LMFDB - Embedded newform 525.2.w.a.104.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(104,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1, 5]))

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

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

chi := DirichletCharacter("525.104");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.w (of order $10$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			104.4
Character	$\chi$	$=$	525.104
Dual form			525.2.w.a.419.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.825889 + 2.54182i) q^{2} +(1.65709 + 0.504029i) q^{3} +(-4.16074 - 3.02296i) q^{4} +(1.82317 - 1.29462i) q^{5} +(-2.64973 + 3.79577i) q^{6} +(-2.62130 - 0.358847i) q^{7} +(6.79573 - 4.93738i) q^{8} +(2.49191 + 1.67044i) q^{9} +O(q^{10})$	\(q+(-0.825889 + 2.54182i) q^{2} +(1.65709 + 0.504029i) q^{3} +(-4.16074 - 3.02296i) q^{4} +(1.82317 - 1.29462i) q^{5} +(-2.64973 + 3.79577i) q^{6} +(-2.62130 - 0.358847i) q^{7} +(6.79573 - 4.93738i) q^{8} +(2.49191 + 1.67044i) q^{9} +(1.78496 + 5.70340i) q^{10} +(4.91118 + 1.59574i) q^{11} +(-5.37108 - 7.10645i) q^{12} +(0.892552 + 2.74699i) q^{13} +(3.07703 - 6.36652i) q^{14} +(3.67369 - 1.22637i) q^{15} +(3.75892 + 11.5688i) q^{16} +(2.10823 + 2.90173i) q^{17} +(-6.30401 + 4.95440i) q^{18} +(-1.65683 - 2.28042i) q^{19} +(-11.4993 - 0.124789i) q^{20} +(-4.16287 - 1.91585i) q^{21} +(-8.11218 + 11.1655i) q^{22} +(0.0415129 - 0.127763i) q^{23} +(13.7497 - 4.75646i) q^{24} +(1.64792 - 4.72063i) q^{25} -7.71952 q^{26} +(3.28737 + 4.02407i) q^{27} +(9.82179 + 9.41716i) q^{28} +(-4.19982 + 5.78055i) q^{29} +(0.0831689 + 10.3507i) q^{30} +(-0.637066 - 0.876845i) q^{31} -15.7103 q^{32} +(7.33398 + 5.11966i) q^{33} +(-9.11686 + 2.96225i) q^{34} +(-5.24366 + 2.73935i) q^{35} +(-5.31852 - 14.4832i) q^{36} +(3.64053 - 1.18288i) q^{37} +(7.16479 - 2.32798i) q^{38} +(0.0944786 + 5.00189i) q^{39} +(5.99774 - 17.7996i) q^{40} +(-2.41638 - 7.43686i) q^{41} +(8.30783 - 8.99901i) q^{42} +9.29611i q^{43} +(-15.6103 - 21.4858i) q^{44} +(6.70577 - 0.180571i) q^{45} +(0.290467 + 0.211037i) q^{46} +(0.582787 - 0.802138i) q^{47} +(0.397890 + 21.0651i) q^{48} +(6.74246 + 1.88129i) q^{49} +(10.6380 + 8.08743i) q^{50} +(2.03098 + 5.87105i) q^{51} +(4.59036 - 14.1277i) q^{52} +(6.05976 + 4.40267i) q^{53} +(-12.9435 + 5.03249i) q^{54} +(11.0198 - 3.44881i) q^{55} +(-19.5854 + 10.5038i) q^{56} +(-1.59611 - 4.61396i) q^{57} +(-11.2246 - 15.4493i) q^{58} +(-1.62429 - 4.99904i) q^{59} +(-18.9926 - 6.00278i) q^{60} +(-10.9370 - 3.55366i) q^{61} +(2.75493 - 0.895132i) q^{62} +(-5.93262 - 5.27295i) q^{63} +(5.45711 - 16.7952i) q^{64} +(5.18359 + 3.85273i) q^{65} +(-19.0703 + 14.4134i) q^{66} +(-1.37048 - 1.88630i) q^{67} -18.4465i q^{68} +(0.133187 - 0.190792i) q^{69} +(-2.63227 - 15.5909i) q^{70} +(7.53120 - 10.3658i) q^{71} +(25.1820 - 0.951642i) q^{72} +(1.24381 - 3.82806i) q^{73} +10.2305i q^{74} +(5.11008 - 6.99193i) q^{75} +14.4968i q^{76} +(-12.3011 - 5.94528i) q^{77} +(-12.7920 - 3.89086i) q^{78} +(-12.0766 - 8.77413i) q^{79} +(21.8303 + 16.2255i) q^{80} +(3.41924 + 8.32519i) q^{81} +20.8989 q^{82} +(-0.825199 - 1.13579i) q^{83} +(11.5291 + 20.5556i) q^{84} +(7.60031 + 2.56100i) q^{85} +(-23.6291 - 7.67755i) q^{86} +(-9.87305 + 7.46208i) q^{87} +(41.2538 - 13.4042i) q^{88} +(-0.109938 + 0.338354i) q^{89} +(-5.07924 + 17.1940i) q^{90} +(-1.35390 - 7.52099i) q^{91} +(-0.558948 + 0.406099i) q^{92} +(-0.613721 - 1.77411i) q^{93} +(1.55758 + 2.14382i) q^{94} +(-5.97296 - 2.01265i) q^{95} +(-26.0334 - 7.91844i) q^{96} +(2.45844 + 1.78616i) q^{97} +(-10.3504 + 15.5844i) q^{98} +(9.57263 + 12.1803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q - 84 q^{4} - 6 q^{9}+O(q^{10}) $ 304 * q - 84 * q^4 - 6 * q^9	$ 304 q - 84 q^{4} - 6 q^{9} - 36 q^{15} - 60 q^{16} - 18 q^{21} - 40 q^{22} - 8 q^{25} + 60 q^{28} + 14 q^{30} + 28 q^{36} - 20 q^{37} - 2 q^{39} - 35 q^{42} - 24 q^{46} - 20 q^{49} - 52 q^{51} - 80 q^{58} + 4 q^{60} + 55 q^{63} - 76 q^{64} - 20 q^{67} + 6 q^{70} + 30 q^{72} - 40 q^{78} - 68 q^{79} - 10 q^{81} + 80 q^{84} - 88 q^{85} - 20 q^{88} - 82 q^{91} - 36 q^{99}+O(q^{100}) $ 304 * q - 84 * q^4 - 6 * q^9 - 36 * q^15 - 60 * q^16 - 18 * q^21 - 40 * q^22 - 8 * q^25 + 60 * q^28 + 14 * q^30 + 28 * q^36 - 20 * q^37 - 2 * q^39 - 35 * q^42 - 24 * q^46 - 20 * q^49 - 52 * q^51 - 80 * q^58 + 4 * q^60 + 55 * q^63 - 76 * q^64 - 20 * q^67 + 6 * q^70 + 30 * q^72 - 40 * q^78 - 68 * q^79 - 10 * q^81 + 80 * q^84 - 88 * q^85 - 20 * q^88 - 82 * q^91 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$-1$

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 $

$2$	−0.825889	+	2.54182i	−0.583992	+	1.79734i	0.0192915	+	0.999814i	$0.493859\pi$
$2$	−0.825889	+	2.54182i	−0.583992	+	1.79734i	−0.603283	+	0.797527i	$0.706141\pi$
$3$	1.65709	+	0.504029i	0.956723	+	0.291001i
$3$	1.65709	+	0.504029i	0.956723	+	0.291001i
$4$	−4.16074	−	3.02296i	−2.08037	−	1.51148i
$5$	1.82317	−	1.29462i	0.815348	−	0.578972i
$5$	1.82317	−	1.29462i	0.815348	−	0.578972i
$6$	−2.64973	+	3.79577i	−1.08175	+	1.54961i
$7$	−2.62130	−	0.358847i	−0.990759	−	0.135631i
$7$	−2.62130	−	0.358847i	−0.990759	−	0.135631i
$8$	6.79573	−	4.93738i	2.40265	−	1.74563i
$9$	2.49191	+	1.67044i	0.830637	+	0.556815i
$10$	1.78496	+	5.70340i	0.564454	+	1.80357i
$11$	4.91118	+	1.59574i	1.48078	+	0.481133i	0.934345	−	0.356370i	$-0.115986\pi$
$11$	4.91118	+	1.59574i	1.48078	+	0.481133i	0.546432	+	0.837504i	$0.315986\pi$
$12$	−5.37108	−	7.10645i	−1.55050	−	2.05146i
$13$	0.892552	+	2.74699i	0.247549	+	0.761879i	0.995207	+	0.0977941i	$0.0311787\pi$
$13$	0.892552	+	2.74699i	0.247549	+	0.761879i	−0.747657	+	0.664085i	$0.768821\pi$
$14$	3.07703	−	6.36652i	0.822371	−	1.70152i
$15$	3.67369	−	1.22637i	0.948543	−	0.316649i
$16$	3.75892	+	11.5688i	0.939731	+	2.89219i
$17$	2.10823	+	2.90173i	0.511321	+	0.703773i	0.984141	−	0.177386i	$-0.0567640\pi$
$17$	2.10823	+	2.90173i	0.511321	+	0.703773i	−0.472820	+	0.881159i	$0.656764\pi$
$18$	−6.30401	+	4.95440i	−1.48587	+	1.16776i
$19$	−1.65683	−	2.28042i	−0.380102	−	0.523165i	0.575510	−	0.817795i	$-0.304804\pi$
$19$	−1.65683	−	2.28042i	−0.380102	−	0.523165i	−0.955611	+	0.294630i	$0.904804\pi$
$20$	−11.4993	−	0.124789i	−2.57133	−	0.0279037i
$21$	−4.16287	−	1.91585i	−0.908413	−	0.418074i
$22$	−8.11218	+	11.1655i	−1.72952	+	2.38048i
$23$	0.0415129	−	0.127763i	0.00865603	−	0.0266405i	−0.946635	−	0.322307i	$-0.895542\pi$
$23$	0.0415129	−	0.127763i	0.00865603	−	0.0266405i	0.955291	+	0.295666i	$0.0955417\pi$
$24$	13.7497	−	4.75646i	2.80665	−	0.970909i
$25$	1.64792	−	4.72063i	0.329583	−	0.944127i
$26$	−7.71952			−1.51392
$27$	3.28737	+	4.02407i	0.632656	+	0.774433i
$28$	9.82179	+	9.41716i	1.85614	+	1.77968i
$29$	−4.19982	+	5.78055i	−0.779887	+	1.07342i	0.215408	+	0.976524i	$0.430892\pi$
$29$	−4.19982	+	5.78055i	−0.779887	+	1.07342i	−0.995294	+	0.0968976i	$0.969108\pi$
$30$	0.0831689	+	10.3507i	0.0151845	+	1.88978i
$31$	−0.637066	−	0.876845i	−0.114420	−	0.157486i	0.747966	−	0.663737i	$-0.231031\pi$
$31$	−0.637066	−	0.876845i	−0.114420	−	0.157486i	−0.862386	+	0.506251i	$0.831031\pi$
$32$	−15.7103			−2.77721
$33$	7.33398	+	5.11966i	1.27668	+	0.891219i
$34$	−9.11686	+	2.96225i	−1.56353	+	0.508021i
$35$	−5.24366	+	2.73935i	−0.886340	+	0.463035i
$36$	−5.31852	−	14.4832i	−0.886420	−	2.41387i
$37$	3.64053	−	1.18288i	0.598500	−	0.194464i	0.00592877	−	0.999982i	$-0.498113\pi$
$37$	3.64053	−	1.18288i	0.598500	−	0.194464i	0.592571	+	0.805518i	$0.298113\pi$
$38$	7.16479	−	2.32798i	1.16228	−	0.377648i
$39$	0.0944786	+	5.00189i	0.0151287	+	0.800944i
$40$	5.99774	−	17.7996i	0.948327	−	2.81436i
$41$	−2.41638	−	7.43686i	−0.377376	−	1.16144i	−0.941862	−	0.336001i	$-0.890926\pi$
$41$	−2.41638	−	7.43686i	−0.377376	−	1.16144i	0.564486	−	0.825443i	$-0.309074\pi$
$42$	8.30783	−	8.99901i	1.28193	−	1.38858i
$43$			9.29611i			1.41764i	0.705388	+	0.708822i	$0.250773\pi$
$43$			9.29611i			1.41764i	−0.705388	+	0.708822i	$0.749227\pi$
$44$	−15.6103	−	21.4858i	−2.35334	−	3.23910i
$45$	6.70577	−	0.180571i	0.999638	−	0.0269180i
$46$	0.290467	+	0.211037i	0.0428271	+	0.0311157i
$47$	0.582787	−	0.802138i	0.0850083	−	0.117004i	−0.764395	−	0.644748i	$-0.776962\pi$
$47$	0.582787	−	0.802138i	0.0850083	−	0.117004i	0.849403	+	0.527745i	$0.176962\pi$
$48$	0.397890	+	21.0651i	0.0574305	+	3.04049i
$49$	6.74246	+	1.88129i	0.963208	+	0.268756i
$50$	10.6380	+	8.08743i	1.50444	+	1.14374i
$51$	2.03098	+	5.87105i	0.284394	+	0.822111i
$52$	4.59036	−	14.1277i	0.636569	−	1.95916i
$53$	6.05976	+	4.40267i	0.832372	+	0.604754i	0.920229	−	0.391379i	$-0.128002\pi$
$53$	6.05976	+	4.40267i	0.832372	+	0.604754i	−0.0878575	+	0.996133i	$0.528002\pi$
$54$	−12.9435	+	5.03249i	−1.76139	+	0.684835i
$55$	11.0198	−	3.44881i	1.48591	−	0.465037i
$56$	−19.5854	+	10.5038i	−2.61721	+	1.40362i
$57$	−1.59611	−	4.61396i	−0.211410	−	0.611134i
$58$	−11.2246	−	15.4493i	−1.47386	−	2.02859i
$59$	−1.62429	−	4.99904i	−0.211464	−	0.650820i	−0.999386	−	0.0350441i	$-0.988843\pi$
$59$	−1.62429	−	4.99904i	−0.211464	−	0.650820i	0.787922	−	0.615776i	$-0.211157\pi$
$60$	−18.9926	−	6.00278i	−2.45193	−	0.774956i
$61$	−10.9370	−	3.55366i	−1.40034	−	0.454999i	−0.491041	−	0.871136i	$-0.663384\pi$
$61$	−10.9370	−	3.55366i	−1.40034	−	0.454999i	−0.909302	+	0.416137i	$0.863384\pi$
$62$	2.75493	−	0.895132i	0.349877	−	0.113682i
