LMFDB - Embedded newform 525.2.z.a.64.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(64,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("525.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.z (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.13
Character	$\chi$	$=$	525.64
Dual form			525.2.z.a.484.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22763 + 1.68969i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.729938 + 2.24652i) q^{4} +(1.98040 - 1.03828i) q^{5} +(-0.645404 - 1.98635i) q^{6} -1.00000i q^{7} +(-0.719317 + 0.233720i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.22763 + 1.68969i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.729938 + 2.24652i) q^{4} +(1.98040 - 1.03828i) q^{5} +(-0.645404 - 1.98635i) q^{6} -1.00000i q^{7} +(-0.719317 + 0.233720i) q^{8} +(0.809017 + 0.587785i) q^{9} +(4.18557 + 2.07164i) q^{10} +(2.37275 - 1.72390i) q^{11} +(1.38843 - 1.91100i) q^{12} +(-2.85292 + 3.92671i) q^{13} +(1.68969 - 1.22763i) q^{14} +(-2.20432 + 0.375483i) q^{15} +(2.54404 + 1.84835i) q^{16} +(5.37669 - 1.74699i) q^{17} +2.08857i q^{18} +(-0.451469 - 1.38948i) q^{19} +(0.886941 + 5.20688i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(5.82571 + 1.89289i) q^{22} +(1.60914 + 2.21479i) q^{23} +0.756335 q^{24} +(2.84396 - 4.11241i) q^{25} -10.1373 q^{26} +(-0.587785 - 0.809017i) q^{27} +(2.24652 + 0.729938i) q^{28} +(-2.70753 + 8.33292i) q^{29} +(-3.34054 - 3.26366i) q^{30} +(-1.88287 - 5.79487i) q^{31} +8.08039i q^{32} +(-2.78933 + 0.906308i) q^{33} +(9.55247 + 6.94027i) q^{34} +(-1.03828 - 1.98040i) q^{35} +(-1.91100 + 1.38843i) q^{36} +(-1.56643 + 2.15601i) q^{37} +(1.79355 - 2.46861i) q^{38} +(3.92671 - 2.85292i) q^{39} +(-1.18187 + 1.20971i) q^{40} +(-5.68654 - 4.13151i) q^{41} +(-1.98635 + 0.645404i) q^{42} +6.50614i q^{43} +(2.14082 + 6.58876i) q^{44} +(2.21246 + 0.324065i) q^{45} +(-1.76687 + 5.43788i) q^{46} +(-12.1833 - 3.95860i) q^{47} +(-1.84835 - 2.54404i) q^{48} -1.00000 q^{49} +(10.4400 - 0.243109i) q^{50} -5.65339 q^{51} +(-6.73898 - 9.27541i) q^{52} +(-7.32646 - 2.38051i) q^{53} +(0.645404 - 1.98635i) q^{54} +(2.90910 - 5.87758i) q^{55} +(0.233720 + 0.719317i) q^{56} +1.46098i q^{57} +(-17.4039 + 5.65487i) q^{58} +(2.83333 + 2.05853i) q^{59} +(0.765484 - 5.22612i) q^{60} +(10.0621 - 7.31058i) q^{61} +(7.48007 - 10.2954i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-8.56529 + 6.22304i) q^{64} +(-1.57291 + 10.7386i) q^{65} +(-4.95565 - 3.60049i) q^{66} +(0.963972 - 0.313214i) q^{67} +13.3540i q^{68} +(-0.845973 - 2.60364i) q^{69} +(2.07164 - 4.18557i) q^{70} +(1.98572 - 6.11143i) q^{71} +(-0.719317 - 0.233720i) q^{72} +(5.85613 + 8.06027i) q^{73} -5.56600 q^{74} +(-3.97557 + 3.03230i) q^{75} +3.45103 q^{76} +(-1.72390 - 2.37275i) q^{77} +(9.64111 + 3.13259i) q^{78} +(5.33121 - 16.4078i) q^{79} +(6.95731 + 1.01906i) q^{80} +(0.309017 + 0.951057i) q^{81} -14.6805i q^{82} +(7.18826 - 2.33561i) q^{83} +(-1.91100 - 1.38843i) q^{84} +(8.83413 - 9.04224i) q^{85} +(-10.9934 + 7.98714i) q^{86} +(5.15003 - 7.08840i) q^{87} +(-1.30385 + 1.79459i) q^{88} +(-11.1282 + 8.08512i) q^{89} +(2.16852 + 4.13620i) q^{90} +(3.92671 + 2.85292i) q^{91} +(-6.15013 + 1.99830i) q^{92} +6.09309i q^{93} +(-8.26782 - 25.4457i) q^{94} +(-2.33675 - 2.28297i) q^{95} +(2.49698 - 7.68491i) q^{96} +(-5.18932 - 1.68611i) q^{97} +(-1.22763 - 1.68969i) q^{98} +2.93287 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9}+O(q^{10}) $ 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9	$ 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9} + 36 q^{10} + 12 q^{11} + 20 q^{13} - 4 q^{15} + 4 q^{16} - 22 q^{19} - 22 q^{20} + 14 q^{21} + 30 q^{22} - 10 q^{23} + 16 q^{25} - 60 q^{26} - 20 q^{28} - 18 q^{29} - 18 q^{30} + 16 q^{31} - 10 q^{33} + 6 q^{35} - 12 q^{36} + 10 q^{37} + 100 q^{38} - 22 q^{40} + 8 q^{41} - 66 q^{44} + 2 q^{45} + 40 q^{46} - 100 q^{47} - 56 q^{49} + 62 q^{50} + 32 q^{51} + 80 q^{52} - 30 q^{53} - 58 q^{55} - 40 q^{58} - 20 q^{59} + 66 q^{60} + 28 q^{61} - 50 q^{62} - 12 q^{64} + 78 q^{65} - 20 q^{67} + 4 q^{69} - 18 q^{70} + 40 q^{71} - 20 q^{73} + 100 q^{74} - 8 q^{75} - 164 q^{76} + 20 q^{77} - 90 q^{78} - 4 q^{79} - 158 q^{80} - 14 q^{81} + 30 q^{83} - 12 q^{84} + 46 q^{85} + 80 q^{86} - 40 q^{87} + 130 q^{88} - 38 q^{89} + 4 q^{90} - 100 q^{92} - 10 q^{94} + 8 q^{95} + 10 q^{96} - 130 q^{97} + 48 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9 + 36 * q^10 + 12 * q^11 + 20 * q^13 - 4 * q^15 + 4 * q^16 - 22 * q^19 - 22 * q^20 + 14 * q^21 + 30 * q^22 - 10 * q^23 + 16 * q^25 - 60 * q^26 - 20 * q^28 - 18 * q^29 - 18 * q^30 + 16 * q^31 - 10 * q^33 + 6 * q^35 - 12 * q^36 + 10 * q^37 + 100 * q^38 - 22 * q^40 + 8 * q^41 - 66 * q^44 + 2 * q^45 + 40 * q^46 - 100 * q^47 - 56 * q^49 + 62 * q^50 + 32 * q^51 + 80 * q^52 - 30 * q^53 - 58 * q^55 - 40 * q^58 - 20 * q^59 + 66 * q^60 + 28 * q^61 - 50 * q^62 - 12 * q^64 + 78 * q^65 - 20 * q^67 + 4 * q^69 - 18 * q^70 + 40 * q^71 - 20 * q^73 + 100 * q^74 - 8 * q^75 - 164 * q^76 + 20 * q^77 - 90 * q^78 - 4 * q^79 - 158 * q^80 - 14 * q^81 + 30 * q^83 - 12 * q^84 + 46 * q^85 + 80 * q^86 - 40 * q^87 + 130 * q^88 - 38 * q^89 + 4 * q^90 - 100 * q^92 - 10 * q^94 + 8 * q^95 + 10 * q^96 - 130 * q^97 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.22763	+	1.68969i	0.868067	+	1.19479i	0.979585	+	0.201029i	$0.0644285\pi$
$2$	1.22763	+	1.68969i	0.868067	+	1.19479i	−0.111519	+	0.993762i	$0.535572\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	−0.729938	+	2.24652i	−0.364969	+	1.12326i
$5$	1.98040	−	1.03828i	0.885661	−	0.464332i
$5$	1.98040	−	1.03828i	0.885661	−	0.464332i
$6$	−0.645404	−	1.98635i	−0.263485	−	0.810924i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.719317	+	0.233720i	−0.254317	+	0.0826326i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	4.18557	+	2.07164i	1.32359	+	0.655109i
$11$	2.37275	−	1.72390i	0.715410	−	0.519776i	−0.169505	−	0.985529i	$-0.554217\pi$
$11$	2.37275	−	1.72390i	0.715410	−	0.519776i	0.884914	+	0.465754i	$0.154217\pi$
$12$	1.38843	−	1.91100i	0.400804	−	0.551659i
$13$	−2.85292	+	3.92671i	−0.791259	+	1.08907i	0.202692	+	0.979243i	$0.435031\pi$
$13$	−2.85292	+	3.92671i	−0.791259	+	1.08907i	−0.993950	+	0.109831i	$0.964969\pi$
$14$	1.68969	−	1.22763i	0.451589	−	0.328098i
$15$	−2.20432	+	0.375483i	−0.569152	+	0.0969494i
$16$	2.54404	+	1.84835i	0.636009	+	0.462088i
$17$	5.37669	−	1.74699i	1.30404	−	0.423708i	0.427054	−	0.904226i	$-0.359551\pi$
$17$	5.37669	−	1.74699i	1.30404	−	0.423708i	0.876985	+	0.480518i	$0.159551\pi$
$18$			2.08857i			0.492281i
$19$	−0.451469	−	1.38948i	−0.103574	−	0.318768i	0.885819	−	0.464031i	$-0.153597\pi$
$19$	−0.451469	−	1.38948i	−0.103574	−	0.318768i	−0.989393	+	0.145263i	$0.953597\pi$
$20$	0.886941	+	5.20688i	0.198326	+	1.16429i
$21$	−0.309017	+	0.951057i	−0.0674330	+	0.207538i
$22$	5.82571	+	1.89289i	1.24205	+	0.403565i
$23$	1.60914	+	2.21479i	0.335528	+	0.461815i	0.943129	−	0.332428i	$-0.107868\pi$
$23$	1.60914	+	2.21479i	0.335528	+	0.461815i	−0.607601	+	0.794243i	$0.707868\pi$
$24$	0.756335			0.154386
$25$	2.84396	−	4.11241i	0.568792	−	0.822481i
$26$	−10.1373			−1.98808
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	2.24652	+	0.729938i	0.424552	+	0.137945i
$29$	−2.70753	+	8.33292i	−0.502776	+	1.54738i	0.301703	+	0.953402i	$0.402445\pi$
$29$	−2.70753	+	8.33292i	−0.502776	+	1.54738i	−0.804478	+	0.593982i	$0.797555\pi$
$30$	−3.34054	−	3.26366i	−0.609896	−	0.595859i
$31$	−1.88287	−	5.79487i	−0.338173	−	1.04079i	−0.965138	−	0.261742i	$-0.915703\pi$
$31$	−1.88287	−	5.79487i	−0.338173	−	1.04079i	0.626965	−	0.779048i	$-0.284297\pi$
$32$			8.08039i			1.42843i
$33$	−2.78933	+	0.906308i	−0.485560	+	0.157768i
$34$	9.55247	+	6.94027i	1.63823	+	1.19025i
$35$	−1.03828	−	1.98040i	−0.175501	−	0.334749i
$36$	−1.91100	+	1.38843i	−0.318501	+	0.231404i
$37$	−1.56643	+	2.15601i	−0.257520	+	0.354446i	−0.918127	−	0.396286i	$-0.870299\pi$
$37$	−1.56643	+	2.15601i	−0.257520	+	0.354446i	0.660607	+	0.750732i	$0.270299\pi$
$38$	1.79355	−	2.46861i	0.290952	−	0.400461i
$39$	3.92671	−	2.85292i	0.628777	−	0.456833i
$40$	−1.18187	+	1.20971i	−0.186870	+	0.191272i
$41$	−5.68654	−	4.13151i	−0.888088	−	0.645233i	0.0472910	−	0.998881i	$-0.484941\pi$
$41$	−5.68654	−	4.13151i	−0.888088	−	0.645233i	−0.935379	+	0.353648i	$0.884941\pi$
$42$	−1.98635	+	0.645404i	−0.306500	+	0.0995880i
$43$			6.50614i			0.992177i	0.868272	+	0.496088i	$0.165231\pi$
$43$			6.50614i			0.992177i	−0.868272	+	0.496088i	$0.834769\pi$
$44$	2.14082	+	6.58876i	0.322740	+	0.993293i
$45$	2.21246	+	0.324065i	0.329814	+	0.0483088i
$46$	−1.76687	+	5.43788i	−0.260511	+	0.801772i
$47$	−12.1833	−	3.95860i	−1.77712	−	0.577422i	−0.778390	−	0.627782i	$-0.783963\pi$
$47$	−12.1833	−	3.95860i	−1.77712	−	0.577422i	−0.998731	+	0.0503600i	$0.983963\pi$
$48$	−1.84835	−	2.54404i	−0.266786	−	0.367200i
$49$	−1.00000			−0.142857
$50$	10.4400	−	0.243109i	1.47644	−	0.0343808i
$51$	−5.65339			−0.791632
$52$	−6.73898	−	9.27541i	−0.934528	−	1.28627i
$53$	−7.32646	−	2.38051i	−1.00637	−	0.326988i	−0.240960	−	0.970535i	$-0.577462\pi$
$53$	−7.32646	−	2.38051i	−1.00637	−	0.326988i	−0.765407	+	0.643547i	$0.777462\pi$
$54$	0.645404	−	1.98635i	0.0878284	−	0.270308i
$55$	2.90910	−	5.87758i	0.392262	−	0.792533i
$56$	0.233720	+	0.719317i	0.0312322	+	0.0961228i
