LMFDB - Embedded newform 525.2.bm.a.131.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(131,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 12, 25]))

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

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

chi := DirichletCharacter("525.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bm (of order $30$, degree $8$, 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:	$608$
Relative dimension:	$76$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			131.9
Character	$\chi$	$=$	525.131
Dual form			525.2.bm.a.521.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.478695 + 2.25208i) q^{2} +(-0.600734 - 1.62454i) q^{3} +(-3.01563 - 1.34265i) q^{4} +(-2.22631 + 0.208681i) q^{5} +(3.94616 - 0.575244i) q^{6} +(0.695446 + 2.55272i) q^{7} +(1.76069 - 2.42338i) q^{8} +(-2.27824 + 1.95183i) q^{9} +O(q^{10})$	\(q+(-0.478695 + 2.25208i) q^{2} +(-0.600734 - 1.62454i) q^{3} +(-3.01563 - 1.34265i) q^{4} +(-2.22631 + 0.208681i) q^{5} +(3.94616 - 0.575244i) q^{6} +(0.695446 + 2.55272i) q^{7} +(1.76069 - 2.42338i) q^{8} +(-2.27824 + 1.95183i) q^{9} +(0.595755 - 5.11372i) q^{10} +(1.28591 + 1.15784i) q^{11} +(-0.369585 + 5.70558i) q^{12} +(-0.199947 - 0.0649666i) q^{13} +(-6.08183 + 0.344230i) q^{14} +(1.67643 + 3.49136i) q^{15} +(0.197191 + 0.219003i) q^{16} +(0.590755 - 5.62066i) q^{17} +(-3.30510 - 6.06511i) q^{18} +(-2.77393 - 6.23035i) q^{19} +(6.99392 + 2.35984i) q^{20} +(3.72920 - 2.66328i) q^{21} +(-3.22310 + 2.34172i) q^{22} +(0.331384 - 1.55904i) q^{23} +(-4.99458 - 1.40450i) q^{24} +(4.91290 - 0.929178i) q^{25} +(0.242024 - 0.419197i) q^{26} +(4.53943 + 2.52855i) q^{27} +(1.33018 - 8.63179i) q^{28} +(-3.30323 - 4.54650i) q^{29} +(-8.66532 + 2.10416i) q^{30} +(-7.86781 - 0.826940i) q^{31} +(4.60069 - 2.65621i) q^{32} +(1.10846 - 2.78455i) q^{33} +(12.3754 + 4.02101i) q^{34} +(-2.08098 - 5.53801i) q^{35} +(9.49094 - 2.82713i) q^{36} +(0.538835 + 0.598437i) q^{37} +(15.3591 - 3.26468i) q^{38} +(0.0145741 + 0.363849i) q^{39} +(-3.41412 + 5.76262i) q^{40} +(3.41013 - 10.4953i) q^{41} +(4.21277 + 9.67336i) q^{42} +2.28781 q^{43} +(-2.32326 - 5.21812i) q^{44} +(4.66475 - 4.82080i) q^{45} +(3.35245 + 1.49261i) q^{46} +(-0.438575 - 4.17277i) q^{47} +(0.237319 - 0.451906i) q^{48} +(-6.03271 + 3.55055i) q^{49} +(-0.259198 + 11.5091i) q^{50} +(-9.48585 + 2.41682i) q^{51} +(0.515739 + 0.464373i) q^{52} +(-4.24505 + 9.53454i) q^{53} +(-7.86751 + 9.01276i) q^{54} +(-3.10444 - 2.30935i) q^{55} +(7.41067 + 2.80921i) q^{56} +(-8.45504 + 8.24913i) q^{57} +(11.8203 - 5.26275i) q^{58} +(-6.50233 + 1.38211i) q^{59} +(-0.367835 - 12.7795i) q^{60} +(-2.08443 + 9.80649i) q^{61} +(5.62861 - 17.3231i) q^{62} +(-6.56685 - 4.45830i) q^{63} +(3.96181 + 12.1932i) q^{64} +(0.458701 + 0.102911i) q^{65} +(5.74043 + 3.82929i) q^{66} +(-0.00569497 + 0.0541840i) q^{67} +(-9.32806 + 16.1567i) q^{68} +(-2.73179 + 0.398222i) q^{69} +(13.4682 - 2.03552i) q^{70} +(-3.65554 - 5.03142i) q^{71} +(0.718753 + 8.95760i) q^{72} +(-1.99738 - 1.79844i) q^{73} +(-1.60567 + 0.927031i) q^{74} +(-4.46083 - 7.42300i) q^{75} +22.5129i q^{76} +(-2.06135 + 4.08776i) q^{77} +(-0.826393 - 0.141350i) q^{78} +(-0.311572 - 2.96441i) q^{79} +(-0.484710 - 0.446418i) q^{80} +(1.38074 - 8.89346i) q^{81} +(22.0039 + 12.7039i) q^{82} +(3.75466 + 2.72792i) q^{83} +(-14.8217 + 3.02447i) q^{84} +(-0.142278 + 12.6366i) q^{85} +(-1.09516 + 5.15234i) q^{86} +(-5.40160 + 8.09745i) q^{87} +(5.06996 - 1.07765i) q^{88} +(9.19415 + 1.95428i) q^{89} +(8.62384 + 12.8131i) q^{90} +(0.0267892 - 0.555588i) q^{91} +(-3.09257 + 4.25656i) q^{92} +(3.38306 + 13.2783i) q^{93} +(9.60735 + 1.00977i) q^{94} +(7.47579 + 13.2918i) q^{95} +(-7.07890 - 5.87831i) q^{96} +(-5.09988 - 7.01939i) q^{97} +(-5.10830 - 15.2858i) q^{98} +(-5.18950 - 0.127956i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9}+O(q^{10}) $ 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9	$ 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9} - 30 q^{10} + 3 q^{12} + 16 q^{15} + 50 q^{16} - 8 q^{18} - 18 q^{19} - 21 q^{21} - 24 q^{22} - 66 q^{24} - 10 q^{25} - 30 q^{28} - 7 q^{30} - 36 q^{31} + 36 q^{33} - 100 q^{36} - 14 q^{37} - 31 q^{39} - 30 q^{40} + 20 q^{42} - 96 q^{43} - 117 q^{45} + 42 q^{46} - 28 q^{49} - 8 q^{51} - 66 q^{52} + 3 q^{54} + 48 q^{57} - 38 q^{58} - 49 q^{60} - 18 q^{61} + 4 q^{63} - 32 q^{64} - 3 q^{66} - 22 q^{67} - 270 q^{70} + 45 q^{72} + 102 q^{73} + 135 q^{75} + 58 q^{78} - 34 q^{79} - 55 q^{81} + 108 q^{82} - 75 q^{84} - 96 q^{85} - 9 q^{87} + 36 q^{88} + 38 q^{91} - 22 q^{93} + 30 q^{94} - 81 q^{96} + 36 q^{99}+O(q^{100}) $ 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9 - 30 * q^10 + 3 * q^12 + 16 * q^15 + 50 * q^16 - 8 * q^18 - 18 * q^19 - 21 * q^21 - 24 * q^22 - 66 * q^24 - 10 * q^25 - 30 * q^28 - 7 * q^30 - 36 * q^31 + 36 * q^33 - 100 * q^36 - 14 * q^37 - 31 * q^39 - 30 * q^40 + 20 * q^42 - 96 * q^43 - 117 * q^45 + 42 * q^46 - 28 * q^49 - 8 * q^51 - 66 * q^52 + 3 * q^54 + 48 * q^57 - 38 * q^58 - 49 * q^60 - 18 * q^61 + 4 * q^63 - 32 * q^64 - 3 * q^66 - 22 * q^67 - 270 * q^70 + 45 * q^72 + 102 * q^73 + 135 * q^75 + 58 * q^78 - 34 * q^79 - 55 * q^81 + 108 * q^82 - 75 * q^84 - 96 * q^85 - 9 * q^87 + 36 * q^88 + 38 * q^91 - 22 * q^93 + 30 * q^94 - 81 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.478695	+	2.25208i	−0.338488	+	1.59246i	0.398901	+	0.916994i	$0.369392\pi$
$2$	−0.478695	+	2.25208i	−0.338488	+	1.59246i	−0.737389	+	0.675468i	$0.763942\pi$
$3$	−0.600734	−	1.62454i	−0.346834	−	0.937927i
$3$	−0.600734	−	1.62454i	−0.346834	−	0.937927i
$4$	−3.01563	−	1.34265i	−1.50782	−	0.671323i
$5$	−2.22631	+	0.208681i	−0.995636	+	0.0933251i
$5$	−2.22631	+	0.208681i	−0.995636	+	0.0933251i
$6$	3.94616	−	0.575244i	1.61101	−	0.234843i
$7$	0.695446	+	2.55272i	0.262854	+	0.964836i
$7$	0.695446	+	2.55272i	0.262854	+	0.964836i
$8$	1.76069	−	2.42338i	0.622498	−	0.856795i
$9$	−2.27824	+	1.95183i	−0.759413	+	0.650609i
$10$	0.595755	−	5.11372i	0.188394	−	1.61710i
$11$	1.28591	+	1.15784i	0.387715	+	0.349100i	0.839821	−	0.542864i	$-0.182660\pi$
$11$	1.28591	+	1.15784i	0.387715	+	0.349100i	−0.452105	+	0.891965i	$0.649327\pi$
$12$	−0.369585	+	5.70558i	−0.106690	+	1.64706i
$13$	−0.199947	−	0.0649666i	−0.0554553	−	0.0180185i	0.281158	−	0.959661i	$-0.409281\pi$
$13$	−0.199947	−	0.0649666i	−0.0554553	−	0.0180185i	−0.336613	+	0.941643i	$0.609281\pi$
$14$	−6.08183	+	0.344230i	−1.62544	+	0.0919992i
$15$	1.67643	+	3.49136i	0.432852	+	0.901465i
$16$	0.197191	+	0.219003i	0.0492978	+	0.0547507i
$17$	0.590755	−	5.62066i	0.143279	−	1.36321i	−0.652576	−	0.757723i	$-0.726312\pi$
$17$	0.590755	−	5.62066i	0.143279	−	1.36321i	0.795855	−	0.605487i	$-0.207022\pi$
$18$	−3.30510	−	6.06511i	−0.779018	−	1.42956i
$19$	−2.77393	−	6.23035i	−0.636383	−	1.42934i	−0.887236	−	0.461315i	$-0.847378\pi$
$19$	−2.77393	−	6.23035i	−0.636383	−	1.42934i	0.250853	−	0.968025i	$-0.419289\pi$
$20$	6.99392	+	2.35984i	1.56389	+	0.527676i
$21$	3.72920	−	2.66328i	0.813778	−	0.581175i
$22$	−3.22310	+	2.34172i	−0.687166	+	0.499256i
$23$	0.331384	−	1.55904i	0.0690984	−	0.325082i	−0.929999	−	0.367562i	$-0.880192\pi$
$23$	0.331384	−	1.55904i	0.0690984	−	0.325082i	0.999097	+	0.0424799i	$0.0135258\pi$
$24$	−4.99458	−	1.40450i	−1.01951	−	0.286692i
$25$	4.91290	−	0.929178i	0.982581	−	0.185836i
$26$	0.242024	−	0.419197i	0.0474647	−	0.0822114i
$27$	4.53943	+	2.52855i	0.873614	+	0.486620i
$28$	1.33018	−	8.63179i	0.251381	−	1.63125i
$29$	−3.30323	−	4.54650i	−0.613394	−	0.844265i	0.383457	−	0.923559i	$-0.374733\pi$
$29$	−3.30323	−	4.54650i	−0.613394	−	0.844265i	−0.996851	+	0.0792941i	$0.974733\pi$
$30$	−8.66532	+	2.10416i	−1.58206	+	0.384165i
$31$	−7.86781	−	0.826940i	−1.41310	−	0.148523i	−0.632987	−	0.774162i	$-0.718171\pi$
$31$	−7.86781	−	0.826940i	−1.41310	−	0.148523i	−0.780112	+	0.625640i	$0.784838\pi$
$32$	4.60069	−	2.65621i	0.813295	−	0.469556i
$33$	1.10846	−	2.78455i	0.192958	−	0.484728i
$34$	12.3754	+	4.02101i	2.12236	+	0.689597i
$35$	−2.08098	−	5.53801i	−0.351750	−	0.936094i
$36$	9.49094	−	2.82713i	1.58182	−	0.471188i
$37$	0.538835	+	0.598437i	0.0885839	+	0.0983824i	0.785807	−	0.618472i	$-0.212248\pi$
$37$	0.538835	+	0.598437i	0.0885839	+	0.0983824i	−0.697223	+	0.716854i	$0.745581\pi$
$38$	15.3591	−	3.26468i	2.49158	−	0.529602i
$39$	0.0145741	+	0.363849i	0.00233372	+	0.0582624i
$40$	−3.41412	+	5.76262i	−0.539821	+	0.911150i
$41$	3.41013	−	10.4953i	0.532573	−	1.63909i	−0.216262	−	0.976335i	$-0.569386\pi$
$41$	3.41013	−	10.4953i	0.532573	−	1.63909i	0.748835	−	0.662757i	$-0.230614\pi$
$42$	4.21277	+	9.67336i	0.650045	+	1.49263i
$43$	2.28781			0.348888			0.174444	−	0.984667i	$-0.444187\pi$
$43$	2.28781			0.348888			0.174444	+	0.984667i	$0.444187\pi$
$44$	−2.32326	−	5.21812i	−0.350244	−	0.786662i
$45$	4.66475	−	4.82080i	0.695380	−	0.718642i
$46$	3.35245	+	1.49261i	0.494292	+	0.220073i
$47$	−0.438575	−	4.17277i	−0.0639728	−	0.608660i	−0.978800	−	0.204816i	$-0.934340\pi$
$47$	−0.438575	−	4.17277i	−0.0639728	−	0.608660i	0.914828	−	0.403844i	$-0.132326\pi$
$48$	0.237319	−	0.451906i	0.0342540	−	0.0652271i
$49$	−6.03271	+	3.55055i	−0.861816	+	0.507221i
$50$	−0.259198	+	11.5091i	−0.0366561	+	1.62763i
$51$	−9.48585	+	2.41682i	−1.32829	+	0.338422i
$52$	0.515739	+	0.464373i	0.0715201	+	0.0643970i
$53$	−4.24505	+	9.53454i	−0.583102	+	1.30967i	0.345439	+	0.938441i	$0.387730\pi$
$53$	−4.24505	+	9.53454i	−0.583102	+	1.30967i	−0.928542	+	0.371228i	$0.878937\pi$
$54$	−7.86751	+	9.01276i	−1.07063	+	1.22648i
$55$	−3.10444	−	2.30935i	−0.418603	−	0.311393i
$56$	7.41067	+	2.80921i	0.990292	+	0.375396i
$57$	−8.45504	+	8.24913i	−1.11990	+	1.09262i
$58$	11.8203	−	5.26275i	1.55209	−	0.691033i
$59$	−6.50233	+	1.38211i	−0.846531	+	0.179936i	−0.610704	−	0.791859i	$-0.709113\pi$
