LMFDB - Embedded newform 507.2.m.a.40.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$15$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			40.5
Character	$\chi$	$=$	507.40
Dual form			507.2.m.a.469.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56270 - 0.385172i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(0.522773 + 0.274373i) q^{4} +(-0.878504 + 1.27273i) q^{5} +(0.570727 - 1.50488i) q^{6} +(0.273931 + 0.242682i) q^{7} +(1.69816 + 1.50443i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})$	\(q+(-1.56270 - 0.385172i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(0.522773 + 0.274373i) q^{4} +(-0.878504 + 1.27273i) q^{5} +(0.570727 - 1.50488i) q^{6} +(0.273931 + 0.242682i) q^{7} +(1.69816 + 1.50443i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(1.86306 - 1.65053i) q^{10} +(4.72254 - 1.16400i) q^{11} +(-0.335385 + 0.485890i) q^{12} +(-3.52332 - 0.765668i) q^{13} +(-0.334599 - 0.484750i) q^{14} +(-1.15756 - 1.02551i) q^{15} +(-2.74502 - 3.97685i) q^{16} +(5.97008 + 5.28903i) q^{17} +(1.42512 + 0.747959i) q^{18} -4.56274 q^{19} +(-0.808461 + 0.424313i) q^{20} +(-0.273931 + 0.242682i) q^{21} -7.82827 q^{22} -3.46519 q^{23} +(-1.69816 + 1.50443i) q^{24} +(0.924946 + 2.43888i) q^{25} +(5.21098 + 2.55359i) q^{26} +(0.354605 - 0.935016i) q^{27} +(0.0766186 + 0.202027i) q^{28} +(-4.09901 - 1.01032i) q^{29} +(1.41393 + 2.04843i) q^{30} +(-1.09769 + 2.89437i) q^{31} +(1.14889 + 3.02937i) q^{32} +(0.586276 + 4.82841i) q^{33} +(-7.29228 - 10.5647i) q^{34} +(-0.549518 + 0.135444i) q^{35} +(-0.441921 - 0.391508i) q^{36} +(-2.95482 + 7.79121i) q^{37} +(7.13021 + 1.75744i) q^{38} +(1.18477 - 3.40534i) q^{39} +(-3.40658 + 0.839646i) q^{40} +(-0.424060 + 3.49245i) q^{41} +(0.521547 - 0.273729i) q^{42} +(0.408248 + 1.07646i) q^{43} +(2.78819 + 0.687227i) q^{44} +(1.15756 - 1.02551i) q^{45} +(5.41507 + 1.33469i) q^{46} +(-6.59542 + 3.46154i) q^{47} +(4.27873 - 2.24565i) q^{48} +(-0.827613 - 6.81601i) q^{49} +(-0.506028 - 4.16751i) q^{50} +(-5.97008 + 5.28903i) q^{51} +(-1.63182 - 1.36697i) q^{52} +(0.180951 + 0.160308i) q^{53} +(-0.914284 + 1.32457i) q^{54} +(-2.66731 + 7.03311i) q^{55} +(0.100079 + 0.824222i) q^{56} +(0.549977 - 4.52947i) q^{57} +(6.01640 + 3.15765i) q^{58} +(-6.33698 + 9.18070i) q^{59} +(-0.323770 - 0.853712i) q^{60} +(-2.28748 + 2.02653i) q^{61} +(2.83019 - 4.10024i) q^{62} +(-0.207893 - 0.301186i) q^{63} +(0.536377 + 4.41746i) q^{64} +(4.06974 - 3.81159i) q^{65} +(0.943594 - 7.77120i) q^{66} +(11.3526 - 5.95833i) q^{67} +(1.66983 + 4.40299i) q^{68} +(0.417683 - 3.43993i) q^{69} +0.910903 q^{70} +(-0.725999 + 5.97914i) q^{71} +(-1.28878 - 1.86711i) q^{72} +(-9.32671 + 2.29883i) q^{73} +(7.61846 - 11.0372i) q^{74} +(-2.53259 + 0.624227i) q^{75} +(-2.38528 - 1.25189i) q^{76} +(1.57613 + 0.827218i) q^{77} +(-3.16309 + 4.86519i) q^{78} +(-4.79957 + 2.51901i) q^{79} +7.47297 q^{80} +(0.885456 + 0.464723i) q^{81} +(2.00787 - 5.29433i) q^{82} +(2.08260 + 17.1517i) q^{83} +(-0.209789 + 0.0517083i) q^{84} +(-11.9763 + 2.95188i) q^{85} +(-0.223348 - 1.83943i) q^{86} +(1.49703 - 3.94735i) q^{87} +(9.77077 + 5.12810i) q^{88} +9.59411 q^{89} +(-2.20392 + 1.15671i) q^{90} +(-0.779331 - 1.06478i) q^{91} +(-1.81151 - 0.950754i) q^{92} +(-2.74095 - 1.43856i) q^{93} +(11.6400 - 2.86900i) q^{94} +(4.00838 - 5.80714i) q^{95} +(-3.14577 + 0.775362i) q^{96} +(0.986463 + 1.42914i) q^{97} +(-1.33202 + 10.9702i) q^{98} -4.86388 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) $ 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{13}\right)$

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 $

$2$	−1.56270	−	0.385172i	−1.10500	−	0.272358i	−0.355707	−	0.934598i	$-0.615760\pi$
$2$	−1.56270	−	0.385172i	−1.10500	−	0.272358i	−0.749292	+	0.662240i	$0.769606\pi$
$3$	−0.120537	+	0.992709i	−0.0695919	+	0.573141i
$3$	−0.120537	+	0.992709i	−0.0695919	+	0.573141i
$4$	0.522773	+	0.274373i	0.261387	+	0.137186i
$5$	−0.878504	+	1.27273i	−0.392879	+	0.569183i	−0.968651	−	0.248427i	$-0.920086\pi$
$5$	−0.878504	+	1.27273i	−0.392879	+	0.569183i	0.575772	+	0.817610i	$0.304702\pi$
$6$	0.570727	−	1.50488i	0.232998	−	0.614366i
$7$	0.273931	+	0.242682i	0.103536	+	0.0917250i	0.713303	−	0.700856i	$-0.247198\pi$
$7$	0.273931	+	0.242682i	0.103536	+	0.0917250i	−0.609767	+	0.792581i	$0.708737\pi$
$8$	1.69816	+	1.50443i	0.600388	+	0.531898i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	1.86306	−	1.65053i	0.589152	−	0.521943i
$11$	4.72254	−	1.16400i	1.42390	−	0.350960i	0.549227	−	0.835673i	$-0.314922\pi$
$11$	4.72254	−	1.16400i	1.42390	−	0.350960i	0.874673	+	0.484714i	$0.161076\pi$
$12$	−0.335385	+	0.485890i	−0.0968174	+	0.140264i
$13$	−3.52332	−	0.765668i	−0.977192	−	0.212358i
$13$	−3.52332	−	0.765668i	−0.977192	−	0.212358i
$14$	−0.334599	−	0.484750i	−0.0894253	−	0.129555i
$15$	−1.15756	−	1.02551i	−0.298881	−	0.264785i
$16$	−2.74502	−	3.97685i	−0.686255	−	0.994211i
$17$	5.97008	+	5.28903i	1.44796	+	1.28278i	0.892359	+	0.451327i	$0.149049\pi$
$17$	5.97008	+	5.28903i	1.44796	+	1.28278i	0.555598	+	0.831451i	$0.312489\pi$
$18$	1.42512	+	0.747959i	0.335903	+	0.176296i
$19$	−4.56274			−1.04676			−0.523382	−	0.852098i	$-0.675330\pi$
$19$	−4.56274			−1.04676			−0.523382	+	0.852098i	$0.675330\pi$
$20$	−0.808461	+	0.424313i	−0.180777	+	0.0948793i
$21$	−0.273931	+	0.242682i	−0.0597766	+	0.0529575i
$22$	−7.82827			−1.66899
$23$	−3.46519			−0.722542			−0.361271	−	0.932461i	$-0.617657\pi$
$23$	−3.46519			−0.722542			−0.361271	+	0.932461i	$0.617657\pi$
$24$	−1.69816	+	1.50443i	−0.346634	+	0.307091i
$25$	0.924946	+	2.43888i	0.184989	+	0.487776i
$26$	5.21098	+	2.55359i	1.02196	+	0.500801i
$27$	0.354605	−	0.935016i	0.0682437	−	0.179944i
$28$	0.0766186	+	0.202027i	0.0144795	+	0.0381794i
$29$	−4.09901	−	1.01032i	−0.761168	−	0.187611i	−0.160419	−	0.987049i	$-0.551285\pi$
$29$	−4.09901	−	1.01032i	−0.761168	−	0.187611i	−0.600749	+	0.799438i	$0.705131\pi$
$30$	1.41393	+	2.04843i	0.258147	+	0.373990i
$31$	−1.09769	+	2.89437i	−0.197151	+	0.519844i	−0.996738	−	0.0807062i	$-0.974282\pi$
$31$	−1.09769	+	2.89437i	−0.197151	+	0.519844i	0.799587	+	0.600550i	$0.205052\pi$
$32$	1.14889	+	3.02937i	0.203097	+	0.535522i
$33$	0.586276	+	4.82841i	0.102057	+	0.840519i
$34$	−7.29228	−	10.5647i	−1.25062	−	1.81183i
$35$	−0.549518	+	0.135444i	−0.0928855	+	0.0228942i
$36$	−0.441921	−	0.391508i	−0.0736535	−	0.0652513i
$37$	−2.95482	+	7.79121i	−0.485769	+	1.28087i	0.438365	+	0.898797i	$0.355558\pi$
$37$	−2.95482	+	7.79121i	−0.485769	+	1.28087i	−0.924133	+	0.382070i	$0.875211\pi$
$38$	7.13021	+	1.75744i	1.15667	+	0.285094i
$39$	1.18477	−	3.40534i	0.189716	−	0.545290i
$40$	−3.40658	+	0.839646i	−0.538627	+	0.132760i
$41$	−0.424060	+	3.49245i	−0.0662271	+	0.545429i	0.921401	+	0.388614i	$0.127046\pi$
$41$	−0.424060	+	3.49245i	−0.0662271	+	0.545429i	−0.987628	+	0.156815i	$0.949877\pi$
$42$	0.521547	−	0.273729i	0.0804764	−	0.0422373i
$43$	0.408248	+	1.07646i	0.0622572	+	0.164159i	0.962535	−	0.271157i	$-0.0874061\pi$
$43$	0.408248	+	1.07646i	0.0622572	+	0.164159i	−0.900278	+	0.435315i	$0.856637\pi$
$44$	2.78819	+	0.687227i	0.420335	+	0.103603i
$45$	1.15756	−	1.02551i	0.172559	−	0.152874i
$46$	5.41507	+	1.33469i	0.798408	+	0.196790i
$47$	−6.59542	+	3.46154i	−0.962041	+	0.504918i	−0.871190	−	0.490947i	$-0.836651\pi$
$47$	−6.59542	+	3.46154i	−0.962041	+	0.504918i	−0.0908509	+	0.995865i	$0.528959\pi$
$48$	4.27873	−	2.24565i	0.617581	−	0.324131i
$49$	−0.827613	−	6.81601i	−0.118230	−	0.973715i
$50$	−0.506028	−	4.16751i	−0.0715631	−	0.589375i
$51$	−5.97008	+	5.28903i	−0.835978	+	0.740612i
$52$	−1.63182	−	1.36697i	−0.226292	−	0.189565i
$53$	0.180951	+	0.160308i	0.0248555	+	0.0220201i	0.675459	−	0.737398i	$-0.263946\pi$
$53$	0.180951	+	0.160308i	0.0248555	+	0.0220201i	−0.650603	+	0.759418i	$0.725484\pi$
$54$	−0.914284	+	1.32457i	−0.124418	+	0.180251i
$55$	−2.66731	+	7.03311i	−0.359660	+	0.948344i
$56$	0.100079	+	0.824222i	0.0133736	+	0.110141i
$57$	0.549977	−	4.52947i	0.0728463	−	0.599943i
$58$	6.01640	+	3.15765i	0.789992	+	0.414620i
$59$	−6.33698	+	9.18070i	−0.825004	+	1.19523i	0.153326	+	0.988176i	$0.451002\pi$
$59$	−6.33698	+	9.18070i	−0.825004	+	1.19523i	−0.978330	+	0.207049i	$0.933614\pi$
$60$	−0.323770	−	0.853712i	−0.0417985	−	0.110214i
$61$	−2.28748	+	2.02653i	−0.292882	+	0.259471i	−0.796749	−	0.604310i	$-0.793449\pi$
$61$	−2.28748	+	2.02653i	−0.292882	+	0.259471i	0.503867	+	0.863781i	$0.331910\pi$
$62$	2.83019	−	4.10024i	0.359435	−	0.520731i
$63$	−0.207893	−	0.301186i	−0.0261921	−	0.0379458i
$64$	0.536377	+	4.41746i	0.0670471	+	0.552183i
$65$	4.06974	−	3.81159i	0.504789	−	0.472770i
$66$	0.943594	−	7.77120i	0.116148	−	0.956568i
$67$	11.3526	−	5.95833i	1.38695	−	0.727926i	0.404512	−	0.914533i	$-0.367441\pi$
$67$	11.3526	−	5.95833i	1.38695	−	0.727926i	0.982435	+	0.186607i	$0.0597491\pi$
$68$	1.66983	+	4.40299i	0.202497	+	0.533941i
$69$	0.417683	−	3.43993i	0.0502831	−	0.414119i
$70$	0.910903			0.108874
$71$	−0.725999	+	5.97914i	−0.0861603	+	0.709594i	0.884061	+	0.467372i	$0.154799\pi$
$71$	−0.725999	+	5.97914i	−0.0861603	+	0.709594i	−0.970221	+	0.242221i	$0.922124\pi$
$72$	−1.28878	−	1.86711i	−0.151884	−	0.220041i
$73$	−9.32671	+	2.29883i	−1.09161	+	0.269057i	−0.743729	−	0.668482i	$-0.766944\pi$
