LMFDB - Embedded newform 529.2.c.e.255.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,2,Mod(118,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("529.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	529.c (of order $11$, degree $10$, not 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:	$4.22408626693$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			255.1
Root			$0.142315 - 0.989821i$ of defining polynomial
Character	$\chi$	$=$	529.255
Dual form			529.2.c.e.334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.402869 + 0.258908i) q^{2} +(-0.313607 - 2.18119i) q^{3} +(-0.735560 - 1.61065i) q^{4} +(-2.48926 - 0.730913i) q^{5} +(0.438384 - 0.959928i) q^{6} +(-2.22514 + 2.56794i) q^{7} +(0.256983 - 1.78736i) q^{8} +(-1.78074 + 0.522874i) q^{9} +O(q^{10})$	\(q+(0.402869 + 0.258908i) q^{2} +(-0.313607 - 2.18119i) q^{3} +(-0.735560 - 1.61065i) q^{4} +(-2.48926 - 0.730913i) q^{5} +(0.438384 - 0.959928i) q^{6} +(-2.22514 + 2.56794i) q^{7} +(0.256983 - 1.78736i) q^{8} +(-1.78074 + 0.522874i) q^{9} +(-0.813607 - 0.938953i) q^{10} +(-0.192401 + 0.123649i) q^{11} +(-3.28245 + 2.10951i) q^{12} +(2.00357 + 2.31224i) q^{13} +(-1.56130 + 0.458439i) q^{14} +(-0.813607 + 5.65876i) q^{15} +(-1.75278 + 2.02282i) q^{16} +(0.800404 - 1.75264i) q^{17} +(-0.852783 - 0.250400i) q^{18} +(-0.803526 - 1.75948i) q^{19} +(0.653755 + 4.54696i) q^{20} +(6.29898 + 4.04811i) q^{21} -0.109526 q^{22} -3.97915 q^{24} +(1.45592 + 0.935664i) q^{25} +(0.208518 + 1.45027i) q^{26} +(-1.04731 - 2.29328i) q^{27} +(5.77279 + 1.69504i) q^{28} +(-2.68886 + 5.88778i) q^{29} +(-1.79288 + 2.06909i) q^{30} +(-0.214354 + 1.49086i) q^{31} +(-4.69505 + 1.37859i) q^{32} +(0.330039 + 0.380885i) q^{33} +(0.776231 - 0.498853i) q^{34} +(7.41589 - 4.76590i) q^{35} +(2.15201 + 2.48355i) q^{36} +(-6.47580 + 1.90147i) q^{37} +(0.131827 - 0.916879i) q^{38} +(4.41510 - 5.09530i) q^{39} +(-1.94610 + 4.26137i) q^{40} +(-7.73992 - 2.27265i) q^{41} +(1.48958 + 3.26172i) q^{42} +(0.378479 + 2.63238i) q^{43} +(0.340677 + 0.218940i) q^{44} +4.81491 q^{45} -1.43889 q^{47} +(4.96183 + 3.18877i) q^{48} +(-0.646902 - 4.49930i) q^{49} +(0.344295 + 0.753900i) q^{50} +(-4.07385 - 1.19619i) q^{51} +(2.25047 - 4.92785i) q^{52} +(5.61926 - 6.48497i) q^{53} +(0.171822 - 1.19505i) q^{54} +(0.569313 - 0.167165i) q^{55} +(4.01801 + 4.63704i) q^{56} +(-3.58576 + 2.30442i) q^{57} +(-2.60765 + 1.67584i) q^{58} +(-0.0404373 - 0.0466671i) q^{59} +(9.71275 - 2.85192i) q^{60} +(-0.00632292 + 0.0439769i) q^{61} +(-0.472354 + 0.545125i) q^{62} +(2.61969 - 5.73632i) q^{63} +(2.88789 + 0.847960i) q^{64} +(-3.29736 - 7.22022i) q^{65} +(0.0343481 + 0.238897i) q^{66} +(-10.4382 - 6.70824i) q^{67} -3.41164 q^{68} +4.22157 q^{70} +(-7.01302 - 4.50700i) q^{71} +(0.476941 + 3.31720i) q^{72} +(-0.277590 - 0.607837i) q^{73} +(-3.10120 - 0.910596i) q^{74} +(1.58427 - 3.46907i) q^{75} +(-2.24286 + 2.58840i) q^{76} +(0.110596 - 0.769210i) q^{77} +(3.09792 - 0.909632i) q^{78} +(-7.83807 - 9.04561i) q^{79} +(5.84164 - 3.75419i) q^{80} +(-9.35753 + 6.01372i) q^{81} +(-2.52977 - 2.91951i) q^{82} +(-0.345930 + 0.101574i) q^{83} +(1.88682 - 13.1231i) q^{84} +(-3.27344 + 3.77775i) q^{85} +(-0.529067 + 1.15850i) q^{86} +(13.6856 + 4.01845i) q^{87} +(0.171560 + 0.375665i) q^{88} +(-2.29409 - 15.9557i) q^{89} +(1.93978 + 1.24662i) q^{90} -10.3959 q^{91} +3.31908 q^{93} +(-0.579683 - 0.372540i) q^{94} +(0.714162 + 4.96711i) q^{95} +(4.47937 + 9.80845i) q^{96} +(-0.382418 - 0.112288i) q^{97} +(0.904290 - 1.98012i) q^{98} +(0.277964 - 0.320788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - 7 q^{3} + 8 q^{4} + 3 q^{5} - 5 q^{6} - 6 q^{7} + 15 q^{8} - 2 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 + 3 * q^5 - 5 * q^6 - 6 * q^7 + 15 * q^8 - 2 * q^9	\( 10 q + 4 q^{2} - 7 q^{3} + 8 q^{4} + 3 q^{5} - 5 q^{6} - 6 q^{7} + 15 q^{8} - 2 q^{9} - 12 q^{10} - 7 q^{11} - 10 q^{12} + 8 q^{13} + 2 q^{14} - 12 q^{15} + 12 q^{16} - q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{20} + 24 q^{21} + 6 q^{22} - 38 q^{24} + 18 q^{25} - 10 q^{26} - 4 q^{27} + 26 q^{28} - 8 q^{29} + 4 q^{30} - 12 q^{31} - 23 q^{32} + 17 q^{33} + 26 q^{34} + 18 q^{35} - 6 q^{36} - 25 q^{37} + 52 q^{38} + 12 q^{39} - 12 q^{40} - 26 q^{41} + 14 q^{42} - 22 q^{43} - 32 q^{44} + 6 q^{45} - 18 q^{47} - 15 q^{48} + 15 q^{49} + 5 q^{50} - 18 q^{51} + 13 q^{52} + 48 q^{53} - 17 q^{54} + 32 q^{55} + 2 q^{56} + 8 q^{57} - q^{58} + q^{59} + 8 q^{60} - 36 q^{61} - 18 q^{62} + 21 q^{63} + 13 q^{64} - 13 q^{65} - 2 q^{66} + 10 q^{67} + 30 q^{68} + 38 q^{70} - 14 q^{71} - 3 q^{72} - 3 q^{73} - 32 q^{74} - 6 q^{75} - 50 q^{76} + 13 q^{77} + 7 q^{78} - 18 q^{79} - 14 q^{80} + 11 q^{81} - 6 q^{82} + 15 q^{83} - 16 q^{84} - 19 q^{85} - 22 q^{86} + 10 q^{87} - 16 q^{88} + 19 q^{89} - 24 q^{90} + 4 q^{91} + 4 q^{93} - 5 q^{94} + 28 q^{95} - 7 q^{96} - 21 q^{97} + 39 q^{98} - 25 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 + 3 * q^5 - 5 * q^6 - 6 * q^7 + 15 * q^8 - 2 * q^9 - 12 * q^10 - 7 * q^11 - 10 * q^12 + 8 * q^13 + 2 * q^14 - 12 * q^15 + 12 * q^16 - q^17 - 3 * q^18 - 2 * q^19 - 2 * q^20 + 24 * q^21 + 6 * q^22 - 38 * q^24 + 18 * q^25 - 10 * q^26 - 4 * q^27 + 26 * q^28 - 8 * q^29 + 4 * q^30 - 12 * q^31 - 23 * q^32 + 17 * q^33 + 26 * q^34 + 18 * q^35 - 6 * q^36 - 25 * q^37 + 52 * q^38 + 12 * q^39 - 12 * q^40 - 26 * q^41 + 14 * q^42 - 22 * q^43 - 32 * q^44 + 6 * q^45 - 18 * q^47 - 15 * q^48 + 15 * q^49 + 5 * q^50 - 18 * q^51 + 13 * q^52 + 48 * q^53 - 17 * q^54 + 32 * q^55 + 2 * q^56 + 8 * q^57 - q^58 + q^59 + 8 * q^60 - 36 * q^61 - 18 * q^62 + 21 * q^63 + 13 * q^64 - 13 * q^65 - 2 * q^66 + 10 * q^67 + 30 * q^68 + 38 * q^70 - 14 * q^71 - 3 * q^72 - 3 * q^73 - 32 * q^74 - 6 * q^75 - 50 * q^76 + 13 * q^77 + 7 * q^78 - 18 * q^79 - 14 * q^80 + 11 * q^81 - 6 * q^82 + 15 * q^83 - 16 * q^84 - 19 * q^85 - 22 * q^86 + 10 * q^87 - 16 * q^88 + 19 * q^89 - 24 * q^90 + 4 * q^91 + 4 * q^93 - 5 * q^94 + 28 * q^95 - 7 * q^96 - 21 * q^97 + 39 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/529\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.402869	+	0.258908i	0.284871	+	0.183076i	0.675271	−	0.737570i	$-0.264027\pi$
$2$	0.402869	+	0.258908i	0.284871	+	0.183076i	−0.390399	+	0.920646i	$0.627663\pi$
$3$	−0.313607	−	2.18119i	−0.181061	−	1.25931i	−0.854260	−	0.519846i	$-0.825989\pi$
$3$	−0.313607	−	2.18119i	−0.181061	−	1.25931i	0.673198	−	0.739462i	$-0.264920\pi$
$4$	−0.735560	−	1.61065i	−0.367780	−	0.805326i
$5$	−2.48926	−	0.730913i	−1.11323	−	0.326874i	−0.327135	−	0.944978i	$-0.606083\pi$
$5$	−2.48926	−	0.730913i	−1.11323	−	0.326874i	−0.786097	+	0.618103i	$0.787901\pi$
$6$	0.438384	−	0.959928i	0.178970	−	0.391889i
$7$	−2.22514	+	2.56794i	−0.841023	+	0.970592i	−0.999860	−	0.0167129i	$-0.994680\pi$
$7$	−2.22514	+	2.56794i	−0.841023	+	0.970592i	0.158838	+	0.987305i	$0.449225\pi$
$8$	0.256983	−	1.78736i	0.0908573	−	0.631927i
$9$	−1.78074	+	0.522874i	−0.593581	+	0.174291i
$10$	−0.813607	−	0.938953i	−0.257285	−	0.296923i
$11$	−0.192401	+	0.123649i	−0.0580111	+	0.0372814i	−0.569325	−	0.822113i	$-0.692795\pi$
$11$	−0.192401	+	0.123649i	−0.0580111	+	0.0372814i	0.511314	+	0.859394i	$0.329159\pi$
$12$	−3.28245	+	2.10951i	−0.947563	+	0.608962i
$13$	2.00357	+	2.31224i	0.555691	+	0.641301i	0.962199	−	0.272346i	$-0.0877994\pi$
$13$	2.00357	+	2.31224i	0.555691	+	0.641301i	−0.406509	+	0.913647i	$0.633254\pi$
$14$	−1.56130	+	0.458439i	−0.417275	+	0.122523i
$15$	−0.813607	+	5.65876i	−0.210072	+	1.46109i
$16$	−1.75278	+	2.02282i	−0.438196	+	0.505705i
$17$	0.800404	−	1.75264i	0.194126	−	0.425078i	−0.787390	−	0.616455i	$-0.788568\pi$
$17$	0.800404	−	1.75264i	0.194126	−	0.425078i	0.981517	+	0.191377i	$0.0612954\pi$
$18$	−0.852783	−	0.250400i	−0.201003	−	0.0590198i
$19$	−0.803526	−	1.75948i	−0.184342	−	0.403652i	0.794788	−	0.606887i	$-0.207582\pi$
$19$	−0.803526	−	1.75948i	−0.184342	−	0.403652i	−0.979130	+	0.203235i	$0.934855\pi$
$20$	0.653755	+	4.54696i	0.146184	+	1.01673i
$21$	6.29898	+	4.04811i	1.37455	+	0.883370i
$22$	−0.109526			−0.0233510
$23$		0			0
$23$		0			0
$24$	−3.97915			−0.812241
$25$	1.45592	+	0.935664i	0.291184	+	0.187133i
$26$	0.208518	+	1.45027i	0.0408937	+	0.284422i
$27$	−1.04731	−	2.29328i	−0.201554	−	0.441342i
$28$	5.77279	+	1.69504i	1.09095	+	0.320333i
$29$	−2.68886	+	5.88778i	−0.499308	+	1.09333i	0.477385	+	0.878694i	$0.341585\pi$
$29$	−2.68886	+	5.88778i	−0.499308	+	1.09333i	−0.976694	+	0.214639i	$0.931143\pi$
$30$	−1.79288	+	2.06909i	−0.327333	+	0.377763i
$31$	−0.214354	+	1.49086i	−0.0384991	+	0.267767i	−0.999975	−	0.00712341i	$-0.997733\pi$
$31$	−0.214354	+	1.49086i	−0.0384991	+	0.267767i	0.961476	+	0.274891i	$0.0886416\pi$
$32$	−4.69505	+	1.37859i	−0.829976	+	0.243703i
$33$	0.330039	+	0.380885i	0.0574524	+	0.0663036i
$34$	0.776231	−	0.498853i	0.133123	−	0.0855527i
$35$	7.41589	−	4.76590i	1.25351	−	0.805585i
$36$	2.15201	+	2.48355i	0.358669	+	0.413926i
$37$	−6.47580	+	1.90147i	−1.06461	+	0.312599i	−0.766708	−	0.641996i	$-0.778107\pi$
$37$	−6.47580	+	1.90147i	−1.06461	+	0.312599i	−0.297907	+	0.954595i	$0.596288\pi$
$38$	0.131827	−	0.916879i	0.0213852	−	0.148737i
$39$	4.41510	−	5.09530i	0.706982	−	0.815901i
$40$	−1.94610	+	4.26137i	−0.307706	+	0.673782i
$41$	−7.73992	−	2.27265i	−1.20877	−	0.354928i	−0.385572	−	0.922678i	$-0.625996\pi$
$41$	−7.73992	−	2.27265i	−1.20877	−	0.354928i	−0.823201	+	0.567750i	$0.807814\pi$
$42$	1.48958	+	3.26172i	0.229847	+	0.503294i
$43$	0.378479	+	2.63238i	0.0577175	+	0.401434i	0.998116	+	0.0613589i	$0.0195434\pi$
$43$	0.378479	+	2.63238i	0.0577175	+	0.401434i	−0.940398	+	0.340075i	$0.889547\pi$
$44$	0.340677	+	0.218940i	0.0513590	+	0.0330064i
$45$	4.81491			0.717765
$46$		0			0
$47$	−1.43889			−0.209883			−0.104942	−	0.994478i	$-0.533466\pi$
$47$	−1.43889			−0.209883			−0.104942	+	0.994478i	$0.533466\pi$
$48$	4.96183	+	3.18877i	0.716179	+	0.460260i
$49$	−0.646902	−	4.49930i	−0.0924146	−	0.642758i