$59$	−6.50233	+	1.38211i	−0.846531	+	0.179936i	−0.235827	+	0.971795i	$0.575780\pi$
$60$	−0.367835	−	12.7795i	−0.0474873	−	1.64983i
$61$	−2.08443	+	9.80649i	−0.266885	+	1.25559i	0.616654	+	0.787234i	$0.288488\pi$
$61$	−2.08443	+	9.80649i	−0.266885	+	1.25559i	−0.883538	+	0.468359i	$0.844846\pi$
$62$	5.62861	−	17.3231i	0.714835	−	2.20003i
$63$	−6.56685	−	4.45830i	−0.827346	−	0.561693i
$64$	3.96181	+	12.1932i	0.495226	+	1.52415i
$65$	0.458701	+	0.102911i	0.0568948	+	0.0127645i
$66$	5.74043	+	3.82929i	0.706598	+	0.471353i
$67$	−0.00569497	+	0.0541840i	−0.000695751	+	0.00661963i	−0.994864	−	0.101218i	$-0.967726\pi$
$67$	−0.00569497	+	0.0541840i	−0.000695751	+	0.00661963i	0.994169	+	0.107838i	$0.0343927\pi$
$68$	−9.32806	+	16.1567i	−1.13119	+	1.95928i
$69$	−2.73179	+	0.398222i	−0.328869	+	0.0479403i
$70$	13.4682	−	2.03552i	1.60976	−	0.243292i
$71$	−3.65554	−	5.03142i	−0.433833	−	0.597120i	0.534995	−	0.844855i	$-0.320314\pi$
$71$	−3.65554	−	5.03142i	−0.433833	−	0.597120i	−0.968828	+	0.247735i	$0.920314\pi$
$72$	0.718753	+	8.95760i	0.0847059	+	1.05566i
$73$	−1.99738	−	1.79844i	−0.233775	−	0.210492i	0.543914	−	0.839141i	$-0.316942\pi$
$73$	−1.99738	−	1.79844i	−0.233775	−	0.210492i	−0.777689	+	0.628649i	$0.783608\pi$
$74$	−1.60567	+	0.927031i	−0.186655	+	0.107765i
$75$	−4.46083	−	7.42300i	−0.515092	−	0.857135i
$76$			22.5129i			2.58240i
$77$	−2.06135	+	4.08776i	−0.234912	+	0.465844i
$78$	−0.826393	−	0.141350i	−0.0935706	−	0.0160048i
$79$	−0.311572	−	2.96441i	−0.0350546	−	0.333523i	−0.997968	−	0.0637128i	$-0.979706\pi$
$79$	−0.311572	−	2.96441i	−0.0350546	−	0.333523i	0.962914	−	0.269810i	$-0.0869608\pi$
$80$	−0.484710	−	0.446418i	−0.0541922	−	0.0499110i
$81$	1.38074	−	8.89346i	0.153415	−	0.988162i
$82$	22.0039	+	12.7039i	2.42992	+	1.40292i
$83$	3.75466	+	2.72792i	0.412127	+	0.299428i	0.774463	−	0.632620i	$-0.218020\pi$
$83$	3.75466	+	2.72792i	0.412127	+	0.299428i	−0.362335	+	0.932048i	$0.618020\pi$
$84$	−14.8217	+	3.02447i	−1.61718	+	0.329997i
$85$	−0.142278	+	12.6366i	−0.0154322	+	1.37063i
$86$	−1.09516	+	5.15234i	−0.118095	+	0.555591i
$87$	−5.40160	+	8.09745i	−0.579112	+	0.868138i
$88$	5.06996	−	1.07765i	0.540459	−	0.114878i
$89$	9.19415	+	1.95428i	0.974578	+	0.207153i	0.667564	−	0.744552i	$-0.267337\pi$
$89$	9.19415	+	1.95428i	0.974578	+	0.207153i	0.307014	+	0.951705i	$0.400670\pi$
$90$	8.62384	+	12.8131i	0.909032	+	1.35062i
$91$	0.0267892	−	0.555588i	0.00280827	−	0.0582414i
$92$	−3.09257	+	4.25656i	−0.322423	+	0.443777i
$93$	3.38306	+	13.2783i	0.350807	+	1.37690i
$94$	9.60735	+	1.00977i	0.990923	+	0.104150i
$95$	7.47579	+	13.2918i	0.766999	+	1.36371i
$96$	−7.07890	−	5.87831i	−0.722487	−	0.599953i
$97$	−5.09988	−	7.01939i	−0.517815	−	0.712711i	0.467398	−	0.884047i	$-0.345192\pi$
$97$	−5.09988	−	7.01939i	−0.517815	−	0.712711i	−0.985213	+	0.171336i	$0.945192\pi$
$98$	−5.10830	−	15.2858i	−0.516017	−	1.54410i
$99$	−5.18950	−	0.127956i	−0.521564	−	0.0128601i
$100$	−16.0631	−	3.79423i	−1.60631	−	0.379423i
$101$	−1.45943	−	2.52780i	−0.145219	−	0.251526i	0.784236	−	0.620463i	$-0.213055\pi$
$101$	−1.45943	−	2.52780i	−0.145219	−	0.251526i	−0.929454	+	0.368937i	$0.879722\pi$
$102$	−0.902041	−	22.5198i	−0.0893153	−	2.22980i
$103$	19.8959	−	2.09114i	1.96040	−	0.206046i	0.962524	−	0.271198i	$-0.0874199\pi$
$103$	19.8959	−	2.09114i	1.96040	−	0.206046i	0.997875	+	0.0651521i	$0.0207532\pi$
$104$	−0.509483	+	0.370161i	−0.0499589	+	0.0362973i
$105$	−7.74658	+	6.70750i	−0.755989	+	0.654585i
$106$	−19.4405	−	14.1243i	−1.88823	−	1.37188i
$107$	1.91505	+	1.10566i	0.185135	+	0.106888i	0.589703	−	0.807620i	$-0.299245\pi$
$107$	1.91505	+	1.10566i	0.185135	+	0.106888i	−0.404568	+	0.914508i	$0.632578\pi$
$108$	−10.2943	−	13.7200i	−0.990570	−	1.32021i
$109$	−14.3630	+	3.05295i	−1.37572	+	0.292419i	−0.835680	−	0.549217i	$-0.814926\pi$
$109$	−14.3630	+	3.05295i	−1.37572	+	0.292419i	−0.540045	+	0.841636i	$0.681593\pi$
$110$	6.68694	−	5.88598i	0.637574	−	0.561207i
$111$	0.648486	−	1.23486i	0.0615516	−	0.117208i
$112$	−0.421916	+	0.655677i	−0.0398673	+	0.0619557i
$113$	5.44886	+	1.77044i	0.512586	+	0.166549i	0.553878	−	0.832598i	$-0.313147\pi$
$113$	5.44886	+	1.77044i	0.512586	+	0.166549i	−0.0412921	+	0.999147i	$0.513147\pi$
$114$	−14.5303	−	22.9903i	−1.36089	−	2.15323i
$115$	−0.412421	+	3.54006i	−0.0384585	+	0.330112i
$116$	3.85698	+	18.1457i	0.358111	+	1.68478i
$117$	0.582330	−	0.242252i	0.0538364	−	0.0223962i
$118$		−	15.3054i		−	1.40897i
$119$	14.7588	−	2.40084i	1.35294	−	0.220084i
$120$	11.4126	+	2.08457i	1.04182	+	0.190294i
$121$	−0.836840	−	7.96201i	−0.0760764	−	0.723819i
$122$	−21.0872	−	9.38864i	−1.90915	−	0.850007i
$123$	−19.0986	+	0.765001i	−1.72206	+	0.0689779i
$124$	22.6161	+	13.0574i	2.03099	+	1.17259i
$125$	−10.7437	+	3.09387i	−0.960949	+	0.276724i
$126$	13.1840	−	12.6549i	1.17452	−	1.12739i
$127$	−3.37917	−	10.4000i	−0.299853	−	0.922853i	−0.981548	−	0.191216i	$-0.938757\pi$
$127$	−3.37917	−	10.4000i	−0.299853	−	0.922853i	0.681695	−	0.731637i	$-0.261243\pi$
$128$	−18.7899	+	1.97490i	−1.66081	+	0.174558i
$129$	−1.37437	−	3.71663i	−0.121006	−	0.327231i
$130$	−0.451341	+	0.983769i	−0.0395852	+	0.0862822i
$131$	−17.0882	+	7.60815i	−1.49300	+	0.664727i	−0.980956	−	0.194231i	$-0.937779\pi$
$131$	−17.0882	+	7.60815i	−1.49300	+	0.664727i	−0.512046	+	0.858958i	$0.671112\pi$
$132$	−7.08137	+	6.90892i	−0.616354	+	0.601344i
$133$	13.9752	−	11.4139i	1.21180	−	0.989713i
$134$	−0.119301	−	0.0387631i	−0.0103060	−	0.00334862i
$135$	−10.6338	−	4.68204i	−0.915215	−	0.402966i
$136$	−12.5809	−	11.3279i	−1.07880	−	0.971356i
$137$	−0.297542	−	1.39983i	−0.0254208	−	0.119595i	0.963608	−	0.267320i	$-0.0861382\pi$
$137$	−0.297542	−	1.39983i	−0.0254208	−	0.119595i	−0.989028	+	0.147725i	$0.952805\pi$
$138$	0.410865	−	6.34284i	0.0349752	−	0.539939i
$139$	10.2598	−	3.33360i	0.870222	−	0.282752i	0.160331	−	0.987063i	$-0.448744\pi$
$139$	10.2598	−	3.33360i	0.870222	−	0.282752i	0.709892	+	0.704311i	$0.248744\pi$
$140$	−1.16011	+	19.4946i	−0.0980471	+	1.64760i
$141$	−6.51534	+	3.21920i	−0.548691	+	0.271106i
$142$	13.0811	−	5.82406i	1.09774	−	0.488745i
$143$	−0.181892	−	0.315046i	−0.0152106	−	0.0263455i
$144$	−0.876704	−	0.114058i	−0.0730587	−	0.00950480i
$145$	8.30278	+	9.43260i	0.689508	+	0.783335i
$146$	5.00638	−	3.63735i	0.414331	−	0.301029i
$147$	9.39205	+	7.66742i	0.774643	+	0.632398i
$148$	−0.821439	−	2.52813i	−0.0675219	−	0.207811i
$149$	−17.7268	−	10.2346i	−1.45223	−	0.838447i	−0.453626	−	0.891192i	$-0.649870\pi$
$149$	−17.7268	−	10.2346i	−1.45223	−	0.838447i	−0.998608	+	0.0527449i	$0.983203\pi$
$150$	18.8526	−	6.49280i	1.53931	−	0.530135i
$151$	0.783250	+	1.35663i	0.0637400	+	0.110401i	0.896134	−	0.443783i	$-0.146364\pi$
$151$	0.783250	+	1.35663i	0.0637400	+	0.110401i	−0.832394	+	0.554184i	$0.813031\pi$
$152$	−19.9825	−	4.24742i	−1.62080	−	0.344511i
$153$	9.62468	+	13.9583i	0.778109	+	1.12846i
$154$	−8.21922	−	6.59911i	−0.662324	−	0.531771i
$155$	17.6887	+	0.199160i	1.42079	+	0.0159970i
$156$	0.444570	−	1.11680i	0.0355941	−	0.0894157i
$157$	−7.52534	+	4.34475i	−0.600587	+	0.346749i	−0.769273	−	0.638921i	$-0.779381\pi$
$157$	−7.52534	+	4.34475i	−0.600587	+	0.346749i	0.168685	+	0.985670i	$0.446048\pi$
$158$	6.82525	+	0.717363i	0.542988	+	0.0570703i
$159$	18.0394	+	1.16852i	1.43061	+	0.0926696i
$160$	−9.68825	+	6.87362i	−0.765924	+	0.543407i
$161$	4.21025	−	0.238298i	0.331814	−	0.0187806i
$162$	19.3678	+	7.36678i	1.52168	+	0.578789i
$163$	−10.8787	−	12.0820i	−0.852083	−	0.946334i	0.147001	−	0.989136i	$-0.453038\pi$
$163$	−10.8787	−	12.0820i	−0.852083	−	0.946334i	−0.999084	+	0.0428024i	$0.986371\pi$
$164$	−24.3752	+	27.0714i	−1.90338	+	2.11392i
$165$	−1.88669	+	6.43059i	−0.146878	+	0.500621i
$166$	−7.94083	+	7.14996i	−0.616328	+	0.554944i
$167$	1.98579	+	1.44276i	0.153665	+	0.111644i	0.661961	−	0.749538i	$-0.269724\pi$
$167$	1.98579	+	1.44276i	0.153665	+	0.111644i	−0.508296	+	0.861182i	$0.669724\pi$
$168$	0.111824	−	13.7265i	0.00862744	−	1.05902i
$169$	−10.4815	−	7.61523i	−0.806266	−	0.585787i
$170$	−28.3906	−	6.36950i	−2.17746	−	0.488518i
$171$	18.4802	+	8.77999i	1.41322	+	0.671422i
$172$	−6.89920	−	3.07172i	−0.526059	−	0.234217i
$173$	−16.5995	−	3.52834i	−1.26204	−	0.268255i	−0.472158	−	0.881514i	$-0.656525\pi$
$173$	−16.5995	−	3.52834i	−1.26204	−	0.268255i	−0.789882	+	0.613259i	$0.789858\pi$
$174$	−15.6504	−	16.0411i	−1.18645	−	1.21607i
$175$	5.78858	+	11.8951i	0.437576	+	0.899181i
$176$			0.509932i			0.0384376i
$177$	6.15146	+	9.73299i	0.462372	+	0.731576i
$178$	−8.80239	+	19.7705i	−0.659767	+	1.48186i
$179$	1.01668	−	2.28351i	0.0759906	−	0.170678i	−0.871555	−	0.490297i	$-0.836888\pi$
$179$	1.01668	−	2.28351i	0.0759906	−	0.170678i	0.947546	+	0.319619i	$0.103555\pi$
$180$	−20.5398	+	8.27464i	−1.53095	+	0.616755i
$181$	−4.49699	+	6.18958i	−0.334259	+	0.460068i	−0.942754	−	0.333490i	$-0.891774\pi$
$181$	−4.49699	+	6.18958i	−0.334259	+	0.460068i	0.608495	+	0.793558i	$0.291774\pi$
$182$	1.23841	+	0.326289i	0.0917967	+	0.0241861i
$183$	17.1832	−	2.50485i	1.27022	−	0.185164i
$184$	−3.19468	−	3.54806i	−0.235515	−	0.261566i
$185$	−1.32450	−	1.21986i	−0.0973788	−	0.0896859i
$186$	−31.5233	+	1.26268i	−2.31140	+	0.0925840i
$187$	7.26745	−	6.54365i	0.531449	−	0.478519i
$188$	−4.27997	+	13.1724i	−0.312149	+	0.960695i
$189$	−3.29774	+	13.3463i	−0.239876	+	0.970804i
$190$	−33.5129	+	10.4734i	−2.43128	+	0.759817i
$191$	−3.02693	+	2.72546i	−0.219021	+	0.197207i	−0.771336	−	0.636428i	$-0.780411\pi$
$191$	−3.02693	+	2.72546i	−0.219021	+	0.197207i	0.552315	+	0.833635i	$0.313745\pi$
$192$	17.4283	−	13.7610i	1.25778	−	0.993112i
$193$	1.79282	+	3.10526i	0.129050	+	0.223522i	0.923309	−	0.384058i	$-0.125474\pi$
$193$	1.79282	+	3.10526i	0.129050	+	0.223522i	−0.794259	+	0.607580i	$0.792140\pi$