$63$	−5.93262	−	5.27295i	−0.747440	−	0.664330i
$64$	5.45711	−	16.7952i	0.682138	−	2.09941i
$65$	5.18359	+	3.85273i	0.642945	+	0.477872i
$66$	−19.0703	+	14.4134i	−2.34740	+	1.77417i
$67$	−1.37048	−	1.88630i	−0.167430	−	0.230448i	0.717054	−	0.697017i	$-0.245490\pi$
$67$	−1.37048	−	1.88630i	−0.167430	−	0.230448i	−0.884485	+	0.466569i	$0.845490\pi$
$68$		−	18.4465i		−	2.23696i
$69$	0.133187	−	0.190792i	0.0160338	−	0.0229687i
$70$	−2.63227	−	15.5909i	−0.314617	−	1.86346i
$71$	7.53120	−	10.3658i	0.893789	−	1.23019i	−0.0786184	−	0.996905i	$-0.525051\pi$
$71$	7.53120	−	10.3658i	0.893789	−	1.23019i	0.972407	−	0.233290i	$-0.0749491\pi$
$72$	25.1820	−	0.951642i	2.96772	−	0.112152i
$73$	1.24381	−	3.82806i	0.145577	−	0.448040i	−0.851508	−	0.524342i	$-0.824311\pi$
$73$	1.24381	−	3.82806i	0.145577	−	0.448040i	0.997085	+	0.0763019i	$0.0243113\pi$
$74$			10.2305i			1.18927i
$75$	5.11008	−	6.99193i	0.590062	−	0.807358i
$76$			14.4968i			1.66289i
$77$	−12.3011	−	5.94528i	−1.40184	−	0.677527i
$78$	−12.7920	−	3.89086i	−1.44840	−	0.440553i
$79$	−12.0766	−	8.77413i	−1.35872	−	0.987166i	−0.998525	−	0.0542886i	$-0.982711\pi$
$79$	−12.0766	−	8.77413i	−1.35872	−	0.987166i	−0.360193	−	0.932878i	$-0.617289\pi$
$80$	21.8303	+	16.2255i	2.44071	+	1.81407i
$81$	3.41924	+	8.32519i	0.379915	+	0.925021i
$82$	20.8989			2.30789
$83$	−0.825199	−	1.13579i	−0.0905773	−	0.124669i	0.761323	−	0.648372i	$-0.224550\pi$
$83$	−0.825199	−	1.13579i	−0.0905773	−	0.124669i	−0.851901	+	0.523703i	$0.824550\pi$
$84$	11.5291	+	20.5556i	1.25793	+	2.24280i
$85$	7.60031	+	2.56100i	0.824369	+	0.277779i
$86$	−23.6291	−	7.67755i	−2.54799	−	0.827892i
$87$	−9.87305	+	7.46208i	−1.05850	+	0.800019i
$88$	41.2538	−	13.4042i	4.39767	−	1.42889i
$89$	−0.109938	+	0.338354i	−0.0116534	+	0.0358654i	−0.956714	−	0.291029i	$-0.906002\pi$
$89$	−0.109938	+	0.338354i	−0.0116534	+	0.0358654i	0.945061	+	0.326895i	$0.106002\pi$
$90$	−5.07924	+	17.1940i	−0.535399	+	1.81241i
$91$	−1.35390	−	7.52099i	−0.141927	−	0.788414i
$92$	−0.558948	+	0.406099i	−0.0582743	+	0.0423388i
$93$	−0.613721	−	1.77411i	−0.0636399	−	0.183967i
$94$	1.55758	+	2.14382i	0.160652	+	0.221118i
$95$	−5.97296	−	2.01265i	−0.612813	−	0.206493i
$96$	−26.0334	−	7.91844i	−2.65702	−	0.808172i
$97$	2.45844	+	1.78616i	0.249617	+	0.181357i	0.705557	−	0.708653i	$-0.250697\pi$
$97$	2.45844	+	1.78616i	0.249617	+	0.181357i	−0.455940	+	0.890010i	$0.650697\pi$
$98$	−10.3504	+	15.5844i	−1.04555	+	1.57426i
$99$	9.57263	+	12.1803i	0.962085	+	1.22417i
$100$	−21.1268	+	14.6598i	−2.11268	+	1.46598i
$101$	7.82720			0.778836			0.389418	−	0.921061i	$-0.372676\pi$
$101$	7.82720			0.778836			0.389418	+	0.921061i	$0.372676\pi$
$102$	−16.6005	+	0.313560i	−1.64370	+	0.0310471i
$103$	−4.70751	−	3.42020i	−0.463844	−	0.337003i	0.331193	−	0.943563i	$-0.392549\pi$
$103$	−4.70751	−	3.42020i	−0.463844	−	0.337003i	−0.795037	+	0.606560i	$0.792549\pi$
$104$	19.6285	+	14.2609i	1.92473	+	1.39840i
$105$	−10.0699	+	1.89641i	−0.982725	+	0.185070i
$106$	−16.1955	+	11.7667i	−1.57305	+	1.14289i
$107$	−4.08050			−0.394477			−0.197239	−	0.980356i	$-0.563197\pi$
$107$	−4.08050			−0.394477			−0.197239	+	0.980356i	$0.563197\pi$
$108$	−1.51332	−	26.6807i	−0.145620	−	2.56735i
$109$	2.43326	+	7.48880i	0.233064	+	0.717297i	0.997372	+	0.0724462i	$0.0230806\pi$
$109$	2.43326	+	7.48880i	0.233064	+	0.717297i	−0.764308	+	0.644851i	$0.776919\pi$
$110$	−0.334874	+	30.8587i	−0.0319290	+	2.94227i
$111$	6.62891	−	0.125211i	0.629188	−	0.0118845i
$112$	−5.70186	−	31.6742i	−0.538775	−	2.99293i
$113$	2.04165	+	6.28356i	0.192062	+	0.591108i	0.999998	+	0.00183707i	$0.000584757\pi$
$113$	2.04165	+	6.28356i	0.192062	+	0.591108i	−0.807936	+	0.589270i	$0.799415\pi$
$114$	13.0461	−	0.246422i	1.22188	−	0.0230795i
$115$	−0.0897201	−	0.286678i	−0.00836644	−	0.0267329i
$116$	34.9487	−	11.3555i	3.24491	−	1.05433i
$117$	−2.36454	+	8.33622i	−0.218602	+	0.770684i
$118$	14.0482			1.29324
$119$	−4.48504	−	8.36285i	−0.411143	−	0.766621i
$120$	18.9103	−	26.4725i	1.72627	−	2.41660i
$121$	12.6741	+	9.20829i	1.15219	+	0.837117i
$122$	18.0655	−	24.8651i	1.63558	−	2.25118i
$123$	−0.255780	−	13.5415i	−0.0230629	−	1.22100i
$124$			5.57415i			0.500574i
$125$	−3.10699	−	10.7400i	−0.277898	−	0.960611i
$126$	18.3026	−	10.7248i	1.63053	−	0.955441i
$127$	−4.72566	−	1.53546i	−0.419335	−	0.136250i	0.0917468	−	0.995782i	$-0.470755\pi$
$127$	−4.72566	−	1.53546i	−0.419335	−	0.136250i	−0.511081	+	0.859532i	$0.670755\pi$
$128$	12.7638	+	9.27345i	1.12817	+	0.819665i
$129$	−4.68551	+	15.4045i	−0.412536	+	1.35629i
$130$	−14.0740	+	9.99385i	−1.23437	+	0.876519i
$131$	11.0796	−	8.04982i	0.968032	−	0.703316i	0.0130296	−	0.999915i	$-0.495852\pi$
$131$	11.0796	−	8.04982i	0.968032	−	0.703316i	0.955002	+	0.296599i	$0.0958524\pi$
$132$	−15.0383	−	43.4719i	−1.30892	−	3.78374i
$133$	3.52472	+	6.57223i	0.305632	+	0.569885i
$134$	5.92650	−	1.92564i	0.511972	−	0.166350i
$135$	11.2031	+	3.08068i	0.964209	+	0.265143i
$136$	28.6539	+	9.31023i	2.45705	+	0.798345i
$137$	1.51841	+	4.67318i	0.129726	+	0.399256i	0.994733	−	0.102505i	$-0.0326857\pi$
$137$	1.51841	+	4.67318i	0.129726	+	0.399256i	−0.865006	+	0.501761i	$0.832686\pi$
$138$	0.374962	+	0.496111i	0.0319189	+	0.0422318i
$139$	−19.9413	−	6.47933i	−1.69140	−	0.549570i	−0.704333	−	0.709870i	$-0.748754\pi$
$139$	−19.9413	−	6.47933i	−1.69140	−	0.549570i	−0.987068	+	0.160300i	$0.948754\pi$
$140$	30.0985	+	4.45361i	2.54378	+	0.376399i
$141$	1.37003	−	1.03548i	0.115378	−	0.0872027i
$142$	20.1281	+	27.7040i	1.68911	+	2.32487i
$143$			14.9153i			1.24728i
$144$	−9.95809	+	35.1074i	−0.829841	+	2.92562i
$145$	−0.173370	+	15.9761i	−0.0143976	+	1.32674i
$146$	8.70300	+	6.32310i	0.720265	+	0.523303i
$147$	10.2247	+	6.51587i	0.843315	+	0.537420i
$148$	−18.7231	−	6.08351i	−1.53903	−	0.500062i
$149$		−	7.33093i		−	0.600573i	−0.953849	−	0.300287i	$-0.902918\pi$
$149$		−	7.33093i		−	0.600573i	0.953849	−	0.300287i	$-0.0970823\pi$
$150$	13.5519	+	18.7635i	1.10651	+	1.53203i
$151$	−8.03176			−0.653615			−0.326808	−	0.945091i	$-0.605973\pi$
$151$	−8.03176			−0.653615			−0.326808	+	0.945091i	$0.605973\pi$
$152$	−22.5187	−	7.31676i	−1.82650	−	0.593467i
$153$	0.406345	+	10.7525i	0.0328510	+	0.869291i
$154$	25.2712	−	26.3570i	2.03641	−	2.12391i
$155$	−2.29666	−	0.773883i	−0.184472	−	0.0621597i
$156$	14.7274	−	21.0972i	1.17914	−	1.68913i
$157$	−7.12103			−0.568320			−0.284160	−	0.958777i	$-0.591715\pi$
$157$	−7.12103			−0.568320			−0.284160	+	0.958777i	$0.591715\pi$
$158$	32.2762	−	23.4500i	2.56775	−	1.86558i
$159$	7.82251	+	10.3499i	0.620365	+	0.820803i
$160$	−28.6426	+	20.3389i	−2.26439	+	1.60793i
$161$	−0.154665	+	0.320010i	−0.0121893	+	0.0252203i
$162$	−23.9851	+	1.81541i	−1.88445	+	0.142632i
$163$	7.15707	−	2.32547i	0.560585	−	0.182145i	−0.0149995	−	0.999888i	$-0.504775\pi$
$163$	7.15707	−	2.32547i	0.560585	−	0.182145i	0.575584	+	0.817742i	$0.304775\pi$
$164$	−12.4274	+	38.2475i	−0.970415	+	2.98663i
$165$	19.9991	−	0.160695i	1.55693	−	0.0125101i
$166$	3.56850	−	1.15947i	0.276969	−	0.0899927i
$167$	−1.51807	−	2.08945i	−0.117472	−	0.161686i	0.746232	−	0.665686i	$-0.231861\pi$
$167$	−1.51807	−	2.08945i	−0.117472	−	0.161686i	−0.863704	+	0.504000i	$0.831861\pi$
$168$	−37.7491	+	7.53408i	−2.91240	+	0.581267i
$169$	3.76790	−	2.73754i	0.289838	−	0.210580i
$170$	−12.7866	+	17.2036i	−0.980689	+	1.31945i
$171$	−0.319340	−	8.45025i	−0.0244205	−	0.646207i
$172$	28.1017	−	38.6787i	2.14274	−	2.94923i
$173$	−8.78774	−	2.85531i	−0.668120	−	0.217085i	−0.0447330	−	0.998999i	$-0.514244\pi$
$173$	−8.78774	−	2.85531i	−0.668120	−	0.217085i	−0.623387	+	0.781914i	$0.714244\pi$
$174$	−10.8133	−	31.2584i	−0.819751	−	2.36969i
$175$	−6.01367	+	11.7829i	−0.454591	+	0.890700i
$176$			62.8146i			4.73483i
$177$	−0.171934	−	9.10256i	−0.0129234	−	0.684190i
$178$	−0.769239	−	0.558885i	−0.0576569	−	0.0418902i
$179$	−3.54867	+	4.88433i	−0.265240	+	0.365072i	−0.920776	−	0.390093i	$-0.872443\pi$
$179$	−3.54867	+	4.88433i	−0.265240	+	0.365072i	0.655535	+	0.755164i	$0.272443\pi$
$180$	−28.4469	−	19.5200i	−2.12030	−	1.45493i
$181$	−11.7846	−	16.2201i	−0.875942	−	1.20563i	−0.977528	−	0.210804i	$-0.932392\pi$
$181$	−11.7846	−	16.2201i	−0.875942	−	1.20563i	0.101586	−	0.994827i	$-0.467608\pi$
$182$	20.2352	+	2.77013i	1.49993	+	0.205335i
$183$	−16.3325	−	11.4013i	−1.20733	−	0.842809i
$184$	−0.348707	−	1.07321i	−0.0257070	−	0.0791181i
$185$	5.10594	−	6.86971i	0.375396	−	0.505071i
$186$	5.01635	−	0.0947517i	0.367817	−	0.00694753i
$187$	5.72350	+	17.6151i	0.418544	+	1.28814i
$188$	−4.84966	+	1.57575i	−0.353698	+	0.114923i
$189$	−7.17318	−	11.7280i	−0.521772	−	0.853085i
$190$	10.0488	−	13.5200i	0.729016	−	0.980844i
$191$	−6.33023	+	2.05682i	−0.458039	+	0.148826i	−0.528943	−	0.848657i	$-0.677412\pi$
$191$	−6.33023	+	2.05682i	−0.458039	+	0.148826i	0.0709040	+	0.997483i	$0.477412\pi$
$192$	17.5082	−	25.0807i	1.26355	−	1.81005i
$193$			10.0244i			0.721570i	0.932649	+	0.360785i	$0.117491\pi$
$193$			10.0244i			0.721570i	−0.932649	+	0.360785i	$0.882509\pi$
$194$	−6.57051	+	4.77376i	−0.471735	+	0.342736i
$195$	6.64781	+	8.99700i	0.476059	+	0.644289i
$196$	−22.3666	−	28.2097i	−1.59761	−	2.01498i
$197$	−17.3158	−	12.5807i	−1.23370	−	0.896334i	−0.236537	−	0.971623i	$-0.576012\pi$
$197$	−17.3158	−	12.5807i	−1.23370	−	0.896334i	−0.997162	+	0.0752881i	$0.976012\pi$
$198$	−38.8661	+	14.2724i	−2.76209	+	1.01429i