$50$	0.344295	+	0.753900i	0.0486906	+	0.106618i
$51$	−4.07385	−	1.19619i	−0.570453	−	0.167500i
$52$	2.25047	−	4.92785i	0.312084	−	0.683370i
$53$	5.61926	−	6.48497i	0.771864	−	0.890779i	−0.224630	−	0.974444i	$-0.572117\pi$
$53$	5.61926	−	6.48497i	0.771864	−	0.890779i	0.996494	+	0.0836655i	$0.0266627\pi$
$54$	0.171822	−	1.19505i	0.0233820	−	0.162625i
$55$	0.569313	−	0.167165i	0.0767661	−	0.0225406i
$56$	4.01801	+	4.63704i	0.536930	+	0.619650i
$57$	−3.58576	+	2.30442i	−0.474945	+	0.305229i
$58$	−2.60765	+	1.67584i	−0.342401	+	0.220048i
$59$	−0.0404373	−	0.0466671i	−0.00526449	−	0.00607554i	0.753111	−	0.657893i	$-0.228552\pi$
$59$	−0.0404373	−	0.0466671i	−0.00526449	−	0.00607554i	−0.758376	+	0.651818i	$0.774007\pi$
$60$	9.71275	−	2.85192i	1.25391	−	0.368181i
$61$	−0.00632292	+	0.0439769i	−0.000809567	+	0.00563066i	−0.990222	−	0.139499i	$-0.955451\pi$
$61$	−0.00632292	+	0.0439769i	−0.000809567	+	0.00563066i	0.989413	+	0.145130i	$0.0463599\pi$
$62$	−0.472354	+	0.545125i	−0.0599890	+	0.0692310i
$63$	2.61969	−	5.73632i	0.330050	−	0.722708i
$64$	2.88789	+	0.847960i	0.360986	+	0.105995i
$65$	−3.29736	−	7.22022i	−0.408988	−	0.895558i
$66$	0.0343481	+	0.238897i	0.00422796	+	0.0294061i
$67$	−10.4382	−	6.70824i	−1.27523	−	0.819542i	−0.284941	−	0.958545i	$-0.591974\pi$
$67$	−10.4382	−	6.70824i	−1.27523	−	0.819542i	−0.990292	+	0.139003i	$0.955610\pi$
$68$	−3.41164			−0.413722
$69$		0			0
$70$	4.22157			0.504574
$71$	−7.01302	−	4.50700i	−0.832293	−	0.534882i	0.0537130	−	0.998556i	$-0.482894\pi$
$71$	−7.01302	−	4.50700i	−0.832293	−	0.534882i	−0.886006	+	0.463674i	$0.846531\pi$
$72$	0.476941	+	3.31720i	0.0562080	+	0.390935i
$73$	−0.277590	−	0.607837i	−0.0324895	−	0.0711420i	0.892692	−	0.450668i	$-0.148814\pi$
$73$	−0.277590	−	0.607837i	−0.0324895	−	0.0711420i	−0.925181	+	0.379526i	$0.876087\pi$
$74$	−3.10120	−	0.910596i	−0.360508	−	0.105855i
$75$	1.58427	−	3.46907i	0.182936	−	0.400573i
$76$	−2.24286	+	2.58840i	−0.257274	+	0.296910i
$77$	0.110596	−	0.769210i	0.0126035	−	0.0876596i
$78$	3.09792	−	0.909632i	0.350771	−	0.102996i
$79$	−7.83807	−	9.04561i	−0.881852	−	1.01771i	−0.999695	−	0.0246790i	$-0.992144\pi$
$79$	−7.83807	−	9.04561i	−0.881852	−	1.01771i	0.117844	−	0.993032i	$-0.462402\pi$
$80$	5.84164	−	3.75419i	0.653115	−	0.419732i
$81$	−9.35753	+	6.01372i	−1.03973	+	0.668191i
$82$	−2.52977	−	2.91951i	−0.279366	−	0.322406i
$83$	−0.345930	+	0.101574i	−0.0379708	+	0.0111492i	−0.300663	−	0.953731i	$-0.597208\pi$
$83$	−0.345930	+	0.101574i	−0.0379708	+	0.0111492i	0.262692	+	0.964880i	$0.415390\pi$
$84$	1.88682	−	13.1231i	0.205869	−	1.43185i
$85$	−3.27344	+	3.77775i	−0.355055	+	0.409755i
$86$	−0.529067	+	1.15850i	−0.0570508	+	0.124924i
$87$	13.6856	+	4.01845i	1.46725	+	0.430823i
$88$	0.171560	+	0.375665i	0.0182884	+	0.0400460i
$89$	−2.29409	−	15.9557i	−0.243173	−	1.69130i	−0.635999	−	0.771690i	$-0.719412\pi$
$89$	−2.29409	−	15.9557i	−0.243173	−	1.69130i	0.392826	−	0.919613i	$-0.371497\pi$
$90$	1.93978	+	1.24662i	0.204471	+	0.131405i
$91$	−10.3959			−1.08979
$92$		0			0
$93$	3.31908			0.344172
$94$	−0.579683	−	0.372540i	−0.0597897	−	0.0384245i
$95$	0.714162	+	4.96711i	0.0732715	+	0.509614i
$96$	4.47937	+	9.80845i	0.457174	+	1.00107i
$97$	−0.382418	−	0.112288i	−0.0388287	−	0.0114011i	0.262261	−	0.964997i	$-0.415532\pi$
$97$	−0.382418	−	0.112288i	−0.0388287	−	0.0114011i	−0.301089	+	0.953596i	$0.597350\pi$
$98$	0.904290	−	1.98012i	0.0913471	−	0.200022i
$99$	0.277964	−	0.320788i	0.0279365	−	0.0322404i
$100$	0.436111	−	3.03322i	0.0436111	−	0.303322i
$101$	18.6952	−	5.48941i	1.86024	−	0.546216i	0.860947	−	0.508695i	$-0.169872\pi$
$101$	18.6952	−	5.48941i	1.86024	−	0.546216i	0.999296	−	0.0375212i	$-0.0119462\pi$
$102$	−1.33152	−	1.53666i	−0.131840	−	0.152152i
$103$	−5.48883	+	3.52746i	−0.540830	+	0.347571i	−0.782364	−	0.622822i	$-0.785986\pi$
$103$	−5.48883	+	3.52746i	−0.540830	+	0.347571i	0.241533	+	0.970393i	$0.422350\pi$
$104$	4.64769	−	2.98689i	0.455744	−	0.292889i
$105$	−12.7210	−	14.6808i	−1.24144	−	1.43270i
$106$	3.94284	−	1.15772i	0.382962	−	0.112448i
$107$	−0.184025	+	1.27992i	−0.0177904	+	0.123735i	−0.996781	−	0.0801691i	$-0.974454\pi$
$107$	−0.184025	+	1.27992i	−0.0177904	+	0.123735i	0.978991	+	0.203904i	$0.0653631\pi$
$108$	−2.92332	+	3.37369i	−0.281297	+	0.324634i
$109$	−2.94199	+	6.44205i	−0.281791	+	0.617037i	−0.996610	−	0.0822732i	$-0.973782\pi$
$109$	−2.94199	+	6.44205i	−0.281791	+	0.617037i	0.714819	+	0.699310i	$0.246509\pi$
$110$	0.272639	+	0.0800540i	0.0259951	+	0.00763285i
$111$	6.17831	+	13.5286i	0.586419	+	1.28408i
$112$	−1.29431	−	9.00210i	−0.122300	−	0.850618i
$113$	−1.13732	−	0.730913i	−0.106990	−	0.0687585i	0.486051	−	0.873930i	$-0.338437\pi$
$113$	−1.13732	−	0.730913i	−0.106990	−	0.0687585i	−0.593042	+	0.805172i	$0.702073\pi$
$114$	−2.04122			−0.191178
$115$		0			0
$116$	11.4610			1.06412
$117$	−4.77686	−	3.06990i	−0.441621	−	0.283812i
$118$	−0.00420843	−	0.0292703i	−0.000387417	−	0.00269455i
$119$	2.71967	+	5.95526i	0.249312	+	0.545917i
$120$	9.90515	+	2.90842i	0.904213	+	0.265501i
$121$	−4.54784	+	9.95837i	−0.413440	+	0.905307i
$122$	−0.0139333	+	0.0160799i	−0.00126146	+	0.00145580i
$123$	−2.52977	+	17.5949i	−0.228102	+	1.58648i
$124$	2.55893	−	0.751371i	0.229799	−	0.0674751i
$125$	5.55441	+	6.41013i	0.496802	+	0.573340i
$126$	2.54057	−	1.63273i	0.226332	−	0.145455i
$127$	8.21319	−	5.27830i	0.728803	−	0.468373i	−0.122886	−	0.992421i	$-0.539215\pi$
$127$	8.21319	−	5.27830i	0.728803	−	0.468373i	0.851689	+	0.524048i	$0.175579\pi$
$128$	7.35271	+	8.48548i	0.649894	+	0.750018i
$129$	5.62301	−	1.65107i	0.495079	−	0.145368i
$130$	0.540968	−	3.76252i	0.0474461	−	0.329995i
$131$	3.29049	−	3.79743i	0.287491	−	0.331783i	−0.593572	−	0.804781i	$-0.702283\pi$
$131$	3.29049	−	3.79743i	0.287491	−	0.331783i	0.881063	+	0.472998i	$0.156828\pi$
$132$	0.370710	−	0.811741i	0.0322662	−	0.0706530i
$133$	6.30619	+	1.85167i	0.546816	+	0.160560i
$134$	−2.46842	−	5.40509i	−0.213239	−	0.466929i
$135$	0.930830	+	6.47407i	0.0801131	+	0.557199i
$136$	−2.92691	−	1.88101i	−0.250980	−	0.161295i
$137$	11.6182			0.992608			0.496304	−	0.868149i	$-0.334690\pi$
$137$	11.6182			0.992608			0.496304	+	0.868149i	$0.334690\pi$
$138$		0			0
$139$	−17.3118			−1.46837			−0.734183	−	0.678952i	$-0.762435\pi$
$139$	−17.3118			−1.46837			−0.734183	+	0.678952i	$0.762435\pi$
$140$	−13.1310	−	8.43881i	−1.10978	−	0.713210i
$141$	0.451245	+	3.13848i	0.0380017	+	0.264308i
$142$	−1.65843	−	3.63146i	−0.139172	−	0.304745i
$143$	−0.671395	−	0.197139i	−0.0561448	−	0.0164856i
$144$	2.06358	−	4.51861i	0.171965	−	0.376551i
$145$	10.9967	−	12.6909i	0.913228	−	1.05392i
$146$	0.0455417	−	0.316749i	0.00376905	−	0.0262144i
$147$	−9.61094	+	2.82203i	−0.792697	+	0.232757i
$148$	7.82594	+	9.03161i	0.643288	+	0.742394i
$149$	6.16716	−	3.96339i	0.505233	−	0.324694i	−0.263073	−	0.964776i	$-0.584736\pi$
$149$	6.16716	−	3.96339i	0.505233	−	0.324694i	0.768306	+	0.640082i	$0.221100\pi$
$150$	1.53642	−	0.987400i	0.125448	−	0.0806208i
$151$	−11.2018	−	12.9275i	−0.911587	−	1.05203i	−0.998442	−	0.0558060i	$-0.982227\pi$
$151$	−11.2018	−	12.9275i	−0.911587	−	1.05203i	0.0868551	−	0.996221i	$-0.472318\pi$
$152$	−3.35131	+	0.984033i	−0.271827	+	0.0798156i
$153$	−0.508905	+	3.53951i	−0.0411425	+	0.286153i
$154$	0.243710	−	0.281257i	0.0196387	−	0.0226643i
$155$	1.62328	−	3.55448i	0.130385	−	0.285502i
$156$	−11.4543	−	3.36329i	−0.917080	−	0.269279i
$157$	7.47860	+	16.3759i	0.596858	+	1.30694i	0.931208	+	0.364487i	$0.118756\pi$
$157$	7.47860	+	16.3759i	0.596858	+	1.30694i	−0.334351	+	0.942449i	$0.608517\pi$
$158$	−0.815732	−	5.67354i	−0.0648961	−	0.451363i
$159$	−15.9072	−	10.2229i	−1.26152	−	0.810729i
$160$	12.6948			1.00362
$161$		0			0
$162$	−5.32686			−0.418518
$163$	12.5391	+	8.05836i	0.982135	+	0.631180i	0.930038	−	0.367462i	$-0.119773\pi$
$163$	12.5391	+	8.05836i	0.982135	+	0.631180i	0.0520963	+	0.998642i	$0.483410\pi$
$164$	2.03274	+	14.1380i	0.158730	+	1.10399i
$165$	−0.543159	−	1.18935i	−0.0422849	−	0.0925910i
$166$	−0.165663	−	0.0486431i	−0.0128580	−	0.00377544i
$167$	3.17363	−	6.94928i	0.245583	−	0.537751i	−0.746194	−	0.665728i	$-0.768121\pi$
$167$	3.17363	−	6.94928i	0.245583	−	0.537751i	0.991777	+	0.127977i	$0.0408483\pi$
$168$	8.85416	−	10.2182i	0.683113	−	0.788355i
$169$	0.517917	−	3.60219i	0.0398397	−	0.277091i
$170$	−2.29686	+	0.674419i	−0.176161	+	0.0517256i
$171$	2.35086	+	2.71304i	0.179775	+	0.207471i
$172$	3.96145	−	2.54587i	0.302058	−	0.194121i
$173$	5.03407	−	3.23520i	0.382733	−	0.245968i	−0.335100	−	0.942182i	$-0.608770\pi$
$173$	5.03407	−	3.23520i	0.382733	−	0.245968i	0.717833	+	0.696215i	$0.245134\pi$
$174$	4.47309	+	5.16222i	0.339104	+	0.391347i
$175$	−5.64236	+	1.65675i	−0.426522	+	0.125238i
$176$	0.0871183	−	0.605921i	0.00656679	−	0.0456730i
$177$	−0.0891082	+	0.102836i	−0.00669778	+	0.00772965i
$178$	3.20685	−	7.02202i	0.240364	−	0.526323i
$179$	−3.44615	−	1.01188i	−0.257577	−	0.0756315i	0.150395	−	0.988626i	$-0.451946\pi$
$179$	−3.44615	−	1.01188i	−0.257577	−	0.0756315i	−0.407972	+	0.912995i	$0.633764\pi$
$180$	−3.54166	−	7.75515i	−0.263980	−	0.578035i
$181$	2.71480	+	18.8818i	0.201789	+	1.40347i	0.798972	+	0.601369i	$0.205378\pi$
$181$	2.71480	+	18.8818i	0.201789	+	1.40347i	−0.597182	+	0.802105i	$0.703713\pi$
$182$	−4.18820	−	2.69159i	−0.310450	−	0.199514i
$183$	0.0979047			0.00723732
$184$		0			0
$185$	17.5098			1.28734
$186$	1.33715	+	0.859336i	0.0980448	+	0.0630096i
$187$	0.0627130	+	0.436178i	0.00458603	+	0.0318965i
$188$	1.05839	+	2.31754i	0.0771908	+	0.169024i
$189$	8.21942	+	2.41344i	0.597875	+	0.175552i
$190$	−0.998311	+	2.18600i	−0.0724251	+	0.158589i
$191$	−8.57191	+	9.89251i	−0.620241	+	0.715797i	−0.975753	−	0.218875i	$-0.929761\pi$
$191$	−8.57191	+	9.89251i	−0.620241	+	0.715797i	0.355511	+	0.934672i	$0.384307\pi$
$192$	0.943896	−	6.56494i	0.0681198	−	0.473784i
$193$	−9.00358	+	2.64369i	−0.648092	+	0.190297i	−0.589225	−	0.807969i	$-0.700567\pi$