$73$	−9.32671	+	2.29883i	−1.09161	+	0.269057i	−0.347880	+	0.937539i	$0.613098\pi$
$74$	7.61846	−	11.0372i	0.885628	−	1.28305i
$75$	−2.53259	+	0.624227i	−0.292438	+	0.0720796i
$76$	−2.38528	−	1.25189i	−0.273610	−	0.143602i
$77$	1.57613	+	0.827218i	0.179617	+	0.0942702i
$78$	−3.16309	+	4.86519i	−0.358150	+	0.550874i
$79$	−4.79957	+	2.51901i	−0.539994	+	0.283411i	−0.712588	−	0.701582i	$-0.752477\pi$
$79$	−4.79957	+	2.51901i	−0.539994	+	0.283411i	0.172595	+	0.984993i	$0.444785\pi$
$80$	7.47297			0.835503
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	2.00787	−	5.29433i	0.221733	−	0.584661i
$83$	2.08260	+	17.1517i	0.228595	+	1.88265i	0.429543	+	0.903046i	$0.358675\pi$
$83$	2.08260	+	17.1517i	0.228595	+	1.88265i	−0.200949	+	0.979602i	$0.564402\pi$
$84$	−0.209789	+	0.0517083i	−0.0228898	+	0.00564184i
$85$	−11.9763	+	2.95188i	−1.29901	+	0.320176i
$86$	−0.223348	−	1.83943i	−0.0240842	−	0.198351i
$87$	1.49703	−	3.94735i	0.160499	−	0.423200i
$88$	9.77077	+	5.12810i	1.04157	+	0.546657i
$89$	9.59411			1.01697			0.508487	−	0.861070i	$-0.330205\pi$
$89$	9.59411			1.01697			0.508487	+	0.861070i	$0.330205\pi$
$90$	−2.20392	+	1.15671i	−0.232314	+	0.121928i
$91$	−0.779331	−	1.06478i	−0.0816961	−	0.111620i
$92$	−1.81151	−	0.950754i	−0.188863	−	0.0991229i
$93$	−2.74095	−	1.43856i	−0.284224	−	0.149172i
$94$	11.6400	−	2.86900i	1.20057	−	0.295914i
$95$	4.00838	−	5.80714i	0.411251	−	0.595800i
$96$	−3.14577	+	0.775362i	−0.321063	+	0.0791350i
$97$	0.986463	+	1.42914i	0.100160	+	0.145107i	0.869860	−	0.493299i	$-0.164209\pi$
$97$	0.986463	+	1.42914i	0.100160	+	0.145107i	−0.769699	+	0.638406i	$0.779594\pi$
$98$	−1.33202	+	10.9702i	−0.134554	+	1.10815i
$99$	−4.86388			−0.488838
$100$	−0.185625	+	1.52876i	−0.0185625	+	0.152876i
$101$	−3.22157	−	8.49458i	−0.320558	−	0.845243i	−0.994333	−	0.106306i	$-0.966098\pi$
$101$	−3.22157	−	8.49458i	−0.320558	−	0.845243i	0.673775	−	0.738936i	$-0.264672\pi$
$102$	11.3666	−	5.96568i	1.12547	−	0.590690i
$103$	1.66865	−	13.7426i	0.164417	−	1.35410i	−0.643791	−	0.765201i	$-0.722639\pi$
$103$	1.66865	−	13.7426i	0.164417	−	1.35410i	0.808208	−	0.588897i	$-0.200438\pi$
$104$	−4.83124	−	6.60082i	−0.473742	−	0.647264i
$105$	−0.0682194	−	0.561837i	−0.00665753	−	0.0548297i
$106$	−0.221026	−	0.320212i	−0.0214680	−	0.0311017i
$107$	7.62440	−	11.0458i	0.737078	−	1.06784i	−0.257744	−	0.966213i	$-0.582979\pi$
$107$	7.62440	−	11.0458i	0.737078	−	1.06784i	0.994822	−	0.101629i	$-0.0324055\pi$
$108$	0.441921	−	0.391508i	0.0425238	−	0.0376728i
$109$	−3.96459	−	10.4538i	−0.379739	−	1.00129i	−0.979560	−	0.201154i	$-0.935531\pi$
$109$	−3.96459	−	10.4538i	−0.379739	−	1.00129i	0.599821	−	0.800134i	$-0.295238\pi$
$110$	6.87717	−	9.96329i	0.655712	−	0.949963i
$111$	−7.37824	−	3.87240i	−0.700312	−	0.367552i
$112$	0.213162	−	1.75555i	0.0201419	−	0.165884i
$113$	−0.427279	−	3.51896i	−0.0401950	−	0.331036i	−0.998910	−	0.0466685i	$-0.985140\pi$
$113$	−0.427279	−	3.51896i	−0.0401950	−	0.331036i	0.958715	−	0.284367i	$-0.0917835\pi$
$114$	−2.60408	+	6.86638i	−0.243894	+	0.643096i
$115$	3.04418	−	4.41026i	0.283872	−	0.411259i
$116$	−1.86565	−	1.65282i	−0.173221	−	0.153461i
$117$	3.23770	+	1.58660i	0.299325	+	0.146682i
$118$	13.4390	−	11.9059i	1.23716	−	1.09603i
$119$	0.351839	+	2.89766i	0.0322530	+	0.265628i
$120$	−0.422906	−	3.48295i	−0.0386059	−	0.317948i
$121$	11.2075	−	5.88214i	1.01886	−	0.534740i
$122$	4.35522	−	2.28580i	0.394303	−	0.206946i
$123$	−3.41587	−	0.841936i	−0.307999	−	0.0759149i
$124$	−1.36798	+	1.21192i	−0.122848	+	0.108834i
$125$	−11.4243	−	2.81585i	−1.02182	−	0.251857i
$126$	0.208868	+	0.550739i	0.0186074	+	0.0490637i
$127$	12.0619	−	6.33059i	1.07032	−	0.561749i	0.164922	−	0.986307i	$-0.447263\pi$
$127$	12.0619	−	6.33059i	1.07032	−	0.561749i	0.905401	+	0.424558i	$0.139570\pi$
$128$	1.64434	−	13.5424i	0.145341	−	1.19699i
$129$	−1.11782	+	0.275518i	−0.0984186	+	0.0242580i
$130$	−7.82791	+	4.38884i	−0.686553	+	0.384927i
$131$	5.43512	+	1.33964i	0.474869	+	0.117045i	0.469484	−	0.882941i	$-0.344440\pi$
$131$	5.43512	+	1.33964i	0.474869	+	0.117045i	0.00538452	+	0.999986i	$0.498286\pi$
$132$	−1.01830	+	2.68502i	−0.0886312	+	0.233701i
$133$	−1.24987	−	1.10729i	−0.108378	−	0.0960144i
$134$	−20.0358	+	4.93838i	−1.73083	+	0.426611i
$135$	0.878504	+	1.27273i	0.0756095	+	0.109539i
$136$	2.18112	+	17.9632i	0.187030	+	1.54033i
$137$	4.34118	+	11.4468i	0.370892	+	0.977962i	0.982411	+	0.186732i	$0.0597897\pi$
$137$	4.34118	+	11.4468i	0.370892	+	0.977962i	−0.611519	+	0.791230i	$0.709441\pi$
$138$	−1.97768	+	5.21471i	−0.168351	+	0.443905i
$139$	−8.48803	−	12.2970i	−0.719945	−	1.04302i	−0.996627	−	0.0820590i	$-0.973850\pi$
$139$	−8.48803	−	12.2970i	−0.719945	−	1.04302i	0.276682	−	0.960961i	$-0.410765\pi$
$140$	−0.324435	−	0.0799661i	−0.0274198	−	0.00675837i
$141$	−2.64131	−	6.96457i	−0.222439	−	0.586523i
$142$	3.43752	−	9.06399i	0.288470	−	0.760633i
$143$	−17.5302	+	0.485245i	−1.46595	+	0.0405782i
$144$	1.71353	+	4.51821i	0.142794	+	0.376518i
$145$	4.88686	−	4.32938i	0.405832	−	0.359535i
$146$	15.4603			1.27951
$147$	6.86607			0.566304
$148$	−3.68239	+	3.26232i	−0.302691	+	0.268161i
$149$	−13.4512	+	7.05974i	−1.10197	+	0.578356i	−0.914774	−	0.403967i	$-0.867631\pi$
$149$	−13.4512	+	7.05974i	−1.10197	+	0.578356i	−0.187192	+	0.982323i	$0.559939\pi$
$150$	4.19812			0.342775
$151$	9.14549	+	4.79992i	0.744249	+	0.390612i	0.793815	−	0.608159i	$-0.208092\pi$
$151$	9.14549	+	4.79992i	0.744249	+	0.390612i	−0.0495662	+	0.998771i	$0.515784\pi$
$152$	−7.74824	−	6.86434i	−0.628465	−	0.556771i
$153$	−4.53085	−	6.56407i	−0.366298	−	0.530674i
$154$	−2.14441	−	1.89978i	−0.172801	−	0.153088i
$155$	−2.71943	−	3.93978i	−0.218430	−	0.316450i
$156$	1.55370	−	1.45515i	0.124395	−	0.116505i
$157$	−8.65480	+	12.5386i	−0.690729	+	1.00069i	0.308054	+	0.951369i	$0.400322\pi$
$157$	−8.65480	+	12.5386i	−0.690729	+	1.00069i	−0.998783	+	0.0493243i	$0.984293\pi$
$158$	8.47056	−	2.08780i	0.673881	−	0.166097i
$159$	−0.180951	+	0.160308i	−0.0143503	+	0.0127133i
$160$	−4.86488	−	1.19909i	−0.384602	−	0.0947960i
$161$	−0.949223	−	0.840938i	−0.0748093	−	0.0662752i
$162$	−1.20471	−	1.06728i	−0.0946507	−	0.0838532i
$163$	1.28787	−	3.39584i	0.100874	−	0.265982i	−0.875073	−	0.483991i	$-0.839187\pi$
$163$	1.28787	−	3.39584i	0.100874	−	0.265982i	0.975947	+	0.218008i	$0.0699560\pi$
$164$	−1.17992	+	1.70941i	−0.0921362	+	0.133482i
$165$	−6.66032	−	3.49561i	−0.518505	−	0.272133i
$166$	3.35188	−	27.6052i	0.260157	−	2.14258i
$167$	18.4509	+	4.54775i	1.42778	+	0.351915i	0.876095	−	0.482139i	$-0.160140\pi$
$167$	18.4509	+	4.54775i	1.42778	+	0.351915i	0.551682	+	0.834055i	$0.313986\pi$
$168$	−0.830276			−0.0640572
$169$	11.8275	+	5.39538i	0.909808	+	0.415029i
$170$	19.8523			1.52260
$171$	4.43015	+	1.09193i	0.338782	+	0.0835023i
$172$	−0.0819303	+	0.674757i	−0.00624713	+	0.0514497i
$173$	10.7969	+	5.66665i	0.820874	+	0.430828i	0.822219	−	0.569171i	$-0.192736\pi$
$173$	10.7969	+	5.66665i	0.820874	+	0.430828i	−0.00134532	+	0.999999i	$0.500428\pi$
$174$	−3.85982	+	5.59192i	−0.292612	+	0.423922i
$175$	−0.338501	+	0.892553i	−0.0255882	+	0.0674706i
$176$	−17.5925	−	15.5856i	−1.32609	−	1.17481i
$177$	−8.34992	−	7.39739i	−0.627619	−	0.556022i
$178$	−14.9927	−	3.69538i	−1.12375	−	0.276980i
$179$	6.98738	−	6.19028i	0.522261	−	0.462683i	−0.360330	−	0.932825i	$-0.617336\pi$
$179$	6.98738	−	6.19028i	0.522261	−	0.462683i	0.882591	+	0.470142i	$0.155797\pi$
$180$	0.886513	−	0.218506i	0.0660768	−	0.0162865i
$181$	0.0485975	−	0.0704056i	0.00361222	−	0.00523321i	−0.821174	−	0.570678i	$-0.806680\pi$
$181$	0.0485975	−	0.0704056i	0.00361222	−	0.00523321i	0.824786	+	0.565445i	$0.191296\pi$
$182$	0.807739	+	1.96412i	0.0598736	+	0.145590i
$183$	−1.73603	−	2.51508i	−0.128331	−	0.185920i
$184$	−5.88443	−	5.21315i	−0.433806	−	0.384319i
$185$	−7.32031	−	10.6053i	−0.538200	−	0.779717i
$186$	3.72920	+	3.30379i	0.273438	+	0.242245i
$187$	34.3504	+	18.0285i	2.51195	+	1.31837i
$188$	−4.39766			−0.320732
$189$	0.324048	−	0.170074i	0.0235711	−	0.0123710i
$190$	−8.50066	+	7.53093i	−0.616703	+	0.546351i
$191$	1.49158			0.107927			0.0539633	−	0.998543i	$-0.482815\pi$
$191$	1.49158			0.107927			0.0539633	+	0.998543i	$0.482815\pi$
$192$	−4.44991			−0.321144
$193$	−8.05021	+	7.13187i	−0.579467	+	0.513363i	−0.901163	−	0.433480i	$-0.857285\pi$
$193$	−8.05021	+	7.13187i	−0.579467	+	0.513363i	0.321696	+	0.946843i	$0.395747\pi$
$194$	−0.991085	−	2.61328i	−0.0711558	−	0.187622i
$195$	3.29325	+	4.49950i	0.235835	+	0.322216i
$196$	1.43747	−	3.79030i	0.102677	−	0.270736i
$197$	−2.23576	−	5.89521i	−0.159291	−	0.420016i	0.831481	−	0.555553i	$-0.187493\pi$
$197$	−2.23576	−	5.89521i	−0.159291	−	0.420016i	−0.990772	+	0.135537i	$0.956724\pi$
$198$	7.60080	+	1.87343i	0.540165	+	0.133139i
$199$	14.1819	+	20.5461i	1.00533	+	1.45647i	0.886038	+	0.463613i	$0.153447\pi$
$199$	14.1819	+	20.5461i	1.00533	+	1.45647i	0.119293	+	0.992859i	$0.461937\pi$
$200$	−2.09844	+	5.53312i	−0.148382	+	0.391251i
$201$	4.54648	+	11.9881i	0.320684	+	0.845573i
$202$	1.76249	+	14.5154i	0.124008	+	1.02130i
$203$	−0.877661	−	1.27151i	−0.0615998	−	0.0892427i
$204$	−4.57216	+	1.12694i	−0.320115	+	0.0789013i
$205$	−4.07241	−	3.60784i	−0.284430	−	0.251983i
$206$	−7.90087	+	20.8329i	−0.550480	+	1.45150i
