LMFDB - Embedded newform 525.2.bs.a.2.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 3, 20]))

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

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

chi := DirichletCharacter("525.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bs (of order $60$, degree $16$, 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:	$1216$
Relative dimension:	$76$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			2.8
Character	$\chi$	$=$	525.2
Dual form			525.2.bs.a.263.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.82030 - 1.47405i) q^{2} +(1.15573 - 1.29008i) q^{3} +(0.724840 + 3.41011i) q^{4} +(-1.83998 - 1.27061i) q^{5} +(-4.00540 + 0.644724i) q^{6} +(0.479622 + 2.60192i) q^{7} +(1.58048 - 3.10187i) q^{8} +(-0.328590 - 2.98195i) q^{9} +O(q^{10})$	\(q+(-1.82030 - 1.47405i) q^{2} +(1.15573 - 1.29008i) q^{3} +(0.724840 + 3.41011i) q^{4} +(-1.83998 - 1.27061i) q^{5} +(-4.00540 + 0.644724i) q^{6} +(0.479622 + 2.60192i) q^{7} +(1.58048 - 3.10187i) q^{8} +(-0.328590 - 2.98195i) q^{9} +(1.47637 + 5.02511i) q^{10} +(-0.430837 + 0.967676i) q^{11} +(5.23701 + 3.00605i) q^{12} +(-6.32773 + 1.00221i) q^{13} +(2.96229 - 5.44324i) q^{14} +(-3.76571 + 0.905237i) q^{15} +(-1.07948 + 0.480614i) q^{16} +(0.167881 + 3.20335i) q^{17} +(-3.79740 + 5.91239i) q^{18} +(-0.173056 + 0.814164i) q^{19} +(2.99923 - 7.19553i) q^{20} +(3.91098 + 2.38836i) q^{21} +(2.21065 - 1.12638i) q^{22} +(-3.32232 + 4.10272i) q^{23} +(-2.17504 - 5.62386i) q^{24} +(1.77109 + 4.67582i) q^{25} +(12.9957 + 7.50304i) q^{26} +(-4.22670 - 3.02242i) q^{27} +(-8.52516 + 3.52153i) q^{28} +(-1.92973 + 5.93910i) q^{29} +(8.18906 + 3.90303i) q^{30} +(2.39395 - 2.65875i) q^{31} +(-4.05196 - 1.08572i) q^{32} +(0.750445 + 1.67418i) q^{33} +(4.41630 - 6.07851i) q^{34} +(2.42353 - 5.39690i) q^{35} +(9.93059 - 3.28196i) q^{36} +(-4.19920 - 1.61192i) q^{37} +(1.51513 - 1.22693i) q^{38} +(-6.02020 + 9.32154i) q^{39} +(-6.84934 + 3.69921i) q^{40} +(0.195079 - 0.268503i) q^{41} +(-3.59859 - 10.1125i) q^{42} +(-2.83047 + 2.83047i) q^{43} +(-3.61216 - 0.767789i) q^{44} +(-3.18430 + 5.90425i) q^{45} +(12.0952 - 2.57092i) q^{46} +(8.90311 + 0.466592i) q^{47} +(-0.627552 + 1.94806i) q^{48} +(-6.53993 + 2.49587i) q^{49} +(3.66847 - 11.1220i) q^{50} +(4.32659 + 3.48562i) q^{51} +(-8.00425 - 20.8518i) q^{52} +(-7.04869 - 4.57747i) q^{53} +(3.23867 + 11.7320i) q^{54} +(2.02227 - 1.23308i) q^{55} +(8.82884 + 2.62456i) q^{56} +(0.850328 + 1.16421i) q^{57} +(12.2672 - 7.96641i) q^{58} +(0.822175 - 7.82247i) q^{59} +(-5.81649 - 12.1853i) q^{60} +(-0.208933 - 1.98786i) q^{61} +(-8.27682 + 1.31092i) q^{62} +(7.60118 - 2.28517i) q^{63} +(7.16446 + 9.86103i) q^{64} +(12.9164 + 6.19604i) q^{65} +(1.10179 - 4.15370i) q^{66} +(10.2201 - 0.535612i) q^{67} +(-10.8021 + 2.89441i) q^{68} +(1.45313 + 9.02767i) q^{69} +(-12.3668 + 6.25155i) q^{70} +(9.31379 + 3.02623i) q^{71} +(-9.76895 - 3.69368i) q^{72} +(-1.07684 + 0.413358i) q^{73} +(5.26774 + 9.12399i) q^{74} +(8.07905 + 3.11913i) q^{75} -2.90182 q^{76} +(-2.72445 - 0.656883i) q^{77} +(24.6989 - 8.09390i) q^{78} +(-0.499299 + 0.449571i) q^{79} +(2.59689 + 0.487274i) q^{80} +(-8.78406 + 1.95968i) q^{81} +(-0.750887 + 0.201200i) q^{82} +(-4.74517 + 9.31293i) q^{83} +(-5.30971 + 15.0680i) q^{84} +(3.76132 - 6.10743i) q^{85} +(9.32453 - 0.980048i) q^{86} +(5.43165 + 9.35348i) q^{87} +(2.32067 + 2.86579i) q^{88} +(0.0615555 + 0.585661i) q^{89} +(14.4995 - 6.05367i) q^{90} +(-5.64259 - 15.9835i) q^{91} +(-16.3989 - 8.35564i) q^{92} +(-0.663236 - 6.16116i) q^{93} +(-15.5185 - 13.9729i) q^{94} +(1.35291 - 1.27816i) q^{95} +(-6.08362 + 3.97254i) q^{96} +(2.73593 - 1.39403i) q^{97} +(15.5836 + 5.09693i) q^{98} +(3.02713 + 0.966766i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9}+O(q^{10}) $ 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9	$ 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9} - 12 q^{10} - 64 q^{13} - 44 q^{15} - 140 q^{16} - 24 q^{18} - 20 q^{19} - 12 q^{21} + 8 q^{22} - 24 q^{25} - 80 q^{27} - 40 q^{28} - 50 q^{30} - 12 q^{31} - 6 q^{33} - 80 q^{34} + 8 q^{36} - 24 q^{37} - 50 q^{39} - 4 q^{40} - 34 q^{42} - 96 q^{43} + 30 q^{45} - 12 q^{46} - 44 q^{48} - 16 q^{51} - 136 q^{52} - 10 q^{54} - 40 q^{55} - 112 q^{57} - 76 q^{58} - 60 q^{60} - 12 q^{61} - 14 q^{63} - 80 q^{64} - 30 q^{66} - 32 q^{67} + 100 q^{69} - 100 q^{70} + 24 q^{72} - 72 q^{73} - 96 q^{75} - 64 q^{76} + 20 q^{78} - 20 q^{79} - 6 q^{81} - 204 q^{82} + 100 q^{84} - 56 q^{85} + 36 q^{87} - 140 q^{88} + 164 q^{90} - 24 q^{91} + 34 q^{93} - 20 q^{94} - 30 q^{96} - 240 q^{97}+O(q^{100}) $ 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9 - 12 * q^10 - 64 * q^13 - 44 * q^15 - 140 * q^16 - 24 * q^18 - 20 * q^19 - 12 * q^21 + 8 * q^22 - 24 * q^25 - 80 * q^27 - 40 * q^28 - 50 * q^30 - 12 * q^31 - 6 * q^33 - 80 * q^34 + 8 * q^36 - 24 * q^37 - 50 * q^39 - 4 * q^40 - 34 * q^42 - 96 * q^43 + 30 * q^45 - 12 * q^46 - 44 * q^48 - 16 * q^51 - 136 * q^52 - 10 * q^54 - 40 * q^55 - 112 * q^57 - 76 * q^58 - 60 * q^60 - 12 * q^61 - 14 * q^63 - 80 * q^64 - 30 * q^66 - 32 * q^67 + 100 * q^69 - 100 * q^70 + 24 * q^72 - 72 * q^73 - 96 * q^75 - 64 * q^76 + 20 * q^78 - 20 * q^79 - 6 * q^81 - 204 * q^82 + 100 * q^84 - 56 * q^85 + 36 * q^87 - 140 * q^88 + 164 * q^90 - 24 * q^91 + 34 * q^93 - 20 * q^94 - 30 * q^96 - 240 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.82030	−	1.47405i	−1.28714	−	1.04231i	−0.996336	−	0.0855266i	$-0.972743\pi$
$2$	−1.82030	−	1.47405i	−1.28714	−	1.04231i	−0.290808	−	0.956782i	$-0.593924\pi$
$3$	1.15573	−	1.29008i	0.667259	−	0.744825i
$3$	1.15573	−	1.29008i	0.667259	−	0.744825i
$4$	0.724840	+	3.41011i	0.362420	+	1.70505i
$5$	−1.83998	−	1.27061i	−0.822866	−	0.568235i
$5$	−1.83998	−	1.27061i	−0.822866	−	0.568235i
$6$	−4.00540	+	0.644724i	−1.63520	+	0.263207i
$7$	0.479622	+	2.60192i	0.181280	+	0.983432i
$7$	0.479622	+	2.60192i	0.181280	+	0.983432i
$8$	1.58048	−	3.10187i	0.558785	−	1.09668i
$9$	−0.328590	−	2.98195i	−0.109530	−	0.993984i
$10$	1.47637	+	5.02511i	0.466870	+	1.58908i
$11$	−0.430837	+	0.967676i	−0.129902	+	0.291765i	−0.966773	−	0.255635i	$-0.917716\pi$
$11$	−0.430837	+	0.967676i	−0.129902	+	0.291765i	0.836871	+	0.547400i	$0.184382\pi$
$12$	5.23701	+	3.00605i	1.51179	+	0.867773i
$13$	−6.32773	+	1.00221i	−1.75500	+	0.277964i	−0.949302	−	0.314366i	$-0.898208\pi$
$13$	−6.32773	+	1.00221i	−1.75500	+	0.277964i	−0.805695	+	0.592331i	$0.798208\pi$
$14$	2.96229	−	5.44324i	0.791705	−	1.45477i
$15$	−3.76571	+	0.905237i	−0.972301	+	0.233731i
$16$	−1.07948	+	0.480614i	−0.269869	+	0.120153i
$17$	0.167881	+	3.20335i	0.0407170	+	0.776927i	0.940335	+	0.340250i	$0.110512\pi$
$17$	0.167881	+	3.20335i	0.0407170	+	0.776927i	−0.899618	+	0.436677i	$0.856155\pi$
$18$	−3.79740	+	5.91239i	−0.895056	+	1.39356i
$19$	−0.173056	+	0.814164i	−0.0397017	+	0.186782i	−0.993530	−	0.113571i	$-0.963771\pi$
$19$	−0.173056	+	0.814164i	−0.0397017	+	0.186782i	0.953828	+	0.300353i	$0.0971044\pi$
$20$	2.99923	−	7.19553i	0.670648	−	1.60897i
$21$	3.91098	+	2.38836i	0.853446	+	0.521182i
$22$	2.21065	−	1.12638i	0.471312	−	0.240146i
$23$	−3.32232	+	4.10272i	−0.692752	+	0.855477i	−0.995218	−	0.0976831i	$-0.968857\pi$
$23$	−3.32232	+	4.10272i	−0.692752	+	0.855477i	0.302466	+	0.953160i	$0.402190\pi$
$24$	−2.17504	−	5.62386i	−0.443978	−	1.14796i
$25$	1.77109	+	4.67582i	0.354217	+	0.935163i
$26$	12.9957	+	7.50304i	2.54866	+	1.47147i
$27$	−4.22670	−	3.02242i	−0.813429	−	0.581664i
$28$	−8.52516	+	3.52153i	−1.61110	+	0.665507i
$29$	−1.92973	+	5.93910i	−0.358342	+	1.10286i	0.595704	+	0.803204i	$0.296873\pi$
$29$	−1.92973	+	5.93910i	−0.358342	+	1.10286i	−0.954046	+	0.299660i	$0.903127\pi$
$30$	8.18906	+	3.90303i	1.49511	+	0.712592i
$31$	2.39395	−	2.65875i	0.429966	−	0.477526i	−0.488762	−	0.872417i	$-0.662551\pi$
$31$	2.39395	−	2.65875i	0.429966	−	0.477526i	0.918728	+	0.394892i	$0.129218\pi$
$32$	−4.05196	−	1.08572i	−0.716292	−	0.191930i
$33$	0.750445	+	1.67418i	0.130636	+	0.291438i
$34$	4.41630	−	6.07851i	0.757389	−	1.04246i
$35$	2.42353	−	5.39690i	0.409651	−	0.912242i
$36$	9.93059	−	3.28196i	1.65510	−	0.546994i
$37$	−4.19920	−	1.61192i	−0.690344	−	0.264998i	−0.0121982	−	0.999926i	$-0.503883\pi$
$37$	−4.19920	−	1.61192i	−0.690344	−	0.264998i	−0.678146	+	0.734927i	$0.737216\pi$
$38$	1.51513	−	1.22693i	0.245786	−	0.199034i
$39$	−6.02020	+	9.32154i	−0.964003	+	1.49264i
$40$	−6.84934	+	3.69921i	−1.08298	+	0.584897i
$41$	0.195079	−	0.268503i	0.0304662	−	0.0419331i	−0.793512	−	0.608554i	$-0.791750\pi$
$41$	0.195079	−	0.268503i	0.0304662	−	0.0419331i	0.823978	+	0.566621i	$0.191750\pi$
$42$	−3.59859	−	10.1125i	−0.555275	−	1.56039i
$43$	−2.83047	+	2.83047i	−0.431642	+	0.431642i	−0.889187	−	0.457544i	$-0.848729\pi$
$43$	−2.83047	+	2.83047i	−0.431642	+	0.431642i	0.457544	+	0.889187i	$0.348729\pi$
$44$	−3.61216	−	0.767789i	−0.544554	−	0.115749i
$45$	−3.18430	+	5.90425i	−0.474688	+	0.880154i
$46$	12.0952	−	2.57092i	1.78334	−	0.379061i
$47$	8.90311	+	0.466592i	1.29865	+	0.0680595i	0.689088	−	0.724677i	$-0.258011\pi$
$47$	8.90311	+	0.466592i	1.29865	+	0.0680595i	0.609564	+	0.792737i	$0.291344\pi$
$48$	−0.627552	+	1.94806i	−0.0905793	+	0.281179i
$49$	−6.53993	+	2.49587i	−0.934275	+	0.356553i
$50$	3.66847	−	11.1220i	0.518800	−	1.57289i
$51$	4.32659	+	3.48562i	0.605844	+	0.488085i
$52$	−8.00425	−	20.8518i	−1.10999	−	2.89162i
$53$	−7.04869	−	4.57747i	−0.968212	−	0.628764i	−0.0393638	−	0.999225i	$-0.512533\pi$
$53$	−7.04869	−	4.57747i	−0.968212	−	0.628764i	−0.928848	+	0.370461i	$0.879200\pi$
$54$	3.23867	+	11.7320i	0.440727	+	1.59653i
$55$	2.02227	−	1.23308i	0.272683	−	0.166269i
$56$	8.82884	+	2.62456i	1.17980	+	0.350721i
$57$	0.850328	+	1.16421i	0.112629	+	0.154203i
$58$	12.2672	−	7.96641i	1.61076	−	1.04604i