$193$	−9.00358	+	2.64369i	−0.648092	+	0.190297i	−0.0588666	+	0.998266i	$0.518749\pi$
$194$	−0.124992	−	0.144249i	−0.00897391	−	0.0103564i
$195$	−14.7146	+	9.45647i	−1.05373	+	0.677192i
$196$	−6.77098	+	4.35144i	−0.483641	+	0.310817i
$197$	6.78624	+	7.83174i	0.483500	+	0.557988i	0.944117	−	0.329611i	$-0.106917\pi$
$197$	6.78624	+	7.83174i	0.483500	+	0.557988i	−0.460617	+	0.887599i	$0.652372\pi$
$198$	0.195038	−	0.0572683i	0.0138607	−	0.00406988i
$199$	1.45966	−	10.1522i	0.103473	−	0.719670i	−0.870362	−	0.492413i	$-0.836115\pi$
$199$	1.45966	−	10.1522i	0.103473	−	0.719670i	0.973835	−	0.227257i	$-0.0729758\pi$
$200$	2.04652	−	2.36180i	0.144710	−	0.167005i
$201$	−11.3584	+	24.8715i	−0.801161	+	1.75430i
$202$	8.95297	+	2.62883i	0.629929	+	0.184964i
$203$	−9.13641	−	20.0059i	−0.641250	−	1.40414i
$204$	1.06991	+	7.44142i	0.0749090	+	0.521003i
$205$	17.6056	+	11.3144i	1.22963	+	0.790234i
$206$	−3.12457			−0.217699
$207$		0			0
$208$	−8.18908			−0.567810
$209$	0.372156	+	0.239170i	0.0257426	+	0.0165437i
$210$	−1.32391	−	9.20802i	−0.0913587	−	0.635414i
$211$	−3.43579	−	7.52333i	−0.236530	−	0.517928i	0.753726	−	0.657189i	$-0.228255\pi$
$211$	−3.43579	−	7.52333i	−0.236530	−	0.517928i	−0.990256	+	0.139261i	$0.955527\pi$
$212$	−14.5783	−	4.28058i	−1.00124	−	0.293992i
$213$	−7.63126	+	16.7101i	−0.522885	+	1.14496i
$214$	−0.405521	+	0.467996i	−0.0277209	+	0.0319916i
$215$	0.981907	−	6.82931i	0.0669655	−	0.465755i
$216$	−4.36806	+	1.28258i	−0.297209	+	0.0872683i
$217$	−3.35149	−	3.86783i	−0.227514	−	0.262565i
$218$	−2.85314	+	1.83360i	−0.193239	+	0.124187i
$219$	−1.23875	+	0.796098i	−0.0837071	+	0.0537953i
$220$	−0.688009	−	0.794004i	−0.0463855	−	0.0535318i
$221$	5.65620	−	1.66081i	0.380477	−	0.111718i
$222$	−1.01362	+	7.04987i	−0.0680296	+	0.473156i
$223$	7.06865	−	8.15766i	0.473352	−	0.546277i	−0.467989	−	0.883734i	$-0.655021\pi$
$223$	7.06865	−	8.15766i	0.473352	−	0.546277i	0.941341	+	0.337457i	$0.109567\pi$
$224$	6.90699	−	15.1242i	0.461492	−	1.01053i
$225$	−3.08186	−	0.904915i	−0.205457	−	0.0603277i
$226$	−0.268953	−	0.588925i	−0.0178905	−	0.0391747i
$227$	−3.30408	−	22.9804i	−0.219299	−	1.52526i	−0.740635	−	0.671908i	$-0.765475\pi$
$227$	−3.30408	−	22.9804i	−0.219299	−	1.52526i	0.521335	−	0.853352i	$-0.325434\pi$
$228$	6.34916	+	4.08036i	0.420484	+	0.270228i
$229$	−14.1883			−0.937587			−0.468794	−	0.883308i	$-0.655311\pi$
$229$	−14.1883			−0.937587			−0.468794	+	0.883308i	$0.655311\pi$
$230$		0			0
$231$	−1.71247			−0.112672
$232$	9.83258	+	6.31901i	0.645540	+	0.414864i
$233$	−3.50398	−	24.3707i	−0.229553	−	1.59658i	−0.699995	−	0.714148i	$-0.746814\pi$
$233$	−3.50398	−	24.3707i	−0.229553	−	1.59658i	0.470441	−	0.882431i	$-0.344095\pi$
$234$	−1.12963	−	2.47354i	−0.0738460	−	0.161700i
$235$	3.58176	+	1.05170i	0.233649	+	0.0686054i
$236$	−0.0454204	+	0.0994568i	−0.00295662	+	0.00647409i
$237$	−17.2721	+	19.9331i	−1.12194	+	1.29479i
$238$	−0.446192	+	3.10334i	−0.0289223	+	0.201159i
$239$	−0.225362	+	0.0661722i	−0.0145774	+	0.00428032i	−0.289013	−	0.957325i	$-0.593327\pi$
$239$	−0.225362	+	0.0661722i	−0.0145774	+	0.00428032i	0.274436	+	0.961605i	$0.411509\pi$
$240$	−10.0206	−	11.5644i	−0.646825	−	0.746476i
$241$	−4.43149	+	2.84794i	−0.285457	+	0.183452i	−0.675531	−	0.737331i	$-0.736086\pi$
$241$	−4.43149	+	2.84794i	−0.285457	+	0.183452i	0.390074	+	0.920783i	$0.372449\pi$
$242$	−4.41049	+	2.83445i	−0.283517	+	0.182205i
$243$	11.0987	+	12.8086i	0.711982	+	0.821672i
$244$	0.0754823	−	0.0221636i	0.00483226	−	0.00141888i
$245$	−1.67829	+	11.6728i	−0.107222	+	0.745746i
$246$	−5.57464	+	6.43348i	−0.355426	+	0.410183i
$247$	2.45842	−	5.38319i	0.156425	−	0.342524i
$248$	2.60962	+	0.766255i	0.165711	+	0.0486572i
$249$	0.330039	+	0.722684i	0.0209154	+	0.0457983i
$250$	0.578065	+	4.02053i	0.0365600	+	0.254281i
$251$	24.5542	+	15.7800i	1.54985	+	0.996026i	0.985341	+	0.170597i	$0.0545696\pi$
$251$	24.5542	+	15.7800i	1.54985	+	0.996026i	0.564506	+	0.825429i	$0.309067\pi$
$252$	−11.1661			−0.703401
$253$		0			0
$254$	4.67544			0.293363
$255$	9.26656	+	5.95526i	0.580294	+	0.372933i
$256$	−0.0914606	−	0.636123i	−0.00571629	−	0.0397577i
$257$	4.69752	+	10.2861i	0.293023	+	0.641632i	0.997692	−	0.0679050i	$-0.0216315\pi$
$257$	4.69752	+	10.2861i	0.293023	+	0.641632i	−0.704668	+	0.709537i	$0.748904\pi$
$258$	2.69281	+	0.790681i	0.167647	+	0.0492257i
$259$	9.52667	−	20.8605i	0.591959	−	1.29621i
$260$	−9.20385	+	10.6218i	−0.570798	+	0.658736i
$261$	1.70960	−	11.8906i	0.105822	−	0.736007i
$262$	2.30882	−	0.677931i	0.142640	−	0.0418827i
$263$	−15.7721	−	18.2020i	−0.972550	−	1.12238i	−0.992459	−	0.122581i	$-0.960883\pi$
$263$	−15.7721	−	18.2020i	−0.972550	−	1.12238i	0.0199083	−	0.999802i	$-0.493663\pi$
$264$	0.765593	−	0.492017i	0.0471190	−	0.0302815i
$265$	−18.7277	+	12.0356i	−1.15044	+	0.739341i
$266$	2.06116	+	2.37870i	0.126378	+	0.145848i
$267$	−34.0829	+	10.0077i	−2.08584	+	0.612459i
$268$	−3.12670	+	21.7467i	−0.190994	+	1.32839i
$269$	−4.29818	+	4.96037i	−0.262065	+	0.302439i	−0.871499	−	0.490398i	$-0.836851\pi$
$269$	−4.29818	+	4.96037i	−0.262065	+	0.302439i	0.609434	+	0.792837i	$0.291397\pi$
$270$	−1.30119	+	2.84920i	−0.0791877	+	0.173397i
$271$	−19.2220	−	5.64408i	−1.16765	−	0.342853i	−0.360250	−	0.932856i	$-0.617309\pi$
$271$	−19.2220	−	5.64408i	−1.16765	−	0.342853i	−0.807402	+	0.590002i	$0.799127\pi$
$272$	2.14234	+	4.69107i	0.129898	+	0.284438i
$273$	3.26024	+	22.6755i	0.197319	+	1.37238i
$274$	4.68061	+	3.00804i	0.282766	+	0.181723i
$275$	−0.395814			−0.0238685
$276$		0			0
$277$	−7.60036			−0.456661			−0.228331	−	0.973584i	$-0.573327\pi$
$277$	−7.60036			−0.456661			−0.228331	+	0.973584i	$0.573327\pi$
$278$	−6.97438	−	4.48216i	−0.418296	−	0.268822i
$279$	−0.397824	−	2.76693i	−0.0238171	−	0.165652i
$280$	−6.61262	−	14.4796i	−0.395180	−	0.865322i
$281$	−30.8246	−	9.05091i	−1.83884	−	0.539932i	−0.838850	−	0.544363i	$-0.816771\pi$
$281$	−30.8246	−	9.05091i	−1.83884	−	0.539932i	−0.999990	+	0.00443068i	$0.998590\pi$
$282$	−0.630785	+	1.38123i	−0.0375627	+	0.0822509i
$283$	−3.95497	+	4.56428i	−0.235099	+	0.271318i	−0.861024	−	0.508565i	$-0.830176\pi$
$283$	−3.95497	+	4.56428i	−0.235099	+	0.271318i	0.625925	+	0.779883i	$0.284722\pi$
$284$	−2.10070	+	14.6107i	−0.124654	+	0.866986i
$285$	10.6102	−	3.11544i	0.628495	−	0.184543i
$286$	−0.219443	−	0.253251i	−0.0129759	−	0.0149750i
$287$	23.0584	−	14.8187i	1.36110	−	0.874723i
$288$	7.63986	−	4.90984i	0.450183	−	0.289315i
$289$	8.70153	+	10.0421i	0.511855	+	0.590712i
$290$	7.71602	−	2.26563i	0.453100	−	0.133042i
$291$	−0.124992	+	0.869339i	−0.00732716	+	0.0509616i
$292$	−0.774830	+	0.894202i	−0.0453435	+	0.0523292i
$293$	12.1538	−	26.6131i	0.710032	−	1.55475i	−0.117336	−	0.993092i	$-0.537436\pi$
$293$	12.1538	−	26.6131i	0.710032	−	1.55475i	0.827368	−	0.561660i	$-0.189837\pi$
$294$	−4.60260	−	1.35145i	−0.268429	−	0.0788179i
$295$	0.0665494	+	0.145723i	0.00387465	+	0.00848431i
$296$	1.73443	+	12.0632i	0.100812	+	0.701160i
$297$	0.485064	+	0.311731i	0.0281462	+	0.0180885i
$298$	3.51071			0.203370
$299$		0			0
$300$	−6.75279			−0.389872
$301$	−7.60197	−	4.88549i	−0.438170	−	0.281595i
$302$	−1.16580	−	8.10833i	−0.0670843	−	0.466582i
$303$	−17.8364	−	39.0562i	−1.02467	−	2.24372i
$304$	4.96751	+	1.45859i	0.284906	+	0.0836560i
$305$	0.0478827	−	0.104848i	0.00274175	−	0.00600361i
$306$	−1.12143	+	1.29420i	−0.0641080	+	0.0739845i
$307$	1.21975	−	8.48357i	0.0696150	−	0.484183i	−0.924952	−	0.380084i	$-0.875895\pi$
$307$	1.21975	−	8.48357i	0.0696150	−	0.484183i	0.994567	−	0.104099i	$-0.0331958\pi$
$308$	−1.32028	+	0.387669i	−0.0752299	+	0.0220895i
$309$	9.41538	+	10.8659i	0.535622	+	0.618141i
$310$	1.57425	−	1.01171i	0.0894115	−	0.0574613i
$311$	0.177590	−	0.114130i	0.0100702	−	0.00647172i	−0.535596	−	0.844474i	$-0.679913\pi$
$311$	0.177590	−	0.114130i	0.0100702	−	0.00647172i	0.545666	+	0.838003i	$0.316277\pi$
$312$	−7.97252	−	9.20077i	−0.451355	−	0.520891i
$313$	28.2713	−	8.30121i	1.59799	−	0.469212i	0.643004	−	0.765863i	$-0.277688\pi$
$313$	28.2713	−	8.30121i	1.59799	−	0.469212i	0.954986	+	0.296651i	$0.0958697\pi$
$314$	−1.22695	+	8.53360i	−0.0692406	+	0.481579i
$315$	−10.7138	+	12.3644i	−0.603656	+	0.696657i
$316$	−8.80396	+	19.2780i	−0.495262	+	1.08447i
$317$	−25.2074	−	7.40157i	−1.41579	−	0.415714i	−0.517714	−	0.855553i	$-0.673217\pi$
$317$	−25.2074	−	7.40157i	−1.41579	−	0.415714i	−0.898076	+	0.439840i	$0.855035\pi$
$318$	−3.76171	−	8.23699i	−0.210946	−	0.461907i
$319$	−0.210676	−	1.46529i	−0.0117956	−	0.0820403i
$320$	−6.56892	−	4.22159i	−0.367214	−	0.235994i
$321$	2.84947			0.159042
$322$		0			0
$323$	−3.72688			−0.207369
$324$	16.5690	+	10.6483i	0.920502	+	0.591571i
$325$	0.753559	+	5.24112i	0.0417999	+	0.290725i
$326$	2.96522	+	6.49293i	0.164228	+	0.359610i
$327$	14.9739	+	4.39675i	0.828061	+	0.243141i
$328$	−6.05106	+	13.2500i	−0.334114	+	0.731608i
$329$	3.20172	−	3.69498i	0.176516	−	0.203711i
$330$	0.0891112	−	0.619782i	0.00490541	−	0.0341179i
$331$	−21.8357	+	6.41153i	−1.20020	+	0.352409i	−0.819928	−	0.572467i	$-0.805987\pi$
$331$	−21.8357	+	6.41153i	−1.20020	+	0.352409i	−0.380268	+	0.924876i	$0.624168\pi$
$332$	0.418054	+	0.482459i	0.0229437	+	0.0264784i
$333$	10.5375	−	6.77205i	0.577452	−	0.371106i
$334$	3.07778	−	1.97797i	0.168409	−	0.108230i
$335$	21.0803	+	24.3280i	1.15174	+	1.32918i
$336$	−19.2293	+	5.64625i	−1.04905	+	0.308028i
$337$	0.0850657	−	0.591645i	0.00463382	−	0.0322290i	−0.987373	−	0.158410i	$-0.949363\pi$
$337$	0.0850657	−	0.591645i	0.00463382	−	0.0322290i	0.992007	+	0.126182i	$0.0402722\pi$
$338$	1.14129	−	1.31712i	0.0620779	−	0.0716418i
$339$	−1.23758	+	2.70993i	−0.0672164	+	0.147183i
$340$	8.49246	+	2.49361i	0.460568	+	0.135235i
$341$	−0.143101	−	0.313348i	−0.00774937	−	0.0169688i
$342$	0.244661	+	1.70165i	0.0132298	+	0.0920150i
$343$	−7.01593	−	4.50886i	−0.378825	−	0.243456i
$344$	4.80227			0.258921
$345$		0			0
$346$	2.86569			0.154060
$347$	0.487426	+	0.313250i	0.0261664	+	0.0168161i	0.553659	−	0.832744i	$-0.313231\pi$
