LMFDB - Embedded newform 115.2.g.c.41.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			41.4
Character	$\chi$	$=$	115.41
Dual form			115.2.g.c.101.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29680 + 0.380775i) q^{2} +(-1.87580 + 2.16478i) q^{3} +(-0.145804 - 0.0937028i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-3.25683 + 2.09304i) q^{6} +(1.66529 + 3.64647i) q^{7} +(-1.92355 - 2.21990i) q^{8} +(-0.740735 - 5.15193i) q^{9} +O(q^{10})$	\(q+(1.29680 + 0.380775i) q^{2} +(-1.87580 + 2.16478i) q^{3} +(-0.145804 - 0.0937028i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-3.25683 + 2.09304i) q^{6} +(1.66529 + 3.64647i) q^{7} +(-1.92355 - 2.21990i) q^{8} +(-0.740735 - 5.15193i) q^{9} +(-0.561453 + 1.22941i) q^{10} +(5.32356 - 1.56314i) q^{11} +(0.476346 - 0.139868i) q^{12} +(0.162683 - 0.356227i) q^{13} +(0.771061 + 5.36284i) q^{14} +(-1.87580 - 2.16478i) q^{15} +(-1.50518 - 3.29589i) q^{16} +(-0.659097 + 0.423576i) q^{17} +(1.00114 - 6.96308i) q^{18} +(-0.661374 - 0.425039i) q^{19} +(0.113499 - 0.130985i) q^{20} +(-11.0176 - 3.23505i) q^{21} +7.49880 q^{22} +(4.73133 + 0.783914i) q^{23} +8.41379 q^{24} +(-0.959493 - 0.281733i) q^{25} +(0.346610 - 0.400009i) q^{26} +(5.31317 + 3.41457i) q^{27} +(0.0988782 - 0.687713i) q^{28} +(-0.130841 + 0.0840862i) q^{29} +(-1.60824 - 3.52155i) q^{30} +(-2.02743 - 2.33978i) q^{31} +(0.139125 + 0.967639i) q^{32} +(-6.60206 + 14.4565i) q^{33} +(-1.01601 + 0.298326i) q^{34} +(-3.84635 + 1.12939i) q^{35} +(-0.374747 + 0.820583i) q^{36} +(-1.58547 - 11.0272i) q^{37} +(-0.695826 - 0.803026i) q^{38} +(0.465993 + 1.02038i) q^{39} +(2.47105 - 1.58805i) q^{40} +(-1.44931 + 10.0802i) q^{41} +(-13.0558 - 8.39042i) q^{42} +(-1.99607 + 2.30359i) q^{43} +(-0.922669 - 0.270920i) q^{44} +5.20491 q^{45} +(5.83710 + 2.81815i) q^{46} +2.46641 q^{47} +(9.95832 + 2.92403i) q^{48} +(-5.93953 + 6.85459i) q^{49} +(-1.13699 - 0.730702i) q^{50} +(0.319381 - 2.22135i) q^{51} +(-0.0570994 + 0.0366955i) q^{52} +(-2.03164 - 4.44868i) q^{53} +(5.58994 + 6.45114i) q^{54} +(0.789606 + 5.49183i) q^{55} +(4.89152 - 10.7109i) q^{56} +(2.16072 - 0.634445i) q^{57} +(-0.201692 + 0.0592222i) q^{58} +(4.65335 - 10.1894i) q^{59} +(0.0706530 + 0.491402i) q^{60} +(-4.03735 - 4.65935i) q^{61} +(-1.73825 - 3.80623i) q^{62} +(17.5528 - 11.2805i) q^{63} +(-1.21934 + 8.48070i) q^{64} +(0.329449 + 0.211724i) q^{65} +(-14.0662 + 16.2333i) q^{66} +(-5.93489 - 1.74264i) q^{67} +0.135790 q^{68} +(-10.5720 + 8.77185i) q^{69} -5.41799 q^{70} +(4.07908 + 1.19772i) q^{71} +(-10.0119 + 11.5544i) q^{72} +(-0.795440 - 0.511198i) q^{73} +(2.14284 - 14.9037i) q^{74} +(2.40970 - 1.54862i) q^{75} +(0.0566039 + 0.123945i) q^{76} +(14.5652 + 16.8091i) q^{77} +(0.215764 + 1.50067i) q^{78} +(-0.726576 + 1.59098i) q^{79} +(3.47655 - 1.02081i) q^{80} +(-2.37603 + 0.697664i) q^{81} +(-5.71776 + 12.5201i) q^{82} +(1.38922 + 9.66226i) q^{83} +(1.30328 + 1.50406i) q^{84} +(-0.325465 - 0.712670i) q^{85} +(-3.46565 + 2.22724i) q^{86} +(0.0634020 - 0.440971i) q^{87} +(-13.7101 - 8.81098i) q^{88} +(5.26061 - 6.07106i) q^{89} +(6.74973 + 1.98190i) q^{90} +1.56988 q^{91} +(-0.616393 - 0.557637i) q^{92} +8.86818 q^{93} +(3.19844 + 0.939147i) q^{94} +(0.514836 - 0.594153i) q^{95} +(-2.35570 - 1.51392i) q^{96} +(1.60637 - 11.1726i) q^{97} +(-10.3124 + 6.62741i) q^{98} +(-11.9965 - 26.2687i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	1.29680	+	0.380775i	0.916977	+	0.269249i	0.705975	−	0.708237i	$-0.250509\pi$
$2$	1.29680	+	0.380775i	0.916977	+	0.269249i	0.211002	+	0.977486i	$0.432327\pi$
$3$	−1.87580	+	2.16478i	−1.08299	+	1.24984i	−0.116487	+	0.993192i	$0.537163\pi$
$3$	−1.87580	+	2.16478i	−1.08299	+	1.24984i	−0.966505	+	0.256647i	$0.917382\pi$
$4$	−0.145804	−	0.0937028i	−0.0729022	−	0.0468514i
$5$	−0.142315	+	0.989821i	−0.0636451	+	0.442662i
$5$	−0.142315	+	0.989821i	−0.0636451	+	0.442662i
$6$	−3.25683	+	2.09304i	−1.32960	+	0.854479i
$7$	1.66529	+	3.64647i	0.629419	+	1.37824i	0.908466	+	0.417958i	$0.137254\pi$
$7$	1.66529	+	3.64647i	0.629419	+	1.37824i	−0.279047	+	0.960277i	$0.590019\pi$
$8$	−1.92355	−	2.21990i	−0.680078	−	0.784852i
$9$	−0.740735	−	5.15193i	−0.246912	−	1.71731i
$10$	−0.561453	+	1.22941i	−0.177547	+	0.388774i
$11$	5.32356	−	1.56314i	1.60511	−	0.471304i	0.648151	−	0.761512i	$-0.275543\pi$
$11$	5.32356	−	1.56314i	1.60511	−	0.471304i	0.956964	+	0.290208i	$0.0937246\pi$
$12$	0.476346	−	0.139868i	0.137509	−	0.0403763i
$13$	0.162683	−	0.356227i	0.0451202	−	0.0987995i	−0.885730	−	0.464202i	$-0.846341\pi$
$13$	0.162683	−	0.356227i	0.0451202	−	0.0987995i	0.930850	+	0.365402i	$0.119069\pi$
$14$	0.771061	+	5.36284i	0.206075	+	1.43328i
$15$	−1.87580	−	2.16478i	−0.484329	−	0.558945i
$16$	−1.50518	−	3.29589i	−0.376296	−	0.823973i
$17$	−0.659097	+	0.423576i	−0.159855	+	0.102732i	−0.618122	−	0.786082i	$-0.712106\pi$
$17$	−0.659097	+	0.423576i	−0.159855	+	0.102732i	0.458268	+	0.888814i	$0.348470\pi$
$18$	1.00114	−	6.96308i	0.235971	−	1.64121i
$19$	−0.661374	−	0.425039i	−0.151730	−	0.0975107i	0.462573	−	0.886581i	$-0.346926\pi$
$19$	−0.661374	−	0.425039i	−0.151730	−	0.0975107i	−0.614303	+	0.789070i	$0.710563\pi$
$20$	0.113499	−	0.130985i	0.0253792	−	0.0292891i
$21$	−11.0176	−	3.23505i	−2.40423	−	0.705945i
$22$	7.49880			1.59875
$23$	4.73133	+	0.783914i	0.986550	+	0.163457i
$23$	4.73133	+	0.783914i	0.986550	+	0.163457i
$24$	8.41379			1.71746
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$	0.346610	−	0.400009i	0.0679758	−	0.0784483i
$27$	5.31317	+	3.41457i	1.02252	+	0.657134i
$28$	0.0988782	−	0.687713i	0.0186862	−	0.129966i
$29$	−0.130841	+	0.0840862i	−0.0242965	+	0.0156144i	−0.552733	−	0.833359i	$-0.686415\pi$
$29$	−0.130841	+	0.0840862i	−0.0242965	+	0.0156144i	0.528436	+	0.848973i	$0.322779\pi$
$30$	−1.60824	−	3.52155i	−0.293623	−	0.642944i
$31$	−2.02743	−	2.33978i	−0.364138	−	0.420237i	0.543884	−	0.839160i	$-0.316953\pi$
$31$	−2.02743	−	2.33978i	−0.364138	−	0.420237i	−0.908022	+	0.418923i	$0.862408\pi$
$32$	0.139125	+	0.967639i	0.0245941	+	0.171056i
$33$	−6.60206	+	14.4565i	−1.14927	+	2.51655i
$34$	−1.01601	+	0.298326i	−0.174243	+	0.0511625i
$35$	−3.84635	+	1.12939i	−0.650152	+	0.190902i
$36$	−0.374747	+	0.820583i	−0.0624579	+	0.136764i
$37$	−1.58547	−	11.0272i	−0.260649	−	1.81286i	−0.527987	−	0.849252i	$-0.677053\pi$
$37$	−1.58547	−	11.0272i	−0.260649	−	1.81286i	0.267338	−	0.963603i	$-0.413856\pi$
$38$	−0.695826	−	0.803026i	−0.112878	−	0.130268i
$39$	0.465993	+	1.02038i	0.0746187	+	0.163392i
$40$	2.47105	−	1.58805i	0.390707	−	0.251092i
$41$	−1.44931	+	10.0802i	−0.226345	+	1.57426i	0.486970	+	0.873418i	$0.338102\pi$
$41$	−1.44931	+	10.0802i	−0.226345	+	1.57426i	−0.713315	+	0.700843i	$0.752807\pi$
$42$	−13.0558	−	8.39042i	−2.01455	−	1.29467i
$43$	−1.99607	+	2.30359i	−0.304398	+	0.351294i	−0.887254	−	0.461282i	$-0.847390\pi$
$43$	−1.99607	+	2.30359i	−0.304398	+	0.351294i	0.582856	+	0.812575i	$0.301935\pi$
$44$	−0.922669	−	0.270920i	−0.139098	−	0.0408427i
$45$	5.20491			0.775902
$46$	5.83710	+	2.81815i	0.860633	+	0.415514i
$47$	2.46641			0.359763			0.179881	−	0.983688i	$-0.442429\pi$
$47$	2.46641			0.359763			0.179881	+	0.983688i	$0.442429\pi$
$48$	9.95832	+	2.92403i	1.43736	+	0.422047i
$49$	−5.93953	+	6.85459i	−0.848505	+	0.979226i
$50$	−1.13699	−	0.730702i	−0.160795	−	0.103337i
$51$	0.319381	−	2.22135i	0.0447223	−	0.311051i
$52$	−0.0570994	+	0.0366955i	−0.00791826	+	0.00508875i
$53$	−2.03164	−	4.44868i	−0.279068	−	0.611073i	0.717249	−	0.696817i	$-0.245401\pi$
$53$	−2.03164	−	4.44868i	−0.279068	−	0.611073i	−0.996317	+	0.0857432i	$0.972674\pi$
$54$	5.58994	+	6.45114i	0.760695	+	0.877889i
$55$	0.789606	+	5.49183i	0.106471	+	0.740519i
$56$	4.89152	−	10.7109i	0.653657	−	1.43131i
$57$	2.16072	−	0.634445i	0.286195	−	0.0840343i
$58$	−0.201692	+	0.0592222i	−0.0264835	+	0.00777625i
$59$	4.65335	−	10.1894i	0.605814	−	1.32655i	−0.319586	−	0.947557i	$-0.603544\pi$
$59$	4.65335	−	10.1894i	0.605814	−	1.32655i	0.925400	−	0.378991i	$-0.123729\pi$
$60$	0.0706530	+	0.491402i	0.00912126	+	0.0634398i
$61$	−4.03735	−	4.65935i	−0.516929	−	0.596568i	0.435930	−	0.899981i	$-0.356419\pi$
$61$	−4.03735	−	4.65935i	−0.516929	−	0.596568i	−0.952859	+	0.303412i	$0.901874\pi$
$62$	−1.73825	−	3.80623i	−0.220757	−	0.483391i
$63$	17.5528	−	11.2805i	2.21145	−	1.42121i
$64$	−1.21934	+	8.48070i	−0.152418	+	1.06009i
$65$	0.329449	+	0.211724i	0.0408631	+	0.0262611i
$66$	−14.0662	+	16.2333i	−1.73143	+	1.99818i
$67$	−5.93489	−	1.74264i	−0.725062	−	0.212898i	−0.101683	−	0.994817i	$-0.532423\pi$
$67$	−5.93489	−	1.74264i	−0.725062	−	0.212898i	−0.623380	+	0.781919i	$0.714241\pi$
$68$	0.135790			0.0164669
$69$	−10.5720	+	8.77185i	−1.27272	+	1.05601i
$70$	−5.41799			−0.647574
$71$	4.07908	+	1.19772i	0.484097	+	0.142144i	0.514669	−	0.857389i	$-0.327915\pi$
$71$	4.07908	+	1.19772i	0.484097	+	0.142144i	−0.0305720	+	0.999533i	$0.509733\pi$
$72$	−10.0119	+	11.5544i	−1.17991	+	1.36169i
$73$	−0.795440	−	0.511198i	−0.0930992	−	0.0598312i	0.493263	−	0.869880i	$-0.335804\pi$
$73$	−0.795440	−	0.511198i	−0.0930992	−	0.0598312i	−0.586362	+	0.810049i	$0.699440\pi$
$74$	2.14284	−	14.9037i	0.249100	−	1.73253i
$75$	2.40970	−	1.54862i	0.278249	−	0.178820i
$76$	0.0566039	+	0.123945i	0.00649291	+	0.0142175i