$199$		−	0.284386i		−	0.0201596i	−0.999949	−	0.0100798i	$-0.996791\pi$
$199$		−	0.284386i		−	0.0201596i	0.999949	−	0.0100798i	$-0.00320855\pi$
$200$	−12.1088	−	40.2165i	−0.856221	−	2.84374i
$201$	−1.32026	−	3.81653i	−0.0931238	−	0.269197i
$202$	−6.46440	+	19.8954i	−0.454834	+	1.39983i
$203$	13.0833	−	13.6455i	0.918270	−	0.957726i
$204$	9.29754	−	30.5675i	0.650958	−	2.14015i
$205$	−14.0334	−	10.4304i	−0.980135	−	0.728490i
$206$	12.5814	−	9.14095i	0.876590	−	0.636880i
$207$	0.316868	−	0.249030i	0.0220238	−	0.0173088i
$208$	−28.4243	+	20.6515i	−1.97087	+	1.43192i
$209$	−4.49801	−	13.8434i	−0.311134	−	0.957571i
$210$	3.49631	−	27.1622i	0.241269	−	1.87437i
$211$	2.85557	−	8.78855i	0.196586	−	0.605029i	−0.803369	−	0.595482i	$-0.796961\pi$
$211$	2.85557	−	8.78855i	0.196586	−	0.605029i	0.999954	−	0.00954673i	$-0.00303886\pi$
$212$	−11.9040	−	36.6368i	−0.817571	−	2.51622i
$213$	17.7046	−	13.3812i	1.21310	−	0.916862i
$214$	3.37004	−	10.3719i	0.230371	−	0.709010i
$215$	12.0349	+	16.9484i	0.820776	+	1.15587i
$216$	42.2085	+	11.1155i	2.87192	+	0.756312i
$217$	1.35529	+	2.52709i	0.0920030	+	0.171550i
$218$	−21.0448			−1.42534
$219$	3.99056	−	5.71653i	0.269657	−	0.386287i
$220$	−56.2762	−	18.9628i	−3.79414	−	1.27847i
$221$	−6.08933	+	8.38125i	−0.409613	+	0.563784i
$222$	−5.15648	+	16.9529i	−0.346080	+	1.13781i
$223$	7.63141	−	23.4871i	0.511037	−	1.57281i	−0.279341	−	0.960192i	$-0.590116\pi$
$223$	7.63141	−	23.4871i	0.511037	−	1.57281i	0.790378	−	0.612619i	$-0.209884\pi$
$224$	41.1814	+	5.63759i	2.75155	+	0.376677i
$225$	11.9920	−	9.01064i	0.799467	−	0.600710i
$226$	−17.6579			−1.17458
$227$	−7.56273	−	2.45728i	−0.501956	−	0.163095i	0.0470848	−	0.998891i	$-0.485007\pi$
$227$	−7.56273	−	2.45728i	−0.501956	−	0.163095i	−0.549041	+	0.835795i	$0.685007\pi$
$228$	−7.30679	+	24.0225i	−0.483904	+	1.59093i
$229$	−16.0699	+	22.1183i	−1.06193	+	1.46162i	−0.183939	+	0.982938i	$0.558885\pi$
$229$	−16.0699	+	22.1183i	−1.06193	+	1.46162i	−0.877989	+	0.478681i	$0.841115\pi$
$230$	0.802784	+	0.00871169i	0.0529340	+	0.000574432i
$231$	−17.3874	−	16.0520i	−1.14401	−	1.05614i
$232$			60.0192i			3.94045i
$233$	−3.14439	+	2.28453i	−0.205996	+	0.149665i	−0.686000	−	0.727601i	$-0.740635\pi$
$233$	−3.14439	+	2.28453i	−0.205996	+	0.149665i	0.480004	+	0.877266i	$0.340635\pi$
$234$	−19.2364	−	12.8950i	−1.25752	−	0.842974i
$235$	0.0240577	−	2.21692i	0.00156935	−	0.144616i
$236$	−8.35365	+	25.7099i	−0.543776	+	1.67357i
$237$	−15.5895	−	20.6265i	−1.01265	−	1.33983i
$238$	24.9610	−	4.49339i	1.61798	−	0.291263i
$239$	11.8426	+	3.84789i	0.766033	+	0.248899i	0.665866	−	0.746071i	$-0.268062\pi$
$239$	11.8426	+	3.84789i	0.766033	+	0.248899i	0.100167	+	0.994971i	$0.468062\pi$
$240$	27.9968	+	37.8903i	1.80718	+	2.44581i
$241$	5.68929	−	1.84856i	0.366480	−	0.119076i	−0.119987	−	0.992775i	$-0.538285\pi$
$241$	5.68929	−	1.84856i	0.366480	−	0.119076i	0.486467	+	0.873699i	$0.338285\pi$
$242$	−33.8733	+	24.6104i	−2.17746	+	1.58201i
$243$	1.46986	+	15.5190i	0.0942913	+	0.995545i
$244$	34.7636	+	47.8480i	2.22551	+	3.06316i
$245$	14.7282	−	5.29900i	0.940952	−	0.338541i
$246$	34.6314	+	10.5336i	2.20801	+	0.671599i
$247$	4.78551	−	6.58669i	0.304495	−	0.419101i
$248$	−8.65865	−	2.81337i	−0.549825	−	0.178649i
$249$	−0.794961	−	2.29803i	−0.0503786	−	0.145632i
$250$	29.8651	+	0.972579i	1.88883	+	0.0615113i
$251$	−19.7143			−1.24435			−0.622177	−	0.782877i	$-0.713752\pi$
$251$	−19.7143			−1.24435			−0.622177	+	0.782877i	$0.713752\pi$
$252$	8.74419	+	39.8735i	0.550833	+	2.51179i
$253$	0.407754	−	0.561226i	0.0256353	−	0.0352840i
$254$	7.80574	−	10.7437i	0.489776	−	0.674119i
$255$	11.3036	+	8.07458i	0.707859	+	0.505650i
$256$	−5.53918	+	4.02445i	−0.346199	+	0.251528i
$257$			22.7268i			1.41766i	0.705380	+	0.708830i	$0.250777\pi$
$257$			22.7268i			1.41766i	−0.705380	+	0.708830i	$0.749223\pi$
$258$	−35.2859	−	24.6321i	−2.19680	−	1.53353i
$259$	−9.96742	+	1.79430i	−0.619345	+	0.111492i
$260$	−9.92096	−	31.7000i	−0.615272	−	1.96595i
$261$	−20.1217	+	7.38906i	−1.24550	+	0.457371i
$262$	11.3107	+	34.8107i	0.698777	+	2.15061i
$263$	−9.98243	−	30.7228i	−0.615543	−	1.89445i	−0.393073	−	0.919507i	$-0.628588\pi$
$263$	−9.98243	−	30.7228i	−0.615543	−	1.89445i	−0.222470	−	0.974939i	$-0.571412\pi$
$264$	75.1175	−	1.41886i	4.62316	−	0.0873249i
$265$	16.7478	+	0.181744i	1.02881	+	0.0111645i
$266$	−19.6165	+	3.53128i	−1.20276	+	0.216517i
$267$	−0.352717	+	0.505271i	−0.0215859	+	0.0309221i
$268$			11.9913i			0.732485i
$269$	7.53735	−	5.47620i	0.459560	−	0.333890i	−0.333799	−	0.942644i	$-0.608331\pi$
$269$	7.53735	−	5.47620i	0.459560	−	0.333890i	0.793359	+	0.608754i	$0.208331\pi$
$270$	−17.0831	+	25.9320i	−1.03964	+	1.57817i
$271$	−10.0272	+	13.8013i	−0.609110	+	0.838369i	−0.996504	−	0.0835459i	$-0.973375\pi$
$271$	−10.0272	+	13.8013i	−0.609110	+	0.838369i	0.387394	+	0.921914i	$0.373375\pi$
$272$	−25.6448	+	35.2971i	−1.55494	+	2.14020i
$273$	1.54726	−	13.1454i	0.0936443	−	0.795595i
$274$	−13.1324			−0.793359
$275$	15.6261	−	20.5542i	0.942290	−	1.23947i
$276$	−1.13091	+	0.391219i	−0.0680730	+	0.0235486i
$277$	12.2919	+	3.99388i	0.738549	+	0.239969i	0.654047	−	0.756454i	$-0.273070\pi$
$277$	12.2919	+	3.99388i	0.738549	+	0.239969i	0.0845023	+	0.996423i	$0.473070\pi$
$278$	32.9386	−	45.3361i	1.97553	−	2.71908i
$279$	−0.122789	−	3.24920i	−0.00735121	−	0.194525i
$280$	−22.1092	+	44.5058i	−1.32128	+	2.65973i
$281$	6.70687	+	9.23121i	0.400098	+	0.550688i	0.960769	−	0.277351i	$-0.0894565\pi$
$281$	6.70687	+	9.23121i	0.400098	+	0.550688i	−0.560670	+	0.828039i	$0.689457\pi$
$282$	1.50050	+	4.33757i	0.0893535	+	0.258298i
$283$	12.7196	−	9.24136i	0.756104	−	0.549342i	−0.141609	−	0.989923i	$-0.545228\pi$
$283$	12.7196	−	9.24136i	0.756104	−	0.549342i	0.897713	+	0.440581i	$0.145228\pi$
$284$	−62.6708	+	20.3630i	−3.71883	+	1.20832i
$285$	−8.88332	−	6.34569i	−0.526202	−	0.375886i
$286$	−37.9120	−	12.3183i	−2.24178	−	0.728399i
$287$	3.66538	+	20.3614i	0.216360	+	1.20189i
$288$	−39.1486	−	26.2432i	−2.30686	−	1.54639i
$289$	1.27788	−	3.93292i	0.0751696	−	0.231348i
$290$	−40.4653	−	13.6352i	−2.37620	−	0.800685i
$291$	3.17359	+	4.19896i	0.186039	+	0.246148i
$292$	−16.7472	+	12.1676i	−0.980058	+	0.712054i
$293$			10.9949i			0.642329i	0.947023	+	0.321165i	$0.104074\pi$
$293$			10.9949i			0.642329i	−0.947023	+	0.321165i	$0.895926\pi$
$294$	−25.0066	+	20.6079i	−1.45842	+	1.20188i
$295$	−9.43322	−	7.01128i	−0.549223	−	0.408212i
$296$	18.8997	−	26.0133i	1.09853	−	1.51199i
$297$	9.72352	+	25.0087i	0.564216	+	1.45115i
$298$	18.6339	+	6.05453i	1.07944	+	0.350730i
$299$	0.388018			0.0224396
$300$	−42.3980	+	13.6441i	−2.44785	+	0.787740i
$301$	3.33588	−	24.3679i	0.192277	−	1.40454i
$302$	6.63334	−	20.4153i	0.381706	−	1.17477i
$303$	12.9704	+	3.94513i	0.745130	+	0.226642i
$304$	20.1538	−	27.7394i	1.15590	−	1.59096i
$305$	−24.5407	+	7.68037i	−1.40520	+	0.439777i
$306$	−27.6667	−	7.84754i	−1.58160	−	0.448614i
$307$	11.6700			0.666043			0.333022	−	0.942919i	$-0.391932\pi$
$307$	11.6700			0.666043			0.333022	+	0.942919i	$0.391932\pi$
$308$	33.2093	+	61.9224i	1.89227	+	3.52835i
$309$	−6.07689	−	8.04031i	−0.345702	−	0.457397i
$310$	3.86386	−	5.19857i	0.219453	−	0.295259i
$311$	−1.26988	+	3.90830i	−0.0720085	+	0.221619i	−0.980583	−	0.196103i	$-0.937171\pi$
$311$	−1.26988	+	3.90830i	−0.0720085	+	0.221619i	0.908575	+	0.417722i	$0.137171\pi$
$312$	25.3383	+	33.5250i	1.43450	+	1.89798i
$313$	−3.25065	−	10.0045i	−0.183737	−	0.565486i	0.816187	−	0.577788i	$-0.196084\pi$
$313$	−3.25065	−	10.0045i	−0.183737	−	0.565486i	−0.999924	+	0.0123024i	$0.996084\pi$
$314$	5.88118	−	18.1004i	0.331894	−	1.02146i
$315$	−17.6427	−	1.93301i	−0.994051	−	0.108913i
$316$	23.7236	+	73.0138i	1.33456	+	4.10735i
$317$	−0.931973	+	0.677118i	−0.0523448	+	0.0380307i	−0.613650	−	0.789578i	$-0.710299\pi$
$317$	−0.931973	+	0.677118i	−0.0523448	+	0.0380307i	0.561305	+	0.827609i	$0.310299\pi$
$318$	−32.7682	+	11.3356i	−1.83755	+	0.635666i
$319$	−29.8503	+	21.6875i	−1.67130	+	1.21427i
$320$	−11.7942	−	37.6855i	−0.659317	−	2.10668i
$321$	−6.76177	−	2.05669i	−0.377405	−	0.114793i
$322$	−0.685673	−	0.657425i	−0.0382110	−	0.0366368i
$323$	3.12421	−	9.61532i	0.173836	−	0.535011i
$324$	10.9401	−	44.9752i	0.607785	−	2.49862i
$325$	14.4384	+	0.313403i	0.800898	+	0.0173845i
$326$			20.1126i			1.11393i
$327$	0.257566	+	13.6361i	0.0142434	+	0.754076i
$328$	−53.1397	−	38.6083i	−2.93415	−	2.13179i
$329$	−1.81551	+	1.89351i	−0.100092	+	0.104393i
$330$	−16.1086	+	50.9670i	−0.886749	+	2.80564i
$331$	−7.85939	+	5.71018i	−0.431991	+	0.313860i	−0.782444	−	0.622720i	$-0.786027\pi$
$331$	−7.85939	+	5.71018i	−0.431991	+	0.313860i	0.350454	+	0.936580i	$0.386027\pi$
$332$			7.22026i			0.396264i
$333$	11.0478	+	3.13367i	0.605417	+	0.171724i
$334$	6.56476	−	2.13302i	0.359208	−	0.116714i
$335$	−4.94065	−	1.66480i	−0.269937	−	0.0909578i
$336$	6.51617	−	55.3609i	0.355486	−	3.02018i
$337$	29.8202	−	9.68918i	1.62441	−	0.527803i	0.651434	−	0.758705i	$-0.274168\pi$
$337$	29.8202	−	9.68918i	1.62441	−	0.527803i	0.972977	+	0.230902i	$0.0741678\pi$
$338$	3.84647	+	11.8382i	0.209221	+	0.643915i
$339$	0.216113	+	11.4415i	0.0117377	+	0.621416i
$340$	−23.8812	−	33.6311i	−1.29514	−	1.82390i
$341$	−1.72953	−	5.32294i	−0.0936591	−	0.288253i
$342$	21.7428	+	6.16726i	1.17571	+	0.333487i
$343$	−16.9989	−	7.35095i	−0.917856	−	0.396914i