$347$	0.487426	+	0.313250i	0.0261664	+	0.0168161i	−0.527492	+	0.849560i	$0.676868\pi$
$348$	−3.59424	−	24.9985i	−0.192672	−	1.34006i
$349$	9.02222	+	19.7559i	0.482948	+	1.05751i	0.981642	+	0.190731i	$0.0610859\pi$
$349$	9.02222	+	19.7559i	0.482948	+	1.05751i	−0.498694	+	0.866778i	$0.666187\pi$
$350$	−2.70208	−	0.793402i	−0.144432	−	0.0424091i
$351$	3.20427	−	7.01638i	0.171031	−	0.374507i
$352$	0.732872	−	0.845779i	0.0390622	−	0.0450802i
$353$	−0.0950636	+	0.661182i	−0.00505972	+	0.0351912i	−0.992195	−	0.124697i	$-0.960204\pi$
$353$	−0.0950636	+	0.661182i	−0.00505972	+	0.0351912i	0.987135	+	0.159888i	$0.0511133\pi$
$354$	−0.0625241	+	0.0183587i	−0.00332312	+	0.000975756i
$355$	14.1630	+	16.3450i	0.751695	+	0.867503i
$356$	−24.0117	+	15.4314i	−1.27262	+	0.817860i
$357$	12.1366	−	7.79973i	0.642338	−	0.412805i
$358$	−1.12636	−	1.29989i	−0.0595301	−	0.0687014i
$359$	−15.4539	+	4.53768i	−0.815627	+	0.239490i	−0.662832	−	0.748768i	$-0.730646\pi$
$359$	−15.4539	+	4.53768i	−0.815627	+	0.239490i	−0.152795	+	0.988258i	$0.548827\pi$
$360$	1.23735	−	8.60598i	0.0652142	−	0.453575i
$361$	9.99225	−	11.5317i	0.525908	−	0.606930i
$362$	−3.79495	+	8.30978i	−0.199458	+	0.436753i
$363$	23.1473	+	6.79666i	1.21492	+	0.356732i
$364$	7.64683	+	16.7442i	0.400803	+	0.877636i
$365$	0.246718	+	1.71596i	0.0129138	+	0.0898175i
$366$	0.0394428	+	0.0253483i	0.00206171	+	0.00132498i
$367$	27.2461			1.42223			0.711117	−	0.703074i	$-0.248190\pi$
$367$	27.2461			1.42223			0.711117	+	0.703074i	$0.248190\pi$
$368$		0			0
$369$	14.9711			0.779366
$370$	7.05414	+	4.53342i	0.366727	+	0.235681i
$371$	4.14942	+	28.8599i	0.215427	+	1.49833i
$372$	−2.44138	−	5.34587i	−0.126580	−	0.277171i
$373$	15.8907	+	4.66592i	0.822787	+	0.241592i	0.665916	−	0.746027i	$-0.268041\pi$
$373$	15.8907	+	4.66592i	0.822787	+	0.241592i	0.156871	+	0.987619i	$0.449859\pi$
$374$	−0.0876651	+	0.191960i	−0.00453305	+	0.00992600i
$375$	12.2398	−	14.1255i	0.632060	−	0.729436i
$376$	−0.369770	+	2.57181i	−0.0190694	+	0.132631i
$377$	−19.0013	+	5.57928i	−0.978616	+	0.287348i
$378$	2.68649	+	3.10038i	0.138178	+	0.159466i
$379$	−9.88901	+	6.35528i	−0.507964	+	0.326449i	−0.769395	−	0.638773i	$-0.779442\pi$
$379$	−9.88901	+	6.35528i	−0.507964	+	0.326449i	0.261431	+	0.965222i	$0.415806\pi$
$380$	7.47497	−	4.80387i	0.383458	−	0.246433i
$381$	−14.0887	−	16.2592i	−0.721784	−	0.832983i
$382$	−6.01461	+	1.76605i	−0.307734	+	0.0903589i
$383$	1.59567	−	11.0981i	0.0815349	−	0.567088i	−0.907573	−	0.419895i	$-0.862067\pi$
$383$	1.59567	−	11.0981i	0.0815349	−	0.567088i	0.989108	−	0.147193i	$-0.0470239\pi$
$384$	16.2025	−	18.6987i	0.826833	−	0.954216i
$385$	−0.837527	+	1.83393i	−0.0426843	+	0.0934657i
$386$	−4.31174	−	1.26604i	−0.219462	−	0.0644397i
$387$	−2.05038	−	4.48970i	−0.104226	−	0.228224i
$388$	0.100434	+	0.698537i	0.00509878	+	0.0354628i
$389$	3.44329	+	2.21287i	0.174582	+	0.112197i	0.625013	−	0.780614i	$-0.285094\pi$
$389$	3.44329	+	2.21287i	0.174582	+	0.112197i	−0.450432	+	0.892811i	$0.648730\pi$
$390$	−8.37640			−0.424156
$391$		0			0
$392$	−8.20811			−0.414572
$393$	−9.31482	−	5.98627i	−0.469870	−	0.301967i
$394$	0.706265	+	4.91218i	0.0355811	+	0.247472i
$395$	12.8994	+	28.2458i	0.649042	+	1.42120i
$396$	−0.721137	−	0.211745i	−0.0362385	−	0.0106406i
$397$	1.12889	−	2.47191i	0.0566571	−	0.124062i	−0.879186	−	0.476479i	$-0.841913\pi$
$397$	1.12889	−	2.47191i	0.0566571	−	0.124062i	0.935843	+	0.352417i	$0.114640\pi$
$398$	3.21654	−	3.71209i	0.161231	−	0.186070i
$399$	2.06116	−	14.3357i	0.103187	−	0.717682i
$400$	−4.44459	+	1.30505i	−0.222230	+	0.0652525i
$401$	11.9343	+	13.7729i	0.595968	+	0.687784i	0.970959	−	0.239244i	$-0.0768997\pi$
$401$	11.9343	+	13.7729i	0.595968	+	0.687784i	−0.374991	+	0.927028i	$0.622354\pi$
$402$	−11.0154	+	7.07916i	−0.549398	+	0.353076i
$403$	−3.87672	+	2.49141i	−0.193113	+	0.124106i
$404$	−22.5930	−	26.0737i	−1.12404	−	1.29721i
$405$	27.6889	−	8.13018i	1.37587	−	0.403992i
$406$	1.49893	−	10.4253i	0.0743905	−	0.517397i
$407$	1.01084	−	1.16657i	0.0501053	−	0.0578246i
$408$	−3.18493	+	6.97402i	−0.157678	+	0.345266i
$409$	12.5570	+	3.68706i	0.620902	+	0.182313i	0.577029	−	0.816724i	$-0.304212\pi$
$409$	12.5570	+	3.68706i	0.620902	+	0.182313i	0.0438731	+	0.999037i	$0.486030\pi$
$410$	4.16335	+	9.11646i	0.205613	+	0.450230i
$411$	−3.64355	−	25.3414i	−0.179723	−	1.25000i
$412$	9.71887	+	6.24594i	0.478814	+	0.307715i
$413$	0.209817			0.0103244
$414$		0			0
$415$	0.935353			0.0459147
$416$	−12.5945	−	8.09400i	−0.617497	−	0.396841i
$417$	5.42910	+	37.7602i	0.265864	+	1.84913i
$418$	0.0880070	+	0.192709i	0.00430456	+	0.00942568i
$419$	1.94364	+	0.570703i	0.0949529	+	0.0278807i	0.328864	−	0.944377i	$-0.393334\pi$
$419$	1.94364	+	0.570703i	0.0949529	+	0.0278807i	−0.233911	+	0.972258i	$0.575152\pi$
$420$	−14.2886	+	31.2877i	−0.697213	+	1.52668i
$421$	−9.43724	+	10.8912i	−0.459943	+	0.530802i	−0.937587	−	0.347751i	$-0.886945\pi$
$421$	−9.43724	+	10.8912i	−0.459943	+	0.530802i	0.477644	+	0.878553i	$0.341491\pi$
$422$	0.563679	−	3.92047i	0.0274395	−	0.190846i
$423$	2.56229	−	0.752356i	0.124583	−	0.0365808i
$424$	−10.1469	−	11.7102i	−0.492777	−	0.568695i
$425$	2.80521	−	1.80280i	0.136073	−	0.0874486i
$426$	−7.40079	+	4.75620i	−0.358569	+	0.230439i
$427$	−0.0988608	−	0.114091i	−0.00478421	−	0.00552127i
$428$	2.19687	−	0.645060i	0.106190	−	0.0311802i
$429$	−0.219443	+	1.52626i	−0.0105948	+	0.0736886i
$430$	2.16375	−	2.49710i	0.104345	−	0.120421i
$431$	5.53130	−	12.1119i	0.266433	−	0.583408i	−0.728374	−	0.685179i	$-0.759724\pi$
$431$	5.53130	−	12.1119i	0.266433	−	0.583408i	0.994808	+	0.101772i	$0.0324511\pi$
$432$	6.47459	+	1.90111i	0.311509	+	0.0914673i
$433$	−14.6800	−	32.1448i	−0.705477	−	1.54478i	−0.833201	−	0.552970i	$-0.813494\pi$
$433$	−14.6800	−	32.1448i	−0.705477	−	1.54478i	0.127724	−	0.991810i	$-0.459233\pi$
$434$	−0.348800	−	2.42596i	−0.0167429	−	0.116450i
$435$	−31.1299	−	20.0059i	−1.49256	−	0.959212i
$436$	12.5399			0.600553
$437$		0			0
$438$	−0.705171			−0.0336944
$439$	−10.8649	−	6.98248i	−0.518556	−	0.333255i	0.255045	−	0.966929i	$-0.417910\pi$
$439$	−10.8649	−	6.98248i	−0.518556	−	0.333255i	−0.773600	+	0.633674i	$0.781546\pi$
$440$	−0.152480	−	1.06052i	−0.00726922	−	0.0505585i
$441$	3.50453	+	7.67386i	0.166883	+	0.365422i
$442$	2.70870	+	0.795348i	0.128840	+	0.0378308i
$443$	−2.96436	+	6.49103i	−0.140841	+	0.308398i	−0.966887	−	0.255204i	$-0.917858\pi$
$443$	−2.96436	+	6.49103i	−0.140841	+	0.308398i	0.826047	+	0.563602i	$0.190585\pi$
$444$	17.2454	−	19.9022i	0.818428	−	0.944517i
$445$	−5.95166	+	41.3947i	−0.282136	+	1.96230i
$446$	4.95983	−	1.45634i	0.234855	−	0.0689595i
$447$	−10.5790	−	12.2088i	−0.500367	−	0.577455i
$448$	−8.60345	+	5.52910i	−0.406475	+	0.261226i
$449$	−2.57777	+	1.65663i	−0.121652	+	0.0781812i	−0.600052	−	0.799961i	$-0.704853\pi$
$449$	−2.57777	+	1.65663i	−0.121652	+	0.0781812i	0.478400	+	0.878142i	$0.341217\pi$
$450$	−1.00730	−	1.16248i	−0.0474844	−	0.0547999i
$451$	1.77018	−	0.519771i	0.0833544	−	0.0244751i
$452$	−0.340677	+	2.36946i	−0.0160241	+	0.111450i
$453$	−24.6844	+	28.4873i	−1.15977	+	1.33845i
$454$	4.61869	−	10.1135i	0.216766	−	0.474651i
$455$	25.8782	+	7.59852i	1.21319	+	0.356224i
$456$	3.19735	+	7.00123i	0.149730	+	0.327863i
$457$	2.40830	+	16.7501i	0.112655	+	0.783536i	0.965319	+	0.261075i	$0.0840769\pi$
$457$	2.40830	+	16.7501i	0.112655	+	0.783536i	−0.852663	+	0.522461i	$0.825014\pi$
$458$	−5.71601	−	3.67346i	−0.267092	−	0.171649i
$459$	−4.85756			−0.226732
$460$		0			0
$461$	−3.84880			−0.179257			−0.0896283	−	0.995975i	$-0.528568\pi$
$461$	−3.84880			−0.179257			−0.0896283	+	0.995975i	$0.528568\pi$
$462$	−0.689903	−	0.443373i	−0.0320972	−	0.0206276i
$463$	−1.62503	−	11.3024i	−0.0755217	−	0.525265i	−0.992104	−	0.125419i	$-0.959973\pi$
$463$	−1.62503	−	11.3024i	−0.0755217	−	0.525265i	0.916582	−	0.399846i	$-0.130937\pi$
$464$	−7.19693	−	15.7591i	−0.334109	−	0.731596i
$465$	−8.26205	−	2.42596i	−0.383143	−	0.112501i
$466$	4.89814	−	10.7254i	0.226902	−	0.496846i
$467$	18.4225	−	21.2607i	0.852492	−	0.983829i	−0.147494	−	0.989063i	$-0.547121\pi$
$467$	18.4225	−	21.2607i	0.852492	−	0.983829i	0.999986	+	0.00523432i	$0.00166614\pi$
$468$	−1.43087	+	9.95195i	−0.0661422	+	0.460029i
$469$	40.4529	−	11.8780i	1.86794	−	0.548477i
$470$	1.17069	+	1.35105i	0.0539998	+	0.0623191i
$471$	33.3735	−	21.4478i	1.53777	−	0.988263i
$472$	−0.0938026	+	0.0602832i	−0.00431761	+	0.00277476i
$473$	−0.398310	−	0.459674i	−0.0183143	−	0.0211358i
$474$	−12.1192	+	3.55853i	−0.556654	+	0.163448i
$475$	0.476408	−	3.31349i	0.0218591	−	0.152033i
$476$	7.59136	−	8.76090i	0.347949	−	0.401555i
$477$	−6.61564	+	14.4862i	−0.302909	+	0.663279i
$478$	−0.107924	−	0.0316893i	−0.00493632	−	0.00144943i
$479$	9.90583	+	21.6907i	0.452609	+	0.991075i	0.989110	+	0.147176i	$0.0470184\pi$
$479$	9.90583	+	21.6907i	0.452609	+	0.991075i	−0.536501	+	0.843899i	$0.680254\pi$
$480$	−3.98120	−	27.6898i	−0.181716	−	1.26386i
$481$	−17.3714	−	11.1639i	−0.792066	−	0.509030i
$482$	−2.52266			−0.114904
$483$		0			0
$484$	19.3847			0.881122
$485$	0.869865	+	0.559029i	0.0394986	+	0.0253842i
$486$	1.15508	+	8.03373i	0.0523953	+	0.364418i
$487$	7.14442	+	15.6441i	0.323745	+	0.708902i	0.999604	−	0.0281285i	$-0.00895475\pi$
$487$	7.14442	+	15.6441i	0.323745	+	0.708902i	−0.675860	+	0.737030i	$0.736227\pi$
$488$	0.0769776	+	0.0226027i	0.00348461	+	0.00102317i
$489$	13.6444	−	29.8772i	0.617023	−	1.35109i
$490$	−3.69831	+	4.26808i	−0.167073	+	0.192812i
$491$	4.86047	−	33.8053i	0.219350	−	1.52561i	−0.521098	−	0.853497i	$-0.674477\pi$
$491$	4.86047	−	33.8053i	0.219350	−	1.52561i	0.740448	−	0.672114i	$-0.234614\pi$
$492$	30.2001	−	8.86755i	1.36153	−	0.399780i
$493$	8.16698	+	9.42520i	0.367822	+	0.424490i
$494$	2.38417	−	1.53221i	0.107269	−	0.0689376i
$495$	−0.926394	+	0.595357i	−0.0416383	+	0.0267593i
$496$	−2.64003	−	3.04676i	−0.118541	−	0.136804i
$497$	27.1786	−	7.98037i	1.21913	−	0.357969i