$57$			1.46098i			0.193512i
$58$	−17.4039	+	5.65487i	−2.28524	+	0.742521i
$59$	2.83333	+	2.05853i	0.368868	+	0.267998i	0.756741	−	0.653715i	$-0.226790\pi$
$59$	2.83333	+	2.05853i	0.368868	+	0.267998i	−0.387874	+	0.921713i	$0.626790\pi$
$60$	0.765484	−	5.22612i	0.0988236	−	0.674689i
$61$	10.0621	−	7.31058i	1.28833	−	0.936023i	0.288556	−	0.957463i	$-0.406825\pi$
$61$	10.0621	−	7.31058i	1.28833	−	0.936023i	0.999770	+	0.0214398i	$0.00682502\pi$
$62$	7.48007	−	10.2954i	0.949970	−	1.30752i
$63$	0.587785	−	0.809017i	0.0740540	−	0.101927i
$64$	−8.56529	+	6.22304i	−1.07066	+	0.777881i
$65$	−1.57291	+	10.7386i	−0.195096	+	1.33196i
$66$	−4.95565	−	3.60049i	−0.609998	−	0.443190i
$67$	0.963972	−	0.313214i	0.117768	−	0.0382651i	−0.249540	−	0.968364i	$-0.580279\pi$
$67$	0.963972	−	0.313214i	0.117768	−	0.0382651i	0.367308	+	0.930099i	$0.380279\pi$
$68$			13.3540i			1.61941i
$69$	−0.845973	−	2.60364i	−0.101843	−	0.313441i
$70$	2.07164	−	4.18557i	0.247608	−	0.500271i
$71$	1.98572	−	6.11143i	0.235662	−	0.725293i	−0.761371	−	0.648317i	$-0.775473\pi$
$71$	1.98572	−	6.11143i	0.235662	−	0.725293i	0.997033	−	0.0769767i	$-0.0245267\pi$
$72$	−0.719317	−	0.233720i	−0.0847723	−	0.0275442i
$73$	5.85613	+	8.06027i	0.685408	+	0.943384i	0.999983	−	0.00584900i	$-0.00186180\pi$
$73$	5.85613	+	8.06027i	0.685408	+	0.943384i	−0.314574	+	0.949233i	$0.601862\pi$
$74$	−5.56600			−0.647034
$75$	−3.97557	+	3.03230i	−0.459059	+	0.350140i
$76$	3.45103			0.395861
$77$	−1.72390	−	2.37275i	−0.196457	−	0.270399i
$78$	9.64111	+	3.13259i	1.09164	+	0.354696i
$79$	5.33121	−	16.4078i	0.599808	−	1.84602i	0.0706390	−	0.997502i	$-0.477496\pi$
$79$	5.33121	−	16.4078i	0.599808	−	1.84602i	0.529169	−	0.848517i	$-0.322504\pi$
$80$	6.95731	+	1.01906i	0.777851	+	0.113934i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	14.6805i		−	1.62118i
$83$	7.18826	−	2.33561i	0.789014	−	0.256366i	0.113330	−	0.993557i	$-0.463848\pi$
$83$	7.18826	−	2.33561i	0.789014	−	0.256366i	0.675684	+	0.737191i	$0.263848\pi$
$84$	−1.91100	−	1.38843i	−0.208508	−	0.151490i
$85$	8.83413	−	9.04224i	0.958196	−	0.980768i
$86$	−10.9934	+	7.98714i	−1.18544	+	0.861276i
$87$	5.15003	−	7.08840i	0.552141	−	0.759957i
$88$	−1.30385	+	1.79459i	−0.138990	+	0.191304i
$89$	−11.1282	+	8.08512i	−1.17959	+	0.857021i	−0.992125	−	0.125250i	$-0.960027\pi$
$89$	−11.1282	+	8.08512i	−1.17959	+	0.857021i	−0.187463	+	0.982272i	$0.560027\pi$
$90$	2.16852	+	4.13620i	0.228582	+	0.435994i
$91$	3.92671	+	2.85292i	0.411631	+	0.299068i
$92$	−6.15013	+	1.99830i	−0.641195	+	0.208337i
$93$			6.09309i			0.631824i
$94$	−8.26782	−	25.4457i	−0.852761	−	2.62453i
$95$	−2.33675	−	2.28297i	−0.239746	−	0.234228i
$96$	2.49698	−	7.68491i	0.254847	−	0.784338i
$97$	−5.18932	−	1.68611i	−0.526896	−	0.171199i	0.0334768	−	0.999439i	$-0.489342\pi$
$97$	−5.18932	−	1.68611i	−0.526896	−	0.171199i	−0.560373	+	0.828241i	$0.689342\pi$
$98$	−1.22763	−	1.68969i	−0.124010	−	0.170684i
$99$	2.93287			0.294765
$100$	7.16269	+	9.39082i	0.716269	+	0.939082i
$101$	−2.87628			−0.286201			−0.143100	−	0.989708i	$-0.545707\pi$
$101$	−2.87628			−0.286201			−0.143100	+	0.989708i	$0.545707\pi$
$102$	−6.94027	−	9.55247i	−0.687189	−	0.945835i
$103$	−14.5884	−	4.74007i	−1.43744	−	0.467053i	−0.516343	−	0.856382i	$-0.672707\pi$
$103$	−14.5884	−	4.74007i	−1.43744	−	0.467053i	−0.921099	+	0.389329i	$0.872707\pi$
$104$	1.13440	−	3.49134i	0.111237	−	0.342354i
$105$	0.375483	+	2.20432i	0.0366434	+	0.215119i
$106$	−4.97187	−	15.3018i	−0.482911	−	1.48625i
$107$			17.0034i			1.64378i	0.569645	+	0.821891i	$0.307081\pi$
$107$			17.0034i			1.64378i	−0.569645	+	0.821891i	$0.692919\pi$
$108$	2.24652	−	0.729938i	0.216171	−	0.0702384i
$109$	−6.06390	−	4.40568i	−0.580816	−	0.421988i	0.258202	−	0.966091i	$-0.416870\pi$
$109$	−6.06390	−	4.40568i	−0.580816	−	0.421988i	−0.839018	+	0.544103i	$0.816870\pi$
$110$	13.5026	−	2.30003i	1.28742	−	0.219299i
$111$	2.15601	−	1.56643i	0.204640	−	0.148679i
$112$	1.84835	−	2.54404i	0.174653	−	0.240389i
$113$	−4.80644	+	6.61550i	−0.452152	+	0.622334i	−0.972858	−	0.231402i	$-0.925669\pi$
$113$	−4.80644	+	6.61550i	−0.452152	+	0.622334i	0.520706	+	0.853736i	$0.325669\pi$
$114$	−2.46861	+	1.79355i	−0.231207	+	0.167981i
$115$	5.48629	+	2.71543i	0.511600	+	0.253215i
$116$	−16.7437	−	12.1650i	−1.55462	−	1.12950i
$117$	−4.61613	+	1.49987i	−0.426761	+	0.138663i
$118$			7.31456i			0.673360i
$119$	−1.74699	−	5.37669i	−0.160147	−	0.492880i
$120$	1.49784	−	0.785285i	0.136734	−	0.0716864i
$121$	−0.741098	+	2.28087i	−0.0673726	+	0.207351i
$122$	24.7052	+	8.02721i	2.23670	+	0.726749i
$123$	4.13151	+	5.68654i	0.372526	+	0.512738i
$124$	14.3927			1.29250
$125$	1.36236	−	11.0970i	0.121853	−	0.992548i
$126$	2.08857			0.186065
$127$	−2.85099	−	3.92405i	−0.252984	−	0.348203i	0.663569	−	0.748115i	$-0.269041\pi$
$127$	−2.85099	−	3.92405i	−0.252984	−	0.348203i	−0.916554	+	0.399912i	$0.869041\pi$
$128$	−5.66021	−	1.83911i	−0.500296	−	0.162556i
$129$	2.01051	−	6.18771i	0.177015	−	0.544797i
$130$	−20.0758	+	10.5253i	−1.76077	+	0.923129i
$131$	−3.68587	−	11.3440i	−0.322036	−	0.991126i	−0.972761	−	0.231812i	$-0.925535\pi$
$131$	−3.68587	−	11.3440i	−0.322036	−	0.991126i	0.650724	−	0.759314i	$-0.274465\pi$
$132$		−	6.92783i		−	0.602990i
$133$	−1.38948	+	0.451469i	−0.120483	+	0.0391473i
$134$	1.71264	+	1.24430i	0.147949	+	0.107491i
$135$	−2.00403	−	0.991892i	−0.172480	−	0.0853685i
$136$	−3.45924	+	2.51328i	−0.296627	+	0.215512i
$137$	−3.05438	+	4.20400i	−0.260953	+	0.359172i	−0.919310	−	0.393535i	$-0.871252\pi$
$137$	−3.05438	+	4.20400i	−0.260953	+	0.359172i	0.658356	+	0.752706i	$0.271252\pi$
$138$	3.36080	−	4.62574i	0.286090	−	0.393769i
$139$	−11.7974	+	8.57131i	−1.00064	+	0.727009i	−0.962226	−	0.272253i	$-0.912231\pi$
$139$	−11.7974	+	8.57131i	−1.00064	+	0.727009i	−0.0384159	+	0.999262i	$0.512231\pi$
$140$	5.20688	−	0.886941i	0.440062	−	0.0749602i
$141$	10.3638	+	7.52971i	0.872786	+	0.634116i
$142$	12.7642	−	4.14733i	1.07114	−	0.348036i
$143$			14.2352i			1.19041i
$144$	0.971735	+	2.99069i	0.0809779	+	0.249224i
$145$	3.28989	+	19.3137i	0.273211	+	1.60391i
$146$	−6.43019	+	19.7901i	−0.532166	+	1.63784i
$147$	0.951057	+	0.309017i	0.0784418	+	0.0254873i
$148$	−3.70012	−	5.09278i	−0.304148	−	0.418624i
$149$	−9.61250			−0.787487			−0.393744	−	0.919220i	$-0.628820\pi$
$149$	−9.61250			−0.787487			−0.393744	+	0.919220i	$0.628820\pi$
$150$	−10.0042	−	2.99494i	−0.816838	−	0.244535i
$151$	2.06396			0.167962			0.0839812	−	0.996467i	$-0.473236\pi$
$151$	2.06396			0.167962			0.0839812	+	0.996467i	$0.473236\pi$
$152$	0.649499	+	0.893958i	0.0526813	+	0.0725096i
$153$	5.37669	+	1.74699i	0.434680	+	0.141236i
$154$	1.89289	−	5.82571i	0.152533	−	0.469449i
$155$	−9.74552	−	9.52122i	−0.782779	−	0.764763i
$156$	3.54289	+	10.9039i	0.283658	+	0.873010i
$157$			15.4477i			1.23286i	0.787411	+	0.616429i	$0.211421\pi$
$157$			15.4477i			1.23286i	−0.787411	+	0.616429i	$0.788579\pi$
$158$	34.2688	−	11.1346i	2.72628	−	0.885822i
$159$	6.23226	+	4.52800i	0.494250	+	0.359094i
$160$	8.38969	+	16.0024i	0.663263	+	1.26510i
$161$	2.21479	−	1.60914i	0.174550	−	0.126818i
$162$	−1.22763	+	1.68969i	−0.0964518	+	0.132755i
$163$	4.53940	−	6.24795i	0.355553	−	0.489377i	−0.593350	−	0.804945i	$-0.702195\pi$
$163$	4.53940	−	6.24795i	0.355553	−	0.489377i	0.948903	+	0.315568i	$0.102195\pi$
$164$	13.4323	−	9.75916i	1.04889	−	0.762063i
$165$	−4.58299	+	4.69095i	−0.356785	+	0.365190i
$166$	12.7710	+	9.27867i	0.991221	+	0.720164i
$167$	−3.79251	+	1.23226i	−0.293473	+	0.0953553i	−0.452053	−	0.891991i	$-0.649308\pi$
$167$	−3.79251	+	1.23226i	−0.293473	+	0.0953553i	0.158580	+	0.987346i	$0.449308\pi$
$168$		−	0.756335i		−	0.0583525i
$169$	−3.26268	−	10.0415i	−0.250975	−	0.772422i
$170$	26.1236	+	3.82640i	2.00359	+	0.293472i
$171$	0.451469	−	1.38948i	0.0345247	−	0.106256i
$172$	−14.6162	−	4.74908i	−1.11447	−	0.362114i
$173$	4.56999	+	6.29005i	0.347450	+	0.478223i	0.946599	−	0.322414i	$-0.104494\pi$
$173$	4.56999	+	6.29005i	0.347450	+	0.478223i	−0.599149	+	0.800637i	$0.704494\pi$
$174$	18.2995			1.38728
$175$	−4.11241	−	2.84396i	−0.310869	−	0.214983i
$176$	9.22272			0.695189
$177$	−2.05853	−	2.83333i	−0.154729	−	0.212966i
$178$	−27.3227	−	8.87768i	−2.04792	−	0.665410i
$179$	4.76555	−	14.6668i	0.356194	−	1.09625i	−0.599120	−	0.800659i	$-0.704483\pi$
$179$	4.76555	−	14.6668i	0.356194	−	1.09625i	0.955314	−	0.295593i	$-0.0955171\pi$
$180$	−2.34298	+	4.73379i	−0.174635	+	0.352836i
$181$	1.14756	+	3.53184i	0.0852977	+	0.262519i	0.984604	−	0.174800i	$-0.0559279\pi$
$181$	1.14756	+	3.53184i	0.0852977	+	0.262519i	−0.899306	+	0.437319i	$0.855928\pi$
$182$			10.1373i			0.751424i
$183$	−11.8288	+	3.84340i	−0.874407	+	0.284112i
$184$	−1.67512	−	1.21705i	−0.123491	−	0.0897218i
$185$	−0.863627	+	5.89616i	−0.0634951	+	0.433494i
$186$	−10.2954	+	7.48007i	−0.754898	+	0.548465i
$187$	9.74587	−	13.4140i	0.712689	−	0.980932i
$188$	17.7862	−	24.4805i	1.29719	−	1.78543i
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	0.988843	−	6.75104i	0.0717382	−	0.489772i
$191$	0.633834	+	0.460507i	0.0458626	+	0.0333211i	0.610480	−	0.792031i	$-0.290976\pi$
$191$	0.633834	+	0.460507i	0.0458626	+	0.0333211i	−0.564618	+	0.825352i	$0.690976\pi$
$192$	10.0691	−	3.27165i	0.726675	−	0.236111i
$193$			5.27337i			0.379585i	0.981824	+	0.189793i	$0.0607816\pi$