$59$	0.822175	−	7.82247i	0.107038	−	1.01840i	−0.800758	−	0.598988i	$-0.795570\pi$
$59$	0.822175	−	7.82247i	0.107038	−	1.01840i	0.907796	−	0.419411i	$-0.137764\pi$
$60$	−5.81649	−	12.1853i	−0.750906	−	1.57312i
$61$	−0.208933	−	1.98786i	−0.0267511	−	0.254519i	−0.999722	−	0.0235906i	$-0.992490\pi$
$61$	−0.208933	−	1.98786i	−0.0267511	−	0.254519i	0.972971	−	0.230929i	$-0.0741765\pi$
$62$	−8.27682	+	1.31092i	−1.05116	+	0.166487i
$63$	7.60118	−	2.28517i	0.957659	−	0.287904i
$64$	7.16446	+	9.86103i	0.895557	+	1.23263i
$65$	12.9164	+	6.19604i	1.60208	+	0.768524i
$66$	1.10179	−	4.15370i	0.135621	−	0.511285i
$67$	10.2201	−	0.535612i	1.24858	−	0.0654354i	0.583442	−	0.812155i	$-0.301706\pi$
$67$	10.2201	−	0.535612i	1.24858	−	0.0654354i	0.665139	+	0.746719i	$0.268372\pi$
$68$	−10.8021	+	2.89441i	−1.30994	+	0.350999i
$69$	1.45313	+	9.02767i	0.174936	+	1.08680i
$70$	−12.3668	+	6.25155i	−1.47812	+	0.747203i
$71$	9.31379	+	3.02623i	1.10534	+	0.359148i	0.804157	−	0.594417i	$-0.202617\pi$
$71$	9.31379	+	3.02623i	1.10534	+	0.359148i	0.301187	+	0.953565i	$0.402617\pi$
$72$	−9.76895	−	3.69368i	−1.15128	−	0.435304i
$73$	−1.07684	+	0.413358i	−0.126034	+	0.0483799i	−0.420568	−	0.907261i	$-0.638169\pi$
$73$	−1.07684	+	0.413358i	−0.126034	+	0.0483799i	0.294534	+	0.955641i	$0.404836\pi$
$74$	5.26774	+	9.12399i	0.612362	+	1.06064i
$75$	8.07905	+	3.11913i	0.932888	+	0.360166i
$76$	−2.90182			−0.332862
$77$	−2.72445	−	0.656883i	−0.310480	−	0.0748588i
$78$	24.6989	−	8.09390i	2.79660	−	0.916454i
$79$	−0.499299	+	0.449571i	−0.0561755	+	0.0505807i	−0.696740	−	0.717323i	$-0.745367\pi$
$79$	−0.499299	+	0.449571i	−0.0561755	+	0.0505807i	0.640565	+	0.767904i	$0.278700\pi$
$80$	2.59689	+	0.487274i	0.290342	+	0.0544789i
$81$	−8.78406	+	1.95968i	−0.976006	+	0.217742i
$82$	−0.750887	+	0.201200i	−0.0829216	+	0.0222188i
$83$	−4.74517	+	9.31293i	−0.520851	+	1.02223i	0.469407	+	0.882982i	$0.344468\pi$
$83$	−4.74517	+	9.31293i	−0.520851	+	1.02223i	−0.990258	+	0.139245i	$0.955532\pi$
$84$	−5.30971	+	15.0680i	−0.579337	+	1.64406i
$85$	3.76132	−	6.10743i	0.407973	−	0.662444i
$86$	9.32453	−	0.980048i	1.00549	−	0.105681i
$87$	5.43165	+	9.35348i	0.582334	+	1.00280i
$88$	2.32067	+	2.86579i	0.247385	+	0.305495i
$89$	0.0615555	+	0.585661i	0.00652487	+	0.0620799i	0.997300	−	0.0734376i	$-0.0233970\pi$
$89$	0.0615555	+	0.585661i	0.00652487	+	0.0620799i	−0.990775	+	0.135518i	$0.956730\pi$
$90$	14.4995	−	6.05367i	1.52838	−	0.638113i
$91$	−5.64259	−	15.9835i	−0.591504	−	1.67553i
$92$	−16.3989	−	8.35564i	−1.70970	−	0.871136i
$93$	−0.663236	−	6.16116i	−0.0687744	−	0.638883i
$94$	−15.5185	−	13.9729i	−1.60061	−	1.44120i
$95$	1.35291	−	1.27816i	0.138805	−	0.131137i
$96$	−6.08362	+	3.97254i	−0.620907	+	0.405446i
$97$	2.73593	−	1.39403i	0.277792	−	0.141542i	−0.309545	−	0.950885i	$-0.600177\pi$
$97$	2.73593	−	1.39403i	0.277792	−	0.141542i	0.587336	+	0.809343i	$0.300177\pi$
$98$	15.5836	+	5.09693i	1.57418	+	0.514868i
$99$	3.02713	+	0.966766i	0.304238	+	0.0971637i
$100$	−14.6613	+	9.42881i	−1.46613	+	0.942881i
$101$	−11.5077	+	6.64398i	−1.14506	+	0.661100i	−0.947678	−	0.319227i	$-0.896577\pi$
$101$	−11.5077	+	6.64398i	−1.14506	+	0.661100i	−0.197381	+	0.980327i	$0.563244\pi$
$102$	−2.73771	−	12.7225i	−0.271073	−	1.25971i
$103$	−18.9806	−	0.994734i	−1.87022	−	0.0980140i	−0.916742	−	0.399480i	$-0.869191\pi$
$103$	−18.9806	−	0.994734i	−1.87022	−	0.0980140i	−0.953477	+	0.301466i	$0.902524\pi$
$104$	−6.89212	+	21.2118i	−0.675828	+	2.07999i
$105$	−4.16147	−	9.36388i	−0.406117	−	0.913821i
$106$	6.08329	+	18.7224i	0.590862	+	1.81848i
$107$	1.39847	+	5.21915i	0.135195	+	0.504555i	0.999997	+	0.00244166i	$0.000777205\pi$
$107$	1.39847	+	5.21915i	0.135195	+	0.504555i	−0.864802	+	0.502113i	$0.832556\pi$
$108$	7.24307	−	16.6043i	0.696965	−	1.59775i
$109$	−11.7324	−	1.23312i	−1.12376	−	0.118112i	−0.475632	−	0.879644i	$-0.657781\pi$
$109$	−11.7324	−	1.23312i	−1.12376	−	0.118112i	−0.648127	+	0.761532i	$0.724447\pi$
$110$	−5.49876	−	0.736354i	−0.524286	−	0.0702086i
$111$	−6.93263	+	3.55434i	−0.658016	+	0.337363i
$112$	−1.76826	−	2.57819i	−0.167085	−	0.243616i
$113$	−1.79721	−	11.3471i	−0.169067	−	1.06745i	−0.915598	−	0.402096i	$-0.868282\pi$
$113$	−1.79721	−	11.3471i	−0.169067	−	1.06745i	0.746531	−	0.665351i	$-0.231718\pi$
$114$	0.168247	−	3.37262i	0.0157578	−	0.315875i
$115$	11.3260	−	3.32757i	1.05615	−	0.310297i
$116$	−21.6517	−	2.27569i	−2.01031	−	0.211292i
$117$	5.06778	+	18.5397i	0.468516	+	1.71399i
$118$	−13.0273	+	13.0273i	−1.19926	+	1.19926i
$119$	−8.25433	+	1.97321i	−0.756673	+	0.180884i
$120$	−3.14370	+	13.1114i	−0.286979	+	1.19691i
$121$	6.60966	+	7.34077i	0.600878	+	0.667343i
$122$	−2.54988	+	3.92647i	−0.230855	+	0.355486i
$123$	−0.120931	−	0.561983i	−0.0109040	−	0.0506723i
$124$	10.8018	+	6.23645i	0.970035	+	0.560050i
$125$	2.68238	−	10.8538i	0.239919	−	0.970793i
$126$	−17.2048	−	7.04481i	−1.53273	−	0.627602i
$127$	−17.6774	−	2.79982i	−1.56862	−	0.248444i	−0.689226	−	0.724547i	$-0.742049\pi$
$127$	−17.6774	−	2.79982i	−1.56862	−	0.248444i	−0.879390	+	0.476103i	$0.842049\pi$
$128$	1.05510	−	20.1324i	0.0932582	−	1.77947i
$129$	0.380269	+	6.92277i	0.0334808	+	0.609516i
$130$	−14.3783	−	30.3179i	−1.26106	−	2.65906i
$131$	3.08127	−	14.4962i	0.269212	−	1.26654i	−0.610874	−	0.791728i	$-0.709182\pi$
$131$	3.08127	−	14.4962i	0.269212	−	1.26654i	0.880086	−	0.474815i	$-0.157485\pi$
$132$	−5.16518	+	3.77261i	−0.449571	+	0.328364i
$133$	−2.20139	−	0.0597861i	−0.190884	−	0.00518411i
$134$	−19.3931	−	14.0899i	−1.67531	−	1.21718i
$135$	3.93675	+	10.9317i	0.338821	+	0.940851i
$136$	10.2017	+	4.54210i	0.874790	+	0.389482i
$137$	−4.62132	−	5.70686i	−0.394826	−	0.487570i	0.540506	−	0.841340i	$-0.318233\pi$
$137$	−4.62132	−	5.70686i	−0.394826	−	0.487570i	−0.935332	+	0.353770i	$0.884900\pi$
$138$	10.6621	−	18.5750i	0.907617	−	1.58121i
$139$	−9.51954	−	13.1025i	−0.807437	−	1.11134i	−0.991714	−	0.128467i	$-0.958994\pi$
$139$	−9.51954	−	13.1025i	−0.807437	−	1.11134i	0.184277	−	0.982874i	$-0.441006\pi$
$140$	20.1607	+	4.35261i	1.70389	+	0.367862i
$141$	10.8915	−	10.9464i	0.917231	−	0.921856i
$142$	−12.4930	−	19.2376i	−1.04839	−	1.61438i
$143$	1.75640	−	6.55498i	0.146878	−	0.548155i
$144$	1.78787	+	3.06102i	0.148989	+	0.255085i
$145$	11.0970	−	8.47592i	0.921554	−	0.703886i
$146$	2.56947	+	0.834871i	0.212651	+	0.0690944i
$147$	−4.33851	+	11.3215i	−0.357834	+	0.933785i
$148$	2.45307	−	15.4881i	0.201641	−	1.27311i
$149$	−11.2245	+	19.4415i	−0.919549	+	1.59271i	−0.119449	+	0.992840i	$0.538113\pi$
$149$	−11.2245	+	19.4415i	−0.919549	+	1.59271i	−0.800101	+	0.599866i	$0.795221\pi$
$150$	−10.1085	−	17.5866i	−0.825356	−	1.43594i
$151$	6.81324	+	11.8009i	0.554453	+	0.960341i	0.997946	+	0.0640632i	$0.0204059\pi$
$151$	6.81324	+	11.8009i	0.554453	+	0.960341i	−0.443493	+	0.896278i	$0.646261\pi$
$152$	2.25192	+	1.82357i	0.182655	+	0.147911i
$153$	9.49707	−	1.55320i	0.767793	−	0.125569i
$154$	3.99103	+	5.21169i	0.321606	+	0.419970i
$155$	−7.78307	+	1.85028i	−0.625151	+	0.148618i
$156$	−36.1511	−	13.7729i	−2.89440	−	1.10271i
$157$	−4.61650	+	17.2290i	−0.368437	+	1.37502i	0.494265	+	0.869311i	$0.335437\pi$
$157$	−4.61650	+	17.2290i	−0.368437	+	1.37502i	−0.862702	+	0.505713i	$0.831229\pi$
$158$	1.57156	−	0.0823620i	0.125027	−	0.00655237i
$159$	−14.0516	+	3.80303i	−1.11437	+	0.301600i
$160$	6.07602	+	7.14618i	0.480351	+	0.564955i
$161$	−12.2684	−	6.67664i	−0.966885	−	0.526193i
$162$	18.8782	+	9.38092i	1.48321	+	0.737035i
$163$	−7.54351	+	19.6515i	−0.590853	+	1.53923i	0.233032	+	0.972469i	$0.425135\pi$
$163$	−7.54351	+	19.6515i	−0.590853	+	1.53923i	−0.823886	+	0.566756i	$0.808198\pi$
$164$	1.05702	+	0.470618i	0.0825397	+	0.0367491i
$165$	0.746430	−	4.03399i	0.0581095	−	0.314046i
$166$	22.3653	−	9.95768i	1.73588	−	0.772866i
$167$	−7.64511	−	3.89538i	−0.591596	−	0.301433i	0.132445	−	0.991190i	$-0.457717\pi$
$167$	−7.64511	−	3.89538i	−0.591596	−	0.301433i	−0.724041	+	0.689757i	$0.757717\pi$
$168$	13.5896	−	8.35659i	1.04846	−	0.644725i
$169$	26.6720	−	8.66626i	2.05169	−	0.666635i
$170$	−15.8494	+	5.57296i	−1.21559	+	0.427427i
$171$	2.48466	+	0.248518i	0.190007	+	0.0190047i
$172$	−11.7038	−	7.60056i	−0.892409	−	0.579537i
$173$	4.87318	−	6.01788i	0.370501	−	0.457531i	−0.557462	−	0.830202i	$-0.688225\pi$
$173$	4.87318	−	6.01788i	0.370501	−	0.457531i	0.927963	+	0.372671i	$0.121558\pi$
$174$	3.90026	−	25.0326i	0.295678	−	1.89772i
$175$	−11.3166	+	6.85084i	−0.855456	+	0.517875i
$176$		−	1.25165i		−	0.0943466i
$177$	−9.14137	−	10.1013i	−0.687107	−	0.759261i
$178$	0.751242	−	1.15681i	0.0563080	−	0.0867067i
$179$	−18.7019	+	3.97520i	−1.39784	+	0.297121i	−0.844376	−	0.535751i	$-0.820029\pi$
$179$	−18.7019	+	3.97520i	−1.39784	+	0.297121i	−0.553466	+	0.832871i	$0.686695\pi$
$180$	−22.4422	−	6.57917i	−1.67275	−	0.490383i
$181$	2.14702	+	6.60786i	0.159587	+	0.491158i	0.998597	−	0.0529582i	$-0.0168650\pi$
$181$	2.14702	+	6.60786i	0.159587	+	0.491158i	−0.839010	+	0.544116i	$0.816865\pi$
$182$	−13.2893	+	37.4122i	−0.985067	+	2.77318i
$183$	−2.80596	−	2.02789i	−0.207422	−	0.149906i
$184$	7.47525	+	16.7897i	0.551083	+	1.23775i
$185$	5.67833	+	8.30147i	0.417479	+	0.610336i
$186$	−7.87456	+	12.1928i	−0.577390	+	0.894018i
$187$	−3.17214	−	1.21767i	−0.231970	−	0.0890448i
$188$	4.86221	+	30.6988i	0.354613	+	2.23894i
$189$	5.83685	−	12.4471i	0.424568	−	0.905396i
$190$	−4.34676	+	0.332385i	−0.315347	+	0.0241137i
$191$	2.49322	+	5.59985i	0.180403	+	0.405191i	0.980999	−	0.194013i	$-0.0621504\pi$
$191$	2.49322	+	5.59985i	0.180403	+	0.405191i	−0.800596	+	0.599204i	$0.795484\pi$
$192$	21.0016	+	2.15397i	1.51566	+	0.155449i
$193$	17.6299	+	4.72393i	1.26903	+	0.340036i	0.829659	−	0.558270i	$-0.188535\pi$
$193$	17.6299	+	4.72393i	1.26903	+	0.340036i	0.439371	+	0.898306i	$0.355201\pi$
$194$	−7.03506	−	1.49535i	−0.505088	−	0.107360i
$195$	22.9211	−	9.50214i	1.64142	−	0.680463i