$498$	−0.0541465	+	0.376597i	−0.00242636	+	0.0168757i
$499$	−20.0190	+	23.1032i	−0.896175	+	1.03424i	0.103042	+	0.994677i	$0.467142\pi$
$499$	−20.0190	+	23.1032i	−0.896175	+	1.03424i	−0.999217	+	0.0395637i	$0.987403\pi$
$500$	6.23889	−	13.6613i	0.279012	−	0.610950i
$501$	−16.1529	−	4.74293i	−0.721660	−	0.211899i
$502$	5.80655	+	12.7146i	0.259159	+	0.567479i
$503$	−2.78627	−	19.3789i	−0.124233	−	0.864063i	−0.952676	−	0.303988i	$-0.901682\pi$
$503$	−2.78627	−	19.3789i	−0.124233	−	0.864063i	0.828442	−	0.560075i	$-0.189228\pi$
$504$	−9.57964	−	6.15646i	−0.426711	−	0.274230i
$505$	−50.5495			−2.24942
$506$		0			0
$507$	−8.01947			−0.356157
$508$	−14.5428	−	9.34609i	−0.645232	−	0.414666i
$509$	0.416422	+	2.89628i	0.0184576	+	0.128375i	0.996967	−	0.0778277i	$-0.0247984\pi$
$509$	0.416422	+	2.89628i	0.0184576	+	0.128375i	−0.978509	+	0.206203i	$0.933889\pi$
$510$	2.19135	+	4.79838i	0.0970344	+	0.212476i
$511$	2.17857	+	0.639685i	0.0963742	+	0.0282980i
$512$	9.45633	−	20.7065i	0.417915	−	0.915105i
$513$	−3.19344	+	3.68542i	−0.140994	+	0.162715i
$514$	−0.770680	+	5.36020i	−0.0339932	+	0.236428i
$515$	16.2414	−	4.76890i	0.715681	−	0.210143i
$516$	−6.79536	−	7.84226i	−0.299149	−	0.345236i
$517$	0.276843	−	0.177916i	0.0121755	−	0.00782475i
$518$	9.23896	−	5.93752i	0.405937	−	0.260880i
$519$	−8.63529	−	9.96565i	−0.379047	−	0.437444i
$520$	−13.7525	+	4.03809i	−0.603086	+	0.177082i
$521$	4.89880	−	34.0719i	0.214620	−	1.49272i	−0.542841	−	0.839836i	$-0.682651\pi$
$521$	4.89880	−	34.0719i	0.214620	−	1.49272i	0.757461	−	0.652881i	$-0.226440\pi$
$522$	3.76731	−	4.34771i	0.164891	−	0.190294i
$523$	−1.73654	+	3.80249i	−0.0759335	+	0.166271i	−0.943792	−	0.330541i	$-0.892769\pi$
$523$	−1.73654	+	3.80249i	−0.0759335	+	0.166271i	0.867858	+	0.496812i	$0.165496\pi$
$524$	−8.53669	−	2.50660i	−0.372927	−	0.109501i
$525$	5.38316	+	11.7875i	0.234940	+	0.514447i
$526$	−1.64145	−	11.4166i	−0.0715707	−	0.497785i
$527$	2.44138	+	1.56898i	0.106348	+	0.0683458i
$528$	−1.34895			−0.0587054
$529$		0			0
$530$	−10.6609			−0.463082
$531$	0.0964094	+	0.0619586i	0.00418381	+	0.00268877i
$532$	−1.65620	−	11.5191i	−0.0718052	−	0.499416i
$533$	−10.2526	−	22.4500i	−0.444088	−	0.972417i
$534$	−16.3220	−	4.79258i	−0.706323	−	0.207395i
$535$	1.39360	−	3.05156i	0.0602506	−	0.131930i
$536$	−14.6725	+	16.9330i	−0.633755	+	0.731392i
$537$	−1.12636	+	7.83402i	−0.0486061	+	0.338063i
$538$	−3.01588	+	0.885544i	−0.130024	+	0.0381785i
$539$	0.680797	+	0.785682i	0.0293240	+	0.0338417i
$540$	9.74278	−	6.26131i	0.419263	−	0.269444i
$541$	6.25381	−	4.01908i	0.268872	−	0.172794i	−0.399257	−	0.916839i	$-0.630732\pi$
$541$	6.25381	−	4.01908i	0.268872	−	0.172794i	0.668129	+	0.744045i	$0.267095\pi$
$542$	−6.28264	−	7.25055i	−0.269863	−	0.311438i
$543$	40.3334	−	11.8429i	1.73087	−	0.508230i
$544$	−1.34176	+	9.33217i	−0.0575276	+	0.400113i
$545$	12.0320	−	13.8856i	0.515392	−	0.594795i
$546$	−4.55742	+	9.97935i	−0.195039	+	0.427077i
$547$	−12.9654	−	3.80699i	−0.554362	−	0.162775i	−0.00746009	−	0.999972i	$-0.502375\pi$
$547$	−12.9654	−	3.80699i	−0.554362	−	0.162775i	−0.546902	+	0.837197i	$0.684193\pi$
$548$	−8.54587	−	18.7128i	−0.365062	−	0.799373i
$549$	−0.0117348	−	0.0816177i	−0.000500831	−	0.00348336i
$550$	−0.159461	−	0.102480i	−0.00679945	−	0.00436974i
$551$	12.5200			0.533369
$552$		0			0
$553$	40.6694			1.72944
$554$	−3.06195	−	1.96780i	−0.130090	−	0.0836037i
$555$	−5.49119	−	38.1920i	−0.233088	−	1.62116i
$556$	12.7338	+	27.8832i	0.540036	+	1.18251i
$557$	21.4186	+	6.28906i	0.907534	+	0.266476i	0.702003	−	0.712174i	$-0.252289\pi$
$557$	21.4186	+	6.28906i	0.907534	+	0.266476i	0.205532	+	0.978650i	$0.434108\pi$
$558$	0.556109	−	1.21771i	0.0235420	−	0.0515498i
$559$	−5.32839	+	6.14929i	−0.225367	+	0.260087i
$560$	−3.35788	+	23.3546i	−0.141897	+	0.986912i
$561$	0.931719	−	0.273577i	0.0393372	−	0.0115504i
$562$	−10.0749	−	11.6271i	−0.424985	−	0.490458i
$563$	12.3698	−	7.94960i	0.521326	−	0.335036i	−0.253371	−	0.967369i	$-0.581539\pi$
$563$	12.3698	−	7.94960i	0.521326	−	0.335036i	0.774696	+	0.632334i	$0.217903\pi$
$564$	4.72308	−	3.03534i	0.198877	−	0.127811i
$565$	2.29686	+	2.65072i	0.0966297	+	0.111517i
$566$	−2.77506	+	0.814832i	−0.116645	+	0.0342500i
$567$	5.37889	−	37.4110i	0.225892	−	1.57111i
$568$	−9.85785	+	11.3766i	−0.413626	+	0.477350i
$569$	−14.4346	+	31.6074i	−0.605131	+	1.32505i	0.320725	+	0.947172i	$0.396074\pi$
$569$	−14.4346	+	31.6074i	−0.605131	+	1.32505i	−0.925855	+	0.377879i	$0.876654\pi$
$570$	5.08114	+	1.49196i	0.212826	+	0.0624912i
$571$	9.25542	+	20.2665i	0.387327	+	0.848128i	0.998400	+	0.0565534i	$0.0180111\pi$
$571$	9.25542	+	20.2665i	0.387327	+	0.848128i	−0.611072	+	0.791575i	$0.709262\pi$
$572$	0.176328	+	1.22639i	0.00737266	+	0.0512780i
$573$	24.2656	+	15.5946i	1.01371	+	0.651472i
$574$	13.1262			0.547878
$575$		0			0
$576$	−5.58596			−0.232748
$577$	−1.76606	−	1.13498i	−0.0735220	−	0.0472497i	0.503363	−	0.864075i	$-0.332096\pi$
$577$	−1.76606	−	1.13498i	−0.0735220	−	0.0472497i	−0.576885	+	0.816825i	$0.695732\pi$
$578$	0.905595	+	6.29855i	0.0376678	+	0.261985i
$579$	8.58996	+	18.8094i	0.356987	+	0.781692i
$580$	−28.5294	−	8.37698i	−1.18462	−	0.347835i
$581$	0.508905	−	1.11435i	0.0211129	−	0.0462309i
$582$	−0.275434	+	0.317868i	−0.0114171	+	0.0131761i
$583$	−0.279293	+	1.94253i	−0.0115671	+	0.0804512i
$584$	−1.15776	+	0.339949i	−0.0479084	+	0.0140672i
$585$	9.64702	+	11.1333i	0.398855	+	0.460303i
$586$	11.7867	−	7.57487i	0.486905	−	0.312915i
$587$	−14.0507	+	9.02983i	−0.579934	+	0.372701i	−0.797477	−	0.603350i	$-0.793832\pi$
$587$	−14.0507	+	9.02983i	−0.579934	+	0.372701i	0.217543	+	0.976051i	$0.430196\pi$
$588$	11.6147	+	13.4041i	0.478983	+	0.552776i
$589$	2.79538	−	0.820798i	0.115182	−	0.0338204i
$590$	−0.0109181	+	0.0759374i	−0.000449493	+	0.00312629i
$591$	14.9543	−	17.2581i	0.615136	−	0.709905i
$592$	7.50434	−	16.4322i	0.308427	−	0.675360i
$593$	30.4220	+	8.93272i	1.24928	+	0.366823i	0.838496	−	0.544908i	$-0.183436\pi$
$593$	30.4220	+	8.93272i	1.24928	+	0.366823i	0.410788	+	0.911731i	$0.365254\pi$
$594$	0.114707	+	0.251174i	0.00470650	+	0.0103058i
$595$	−2.41721	−	16.8120i	−0.0990958	−	0.689226i
$596$	−10.9200	−	7.01783i	−0.447299	−	0.287461i
$597$	−22.6016			−0.925021
$598$		0			0
$599$	−2.96111			−0.120988			−0.0604938	−	0.998169i	$-0.519268\pi$
$599$	−2.96111			−0.120988			−0.0604938	+	0.998169i	$0.519268\pi$
$600$	−5.79334	−	3.72315i	−0.236512	−	0.151997i
$601$	2.92096	+	20.3158i	0.119149	+	0.828697i	0.958497	+	0.285103i	$0.0920278\pi$
$601$	2.92096	+	20.3158i	0.119149	+	0.828697i	−0.839348	+	0.543594i	$0.817063\pi$
$602$	−1.79771	−	3.93643i	−0.0732690	−	0.160437i
$603$	22.0954	+	6.48779i	0.899793	+	0.264203i
$604$	−12.5822	+	27.5511i	−0.511961	+	1.12104i
$605$	18.5995	−	21.4649i	0.756176	−	0.872673i
$606$	2.92625	−	20.3525i	0.118871	−	0.826765i
$607$	5.18594	−	1.52273i	0.210491	−	0.0618056i	−0.174787	−	0.984606i	$-0.555924\pi$
$607$	5.18594	−	1.52273i	0.210491	−	0.0618056i	0.385278	+	0.922801i	$0.374106\pi$
$608$	6.19820	+	7.15310i	0.251370	+	0.290097i
$609$	−40.7714	+	26.2022i	−1.65214	+	1.06177i
$610$	0.0464366	−	0.0298430i	0.00188016	−	0.00120831i
$611$	−2.88291	−	3.32706i	−0.116630	−	0.134598i
$612$	6.07525	−	1.78386i	0.245578	−	0.0721081i
$613$	1.49069	−	10.3680i	0.0602084	−	0.418759i	−0.937319	−	0.348474i	$-0.886700\pi$
$613$	1.49069	−	10.3680i	0.0602084	−	0.418759i	0.997527	−	0.0702849i	$-0.0223908\pi$
$614$	2.68787	−	3.10196i	0.108473	−	0.125185i
$615$	19.1576	−	41.9493i	0.772510	−	1.69156i
$616$	−1.34643	−	0.395348i	−0.0542493	−	0.0159290i
$617$	−8.01430	−	17.5489i	−0.322643	−	0.706490i	0.676919	−	0.736057i	$-0.263315\pi$
$617$	−8.01430	−	17.5489i	−0.322643	−	0.706490i	−0.999563	+	0.0295667i	$0.990587\pi$
$618$	0.979887	+	6.81526i	0.0394168	+	0.274150i
$619$	0.232161	+	0.149201i	0.00933134	+	0.00599689i	0.545298	−	0.838242i	$-0.316416\pi$
$619$	0.232161	+	0.149201i	0.00933134	+	0.00599689i	−0.535967	+	0.844239i	$0.680053\pi$
$620$	−6.91904			−0.277875
$621$		0			0
$622$	0.101095			0.00405353
$623$	46.0780	+	29.6126i	1.84608	+	1.18640i
$624$	2.56815	+	17.8619i	0.102808	+	0.715048i
$625$	−12.7358	−	27.8876i	−0.509434	−	1.11550i
$626$	13.5389	+	3.97538i	0.541123	+	0.158888i
$627$	0.404964	−	0.886747i	0.0161727	−	0.0354133i
$628$	20.8748	−	24.0909i	0.832997	−	0.961330i
$629$	−1.85067	+	12.8717i	−0.0737910	+	0.513228i
$630$	−7.51753	+	2.20735i	−0.299505	+	0.0879427i
$631$	−24.8043	−	28.6257i	−0.987445	−	1.13957i	−0.990211	−	0.139576i	$-0.955426\pi$
$631$	−24.8043	−	28.6257i	−0.987445	−	1.13957i	0.00276642	−	0.999996i	$-0.499119\pi$
$632$	−18.1820	+	11.6849i	−0.723241	+	0.464799i
$633$	−15.3323	+	9.85347i	−0.609404	+	0.391640i
$634$	−8.23897	−	9.50828i	−0.327211	−	0.377622i
$635$	−24.3028	+	7.13593i	−0.964426	+	0.283181i
$636$	−4.76488	+	33.1405i	−0.188940	+	1.31410i
$637$	9.10737	−	10.5105i	0.360847	−	0.416440i
$638$	0.294500	−	0.644865i	0.0116594	−	0.0255304i
$639$	14.8450	+	4.35888i	0.587259	+	0.172435i
$640$	−12.1007	−	26.4968i	−0.478321	−	1.04738i
$641$	3.07550	+	21.3905i	0.121475	+	0.844876i	0.955887	+	0.293735i	$0.0948983\pi$
$641$	3.07550	+	21.3905i	0.121475	+	0.844876i	−0.834412	+	0.551141i	$0.814193\pi$
$642$	1.14796	+	0.737750i	0.0453064	+	0.0291167i
$643$	26.9690			1.06355			0.531777	−	0.846884i	$-0.321524\pi$
$643$	26.9690			1.06355			0.531777	+	0.846884i	$0.321524\pi$
$644$		0			0
$645$	−15.2039			−0.598655
$646$	−1.50144	−	0.964919i	−0.0590735	−	0.0379642i
$647$	1.35025	+	9.39117i	0.0530837	+	0.369205i	0.998997	+	0.0447846i	$0.0142601\pi$
$647$	1.35025	+	9.39117i	0.0530837	+	0.369205i	−0.945913	+	0.324420i	$0.894831\pi$
$648$	8.34394	+	18.2707i	0.327781	+	0.717740i
$649$	0.0135505	+	0.00397878i	0.000531903	+	0.000156181i
$650$	−1.05338	+	2.30659i	−0.0413171	+	0.0904718i
$651$	−7.38540	+	8.52320i	−0.289456	+	0.334051i
$652$	3.75599	−	26.1235i	0.147096	−	1.02307i
$653$	−21.9405	+	6.44231i	−0.858598	+	0.252107i	−0.681259	−	0.732043i	$-0.738567\pi$