$344$	45.8985	+	63.1738i	2.47468	+	3.40611i
$345$	−0.00418044	−	0.520274i	−0.000225067	−	0.0280106i
$346$	14.5154	−	19.9787i	0.780352	−	1.07406i
$347$	−4.42584	−	3.21556i	−0.237591	−	0.172620i	0.462618	−	0.886558i	$-0.346910\pi$
$347$	−4.42584	−	3.21556i	−0.237591	−	0.172620i	−0.700210	+	0.713937i	$0.746910\pi$
$348$	63.6368	−	1.20201i	3.41129	−	0.0644344i
$349$			23.3526i			1.25004i	0.780610	+	0.625018i	$0.214908\pi$
$349$			23.3526i			1.25004i	−0.780610	+	0.625018i	$0.785092\pi$
$350$	−24.9833	−	25.0170i	−1.33542	−	1.33722i
$351$	−8.11995	+	12.6221i	−0.433411	+	0.673718i
$352$	−77.1561	−	25.0695i	−4.11243	−	1.33621i
$353$	−7.16551	+	9.86248i	−0.381382	+	0.524927i	−0.955950	−	0.293530i	$-0.905170\pi$
$353$	−7.16551	+	9.86248i	−0.381382	+	0.524927i	0.574568	+	0.818457i	$0.305170\pi$
$354$	23.2791	+	7.08067i	1.23727	+	0.376334i
$355$	0.310891	−	28.6487i	0.0165004	−	1.52051i
$356$	1.48025	−	1.07547i	0.0784532	−	0.0569996i
$357$	−3.21700	−	16.1186i	−0.170262	−	0.853087i
$358$	−9.48429	−	13.0540i	−0.501260	−	0.689926i
$359$	18.4881	−	6.00716i	0.975767	−	0.317046i	0.222625	−	0.974904i	$-0.428537\pi$
$359$	18.4881	−	6.00716i	0.975767	−	0.317046i	0.753142	+	0.657858i	$0.228537\pi$
$360$	44.6791	−	34.3361i	2.35479	−	1.80967i
$361$	3.41606	−	10.5135i	0.179793	−	0.553344i
$362$	50.9614	−	16.5584i	2.67847	−	0.870288i
$363$	16.3610	+	21.6471i	0.858727	+	1.13618i
$364$	−17.1024	+	35.3857i	−0.896410	+	1.85471i
$365$	−2.68820	−	8.58947i	−0.140707	−	0.449594i
$366$	42.4690	−	32.0982i	2.21989	−	1.67780i
$367$	−6.64005	+	4.82428i	−0.346608	+	0.251825i	−0.747445	−	0.664324i	$-0.768719\pi$
$367$	−6.64005	+	4.82428i	−0.346608	+	0.251825i	0.400837	+	0.916149i	$0.368719\pi$
$368$	1.63411			0.0851839
$369$	6.40145	−	22.5684i	0.333246	−	1.17487i
$370$	13.2446	+	18.6520i	0.688556	+	0.969672i
$371$	−14.3046	−	13.7153i	−0.742657	−	0.712061i
$372$	−2.80953	+	9.23688i	−0.145667	+	0.478910i
$373$	3.74076	+	1.21545i	0.193689	+	0.0629335i	0.404255	−	0.914646i	$-0.367531\pi$
$373$	3.74076	+	1.21545i	0.193689	+	0.0629335i	−0.210566	+	0.977580i	$0.567531\pi$
$374$	−49.5015			−2.55966
$375$	0.264670	−	19.3631i	0.0136675	−	0.999907i
$376$		−	8.32855i		−	0.429512i
$377$	−19.6277	−	6.37743i	−1.01088	−	0.328454i
$378$	35.7347	−	8.54695i	1.83800	−	0.439608i
$379$	−15.2627	−	11.0890i	−0.783990	−	0.569602i	0.122184	−	0.992507i	$-0.461010\pi$
$379$	−15.2627	−	11.0890i	−0.783990	−	0.569602i	−0.906174	+	0.422905i	$0.861010\pi$
$380$	18.7678	+	26.4301i	0.962769	+	1.35584i
$381$	−7.05694	−	4.92627i	−0.361538	−	0.252380i
$382$		−	17.7890i		−	0.910166i
$383$	13.5050	+	18.5881i	0.690075	+	0.949807i	1.00000		0.000954319i	$-0.000303769\pi$
$383$	13.5050	+	18.5881i	0.690075	+	0.949807i	−0.309924	+	0.950761i	$0.600304\pi$
$384$	16.4767	+	21.8003i	0.840824	+	1.11249i
$385$	−30.1238	+	5.08594i	−1.53525	+	0.259204i
$386$	−25.4802	−	8.27901i	−1.29691	−	0.421391i
$387$	−15.5286	+	23.1651i	−0.789365	+	1.17755i
$388$	−4.82945	−	14.8635i	−0.245178	−	0.754582i
$389$	9.03650	+	2.93614i	0.458169	+	0.148868i	0.529003	−	0.848620i	$-0.322566\pi$
$389$	9.03650	+	2.93614i	0.458169	+	0.148868i	−0.0708340	+	0.997488i	$0.522566\pi$
$390$	−28.3591	+	9.46703i	−1.43602	+	0.479382i
$391$	0.458254	−	0.148896i	0.0231749	−	0.00752998i
$392$	55.1086	−	20.5054i	2.78340	−	1.03568i
$393$	22.4173	−	7.75485i	1.13080	−	0.391180i
$394$	46.2787	−	33.6235i	2.33149	−	1.69393i
$395$	−33.3768	−	0.362200i	−1.67937	−	0.0182242i
$396$	−3.00876	−	79.6167i	−0.151196	−	4.00089i
$397$	−22.4386	−	16.3026i	−1.12616	−	0.818203i	−0.141029	−	0.990005i	$-0.545041\pi$
$397$	−22.4386	−	16.3026i	−1.12616	−	0.818203i	−0.985131	+	0.171802i	$0.945041\pi$
$398$	0.722859	+	0.234871i	0.0362336	+	0.0117730i
$399$	2.52819	+	12.6673i	0.126568	+	0.634161i
$400$	60.8063	+	1.31988i	3.04032	+	0.0659938i
$401$			7.67254i			0.383148i	0.981478	+	0.191574i	$0.0613592\pi$
$401$			7.67254i			0.383148i	−0.981478	+	0.191574i	$0.938641\pi$
$402$	10.7913	−	0.203833i	0.538223	−	0.0101663i
$403$	1.84007	−	2.53265i	0.0916607	−	0.126160i
$404$	−32.5670	−	23.6613i	−1.62027	−	1.17719i
$405$	17.0118	+	10.7516i	0.845324	+	0.534254i
$406$	23.8791	+	44.5252i	1.18510	+	2.20975i
$407$	19.7669			0.979808
$408$	42.7896	+	29.8703i	2.11840	+	1.47880i
$409$	31.1297	−	10.1147i	1.53927	−	0.500138i	0.588093	−	0.808793i	$-0.299879\pi$
$409$	31.1297	−	10.1147i	1.53927	−	0.500138i	0.951174	+	0.308655i	$0.0998790\pi$
$410$	38.1022	−	27.0561i	1.88174	−	1.33621i
$411$	0.160727	+	8.50920i	0.00792806	+	0.419728i
$412$	9.24760	+	28.4612i	0.455597	+	1.40218i
$413$	2.46386	+	13.6869i	0.121239	+	0.673487i
$414$	0.371293	+	1.01109i	0.0182481	+	0.0496926i
$415$	−2.97489	−	1.00242i	−0.146032	−	0.0492068i
$416$	−14.0223	−	43.1561i	−0.687498	−	2.11590i
$417$	−29.7789	−	20.7878i	−1.45828	−	1.01799i
$418$	38.9024			1.90278
$419$	24.6420	−	17.9034i	1.20384	−	0.874640i	0.209181	−	0.977877i	$-0.432920\pi$
$419$	24.6420	−	17.9034i	1.20384	−	0.874640i	0.994657	+	0.103237i	$0.0329201\pi$
$420$	47.6312	+	22.5505i	2.32416	+	1.10035i
$421$	−4.23993	−	3.08049i	−0.206641	−	0.150134i	0.479651	−	0.877459i	$-0.340763\pi$
$421$	−4.23993	−	3.08049i	−0.206641	−	0.150134i	−0.686293	+	0.727325i	$0.740763\pi$
$422$	19.9806	+	14.5167i	0.972638	+	0.706663i
$423$	2.79218	−	1.02534i	0.135760	−	0.0498539i
$424$	62.9182			3.05558
$425$	17.1722	−	5.17038i	0.832974	−	0.250800i
$426$	19.3906	+	56.0532i	0.939476	+	2.71579i
$427$	27.3940	+	13.2399i	1.32569	+	0.640725i
$428$	16.9779	+	12.3352i	0.820659	+	0.596244i
$429$	−7.51772	+	24.7160i	−0.362959	+	1.19330i
$430$	−53.0194	+	16.5932i	−2.55682	+	0.800194i
$431$	−4.20080	−	5.78191i	−0.202346	−	0.278505i	0.695770	−	0.718265i	$-0.255063\pi$
$431$	−4.20080	−	5.78191i	−0.202346	−	0.278505i	−0.898115	+	0.439760i	$0.855063\pi$
$432$	−34.1966	+	53.1571i	−1.64529	+	2.55752i
$433$	13.1786	−	9.57479i	0.633321	−	0.460135i	−0.224228	−	0.974537i	$-0.571986\pi$
$433$	13.1786	−	9.57479i	0.633321	−	0.460135i	0.857549	+	0.514402i	$0.171986\pi$
$434$	−7.54273	+	1.35781i	−0.362062	+	0.0651771i
$435$	−8.33971	+	26.3865i	−0.399858	+	1.26514i
$436$	12.5142	−	38.5146i	0.599320	−	1.84452i
$437$	−0.360134	+	0.117015i	−0.0172276	+	0.00559758i
$438$	11.2347	+	14.8645i	0.536812	+	0.710254i
$439$	−14.5351	−	4.72275i	−0.693725	−	0.225405i	−0.0591304	−	0.998250i	$-0.518833\pi$
$439$	−14.5351	−	4.72275i	−0.693725	−	0.225405i	−0.634594	+	0.772845i	$0.718833\pi$
$440$	57.8595	−	77.8462i	2.75834	−	3.71117i
$441$	13.6590	+	15.9509i	0.650429	+	0.759567i
$442$	−16.2745	−	22.4000i	−0.774101	−	1.06546i
$443$	−15.2591			−0.724980			−0.362490	−	0.931988i	$-0.618073\pi$
$443$	−15.2591			−0.724980			−0.362490	+	0.931988i	$0.618073\pi$
$444$	−27.9597	−	19.5179i	−1.32691	−	0.926280i
$445$	0.237604	+	0.759205i	0.0112635	+	0.0359898i
$446$	53.3973	+	38.7954i	2.52844	+	1.83702i
$447$	3.69500	−	12.1480i	0.174767	−	0.574582i
$448$	−20.3316	+	42.0672i	−0.960580	+	1.98749i
$449$		−	26.2787i		−	1.24017i	−0.784534	−	0.620085i	$-0.787098\pi$
$449$		−	26.2787i		−	1.24017i	0.784534	−	0.620085i	$-0.212902\pi$
$450$	12.9994	+	37.9234i	0.612798	+	1.78772i
$451$		−	40.3797i		−	1.90141i
$452$	10.5001	−	32.3161i	0.493885	−	1.52002i
$453$	−13.3094	−	4.04824i	−0.625329	−	0.190203i
$454$	12.4919	−	17.1937i	0.586276	−	0.806940i
$455$	−12.2052	−	11.9593i	−0.572190	−	0.560660i
$456$	−33.6277	−	23.4746i	−1.57476	−	1.09930i
$457$			33.8353i			1.58275i	0.611331	+	0.791375i	$0.290634\pi$
$457$			33.8353i			1.58275i	−0.611331	+	0.791375i	$0.709366\pi$
$458$	−42.9489	−	59.1141i	−2.00687	−	2.76222i
$459$	−4.74623	+	18.0228i	−0.221535	+	0.841230i
$460$	−0.493314	+	1.46401i	−0.0230009	+	0.0682600i
$461$	4.20166	−	12.9314i	0.195691	−	0.602275i	−0.804277	−	0.594255i	$-0.797447\pi$
$461$	4.20166	−	12.9314i	0.195691	−	0.602275i	0.999968	−	0.00802015i	$-0.00255292\pi$
$462$	55.1613	−	30.9386i	2.56634	−	1.43939i
$463$	−19.4483	+	6.31913i	−0.903838	+	0.293675i	−0.723820	−	0.689989i	$-0.757616\pi$
$463$	−19.4483	+	6.31913i	−0.903838	+	0.293675i	−0.180018	+	0.983663i	$0.557616\pi$
$464$	−82.6607	−	26.8581i	−3.83743	−	1.24686i
$465$	−3.41572	−	2.43998i	−0.158400	−	0.113151i
$466$	−3.20996	−	9.87924i	−0.148699	−	0.457647i
$467$	−7.69411	−	10.5900i	−0.356041	−	0.490049i	0.592999	−	0.805203i	$-0.297944\pi$
$467$	−7.69411	−	10.5900i	−0.356041	−	0.490049i	−0.949040	+	0.315154i	$0.897944\pi$
$468$	35.0383	−	27.5370i	1.61964	−	1.27290i
$469$	2.91554	+	5.43635i	0.134627	+	0.251027i
$470$	5.61516	+	1.89208i	0.259008	+	0.0872753i
$471$	−11.8002	−	3.58920i	−0.543725	−	0.165382i
$472$	−35.7204	−	25.9524i	−1.64416	−	1.19456i
$473$	−14.8342	+	45.6549i	−0.682076	+	2.09921i
$474$	65.3041	−	22.5907i	2.99952	−	1.03763i
$475$	−13.4954	+	4.06332i	−0.619209	+	0.186438i
$476$	−6.61945	+	48.3537i	−0.303402	+	2.21629i
$477$	7.74596	+	21.0936i	0.354663	+	0.965807i
$478$	−19.5613	+	26.9238i	−0.894713	+	1.23147i
$479$	33.9559	+	24.6704i	1.55148	+	1.12722i	0.942582	+	0.333975i	$0.108390\pi$
$479$	33.9559	+	24.6704i	1.55148	+	1.12722i	0.608903	+	0.793245i	$0.291610\pi$
$480$	−57.7148	+	19.2667i	−2.63431	+	0.879401i
$481$	6.49874	+	8.94474i	0.296317	+	0.407845i
$482$			15.9879i			0.728229i
$483$	−0.417589	+	0.452330i	−0.0190009	+	0.0205817i
$484$	−24.8975	−	76.6267i	−1.13171	−	3.48303i
$485$	6.79457	+	0.0737335i	0.308525	+	0.00334807i
$486$	−40.6605	−	9.08086i	−1.84440	−	0.411916i