$193$			5.27337i			0.379585i	−0.981824	+	0.189793i	$0.939218\pi$
$194$	−3.52157	−	10.8383i	−0.252834	−	0.778142i
$195$	4.81433	−	9.72694i	0.344761	−	0.696561i
$196$	0.729938	−	2.24652i	0.0521385	−	0.160466i
$197$	−4.26956	−	1.38726i	−0.304194	−	0.0988385i	0.152943	−	0.988235i	$-0.451125\pi$
$197$	−4.26956	−	1.38726i	−0.304194	−	0.0988385i	−0.457137	+	0.889397i	$0.651125\pi$
$198$	3.60049	+	4.95565i	0.255876	+	0.352183i
$199$	−4.25442			−0.301588			−0.150794	−	0.988565i	$-0.548183\pi$
$199$	−4.25442			−0.301588			−0.150794	+	0.988565i	$0.548183\pi$
$200$	−1.08456	+	3.62282i	−0.0766897	+	0.256172i
$201$	−1.01358			−0.0714924
$202$	−3.53102	−	4.86003i	−0.248441	−	0.341950i
$203$	8.33292	+	2.70753i	0.584856	+	0.190031i
$204$	4.12662	−	12.7004i	0.288921	−	0.889209i
$205$	−15.5513	−	2.27784i	−1.08615	−	0.159091i
$206$	−9.89998	−	30.4690i	−0.689764	−	2.12288i
$207$			2.73763i			0.190278i
$208$	−14.5159	+	4.71650i	−1.00650	+	0.327030i
$209$	−3.46654	−	2.51859i	−0.239786	−	0.174215i
$210$	−3.26366	+	3.34054i	−0.225214	+	0.230519i
$211$	16.0653	−	11.6721i	1.10598	−	0.803541i	0.123954	−	0.992288i	$-0.460443\pi$
$211$	16.0653	−	11.6721i	1.10598	−	0.803541i	0.982026	+	0.188747i	$0.0604425\pi$
$212$	10.6957	−	14.7214i	0.734586	−	1.01107i
$213$	−3.77707	+	5.19869i	−0.258801	+	0.356209i
$214$	−28.7305	+	20.8739i	−1.96398	+	1.42691i
$215$	6.75518	+	12.8848i	0.460699	+	0.878733i
$216$	0.611888	+	0.444562i	0.0416337	+	0.0302486i
$217$	−5.79487	+	1.88287i	−0.393382	+	0.127817i
$218$		−	15.6547i		−	1.06027i
$219$	−3.07875	−	9.47542i	−0.208043	−	0.640290i
$220$	11.0806	+	10.8256i	0.747056	+	0.729863i
$221$	−8.47935	+	26.0967i	−0.570383	+	1.75546i
$222$	5.29358	+	1.71999i	0.355282	+	0.115438i
$223$	3.20303	+	4.40860i	0.214491	+	0.295222i	0.902682	−	0.430308i	$-0.141595\pi$
$223$	3.20303	+	4.40860i	0.214491	+	0.295222i	−0.688191	+	0.725529i	$0.741595\pi$
$224$	8.08039			0.539894
$225$	4.71802	−	1.65537i	0.314535	−	0.110358i
$226$	−17.0787			−1.13606
$227$	4.78734	+	6.58921i	0.317747	+	0.437341i	0.937778	−	0.347236i	$-0.112880\pi$
$227$	4.78734	+	6.58921i	0.317747	+	0.437341i	−0.620031	+	0.784578i	$0.712880\pi$
$228$	−3.28213	−	1.06643i	−0.217364	−	0.0706259i
$229$	1.83906	−	5.66006i	0.121529	−	0.374027i	−0.871724	−	0.489997i	$-0.836998\pi$
$229$	1.83906	−	5.66006i	0.121529	−	0.374027i	0.993253	+	0.115970i	$0.0369977\pi$
$230$	2.14691	+	12.6037i	0.141563	+	0.831062i
$231$	0.906308	+	2.78933i	0.0596307	+	0.183524i
$232$		−	6.62681i		−	0.435072i
$233$	−16.5575	+	5.37985i	−1.08472	+	0.352446i	−0.796203	−	0.605030i	$-0.793161\pi$
$233$	−16.5575	+	5.37985i	−1.08472	+	0.352446i	−0.288514	+	0.957476i	$0.593161\pi$
$234$	−8.20122	−	5.95853i	−0.536130	−	0.389522i
$235$	−28.2380	+	4.81006i	−1.84204	+	0.313774i
$236$	−6.69269	+	4.86252i	−0.435657	+	0.316523i
$237$	−10.1406	+	13.9573i	−0.658700	+	0.906623i
$238$	6.94027	−	9.55247i	0.449871	−	0.619194i
$239$	−11.0057	+	7.99613i	−0.711902	+	0.517227i	−0.883787	−	0.467890i	$-0.845014\pi$
$239$	−11.0057	+	7.99613i	−0.711902	+	0.517227i	0.171885	+	0.985117i	$0.445014\pi$
$240$	−6.30189	−	3.11911i	−0.406785	−	0.201337i
$241$	4.75345	+	3.45359i	0.306197	+	0.222465i	0.730263	−	0.683166i	$-0.239398\pi$
$241$	4.75345	+	3.45359i	0.306197	+	0.222465i	−0.424066	+	0.905631i	$0.639398\pi$
$242$	−4.76375	+	1.54784i	−0.306226	+	0.0994987i
$243$		−	1.00000i		−	0.0641500i
$244$	9.07860	+	27.9411i	0.581198	+	1.78874i
$245$	−1.98040	+	1.03828i	−0.126523	+	0.0663331i
$246$	−4.53651	+	13.9619i	−0.289237	+	0.890181i
$247$	6.74409	+	2.19129i	0.429116	+	0.139428i
$248$	2.70876	+	3.72829i	0.172006	+	0.236746i
$249$	−7.55819			−0.478981
$250$	20.4230	−	11.3211i	1.29166	−	0.716009i
$251$	−1.90092			−0.119985			−0.0599927	−	0.998199i	$-0.519108\pi$
$251$	−1.90092			−0.119985			−0.0599927	+	0.998199i	$0.519108\pi$
$252$	1.38843	+	1.91100i	0.0874626	+	0.120382i
$253$	7.63614	+	2.48113i	0.480080	+	0.155987i
$254$	3.13046	−	9.63457i	0.196423	−	0.604526i
$255$	−11.1960	+	5.86978i	−0.701118	+	0.367580i
$256$	2.70218	+	8.31645i	0.168886	+	0.519778i
$257$			25.9348i			1.61777i	0.587966	+	0.808886i	$0.299929\pi$
$257$			25.9348i			1.61777i	−0.587966	+	0.808886i	$0.700071\pi$
$258$	12.9235	−	4.19909i	0.804580	−	0.261424i
$259$	2.15601	+	1.56643i	0.133968	+	0.0973335i
$260$	−22.9763	−	11.3721i	−1.42493	−	0.705266i
$261$	−7.08840	+	5.15003i	−0.438761	+	0.318779i
$262$	14.6429	−	20.1542i	0.904639	−	1.24513i
$263$	5.11303	−	7.03749i	0.315283	−	0.433950i	−0.621737	−	0.783226i	$-0.713573\pi$
$263$	5.11303	−	7.03749i	0.315283	−	0.433950i	0.937020	+	0.349276i	$0.113573\pi$
$264$	1.79459	−	1.30385i	0.110449	−	0.0802462i
$265$	−16.9809	+	2.89254i	−1.04313	+	0.177687i
$266$	−2.46861	−	1.79355i	−0.151360	−	0.109970i
$267$	13.0820	−	4.25060i	0.800605	−	0.260132i
$268$			2.39421i			0.146250i
$269$	−7.55357	−	23.2475i	−0.460549	−	1.41742i	−0.864495	−	0.502642i	$-0.832361\pi$
$269$	−7.55357	−	23.2475i	−0.460549	−	1.41742i	0.403945	−	0.914783i	$-0.367639\pi$
$270$	−0.784224	−	4.60387i	−0.0477264	−	0.280183i
$271$	−0.436364	+	1.34299i	−0.0265072	+	0.0815809i	−0.963435	−	0.267942i	$-0.913656\pi$
$271$	−0.436364	+	1.34299i	−0.0265072	+	0.0815809i	0.936928	+	0.349523i	$0.113656\pi$
$272$	16.9075	+	5.49359i	1.02517	+	0.333098i
$273$	−2.85292	−	3.92671i	−0.172667	−	0.237655i
$274$	−10.8531			−0.655660
$275$	−0.341386	−	14.6604i	−0.0205863	−	0.884055i
$276$	6.46663			0.389245
$277$	5.87566	+	8.08715i	0.353034	+	0.485910i	0.948191	−	0.317700i	$-0.102910\pi$
$277$	5.87566	+	8.08715i	0.353034	+	0.485910i	−0.595157	+	0.803609i	$0.702910\pi$
$278$	−28.9657	−	9.41152i	−1.73725	−	0.564466i
$279$	1.88287	−	5.79487i	0.112724	−	0.346930i
$280$	1.20971	+	1.18187i	0.0722940	+	0.0706301i
$281$	6.14536	+	18.9135i	0.366601	+	1.12828i	0.948972	+	0.315360i	$0.102125\pi$
$281$	6.14536	+	18.9135i	0.366601	+	1.12828i	−0.582371	+	0.812923i	$0.697875\pi$
$282$			26.7552i			1.59325i
$283$	1.29544	−	0.420912i	0.0770056	−	0.0250206i	−0.270261	−	0.962787i	$-0.587110\pi$
$283$	1.29544	−	0.420912i	0.0770056	−	0.0250206i	0.347266	+	0.937766i	$0.387110\pi$
$284$	12.2800	+	8.92193i	0.728683	+	0.529419i
$285$	1.51691	+	2.89333i	0.0898538	+	0.171386i
$286$	−24.0532	+	17.4756i	−1.42229	+	1.03336i
$287$	−4.13151	+	5.68654i	−0.243875	+	0.335666i
$288$	−4.74954	+	6.53718i	−0.279869	+	0.385207i
$289$	12.1035	−	8.79372i	0.711971	−	0.517278i
$290$	−28.5953	+	29.2690i	−1.67918	+	1.71873i
$291$	4.41430	+	3.20718i	0.258771	+	0.188008i
$292$	−22.3822	+	7.27241i	−1.30982	+	0.425586i
$293$		−	21.3372i		−	1.24653i	−0.782010	−	0.623266i	$-0.785806\pi$
$293$		−	21.3372i		−	1.24653i	0.782010	−	0.623266i	$-0.214194\pi$
$294$	0.645404	+	1.98635i	0.0376407	+	0.115846i
$295$	7.74845	+	1.13494i	0.451132	+	0.0660786i
$296$	0.622859	−	1.91696i	0.0362030	−	0.111421i
$297$	−2.78933	−	0.906308i	−0.161853	−	0.0525893i
$298$	−11.8006	−	16.2421i	−0.683591	−	0.940882i
$299$	−13.2876			−0.768440
$300$	−3.91020	−	11.1446i	−0.225755	−	0.643433i
$301$	6.50614			0.375008
$302$	2.53378	+	3.48744i	0.145802	+	0.200680i
$303$	2.73551	+	0.888820i	0.157151	+	0.0510614i
$304$	1.41969	−	4.36936i	0.0814248	−	0.250600i
$305$	12.3367	−	24.9252i	0.706395	−	1.42721i
$306$	3.64872	+	11.2296i	0.208583	+	0.641953i
$307$		−	21.0570i		−	1.20179i	−0.799329	−	0.600894i	$-0.794811\pi$
$307$		−	21.0570i		−	1.20179i	0.799329	−	0.600894i	$-0.205189\pi$
$308$	6.58876	−	2.14082i	0.375429	−	0.121984i
$309$	12.4097	+	9.01615i	0.705961	+	0.512911i
$310$	4.12401	−	28.1555i	0.234228	−	1.59912i
$311$	−6.55774	+	4.76448i	−0.371855	+	0.270169i	−0.757980	−	0.652278i	$-0.773813\pi$
$311$	−6.55774	+	4.76448i	−0.371855	+	0.270169i	0.386125	+	0.922447i	$0.373813\pi$
$312$	−2.15777	+	2.96991i	−0.122159	+	0.168138i
$313$	−5.95556	+	8.19713i	−0.336628	+	0.463329i	−0.943453	−	0.331507i	$-0.892443\pi$
$313$	−5.95556	+	8.19713i	−0.336628	+	0.463329i	0.606825	+	0.794836i	$0.292443\pi$
$314$	−26.1018	+	18.9640i	−1.47301	+	1.07020i
$315$	0.324065	−	2.21246i	0.0182590	−	0.124658i
$316$	32.9689	+	23.9533i	1.85465	+	1.34748i
$317$	28.8293	−	9.36721i	1.61922	−	0.526115i	0.647459	−	0.762100i	$-0.275832\pi$
$317$	28.8293	−	9.36721i	1.61922	−	0.526115i	0.971757	+	0.235985i	$0.0758318\pi$
$318$			16.0893i			0.902243i
$319$	7.94085	+	24.4394i	0.444602	+	1.36834i
$320$	−10.5014	+	21.2173i	−0.587048	+	1.18608i
$321$	5.25434	−	16.1712i	0.293269	−	0.902589i
$322$	5.43788	+	1.76687i	0.303041	+	0.0984641i
$323$	−4.85482	−	6.68208i	−0.270129	−	0.371801i
$324$	−2.36213			−0.131229
$325$	8.03464	+	22.8998i	0.445681	+	1.27025i
$326$	16.1298			0.893347
$327$	4.40568	+	6.06390i	0.243635	+	0.335334i
$328$	5.05604	+	1.64281i	0.279173	+	0.0907088i
$329$	−3.95860	+	12.1833i	−0.218245	+	0.671688i
$330$	−13.5525	−	1.98507i	−0.746039	−	0.109274i
$331$	1.21351	+	3.73480i	0.0667005	+	0.205283i	0.978852	−	0.204571i	$-0.0655798\pi$
$331$	1.21351	+	3.73480i	0.0667005	+	0.205283i	−0.912151	+	0.409854i	$0.865580\pi$
$332$			17.8534i			0.979834i
$333$	−2.53454	+	0.823523i	−0.138892	+	0.0451288i
$334$	−6.73795	−	4.89540i	−0.368684	−	0.267865i
$335$	1.58385	−	1.62116i	0.0865348	−	0.0885733i
$336$	−2.54404	+	1.84835i	−0.138789	+	0.100836i
$337$	7.81967	−	10.7629i	0.425965	−	0.586290i	−0.541056	−	0.840986i	$-0.681975\pi$
$337$	7.81967	−	10.7629i	0.425965	−	0.586290i	0.967021	+	0.254696i	$0.0819755\pi$
$338$	12.9616	−	17.8402i	0.705020	−	0.970377i