$653$	−21.9405	+	6.44231i	−0.858598	+	0.252107i	−0.177339	+	0.984150i	$0.556749\pi$
$654$	4.89419	+	5.64819i	0.191378	+	0.220862i
$655$	−10.9665	+	7.04773i	−0.428496	+	0.275378i
$656$	18.1636	−	11.6730i	0.709168	−	0.455754i
$657$	0.812139	+	0.937258i	0.0316846	+	0.0365659i
$658$	2.24653	−	0.659642i	0.0875790	−	0.0257155i
$659$	−3.61515	+	25.1440i	−0.140826	+	0.979469i	0.789765	+	0.613410i	$0.210202\pi$
$659$	−3.61515	+	25.1440i	−0.140826	+	0.979469i	−0.930591	+	0.366060i	$0.880707\pi$
$660$	−1.51611	+	1.74968i	−0.0590144	+	0.0681062i
$661$	−6.41009	+	14.0361i	−0.249323	+	0.545942i	−0.992370	−	0.123298i	$-0.960653\pi$
$661$	−6.41009	+	14.0361i	−0.249323	+	0.545942i	0.743046	+	0.669240i	$0.233380\pi$
$662$	−10.4569	−	3.07043i	−0.406419	−	0.119335i
$663$	−5.39636	−	11.8164i	−0.209577	−	0.458910i
$664$	0.0926514	+	0.644405i	0.00359557	+	0.0250078i
$665$	−14.3444	−	9.21856i	−0.556251	−	0.357480i
$666$	5.99858			0.232440
$667$		0			0
$668$	−13.5273			−0.523386
$669$	−20.0102	−	12.8597i	−0.773637	−	0.497186i
$670$	2.19390	+	15.2589i	0.0847576	+	0.589502i
$671$	−0.00422114	−	0.00924301i	−0.000162955	−	0.000356823i
$672$	−35.1548	−	10.3224i	−1.35612	−	0.398194i
$673$	−9.91371	+	21.7080i	−0.382145	+	0.836781i	0.616628	+	0.787255i	$0.288498\pi$
$673$	−9.91371	+	21.7080i	−0.382145	+	0.836781i	−0.998773	+	0.0495264i	$0.984229\pi$
$674$	0.187452	−	0.216331i	0.00722039	−	0.00833277i
$675$	0.620945	−	4.31877i	0.0239002	−	0.166229i
$676$	−6.18283	+	1.81544i	−0.237801	+	0.0698247i
$677$	6.92333	+	7.98995i	0.266085	+	0.307079i	0.873031	−	0.487664i	$-0.162151\pi$
$677$	6.92333	+	7.98995i	0.266085	+	0.307079i	−0.606946	+	0.794743i	$0.707606\pi$
$678$	−1.20021	+	0.771327i	−0.0460937	+	0.0296226i
$679$	1.13928	−	0.732172i	0.0437216	−	0.0280982i
$680$	5.91098	+	6.82164i	0.226676	+	0.261598i
$681$	−49.0883	+	14.4136i	−1.88107	+	0.552331i
$682$	0.0234773	−	0.163288i	0.000898994	−	0.00625264i
$683$	−4.85481	+	5.60275i	−0.185764	+	0.214383i	−0.840991	−	0.541049i	$-0.818027\pi$
$683$	−4.85481	+	5.60275i	−0.185764	+	0.214383i	0.655227	+	0.755432i	$0.272573\pi$
$684$	2.64056	−	5.78201i	0.100964	−	0.221081i
$685$	−28.9207	−	8.49188i	−1.10500	−	0.324458i
$686$	−1.65912	−	3.63296i	−0.0633455	−	0.138707i
$687$	4.44954	+	30.9473i	0.169761	+	1.18071i
$688$	−5.98822	−	3.84839i	−0.228299	−	0.146719i
$689$	26.2534			1.00018
$690$		0			0
$691$	−29.9490			−1.13932			−0.569658	−	0.821882i	$-0.692924\pi$
$691$	−29.9490			−1.13932			−0.569658	+	0.821882i	$0.692924\pi$
$692$	−8.91364	−	5.72845i	−0.338846	−	0.217763i
$693$	0.205257	+	1.42759i	0.00779707	+	0.0542298i
$694$	0.115266	+	0.252397i	0.00437544	+	0.00958087i
$695$	43.0935	+	12.6534i	1.63463	+	0.479971i
$696$	10.6994	−	23.4284i	0.405559	−	0.888050i
$697$	−10.1782	+	11.7463i	−0.385527	+	0.444921i
$698$	−1.48019	+	10.2950i	−0.0560261	+	0.389670i
$699$	−52.0582	+	15.2857i	−1.96902	+	0.578157i
$700$	6.81873	+	7.86924i	0.257724	+	0.297429i
$701$	−4.51644	+	2.90254i	−0.170584	+	0.109627i	−0.623147	−	0.782105i	$-0.714146\pi$
$701$	−4.51644	+	2.90254i	−0.170584	+	0.109627i	0.452563	+	0.891732i	$0.350510\pi$
$702$	3.10750	−	1.99707i	0.117285	−	0.0753745i
$703$	8.54906	+	9.86614i	0.322434	+	0.372108i
$704$	−0.660481	+	0.193935i	−0.0248928	+	0.00730919i
$705$	1.17069	−	8.14232i	0.0440907	−	0.306657i
$706$	−0.209484	+	0.241757i	−0.00788402	+	0.00909864i
$707$	−27.5029	+	60.2229i	−1.03435	+	2.26492i
$708$	0.231178	+	0.0678800i	0.00868820	+	0.00255109i
$709$	−3.14017	−	6.87601i	−0.117932	−	0.258234i	0.841456	−	0.540326i	$-0.181699\pi$
$709$	−3.14017	−	6.87601i	−0.117932	−	0.258234i	−0.959387	+	0.282092i	$0.908972\pi$
$710$	1.47399	+	10.2518i	0.0553178	+	0.384744i
$711$	18.6873	+	12.0096i	0.700829	+	0.450395i
$712$	−29.1081			−1.09087
$713$		0			0
$714$	6.90888			0.258558
$715$	1.52719	+	0.981462i	0.0571135	+	0.0367046i
$716$	0.905061	+	6.29484i	0.0338237	+	0.235249i
$717$	0.215009	+	0.470804i	0.00802965	+	0.0175825i
$718$	−7.40075	−	2.17306i	−0.276194	−	0.0810977i
$719$	−14.0360	+	30.7345i	−0.523454	+	1.14620i	0.444661	+	0.895699i	$0.353324\pi$
$719$	−14.0360	+	30.7345i	−0.523454	+	1.14620i	−0.968115	+	0.250505i	$0.919403\pi$
$720$	−8.43950	+	9.73970i	−0.314521	+	0.362977i
$721$	3.15508	−	21.9441i	0.117501	−	0.817240i
$722$	7.01121	−	2.05868i	0.260930	−	0.0766161i
$723$	7.60164	+	8.77276i	0.282708	+	0.326262i
$724$	28.4151	−	18.2613i	1.05604	−	0.678676i
$725$	−9.42375	+	6.05628i	−0.349989	+	0.224924i
$726$	7.56562	+	8.73119i	0.280786	+	0.324045i
$727$	8.99199	−	2.64029i	0.333494	−	0.0979228i	−0.110698	−	0.993854i	$-0.535309\pi$
$727$	8.99199	−	2.64029i	0.333494	−	0.0979228i	0.444193	+	0.895931i	$0.353491\pi$
$728$	−2.67158	+	18.5813i	−0.0990154	+	0.688667i
$729$	2.60461	−	3.00588i	0.0964670	−	0.111329i
$730$	−0.344881	+	0.755185i	−0.0127646	+	0.0279506i
$731$	4.91655	+	1.44363i	0.181845	+	0.0533945i
$732$	−0.0720148	−	0.157690i	−0.00266174	−	0.00582840i
$733$	2.87062	+	19.9656i	0.106029	+	0.737447i	0.971595	+	0.236652i	$0.0760501\pi$
$733$	2.87062	+	19.9656i	0.106029	+	0.737447i	−0.865566	+	0.500796i	$0.833041\pi$
$734$	10.9766	+	7.05424i	0.405154	+	0.260377i
$735$	25.9868			0.958538
$736$		0			0
$737$	2.83779			0.104531
$738$	6.03140	+	3.87615i	0.222019	+	0.142683i
$739$	−4.71756	−	32.8114i	−0.173538	−	1.20699i	−0.871334	−	0.490690i	$-0.836745\pi$
$739$	−4.71756	−	32.8114i	−0.173538	−	1.20699i	0.697796	−	0.716297i	$-0.254164\pi$
$740$	−12.8795	−	28.2021i	−0.473459	−	1.03673i
$741$	−12.5127	−	3.67406i	−0.459666	−	0.134970i
$742$	−5.80039	+	12.7011i	−0.212939	+	0.466271i
$743$	8.64614	−	9.97818i	0.317196	−	0.366064i	−0.574653	−	0.818397i	$-0.694863\pi$
$743$	8.64614	−	9.97818i	0.317196	−	0.366064i	0.891849	+	0.452333i	$0.149408\pi$
$744$	0.852947	−	5.93238i	0.0312706	−	0.217492i
$745$	−18.2486	+	5.35826i	−0.668575	+	0.196311i
$746$	5.19381	+	5.99398i	0.190159	+	0.219455i
$747$	0.562903	−	0.361756i	0.0205955	−	0.0132360i
$748$	0.656402	−	0.421844i	0.0240004	−	0.0154241i
$749$	−2.87729	−	3.32057i	−0.105134	−	0.121331i
$750$	8.58823	−	2.52173i	0.313598	−	0.0920807i
$751$	−3.54101	+	24.6282i	−0.129213	+	0.898697i	0.817342	+	0.576154i	$0.195447\pi$
$751$	−3.54101	+	24.6282i	−0.129213	+	0.898697i	−0.946555	+	0.322544i	$0.895462\pi$
$752$	2.52206	−	2.91061i	0.0919699	−	0.106139i
$753$	26.7188	−	58.5060i	0.973687	−	2.13208i
$754$	−9.09956	−	2.67187i	−0.331386	−	0.0973038i
$755$	18.4352	+	40.3675i	0.670926	+	1.46912i
$756$	−2.15867	−	15.0138i	−0.0785099	−	0.546048i
$757$	21.5184	+	13.8291i	0.782101	+	0.502626i	0.869730	−	0.493527i	$-0.164293\pi$
$757$	21.5184	+	13.8291i	0.782101	+	0.502626i	−0.0876293	+	0.996153i	$0.527929\pi$
$758$	−5.62941			−0.204469
$759$		0			0
$760$	9.06153			0.328696
$761$	27.6306	+	17.7571i	1.00161	+	0.643696i	0.935209	−	0.354097i	$-0.115212\pi$
$761$	27.6306	+	17.7571i	1.00161	+	0.643696i	0.0664016	+	0.997793i	$0.478848\pi$
$762$	−1.46625	−	10.1980i	−0.0531167	−	0.369434i
$763$	−9.99651	−	21.8893i	−0.361898	−	0.792446i
$764$	22.2385	+	6.52982i	0.804562	+	0.236241i
$765$	3.85388	−	8.43881i	0.139337	−	0.305106i
$766$	3.51624	−	4.05796i	0.127047	−	0.146620i
$767$	0.0268868	−	0.187002i	0.000970826	−	0.00675224i
$768$	−1.35882	+	0.398985i	−0.0490322	+	0.0143971i
$769$	20.4643	+	23.6170i	0.737960	+	0.851651i	0.993344	−	0.115189i	$-0.0367472\pi$
$769$	20.4643	+	23.6170i	0.737960	+	0.851651i	−0.255384	+	0.966840i	$0.582202\pi$
$770$	−0.812233	+	0.521991i	−0.0292708	+	0.0188112i
$771$	20.9628	−	13.4720i	0.754957	−	0.485181i
$772$	10.8807	+	12.5570i	0.391606	+	0.451938i
$773$	−6.55151	+	1.92370i	−0.235641	+	0.0691906i	−0.397421	−	0.917636i	$-0.630095\pi$
$773$	−6.55151	+	1.92370i	−0.235641	+	0.0691906i	0.161780	+	0.986827i	$0.448277\pi$
$774$	0.336386	−	2.33962i	0.0120912	−	0.0840959i
$775$	−1.70703	+	1.97002i	−0.0613184	+	0.0707652i
$776$	−0.298974	+	0.654662i	−0.0107325	+	0.0235010i
$777$	−48.4883	−	14.2374i	−1.73951	−	0.510765i
$778$	0.814265	+	1.78299i	0.0291928	+	0.0639234i
$779$	2.22056	+	15.4443i	0.0795599	+	0.553351i
$780$	26.0545	+	16.7442i	0.932902	+	0.599540i
$781$	1.90660			0.0682234
$782$		0			0
$783$	16.3184			0.583172
$784$	10.2352	+	6.57774i	0.365541	+	0.234919i
$785$	−6.64687	−	46.2300i	−0.237237	−	1.65002i
$786$	−2.20276	−	4.82337i	−0.0785698	−	0.172044i
$787$	−29.1245	−	8.55173i	−1.03818	−	0.304836i	−0.282146	−	0.959372i	$-0.591046\pi$
$787$	−29.1245	−	8.55173i	−1.03818	−	0.304836i	−0.756031	+	0.654535i	$0.772864\pi$
$788$	7.62252	−	16.6910i	0.271541	−	0.594592i
$789$	−34.7557	+	40.1102i	−1.23733	+	1.42796i
$790$	−2.11629	+	14.7192i	−0.0752944	+	0.523684i
$791$	4.40764	−	1.29420i	0.156718	−	0.0460165i
$792$	−0.501931	−	0.579259i	−0.0178353	−	0.0205831i
$793$	−0.114354	+	0.0734907i	−0.00406082	+	0.00260973i
$794$	1.09479	−	0.703580i	0.0388527	−	0.0249691i
$795$	32.1250	+	37.0742i	1.13936	+	1.31489i
$796$	−17.4253	+	5.11653i	−0.617624	+	0.181351i
$797$	−2.81152	+	19.5545i	−0.0995891	+	0.692658i	0.877461	+	0.479648i	$0.159236\pi$
$797$	−2.81152	+	19.5545i	−0.0995891	+	0.692658i	−0.977050	+	0.213010i	$0.931673\pi$
$798$	4.54200	−	5.24175i	0.160785	−	0.185556i
$799$	−1.15169	+	2.52185i	−0.0407439	+	0.0892166i
$800$	−8.12553	−	2.38587i	−0.287281	−	0.0843533i
$801$	12.4280	+	27.2135i	0.439122	+	0.961543i
$802$	1.24203	+	8.63854i	0.0438578	+	0.305037i
$803$	0.128567	+	0.0826249i	0.00453702	+	0.00291577i
$804$	48.4141			1.70743
$805$		0			0
$806$	−2.20686			−0.0777332
$807$	12.1674	+	7.81953i	0.428314	+	0.275260i
$808$	−5.00718	−	34.8257i	−0.176152	−	1.22516i
$809$	−10.7864	−	23.6190i	−0.379231	−	0.830400i	−0.998960	−	0.0455842i	$-0.985485\pi$
$809$	−10.7864	−	23.6190i	−0.379231	−	0.830400i	0.619730	−	0.784815i	$-0.287242\pi$
$810$	13.2600	+	3.89347i	0.465907	+	0.136803i
$811$	22.0312	−	48.2417i	0.773622	−	1.69400i	0.0551099	−	0.998480i	$-0.482449\pi$
$811$	22.0312	−	48.2417i	0.773622	−	1.69400i	0.718512	−	0.695515i	$-0.244824\pi$
$812$	−25.5022	+	29.4311i	−0.894953	+	1.03283i