$194$	18.2495	−	8.12521i	1.31024	−	0.583356i
$195$	−0.108375	−	0.806998i	−0.00776088	−	0.0577903i
$196$	22.9596	−	2.60736i	1.63997	−	0.186240i
$197$	3.82376	+	5.26295i	0.272431	+	0.374970i	0.923209	−	0.384299i	$-0.125557\pi$
$197$	3.82376	+	5.26295i	0.272431	+	0.374970i	−0.650777	+	0.759269i	$0.725557\pi$
$198$	2.77235	−	11.6259i	0.197023	−	0.826218i
$199$	11.0116	−	6.35755i	0.780591	−	0.450674i	−0.0560487	−	0.998428i	$-0.517850\pi$
$199$	11.0116	−	6.35755i	0.780591	−	0.450674i	0.836640	+	0.547754i	$0.184517\pi$
$200$	6.39835	−	13.5418i	0.452431	−	0.957552i
$201$	0.0914450	−	0.0232985i	0.00645004	−	0.00164335i
$202$	6.39144	−	2.07671i	0.449700	−	0.146116i
$203$	9.30871	−	11.5940i	0.653344	−	0.813743i
$204$	31.8508	+	5.44791i	2.23000	+	0.381430i
$205$	−5.40184	+	24.0774i	−0.377281	+	1.68164i
$206$	−4.81463	+	45.8082i	−0.335451	+	3.19161i
$207$	2.28801	+	4.19867i	0.159027	+	0.291828i
$208$	−0.0251998	−	0.0565997i	−0.00174729	−	0.00392449i
$209$	3.64670	−	11.2234i	0.252248	−	0.776339i
$210$	−11.3976	−	20.6568i	−0.786508	−	1.42545i
$211$	0.252721	+	0.777795i	0.0173980	+	0.0535456i	0.959379	−	0.282122i	$-0.0910382\pi$
$211$	0.252721	+	0.777795i	0.0173980	+	0.0535456i	−0.941981	+	0.335667i	$0.891038\pi$
$212$	25.6030	−	23.0531i	1.75842	−	1.58329i
$213$	−5.97772	+	8.96111i	−0.409587	+	0.614005i
$214$	−3.40676	+	3.78359i	−0.232881	+	0.258641i
$215$	−5.09338	+	0.477423i	−0.347365	+	0.0325600i
$216$	14.1202	−	6.54877i	0.960756	−	0.445588i
$217$	−3.36069	−	20.6594i	−0.228139	−	1.40245i
$218$		−	33.8081i		−	2.28977i
$219$	−1.72175	+	4.32520i	−0.116345	+	0.292270i
$220$	6.26121	+	11.1323i	0.422131	+	0.750542i
$221$	−0.483275	+	1.08545i	−0.0325086	+	0.0730155i
$222$	2.47057	+	2.05156i	0.165814	+	0.137692i
$223$	−23.1911	+	7.53524i	−1.55299	+	0.504597i	−0.954924	−	0.296850i	$-0.904064\pi$
$223$	−23.1911	+	7.53524i	−1.55299	+	0.504597i	−0.598066	+	0.801447i	$0.704064\pi$
$224$	9.98007	+	9.89700i	0.666822	+	0.661271i
$225$	−9.37917	+	11.7060i	−0.625278	+	0.780402i
$226$	−6.59552	+	11.4238i	−0.438728	+	0.759899i
$227$	19.2755	−	21.4077i	1.27936	−	1.42088i	0.421641	−	0.906763i	$-0.361454\pi$
$227$	19.2755	−	21.4077i	1.27936	−	1.42088i	0.857722	−	0.514114i	$-0.171879\pi$
$228$	36.5730	−	13.5242i	2.42210	−	0.895664i
$229$	−3.95857	+	0.416062i	−0.261590	+	0.0274942i	−0.234415	−	0.972137i	$-0.575318\pi$
$229$	−3.95857	+	0.416062i	−0.261590	+	0.0274942i	−0.0271743	+	0.999631i	$0.508651\pi$
$230$	−7.77508	−	2.62341i	−0.512673	−	0.172983i
$231$	7.87904	+	0.893073i	0.518403	+	0.0587599i
$232$	−16.8339			−1.10520
$233$	2.20729	+	4.95766i	0.144604	+	0.324787i	0.971298	−	0.237865i	$-0.0764477\pi$
$233$	2.20729	+	4.95766i	0.144604	+	0.324787i	−0.826694	+	0.562652i	$0.809781\pi$
$234$	0.266813	+	1.42742i	0.0174421	+	0.0933134i
$235$	1.84718	+	9.19834i	0.120497	+	0.600034i
$236$	21.4643	+	4.56238i	1.39721	+	0.296986i
$237$	−4.62863	+	2.28698i	−0.300662	+	0.148556i
$238$	−1.65808	+	34.3873i	−0.107477	+	2.22899i
$239$	−9.16755	+	2.97872i	−0.593000	+	0.192677i	−0.590116	−	0.807319i	$-0.700918\pi$
$239$	−9.16755	+	2.97872i	−0.593000	+	0.192677i	−0.00288380	+	0.999996i	$0.500918\pi$
$240$	−0.434041	+	1.05561i	−0.0280172	+	0.0681392i
$241$	3.79687	+	17.8629i	0.244578	+	1.15065i	0.913348	+	0.407180i	$0.133488\pi$
$241$	3.79687	+	17.8629i	0.244578	+	1.15065i	−0.668770	+	0.743470i	$0.733179\pi$
$242$	18.3317	+	1.92674i	1.17840	+	0.123855i
$243$	−15.2772	+	3.09954i	−0.980033	+	0.198836i
$244$	19.4525	−	26.7741i	1.24532	−	1.71404i
$245$	12.6897	−	9.16354i	0.810718	−	0.585437i
$246$	7.41955	−	43.3778i	0.473053	−	2.76567i
$247$	0.149874	+	1.42595i	0.00953623	+	0.0907311i
$248$	−15.8568	+	17.6107i	−1.00690	+	1.11828i
$249$	2.17605	−	7.73833i	0.137902	−	0.490397i
$250$	−1.82467	−	25.6768i	−0.115402	−	1.62394i
$251$	19.8925			1.25560			0.627802	−	0.778373i	$-0.283955\pi$
$251$	19.8925			1.25560			0.627802	+	0.778373i	$0.283955\pi$
$252$	13.8173	+	22.2616i	0.870408	+	1.40235i
$253$	2.23124	−	1.62109i	0.140277	−	0.101917i
$254$	25.0393	−	2.63174i	1.57110	−	0.165130i
$255$	20.6141	−	7.36010i	1.29091	−	0.460907i
$256$	1.86675	−	17.7609i	0.116672	−	1.11006i
$257$	−3.00415	+	5.20334i	−0.187394	+	0.324576i	−0.944381	−	0.328855i	$-0.893337\pi$
$257$	−3.00415	+	5.20334i	−0.187394	+	0.324576i	0.756987	+	0.653430i	$0.226671\pi$
$258$	9.02806	−	1.31605i	0.562063	−	0.0819337i
$259$	−1.15291	+	1.79167i	−0.0716382	+	0.111329i
$260$	−1.24510	−	0.926214i	−0.0772178	−	0.0574413i
$261$	16.3995	+	3.91068i	1.01511	+	0.242065i
$262$	−8.95415	−	42.1260i	−0.553190	−	2.60255i
$263$	5.85998	+	27.5691i	0.361342	+	1.69998i	0.664705	+	0.747106i	$0.268557\pi$
$263$	5.85998	+	27.5691i	0.361342	+	1.69998i	−0.303363	+	0.952875i	$0.598110\pi$
$264$	−4.79638	−	7.58895i	−0.295197	−	0.467068i
$265$	7.46111	−	22.1127i	0.458333	−	1.35837i
$266$	19.0152	+	36.9371i	1.16590	+	2.26476i
$267$	−2.34844	−	16.1102i	−0.143722	−	0.985931i
$268$	0.0899239	−	0.155753i	0.00549297	−	0.00951411i
$269$	0.429087	−	4.08249i	0.0261619	−	0.248914i	−0.973623	−	0.228164i	$-0.926728\pi$
$269$	0.429087	−	4.08249i	0.0261619	−	0.248914i	0.999785	−	0.0207502i	$-0.00660548\pi$
$270$	15.6347	−	21.7070i	0.951498	−	1.32105i
$271$	−18.1108	+	1.90352i	−1.10015	+	0.115631i	−0.637160	−	0.770732i	$-0.719891\pi$
$271$	−18.1108	+	1.90352i	−1.10015	+	0.115631i	−0.462992	+	0.886362i	$0.653224\pi$
$272$	1.34743	−	0.978967i	0.0817001	−	0.0593586i
$273$	−0.918666	+	0.290240i	−0.0556002	+	0.0175662i
$274$	3.29496			0.199056
$275$	7.39337	+	4.49350i	0.445837	+	0.270968i
$276$	8.77275	+	2.46694i	0.528058	+	0.148492i
$277$	−11.0251	+	12.2446i	−0.662436	+	0.735709i	−0.976932	−	0.213549i	$-0.931498\pi$
$277$	−11.0251	+	12.2446i	−0.662436	+	0.735709i	0.314497	+	0.949259i	$0.398164\pi$
$278$	2.59624	+	24.7016i	0.155712	+	1.48150i
$279$	19.5388	−	13.4726i	1.16976	−	0.806586i
$280$	−17.0847	−	4.70770i	−1.02100	−	0.281339i
$281$	4.34626	−	5.98212i	0.259276	−	0.356863i	−0.659457	−	0.751743i	$-0.729214\pi$
$281$	4.34626	−	5.98212i	0.259276	−	0.356863i	0.918733	+	0.394879i	$0.129214\pi$
$282$	−4.13105	−	16.2141i	−0.246000	−	0.965536i
$283$	11.3024	+	1.18793i	0.671857	+	0.0706150i	0.434313	−	0.900762i	$-0.356991\pi$
$283$	11.3024	+	1.18793i	0.671857	+	0.0706150i	0.237544	+	0.971377i	$0.423658\pi$
$284$	4.26835	+	20.0810i	0.253280	+	1.19159i
$285$	17.1021	−	20.1295i	1.01304	−	1.19237i
$286$	0.796581	−	0.258825i	0.0471028	−	0.0153046i
$287$	29.1631	+	1.40618i	1.72144	+	0.0830041i
$288$	−5.29700	+	15.0312i	−0.312129	+	0.885724i
$289$	−14.6143	−	3.10637i	−0.859666	−	0.182728i
$290$	−25.2175	+	14.1832i	−1.48082	+	0.832866i
$291$	−8.33958	+	12.5017i	−0.488875	+	0.732864i
$292$	3.60867	+	8.10522i	0.211182	+	0.474322i
$293$	−27.6513			−1.61541			−0.807704	−	0.589588i	$-0.799290\pi$
$293$	−27.6513			−1.61541			−0.807704	+	0.589588i	$0.799290\pi$
$294$	−21.7636	+	17.4813i	−1.26928	+	1.01953i
$295$	14.1878	−	4.43392i	0.826044	−	0.258153i
$296$	2.39896	−	0.252141i	0.139437	−	0.0146554i
$297$	2.90964	+	8.50739i	0.168834	+	0.493649i
$298$	31.5348	−	35.0229i	1.82676	−	2.02882i
$299$	−0.167545	+	0.290196i	−0.00968937	+	0.0167825i
$300$	3.48576	+	28.3744i	0.201250	+	1.63820i
$301$	1.59105	+	5.84013i	0.0917065	+	0.336620i
$302$	−3.43018	+	1.11453i	−0.197384	+	0.0641341i
$303$	−3.22978	+	3.88943i	−0.185546	+	0.223442i
$304$	0.817470	−	1.83607i	0.0468851	−	0.105306i
$305$	2.59417	−	22.2673i	0.148541	−	1.27502i
$306$	−36.0424	+	14.9938i	−2.06041	+	0.857140i
$307$		−	4.13712i		−	0.236118i	−0.993007	−	0.118059i	$-0.962333\pi$
$307$		−	4.13712i		−	0.236118i	0.993007	−	0.118059i	$-0.0376672\pi$
$308$	11.7047	−	9.55954i	0.666936	−	0.544705i
$309$	−15.3493	−	31.0654i	−0.873189	−	1.76725i
$310$	−8.91603	+	39.7411i	−0.506396	+	2.25714i
$311$	16.8781	−	18.7450i	0.957068	−	1.06293i	−0.0408964	−	0.999163i	$-0.513021\pi$
$311$	16.8781	−	18.7450i	0.957068	−	1.06293i	0.997965	−	0.0637687i	$-0.0203120\pi$
$312$	0.907404	+	0.605306i	0.0513716	+	0.0342687i
$313$	−22.8445	+	20.5693i	−1.29125	+	1.16265i	−0.314264	+	0.949336i	$0.601758\pi$
$313$	−22.8445	+	20.5693i	−1.29125	+	1.16265i	−0.976985	+	0.213310i	$0.931576\pi$
$314$	−6.18240	−	19.0275i	−0.348893	−	1.07378i
$315$	15.5502	+	8.55518i	0.876155	+	0.482030i
$316$	−3.04057	+	9.35791i	−0.171045	+	0.526424i
$317$	9.39060	+	21.0916i	0.527429	+	1.18462i	0.959223	+	0.282652i	$0.0912141\pi$
$317$	9.39060	+	21.0916i	0.527429	+	1.18462i	−0.431794	+	0.901972i	$0.642119\pi$
$318$	−11.2669	+	40.0667i	−0.631819	+	2.24683i
$319$	1.01646	−	9.67097i	0.0569108	−	0.541471i
$320$	−11.3647	−	26.3191i	−0.635306	−	1.47128i
$321$	0.645743	−	3.77528i	0.0360418	−	0.210716i
$322$	−1.47875	+	9.59589i	−0.0824078	+	0.534758i
$323$	−36.6574	+	11.9107i	−2.03967	+	0.662730i
$324$	−16.1046	+	24.9656i	−0.894698	+	1.38698i
$325$	−1.04268	−	0.133389i	−0.0578378	−	0.00739908i
$326$	32.4172	−	18.7161i	1.79542	−	1.03659i
$327$	13.5880	+	21.4992i	0.751416	+	1.18891i
$328$	−19.4299	−	26.7430i	−1.07284	−	1.47664i
$329$	10.3469	−	4.02149i	0.570442	−	0.221712i
$330$	−13.5791	−	7.32726i	−0.747503	−	0.403353i
$331$	14.4176	−	6.41912i	0.792461	−	0.352827i	0.0297432	−	0.999558i	$-0.490531\pi$
$331$	14.4176	−	6.41912i	0.792461	−	0.352827i	0.762718	+	0.646731i	$0.223864\pi$
$332$	−7.66004	−	13.2676i	−0.420399	−	0.728153i
$333$	−2.39564	−	0.311668i	−0.131280	−	0.0170793i
$334$	−4.19981	+	3.78152i	−0.229803	+	0.206916i
$335$	0.00137158	−	0.121819i	7.49373e−5	−	0.00665567i
$336$	1.31863	+	0.291531i	0.0719372	+	0.0159043i
$337$	3.68717	−	11.3479i	0.200853	−	0.618162i	−0.799005	−	0.601324i	$-0.794640\pi$
$337$	3.68717	−	11.3479i	0.200853	−	0.618162i	0.999858	−	0.0168379i	$-0.00535992\pi$
$338$	22.1675	−	19.9597i	1.20576	−	1.08567i
$339$	−0.397167	−	9.91544i	−0.0215711	−	0.538533i
$340$	17.3955	−	37.9163i	0.943406	−	2.05630i