$207$	3.36450	+	0.829275i	0.233849	+	0.0576386i
$208$	6.62662	+	16.1135i	0.459473	+	1.11727i
$209$	−21.5477	+	5.31104i	−1.49049	+	0.367372i
$210$	−0.109797	+	0.904261i	−0.00757673	+	0.0624000i
$211$	1.10103	−	0.577863i	0.0757977	−	0.0397817i	−0.426398	−	0.904535i	$-0.640218\pi$
$211$	1.10103	−	0.577863i	0.0757977	−	0.0397817i	0.502196	+	0.864754i	$0.332526\pi$
$212$	0.0506120	+	0.133453i	0.00347605	+	0.00916558i
$213$	−5.84804	−	1.44141i	−0.400701	−	0.0987639i
$214$	−16.1692	+	14.3247i	−1.10531	+	0.979215i
$215$	−1.72869	−	0.426084i	−0.117896	−	0.0290587i
$216$	2.00884	−	1.05432i	0.136685	−	0.0717376i
$217$	−1.00310	+	0.526468i	−0.0680949	+	0.0357390i
$218$	2.16898	+	17.8632i	0.146902	+	1.20985i
$219$	−1.15786	−	9.53580i	−0.0782406	−	0.644369i
$220$	−3.32409	+	2.94489i	−0.224110	+	0.198544i
$221$	−16.9848	−	23.2060i	−1.14252	−	1.56101i
$222$	10.0385	+	8.89330i	0.673738	+	0.596879i
$223$	−6.72051	+	9.73634i	−0.450039	+	0.651994i	−0.980684	−	0.195600i	$-0.937334\pi$
$223$	−6.72051	+	9.73634i	−0.450039	+	0.651994i	0.530645	+	0.847594i	$0.321950\pi$
$224$	−0.420456	+	1.10865i	−0.0280929	+	0.0740749i
$225$	−0.314406	−	2.58937i	−0.0209604	−	0.172624i
$226$	−0.687694	+	5.66367i	−0.0457447	+	0.376742i
$227$	22.2747	+	11.6906i	1.47842	+	0.775936i	0.995040	−	0.0994741i	$-0.0317161\pi$
$227$	22.2747	+	11.6906i	1.47842	+	0.775936i	0.483382	+	0.875410i	$0.339408\pi$
$228$	1.53028	−	2.21699i	0.101345	−	0.146824i
$229$	8.44754	+	22.2743i	0.558229	+	1.47193i	0.855839	+	0.517242i	$0.173041\pi$
$229$	8.44754	+	22.2743i	0.558229	+	1.47193i	−0.297610	+	0.954688i	$0.596189\pi$
$230$	−6.45586	+	5.71940i	−0.425687	+	0.377126i
$231$	−1.01117	+	1.46493i	−0.0665300	+	0.0963853i
$232$	−5.44081	−	7.88237i	−0.357206	−	0.517503i
$233$	3.06997	+	25.2835i	0.201121	+	1.65638i	0.647895	+	0.761730i	$0.275650\pi$
$233$	3.06997	+	25.2835i	0.201121	+	1.65638i	−0.446774	+	0.894647i	$0.647427\pi$
$234$	−4.44845	−	3.72646i	−0.290804	−	0.243606i
$235$	1.38848	−	11.4352i	0.0905746	−	0.745949i
$236$	−5.83173	+	3.06073i	−0.379614	+	0.199237i
$237$	−1.92212	−	5.06821i	−0.124855	−	0.329216i
$238$	0.566275	−	4.66370i	0.0367062	−	0.302303i
$239$	−16.9115			−1.09391			−0.546956	−	0.837161i	$-0.684214\pi$
$239$	−16.9115			−1.09391			−0.546956	+	0.837161i	$0.684214\pi$
$240$	−0.900767	+	7.41848i	−0.0581442	+	0.478861i
$241$	−13.1997	−	19.1231i	−0.850268	−	1.23183i	−0.970985	−	0.239139i	$-0.923135\pi$
$241$	−13.1997	−	19.1231i	−0.850268	−	1.23183i	0.120717	−	0.992687i	$-0.461481\pi$
$242$	−19.7796	+	4.87523i	−1.27148	+	0.313392i
$243$	−0.568065	+	0.822984i	−0.0364414	+	0.0527944i
$244$	−1.75186	+	0.431795i	−0.112151	+	0.0276428i
$245$	9.40201	+	4.93456i	0.600672	+	0.315257i
$246$	5.01370	+	2.63139i	0.319662	+	0.167772i
$247$	16.0760	+	3.49354i	1.02289	+	0.222289i
$248$	−6.21843	+	3.26369i	−0.394871	+	0.207244i
$249$	−17.2777			−1.09493
$250$	16.7683	+	8.80067i	1.06052	+	0.556603i
$251$	1.54540	−	4.07489i	0.0975449	−	0.257205i	−0.877358	−	0.479837i	$-0.840696\pi$
$251$	1.54540	−	4.07489i	0.0975449	−	0.257205i	0.974902	+	0.222632i	$0.0714649\pi$
$252$	−0.0260441	−	0.214492i	−0.00164062	−	0.0135117i
$253$	−16.3645	+	4.03349i	−1.02883	+	0.253583i
$254$	−21.2876	+	5.24692i	−1.33570	+	0.329221i
$255$	−1.48678	−	12.2447i	−0.0931058	−	0.766795i
$256$	−4.62984	+	12.2079i	−0.289365	+	0.762992i
$257$	−16.5939	−	8.70913i	−1.03510	−	0.543260i	−0.140474	−	0.990084i	$-0.544863\pi$
$257$	−16.5939	−	8.70913i	−1.03510	−	0.543260i	−0.894622	+	0.446824i	$0.852555\pi$
$258$	1.85294			0.115359
$259$	−2.70020	+	1.41717i	−0.167782	+	0.0880589i
$260$	3.17335	−	0.875976i	0.196803	−	0.0543257i
$261$	3.73812	+	1.96192i	0.231384	+	0.121440i
$262$	−7.97749	−	4.18691i	−0.492851	−	0.258668i
$263$	18.4490	−	4.54728i	1.13762	−	0.280397i	0.374858	−	0.927082i	$-0.377691\pi$
$263$	18.4490	−	4.54728i	1.13762	−	0.280397i	0.762757	+	0.646685i	$0.223845\pi$
$264$	−6.26844	+	9.08141i	−0.385796	+	0.558922i
$265$	−0.362996	+	0.0894704i	−0.0222986	+	0.00549612i
$266$	1.52669	+	2.21179i	0.0936071	+	0.135613i
$267$	−1.15644	+	9.52415i	−0.0707731	+	0.582869i
$268$	7.56966			0.462391
$269$	2.79477	−	23.0170i	0.170400	−	1.40337i	−0.617017	−	0.786950i	$-0.711659\pi$
$269$	2.79477	−	23.0170i	0.170400	−	1.40337i	0.787417	−	0.616421i	$-0.211418\pi$
$270$	−0.882620	−	2.32728i	−0.0537145	−	0.141634i
$271$	10.6856	−	5.60824i	0.649105	−	0.340676i	−0.107828	−	0.994170i	$-0.534389\pi$
$271$	10.6856	−	5.60824i	0.649105	−	0.340676i	0.756932	+	0.653493i	$0.226697\pi$
$272$	4.64567	−	38.2606i	0.281685	−	2.31989i
$273$	1.15096	−	0.645304i	0.0696592	−	0.0390556i
$274$	−2.37501	−	19.5600i	−0.143480	−	1.18166i
$275$	7.20696	+	10.4411i	0.434596	+	0.629621i
$276$	1.16217	−	1.68370i	0.0699547	−	0.101347i
$277$	−6.88527	+	6.09981i	−0.413695	+	0.366502i	−0.844147	−	0.536111i	$-0.819893\pi$
$277$	−6.88527	+	6.09981i	−0.413695	+	0.366502i	0.430452	+	0.902614i	$0.358354\pi$
$278$	8.52780	+	22.4860i	0.511463	+	1.34862i
$279$	1.75846	−	2.54757i	0.105276	−	0.152519i
$280$	−1.13693	−	0.596709i	−0.0679448	−	0.0356602i
$281$	−2.89546	+	23.8463i	−0.172729	+	1.42255i	0.606138	+	0.795360i	$0.292718\pi$
$281$	−2.89546	+	23.8463i	−0.172729	+	1.42255i	−0.778867	+	0.627190i	$0.784205\pi$
$282$	1.44503	+	11.9009i	0.0860505	+	0.708690i
$283$	0.964593	−	2.54342i	0.0573391	−	0.151191i	−0.903286	−	0.429039i	$-0.858852\pi$
$283$	0.964593	−	2.54342i	0.0573391	−	0.151191i	0.960625	+	0.277849i	$0.0896214\pi$
$284$	−2.02005	+	2.92654i	−0.119868	+	0.173658i
$285$	5.28165	+	4.67913i	0.312858	+	0.277168i
$286$	27.5815	+	5.99386i	1.63093	+	0.354424i
$287$	−0.963716	+	0.853778i	−0.0568864	+	0.0503969i
$288$	−0.390528	−	3.21629i	−0.0230121	−	0.189522i
$289$	5.61890	+	46.2758i	0.330523	+	2.72210i
$290$	−9.30427	+	4.88326i	−0.546365	+	0.286755i
$291$	−1.53762	+	0.807007i	−0.0901370	+	0.0473076i
$292$	−5.50649	−	1.35723i	−0.322243	−	0.0794257i
$293$	16.5120	−	14.6283i	0.964641	−	0.854597i	−0.0247771	−	0.999693i	$-0.507888\pi$
$293$	16.5120	−	14.6283i	0.964641	−	0.854597i	0.989418	+	0.145096i	$0.0463491\pi$
$294$	−10.7296	−	2.64462i	−0.625765	−	0.154237i
$295$	−6.11751	−	16.1306i	−0.356175	−	0.939157i
$296$	−16.7391	+	8.78536i	−0.972940	+	0.510638i
$297$	0.586276	−	4.82841i	0.0340192	−	0.280173i
$298$	23.7395	−	5.85125i	1.37519	−	0.338954i
$299$	12.2090	+	2.65319i	0.706063	+	0.153438i
$300$	−1.49524	−	0.368544i	−0.0863278	−	0.0212779i
$301$	−0.149406	+	0.393950i	−0.00861159	+	0.0227069i
$302$	−12.4429	−	11.0234i	−0.716008	−	0.634328i
$303$	8.82096	−	2.17417i	0.506751	−	0.124903i
$304$	12.5248	+	18.1453i	0.718347	+	1.04070i
$305$	−0.569672	−	4.69167i	−0.0326193	−	0.268644i
$306$	4.55208	+	12.0029i	0.260225	+	0.686158i
$307$	0.478319	−	1.26122i	0.0272991	−	0.0719818i	−0.920674	−	0.390333i	$-0.872360\pi$
$307$	0.478319	−	1.26122i	0.0272991	−	0.0719818i	0.947973	+	0.318351i	$0.103129\pi$
$308$	0.596994	+	0.864895i	0.0340169	+	0.0492819i
$309$	13.4413	+	3.31297i	0.764647	+	0.188468i
$310$	2.73217	+	7.20415i	0.155177	+	0.409168i
$311$	−6.37580	+	16.8116i	−0.361538	+	0.953298i	0.623632	+	0.781718i	$0.285656\pi$
$311$	−6.37580	+	16.8116i	−0.361538	+	0.953298i	−0.985170	+	0.171580i	$0.945113\pi$
$312$	7.13503	−	4.00037i	0.403942	−	0.226476i
$313$	−2.14083	−	5.64491i	−0.121007	−	0.319069i	0.860802	−	0.508940i	$-0.169962\pi$
$313$	−2.14083	−	5.64491i	−0.121007	−	0.319069i	−0.981809	+	0.189871i	$0.939193\pi$
$314$	18.3544	−	16.2606i	1.03580	−	0.917639i
$315$	0.565964			0.0318884
$316$	−3.20023			−0.180027
$317$	20.0338	−	17.7484i	1.12521	−	0.996847i	0.125219	−	0.992129i	$-0.460037\pi$
$317$	20.0338	−	17.7484i	1.12521	−	0.996847i	0.999989	−	0.00471842i	$-0.00150192\pi$
$318$	0.344519	−	0.180817i	0.0193197	−	0.0101397i
$319$	−20.5338			−1.14967
$320$	−6.09346	−	3.19809i	−0.340635	−	0.178779i
$321$	10.0463	+	8.90024i	0.560729	+	0.496763i
$322$	1.15945	+	1.67975i	0.0646135	+	0.0936089i
$323$	−27.2399	−	24.1324i	−1.51567	−	1.34277i
$324$	0.335385	+	0.485890i	0.0186325	+	0.0269939i
$325$	−1.39150	−	9.30115i	−0.0771866	−	0.515935i
$326$	−3.32054	+	4.81063i	−0.183908	+	0.266436i
$327$	10.8554	−	2.67562i	0.600306	−	0.147962i
$328$	−5.97428	+	5.29275i	−0.329874	+	0.292243i
$329$	−2.64674	−	0.652363i	−0.145920	−	0.0359659i
$330$	9.06170	+	8.02797i	0.498830	+	0.441925i
$331$	−4.83584	−	4.28418i	−0.265802	−	0.235480i	0.519686	−	0.854358i	$-0.326049\pi$
$331$	−4.83584	−	4.28418i	−0.265802	−	0.235480i	−0.785487	+	0.618878i	$0.787588\pi$
$332$	−3.61724	+	9.53788i	−0.198522	+	0.523459i
$333$	4.73351	−	6.85768i	0.259395	−	0.375798i
$334$	−27.0817	−	14.2136i	−1.48184	−	0.777732i
$335$	−2.38998	+	19.6833i	−0.130579	+	1.07541i
$336$	1.71705	+	0.423215i	0.0936729	+	0.0230883i
$337$	15.5067			0.844702			0.422351	−	0.906432i	$-0.361205\pi$
$337$	15.5067			0.844702			0.422351	+	0.906432i	$0.361205\pi$
$338$	−16.4047	−	12.9870i	−0.892300	−	0.706400i
$339$	3.54481			0.192527
$340$	−7.07078	−	1.74279i	−0.383467	−	0.0945161i
$341$	−1.81483	+	14.9465i	−0.0982787	+	0.809398i
$342$	−6.50243	−	3.41274i	−0.351611	−	0.184540i
$343$	2.88266	−	4.17626i	0.155649	−	0.225497i
$344$	−0.926196	+	2.44218i	−0.0499371	+	0.131673i
$345$	4.01117	+	3.55359i	0.215954	+	0.191319i
$346$	−14.6897	−	13.0140i	−0.789725	−	0.699635i