$77$	14.5652	+	16.8091i	1.65986	+	1.91558i
$78$	0.215764	+	1.50067i	0.0244305	+	0.169918i
$79$	−0.726576	+	1.59098i	−0.0817462	+	0.178999i	−0.946091	−	0.323900i	$-0.895006\pi$
$79$	−0.726576	+	1.59098i	−0.0817462	+	0.178999i	0.864345	+	0.502899i	$0.167733\pi$
$80$	3.47655	−	1.02081i	0.388691	−	0.114130i
$81$	−2.37603	+	0.697664i	−0.264003	+	0.0775183i
$82$	−5.71776	+	12.5201i	−0.631421	+	1.38262i
$83$	1.38922	+	9.66226i	0.152487	+	1.06057i	0.912033	+	0.410117i	$0.134512\pi$
$83$	1.38922	+	9.66226i	0.152487	+	1.06057i	−0.759546	+	0.650454i	$0.774579\pi$
$84$	1.30328	+	1.50406i	0.142199	+	0.164106i
$85$	−0.325465	−	0.712670i	−0.0353017	−	0.0772999i
$86$	−3.46565	+	2.22724i	−0.373711	+	0.240169i
$87$	0.0634020	−	0.440971i	0.00679741	−	0.0472770i
$88$	−13.7101	−	8.81098i	−1.46151	−	0.939253i
$89$	5.26061	−	6.07106i	0.557623	−	0.643532i	−0.405019	−	0.914308i	$-0.632735\pi$
$89$	5.26061	−	6.07106i	0.557623	−	0.643532i	0.962642	+	0.270777i	$0.0872805\pi$
$90$	6.74973	+	1.98190i	0.711484	+	0.208910i
$91$	1.56988			0.164569
$92$	−0.616393	−	0.557637i	−0.0642635	−	0.0581377i
$93$	8.86818			0.919587
$94$	3.19844	+	0.939147i	0.329894	+	0.0968656i
$95$	0.514836	−	0.594153i	0.0528211	−	0.0609588i
$96$	−2.35570	−	1.51392i	−0.240428	−	0.154514i
$97$	1.60637	−	11.1726i	0.163103	−	1.13440i	−0.729638	−	0.683833i	$-0.760312\pi$
$97$	1.60637	−	11.1726i	0.163103	−	1.13440i	0.892741	−	0.450570i	$-0.148779\pi$
$98$	−10.3124	+	6.62741i	−1.04171	+	0.669469i
$99$	−11.9965	−	26.2687i	−1.20570	−	2.64011i
$100$	0.113499	+	0.130985i	0.0113499	+	0.0130985i
$101$	−2.36300	−	16.4350i	−0.235128	−	1.63535i	−0.675377	−	0.737473i	$-0.736019\pi$
$101$	−2.36300	−	16.4350i	−0.235128	−	1.63535i	0.440249	−	0.897876i	$-0.354890\pi$
$102$	1.26001	−	2.75903i	0.124759	−	0.273185i
$103$	−4.44627	+	1.30554i	−0.438104	+	0.128639i	−0.493344	−	0.869834i	$-0.664226\pi$
$103$	−4.44627	+	1.30554i	−0.438104	+	0.128639i	0.0552401	+	0.998473i	$0.482408\pi$
$104$	−1.10372	+	0.324080i	−0.108228	+	0.0317787i
$105$	4.77008	−	10.4450i	0.465512	−	1.01933i
$106$	−0.940692	−	6.54265i	−0.0913680	−	0.635479i
$107$	6.10670	+	7.04751i	0.590357	+	0.681308i	0.969799	−	0.243907i	$-0.0784293\pi$
$107$	6.10670	+	7.04751i	0.590357	+	0.681308i	−0.379441	+	0.925216i	$0.623884\pi$
$108$	−0.454729	−	0.995718i	−0.0437563	−	0.0958130i
$109$	−8.32035	+	5.34717i	−0.796945	+	0.512166i	−0.874618	−	0.484813i	$-0.838888\pi$
$109$	−8.32035	+	5.34717i	−0.796945	+	0.512166i	0.0776724	+	0.996979i	$0.475251\pi$
$110$	−1.06719	+	7.42248i	−0.101753	+	0.707705i
$111$	26.8455	+	17.2525i	2.54806	+	1.63754i
$112$	9.51181	−	10.9772i	0.898781	−	1.03725i
$113$	6.52967	+	1.91728i	0.614259	+	0.180363i	0.574039	−	0.818828i	$-0.305376\pi$
$113$	6.52967	+	1.91728i	0.614259	+	0.180363i	0.0402204	+	0.999191i	$0.487194\pi$
$114$	3.04361			0.285060
$115$	−1.44927	+	4.57161i	−0.135145	+	0.426305i
$116$	0.0269563			0.00250283
$117$	−1.95576	−	0.574263i	−0.180810	−	0.0530906i
$118$	9.91434	−	11.4418i	0.912689	−	1.05330i
$119$	−2.64214	−	1.69800i	−0.242205	−	0.155656i
$120$	−1.19741	+	8.32815i	−0.109308	+	0.760252i
$121$	16.6431	−	10.6959i	1.51301	−	0.972353i
$122$	−3.46147	−	7.57956i	−0.313387	−	0.686222i
$123$	−19.1028	−	22.0458i	−1.72244	−	1.98781i
$124$	0.0763645	+	0.531126i	0.00685773	+	0.0476966i
$125$	0.415415	−	0.909632i	0.0371558	−	0.0813600i
$126$	27.0578	−	7.94490i	2.41050	−	0.707788i
$127$	−19.5304	+	5.73464i	−1.73304	+	0.508867i	−0.987504	−	0.157596i	$-0.949626\pi$
$127$	−19.5304	+	5.73464i	−1.73304	+	0.508867i	−0.745538	+	0.666463i	$0.767807\pi$
$128$	−3.99827	+	8.75499i	−0.353401	+	0.773839i
$129$	−1.24255	−	8.64212i	−0.109400	−	0.760896i
$130$	0.346610	+	0.400009i	0.0303997	+	0.0350831i
$131$	3.83677	+	8.40135i	0.335220	+	0.734029i	0.999914	−	0.0130862i	$-0.00416558\pi$
$131$	3.83677	+	8.40135i	0.335220	+	0.734029i	−0.664695	+	0.747115i	$0.731438\pi$
$132$	2.31722	−	1.48919i	0.201688	−	0.129617i
$133$	0.448515	−	3.11949i	0.0388912	−	0.270494i
$134$	−7.03282	−	4.51972i	−0.607543	−	0.390444i
$135$	−4.13596	+	4.77315i	−0.355967	+	0.410807i
$136$	2.20810	+	0.648357i	0.189343	+	0.0555962i
$137$	−13.3739			−1.14261			−0.571306	−	0.820737i	$-0.693563\pi$
$137$	−13.3739			−1.14261			−0.571306	+	0.820737i	$0.693563\pi$
$138$	−17.0499	+	7.34978i	−1.45138	+	0.625654i
$139$	4.41265			0.374276			0.187138	−	0.982334i	$-0.440079\pi$
$139$	4.41265			0.374276			0.187138	+	0.982334i	$0.440079\pi$
$140$	0.666641	+	0.195744i	0.0563415	+	0.0165433i
$141$	−4.62648	+	5.33924i	−0.389620	+	0.449645i
$142$	4.83369	+	3.10642i	0.405634	+	0.260685i
$143$	0.309223	−	2.15069i	0.0258585	−	0.179850i
$144$	−15.8653	+	10.1960i	−1.32210	+	0.849665i
$145$	−0.0646098	−	0.141476i	−0.00536555	−	0.0117489i
$146$	−0.836876	−	0.965806i	−0.0692603	−	0.0799307i
$147$	−3.69735	−	25.7156i	−0.304952	−	2.12099i
$148$	−0.802108	+	1.75637i	−0.0659329	+	0.144373i
$149$	−3.14930	+	0.924717i	−0.258001	+	0.0757558i	−0.408175	−	0.912904i	$-0.633835\pi$
$149$	−3.14930	+	0.924717i	−0.258001	+	0.0757558i	0.150174	+	0.988660i	$0.452016\pi$
$150$	3.71458	−	1.09070i	0.303294	−	0.0890553i
$151$	−3.58667	+	7.85371i	−0.291879	+	0.639126i	−0.997591	−	0.0693732i	$-0.977900\pi$
$151$	−3.58667	+	7.85371i	−0.291879	+	0.639126i	0.705712	+	0.708499i	$0.250627\pi$
$152$	0.328644	+	2.28577i	0.0266565	+	0.185400i
$153$	2.67045	+	3.08186i	0.215893	+	0.249154i
$154$	12.4877	+	27.3442i	1.00628	+	2.20345i
$155$	2.60450	−	1.67381i	0.209198	−	0.134444i
$156$	0.0276689	−	0.192441i	0.00221528	−	0.0154076i
$157$	−5.02527	−	3.22954i	−0.401060	−	0.257746i	0.324526	−	0.945877i	$-0.394795\pi$
$157$	−5.02527	−	3.22954i	−0.401060	−	0.257746i	−0.725586	+	0.688131i	$0.758431\pi$
$158$	−1.54803	+	1.78652i	−0.123155	+	0.142128i
$159$	13.4414	+	3.94675i	1.06597	+	0.312997i
$160$	−0.977589			−0.0772852
$161$	5.02050	+	18.5581i	0.395671	+	1.46258i
$162$	−3.34689			−0.262956
$163$	−3.58414	−	1.05240i	−0.280731	−	0.0824302i	0.138336	−	0.990385i	$-0.455825\pi$
$163$	−3.58414	−	1.05240i	−0.280731	−	0.0824302i	−0.419067	+	0.907955i	$0.637643\pi$
$164$	1.15586	−	1.33393i	0.0902574	−	0.104163i
$165$	−13.3698	−	8.59223i	−1.04084	−	0.668905i
$166$	−1.87760	+	13.0590i	−0.145730	+	1.01358i
$167$	−6.45290	+	4.14703i	−0.499340	+	0.320907i	−0.765952	−	0.642897i	$-0.777732\pi$
$167$	−6.45290	+	4.14703i	−0.499340	+	0.320907i	0.266612	+	0.963804i	$0.414096\pi$
$168$	14.0114	+	30.6806i	1.08100	+	2.36706i
$169$	8.41276	+	9.70884i	0.647135	+	0.746834i
$170$	−0.150697	−	1.04812i	−0.0115579	−	0.0803871i
$171$	−1.69987	+	3.72219i	−0.129992	+	0.284643i
$172$	0.506888	−	0.148836i	0.0386498	−	0.0113486i
$173$	−15.1360	+	4.44434i	−1.15077	+	0.337897i	−0.800840	−	0.598879i	$-0.795613\pi$
$173$	−15.1360	+	4.44434i	−1.15077	+	0.337897i	−0.349931	+	0.936775i	$0.613795\pi$
$174$	0.250130	−	0.547709i	0.0189623	−	0.0415217i
$175$	−0.570502	−	3.96793i	−0.0431259	−	0.299947i
$176$	−13.1649	−	15.1931i	−0.992340	−	1.14522i
$177$	13.3291	+	29.1868i	1.00188	+	2.19381i
$178$	9.13367	−	5.86985i	0.684598	−	0.439964i
$179$	1.90287	−	13.2347i	0.142227	−	0.989211i	−0.786273	−	0.617879i	$-0.787992\pi$
$179$	1.90287	−	13.2347i	0.142227	−	0.989211i	0.928500	−	0.371332i	$-0.121099\pi$
$180$	−0.758898	−	0.487714i	−0.0565649	−	0.0363521i
$181$	−0.453768	+	0.523677i	−0.0337283	+	0.0389246i	−0.772363	−	0.635181i	$-0.780925\pi$
$181$	−0.453768	+	0.523677i	−0.0337283	+	0.0389246i	0.738635	+	0.674106i	$0.235471\pi$
$182$	2.03583	+	0.597773i	0.150906	+	0.0443099i
$183$	17.6597			1.30544
$184$	−7.36074	−	12.0110i	−0.542641	−	0.885460i
$185$	11.1406			0.819070
$186$	11.5003	+	3.37678i	0.843240	+	0.247598i
$187$	−2.84664	+	3.28519i	−0.208167	+	0.240237i
$188$	−0.359613	−	0.231109i	−0.0262275	−	0.0168554i
$189$	−3.60316	+	25.0606i	−0.262092	+	1.82289i
$190$	0.893879	−	0.574461i	0.0648488	−	0.0416758i
$191$	4.37397	+	9.57765i	0.316489	+	0.693015i	0.999293	−	0.0375868i	$-0.0119671\pi$
$191$	4.37397	+	9.57765i	0.316489	+	0.693015i	−0.682804	+	0.730601i	$0.739240\pi$
$192$	−16.0717	−	18.5477i	−1.15987	−	1.33856i
$193$	2.13793	+	14.8696i	0.153892	+	1.07034i	0.909616	+	0.415450i	$0.136376\pi$
$193$	2.13793	+	14.8696i	0.153892	+	1.07034i	−0.755724	+	0.654890i	$0.772715\pi$
$194$	6.33739	−	13.8769i	0.454998	−	0.996306i
$195$	−1.07631	+	0.316035i	−0.0770765	+	0.0226317i
$196$	1.50830	−	0.442878i	0.107736	−	0.0316341i
$197$	−4.56121	+	9.98766i	−0.324973	+	0.711591i	−0.999648	−	0.0265235i	$-0.991556\pi$
$197$	−4.56121	+	9.98766i	−0.324973	+	0.711591i	0.674675	+	0.738115i	$0.264284\pi$
$198$	−5.55463	−	38.6333i	−0.394750	−	2.74555i
$199$	6.98763	+	8.06416i	0.495340	+	0.571653i	0.947285	−	0.320393i	$-0.103815\pi$
$199$	6.98763	+	8.06416i	0.495340	+	0.571653i	−0.451945	+	0.892046i	$0.649270\pi$
$200$	1.22022	+	2.67190i	0.0862823	+	0.188932i
$201$	14.9051	−	9.57892i	1.05132	−	0.675645i
$202$	3.19371	−	22.2128i	0.224709	−	1.56288i
$203$	−0.524505	−	0.337079i	−0.0368130	−	0.0236583i
$204$	−0.254714	+	0.293955i	−0.0178335	+	0.0205810i
$205$	−9.77133	−	2.86912i	−0.682460	−	0.200388i
$206$	−6.26305			−0.436367
$207$	0.534008	−	24.9561i	0.0371161	−	1.73457i
$208$	−1.41895			−0.0983867
$209$	−4.18526	−	1.22890i	−0.289501	−	0.0850050i
$210$	10.1630	−	11.7288i	0.701317	−	0.809363i
$211$	−10.9135	−	7.01366i	−0.751314	−	0.482840i	0.108088	−	0.994141i	$-0.465527\pi$