$339$	6.61550	−	4.80644i	0.359305	−	0.261050i
$340$	13.8652	+	26.4463i	0.751945	+	1.43425i
$341$	−14.4574	−	10.5039i	−0.782910	−	0.568817i
$342$	2.90203	−	0.942925i	0.156924	−	0.0509876i
$343$			1.00000i			0.0539949i
$344$	−1.52062	−	4.67998i	−0.0819862	−	0.252327i
$345$	−4.37866	−	4.27789i	−0.235739	−	0.230314i
$346$	−5.01797	+	15.4437i	−0.269768	+	0.830259i
$347$	1.28730	+	0.418270i	0.0691061	+	0.0224539i	0.343366	−	0.939202i	$-0.388433\pi$
$347$	1.28730	+	0.418270i	0.0691061	+	0.0224539i	−0.274260	+	0.961656i	$0.588433\pi$
$348$	12.1650	+	16.7437i	0.652114	+	0.897558i
$349$	29.0786			1.55654			0.778270	−	0.627930i	$-0.216097\pi$
$349$	29.0786			1.55654			0.778270	+	0.627930i	$0.216097\pi$
$350$	−0.243109	−	10.4400i	−0.0129947	−	0.558043i
$351$	4.85368			0.259070
$352$	13.9298	+	19.1727i	0.742461	+	1.02191i
$353$	18.3982	+	5.97795i	0.979240	+	0.318174i	0.754540	−	0.656254i	$-0.227860\pi$
$353$	18.3982	+	5.97795i	0.979240	+	0.318174i	0.224699	+	0.974428i	$0.427860\pi$
$354$	2.26032	−	6.95656i	0.120135	−	0.369737i
$355$	−2.41283	−	14.1648i	−0.128060	−	0.751790i
$356$	−10.0405	−	30.9014i	−0.532144	−	1.63777i
$357$			5.65339i			0.299209i
$358$	30.6328	−	9.95319i	1.61899	−	0.526042i
$359$	−28.1064	−	20.4205i	−1.48340	−	1.07775i	−0.976442	−	0.215779i	$-0.930771\pi$
$359$	−28.1064	−	20.4205i	−1.48340	−	1.07775i	−0.506955	−	0.861973i	$-0.669229\pi$
$360$	−1.66720	+	0.283991i	−0.0878692	+	0.0149676i
$361$	13.6445	−	9.91331i	0.718131	−	0.521753i
$362$	−4.55893	+	6.27482i	−0.239612	+	0.329797i
$363$	1.40965	−	1.94022i	0.0739876	−	0.101835i
$364$	−9.27541	+	6.73898i	−0.486163	+	0.353218i
$365$	19.9663	+	9.88227i	1.04508	+	0.517262i
$366$	−21.0155	−	15.2687i	−1.09850	−	0.798106i
$367$	17.3932	−	5.65139i	0.907917	−	0.295000i	0.182416	−	0.983221i	$-0.441608\pi$
$367$	17.3932	−	5.65139i	0.907917	−	0.295000i	0.725501	+	0.688221i	$0.241608\pi$
$368$			8.60874i			0.448762i
$369$	−2.17206	−	6.68492i	−0.113073	−	0.348003i
$370$	−11.0229	+	5.77905i	−0.573053	+	0.300438i
$371$	−2.38051	+	7.32646i	−0.123590	+	0.380371i
$372$	−13.6882	−	4.44758i	−0.709702	−	0.230596i
$373$	−8.29150	−	11.4123i	−0.429317	−	0.590905i	0.538479	−	0.842639i	$-0.318999\pi$
$373$	−8.29150	−	11.4123i	−0.429317	−	0.590905i	−0.967796	+	0.251734i	$0.918999\pi$
$374$	34.6299			1.79067
$375$	−4.72485	+	10.1329i	−0.243990	+	0.523261i
$376$	9.68888			0.499666
$377$	−24.9966	−	34.4049i	−1.28739	−	1.77194i
$378$	−1.98635	−	0.645404i	−0.102167	−	0.0331960i
$379$	−8.23504	+	25.3448i	−0.423005	+	1.30188i	0.481886	+	0.876234i	$0.339952\pi$
$379$	−8.23504	+	25.3448i	−0.423005	+	1.30188i	−0.904891	+	0.425643i	$0.860048\pi$
$380$	6.83443	−	3.58313i	0.350599	−	0.183811i
$381$	1.49885	+	4.61299i	0.0767885	+	0.236331i
$382$			1.63631i			0.0837212i
$383$	−12.2103	+	3.96737i	−0.623918	+	0.202723i	−0.603879	−	0.797076i	$-0.706379\pi$
$383$	−12.2103	+	3.96737i	−0.623918	+	0.202723i	−0.0200390	+	0.999799i	$0.506379\pi$
$384$	4.81486	+	3.49820i	0.245707	+	0.178517i
$385$	−5.87758	−	2.90910i	−0.299549	−	0.148261i
$386$	−8.91036	+	6.47375i	−0.453525	+	0.329505i
$387$	−3.82421	+	5.26358i	−0.194396	+	0.267563i
$388$	7.57577	−	10.4272i	0.384601	−	0.529358i
$389$	−0.221136	+	0.160665i	−0.0112121	+	0.00814603i	−0.593377	−	0.804925i	$-0.702206\pi$
$389$	−0.221136	+	0.160665i	−0.0112121	+	0.00814603i	0.582165	+	0.813071i	$0.302206\pi$
$390$	22.3457	−	3.80638i	1.13152	−	0.192743i
$391$	12.5210	+	9.09707i	0.633216	+	0.460058i
$392$	0.719317	−	0.233720i	0.0363310	−	0.0118047i
$393$			11.9277i			0.601675i
$394$	−2.89740	−	8.91728i	−0.145969	−	0.449246i
$395$	−6.47790	−	38.0292i	−0.325938	−	1.91346i
$396$	−2.14082	+	6.58876i	−0.107580	+	0.331098i
$397$	29.7947	+	9.68087i	1.49535	+	0.485869i	0.938658	−	0.344850i	$-0.112070\pi$
$397$	29.7947	+	9.68087i	1.49535	+	0.485869i	0.556693	+	0.830718i	$0.312070\pi$
$398$	−5.22286	−	7.18865i	−0.261798	−	0.360334i
$399$	1.46098			0.0731407
$400$	14.8363	−	5.20548i	0.741815	−	0.260274i
$401$	17.6248			0.880138			0.440069	−	0.897964i	$-0.354954\pi$
$401$	17.6248			0.880138			0.440069	+	0.897964i	$0.354954\pi$
$402$	−1.24430	−	1.71264i	−0.0620602	−	0.0854185i
$403$	28.1265	+	9.13885i	1.40108	+	0.455238i
$404$	2.09951	−	6.46162i	0.104454	−	0.321478i
$405$	1.59944	+	1.56263i	0.0794767	+	0.0776475i
$406$	5.65487	+	17.4039i	0.280646	+	0.863741i
$407$			7.81605i			0.387427i
$408$	4.06658	−	1.32131i	0.201326	−	0.0654146i
$409$	30.1942	+	21.9374i	1.49301	+	1.08473i	0.973065	+	0.230533i	$0.0740468\pi$
$409$	30.1942	+	21.9374i	1.49301	+	1.08473i	0.519943	+	0.854201i	$0.325953\pi$
$410$	−15.2424	−	29.0732i	−0.752768	−	1.43582i
$411$	4.20400	−	3.05438i	0.207368	−	0.150662i
$412$	21.2973	−	29.3133i	1.04924	−	1.44416i
$413$	2.05853	−	2.83333i	0.101294	−	0.139419i
$414$	−4.62574	+	3.36080i	−0.227343	+	0.165174i
$415$	11.8106	−	12.0888i	0.579761	−	0.593418i
$416$	−31.7294	−	23.0527i	−1.55566	−	1.13025i
$417$	13.8687	−	4.50620i	0.679151	−	0.220670i
$418$		−	8.94929i		−	0.437724i
$419$	7.62087	+	23.4546i	0.372304	+	1.14583i	0.945280	+	0.326261i	$0.105789\pi$
$419$	7.62087	+	23.4546i	0.372304	+	1.14583i	−0.572976	+	0.819572i	$0.694211\pi$
$420$	−5.22612	−	0.765484i	−0.255009	−	0.0373518i
$421$	2.76602	−	8.51294i	0.134808	−	0.414895i	−0.860752	−	0.509024i	$-0.830006\pi$
$421$	2.76602	−	8.51294i	0.134808	−	0.414895i	0.995560	+	0.0941285i	$0.0300065\pi$
$422$	39.4445	+	12.8163i	1.92013	+	0.623887i
$423$	−7.52971	−	10.3638i	−0.366107	−	0.503903i
$424$	5.82642			0.282956
$425$	8.10675	−	27.0795i	0.393235	−	1.31355i
$426$	−13.4210			−0.650251
$427$	−7.31058	−	10.0621i	−0.353784	−	0.486941i
$428$	−38.1985	−	12.4114i	−1.84639	−	0.599930i
$429$	4.39893	−	13.5385i	0.212383	−	0.653646i
$430$	−13.4784	+	27.2319i	−0.649984	+	1.31324i
$431$	10.9388	+	33.6662i	0.526904	+	1.62164i	0.760520	+	0.649315i	$0.224944\pi$
$431$	10.9388	+	33.6662i	0.526904	+	1.62164i	−0.233615	+	0.972329i	$0.575056\pi$
$432$		−	3.14460i		−	0.151295i
$433$	−6.85955	+	2.22880i	−0.329649	+	0.107109i	−0.469165	−	0.883110i	$-0.655445\pi$
$433$	−6.85955	+	2.22880i	−0.329649	+	0.107109i	0.139516	+	0.990220i	$0.455445\pi$
$434$	−10.2954	−	7.48007i	−0.494197	−	0.359055i
$435$	2.83938	−	19.3850i	0.136138	−	0.929441i
$436$	14.3237	−	10.4068i	0.685982	−	0.498395i
$437$	2.35092	−	3.23577i	0.112460	−	0.154788i
$438$	12.2310	−	16.8345i	0.584417	−	0.804382i
$439$	−13.8582	+	10.0685i	−0.661414	+	0.480545i	−0.867140	−	0.498064i	$-0.834044\pi$
$439$	−13.8582	+	10.0685i	−0.661414	+	0.480545i	0.205726	+	0.978610i	$0.434044\pi$
$440$	−0.718853	+	4.90776i	−0.0342700	+	0.233968i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	−54.5049	+	17.7097i	−2.59253	+	0.842366i
$443$		−	7.91325i		−	0.375970i	−0.982172	−	0.187985i	$-0.939804\pi$
$443$		−	7.91325i		−	0.375970i	0.982172	−	0.187985i	$-0.0601956\pi$
$444$	1.94527	+	5.98692i	0.0923184	+	0.284127i
$445$	−13.6437	+	27.5659i	−0.646774	+	1.30675i
$446$	−3.51702	+	10.8243i	−0.166536	+	0.512544i
$447$	9.14203	+	2.97043i	0.432403	+	0.140496i
$448$	6.22304	+	8.56529i	0.294011	+	0.404672i
$449$	25.2096			1.18971			0.594857	−	0.803831i	$-0.297208\pi$
$449$	25.2096			1.18971			0.594857	+	0.803831i	$0.297208\pi$
$450$	8.58905	+	5.93981i	0.404892	+	0.280006i
$451$	−20.6150			−0.970723
$452$	−11.3534	−	15.6267i	−0.534021	−	0.735017i
$453$	−1.96294	−	0.637797i	−0.0922269	−	0.0299663i
$454$	−5.25663	+	16.1783i	−0.246706	+	0.759283i
$455$	10.7386	+	1.57291i	0.503433	+	0.0737392i
$456$	−0.341462	−	1.05091i	−0.0159904	−	0.0492134i
$457$		−	39.7954i		−	1.86155i	−0.365595	−	0.930774i	$-0.619134\pi$
$457$		−	39.7954i		−	1.86155i	0.365595	−	0.930774i	$-0.380866\pi$
$458$	11.8214	−	3.84102i	0.552379	−	0.179479i
$459$	−4.57368	−	3.32298i	−0.213481	−	0.155103i
$460$	−10.1049	+	10.3430i	−0.471144	+	0.482243i
$461$	19.5530	−	14.2061i	0.910676	−	0.661645i	−0.0305098	−	0.999534i	$-0.509713\pi$
$461$	19.5530	−	14.2061i	0.910676	−	0.661645i	0.941186	+	0.337890i	$0.109713\pi$
$462$	−3.60049	+	4.95565i	−0.167510	+	0.230558i
$463$	16.7129	−	23.0033i	0.776713	−	1.06905i	−0.218924	−	0.975742i	$-0.570255\pi$
$463$	16.7129	−	23.0033i	0.776713	−	1.06905i	0.995637	−	0.0933121i	$-0.0297454\pi$
$464$	−22.2902	+	16.1948i	−1.03480	+	0.751824i
$465$	6.32632	+	12.0668i	0.293376	+	0.559582i
$466$	−29.4168	−	21.3725i	−1.36271	−	0.990063i
$467$	−24.5812	+	7.98691i	−1.13748	+	0.369590i	−0.816414	−	0.577467i	$-0.804041\pi$
$467$	−24.5812	+	7.98691i	−1.13748	+	0.369590i	−0.321067	+	0.947057i	$0.604041\pi$
$468$		−	11.4650i		−	0.529971i
$469$	−0.313214	−	0.963972i	−0.0144629	−	0.0445121i
$470$	−42.7933	−	41.8084i	−1.97391	−	1.92848i
$471$	4.77359	−	14.6916i	0.219955	−	0.676953i
$472$	−2.51918	−	0.818531i	−0.115955	−	0.0376760i
$473$	11.2159	+	15.4374i	0.515709	+	0.709813i
$474$	−36.0323			−1.65502
$475$	−6.99806	−	2.09500i	−0.321093	−	0.0961251i
$476$	13.3540			0.612081
$477$	−4.52800	−	6.23226i	−0.207323	−	0.285356i
$478$	−27.0220	−	8.77997i	−1.23596	−	0.401586i
$479$	7.95986	−	24.4979i	0.363695	−	1.11934i	−0.587099	−	0.809515i	$-0.699730\pi$
$479$	7.95986	−	24.4979i	0.363695	−	1.11934i	0.950794	−	0.309824i	$-0.100270\pi$
$480$	−3.03405	−	17.8117i	−0.138485	−	0.812991i
$481$	−3.99712	−	12.3019i	−0.182253	−	0.560917i
$482$			12.2716i			0.558956i
$483$	−2.60364	+	0.845973i	−0.118470	+	0.0384931i
$484$	−4.58305	−	3.32978i	−0.208321	−	0.151354i