$487$	−21.4968	+	6.98474i	−0.974113	+	0.316509i	−0.752475	−	0.658620i	$-0.771140\pi$
$487$	−21.4968	+	6.98474i	−0.974113	+	0.316509i	−0.221638	+	0.975129i	$0.571140\pi$
$488$	−91.8708	+	29.8506i	−4.15880	+	1.35128i
$489$	13.0320	−	0.246156i	0.589329	−	0.0111316i
$490$	1.30526	+	41.8129i	0.0589655	+	1.88892i
$491$	−22.9353	+	7.45214i	−1.03506	+	0.336311i	−0.776788	−	0.629762i	$-0.783152\pi$
$491$	−22.9353	+	7.45214i	−1.03506	+	0.336311i	−0.258270	+	0.966073i	$0.583152\pi$
$492$	−39.8711	+	57.1159i	−1.79753	+	2.57498i
$493$	−25.6278			−1.15422
$494$	12.7899	+	17.6038i	0.575445	+	0.792032i
$495$	33.2214	+	9.81385i	1.49319	+	0.441100i
$496$	7.74935	−	10.6661i	0.347956	−	0.478920i
$497$	−23.4613	+	24.4694i	−1.05238	+	1.09760i
$498$	6.49774	−	0.122733i	0.291171	−	0.00549980i
$499$	−27.7320			−1.24146			−0.620728	−	0.784026i	$-0.713163\pi$
$499$	−27.7320			−1.24146			−0.620728	+	0.784026i	$0.713163\pi$
$500$	−19.5390	+	54.0785i	−0.873812	+	2.41846i
$501$	−1.46244	−	4.22756i	−0.0653372	−	0.188873i
$502$	16.2818	−	50.1102i	0.726692	−	2.23653i
$503$	−11.1370	+	15.3288i	−0.496576	+	0.683479i	−0.981584	−	0.191031i	$-0.938817\pi$
$503$	−11.1370	+	15.3288i	−0.496576	+	0.683479i	0.485008	+	0.874510i	$0.338817\pi$
$504$	−66.3511	−	6.54193i	−2.95551	−	0.291401i
$505$	14.2703	−	10.1333i	0.635022	−	0.450924i
$506$	1.08978	+	1.49995i	0.0484465	+	0.0666809i
$507$	7.62355	−	2.63722i	0.338574	−	0.117123i
$508$	15.0206	+	20.6741i	0.666433	+	0.917266i
$509$	0.636297	+	1.95832i	0.0282034	+	0.0868011i	0.964167	−	0.265295i	$-0.0854692\pi$
$509$	0.636297	+	1.95832i	0.0282034	+	0.0868011i	−0.935964	+	0.352096i	$0.885469\pi$
$510$	−29.8597	+	22.0631i	−1.32221	+	0.976969i
$511$	−4.63409	+	9.58816i	−0.205000	+	0.424155i
$512$	4.09598	+	12.6061i	0.181019	+	0.557118i
$513$	3.72999	−	14.1638i	0.164683	−	0.625347i
$514$	−57.7675	−	18.7698i	−2.54802	−	0.827901i
$515$	−13.0105	−	0.141187i	−0.573310	−	0.00622146i
$516$	66.0624	−	49.9302i	2.90823	−	2.19805i
$517$	4.14218	−	3.00947i	0.182173	−	0.132356i
$518$	3.67119	−	26.8173i	0.161303	−	1.17828i
$519$	−13.1229	−	9.16079i	−0.576033	−	0.402114i
$520$	54.2487	+	0.588698i	2.37896	+	0.0258161i
$521$	20.6922	+	15.0337i	0.906540	+	0.658640i	0.940137	−	0.340796i	$-0.110696\pi$
$521$	20.6922	+	15.0337i	0.906540	+	0.658640i	−0.0335974	+	0.999435i	$0.510696\pi$
$522$	−2.16345	−	57.2483i	−0.0946915	−	2.50569i
$523$	−10.6260	+	32.7035i	−0.464643	+	1.43002i	0.394788	+	0.918772i	$0.370818\pi$
$523$	−10.6260	+	32.7035i	−0.464643	+	1.43002i	−0.859431	+	0.511252i	$0.829182\pi$
$524$	−70.4338			−3.07691
$525$	−15.9041	+	16.4942i	−0.694112	+	0.719867i
$526$	86.3362			3.76444
$527$	1.20129	−	3.69719i	0.0523290	−	0.161052i
$528$	−31.6604	+	104.090i	−1.37784	+	4.52992i
$529$	18.5928	+	13.5085i	0.808382	+	0.587324i
$530$	−14.2938	+	42.4198i	−0.620881	+	1.84260i
$531$	4.30304	−	15.1704i	0.186736	−	0.658341i
$532$	5.20212	−	38.0004i	0.225541	−	1.64753i
$533$	18.2723	−	13.2756i	0.791460	−	0.575029i
$534$	−0.993006	−	1.31384i	−0.0429716	−	0.0568555i
$535$	−7.43946	+	5.28270i	−0.321636	+	0.228391i
$536$	−18.6268	−	6.05220i	−0.804554	−	0.261415i
$537$	−8.34232	+	6.30515i	−0.359998	+	0.272087i
$538$	7.69453	+	23.6813i	0.331735	+	1.02098i
$539$	30.1114	+	19.9986i	1.29699	+	0.861399i
$540$	−37.3005	−	46.6844i	−1.60516	−	2.00898i
$541$	0.236536	+	0.727984i	0.0101695	+	0.0312985i	0.956013	−	0.293326i	$-0.0947621\pi$
$541$	0.236536	+	0.727984i	0.0101695	+	0.0312985i	−0.945843	+	0.324624i	$0.894762\pi$
$542$	−26.7991	−	36.8858i	−1.15112	−	1.58438i
$543$	−11.3528	−	32.8180i	−0.487194	−	1.40835i
$544$	−33.1209	−	45.5871i	−1.42005	−	1.95453i
$545$	14.1314	+	10.5032i	0.605323	+	0.449909i
$546$	32.1354	+	14.7895i	1.37527	+	0.632931i
$547$	−12.3896	+	17.0528i	−0.529742	+	0.729127i	−0.987091	−	0.160160i	$-0.948799\pi$
$547$	−12.3896	+	17.0528i	−0.529742	+	0.729127i	0.457349	+	0.889287i	$0.348799\pi$
$548$	7.80911	−	24.0340i	0.333589	−	1.02668i
$549$	−21.3179	−	27.1251i	−0.909827	−	1.15767i
$550$	39.3398	+	56.6943i	1.67746	+	2.41745i
$551$	20.1405			0.858013
$552$	−0.0369114	−	1.95417i	−0.00157105	−	0.0831749i
$553$	28.5077	+	27.3333i	1.21227	+	1.16233i
$554$	−20.3035	+	27.9454i	−0.862613	+	1.18728i
$555$	11.9235	−	8.81020i	0.506126	−	0.373972i
$556$	63.3840	+	87.2406i	2.68808	+	3.69983i
$557$	31.8703			1.35039			0.675193	−	0.737641i	$-0.264060\pi$
$557$	31.8703			1.35039			0.675193	+	0.737641i	$0.264060\pi$
$558$	8.36031	+	2.37137i	0.353920	+	0.100388i
$559$	−25.5364	+	8.29727i	−1.08007	+	0.350937i
$560$	−51.4015	−	50.3657i	−2.17211	−	2.12834i
$561$	0.605845	+	32.0747i	0.0255788	+	1.35419i
$562$	−29.0032	+	9.42373i	−1.22343	+	0.397516i
$563$	28.3068	−	9.19743i	1.19299	−	0.387626i	0.355812	−	0.934558i	$-0.384204\pi$
$563$	28.3068	−	9.19743i	1.19299	−	0.387626i	0.837177	+	0.546932i	$0.184204\pi$
$564$	−8.83055	+	0.166796i	−0.371833	+	0.00702340i
$565$	11.8571	+	8.81285i	0.498832	+	0.370759i
$566$	12.9849	+	39.9634i	0.545796	+	1.67979i
$567$	−5.97538	−	23.0498i	−0.250943	−	0.968002i
$568$		−	107.628i		−	4.51595i
$569$	−12.0733	−	16.6175i	−0.506139	−	0.696640i	0.477124	−	0.878836i	$-0.341679\pi$
$569$	−12.0733	−	16.6175i	−0.506139	−	0.696640i	−0.983262	+	0.182196i	$0.941679\pi$
$570$	23.4662	−	17.3390i	0.982893	−	0.726251i
$571$	−9.56464	−	6.94912i	−0.400268	−	0.290812i	0.369382	−	0.929278i	$-0.379569\pi$
$571$	−9.56464	−	6.94912i	−0.400268	−	0.290812i	−0.769650	+	0.638466i	$0.779569\pi$
$572$	45.0882	−	62.0586i	1.88523	−	2.59480i
$573$	−11.5265	+	0.217718i	−0.481525	+	0.00909532i
$574$	−54.7823	−	7.49949i	−2.28657	−	0.313023i
$575$	−0.534715	−	0.406510i	−0.0222991	−	0.0169527i
$576$	41.6541	−	32.7365i	1.73559	−	1.36402i
$577$	−5.47010	+	16.8352i	−0.227723	+	0.700860i	0.770280	+	0.637705i	$0.220116\pi$
$577$	−5.47010	+	16.8352i	−0.227723	+	0.700860i	−0.998004	+	0.0631550i	$0.979884\pi$
$578$	8.94140	+	6.49631i	0.371913	+	0.270211i
$579$	−5.05257	+	16.6113i	−0.209978	+	0.690342i
$580$	49.0165	−	65.9484i	2.03530	−	2.73836i
$581$	1.75552	+	3.27337i	0.0728313	+	0.135802i
$582$	−13.2941	+	4.59883i	−0.551056	+	0.190628i
$583$	22.7351	+	31.2921i	0.941590	+	1.29599i
$584$	−10.4480	−	32.1556i	−0.432341	−	1.33061i
$585$	6.48128	+	18.2595i	0.267968	+	0.754939i
$586$	−27.9471	−	9.08057i	−1.15448	−	0.375115i
$587$	15.8963	−	5.16501i	0.656110	−	0.213183i	0.0380034	−	0.999278i	$-0.487900\pi$
$587$	15.8963	−	5.16501i	0.656110	−	0.213183i	0.618106	+	0.786095i	$0.287900\pi$
$588$	−22.8450	−	58.0195i	−0.942110	−	2.39269i
$589$	−0.944074	+	2.90556i	−0.0388999	+	0.119721i
$590$	25.6122	−	18.1870i	1.05444	−	0.748748i
$591$	−22.3528	−	29.5750i	−0.919473	−	1.21655i
$592$	27.3690	+	37.6702i	1.12486	+	1.54823i
$593$			21.2580i			0.872963i	0.899713	+	0.436482i	$0.143776\pi$
$593$			21.2580i			0.872963i	−0.899713	+	0.436482i	$0.856224\pi$
$594$	−71.5984	+	4.06104i	−2.93772	+	0.166626i
$595$	−19.0037	−	9.44050i	−0.779076	−	0.387023i
$596$	−22.1611	+	30.5021i	−0.907754	+	1.24942i
$597$	0.143339	−	0.471254i	0.00586646	−	0.0192871i
$598$	−0.320460	+	0.986273i	−0.0131046	+	0.0403317i
$599$			1.77189i			0.0723976i	0.999345	+	0.0361988i	$0.0115250\pi$
$599$			1.77189i			0.0723976i	−0.999345	+	0.0361988i	$0.988475\pi$
$600$	0.204889	−	72.7457i	0.00836455	−	2.96983i
$601$			43.1204i			1.75892i	0.475974	+	0.879459i	$0.342095\pi$
$601$			43.1204i			1.75892i	−0.475974	+	0.879459i	$0.657905\pi$
$602$	59.1839	+	28.6044i	2.41216	+	1.16583i
$603$	−0.264148	−	6.98979i	−0.0107570	−	0.284646i
$604$	33.4181	+	24.2797i	1.35976	+	0.987926i
$605$	35.0283	+	0.380122i	1.42410	+	0.0154542i
$606$	−20.7399	+	29.7102i	−0.842503	+	1.20690i
$607$	−9.88379			−0.401171			−0.200585	−	0.979676i	$-0.564284\pi$
$607$	−9.88379			−0.401171			−0.200585	+	0.979676i	$0.564284\pi$
$608$	26.0292	+	35.8261i	1.05562	+	1.45294i
$609$	28.5580	−	16.0175i	1.15723	−	0.649061i
$610$	0.745753	−	68.7213i	0.0301947	−	2.78245i
$611$	2.72364	+	0.884963i	0.110187	+	0.0358018i
$612$	30.8138	−	45.9669i	1.24557	−	1.85810i
$613$	−37.2992	+	12.1192i	−1.50650	+	0.489491i	−0.941906	−	0.335878i	$-0.890967\pi$
$613$	−37.2992	+	12.1192i	−1.50650	+	0.489491i	−0.564594	+	0.825369i	$0.690967\pi$
$614$	−9.63814	+	29.6631i	−0.388964	+	1.19711i
$615$	−17.9974	−	24.3574i	−0.725726	−	0.982183i
$616$	−112.949	+	20.3326i	−4.55084	+	0.819224i
$617$	−15.2962	+	11.1133i	−0.615802	+	0.447406i	−0.851453	−	0.524432i	$-0.824278\pi$
$617$	−15.2962	+	11.1133i	−0.615802	+	0.447406i	0.235651	+	0.971838i	$0.424278\pi$
$618$	25.4559	−	8.80599i	1.02399	−	0.354229i
$619$	24.0767	+	33.1387i	0.967724	+	1.33196i	0.943188	+	0.332259i	$0.107811\pi$
$619$	24.0767	+	33.1387i	0.967724	+	1.33196i	0.0245362	+	0.999699i	$0.492189\pi$
$620$	7.21641	+	10.1626i	0.289818	+	0.408141i
$621$	0.650598	−	0.252956i	0.0261076	−	0.0101508i
$622$	−8.88542	−	6.45564i	−0.356273	−	0.258847i
$623$	0.409597	−	0.847476i	0.0164102	−	0.0339534i
$624$	−57.5107	+	19.8947i	−2.30227	+	0.796427i
$625$	−19.5687	−	15.5584i	−0.782750	−	0.622337i
$626$	28.1142			1.12367
$627$	−0.476124	−	25.2070i	−0.0190145	−	1.00667i
$628$	29.6288	+	21.5266i	1.18232	+	0.859003i
$629$	11.1075	+	8.07007i	0.442885	+	0.321775i
$630$	19.4843	−	43.2481i	0.776271	−	1.72304i
$631$	19.9639	−	14.5046i	0.794751	−	0.577420i	−0.114619	−	0.993410i	$-0.536565\pi$
$631$	19.9639	−	14.5046i	0.794751	−	0.577420i	0.909369	+	0.415989i	$0.136565\pi$