$196$	−13.2516	−	20.4927i	−0.946542	−	1.46377i
$197$	2.15454	+	4.22853i	0.153505	+	0.301270i	0.954933	−	0.296820i	$-0.0959263\pi$
$197$	2.15454	+	4.22853i	0.153505	+	0.301270i	−0.801428	+	0.598091i	$0.795926\pi$
$198$	−4.08521	−	6.22193i	−0.290323	−	0.442173i
$199$	2.18314	−	1.26043i	0.154759	−	0.0893499i	−0.420621	−	0.907236i	$-0.638188\pi$
$199$	2.18314	−	1.26043i	0.154759	−	0.0893499i	0.575379	+	0.817887i	$0.304854\pi$
$200$	17.3029	+	1.89636i	1.22350	+	0.134093i
$201$	11.1206	−	13.8037i	0.784390	−	0.973637i
$202$	30.7410	+	4.86889i	2.16293	+	0.342574i
$203$	−16.3786	−	2.17248i	−1.14955	−	0.152478i
$204$	−8.75025	+	17.2807i	−0.612640	+	1.20989i
$205$	−0.700105	+	0.246172i	−0.0488975	+	0.0171934i
$206$	33.0841	+	29.7891i	2.30508	+	2.07550i
$207$	13.3258	+	8.55888i	0.926207	+	0.594883i
$208$	6.34896	−	4.12306i	0.440221	−	0.285883i
$209$	−0.713288	−	0.518234i	−0.0493392	−	0.0358470i
$210$	−6.22769	+	23.1792i	−0.429752	+	1.59952i
$211$	−6.66677	+	4.84369i	−0.458959	+	0.333453i	−0.793123	−	0.609062i	$-0.791546\pi$
$211$	−6.66677	+	4.84369i	−0.458959	+	0.333453i	0.334164	+	0.942515i	$0.391546\pi$
$212$	10.5005	−	27.3547i	0.721177	−	1.87873i
$213$	14.6683	−	8.51799i	1.00505	−	0.583643i
$214$	5.14765	−	11.5618i	0.351886	−	0.790349i
$215$	8.80445	−	1.61159i	0.600458	−	0.109909i
$216$	−16.0554	+	8.33380i	−1.09243	+	0.567044i
$217$	8.06603	+	4.95366i	0.547558	+	0.336276i
$218$	19.5387	+	19.5387i	1.32333	+	1.32333i
$219$	−0.711264	+	1.86693i	−0.0480628	+	0.126155i
$220$	5.67076	+	6.00238i	0.382323	+	0.404681i
$221$	−4.27275	−	20.1017i	−0.287416	−	1.35219i
$222$	17.8587	+	3.74906i	1.19860	+	0.251621i
$223$	−0.982722	+	6.20466i	−0.0658079	+	0.415495i	0.932689	+	0.360682i	$0.117456\pi$
$223$	−0.982722	+	6.20466i	−0.0658079	+	0.415495i	−0.998497	+	0.0548126i	$0.982544\pi$
$224$	0.881542	−	11.0636i	0.0589005	−	0.739217i
$225$	13.3611	−	6.81772i	0.890739	−	0.454514i
$226$	−13.4547	+	23.3043i	−0.894995	+	1.55018i
$227$	22.2168	−	8.52824i	1.47458	−	0.566039i	0.517456	−	0.855710i	$-0.326879\pi$
$227$	22.2168	−	8.52824i	1.47458	−	0.566039i	0.957126	+	0.289671i	$0.0935459\pi$
$228$	−3.35372	+	3.74357i	−0.222105	+	0.247924i
$229$	16.0884	−	14.4860i	1.06315	−	0.957264i	0.0639778	−	0.997951i	$-0.479621\pi$
$229$	16.0884	−	14.4860i	1.06315	−	0.957264i	0.999172	+	0.0406870i	$0.0129546\pi$
$230$	−25.5216	−	10.6379i	−1.68285	−	0.701441i
$231$	−3.99615	+	2.75557i	−0.262927	+	0.181303i
$232$	15.3724	+	15.3724i	1.00925	+	1.00925i
$233$	−3.86268	−	5.94801i	−0.253053	−	0.389667i	0.689199	−	0.724572i	$-0.257962\pi$
$233$	−3.86268	−	5.94801i	−0.253053	−	0.389667i	−0.942252	+	0.334905i	$0.891296\pi$
$234$	18.1035	−	41.2178i	1.18346	−	2.69449i
$235$	−15.7887	−	12.1709i	−1.02994	−	0.793944i
$236$	27.2714	−	2.86634i	1.77522	−	0.186583i
$237$	0.00292694	+	1.16371i	0.000190125	+	0.0755914i
$238$	17.9339	+	8.57545i	1.16248	+	0.555864i
$239$	3.74481	−	2.72077i	0.242232	−	0.175992i	−0.460045	−	0.887896i	$-0.652167\pi$
$239$	3.74481	−	2.72077i	0.242232	−	0.175992i	0.702277	+	0.711904i	$0.252167\pi$
$240$	3.62992	−	2.78703i	0.234310	−	0.179902i
$241$	−0.467059	+	4.44377i	−0.0300859	+	0.286249i	0.969126	+	0.246565i	$0.0793018\pi$
$241$	−0.467059	+	4.44377i	−0.0300859	+	0.286249i	−0.999212	+	0.0396840i	$0.987365\pi$
$242$	−1.21090	−	23.1053i	−0.0778395	−	1.48527i
$243$	−7.62384	+	13.5969i	−0.489070	+	0.872245i
$244$	6.62737	−	2.15336i	0.424274	−	0.137855i
$245$	15.2046	+	3.71735i	0.971389	+	0.237493i
$246$	−0.608258	+	1.20123i	−0.0387811	+	0.0765878i
$247$	0.279084	−	5.32525i	0.0177577	−	0.338837i
$248$	−4.46350	−	11.6278i	−0.283433	−	0.738368i
$249$	6.53026	+	16.8848i	0.413838	+	1.07003i
$250$	−20.8817	+	15.8032i	−1.32068	+	0.999480i
$251$		−	19.6720i		−	1.24169i	−0.783934	−	0.620844i	$-0.786790\pi$
$251$		−	19.6720i		−	1.24169i	0.783934	−	0.620844i	$-0.213210\pi$
$252$	13.3023	+	24.2645i	0.837967	+	1.52852i
$253$	−2.53873	−	4.98253i	−0.159608	−	0.313249i
$254$	28.0510	+	31.1538i	1.76008	+	1.95476i
$255$	−3.53198	−	11.9109i	−0.221181	−	0.745890i
$256$	−15.2848	+	16.9755i	−0.955300	+	1.06097i
$257$	−5.68073	−	21.2008i	−0.354354	−	1.32247i	−0.881296	−	0.472566i	$-0.843328\pi$
$257$	−5.68073	−	21.2008i	−0.354354	−	1.32247i	0.526942	−	0.849902i	$-0.323339\pi$
$258$	9.51228	−	13.1620i	0.592209	−	0.819431i
$259$	2.18006	−	11.6991i	0.135462	−	0.726945i
$260$	−11.7668	+	48.5373i	−0.729749	+	3.01015i
$261$	18.3442	+	3.80284i	1.13548	+	0.235390i
$262$	−26.9770	+	21.8455i	−1.66664	+	1.34962i
$263$	13.7943	−	11.1704i	0.850594	−	0.688798i	−0.101422	−	0.994843i	$-0.532339\pi$
$263$	13.7943	−	11.1704i	0.850594	−	0.688798i	0.952017	+	0.306046i	$0.0990060\pi$
$264$	6.37916	+	0.318231i	0.392610	+	0.0195858i
$265$	7.15328	+	17.3786i	0.439423	+	1.06756i
$266$	3.91905	+	3.35377i	0.240292	+	0.205633i
$267$	0.826688	+	0.597453i	0.0505925	+	0.0365635i
$268$	9.23442	+	34.4633i	0.564082	+	2.10518i
$269$	1.92964	−	2.14308i	0.117652	−	0.130666i	−0.681441	−	0.731873i	$-0.738647\pi$
$269$	1.92964	−	2.14308i	0.117652	−	0.130666i	0.799094	+	0.601207i	$0.205313\pi$
$270$	8.94779	−	25.7019i	0.544545	−	1.56417i
$271$	−1.35736	−	1.50751i	−0.0824540	−	0.0915745i	0.700506	−	0.713647i	$-0.252958\pi$
$271$	−1.35736	−	1.50751i	−0.0824540	−	0.0915745i	−0.782960	+	0.622072i	$0.786291\pi$
$272$	−1.72080	−	3.37726i	−0.104339	−	0.204776i
$273$	−27.1413	−	11.1932i	−1.64266	−	0.677445i
$274$			17.2002i			1.03910i
$275$	−5.28772	−	0.300677i	−0.318862	−	0.0181315i
$276$	−29.7320	+	11.4989i	−1.78966	+	0.692155i
$277$	−1.19195	−	3.10513i	−0.0716171	−	0.186569i	0.893100	−	0.449859i	$-0.148526\pi$
$277$	−1.19195	−	3.10513i	−0.0716171	−	0.186569i	−0.964717	+	0.263290i	$0.915192\pi$
$278$	−1.98535	+	37.8827i	−0.119073	+	2.27205i
$279$	−8.71489	−	6.26500i	−0.521747	−	0.375076i
$280$	−12.9101	−	16.0472i	−0.771528	−	0.959002i
$281$	−24.7883	+	8.05419i	−1.47874	+	0.480473i	−0.933737	−	0.357959i	$-0.883473\pi$
$281$	−24.7883	+	8.05419i	−1.47874	+	0.480473i	−0.545006	+	0.838432i	$0.683473\pi$
$282$	−35.9613	+	3.87116i	−2.14147	+	0.230524i
$283$	−0.710894	−	13.5647i	−0.0422582	−	0.806335i	−0.934757	−	0.355286i	$-0.884383\pi$
$283$	−0.710894	−	13.5647i	−0.0422582	−	0.806335i	0.892499	−	0.451049i	$-0.148950\pi$
$284$	−3.56877	+	33.9545i	−0.211767	+	2.01483i
$285$	−0.0853339	−	3.22256i	−0.00505475	−	0.190888i
$286$	−12.8595	+	9.34299i	−0.760399	+	0.552462i
$287$	0.792186	+	0.378799i	0.0467613	+	0.0223598i
$288$	−1.90613	+	12.4395i	−0.112320	+	0.733005i
$289$	6.67359	−	0.701422i	0.392564	−	0.0412601i
$290$	−32.6937	−	0.928784i	−1.91984	−	0.0545401i
$291$	1.36359	−	5.14067i	0.0799351	−	0.301351i
$292$	−2.19013	−	3.37250i	−0.128168	−	0.197361i
$293$	1.85036	+	1.85036i	0.108099	+	0.108099i	0.759088	−	0.650988i	$-0.225645\pi$
$293$	1.85036	+	1.85036i	0.108099	+	0.108099i	−0.650988	+	0.759088i	$0.725645\pi$
$294$	24.5858	−	14.2134i	1.43388	−	0.828942i
$295$	−11.4521	+	13.3486i	−0.666768	+	0.777183i
$296$	−11.6367	+	10.4778i	−0.676371	+	0.609007i
$297$	4.74574	−	2.78791i	0.275376	−	0.161771i
$298$	49.0896	−	18.8437i	2.84368	−	1.09159i
$299$	16.9109	−	29.2906i	0.977985	−	1.69392i
$300$	−4.78055	+	29.8113i	−0.276005	+	1.72115i
$301$	−8.72219	−	6.00709i	−0.502739	−	0.346243i
$302$	4.99293	−	31.5241i	0.287311	−	1.81401i
$303$	−4.72853	+	22.5244i	−0.271647	+	1.29399i
$304$	−0.204489	−	0.962044i	−0.0117282	−	0.0551770i
$305$	−2.14137	+	3.92310i	−0.122614	+	0.224636i
$306$	−19.5770	−	11.1718i	−1.11914	−	0.638652i
$307$	2.55002	+	2.55002i	0.145537	+	0.145537i	0.776121	−	0.630584i	$-0.217185\pi$
$307$	2.55002	+	2.55002i	0.145537	+	0.145537i	−0.630584	+	0.776121i	$0.717185\pi$
$308$	0.265250	−	9.76679i	0.0151140	−	0.556515i
$309$	−23.2197	+	23.3368i	−1.32092	+	1.32759i
$310$	16.8949	+	8.10456i	0.959565	+	0.460308i
$311$	−13.6919	+	30.7524i	−0.776394	+	1.74381i	−0.115531	+	0.993304i	$0.536857\pi$
$311$	−13.6919	+	30.7524i	−0.776394	+	1.74381i	−0.660863	+	0.750506i	$0.729810\pi$
$312$	19.3994	+	33.4064i	1.09827	+	1.89126i
$313$	−0.483231	+	1.25886i	−0.0273139	+	0.0711550i	−0.946559	−	0.322530i	$-0.895467\pi$
$313$	−0.483231	+	1.25886i	−0.0273139	+	0.0711550i	0.919245	+	0.393685i	$0.128800\pi$
$314$	33.7997	−	24.5569i	1.90743	−	1.38583i
$315$	−16.8896	−	5.45348i	−0.951623	−	0.307269i
$316$	−1.89500	−	1.37680i	−0.106602	−	0.0774508i
$317$	−0.739676	+	0.480351i	−0.0415443	+	0.0269792i	−0.565244	−	0.824924i	$-0.691218\pi$
$317$	−0.739676	+	0.480351i	−0.0415443	+	0.0269792i	0.523700	+	0.851903i	$0.324551\pi$
$318$	31.1840	+	13.7901i	1.74871	+	0.773312i
$319$	−4.91573	−	4.42614i	−0.275228	−	0.247816i
$320$	−0.652941	−	27.2474i	−0.0365005	−	1.52318i
$321$	8.34935	+	4.22779i	0.466015	+	0.235972i
$322$	12.4904	+	30.2376i	0.696065	+	1.68508i
$323$	−2.63711	−	0.417677i	−0.146733	−	0.0232402i
$324$	−13.0497	−	28.5341i	−0.724986	−	1.58523i
$325$	−15.8931	−	27.8123i	−0.881592	−	1.54275i
$326$	42.6987	−	24.6521i	2.36486	−	1.36535i
$327$	−15.1503	+	13.7105i	−0.837811	+	0.758193i
$328$	−0.524543	−	1.02947i	−0.0289630	−	0.0568431i
$329$	3.05609	+	23.3889i	0.168488	+	1.28947i
$330$	−7.30502	+	6.24279i	−0.402128	+	0.343654i
$331$	16.9588	+	3.60471i	0.932141	+	0.198133i	0.648863	−	0.760905i	$-0.275245\pi$
$331$	16.9588	+	3.60471i	0.932141	+	0.198133i	0.283278	+	0.959038i	$0.408578\pi$
$332$	−35.1976	−	9.43116i	−1.93172	−	0.517602i
$333$	−3.42686	+	13.0515i	−0.187791	+	0.715216i
$334$	8.17439	+	18.3600i	0.447283	+	1.00461i
$335$	−19.4853	−	12.0002i	−1.06460	−	0.655643i
$336$	−5.36969	−	0.698503i	−0.292940	−	0.0381065i
$337$	−1.79431	−	11.3289i	−0.0977425	−	0.617122i	−0.987124	−	0.159956i	$-0.948865\pi$
$337$	−1.79431	−	11.3289i	−0.0977425	−	0.617122i	0.889382	−	0.457166i	$-0.151135\pi$
$338$	−61.3254	−	23.5406i	−3.33566	−	1.28044i
$339$	−16.7157	−	10.7956i	−0.907873	−	0.586338i
$340$	23.5533	+	8.39960i	1.27736	+	0.455532i