$485$	−12.0276	+	2.04878i	−0.546144	+	0.0930302i
$486$	1.68969	−	1.22763i	0.0766459	−	0.0556865i
$487$	−3.00235	+	4.13237i	−0.136049	+	0.187256i	−0.871606	−	0.490208i	$-0.836921\pi$
$487$	−3.00235	+	4.13237i	−0.136049	+	0.187256i	0.735556	+	0.677464i	$0.236921\pi$
$488$	−5.52924	+	7.61035i	−0.250297	+	0.344504i
$489$	−6.24795	+	4.53940i	−0.282542	+	0.205279i
$490$	−4.18557	−	2.07164i	−0.189085	−	0.0935871i
$491$	23.8279	+	17.3120i	1.07534	+	0.781277i	0.976864	−	0.213862i	$-0.0686044\pi$
$491$	23.8279	+	17.3120i	1.07534	+	0.781277i	0.0984723	+	0.995140i	$0.468604\pi$
$492$	−15.7907	+	5.13070i	−0.711898	+	0.231310i
$493$			49.5335i			2.23088i
$494$	4.57666	+	14.0855i	0.205914	+	0.633737i
$495$	5.80826	−	3.04514i	0.261062	−	0.136869i
$496$	5.92087	−	18.2226i	0.265855	−	0.818217i
$497$	−6.11143	−	1.98572i	−0.274135	−	0.0890719i
$498$	−9.27867	−	12.7710i	−0.415787	−	0.572282i
$499$	21.8402			0.977701			0.488851	−	0.872368i	$-0.337416\pi$
$499$	21.8402			0.977701			0.488851	+	0.872368i	$0.337416\pi$
$500$	23.9352	+	11.1607i	1.07042	+	0.499122i
$501$	3.98768			0.178157
$502$	−2.33364	−	3.21197i	−0.104155	−	0.143357i
$503$	2.04257	+	0.663672i	0.0910738	+	0.0295917i	0.354199	−	0.935170i	$-0.384753\pi$
$503$	2.04257	+	0.663672i	0.0910738	+	0.0295917i	−0.263126	+	0.964762i	$0.584753\pi$
$504$	−0.233720	+	0.719317i	−0.0104107	+	0.0320409i
$505$	−5.69619	+	2.98638i	−0.253477	+	0.132892i
$506$	5.18202	+	15.9486i	0.230369	+	0.709003i
$507$			10.5582i			0.468908i
$508$	10.8965	−	3.54048i	0.483454	−	0.157084i
$509$	−18.4466	−	13.4022i	−0.817629	−	0.594042i	0.0984032	−	0.995147i	$-0.468627\pi$
$509$	−18.4466	−	13.4022i	−0.817629	−	0.594042i	−0.916032	+	0.401104i	$0.868627\pi$
$510$	−23.6626	−	11.7118i	−1.04780	−	0.518606i
$511$	8.06027	−	5.85613i	0.356566	−	0.259060i
$512$	−17.7313	+	24.4051i	−0.783622	+	1.07856i
$513$	−0.858745	+	1.18196i	−0.0379145	+	0.0521849i
$514$	−43.8218	+	31.8384i	−1.93290	+	1.40433i
$515$	−33.8124	+	5.75961i	−1.48995	+	0.253799i
$516$	12.4333	+	9.03329i	0.547344	+	0.397668i
$517$	−35.7322	+	11.6101i	−1.57150	+	0.510611i
$518$			5.56600i			0.244556i
$519$	−2.40258	−	7.39439i	−0.105462	−	0.324578i
$520$	−1.37840	−	8.09207i	−0.0604470	−	0.354861i
$521$	−0.910226	+	2.80139i	−0.0398777	+	0.122731i	−0.969014	−	0.247008i	$-0.920553\pi$
$521$	−0.910226	+	2.80139i	−0.0398777	+	0.122731i	0.929136	+	0.369739i	$0.120553\pi$
$522$	−17.4039	−	5.65487i	−0.761748	−	0.247507i
$523$	4.11059	+	5.65774i	0.179744	+	0.247396i	0.889376	−	0.457176i	$-0.151139\pi$
$523$	4.11059	+	5.65774i	0.179744	+	0.247396i	−0.709633	+	0.704572i	$0.751139\pi$
$524$	28.1749			1.23082
$525$	3.03230	+	3.97557i	0.132340	+	0.173508i
$526$	18.1681			0.792166
$527$	−20.2472	−	27.8679i	−0.881982	−	1.21394i
$528$	−8.77133	−	2.84998i	−0.381723	−	0.124029i
$529$	4.79143	−	14.7465i	0.208323	−	0.641153i
$530$	−25.7338	−	25.1416i	−1.11781	−	1.09208i
$531$	1.08223	+	3.33078i	0.0469650	+	0.144543i
$532$		−	3.45103i		−	0.149621i
$533$	32.4465	−	10.5425i	1.40541	−	0.456647i
$534$	23.2421	+	16.8864i	1.00578	+	0.730744i
$535$	17.6543	+	33.6735i	0.763260	+	1.45583i
$536$	−0.620197	+	0.450600i	−0.0267884	+	0.0194629i
$537$	−9.06461	+	12.4764i	−0.391167	+	0.538395i
$538$	30.0081	−	41.3025i	1.29374	−	1.78068i
$539$	−2.37275	+	1.72390i	−0.102201	+	0.0742537i
$540$	3.69113	−	3.77808i	0.158841	−	0.162583i
$541$	−15.4464	−	11.2225i	−0.664093	−	0.482492i	0.203949	−	0.978981i	$-0.434622\pi$
$541$	−15.4464	−	11.2225i	−0.664093	−	0.482492i	−0.868043	+	0.496489i	$0.834622\pi$
$542$	−2.80493	+	0.911377i	−0.120482	+	0.0391470i
$543$		−	3.71359i		−	0.159366i
$544$	14.1164	+	43.4458i	0.605235	+	1.86272i
$545$	−16.5833	−	2.42900i	−0.710349	−	0.104047i
$546$	3.13259	−	9.64111i	0.134062	−	0.412601i
$547$	10.6670	+	3.46591i	0.456087	+	0.148192i	0.528046	−	0.849216i	$-0.322925\pi$
$547$	10.6670	+	3.46591i	0.456087	+	0.148192i	−0.0719586	+	0.997408i	$0.522925\pi$
$548$	−7.21485	−	9.93039i	−0.308203	−	0.424205i
$549$	12.4375			0.530819
$550$	24.3524	−	18.5744i	1.03839	−	0.792015i
$551$	12.8008			0.545331
$552$	1.21705	+	1.67512i	0.0518009	+	0.0712978i
$553$	−16.4078	−	5.33121i	−0.697729	−	0.226706i
$554$	−6.45163	+	19.8561i	−0.274103	+	0.843604i
$555$	2.64337	−	5.34070i	0.112205	−	0.226700i
$556$	−10.6442	−	32.7596i	−0.451416	−	1.38932i
$557$		−	37.1852i		−	1.57559i	−0.615940	−	0.787793i	$-0.711224\pi$
$557$		−	37.1852i		−	1.57559i	0.615940	−	0.787793i	$-0.288776\pi$
$558$	12.1030	−	3.93251i	0.512361	−	0.166476i
$559$	−25.5477	−	18.5615i	−1.08055	−	0.785069i
$560$	1.01906	−	6.95731i	0.0430630	−	0.294000i
$561$	−13.4140	+	9.74587i	−0.566341	+	0.411471i
$562$	−24.4137	+	33.6025i	−1.02983	+	1.41744i
$563$	−24.5790	+	33.8302i	−1.03588	+	1.42577i	−0.135446	+	0.990785i	$0.543247\pi$
$563$	−24.5790	+	33.8302i	−1.03588	+	1.42577i	−0.900437	+	0.434986i	$0.856753\pi$
$564$	−24.4805	+	17.7862i	−1.03082	+	0.748932i
$565$	−2.64995	+	18.0918i	−0.111484	+	0.761126i
$566$	2.30153	+	1.67216i	0.0967405	+	0.0702861i
$567$	0.951057	−	0.309017i	0.0399406	−	0.0129775i
$568$			4.86016i			0.203928i
$569$	−6.89535	−	21.2217i	−0.289068	−	0.889660i	−0.985150	−	0.171698i	$-0.945075\pi$
$569$	−6.89535	−	21.2217i	−0.289068	−	0.889660i	0.696081	−	0.717963i	$-0.254925\pi$
$570$	−3.02663	+	6.11505i	−0.126772	+	0.256131i
$571$	10.3243	−	31.7750i	0.432059	−	1.32974i	−0.464012	−	0.885829i	$-0.653590\pi$
$571$	10.3243	−	31.7750i	0.432059	−	1.32974i	0.896071	−	0.443912i	$-0.146410\pi$
$572$	−31.9798	−	10.3909i	−1.33714	−	0.434463i
$573$	−0.460507	−	0.633834i	−0.0192380	−	0.0264788i
$574$	−14.6805			−0.612750
$575$	13.6844	−	0.318659i	0.570680	−	0.0132890i
$576$	−10.5873			−0.441136
$577$	12.8368	+	17.6683i	0.534403	+	0.735543i	0.987793	−	0.155769i	$-0.0497856\pi$
$577$	12.8368	+	17.6683i	0.534403	+	0.735543i	−0.453390	+	0.891312i	$0.649786\pi$
$578$	29.7173	+	9.65574i	1.23608	+	0.401626i
$579$	1.62956	−	5.01527i	0.0677222	−	0.208428i
$580$	−45.7900	−	6.70698i	−1.90132	−	0.278492i
$581$	−2.33561	−	7.18826i	−0.0968974	−	0.298219i
$582$			11.3960i			0.472381i
$583$	−21.4876	+	6.98174i	−0.889925	+	0.289154i
$584$	−6.09627	−	4.42920i	−0.252265	−	0.183281i
$585$	−7.58449	+	7.76316i	−0.313580	+	0.320967i
$586$	36.0532	−	26.1942i	1.48934	−	1.08207i
$587$	8.04321	−	11.0705i	0.331979	−	0.456930i	−0.610098	−	0.792326i	$-0.708870\pi$
$587$	8.04321	−	11.0705i	0.331979	−	0.456930i	0.942077	+	0.335396i	$0.108870\pi$
$588$	−1.38843	+	1.91100i	−0.0572577	+	0.0788085i
$589$	−7.20180	+	5.23241i	−0.296745	+	0.215598i
$590$	7.59454	+	14.4858i	0.312662	+	0.596369i
$591$	3.63191	+	2.63873i	0.149397	+	0.108543i
$592$	−7.97013	+	2.58965i	−0.327570	+	0.106434i
$593$		−	1.54413i		−	0.0634100i	−0.999497	−	0.0317050i	$-0.989906\pi$
$593$		−	1.54413i		−	0.0634100i	0.999497	−	0.0317050i	$-0.0100937\pi$
$594$	−1.89289	−	5.82571i	−0.0776662	−	0.239032i
$595$	−9.04224	−	8.83413i	−0.370696	−	0.362164i
$596$	7.01654	−	21.5947i	0.287409	−	0.884552i
$597$	4.04619	+	1.31469i	0.165600	+	0.0538066i
$598$	−16.3122	−	22.4519i	−0.667057	−	0.918125i
$599$	10.0585			0.410979			0.205490	−	0.978659i	$-0.434121\pi$
$599$	10.0585			0.410979			0.205490	+	0.978659i	$0.434121\pi$
$600$	2.15099	−	3.11036i	0.0878136	−	0.126980i
$601$	−31.8963			−1.30108			−0.650539	−	0.759472i	$-0.725457\pi$
$601$	−31.8963			−1.30108			−0.650539	+	0.759472i	$0.725457\pi$
$602$	7.98714	+	10.9934i	0.325532	+	0.448056i
$603$	0.963972	+	0.313214i	0.0392560	+	0.0127550i
$604$	−1.50656	+	4.63672i	−0.0613011	+	0.188665i
$605$	0.900501	+	5.28649i	0.0366106	+	0.214926i
$606$	1.85636	+	5.71330i	0.0754097	+	0.232087i
$607$		−	19.6473i		−	0.797458i	−0.917069	−	0.398729i	$-0.869451\pi$
$607$		−	19.6473i		−	0.797458i	0.917069	−	0.398729i	$-0.130549\pi$
$608$	11.2275	−	3.64805i	0.455337	−	0.147948i
$609$	−7.08840	−	5.15003i	−0.287237	−	0.208690i
$610$	57.2606	−	9.75378i	2.31842	−	0.394919i
$611$	50.3024	−	36.5468i	2.03502	−	1.47853i
$612$	−7.84930	+	10.8036i	−0.317289	+	0.436711i
$613$	−2.95055	+	4.06108i	−0.119171	+	0.164025i	−0.864435	−	0.502745i	$-0.832324\pi$
$613$	−2.95055	+	4.06108i	−0.119171	+	0.164025i	0.745264	+	0.666770i	$0.232324\pi$
$614$	35.5799	−	25.8503i	1.43589	−	1.04323i
$615$	14.0862	+	6.97196i	0.568012	+	0.281136i
$616$	1.79459	+	1.30385i	0.0723061	+	0.0525334i
$617$	−36.2848	+	11.7896i	−1.46077	+	0.474633i	−0.928305	−	0.371820i	$-0.878734\pi$
$617$	−36.2848	+	11.7896i	−1.46077	+	0.474633i	−0.532465	+	0.846452i	$0.678734\pi$
$618$			32.0370i			1.28872i
$619$	−13.2989	−	40.9299i	−0.534530	−	1.64511i	−0.744663	−	0.667441i	$-0.767390\pi$
$619$	−13.2989	−	40.9299i	−0.534530	−	1.64511i	0.210133	−	0.977673i	$-0.432610\pi$
$620$	28.5032	−	14.9436i	1.14472	−	0.600149i
$621$	0.845973	−	2.60364i	0.0339477	−	0.104480i
$622$	−16.1010	−	5.23152i	−0.645590	−	0.209765i
$623$	8.08512	+	11.1282i	0.323924	+	0.445843i
$624$	15.2629			0.611005
$625$	−8.82378	−	23.3910i	−0.352951	−	0.935642i
$626$	−21.1618			−0.845797
$627$	2.51859	+	3.46654i	0.100583	+	0.138440i
$628$	−34.7035	−	11.2758i	−1.38482	−	0.449955i
$629$	−4.65570	+	14.3288i	−0.185635	+	0.571325i
$630$	4.13620	−	2.16852i	0.164790	−	0.0863958i
$631$	−2.56214	−	7.88545i	−0.101997	−	0.313915i	0.887017	−	0.461737i	$-0.152774\pi$
$631$	−2.56214	−	7.88545i	−0.101997	−	0.313915i	−0.989014	+	0.147822i	$0.952774\pi$
$632$			13.0484i			0.519038i