$341$	−9.15980	−	10.1730i	−0.496031	−	0.550898i
$342$	−28.6196	+	37.4161i	−1.54757	+	2.02323i
$343$	−13.2590	−	12.9306i	−0.715917	−	0.698185i
$344$	4.02813	−	5.54424i	0.217182	−	0.298925i
$345$	5.99871	−	1.45664i	0.322960	−	0.0784228i
$346$	15.8922	−	35.6945i	0.854371	−	1.91895i
$347$	−4.18061	+	9.38980i	−0.224427	+	0.504071i	−0.990304	−	0.138916i	$-0.955638\pi$
$347$	−4.18061	+	9.38980i	−0.224427	+	0.504071i	0.765877	+	0.642987i	$0.222305\pi$
$348$	27.1613	−	17.1665i	1.45600	−	0.920221i
$349$		−	34.0859i		−	1.82458i	−0.409550	−	0.912288i	$-0.634314\pi$
$349$		−	34.0859i		−	1.82458i	0.409550	−	0.912288i	$-0.365686\pi$
$350$	−29.5596	+	7.34227i	−1.58003	+	0.392461i
$351$	−0.743373	−	0.800487i	−0.0396783	−	0.0427269i
$352$	8.99151	+	1.91120i	0.479249	+	0.101868i
$353$	−18.5967	−	8.27977i	−0.989801	−	0.440688i	−0.153018	−	0.988223i	$-0.548899\pi$
$353$	−18.5967	−	8.27977i	−0.989801	−	0.440688i	−0.836782	+	0.547536i	$0.815566\pi$
$354$	−24.8642	+	9.19446i	−1.32151	+	0.488680i
$355$	9.18833	+	10.4387i	0.487666	+	0.554026i
$356$	−25.1023	−	18.2379i	−1.33042	−	0.966606i
$357$	−12.7663	−	22.5339i	−0.675667	−	1.19262i
$358$	4.65597	+	3.38276i	0.246076	+	0.178785i
$359$	18.3990	−	16.5665i	0.971060	−	0.874346i	−0.0210425	−	0.999779i	$-0.506699\pi$
$359$	18.3990	−	16.5665i	0.971060	−	0.874346i	0.992102	+	0.125433i	$0.0400319\pi$
$360$	−3.46945	−	19.7924i	−0.182856	−	1.04315i
$361$	−18.4091	+	20.4454i	−0.968900	+	1.07607i
$362$	−11.7868	−	13.0905i	−0.619498	−	0.688022i
$363$	−12.4319	+	6.14252i	−0.652503	+	0.322399i
$364$	−0.826744	+	1.63948i	−0.0433332	+	0.0859321i
$365$	4.82208	+	3.58708i	0.252399	+	0.187756i
$366$	−2.58438	+	39.8970i	−0.135088	+	2.08545i
$367$	4.74292	+	0.498501i	0.247578	+	0.0260215i	0.227505	−	0.973777i	$-0.426943\pi$
$367$	4.74292	+	0.498501i	0.247578	+	0.0260215i	0.0200737	+	0.999799i	$0.493610\pi$
$368$	0.406780	−	0.234855i	0.0212049	−	0.0122426i
$369$	12.7159	+	30.5668i	0.661966	+	1.59124i
$370$	3.38125	−	2.39893i	0.175783	−	0.124714i
$371$	−27.2912	−	4.20565i	−1.41689	−	0.218346i
$372$	7.62599	−	44.5848i	0.395389	−	2.31161i
$373$	4.14911	+	0.881920i	0.214833	+	0.0456641i	0.314071	−	0.949400i	$-0.398307\pi$
$373$	4.14911	+	0.881920i	0.214833	+	0.0456641i	−0.0992379	+	0.995064i	$0.531640\pi$
$374$	11.2579	+	19.4993i	0.582134	+	1.00829i
$375$	11.4802	+	15.5950i	0.592836	+	0.805323i
$376$	−10.8844	−	6.28411i	−0.561320	−	0.324078i
$377$	0.365099	+	1.12366i	0.0188035	+	0.0578714i
$378$	−28.4784	−	13.8156i	−1.46477	−	0.710599i
$379$	2.19341	−	1.59360i	0.112668	−	0.0818579i	−0.530025	−	0.847982i	$-0.677817\pi$
$379$	2.19341	−	1.59360i	0.112668	−	0.0818579i	0.642692	+	0.766124i	$0.277817\pi$
$380$	−4.69801	−	50.1206i	−0.241003	−	2.57113i
$381$	−14.8652	+	11.7372i	−0.761569	+	0.601317i
$382$	−4.68898	−	8.12156i	−0.239909	−	0.415535i
$383$	−25.3225	+	11.2743i	−1.29392	+	0.576089i	−0.934126	−	0.356943i	$-0.883819\pi$
$383$	−25.3225	+	11.2743i	−1.29392	+	0.576089i	−0.359792	+	0.933033i	$0.617152\pi$
$384$	14.4960	+	29.3385i	0.739748	+	1.49718i
$385$	3.73615	−	9.53079i	0.190412	−	0.485734i
$386$	−7.85152	+	2.55111i	−0.399632	+	0.129848i
$387$	−5.21218	+	4.46541i	−0.264950	+	0.226990i
$388$	5.95482	+	28.0152i	0.302310	+	1.42226i
$389$	20.3955	+	18.3642i	1.03409	+	0.931103i	0.997669	−	0.0682333i	$-0.0217362\pi$
$389$	20.3955	+	18.3642i	1.03409	+	0.931103i	0.0364254	+	0.999336i	$0.488403\pi$
$390$	1.86930	+	0.142237i	0.0946559	+	0.00720244i
$391$	−8.56707	−	2.78361i	−0.433255	−	0.140773i
$392$	−2.01739	+	20.8710i	−0.101894	+	1.05414i
$393$	22.6252	+	23.1899i	1.14129	+	1.16978i
$394$	−13.6830	+	6.09207i	−0.689340	+	0.306914i
$395$	1.31227	+	6.53468i	0.0660277	+	0.328795i
$396$	15.4778	+	7.35353i	0.777789	+	0.369529i
$397$	2.41439	−	0.253762i	0.121175	−	0.0127360i	−0.0437470	−	0.999043i	$-0.513930\pi$
$397$	2.41439	−	0.253762i	0.121175	−	0.0127360i	0.164922	+	0.986307i	$0.447263\pi$
$398$	9.04652	+	27.8423i	0.453461	+	1.39561i
$399$	−26.9377	−	15.8465i	−1.34857	−	0.793316i
$400$	1.17227	+	0.892714i	0.0586137	+	0.0446357i
$401$	−9.93938	−	5.73850i	−0.496349	−	0.286567i	0.230856	−	0.972988i	$-0.425847\pi$
$401$	−9.93938	−	5.73850i	−0.496349	−	0.286567i	−0.727204	+	0.686421i	$0.759181\pi$
$402$	0.00869580	+	0.217095i	0.000433707	+	0.0108277i
$403$	1.51942	+	0.676489i	0.0756876	+	0.0336983i
$404$	1.00715	+	9.58242i	0.0501078	+	0.476743i
$405$	−1.21805	+	20.0877i	−0.0605253	+	0.998167i
$406$	21.6547	+	26.5140i	1.07471	+	1.31587i
$407$			1.39342i			0.0690690i
$408$	−10.8448	+	27.2431i	−0.536896	+	1.34873i
$409$	3.65573	+	17.1989i	0.180764	+	0.850430i	0.971271	+	0.237976i	$0.0764840\pi$
$409$	3.65573	+	17.1989i	0.180764	+	0.850430i	−0.790507	+	0.612454i	$0.790183\pi$
$410$	−51.6385	−	23.6911i	−2.55024	−	1.17002i
$411$	−2.09533	+	1.32429i	−0.103355	+	0.0653225i
$412$	−62.8063	−	20.4070i	−3.09425	−	1.00538i
$413$	−8.05016	−	15.6374i	−0.396122	−	0.769466i
$414$	−10.5510	+	3.14290i	−0.518554	+	0.154465i
$415$	−8.92830	−	5.28967i	−0.438273	−	0.259659i
$416$	−1.09246	+	0.232209i	−0.0535622	+	0.0113850i
$417$	−11.5789	−	14.6648i	−0.567023	−	0.718137i
$418$	23.5304	+	13.5853i	1.15091	+	0.664477i
$419$	−3.88058	−	2.81941i	−0.189579	−	0.137737i	0.488947	−	0.872313i	$-0.337381\pi$
$419$	−3.88058	−	2.81941i	−0.189579	−	0.137737i	−0.678526	+	0.734576i	$0.737381\pi$
$420$	32.3666	−	9.82643i	1.57933	−	0.479481i
$421$	17.8661	−	12.9805i	0.870741	−	0.632631i	−0.0600445	−	0.998196i	$-0.519124\pi$
$421$	17.8661	−	12.9805i	0.870741	−	0.632631i	0.930786	+	0.365565i	$0.119124\pi$
$422$	−1.87263	+	0.196822i	−0.0911584	+	0.00958113i
$423$	9.14370	+	8.65053i	0.444582	+	0.420603i
$424$	15.6316	+	27.0747i	0.759138	+	1.31487i
$425$	−2.32027	−	28.1627i	−0.112550	−	1.36609i
$426$	−17.3196	−	17.7520i	−0.839139	−	0.860085i
$427$	−26.4828	+	1.49892i	−1.28159	+	0.0725377i
$428$	−4.29060	−	5.90550i	−0.207394	−	0.285453i
$429$	−0.402536	+	0.484750i	−0.0194346	+	0.0234039i
$430$	1.36298	−	11.6992i	0.0657285	−	0.564187i
$431$	24.4906	+	2.57406i	1.17967	+	0.123988i	0.673994	−	0.738736i	$-0.264577\pi$
$431$	24.4906	+	2.57406i	1.17967	+	0.123988i	0.505674	+	0.862725i	$0.331244\pi$
$432$	0.341375	+	1.49276i	0.0164244	+	0.0718202i
$433$	−7.00061	+	9.63552i	−0.336428	+	0.463053i	−0.943394	−	0.331674i	$-0.892386\pi$
$433$	−7.00061	+	9.63552i	−0.336428	+	0.463053i	0.606966	+	0.794728i	$0.292386\pi$
$434$	48.1353	+	2.32098i	2.31057	+	0.111410i
$435$	10.3358	−	19.1546i	0.495566	−	0.918395i
$436$	47.4125	+	10.0778i	2.27065	+	0.482641i
$437$	−10.6326	+	2.26003i	−0.508626	+	0.108112i
$438$	−8.91650	−	5.94797i	−0.426047	−	0.284205i
$439$	7.56505	−	35.5908i	0.361060	−	1.69865i	−0.304667	−	0.952459i	$-0.598545\pi$
$439$	7.56505	−	35.5908i	0.361060	−	1.69865i	0.665727	−	0.746196i	$-0.268122\pi$
$440$	−11.0624	+	3.45719i	−0.527380	+	0.164815i
$441$	6.81389	−	19.8638i	0.324471	−	0.945896i
$442$	−2.21319	−	1.60798i	−0.105271	−	0.0764836i
$443$	6.28381	+	3.62796i	0.298553	+	0.172370i	0.641793	−	0.766878i	$-0.278191\pi$
$443$	6.28381	+	3.62796i	0.298553	+	0.172370i	−0.343240	+	0.939248i	$0.611524\pi$
$444$	−3.61357	+	2.85319i	−0.171493	+	0.135406i
$445$	−20.8769	−	2.43218i	−0.989658	−	0.115296i
$446$	−5.86852	−	55.8353i	−0.277883	−	2.64388i
$447$	−5.97734	+	34.9460i	−0.282718	+	1.65289i
$448$	−28.3705	+	18.5931i	−1.34038	+	0.878440i
$449$		−	12.2818i		−	0.579615i	−0.957085	−	0.289807i	$-0.906409\pi$
$449$		−	12.2818i		−	0.579615i	0.957085	−	0.289807i	$-0.0935912\pi$
$450$	−21.8732	−	26.7263i	−1.03111	−	1.25989i
$451$	16.5370	−	9.54761i	0.778695	−	0.449580i
$452$	−14.0547	−	12.6549i	−0.661077	−	0.595236i
$453$	1.73337	−	2.08739i	0.0814407	−	0.0980741i
$454$	38.9847	+	53.6578i	1.82964	+	2.51829i
$455$	0.0562997	+	1.24250i	0.00263937	+	0.0582493i
$456$	5.10410	+	35.0139i	0.239021	+	1.63968i
$457$	−2.26175	+	3.91747i	−0.105800	+	0.183251i	−0.914065	−	0.405568i	$-0.867074\pi$
$457$	−2.26175	+	3.91747i	−0.105800	+	0.183251i	0.808265	+	0.588819i	$0.200407\pi$
$458$	0.957940	−	9.11419i	0.0447616	−	0.425878i
$459$	16.8938	−	24.0208i	0.788536	−	1.12120i
$460$	5.99676	−	10.1218i	0.279600	−	0.471931i
$461$	3.18815	+	9.81210i	0.148487	+	0.456995i	0.997443	−	0.0714681i	$-0.0227684\pi$
$461$	3.18815	+	9.81210i	0.148487	+	0.456995i	−0.848956	+	0.528463i	$0.822768\pi$
$462$	−5.78293	+	17.3167i	−0.269046	+	0.805648i
$463$	10.1566	−	31.2588i	0.472018	−	1.45272i	−0.377920	−	0.925838i	$-0.623361\pi$
$463$	10.1566	−	31.2588i	0.472018	−	1.45272i	0.849938	−	0.526883i	$-0.176639\pi$
$464$	0.344330	−	1.61995i	0.0159851	−	0.0752041i
$465$	−10.3027	−	28.8556i	−0.477775	−	1.33815i
$466$	−12.2217	+	2.59779i	−0.566158	+	0.120341i
$467$	−24.5024	+	10.9092i	−1.13384	+	0.504816i	−0.885861	−	0.463950i	$-0.846432\pi$
$467$	−24.5024	+	10.9092i	−1.13384	+	0.504816i	−0.247975	+	0.968766i	$0.579765\pi$
$468$	−2.08135	−	0.0513195i	−0.0962106	−	0.00237224i
$469$	−0.142277	+	0.0231444i	−0.00656973	+	0.00106871i
$470$	−21.5997	−	0.243194i	−0.996318	−	0.0112177i
$471$	11.5789	+	9.61514i	0.533529	+	0.443042i
$472$	−8.09919	+	18.1911i	−0.372796	+	0.837313i
$473$	2.94191	+	2.64891i	0.135269	+	0.121797i
$474$	−2.93478	−	11.5188i	−0.134799	−	0.529076i
$475$	−19.4172	−	28.0316i	−0.890920	−	1.28618i
$476$	−47.7305	−	12.5758i	−2.18773	−	0.576410i
$477$	−8.93854	−	30.0076i	−0.409268	−	1.37395i
$478$	−2.31986	−	22.0720i	−0.106108	−	1.00955i
$479$	−1.54657	−	0.688578i	−0.0706647	−	0.0314619i	0.371100	−	0.928593i	$-0.378981\pi$
$479$	−1.54657	−	0.688578i	−0.0706647	−	0.0314619i	−0.441765	+	0.897131i	$0.645647\pi$
$480$	16.9865	+	11.6097i	0.775324	+	0.529908i
$481$	−0.0688599	−	0.154662i	−0.00313974	−	0.00705197i
$482$	−42.0462			−1.91515
$483$	−2.91636	−	6.69654i	−0.132699	−	0.304703i
$484$	−8.16655	+	25.1341i	−0.371207	+	1.14246i
$485$	12.8187	+	14.5631i	0.582069	+	0.661275i