$347$	−10.7819	−	2.65749i	−0.578801	−	0.142662i	−0.0609625	−	0.998140i	$-0.519417\pi$
$347$	−10.7819	−	2.65749i	−0.578801	−	0.142662i	−0.517838	+	0.855478i	$0.673263\pi$
$348$	1.86565	−	1.65282i	0.100009	−	0.0886006i
$349$	−18.7202	+	4.61411i	−1.00207	+	0.246988i	−0.706025	−	0.708187i	$-0.749514\pi$
$349$	−18.7202	+	4.61411i	−1.00207	+	0.246988i	−0.296044	+	0.955174i	$0.595667\pi$
$350$	0.872762	−	1.26441i	0.0466511	−	0.0675858i
$351$	−1.96530	+	3.02285i	−0.104900	+	0.161348i
$352$	8.95187	+	12.9690i	0.477136	+	0.691251i
$353$	−6.74620	−	5.97661i	−0.359064	−	0.318103i	0.464234	−	0.885713i	$-0.346330\pi$
$353$	−6.74620	−	5.97661i	−0.359064	−	0.318103i	−0.823298	+	0.567610i	$0.807868\pi$
$354$	10.1992	+	14.7761i	0.542081	+	0.785340i
$355$	−6.97205	−	6.17670i	−0.370038	−	0.327825i
$356$	5.01554	+	2.63236i	0.265823	+	0.139515i
$357$	−2.91894			−0.154487
$358$	−13.3035	+	6.98223i	−0.703113	+	0.369022i
$359$	18.7031	−	16.5695i	0.987111	−	0.874504i	−0.00498433	−	0.999988i	$-0.501587\pi$
$359$	18.7031	−	16.5695i	0.987111	−	0.874504i	0.992096	+	0.125483i	$0.0400481\pi$
$360$	3.50853			0.184916
$361$	1.81858			0.0957146
$362$	−0.103062	+	0.0913048i	−0.00541681	+	0.00479887i
$363$	4.48834	+	11.8348i	0.235577	+	0.621165i
$364$	−0.115266	−	0.770468i	−0.00604158	−	0.0403835i
$365$	5.26775	−	13.8899i	0.275727	−	0.727032i
$366$	1.74417	+	4.59899i	0.0911691	+	0.240393i
$367$	−6.08280	−	1.49928i	−0.317520	−	0.0782616i	0.0773350	−	0.997005i	$-0.475359\pi$
$367$	−6.08280	−	1.49928i	−0.317520	−	0.0782616i	−0.394855	+	0.918744i	$0.629205\pi$
$368$	9.51201	+	13.7805i	0.495848	+	0.718360i
$369$	1.24754	−	3.28948i	0.0649441	−	0.171244i
$370$	7.35461	+	19.3925i	0.382348	+	1.00817i
$371$	0.0106641	+	0.0878269i	0.000553653	+	0.00455974i
$372$	−1.03819	−	1.50408i	−0.0538279	−	0.0779832i
$373$	10.2712	−	2.53161i	0.531821	−	0.131082i	0.0357443	−	0.999361i	$-0.488620\pi$
$373$	10.2712	−	2.53161i	0.531821	−	0.131082i	0.496076	+	0.868279i	$0.334774\pi$
$374$	−46.7354	−	41.4040i	−2.41663	−	2.14095i
$375$	4.17237	−	11.0016i	0.215460	−	0.568122i
$376$	−16.4077	−	4.04414i	−0.846163	−	0.208560i
$377$	13.6686	+	6.69815i	0.703966	+	0.344972i
$378$	−0.571899	+	0.140961i	−0.0294153	+	0.00725023i
$379$	2.39650	−	19.7369i	0.123100	−	1.01382i	−0.791981	−	0.610546i	$-0.790950\pi$
$379$	2.39650	−	19.7369i	0.123100	−	1.01382i	0.915080	−	0.403272i	$-0.132127\pi$
$380$	3.68880	−	1.93603i	0.189231	−	0.0993162i
$381$	4.83053	+	12.7370i	0.247475	+	0.652539i
$382$	−2.33089	−	0.574513i	−0.119259	−	0.0293946i
$383$	0.616147	−	0.545859i	0.0314837	−	0.0278921i	−0.647234	−	0.762291i	$-0.724074\pi$
$383$	0.616147	−	0.545859i	0.0314837	−	0.0278921i	0.678718	+	0.734399i	$0.262536\pi$
$384$	13.2454	+	3.26470i	0.675927	+	0.166601i
$385$	−2.43746	+	1.27928i	−0.124225	+	0.0651981i
$386$	15.3271	−	8.04428i	0.780128	−	0.409443i
$387$	−0.138771	−	1.14288i	−0.00705412	−	0.0580959i
$388$	0.123580	+	1.01777i	0.00627383	+	0.0516696i
$389$	13.5979	−	12.0467i	0.689443	−	0.610793i	−0.243891	−	0.969803i	$-0.578424\pi$
$389$	13.5979	−	12.0467i	0.689443	−	0.610793i	0.933334	+	0.359010i	$0.116885\pi$
$390$	−3.41329	−	8.29985i	−0.172839	−	0.420279i
$391$	−20.6875	−	18.3275i	−1.04621	−	0.926861i
$392$	8.84882	−	12.8197i	0.446933	−	0.647494i
$393$	−1.98500	+	5.23402i	−0.100130	+	0.264021i
$394$	1.22316	+	10.0736i	0.0616218	+	0.507501i
$395$	1.01042	−	8.32152i	0.0508395	−	0.418701i
$396$	−2.54270	−	1.33451i	−0.127776	−	0.0670619i
$397$	9.51403	−	13.7835i	0.477496	−	0.691772i	−0.508022	−	0.861344i	$-0.669623\pi$
$397$	9.51403	−	13.7835i	0.477496	−	0.691772i	0.985518	+	0.169572i	$0.0542386\pi$
$398$	−14.2484	−	37.5699i	−0.714207	−	1.88321i
$399$	1.24987	−	1.10729i	0.0625720	−	0.0554340i
$400$	7.16006	−	10.3731i	0.358003	−	0.518657i
$401$	−12.9657	−	18.7840i	−0.647476	−	0.938031i	−0.999998	−	0.00222696i	$-0.999291\pi$
$401$	−12.9657	−	18.7840i	−0.647476	−	0.938031i	0.352522	−	0.935804i	$-0.385324\pi$
$402$	−2.48733	−	20.4850i	−0.124057	−	1.02170i
$403$	6.08363	−	9.35731i	0.303047	−	0.466121i
$404$	0.646530	−	5.32465i	0.0321661	−	0.264911i
$405$	−1.36934	+	0.718687i	−0.0680433	+	0.0357119i
$406$	0.881774	+	2.32505i	0.0437617	+	0.115390i
$407$	−4.88526	+	40.2337i	−0.242153	+	1.99431i
$408$	−18.0951			−0.895842
$409$	−0.865870	+	7.13108i	−0.0428145	+	0.352609i	0.955520	+	0.294925i	$0.0952947\pi$
$409$	−0.865870	+	7.13108i	−0.0428145	+	0.352609i	−0.998335	+	0.0576842i	$0.981628\pi$
$410$	4.97434	+	7.20657i	0.245665	+	0.355907i
$411$	−11.8866	+	2.92978i	−0.586321	+	0.144515i
$412$	4.64292	−	6.72643i	0.228740	−	0.331387i
$413$	−3.96388	+	0.977009i	−0.195050	+	0.0480755i
$414$	−4.93830	−	2.59182i	−0.242704	−	0.127381i
$415$	−23.6591	−	12.4173i	−1.16138	−	0.609540i
$416$	−1.72840	−	11.5531i	−0.0847420	−	0.566437i
$417$	13.2305	−	6.94390i	0.647900	−	0.340044i
$418$	35.7184			1.74704
$419$	−11.7312	−	6.15698i	−0.573104	−	0.300788i	0.153163	−	0.988201i	$-0.451054\pi$
$419$	−11.7312	−	6.15698i	−0.573104	−	0.300788i	−0.726267	+	0.687413i	$0.758746\pi$
$420$	0.118489	−	0.312431i	0.00578169	−	0.0152451i
$421$	−3.34221	−	27.5255i	−0.162889	−	1.34151i	−0.813262	−	0.581898i	$-0.802310\pi$
$421$	−3.34221	−	27.5255i	−0.162889	−	1.34151i	0.650373	−	0.759615i	$-0.274613\pi$
$422$	−1.94315	+	0.478944i	−0.0945912	+	0.0233146i
$423$	7.23217	−	1.78257i	0.351640	−	0.0866715i
$424$	0.0661091	+	0.544457i	0.00321054	+	0.0264412i
$425$	−7.37732	+	19.4524i	−0.357852	+	0.943579i
$426$	8.58356	+	4.50500i	0.415875	+	0.218268i
$427$	−1.11841			−0.0541239
$428$	7.01651	−	3.68255i	0.339156	−	0.178003i
$429$	1.63133	−	17.4609i	0.0787614	−	0.843021i
$430$	2.53732	+	1.33169i	0.122360	+	0.0642197i
$431$	31.3418	+	16.4494i	1.50968	+	0.792341i	0.997773	−	0.0667006i	$-0.0212472\pi$
$431$	31.3418	+	16.4494i	1.50968	+	0.792341i	0.511906	+	0.859041i	$0.328940\pi$
$432$	−4.69181	+	1.15643i	−0.225735	+	0.0556387i
$433$	16.7958	−	24.3329i	0.807154	−	1.16936i	−0.175603	−	0.984461i	$-0.556187\pi$
$433$	16.7958	−	24.3329i	0.807154	−	1.16936i	0.982757	−	0.184903i	$-0.0591972\pi$
$434$	1.77033	−	0.436347i	0.0849786	−	0.0209453i
$435$	3.70877	+	5.37308i	0.177822	+	0.257619i
$436$	0.795644	−	6.55272i	0.0381044	−	0.313818i
$437$	15.8108			0.756331
$438$	−1.86354	+	15.3476i	−0.0890432	+	0.733337i
$439$	8.50138	+	22.4163i	0.405749	+	1.06987i	0.969751	+	0.244098i	$0.0784918\pi$
$439$	8.50138	+	22.4163i	0.405749	+	1.06987i	−0.564002	+	0.825773i	$0.690739\pi$
$440$	−15.1104	+	7.93052i	−0.720358	+	0.378073i
$441$	−0.827613	+	6.81601i	−0.0394101	+	0.324572i
$442$	17.6039	+	42.8062i	0.837334	+	2.03608i
$443$	3.41195	+	28.0999i	0.162107	+	1.33507i	0.815811	+	0.578318i	$0.196291\pi$
$443$	3.41195	+	28.0999i	0.162107	+	1.33507i	−0.653705	+	0.756750i	$0.726786\pi$
$444$	−2.79467	−	4.04877i	−0.132629	−	0.192146i
$445$	−8.42846	+	12.2107i	−0.399547	+	0.578844i
$446$	14.2523	−	12.6265i	0.674868	−	0.597881i
$447$	−5.38690	−	14.2041i	−0.254792	−	0.671831i
$448$	−0.925107	+	1.34025i	−0.0437072	+	0.0633208i
$449$	−17.8245	−	9.35504i	−0.841192	−	0.441492i	−0.0116477	−	0.999932i	$-0.503708\pi$
$449$	−17.8245	−	9.35504i	−0.841192	−	0.441492i	−0.829545	+	0.558440i	$0.811400\pi$
$450$	−0.506028	+	4.16751i	−0.0238544	+	0.196458i
$451$	2.06258	+	16.9868i	0.0971229	+	0.799879i
$452$	0.742136	−	1.95685i	0.0349071	−	0.0920426i
$453$	−5.86729	+	8.50024i	−0.275669	+	0.399376i
$454$	−30.3058	−	26.8486i	−1.42232	−	1.26007i
$455$	2.03983	−	0.0564634i	0.0956287	−	0.00264705i
$456$	7.74824	−	6.86434i	0.362844	−	0.321452i
$457$	−1.55404	−	12.7987i	−0.0726951	−	0.598698i	−0.982847	−	0.184423i	$-0.940958\pi$
$457$	−1.55404	−	12.7987i	−0.0726951	−	0.598698i	0.910152	−	0.414275i	$-0.135965\pi$
$458$	−4.62156	−	38.0619i	−0.215951	−	1.77852i
$459$	7.06235	−	3.70661i	0.329642	−	0.173010i
$460$	2.80147	−	1.47033i	0.130619	−	0.0685543i
$461$	−17.0832	−	4.21064i	−0.795646	−	0.196109i	−0.179518	−	0.983755i	$-0.557454\pi$
$461$	−17.0832	−	4.21064i	−0.795646	−	0.196109i	−0.616129	+	0.787646i	$0.711300\pi$
$462$	2.14441	−	1.89978i	0.0997668	−	0.0883857i
$463$	14.4058	+	3.55071i	0.669493	+	0.165015i	0.559390	−	0.828905i	$-0.311036\pi$
$463$	14.4058	+	3.55071i	0.669493	+	0.165015i	0.110104	+	0.993920i	$0.464882\pi$
$464$	7.23400	+	19.0745i	0.335830	+	0.885511i
$465$	4.23884	−	2.22472i	0.196572	−	0.103169i
$466$	4.94103	−	40.6931i	0.228889	−	1.88507i
$467$	30.4453	−	7.50410i	1.40884	−	0.347248i	0.539720	−	0.841845i	$-0.318530\pi$
$467$	30.4453	−	7.50410i	1.40884	−	0.347248i	0.869123	+	0.494596i	$0.164684\pi$
$468$	1.25726	+	1.71777i	0.0581169	+	0.0794039i
$469$	4.55582	+	1.12291i	0.210368	+	0.0518511i
$470$	−6.57429	+	17.3350i	−0.303250	+	0.799603i
$471$	−11.4040	−	10.1031i	−0.525469	−	0.465525i
$472$	−24.5729	+	6.05668i	−1.13106	+	0.278781i
$473$	3.18097	+	4.60843i	0.146261	+	0.211896i
$474$	1.05157	+	8.66045i	0.0483002	+	0.397788i
$475$	−4.22029	−	11.1280i	−0.193640	−	0.510587i
$476$	−0.611105	+	1.61135i	−0.0280100	+	0.0738562i
$477$	−0.137328	−	0.198954i	−0.00628783	−	0.00910950i
$478$	26.4276	+	6.51382i	1.20877	+	0.297935i
$479$	4.44547	+	11.7217i	0.203119	+	0.535580i	0.997407	−	0.0719604i	$-0.0229255\pi$
$479$	4.44547	+	11.7217i	0.203119	+	0.535580i	−0.794289	+	0.607540i	$0.792156\pi$
$480$	1.77674	−	4.68488i	0.0810967	−	0.213834i