$633$	−18.8859	+	6.13639i	−0.750646	+	0.243900i
$634$	51.2194	+	37.2131i	2.03418	+	1.47792i
$635$	−9.72034	−	4.81106i	−0.385740	−	0.190921i
$636$	−14.7214	+	10.6957i	−0.583742	+	0.424113i
$637$	2.85292	−	3.92671i	0.113037	−	0.155582i
$638$	−31.5466	+	43.4202i	−1.24894	+	1.71902i
$639$	5.19869	−	3.77707i	0.205657	−	0.149419i
$640$	−13.1190	+	2.23469i	−0.518573	+	0.0883338i
$641$	9.16593	+	6.65944i	0.362032	+	0.263032i	0.753899	−	0.656990i	$-0.228171\pi$
$641$	9.16593	+	6.65944i	0.362032	+	0.263032i	−0.391867	+	0.920022i	$0.628171\pi$
$642$	33.7747	−	10.9741i	1.33298	−	0.433112i
$643$			17.0336i			0.671738i	0.941909	+	0.335869i	$0.109030\pi$
$643$			17.0336i			0.671738i	−0.941909	+	0.335869i	$0.890970\pi$
$644$	1.99830	+	6.15013i	0.0787440	+	0.242349i
$645$	−2.44295	−	14.3416i	−0.0961910	−	0.564700i
$646$	5.33072	−	16.4063i	0.209734	−	0.645496i
$647$	−33.0524	−	10.7394i	−1.29942	−	0.422208i	−0.424043	−	0.905642i	$-0.639389\pi$
$647$	−33.0524	−	10.7394i	−1.29942	−	0.422208i	−0.875381	+	0.483434i	$0.839389\pi$
$648$	−0.444562	−	0.611888i	−0.0174641	−	0.0240372i
$649$	10.2715			0.403190
$650$	−28.8300	+	41.6886i	−1.13080	+	1.63516i
$651$	6.09309			0.238807
$652$	10.7227	+	14.7585i	0.419932	+	0.577986i
$653$	−24.9627	−	8.11088i	−0.976867	−	0.317403i	−0.223282	−	0.974754i	$-0.571677\pi$
$653$	−24.9627	−	8.11088i	−0.976867	−	0.317403i	−0.753585	+	0.657350i	$0.771677\pi$
$654$	−4.83755	+	14.8885i	−0.189163	+	0.582185i
$655$	−19.0777	−	18.6386i	−0.745426	−	0.728270i
$656$	−6.83027	−	21.0214i	−0.266677	−	0.820749i
$657$			9.96305i			0.388696i
$658$	−25.4457	+	8.26782i	−0.991978	+	0.322313i
$659$	−6.09437	−	4.42782i	−0.237403	−	0.172483i	0.462723	−	0.886503i	$-0.346873\pi$
$659$	−6.09437	−	4.42782i	−0.237403	−	0.172483i	−0.700125	+	0.714020i	$0.746873\pi$
$660$	−7.19301	−	13.7199i	−0.279988	−	0.534045i
$661$	11.1056	−	8.06869i	0.431958	−	0.313836i	−0.350473	−	0.936573i	$-0.613979\pi$
$661$	11.1056	−	8.06869i	0.431958	−	0.313836i	0.782431	+	0.622737i	$0.213979\pi$
$662$	−4.82091	+	6.63541i	−0.187370	+	0.257893i
$663$	16.1287	−	22.1992i	0.626386	−	0.862146i
$664$	−4.62476	+	3.36009i	−0.179476	+	0.130397i
$665$	−2.28297	+	2.33675i	−0.0885299	+	0.0906154i
$666$	−4.50299	−	3.27161i	−0.174487	−	0.126772i
$667$	−22.8124	+	7.41220i	−0.883300	+	0.287002i
$668$		−	9.41942i		−	0.364448i
$669$	−1.68394	−	5.18262i	−0.0651047	−	0.200372i
$670$	4.68363	+	0.686025i	0.180945	+	0.0265035i
$671$	11.2722	−	34.6923i	0.435159	−	1.33928i
$672$	−7.68491	−	2.49698i	−0.296452	−	0.0963231i
$673$	−27.6830	−	38.1024i	−1.06710	−	1.46874i	−0.872977	−	0.487762i	$-0.837813\pi$
$673$	−27.6830	−	38.1024i	−1.06710	−	1.46874i	−0.194124	−	0.980977i	$-0.562187\pi$
$674$	27.7856			1.07026
$675$	−4.99864	+	0.116400i	−0.192398	+	0.00448023i
$676$	24.9399			0.959229
$677$	26.3499	+	36.2675i	1.01271	+	1.39387i	0.917192	+	0.398446i	$0.130450\pi$
$677$	26.3499	+	36.2675i	1.01271	+	1.39387i	0.0955171	+	0.995428i	$0.469550\pi$
$678$	16.2428	+	5.27760i	0.623801	+	0.202685i
$679$	−1.68611	+	5.18932i	−0.0647071	+	0.199148i
$680$	−4.24118	+	8.56895i	−0.162642	+	0.328604i
$681$	−2.51686	−	7.74609i	−0.0964461	−	0.296831i
$682$		−	37.3233i		−	1.42918i
$683$	24.5217	−	7.96759i	0.938298	−	0.304872i	0.200346	−	0.979725i	$-0.435793\pi$
$683$	24.5217	−	7.96759i	0.938298	−	0.304872i	0.737952	+	0.674854i	$0.235793\pi$
$684$	2.79195	+	2.02847i	0.106753	+	0.0775604i
$685$	−1.68398	+	11.4969i	−0.0643416	+	0.439273i
$686$	−1.68969	+	1.22763i	−0.0645127	+	0.0468712i
$687$	−3.49811	+	4.81473i	−0.133461	+	0.183693i
$688$	−12.0256	+	16.5519i	−0.458473	+	0.631033i
$689$	30.2494	−	21.9775i	1.15241	−	0.837276i
$690$	1.85292	−	12.6502i	0.0705393	−	0.481587i
$691$	37.7084	+	27.3968i	1.43450	+	1.04222i	0.989157	+	0.146861i	$0.0469171\pi$
$691$	37.7084	+	27.3968i	1.43450	+	1.04222i	0.445340	+	0.895362i	$0.353083\pi$
$692$	−17.4665	+	5.67522i	−0.663977	+	0.215739i
$693$		−	2.93287i		−	0.111411i
$694$	0.873587	+	2.68863i	0.0331609	+	0.102059i
$695$	−14.4641	+	29.2236i	−0.548656	+	1.10851i
$696$	−2.04780	+	6.30248i	−0.0776216	+	0.238895i
$697$	−37.7924	−	12.2795i	−1.43149	−	0.465120i
$698$	35.6978	+	49.1338i	1.35118	+	1.85974i
$699$	17.4096			0.658490
$700$	9.39082	−	7.16269i	0.354939	−	0.270724i
$701$	18.7408			0.707831			0.353915	−	0.935277i	$-0.384850\pi$
$701$	18.7408			0.707831			0.353915	+	0.935277i	$0.384850\pi$
$702$	5.95853	+	8.20122i	0.224890	+	0.309535i
$703$	3.70293	+	1.20315i	0.139659	+	0.0453778i
$704$	−9.59533	+	29.5314i	−0.361638	+	1.11301i
$705$	28.3423	+	4.15138i	1.06743	+	0.156350i
$706$	12.4854	+	38.4260i	0.469893	+	1.44618i
$707$			2.87628i			0.108174i
$708$	7.86773	−	2.55638i	0.295687	−	0.0960746i
$709$	28.1953	+	20.4851i	1.05890	+	0.769333i	0.973884	−	0.227047i	$-0.0729072\pi$
$709$	28.1953	+	20.4851i	1.05890	+	0.769333i	0.0850120	+	0.996380i	$0.472907\pi$
$710$	20.9721	−	21.4661i	0.787067	−	0.805608i
$711$	13.9573	−	10.1406i	0.523439	−	0.380301i
$712$	6.11506	−	8.41665i	0.229171	−	0.315427i
$713$	9.80461	−	13.4949i	0.367186	−	0.505388i
$714$	−9.55247	+	6.94027i	−0.357492	+	0.259733i
$715$	14.7801	+	28.1915i	0.552746	+	1.05430i
$716$	29.4708	+	21.4118i	1.10138	+	0.800196i
$717$	12.9380	−	4.20382i	0.483179	−	0.156994i
$718$		−	72.5598i		−	2.70791i
$719$	13.2223	+	40.6941i	0.493109	+	1.51763i	0.819883	+	0.572531i	$0.194038\pi$
$719$	13.2223	+	40.6941i	0.493109	+	1.51763i	−0.326775	+	0.945102i	$0.605962\pi$
$720$	5.02959	+	4.91384i	0.187442	+	0.183128i
$721$	−4.74007	+	14.5884i	−0.176530	+	0.543302i
$722$	33.5008	+	10.8851i	1.24677	+	0.405101i
$723$	−3.45359	−	4.75345i	−0.128440	−	0.176783i
$724$	−8.77199			−0.326009
$725$	26.5682	+	34.8330i	0.986720	+	1.29366i
$726$	5.00890			0.185898
$727$	−1.27385	−	1.75330i	−0.0472444	−	0.0650263i	0.784741	−	0.619824i	$-0.212796\pi$
$727$	−1.27385	−	1.75330i	−0.0472444	−	0.0650263i	−0.831986	+	0.554797i	$0.812796\pi$
$728$	−3.49134	−	1.13440i	−0.129398	−	0.0420438i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	7.81326	+	45.8686i	0.289182	+	1.69767i
$731$	11.3662	+	34.9815i	0.420393	+	1.29384i
$732$		−	29.3790i		−	1.08588i
$733$	38.5816	−	12.5359i	1.42504	−	0.463025i	0.507843	−	0.861450i	$-0.330443\pi$
$733$	38.5816	−	12.5359i	1.42504	−	0.463025i	0.917201	+	0.398425i	$0.130443\pi$
$734$	30.9015	+	22.4513i	1.14060	+	0.828691i
$735$	2.20432	−	0.375483i	0.0813074	−	0.0138499i
$736$	−17.8963	+	13.0025i	−0.659668	+	0.479277i
$737$	1.74731	−	2.40497i	0.0643631	−	0.0885881i
$738$	8.62895	−	11.8767i	0.317636	−	0.437189i
$739$	23.0841	−	16.7716i	0.849162	−	0.616952i	−0.0757528	−	0.997127i	$-0.524136\pi$
$739$	23.0841	−	16.7716i	0.849162	−	0.616952i	0.924915	+	0.380174i	$0.124136\pi$
$740$	−12.6154	−	6.24399i	−0.463753	−	0.229534i
$741$	−5.73687	−	4.16808i	−0.210749	−	0.153118i
$742$	−15.3018	+	4.97187i	−0.561748	+	0.182523i
$743$			3.69060i			0.135395i	0.997706	+	0.0676975i	$0.0215653\pi$
$743$			3.69060i			0.135395i	−0.997706	+	0.0676975i	$0.978435\pi$
$744$	−1.42408	−	4.38286i	−0.0522093	−	0.160684i
$745$	−19.0366	+	9.98045i	−0.697447	+	0.365655i
$746$	9.10429	−	28.0201i	0.333332	−	1.02589i
$747$	7.18826	+	2.33561i	0.263005	+	0.0854555i
$748$	23.0210	+	31.6857i	0.841732	+	1.15854i
$749$	17.0034			0.621291
$750$	−22.9218	+	4.45595i	−0.836987	+	0.162708i
$751$	4.57741			0.167032			0.0835161	−	0.996506i	$-0.473385\pi$
$751$	4.57741			0.167032			0.0835161	+	0.996506i	$0.473385\pi$
$752$	−23.6779	−	32.5899i	−0.863445	−	1.18843i
$753$	1.80789	+	0.587418i	0.0658831	+	0.0214067i
$754$	27.4469	−	84.4730i	0.999559	−	3.07633i
$755$	4.08746	−	2.14296i	0.148758	−	0.0779902i
$756$	−0.729938	−	2.24652i	−0.0265476	−	0.0817051i
$757$			11.6163i			0.422203i	0.977464	+	0.211101i	$0.0677050\pi$
$757$			11.6163i			0.422203i	−0.977464	+	0.211101i	$0.932295\pi$
$758$	−52.9345	+	17.1995i	−1.92267	+	0.624712i
$759$	−6.49569	−	4.71940i	−0.235779	−	0.171303i
$760$	2.21444	+	1.09603i	0.0803263	+	0.0397573i
$761$	−38.2772	+	27.8100i	−1.38755	+	1.00811i	−0.391417	+	0.920213i	$0.628015\pi$
$761$	−38.2772	+	27.8100i	−1.38755	+	1.00811i	−0.996129	+	0.0878981i	$0.971985\pi$
$762$	−5.95449	+	8.19565i	−0.215708	+	0.296897i
$763$	−4.40568	+	6.06390i	−0.159496	+	0.219528i
$764$	−1.49720	+	1.08778i	−0.0541667	+	0.0393544i
$765$	12.4619	−	2.12275i	0.450559	−	0.0767483i
$766$	−21.6934	−	15.7612i	−0.783814	−	0.569474i
$767$	−16.1665	+	5.25282i	−0.583740	+	0.189668i
$768$		−	8.74443i		−	0.315538i
$769$	8.81265	+	27.1226i	0.317792	+	0.978064i	0.974590	+	0.223997i	$0.0719107\pi$
$769$	8.81265	+	27.1226i	0.317792	+	0.978064i	−0.656797	+	0.754067i	$0.728089\pi$
$770$	−2.30003	−	13.5026i	−0.0828874	−	0.486599i
$771$	8.01431	−	24.6655i	0.288628	−	0.888306i
$772$	−11.8467	−	3.84923i	−0.426373	−	0.138537i
$773$	3.42987	+	4.72082i	0.123364	+	0.169796i	0.866232	−	0.499642i	$-0.166535\pi$
$773$	3.42987	+	4.72082i	0.123364	+	0.169796i	−0.742868	+	0.669438i	$0.766535\pi$
$774$	−13.5885			−0.488430
$775$	−29.1857	−	8.73727i	−1.04838	−	0.313852i
$776$	4.12685			0.148145
$777$	−1.56643	−	2.15601i	−0.0561955	−	0.0773465i
$778$	−0.542947	−	0.176414i	−0.0194656	−	0.00632476i
$779$	−3.17335	+	9.76657i	−0.113697	+	0.349924i
$780$	18.3376	+	17.9156i	0.656591	+	0.641480i
$781$	−5.82388	−	17.9241i	−0.208395	−	0.641373i
$782$			32.3245i			1.15592i
$783$	8.33292	−	2.70753i	0.297794	−	0.0967592i