$341$	1.54141	+	3.46205i	0.0834718	+	0.187481i
$342$	−4.15649	−	4.11488i	−0.224757	−	0.222507i
$343$	−9.63073	−	15.8193i	−0.520011	−	0.854160i
$344$	4.30624	+	13.2532i	0.232177	+	0.714567i
$345$	8.79694	−	18.4571i	0.473612	−	0.993699i
$346$	−17.7413	+	3.77102i	−0.953777	+	0.202732i
$347$	−19.5254	+	30.0665i	−1.04818	+	1.61406i	−0.295893	+	0.955221i	$0.595617\pi$
$347$	−19.5254	+	30.0665i	−1.04818	+	1.61406i	−0.752287	+	0.658836i	$0.771049\pi$
$348$	−27.9593	+	25.3023i	−1.49877	+	1.35634i
$349$		−	31.1563i		−	1.66776i	−0.551948	−	0.833879i	$-0.686115\pi$
$349$		−	31.1563i		−	1.66776i	0.551948	−	0.833879i	$-0.313885\pi$
$350$	30.6981	+	4.21068i	1.64088	+	0.225070i
$351$	29.7745	+	14.8890i	1.58925	+	0.794715i
$352$	2.79636	−	3.45322i	0.149046	−	0.184057i
$353$	25.4193	+	16.5075i	1.35293	+	0.878604i	0.998406	−	0.0564417i	$-0.0179755\pi$
$353$	25.4193	+	16.5075i	1.35293	+	0.878604i	0.354526	+	0.935046i	$0.384642\pi$
$354$	1.75020	+	31.8622i	0.0930218	+	1.69346i
$355$	−13.2921	−	17.4024i	−0.705469	−	0.923626i
$356$	−1.95255	+	0.634421i	−0.103485	+	0.0336243i
$357$	−6.99417	+	12.9292i	−0.370171	+	0.684286i
$358$	39.9025	+	20.3314i	2.10892	+	1.07455i
$359$	0.514210	−	0.228941i	0.0271389	−	0.0120830i	−0.393122	−	0.919486i	$-0.628605\pi$
$359$	0.514210	−	0.228941i	0.0271389	−	0.0120830i	0.420261	+	0.907403i	$0.361938\pi$
$360$	13.2815	+	19.2089i	0.699996	+	1.01240i
$361$	16.7244	+	7.44620i	0.880234	+	0.391906i
$362$	5.83207	−	15.1931i	0.306527	−	0.798530i
$363$	17.1091	−	0.0430323i	0.897996	−	0.00225861i
$364$	50.4156	−	30.8273i	2.64249	−	1.61579i
$365$	2.50658	+	0.607668i	0.131200	+	0.0318068i
$366$	2.11848	+	7.82746i	0.110735	+	0.409148i
$367$	19.4748	−	1.02063i	1.01658	−	0.0532765i	0.463239	−	0.886233i	$-0.346687\pi$
$367$	19.4748	−	1.02063i	1.01658	−	0.0532765i	0.553338	+	0.832957i	$0.313354\pi$
$368$	1.61454	−	6.02555i	0.0841637	−	0.314103i
$369$	−0.864763	−	0.493488i	−0.0450178	−	0.0256900i
$370$	1.90050	−	23.4813i	0.0988024	−	1.22073i
$371$	8.52949	−	20.5355i	0.442829	−	1.06615i
$372$	20.5295	−	6.72757i	1.06440	−	0.348808i
$373$	0.918171	+	0.743520i	0.0475411	+	0.0384980i	0.652796	−	0.757533i	$-0.273596\pi$
$373$	0.918171	+	0.743520i	0.0475411	+	0.0384980i	−0.605255	+	0.796031i	$0.706929\pi$
$374$	3.97933	+	6.89239i	0.205766	+	0.356397i
$375$	−10.9021	−	16.0045i	−0.562983	−	0.826469i
$376$	15.5185	−	26.8789i	0.800306	−	1.38617i
$377$	6.25857	−	39.5150i	0.322333	−	2.03513i
$378$	−28.9724	+	14.0537i	−1.49018	+	0.722843i
$379$	−8.99154	−	2.92153i	−0.461864	−	0.150069i	0.0688367	−	0.997628i	$-0.478071\pi$
$379$	−8.99154	−	2.92153i	−0.461864	−	0.150069i	−0.530701	+	0.847559i	$0.678071\pi$
$380$	5.33931	+	3.68709i	0.273901	+	0.189144i
$381$	−24.0422	+	19.5693i	−1.23172	+	1.00257i
$382$	3.71605	−	13.8685i	0.190130	−	0.709574i
$383$	−8.34837	−	12.8554i	−0.426582	−	0.656878i	0.558393	−	0.829577i	$-0.311418\pi$
$383$	−8.34837	−	12.8554i	−0.426582	−	0.656878i	−0.984975	+	0.172698i	$0.944751\pi$
$384$	−24.7530	−	24.6288i	−1.26317	−	1.25683i
$385$	4.17830	+	4.67037i	0.212946	+	0.238024i
$386$	−25.1284	−	34.5863i	−1.27900	−	1.76040i
$387$	9.37038	+	7.51025i	0.476323	+	0.381768i
$388$	6.73689	+	8.31936i	0.342014	+	0.422352i
$389$	6.99623	+	3.11492i	0.354723	+	0.157933i	0.576359	−	0.817197i	$-0.304473\pi$
$389$	6.99623	+	3.11492i	0.354723	+	0.157933i	−0.221636	+	0.975129i	$0.571140\pi$
$390$	−55.7298	−	16.4901i	−2.82199	−	0.835009i
$391$	−13.7002	−	9.95380i	−0.692850	−	0.503385i
$392$	−2.59437	+	24.2307i	−0.131035	+	1.22383i
$393$	−15.1401	−	20.7288i	−0.763719	−	1.04563i
$394$	2.31114	−	10.8731i	0.116434	−	0.547777i
$395$	1.48993	−	0.192788i	0.0749667	−	0.00970020i
$396$	−1.10259	+	11.0236i	−0.0554072	+	0.553956i
$397$	0.370614	−	7.07174i	0.0186006	−	0.354921i	−0.973435	−	0.228963i	$-0.926466\pi$
$397$	0.370614	−	7.07174i	0.0186006	−	0.354921i	0.992036	−	0.125957i	$-0.0402002\pi$
$398$	−5.83189	−	0.923681i	−0.292326	−	0.0463000i
$399$	−2.62133	+	2.77086i	−0.131231	+	0.138716i
$400$	−4.15911	−	4.19622i	−0.207955	−	0.209811i
$401$	4.04973	+	2.33811i	0.202234	+	0.116760i	0.597697	−	0.801722i	$-0.296083\pi$
$401$	4.04973	+	2.33811i	0.202234	+	0.116760i	−0.395463	+	0.918482i	$0.629416\pi$
$402$	−40.5901	+	8.73446i	−2.02445	+	0.435635i
$403$	−12.4836	+	19.2231i	−0.621854	+	0.957571i
$404$	−30.9979	−	34.4267i	−1.54220	−	1.71279i
$405$	18.6525	+	7.55536i	0.926851	+	0.375429i
$406$	26.6115	+	28.0973i	1.32071	+	1.39445i
$407$	3.36899	−	3.36899i	0.166995	−	0.166995i
$408$	17.6500	−	7.91156i	0.873807	−	0.391681i
$409$	23.1881	+	2.43717i	1.14658	+	0.120510i	0.658703	−	0.752403i	$-0.271105\pi$
$409$	23.1881	+	2.43717i	1.14658	+	0.120510i	0.487876	+	0.872913i	$0.337772\pi$
$410$	1.63727	+	0.583883i	0.0808589	+	0.0288359i
$411$	−12.7033	−	0.633716i	−0.626606	−	0.0312589i
$412$	−10.3658	−	65.4470i	−0.510686	−	3.22434i
$413$	20.7477	−	1.61260i	1.02093	−	0.0793507i
$414$	−11.6407	−	35.2225i	−0.572110	−	1.73109i
$415$	20.5642	−	11.1064i	1.00946	−	0.545190i
$416$	26.7278	+	2.80921i	1.31044	+	0.137733i
$417$	−27.9052	−	2.86202i	−1.36653	−	0.140154i
$418$	0.534494	+	1.99476i	0.0261430	+	0.0975668i
$419$	8.74668	+	26.9195i	0.427303	+	1.31510i	0.900772	+	0.434293i	$0.143002\pi$
$419$	8.74668	+	26.9195i	0.427303	+	1.31510i	−0.473468	+	0.880811i	$0.656998\pi$
$420$	28.9154	−	20.9784i	1.41093	−	1.02364i
$421$	3.61225	−	11.1174i	0.176051	−	0.541828i	−0.823629	−	0.567128i	$-0.808054\pi$
$421$	3.61225	−	11.1174i	0.176051	−	0.541828i	0.999680	+	0.0253007i	$0.00805431\pi$
$422$	19.2753	+	1.01018i	0.938307	+	0.0491746i
$423$	−1.53412	−	26.7020i	−0.0745913	−	1.29829i
$424$	−25.3390	+	14.6295i	−1.23057	+	0.710472i
$425$	−14.6810	+	6.45839i	−0.712131	+	0.313278i
$426$	−39.2565	−	6.11645i	−1.90198	−	0.296343i
$427$	5.07204	−	1.49705i	0.245453	−	0.0724471i
$428$	−16.7842	+	8.55198i	−0.811295	+	0.413375i
$429$	−6.42650	−	9.84166i	−0.310274	−	0.475160i
$430$	−18.4023	−	10.0446i	−0.887436	−	0.484393i
$431$	3.09869	+	2.79007i	0.149259	+	0.134393i	0.740377	−	0.672191i	$-0.234647\pi$
$431$	3.09869	+	2.79007i	0.149259	+	0.134393i	−0.591119	+	0.806585i	$0.701314\pi$
$432$	6.01524	+	1.23121i	0.289408	+	0.0592369i
$433$	4.56539	+	2.32618i	0.219399	+	0.111789i	0.560236	−	0.828333i	$-0.310710\pi$
$433$	4.56539	+	2.32618i	0.219399	+	0.111789i	−0.340837	+	0.940122i	$0.610710\pi$
$434$	−7.38064	−	20.9068i	−0.354282	−	1.00356i
$435$	1.89050	−	24.1118i	0.0906428	−	1.15607i
$436$	−4.29903	−	40.9025i	−0.205886	−	1.95887i
$437$	−2.76534	−	3.41491i	−0.132284	−	0.163357i
$438$	4.04665	−	2.34992i	0.193356	−	0.112284i
$439$	4.67719	−	0.491593i	0.223230	−	0.0234625i	0.00774707	−	0.999970i	$-0.497534\pi$
$439$	4.67719	−	0.491593i	0.223230	−	0.0234625i	0.215483	+	0.976508i	$0.430867\pi$
$440$	−0.628690	−	8.22170i	−0.0299716	−	0.391954i
$441$	9.59151	+	18.6816i	0.456739	+	0.889601i
$442$	−21.8532	+	42.8893i	−1.03945	+	2.04003i
$443$	10.5516	−	2.82728i	0.501320	−	0.134328i	0.000707226	−	1.00000i	$-0.499775\pi$
$443$	10.5516	−	2.82728i	0.501320	−	0.134328i	0.500612	+	0.865672i	$0.333108\pi$
$444$	−17.1457	−	21.0647i	−0.813700	−	0.999685i
$445$	0.630887	−	1.15582i	0.0299069	−	0.0547911i
$446$	10.9348	−	9.84574i	0.517778	−	0.466209i
$447$	12.1085	+	36.9495i	0.572710	+	1.74765i
$448$	−22.2213	+	23.3709i	−1.04986	+	1.10417i
$449$	18.4633			0.871338			0.435669	−	0.900107i	$-0.356512\pi$
$449$	18.4633			0.871338			0.435669	+	0.900107i	$0.356512\pi$
$450$	−34.3708	−	7.28461i	−1.62025	−	0.343400i
$451$	0.175777	+	0.304454i	0.00827700	+	0.0143362i
$452$	37.3922	−	14.3535i	1.75878	−	0.675132i
$453$	23.0983	+	4.84900i	1.08525	+	0.227826i
$454$	−53.0122	−	17.2247i	−2.48799	−	0.808396i
$455$	−9.92660	+	36.5790i	−0.465366	+	1.71485i
$456$	4.95514	−	0.797598i	0.232046	−	0.0373510i
$457$	20.3503	−	5.45285i	0.951947	−	0.255074i	0.250759	−	0.968050i	$-0.419320\pi$
$457$	20.3503	−	5.45285i	0.951947	−	0.255074i	0.701188	+	0.712976i	$0.252653\pi$
$458$	−50.6387	+	2.65386i	−2.36619	+	0.124007i
$459$	8.97228	−	14.0470i	0.418790	−	0.655659i
$460$	19.5569	+	36.2109i	0.911845	+	1.68834i
$461$	10.3720	+	14.2758i	0.483070	+	0.664889i	0.979091	−	0.203422i	$-0.0652062\pi$
$461$	10.3720	+	14.2758i	0.483070	+	0.664889i	−0.496021	+	0.868310i	$0.665206\pi$
$462$	11.3360	+	0.874561i	0.527399	+	0.0406882i
$463$	−23.6968	+	3.75320i	−1.10128	+	0.174426i	−0.680509	−	0.732740i	$-0.738241\pi$
$463$	−23.6968	+	3.75320i	−1.10128	+	0.174426i	−0.420773	+	0.907166i	$0.638241\pi$
$464$	−0.771315	−	7.33858i	−0.0358074	−	0.340685i
$465$	−6.60811	+	12.1792i	−0.306444	+	0.564795i
$466$	−1.73642	+	16.5209i	−0.0804380	+	0.765316i
$467$	−2.86788	+	1.86242i	−0.132710	+	0.0861826i	−0.609286	−	0.792950i	$-0.708544\pi$
$467$	−2.86788	+	1.86242i	−0.132710	+	0.0861826i	0.476577	+	0.879133i	$0.341877\pi$
$468$	−59.5489	+	30.7200i	−2.75265	+	1.42003i
$469$	6.29539	+	26.3349i	0.290694	+	1.21603i
$470$	10.7996	+	45.4280i	0.498150	+	2.09544i
$471$	16.8913	+	25.8677i	0.778310	+	1.19192i
$472$	−22.9649	−	14.9136i	−1.05704	−	0.686452i
$473$	−1.51951	−	3.95845i	−0.0698669	−	0.182010i
$474$	1.71004	−	2.12262i	0.0785448	−	0.0974952i
$475$	−4.11338	+	0.632777i	−0.188735	+	0.0290338i
$476$	−12.7119	−	26.7179i	−0.582650	−	1.22461i
$477$	−11.3337	+	22.5230i	−0.518933	+	1.03126i
$478$	−10.8272	−	0.567430i	−0.495225	−	0.0259536i
$479$	−12.8990	+	2.74177i	−0.589371	+	0.125275i	−0.492937	−	0.870065i	$-0.664077\pi$
$479$	−12.8990	+	2.74177i	−0.589371	+	0.125275i	−0.0964335	+	0.995339i	$0.530744\pi$
$480$	16.2413	+	0.420515i	0.741312	+	0.0191938i
$481$	28.1869	+	5.99131i	1.28521	+	0.273180i
$482$	7.40052	−	7.40052i	0.337084	−	0.337084i
$483$	−22.7923	+	8.11078i	−1.03709	+	0.369053i
$484$	−20.2419	+	27.8605i	−0.920084	+	1.26639i
$485$	−6.80534	−	0.911322i	−0.309014	−	0.0413810i
$486$	33.9202	−	13.5126i	1.53865	−	0.612943i