$481$	16.3762	−	25.1885i	0.746692	−	1.14850i
$482$	13.2616	+	34.9679i	0.604048	+	1.59274i
$483$	0.949223	−	0.840938i	0.0431911	−	0.0382640i
$484$	7.47287			0.339676
$485$	−2.68552			−0.121943
$486$	1.20471	−	1.06728i	0.0546466	−	0.0484127i
$487$	1.47519	−	0.774238i	0.0668471	−	0.0350841i	−0.430968	−	0.902367i	$-0.641828\pi$
$487$	1.47519	−	0.774238i	0.0668471	−	0.0350841i	0.497816	+	0.867283i	$0.334136\pi$
$488$	−6.93329			−0.313855
$489$	3.21584	+	1.68780i	0.145425	+	0.0763251i
$490$	−12.7919	−	11.3326i	−0.577879	−	0.511956i
$491$	−2.84172	−	4.11694i	−0.128245	−	0.185795i	0.753602	−	0.657332i	$-0.228315\pi$
$491$	−2.84172	−	4.11694i	−0.128245	−	0.185795i	−0.881846	+	0.471537i	$0.843699\pi$
$492$	−1.55472	−	1.37736i	−0.0700923	−	0.0620963i
$493$	−19.1278	−	27.7115i	−0.861475	−	1.24806i
$494$	−23.7764	−	11.6514i	−1.06975	−	0.524221i
$495$	4.27293	−	6.19041i	0.192054	−	0.278238i
$496$	14.5236	−	3.57975i	0.652130	−	0.160736i
$497$	−1.64990	+	1.46168i	−0.0740082	+	0.0655655i
$498$	26.9999	+	6.65489i	1.20990	+	0.298213i
$499$	−13.6550	−	12.0973i	−0.611282	−	0.541549i	0.299679	−	0.954040i	$-0.403120\pi$
$499$	−13.6550	−	12.0973i	−0.611282	−	0.541549i	−0.910962	+	0.412491i	$0.864659\pi$
$500$	−5.19975	−	4.60658i	−0.232540	−	0.206012i
$501$	−6.73860	+	17.7682i	−0.301059	+	0.793826i
$502$	−3.98454	+	5.77260i	−0.177839	+	0.257644i
$503$	25.3730	+	13.3168i	1.13132	+	0.593765i	0.923193	−	0.384336i	$-0.125569\pi$
$503$	25.3730	+	13.3168i	1.13132	+	0.593765i	0.208132	+	0.978101i	$0.433262\pi$
$504$	0.100079	−	0.824222i	0.00445786	−	0.0367138i
$505$	13.6415	+	3.36232i	0.607038	+	0.149621i
$506$	27.1265			1.20592
$507$	−6.78169	+	11.0909i	−0.301186	+	0.492565i
$508$	8.04259			0.356832
$509$	4.82014	+	1.18806i	0.213649	+	0.0526597i	0.344687	−	0.938718i	$-0.387985\pi$
$509$	4.82014	+	1.18806i	0.213649	+	0.0526597i	−0.131038	+	0.991377i	$0.541831\pi$
$510$	−2.39293	+	19.7076i	−0.105961	+	0.872666i
$511$	−3.11276	−	1.63370i	−0.137700	−	0.0722707i
$512$	−3.56169	+	5.16000i	−0.157406	+	0.228042i
$513$	−1.61797	+	4.26623i	−0.0714351	+	0.188359i
$514$	22.5768	+	20.0013i	0.995818	+	0.882218i
$515$	16.0247	+	14.1967i	0.706134	+	0.625580i
$516$	−0.659961	−	0.162666i	−0.0290532	−	0.00716096i
$517$	−27.1179	+	24.0244i	−1.19264	+	1.05659i
$518$	4.76547	−	1.17458i	0.209383	−	0.0516082i
$519$	−6.92676	+	10.0351i	−0.304051	+	0.440494i
$520$	12.6453	−	0.350029i	0.554535	−	0.0153498i
$521$	−0.0103085	−	0.0149345i	−0.000451624	−	0.000654290i	0.822758	−	0.568392i	$-0.192434\pi$
$521$	−0.0103085	−	0.0149345i	−0.000451624	−	0.000654290i	−0.823210	+	0.567738i	$0.807819\pi$
$522$	−5.08590	−	4.50571i	−0.222604	−	0.197210i
$523$	6.86509	+	9.94580i	0.300189	+	0.434899i	0.943831	−	0.330427i	$-0.107193\pi$
$523$	6.86509	+	9.94580i	0.300189	+	0.434899i	−0.643642	+	0.765327i	$0.722577\pi$
$524$	2.47378	+	2.19157i	0.108067	+	0.0957394i
$525$	−0.845243	−	0.443618i	−0.0368894	−	0.0193611i
$526$	−30.5818			−1.33343
$527$	−21.8617	+	11.4739i	−0.952310	+	0.499811i
$528$	17.5925	−	15.5856i	0.765616	−	0.678277i
$529$	−10.9924			−0.477932
$530$	0.601716			0.0261369
$531$	8.34992	−	7.39739i	0.362356	−	0.321019i
$532$	−0.349590	−	0.921794i	−0.0151567	−	0.0399649i
$533$	4.16816	−	11.9803i	0.180543	−	0.518925i
$534$	5.47561	−	14.4380i	0.236953	−	0.624793i
$535$	7.36034	+	19.4076i	0.318215	+	0.839065i
$536$	28.2425	+	6.96114i	1.21989	+	0.300676i
$537$	5.30291	+	7.68259i	0.228837	+	0.331528i
$538$	−13.2329	+	34.8923i	−0.570511	+	1.50431i
$539$	−11.8423	−	31.2255i	−0.510083	−	1.34498i
$540$	0.110055	+	0.906388i	0.00473603	+	0.0390047i
$541$	10.5824	+	15.3313i	0.454975	+	0.659145i	0.981599	−	0.190953i	$-0.0611579\pi$
$541$	10.5824	+	15.3313i	0.454975	+	0.659145i	−0.526624	+	0.850098i	$0.676542\pi$
$542$	−18.8586	+	4.64822i	−0.810045	+	0.199658i
$543$	0.0640345	+	0.0567296i	0.00274798	+	0.00243450i
$544$	−9.16347	+	24.1621i	−0.392881	+	1.03594i
$545$	16.7877	+	4.13780i	0.719107	+	0.177244i
$546$	−2.04716	+	0.565101i	−0.0876104	+	0.0241841i
$547$	17.9148	−	4.41560i	0.765982	−	0.188798i	0.163080	−	0.986613i	$-0.447857\pi$
$547$	17.9148	−	4.41560i	0.765982	−	0.188798i	0.602902	+	0.797815i	$0.294011\pi$
$548$	−0.871222	+	7.17516i	−0.0372168	+	0.306508i
$549$	2.70599	−	1.42022i	0.115489	−	0.0606133i
$550$	−7.24073	−	19.0922i	−0.308746	−	0.814096i
$551$	18.7027	+	4.60981i	0.796763	+	0.196384i
$552$	5.88443	−	5.21315i	0.250458	−	0.221887i
$553$	−1.92607	−	0.474733i	−0.0819047	−	0.0201877i
$554$	13.1091	−	6.88019i	0.556953	−	0.292311i
$555$	11.4103	−	5.98861i	0.484342	−	0.254202i
$556$	−1.06335	−	8.75744i	−0.0450959	−	0.371398i
$557$	−2.04443	−	16.8374i	−0.0866254	−	0.713425i	−0.969718	−	0.244226i	$-0.921466\pi$
$557$	−2.04443	−	16.8374i	−0.0866254	−	0.713425i	0.883093	−	0.469198i	$-0.155457\pi$
$558$	−3.72920	+	3.30379i	−0.157870	+	0.139860i
$559$	−0.614173	−	4.10529i	−0.0259768	−	0.173635i
$560$	2.04708	+	1.81355i	0.0865048	+	0.0766365i
$561$	−22.0375	+	31.9268i	−0.930424	+	1.34795i
$562$	13.7097	−	36.1494i	0.578307	−	1.52487i
$563$	0.792745	+	6.52884i	0.0334102	+	0.275158i	0.999834	+	0.0182054i	$0.00579528\pi$
$563$	0.792745	+	6.52884i	0.0334102	+	0.275158i	−0.966424	+	0.256952i	$0.917282\pi$
$564$	0.530079	−	4.36560i	0.0223204	−	0.183825i
$565$	4.85406	+	2.54761i	0.204212	+	0.107179i
$566$	−2.48703	+	3.60308i	−0.104538	+	0.151449i
$567$	0.129774	+	0.342186i	0.00545000	+	0.0143705i
$568$	−10.2281	+	9.06129i	−0.429161	+	0.380203i
$569$	8.44525	−	12.2351i	0.354043	−	0.512920i	−0.604983	−	0.796239i	$-0.706820\pi$
$569$	8.44525	−	12.2351i	0.354043	−	0.512920i	0.959026	+	0.283318i	$0.0914353\pi$
$570$	−6.45138	−	9.34643i	−0.270218	−	0.391479i
$571$	−4.07298	−	33.5440i	−0.170449	−	1.40377i	−0.787240	−	0.616647i	$-0.788490\pi$
$571$	−4.07298	−	33.5440i	−0.170449	−	1.40377i	0.616790	−	0.787127i	$-0.288433\pi$
$572$	−9.29748	−	4.55614i	−0.388747	−	0.190502i
$573$	−0.179790	+	1.48070i	−0.00751082	+	0.0618571i
$574$	1.83485	−	0.963006i	0.0765853	−	0.0401951i
$575$	−3.20512	−	8.45119i	−0.133663	−	0.352439i
$576$	0.536377	−	4.41746i	0.0223490	−	0.184061i
$577$	−33.7145			−1.40355			−0.701777	−	0.712397i	$-0.747610\pi$
$577$	−33.7145			−1.40355			−0.701777	+	0.712397i	$0.747610\pi$
$578$	9.04346	−	74.4796i	0.376158	−	3.09794i
$579$	−6.10952	−	8.85117i	−0.253903	−	0.367842i
$580$	3.74258	−	0.922464i	0.155402	−	0.0383032i
$581$	−3.59192	+	5.20380i	−0.149018	+	0.215890i
$582$	2.71368	−	0.668863i	0.112486	−	0.0277253i
$583$	1.04115	+	0.546436i	0.0431199	+	0.0226311i
$584$	−19.2966	−	10.1277i	−0.798500	−	0.419085i
$585$	−4.86365	+	2.72688i	−0.201087	+	0.112743i
$586$	−31.4378	+	16.4998i	−1.29868	+	0.681601i
$587$	−15.6238			−0.644862			−0.322431	−	0.946593i	$-0.604500\pi$
$587$	−15.6238			−0.644862			−0.322431	+	0.946593i	$0.604500\pi$
$588$	3.58940	+	1.88386i	0.148024	+	0.0776891i
$589$	5.00847	−	13.2062i	0.206370	−	0.544154i
$590$	3.34682	+	27.5636i	0.137787	+	1.13477i
$591$	6.12172	−	1.50887i	0.251814	−	0.0620665i
$592$	39.0955	−	9.63617i	1.60681	−	0.396044i
$593$	3.38762	+	27.8995i	0.139113	+	1.14570i	0.880307	+	0.474405i	$0.157337\pi$
$593$	3.38762	+	27.8995i	0.139113	+	1.14570i	−0.741194	+	0.671291i	$0.765740\pi$
$594$	−2.77594	+	7.31956i	−0.113898	+	0.300325i
$595$	−3.99703	−	2.09780i	−0.163862	−	0.0860016i
$596$	−8.96893			−0.367382
$597$	−22.1057	+	11.6020i	−0.904727	+	0.474837i
$598$	−18.0571	−	8.84870i	−0.738408	−	0.361850i
$599$	6.76078	+	3.54833i	0.276238	+	0.144981i	0.597154	−	0.802127i	$-0.296298\pi$
$599$	6.76078	+	3.54833i	0.276238	+	0.144981i	−0.320916	+	0.947108i	$0.603991\pi$
$600$	−5.23984	−	2.75008i	−0.213916	−	0.112272i
$601$	19.9925	−	4.92772i	0.815512	−	0.201006i	0.190567	−	0.981674i	$-0.438967\pi$
$601$	19.9925	−	4.92772i	0.815512	−	0.201006i	0.624945	+	0.780668i	$0.285121\pi$
$602$	0.385215	−	0.558080i	0.0157002	−	0.0227457i
$603$	−12.4487	+	3.06832i	−0.506950	+	0.124952i
$604$	3.46405	+	5.01854i	0.140950	+	0.204202i
$605$	−2.35942	+	19.4316i	−0.0959242	+	0.790007i
$606$	−14.6220			−0.593977
$607$	−0.974213	+	8.02337i	−0.0395421	+	0.325658i	0.959493	+	0.281733i	$0.0909094\pi$
$607$	−0.974213	+	8.02337i	−0.0395421	+	0.325658i	−0.999035	+	0.0439250i	$0.986014\pi$
$608$	−5.24208	−	13.8222i	−0.212594	−	0.560565i
$609$	1.36803	−	0.717998i	0.0554354	−	0.0290948i
$610$	−0.916871	+	7.55111i	−0.0371230	+	0.305736i
$611$	25.8881	−	7.14620i	1.04732	−	0.289104i
$612$	−0.567607	−	4.67466i	−0.0229441	−	0.188962i
$613$	23.1895	+	33.5957i	0.936613	+	1.35692i	0.934134	+	0.356922i	$0.116174\pi$
$613$	23.1895	+	33.5957i	0.936613	+	1.35692i	0.00247925	+	0.999997i	$0.499211\pi$
$614$	−1.23326	+	1.78668i	−0.0497702	+	0.0721046i
$615$	4.07241	−	3.60784i	0.164216	−	0.145482i
$616$	1.43202	+	3.77593i	0.0576978	+	0.152137i
$617$	−13.4361	+	19.4655i	−0.540916	+	0.783652i	−0.994181	−	0.107724i	$-0.965644\pi$
$617$	−13.4361	+	19.4655i	−0.540916	+	0.783652i	0.453265	+	0.891376i	$0.350259\pi$
$618$	−19.7286	−	10.3544i	−0.793603	−	0.416515i
$619$	−0.768528	+	6.32939i	−0.0308897	+	0.254400i	0.969081	+	0.246743i	$0.0793603\pi$
$619$	−0.768528	+	6.32939i	−0.0308897	+	0.254400i	−0.999971	+	0.00765682i	$0.997563\pi$
$620$	−0.340679	−	2.80575i	−0.0136820	−	0.112682i
$621$	−1.22877	+	3.24001i	−0.0493090	+	0.130017i
$622$	16.4388	−	23.8158i	0.659137	−	0.954925i