$784$	−2.54404	−	1.84835i	−0.0908584	−	0.0660125i
$785$	16.0390	+	30.5925i	0.572455	+	1.09189i
$786$	−20.1542	+	14.6429i	−0.718875	+	0.522294i
$787$	−3.28861	+	4.52638i	−0.117226	+	0.161348i	−0.863598	−	0.504182i	$-0.831794\pi$
$787$	−3.28861	+	4.52638i	−0.117226	+	0.161348i	0.746371	+	0.665530i	$0.231794\pi$
$788$	6.23303	−	8.57903i	0.222043	−	0.305615i
$789$	−7.03749	+	5.11303i	−0.250541	+	0.182029i
$790$	56.3051	−	57.6315i	2.00325	−	2.05044i
$791$	6.61550	+	4.80644i	0.235220	+	0.170897i
$792$	−2.10967	+	0.685472i	−0.0749637	+	0.0243572i
$793$			60.3677i			2.14372i
$794$	20.2192	+	62.2283i	0.717552	+	2.20840i
$795$	17.0437	+	2.49644i	0.604477	+	0.0885395i
$796$	3.10546	−	9.55763i	0.110070	−	0.338761i
$797$	−3.07687	−	0.999737i	−0.108988	−	0.0354125i	0.254015	−	0.967200i	$-0.418249\pi$
$797$	−3.07687	−	0.999737i	−0.108988	−	0.0354125i	−0.363004	+	0.931788i	$0.618249\pi$
$798$	1.79355	+	2.46861i	0.0634910	+	0.0873878i
$799$	−72.4216			−2.56209
$800$	33.2299	+	22.9803i	1.17485	+	0.812477i
$801$	−13.7552			−0.486017
$802$	21.6367	+	29.7804i	0.764019	+	1.05158i
$803$	27.7902	+	9.02959i	0.980696	+	0.318647i
$804$	0.739851	−	2.27703i	0.0260925	−	0.0803046i
$805$	2.71543	−	5.48629i	0.0957063	−	0.193366i
$806$	19.0871	+	58.7442i	0.672316	+	2.06917i
$807$			24.4439i			0.860465i
$808$	2.06896	−	0.672246i	0.0727857	−	0.0236495i
$809$	23.7896	+	17.2841i	0.836397	+	0.607678i	0.921362	−	0.388706i	$-0.127078\pi$
$809$	23.7896	+	17.2841i	0.836397	+	0.607678i	−0.0849647	+	0.996384i	$0.527078\pi$
$810$	−0.676834	+	4.62088i	−0.0237815	+	0.162361i
$811$	−7.55315	+	5.48768i	−0.265227	+	0.192699i	−0.712448	−	0.701725i	$-0.752414\pi$
$811$	−7.55315	+	5.48768i	−0.265227	+	0.192699i	0.447221	+	0.894423i	$0.352414\pi$
$812$	−12.1650	+	16.7437i	−0.426909	+	0.587590i
$813$	0.830014	−	1.14242i	0.0291099	−	0.0400663i
$814$	−13.2067	+	9.59523i	−0.462894	+	0.336312i
$815$	2.50272	−	17.0866i	0.0876665	−	0.598517i
$816$	−14.3824	−	10.4494i	−0.503485	−	0.365803i
$817$	9.04014	−	2.93732i	0.316275	−	0.102764i
$818$			77.9499i			2.72545i
$819$	1.49987	+	4.61613i	0.0524097	+	0.161301i
$820$	16.4687	−	33.2735i	0.575111	−	1.16196i
$821$	−8.92423	+	27.4660i	−0.311458	+	0.958569i	0.665730	+	0.746193i	$0.268120\pi$
$821$	−8.92423	+	27.4660i	−0.311458	+	0.958569i	−0.977188	+	0.212376i	$0.931880\pi$
$822$	10.3219	+	3.35379i	0.360018	+	0.116977i
$823$	−31.4598	−	43.3007i	−1.09662	−	1.50937i	−0.839791	−	0.542909i	$-0.817323\pi$
$823$	−31.4598	−	43.3007i	−1.09662	−	1.50937i	−0.256828	−	0.966457i	$-0.582677\pi$
$824$	11.6016			0.404160
$825$	−4.20564	+	14.0484i	−0.146421	+	0.489101i
$826$	7.31456			0.254506
$827$	−12.1238	−	16.6870i	−0.421587	−	0.580265i	0.544409	−	0.838820i	$-0.316754\pi$
$827$	−12.1238	−	16.6870i	−0.421587	−	0.580265i	−0.965997	+	0.258555i	$0.916754\pi$
$828$	−6.15013	−	1.99830i	−0.213732	−	0.0694457i
$829$	−7.65763	+	23.5678i	−0.265961	+	0.818543i	0.725510	+	0.688212i	$0.241604\pi$
$829$	−7.65763	+	23.5678i	−0.265961	+	0.818543i	−0.991471	+	0.130331i	$0.958396\pi$
$830$	34.9255	+	5.11564i	1.21228	+	0.177566i
$831$	−3.08902	−	9.50701i	−0.107157	−	0.329795i
$832$		−	51.3873i		−	1.78153i
$833$	−5.37669	+	1.74699i	−0.186291	+	0.0605297i
$834$	24.6397	+	17.9018i	0.853203	+	0.619888i
$835$	−6.23126	+	6.37805i	−0.215642	+	0.220721i
$836$	8.18843	−	5.94924i	0.283203	−	0.205759i
$837$	−3.58143	+	4.92941i	−0.123792	+	0.170385i
$838$	−30.2754	+	41.6706i	−1.04585	+	1.43949i
$839$	−20.5367	+	14.9208i	−0.709006	+	0.515123i	−0.882853	−	0.469650i	$-0.844380\pi$
$839$	−20.5367	+	14.9208i	−0.709006	+	0.515123i	0.173847	+	0.984773i	$0.444380\pi$
$840$	−0.785285	−	1.49784i	−0.0270949	−	0.0516805i
$841$	−38.6453	−	28.0775i	−1.33260	−	0.968189i
$842$	17.7799	−	5.77704i	0.612735	−	0.199090i
$843$		−	19.8868i		−	0.684938i
$844$	14.4950	+	44.6109i	0.498937	+	1.53557i
$845$	−16.8873	−	16.4986i	−0.580939	−	0.567569i
$846$	8.26782	−	25.4457i	0.284254	−	0.874843i
$847$	2.28087	+	0.741098i	0.0783715	+	0.0254644i
$848$	−14.2388	−	19.5980i	−0.488961	−	0.672997i
$849$	−1.36210			−0.0467472
$850$	55.7081	−	19.5458i	1.91077	−	0.670414i
$851$	−7.29571			−0.250094
$852$	−8.92193	−	12.2800i	−0.305660	−	0.420706i
$853$	−7.07838	−	2.29991i	−0.242359	−	0.0787473i	0.185319	−	0.982678i	$-0.440668\pi$
$853$	−7.07838	−	2.29991i	−0.242359	−	0.0787473i	−0.427678	+	0.903931i	$0.640668\pi$
$854$	8.02721	−	24.7052i	0.274685	−	0.845395i
$855$	−0.548575	−	3.22047i	−0.0187609	−	0.110138i
$856$	−3.97404	−	12.2308i	−0.135830	−	0.418042i
$857$			13.7033i			0.468097i	0.972225	+	0.234048i	$0.0751975\pi$
$857$			13.7033i			0.468097i	−0.972225	+	0.234048i	$0.924803\pi$
$858$	28.2762	−	9.18749i	0.965333	−	0.313656i
$859$	3.38238	+	2.45745i	0.115405	+	0.0838470i	0.643991	−	0.765033i	$-0.277277\pi$
$859$	3.38238	+	2.45745i	0.115405	+	0.0838470i	−0.528586	+	0.848880i	$0.677277\pi$
$860$	−33.8767	+	5.77056i	−1.15519	+	0.196774i
$861$	5.68654	−	4.13151i	0.193797	−	0.140801i
$862$	−43.4566	+	59.8129i	−1.48014	+	2.03724i
$863$	14.8096	−	20.3837i	0.504126	−	0.693869i	−0.478789	−	0.877930i	$-0.658924\pi$
$863$	14.8096	−	20.3837i	0.504126	−	0.693869i	0.982915	+	0.184060i	$0.0589242\pi$
$864$	6.53718	−	4.74954i	0.222399	−	0.161583i
$865$	15.5812	+	7.71189i	0.529777	+	0.262212i
$866$	−12.1870	−	8.85437i	−0.414131	−	0.300884i
$867$	−14.2285	+	4.62313i	−0.483226	+	0.157010i
$868$		−	14.3927i		−	0.488519i
$869$	−15.6358	−	48.1219i	−0.530407	−	1.63243i
$870$	36.2404	−	19.0000i	1.22866	−	0.644160i
$871$	−1.52024	+	4.67882i	−0.0515113	+	0.158536i
$872$	5.39156	+	1.75182i	0.182581	+	0.0593243i
$873$	−3.20718	−	4.41430i	−0.108546	−	0.149401i
$874$	8.35351			0.282562
$875$	−11.0970	−	1.36236i	−0.375148	−	0.0460561i
$876$	23.5340			0.795141
$877$	15.1051	+	20.7904i	0.510064	+	0.702042i	0.983930	−	0.178554i	$-0.0571420\pi$
$877$	15.1051	+	20.7904i	0.510064	+	0.702042i	−0.473866	+	0.880597i	$0.657142\pi$
$878$	−34.0254	−	11.0555i	−1.14830	−	0.373106i
$879$	−6.59355	+	20.2929i	−0.222395	+	0.684461i
$880$	18.2647	−	9.57574i	0.615702	−	0.322798i
$881$	8.01215	+	24.6589i	0.269936	+	0.830778i	0.990515	+	0.137405i	$0.0438762\pi$
$881$	8.01215	+	24.6589i	0.269936	+	0.830778i	−0.720579	+	0.693373i	$0.756124\pi$
$882$		−	2.08857i		−	0.0703259i
$883$	27.9600	−	9.08476i	0.940930	−	0.305727i	0.201905	−	0.979405i	$-0.435287\pi$
$883$	27.9600	−	9.08476i	0.940930	−	0.305727i	0.739025	+	0.673678i	$0.235287\pi$
$884$	−52.4374	−	38.0980i	−1.76366	−	1.28138i
$885$	−7.01849	−	3.47379i	−0.235924	−	0.116770i
$886$	13.3709	−	9.71456i	0.449206	−	0.326367i
$887$	3.69868	−	5.09080i	0.124189	−	0.170932i	−0.742395	−	0.669962i	$-0.766310\pi$
$887$	3.69868	−	5.09080i	0.124189	−	0.170932i	0.866585	+	0.499030i	$0.166310\pi$
$888$	−1.18475	+	1.63067i	−0.0397576	+	0.0547216i
$889$	−3.92405	+	2.85099i	−0.131608	+	0.0956190i
$890$	−63.3273	+	10.7872i	−2.12274	+	0.361587i
$891$	2.37275	+	1.72390i	0.0794900	+	0.0577528i
$892$	−12.2420	+	3.97767i	−0.409893	+	0.133182i
$893$			18.7157i			0.626296i
$894$	6.20395	+	19.0938i	0.207491	+	0.638592i
$895$	−5.79057	−	33.9942i	−0.193557	−	1.13630i
$896$	−1.83911	+	5.66021i	−0.0614404	+	0.189094i
$897$	12.6372	+	4.10608i	0.421945	+	0.137098i
$898$	30.9481	+	42.5964i	1.03275	+	1.42146i
$899$	53.3861			1.78053
$900$	0.274951	+	11.8074i	0.00916504	+	0.393582i
$901$	−43.5508			−1.45089
$902$	−25.3076	−	34.8330i	−0.842652	−	1.15981i
$903$	−6.18771	−	2.01051i	−0.205914	−	0.0669055i
$904$	1.91118	−	5.88201i	0.0635649	−	0.195633i
$905$	5.93966	+	5.80296i	0.197441	+	0.192897i
$906$	−1.33209	−	4.09974i	−0.0442556	−	0.136205i
$907$		−	38.4319i		−	1.27611i	−0.769991	−	0.638055i	$-0.779739\pi$
$907$		−	38.4319i		−	1.27611i	0.769991	−	0.638055i	$-0.220261\pi$
$908$	−18.2973	+	5.94514i	−0.607216	+	0.197296i
$909$	−2.32696	−	1.69064i	−0.0771804	−	0.0560749i
$910$	10.5253	+	20.0758i	0.348910	+	0.665507i
$911$	−30.7255	+	22.3234i	−1.01798	+	0.739606i	−0.965868	−	0.259035i	$-0.916595\pi$
$911$	−30.7255	+	22.3234i	−1.01798	+	0.739606i	−0.0521124	+	0.998641i	$0.516595\pi$
$912$	−2.70041	+	3.71680i	−0.0894195	+	0.123075i
$913$	13.0296	−	17.9337i	0.431216	−	0.593517i
$914$	67.2418	−	48.8540i	2.22416	−	1.61595i
$915$	−19.4352	+	19.8930i	−0.642506	+	0.657642i
$916$	11.3730	+	8.26299i	0.375775	+	0.273017i
$917$	−11.3440	+	3.68587i	−0.374610	+	0.121718i
$918$		−	11.8075i		−	0.389706i
$919$	5.35417	+	16.4785i	0.176618	+	0.543574i	0.999704	−	0.0243431i	$-0.00774942\pi$
$919$	5.35417	+	16.4785i	0.176618	+	0.543574i	−0.823086	+	0.567917i	$0.807749\pi$
$920$	−4.58104	−	0.670997i	−0.151032	−	0.0221221i
$921$	−6.50698	+	20.0264i	−0.214412	+	0.659893i
$922$	48.0079	+	15.5987i	1.58105	+	0.513716i
$923$	18.3327	+	25.2328i	0.603428	+	0.830548i
$924$	−6.92783			−0.227909
$925$	4.41152	+	12.5734i	0.145050	+	0.413412i
$926$	59.3857			1.95154
$927$	−9.01615	−	12.4097i	−0.296129	−	0.407587i
$928$	−67.3333	−	21.8779i	−2.21032	−	0.718177i
$929$	11.5291	−	35.4829i	0.378257	−	1.16416i	−0.562998	−	0.826459i	$-0.690352\pi$
$929$	11.5291	−	35.4829i	0.378257	−	1.16416i	0.941255	−	0.337697i	$-0.109648\pi$
$930$	−12.6227	+	25.5030i	−0.413914	+	0.836277i
$931$	0.451469	+	1.38948i	0.0147963	+	0.0455383i
$932$		−	41.1237i		−	1.34705i
$933$	7.70908	−	2.50483i	0.252384	−	0.0820046i
$934$	−43.6720	−	31.7296i	−1.42899	−	1.03822i
$935$	5.37322	−	36.6841i	0.175723	−	1.19970i
$936$	2.96991	−	2.15777i	0.0970745	−	0.0705288i