$211$	−10.9135	−	7.01366i	−0.751314	−	0.482840i	−0.859402	+	0.511301i	$0.829164\pi$
$212$	−0.120631	+	0.839008i	−0.00828498	+	0.0576233i
$213$	−10.2443	+	6.58363i	−0.701930	+	0.451103i
$214$	5.23566	+	11.4645i	0.357902	+	0.783697i
$215$	−1.99607	−	2.30359i	−0.136131	−	0.157103i
$216$	−2.64017	−	18.3628i	−0.179641	−	1.24943i
$217$	5.15569	−	11.2894i	0.349991	−	0.766373i
$218$	−12.8259	+	3.76603i	−0.868680	+	0.255067i
$219$	2.59872	−	0.763053i	0.175605	−	0.0515623i
$220$	0.399472	−	0.874721i	0.0269324	−	0.0589737i
$221$	0.0436650	+	0.303697i	0.00293723	+	0.0204289i
$222$	28.2439	+	32.5952i	1.89561	+	2.18765i
$223$	8.17106	+	17.8921i	0.547174	+	1.19814i	0.958089	+	0.286471i	$0.0924822\pi$
$223$	8.17106	+	17.8921i	0.547174	+	1.19814i	−0.410914	+	0.911674i	$0.634791\pi$
$224$	−3.29678	+	2.11871i	−0.220276	+	0.141562i
$225$	−0.740735	+	5.15193i	−0.0493824	+	0.343462i
$226$	7.73762	+	4.97267i	0.514699	+	0.330777i
$227$	−2.70069	+	3.11677i	−0.179251	+	0.206867i	−0.838264	−	0.545265i	$-0.816429\pi$
$227$	−2.70069	+	3.11677i	−0.179251	+	0.206867i	0.659012	+	0.752132i	$0.270974\pi$
$228$	−0.374492	−	0.109961i	−0.0248013	−	0.00728233i
$229$	−4.14670			−0.274022			−0.137011	−	0.990570i	$-0.543750\pi$
$229$	−4.14670			−0.274022			−0.137011	+	0.990570i	$0.543750\pi$
$230$	−3.62017	+	5.37662i	−0.238707	+	0.354524i
$231$	−63.7095			−4.19178
$232$	0.438341	+	0.128709i	0.0287785	+	0.00845014i
$233$	15.5834	−	17.9842i	1.02090	−	1.17818i	0.0370295	−	0.999314i	$-0.488210\pi$
$233$	15.5834	−	17.9842i	1.02090	−	1.17818i	0.983873	−	0.178870i	$-0.0572441\pi$
$234$	−2.31757	−	1.48941i	−0.151504	−	0.0973657i
$235$	−0.351006	+	2.44130i	−0.0228971	+	0.159253i
$236$	−1.63325	+	1.04963i	−0.106316	+	0.0683250i
$237$	−2.08122	−	4.55724i	−0.135190	−	0.296024i
$238$	−2.77978	−	3.20803i	−0.180186	−	0.207946i
$239$	0.636804	+	4.42907i	0.0411915	+	0.286493i	0.999997	+	0.00242977i	$0.000773419\pi$
$239$	0.636804	+	4.42907i	0.0411915	+	0.286493i	−0.958806	+	0.284063i	$0.908317\pi$
$240$	−4.31148	+	9.44082i	−0.278305	+	0.609402i
$241$	6.32560	−	1.85736i	0.407468	−	0.119643i	−0.0715743	−	0.997435i	$-0.522802\pi$
$241$	6.32560	−	1.85736i	0.407468	−	0.119643i	0.479042	+	0.877792i	$0.340984\pi$
$242$	25.6555	−	7.53314i	1.64920	−	0.484249i
$243$	−4.92436	+	10.7828i	−0.315898	+	0.691720i
$244$	0.152069	+	1.05766i	0.00973522	+	0.0677100i
$245$	−5.93953	−	6.85459i	−0.379463	−	0.437923i
$246$	−16.3781	−	35.8630i	−1.04423	−	2.28654i
$247$	−0.259005	+	0.166452i	−0.0164801	+	0.0105911i
$248$	−1.29420	+	9.00138i	−0.0821820	+	0.571588i
$249$	−23.5226	−	15.1171i	−1.49068	−	0.958005i
$250$	0.885076	−	1.02143i	0.0559771	−	0.0646010i
$251$	0.577885	+	0.169682i	0.0364758	+	0.0107103i	0.299920	−	0.953964i	$-0.403040\pi$
$251$	0.577885	+	0.169682i	0.0364758	+	0.0107103i	−0.263444	+	0.964675i	$0.584858\pi$
$252$	−3.61629			−0.227805
$253$	26.4129	−	3.22251i	1.66056	−	0.202597i
$254$	−27.5106			−1.72617
$255$	2.15328	+	0.632261i	0.134844	+	0.0395937i
$256$	2.70293	−	3.11935i	0.168933	−	0.194959i
$257$	−8.71003	−	5.59759i	−0.543317	−	0.349168i	0.240018	−	0.970768i	$-0.422847\pi$
$257$	−8.71003	−	5.59759i	−0.543317	−	0.349168i	−0.783335	+	0.621600i	$0.786483\pi$
$258$	1.67936	−	11.6802i	0.104553	−	0.727180i
$259$	37.5700	−	24.1448i	2.33448	−	1.50028i
$260$	−0.0281959	−	0.0617405i	−0.00174864	−	0.00382898i
$261$	0.530124	+	0.611796i	0.0328139	+	0.0378692i
$262$	1.77650	+	12.3558i	0.109752	+	0.763345i
$263$	7.39344	−	16.1894i	0.455899	−	0.998280i	−0.532504	−	0.846427i	$-0.678749\pi$
$263$	7.39344	−	16.1894i	0.455899	−	0.998280i	0.988403	−	0.151852i	$-0.0485238\pi$
$264$	44.7913	−	13.1519i	2.75672	−	0.809445i
$265$	4.69253	−	1.37785i	0.288260	−	0.0846408i
$266$	1.76946	−	3.87458i	0.108493	−	0.237566i
$267$	3.27472	+	22.7762i	0.200410	+	1.39388i
$268$	0.702043	+	0.810200i	0.0428841	+	0.0494909i
$269$	2.45865	+	5.38369i	0.149907	+	0.328249i	0.969656	−	0.244472i	$-0.0786148\pi$
$269$	2.45865	+	5.38369i	0.149907	+	0.328249i	−0.819750	+	0.572722i	$0.805887\pi$
$270$	−7.18101	+	4.61495i	−0.437022	+	0.280857i
$271$	−0.0295042	+	0.205206i	−0.00179225	+	0.0124654i	−0.990698	−	0.136079i	$-0.956550\pi$
$271$	−0.0295042	+	0.205206i	−0.00179225	+	0.0124654i	0.988906	+	0.148545i	$0.0474589\pi$
$272$	2.38812	+	1.53475i	0.144801	+	0.0930581i
$273$	−2.94478	+	3.39846i	−0.178226	+	0.205684i
$274$	−17.3433	−	5.09246i	−1.04775	−	0.307647i
$275$	−5.54831			−0.334575
$276$	2.36339	−	0.288346i	0.142260	−	0.0173564i
$277$	24.8826			1.49505			0.747524	−	0.664235i	$-0.231242\pi$
$277$	24.8826			1.49505			0.747524	+	0.664235i	$0.231242\pi$
$278$	5.72232	+	1.68023i	0.343202	+	0.100773i
$279$	−10.5526	+	12.1783i	−0.631768	+	0.729099i
$280$	9.90577	+	6.36605i	0.591983	+	0.380445i
$281$	1.01670	−	7.07133i	0.0606515	−	0.421840i	−0.936762	−	0.349966i	$-0.886193\pi$
$281$	1.01670	−	7.07133i	0.0606515	−	0.421840i	0.997414	−	0.0718740i	$-0.0228979\pi$
$282$	−8.03267	+	5.16229i	−0.478339	+	0.307410i
$283$	−13.1197	−	28.7281i	−0.779884	−	1.70771i	−0.703572	−	0.710624i	$-0.748413\pi$
$283$	−13.1197	−	28.7281i	−0.779884	−	1.70771i	−0.0763123	−	0.997084i	$-0.524315\pi$
$284$	−0.482517	−	0.556854i	−0.0286321	−	0.0330432i
$285$	0.320485	+	2.22902i	0.0189839	+	0.132036i
$286$	1.21993	−	2.67127i	0.0721360	−	0.157956i
$287$	−39.1706	+	11.5015i	−2.31217	+	0.678914i
$288$	4.88215	−	1.43353i	0.287684	−	0.0844715i
$289$	−6.80706	+	14.9054i	−0.400415	+	0.876788i
$290$	−0.0299156	−	0.208068i	−0.00175670	−	0.0122181i
$291$	21.1730	+	24.4349i	1.24118	+	1.43240i
$292$	0.0680779	+	0.149070i	0.00398396	+	0.00872365i
$293$	−8.85730	+	5.69224i	−0.517449	+	0.332544i	−0.773162	−	0.634208i	$-0.781326\pi$
$293$	−8.85730	+	5.69224i	−0.517449	+	0.332544i	0.255713	+	0.966753i	$0.417690\pi$
$294$	4.99714	−	34.7559i	0.291439	−	2.02700i
$295$	9.42346	+	6.05609i	0.548655	+	0.352599i
$296$	−21.4294	+	24.7309i	−1.24556	+	1.43745i
$297$	33.6224	+	9.87244i	1.95097	+	0.572857i
$298$	−4.43612			−0.256978
$299$	1.04896	−	1.55790i	0.0606629	−	0.0900955i
$300$	−0.496456			−0.0286629
$301$	−11.7240	−	3.44247i	−0.675759	−	0.198421i
$302$	−7.64169	+	8.81898i	−0.439730	+	0.507475i
$303$	40.0109	+	25.7134i	2.29856	+	1.47720i
$304$	−0.405394	+	2.81958i	−0.0232510	+	0.161714i
$305$	5.18649	−	3.33316i	0.296978	−	0.190856i
$306$	2.28955	+	5.01341i	0.130885	+	0.286597i
$307$	7.74575	+	8.93907i	0.442073	+	0.510180i	0.932434	−	0.361340i	$-0.117681\pi$
$307$	7.74575	+	8.93907i	0.442073	+	0.510180i	−0.490361	+	0.871519i	$0.663135\pi$
$308$	−0.548607	−	3.81564i	−0.0312598	−	0.217416i
$309$	5.51408	−	12.0742i	0.313685	−	0.686875i
$310$	4.01486	−	1.17887i	0.228029	−	0.0669553i
$311$	−20.3520	+	5.97588i	−1.15405	+	0.338861i	−0.802120	−	0.597163i	$-0.796294\pi$
$311$	−20.3520	+	5.97588i	−1.15405	+	0.338861i	−0.351935	+	0.936024i	$0.614476\pi$
$312$	1.36878	−	2.99722i	0.0774921	−	0.169684i
$313$	−2.88409	−	20.0593i	−0.163018	−	1.13382i	−0.892904	−	0.450248i	$-0.851336\pi$
$313$	−2.88409	−	20.0593i	−0.163018	−	1.13382i	0.729885	−	0.683569i	$-0.239573\pi$
$314$	−5.28704	−	6.10157i	−0.298365	−	0.344332i
$315$	8.66766	+	18.9795i	0.488367	+	1.06938i
$316$	0.255017	−	0.163890i	0.0143458	−	0.00921951i
$317$	0.460294	−	3.20142i	0.0258527	−	0.179810i	−0.972804	−	0.231631i	$-0.925594\pi$
$317$	0.460294	−	3.20142i	0.0258527	−	0.179810i	0.998656	+	0.0518218i	$0.0165028\pi$
$318$	15.9280	+	10.2363i	0.893197	+	0.574023i
$319$	−0.565100	+	0.652160i	−0.0316395	+	0.0365140i
$320$	−8.22085	−	2.41386i	−0.459559	−	0.134939i
$321$	−26.7113			−1.49088
$322$	−0.555870	+	25.9778i	−0.0309774	+	1.44769i
$323$	0.615946			0.0342722
$324$	0.411808	+	0.120918i	0.0228782	+	0.00671765i
$325$	−0.256454	+	0.295964i	−0.0142255	+	0.0164171i
$326$	−4.24719	−	2.72950i	−0.235230	−	0.151173i
$327$	4.03183	−	28.0420i	0.222961	−	1.55072i
$328$	25.1648	−	16.1724i	1.38949	−	0.892974i
$329$	4.10728	+	8.99368i	0.226441	+	0.495838i
$330$	−14.0662	−	16.2333i	−0.774320	−	0.893613i
$331$	−1.68721	−	11.7348i	−0.0927377	−	0.645005i	−0.982178	−	0.187953i	$-0.939815\pi$
$331$	−1.68721	−	11.7348i	−0.0927377	−	0.645005i	0.889440	−	0.457051i	$-0.151094\pi$
$332$	0.702826	−	1.53897i	0.0385726	−	0.0844621i
$333$	−55.6368	+	16.3364i	−3.04888	+	0.895231i
$334$	−9.94721	+	2.92076i	−0.544287	+	0.159817i
$335$	2.56953	−	5.62648i	0.140388	−	0.307407i
$336$	5.92108	+	41.1820i	0.323022	+	2.24666i
$337$	−15.3769	−	17.7459i	−0.837632	−	0.966678i	0.162167	−	0.986763i	$-0.448152\pi$
$337$	−15.3769	−	17.7459i	−0.837632	−	0.966678i	−0.999798	+	0.0200850i	$0.993606\pi$
$338$	7.21279	+	15.7938i	0.392324	+	0.859069i
$339$	−16.3988	+	10.5389i	−0.890662	+	0.572394i
$340$	−0.0193249	+	0.134407i	−0.00104804	+	0.00728926i
$341$	−14.4506	−	9.28681i	−0.782542	−	0.502909i
$342$	−3.62171	+	4.17968i	−0.195840	+	0.226011i
$343$	−7.96162	−	2.33774i	−0.429887	−	0.126226i
$344$	8.95326			0.482728
$345$	−7.17801	−	11.7128i	−0.386451	−	0.630595i
$346$	−21.3207			−1.14621
$347$	28.6066	+	8.39965i	1.53568	+	0.450917i	0.936784	−	0.349908i	$-0.113787\pi$
$347$	28.6066	+	8.39965i	1.53568	+	0.450917i	0.598898	+	0.800825i	$0.295605\pi$
$348$	−0.0505644	+	0.0583545i	−0.00271054	+	0.00312813i
$349$	−15.9566	−	10.2547i	−0.854138	−	0.548921i	0.0387251	−	0.999250i	$-0.487670\pi$