$632$	−125.390			−4.98775
$633$	9.16163	−	13.1241i	0.364142	−	0.521638i
$634$	−0.951409	−	2.92814i	−0.0377853	−	0.116291i
$635$	−10.6035	+	3.31853i	−0.420788	+	0.131692i
$636$	−1.26007	−	66.7105i	−0.0499649	−	2.64524i
$637$	0.850097	+	20.2006i	0.0336821	+	0.800379i
$638$	−30.4728	−	93.7857i	−1.20643	−	3.71301i
$639$	36.0826	−	13.2502i	1.42740	−	0.524170i
$640$	35.2762	+	0.382812i	1.39441	+	0.0151320i
$641$	34.1211	−	11.0866i	1.34770	−	0.437895i	0.455784	−	0.890090i	$-0.349359\pi$
$641$	34.1211	−	11.0866i	1.34770	−	0.437895i	0.891919	+	0.452195i	$0.149359\pi$
$642$	10.8122	−	15.4886i	0.426724	−	0.611288i
$643$	−3.70545			−0.146129			−0.0730644	−	0.997327i	$-0.523278\pi$
$643$	−3.70545			−0.146129			−0.0730644	+	0.997327i	$0.523278\pi$
$644$	1.61090	−	0.863933i	0.0634783	−	0.0340437i
$645$	11.4005	+	34.1510i	0.448895	+	1.34470i
$646$	21.8602	+	15.8824i	0.860079	+	0.624884i
$647$	−6.83318	+	9.40507i	−0.268640	+	0.369751i	−0.921930	−	0.387356i	$-0.873388\pi$
$647$	−6.83318	+	9.40507i	−0.268640	+	0.369751i	0.653290	+	0.757108i	$0.273388\pi$
$648$	64.3409	+	39.6936i	2.52755	+	1.55931i
$649$		−	27.1431i		−	1.06546i
$650$	−12.7211	+	36.4410i	−0.498964	+	1.42934i
$651$	0.972115	+	4.87072i	0.0381002	+	0.190899i
$652$	−36.8085	−	11.9598i	−1.44153	−	0.468382i
$653$	25.5185	+	18.5403i	0.998617	+	0.725538i	0.961791	−	0.273784i	$-0.0882753\pi$
$653$	25.5185	+	18.5403i	0.998617	+	0.725538i	0.0368259	+	0.999322i	$0.488275\pi$
$654$	−34.8732	−	10.6072i	−1.36365	−	0.414774i
$655$	9.77861	−	29.0201i	0.382082	−	1.13391i
$656$	76.9524	−	55.9092i	3.00449	−	2.18289i
$657$	9.49402	−	7.46146i	0.370397	−	0.291099i
$658$	−3.31358	−	6.17853i	−0.129177	−	0.240864i
$659$	−0.512658	+	0.166573i	−0.0199703	+	0.00648875i	−0.318985	−	0.947760i	$-0.603342\pi$
$659$	−0.512658	+	0.166573i	−0.0199703	+	0.00648875i	0.299015	+	0.954248i	$0.403342\pi$
$660$	−83.6970	−	59.7879i	−3.25790	−	2.32724i
$661$	37.9795	+	12.3403i	1.47723	+	0.479982i	0.933285	−	0.359137i	$-0.116929\pi$
$661$	37.9795	+	12.3403i	1.47723	+	0.479982i	0.543948	+	0.839119i	$0.316929\pi$
$662$	−8.02329	−	24.6931i	−0.311834	−	0.959726i
$663$	−14.3150	+	10.8193i	−0.555947	+	0.420187i
$664$	−11.2156	−	3.64419i	−0.435252	−	0.141422i
$665$	14.9347	+	7.41914i	0.579143	+	0.287702i
$666$	−17.0895	+	25.4936i	−0.662205	+	0.987855i
$667$	0.564197	+	0.776550i	0.0218458	+	0.0300682i
$668$			13.2827i			0.513924i
$669$	24.4841	−	35.0738i	0.946610	−	1.35603i
$670$	8.31206	−	11.1833i	0.321123	−	0.432050i
$671$	−48.0430	−	34.9053i	−1.85468	−	1.34750i
$672$	65.3999	+	30.0986i	2.52286	+	1.16108i
$673$	−13.3340	−	4.33248i	−0.513988	−	0.167005i	0.0405270	−	0.999178i	$-0.487096\pi$
$673$	−13.3340	−	4.33248i	−0.513988	−	0.167005i	−0.554515	+	0.832173i	$0.687096\pi$
$674$			83.7999i			3.22785i
$675$	24.4135	−	8.88715i	0.939676	−	0.342067i
$676$	−23.9527			−0.921258
$677$	6.78909	+	2.20591i	0.260926	+	0.0847799i	0.436559	−	0.899676i	$-0.356197\pi$
$677$	6.78909	+	2.20591i	0.260926	+	0.0847799i	−0.175633	+	0.984456i	$0.556197\pi$
$678$	−29.2607	−	8.90007i	−1.12375	−	0.341805i
$679$	−5.80336	−	5.56428i	−0.222713	−	0.213537i
$680$	64.2943	−	20.1218i	2.46557	−	0.771636i
$681$	−11.2936	−	7.88377i	−0.432772	−	0.302107i
$682$	14.9584			0.572785
$683$	−24.9902	+	18.1564i	−0.956222	+	0.694736i	−0.952270	−	0.305256i	$-0.901258\pi$
$683$	−24.9902	+	18.1564i	−0.956222	+	0.694736i	−0.00395199	+	0.999992i	$0.501258\pi$
$684$	−24.2160	+	36.1247i	−0.925924	+	1.38126i
$685$	8.81831	+	6.55425i	0.336930	+	0.250425i
$686$	32.7240	−	37.1372i	1.24941	−	1.41791i
$687$	−37.7775	+	28.5524i	−1.44130	+	1.08934i
$688$	−107.545	+	34.9434i	−4.10010	+	1.33220i
$689$	−6.68546	+	20.5757i	−0.254696	+	0.783873i
$690$	1.32590	+	0.419062i	0.0504760	+	0.0159534i
$691$	−3.98588	+	1.29509i	−0.151630	+	0.0492676i	−0.383849	−	0.923396i	$-0.625402\pi$
$691$	−3.98588	+	1.29509i	−0.151630	+	0.0492676i	0.232219	+	0.972664i	$0.425402\pi$
$692$	27.9321	+	38.4452i	1.06182	+	1.46147i
$693$	−20.7219	−	35.3633i	−0.787160	−	1.34334i
$694$	11.8286	−	8.59401i	0.449009	−	0.326224i
$695$	−44.7447	+	14.0035i	−1.69727	+	0.531183i
$696$	−30.2514	+	99.4573i	−1.14668	+	3.76992i
$697$	16.4855	−	22.6903i	0.624432	−	0.859457i
$698$	−59.3582	−	19.2866i	−2.24674	−	0.730010i
$699$	−6.36201	+	2.20082i	−0.240633	+	0.0832426i
$700$	60.6404	−	30.8464i	2.29199	−	1.16588i
$701$		−	19.4866i		−	0.735999i	−0.929826	−	0.368000i	$-0.880043\pi$
$701$		−	19.4866i		−	0.735999i	0.929826	−	0.368000i	$-0.119957\pi$
$702$	−25.3770	−	31.0639i	−0.957792	−	1.17243i
$703$	−8.72920	−	6.34214i	−0.329228	−	0.239198i
$704$	53.6017	−	73.7764i	2.02019	−	2.78055i
$705$	1.15726	−	3.66152i	0.0435849	−	0.137901i
$706$	−19.1508	−	26.3588i	−0.720749	−	0.992026i
$707$	−20.5175	−	2.80877i	−0.771639	−	0.105635i
$708$	−26.8013	+	38.3932i	−1.00725	+	1.44290i
$709$	3.22079	+	9.91257i	0.120959	+	0.372274i	0.993143	−	0.116904i	$-0.0372969\pi$
$709$	3.22079	+	9.91257i	0.120959	+	0.372274i	−0.872184	+	0.489178i	$0.837297\pi$
$710$	72.5632	+	24.4509i	2.72325	+	0.917625i
$711$	−15.4370	−	42.0375i	−0.578933	−	1.57653i
$712$	0.923475	+	2.84216i	0.0346087	+	0.106515i
$713$	−0.138475	+	0.0449933i	−0.00518594	+	0.00168501i
$714$	43.6275	+	5.13511i	1.63272	+	0.192177i
$715$	19.3096	+	27.1931i	0.722138	+	1.01696i
$716$	29.5302	−	9.59495i	1.10360	−	0.358580i
$717$	17.6848	+	12.3453i	0.660451	+	0.461044i
$718$			51.9548i			1.93894i
$719$	−40.4973	+	29.4230i	−1.51029	+	1.09729i	−0.544247	+	0.838925i	$0.683185\pi$
$719$	−40.4973	+	29.4230i	−1.51029	+	1.09729i	−0.966047	+	0.258368i	$0.916815\pi$
$720$	27.2955	+	76.8989i	1.01724	+	2.86585i
$721$	11.1125	+	10.6547i	0.413850	+	0.396800i
$722$	23.9023	+	17.3660i	0.889551	+	0.646297i
$723$	10.3594	−	0.195675i	0.385271	−	0.00727721i
$724$			103.112i			3.83213i
$725$	20.3669	+	29.3517i	0.756408	+	1.09009i
$726$	−68.5355	+	23.7086i	−2.54359	+	0.879907i
$727$	9.79540	−	30.1471i	0.363291	−	1.11810i	−0.587753	−	0.809041i	$-0.699987\pi$
$727$	9.79540	−	30.1471i	0.363291	−	1.11810i	0.951044	−	0.309055i	$-0.100013\pi$
$728$	−46.3348	−	44.4259i	−1.71728	−	1.64653i
$729$	−5.38633	+	26.4573i	−0.199494	+	0.979899i
$730$	24.0531	+	0.261020i	0.890245	+	0.00966079i
$731$	−26.9748	+	19.5984i	−0.997700	+	0.724871i
$732$	33.4898	+	96.8105i	1.23782	+	3.57822i
$733$	−11.3912	+	8.27618i	−0.420743	+	0.305688i	−0.777937	−	0.628343i	$-0.783734\pi$
$733$	−11.3912	+	8.27618i	−0.420743	+	0.305688i	0.357194	+	0.934030i	$0.383734\pi$
$734$	−6.77853	−	20.8622i	−0.250200	−	0.770036i
$735$	27.0769	−	1.35749i	0.998746	−	0.0500718i
$736$	−0.652179	+	2.00720i	−0.0240396	+	0.0739864i
$737$	−3.72061	−	11.4509i	−0.137051	−	0.421798i
$738$	52.0781	+	34.9104i	1.91702	+	1.28507i
$739$	−13.1013	+	40.3215i	−0.481938	+	1.48325i	0.354430	+	0.935082i	$0.384675\pi$
$739$	−13.1013	+	40.3215i	−0.481938	+	1.48325i	−0.836368	+	0.548169i	$0.815325\pi$
$740$	−42.0113	+	13.1481i	−1.54437	+	0.483332i
$741$	11.2499	−	8.50272i	0.413276	−	0.312355i
$742$	46.6758	−	25.0324i	1.71352	−	0.918970i
$743$	17.3685			0.637188			0.318594	−	0.947891i	$-0.396789\pi$
$743$	17.3685			0.637188			0.318594	+	0.947891i	$0.396789\pi$
$744$	−12.9302	−	9.02621i	−0.474043	−	0.330917i
$745$	−9.49077	−	13.3656i	−0.347715	−	0.489676i
$746$	−6.17891	+	8.50454i	−0.226226	+	0.311373i
$747$	−0.159051	−	4.20873i	−0.00581936	−	0.153989i
$748$	29.4357	−	90.5939i	1.07628	−	3.31244i
$749$	10.6962	+	1.46428i	0.390832	+	0.0535035i
$750$	48.9990	+	16.6645i	1.78919	+	0.608502i
$751$	−31.7620			−1.15901			−0.579506	−	0.814968i	$-0.696754\pi$
$751$	−31.7620			−1.15901			−0.579506	+	0.814968i	$0.696754\pi$
$752$	11.4704	+	3.72696i	0.418283	+	0.135908i
$753$	−32.6684	−	9.93655i	−1.19050	−	0.362108i
$754$	32.4206	−	44.6231i	1.18069	−	1.62508i
$755$	−14.6433	+	10.3981i	−0.532924	+	0.378425i
$756$	−5.60742	+	70.4813i	−0.203940	+	2.56338i
$757$			13.1944i			0.479560i	0.970827	+	0.239780i	$0.0770754\pi$
$757$			13.1944i			0.479560i	−0.970827	+	0.239780i	$0.922925\pi$
$758$	40.7915	−	29.6367i	1.48161	−	1.07645i
$759$	0.958560	−	0.724483i	0.0347935	−	0.0262971i
$760$	−50.5278	+	15.8134i	−1.83284	+	0.573613i
$761$	−1.37350	+	4.22720i	−0.0497894	+	0.153236i	−0.972860	−	0.231395i	$-0.925671\pi$
$761$	−1.37350	+	4.22720i	−0.0497894	+	0.153236i	0.923071	+	0.384631i	$0.125671\pi$
$762$	18.3500	−	13.8690i	0.664749	−	0.502419i
$763$	−3.69098	−	20.5036i	−0.133622	−	0.742280i
$764$	32.5561	+	10.5781i	1.17784	+	0.382703i
$765$	14.6613	+	19.0777i	0.530080	+	0.689755i
$766$	−58.4013	+	18.9757i	−2.11012	+	0.685621i
$767$	12.2826	−	8.92381i	0.443498	−	0.322220i
$768$	−11.2074	+	3.87698i	−0.404411	+	0.139898i
$769$	−25.3914	−	34.9483i	−0.915638	−	1.26027i	−0.965204	−	0.261497i	$-0.915784\pi$
$769$	−25.3914	−	34.9483i	−0.915638	−	1.26027i	0.0495664	−	0.998771i	$-0.484216\pi$
$770$	11.9514	−	80.7699i	0.430697	−	2.91075i
$771$	−11.4550	+	37.6604i	−0.412540	+	1.35631i
$772$	30.3032	−	41.7088i	1.09064	−	1.50113i
$773$	−39.9911	−	12.9939i	−1.43838	−	0.467358i	−0.516988	−	0.855992i	$-0.672947\pi$
$773$	−39.9911	−	12.9939i	−1.43838	−	0.467358i	−0.921392	+	0.388634i	$0.872947\pi$
$774$	−46.0566	−	58.6028i	−1.65547	−	2.10644i
$775$	−5.18910	+	1.56238i	−0.186398	+	0.0561225i
$776$	25.5259			0.916326
$777$	−17.4213	−	2.05055i	−0.624986	−	0.0735630i
$778$	−14.9263	+	20.5443i	−0.535133	+	0.736548i
$779$	−12.9557	+	17.8320i	−0.464185	+	0.638896i