$937$	25.6294	−	35.2759i	0.837276	−	1.15241i	−0.149248	−	0.988800i	$-0.547685\pi$
$937$	25.6294	−	35.2759i	0.837276	−	1.15241i	0.986525	−	0.163612i	$-0.0523147\pi$
$938$	1.24430	−	1.71264i	0.0406279	−	0.0559196i
$939$	8.19713	−	5.95556i	0.267503	−	0.194352i
$940$	9.80609	−	66.9482i	0.319839	−	2.18361i
$941$	−40.2236	−	29.2242i	−1.31125	−	0.952681i	−0.999997	−	0.00235433i	$-0.999251\pi$
$941$	−40.2236	−	29.2242i	−1.31125	−	0.952681i	−0.311255	−	0.950326i	$-0.600749\pi$
$942$	30.6845	−	9.96998i	0.999753	−	0.324840i
$943$		−	19.2426i		−	0.626626i
$944$	3.40320	+	10.4740i	0.110765	+	0.340898i
$945$	−0.991892	+	2.00403i	−0.0322663	+	0.0651912i
$946$	−12.3154	+	37.9029i	−0.400408	+	1.23233i
$947$	−7.40057	−	2.40459i	−0.240486	−	0.0781387i	0.186294	−	0.982494i	$-0.440352\pi$
$947$	−7.40057	−	2.40459i	−0.240486	−	0.0781387i	−0.426780	+	0.904355i	$0.640352\pi$
$948$	−23.9533	−	32.9689i	−0.777968	−	1.07078i
$949$	−48.3575			−1.56975
$950$	−5.05114	−	14.3964i	−0.163881	−	0.467082i
$951$	−30.3129			−0.982964
$952$	2.51328	+	3.45924i	0.0814559	+	0.112114i
$953$	−4.59307	−	1.49238i	−0.148784	−	0.0483429i	0.233678	−	0.972314i	$-0.424924\pi$
$953$	−4.59307	−	1.49238i	−0.148784	−	0.0483429i	−0.382462	+	0.923971i	$0.624924\pi$
$954$	4.97187	−	15.3018i	0.160970	−	0.495415i
$955$	1.73338	+	0.253893i	0.0560908	+	0.00821577i
$956$	−9.92996	−	30.5613i	−0.321158	−	0.988422i
$957$		−	25.6971i		−	0.830670i
$958$	51.1657	−	16.6247i	1.65309	−	0.537121i
$959$	4.20400	+	3.05438i	0.135754	+	0.0986311i
$960$	16.5440	−	16.9337i	0.533954	−	0.546532i
$961$	−4.95584	+	3.60063i	−0.159866	+	0.116149i
$962$	15.8794	−	21.8561i	0.511971	−	0.704668i
$963$	−9.99436	+	13.7561i	−0.322064	+	0.443283i
$964$	−11.2283	+	8.15782i	−0.361638	+	0.262746i
$965$	5.47522	+	10.4434i	0.176254	+	0.336184i
$966$	−4.62574	−	3.36080i	−0.148831	−	0.108132i
$967$	−38.2638	+	12.4326i	−1.23048	+	0.399807i	−0.850888	−	0.525347i	$-0.823935\pi$
$967$	−38.2638	+	12.4326i	−1.23048	+	0.399807i	−0.379591	+	0.925154i	$0.623935\pi$
$968$		−	1.81388i		−	0.0583002i
$969$	2.55233	+	7.85526i	0.0819926	+	0.252347i
$970$	−18.2272	−	17.8077i	−0.585241	−	0.571772i
$971$	−3.45749	+	10.6411i	−0.110956	+	0.341488i	−0.991082	−	0.133252i	$-0.957458\pi$
$971$	−3.45749	+	10.6411i	−0.110956	+	0.341488i	0.880126	+	0.474740i	$0.157458\pi$
$972$	2.24652	+	0.729938i	0.0720571	+	0.0234128i
$973$	8.57131	+	11.7974i	0.274783	+	0.378207i
$974$	−10.6682			−0.341831
$975$	−0.564967	−	24.2618i	−0.0180934	−	0.777001i
$976$	39.1110			1.25191
$977$	−1.87049	−	2.57451i	−0.0598423	−	0.0823659i	0.778047	−	0.628206i	$-0.216211\pi$
$977$	−1.87049	−	2.57451i	−0.0598423	−	0.0823659i	−0.837889	+	0.545840i	$0.816211\pi$
$978$	−15.3404	−	4.98438i	−0.490531	−	0.159383i
$979$	−12.4665	+	38.3679i	−0.398430	+	1.22624i
$980$	−0.886941	−	5.20688i	−0.0283323	−	0.166328i
$981$	−2.31620	−	7.12854i	−0.0739507	−	0.227597i
$982$			61.5144i			1.96300i
$983$	−8.96292	+	2.91223i	−0.285873	+	0.0928857i	−0.448443	−	0.893811i	$-0.648021\pi$
$983$	−8.96292	+	2.91223i	−0.285873	+	0.0928857i	0.162571	+	0.986697i	$0.448021\pi$
$984$	−4.30092	−	3.12480i	−0.137108	−	0.0996151i
$985$	−9.89580	+	1.68565i	−0.315306	+	0.0537093i
$986$	−83.6963	+	60.8089i	−2.66543	+	1.93655i
$987$	7.52971	−	10.3638i	0.239673	−	0.329882i
$988$	−9.84554	+	13.5512i	−0.313228	+	0.431122i
$989$	−14.4097	+	10.4693i	−0.458202	+	0.332903i
$990$	12.2757	+	6.07586i	0.390149	+	0.193103i
$991$	37.2551	+	27.0674i	1.18345	+	0.859825i	0.992556	−	0.121787i	$-0.0388624\pi$
$991$	37.2551	+	27.0674i	1.18345	+	0.859825i	0.190891	+	0.981611i	$0.438862\pi$
$992$	46.8249	−	15.2143i	1.48669	−	0.483055i
$993$		−	3.92700i		−	0.124620i
$994$	−4.14733	−	12.7642i	−0.131545	−	0.404854i
$995$	−8.42545	+	4.41727i	−0.267105	+	0.140037i
$996$	5.51701	−	16.9796i	0.174813	−	0.538020i
$997$	−3.96031	−	1.28678i	−0.125424	−	0.0407529i	0.245632	−	0.969363i	$-0.421004\pi$
$997$	−3.96031	−	1.28678i	−0.125424	−	0.0407529i	−0.371057	+	0.928610i	$0.621004\pi$
$998$	26.8117	+	36.9031i	0.848710	+	1.16815i
$999$	2.66498			0.0843162

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.a.64.13	✓	56
25.9	even	10	inner	525.2.z.a.484.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.a.64.13	✓	56	1.1	even	1	trivial
525.2.z.a.484.13	yes	56	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22763 + 1.68969i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.729938 + 2.24652i) q^{4} +(1.98040 - 1.03828i) q^{5} +(-0.645404 - 1.98635i) q^{6} -1.00000i q^{7} +(-0.719317 + 0.233720i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.22763 + 1.68969i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.729938 + 2.24652i) q^{4} +(1.98040 - 1.03828i) q^{5} +(-0.645404 - 1.98635i) q^{6} -1.00000i q^{7} +(-0.719317 + 0.233720i) q^{8} +(0.809017 + 0.587785i) q^{9} +(4.18557 + 2.07164i) q^{10} +(2.37275 - 1.72390i) q^{11} +(1.38843 - 1.91100i) q^{12} +(-2.85292 + 3.92671i) q^{13} +(1.68969 - 1.22763i) q^{14} +(-2.20432 + 0.375483i) q^{15} +(2.54404 + 1.84835i) q^{16} +(5.37669 - 1.74699i) q^{17} +2.08857i q^{18} +(-0.451469 - 1.38948i) q^{19} +(0.886941 + 5.20688i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(5.82571 + 1.89289i) q^{22} +(1.60914 + 2.21479i) q^{23} +0.756335 q^{24} +(2.84396 - 4.11241i) q^{25} -10.1373 q^{26} +(-0.587785 - 0.809017i) q^{27} +(2.24652 + 0.729938i) q^{28} +(-2.70753 + 8.33292i) q^{29} +(-3.34054 - 3.26366i) q^{30} +(-1.88287 - 5.79487i) q^{31} +8.08039i q^{32} +(-2.78933 + 0.906308i) q^{33} +(9.55247 + 6.94027i) q^{34} +(-1.03828 - 1.98040i) q^{35} +(-1.91100 + 1.38843i) q^{36} +(-1.56643 + 2.15601i) q^{37} +(1.79355 - 2.46861i) q^{38} +(3.92671 - 2.85292i) q^{39} +(-1.18187 + 1.20971i) q^{40} +(-5.68654 - 4.13151i) q^{41} +(-1.98635 + 0.645404i) q^{42} +6.50614i q^{43} +(2.14082 + 6.58876i) q^{44} +(2.21246 + 0.324065i) q^{45} +(-1.76687 + 5.43788i) q^{46} +(-12.1833 - 3.95860i) q^{47} +(-1.84835 - 2.54404i) q^{48} -1.00000 q^{49} +(10.4400 - 0.243109i) q^{50} -5.65339 q^{51} +(-6.73898 - 9.27541i) q^{52} +(-7.32646 - 2.38051i) q^{53} +(0.645404 - 1.98635i) q^{54} +(2.90910 - 5.87758i) q^{55} +(0.233720 + 0.719317i) q^{56} +1.46098i q^{57} +(-17.4039 + 5.65487i) q^{58} +(2.83333 + 2.05853i) q^{59} +(0.765484 - 5.22612i) q^{60} +(10.0621 - 7.31058i) q^{61} +(7.48007 - 10.2954i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-8.56529 + 6.22304i) q^{64} +(-1.57291 + 10.7386i) q^{65} +(-4.95565 - 3.60049i) q^{66} +(0.963972 - 0.313214i) q^{67} +13.3540i q^{68} +(-0.845973 - 2.60364i) q^{69} +(2.07164 - 4.18557i) q^{70} +(1.98572 - 6.11143i) q^{71} +(-0.719317 - 0.233720i) q^{72} +(5.85613 + 8.06027i) q^{73} -5.56600 q^{74} +(-3.97557 + 3.03230i) q^{75} +3.45103 q^{76} +(-1.72390 - 2.37275i) q^{77} +(9.64111 + 3.13259i) q^{78} +(5.33121 - 16.4078i) q^{79} +(6.95731 + 1.01906i) q^{80} +(0.309017 + 0.951057i) q^{81} -14.6805i q^{82} +(7.18826 - 2.33561i) q^{83} +(-1.91100 - 1.38843i) q^{84} +(8.83413 - 9.04224i) q^{85} +(-10.9934 + 7.98714i) q^{86} +(5.15003 - 7.08840i) q^{87} +(-1.30385 + 1.79459i) q^{88} +(-11.1282 + 8.08512i) q^{89} +(2.16852 + 4.13620i) q^{90} +(3.92671 + 2.85292i) q^{91} +(-6.15013 + 1.99830i) q^{92} +6.09309i q^{93} +(-8.26782 - 25.4457i) q^{94} +(-2.33675 - 2.28297i) q^{95} +(2.49698 - 7.68491i) q^{96} +(-5.18932 - 1.68611i) q^{97} +(-1.22763 - 1.68969i) q^{98} +2.93287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9}+O(q^{10}) \) 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9	\( 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9} + 36 q^{10} + 12 q^{11} + 20 q^{13} - 4 q^{15} + 4 q^{16} - 22 q^{19} - 22 q^{20} + 14 q^{21} + 30 q^{22} - 10 q^{23} + 16 q^{25} - 60 q^{26} - 20 q^{28} - 18 q^{29} - 18 q^{30} + 16 q^{31} - 10 q^{33} + 6 q^{35} - 12 q^{36} + 10 q^{37} + 100 q^{38} - 22 q^{40} + 8 q^{41} - 66 q^{44} + 2 q^{45} + 40 q^{46} - 100 q^{47} - 56 q^{49} + 62 q^{50} + 32 q^{51} + 80 q^{52} - 30 q^{53} - 58 q^{55} - 40 q^{58} - 20 q^{59} + 66 q^{60} + 28 q^{61} - 50 q^{62} - 12 q^{64} + 78 q^{65} - 20 q^{67} + 4 q^{69} - 18 q^{70} + 40 q^{71} - 20 q^{73} + 100 q^{74} - 8 q^{75} - 164 q^{76} + 20 q^{77} - 90 q^{78} - 4 q^{79} - 158 q^{80} - 14 q^{81} + 30 q^{83} - 12 q^{84} + 46 q^{85} + 80 q^{86} - 40 q^{87} + 130 q^{88} - 38 q^{89} + 4 q^{90} - 100 q^{92} - 10 q^{94} + 8 q^{95} + 10 q^{96} - 130 q^{97} + 48 q^{99}+O(q^{100}) \) 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9 + 36 * q^10 + 12 * q^11 + 20 * q^13 - 4 * q^15 + 4 * q^16 - 22 * q^19 - 22 * q^20 + 14 * q^21 + 30 * q^22 - 10 * q^23 + 16 * q^25 - 60 * q^26 - 20 * q^28 - 18 * q^29 - 18 * q^30 + 16 * q^31 - 10 * q^33 + 6 * q^35 - 12 * q^36 + 10 * q^37 + 100 * q^38 - 22 * q^40 + 8 * q^41 - 66 * q^44 + 2 * q^45 + 40 * q^46 - 100 * q^47 - 56 * q^49 + 62 * q^50 + 32 * q^51 + 80 * q^52 - 30 * q^53 - 58 * q^55 - 40 * q^58 - 20 * q^59 + 66 * q^60 + 28 * q^61 - 50 * q^62 - 12 * q^64 + 78 * q^65 - 20 * q^67 + 4 * q^69 - 18 * q^70 + 40 * q^71 - 20 * q^73 + 100 * q^74 - 8 * q^75 - 164 * q^76 + 20 * q^77 - 90 * q^78 - 4 * q^79 - 158 * q^80 - 14 * q^81 + 30 * q^83 - 12 * q^84 + 46 * q^85 + 80 * q^86 - 40 * q^87 + 130 * q^88 - 38 * q^89 + 4 * q^90 - 100 * q^92 - 10 * q^94 + 8 * q^95 + 10 * q^96 - 130 * q^97 + 48 * q^99

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