$623$	2.62812	+	2.32831i	0.105293	+	0.0932819i
$624$	−16.7947	+	4.63604i	−0.672327	+	0.185590i
$625$	3.85813	−	3.41800i	0.154325	−	0.136720i
$626$	1.17123	+	9.64591i	0.0468116	+	0.385528i
$627$	−2.67502	−	22.0308i	−0.106830	−	0.879825i
$628$	−7.96476	+	4.18023i	−0.317829	+	0.166809i
$629$	−58.8484	+	30.8860i	−2.34644	+	1.23151i
$630$	−0.884434	−	0.217993i	−0.0352367	−	0.00868506i
$631$	25.7256	−	22.7909i	1.02412	−	0.907292i	0.0283904	−	0.999597i	$-0.490962\pi$
$631$	25.7256	−	22.7909i	1.02412	−	0.907292i	0.995731	+	0.0923047i	$0.0294234\pi$
$632$	−11.9401	−	2.94297i	−0.474952	−	0.117065i
$633$	0.440936	+	1.16265i	0.0175256	+	0.0462113i
$634$	−38.1430	+	20.0190i	−1.51485	+	0.795056i
$635$	−2.53930	+	20.9130i	−0.100769	+	0.829909i
$636$	−0.138580	+	0.0341570i	−0.00549507	+	0.00135441i
$637$	−2.30286	+	24.6486i	−0.0912426	+	0.976614i
$638$	32.0882	+	7.90903i	1.27038	+	0.313122i
$639$	2.13581	−	5.63166i	0.0844911	−	0.222785i
$640$	15.7912	+	13.9898i	0.624204	+	0.552996i
$641$	15.3389	−	3.78069i	0.605848	−	0.149328i	0.0755538	−	0.997142i	$-0.475928\pi$
$641$	15.3389	−	3.78069i	0.605848	−	0.149328i	0.530294	+	0.847814i	$0.322081\pi$
$642$	−12.2713	−	17.7780i	−0.484308	−	0.701641i
$643$	4.10982	+	33.8474i	0.162076	+	1.33481i	0.815912	+	0.578176i	$0.196235\pi$
$643$	4.10982	+	33.8474i	0.162076	+	1.33481i	−0.653836	+	0.756636i	$0.726841\pi$
$644$	−0.265498	−	0.700061i	−0.0104621	−	0.0275863i
$645$	0.631349	−	1.66473i	0.0248593	−	0.0655487i
$646$	33.2728	+	48.2039i	1.30910	+	1.89656i
$647$	−27.3066	−	6.73047i	−1.07353	−	0.264602i	−0.337347	−	0.941380i	$-0.609529\pi$
$647$	−27.3066	−	6.73047i	−1.07353	−	0.264602i	−0.736187	+	0.676778i	$0.763376\pi$
$648$	0.804496	+	2.12128i	0.0316036	+	0.0833318i
$649$	−19.2403	+	50.7325i	−0.755248	+	1.99142i
$650$	−1.40804	+	15.0709i	−0.0552278	+	0.591130i
$651$	−0.401719	−	1.05925i	−0.0157446	−	0.0415151i
$652$	1.60499	−	1.42190i	0.0628562	−	0.0556857i
$653$	−20.8926			−0.817590			−0.408795	−	0.912626i	$-0.634051\pi$
$653$	−20.8926			−0.817590			−0.408795	+	0.912626i	$0.634051\pi$
$654$	−17.9944			−0.703635
$655$	−6.47977	+	5.74058i	−0.253186	+	0.224303i
$656$	15.0530	−	7.90042i	0.587720	−	0.308459i
$657$	9.60583			0.374759
$658$	3.88480	+	2.03890i	0.151445	+	0.0794846i
$659$	−18.4805	−	16.3723i	−0.719900	−	0.637776i	0.221464	−	0.975169i	$-0.428916\pi$
$659$	−18.4805	−	16.3723i	−0.719900	−	0.637776i	−0.941364	+	0.337393i	$0.890455\pi$
$660$	−2.52274	−	3.65482i	−0.0981975	−	0.142264i
$661$	−22.2041	−	19.6711i	−0.863640	−	0.765118i	0.109826	−	0.993951i	$-0.464971\pi$
$661$	−22.2041	−	19.6711i	−0.863640	−	0.765118i	−0.973466	+	0.228833i	$0.926509\pi$
$662$	5.90683	+	8.55753i	0.229576	+	0.332598i
$663$	25.0841	−	14.0638i	0.974186	−	0.546193i
$664$	−22.2671	+	32.2594i	−0.864131	+	1.25191i
$665$	2.50731	−	0.617995i	0.0972292	−	0.0239648i
$666$	−10.0385	+	8.89330i	−0.388983	+	0.344608i
$667$	14.2039	+	3.50094i	0.549976	+	0.135557i
$668$	8.39788	+	7.43987i	0.324924	+	0.287857i
$669$	−8.85529	−	7.84510i	−0.342365	−	0.303309i
$670$	11.3163	−	29.8386i	0.437186	−	1.15277i
$671$	−8.44385	+	12.2330i	−0.325971	+	0.472251i
$672$	−1.04989	−	0.551024i	−0.0405003	−	0.0212562i
$673$	1.27652	−	10.5131i	0.0492061	−	0.405249i	−0.947207	−	0.320623i	$-0.896108\pi$
$673$	1.27652	−	10.5131i	0.0492061	−	0.405249i	0.996413	−	0.0846252i	$-0.0269693\pi$
$674$	−24.2323	−	5.97273i	−0.933395	−	0.230061i
$675$	2.60838			0.100397
$676$	4.70276	+	6.06570i	0.180875	+	0.233296i
$677$	3.23015			0.124145			0.0620723	−	0.998072i	$-0.480229\pi$
$677$	3.23015			0.124145			0.0620723	+	0.998072i	$0.480229\pi$
$678$	−5.53948	−	1.36536i	−0.212742	−	0.0524363i
$679$	−0.0766029	+	0.630881i	−0.00293975	+	0.0242110i
$680$	−24.7784	−	13.0047i	−0.950210	−	0.498709i
$681$	−14.2903	+	20.7031i	−0.547606	+	0.793345i
$682$	8.59301	−	22.6579i	0.329043	−	0.867616i
$683$	−4.88630	−	4.32889i	−0.186969	−	0.165640i	0.564446	−	0.825470i	$-0.309090\pi$
$683$	−4.88630	−	4.32889i	−0.186969	−	0.165640i	−0.751415	+	0.659830i	$0.770628\pi$
$684$	2.01637	+	1.78635i	0.0770978	+	0.0683027i
$685$	−18.3824	−	4.53085i	−0.702355	−	0.173115i
$686$	−6.11333	+	5.41594i	−0.233408	+	0.206781i
$687$	−23.1302	+	5.70108i	−0.882471	+	0.217510i
$688$	3.16027	−	4.57844i	0.120484	−	0.174551i
$689$	−0.514804	−	0.703365i	−0.0196125	−	0.0267961i
$690$	−4.89953	−	7.09819i	−0.186522	−	0.270224i
$691$	−8.80660	−	7.80197i	−0.335019	−	0.296801i	0.478795	−	0.877927i	$-0.341074\pi$
$691$	−8.80660	−	7.80197i	−0.335019	−	0.296801i	−0.813814	+	0.581126i	$0.802612\pi$
$692$	4.08956	+	5.92475i	0.155462	+	0.225225i
$693$	−1.33237	−	1.18037i	−0.0506124	−	0.0448387i
$694$	15.8253	+	8.30574i	0.600719	+	0.315282i
$695$	23.1076			0.876521
$696$	8.48072	−	4.45102i	0.321461	−	0.168716i
$697$	−21.0033	+	18.6073i	−0.795558	+	0.704803i
$698$	31.0313			1.17455
$699$	−25.4692			−0.963333
$700$	−0.421851	+	0.373727i	−0.0159445	+	0.0141256i
$701$	−3.85402	−	10.1622i	−0.145564	−	0.383822i	0.842327	−	0.538966i	$-0.181185\pi$
$701$	−3.85402	−	10.1622i	−0.145564	−	0.383822i	−0.987892	+	0.155145i	$0.950416\pi$
$702$	4.23549	−	3.96684i	0.159858	−	0.149719i
$703$	13.4821	−	35.5493i	0.508485	−	1.34077i
$704$	7.67500	+	20.2373i	0.289262	+	0.762722i
$705$	11.1844	+	2.75672i	0.421230	+	0.103824i
$706$	8.24028	+	11.9381i	0.310127	+	0.449297i
$707$	1.17899	−	3.10874i	0.0443405	−	0.116916i
$708$	−2.33548	−	6.15815i	−0.0877726	−	0.231437i
$709$	−4.96412	−	40.8832i	−0.186431	−	1.53540i	−0.722586	−	0.691281i	$-0.757047\pi$
$709$	−4.96412	−	40.8832i	−0.186431	−	1.53540i	0.536155	−	0.844119i	$-0.319876\pi$
$710$	8.51616	+	12.3378i	0.319606	+	0.463029i
$711$	5.26294	−	1.29720i	0.197376	−	0.0486487i
$712$	16.2923	+	14.4337i	0.610579	+	0.540926i
$713$	3.80370	−	10.0295i	0.142450	−	0.375609i
$714$	4.56144	+	1.12429i	0.170707	+	0.0420756i
$715$	14.7828	−	22.7376i	0.552845	−	0.850338i
$716$	5.35126	−	1.31897i	0.199986	−	0.0492921i
$717$	2.03845	−	16.7882i	0.0761274	−	0.626966i
$718$	−35.6095	+	18.6893i	−1.32893	+	0.697479i
$719$	3.32368	+	8.76382i	0.123952	+	0.326835i	0.982601	−	0.185729i	$-0.0594648\pi$
$719$	3.32368	+	8.76382i	0.123952	+	0.326835i	−0.858649	+	0.512565i	$0.828696\pi$
$720$	−7.25582	−	1.78840i	−0.270408	−	0.0666497i
$721$	3.79217	−	3.35957i	0.141228	−	0.125117i
$722$	−2.84190	−	0.700465i	−0.105765	−	0.0260686i
$723$	20.5747	−	10.7984i	0.765182	−	0.401598i
$724$	0.0447229	−	0.0234724i	0.00166211	−	0.000872344i
$725$	−1.32732	−	10.9315i	−0.0492956	−	0.405986i
$726$	−2.45552	−	20.2230i	−0.0911329	−	0.750547i
$727$	15.8952	−	14.0819i	0.589521	−	0.522270i	−0.314780	−	0.949165i	$-0.601931\pi$
$727$	15.8952	−	14.0819i	0.589521	−	0.522270i	0.904302	+	0.426894i	$0.140392\pi$
$728$	0.278472	−	2.98062i	0.0103209	−	0.110469i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	−13.5819	+	19.6768i	−0.502690	+	0.728273i
$731$	−3.25616	+	8.58579i	−0.120433	+	0.317557i
$732$	−0.217483	−	1.79113i	−0.00803841	−	0.0662022i
$733$	3.72666	−	30.6918i	0.137647	−	1.13363i	−0.746157	−	0.665770i	$-0.768103\pi$
$733$	3.72666	−	30.6918i	0.137647	−	1.13363i	0.883804	−	0.467857i	$-0.154974\pi$
$734$	8.92814	+	4.68585i	0.329544	+	0.172958i
$735$	−6.03186	+	8.73866i	−0.222489	+	0.322330i
$736$	−3.98112	−	10.4973i	−0.146746	−	0.386937i
$737$	46.6778	−	41.3530i	1.71940	−	1.52326i
$738$	−3.21654	+	4.65997i	−0.118403	+	0.171536i
$739$	9.63257	+	13.9552i	0.354340	+	0.513350i	0.959104	−	0.283055i	$-0.0913479\pi$
$739$	9.63257	+	13.9552i	0.354340	+	0.513350i	−0.604764	+	0.796405i	$0.706733\pi$
$740$	−0.917058	−	7.55266i	−0.0337117	−	0.277641i
$741$	−5.40582	+	15.5377i	−0.198588	+	0.570790i
$742$	0.0171636	−	0.141355i	0.000630095	−	0.00518930i
$743$	18.3552	−	9.63354i	0.673386	−	0.353420i	−0.0931222	−	0.995655i	$-0.529685\pi$
$743$	18.3552	−	9.63354i	0.673386	−	0.353420i	0.766508	+	0.642234i	$0.221992\pi$
$744$	−2.49034	−	6.56649i	−0.0913003	−	0.240739i
$745$	2.83178	−	23.3218i	0.103748	−	0.854444i
$746$	−17.0259			−0.623362
$747$	2.08260	−	17.1517i	0.0761983	−	0.627549i
$748$	13.0109	+	18.8496i	0.475727	+	0.689210i
$749$	4.76918	−	1.17550i	0.174262	−	0.0429518i
$750$	−10.7577	+	15.5852i	−0.392816	+	0.569092i
$751$	18.0652	−	4.45266i	0.659207	−	0.162480i	0.104499	−	0.994525i	$-0.466676\pi$
$751$	18.0652	−	4.45266i	0.659207	−	0.162480i	0.554708	+	0.832045i	$0.312830\pi$
$752$	31.8706	+	16.7270i	1.16220	+	0.609969i
$753$	3.85890	+	2.02531i	0.140626	+	0.0738063i
$754$	−18.7800	−	15.7320i	−0.683926	−	0.572924i
$755$	−14.1434	+	7.42301i	−0.514730	+	0.270151i
$756$	0.216067			0.00785830
$757$	−25.3852	−	13.3232i	−0.922641	−	0.484240i	−0.0646526	−	0.997908i	$-0.520594\pi$
$757$	−25.3852	−	13.3232i	−0.922641	−	0.484240i	−0.857989	+	0.513668i	$0.828286\pi$
$758$	−11.3471	+	29.9199i	−0.412146	+	1.08674i
$759$	−2.03156	−	16.7314i	−0.0737409	−	0.607311i
$760$	15.5433	−	3.83108i	0.563815	−	0.138968i
$761$	12.6322	−	3.11355i	0.457915	−	0.112866i	−0.00360918	−	0.999993i	$-0.501149\pi$
$761$	12.6322	−	3.11355i	0.457915	−	0.112866i	0.461524	+	0.887128i	$0.347303\pi$
$762$	−2.64273	−	21.7648i	−0.0957359	−	0.788456i
$763$	1.45091	−	3.82574i	0.0525265	−	0.138501i
$764$	0.779756	+	0.409247i	0.0282106	+	0.0148061i
$765$	12.3347			0.445961
$766$	−1.17311	+	0.615693i	−0.0423860	+	0.0222459i