$349$	−15.9566	−	10.2547i	−0.854138	−	0.548921i	−0.892863	+	0.450329i	$0.851307\pi$
$350$	0.771061	−	5.36284i	0.0412149	−	0.286656i
$351$	2.08073	−	1.33720i	0.111061	−	0.0713745i
$352$	2.25320	+	4.93381i	0.120096	+	0.262973i
$353$	3.40292	+	3.92718i	0.181119	+	0.209023i	0.839048	−	0.544057i	$-0.183113\pi$
$353$	3.40292	+	3.92718i	0.181119	+	0.209023i	−0.657929	+	0.753080i	$0.728567\pi$
$354$	6.17166	+	42.9248i	0.328020	+	2.28143i
$355$	−1.76605	+	3.86710i	−0.0937320	+	0.205245i
$356$	−1.33590	+	0.392254i	−0.0708023	+	0.0207894i
$357$	8.63193	−	2.53456i	0.456850	−	0.134143i
$358$	7.50710	−	16.4383i	0.396763	−	0.868789i
$359$	1.13371	+	7.88513i	0.0598349	+	0.416161i	0.997620	+	0.0689458i	$0.0219636\pi$
$359$	1.13371	+	7.88513i	0.0598349	+	0.416161i	−0.937785	+	0.347215i	$0.887127\pi$
$360$	−10.0119	−	11.5544i	−0.527674	−	0.608968i
$361$	−7.63613	−	16.7208i	−0.401901	−	0.880041i
$362$	−0.787850	+	0.506321i	−0.0414085	+	0.0266116i
$363$	−8.06482	+	56.0921i	−0.423293	+	2.94407i
$364$	−0.228896	−	0.147102i	−0.0119974	−	0.00771026i
$365$	0.619198	−	0.714593i	0.0324103	−	0.0374035i
$366$	22.9011	+	6.72438i	1.19706	+	0.351489i
$367$	−2.05395			−0.107215			−0.0536077	−	0.998562i	$-0.517072\pi$
$367$	−2.05395			−0.107215			−0.0536077	+	0.998562i	$0.517072\pi$
$368$	−4.53782	−	16.7739i	−0.236550	−	0.874399i
$369$	53.0060			2.75938
$370$	14.4471	+	4.24205i	0.751069	+	0.220534i
$371$	12.8387	−	14.8167i	0.666552	−	0.769243i
$372$	−1.29302	−	0.830973i	−0.0670399	−	0.0430839i
$373$	4.42979	−	30.8098i	0.229366	−	1.59527i	−0.471425	−	0.881906i	$-0.656260\pi$
$373$	4.42979	−	30.8098i	0.229366	−	1.59527i	0.700791	−	0.713367i	$-0.252831\pi$
$374$	−4.94244	+	3.17631i	−0.255568	+	0.164243i
$375$	1.18992	+	2.60557i	0.0614474	+	0.134551i
$376$	−4.74426	−	5.47517i	−0.244667	−	0.282360i
$377$	0.00866816	+	0.0602884i	0.000446433	+	0.00310501i
$378$	−14.2150	+	31.1266i	−0.731142	+	1.60098i
$379$	−14.5871	+	4.28316i	−0.749290	+	0.220011i	−0.634013	−	0.773322i	$-0.718594\pi$
$379$	−14.5871	+	4.28316i	−0.749290	+	0.220011i	−0.115276	+	0.993333i	$0.536775\pi$
$380$	−0.130739	+	0.0383885i	−0.00670678	+	0.00196929i
$381$	24.2208	−	53.0361i	1.24087	−	2.71712i
$382$	2.02523	+	14.0858i	0.103620	+	0.720693i
$383$	−17.2237	−	19.8772i	−0.880088	−	1.01568i	−0.999739	−	0.0228598i	$-0.992723\pi$
$383$	−17.2237	−	19.8772i	−0.880088	−	1.01568i	0.119651	−	0.992816i	$-0.461823\pi$
$384$	−11.4527	−	25.0780i	−0.584445	−	1.27976i
$385$	−18.7109	+	12.0248i	−0.953595	+	0.612838i
$386$	−2.88952	+	20.0970i	−0.147073	+	1.02291i
$387$	13.3465	+	8.57726i	0.678439	+	0.436006i
$388$	−1.28112	+	1.47849i	−0.0650389	+	0.0750589i
$389$	29.0738	+	8.53685i	1.47410	+	0.432836i	0.917430	−	0.397897i	$-0.130260\pi$
$389$	29.0738	+	8.53685i	1.47410	+	0.432836i	0.556672	+	0.830732i	$0.312078\pi$
$390$	−1.51610			−0.0767709
$391$	−3.45045	+	1.48740i	−0.174497	+	0.0752212i
$392$	26.6415			1.34560
$393$	−25.3841	−	7.45344i	−1.28046	−	0.375977i
$394$	−9.71803	+	11.2152i	−0.489587	+	0.565014i
$395$	−1.47138	−	0.945601i	−0.0740333	−	0.0475783i
$396$	−0.712307	+	4.95420i	−0.0357948	+	0.248958i
$397$	−19.3869	+	12.4592i	−0.972999	+	0.625308i	−0.927566	−	0.373659i	$-0.878103\pi$
$397$	−19.3869	+	12.4592i	−0.972999	+	0.625308i	−0.0454328	+	0.998967i	$0.514467\pi$
$398$	5.99094	+	13.1183i	0.300299	+	0.657562i
$399$	5.91171	+	6.82247i	0.295955	+	0.341551i
$400$	0.515653	+	3.58644i	0.0257826	+	0.179322i
$401$	6.98693	−	15.2992i	0.348911	−	0.764008i	−0.651077	−	0.759012i	$-0.725682\pi$
$401$	6.98693	−	15.2992i	0.348911	−	0.764008i	0.999988	−	0.00499590i	$-0.00159025\pi$
$402$	22.9763	−	6.74647i	1.14596	−	0.336483i
$403$	−1.16332	+	0.341582i	−0.0579492	+	0.0170154i
$404$	−1.19547	+	2.61772i	−0.0594770	+	0.130236i
$405$	−0.352419	−	2.45113i	−0.0175119	−	0.121798i
$406$	−0.551827	−	0.636843i	−0.0273867	−	0.0316060i
$407$	−25.6773	−	56.2255i	−1.27278	−	2.78699i
$408$	−5.54551	+	3.56388i	−0.274543	+	0.176438i
$409$	−4.05117	+	28.1765i	−0.200317	+	1.39324i	0.603025	+	0.797722i	$0.293962\pi$
$409$	−4.05117	+	28.1765i	−0.200317	+	1.39324i	−0.803343	+	0.595517i	$0.796947\pi$
$410$	−11.5790	−	7.44136i	−0.571845	−	0.367503i
$411$	25.0868	−	28.9517i	1.23744	−	1.42808i
$412$	0.770619	+	0.226274i	0.0379657	+	0.0111477i
$413$	44.9045			2.20961
$414$	10.1952	−	32.1598i	0.501066	−	1.58057i
$415$	−9.76162			−0.479179
$416$	0.367332	+	0.107858i	0.0180099	+	0.00528820i
$417$	−8.27723	+	9.55243i	−0.405338	+	0.467785i
$418$	−4.95951	−	3.18729i	−0.242578	−	0.155895i
$419$	−4.94966	+	34.4256i	−0.241807	+	1.68180i	0.401239	+	0.915974i	$0.368580\pi$
$419$	−4.94966	+	34.4256i	−0.241807	+	1.68180i	−0.643045	+	0.765828i	$0.722329\pi$
$420$	−1.67423	+	1.07596i	−0.0816939	+	0.0525015i
$421$	−0.959260	−	2.10049i	−0.0467515	−	0.102371i	0.884815	−	0.465943i	$-0.154285\pi$
$421$	−0.959260	−	2.10049i	−0.0467515	−	0.102371i	−0.931566	+	0.363571i	$0.881557\pi$
$422$	−11.4820	−	13.2509i	−0.558933	−	0.645043i
$423$	−1.82696	−	12.7068i	−0.0888296	−	0.617824i
$424$	−5.96764	+	13.0673i	−0.289814	+	0.634604i
$425$	0.751734	−	0.220729i	0.0364645	−	0.0107069i
$426$	−15.7917	+	4.63688i	−0.765113	+	0.224657i
$427$	10.2668	−	22.4812i	0.496846	−	1.08794i
$428$	−0.230013	−	1.59977i	−0.0111181	−	0.0773279i
$429$	4.07574	+	4.70366i	0.196779	+	0.227095i
$430$	−1.71136	−	3.74735i	−0.0825289	−	0.180713i
$431$	1.15392	−	0.741577i	0.0555822	−	0.0357205i	−0.512555	−	0.858655i	$-0.671301\pi$
$431$	1.15392	−	0.741577i	0.0555822	−	0.0357205i	0.568137	+	0.822934i	$0.307664\pi$
$432$	3.25675	−	22.6512i	0.156691	−	1.08981i
$433$	30.5033	+	19.6033i	1.46589	+	0.942073i	0.998309	+	0.0581253i	$0.0185123\pi$
$433$	30.5033	+	19.6033i	1.46589	+	0.942073i	0.467585	+	0.883948i	$0.345124\pi$
$434$	10.9846	−	12.6769i	0.527278	−	0.608512i
$435$	0.427459	+	0.125513i	0.0204951	+	0.00601790i
$436$	1.71419			0.0820947
$437$	−2.79598	−	2.52946i	−0.133750	−	0.121001i
$438$	3.66057			0.174909
$439$	−6.64051	−	1.94983i	−0.316934	−	0.0930603i	0.119396	−	0.992847i	$-0.461904\pi$
$439$	−6.64051	−	1.94983i	−0.316934	−	0.0930603i	−0.436331	+	0.899786i	$0.643722\pi$
$440$	10.6725	−	12.3167i	0.508789	−	0.587174i
$441$	39.7140	+	25.5226i	1.89114	+	1.21536i
$442$	−0.0590154	+	0.410461i	−0.00280707	+	0.0195236i
$443$	−12.4645	+	8.01047i	−0.592208	+	0.380589i	−0.802148	−	0.597125i	$-0.796309\pi$
$443$	−12.4645	+	8.01047i	−0.592208	+	0.380589i	0.209940	+	0.977714i	$0.432673\pi$
$444$	−2.29758	−	5.03099i	−0.109038	−	0.238760i
$445$	5.26061	+	6.07106i	0.249377	+	0.287796i
$446$	3.78336	+	26.3139i	0.179147	+	1.24600i
$447$	3.90563	−	8.55213i	0.184730	−	0.404502i
$448$	−32.9552	+	9.67651i	−1.55699	+	0.457172i
$449$	34.8588	−	10.2355i	1.64509	−	0.483042i	0.677490	−	0.735532i	$-0.263068\pi$
$449$	34.8588	−	10.2355i	1.64509	−	0.483042i	0.967599	+	0.252490i	$0.0812495\pi$
$450$	−2.92231	+	6.39897i	−0.137759	+	0.301650i
$451$	8.04123	+	55.9280i	0.378647	+	2.63355i
$452$	−0.772399	−	0.891396i	−0.0363306	−	0.0419277i
$453$	−10.2737	−	22.4963i	−0.482702	−	1.05697i
$454$	−4.68905	+	3.01347i	−0.220068	+	0.141429i
$455$	−0.223418	+	1.55390i	−0.0104740	+	0.0728482i
$456$	−5.56466	−	3.57619i	−0.260589	−	0.167470i
$457$	2.67084	−	3.08231i	0.124937	−	0.144184i	−0.689835	−	0.723967i	$-0.742317\pi$
$457$	2.67084	−	3.08231i	0.124937	−	0.144184i	0.814771	+	0.579782i	$0.196862\pi$
$458$	−5.37745	−	1.57896i	−0.251272	−	0.0737800i
$459$	−4.94823			−0.230964
$460$	0.639683	−	0.530759i	0.0298254	−	0.0247468i
$461$	17.9865			0.837715			0.418858	−	0.908052i	$-0.362431\pi$
$461$	17.9865			0.837715			0.418858	+	0.908052i	$0.362431\pi$
$462$	−82.6185	−	24.2590i	−3.84376	−	1.12863i
$463$	−6.53624	+	7.54322i	−0.303765	+	0.350563i	−0.887024	−	0.461723i	$-0.847232\pi$
$463$	−6.53624	+	7.54322i	−0.303765	+	0.350563i	0.583260	+	0.812286i	$0.301777\pi$
$464$	0.474078	+	0.304672i	0.0220085	+	0.0141440i
$465$	−1.26207	+	8.77791i	−0.0585272	+	0.407066i
$466$	27.0565	−	17.3882i	1.25337	−	0.805491i
$467$	−5.76628	−	12.6264i	−0.266831	−	0.584279i	0.728028	−	0.685548i	$-0.240437\pi$
$467$	−5.76628	−	12.6264i	−0.266831	−	0.584279i	−0.994859	+	0.101268i	$0.967710\pi$
$468$	0.231348	+	0.266990i	0.0106941	+	0.0123416i
$469$	−3.52881	−	24.5434i	−0.162945	−	1.13331i
$470$	−1.38477	+	3.03223i	−0.0638748	+	0.139866i
$471$	16.4176	−	4.82066i	0.756485	−	0.222124i
$472$	−31.5704	+	9.26990i	−1.45314	+	0.426682i
$473$	−7.02537	+	15.3834i	−0.323027	+	0.707330i
$474$	−0.963646	−	6.70230i	−0.0442617	−	0.307847i
$475$	0.514836	+	0.594153i	0.0236223	+	0.0272616i
$476$	0.226128	+	0.495152i	0.0103646	+	0.0226953i
$477$	−21.4144	+	13.7622i	−0.980497	+	0.630127i
$478$	−0.860672	+	5.98610i	−0.0393662	+	0.273798i
$479$	−35.2789	−	22.6724i	−1.61193	−	1.03593i	−0.960906	−	0.276875i	$-0.910701\pi$
$479$	−35.2789	−	22.6724i	−1.61193	−	1.03593i	−0.651029	−	0.759053i	$-0.725662\pi$
$480$	1.83376	−	2.11627i	0.0836993	−	0.0965941i
$481$	−4.18610	−	1.22915i	−0.190870	−	0.0560444i
$482$	8.91028			0.405852
$483$	−49.5917	−	23.9429i	−2.25650	−	1.08944i
$484$	−3.42887			−0.155858
$485$	10.8302	+	3.18005i	0.491776	+	0.144399i
$486$	−10.4918	+	12.1081i	−0.475916	+	0.549236i
$487$	21.9252	+	14.0905i	0.993527	+	0.638501i	0.933079	−	0.359670i	$-0.117111\pi$