$487$	−17.6224	+	14.2703i	−0.798546	+	0.646650i	−0.939185	−	0.343411i	$-0.888418\pi$
$487$	−17.6224	+	14.2703i	−0.798546	+	0.646650i	0.140639	+	0.990061i	$0.455084\pi$
$488$	−6.49630	−	2.49369i	−0.294074	−	0.112884i
$489$	16.6337	+	32.4435i	0.752202	+	1.46714i
$490$	−22.1974	−	29.1790i	−1.00278	−	1.31817i
$491$	10.1363	−	13.9515i	0.457446	−	0.629620i	−0.516531	−	0.856269i	$-0.672777\pi$
$491$	10.1363	−	13.9515i	0.457446	−	0.629620i	0.973977	+	0.226648i	$0.0727768\pi$
$492$	1.82876	−	0.819736i	0.0824470	−	0.0369565i
$493$	−19.3490	−	5.18455i	−0.871435	−	0.233500i
$494$	−8.35768	+	9.28214i	−0.376030	+	0.417623i
$495$	−4.34149	−	5.62515i	−0.195135	−	0.252831i
$496$	−1.30638	+	4.02062i	−0.0586582	+	0.180531i
$497$	−3.40691	+	25.6851i	−0.152821	+	1.15214i
$498$	13.0020	−	40.3613i	0.582635	−	1.80863i
$499$	−36.0263	−	20.7998i	−1.61276	−	0.931127i	−0.988727	−	0.149728i	$-0.952160\pi$
$499$	−36.0263	−	20.7998i	−1.61276	−	0.931127i	−0.624032	−	0.781399i	$-0.714507\pi$
$500$	38.9569	+	1.27993i	1.74220	+	0.0572403i
$501$	−13.8610	+	5.36078i	−0.619264	+	0.239502i
$502$	−28.9975	+	35.8089i	−1.29422	+	1.59823i
$503$	12.8048	−	6.52436i	0.570937	−	0.290907i	−0.144591	−	0.989492i	$-0.546187\pi$
$503$	12.8048	−	6.52436i	0.570937	−	0.290907i	0.715527	+	0.698585i	$0.246187\pi$
$504$	4.92523	−	27.1896i	0.219387	−	1.21112i
$505$	29.6159	+	2.39702i	1.31789	+	0.106666i
$506$	−2.72325	+	12.8119i	−0.121063	+	0.569558i
$507$	19.6454	−	44.4247i	0.872484	−	1.97297i
$508$	−3.26559	−	62.3112i	−0.144887	−	2.76461i
$509$	−36.5493	+	16.2728i	−1.62002	+	0.721279i	−0.998089	−	0.0617940i	$-0.980318\pi$
$509$	−36.5493	+	16.2728i	−1.62002	+	0.721279i	−0.621930	+	0.783073i	$0.713651\pi$
$510$	−11.1280	+	26.8877i	−0.492755	+	1.19061i
$511$	−1.59200	−	2.60358i	−0.0704258	−	0.115176i
$512$	13.0218	−	2.06245i	0.575487	−	0.0911482i
$513$	3.19220	−	2.91818i	0.140939	−	0.128841i
$514$	−20.9103	+	46.9653i	−0.922314	+	2.07155i
$515$	33.6602	+	25.9473i	1.48324	+	1.14338i
$516$	−23.3317	+	6.31466i	−1.02712	+	0.277987i
$517$	−4.28730	+	8.41430i	−0.188555	+	0.370061i
$518$	−21.2133	+	18.0823i	−0.932060	+	0.794489i
$519$	−2.13145	−	13.2418i	−0.0935603	−	0.581251i
$520$	39.6334	−	30.2721i	1.73804	−	1.32752i
$521$	−5.50211	−	25.8854i	−0.241052	−	1.13406i	−0.917552	−	0.397617i	$-0.869837\pi$
$521$	−5.50211	−	25.8854i	−0.241052	−	1.13406i	0.676500	−	0.736443i	$-0.263496\pi$
$522$	−27.7863	−	33.9625i	−1.21617	−	1.48650i
$523$	0.777545	+	0.629643i	0.0339997	+	0.0275324i	0.646170	−	0.763194i	$-0.276370\pi$
$523$	0.777545	+	0.629643i	0.0339997	+	0.0275324i	−0.612170	+	0.790726i	$0.709703\pi$
$524$	51.6672			2.25709
$525$	−4.24083	+	22.5170i	−0.185085	+	0.982723i
$526$	−41.5755			−1.81278
$527$	8.91881	+	7.22231i	0.388509	+	0.314609i
$528$	−1.61472	−	1.44656i	−0.0702718	−	0.0629537i
$529$	−1.01256	−	4.76373i	−0.0440245	−	0.207119i
$530$	12.5958	−	42.1785i	0.547127	−	1.83212i
$531$	−23.5964	+	0.118699i	−1.02400	+	0.00515108i
$532$	−1.39178	−	7.55030i	−0.0603412	−	0.327347i
$533$	−0.965309	+	1.89453i	−0.0418122	+	0.0820610i
$534$	−0.624143	−	2.30612i	−0.0270093	−	0.0997955i
$535$	4.05836	−	11.3801i	0.175458	−	0.492004i
$536$	14.4912	−	32.5479i	0.625927	−	1.40585i
$537$	−16.4859	+	28.7211i	−0.711421	+	1.23941i
$538$	−6.67152	+	1.05667i	−0.287630	+	0.0455561i
$539$	0.402449	−	7.40384i	0.0173347	−	0.318906i
$540$	−34.4247	+	21.3485i	−1.48140	+	0.918691i
$541$	0.979215	−	0.435975i	0.0420997	−	0.0187440i	−0.385579	−	0.922675i	$-0.625998\pi$
$541$	0.979215	−	0.435975i	0.0420997	−	0.0187440i	0.427679	+	0.903931i	$0.359332\pi$
$542$	0.248671	+	4.74492i	0.0106813	+	0.203812i
$543$	11.0060	+	4.86706i	0.472313	+	0.208865i
$544$	2.79770	−	13.1621i	0.119950	−	0.564322i
$545$	20.0206	+	17.1762i	0.857588	+	0.735750i
$546$	32.9058	+	60.3825i	1.40824	+	2.58413i
$547$	−1.86448	+	0.949998i	−0.0797192	+	0.0406190i	−0.493396	−	0.869805i	$-0.664245\pi$
$547$	−1.86448	+	0.949998i	−0.0797192	+	0.0406190i	0.413676	+	0.910424i	$0.364245\pi$
$548$	16.1113	−	19.8958i	0.688240	−	0.849905i
$549$	−5.85905	+	1.27622i	−0.250058	+	0.0544676i
$550$	9.18201	+	8.34167i	0.391522	+	0.355690i
$551$	−4.50145	−	2.59891i	−0.191768	−	0.110717i
$552$	30.2993	+	9.76066i	1.28962	+	0.415441i
$553$	−1.40922	−	1.08351i	−0.0599261	−	0.0460755i
$554$	−2.40741	+	7.40924i	−0.102281	+	0.314788i
$555$	17.2721	+	2.26875i	0.733161	+	0.0963031i
$556$	37.7808	−	41.9599i	1.60226	−	1.77950i
$557$	38.5639	+	10.3332i	1.63400	+	0.437830i	0.955073	−	0.296372i	$-0.0957767\pi$
$557$	38.5639	+	10.3332i	1.63400	+	0.437830i	0.678931	+	0.734202i	$0.262443\pi$
$558$	6.62877	+	24.2503i	0.280618	+	1.02660i
$559$	15.0737	−	20.7472i	0.637550	−	0.877512i
$560$	−0.0223201	+	6.99060i	−0.000943196	+	0.295407i
$561$	−5.23701	+	2.68500i	−0.221107	+	0.113361i
$562$	56.9942	+	21.8780i	2.40416	+	0.922869i
$563$	−5.17878	+	4.19369i	−0.218259	+	0.176743i	−0.732214	−	0.681074i	$-0.761513\pi$
$563$	−5.17878	+	4.19369i	−0.218259	+	0.176743i	0.513955	+	0.857817i	$0.328180\pi$
$564$	45.2231	+	29.2068i	1.90424	+	1.22983i
$565$	−11.1110	+	23.1621i	−0.467441	+	0.974435i
$566$	−18.7009	+	25.7396i	−0.786058	+	1.08192i
$567$	−9.31194	−	21.9155i	−0.391065	−	0.920363i
$568$	24.1073	−	24.1073i	1.01152	−	1.01152i
$569$	−7.73745	−	1.64465i	−0.324371	−	0.0689472i	0.0428483	−	0.999082i	$-0.486357\pi$
$569$	−7.73745	−	1.64465i	−0.324371	−	0.0689472i	−0.367219	+	0.930134i	$0.619690\pi$
$570$	−4.59487	+	5.99180i	−0.192458	+	0.250969i
$571$	−21.7720	+	4.62777i	−0.911128	+	0.193666i	−0.639550	−	0.768750i	$-0.720879\pi$
$571$	−21.7720	+	4.62777i	−0.911128	+	0.193666i	−0.271579	+	0.962416i	$0.587546\pi$
$572$	23.6263	+	1.23820i	0.987865	+	0.0517718i
$573$	10.1057	+	3.25547i	0.422172	+	0.135999i
$574$	−0.883646	−	1.85724i	−0.0368827	−	0.0775199i
$575$	−25.0677	−	8.26828i	−1.04540	−	0.344811i
$576$	27.0509	−	24.6043i	1.12712	−	1.02518i
$577$	10.7768	+	28.0746i	0.448645	+	1.16876i	0.952383	+	0.304903i	$0.0986241\pi$
$577$	10.7768	+	28.0746i	0.448645	+	1.16876i	−0.503739	+	0.863856i	$0.668043\pi$
$578$	−13.1818	−	8.56038i	−0.548292	−	0.356065i
$579$	26.4696	−	17.2844i	1.10004	−	0.718314i
$580$	36.9473	+	31.6982i	1.53415	+	1.31619i
$581$	−26.5073	−	7.87986i	−1.09971	−	0.326912i
$582$	−10.0597	+	7.34755i	−0.416989	+	0.304566i
$583$	7.46635	−	4.84870i	0.309224	−	0.200813i
$584$	−0.419735	+	3.99351i	−0.0173687	+	0.165253i
$585$	14.2321	−	40.5519i	0.588425	−	1.67661i
$586$	−0.640687	−	6.09573i	−0.0264665	−	0.251812i
$587$	−14.1132	+	2.23531i	−0.582515	+	0.0922613i	−0.440735	−	0.897637i	$-0.645282\pi$
$587$	−14.1132	+	2.23531i	−0.582515	+	0.0922613i	−0.141779	+	0.989898i	$0.545282\pi$
$588$	−41.7524	−	6.58846i	−1.72184	−	0.271704i
$589$	1.75037	+	2.40918i	0.0721228	+	0.0992685i
$590$	40.5226	−	7.41737i	1.66829	−	0.305368i
$591$	7.94519	+	2.10750i	0.326821	+	0.0866911i
$592$	5.30765	−	0.278162i	0.218143	−	0.0114324i
$593$	28.6351	−	7.67275i	1.17590	−	0.315082i	0.382602	−	0.923913i	$-0.375028\pi$
$593$	28.6351	−	7.67275i	1.17590	−	0.315082i	0.793300	+	0.608831i	$0.208361\pi$
$594$	−12.7482	−	1.92062i	−0.523063	−	0.0788040i
$595$	17.6950	+	6.85739i	0.725425	+	0.281125i
$596$	−74.4334	−	24.1849i	−3.04891	−	0.990651i
$597$	0.897055	−	4.27313i	0.0367140	−	0.174888i
$598$	−73.9586	+	28.3901i	−3.02439	+	1.16096i
$599$	−7.68207	−	13.3057i	−0.313881	−	0.543658i	0.665318	−	0.746560i	$-0.268296\pi$
$599$	−7.68207	−	13.3057i	−0.313881	−	0.543658i	−0.979199	+	0.202902i	$0.934963\pi$
$600$	22.4439	−	20.1304i	0.916269	−	0.821821i
$601$	−17.9295			−0.731360			−0.365680	−	0.930741i	$-0.619164\pi$
$601$	−17.9295			−0.731360			−0.365680	+	0.930741i	$0.619164\pi$
$602$	7.02225	+	23.7916i	0.286206	+	0.969673i
$603$	−4.95538	−	30.2998i	−0.201799	−	1.23390i
$604$	−35.3037	+	31.7876i	−1.43649	+	1.29342i
$605$	−2.83439	−	21.9052i	−0.115235	−	0.890574i
$606$	41.8094	−	34.0310i	1.69839	−	1.38242i
$607$	30.6727	−	8.21873i	1.24497	−	0.333588i	0.424576	−	0.905392i	$-0.360423\pi$
$607$	30.6727	−	8.21873i	1.24497	−	0.333588i	0.820390	+	0.571804i	$0.193756\pi$
$608$	1.58517	−	3.11107i	0.0642871	−	0.126171i
$609$	−21.7318	+	18.6188i	−0.880618	+	0.754473i
$610$	9.68076	−	3.98473i	0.391963	−	0.161337i
$611$	−56.8041	+	5.97036i	−2.29805	+	0.241535i
$612$	12.1804	+	31.2602i	0.492365	+	1.26362i
$613$	1.57677	+	1.94715i	0.0636850	+	0.0786445i	0.807993	−	0.589192i	$-0.200554\pi$
$613$	1.57677	+	1.94715i	0.0636850	+	0.0786445i	−0.744308	+	0.667837i	$0.767221\pi$
$614$	−0.882942	−	8.40063i	−0.0356326	−	0.339022i
$615$	−0.491551	+	1.18770i	−0.0198212	+	0.0478925i
$616$	−6.34351	+	7.41269i	−0.255587	+	0.298666i
$617$	11.7086	+	5.96584i	0.471371	+	0.240176i	0.673505	−	0.739182i	$-0.264788\pi$
$617$	11.7086	+	5.96584i	0.471371	+	0.240176i	−0.202134	+	0.979358i	$0.564788\pi$
$618$	76.6663	−	8.25297i	3.08397	−	0.331983i
$619$	−17.5886	−	15.8368i	−0.706944	−	0.636535i	0.235121	−	0.971966i	$-0.424451\pi$
$619$	−17.5886	−	15.8368i	−0.706944	−	0.636535i	−0.942065	+	0.335431i	$0.891118\pi$
$620$	−11.9511	−	25.1999i	−0.479969	−	1.01205i
$621$	26.4426	−	7.29956i	1.06110	−	0.292921i
$622$	70.2537	−	35.7961i	2.81692	−	1.43529i
$623$	−1.49432	+	0.441058i	−0.0598685	+	0.0176706i
$624$	2.01860	−	12.9558i	0.0808087	−	0.518646i
$625$	−18.7265	+	16.5625i	−0.749060	+	0.662502i
$626$	2.73524	−	1.57919i	0.109322	−	0.0631173i
$627$	−1.49293	+	0.321258i	−0.0596218	+	0.0128298i
$628$	−62.0989	−	3.25447i	−2.47802	−	0.129867i
$629$	4.45859	−	13.7221i	0.177776	−	0.547137i
$630$	22.7054	+	34.8230i	0.904606	+	1.38738i
$631$	−13.0081	−	40.0347i	−0.517842	−	1.59375i	−0.778050	−	0.628202i	$-0.783791\pi$
$631$	−13.0081	−	40.0347i	−0.517842	−	1.59375i	0.260208	−	0.965553i	$-0.416209\pi$
$632$	0.605377	+	2.25930i	0.0240806	+	0.0898701i
$633$	−1.45624	+	14.1986i	−0.0578803	+	0.564344i
$634$	2.05449	+	0.215936i	0.0815942	+	0.00857589i
$635$	28.9686	+	27.6128i	1.14959	+	1.09578i