$780$	−0.462260	−	57.5303i	−0.0165516	−	2.05991i
$781$	53.5282	−	38.8905i	1.91539	−	1.39161i
$782$			1.28777i			0.0460506i
$783$	−37.0677	+	2.10247i	−1.32469	+	0.0751362i
$784$	3.58013	+	85.0736i	0.127862	+	3.03834i
$785$	−12.9829	+	9.21903i	−0.463378	+	0.329041i
$786$	1.19726	+	63.3855i	0.0427049	+	2.26089i
$787$	−9.46805	−	29.1397i	−0.337499	−	1.03872i	−0.965478	−	0.260486i	$-0.916117\pi$
$787$	−9.46805	−	29.1397i	−0.337499	−	1.03872i	0.627978	−	0.778231i	$-0.283883\pi$
$788$	34.0158	+	104.690i	1.21176	+	3.72942i
$789$	−1.05666	−	55.9419i	−0.0376182	−	1.99158i
$790$	28.4862	−	84.5388i	1.01349	−	3.00776i
$791$	−3.09695	−	17.2038i	−0.110115	−	0.611695i
$792$	125.192	+	35.5102i	4.44850	+	1.26180i
$793$		−	33.2158i		−	1.17953i
$794$	59.9701	−	43.5708i	2.12826	−	1.54627i
$795$	27.6610	+	8.74252i	0.981035	+	0.310065i
$796$	−0.859686	+	1.18326i	−0.0304708	+	0.0419394i
$797$	−14.5470	+	20.0222i	−0.515280	+	0.709223i	−0.984799	−	0.173700i	$-0.944428\pi$
$797$	−14.5470	+	20.0222i	−0.515280	+	0.709223i	0.469518	+	0.882923i	$0.344428\pi$
$798$	−34.2862	−	4.03560i	−1.21372	−	0.142859i
$799$	3.55624			0.125811
$800$	−25.8892	+	74.1625i	−0.915323	+	2.62204i
$801$	−0.839156	+	0.659502i	−0.0296501	+	0.0233024i
$802$	−19.5022	−	6.33666i	−0.688648	−	0.223755i
$803$	12.2172	−	16.8155i	0.431134	−	0.593406i
$804$	−6.04395	+	19.8707i	−0.213154	+	0.700785i
$805$	0.132310	+	0.783666i	0.00466331	+	0.0276206i
$806$	4.91784	+	6.76883i	0.173224	+	0.238422i
$807$	15.2502	−	5.27554i	0.536834	−	0.185708i
$808$	53.1915	−	38.6459i	1.87127	−	1.35956i
$809$	28.8811	−	9.38405i	1.01541	−	0.329926i	0.246401	−	0.969168i	$-0.420752\pi$
$809$	28.8811	−	9.38405i	1.01541	−	0.329926i	0.769005	+	0.639242i	$0.220752\pi$
$810$	−41.3787	+	34.3614i	−1.45390	+	1.20734i
$811$	−0.475614	−	0.154536i	−0.0167011	−	0.00542650i	0.300655	−	0.953733i	$-0.402795\pi$
$811$	−0.475614	−	0.154536i	−0.0167011	−	0.00542650i	−0.317356	+	0.948307i	$0.602795\pi$
$812$	−95.6861	+	17.2250i	−3.35792	+	0.604480i
$813$	−23.5723	+	17.8160i	−0.826716	+	0.624835i
$814$	−16.3253	+	50.2440i	−0.572200	+	1.76105i
$815$	10.0380	−	13.5054i	0.351615	−	0.473074i
$816$	−60.2865	+	45.5648i	−2.11045	+	1.59509i
$817$	21.1991	−	15.4020i	0.741662	−	0.538849i
$818$			87.4799i			3.05866i
$819$	9.18960	−	21.0033i	0.321110	−	0.733913i
$820$	26.8588	+	85.8205i	0.937949	+	2.99698i
$821$	13.1264	−	18.0669i	0.458115	−	0.630541i	−0.516002	−	0.856587i	$-0.672580\pi$
$821$	13.1264	−	18.0669i	0.458115	−	0.630541i	0.974116	+	0.226047i	$0.0725802\pi$
$822$	−21.7616	−	6.61912i	−0.759024	−	0.230868i
$823$	−41.9328	−	13.6248i	−1.46169	−	0.474931i	−0.533101	−	0.846051i	$-0.678974\pi$
$823$	−41.9328	−	13.6248i	−1.46169	−	0.474931i	−0.928585	+	0.371121i	$0.878974\pi$
$824$	−48.8778			−1.70274
$825$	36.2538	−	26.1843i	1.26220	−	0.911619i
$826$	−36.8245	−	5.04114i	−1.28129	−	0.175404i
$827$	11.7426	−	36.1400i	0.408330	−	1.25671i	−0.509752	−	0.860321i	$-0.670263\pi$
$827$	11.7426	−	36.1400i	0.408330	−	1.25671i	0.918082	−	0.396389i	$-0.129737\pi$
$828$	−2.07121	+	0.0782725i	−0.0719797	+	0.00272016i
$829$	7.15740	−	9.85131i	0.248587	−	0.342150i	−0.666429	−	0.745568i	$-0.732178\pi$
$829$	7.15740	−	9.85131i	0.248587	−	0.342150i	0.915016	+	0.403418i	$0.132178\pi$
$830$	5.00491	−	6.73377i	0.173723	−	0.233733i
$831$	18.3558	+	12.8137i	0.636755	+	0.444502i
$832$	51.0072			1.76836
$833$	8.75565	+	23.5310i	0.303365	+	0.815301i
$834$	77.4331	−	58.5242i	2.68129	−	2.02653i
$835$	−5.47275	−	1.84409i	−0.189392	−	0.0638175i
$836$	−23.1331	+	71.1963i	−0.800074	+	2.46237i
$837$	1.43422	−	5.44612i	0.0495738	−	0.188245i
$838$	25.1559	+	77.4217i	0.868994	+	2.67449i
$839$	0.544478	−	1.67573i	0.0187975	−	0.0578526i	−0.941218	−	0.337800i	$-0.890317\pi$
$839$	0.544478	−	1.67573i	0.0187975	−	0.0578526i	0.960015	+	0.279948i	$0.0903171\pi$
$840$	−59.0693	+	62.6066i	−2.03808	+	2.16013i
$841$	−6.81483	−	20.9739i	−0.234994	−	0.723238i
$842$	11.3318	−	8.23301i	0.390518	−	0.283728i
$843$	6.46111	+	18.6774i	0.222532	+	0.643285i
$844$	−38.4487	+	27.9346i	−1.32346	+	0.961549i
$845$	3.32545	−	9.86900i	0.114399	−	0.339504i
$846$	0.300211	+	7.94405i	0.0103214	+	0.273122i
$847$	−29.9183	−	28.6858i	−1.02801	−	0.985655i
$848$	−28.1554	+	86.6533i	−0.966859	+	2.97569i
$849$	25.7355	−	8.90273i	0.883241	−	0.305541i
$850$	−1.04014	+	47.9189i	−0.0356764	+	1.64360i
$851$		−	0.514232i		−	0.0176276i
$852$	−114.115	+	2.15546i	−3.90951	+	0.0738450i
$853$	28.0737	+	20.3968i	0.961227	+	0.698372i	0.953435	−	0.301597i	$-0.0975199\pi$
$853$	28.0737	+	20.3968i	0.961227	+	0.698372i	0.00779149	+	0.999970i	$0.497520\pi$
$854$	−56.2780	+	58.6961i	−1.92579	+	2.00854i
$855$	−11.5221	−	14.9928i	−0.394047	−	0.512744i
$856$	−27.7300	+	20.1470i	−0.947792	+	0.688611i
$857$		−	9.55489i		−	0.326389i	−0.986594	−	0.163194i	$-0.947820\pi$
$857$		−	9.55489i		−	0.326389i	0.986594	−	0.163194i	$-0.0521798\pi$
$858$	−56.6148	−	39.5214i	−1.93280	−	1.34924i
$859$	19.6846	−	6.39590i	0.671629	−	0.218225i	0.0467020	−	0.998909i	$-0.485129\pi$
$859$	19.6846	−	6.39590i	0.671629	−	0.218225i	0.624927	+	0.780683i	$0.285129\pi$
$860$	1.16005	−	106.899i	0.0395574	−	3.64523i
$861$	−4.18885	+	35.5882i	−0.142756	+	1.21284i
$862$	18.1660	−	5.90249i	0.618736	−	0.201040i
$863$	−3.12957	−	9.63181i	−0.106532	−	0.327871i	0.883555	−	0.468327i	$-0.155143\pi$
$863$	−3.12957	−	9.63181i	−0.106532	−	0.327871i	−0.990087	+	0.140456i	$0.955143\pi$
$864$	−51.6456	−	63.2194i	−1.75702	−	2.15077i
$865$	−19.7181	+	6.17107i	−0.670436	+	0.209823i
$866$	13.4534	+	41.4053i	0.457165	+	1.40701i
$867$	4.09987	−	5.87312i	0.139239	−	0.199462i
$868$	2.00027	−	14.6115i	0.0678935	−	0.495948i
$869$	−45.3089	−	62.3623i	−1.53700	−	2.11550i
$870$	−60.1822	−	42.9904i	−2.04037	−	1.45751i
$871$	3.95843	−	5.44831i	0.134126	−	0.184609i
$872$	53.5109	+	38.8779i	1.81211	+	1.31657i
$873$	3.14253	+	8.55765i	0.106359	+	0.289632i
$874$		−	1.01204i		−	0.0342327i
$875$	4.29037	+	29.2676i	0.145041	+	0.989426i
$876$	−33.8845	+	11.7217i	−1.14485	+	0.396040i
$877$	3.73429	+	1.21334i	0.126098	+	0.0409717i	0.371386	−	0.928478i	$-0.378883\pi$
$877$	3.73429	+	1.21334i	0.126098	+	0.0409717i	−0.245288	+	0.969450i	$0.578883\pi$
$878$	24.0088	−	33.0453i	0.810259	−	1.11523i
$879$	−5.54174	+	18.2196i	−0.186918	+	0.614531i
$880$	81.3211	+	114.522i	2.74133	+	3.86053i
$881$	−29.2690	+	21.2652i	−0.986097	+	0.716441i	−0.959063	−	0.283193i	$-0.908606\pi$
$881$	−29.2690	+	21.2652i	−0.986097	+	0.716441i	−0.0270339	+	0.999635i	$0.508606\pi$
$882$	−51.8252	+	21.5451i	−1.74505	+	0.725462i
$883$	29.8514	+	41.0869i	1.00458	+	1.38269i	0.922473	+	0.386062i	$0.126165\pi$
$883$	29.8514	+	41.0869i	1.00458	+	1.38269i	0.0821070	+	0.996624i	$0.473835\pi$
$884$	50.6723	−	16.4644i	1.70429	−	0.553759i
$885$	−12.0978	−	16.3729i	−0.406664	−	0.550371i
$886$	12.6023	−	38.7859i	0.423382	−	1.30304i
$887$	32.8801	−	10.6834i	1.10401	−	0.358713i	0.300363	−	0.953825i	$-0.402892\pi$
$887$	32.8801	−	10.6834i	1.10401	−	0.358713i	0.803643	+	0.595112i	$0.202892\pi$
$888$	44.4300	−	33.5804i	1.49097	−	1.12688i
$889$	11.8364	+	5.72070i	0.396980	+	0.191866i
$890$	−2.12600	−	0.0230710i	−0.0712637	−	0.000773342i
$891$	3.50765	+	46.3427i	0.117511	+	1.55254i
$892$	−102.753	+	74.6543i	−3.44042	+	2.49961i
$893$	−2.79479			−0.0935241
$894$	27.8265	+	19.4250i	0.930657	+	0.649668i
$895$	−0.146491	+	13.4992i	−0.00489664	+	0.451227i
$896$	−30.1300	−	28.8888i	−1.00657	−	0.965106i
$897$	0.642981	+	0.195572i	0.0214685	+	0.00652996i
$898$	66.7959	+	21.7033i	2.22901	+	0.724249i
$899$	7.74421			0.258284
$900$	−77.1345	+	1.23964i	−2.57115	+	0.0413215i
$901$			26.8656i			0.895024i
$902$	102.638	+	33.3491i	3.41747	+	1.11040i
$903$	17.8100	−	38.6985i	0.592679	−	1.28781i
$904$	44.8989	+	32.6209i	1.49331	+	1.08496i
$905$	−42.4842	−	14.3155i	−1.41222	−	0.475862i
$906$	21.2820	−	30.4867i	0.707046	−	1.01285i
$907$		−	27.3297i		−	0.907469i	−0.891137	−	0.453734i	$-0.850092\pi$
$907$		−	27.3297i		−	0.907469i	0.891137	−	0.453734i	$-0.149908\pi$
$908$	24.0383	+	33.0859i	0.797740	+	1.09800i
$909$	19.5047	+	13.0749i	0.646930	+	0.433667i
$910$	40.4785	−	21.1465i	1.34185	−	0.701000i
$911$	28.8612	+	9.37756i	0.956213	+	0.310692i	0.745238	−	0.666799i	$-0.232336\pi$
$911$	28.8612	+	9.37756i	0.956213	+	0.310692i	0.210975	+	0.977491i	$0.432336\pi$
$912$	47.3782	−	35.8086i	1.56885	−	1.18574i
$913$	−2.24028	−	6.89486i	−0.0741423	−	0.228187i
$914$	−86.0035	−	27.9442i	−2.84474	−	0.924313i
$915$	−44.5374	+	0.357862i	−1.47236	+	0.0118305i
$916$	133.725	−	43.4500i	4.41841	−	1.43563i
$917$	−31.9317	+	17.1251i	−1.05448	+	0.565522i
$918$	−41.8908	−	26.9489i	−1.38260	−	0.889446i
$919$	22.9280	−	16.6582i	0.756326	−	0.549503i	−0.141455	−	0.989945i	$-0.545178\pi$
$919$	22.9280	−	16.6582i	0.756326	−	0.549503i	0.897781	+	0.440442i	$0.145178\pi$
$920$	−2.02515	−	1.50520i	−0.0667673	−	0.0496251i
$921$	19.3383	+	5.88202i	0.637219	+	0.193819i
$922$	29.3992	+	21.3598i	0.968212	+	0.703447i
$923$	35.1968	+	11.4361i	1.15852	+	0.376425i
$924$	23.8202	+	119.350i	0.783626	+	3.92631i
$925$	0.415347	−	19.1349i	0.0136565	−	0.629152i
$926$		−	54.6530i		−	1.79601i
$927$	−6.01743	−	16.3865i	−0.197638	−	0.538202i
$928$	65.9804	−	90.8142i	2.16591	−	2.98112i
$929$	−7.67581	−	5.57680i	−0.251835	−	0.182969i	0.454705	−	0.890642i	$-0.349745\pi$
$929$	−7.67581	−	5.57680i	−0.251835	−	0.182969i	−0.706540	+	0.707673i	$0.749745\pi$