$487$	21.9252	+	14.0905i	0.993527	+	0.638501i	0.0604477	+	0.998171i	$0.480747\pi$
$488$	−2.57722	+	17.9250i	−0.116665	+	0.811426i
$489$	9.00133	−	5.78480i	0.407054	−	0.261598i
$490$	−5.09233	−	11.1507i	−0.230048	−	0.503735i
$491$	18.2415	+	21.0518i	0.823226	+	0.950053i	0.999411	−	0.0343035i	$-0.0109213\pi$
$491$	18.2415	+	21.0518i	0.823226	+	0.950053i	−0.176185	+	0.984357i	$0.556376\pi$
$492$	0.719520	+	5.00437i	0.0324384	+	0.225614i
$493$	0.0506198	−	0.110842i	0.00227980	−	0.00499207i
$494$	−0.399259	+	0.117233i	−0.0179635	+	0.00527456i
$495$	27.7086	−	8.13599i	1.24541	−	0.365686i
$496$	−4.66001	+	10.2040i	−0.209241	+	0.458173i
$497$	2.42536	+	16.8688i	0.108792	+	0.756668i
$498$	−24.7479	−	28.5606i	−1.10898	−	1.27983i
$499$	1.16697	+	2.55531i	0.0522408	+	0.114392i	0.933952	−	0.357397i	$-0.116336\pi$
$499$	1.16697	+	2.55531i	0.0522408	+	0.114392i	−0.881712	+	0.471789i	$0.843608\pi$
$500$	−0.145804	+	0.0937028i	−0.00652057	+	0.00419051i
$501$	3.12691	−	21.7481i	0.139700	−	0.971634i
$502$	0.684791	+	0.440088i	0.0305637	+	0.0196421i
$503$	9.13764	−	10.5454i	0.407427	−	0.470196i	−0.514539	−	0.857467i	$-0.672037\pi$
$503$	9.13764	−	10.5454i	0.407427	−	0.470196i	0.921966	+	0.387271i	$0.126582\pi$
$504$	−58.8053	−	17.2668i	−2.61940	−	0.769124i
$505$	16.6041			0.738871
$506$	35.4793	+	5.87842i	1.57725	+	0.261328i
$507$	−36.7982			−1.63426
$508$	3.38497	+	0.993916i	0.150184	+	0.0440979i
$509$	19.7362	−	22.7768i	0.874791	−	1.00956i	−0.125057	−	0.992150i	$-0.539911\pi$
$509$	19.7362	−	22.7768i	0.874791	−	1.00956i	0.999848	−	0.0174134i	$-0.00554314\pi$
$510$	2.55163	+	1.63983i	0.112988	+	0.0726131i
$511$	0.539433	−	3.75184i	0.0238631	−	0.165972i
$512$	20.8867	−	13.4230i	0.923069	−	0.593220i
$513$	−2.06267	−	4.51661i	−0.0910691	−	0.199413i
$514$	−9.16375	−	10.5755i	−0.404195	−	0.466466i
$515$	−0.659484	−	4.58682i	−0.0290604	−	0.202119i
$516$	−0.628621	+	1.37649i	−0.0276735	+	0.0605965i
$517$	13.1301	−	3.85534i	0.577460	−	0.169558i
$518$	57.9145	−	17.0052i	2.54462	−	0.747167i
$519$	18.7711	−	41.1029i	0.823959	−	1.80422i
$520$	−0.163706	−	1.13860i	−0.00717900	−	0.0499310i
$521$	5.63542	+	6.50362i	0.246892	+	0.284929i	0.865646	−	0.500656i	$-0.166908\pi$
$521$	5.63542	+	6.50362i	0.246892	+	0.284929i	−0.618754	+	0.785585i	$0.712362\pi$
$522$	0.454509	+	0.995236i	0.0198933	+	0.0435603i
$523$	22.7486	−	14.6196i	0.994726	−	0.639272i	0.0613296	−	0.998118i	$-0.480466\pi$
$523$	22.7486	−	14.6196i	0.994726	−	0.639272i	0.933397	+	0.358846i	$0.116830\pi$
$524$	0.227812	−	1.58447i	0.00995202	−	0.0692178i
$525$	9.65985	+	6.20801i	0.421591	+	0.270940i
$526$	15.7523	−	18.1792i	0.686834	−	0.792649i
$527$	2.32735	+	0.683372i	0.101381	+	0.0297682i
$528$	57.5844			2.50604
$529$	21.7710	+	7.41792i	0.946563	+	0.322518i
$530$	6.60993			0.287117
$531$	−55.9420	−	16.4261i	−2.42768	−	0.712830i
$532$	−0.357701	+	0.412808i	−0.0155083	+	0.0178975i
$533$	3.35506	+	2.15616i	0.145324	+	0.0933938i
$534$	−4.42594	+	30.7831i	−0.191529	+	1.33211i
$535$	−7.84485	+	5.04158i	−0.339162	+	0.217966i
$536$	7.54758	+	16.5269i	0.326006	+	0.713853i
$537$	25.0810	+	28.9450i	1.08232	+	1.24907i
$538$	1.13840	+	7.91777i	0.0490800	+	0.341359i
$539$	−20.9048	+	45.7751i	−0.900433	+	1.97167i
$540$	1.05030	−	0.308395i	0.0451976	−	0.0132712i
$541$	−37.0589	+	10.8815i	−1.59329	+	0.467831i	−0.953668	−	0.300862i	$-0.902726\pi$
$541$	−37.0589	+	10.8815i	−1.59329	+	0.467831i	−0.639618	+	0.768693i	$0.720907\pi$
$542$	−0.116398	+	0.254877i	−0.00499974	+	0.0109479i
$543$	−0.282470	−	1.96462i	−0.0121219	−	0.0843100i
$544$	−0.501566	−	0.578838i	−0.0215045	−	0.0248175i
$545$	−4.10863	−	8.99664i	−0.175994	−	0.385374i
$546$	−5.11285	+	3.28583i	−0.218810	+	0.140620i
$547$	1.30597	−	9.08325i	0.0558395	−	0.388372i	−0.942667	−	0.333735i	$-0.891691\pi$
$547$	1.30597	−	9.08325i	0.0558395	−	0.388372i	0.998506	−	0.0546367i	$-0.0174001\pi$
$548$	1.94998	+	1.25317i	0.0832989	+	0.0535329i
$549$	−21.0140	+	24.2515i	−0.896856	+	1.03503i
$550$	−7.19505	−	2.11266i	−0.306798	−	0.0900840i
$551$	0.122275			0.00520907
$552$	39.8084	+	6.59569i	1.69436	+	0.280731i
$553$	−7.01142			−0.298156
$554$	32.2677	+	9.47466i	1.37092	+	0.402540i
$555$	−20.8974	+	24.1169i	−0.887047	+	1.02371i
$556$	−0.643383	−	0.413477i	−0.0272855	−	0.0175353i
$557$	−5.05484	+	35.1572i	−0.214180	+	1.48966i	0.544812	+	0.838558i	$0.316601\pi$
$557$	−5.05484	+	35.1572i	−0.214180	+	1.48966i	−0.758992	+	0.651099i	$0.774308\pi$
$558$	−18.3218	+	11.7747i	−0.775625	+	0.498464i
$559$	0.495872	+	1.08581i	0.0209731	+	0.0459248i
$560$	9.51181	+	10.9772i	0.401947	+	0.463872i
$561$	−1.77203	−	12.3247i	−0.0748150	−	0.520350i
$562$	4.01105	−	8.78298i	0.169196	−	0.370488i
$563$	5.69658	−	1.67267i	0.240082	−	0.0704945i	−0.159478	−	0.987202i	$-0.550981\pi$
$563$	5.69658	−	1.67267i	0.240082	−	0.0704945i	0.399560	+	0.916707i	$0.369163\pi$
$564$	1.17486	−	0.344971i	0.0494706	−	0.0145259i
$565$	−2.82704	+	6.19035i	−0.118934	+	0.260430i
$566$	−6.07467	−	42.2503i	−0.255337	−	1.77591i
$567$	−6.50078	−	7.50230i	−0.273007	−	0.315067i
$568$	−5.18749	−	11.3590i	−0.217662	−	0.476614i
$569$	−6.75930	+	4.34394i	−0.283365	+	0.182107i	−0.674600	−	0.738183i	$-0.735684\pi$
$569$	−6.75930	+	4.34394i	−0.283365	+	0.182107i	0.391236	+	0.920290i	$0.372048\pi$
$570$	−0.433150	+	3.01263i	−0.0181427	+	0.126185i
$571$	14.8771	+	9.56094i	0.622588	+	0.400113i	0.813559	−	0.581483i	$-0.197527\pi$
$571$	14.8771	+	9.56094i	0.622588	+	0.400113i	−0.190971	+	0.981596i	$0.561164\pi$
$572$	−0.246612	+	0.284605i	−0.0103114	+	0.0118999i
$573$	−28.9382	−	8.49703i	−1.20891	−	0.354969i
$574$	−55.1760			−2.30300
$575$	−4.31882	−	2.08513i	−0.180107	−	0.0869559i
$576$	44.5952			1.85813
$577$	15.7550	+	4.62608i	0.655888	+	0.192586i	0.592710	−	0.805416i	$-0.298058\pi$
$577$	15.7550	+	4.62608i	0.655888	+	0.192586i	0.0631785	+	0.998002i	$0.479876\pi$
$578$	−14.5030	+	16.7374i	−0.603245	+	0.696182i
$579$	−36.1999	−	23.2643i	−1.50442	−	0.966830i
$580$	−0.00383627	+	0.0266819i	−0.000159293	+	0.00110790i
$581$	−32.9197	+	21.1562i	−1.36574	+	0.877707i
$582$	18.1529	+	39.7494i	0.752464	+	1.64767i
$583$	−17.7695	−	20.5071i	−0.735937	−	0.849317i
$584$	0.395262	+	2.74911i	0.0163561	+	0.113759i
$585$	0.846751	−	1.85413i	0.0350089	−	0.0766587i
$586$	−13.6536	+	4.00906i	−0.564026	+	0.165613i
$587$	−11.3549	+	3.33411i	−0.468668	+	0.137613i	−0.507535	−	0.861631i	$-0.669443\pi$
$587$	−11.3549	+	3.33411i	−0.468668	+	0.137613i	0.0388670	+	0.999244i	$0.487625\pi$
$588$	−1.87053	+	4.09590i	−0.0771396	+	0.168912i
$589$	0.346392	+	2.40921i	0.0142728	+	0.0992698i
$590$	9.91434	+	11.4418i	0.408167	+	0.471050i
$591$	−13.0652	−	28.6089i	−0.537432	−	1.17681i
$592$	−33.9579	+	21.8234i	−1.39566	+	0.896938i
$593$	−3.02783	+	21.0590i	−0.124338	+	0.864789i	0.828214	+	0.560412i	$0.189357\pi$
$593$	−3.02783	+	21.0590i	−0.124338	+	0.864789i	−0.952552	+	0.304377i	$0.901552\pi$
$594$	39.8424	+	25.6052i	1.63476	+	1.05059i
$595$	2.05674	−	2.37360i	0.0843179	−	0.0973081i
$596$	0.545830	+	0.160270i	0.0223581	+	0.00656492i
$597$	−30.5645			−1.25092
$598$	1.95350	−	1.62086i	0.0798845	−	0.0662820i
$599$	−20.8310			−0.851130			−0.425565	−	0.904928i	$-0.639925\pi$
$599$	−20.8310			−0.851130			−0.425565	+	0.904928i	$0.639925\pi$
$600$	−8.07297	−	2.37044i	−0.329578	−	0.0967727i
$601$	−10.9779	+	12.6692i	−0.447797	+	0.516786i	−0.934103	−	0.357003i	$-0.883799\pi$
$601$	−10.9779	+	12.6692i	−0.447797	+	0.516786i	0.486306	+	0.873789i	$0.338344\pi$
$602$	−13.8929	−	8.92840i	−0.566231	−	0.363894i
$603$	−4.58178	+	31.8670i	−0.186584	+	1.29772i
$604$	1.25887	−	0.809024i	0.0512225	−	0.0329187i
$605$	8.21845	+	17.9959i	0.334127	+	0.731637i
$606$	42.0951	+	48.5803i	1.71000	+	1.97344i
$607$	5.69449	+	39.6060i	0.231132	+	1.60756i	0.693220	+	0.720726i	$0.256191\pi$
$607$	5.69449	+	39.6060i	0.231132	+	1.60756i	−0.462088	+	0.886834i	$0.652900\pi$
$608$	0.319271	−	0.699105i	0.0129481	−	0.0283525i
$609$	1.71357	−	0.503149i	0.0694373	−	0.0203886i
$610$	7.99503	−	2.34755i	0.323709	−	0.0950497i
$611$	0.401243	−	0.878600i	0.0162326	−	0.0355444i
$612$	−0.100584	−	0.699578i	−0.00406587	−	0.0282788i
$613$	10.4758	+	12.0897i	0.423113	+	0.488299i	0.926783	−	0.375598i	$-0.122563\pi$
$613$	10.4758	+	12.0897i	0.423113	+	0.488299i	−0.503670	+	0.863896i	$0.668017\pi$
$614$	6.64092	+	14.5416i	0.268006	+	0.586851i
$615$	24.5401	−	15.7709i	0.989551	−	0.635946i
$616$	9.29763	−	64.6664i	0.374612	−	2.60548i
$617$	−12.0807	−	7.76379i	−0.486350	−	0.312558i	0.274386	−	0.961620i	$-0.411525\pi$
$617$	−12.0807	−	7.76379i	−0.486350	−	0.312558i	−0.760736	+	0.649061i	$0.775162\pi$
$618$	11.7482	−	13.5582i	0.472582	−	0.545389i
$619$	−1.66030	−	0.487507i	−0.0667329	−	0.0195946i	0.248196	−	0.968710i	$-0.420162\pi$
$619$	−1.66030	−	0.487507i	−0.0667329	−	0.0195946i	−0.314929	+	0.949115i	$0.601981\pi$
$620$	−0.536588			−0.0215499
$621$	22.4616	+	20.3205i	0.901355	+	0.815435i
$622$	−28.6679			−1.14948
$623$	30.8984	+	9.07258i	1.23792	+	0.363485i
$624$	2.66167	−	3.07173i	0.106552	−	0.122968i
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$	3.89798	−	27.1111i	0.155795	−	1.08358i
$627$	10.5110	−	6.75502i	0.419769	−	0.269769i
$628$	0.430089	+	0.941763i	0.0171624	+	0.0375804i
$629$	5.71582	+	6.59641i	0.227905	+	0.263016i
$630$	4.01330	+	27.9131i	0.159894	+	1.11208i