$813$	−6.28264	+	43.6967i	−0.220342	+	1.53251i
$814$	0.709268	−	0.208260i	0.0248598	−	0.00729951i
$815$	−25.3230	−	29.2243i	−0.887027	−	1.02368i
$816$	9.56024	−	6.14400i	0.334675	−	0.215083i
$817$	4.32749	−	2.78111i	0.151400	−	0.0972987i
$818$	4.10420	+	4.73650i	0.143500	+	0.165608i
$819$	18.5125	−	5.43576i	0.646879	−	0.189941i
$820$	5.27363	−	36.6789i	0.184163	−	1.28088i
$821$	−27.9134	+	32.2137i	−0.974183	+	1.12427i	0.0180456	+	0.999837i	$0.494256\pi$
$821$	−27.9134	+	32.2137i	−0.974183	+	1.12427i	−0.992228	+	0.124430i	$0.960290\pi$
$822$	5.09323	−	11.1526i	0.177647	−	0.388992i
$823$	29.1861	+	8.56980i	1.01736	+	0.298724i	0.747562	−	0.664192i	$-0.231224\pi$
$823$	29.1861	+	8.56980i	1.01736	+	0.298724i	0.269800	+	0.962916i	$0.413042\pi$
$824$	4.89429	+	10.7170i	0.170501	+	0.373345i
$825$	0.124130	+	0.863345i	0.00432166	+	0.0300578i
$826$	0.0845288	+	0.0543234i	0.00294113	+	0.00189015i
$827$	−41.6718			−1.44907			−0.724535	−	0.689238i	$-0.757945\pi$
$827$	−41.6718			−1.44907			−0.724535	+	0.689238i	$0.757945\pi$
$828$		0			0
$829$	−7.98458			−0.277316			−0.138658	−	0.990340i	$-0.544279\pi$
$829$	−7.98458			−0.277316			−0.138658	+	0.990340i	$0.544279\pi$
$830$	0.376825	+	0.242171i	0.0130798	+	0.00840587i
$831$	2.38353	+	16.5778i	0.0826837	+	0.575078i
$832$	3.82539	+	8.37645i	0.132622	+	0.290401i
$833$	−8.40344	−	2.46747i	−0.291162	−	0.0854929i
$834$	−7.58921	+	16.6181i	−0.262793	+	0.575436i
$835$	−12.9793	+	14.9789i	−0.449168	+	0.518367i
$836$	0.111477	−	0.775338i	0.00385550	−	0.0268156i
$837$	3.64347	−	1.06982i	0.125937	−	0.0369783i
$838$	0.635271	+	0.733142i	0.0219451	+	0.0253260i
$839$	28.4352	−	18.2742i	0.981693	−	0.630896i	0.0517738	−	0.998659i	$-0.483513\pi$
$839$	28.4352	−	18.2742i	0.981693	−	0.630896i	0.929920	+	0.367763i	$0.119876\pi$
$840$	−29.5090	+	18.9643i	−1.01816	+	0.654329i
$841$	−8.44500	−	9.74605i	−0.291207	−	0.336071i
$842$	−6.62178	+	1.94433i	−0.228202	+	0.0670061i
$843$	−10.0749	+	70.0726i	−0.346998	+	2.41343i
$844$	−9.59024	+	11.0677i	−0.330110	+	0.380967i
$845$	−3.92212	+	8.58824i	−0.134925	+	0.295444i
$846$	1.22706	+	0.360297i	0.0421871	+	0.0123873i
$847$	−15.4530	−	33.8373i	−0.530971	−	1.16266i
$848$	3.26858	+	22.7335i	0.112244	+	0.780671i
$849$	11.1958	+	7.19513i	0.384240	+	0.246936i
$850$	1.59689			0.0547729
$851$		0			0
$852$	32.5275			1.11437
$853$	−24.4558	−	15.7168i	−0.837352	−	0.538134i	0.0502542	−	0.998736i	$-0.483997\pi$
$853$	−24.4558	−	15.7168i	−0.837352	−	0.538134i	−0.887606	+	0.460603i	$0.847633\pi$
$854$	−0.0102887	−	0.0715598i	−0.000352074	−	0.00244873i
$855$	−3.86891	−	8.47173i	−0.132314	−	0.289727i
$856$	2.24039	+	0.657839i	0.0765750	+	0.0224845i
$857$	−7.26081	+	15.8990i	−0.248024	+	0.543098i	−0.992166	−	0.124924i	$-0.960131\pi$
$857$	−7.26081	+	15.8990i	−0.248024	+	0.543098i	0.744142	+	0.668022i	$0.232859\pi$
$858$	−0.483568	+	0.558068i	−0.0165088	+	0.0190521i
$859$	6.30974	−	43.8852i	0.215286	−	1.49734i	−0.539842	−	0.841766i	$-0.681516\pi$
$859$	6.30974	−	43.8852i	0.215286	−	1.49734i	0.755128	−	0.655578i	$-0.227575\pi$
$860$	−11.7219	+	3.44186i	−0.399713	+	0.117366i
$861$	−39.5537	−	45.6474i	−1.34799	−	1.55566i
$862$	5.36425	−	3.44739i	0.182707	−	0.117419i
$863$	−9.29363	+	5.97265i	−0.316359	+	0.203311i	−0.689177	−	0.724593i	$-0.742028\pi$
$863$	−9.29363	+	5.97265i	−0.316359	+	0.203311i	0.372818	+	0.927904i	$0.378391\pi$
$864$	8.07866	+	9.32327i	0.274842	+	0.317184i
$865$	−14.8958	+	4.37379i	−0.506471	+	0.148713i
$866$	2.40842	−	16.7509i	0.0818414	−	0.569219i
$867$	19.1748	−	22.1289i	0.651211	−	0.751538i
$868$	−3.76450	+	8.24310i	−0.127775	+	0.279789i
$869$	2.62653	+	0.771218i	0.0890989	+	0.0261618i
$870$	−7.36155	−	16.1196i	−0.249580	−	0.546504i
$871$	−5.40264	−	37.5762i	−0.183061	−	1.27322i
$872$	10.7582	+	6.91389i	0.364319	+	0.234134i
$873$	0.739701			0.0250351
$874$		0			0
$875$	−28.8202			−0.974300
$876$	2.19341	+	1.40962i	0.0741085	+	0.0476267i
$877$	2.79964	+	19.4719i	0.0945371	+	0.657520i	0.980898	+	0.194525i	$0.0623164\pi$
$877$	2.79964	+	19.4719i	0.0945371	+	0.657520i	−0.886361	+	0.462996i	$0.846775\pi$
$878$	−2.56933	−	5.62605i	−0.0867107	−	0.189870i
$879$	−61.8596	−	18.1636i	−2.08647	−	0.612643i
$880$	−0.659736	+	1.44462i	−0.0222397	+	0.0486982i
$881$	−13.7208	+	15.8346i	−0.462265	+	0.533483i	−0.938244	−	0.345974i	$-0.887549\pi$
$881$	−13.7208	+	15.8346i	−0.462265	+	0.533483i	0.475979	+	0.879457i	$0.342094\pi$
$882$	−0.574957	+	3.99891i	−0.0193598	+	0.134650i
$883$	39.4453	−	11.5822i	1.32744	−	0.389771i	0.460268	−	0.887780i	$-0.347753\pi$
$883$	39.4453	−	11.5822i	1.32744	−	0.389771i	0.867172	+	0.498009i	$0.165935\pi$
$884$	−6.83546	−	7.88854i	−0.229901	−	0.265320i
$885$	0.296978	−	0.190856i	0.00998281	−	0.00641556i
$886$	−2.87483	+	1.84754i	−0.0965818	+	0.0620694i
$887$	−26.0976	−	30.1182i	−0.876270	−	1.01127i	−0.999821	−	0.0189314i	$-0.993974\pi$
$887$	−26.0976	−	30.1182i	−0.876270	−	1.01127i	0.123551	−	0.992338i	$-0.460572\pi$
$888$	25.7682	−	7.56622i	0.864724	−	0.253906i
$889$	−4.72110	+	32.8360i	−0.158341	+	1.10128i
$890$	−13.1152	+	15.1357i	−0.439622	+	0.507351i
$891$	1.05681	−	2.31409i	0.0354045	−	0.0775250i
$892$	−18.3386	−	5.38469i	−0.614021	−	0.180293i
$893$	1.15618	+	2.53169i	0.0386902	+	0.0847197i
$894$	−1.10098	−	7.65751i	−0.0368224	−	0.256106i
$895$	7.83876	+	5.03767i	0.262021	+	0.168391i
$896$	−38.1510			−1.27454
$897$		0			0
$898$	−1.46742			−0.0489683
$899$	−8.20151	−	5.27079i	−0.273536	−	0.175791i
$900$	0.809388	+	5.62942i	0.0269796	+	0.187647i
$901$	−6.86814	−	15.0391i	−0.228811	−	0.501026i
$902$	0.847723	+	0.248914i	0.0282261	+	0.00828793i
$903$	−8.27213	+	18.1134i	−0.275279	+	0.602777i
$904$	−1.59868	+	1.84497i	−0.0531712	+	0.0613628i
$905$	7.04313	−	48.9861i	0.234122	−	1.62835i
$906$	−17.3202	+	5.08566i	−0.575424	+	0.168960i
$907$	24.9248	+	28.7648i	0.827615	+	0.955118i	0.999550	−	0.0299898i	$-0.00954747\pi$
$907$	24.9248	+	28.7648i	0.827615	+	0.955118i	−0.171935	+	0.985108i	$0.555002\pi$
$908$	−34.5830	+	22.2251i	−1.14768	+	0.737567i
$909$	−30.4211	+	19.5505i	−1.00900	+	0.648448i
$910$	8.45821	+	9.76129i	0.280387	+	0.323584i
$911$	−48.1919	+	14.1504i	−1.59667	+	0.468824i	−0.954617	−	0.297837i	$-0.903735\pi$
$911$	−48.1919	+	14.1504i	−1.59667	+	0.468824i	−0.642052	+	0.766661i	$0.721917\pi$
$912$	1.62362	−	11.2925i	0.0537633	−	0.373932i
$913$	0.0539978	−	0.0623168i	0.00178707	−	0.00206239i
$914$	−3.36651	+	7.37162i	−0.111354	+	0.243831i
$915$	−0.243710	−	0.0715598i	−0.00805682	−	0.00236569i
$916$	10.4363	+	22.8524i	0.344826	+	0.755063i
$917$	2.42979	+	16.8996i	0.0802389	+	0.558074i
$918$	−1.95696	−	1.25766i	−0.0645894	−	0.0415091i
$919$	−50.0605			−1.65134			−0.825671	−	0.564152i	$-0.809203\pi$
$919$	−50.0605			−1.65134			−0.825671	+	0.564152i	$0.809203\pi$
$920$		0			0
$921$	−18.8868			−0.622340
$922$	−1.55056	−	0.996487i	−0.0510651	−	0.0328175i
$923$	−3.62981	−	25.2459i	−0.119477	−	0.830979i
$924$	1.25963	+	2.75820i	0.0414387	+	0.0907381i
$925$	−11.2074	−	3.29079i	−0.368497	−	0.108200i
$926$	2.27160	−	4.97411i	0.0746493	−	0.163459i
$927$	7.92979	−	9.15146i	0.260448	−	0.300573i
$928$	4.50749	−	31.3503i	0.147966	−	1.02912i
$929$	3.45822	−	1.01542i	0.113461	−	0.0333150i	−0.224509	−	0.974472i	$-0.572078\pi$
$929$	3.45822	−	1.01542i	0.113461	−	0.0333150i	0.337970	+	0.941157i	$0.390260\pi$
$930$	−2.70042	−	3.11645i	−0.0885504	−	0.102193i
$931$	−7.39662	+	4.75352i	−0.242414	+	0.155790i
$932$	−36.6754	+	23.5698i	−1.20134	+	0.772055i
$933$	−0.304632	−	0.351564i	−0.00997321	−	0.0115097i
$934$	12.9264	−	3.79554i	0.422966	−	0.124194i
$935$	0.162700	−	1.13160i	0.00532084	−	0.0370073i
$936$	−6.71459	+	7.74904i	−0.219473	+	0.253285i
$937$	14.0160	−	30.6909i	0.457884	−	1.00263i	−0.530081	−	0.847947i	$-0.677838\pi$
$937$	14.0160	−	30.6909i	0.457884	−	1.00263i	0.987965	−	0.154679i	$-0.0494344\pi$
$938$	19.3725	+	5.68829i	0.632536	+	0.185729i
$939$	−26.9726	−	59.0617i	−0.880217	−	1.92741i
$940$	−0.940679	−	6.54256i	−0.0306816	−	0.213395i
$941$	−27.2088	−	17.4860i	−0.886981	−	0.570028i	0.0159219	−	0.999873i	$-0.494932\pi$
$941$	−27.2088	−	17.4860i	−0.886981	−	0.570028i	−0.902903	+	0.429845i	$0.858568\pi$
$942$	18.9981			0.618993
$943$		0			0
$944$	0.165277			0.00537930
$945$	−18.6963	−	12.0154i	−0.608190	−	0.390860i
$946$	−0.0414533	−	0.288314i	−0.00134776	−	0.00937390i
$947$	16.3675	+	35.8399i	0.531874	+	1.16464i	0.964745	+	0.263185i	$0.0847731\pi$
$947$	16.3675	+	35.8399i	0.531874	+	1.16464i	−0.432872	+	0.901456i	$0.642500\pi$
$948$	44.8099	+	13.1574i	1.45536	+	0.427331i
$949$	0.849297	−	1.85970i	0.0275693	−	0.0603685i
$950$	1.04982	−	1.21156i	0.0340607	−	0.0393081i
$951$	−8.23897	+	57.3033i	−0.267167	+	1.85819i
$952$	11.3431	−	3.33063i	0.367632	−	0.107946i
$953$	−20.3574	−	23.4936i	−0.659439	−	0.761034i	0.323246	−	0.946315i	$-0.395226\pi$
$953$	−20.3574	−	23.4936i	−0.659439	−	0.761034i	−0.982686	+	0.185281i	$0.940680\pi$
$954$	−6.41584	+	4.12321i	−0.207720	+	0.133494i
$955$	28.5683	−	18.3597i	0.924448	−	0.594107i
$956$	0.272347	+	0.314306i	0.00880834	+	0.0101654i
$957$	−3.12999	+	0.919049i	−0.101178	+	0.0297086i
$958$	−1.62516	+	11.3032i	−0.0525065	+	0.365191i
$959$	−25.8520	+	29.8348i	−0.834806	+	0.963418i
$960$	−7.14801	+	15.6520i	−0.230701	+	0.505165i
$961$	27.5676	+	8.09456i	0.889276	+	0.261115i
$962$	−4.10796	−	8.99518i	−0.132446	−	0.290016i
$963$	−0.341537	−	2.37544i	−0.0110059	−	0.0765475i
$964$	7.84667	+	5.04275i	0.252724	+	0.162416i
$965$	24.3446			0.783679
$966$		0			0
$967$	33.5947			1.08033			0.540167	−	0.841558i	$-0.318361\pi$
$967$	33.5947			1.08033			0.540167	+	0.841558i	$0.318361\pi$
$968$	16.6305	+	10.6877i	0.534523	+	0.343517i
$969$	1.16878	+	8.12901i	0.0375465	+	0.261141i
$970$	0.205705	+	0.450431i	0.00660478	+	0.0144625i
$971$	−11.8399	−	3.47650i	−0.379960	−	0.111566i	0.0861748	−	0.996280i	$-0.472536\pi$
$971$	−11.8399	−	3.47650i	−0.379960	−	0.111566i	−0.466135	+	0.884714i	$0.654354\pi$
$972$	12.4664	−	27.2976i	0.399860	−	0.875572i