$486$	0.332690	−	35.8892i	0.0150911	−	1.62797i
$487$	28.6872	−	6.09765i	1.29994	−	0.276311i	0.494599	−	0.869122i	$-0.335315\pi$
$487$	28.6872	−	6.09765i	1.29994	−	0.276311i	0.805342	+	0.592811i	$0.201982\pi$
$488$	20.0948	+	22.3176i	0.909650	+	1.01027i
$489$	−13.0924	+	24.9308i	−0.592061	+	1.12741i
$490$	14.5625	+	32.9649i	0.657867	+	1.48920i
$491$	27.3898	+	8.89948i	1.23608	+	0.401628i	0.852915	−	0.522051i	$-0.174833\pi$
$491$	27.3898	+	8.89948i	1.23608	+	0.401628i	0.383169	+	0.923678i	$0.374833\pi$
$492$	58.6215	+	23.3357i	2.64286	+	1.05205i
$493$	−27.5058	+	15.8805i	−1.23880	+	0.715220i
$494$	−3.28310	−	0.345068i	−0.147714	−	0.0155253i
$495$	11.5801	−	0.798080i	0.520488	−	0.0358710i
$496$	−1.37036	−	1.88614i	−0.0615309	−	0.0846900i
$497$	10.3016	−	12.8306i	0.462088	−	0.575533i
$498$	16.3857	+	8.60495i	0.734261	+	0.385597i
$499$	−2.94988	+	5.10934i	−0.132055	+	0.228726i	−0.924469	−	0.381258i	$-0.875491\pi$
$499$	−2.94988	+	5.10934i	−0.132055	+	0.228726i	0.792414	+	0.609984i	$0.208824\pi$
$500$	36.5531	+	5.09508i	1.63471	+	0.227859i
$501$	1.15089	−	4.09271i	0.0514179	−	0.182849i
$502$	−9.52244	+	44.7995i	−0.425007	+	1.99950i
$503$	7.70826	−	5.60038i	0.343694	−	0.249709i	−0.402525	−	0.915409i	$-0.631867\pi$
$503$	7.70826	−	5.60038i	0.343694	−	0.249709i	0.746219	+	0.665701i	$0.231867\pi$
$504$	−22.3663	+	8.06430i	−0.996276	+	0.359212i
$505$	3.77664	+	5.32312i	0.168058	+	0.236876i
$506$	2.58275	+	5.80094i	0.114817	+	0.257883i
$507$	−6.07465	+	21.6022i	−0.269785	+	0.959389i
$508$	−3.77321	+	35.8997i	−0.167409	+	1.59279i
$509$	−2.40035	−	2.66586i	−0.106394	−	0.118162i	0.687596	−	0.726094i	$-0.258666\pi$
$509$	−2.40035	−	2.66586i	−0.106394	−	0.118162i	−0.793989	+	0.607932i	$0.791999\pi$
$510$	6.70769	+	49.9479i	0.297021	+	2.21173i
$511$	3.20185	−	6.34945i	0.141642	−	0.280883i
$512$	3.16803	+	1.02936i	0.140009	+	0.0454915i
$513$	3.16170	−	35.2963i	0.139592	−	1.55837i
$514$	−10.2803	−	9.25641i	−0.453444	−	0.408283i
$515$	−43.8580	+	8.80742i	−1.93261	+	0.388101i
$516$	−0.845542	+	13.0533i	−0.0372229	+	0.574639i
$517$	4.26741	−	5.87358i	0.187680	−	0.258320i
$518$	−3.48310	−	3.45411i	−0.153039	−	0.151765i
$519$	4.23998	+	29.0861i	0.186115	+	1.27674i
$520$	1.05702	−	0.930413i	0.0463534	−	0.0408013i
$521$	3.16944	+	1.41113i	0.138856	+	0.0618226i	0.474988	−	0.879992i	$-0.342452\pi$
$521$	3.16944	+	1.41113i	0.138856	+	0.0618226i	−0.336132	+	0.941815i	$0.609119\pi$
$522$	−16.6576	+	35.0611i	−0.729081	+	1.53458i
$523$	7.70377	−	36.2434i	0.336862	−	1.58481i	−0.405037	−	0.914300i	$-0.632741\pi$
$523$	7.70377	−	36.2434i	0.336862	−	1.58481i	0.741899	−	0.670511i	$-0.233925\pi$
$524$	61.7468			2.69742
$525$	15.8465	−	16.5495i	0.691600	−	0.722281i
$526$	−64.8929			−2.82947
$527$	−9.29589	+	43.7337i	−0.404935	+	1.90507i
$528$	0.828403	−	0.306333i	0.0360516	−	0.0133314i
$529$	18.6908	+	8.32166i	0.812642	+	0.361811i
$530$	46.2280	+	27.3883i	2.00802	+	1.18967i
$531$	12.1162	−	15.8402i	0.525798	−	0.687406i
$532$	−57.4689	+	15.6565i	−2.49159	+	0.678794i
$533$	−1.36369	+	1.87696i	−0.0590680	+	0.0813001i
$534$	37.4058	+	2.42300i	1.61871	+	0.104854i
$535$	−4.49423	−	2.06190i	−0.194303	−	0.0891437i
$536$	0.121281	+	0.109202i	0.00523856	+	0.00471682i
$537$	−4.32040	−	0.279859i	−0.186439	−	0.0120768i
$538$	8.98870	+	2.92061i	0.387531	+	0.125916i
$539$	−11.8685	−	2.41921i	−0.511210	−	0.104203i
$540$	25.7814	+	28.3968i	1.10946	+	1.22200i
$541$	20.2797	+	22.5229i	0.871892	+	0.968334i	0.999725	−	0.0234617i	$-0.00746877\pi$
$541$	20.2797	+	22.5229i	0.871892	+	0.968334i	−0.127833	+	0.991796i	$0.540802\pi$
$542$	4.38266	−	41.6982i	0.188251	−	1.79109i
$543$	12.7567	+	3.58724i	0.547442	+	0.153943i
$544$	−12.2118	−	27.4281i	−0.523575	−	1.17597i
$545$	31.3394	−	9.79409i	1.34243	−	0.419533i
$546$	−0.213885	−	2.20785i	−0.00915341	−	0.0944872i
$547$	16.4210	−	11.9306i	0.702112	−	0.510114i	−0.178508	−	0.983939i	$-0.557127\pi$
$547$	16.4210	−	11.9306i	0.702112	−	0.510114i	0.880619	+	0.473825i	$0.157127\pi$
$548$	−0.982193	+	4.62086i	−0.0419572	+	0.197393i
$549$	−14.3918	−	26.4100i	−0.614225	−	1.12715i
$550$	−13.6589	+	14.4995i	−0.582417	+	0.618259i
$551$	−19.1634	+	33.1920i	−0.816388	+	1.41403i
$552$	−3.84479	+	7.32132i	−0.163645	+	0.311616i
$553$	7.35062	−	2.85694i	0.312580	−	0.121490i
$554$	−22.2983	−	30.6909i	−0.947363	−	1.30393i
$555$	−1.18604	+	2.88450i	−0.0503445	+	0.122440i
$556$	−35.4155	−	3.72232i	−1.50195	−	0.157862i
$557$	−2.35128	+	1.35751i	−0.0996269	+	0.0575196i	−0.548986	−	0.835832i	$-0.684986\pi$
$557$	−2.35128	+	1.35751i	−0.0996269	+	0.0575196i	0.449359	+	0.893351i	$0.351653\pi$
$558$	20.9884	+	50.4522i	0.888508	+	2.13581i
$559$	−0.457441	−	0.148631i	−0.0193477	−	0.00628644i
$560$	0.802488	−	1.54779i	0.0339113	−	0.0654059i
$561$	−14.9962	−	7.87526i	−0.633140	−	0.332494i
$562$	11.3917	+	12.6517i	0.480529	+	0.533682i
$563$	29.1390	−	6.19369i	1.22806	−	0.261033i	0.452189	−	0.891922i	$-0.350643\pi$
$563$	29.1390	−	6.19369i	1.22806	−	0.261033i	0.775873	+	0.630889i	$0.217310\pi$
$564$	23.9701	−	0.960133i	1.00932	−	0.0404289i
$565$	−12.5003	−	2.80448i	−0.525892	−	0.117985i
$566$	−8.08570	+	24.8852i	−0.339867	+	1.04600i
$567$	23.6627	−	2.66029i	0.993740	−	0.111722i
$568$	−18.6293			−0.781669
$569$	−2.00785	−	4.50970i	−0.0841734	−	0.189057i	0.866555	−	0.499082i	$-0.166329\pi$
$569$	−2.00785	−	4.50970i	−0.0841734	−	0.189057i	−0.950728	+	0.310025i	$0.899663\pi$
$570$	37.1467	+	48.1512i	1.55590	+	2.01683i
$571$	−12.4668	−	5.55059i	−0.521721	−	0.232285i	0.128942	−	0.991652i	$-0.458842\pi$
$571$	−12.4668	−	5.55059i	−0.521721	−	0.232285i	−0.650662	+	0.759367i	$0.725509\pi$
$572$	0.125524	+	1.19428i	0.00524842	+	0.0499354i
$573$	6.24599	+	3.28008i	0.260930	+	0.137027i
$574$	−17.1271	+	65.0046i	−0.714869	+	2.71324i
$575$	0.179434	−	7.96733i	0.00748291	−	0.332261i
$576$	−32.8249	−	20.0462i	−1.36771	−	0.835259i
$577$	8.06144	+	7.25855i	0.335602	+	0.302178i	0.819651	−	0.572864i	$-0.194168\pi$
$577$	8.06144	+	7.25855i	0.335602	+	0.302178i	−0.484049	+	0.875041i	$0.660834\pi$
$578$	13.9916	−	31.4256i	0.581974	−	1.30713i
$579$	3.96760	−	4.77794i	0.164888	−	0.198565i
$580$	−12.3735	−	39.5930i	−0.513781	−	1.64401i
$581$	−4.35244	+	11.4817i	−0.180570	+	0.476341i
$582$	−24.1628	−	24.7659i	−1.00158	−	1.02658i
$583$	−16.4982	+	7.34546i	−0.683284	+	0.304218i
$584$	−7.87507	+	1.67390i	−0.325873	+	0.0692664i
$585$	−1.24589	+	0.660850i	−0.0515113	+	0.0273228i
$586$	13.2365	−	62.2730i	0.546797	−	2.57248i
$587$	6.87109	−	21.1470i	0.283600	−	0.872832i	−0.703214	−	0.710978i	$-0.748253\pi$
$587$	6.87109	−	21.1470i	0.283600	−	0.872832i	0.986815	−	0.161854i	$-0.0517474\pi$
$588$	−18.0283	−	35.7323i	−0.743476	−	1.47358i
$589$	16.6726	+	51.3131i	0.686984	+	2.11432i
$590$	3.19395	+	34.0745i	0.131493	+	1.40283i
$591$	6.25279	−	9.37346i	0.257206	−	0.385573i
$592$	−0.0248059	+	0.236013i	−0.00101952	+	0.00970006i
$593$	17.0276	−	29.4927i	0.699241	−	1.21112i	−0.269489	−	0.963004i	$-0.586855\pi$
$593$	17.0276	−	29.4927i	0.699241	−	1.21112i	0.968730	−	0.248118i	$-0.0798120\pi$
$594$	−20.5522	+	2.48029i	−0.843266	+	0.101768i
$595$	−32.3566	+	8.42488i	−1.32649	+	0.345386i
$596$	39.7160	+	54.6644i	1.62683	+	2.23914i
$597$	−16.9431	−	14.0695i	−0.693435	−	0.575828i
$598$	−0.573343	−	0.516240i	−0.0234457	−	0.0211106i
$599$	−2.66380	+	1.53795i	−0.108840	+	0.0628388i	−0.553432	−	0.832894i	$-0.686682\pi$
$599$	−2.66380	+	1.53795i	−0.108840	+	0.0628388i	0.444592	+	0.895733i	$0.353349\pi$
$600$	−25.8429	−	2.25931i	−1.05503	−	0.0922361i
$601$		−	22.1561i		−	0.903764i	−0.892078	−	0.451882i	$-0.850753\pi$
$601$		−	22.1561i		−	0.903764i	0.892078	−	0.451882i	$-0.149247\pi$
$602$	−13.9141	+	0.787532i	−0.567096	+	0.0320974i
$603$	−0.0927833	−	0.134560i	−0.00377843	−	0.00547969i
$604$	−0.540522	−	5.14272i	−0.0219935	−	0.209254i
$605$	3.52459	+	17.5513i	0.143295	+	0.713560i
$606$	−7.21324	−	9.13558i	−0.293018	−	0.371108i
$607$	28.4386	+	16.4190i	1.15429	+	0.666428i	0.949928	−	0.312468i	$-0.101156\pi$
$607$	28.4386	+	16.4190i	1.15429	+	0.666428i	0.204359	+	0.978896i	$0.434489\pi$
$608$	−29.3111	−	21.2958i	−1.18872	−	0.863657i
$609$	−24.4270	−	8.15741i	−0.989833	−	0.330555i
$610$	48.9059	+	16.5015i	1.98014	+	0.668126i
$611$	−0.183399	+	0.862824i	−0.00741952	+	0.0349061i
$612$	−10.2835	−	55.0155i	−0.415686	−	2.22387i
$613$	37.2838	−	7.92492i	1.50588	−	0.320085i	0.620223	−	0.784426i	$-0.287042\pi$
$613$	37.2838	−	7.92492i	1.50588	−	0.320085i	0.885656	+	0.464341i	$0.153709\pi$
$614$	9.31713	+	1.98042i	0.376009	+	0.0799232i
$615$	42.3597	−	5.68865i	1.70811	−	0.229388i
$616$	6.27682	+	12.1927i	0.252900	+	0.491258i
$617$	−22.8879	+	31.5025i	−0.921431	+	1.26824i	0.0416779	+	0.999131i	$0.486730\pi$
$617$	−22.8879	+	31.5025i	−0.921431	+	1.26824i	−0.963109	+	0.269110i	$0.913270\pi$
$618$	77.3093	−	19.6970i	3.10984	−	0.792328i
$619$	−10.3342	−	1.08617i	−0.415368	−	0.0436570i	−0.105460	−	0.994424i	$-0.533632\pi$
$619$	−10.3342	−	1.08617i	−0.415368	−	0.0436570i	−0.309908	+	0.950767i	$0.600298\pi$
$620$	−53.0753	−	24.3503i	−2.13156	−	0.977932i
$621$	5.44641	−	6.23923i	0.218557	−	0.250372i
$622$	34.1358	+	46.9840i	1.36872	+	1.88389i
$623$	1.40532	+	24.8292i	0.0563030	+	0.994759i
$624$	−0.0768100	+	0.0749394i	−0.00307486	+	0.00299998i
$625$	23.2733	−	9.12992i	0.930930	−	0.365197i
$626$	−35.3882	−	61.2941i	−1.41440	−	2.44981i
$627$	−20.4235	+	0.818072i	−0.815637	+	0.0326707i
$628$	28.5271	−	2.99832i	1.13836	−	0.119646i
$629$	3.68193	−	2.67508i	0.146808	−	0.106662i
$630$	−26.7108	+	30.9250i	−1.06418	+	1.23208i
$631$	−0.884969	−	0.642967i	−0.0352301	−	0.0255961i	0.570031	−	0.821623i	$-0.306931\pi$
$631$	−0.884969	−	0.642967i	−0.0352301	−	0.0255961i	−0.605261	+	0.796027i	$0.706931\pi$
$632$	−7.73248	−	4.46435i	−0.307582	−	0.177582i
$633$	1.11174	−	0.877802i	0.0441876	−	0.0348895i