$631$	−19.3443	+	42.3580i	−0.770083	+	1.68625i	−0.0436138	+	0.999048i	$0.513887\pi$
$631$	−19.3443	+	42.3580i	−0.770083	+	1.68625i	−0.726469	+	0.687199i	$0.758840\pi$
$632$	4.92942	−	1.44741i	0.196082	−	0.0575748i
$633$	35.6545	−	10.4691i	1.41714	−	0.416110i
$634$	1.81593	−	3.97633i	0.0721198	−	0.157920i
$635$	−2.89681	−	20.1477i	−0.114956	−	0.799538i
$636$	−1.58999	−	1.83495i	−0.0630473	−	0.0727604i
$637$	1.47552	+	3.23095i	0.0584624	+	0.128015i
$638$	−0.981149	+	0.630546i	−0.0388440	+	0.0249636i
$639$	3.14908	−	21.9023i	0.124576	−	0.866442i
$640$	−8.09686	−	5.20354i	−0.320057	−	0.205688i
$641$	9.11771	−	10.5224i	0.360128	−	0.415610i	−0.546555	−	0.837423i	$-0.684061\pi$
$641$	9.11771	−	10.5224i	0.360128	−	0.415610i	0.906683	+	0.421814i	$0.138606\pi$
$642$	−34.6392	−	10.1710i	−1.36710	−	0.401417i
$643$	−10.7589			−0.424290			−0.212145	−	0.977238i	$-0.568045\pi$
$643$	−10.7589			−0.424290			−0.212145	+	0.977238i	$0.568045\pi$
$644$	1.00693	−	3.17628i	0.0396787	−	0.125163i
$645$	8.73099			0.343782
$646$	0.798760	+	0.234537i	0.0314268	+	0.00922774i
$647$	8.03858	−	9.27701i	0.316029	−	0.364717i	−0.575404	−	0.817869i	$-0.695155\pi$
$647$	8.03858	−	9.27701i	0.316029	−	0.364717i	0.891433	+	0.453152i	$0.149701\pi$
$648$	6.11915	+	3.93254i	0.240383	+	0.154485i
$649$	8.84492	−	61.5178i	0.347194	−	2.41478i
$650$	−0.445266	+	0.286155i	−0.0174648	+	0.0112239i
$651$	14.7681	+	32.3375i	0.578806	+	1.26741i
$652$	0.423970	+	0.489288i	0.0166040	+	0.0191620i
$653$	2.63266	+	18.3106i	0.103024	+	0.716547i	0.974218	+	0.225609i	$0.0724370\pi$
$653$	2.63266	+	18.3106i	0.103024	+	0.716547i	−0.871194	+	0.490939i	$0.836654\pi$
$654$	15.9062	−	34.8296i	0.621980	−	1.36195i
$655$	−8.86186	+	2.60208i	−0.346262	+	0.101672i
$656$	35.4047	−	10.3958i	1.38232	−	0.405886i
$657$	−2.04445	+	4.47671i	−0.0797615	+	0.174653i
$658$	1.90175	+	13.2270i	0.0741379	+	0.515641i
$659$	−7.29390	−	8.41761i	−0.284130	−	0.327904i	0.595686	−	0.803217i	$-0.296880\pi$
$659$	−7.29390	−	8.41761i	−0.284130	−	0.327904i	−0.879817	+	0.475313i	$0.842335\pi$
$660$	1.14426	+	2.50557i	0.0445401	+	0.0975292i
$661$	−7.18835	+	4.61967i	−0.279594	+	0.179684i	−0.672921	−	0.739714i	$-0.734961\pi$
$661$	−7.18835	+	4.61967i	−0.279594	+	0.179684i	0.393327	+	0.919399i	$0.371324\pi$
$662$	2.28035	−	15.8602i	0.0886284	−	0.616424i
$663$	−0.739345	−	0.475148i	−0.0287138	−	0.0184532i
$664$	18.7770	−	21.6698i	0.728688	−	0.840951i
$665$	3.02391	+	0.887900i	0.117262	+	0.0344313i
$666$	−78.3703			−3.03679
$667$	−0.684967	+	0.295272i	−0.0265220	+	0.0114330i
$668$	1.32945			0.0514379
$669$	−54.0598	−	15.8734i	−2.09007	−	0.613701i
$670$	5.47459	−	6.31801i	0.211502	−	0.244086i
$671$	−28.7763	−	18.4934i	−1.11090	−	0.713929i
$672$	1.59753	−	11.1111i	0.0616262	−	0.428620i
$673$	−26.8906	+	17.2816i	−1.03656	+	0.666155i	−0.944133	−	0.329565i	$-0.893098\pi$
$673$	−26.8906	+	17.2816i	−1.03656	+	0.666155i	−0.0924246	+	0.995720i	$0.529462\pi$
$674$	−13.1836	−	28.8680i	−0.507812	−	1.11195i
$675$	−4.13596	−	4.77315i	−0.159193	−	0.183719i
$676$	−0.316872	−	2.20389i	−0.0121874	−	0.0847650i
$677$	2.90796	−	6.36755i	0.111762	−	0.244725i	−0.845483	−	0.534002i	$-0.820688\pi$
$677$	2.90796	−	6.36755i	0.111762	−	0.244725i	0.957245	+	0.289277i	$0.0934148\pi$
$678$	−25.2790	+	7.42257i	−0.970833	+	0.285062i
$679$	43.4155	−	12.7480i	1.66614	−	0.489222i
$680$	−0.956004	+	2.09336i	−0.0366611	+	0.0802765i
$681$	−1.68118	−	11.6928i	−0.0644228	−	0.448070i
$682$	−15.2033	−	17.5456i	−0.582165	−	0.671854i
$683$	−7.21415	−	15.7968i	−0.276042	−	0.604447i	0.719937	−	0.694040i	$-0.244171\pi$
$683$	−7.21415	−	15.7968i	−0.276042	−	0.604447i	−0.995979	+	0.0895924i	$0.971444\pi$
$684$	0.596628	−	0.383430i	0.0228126	−	0.0146608i
$685$	1.90331	−	13.2378i	0.0727217	−	0.505790i
$686$	−9.43448	−	6.06317i	−0.360210	−	0.231493i
$687$	7.77837	−	8.97672i	0.296763	−	0.342483i
$688$	10.5968	+	3.11151i	0.404000	+	0.118625i
$689$	−1.91525			−0.0729653
$690$	−4.84851	−	17.9223i	−0.184580	−	0.682292i
$691$	43.5450			1.65653			0.828265	−	0.560336i	$-0.189328\pi$
$691$	43.5450			1.65653			0.828265	+	0.560336i	$0.189328\pi$
$692$	2.62335	+	0.770284i	0.0997246	+	0.0292818i
$693$	75.8105	−	87.4899i	2.87980	−	3.32347i
$694$	33.8987	+	21.7853i	1.28678	+	0.826961i
$695$	−0.627985	+	4.36773i	−0.0238208	+	0.165678i
$696$	−1.10087	+	0.707484i	−0.0417282	+	0.0268171i
$697$	−3.31449	−	7.25772i	−0.125545	−	0.274906i
$698$	−16.7878	−	19.3742i	−0.635428	−	0.733323i
$699$	9.70064	+	67.4694i	0.366912	+	2.55193i
$700$	−0.288624	+	0.631999i	−0.0109090	+	0.0238873i
$701$	−6.45899	+	1.89653i	−0.243953	+	0.0716309i	−0.401423	−	0.915893i	$-0.631484\pi$
$701$	−6.45899	+	1.89653i	−0.243953	+	0.0716309i	0.157470	+	0.987524i	$0.449666\pi$
$702$	3.20746	−	0.941795i	0.121058	−	0.0355458i
$703$	−3.63839	+	7.96697i	−0.137225	+	0.300480i
$704$	6.76528	+	47.0535i	0.254976	+	1.77340i
$705$	−4.62648	−	5.33924i	−0.174243	−	0.201087i
$706$	2.91754	+	6.38852i	0.109803	+	0.240435i
$707$	55.9948	−	35.9857i	2.10590	−	1.35338i
$708$	0.791433	−	5.50454i	0.0297439	−	0.206873i
$709$	37.1903	+	23.9008i	1.39671	+	0.897613i	0.999795	−	0.0202418i	$-0.00644359\pi$
$709$	37.1903	+	23.9008i	1.39671	+	0.897613i	0.396917	+	0.917854i	$0.370080\pi$
$710$	−3.76271	+	4.34240i	−0.141212	+	0.162967i
$711$	8.73481	+	2.56477i	0.327581	+	0.0961865i
$712$	−23.5962			−0.884304
$713$	−7.75826	−	12.6596i	−0.290549	−	0.474106i
$714$	12.1590			0.455039
$715$	2.08479	+	0.612150i	0.0779668	+	0.0228931i
$716$	−1.51758	+	1.75138i	−0.0567146	+	0.0654521i
$717$	−10.7825	−	6.92949i	−0.402680	−	0.258787i
$718$	−1.53226	+	10.6571i	−0.0571836	+	0.397720i
$719$	−24.8887	+	15.9950i	−0.928190	+	0.596512i	−0.915023	−	0.403402i	$-0.867828\pi$
$719$	−24.8887	+	15.9950i	−0.928190	+	0.596512i	−0.0131673	+	0.999913i	$0.504191\pi$
$720$	−7.83434	−	17.1548i	−0.291969	−	0.639322i
$721$	−12.1649	−	14.0391i	−0.453046	−	0.522843i
$722$	−3.53568	−	24.5912i	−0.131584	−	0.915189i
$723$	−7.84475	+	17.1776i	−0.291749	+	0.638842i
$724$	0.115231	−	0.0338350i	0.00428254	−	0.00125747i
$725$	0.149231	−	0.0438180i	0.00554228	−	0.00162736i
$726$	−31.8169	+	69.6693i	−1.18084	+	2.58567i
$727$	−5.57428	−	38.7700i	−0.206739	−	1.43790i	−0.783706	−	0.621132i	$-0.786673\pi$
$727$	−5.57428	−	38.7700i	−0.206739	−	1.43790i	0.576967	−	0.816767i	$-0.304236\pi$
$728$	−3.01975	−	3.48498i	−0.111919	−	0.129162i
$729$	−17.1916	−	37.6443i	−0.636725	−	1.39423i
$730$	1.07508	−	0.690909i	0.0397903	−	0.0255717i
$731$	0.339859	−	2.36377i	0.0125702	−	0.0874274i
$732$	−2.57486	−	1.65476i	−0.0951697	−	0.0611619i
$733$	1.87903	−	2.16851i	0.0694034	−	0.0800958i	−0.719986	−	0.693989i	$-0.755852\pi$
$733$	1.87903	−	2.16851i	0.0694034	−	0.0800958i	0.789389	+	0.613893i	$0.210397\pi$
$734$	−2.66357	−	0.782094i	−0.0983140	−	0.0288676i
$735$	25.9801			0.958289
$736$	−0.100298	+	4.68728i	−0.00369702	+	0.172775i
$737$	−34.3187			−1.26415
$738$	68.7382	+	20.1834i	2.53029	+	0.742960i
$739$	0.260821	−	0.301003i	0.00959445	−	0.0110726i	−0.750932	−	0.660379i	$-0.770395\pi$
$739$	0.260821	−	0.301003i	0.00959445	−	0.0110726i	0.760527	+	0.649307i	$0.224941\pi$
$740$	−1.62434	−	1.04390i	−0.0597120	−	0.0383746i
$741$	0.125507	−	0.872920i	0.00461062	−	0.0320675i
$742$	22.2911	−	14.3256i	0.818331	−	0.525909i
$743$	−14.0856	−	30.8433i	−0.516752	−	1.13153i	−0.970655	−	0.240478i	$-0.922696\pi$
$743$	−14.0856	−	30.8433i	−0.516752	−	1.13153i	0.453902	−	0.891051i	$-0.350032\pi$
$744$	−17.0584	−	19.6864i	−0.625391	−	0.721740i
$745$	−0.467113	−	3.24884i	−0.0171137	−	0.119028i
$746$	17.4762	−	38.2675i	0.639848	−	1.40107i
$747$	48.7502	−	14.3144i	1.78368	−	0.523735i
$748$	0.722884	−	0.212258i	0.0264312	−	0.00776091i
$749$	−15.5291	+	34.0040i	−0.567422	+	1.24248i
$750$	0.550958	+	3.83200i	0.0201181	+	0.139925i
$751$	10.4367	+	12.0445i	0.380839	+	0.439512i	0.913513	−	0.406809i	$-0.133358\pi$
$751$	10.4367	+	12.0445i	0.380839	+	0.439512i	−0.532674	+	0.846320i	$0.678813\pi$
$752$	−3.71240	−	8.12901i	−0.135377	−	0.296435i
$753$	−1.45132	+	0.932707i	−0.0528891	+	0.0339897i
$754$	−0.0117154	+	0.0814826i	−0.000426651	+	0.00296742i
$755$	−7.26333	−	4.66786i	−0.264340	−	0.169881i
$756$	2.87360	−	3.31631i	0.104512	−	0.120613i
$757$	−23.4079	−	6.87318i	−0.850774	−	0.249810i	−0.172856	−	0.984947i	$-0.555300\pi$
$757$	−23.4079	−	6.87318i	−0.850774	−	0.249810i	−0.677918	+	0.735137i	$0.737118\pi$
$758$	−20.5475			−0.746319
$759$	−42.5692	+	63.2230i	−1.54516	+	2.29485i
$760$	−2.30927			−0.0837661
$761$	−24.3751	−	7.15717i	−0.883597	−	0.259447i	−0.191708	−	0.981452i	$-0.561403\pi$
$761$	−24.3751	−	7.15717i	−0.883597	−	0.259447i	−0.691888	+	0.722005i	$0.743221\pi$
$762$	51.6044	−	59.5546i	1.86943	−	2.15744i
$763$	−33.3540	−	21.4353i	−1.20750	−	0.776012i
$764$	0.259709	−	1.80632i	0.00939594	−	0.0653502i
$765$	−3.43054	+	2.20467i	−0.124031	+	0.0797102i
$766$	−14.7669	−	32.3351i	−0.533551	−	1.16831i
$767$	−2.87272	−	3.31529i	−0.103728	−	0.119708i
$768$	1.68257	+	11.7025i	0.0607145	+	0.422279i
$769$	−3.36533	+	7.36905i	−0.121357	+	0.265735i	−0.960554	−	0.278092i	$-0.910298\pi$
$769$	−3.36533	+	7.36905i	−0.121357	+	0.265735i	0.839197	+	0.543827i	$0.183025\pi$
$770$	−28.8430	+	8.46907i	−1.03943	+	0.305204i
$771$	28.4558	−	8.35538i	1.02481	−	0.300912i
$772$	1.08161	−	2.36839i	0.0389279	−	0.0852401i