$636$	−23.1539	−	45.1610i	−0.918114	−	1.79075i
$637$	38.8815	−	22.3476i	1.54054	−	0.885444i
$638$	2.42374	+	15.3029i	0.0959568	+	0.605847i
$639$	5.96366	−	28.7676i	0.235919	−	1.13803i
$640$	−27.5219	+	35.7028i	−1.08790	+	1.41128i
$641$	−16.7156	−	1.75688i	−0.660227	−	0.0693927i	−0.231512	−	0.972832i	$-0.574367\pi$
$641$	−16.7156	−	1.75688i	−0.660227	−	0.0693927i	−0.428716	+	0.903439i	$0.641034\pi$
$642$	−8.96633	−	20.0032i	−0.353873	−	0.789462i
$643$	7.00253	−	7.00253i	0.276153	−	0.276153i	−0.555418	−	0.831571i	$-0.687442\pi$
$643$	7.00253	−	7.00253i	0.276153	−	0.276153i	0.831571	+	0.555418i	$0.187442\pi$
$644$	13.8754	−	46.6760i	0.546768	−	1.83929i
$645$	8.09647	−	13.2210i	0.318798	−	0.520575i
$646$	4.18464	+	4.64751i	0.164642	+	0.182854i
$647$	−7.41942	+	11.4249i	−0.291688	+	0.449160i	−0.953886	−	0.300169i	$-0.902957\pi$
$647$	−7.41942	+	11.4249i	−0.291688	+	0.449160i	0.662198	+	0.749329i	$0.269624\pi$
$648$	−7.80438	+	30.3442i	−0.306585	+	1.19203i
$649$	7.21539	+	4.16581i	0.283229	+	0.163522i
$650$	−12.0664	+	74.0538i	−0.473284	+	2.90463i
$651$	15.7127	−	4.68071i	0.615830	−	0.183452i
$652$	−72.4816	−	11.4800i	−2.83860	−	0.449590i
$653$	−0.722335	+	13.7830i	−0.0282672	+	0.539370i	0.947392	+	0.320076i	$0.103709\pi$
$653$	−0.722335	+	13.7830i	−0.0282672	+	0.539370i	−0.975659	+	0.219293i	$0.929625\pi$
$654$	47.7879	−	2.62500i	1.86865	−	0.102646i
$655$	−24.0886	+	22.7578i	−0.941220	+	0.889220i
$656$	−0.0815367	+	0.383600i	−0.00318347	+	0.0149771i
$657$	1.58645	+	3.07524i	0.0618933	+	0.119977i
$658$	28.9134	−	47.0796i	1.12716	−	1.83535i
$659$	19.9345	+	14.4832i	0.776536	+	0.564187i	0.903938	−	0.427665i	$-0.140664\pi$
$659$	19.9345	+	14.4832i	0.776536	+	0.564187i	−0.127401	+	0.991851i	$0.540664\pi$
$660$	14.2974	−	0.378597i	0.556525	−	0.0147369i
$661$	0.752110	+	0.334861i	0.0292537	+	0.0130246i	0.421311	−	0.906916i	$-0.361570\pi$
$661$	0.752110	+	0.334861i	0.0292537	+	0.0130246i	−0.392058	+	0.919941i	$0.628237\pi$
$662$	−25.5566	−	31.5597i	−0.993284	−	1.22660i
$663$	−30.8708	−	17.7199i	−1.19892	−	0.688184i
$664$	21.3878	+	29.4378i	0.830009	+	1.14241i
$665$	3.97455	+	2.90712i	0.154127	+	0.112733i
$666$	25.4764	−	18.7062i	0.987189	−	0.724850i
$667$	−17.9553	−	27.6488i	−0.695233	−	1.07056i
$668$	7.74217	−	28.8942i	0.299553	−	1.11795i
$669$	6.86872	+	8.43868i	0.265560	+	0.326258i
$670$	17.7802	+	50.5663i	0.686908	+	1.95355i
$671$	2.01362	+	0.654265i	0.0777349	+	0.0252576i
$672$	−13.2540	−	13.9238i	−0.511286	−	0.537120i
$673$	−4.32286	+	27.2935i	−0.166634	+	1.05209i	0.752630	+	0.658444i	$0.228785\pi$
$673$	−4.32286	+	27.2935i	−0.166634	+	1.05209i	−0.919264	+	0.393642i	$0.871215\pi$
$674$	−13.4331	+	23.2668i	−0.517423	+	0.896202i
$675$	6.64641	−	25.1162i	0.255820	−	0.966724i
$676$	48.8858	+	84.6727i	1.88022	+	3.25664i
$677$	20.3020	+	16.4402i	0.780269	+	0.631849i	0.934410	−	0.356200i	$-0.115928\pi$
$677$	20.3020	+	16.4402i	0.780269	+	0.631849i	−0.154141	+	0.988049i	$0.549261\pi$
$678$	14.5143	+	44.2910i	0.557417	+	1.70098i
$679$	4.93935	+	6.45005i	0.189555	+	0.247530i
$680$	−12.9998	−	21.3198i	−0.498518	−	0.817578i
$681$	14.6745	−	38.5177i	0.562328	−	1.47600i
$682$	2.29741	−	8.57407i	0.0879725	−	0.328318i
$683$	5.60144	−	0.293559i	0.214333	−	0.0112327i	0.0551329	−	0.998479i	$-0.482442\pi$
$683$	5.60144	−	0.293559i	0.214333	−	0.0112327i	0.159200	+	0.987246i	$0.449108\pi$
$684$	0.953509	+	8.65309i	0.0364583	+	0.330859i
$685$	1.25196	+	16.3725i	0.0478348	+	0.625559i
$686$	−5.78754	+	42.9919i	−0.220969	+	1.64144i
$687$	−0.0943116	−	37.4971i	−0.00359821	−	1.43060i
$688$	1.69506	−	4.41579i	0.0646236	−	0.168350i
$689$	49.1898	+	21.9007i	1.87398	+	0.834351i
$690$	−43.2197	+	20.6304i	−1.64535	+	0.785384i
$691$	−13.2617	+	5.90449i	−0.504499	+	0.224618i	−0.643173	−	0.765721i	$-0.722383\pi$
$691$	−13.2617	+	5.90449i	−0.504499	+	0.224618i	0.138674	+	0.990338i	$0.455716\pi$
$692$	24.0539	+	12.2561i	0.914392	+	0.465906i
$693$	−1.06357	+	8.34002i	−0.0404016	+	0.316811i
$694$	79.8615	−	25.9486i	3.03150	−	0.984995i
$695$	0.867574	+	36.2041i	0.0329089	+	1.37330i
$696$	37.5979	−	2.06526i	1.42514	−	0.0782835i
$697$	0.892860	+	0.579830i	0.0338195	+	0.0219626i
$698$	−45.9258	+	56.7136i	−1.73832	+	2.14664i
$699$	−12.1376	−	1.89112i	−0.459086	−	0.0715289i
$700$	−31.5648	−	33.6251i	−1.19304	−	1.27091i
$701$			18.3856i			0.694413i	0.937789	+	0.347207i	$0.112870\pi$
$701$			18.3856i			0.694413i	−0.937789	+	0.347207i	$0.887130\pi$
$702$	−32.2514	−	70.9914i	−1.21725	−	2.67940i
$703$	2.03906	−	3.13988i	0.0769048	−	0.118423i
$704$	−12.6290	+	2.68438i	−0.475973	+	0.101171i
$705$	−33.9489	+	6.30238i	−1.27859	+	0.237361i
$706$	−21.9378	−	67.5177i	−0.825641	−	2.54106i
$707$	−22.8064	−	26.7555i	−0.857723	−	1.00624i
$708$	27.8205	−	38.4949i	1.04556	−	1.44673i
$709$	−6.53946	−	14.6879i	−0.245595	−	0.551615i	0.748119	−	0.663564i	$-0.230957\pi$
$709$	−6.53946	−	14.6879i	−0.245595	−	0.551615i	−0.993714	+	0.111950i	$0.964290\pi$
$710$	−1.45653	+	51.2707i	−0.0546627	+	1.92416i
$711$	1.50466	+	1.34116i	0.0564293	+	0.0502975i
$712$	1.91393	+	0.734689i	0.0717276	+	0.0275337i
$713$	2.95465	+	18.6549i	0.110653	+	0.698633i
$714$	31.7897	−	13.2252i	1.18970	−	0.494942i
$715$	−11.5606	+	9.82936i	−0.432342	+	0.367597i
$716$	−27.1117	−	60.8939i	−1.01321	−	2.27571i
$717$	0.817989	−	7.97556i	0.0305484	−	0.297853i
$718$	−1.27348	−	0.341229i	−0.0475260	−	0.0127345i
$719$	5.90097	+	1.25429i	0.220069	+	0.0467771i	0.316626	−	0.948550i	$-0.397450\pi$
$719$	5.90097	+	1.25429i	0.220069	+	0.0467771i	−0.0965575	+	0.995327i	$0.530783\pi$
$720$	0.599716	−	7.90392i	0.0223501	−	0.294562i
$721$	−6.51532	−	49.8631i	−0.242643	−	1.85700i
$722$	−19.4674	−	38.2069i	−0.724501	−	1.42191i
$723$	5.19301	+	5.73833i	0.193130	+	0.213411i
$724$	−20.9772	+	12.1112i	−0.779613	+	0.450110i
$725$	−31.1879	+	1.49559i	−1.15829	+	0.0555450i
$726$	−31.2071	−	25.1413i	−1.15820	−	0.933081i
$727$	40.2750	+	6.37893i	1.49372	+	0.236581i	0.849225	−	0.528031i	$-0.177069\pi$
$727$	40.2750	+	6.37893i	1.49372	+	0.236581i	0.644491	+	0.764612i	$0.277069\pi$
$728$	−58.4969	−	7.75909i	−2.16804	−	0.287571i
$729$	8.73001	+	25.5497i	0.323334	+	0.946285i
$730$	−3.66698	−	4.80095i	−0.135721	−	0.177691i
$731$	−9.54217	−	8.59181i	−0.352930	−	0.317779i
$732$	4.88143	−	11.0385i	0.180423	−	0.407995i
$733$	9.58085	−	6.22188i	0.353877	−	0.229810i	−0.355442	−	0.934698i	$-0.615670\pi$
$733$	9.58085	−	6.22188i	0.353877	−	0.229810i	0.709318	+	0.704888i	$0.249003\pi$
$734$	−36.9544	−	26.8489i	−1.36401	−	0.991012i
$735$	22.3681	−	15.3189i	0.825059	−	0.565046i
$736$	17.9163	−	13.0170i	0.660404	−	0.479812i
$737$	−3.88489	+	10.1205i	−0.143102	+	0.372793i
$738$	0.846701	+	2.17300i	0.0311675	+	0.0799891i
$739$	−9.76997	+	21.9437i	−0.359394	+	0.807213i	0.639856	+	0.768495i	$0.278994\pi$
$739$	−9.76997	+	21.9437i	−0.359394	+	0.807213i	−0.999250	+	0.0387179i	$0.987673\pi$
$740$	−24.1930	+	25.3810i	−0.889352	+	0.933022i
$741$	−6.54743	−	6.51457i	−0.240526	−	0.239319i
$742$	−45.7965	+	24.8079i	−1.68124	+	0.910727i
$743$	27.7250	+	27.7250i	1.01713	+	1.01713i	0.999851	+	0.0172824i	$0.00550145\pi$
$743$	27.7250	+	27.7250i	1.01713	+	1.01713i	0.0172824	+	0.999851i	$0.494499\pi$
$744$	−20.1594	−	7.68033i	−0.739078	−	0.281575i
$745$	45.3555	−	21.5099i	1.66170	−	0.788064i
$746$	−0.575360	−	2.70685i	−0.0210654	−	0.0991050i
$747$	29.3299	+	11.0897i	1.07313	+	0.405753i
$748$	1.85309	−	11.6999i	0.0677556	−	0.427792i
$749$	−12.9091	+	6.14192i	−0.471687	+	0.224421i
$750$	−3.74630	+	45.2031i	−0.136795	+	1.65059i
$751$	−8.65777	+	14.9957i	−0.315927	+	0.547201i	−0.979634	−	0.200791i	$-0.935649\pi$
$751$	−8.65777	+	14.9957i	−0.315927	+	0.547201i	0.663707	+	0.747992i	$0.268982\pi$
$752$	−9.83495	+	3.77528i	−0.358644	+	0.137670i
$753$	−25.3784	−	22.7355i	−0.924841	−	0.828528i
$754$	−69.6395	+	62.7036i	−2.53612	+	2.28353i
$755$	2.45809	−	30.3704i	0.0894590	−	1.10529i
$756$	46.6768	+	10.8821i	1.69762	+	0.395778i
$757$	11.8793	+	11.8793i	0.431759	+	0.431759i	0.889226	−	0.457468i	$-0.151243\pi$
$757$	11.8793	+	11.8793i	0.431759	+	0.431759i	−0.457468	+	0.889226i	$0.651243\pi$
$758$	12.0608	+	18.5720i	0.438068	+	0.674565i
$759$	−9.36192	−	2.48330i	−0.339816	−	0.0901381i
$760$	−1.82645	−	6.21665i	−0.0662522	−	0.225502i
$761$	38.4832	−	4.04475i	1.39502	−	0.146622i	0.622999	−	0.782223i	$-0.285914\pi$
$761$	38.4832	−	4.04475i	1.39502	−	0.146622i	0.772018	+	0.635601i	$0.219248\pi$
$762$	72.6101	−	0.182627i	2.63039	−	0.00661587i
$763$	−2.41862	−	31.1181i	−0.0875601	−	1.12655i
$764$	−17.2889	+	12.5611i	−0.625491	+	0.454446i
$765$	−19.4480	−	9.20924i	−0.703143	−	0.332961i
$766$	−3.75290	+	35.7064i	−0.135598	+	1.29013i
$767$	2.63729	+	50.3225i	0.0952270	+	1.81704i
$768$	4.23461	+	39.3376i	0.152803	+	1.41947i
$769$	−39.6071	+	12.8691i	−1.42827	+	0.464072i	−0.918219	−	0.396073i	$-0.870373\pi$
$769$	−39.6071	+	12.8691i	−1.42827	+	0.464072i	−0.510049	+	0.860146i	$0.670373\pi$
$770$	−0.721393	−	14.6605i	−0.0259972	−	0.528327i
$771$	−33.9160	−	17.1737i	−1.22145	−	0.618497i
$772$	−3.33020	+	63.5440i	−0.119857	+	2.28700i
$773$	−16.5338	−	43.0719i	−0.594678	−	1.54919i	−0.818468	−	0.574552i	$-0.805176\pi$
$773$	−16.5338	−	43.0719i	−0.594678	−	1.54919i	0.223790	−	0.974637i	$-0.428157\pi$
$774$	−5.98640	−	27.4833i	−0.215177	−	0.987865i
$775$	16.6717	+	6.48479i	0.598866	+	0.232941i
$776$		−	10.6897i		−	0.383739i
$777$	−12.5731	−	16.3334i	−0.451059	−	0.585956i
$778$	−8.14367	−	15.9828i	−0.291965	−	0.573013i
$779$	0.184846	+	0.205292i	0.00662279	+	0.00735536i
$780$	49.0175	+	71.2759i	1.75511	+	2.55209i
$781$	−6.94114	+	7.70891i	−0.248373	+	0.275847i
$782$	10.2661	+	38.3136i	0.367115	+	1.37009i
$783$	26.1068	−	19.2704i	0.932982	−	0.688667i
$784$	5.86015	−	5.83741i	0.209291	−	0.208479i
$785$	30.3857	−	25.8353i	1.08451	−	0.922102i
$786$	−2.99565	+	60.0498i	−0.106851	+	2.14191i