$634$	−51.9953	+	11.0519i	−2.06500	+	0.438929i
$635$	9.69337	+	22.4485i	0.384670	+	0.890841i
$636$	−52.8311	−	27.7443i	−2.09489	−	1.10013i
$637$	1.43689	−	0.317996i	0.0569316	−	0.0125995i
$638$	21.2932	+	6.91860i	0.843008	+	0.273910i
$639$	18.1487	+	4.32779i	0.717950	+	0.171205i
$640$	41.4200	−	8.31784i	1.63727	−	0.328792i
$641$	−5.43496	−	25.5695i	−0.214668	−	1.00993i	−0.945058	−	0.326903i	$-0.893995\pi$
$641$	−5.43496	−	25.5695i	−0.214668	−	1.00993i	0.730390	−	0.683030i	$-0.239338\pi$
$642$	8.19313	+	3.26147i	0.323357	+	0.128720i
$643$			13.9349i			0.549540i	0.961510	+	0.274770i	$0.0886018\pi$
$643$			13.9349i			0.549540i	−0.961510	+	0.274770i	$0.911398\pi$
$644$	−13.0165	−	4.93425i	−0.512922	−	0.194437i
$645$	3.83535	+	7.98757i	0.151017	+	0.314510i
$646$	−9.27619	−	88.2571i	−0.364967	−	3.47243i
$647$	22.7642	+	10.1353i	0.894953	+	0.398459i	0.802078	−	0.597219i	$-0.203728\pi$
$647$	22.7642	+	10.1353i	0.894953	+	0.398459i	0.0928745	+	0.995678i	$0.470394\pi$
$648$	−19.1212	−	19.0047i	−0.751151	−	0.746574i
$649$	−9.96164	−	5.75136i	−0.391029	−	0.225761i
$650$	0.799530	−	2.28436i	0.0313602	−	0.0895999i
$651$	−31.5430	+	17.8703i	−1.23627	+	0.700394i
$652$	16.5842	+	51.0410i	0.649489	+	1.99892i
$653$	5.15789	−	0.542117i	0.201844	−	0.0212147i	−0.00306686	−	0.999995i	$-0.500976\pi$
$653$	5.15789	−	0.542117i	0.201844	−	0.0212147i	0.204911	+	0.978781i	$0.434310\pi$
$654$	−54.9224	+	20.3096i	−2.14764	+	0.794170i
$655$	36.4559	−	20.5041i	1.42445	−	0.801161i
$656$	2.97095	−	1.32275i	0.115996	−	0.0516448i
$657$	8.06075	+	0.198752i	0.314480	+	0.00775407i
$658$	4.10373	+	25.2271i	0.159980	+	0.983454i
$659$	−35.1704	−	11.4275i	−1.37004	−	0.445154i	−0.470660	−	0.882315i	$-0.655984\pi$
$659$	−35.1704	−	11.4275i	−1.37004	−	0.445154i	−0.899383	+	0.437161i	$0.855984\pi$
$660$	14.3236	−	16.8591i	0.557544	−	0.656241i
$661$	10.9128	+	9.82593i	0.424459	+	0.382184i	0.853493	−	0.521104i	$-0.174480\pi$
$661$	10.9128	+	9.82593i	0.424459	+	0.382184i	−0.429035	+	0.903288i	$0.641146\pi$
$662$	7.55476	+	35.5423i	0.293624	+	1.38139i
$663$	2.05368	+	0.133029i	0.0797583	+	0.00516643i
$664$	13.2216	−	4.29595i	0.513097	−	0.166715i
$665$	−28.7312	+	28.3273i	−1.11415	+	1.09849i
$666$	1.84868	−	5.24598i	0.0716350	−	0.203278i
$667$	−8.18282	+	3.64323i	−0.316840	+	0.141066i
$668$	−4.05130	−	7.01706i	−0.156750	−	0.271498i
$669$	26.1729	+	33.1481i	1.01190	+	1.28158i
$670$	0.273689	+	0.0614029i	0.0105735	+	0.00237220i
$671$	−14.0347	+	10.1968i	−0.541803	+	0.393643i
$672$	10.0827	−	22.1585i	0.388947	−	0.854781i
$673$	−9.92479	−	30.5454i	−0.382572	−	1.17744i	−0.938226	−	0.346023i	$-0.887532\pi$
$673$	−9.92479	−	30.5454i	−0.382572	−	1.17744i	0.555654	−	0.831414i	$-0.312468\pi$
$674$	23.7915	+	13.7360i	0.916413	+	0.529091i
$675$	24.6513	+	8.20460i	0.948827	+	0.315795i
$676$	21.3837	+	37.0376i	0.822449	+	1.42452i
$677$	−9.96991	−	2.11917i	−0.383175	−	0.0814463i	0.0122972	−	0.999924i	$-0.496086\pi$
$677$	−9.96991	−	2.11917i	−0.383175	−	0.0814463i	−0.395472	+	0.918478i	$0.629419\pi$
$678$	22.5205	+	3.85202i	0.864895	+	0.147936i
$679$	14.3718	−	17.9002i	0.551539	−	0.686945i
$680$	30.3728	+	22.5939i	1.16474	+	0.866438i
$681$	−46.3570	−	18.4535i	−1.77640	−	0.707141i
$682$	27.2952	−	15.7589i	1.04519	−	0.603438i
$683$	33.9382	+	3.56705i	1.29861	+	0.136489i	0.728481	−	0.685066i	$-0.240227\pi$
$683$	33.9382	+	3.56705i	1.29861	+	0.136489i	0.570129	+	0.821555i	$0.306893\pi$
$684$	−43.9412	−	51.2896i	−1.68013	−	1.96111i
$685$	0.954538	+	3.05435i	0.0364710	+	0.116701i
$686$	35.4677	−	23.6705i	1.35416	−	0.903743i
$687$	3.05395	+	6.18090i	0.116516	+	0.235816i
$688$	0.451136	+	0.501037i	0.0171994	+	0.0191019i
$689$	1.46821	−	1.63061i	0.0559344	−	0.0621214i
$690$	0.408920	+	14.2069i	0.0155673	+	0.540846i
$691$	−29.7571	+	26.7934i	−1.13201	+	1.01927i	−0.132407	+	0.991195i	$0.542271\pi$
$691$	−29.7571	+	26.7934i	−1.13201	+	1.01927i	−0.999606	+	0.0280738i	$0.991063\pi$
$692$	45.3208	+	32.9275i	1.72284	+	1.25171i
$693$	−3.28238	−	13.3363i	−0.124687	−	0.506604i
$694$	−19.1454	−	13.9099i	−0.726748	−	0.528013i
$695$	−22.1458	+	9.56265i	−0.840036	+	0.362732i
$696$	10.1127	+	27.3472i	0.383320	+	1.03659i
$697$	−56.9760	−	25.3674i	−2.15812	−	0.960857i
$698$	76.7642	+	16.3167i	2.90557	+	0.617598i
$699$	6.72790	−	6.56406i	0.254473	−	0.248275i
$700$	−1.48540	−	43.6431i	−0.0561428	−	1.64956i
$701$			7.93733i			0.299789i	0.988702	+	0.149894i	$0.0478934\pi$
$701$			7.93733i			0.299789i	−0.988702	+	0.149894i	$0.952107\pi$
$702$	2.15861	−	1.29095i	0.0814715	−	0.0487237i
$703$	2.23378	−	5.01715i	0.0842486	−	0.189225i
$704$	−9.02319	+	20.2664i	−0.340074	+	0.763819i
$705$	13.8334	−	8.52657i	0.520995	−	0.321129i
$706$	27.5488	−	37.9177i	1.03681	−	1.42705i
$707$	5.43781	−	5.48346i	0.204510	−	0.206227i
$708$	−5.48259	−	37.6103i	−0.206048	−	1.41348i
$709$	−25.3288	−	28.1305i	−0.951243	−	1.05646i	−0.998341	−	0.0575725i	$-0.981664\pi$
$709$	−25.3288	−	28.1305i	−0.951243	−	1.05646i	0.0470979	−	0.998890i	$-0.485003\pi$
$710$	−27.9071	+	15.6959i	−1.04734	+	0.589058i
$711$	6.49586	+	6.14550i	0.243614	+	0.230474i
$712$	20.9240	−	18.8401i	0.784160	−	0.706061i
$713$	−3.89650	+	11.9922i	−0.145925	+	0.449111i
$714$	56.8594	−	17.9640i	2.12791	−	0.672285i
$715$	0.470692	+	0.663433i	0.0176029	+	0.0248110i
$716$	−6.13190	+	5.52118i	−0.229160	+	0.206336i
$717$	10.3463	+	13.1036i	0.386389	+	0.489363i
$718$	28.5016	+	49.3662i	1.06367	+	1.84233i
$719$	15.4619	−	6.88409i	0.576632	−	0.256733i	−0.0976330	−	0.995222i	$-0.531127\pi$
$719$	15.4619	−	6.88409i	0.576632	−	0.256733i	0.674265	+	0.738489i	$0.264460\pi$
$720$	1.97562	+	0.0709758i	0.0736268	+	0.00264511i
$721$	19.1746	+	49.3342i	0.714099	+	1.83730i
$722$	−37.2323	−	51.2459i	−1.38564	−	1.90717i
$723$	26.7380	−	16.8990i	0.994397	−	0.628480i
$724$	21.8717	−	12.6276i	0.812855	−	0.469302i
$725$	−20.4530	−	19.2673i	−0.759604	−	0.715568i
$726$	−7.88240	−	30.9379i	−0.292543	−	1.14821i
$727$	12.1255	−	3.93981i	0.449710	−	0.146119i	−0.0754014	−	0.997153i	$-0.524024\pi$
$727$	12.1255	−	3.93981i	0.449710	−	0.146119i	0.525111	+	0.851034i	$0.324024\pi$
$728$	−1.29923	−	1.04314i	−0.0481528	−	0.0386613i
$729$	14.2129	+	22.9564i	0.526402	+	0.850236i
$730$	−10.3867	+	9.14259i	−0.384429	+	0.338383i
$731$	1.35154	−	12.8590i	0.0499884	−	0.475608i
$732$	−55.1813	−	15.5172i	−2.03956	−	0.573534i
$733$	−11.8679	−	26.6557i	−0.438350	−	0.984551i	−0.988740	−	0.149643i	$-0.952188\pi$
$733$	−11.8679	−	26.6557i	−0.438350	−	0.984551i	0.550390	−	0.834908i	$-0.314479\pi$
$734$	−3.39308	+	10.4428i	−0.125241	+	0.385451i
$735$	−22.5097	−	15.1101i	−0.830281	−	0.557345i
$736$	−2.61654	−	8.05288i	−0.0964470	−	0.296833i
$737$	−0.0700593	+	0.0630817i	−0.00258067	+	0.00232364i
$738$	−74.9260	+	14.0052i	−2.75806	+	0.515538i
$739$	−11.0065	+	12.2240i	−0.404881	+	0.449666i	−0.910759	−	0.412939i	$-0.864502\pi$
$739$	−11.0065	+	12.2240i	−0.404881	+	0.449666i	0.505877	+	0.862605i	$0.331169\pi$
$740$	2.35635	+	5.45698i	0.0866212	+	0.200603i
$741$	2.22648	−	1.10009i	0.0817917	−	0.0404129i
$742$	22.5356	−	59.4487i	0.827308	−	2.18243i
$743$			8.43453i			0.309433i	0.987959	+	0.154716i	$0.0494464\pi$
$743$			8.43453i			0.309433i	−0.987959	+	0.154716i	$0.950554\pi$
$744$	38.1349	+	15.1805i	1.39809	+	0.556545i
$745$	41.6010	+	19.0860i	1.52414	+	0.699258i
$746$	−3.97231	+	8.92196i	−0.145437	+	0.326656i
$747$	−13.8784	+	1.11360i	−0.507785	+	0.0407444i
$748$	−30.7018	+	9.97561i	−1.12257	+	0.364744i
$749$	−1.49061	+	5.65751i	−0.0544658	+	0.206721i
$750$	−40.6168	+	18.3892i	−1.48311	+	0.671477i
$751$	−7.47447	+	12.9462i	−0.272747	+	0.472412i	−0.969564	−	0.244837i	$-0.921266\pi$
$751$	−7.47447	+	12.9462i	−0.272747	+	0.472412i	0.696817	+	0.717249i	$0.254599\pi$
$752$	0.827364	−	0.918881i	0.0301709	−	0.0335081i
$753$	−11.9501	−	32.3161i	−0.435486	−	1.17766i
$754$	−2.70534	+	0.284343i	−0.0985227	+	0.0103552i
$755$	−2.02686	−	2.85682i	−0.0737649	−	0.103970i
$756$	27.8642	−	35.8200i	1.01341	−	1.30276i
$757$	21.5294			0.782499			0.391249	−	0.920285i	$-0.372043\pi$
$757$	21.5294			0.782499			0.391249	+	0.920285i	$0.372043\pi$
$758$	2.53895	+	5.70258i	0.0922189	+	0.207127i
$759$	−3.97390	−	2.65089i	−0.144244	−	0.0962211i
$760$	45.3737	+	5.28609i	1.64588	+	0.191747i
$761$	8.78049	+	1.86635i	0.318293	+	0.0676552i	0.364288	−	0.931286i	$-0.381312\pi$
$761$	8.78049	+	1.86635i	0.318293	+	0.0676552i	−0.0459950	+	0.998942i	$0.514646\pi$
$762$	−19.3173	−	39.0963i	−0.699792	−	1.41631i
$763$	−17.7820	−	34.5415i	−0.643751	−	1.25048i
$764$	12.7874	−	4.15489i	0.462633	−	0.150319i
$765$	−24.3403	−	29.0669i	−0.880027	−	1.05092i
$766$	−13.2689	−	62.4252i	−0.479424	−	2.25551i
$767$	1.38991	+	0.146086i	0.0501868	+	0.00527484i
$768$	−29.9747	+	7.63699i	−1.08162	+	0.275576i
$769$	−29.0332	+	39.9608i	−1.04696	+	1.44102i	−0.155554	+	0.987827i	$0.549716\pi$
$769$	−29.0332	+	39.9608i	−1.04696	+	1.44102i	−0.891411	+	0.453196i	$0.850284\pi$
$770$	19.6756	+	12.9765i	0.709061	+	0.467639i
$771$	10.2577	+	1.75453i	0.369423	+	0.0631879i
$772$	−1.23723	−	11.7715i	−0.0445289	−	0.423664i
$773$	−27.0025	+	29.9893i	−0.971212	+	1.07864i	0.0256653	+	0.999671i	$0.491830\pi$
$773$	−27.0025	+	29.9893i	−0.971212	+	1.07864i	−0.996877	+	0.0789694i	$0.974837\pi$
$774$	−7.56144	−	13.8758i	−0.271790	−	0.498756i
$775$	−39.4221	+	3.24791i	−1.41609	+	0.116668i
$776$	−25.9900			−0.932985
$777$	3.60323	+	0.796623i	0.129265	+	0.0285787i
$778$	−51.1210	+	37.1416i	−1.83278	+	1.33159i
$779$	−74.8489	+	7.86694i	−2.68174	+	0.281862i
$780$	−0.756694	+	2.57912i	−0.0270940	+	0.0923472i
$781$	1.12487	−	10.7025i	0.0402511	−	0.382964i
$782$	10.3699	−	17.9612i	0.370828	−	0.642293i
$783$	−3.49870	−	28.9909i	−0.125033	−	1.03605i
$784$	−1.96718	−	0.621044i	−0.0702563	−	0.0221801i
$785$	15.8471	−	11.2432i	0.565606	−	0.401286i
$786$	−63.0561	+	39.8529i	−2.24914	+	1.42150i