$767$	29.3565	−	27.4945i	1.06000	−	0.992768i
$768$	−11.5608	−	6.06757i	−0.417164	−	0.218945i
$769$	−9.93505	−	5.21432i	−0.358267	−	0.188033i	0.275980	−	0.961163i	$-0.410998\pi$
$769$	−9.93505	−	5.21432i	−0.358267	−	0.188033i	−0.634247	+	0.773130i	$0.718690\pi$
$770$	4.30178	−	1.06029i	0.155025	−	0.0382103i
$771$	10.6458	−	15.4231i	0.383399	−	0.555449i
$772$	−6.16522	+	1.51959i	−0.221891	+	0.0546913i
$773$	6.69312	+	9.69665i	0.240735	+	0.348764i	0.924664	−	0.380784i	$-0.124346\pi$
$773$	6.69312	+	9.69665i	0.240735	+	0.348764i	−0.683929	+	0.729548i	$0.739730\pi$
$774$	−0.223348	+	1.83943i	−0.00802807	+	0.0661171i
$775$	−8.07433			−0.290038
$776$	−0.474877	+	3.91097i	−0.0170471	+	0.140395i
$777$	−1.08137	−	2.85133i	−0.0387939	−	0.102291i
$778$	−25.8896	+	13.5879i	−0.928187	+	0.487150i
$779$	1.93488	−	15.9351i	0.0693241	−	0.570935i
$780$	0.487084	+	3.25580i	0.0174404	+	0.116576i
$781$	3.53117	+	29.0818i	0.126355	+	1.04063i
$782$	25.2691	+	36.6087i	0.903623	+	1.30912i
$783$	−2.39819	+	3.47438i	−0.0857044	+	0.124164i
$784$	−24.8344	+	22.0014i	−0.886943	+	0.785763i
$785$	−8.35506	−	22.0305i	−0.298205	−	0.786302i
$786$	5.11796	−	7.41465i	0.182552	−	0.264472i
$787$	37.3071	+	19.5803i	1.32985	+	0.697961i	0.971815	−	0.235746i	$-0.0757532\pi$
$787$	37.3071	+	19.5803i	1.32985	+	0.697961i	0.358039	+	0.933707i	$0.383446\pi$
$788$	0.448689	−	3.69529i	0.0159839	−	0.131639i
$789$	2.29034	+	18.8626i	0.0815382	+	0.671527i
$790$	−4.78420	+	12.6149i	−0.170214	+	0.448818i
$791$	0.736942	−	1.06764i	0.0262026	−	0.0379611i
$792$	−8.25962	−	7.31738i	−0.293493	−	0.260012i
$793$	9.61118	−	5.38866i	0.341303	−	0.191357i
$794$	−20.1766	+	17.8749i	−0.716041	+	0.634357i
$795$	−0.0450637	−	0.371133i	−0.00159825	−	0.0131627i
$796$	1.77666	+	14.6321i	0.0629719	+	0.518620i
$797$	−42.5530	+	22.3335i	−1.50730	+	0.791094i	−0.997599	−	0.0692558i	$-0.977938\pi$
$797$	−42.5530	+	22.3335i	−1.50730	+	0.791094i	−0.509704	+	0.860350i	$0.670245\pi$
$798$	−2.37968	+	1.24895i	−0.0842398	+	0.0442125i
$799$	−57.6834	−	14.2177i	−2.04069	−	0.502985i
$800$	−6.32562	+	5.60401i	−0.223644	+	0.198132i
$801$	−9.31532	−	2.29602i	−0.329141	−	0.0811259i
$802$	13.0264	+	34.3479i	0.459980	+	1.21287i
$803$	−41.3699	+	21.7126i	−1.45991	+	0.766221i
$804$	−0.912422	+	7.51447i	−0.0321786	+	0.265015i
$805$	1.90418	−	0.469339i	0.0671137	−	0.0165420i
$806$	−13.1111	+	12.2795i	−0.461818	+	0.432525i
$807$	22.5123	+	5.54879i	0.792471	+	0.195326i
$808$	7.30881	−	19.2718i	0.257123	−	0.677978i
$809$	9.17186	+	8.12556i	0.322465	+	0.285679i	0.808789	−	0.588100i	$-0.200124\pi$
$809$	9.17186	+	8.12556i	0.322465	+	0.285679i	−0.486323	+	0.873779i	$0.661662\pi$
$810$	2.41670	−	0.595662i	0.0849141	−	0.0209294i
$811$	22.1073	+	32.0280i	0.776293	+	1.12465i	0.989055	+	0.147550i	$0.0471387\pi$
$811$	22.1073	+	32.0280i	0.776293	+	1.12465i	−0.212762	+	0.977104i	$0.568246\pi$
$812$	−0.109950	−	0.905519i	−0.00385848	−	0.0317775i
$813$	4.27934	+	11.2837i	0.150083	+	0.395737i
$814$	23.1311	−	60.9917i	0.810745	−	2.13776i
$815$	3.19059	+	4.62237i	0.111762	+	0.161915i
$816$	37.4216	+	9.22360i	1.31002	+	0.322891i
$817$	−1.86273	−	4.91161i	−0.0651686	−	0.171835i
$818$	4.09979	−	10.8103i	0.143346	−	0.377972i
$819$	0.501866	+	1.22035i	0.0175366	+	0.0426425i
$820$	−1.13906	−	3.00344i	−0.0397775	−	0.104885i
$821$	−7.92215	+	7.01841i	−0.276485	+	0.244944i	−0.789957	−	0.613162i	$-0.789897\pi$
$821$	−7.92215	+	7.01841i	−0.276485	+	0.244944i	0.513472	+	0.858106i	$0.328359\pi$
$822$	19.7036			0.687244
$823$	12.8815			0.449019			0.224510	−	0.974472i	$-0.427922\pi$
$823$	12.8815			0.449019			0.224510	+	0.974472i	$0.427922\pi$
$824$	23.5085	−	20.8267i	0.818956	−	0.725532i
$825$	−11.2337	+	5.89588i	−0.391106	+	0.205268i
$826$	6.57069			0.228623
$827$	30.0884	+	15.7916i	1.04628	+	0.549128i	0.898081	−	0.439830i	$-0.144961\pi$
$827$	30.0884	+	15.7916i	1.04628	+	0.549128i	0.148195	+	0.988958i	$0.452654\pi$
$828$	1.53134	+	1.35665i	0.0532178	+	0.0471468i
$829$	18.4955	+	26.7953i	0.642374	+	0.930640i	0.999995	−	0.00322719i	$-0.00102725\pi$
$829$	18.4955	+	26.7953i	0.642374	+	0.930640i	−0.357621	+	0.933867i	$0.616412\pi$
$830$	32.1894	+	28.5174i	1.11731	+	0.989852i
$831$	−5.22541	−	7.57031i	−0.181268	−	0.262611i
$832$	1.49249	−	15.9748i	0.0517426	−	0.553827i
$833$	31.1091	−	45.0694i	1.07787	−	1.56156i
$834$	−23.3499	+	5.75524i	−0.808542	+	0.199288i
$835$	−21.9973	+	19.4879i	−0.761247	+	0.674406i
$836$	−12.7218	−	3.13564i	−0.439992	−	0.108448i
$837$	2.31704	+	2.05271i	0.0800885	+	0.0709522i
$838$	15.9608	+	14.1401i	0.551357	+	0.488460i
$839$	−18.0261	+	47.5310i	−0.622331	+	1.64095i	0.137246	+	0.990537i	$0.456175\pi$
$839$	−18.0261	+	47.5310i	−0.622331	+	1.64095i	−0.759578	+	0.650416i	$0.774594\pi$
$840$	0.729400	−	1.05672i	0.0251667	−	0.0364602i
$841$	−9.89705	−	5.19437i	−0.341278	−	0.179116i
$842$	−5.37919	+	44.3016i	−0.185379	+	1.52673i
$843$	−23.3234	−	5.74870i	−0.803300	−	0.197996i
$844$	0.734136			0.0252700
$845$	−17.2574	+	10.3134i	−0.593672	+	0.354791i
$846$	−11.9883			−0.412167
$847$	4.49756	+	1.10855i	0.154538	+	0.0380902i
$848$	0.140809	−	1.15966i	0.00483539	−	0.0398230i
$849$	2.40861	+	1.26414i	0.0826633	+	0.0433850i
$850$	19.0211	−	27.5568i	0.652417	−	0.945190i
$851$	10.2390	−	26.9980i	0.350989	−	0.925481i
$852$	−2.66171	−	2.35807i	−0.0911888	−	0.0807862i
$853$	−9.38206	−	8.31178i	−0.321236	−	0.284590i	0.487058	−	0.873370i	$-0.338070\pi$
$853$	−9.38206	−	8.31178i	−0.321236	−	0.284590i	−0.808293	+	0.588780i	$0.799609\pi$
$854$	1.74775	+	0.430782i	0.0598068	+	0.0147411i
$855$	−5.28165	+	4.67913i	−0.180628	+	0.160023i
$856$	29.5652	−	7.28716i	1.01052	−	0.249070i
$857$	−4.73100	+	6.85404i	−0.161608	+	0.234130i	−0.895419	−	0.445224i	$-0.853124\pi$
$857$	−4.73100	+	6.85404i	−0.161608	+	0.234130i	0.733811	+	0.679353i	$0.237740\pi$
$858$	−9.27474	+	26.6579i	−0.316634	+	0.910086i
$859$	−32.1374	−	46.5591i	−1.09652	−	1.58858i	−0.763683	−	0.645591i	$-0.776611\pi$
$859$	−32.1374	−	46.5591i	−1.09652	−	1.58858i	−0.332832	−	0.942986i	$-0.608004\pi$
$860$	−0.786808	−	0.697051i	−0.0268299	−	0.0237693i
$861$	−0.731390	−	1.05960i	−0.0249257	−	0.0361111i
$862$	−42.6420	−	37.7775i	−1.45239	−	1.28671i
$863$	7.40019	+	3.88392i	0.251905	+	0.132210i	0.585950	−	0.810347i	$-0.300721\pi$
$863$	7.40019	+	3.88392i	0.251905	+	0.132210i	−0.334045	+	0.942557i	$0.608414\pi$
$864$	3.23991			0.110224
$865$	−16.6973	+	8.76339i	−0.567724	+	0.297964i
$866$	−35.6192	+	31.5558i	−1.21039	+	1.07231i
$867$	−46.6157			−1.58315
$868$	−0.668843			−0.0227020
$869$	−19.7340	+	17.4828i	−0.669431	+	0.593064i
$870$	−3.72615	−	9.82504i	−0.126328	−	0.333100i
$871$	−44.5611	+	12.3007i	−1.50989	+	0.416794i
$872$	8.99450	−	23.7166i	0.304592	−	0.803144i
$873$	−0.615783	−	1.62369i	−0.0208411	−	0.0549534i
$874$	−24.7075	−	6.08986i	−0.835745	−	0.205993i
$875$	−2.44613	−	3.54383i	−0.0826942	−	0.119803i
$876$	2.01107	−	5.30274i	0.0679476	−	0.179163i
$877$	−6.76427	−	17.8359i	−0.228413	−	0.602276i	0.770989	−	0.636849i	$-0.219762\pi$
$877$	−6.76427	−	17.8359i	−0.228413	−	0.602276i	−0.999402	+	0.0345722i	$0.988993\pi$
$878$	−4.65101	−	38.3045i	−0.156964	−	1.29271i
$879$	12.5314	+	18.1548i	0.422673	+	0.612348i
$880$	35.2914	−	8.69855i	1.18967	−	0.293228i
$881$	21.6110	+	19.1457i	0.728093	+	0.645034i	0.943455	−	0.331500i	$-0.107555\pi$
$881$	21.6110	+	19.1457i	0.728093	+	0.645034i	−0.215362	+	0.976534i	$0.569093\pi$
$882$	3.91865	−	10.3326i	0.131948	−	0.347918i
$883$	−29.1509	−	7.18504i	−0.981005	−	0.241796i	−0.283970	−	0.958833i	$-0.591652\pi$
$883$	−29.1509	−	7.18504i	−0.981005	−	0.241796i	−0.697035	+	0.717037i	$0.745498\pi$
$884$	−2.51212	−	16.7917i	−0.0844917	−	0.564764i
$885$	16.7503	−	4.12858i	0.563056	−	0.138781i
$886$	5.49144	−	45.2260i	0.184488	−	1.51940i
$887$	−36.2623	+	19.0319i	−1.21757	+	0.639030i	−0.946243	−	0.323457i	$-0.895155\pi$
$887$	−36.2623	+	19.0319i	−1.21757	+	0.639030i	−0.271328	+	0.962487i	$0.587463\pi$
$888$	−6.70363	−	17.6760i	−0.224959	−	0.593168i
$889$	4.84045	+	1.19306i	0.162344	+	0.0400141i
$890$	17.8744	−	15.8353i	0.599151	−	0.530802i
$891$	4.72254	+	1.16400i	0.158211	+	0.0389955i
$892$	−6.18469	+	3.24598i	−0.207079	+	0.108683i
$893$	30.0932	−	15.7941i	1.00703	−	0.528530i
$894$	2.94711	+	24.2717i	0.0985663	+	0.811766i
$895$	1.74013	+	14.3312i	0.0581661	+	0.479041i
$896$	3.73692	−	3.31062i	0.124842	−	0.110600i
$897$	−4.10547	+	11.8001i	−0.137078	+	0.393995i
$898$	24.2512	+	21.4847i	0.809273	+	0.716953i
$899$	7.42367	−	10.7550i	0.247593	−	0.358701i
$900$	0.546088	−	1.43992i	0.0182029	−	0.0479972i
$901$	0.232415	+	1.91411i	0.00774286	+	0.0637682i
$902$	3.31966	−	27.3398i	0.110533	−	0.910317i
$903$	−0.373069	−	0.195802i	−0.0124150	−	0.00651587i
$904$	4.56846	−	6.61855i	0.151945	−	0.220130i
$905$	0.0469144	+	0.123703i	0.00155949	+	0.00411203i
$906$	12.4429	−	11.0234i	0.413387	−	0.366229i
$907$	−1.77190	+	2.56704i	−0.0588350	+	0.0852372i	−0.851297	−	0.524684i	$-0.824184\pi$
$907$	−1.77190	+	2.56704i	−0.0588350	+	0.0852372i	0.792462	+	0.609921i	$0.208799\pi$
$908$	8.43701	+	12.2231i	0.279992	+	0.405638i
$909$	1.09507	+	9.01872i	0.0363212	+	0.299132i
$910$	−3.20940	−	0.697450i	−0.106391	−	0.0231202i
$911$	3.06547	−	25.2464i	0.101564	−	0.836452i	−0.849528	−	0.527543i	$-0.823113\pi$