$787$	12.9461	−	10.4835i	0.461478	−	0.373697i	−0.370203	−	0.928951i	$-0.620712\pi$
$787$	12.9461	−	10.4835i	0.461478	−	0.373697i	0.831681	+	0.555253i	$0.187379\pi$
$788$	−12.8580	+	10.4122i	−0.458048	+	0.370920i
$789$	1.53178	−	30.7057i	0.0545330	−	1.09315i
$790$	−2.99630	−	1.84530i	−0.106603	−	0.0656528i
$791$	28.6622	−	10.1185i	1.01911	−	0.359772i
$792$	7.78311	−	7.86181i	0.276561	−	0.279357i
$793$	3.31433	+	12.3692i	0.117695	+	0.439245i
$794$	−11.0987	+	12.3264i	−0.393878	+	0.437446i
$795$	30.6870	+	10.8567i	1.08836	+	0.385047i
$796$	5.88064	+	6.53111i	0.208434	+	0.231489i
$797$	−6.03100	−	11.8365i	−0.213629	−	0.419271i	0.759180	−	0.650881i	$-0.225600\pi$
$797$	−6.03100	−	11.8365i	−0.213629	−	0.419271i	−0.972809	+	0.231611i	$0.925600\pi$
$798$	8.85597	−	1.17982i	0.313498	−	0.0417651i
$799$			28.5981i			1.01173i
$800$	−2.09975	−	20.8691i	−0.0742373	−	0.737835i
$801$	1.72619	−	0.375997i	0.0609918	−	0.0132852i
$802$	−3.92522	−	10.2255i	−0.138604	−	0.361076i
$803$	0.0639436	−	1.22012i	0.00225652	−	0.0430570i
$804$	55.1327	+	27.9171i	1.94438	+	0.984560i
$805$	14.0902	+	27.8733i	0.496616	+	0.982405i
$806$	51.0596	−	16.5903i	1.79850	−	0.584368i
$807$	−0.534601	−	4.96620i	−0.0188188	−	0.174819i
$808$	2.42103	+	46.1961i	0.0851717	+	1.62517i
$809$	−0.998844	+	9.50337i	−0.0351175	+	0.334121i	0.962831	+	0.270103i	$0.0870579\pi$
$809$	−0.998844	+	9.50337i	−0.0351175	+	0.334121i	−0.997949	+	0.0640171i	$0.979609\pi$
$810$	−22.8161	−	41.2477i	−0.801678	−	1.44930i
$811$	2.75148	−	1.99906i	0.0966174	−	0.0701966i	−0.538428	−	0.842672i	$-0.680982\pi$
$811$	2.75148	−	1.99906i	0.0966174	−	0.0701966i	0.635045	+	0.772475i	$0.280982\pi$
$812$	−4.46349	−	57.4274i	−0.156638	−	2.01531i
$813$	−3.51354	+	0.00883715i	−0.123225	+	0.000309932i
$814$	−11.0986	+	1.16651i	−0.389006	+	0.0408861i
$815$	38.8494	−	26.5736i	1.36084	−	0.930833i
$816$	−6.34569	−	1.68323i	−0.222144	−	0.0589248i
$817$	−1.81464	−	2.79429i	−0.0634861	−	0.0977600i
$818$	−38.6167	−	38.6167i	−1.35020	−	1.35020i
$819$	−45.8080	+	22.0780i	−1.60066	+	0.771466i
$820$	−1.34694	−	2.20900i	−0.0470370	−	0.0771416i
$821$	−37.3267	+	33.6091i	−1.30271	+	1.17297i	−0.329216	+	0.944254i	$0.606785\pi$
$821$	−37.3267	+	33.6091i	−1.30271	+	1.17297i	−0.973494	+	0.228711i	$0.926549\pi$
$822$	22.1896	+	19.8788i	0.773951	+	0.693351i
$823$	1.10789	−	0.425280i	0.0386187	−	0.0148243i	−0.338982	−	0.940793i	$-0.610083\pi$
$823$	1.10789	−	0.425280i	0.0386187	−	0.0148243i	0.377601	+	0.925969i	$0.376749\pi$
$824$	−33.0841	+	57.3033i	−1.15254	+	1.99626i
$825$	−6.49906	+	6.47406i	−0.226268	+	0.225398i
$826$	−40.1441	−	27.6477i	−1.39679	−	0.961987i
$827$	−0.529675	+	3.34424i	−0.0184186	+	0.116291i	−0.995185	−	0.0980179i	$-0.968750\pi$
$827$	−0.529675	+	3.34424i	−0.0184186	+	0.116291i	0.976766	+	0.214308i	$0.0687498\pi$
$828$	−19.5276	+	51.6462i	−0.678632	+	1.79483i
$829$	7.76850	+	36.5479i	0.269811	+	1.26936i	0.879186	+	0.476479i	$0.158087\pi$
$829$	7.76850	+	36.5479i	0.269811	+	1.26936i	−0.609375	+	0.792883i	$0.708579\pi$
$830$	−53.8042	−	10.0957i	−1.86757	−	0.350426i
$831$	−5.38341	−	2.05098i	−0.186749	−	0.0711477i
$832$	−55.2176	−	55.2176i	−1.91433	−	1.91433i
$833$	−9.09308	−	20.5307i	−0.315056	−	0.711346i
$834$	46.5770	+	46.3433i	1.61283	+	1.60474i
$835$	9.11737	+	16.8814i	0.315520	+	0.584205i
$836$	1.25021	−	2.80802i	0.0432395	−	0.0971175i
$837$	−18.1544	+	4.00223i	−0.627506	+	0.138337i
$838$	23.7591	−	61.8945i	0.820743	−	2.13811i
$839$	−23.4997	+	17.0735i	−0.811300	+	0.589444i	−0.914207	−	0.405247i	$-0.867185\pi$
$839$	−23.4997	+	17.0735i	−0.811300	+	0.589444i	0.102908	+	0.994691i	$0.467185\pi$
$840$	−35.6226	−	1.89111i	−1.22910	−	0.0652496i
$841$	−8.08758	−	5.87597i	−0.278882	−	0.202620i
$842$	−22.9629	+	14.9123i	−0.791354	+	0.513911i
$843$	−18.2579	+	41.2872i	−0.628837	+	1.42201i
$844$	−21.3498	−	19.2235i	−0.734892	−	0.661699i
$845$	−60.0875	−	17.9440i	−2.06707	−	0.617293i
$846$	−36.5674	+	50.8668i	−1.25721	+	1.74884i
$847$	−15.9299	+	20.7186i	−0.547359	+	0.711899i
$848$	9.80889	+	1.55358i	0.336839	+	0.0533500i
$849$	−18.3210	−	14.7599i	−0.628776	−	0.506560i
$850$	36.2436	+	9.88423i	1.24315	+	0.339026i
$851$	20.5644	−	11.8728i	0.704937	−	0.406996i
$852$	39.6794	+	43.8462i	1.35939	+	1.50214i
$853$	4.10608	+	8.05864i	0.140590	+	0.275923i	0.950556	−	0.310554i	$-0.100515\pi$
$853$	4.10608	+	8.05864i	0.140590	+	0.275923i	−0.809966	+	0.586477i	$0.800515\pi$
$854$	−11.4393	−	4.75135i	−0.391445	−	0.162588i
$855$	−4.25597	−	3.61431i	−0.145551	−	0.123607i
$856$	18.3994	+	3.91091i	0.628878	+	0.133672i
$857$	−39.1183	−	10.4817i	−1.33626	−	0.358049i	−0.481212	−	0.876604i	$-0.659803\pi$
$857$	−39.1183	−	10.4817i	−1.33626	−	0.358049i	−0.855044	+	0.518555i	$0.826470\pi$
$858$	−2.80894	+	27.3877i	−0.0958955	+	0.935001i
$859$	15.0429	+	33.7868i	0.513256	+	1.15279i	0.965383	+	0.260838i	$0.0839988\pi$
$859$	15.0429	+	33.7868i	0.513256	+	1.15279i	−0.452127	+	0.891954i	$0.649335\pi$
$860$	11.8775	+	28.8560i	0.405020	+	0.983980i
$861$	1.40423	−	0.584192i	0.0478560	−	0.0199092i
$862$	−1.52784	−	9.64638i	−0.0520383	−	0.328557i
$863$	−3.17467	−	1.21864i	−0.108067	−	0.0414831i	0.303734	−	0.952757i	$-0.401767\pi$
$863$	−3.17467	−	1.21864i	−0.108067	−	0.0414831i	−0.411801	+	0.911274i	$0.635100\pi$
$864$	13.8449	+	16.8357i	0.471014	+	0.572763i
$865$	−16.6130	+	4.88088i	−0.564858	+	0.165955i
$866$	−4.88146	−	10.9639i	−0.165879	−	0.372570i
$867$	6.80796	−	9.42009i	0.231210	−	0.319923i
$868$	−11.0459	+	31.0966i	−0.374923	+	1.05549i
$869$	−0.219922	−	0.676852i	−0.00746036	−	0.0229606i
$870$	−38.9832	+	41.1039i	−1.32165	+	1.39355i
$871$	−64.1331	+	13.6319i	−2.17307	+	0.461900i
$872$	−22.3678	+	34.4434i	−0.757470	+	1.16640i
$873$	−5.05592	−	7.70035i	−0.171117	−	0.260617i
$874$			10.2924i			0.348146i
$875$	29.5272	+	1.77361i	0.998201	+	0.0599590i
$876$	−6.88197	−	1.07226i	−0.232520	−	0.0362283i
$877$	5.68683	−	7.02265i	0.192031	−	0.237138i	−0.672032	−	0.740522i	$-0.734578\pi$
$877$	5.68683	−	7.02265i	0.192031	−	0.237138i	0.864063	+	0.503384i	$0.167912\pi$
$878$	−9.23851	−	5.99956i	−0.311785	−	0.202475i
$879$	4.52562	−	0.248593i	0.152645	−	0.00838485i
$880$	−1.59036	+	2.30302i	−0.0536111	+	0.0776346i
$881$	−0.430612	+	0.139914i	−0.0145077	+	0.00471384i	−0.316262	−	0.948672i	$-0.602428\pi$
$881$	−0.430612	+	0.139914i	−0.0145077	+	0.00471384i	0.301754	+	0.953386i	$0.402428\pi$
$882$	10.0782	−	48.1444i	0.339350	−	1.62111i
$883$	−15.8586	−	8.08038i	−0.533686	−	0.271927i	0.166310	−	0.986074i	$-0.446815\pi$
$883$	−15.8586	−	8.08038i	−0.533686	−	0.271927i	−0.699996	+	0.714147i	$0.746815\pi$
$884$	65.4519	−	29.1410i	2.20138	−	0.980119i
$885$	3.98512	+	30.2014i	0.133958	+	1.01521i
$886$	−23.3745	−	10.4070i	−0.785282	−	0.349630i
$887$	3.40512	−	8.87064i	0.114333	−	0.297847i	−0.864459	−	0.502703i	$-0.832339\pi$
$887$	3.40512	−	8.87064i	0.114333	−	0.297847i	0.978792	+	0.204856i	$0.0656725\pi$
$888$	0.0682156	+	27.1217i	0.00228917	+	0.910144i
$889$	−1.19356	−	47.3379i	−0.0400306	−	1.58766i
$890$	−2.85213	+	1.17398i	−0.0956038	+	0.0393518i
$891$	1.88817	−	9.34442i	0.0632559	−	0.313050i
$892$	−21.8709	+	1.14620i	−0.732291	+	0.0383777i
$893$	−1.92062	+	7.16785i	−0.0642711	+	0.239863i
$894$	32.4243	−	85.1075i	1.08443	−	2.84642i
$895$	39.4621	+	16.4485i	1.31907	+	0.549813i
$896$	52.8890	−	6.91068i	1.76690	−	0.230870i
$897$	−18.2427	−	55.6683i	−0.609105	−	1.85871i
$898$	−33.6087	−	27.2158i	−1.12154	−	0.908203i
$899$	11.1709	+	19.3486i	0.372571	+	0.645311i
$900$	32.9338	+	40.6210i	1.09779	+	1.35403i
$901$	13.4799	−	23.3479i	0.449081	−	0.777832i
$902$	0.128814	−	0.813299i	0.00428904	−	0.0270799i
$903$	−17.8301	+	4.30974i	−0.593348	+	0.143419i
$904$	−38.0377	−	12.3592i	−1.26512	−	0.411061i
$905$	4.44554	−	14.8864i	0.147775	−	0.494840i
$906$	−34.8980	−	42.8745i	−1.15941	−	1.42441i
$907$	0.00496836	−	0.0185422i	0.000164972	−	0.000615683i	−0.965843	−	0.259127i	$-0.916565\pi$
$907$	0.00496836	−	0.0185422i	0.000164972	−	0.000615683i	0.966008	+	0.258511i	$0.0832319\pi$
$908$	45.1858	+	69.5801i	1.49954	+	2.30910i
$909$	23.5933	+	32.1323i	0.782541	+	1.06576i
$910$	71.9885	−	51.9523i	2.38640	−	1.72220i
$911$	1.91500	+	2.63577i	0.0634467	+	0.0873269i	0.839561	−	0.543265i	$-0.182812\pi$
$911$	1.91500	+	2.63577i	0.0634467	+	0.0873269i	−0.776114	+	0.630592i	$0.782812\pi$
$912$	−1.47744	−	0.848054i	−0.0489230	−	0.0280819i
$913$	−6.96750	−	8.60415i	−0.230591	−	0.284756i
$914$	−45.0813	−	20.0715i	−1.49116	−	0.663906i
$915$	2.58626	+	7.29656i	0.0854992	+	0.241217i
$916$	61.0604	+	44.3630i	2.01749	+	1.46579i
$917$	39.1959	+	1.06450i	1.29436	+	0.0351527i
$918$	−37.0382	+	12.3442i	−1.22244	+	0.407418i
$919$	−6.67565	+	31.4065i	−0.220209	+	1.03600i	0.719622	+	0.694366i	$0.244315\pi$
$919$	−6.67565	+	31.4065i	−0.220209	+	1.03600i	−0.939832	+	0.341638i	$0.889018\pi$
$920$	7.57884	−	40.3909i	0.249867	−	1.33165i
$921$	6.23684	−	0.342591i	0.205511	−	0.0112888i
$922$	2.16312	−	41.2748i	0.0712387	−	1.35931i
$923$	−61.9681	−	9.81478i	−2.03970	−	0.323057i
$924$	−12.2933	−	11.6299i	−0.404421	−	0.382597i
$925$	0.0999042	−	22.4895i	0.00328483	−	0.739451i
$926$	48.6675	+	28.0982i	1.59931	+	0.923364i
$927$	3.27060	+	56.9262i	0.107421	+	1.86970i
$928$	14.2674	−	21.9699i	0.468350	−	0.721196i
$929$	4.84144	+	5.37696i	0.158842	+	0.176412i	0.817313	−	0.576194i	$-0.195463\pi$
$929$	4.84144	+	5.37696i	0.158842	+	0.176412i	−0.658470	+	0.752607i	$0.728796\pi$
$930$	29.9814	−	12.4290i	0.983128	−	0.407564i
$931$	−0.900275	−	5.75650i	−0.0295053	−	0.188662i
$932$	17.4835	−	17.4835i	0.572691	−	0.572691i
$933$	23.8489	+	53.2049i	0.780778	+	1.74185i
$934$	7.96568	+	0.837227i	0.260645	+	0.0273949i
$935$	4.28950	+	6.27105i	0.140282	+	0.205085i
$936$	65.5171	+	13.5820i	2.14149	+	0.443942i
$937$	3.71009	+	23.4246i	0.121203	+	0.765247i	0.971166	+	0.238404i	$0.0766243\pi$