$973$	38.5211	−	44.4557i	1.23493	−	1.42518i
$974$	−1.17212	+	8.15227i	−0.0375572	+	0.261216i
$975$	11.1955	−	3.28730i	0.358544	−	0.105278i
$976$	−0.0778746	−	0.0898720i	−0.00249270	−	0.00287673i
$977$	−38.0479	+	24.4519i	−1.21726	+	0.782286i	−0.981859	−	0.189612i	$-0.939277\pi$
$977$	−38.0479	+	24.4519i	−1.21726	+	0.782286i	−0.235402	+	0.971898i	$0.575641\pi$
$978$	13.2324	−	8.50393i	0.423125	−	0.271926i
$979$	2.41429	+	2.78623i	0.0771609	+	0.0890484i
$980$	20.0353	−	5.88288i	0.640003	−	0.187922i
$981$	1.87055	−	13.0099i	0.0597219	−	0.415375i
$982$	10.7106	−	12.3607i	0.341789	−	0.394445i
$983$	6.34237	−	13.8878i	0.202290	−	0.442954i	−0.781113	−	0.624390i	$-0.785348\pi$
$983$	6.34237	−	13.8878i	0.202290	−	0.442954i	0.983403	+	0.181437i	$0.0580748\pi$
$984$	30.7983	+	9.04321i	0.981815	+	0.288287i
$985$	−11.1684	−	24.4554i	−0.355855	−	0.779214i
$986$	0.849963	+	5.91162i	0.0270683	+	0.188264i
$987$	−9.06352	−	5.82477i	−0.288495	−	0.185405i
$988$	−10.4788			−0.333374
$989$		0			0
$990$	−0.527358			−0.0167605
$991$	16.6149	+	10.6778i	0.527791	+	0.339191i	0.777247	−	0.629195i	$-0.216616\pi$
$991$	16.6149	+	10.6778i	0.527791	+	0.339191i	−0.249456	+	0.968386i	$0.580252\pi$
$992$	−1.04889	−	7.29519i	−0.0333023	−	0.231623i
$993$	20.8326	+	45.6169i	0.661101	+	1.44761i
$994$	13.0156	+	3.82173i	0.412830	+	0.121218i
$995$	−11.0539	+	24.2046i	−0.350431	+	0.767337i
$996$	0.921229	−	1.06316i	0.0291903	−	0.0336874i
$997$	−1.74325	+	12.1246i	−0.0552092	+	0.383988i	0.943418	+	0.331606i	$0.107591\pi$
$997$	−1.74325	+	12.1246i	−0.0552092	+	0.383988i	−0.998627	+	0.0523823i	$0.983319\pi$
$998$	−14.0467	+	4.12447i	−0.444639	+	0.130558i
$999$	11.1427	+	12.8594i	0.352541	+	0.406854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.2.c.e.255.1		10
23.2	even	11		529.2.c.h.399.1		10
23.3	even	11		529.2.c.f.501.1		10
23.4	even	11		529.2.c.f.170.1		10
23.5	odd	22		23.2.c.a.4.1	✓	10
23.6	even	11		529.2.c.h.118.1		10
23.7	odd	22		23.2.c.a.6.1	yes	10
23.8	even	11		529.2.c.c.266.1		10
23.9	even	11		529.2.a.j.1.3		5
23.10	odd	22		529.2.c.b.177.1		10
23.11	odd	22		529.2.c.d.334.1		10
23.12	even	11	inner	529.2.c.e.334.1		10
23.13	even	11		529.2.c.c.177.1		10
23.14	odd	22		529.2.a.i.1.3		5
23.15	odd	22		529.2.c.b.266.1		10
23.16	even	11		529.2.c.a.466.1		10
23.17	odd	22		529.2.c.i.118.1		10
23.18	even	11		529.2.c.a.487.1		10
23.19	odd	22		529.2.c.g.170.1		10
23.20	odd	22		529.2.c.g.501.1		10
23.21	odd	22		529.2.c.i.399.1		10
23.22	odd	2		529.2.c.d.255.1		10
69.5	even	22		207.2.i.c.73.1		10
69.14	even	22		4761.2.a.bo.1.3		5
69.32	odd	22		4761.2.a.bn.1.3		5
69.53	even	22		207.2.i.c.190.1		10
92.7	even	22		368.2.m.c.305.1		10
92.51	even	22		368.2.m.c.257.1		10
92.55	odd	22		8464.2.a.bt.1.1		5
92.83	even	22		8464.2.a.bs.1.1		5
115.7	even	44		575.2.p.b.374.2		20
115.28	even	44		575.2.p.b.349.2		20
115.53	even	44		575.2.p.b.374.1		20
115.74	odd	22		575.2.k.b.326.1		10
115.97	even	44		575.2.p.b.349.1		20
115.99	odd	22		575.2.k.b.351.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.4.1	✓	10	23.5	odd	22
23.2.c.a.6.1	yes	10	23.7	odd	22
207.2.i.c.73.1		10	69.5	even	22
207.2.i.c.190.1		10	69.53	even	22
368.2.m.c.257.1		10	92.51	even	22
368.2.m.c.305.1		10	92.7	even	22
529.2.a.i.1.3		5	23.14	odd	22
529.2.a.j.1.3		5	23.9	even	11
529.2.c.a.466.1		10	23.16	even	11
529.2.c.a.487.1		10	23.18	even	11
529.2.c.b.177.1		10	23.10	odd	22
529.2.c.b.266.1		10	23.15	odd	22
529.2.c.c.177.1		10	23.13	even	11
529.2.c.c.266.1		10	23.8	even	11
529.2.c.d.255.1		10	23.22	odd	2
529.2.c.d.334.1		10	23.11	odd	22
529.2.c.e.255.1		10	1.1	even	1	trivial
529.2.c.e.334.1		10	23.12	even	11	inner
529.2.c.f.170.1		10	23.4	even	11
529.2.c.f.501.1		10	23.3	even	11
529.2.c.g.170.1		10	23.19	odd	22
529.2.c.g.501.1		10	23.20	odd	22
529.2.c.h.118.1		10	23.6	even	11
529.2.c.h.399.1		10	23.2	even	11
529.2.c.i.118.1		10	23.17	odd	22
529.2.c.i.399.1		10	23.21	odd	22
575.2.k.b.326.1		10	115.74	odd	22
575.2.k.b.351.1		10	115.99	odd	22
575.2.p.b.349.1		20	115.97	even	44
575.2.p.b.349.2		20	115.28	even	44
575.2.p.b.374.1		20	115.53	even	44
575.2.p.b.374.2		20	115.7	even	44
4761.2.a.bn.1.3		5	69.32	odd	22
4761.2.a.bo.1.3		5	69.14	even	22
8464.2.a.bs.1.1		5	92.83	even	22
8464.2.a.bt.1.1		5	92.55	odd	22

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:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	529.c (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.402869 + 0.258908i) q^{2} +(-0.313607 - 2.18119i) q^{3} +(-0.735560 - 1.61065i) q^{4} +(-2.48926 - 0.730913i) q^{5} +(0.438384 - 0.959928i) q^{6} +(-2.22514 + 2.56794i) q^{7} +(0.256983 - 1.78736i) q^{8} +(-1.78074 + 0.522874i) q^{9} +O(q^{10})\)	\(q+(0.402869 + 0.258908i) q^{2} +(-0.313607 - 2.18119i) q^{3} +(-0.735560 - 1.61065i) q^{4} +(-2.48926 - 0.730913i) q^{5} +(0.438384 - 0.959928i) q^{6} +(-2.22514 + 2.56794i) q^{7} +(0.256983 - 1.78736i) q^{8} +(-1.78074 + 0.522874i) q^{9} +(-0.813607 - 0.938953i) q^{10} +(-0.192401 + 0.123649i) q^{11} +(-3.28245 + 2.10951i) q^{12} +(2.00357 + 2.31224i) q^{13} +(-1.56130 + 0.458439i) q^{14} +(-0.813607 + 5.65876i) q^{15} +(-1.75278 + 2.02282i) q^{16} +(0.800404 - 1.75264i) q^{17} +(-0.852783 - 0.250400i) q^{18} +(-0.803526 - 1.75948i) q^{19} +(0.653755 + 4.54696i) q^{20} +(6.29898 + 4.04811i) q^{21} -0.109526 q^{22} -3.97915 q^{24} +(1.45592 + 0.935664i) q^{25} +(0.208518 + 1.45027i) q^{26} +(-1.04731 - 2.29328i) q^{27} +(5.77279 + 1.69504i) q^{28} +(-2.68886 + 5.88778i) q^{29} +(-1.79288 + 2.06909i) q^{30} +(-0.214354 + 1.49086i) q^{31} +(-4.69505 + 1.37859i) q^{32} +(0.330039 + 0.380885i) q^{33} +(0.776231 - 0.498853i) q^{34} +(7.41589 - 4.76590i) q^{35} +(2.15201 + 2.48355i) q^{36} +(-6.47580 + 1.90147i) q^{37} +(0.131827 - 0.916879i) q^{38} +(4.41510 - 5.09530i) q^{39} +(-1.94610 + 4.26137i) q^{40} +(-7.73992 - 2.27265i) q^{41} +(1.48958 + 3.26172i) q^{42} +(0.378479 + 2.63238i) q^{43} +(0.340677 + 0.218940i) q^{44} +4.81491 q^{45} -1.43889 q^{47} +(4.96183 + 3.18877i) q^{48} +(-0.646902 - 4.49930i) q^{49} +(0.344295 + 0.753900i) q^{50} +(-4.07385 - 1.19619i) q^{51} +(2.25047 - 4.92785i) q^{52} +(5.61926 - 6.48497i) q^{53} +(0.171822 - 1.19505i) q^{54} +(0.569313 - 0.167165i) q^{55} +(4.01801 + 4.63704i) q^{56} +(-3.58576 + 2.30442i) q^{57} +(-2.60765 + 1.67584i) q^{58} +(-0.0404373 - 0.0466671i) q^{59} +(9.71275 - 2.85192i) q^{60} +(-0.00632292 + 0.0439769i) q^{61} +(-0.472354 + 0.545125i) q^{62} +(2.61969 - 5.73632i) q^{63} +(2.88789 + 0.847960i) q^{64} +(-3.29736 - 7.22022i) q^{65} +(0.0343481 + 0.238897i) q^{66} +(-10.4382 - 6.70824i) q^{67} -3.41164 q^{68} +4.22157 q^{70} +(-7.01302 - 4.50700i) q^{71} +(0.476941 + 3.31720i) q^{72} +(-0.277590 - 0.607837i) q^{73} +(-3.10120 - 0.910596i) q^{74} +(1.58427 - 3.46907i) q^{75} +(-2.24286 + 2.58840i) q^{76} +(0.110596 - 0.769210i) q^{77} +(3.09792 - 0.909632i) q^{78} +(-7.83807 - 9.04561i) q^{79} +(5.84164 - 3.75419i) q^{80} +(-9.35753 + 6.01372i) q^{81} +(-2.52977 - 2.91951i) q^{82} +(-0.345930 + 0.101574i) q^{83} +(1.88682 - 13.1231i) q^{84} +(-3.27344 + 3.77775i) q^{85} +(-0.529067 + 1.15850i) q^{86} +(13.6856 + 4.01845i) q^{87} +(0.171560 + 0.375665i) q^{88} +(-2.29409 - 15.9557i) q^{89} +(1.93978 + 1.24662i) q^{90} -10.3959 q^{91} +3.31908 q^{93} +(-0.579683 - 0.372540i) q^{94} +(0.714162 + 4.96711i) q^{95} +(4.47937 + 9.80845i) q^{96} +(-0.382418 - 0.112288i) q^{97} +(0.904290 - 1.98012i) q^{98} +(0.277964 - 0.320788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 7 q^{3} + 8 q^{4} + 3 q^{5} - 5 q^{6} - 6 q^{7} + 15 q^{8} - 2 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 + 3 * q^5 - 5 * q^6 - 6 * q^7 + 15 * q^8 - 2 * q^9	\( 10 q + 4 q^{2} - 7 q^{3} + 8 q^{4} + 3 q^{5} - 5 q^{6} - 6 q^{7} + 15 q^{8} - 2 q^{9} - 12 q^{10} - 7 q^{11} - 10 q^{12} + 8 q^{13} + 2 q^{14} - 12 q^{15} + 12 q^{16} - q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{20} + 24 q^{21} + 6 q^{22} - 38 q^{24} + 18 q^{25} - 10 q^{26} - 4 q^{27} + 26 q^{28} - 8 q^{29} + 4 q^{30} - 12 q^{31} - 23 q^{32} + 17 q^{33} + 26 q^{34} + 18 q^{35} - 6 q^{36} - 25 q^{37} + 52 q^{38} + 12 q^{39} - 12 q^{40} - 26 q^{41} + 14 q^{42} - 22 q^{43} - 32 q^{44} + 6 q^{45} - 18 q^{47} - 15 q^{48} + 15 q^{49} + 5 q^{50} - 18 q^{51} + 13 q^{52} + 48 q^{53} - 17 q^{54} + 32 q^{55} + 2 q^{56} + 8 q^{57} - q^{58} + q^{59} + 8 q^{60} - 36 q^{61} - 18 q^{62} + 21 q^{63} + 13 q^{64} - 13 q^{65} - 2 q^{66} + 10 q^{67} + 30 q^{68} + 38 q^{70} - 14 q^{71} - 3 q^{72} - 3 q^{73} - 32 q^{74} - 6 q^{75} - 50 q^{76} + 13 q^{77} + 7 q^{78} - 18 q^{79} - 14 q^{80} + 11 q^{81} - 6 q^{82} + 15 q^{83} - 16 q^{84} - 19 q^{85} - 22 q^{86} + 10 q^{87} - 16 q^{88} + 19 q^{89} - 24 q^{90} + 4 q^{91} + 4 q^{93} - 5 q^{94} + 28 q^{95} - 7 q^{96} - 21 q^{97} + 39 q^{98} - 25 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 + 3 * q^5 - 5 * q^6 - 6 * q^7 + 15 * q^8 - 2 * q^9 - 12 * q^10 - 7 * q^11 - 10 * q^12 + 8 * q^13 + 2 * q^14 - 12 * q^15 + 12 * q^16 - q^17 - 3 * q^18 - 2 * q^19 - 2 * q^20 + 24 * q^21 + 6 * q^22 - 38 * q^24 + 18 * q^25 - 10 * q^26 - 4 * q^27 + 26 * q^28 - 8 * q^29 + 4 * q^30 - 12 * q^31 - 23 * q^32 + 17 * q^33 + 26 * q^34 + 18 * q^35 - 6 * q^36 - 25 * q^37 + 52 * q^38 + 12 * q^39 - 12 * q^40 - 26 * q^41 + 14 * q^42 - 22 * q^43 - 32 * q^44 + 6 * q^45 - 18 * q^47 - 15 * q^48 + 15 * q^49 + 5 * q^50 - 18 * q^51 + 13 * q^52 + 48 * q^53 - 17 * q^54 + 32 * q^55 + 2 * q^56 + 8 * q^57 - q^58 + q^59 + 8 * q^60 - 36 * q^61 - 18 * q^62 + 21 * q^63 + 13 * q^64 - 13 * q^65 - 2 * q^66 + 10 * q^67 + 30 * q^68 + 38 * q^70 - 14 * q^71 - 3 * q^72 - 3 * q^73 - 32 * q^74 - 6 * q^75 - 50 * q^76 + 13 * q^77 + 7 * q^78 - 18 * q^79 - 14 * q^80 + 11 * q^81 - 6 * q^82 + 15 * q^83 - 16 * q^84 - 19 * q^85 - 22 * q^86 + 10 * q^87 - 16 * q^88 + 19 * q^89 - 24 * q^90 + 4 * q^91 + 4 * q^93 - 5 * q^94 + 28 * q^95 - 7 * q^96 - 21 * q^97 + 39 * q^98 - 25 * q^99

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