$787$	2.24641	+	10.5685i	0.0800758	+	0.376727i	0.999877	−	0.0156568i	$-0.00498392\pi$
$787$	2.24641	+	10.5685i	0.0800758	+	0.376727i	−0.919802	+	0.392384i	$0.871651\pi$
$788$	−4.46477	−	21.0051i	−0.159051	−	0.748275i
$789$	41.2666	−	26.0814i	1.46913	−	0.928523i
$790$	−15.3448	−	0.172770i	−0.545944	−	0.00614688i
$791$	−0.730047	+	15.1406i	−0.0259575	+	0.538339i
$792$	−9.44718	+	12.3508i	−0.335691	+	0.438868i
$793$	1.05387	−	1.82536i	0.0374241	−	0.0648204i
$794$	−0.584261	+	5.55887i	−0.0207346	+	0.197277i
$795$	−40.4050	+	1.16299i	−1.43302	+	0.0412469i
$796$	−41.7428	+	4.38735i	−1.47954	+	0.155506i
$797$	0.144534	−	0.105010i	0.00511965	−	0.00371964i	−0.585222	−	0.810873i	$-0.698993\pi$
$797$	0.144534	−	0.105010i	0.00511965	−	0.00371964i	0.590342	+	0.807153i	$0.298993\pi$
$798$	48.5825	−	53.0803i	1.71980	−	1.87902i
$799$	−23.7128			−0.838898
$800$	20.1347	−	17.3246i	0.711867	−	0.612516i
$801$	−24.7609	+	13.4931i	−0.874883	+	0.476755i
$802$	17.6815	−	19.6373i	0.624356	−	0.693417i
$803$	−0.486135	−	4.62526i	−0.0171553	−	0.163222i
$804$	−0.307046	−	0.0525187i	−0.0108287	−	0.00185219i
$805$	−9.32358	+	1.40913i	−0.328613	+	0.0496651i
$806$	−2.25085	+	3.09802i	−0.0792827	+	0.109123i
$807$	−6.88993	+	1.75542i	−0.242537	+	0.0617938i
$808$	−8.69543	−	0.913927i	−0.305904	−	0.0321518i
$809$	−0.434561	−	2.04445i	−0.0152784	−	0.0718790i	0.969848	−	0.243711i	$-0.0783648\pi$
$809$	−0.434561	−	2.04445i	−0.0152784	−	0.0718790i	−0.985126	+	0.171832i	$0.945031\pi$
$810$	−44.6561	−	12.3590i	−1.56906	−	0.434252i
$811$	0.00276239		0.000897554i	9.70006e−5		3.15174e-5i	−0.308968	−	0.951072i	$-0.599984\pi$
$811$	0.00276239		0.000897554i	9.70006e−5		3.15174e-5i	0.309065	+	0.951041i	$0.399984\pi$
$812$	−43.6384	+	22.4651i	−1.53141	+	0.788370i
$813$	13.9721	+	28.2781i	0.490023	+	0.991757i
$814$	−3.13809	−	0.667021i	−0.109990	−	0.0233791i
$815$	26.7406	+	24.6281i	0.936681	+	0.862683i
$816$	−2.39981	−	1.60085i	−0.0840103	−	0.0560411i
$817$	−6.34623	−	14.2539i	−0.222027	−	0.498680i
$818$	−40.4833			−1.41546
$819$	1.02338	+	1.31805i	0.0357598	+	0.0460564i
$820$	48.6174	−	65.3559i	1.69779	−	2.28233i
$821$	7.62624	−	0.801550i	0.266158	−	0.0279743i	0.0294904	−	0.999565i	$-0.490612\pi$
$821$	7.62624	−	0.801550i	0.266158	−	0.0279743i	0.236667	+	0.971591i	$0.423945\pi$
$822$	−1.97939	−	5.35278i	−0.0690392	−	0.186699i
$823$	−24.3984	+	27.0972i	−0.850476	+	0.944550i	−0.999016	−	0.0443569i	$-0.985876\pi$
$823$	−24.3984	+	27.0972i	−0.850476	+	0.944550i	0.148539	+	0.988906i	$0.452543\pi$
$824$	29.9628	−	51.8971i	1.04380	−	1.80792i
$825$	2.85841	−	14.7102i	0.0995169	−	0.512143i
$826$	39.0703	−	10.6441i	1.35943	−	0.370354i
$827$	31.9576	−	10.3836i	1.11127	−	0.361075i	0.304843	−	0.952403i	$-0.401396\pi$
$827$	31.9576	−	10.3836i	1.11127	−	0.361075i	0.806431	+	0.591328i	$0.201396\pi$
$828$	−1.26246	−	15.7336i	−0.0438735	−	0.546781i
$829$	3.75690	−	8.43814i	0.130483	−	0.293069i	−0.836475	−	0.548004i	$-0.815388\pi$
$829$	3.75690	−	8.43814i	0.130483	−	0.293069i	0.966958	+	0.254936i	$0.0820543\pi$
$830$	16.1867	−	17.5751i	0.561848	−	0.610041i
$831$	26.5150	+	10.5549i	0.919796	+	0.366147i
$832$		−	2.69537i		−	0.0934453i
$833$	16.3926	+	36.0053i	0.567969	+	1.24751i
$834$	38.5690	−	19.0568i	1.33554	−	0.659883i
$835$	−4.72207	−	2.79764i	−0.163414	−	0.0968163i
$836$	−26.0662	+	28.9494i	−0.901518	+	1.00124i
$837$	−33.6244	−	23.6480i	−1.16223	−	0.817394i
$838$	8.20715	−	7.38975i	0.283511	−	0.255275i
$839$	1.85884	+	5.72092i	0.0641743	+	0.197508i	0.978003	−	0.208592i	$-0.0668882\pi$
$839$	1.85884	+	5.72092i	0.0641743	+	0.197508i	−0.913828	+	0.406101i	$0.866888\pi$
$840$	2.61550	+	30.5827i	0.0902434	+	1.05520i
$841$	−0.797886	+	2.45564i	−0.0275133	+	0.0846772i
$842$	20.6807	+	46.4496i	0.712705	+	1.60076i
$843$	−12.3291	−	3.46700i	−0.424637	−	0.119410i
$844$	0.282190	−	2.68486i	0.00971338	−	0.0924166i
$845$	24.9241	+	14.7666i	0.857416	+	0.507985i
$846$	−23.8587	+	16.4514i	−0.820280	+	0.565611i
$847$	19.7428	−	7.67336i	0.678369	−	0.263660i
$848$	−2.92518	+	0.950447i	−0.100451	+	0.0326385i
$849$	−4.85989	−	19.0748i	−0.166791	−	0.654644i
$850$	64.5354	+	8.25590i	2.21354	+	0.283175i
$851$	1.11155	−	0.641753i	0.0381034	−	0.0219990i
$852$	30.0582	−	18.9974i	1.02978	−	0.650842i
$853$	−18.4644	−	25.4140i	−0.632208	−	0.870160i	0.365962	−	0.930630i	$-0.380740\pi$
$853$	−18.4644	−	25.4140i	−0.632208	−	0.870160i	−0.998170	+	0.0604699i	$0.980740\pi$
$854$	9.30149	−	60.3590i	0.318291	−	2.06544i
$855$	−42.9750	−	15.6905i	−1.46971	−	0.536603i
$856$	6.05125	−	2.69419i	0.206827	−	0.0920855i
$857$	−17.1105	−	29.6362i	−0.584483	−	1.01235i	−0.994940	−	0.100474i	$-0.967964\pi$
$857$	−17.1105	−	29.6362i	−0.584483	−	1.01235i	0.410457	−	0.911880i	$-0.365369\pi$
$858$	−0.899004	−	1.13859i	−0.0306915	−	0.0388708i
$859$	8.72862	−	7.85928i	0.297817	−	0.268155i	−0.506652	−	0.862151i	$-0.669117\pi$
$859$	8.72862	−	7.85928i	0.297817	−	0.268155i	0.804468	+	0.593996i	$0.202450\pi$
$860$	16.0008	+	5.39887i	0.545621	+	0.184100i
$861$	−15.2349	−	48.2213i	−0.519203	−	1.64338i
$862$	−17.5205	+	53.9225i	−0.596750	+	1.83661i
$863$	−19.5643	+	17.6158i	−0.665978	+	0.599649i	−0.931187	−	0.364542i	$-0.881226\pi$
$863$	−19.5643	+	17.6158i	−0.665978	+	0.599649i	0.265209	+	0.964191i	$0.414559\pi$
$864$	27.6009	−	0.424595i	0.939001	−	0.0144450i
$865$	37.6920	+	4.39116i	1.28157	+	0.149304i
$866$	−18.3488	−	20.3784i	−0.623518	−	0.692487i
$867$	3.73290	+	25.6076i	0.126776	+	0.869680i
$868$	−17.6036	+	66.8133i	−0.597505	+	2.26779i
$869$	3.03165	−	4.17271i	0.102842	−	0.141549i
$870$	38.1901	+	32.4464i	1.29477	+	1.10004i
$871$	0.00465884	−	0.0104639i	0.000157859	−	0.000354557i
$872$	−17.8903	+	40.1823i	−0.605842	+	1.36074i
$873$	25.3194	+	6.03774i	0.856931	+	0.204346i
$874$		−	25.0274i		−	0.846563i
$875$	−15.3695	−	25.2741i	−0.519582	−	0.854420i
$876$	10.9994	−	10.7315i	0.371634	−	0.362584i
$877$	0.0978611	+	0.0208010i	0.00330453	+	0.000702400i	0.209564	−	0.977795i	$-0.432796\pi$
$877$	0.0978611	+	0.0208010i	0.00330453	+	0.000702400i	−0.206259	+	0.978497i	$0.566129\pi$
$878$	76.5320	+	34.0742i	2.58283	+	1.14995i
$879$	16.6111	+	44.9206i	0.560278	+	1.51513i
$880$	−0.106413	−	1.13527i	−0.00358719	−	0.0382698i
$881$	17.9086	+	13.0114i	0.603357	+	0.438364i	0.847069	−	0.531483i	$-0.178365\pi$
$881$	17.9086	+	13.0114i	0.603357	+	0.438364i	−0.243712	+	0.969848i	$0.578365\pi$
$882$	41.4732	+	24.8541i	1.39647	+	0.836882i
$883$	−21.5085	−	15.6269i	−0.723820	−	0.525886i	0.163782	−	0.986497i	$-0.447631\pi$
$883$	−21.5085	−	15.6269i	−0.723820	−	0.525886i	−0.887602	+	0.460610i	$0.847631\pi$
$884$	2.91476	−	2.62446i	0.0980340	−	0.0882702i
$885$	−15.7261	−	20.3849i	−0.528628	−	0.685232i
$886$	−11.1785	+	12.4150i	−0.375549	+	0.417089i
$887$	−13.2662	−	14.7336i	−0.445434	−	0.494705i	0.478055	−	0.878330i	$-0.341342\pi$
$887$	−13.2662	−	14.7336i	−0.445434	−	0.494705i	−0.923489	+	0.383625i	$0.874675\pi$
$888$	−1.85075	−	3.74573i	−0.0621071	−	0.125698i
$889$	24.1983	−	15.8587i	0.811584	−	0.531884i
$890$	15.4711	−	45.8521i	0.518593	−	1.53697i
$891$	12.0727	−	9.83749i	0.404449	−	0.329568i
$892$	80.0529	+	8.41390i	2.68037	+	0.281718i
$893$	−24.7812	+	14.3074i	−0.829272	+	0.478780i
$894$	−75.8400	−	30.1899i	−2.53647	−	1.00970i
$895$	−1.78693	+	5.29597i	−0.0597304	+	0.177025i
$896$	−18.1087	−	46.5919i	−0.604970	−	1.55653i
$897$	0.572084	+	0.0978521i	0.0191013	+	0.00326719i
$898$	27.6597	+	5.87924i	0.923015	+	0.196193i
$899$	22.2295	+	38.5026i	0.741394	+	1.28413i
$900$	44.0012	−	22.7082i	1.46671	−	0.756939i
$901$	51.0826	+	29.4926i	1.70181	+	0.982540i
$902$	13.5859	+	41.8130i	0.452359	+	1.39222i
$903$	8.53171	−	6.09308i	0.283918	−	0.202765i
$904$	13.8842	−	10.0875i	0.461782	−	0.335504i
$905$	8.72005	−	14.7184i	0.289864	−	0.489255i
$906$	3.87122	+	4.90291i	0.128613	+	0.162888i
$907$	20.2662	+	35.1022i	0.672930	+	1.16555i	0.977069	+	0.212921i	$0.0682976\pi$
$907$	20.2662	+	35.1022i	0.672930	+	1.16555i	−0.304140	+	0.952627i	$0.598369\pi$
$908$	−86.8709	+	38.6774i	−2.88291	+	1.28355i
$909$	8.25876	+	2.91039i	0.273926	+	0.0965314i
$910$	−2.82516	−	0.467987i	−0.0936533	−	0.0155136i
$911$	8.52956	−	2.77142i	0.282597	−	0.0918213i	−0.164289	−	0.986412i	$-0.552533\pi$
$911$	8.52956	−	2.77142i	0.282597	−	0.0918213i	0.446886	+	0.894591i	$0.352533\pi$
$912$	−3.47384	−	0.225022i	−0.115030	−	0.00745123i
$913$	1.66966	+	7.85513i	0.0552576	+	0.259967i
$914$	−7.73977	−	6.96892i	−0.256009	−	0.230511i
$915$	−37.7324	+	9.16239i	−1.24739	+	0.302899i
$916$	12.4962	+	4.06027i	0.412887	+	0.134155i
$917$	−31.3054	−	38.3302i	−1.03379	−	1.26578i
$918$	46.0099	+	49.5449i	1.51855	+	1.63523i
$919$	−10.0612	+	4.47951i	−0.331887	+	0.147766i	−0.565913	−	0.824465i	$-0.691476\pi$
$919$	−10.0612	+	4.47951i	−0.331887	+	0.147766i	0.234027	+	0.972230i	$0.424810\pi$
$920$	7.85277	+	7.23240i	0.258898	+	0.238445i
$921$	−6.72090	+	2.48531i	−0.221461	+	0.0818937i
$922$	−23.6238	+	2.48296i	−0.778009	+	0.0817720i
$923$	0.404039	+	1.24351i	0.0132991	+	0.0409305i
$924$	−22.5612	−	13.2719i	−0.742210	−	0.436615i
$925$	3.20330	+	2.43939i	0.105324	+	0.0802066i
$926$	65.5355	+	37.8370i	2.15363	+	1.24340i
$927$	−41.2460	+	43.5974i	−1.35470	+	1.43193i
$928$	−27.2736	−	12.1430i	−0.895299	−	0.398613i
$929$	1.79868	+	17.1133i	0.0590128	+	0.561469i	0.983583	+	0.180457i	$0.0577577\pi$
$929$	1.79868	+	17.1133i	0.0590128	+	0.561469i	−0.924570	+	0.381012i	$0.875576\pi$
$930$	69.9171	−	9.38943i	2.29267	−	0.307891i
$931$	38.8555	+	27.7369i	1.27344	+	0.909041i
$932$		−	17.9141i		−	0.586795i
$933$	−40.5912	−	16.1583i	−1.32890	−	0.528999i
$934$	−12.8392	−	60.4036i	−0.420111	−	1.97647i
$935$	−14.8141	+	16.0848i	−0.484472	+	0.526028i
$936$	0.438233	−	1.83774i	0.0143241	−	0.0600684i
$937$	50.9043	+	16.5398i	1.66297	+	0.540332i	0.981492	−	0.191504i	$-0.0613366\pi$