$937$	3.71009	+	23.4246i	0.121203	+	0.765247i	−0.849963	+	0.526843i	$0.823376\pi$
$938$	27.3594	−	57.2170i	0.893315	−	1.86820i
$939$	1.06554	+	2.07830i	0.0347726	+	0.0678229i
$940$	30.0599	−	62.6632i	0.980444	−	2.04385i
$941$	33.4821	+	3.51911i	1.09148	+	0.114720i	0.633127	−	0.774048i	$-0.281771\pi$
$941$	33.4821	+	3.51911i	1.09148	+	0.114720i	0.458358	+	0.888768i	$0.348438\pi$
$942$	7.38296	−	71.9853i	0.240550	−	2.34541i
$943$	0.453479	+	1.69241i	0.0147673	+	0.0551124i
$944$	2.87207	+	8.83932i	0.0934779	+	0.287695i
$945$	−26.5552	+	15.4862i	−0.863841	+	0.503765i
$946$	−3.06899	+	9.44536i	−0.0997813	+	0.307095i
$947$	20.9639	+	1.09867i	0.681234	+	0.0357020i	0.389815	−	0.920893i	$-0.372539\pi$
$947$	20.9639	+	1.09867i	0.681234	+	0.0357020i	0.291420	+	0.956595i	$0.405872\pi$
$948$	−3.96627	+	0.853489i	−0.128818	+	0.0277200i
$949$	6.39965	−	3.69484i	0.207741	−	0.119940i
$950$	8.42031	+	4.91147i	0.273191	+	0.159349i
$951$	−0.235174	+	1.50939i	−0.00762605	+	0.0489454i
$952$	−6.92518	+	28.7225i	−0.224447	+	0.930901i
$953$	35.7635	−	18.2224i	1.15849	−	0.590282i	0.234285	−	0.972168i	$-0.424725\pi$
$953$	35.7635	−	18.2224i	1.15849	−	0.590282i	0.924210	+	0.381886i	$0.124725\pi$
$954$	53.8305	−	24.2921i	1.74283	−	0.786485i
$955$	2.52777	−	13.4716i	0.0817966	−	0.435929i
$956$	11.9925	+	10.7981i	0.387865	+	0.349235i
$957$	−11.3913	+	1.22625i	−0.368228	+	0.0396390i
$958$	27.5215	+	14.0229i	0.889180	+	0.453060i
$959$	12.6323	−	14.7614i	0.407918	−	0.476671i
$960$	−35.9058	−	30.6482i	−1.15886	−	0.989167i
$961$	1.90242	+	18.1004i	0.0613685	+	0.583882i
$962$	−42.4770	−	52.4547i	−1.36951	−	1.69121i
$963$	15.1037	−	5.88512i	0.486711	−	0.189645i
$964$	−15.4923	+	1.62830i	−0.498973	+	0.0524442i
$965$	−26.4365	−	31.0928i	−0.851022	−	1.00091i
$966$	53.4444	+	18.8329i	1.71954	+	0.605938i
$967$	9.02326	−	17.7091i	0.290168	−	0.569488i	−0.699199	−	0.714927i	$-0.746460\pi$
$967$	9.02326	−	17.7091i	0.290168	−	0.569488i	0.989367	+	0.145440i	$0.0464597\pi$
$968$	33.2166	−	8.90035i	1.06762	−	0.286068i
$969$	−3.58661	+	2.91935i	−0.115219	+	0.0937829i
$970$	11.0444	+	11.6903i	0.354614	+	0.375352i
$971$	−19.4804	+	17.5402i	−0.625156	+	0.562893i	−0.919640	−	0.392763i	$-0.871519\pi$
$971$	−19.4804	+	17.5402i	−0.625156	+	0.562893i	0.294483	+	0.955657i	$0.404852\pi$
$972$	−51.8931	−	16.1425i	−1.66447	−	0.517771i
$973$	29.5259	−	31.0533i	0.946556	−	0.995523i
$974$	53.1131			1.70185
$975$	−54.2481	−	11.6401i	−1.73733	−	0.372781i
$976$	1.18093	+	2.04543i	0.0378007	+	0.0654727i
$977$	−20.2170	+	7.76057i	−0.646798	+	0.248283i	−0.659578	−	0.751636i	$-0.729265\pi$
$977$	−20.2170	+	7.76057i	−0.646798	+	0.248283i	0.0127801	+	0.999918i	$0.495932\pi$
$978$	17.5449	−	83.5756i	0.561026	−	2.67245i
$979$	−0.593250	−	0.192759i	−0.0189604	−	0.00616060i
$980$	−1.65562	+	54.5439i	−0.0528868	+	1.74234i
$981$	0.178028	+	35.3906i	0.00568399	+	1.12993i
$982$	−39.0162	+	10.4544i	−1.24506	+	0.333612i
$983$	−23.7659	+	1.24552i	−0.758013	+	0.0397258i	−0.427427	−	0.904050i	$-0.640580\pi$
$983$	−23.7659	+	1.24552i	−0.758013	+	0.0397258i	−0.330586	+	0.943776i	$0.607246\pi$
$984$	−1.93433	−	0.513090i	−0.0616641	−	0.0163567i
$985$	1.40850	−	10.5180i	0.0448784	−	0.335132i
$986$	27.5786	+	37.9587i	0.878283	+	1.20885i
$987$	33.7055	+	23.0886i	1.07286	+	0.734919i
$988$	18.3620	−	2.90825i	0.584172	−	0.0925237i
$989$	−2.20891	−	21.0164i	−0.0702392	−	0.668281i
$990$	−0.388936	+	16.6390i	−0.0123612	+	0.528822i
$991$	−1.41072	+	13.4221i	−0.0448129	+	0.426366i	0.948998	+	0.315282i	$0.102099\pi$
$991$	−1.41072	+	13.4221i	−0.0448129	+	0.426366i	−0.993811	+	0.111084i	$0.964568\pi$
$992$	−12.5868	+	8.17399i	−0.399633	+	0.259525i
$993$	24.2501	−	17.7121i	0.769554	−	0.562076i
$994$	44.0627	−	41.7326i	1.39758	−	1.32368i
$995$	−5.61846	−	0.454741i	−0.178117	−	0.0144163i
$996$	−52.8457	+	34.5077i	−1.67448	+	1.09342i
$997$	−17.0500	−	11.0724i	−0.539979	−	0.350667i	0.245655	−	0.969357i	$-0.420997\pi$
$997$	−17.0500	−	11.0724i	−0.539979	−	0.350667i	−0.785635	+	0.618691i	$0.787663\pi$
$998$	34.9187	+	90.9662i	1.10533	+	2.87949i
$999$	12.8769	+	19.5048i	0.407406	+	0.617106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bs.a.2.8	✓	1216
3.2	odd	2	inner	525.2.bs.a.2.69	yes	1216
7.4	even	3	inner	525.2.bs.a.452.69	yes	1216
21.11	odd	6	inner	525.2.bs.a.452.8	yes	1216
25.13	odd	20	inner	525.2.bs.a.338.8	yes	1216
75.38	even	20	inner	525.2.bs.a.338.69	yes	1216
175.88	odd	60	inner	525.2.bs.a.263.69	yes	1216
525.263	even	60	inner	525.2.bs.a.263.8	yes	1216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bs.a.2.8	✓	1216	1.1	even	1	trivial
525.2.bs.a.2.69	yes	1216	3.2	odd	2	inner
525.2.bs.a.263.8	yes	1216	525.263	even	60	inner
525.2.bs.a.263.69	yes	1216	175.88	odd	60	inner
525.2.bs.a.338.8	yes	1216	25.13	odd	20	inner
525.2.bs.a.338.69	yes	1216	75.38	even	20	inner
525.2.bs.a.452.8	yes	1216	21.11	odd	6	inner
525.2.bs.a.452.69	yes	1216	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.82030 - 1.47405i) q^{2} +(1.15573 - 1.29008i) q^{3} +(0.724840 + 3.41011i) q^{4} +(-1.83998 - 1.27061i) q^{5} +(-4.00540 + 0.644724i) q^{6} +(0.479622 + 2.60192i) q^{7} +(1.58048 - 3.10187i) q^{8} +(-0.328590 - 2.98195i) q^{9} +O(q^{10})\)	\(q+(-1.82030 - 1.47405i) q^{2} +(1.15573 - 1.29008i) q^{3} +(0.724840 + 3.41011i) q^{4} +(-1.83998 - 1.27061i) q^{5} +(-4.00540 + 0.644724i) q^{6} +(0.479622 + 2.60192i) q^{7} +(1.58048 - 3.10187i) q^{8} +(-0.328590 - 2.98195i) q^{9} +(1.47637 + 5.02511i) q^{10} +(-0.430837 + 0.967676i) q^{11} +(5.23701 + 3.00605i) q^{12} +(-6.32773 + 1.00221i) q^{13} +(2.96229 - 5.44324i) q^{14} +(-3.76571 + 0.905237i) q^{15} +(-1.07948 + 0.480614i) q^{16} +(0.167881 + 3.20335i) q^{17} +(-3.79740 + 5.91239i) q^{18} +(-0.173056 + 0.814164i) q^{19} +(2.99923 - 7.19553i) q^{20} +(3.91098 + 2.38836i) q^{21} +(2.21065 - 1.12638i) q^{22} +(-3.32232 + 4.10272i) q^{23} +(-2.17504 - 5.62386i) q^{24} +(1.77109 + 4.67582i) q^{25} +(12.9957 + 7.50304i) q^{26} +(-4.22670 - 3.02242i) q^{27} +(-8.52516 + 3.52153i) q^{28} +(-1.92973 + 5.93910i) q^{29} +(8.18906 + 3.90303i) q^{30} +(2.39395 - 2.65875i) q^{31} +(-4.05196 - 1.08572i) q^{32} +(0.750445 + 1.67418i) q^{33} +(4.41630 - 6.07851i) q^{34} +(2.42353 - 5.39690i) q^{35} +(9.93059 - 3.28196i) q^{36} +(-4.19920 - 1.61192i) q^{37} +(1.51513 - 1.22693i) q^{38} +(-6.02020 + 9.32154i) q^{39} +(-6.84934 + 3.69921i) q^{40} +(0.195079 - 0.268503i) q^{41} +(-3.59859 - 10.1125i) q^{42} +(-2.83047 + 2.83047i) q^{43} +(-3.61216 - 0.767789i) q^{44} +(-3.18430 + 5.90425i) q^{45} +(12.0952 - 2.57092i) q^{46} +(8.90311 + 0.466592i) q^{47} +(-0.627552 + 1.94806i) q^{48} +(-6.53993 + 2.49587i) q^{49} +(3.66847 - 11.1220i) q^{50} +(4.32659 + 3.48562i) q^{51} +(-8.00425 - 20.8518i) q^{52} +(-7.04869 - 4.57747i) q^{53} +(3.23867 + 11.7320i) q^{54} +(2.02227 - 1.23308i) q^{55} +(8.82884 + 2.62456i) q^{56} +(0.850328 + 1.16421i) q^{57} +(12.2672 - 7.96641i) q^{58} +(0.822175 - 7.82247i) q^{59} +(-5.81649 - 12.1853i) q^{60} +(-0.208933 - 1.98786i) q^{61} +(-8.27682 + 1.31092i) q^{62} +(7.60118 - 2.28517i) q^{63} +(7.16446 + 9.86103i) q^{64} +(12.9164 + 6.19604i) q^{65} +(1.10179 - 4.15370i) q^{66} +(10.2201 - 0.535612i) q^{67} +(-10.8021 + 2.89441i) q^{68} +(1.45313 + 9.02767i) q^{69} +(-12.3668 + 6.25155i) q^{70} +(9.31379 + 3.02623i) q^{71} +(-9.76895 - 3.69368i) q^{72} +(-1.07684 + 0.413358i) q^{73} +(5.26774 + 9.12399i) q^{74} +(8.07905 + 3.11913i) q^{75} -2.90182 q^{76} +(-2.72445 - 0.656883i) q^{77} +(24.6989 - 8.09390i) q^{78} +(-0.499299 + 0.449571i) q^{79} +(2.59689 + 0.487274i) q^{80} +(-8.78406 + 1.95968i) q^{81} +(-0.750887 + 0.201200i) q^{82} +(-4.74517 + 9.31293i) q^{83} +(-5.30971 + 15.0680i) q^{84} +(3.76132 - 6.10743i) q^{85} +(9.32453 - 0.980048i) q^{86} +(5.43165 + 9.35348i) q^{87} +(2.32067 + 2.86579i) q^{88} +(0.0615555 + 0.585661i) q^{89} +(14.4995 - 6.05367i) q^{90} +(-5.64259 - 15.9835i) q^{91} +(-16.3989 - 8.35564i) q^{92} +(-0.663236 - 6.16116i) q^{93} +(-15.5185 - 13.9729i) q^{94} +(1.35291 - 1.27816i) q^{95} +(-6.08362 + 3.97254i) q^{96} +(2.73593 - 1.39403i) q^{97} +(15.5836 + 5.09693i) q^{98} +(3.02713 + 0.966766i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9}+O(q^{10}) \) 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9	\( 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9} - 12 q^{10} - 64 q^{13} - 44 q^{15} - 140 q^{16} - 24 q^{18} - 20 q^{19} - 12 q^{21} + 8 q^{22} - 24 q^{25} - 80 q^{27} - 40 q^{28} - 50 q^{30} - 12 q^{31} - 6 q^{33} - 80 q^{34} + 8 q^{36} - 24 q^{37} - 50 q^{39} - 4 q^{40} - 34 q^{42} - 96 q^{43} + 30 q^{45} - 12 q^{46} - 44 q^{48} - 16 q^{51} - 136 q^{52} - 10 q^{54} - 40 q^{55} - 112 q^{57} - 76 q^{58} - 60 q^{60} - 12 q^{61} - 14 q^{63} - 80 q^{64} - 30 q^{66} - 32 q^{67} + 100 q^{69} - 100 q^{70} + 24 q^{72} - 72 q^{73} - 96 q^{75} - 64 q^{76} + 20 q^{78} - 20 q^{79} - 6 q^{81} - 204 q^{82} + 100 q^{84} - 56 q^{85} + 36 q^{87} - 140 q^{88} + 164 q^{90} - 24 q^{91} + 34 q^{93} - 20 q^{94} - 30 q^{96} - 240 q^{97}+O(q^{100}) \) 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9 - 12 * q^10 - 64 * q^13 - 44 * q^15 - 140 * q^16 - 24 * q^18 - 20 * q^19 - 12 * q^21 + 8 * q^22 - 24 * q^25 - 80 * q^27 - 40 * q^28 - 50 * q^30 - 12 * q^31 - 6 * q^33 - 80 * q^34 + 8 * q^36 - 24 * q^37 - 50 * q^39 - 4 * q^40 - 34 * q^42 - 96 * q^43 + 30 * q^45 - 12 * q^46 - 44 * q^48 - 16 * q^51 - 136 * q^52 - 10 * q^54 - 40 * q^55 - 112 * q^57 - 76 * q^58 - 60 * q^60 - 12 * q^61 - 14 * q^63 - 80 * q^64 - 30 * q^66 - 32 * q^67 + 100 * q^69 - 100 * q^70 + 24 * q^72 - 72 * q^73 - 96 * q^75 - 64 * q^76 + 20 * q^78 - 20 * q^79 - 6 * q^81 - 204 * q^82 + 100 * q^84 - 56 * q^85 + 36 * q^87 - 140 * q^88 + 164 * q^90 - 24 * q^91 + 34 * q^93 - 20 * q^94 - 30 * q^96 - 240 * q^97

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