$911$	3.06547	−	25.2464i	0.101564	−	0.836452i	0.951092	−	0.308908i	$-0.0999636\pi$
$912$	−19.5227	+	10.2463i	−0.646461	+	0.339289i
$913$	29.7998	+	78.5757i	0.986230	+	2.60047i
$914$	−2.50119	+	20.5991i	−0.0827320	+	0.681359i
$915$	4.72613			0.156241
$916$	−1.69532	+	13.9622i	−0.0560149	+	0.461324i
$917$	1.16374	+	1.68597i	0.0384302	+	0.0556757i
$918$	−12.4640	+	3.07211i	−0.411374	+	0.101395i
$919$	−8.30208	+	12.0276i	−0.273860	+	0.396755i	−0.935647	−	0.352937i	$-0.885183\pi$
$919$	−8.30208	+	12.0276i	−0.273860	+	0.396755i	0.661787	+	0.749692i	$0.269798\pi$
$920$	11.8044	−	2.90953i	0.389181	−	0.0959245i
$921$	1.19437	+	0.626855i	0.0393559	+	0.0206556i
$922$	25.0742	+	13.1600i	0.825776	+	0.433401i
$923$	7.13596	−	20.5105i	0.234883	−	0.675112i
$924$	−0.930548	+	0.488389i	−0.0306128	+	0.0160668i
$925$	−21.7349			−0.714639
$926$	−21.1443	−	11.0974i	−0.694846	−	0.364683i
$927$	−4.90898	+	12.9439i	−0.161232	+	0.425134i
$928$	−1.64869	−	13.5782i	−0.0541209	−	0.445725i
$929$	33.7022	−	8.30684i	1.10573	−	0.272538i	0.356136	−	0.934434i	$-0.384094\pi$
$929$	33.7022	−	8.30684i	1.10573	−	0.272538i	0.749596	+	0.661896i	$0.230248\pi$
$930$	−7.48095	+	1.84389i	−0.245310	+	0.0604635i
$931$	3.77618	+	31.0997i	0.123759	+	1.01925i
$932$	−5.33220	+	14.0598i	−0.174662	+	0.460546i
$933$	−15.9205	−	8.35573i	−0.521214	−	0.273554i
$934$	−50.4674			−1.65134
$935$	−53.1223	+	27.8808i	−1.73729	+	0.911798i
$936$	3.11117	+	7.56520i	0.101692	+	0.247276i
$937$	23.0170	+	12.0802i	0.751932	+	0.394644i	0.796717	−	0.604352i	$-0.206568\pi$
$937$	23.0170	+	12.0802i	0.751932	+	0.394644i	−0.0447855	+	0.998997i	$0.514260\pi$
$938$	−6.68688	−	3.50955i	−0.218334	−	0.114591i
$939$	5.86180	−	1.44480i	0.191293	−	0.0471494i
$940$	3.86336	−	5.59704i	0.126009	−	0.182555i
$941$	−1.73907	+	0.428643i	−0.0566921	+	0.0139734i	−0.267560	−	0.963541i	$-0.586217\pi$
$941$	−1.73907	+	0.428643i	−0.0566921	+	0.0139734i	0.210868	+	0.977515i	$0.432371\pi$
$942$	13.9297	+	20.1806i	0.453853	+	0.657520i
$943$	1.46945	−	12.1020i	0.0478519	−	0.394096i
$944$	53.9053			1.75447
$945$	−0.0682194	+	0.561837i	−0.00221918	+	0.0182766i
$946$	−3.19587	−	8.42683i	−0.103907	−	0.273980i
$947$	−13.8705	+	7.27980i	−0.450731	+	0.236562i	−0.674784	−	0.738015i	$-0.735763\pi$
$947$	−13.8705	+	7.27980i	−0.450731	+	0.236562i	0.224053	+	0.974577i	$0.428071\pi$
$948$	0.385746	−	3.17690i	0.0125284	−	0.103181i
$949$	34.6211	−	0.958327i	1.12385	−	0.0311086i
$950$	2.30887	+	19.0153i	0.0749097	+	0.616937i
$951$	15.2042	+	22.0270i	0.493029	+	0.714275i
$952$	−3.76186	+	5.44999i	−0.121922	+	0.176635i
$953$	−29.1211	+	25.7990i	−0.943324	+	0.835712i	−0.986568	−	0.163353i	$-0.947769\pi$
$953$	−29.1211	+	25.7990i	−0.943324	+	0.835712i	0.0432440	+	0.999065i	$0.486231\pi$
$954$	0.137972	+	0.363802i	0.00446700	+	0.0117785i
$955$	−1.31035	+	1.89838i	−0.0424021	+	0.0614300i
$956$	−8.84087	−	4.64004i	−0.285934	−	0.150070i
$957$	2.47507	−	20.3841i	0.0800077	−	0.658923i
$958$	−2.43207	−	20.0299i	−0.0785765	−	0.647136i
$959$	−1.58873	+	4.18914i	−0.0513029	+	0.135275i
$960$	3.90926	−	5.66354i	0.126171	−	0.182790i
$961$	16.0314	+	14.2026i	0.517142	+	0.458147i
$962$	−35.2931	+	33.0545i	−1.13790	+	1.06572i
$963$	−10.0463	+	8.90024i	−0.323737	+	0.286806i
$964$	−1.65361	−	13.6187i	−0.0532591	−	0.438628i
$965$	−2.00481	−	16.5111i	−0.0645373	−	0.531512i
$966$	−1.80726	+	0.948523i	−0.0581476	+	0.0305182i
$967$	−9.54274	+	5.00842i	−0.306874	+	0.161060i	−0.611130	−	0.791531i	$-0.709285\pi$
$967$	−9.54274	+	5.00842i	−0.306874	+	0.161060i	0.304256	+	0.952590i	$0.401592\pi$
$968$	27.8813	+	6.87213i	0.896140	+	0.220879i
$969$	27.2399	−	24.1324i	0.875072	−	0.775246i
$970$	4.19667	+	1.03439i	0.134747	+	0.0332122i
$971$	−16.2486	−	42.8440i	−0.521442	−	1.37493i	−0.894478	−	0.447113i	$-0.852452\pi$
$971$	−16.2486	−	42.8440i	−0.521442	−	1.37493i	0.373035	−	0.927817i	$-0.378317\pi$
$972$	−0.522773	+	0.274373i	−0.0167680	+	0.00880050i
$973$	0.659130	−	5.42842i	0.0211307	−	0.174027i
$974$	−2.60350	+	0.641704i	−0.0834214	+	0.0205615i
$975$	9.40106	−	0.260226i	0.301075	−	0.00833390i
$976$	14.3384	+	3.53410i	0.458961	+	0.113124i
$977$	−9.77210	+	25.7669i	−0.312637	+	0.824357i	0.682946	+	0.730469i	$0.260699\pi$
$977$	−9.77210	+	25.7669i	−0.312637	+	0.824357i	−0.995583	+	0.0938875i	$0.970071\pi$
$978$	−4.37531	−	3.87619i	−0.139907	−	0.123947i
$979$	45.3086	−	11.1676i	1.44807	−	0.356917i
$980$	3.56121	+	5.15931i	0.113759	+	0.164808i
$981$	1.34764	+	11.0988i	0.0430267	+	0.354357i
$982$	2.85503	+	7.52810i	0.0911078	+	0.240231i
$983$	−9.23899	+	24.3612i	−0.294678	+	0.777002i	0.703145	+	0.711047i	$0.251779\pi$
$983$	−9.23899	+	24.3612i	−0.294678	+	0.777002i	−0.997823	+	0.0659552i	$0.978991\pi$
$984$	−4.53404	−	6.56869i	−0.144540	−	0.209402i
$985$	9.46714	+	2.33344i	0.301648	+	0.0743496i
$986$	19.2175	+	50.6723i	0.612009	+	1.61374i
$987$	0.966636	−	2.54881i	0.0307684	−	0.0811295i
$988$	7.44555	+	6.23714i	0.236875	+	0.198430i
$989$	−1.41466	−	3.73014i	−0.0449834	−	0.118612i
$990$	−9.06170	+	8.02797i	−0.288000	+	0.255146i
$991$	30.5202			0.969506			0.484753	−	0.874651i	$-0.338909\pi$
$991$	30.5202			0.969506			0.484753	+	0.874651i	$0.338909\pi$
$992$	−10.0292			−0.318429
$993$	4.83584	−	4.28418i	0.153461	−	0.135954i
$994$	3.14131	−	1.64868i	0.0996362	−	0.0522931i
$995$	−38.6085			−1.22397
$996$	−9.03233	−	4.74053i	−0.286200	−	0.150209i
$997$	−20.4375	−	18.1061i	−0.647263	−	0.573425i	0.274304	−	0.961643i	$-0.411552\pi$
$997$	−20.4375	−	18.1061i	−0.647263	−	0.573425i	−0.921568	+	0.388218i	$0.873091\pi$
$998$	16.6792	+	24.1640i	0.527971	+	0.764898i
$999$	6.23712	+	5.52560i	0.197334	+	0.174822i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.a.40.5	✓	180
169.131	even	13	inner	507.2.m.a.469.5	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.a.40.5	✓	180	1.1	even	1	trivial
507.2.m.a.469.5	yes	180	169.131	even	13	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56270 - 0.385172i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(0.522773 + 0.274373i) q^{4} +(-0.878504 + 1.27273i) q^{5} +(0.570727 - 1.50488i) q^{6} +(0.273931 + 0.242682i) q^{7} +(1.69816 + 1.50443i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})\)	\(q+(-1.56270 - 0.385172i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(0.522773 + 0.274373i) q^{4} +(-0.878504 + 1.27273i) q^{5} +(0.570727 - 1.50488i) q^{6} +(0.273931 + 0.242682i) q^{7} +(1.69816 + 1.50443i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(1.86306 - 1.65053i) q^{10} +(4.72254 - 1.16400i) q^{11} +(-0.335385 + 0.485890i) q^{12} +(-3.52332 - 0.765668i) q^{13} +(-0.334599 - 0.484750i) q^{14} +(-1.15756 - 1.02551i) q^{15} +(-2.74502 - 3.97685i) q^{16} +(5.97008 + 5.28903i) q^{17} +(1.42512 + 0.747959i) q^{18} -4.56274 q^{19} +(-0.808461 + 0.424313i) q^{20} +(-0.273931 + 0.242682i) q^{21} -7.82827 q^{22} -3.46519 q^{23} +(-1.69816 + 1.50443i) q^{24} +(0.924946 + 2.43888i) q^{25} +(5.21098 + 2.55359i) q^{26} +(0.354605 - 0.935016i) q^{27} +(0.0766186 + 0.202027i) q^{28} +(-4.09901 - 1.01032i) q^{29} +(1.41393 + 2.04843i) q^{30} +(-1.09769 + 2.89437i) q^{31} +(1.14889 + 3.02937i) q^{32} +(0.586276 + 4.82841i) q^{33} +(-7.29228 - 10.5647i) q^{34} +(-0.549518 + 0.135444i) q^{35} +(-0.441921 - 0.391508i) q^{36} +(-2.95482 + 7.79121i) q^{37} +(7.13021 + 1.75744i) q^{38} +(1.18477 - 3.40534i) q^{39} +(-3.40658 + 0.839646i) q^{40} +(-0.424060 + 3.49245i) q^{41} +(0.521547 - 0.273729i) q^{42} +(0.408248 + 1.07646i) q^{43} +(2.78819 + 0.687227i) q^{44} +(1.15756 - 1.02551i) q^{45} +(5.41507 + 1.33469i) q^{46} +(-6.59542 + 3.46154i) q^{47} +(4.27873 - 2.24565i) q^{48} +(-0.827613 - 6.81601i) q^{49} +(-0.506028 - 4.16751i) q^{50} +(-5.97008 + 5.28903i) q^{51} +(-1.63182 - 1.36697i) q^{52} +(0.180951 + 0.160308i) q^{53} +(-0.914284 + 1.32457i) q^{54} +(-2.66731 + 7.03311i) q^{55} +(0.100079 + 0.824222i) q^{56} +(0.549977 - 4.52947i) q^{57} +(6.01640 + 3.15765i) q^{58} +(-6.33698 + 9.18070i) q^{59} +(-0.323770 - 0.853712i) q^{60} +(-2.28748 + 2.02653i) q^{61} +(2.83019 - 4.10024i) q^{62} +(-0.207893 - 0.301186i) q^{63} +(0.536377 + 4.41746i) q^{64} +(4.06974 - 3.81159i) q^{65} +(0.943594 - 7.77120i) q^{66} +(11.3526 - 5.95833i) q^{67} +(1.66983 + 4.40299i) q^{68} +(0.417683 - 3.43993i) q^{69} +0.910903 q^{70} +(-0.725999 + 5.97914i) q^{71} +(-1.28878 - 1.86711i) q^{72} +(-9.32671 + 2.29883i) q^{73} +(7.61846 - 11.0372i) q^{74} +(-2.53259 + 0.624227i) q^{75} +(-2.38528 - 1.25189i) q^{76} +(1.57613 + 0.827218i) q^{77} +(-3.16309 + 4.86519i) q^{78} +(-4.79957 + 2.51901i) q^{79} +7.47297 q^{80} +(0.885456 + 0.464723i) q^{81} +(2.00787 - 5.29433i) q^{82} +(2.08260 + 17.1517i) q^{83} +(-0.209789 + 0.0517083i) q^{84} +(-11.9763 + 2.95188i) q^{85} +(-0.223348 - 1.83943i) q^{86} +(1.49703 - 3.94735i) q^{87} +(9.77077 + 5.12810i) q^{88} +9.59411 q^{89} +(-2.20392 + 1.15671i) q^{90} +(-0.779331 - 1.06478i) q^{91} +(-1.81151 - 0.950754i) q^{92} +(-2.74095 - 1.43856i) q^{93} +(11.6400 - 2.86900i) q^{94} +(4.00838 - 5.80714i) q^{95} +(-3.14577 + 0.775362i) q^{96} +(0.986463 + 1.42914i) q^{97} +(-1.33202 + 10.9702i) q^{98} -4.86388 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Introduction

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