$937$	50.9043	+	16.5398i	1.66297	+	0.540332i	0.681480	+	0.731837i	$0.261337\pi$
$938$	0.0159841	−	0.331498i	0.000521899	−	0.0108238i
$939$	47.1390	+	24.7551i	1.53832	+	0.807852i
$940$	6.77970	−	30.2189i	0.221129	−	0.985633i
$941$	−54.9435	+	11.6786i	−1.79111	+	0.380712i	−0.979172	−	0.203035i	$-0.934920\pi$
$941$	−54.9435	+	11.6786i	−1.79111	+	0.380712i	−0.811936	+	0.583746i	$0.801586\pi$
$942$	−27.1969	+	21.4740i	−0.886122	+	0.699660i
$943$	−15.2325	−	8.79451i	−0.496040	−	0.286389i
$944$	−1.58489	−	1.15149i	−0.0515837	−	0.0374777i
$945$	4.55667	−	30.4013i	0.148228	−	0.988953i
$946$	−7.37384	+	5.35741i	−0.239744	+	0.174184i
$947$	−6.74901	+	0.709349i	−0.219313	+	0.0230507i	−0.213548	−	0.976933i	$-0.568502\pi$
$947$	−6.74901	+	0.709349i	−0.219313	+	0.0230507i	−0.00576549	+	0.999983i	$0.501835\pi$
$948$	17.0288	−	0.682097i	0.553071	−	0.0221535i
$949$	0.282530	+	0.489356i	0.00917131	+	0.0158852i
$950$	72.4245	−	30.3104i	2.34976	−	0.983400i
$951$	28.6229	−	27.9258i	0.928160	−	0.905557i
$952$	20.1675	−	39.9933i	0.653632	−	1.29619i
$953$	33.6400	+	46.3015i	1.08971	+	1.49985i	0.848364	+	0.529414i	$0.177588\pi$
$953$	33.6400	+	46.3015i	1.08971	+	1.49985i	0.241344	+	0.970440i	$0.422412\pi$
$954$	71.8583	−	5.76587i	2.32650	−	0.186677i
$955$	6.17013	−	6.69938i	0.199661	−	0.216787i
$956$	31.6453	+	3.32606i	1.02348	+	0.107572i
$957$	−16.3215	+	4.15840i	−0.527598	+	0.134422i
$958$	2.29107	−	3.15339i	0.0740211	−	0.101881i
$959$	3.36643	−	1.73304i	0.108708	−	0.0559629i
$960$	−35.9291	+	34.2731i	−1.15961	+	1.10616i
$961$	30.8960	+	6.56714i	0.996644	+	0.211843i
$962$	0.381274	−	0.0810422i	0.0122928	−	0.00261291i
$963$	−6.52100	+	1.21891i	−0.210136	+	0.0392787i
$964$	12.5336	−	58.9658i	0.403679	−	1.89916i
$965$	−4.63939	−	6.53915i	−0.149347	−	0.210503i
$966$	16.4772	−	3.36228i	0.530146	−	0.108180i
$967$	34.9711	+	25.4080i	1.12460	+	0.817067i	0.984899	−	0.173128i	$-0.0553874\pi$
$967$	34.9711	+	25.4080i	1.12460	+	0.817067i	0.139696	+	0.990194i	$0.455387\pi$
$968$	−20.7684	−	11.9906i	−0.667521	−	0.385394i
$969$	41.3707	+	52.3961i	1.32902	+	1.68321i
$970$	−38.9335	+	21.8976i	−1.25008	+	0.703088i
$971$	−1.71934	−	16.3584i	−0.0551762	−	0.524966i	−0.986846	−	0.161661i	$-0.948315\pi$
$971$	−1.71934	−	16.3584i	−0.0551762	−	0.524966i	0.931670	−	0.363305i	$-0.118352\pi$
$972$	50.2320	+	11.1648i	1.61119	+	0.358111i
$973$	15.6448	+	23.8719i	0.501551	+	0.765299i
$974$			67.5248i			2.16363i
$975$	0.409681	+	1.77401i	0.0131203	+	0.0568138i
$976$	−2.55868	+	1.47726i	−0.0819014	+	0.0472858i
$977$	4.08852	+	3.68132i	0.130803	+	0.117776i	0.731936	−	0.681373i	$-0.238617\pi$
$977$	4.08852	+	3.68132i	0.130803	+	0.117776i	−0.601133	+	0.799149i	$0.705284\pi$
$978$	−49.8790	−	41.4195i	−1.59496	−	1.32445i
$979$	9.56009	+	13.1583i	0.305542	+	0.420542i
$980$	−50.5710	+	10.5960i	−1.61543	+	0.338477i
$981$	26.7635	−	34.9894i	0.854492	−	1.11713i
$982$	−33.1537	+	57.4239i	−1.05798	+	1.83247i
$983$	3.53131	−	33.5982i	0.112631	−	1.07162i	−0.781529	−	0.623869i	$-0.785560\pi$
$983$	3.53131	−	33.5982i	0.112631	−	1.07162i	0.894160	−	0.447747i	$-0.147774\pi$
$984$	−31.7728	+	47.6301i	−1.01288	+	1.51839i
$985$	−9.61114	−	10.9190i	−0.306236	−	0.347908i
$986$	−22.5972	−	69.5471i	−0.719642	−	2.21483i
$987$	−12.7488	−	14.3930i	−0.405798	−	0.458135i
$988$	1.46259	−	4.50137i	0.0465310	−	0.143208i
$989$	0.758145	−	3.56679i	0.0241076	−	0.113417i
$990$	−3.74600	+	26.4614i	−0.119056	+	0.840999i
$991$	16.4732	−	3.50149i	0.523289	−	0.111229i	0.0613090	−	0.998119i	$-0.480472\pi$
$991$	16.4732	−	3.50149i	0.523289	−	0.111229i	0.461980	+	0.886890i	$0.347139\pi$
$992$	−38.3938	+	17.0940i	−1.21901	+	0.542736i
$993$	−19.0892	−	19.5657i	−0.605778	−	0.620898i
$994$	23.9643	+	29.3419i	0.760103	+	0.930669i
$995$	−23.1885	+	16.4518i	−0.735125	+	0.521556i
$996$	−16.9520	+	20.4143i	−0.537146	+	0.646852i
$997$	−22.9323	+	51.5068i	−0.726273	+	1.63124i	0.0483639	+	0.998830i	$0.484599\pi$
$997$	−22.9323	+	51.5068i	−0.726273	+	1.63124i	−0.774637	+	0.632406i	$0.782067\pi$
$998$	−10.0946	−	9.08919i	−0.319538	−	0.287713i
$999$	0.932825	+	4.07903i	0.0295133	+	0.129055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bm.a.131.9	✓	608
3.2	odd	2	inner	525.2.bm.a.131.68	yes	608
7.3	odd	6	inner	525.2.bm.a.206.9	yes	608
21.17	even	6	inner	525.2.bm.a.206.68	yes	608
25.21	even	5	inner	525.2.bm.a.446.68	yes	608
75.71	odd	10	inner	525.2.bm.a.446.9	yes	608
175.171	odd	30	inner	525.2.bm.a.521.68	yes	608
525.521	even	30	inner	525.2.bm.a.521.9	yes	608

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bm.a.131.9	✓	608	1.1	even	1	trivial
525.2.bm.a.131.68	yes	608	3.2	odd	2	inner
525.2.bm.a.206.9	yes	608	7.3	odd	6	inner
525.2.bm.a.206.68	yes	608	21.17	even	6	inner
525.2.bm.a.446.9	yes	608	75.71	odd	10	inner
525.2.bm.a.446.68	yes	608	25.21	even	5	inner
525.2.bm.a.521.9	yes	608	525.521	even	30	inner
525.2.bm.a.521.68	yes	608	175.171	odd	30	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.bm (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.478695 + 2.25208i) q^{2} +(-0.600734 - 1.62454i) q^{3} +(-3.01563 - 1.34265i) q^{4} +(-2.22631 + 0.208681i) q^{5} +(3.94616 - 0.575244i) q^{6} +(0.695446 + 2.55272i) q^{7} +(1.76069 - 2.42338i) q^{8} +(-2.27824 + 1.95183i) q^{9} +O(q^{10})\)	\(q+(-0.478695 + 2.25208i) q^{2} +(-0.600734 - 1.62454i) q^{3} +(-3.01563 - 1.34265i) q^{4} +(-2.22631 + 0.208681i) q^{5} +(3.94616 - 0.575244i) q^{6} +(0.695446 + 2.55272i) q^{7} +(1.76069 - 2.42338i) q^{8} +(-2.27824 + 1.95183i) q^{9} +(0.595755 - 5.11372i) q^{10} +(1.28591 + 1.15784i) q^{11} +(-0.369585 + 5.70558i) q^{12} +(-0.199947 - 0.0649666i) q^{13} +(-6.08183 + 0.344230i) q^{14} +(1.67643 + 3.49136i) q^{15} +(0.197191 + 0.219003i) q^{16} +(0.590755 - 5.62066i) q^{17} +(-3.30510 - 6.06511i) q^{18} +(-2.77393 - 6.23035i) q^{19} +(6.99392 + 2.35984i) q^{20} +(3.72920 - 2.66328i) q^{21} +(-3.22310 + 2.34172i) q^{22} +(0.331384 - 1.55904i) q^{23} +(-4.99458 - 1.40450i) q^{24} +(4.91290 - 0.929178i) q^{25} +(0.242024 - 0.419197i) q^{26} +(4.53943 + 2.52855i) q^{27} +(1.33018 - 8.63179i) q^{28} +(-3.30323 - 4.54650i) q^{29} +(-8.66532 + 2.10416i) q^{30} +(-7.86781 - 0.826940i) q^{31} +(4.60069 - 2.65621i) q^{32} +(1.10846 - 2.78455i) q^{33} +(12.3754 + 4.02101i) q^{34} +(-2.08098 - 5.53801i) q^{35} +(9.49094 - 2.82713i) q^{36} +(0.538835 + 0.598437i) q^{37} +(15.3591 - 3.26468i) q^{38} +(0.0145741 + 0.363849i) q^{39} +(-3.41412 + 5.76262i) q^{40} +(3.41013 - 10.4953i) q^{41} +(4.21277 + 9.67336i) q^{42} +2.28781 q^{43} +(-2.32326 - 5.21812i) q^{44} +(4.66475 - 4.82080i) q^{45} +(3.35245 + 1.49261i) q^{46} +(-0.438575 - 4.17277i) q^{47} +(0.237319 - 0.451906i) q^{48} +(-6.03271 + 3.55055i) q^{49} +(-0.259198 + 11.5091i) q^{50} +(-9.48585 + 2.41682i) q^{51} +(0.515739 + 0.464373i) q^{52} +(-4.24505 + 9.53454i) q^{53} +(-7.86751 + 9.01276i) q^{54} +(-3.10444 - 2.30935i) q^{55} +(7.41067 + 2.80921i) q^{56} +(-8.45504 + 8.24913i) q^{57} +(11.8203 - 5.26275i) q^{58} +(-6.50233 + 1.38211i) q^{59} +(-0.367835 - 12.7795i) q^{60} +(-2.08443 + 9.80649i) q^{61} +(5.62861 - 17.3231i) q^{62} +(-6.56685 - 4.45830i) q^{63} +(3.96181 + 12.1932i) q^{64} +(0.458701 + 0.102911i) q^{65} +(5.74043 + 3.82929i) q^{66} +(-0.00569497 + 0.0541840i) q^{67} +(-9.32806 + 16.1567i) q^{68} +(-2.73179 + 0.398222i) q^{69} +(13.4682 - 2.03552i) q^{70} +(-3.65554 - 5.03142i) q^{71} +(0.718753 + 8.95760i) q^{72} +(-1.99738 - 1.79844i) q^{73} +(-1.60567 + 0.927031i) q^{74} +(-4.46083 - 7.42300i) q^{75} +22.5129i q^{76} +(-2.06135 + 4.08776i) q^{77} +(-0.826393 - 0.141350i) q^{78} +(-0.311572 - 2.96441i) q^{79} +(-0.484710 - 0.446418i) q^{80} +(1.38074 - 8.89346i) q^{81} +(22.0039 + 12.7039i) q^{82} +(3.75466 + 2.72792i) q^{83} +(-14.8217 + 3.02447i) q^{84} +(-0.142278 + 12.6366i) q^{85} +(-1.09516 + 5.15234i) q^{86} +(-5.40160 + 8.09745i) q^{87} +(5.06996 - 1.07765i) q^{88} +(9.19415 + 1.95428i) q^{89} +(8.62384 + 12.8131i) q^{90} +(0.0267892 - 0.555588i) q^{91} +(-3.09257 + 4.25656i) q^{92} +(3.38306 + 13.2783i) q^{93} +(9.60735 + 1.00977i) q^{94} +(7.47579 + 13.2918i) q^{95} +(-7.07890 - 5.87831i) q^{96} +(-5.09988 - 7.01939i) q^{97} +(-5.10830 - 15.2858i) q^{98} +(-5.18950 - 0.127956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9}+O(q^{10}) \) 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9	\( 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9} - 30 q^{10} + 3 q^{12} + 16 q^{15} + 50 q^{16} - 8 q^{18} - 18 q^{19} - 21 q^{21} - 24 q^{22} - 66 q^{24} - 10 q^{25} - 30 q^{28} - 7 q^{30} - 36 q^{31} + 36 q^{33} - 100 q^{36} - 14 q^{37} - 31 q^{39} - 30 q^{40} + 20 q^{42} - 96 q^{43} - 117 q^{45} + 42 q^{46} - 28 q^{49} - 8 q^{51} - 66 q^{52} + 3 q^{54} + 48 q^{57} - 38 q^{58} - 49 q^{60} - 18 q^{61} + 4 q^{63} - 32 q^{64} - 3 q^{66} - 22 q^{67} - 270 q^{70} + 45 q^{72} + 102 q^{73} + 135 q^{75} + 58 q^{78} - 34 q^{79} - 55 q^{81} + 108 q^{82} - 75 q^{84} - 96 q^{85} - 9 q^{87} + 36 q^{88} + 38 q^{91} - 22 q^{93} + 30 q^{94} - 81 q^{96} + 36 q^{99}+O(q^{100}) \) 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9 - 30 * q^10 + 3 * q^12 + 16 * q^15 + 50 * q^16 - 8 * q^18 - 18 * q^19 - 21 * q^21 - 24 * q^22 - 66 * q^24 - 10 * q^25 - 30 * q^28 - 7 * q^30 - 36 * q^31 + 36 * q^33 - 100 * q^36 - 14 * q^37 - 31 * q^39 - 30 * q^40 + 20 * q^42 - 96 * q^43 - 117 * q^45 + 42 * q^46 - 28 * q^49 - 8 * q^51 - 66 * q^52 + 3 * q^54 + 48 * q^57 - 38 * q^58 - 49 * q^60 - 18 * q^61 + 4 * q^63 - 32 * q^64 - 3 * q^66 - 22 * q^67 - 270 * q^70 + 45 * q^72 + 102 * q^73 + 135 * q^75 + 58 * q^78 - 34 * q^79 - 55 * q^81 + 108 * q^82 - 75 * q^84 - 96 * q^85 - 9 * q^87 + 36 * q^88 + 38 * q^91 - 22 * q^93 + 30 * q^94 - 81 * q^96 + 36 * q^99

Introduction

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