$930$	9.02300	−	6.66702i	0.295876	−	0.218620i
$931$	−6.88093	−	18.4926i	−0.225513	−	0.606072i
$932$	19.9890			0.654762
$933$	−4.07421	+	5.83635i	−0.133384	+	0.191074i
$934$	33.2725	−	10.8109i	1.08871	−	0.353743i
$935$	33.2398	+	24.7056i	1.08706	+	0.807961i
$936$	25.0904	+	68.3253i	0.820105	+	2.23328i
$937$	−3.91008	−	12.0340i	−0.127737	−	0.393133i	0.866653	−	0.498911i	$-0.166267\pi$
$937$	−3.91008	−	12.0340i	−0.127737	−	0.393133i	−0.994390	+	0.105778i	$0.966267\pi$
$938$	−16.2262	+	2.92097i	−0.529803	+	0.0953731i
$939$	−0.344088	−	18.2167i	−0.0112289	−	0.594481i
$940$	−6.80176	+	9.15133i	−0.221849	+	0.298483i
$941$	12.2379	+	37.6644i	0.398944	+	1.22782i	0.925847	+	0.377898i	$0.123353\pi$
$941$	12.2379	+	37.6644i	0.398944	+	1.22782i	−0.526904	+	0.849925i	$0.676647\pi$
$942$	18.8688	−	27.0298i	0.614778	−	0.880677i
$943$	−1.05047			−0.0342080
$944$	51.7272	−	37.5820i	1.68358	−	1.22319i
$945$	−28.2612	−	12.0956i	−0.919338	−	0.393469i
$946$	−103.795	−	75.4117i	−3.37468	−	2.45185i
$947$	−1.80800	−	1.31359i	−0.0587520	−	0.0426859i	0.558022	−	0.829826i	$-0.311561\pi$
$947$	−1.80800	−	1.31359i	−0.0587520	−	0.0426859i	−0.616774	+	0.787141i	$0.711561\pi$
$948$	2.51120	+	132.948i	0.0815599	+	4.31795i
$949$	11.6258			0.377390
$950$	0.817428	−	37.6587i	0.0265209	−	1.22181i
$951$	−1.88565	+	0.652306i	−0.0611465	+	0.0211525i
$952$	−71.7697	−	34.6873i	−2.32607	−	1.12422i
$953$	−14.5158	−	10.5464i	−0.470214	−	0.341631i	0.327311	−	0.944917i	$-0.393858\pi$
$953$	−14.5158	−	10.5464i	−0.470214	−	0.341631i	−0.797525	+	0.603286i	$0.793858\pi$
$954$	−60.0134	+	2.26794i	−1.94301	+	0.0734274i
$955$	−8.87830	+	11.9452i	−0.287295	+	0.386537i
$956$	−37.6419	−	51.8097i	−1.21743	−	1.67565i
$957$	−60.3959	+	20.8928i	−1.95232	+	0.675369i
$958$	−90.7516	+	65.9349i	−2.93205	+	2.13026i
$959$	−2.30325	−	12.7947i	−0.0743758	−	0.413162i
$960$	−0.549543	−	68.3930i	−0.0177364	−	2.20737i
$961$	9.21652	−	28.3655i	0.297307	−	0.915017i
$962$	−28.1032	+	9.13128i	−0.906083	+	0.294404i
$963$	−10.1683	−	6.81625i	−0.327667	−	0.219651i
$964$	−29.2598	−	9.50709i	−0.942395	−	0.306203i
$965$	12.9778	+	18.2762i	0.417769	+	0.588330i
$966$	−0.804862	−	1.43501i	−0.0258960	−	0.0461707i
$967$	0.183580	+	0.252676i	0.00590352	+	0.00812550i	0.811959	−	0.583715i	$-0.198401\pi$
$967$	0.183580	+	0.252676i	0.00590352	+	0.00812550i	−0.806055	+	0.591841i	$0.798401\pi$
$968$	131.595			4.22962
$969$	10.0235	−	14.3588i	0.322001	−	0.461271i
$970$	−5.79897	+	17.2097i	−0.186194	+	0.552570i
$971$	−34.6426	−	25.1694i	−1.11174	−	0.807723i	−0.128799	−	0.991671i	$-0.541112\pi$
$971$	−34.6426	−	25.1694i	−1.11174	−	0.807723i	−0.982936	+	0.183948i	$0.941112\pi$
$972$	40.7976	−	69.0139i	1.30858	−	2.21362i
$973$	49.9472	+	24.1402i	1.60123	+	0.773898i
$974$		−	60.4097i		−	1.93565i
$975$	23.7678	+	7.79670i	0.761179	+	0.249694i
$976$		−	139.886i		−	4.47764i
$977$	3.55904	−	10.9536i	0.113864	−	0.350437i	−0.877845	−	0.478946i	$-0.841019\pi$
$977$	3.55904	−	10.9536i	0.113864	−	0.350437i	0.991708	+	0.128509i	$0.0410191\pi$
$978$	−10.1373	+	33.3284i	−0.324156	+	1.06573i
$979$	−1.07985	+	1.48628i	−0.0345121	+	0.0475018i
$980$	−77.2990	−	22.4750i	−2.46923	−	0.717938i
$981$	−6.44616	+	22.7260i	−0.205810	+	0.725587i
$982$		−	64.4522i		−	2.05675i
$983$	31.2586	+	43.0238i	0.996995	+	1.37225i	0.927151	+	0.374688i	$0.122250\pi$
$983$	31.2586	+	43.0238i	0.996995	+	1.37225i	0.0698441	+	0.997558i	$0.477750\pi$
$984$	−68.5978	−	90.7614i	−2.18682	−	2.89337i
$985$	−47.8568	−	0.519335i	−1.52485	−	0.0165474i
$986$	21.1657	−	65.1414i	0.674054	−	2.07452i
$987$	−3.96285	+	2.22266i	−0.126139	+	0.0707481i
$988$	−39.8225	+	12.9391i	−1.26692	+	0.411649i
$989$	1.18770	+	0.385908i	0.0377668	+	0.0122712i
$990$	−52.3823	+	76.3378i	−1.66482	+	2.42618i
$991$	−15.1162	−	46.5229i	−0.480183	−	1.47785i	−0.838839	−	0.544380i	$-0.816765\pi$
$991$	−15.1162	−	46.5229i	−0.480183	−	1.47785i	0.358656	−	0.933470i	$-0.383235\pi$
$992$	10.0085	+	13.7755i	0.317770	+	0.437373i
$993$	−15.9018	+	5.50094i	−0.504629	+	0.174567i
$994$	−42.8204	−	79.8434i	−1.35818	−	2.53248i
$995$	−0.368172	−	0.518485i	−0.0116718	−	0.0164371i
$996$	−3.63922	+	11.9646i	−0.115313	+	0.379114i
$997$	22.2732	+	16.1824i	0.705400	+	0.512503i	0.881686	−	0.471836i	$-0.156409\pi$
$997$	22.2732	+	16.1824i	0.705400	+	0.512503i	−0.176287	+	0.984339i	$0.556409\pi$
$998$	22.9036	−	70.4899i	0.725000	−	2.23132i
$999$	16.7278	+	10.7612i	0.529244	+	0.340469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.w.a.104.4	yes	304
3.2	odd	2	inner	525.2.w.a.104.74	yes	304
7.6	odd	2	inner	525.2.w.a.104.3	✓	304
21.20	even	2	inner	525.2.w.a.104.73	yes	304
25.19	even	10	inner	525.2.w.a.419.73	yes	304
75.44	odd	10	inner	525.2.w.a.419.3	yes	304
175.69	odd	10	inner	525.2.w.a.419.74	yes	304
525.419	even	10	inner	525.2.w.a.419.4	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.w.a.104.3	✓	304	7.6	odd	2	inner
525.2.w.a.104.4	yes	304	1.1	even	1	trivial
525.2.w.a.104.73	yes	304	21.20	even	2	inner
525.2.w.a.104.74	yes	304	3.2	odd	2	inner
525.2.w.a.419.3	yes	304	75.44	odd	10	inner
525.2.w.a.419.4	yes	304	525.419	even	10	inner
525.2.w.a.419.73	yes	304	25.19	even	10	inner
525.2.w.a.419.74	yes	304	175.69	odd	10	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.825889 + 2.54182i) q^{2} +(1.65709 + 0.504029i) q^{3} +(-4.16074 - 3.02296i) q^{4} +(1.82317 - 1.29462i) q^{5} +(-2.64973 + 3.79577i) q^{6} +(-2.62130 - 0.358847i) q^{7} +(6.79573 - 4.93738i) q^{8} +(2.49191 + 1.67044i) q^{9} +O(q^{10})\)	\(q+(-0.825889 + 2.54182i) q^{2} +(1.65709 + 0.504029i) q^{3} +(-4.16074 - 3.02296i) q^{4} +(1.82317 - 1.29462i) q^{5} +(-2.64973 + 3.79577i) q^{6} +(-2.62130 - 0.358847i) q^{7} +(6.79573 - 4.93738i) q^{8} +(2.49191 + 1.67044i) q^{9} +(1.78496 + 5.70340i) q^{10} +(4.91118 + 1.59574i) q^{11} +(-5.37108 - 7.10645i) q^{12} +(0.892552 + 2.74699i) q^{13} +(3.07703 - 6.36652i) q^{14} +(3.67369 - 1.22637i) q^{15} +(3.75892 + 11.5688i) q^{16} +(2.10823 + 2.90173i) q^{17} +(-6.30401 + 4.95440i) q^{18} +(-1.65683 - 2.28042i) q^{19} +(-11.4993 - 0.124789i) q^{20} +(-4.16287 - 1.91585i) q^{21} +(-8.11218 + 11.1655i) q^{22} +(0.0415129 - 0.127763i) q^{23} +(13.7497 - 4.75646i) q^{24} +(1.64792 - 4.72063i) q^{25} -7.71952 q^{26} +(3.28737 + 4.02407i) q^{27} +(9.82179 + 9.41716i) q^{28} +(-4.19982 + 5.78055i) q^{29} +(0.0831689 + 10.3507i) q^{30} +(-0.637066 - 0.876845i) q^{31} -15.7103 q^{32} +(7.33398 + 5.11966i) q^{33} +(-9.11686 + 2.96225i) q^{34} +(-5.24366 + 2.73935i) q^{35} +(-5.31852 - 14.4832i) q^{36} +(3.64053 - 1.18288i) q^{37} +(7.16479 - 2.32798i) q^{38} +(0.0944786 + 5.00189i) q^{39} +(5.99774 - 17.7996i) q^{40} +(-2.41638 - 7.43686i) q^{41} +(8.30783 - 8.99901i) q^{42} +9.29611i q^{43} +(-15.6103 - 21.4858i) q^{44} +(6.70577 - 0.180571i) q^{45} +(0.290467 + 0.211037i) q^{46} +(0.582787 - 0.802138i) q^{47} +(0.397890 + 21.0651i) q^{48} +(6.74246 + 1.88129i) q^{49} +(10.6380 + 8.08743i) q^{50} +(2.03098 + 5.87105i) q^{51} +(4.59036 - 14.1277i) q^{52} +(6.05976 + 4.40267i) q^{53} +(-12.9435 + 5.03249i) q^{54} +(11.0198 - 3.44881i) q^{55} +(-19.5854 + 10.5038i) q^{56} +(-1.59611 - 4.61396i) q^{57} +(-11.2246 - 15.4493i) q^{58} +(-1.62429 - 4.99904i) q^{59} +(-18.9926 - 6.00278i) q^{60} +(-10.9370 - 3.55366i) q^{61} +(2.75493 - 0.895132i) q^{62} +(-5.93262 - 5.27295i) q^{63} +(5.45711 - 16.7952i) q^{64} +(5.18359 + 3.85273i) q^{65} +(-19.0703 + 14.4134i) q^{66} +(-1.37048 - 1.88630i) q^{67} -18.4465i q^{68} +(0.133187 - 0.190792i) q^{69} +(-2.63227 - 15.5909i) q^{70} +(7.53120 - 10.3658i) q^{71} +(25.1820 - 0.951642i) q^{72} +(1.24381 - 3.82806i) q^{73} +10.2305i q^{74} +(5.11008 - 6.99193i) q^{75} +14.4968i q^{76} +(-12.3011 - 5.94528i) q^{77} +(-12.7920 - 3.89086i) q^{78} +(-12.0766 - 8.77413i) q^{79} +(21.8303 + 16.2255i) q^{80} +(3.41924 + 8.32519i) q^{81} +20.8989 q^{82} +(-0.825199 - 1.13579i) q^{83} +(11.5291 + 20.5556i) q^{84} +(7.60031 + 2.56100i) q^{85} +(-23.6291 - 7.67755i) q^{86} +(-9.87305 + 7.46208i) q^{87} +(41.2538 - 13.4042i) q^{88} +(-0.109938 + 0.338354i) q^{89} +(-5.07924 + 17.1940i) q^{90} +(-1.35390 - 7.52099i) q^{91} +(-0.558948 + 0.406099i) q^{92} +(-0.613721 - 1.77411i) q^{93} +(1.55758 + 2.14382i) q^{94} +(-5.97296 - 2.01265i) q^{95} +(-26.0334 - 7.91844i) q^{96} +(2.45844 + 1.78616i) q^{97} +(-10.3504 + 15.5844i) q^{98} +(9.57263 + 12.1803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q - 84 q^{4} - 6 q^{9}+O(q^{10}) \) 304 * q - 84 * q^4 - 6 * q^9	\( 304 q - 84 q^{4} - 6 q^{9} - 36 q^{15} - 60 q^{16} - 18 q^{21} - 40 q^{22} - 8 q^{25} + 60 q^{28} + 14 q^{30} + 28 q^{36} - 20 q^{37} - 2 q^{39} - 35 q^{42} - 24 q^{46} - 20 q^{49} - 52 q^{51} - 80 q^{58} + 4 q^{60} + 55 q^{63} - 76 q^{64} - 20 q^{67} + 6 q^{70} + 30 q^{72} - 40 q^{78} - 68 q^{79} - 10 q^{81} + 80 q^{84} - 88 q^{85} - 20 q^{88} - 82 q^{91} - 36 q^{99}+O(q^{100}) \) 304 * q - 84 * q^4 - 6 * q^9 - 36 * q^15 - 60 * q^16 - 18 * q^21 - 40 * q^22 - 8 * q^25 + 60 * q^28 + 14 * q^30 + 28 * q^36 - 20 * q^37 - 2 * q^39 - 35 * q^42 - 24 * q^46 - 20 * q^49 - 52 * q^51 - 80 * q^58 + 4 * q^60 + 55 * q^63 - 76 * q^64 - 20 * q^67 + 6 * q^70 + 30 * q^72 - 40 * q^78 - 68 * q^79 - 10 * q^81 + 80 * q^84 - 88 * q^85 - 20 * q^88 - 82 * q^91 - 36 * q^99

Introduction

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