$773$	0.694449	+	4.83000i	0.0249776	+	0.173723i	0.998492	−	0.0549043i	$-0.0174854\pi$
$773$	0.694449	+	4.83000i	0.0249776	+	0.173723i	−0.973514	+	0.228627i	$0.926576\pi$
$774$	14.0417	+	16.2050i	0.504719	+	0.582477i
$775$	1.28611	+	2.81620i	0.0461986	+	0.101161i
$776$	−27.8919	+	17.9250i	−1.00126	+	0.643472i
$777$	−18.2054	+	126.622i	−0.653116	+	4.54252i
$778$	34.4524	+	22.1412i	1.23518	+	0.793800i
$779$	5.24302	−	6.05076i	0.187851	−	0.216791i
$780$	0.186545	+	0.0547745i	0.00667937	+	0.00196124i
$781$	23.5874			0.844024
$782$	−5.04092	+	0.615018i	−0.180263	+	0.0219930i
$783$	−0.982298			−0.0351044
$784$	31.5321	+	9.25865i	1.12614	+	0.330666i
$785$	3.91184	−	4.51450i	0.139620	−	0.161130i
$786$	−30.0800	−	19.3313i	−1.07292	−	0.689523i
$787$	−2.46558	+	17.1485i	−0.0878883	+	0.611277i	0.897508	+	0.440999i	$0.145376\pi$
$787$	−2.46558	+	17.1485i	−0.0878883	+	0.611277i	−0.985396	+	0.170278i	$0.945533\pi$
$788$	1.60092	−	1.02885i	0.0570302	−	0.0366511i
$789$	21.1779	+	46.3732i	0.753954	+	1.65093i
$790$	−1.54803	−	1.78652i	−0.0550764	−	0.0635616i
$791$	3.88245	+	27.0031i	0.138044	+	0.960118i
$792$	−35.2379	+	77.1603i	−1.25213	+	2.74177i
$793$	−2.31659	+	0.680213i	−0.0822646	+	0.0241551i
$794$	−29.8851	+	8.77504i	−1.06058	+	0.311415i
$795$	−5.81949	+	12.7429i	−0.206396	+	0.451944i
$796$	−0.263193	−	1.83055i	−0.00932864	−	0.0648821i
$797$	8.45287	+	9.75513i	0.299416	+	0.345544i	0.885444	−	0.464746i	$-0.153855\pi$
$797$	8.45287	+	9.75513i	0.299416	+	0.345544i	−0.586028	+	0.810291i	$0.699309\pi$
$798$	5.06848	+	11.0984i	0.179422	+	0.392880i
$799$	−1.62560	+	1.04471i	−0.0575097	+	0.0369592i
$800$	0.139125	−	0.967639i	0.00491883	−	0.0342112i
$801$	−35.1744	−	22.6052i	−1.24283	−	0.798716i
$802$	14.8862	−	17.1796i	0.525651	−	0.606633i
$803$	−5.03365	−	1.47801i	−0.177634	−	0.0521579i
$804$	−3.07080			−0.108299
$805$	−19.0837	+	2.32831i	−0.672612	+	0.0820620i
$806$	−1.63866			−0.0577194
$807$	−16.2665	−	4.77626i	−0.572607	−	0.168132i
$808$	−31.9387	+	36.8593i	−1.12360	+	1.29670i
$809$	14.2175	+	9.13700i	0.499859	+	0.321240i	0.766160	−	0.642650i	$-0.222165\pi$
$809$	14.2175	+	9.13700i	0.499859	+	0.321240i	−0.266301	+	0.963890i	$0.585801\pi$
$810$	0.476312	−	3.31282i	0.0167359	−	0.116401i
$811$	−0.486021	+	0.312347i	−0.0170665	+	0.0109680i	−0.549146	−	0.835726i	$-0.685047\pi$
$811$	−0.486021	+	0.312347i	−0.0170665	+	0.0109680i	0.532080	+	0.846694i	$0.321411\pi$
$812$	0.0448899	+	0.0982951i	0.00157533	+	0.00344948i
$813$	−0.388883	−	0.448795i	−0.0136387	−	0.0157399i
$814$	−11.8891	−	82.6906i	−0.416713	−	2.89830i
$815$	1.55176	−	3.39789i	0.0543559	−	0.119023i
$816$	−7.80205	+	2.29089i	−0.273126	+	0.0801971i
$817$	2.29926	−	0.675124i	0.0804410	−	0.0236196i
$818$	−15.9825	+	34.9967i	−0.558814	+	1.22363i
$819$	−1.16287	−	8.08793i	−0.0406339	−	0.282615i
$820$	1.15586	+	1.33393i	0.0403643	+	0.0465829i
$821$	7.11468	+	15.5790i	0.248304	+	0.543710i	0.992210	−	0.124574i	$-0.0397564\pi$
$821$	7.11468	+	15.5790i	0.248304	+	0.543710i	−0.743906	+	0.668284i	$0.767029\pi$
$822$	43.5566	−	27.9921i	1.51921	−	0.976338i
$823$	5.56514	−	38.7064i	0.193988	−	1.34922i	−0.627332	−	0.778752i	$-0.715853\pi$
$823$	5.56514	−	38.7064i	0.193988	−	1.34922i	0.821320	−	0.570467i	$-0.193238\pi$
$824$	11.4508	+	7.35899i	0.398908	+	0.256362i
$825$	10.4075	−	12.0109i	0.362342	−	0.418166i
$826$	58.2322	+	17.0985i	2.02616	+	0.594934i
$827$	14.9859			0.521112			0.260556	−	0.965459i	$-0.416094\pi$
$827$	14.9859			0.521112			0.260556	+	0.965459i	$0.416094\pi$
$828$	−2.41632	+	3.58868i	−0.0839729	+	0.124715i
$829$	−9.72987			−0.337932			−0.168966	−	0.985622i	$-0.554043\pi$
$829$	−9.72987			−0.337932			−0.168966	+	0.985622i	$0.554043\pi$
$830$	−12.6589	−	3.71698i	−0.439396	−	0.129018i
$831$	−46.6746	+	53.8654i	−1.61913	+	1.86857i
$832$	2.82269	+	1.81403i	0.0978590	+	0.0628902i
$833$	1.01129	−	7.03368i	0.0350392	−	0.243703i
$834$	−14.3712	+	9.23584i	−0.497635	+	0.319811i
$835$	−3.18647	−	6.97740i	−0.110272	−	0.241463i
$836$	0.495078	+	0.571350i	0.0171226	+	0.0197605i
$837$	−2.78275	−	19.3545i	−0.0961860	−	0.668989i
$838$	−19.5271	+	42.7585i	−0.674554	+	1.47707i
$839$	48.3010	−	14.1825i	1.66754	−	0.489633i	0.694347	−	0.719640i	$-0.255693\pi$
$839$	48.3010	−	14.1825i	1.66754	−	0.489633i	0.973189	+	0.230008i	$0.0738751\pi$
$840$	−32.3624	+	9.50245i	−1.11661	+	0.327866i
$841$	−12.0370	+	26.3573i	−0.415069	+	0.908873i
$842$	−0.444156	−	3.08917i	−0.0153066	−	0.106460i
$843$	13.4008	+	15.4653i	0.461548	+	0.532654i
$844$	0.934031	+	2.04524i	0.0321507	+	0.0704002i
$845$	−10.8073	+	6.94542i	−0.371782	+	0.238930i
$846$	2.46922	−	17.1738i	0.0848935	−	0.590447i
$847$	66.7177	+	42.8769i	2.29245	+	1.47327i
$848$	−11.6044	+	13.3922i	−0.398496	+	0.459889i
$849$	86.8000	+	25.4868i	2.97897	+	0.874704i
$850$	1.05890			0.0363199
$851$	1.14299	−	53.4160i	0.0391811	−	1.83108i
$852$	2.11057			0.0723071
$853$	−21.0140	−	6.17027i	−0.719506	−	0.211266i	−0.0985730	−	0.995130i	$-0.531428\pi$
$853$	−21.0140	−	6.17027i	−0.719506	−	0.211266i	−0.620933	+	0.783864i	$0.713246\pi$
$854$	21.8743	−	25.2443i	0.748523	−	0.863842i
$855$	−3.44239	−	2.21229i	−0.117727	−	0.0756587i
$856$	3.89819	−	27.1125i	0.133237	−	0.926686i
$857$	24.5280	−	15.7632i	0.837860	−	0.538460i	−0.0499064	−	0.998754i	$-0.515892\pi$
$857$	24.5280	−	15.7632i	0.837860	−	0.538460i	0.887767	+	0.460294i	$0.152256\pi$
$858$	3.49439	+	7.65165i	0.119297	+	0.261223i
$859$	32.9164	+	37.9876i	1.12309	+	1.29612i	0.950360	+	0.311152i	$0.100715\pi$
$859$	32.9164	+	37.9876i	1.12309	+	1.29612i	0.172734	+	0.984968i	$0.444740\pi$
$860$	0.0751831	+	0.522910i	0.00256372	+	0.0178311i
$861$	48.5778	−	106.371i	1.65553	−	3.62510i
$862$	1.77877	−	0.522295i	0.0605853	−	0.0177895i
$863$	−44.7220	+	13.1316i	−1.52236	+	0.447004i	−0.932701	−	0.360651i	$-0.882554\pi$
$863$	−44.7220	+	13.1316i	−1.52236	+	0.447004i	−0.589655	+	0.807655i	$0.700736\pi$
$864$	−2.56487	+	5.61629i	−0.0872587	+	0.191070i
$865$	−2.24502	−	15.6145i	−0.0763330	−	0.530908i
$866$	32.0923	+	37.0364i	1.09054	+	1.25855i
$867$	−19.4983	−	42.6953i	−0.662197	−	1.45001i
$868$	−1.80957	+	1.16294i	−0.0614207	+	0.0394727i
$869$	−1.38105	+	9.60542i	−0.0468489	+	0.325841i
$870$	0.506537	+	0.325532i	0.0171732	+	0.0110366i
$871$	−1.58628	+	1.83067i	−0.0537491	+	0.0620298i
$872$	27.8748	+	8.18477i	0.943959	+	0.277171i
$873$	−58.7502			−1.98839
$874$	−2.66268	−	4.34485i	−0.0900664	−	0.146967i
$875$	4.00873			0.135520
$876$	−0.450405	−	0.132251i	−0.0152178	−	0.00446834i
$877$	−2.90818	+	3.35622i	−0.0982023	+	0.113332i	−0.802723	−	0.596352i	$-0.796616\pi$
$877$	−2.90818	+	3.35622i	−0.0982023	+	0.113332i	0.704521	+	0.709683i	$0.251162\pi$
$878$	−7.86897	−	5.05708i	−0.265565	−	0.170668i
$879$	4.29202	−	29.8516i	0.144766	−	1.00687i
$880$	16.9120	−	10.8687i	0.570103	−	0.366383i
$881$	−5.56070	−	12.1762i	−0.187345	−	0.410228i	0.792532	−	0.609830i	$-0.208762\pi$
$881$	−5.56070	−	12.1762i	−0.187345	−	0.410228i	−0.979877	+	0.199602i	$0.936035\pi$
$882$	41.7827	+	48.2198i	1.40690	+	1.62365i
$883$	7.12308	+	49.5421i	0.239711	+	1.66722i	0.653557	+	0.756878i	$0.273276\pi$
$883$	7.12308	+	49.5421i	0.239711	+	1.66722i	−0.413846	+	0.910347i	$0.635815\pi$
$884$	0.0220907	−	0.0483718i	0.000742990	−	0.00162692i
$885$	−30.7866	+	9.03977i	−1.03488	+	0.303868i
$886$	−19.2142	+	5.64180i	−0.645514	+	0.189540i
$887$	−15.8530	+	34.7133i	−0.532293	+	1.16556i	0.432279	+	0.901740i	$0.357709\pi$
$887$	−15.8530	+	34.7133i	−0.532293	+	1.16556i	−0.964572	+	0.263819i	$0.915018\pi$
$888$	−13.3398	−	92.7803i	−0.447654	−	3.11350i
$889$	−53.4349	−	61.6671i	−1.79215	−	2.06825i
$890$	4.51025	+	9.87607i	0.151184	+	0.331047i
$891$	−11.5584	+	7.42812i	−0.387220	+	0.248851i
$892$	0.485165	−	3.37440i	0.0162445	−	0.112983i
$893$	−1.63122	−	1.04832i	−0.0545866	−	0.0350807i
$894$	8.32126	−	9.60325i	0.278305	−	0.321181i
$895$	12.8292	+	3.76700i	0.428834	+	0.125917i
$896$	−38.5831			−1.28897
$897$	1.40487	+	5.19307i	0.0469074	+	0.173391i
$898$	49.1024			1.63857
$899$	0.462014	+	0.135660i	0.0154090	+	0.00452450i
$900$	0.590752	−	0.681765i	0.0196917	−	0.0227255i
$901$	3.22341	+	2.07156i	0.107387	+	0.0690136i
$902$	−10.8681	+	75.5894i	−0.361869	+	2.51685i
$903$	29.4440	−	18.9225i	0.979836	−	0.629702i
$904$	−8.30398	−	18.1832i	−0.276186	−	0.604763i
$905$	−0.453768	−	0.523677i	−0.0150838	−	0.0174076i
$906$	−4.75694	−	33.0852i	−0.158039	−	1.09918i
$907$	18.6404	−	40.8167i	0.618943	−	1.35530i	−0.297342	−	0.954771i	$-0.596100\pi$
$907$	18.6404	−	40.8167i	0.618943	−	1.35530i	0.916286	−	0.400526i	$-0.131172\pi$
$908$	0.685822	−	0.201376i	0.0227598	−	0.00668288i
$909$	−82.9218	+	24.3480i	−2.75034	+	0.807574i
$910$	−0.881417	+	1.93003i	−0.0292187	+	0.0639800i
$911$	6.32607	+	43.9988i	0.209592	+	1.45775i	0.774491	+	0.632585i	$0.218006\pi$
$911$	6.32607	+	43.9988i	0.209592	+	1.45775i	−0.564899	+	0.825160i	$0.691085\pi$
$912$	−5.34335	−	6.16655i	−0.176936	−	0.204195i
$913$	22.4991	+	49.2661i	0.744610	+	1.63047i
$914$	4.63721	−	2.98016i	0.153385	−	0.0985748i
$915$	−2.51324	+	17.4800i	−0.0830852	+	0.577870i
$916$	0.604607	+	0.388557i	0.0199768	+	0.0128383i
$917$	−24.2459	+	27.9813i	−0.800671	+	0.924024i
$918$	−6.41687	−	1.88416i	−0.211788	−	0.0621866i
$919$	16.8739			0.556617			0.278309	−	0.960492i	$-0.410226\pi$
$919$	16.8739			0.556617			0.278309	+	0.960492i	$0.410226\pi$
$920$	12.9362	−	5.57649i	0.426495	−	0.183851i
$921$	−33.8806			−1.11640
$922$	23.3249	+	6.84882i	0.768165	+	0.225554i
$923$	1.09026	−	1.25823i	0.0358863	−	0.0414150i
$924$	9.28912	+	5.96975i	0.305590	+	0.196391i
$925$	−1.58547	+	11.0272i	−0.0521298	+	0.362571i
$926$	−11.3485	+	7.29322i	−0.372934	+	0.239670i
$927$	10.0196	+	21.9398i	0.329086	+	0.720598i
$928$	−0.0995684	−	0.114908i	−0.00326849	−	0.00377204i
$929$	−6.63942	−	46.1782i	−0.217832	−	1.51506i	−0.746017	−	0.665927i	$-0.768036\pi$
$929$	−6.63942	−	46.1782i	−0.217832	−	1.51506i	0.528185	−	0.849129i	$-0.322873\pi$
$930$	−4.97907	+	10.9026i	−0.163270	+	0.357512i
$931$	6.84172	−	2.00891i	0.224228	−	0.0658394i
$932$	−3.95730	+	1.16197i	−0.129626	+	0.0380615i
$933$	25.2397	−	55.2672i	0.826310	−	1.80937i
$934$	−2.66990	−	18.5696i	−0.0873618	−	0.607615i
$935$	−2.84664	−	3.28519i	−0.0930950	−	0.107437i
$936$	2.48720	+	5.44621i	0.0812967	+	0.178015i
$937$	−3.97575	+	2.55506i	−0.129882	+	0.0834701i	−0.603969	−	0.797008i	$-0.706415\pi$
$937$	−3.97575	+	2.55506i	−0.129882	+	0.0834701i	0.474087	+	0.880478i	$0.342778\pi$
$938$	4.76935	−	33.1716i	0.155725	−	1.08309i
$939$	48.8340	+	31.3837i	1.59364	+	1.02417i
$940$	0.279935	−	0.323062i	0.00913048	−	0.0105371i
$941$	−37.8360	−	11.1096i	−1.23342	−	0.362164i	−0.400879	−	0.916131i	$-0.631295\pi$
$941$	−37.8360	−	11.1096i	−1.23342	−	0.362164i	−0.832539	+	0.553967i	$0.813113\pi$
$942$	23.1260			0.753486
$943$	−14.7592	+	46.5566i	−0.480625	+	1.51609i
$944$	−40.5873			−1.32101
$945$	−24.2927	−	7.13298i	−0.790241	−	0.232036i
$946$	−14.9681	+	17.2741i	−0.486656	+	0.561631i
$947$	−10.3107	−	6.62628i	−0.335052	−	0.215325i	0.362286	−	0.932067i	$-0.381996\pi$
$947$	−10.3107	−	6.62628i	−0.335052	−	0.215325i	−0.697339	+	0.716742i	$0.745633\pi$
$948$	−0.123575	+	0.859481i	−0.00401352	+	0.0279146i
$949$	−0.311507	+	0.200194i	−0.0101120	+	0.00649856i
$950$	0.441402	+	0.966535i	0.0143210	+	0.0313585i
$951$	6.06696	+	7.00165i	0.196735	+	0.227044i
$952$	1.31291	+	9.13148i	0.0425516	+	0.295953i
$953$	−10.1873	+	22.3071i	−0.329999	+	0.722598i	−0.999801	−	0.0199420i	$-0.993652\pi$
$953$	−10.1873	+	22.3071i	−0.329999	+	0.722598i	0.669802	+	0.742540i	$0.266379\pi$
$954$	−33.0105	+	9.69275i	−1.06875	+	0.313814i
$955$	−10.1026	+	2.96640i	−0.326914	+	0.0959906i
$956$	0.322167	−	0.705448i	0.0104196	−	0.0228158i
$957$	−0.351774	−	2.44664i	−0.0113712	−	0.0790886i
$958$	−37.1167	−	42.8349i	−1.19918	−	1.38393i
$959$	−22.2714	−	48.7676i	−0.719182	−	1.57479i
$960$	20.6461	−	13.2685i	0.666351	−	0.428238i
$961$	3.04766	−	21.1970i	0.0983117	−	0.683773i
$962$	−4.96051	−	3.18793i	−0.159933	−	0.102783i
$963$	31.7848	−	36.6816i	1.02425	−	1.18205i
$964$	−1.09634	−	0.321914i	−0.0353107	−	0.0103682i
$965$	−15.0225			−0.483593
$966$	−55.1937	−	49.9325i	−1.77583	−	1.60655i
$967$	−3.12393			−0.100459			−0.0502295	−	0.998738i	$-0.515995\pi$
$967$	−3.12393			−0.100459			−0.0502295	+	0.998738i	$0.515995\pi$
$968$	−55.7576	−	16.3719i	−1.79212	−	0.526213i
$969$	−1.15539	+	1.33339i	−0.0371165	+	0.0428347i
$970$	12.8338	+	8.24778i	0.412068	+	0.264820i
$971$	0.987896	−	6.87097i	0.0317031	−	0.220500i	−0.967811	−	0.251679i	$-0.919017\pi$
$971$	0.987896	−	6.87097i	0.0317031	−	0.220500i	0.999514	+	0.0311793i	$0.00992629\pi$
$972$	1.72838	−	1.11076i	0.0554377	−	0.0356276i
$973$	7.34832	+	16.0906i	0.235576	+	0.515840i
$974$	23.0674	+	26.6211i	0.739126	+	0.852997i
$975$	−0.159642	−	1.11034i	−0.00511264	−	0.0355592i
$976$	−9.27976	+	20.3198i	−0.297038	+	0.650422i
$977$	22.9440	−	6.73696i	0.734043	−	0.215534i	0.106715	−	0.994290i	$-0.465967\pi$
$977$	22.9440	−	6.73696i	0.734043	−	0.215534i	0.627328	+	0.778755i	$0.284149\pi$
$978$	13.8756	−	4.07426i	0.443694	−	0.130280i
$979$	18.5153	−	40.5427i	0.591750	−	1.29575i
$980$	0.223716	+	1.55598i	0.00714634	+	0.0497039i
$981$	33.7114	+	38.9050i	1.07632	+	1.24214i
$982$	15.6396	+	34.2459i	0.499078	+	1.09283i
$983$	13.2381	−	8.50760i	0.422229	−	0.271350i	−0.312225	−	0.950008i	$-0.601074\pi$
$983$	13.2381	−	8.50760i	0.422229	−	0.271350i	0.734455	+	0.678658i	$0.237438\pi$
$984$	−12.1942	+	84.8126i	−0.388737	+	2.70373i
$985$	−9.23687	−	5.93618i	−0.294311	−	0.189142i
$986$	0.107850	−	0.124465i	0.00343463	−	0.00396378i
$987$	−27.1738	−	7.97895i	−0.864951	−	0.253973i
$988$	0.0533611			0.00169764
$989$	−11.2499	+	9.33428i	−0.357725	+	0.296813i
$990$	39.0306			1.24047
$991$	−20.7873	−	6.10370i	−0.660330	−	0.193890i	−0.0656373	−	0.997844i	$-0.520908\pi$
$991$	−20.7873	−	6.10370i	−0.660330	−	0.193890i	−0.594693	+	0.803953i	$0.702726\pi$
$992$	1.98200	−	2.28735i	0.0629285	−	0.0726233i
$993$	28.5683	+	18.3597i	0.906586	+	0.582628i
$994$	−3.27800	+	22.7990i	−0.103972	+	0.723139i
$995$	−8.97652	+	5.76886i	−0.284575	+	0.182885i
$996$	2.01319	+	4.40827i	0.0637903	+	0.139681i
$997$	−8.29289	−	9.57050i	−0.262638	−	0.303101i	0.609079	−	0.793109i	$-0.291539\pi$
$997$	−8.29289	−	9.57050i	−0.262638	−	0.303101i	−0.871718	+	0.490008i	$0.836994\pi$
$998$	0.540331	+	3.75809i	0.0171039	+	0.118960i
$999$	29.2292	−	64.0029i	0.924770	−	2.02496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.c.41.4	✓	50
5.2	odd	4		575.2.p.d.524.4		100
5.3	odd	4		575.2.p.d.524.7		100
5.4	even	2		575.2.k.d.501.2		50
23.3	even	11		2645.2.a.y.1.7		25
23.9	even	11	inner	115.2.g.c.101.4	yes	50
23.20	odd	22		2645.2.a.x.1.7		25
115.9	even	22		575.2.k.d.101.2		50
115.32	odd	44		575.2.p.d.124.7		100
115.78	odd	44		575.2.p.d.124.4		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.c.41.4	✓	50	1.1	even	1	trivial
115.2.g.c.101.4	yes	50	23.9	even	11	inner
575.2.k.d.101.2		50	115.9	even	22
575.2.k.d.501.2		50	5.4	even	2
575.2.p.d.124.4		100	115.78	odd	44
575.2.p.d.124.7		100	115.32	odd	44
575.2.p.d.524.4		100	5.2	odd	4
575.2.p.d.524.7		100	5.3	odd	4
2645.2.a.x.1.7		25	23.20	odd	22
2645.2.a.y.1.7		25	23.3	even	11

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29680 + 0.380775i) q^{2} +(-1.87580 + 2.16478i) q^{3} +(-0.145804 - 0.0937028i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-3.25683 + 2.09304i) q^{6} +(1.66529 + 3.64647i) q^{7} +(-1.92355 - 2.21990i) q^{8} +(-0.740735 - 5.15193i) q^{9} +O(q^{10})\)	\(q+(1.29680 + 0.380775i) q^{2} +(-1.87580 + 2.16478i) q^{3} +(-0.145804 - 0.0937028i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-3.25683 + 2.09304i) q^{6} +(1.66529 + 3.64647i) q^{7} +(-1.92355 - 2.21990i) q^{8} +(-0.740735 - 5.15193i) q^{9} +(-0.561453 + 1.22941i) q^{10} +(5.32356 - 1.56314i) q^{11} +(0.476346 - 0.139868i) q^{12} +(0.162683 - 0.356227i) q^{13} +(0.771061 + 5.36284i) q^{14} +(-1.87580 - 2.16478i) q^{15} +(-1.50518 - 3.29589i) q^{16} +(-0.659097 + 0.423576i) q^{17} +(1.00114 - 6.96308i) q^{18} +(-0.661374 - 0.425039i) q^{19} +(0.113499 - 0.130985i) q^{20} +(-11.0176 - 3.23505i) q^{21} +7.49880 q^{22} +(4.73133 + 0.783914i) q^{23} +8.41379 q^{24} +(-0.959493 - 0.281733i) q^{25} +(0.346610 - 0.400009i) q^{26} +(5.31317 + 3.41457i) q^{27} +(0.0988782 - 0.687713i) q^{28} +(-0.130841 + 0.0840862i) q^{29} +(-1.60824 - 3.52155i) q^{30} +(-2.02743 - 2.33978i) q^{31} +(0.139125 + 0.967639i) q^{32} +(-6.60206 + 14.4565i) q^{33} +(-1.01601 + 0.298326i) q^{34} +(-3.84635 + 1.12939i) q^{35} +(-0.374747 + 0.820583i) q^{36} +(-1.58547 - 11.0272i) q^{37} +(-0.695826 - 0.803026i) q^{38} +(0.465993 + 1.02038i) q^{39} +(2.47105 - 1.58805i) q^{40} +(-1.44931 + 10.0802i) q^{41} +(-13.0558 - 8.39042i) q^{42} +(-1.99607 + 2.30359i) q^{43} +(-0.922669 - 0.270920i) q^{44} +5.20491 q^{45} +(5.83710 + 2.81815i) q^{46} +2.46641 q^{47} +(9.95832 + 2.92403i) q^{48} +(-5.93953 + 6.85459i) q^{49} +(-1.13699 - 0.730702i) q^{50} +(0.319381 - 2.22135i) q^{51} +(-0.0570994 + 0.0366955i) q^{52} +(-2.03164 - 4.44868i) q^{53} +(5.58994 + 6.45114i) q^{54} +(0.789606 + 5.49183i) q^{55} +(4.89152 - 10.7109i) q^{56} +(2.16072 - 0.634445i) q^{57} +(-0.201692 + 0.0592222i) q^{58} +(4.65335 - 10.1894i) q^{59} +(0.0706530 + 0.491402i) q^{60} +(-4.03735 - 4.65935i) q^{61} +(-1.73825 - 3.80623i) q^{62} +(17.5528 - 11.2805i) q^{63} +(-1.21934 + 8.48070i) q^{64} +(0.329449 + 0.211724i) q^{65} +(-14.0662 + 16.2333i) q^{66} +(-5.93489 - 1.74264i) q^{67} +0.135790 q^{68} +(-10.5720 + 8.77185i) q^{69} -5.41799 q^{70} +(4.07908 + 1.19772i) q^{71} +(-10.0119 + 11.5544i) q^{72} +(-0.795440 - 0.511198i) q^{73} +(2.14284 - 14.9037i) q^{74} +(2.40970 - 1.54862i) q^{75} +(0.0566039 + 0.123945i) q^{76} +(14.5652 + 16.8091i) q^{77} +(0.215764 + 1.50067i) q^{78} +(-0.726576 + 1.59098i) q^{79} +(3.47655 - 1.02081i) q^{80} +(-2.37603 + 0.697664i) q^{81} +(-5.71776 + 12.5201i) q^{82} +(1.38922 + 9.66226i) q^{83} +(1.30328 + 1.50406i) q^{84} +(-0.325465 - 0.712670i) q^{85} +(-3.46565 + 2.22724i) q^{86} +(0.0634020 - 0.440971i) q^{87} +(-13.7101 - 8.81098i) q^{88} +(5.26061 - 6.07106i) q^{89} +(6.74973 + 1.98190i) q^{90} +1.56988 q^{91} +(-0.616393 - 0.557637i) q^{92} +8.86818 q^{93} +(3.19844 + 0.939147i) q^{94} +(0.514836 - 0.594153i) q^{95} +(-2.35570 - 1.51392i) q^{96} +(1.60637 - 11.1726i) q^{97} +(-10.3124 + 6.62741i) q^{98} +(-11.9965 - 26.2687i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Introduction

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