LMFDB - Embedded newform 125.2.g.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(6,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("125.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.g (of order $25$, degree $20$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$11$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	125.11
Dual form			125.2.g.a.91.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26877 + 1.19146i) q^{2} +(-1.66333 - 2.62099i) q^{3} +(0.0646335 - 1.02732i) q^{4} +(0.461407 + 2.18795i) q^{5} +(5.23318 + 1.34365i) q^{6} +(-0.283105 + 0.871308i) q^{7} +(-1.07687 - 1.30172i) q^{8} +(-2.82557 + 6.00465i) q^{9} +O(q^{10})$	\(q+(-1.26877 + 1.19146i) q^{2} +(-1.66333 - 2.62099i) q^{3} +(0.0646335 - 1.02732i) q^{4} +(0.461407 + 2.18795i) q^{5} +(5.23318 + 1.34365i) q^{6} +(-0.283105 + 0.871308i) q^{7} +(-1.07687 - 1.30172i) q^{8} +(-2.82557 + 6.00465i) q^{9} +(-3.19226 - 2.22626i) q^{10} +(-4.44831 + 4.17724i) q^{11} +(-2.80010 + 1.53937i) q^{12} +(-1.21791 + 2.58819i) q^{13} +(-0.678930 - 1.44280i) q^{14} +(4.96711 - 4.84861i) q^{15} +(4.95972 + 0.626558i) q^{16} +(0.114671 + 1.82265i) q^{17} +(-3.56927 - 10.9851i) q^{18} +(2.40062 - 3.78277i) q^{19} +(2.27754 - 0.332598i) q^{20} +(2.75458 - 0.707257i) q^{21} +(0.666891 - 10.5999i) q^{22} +(-0.364380 + 1.91014i) q^{23} +(-1.62059 + 4.98766i) q^{24} +(-4.57421 + 2.01906i) q^{25} +(-1.53847 - 4.73492i) q^{26} +(11.1987 - 1.41473i) q^{27} +(0.876814 + 0.347155i) q^{28} +(-0.541404 - 0.214357i) q^{29} +(-0.525214 + 12.0699i) q^{30} +(-0.408646 - 6.49525i) q^{31} +(-4.30574 + 3.12830i) q^{32} +(18.3475 + 4.71084i) q^{33} +(-2.31710 - 2.17590i) q^{34} +(-2.03700 - 0.217391i) q^{35} +(5.98607 + 3.29087i) q^{36} +(-7.98303 - 1.00849i) q^{37} +(1.46117 + 7.65971i) q^{38} +(8.80941 - 1.11289i) q^{39} +(2.35121 - 2.95676i) q^{40} +(0.198615 + 1.04118i) q^{41} +(-2.65227 + 4.17932i) q^{42} +(0.980592 + 0.712442i) q^{43} +(4.00386 + 4.83983i) q^{44} +(-14.4416 - 3.41162i) q^{45} +(-1.81354 - 2.85768i) q^{46} +(-2.55741 + 3.09138i) q^{47} +(-6.60744 - 14.0415i) q^{48} +(4.98409 + 3.62115i) q^{49} +(3.39800 - 8.01170i) q^{50} +(4.58640 - 3.33221i) q^{51} +(2.58019 + 1.41847i) q^{52} +(4.55704 - 1.17005i) q^{53} +(-12.5230 + 15.1378i) q^{54} +(-11.1921 - 7.80525i) q^{55} +(1.43907 - 0.569766i) q^{56} -13.9076 q^{57} +(0.942316 - 0.373089i) q^{58} +(-2.71744 + 1.49392i) q^{59} +(-4.66004 - 5.41619i) q^{60} +(-0.0312818 + 0.163985i) q^{61} +(8.25729 + 7.75411i) q^{62} +(-4.43196 - 4.16189i) q^{63} +(-0.137725 + 0.721979i) q^{64} +(-6.22478 - 1.47051i) q^{65} +(-28.8916 + 15.8833i) q^{66} +(-1.94939 + 0.771819i) q^{67} +1.87985 q^{68} +(5.61255 - 2.22216i) q^{69} +(2.84350 - 2.15118i) q^{70} +(4.40563 - 5.32550i) q^{71} +(10.8591 - 2.78816i) q^{72} +(9.26703 + 5.09459i) q^{73} +(11.3302 - 8.23189i) q^{74} +(12.9004 + 8.63057i) q^{75} +(-3.73096 - 2.71070i) q^{76} +(-2.38032 - 5.05845i) q^{77} +(-9.85118 + 11.9080i) q^{78} +(4.14756 + 6.53550i) q^{79} +(0.917572 + 11.1407i) q^{80} +(-9.64484 - 11.6586i) q^{81} +(-1.49251 - 1.08438i) q^{82} +(-2.01950 + 3.18223i) q^{83} +(-0.548541 - 2.87555i) q^{84} +(-3.93494 + 1.09188i) q^{85} +(-2.09299 + 0.264406i) q^{86} +(0.338706 + 1.77556i) q^{87} +(10.2279 + 1.29208i) q^{88} +(-1.00344 - 0.551644i) q^{89} +(22.3879 - 12.8780i) q^{90} +(-1.91032 - 1.79391i) q^{91} +(1.93878 + 0.497794i) q^{92} +(-16.3443 + 11.8748i) q^{93} +(-0.438471 - 6.96930i) q^{94} +(9.38416 + 3.50703i) q^{95} +(15.3611 + 6.08189i) q^{96} +(14.1417 + 5.59910i) q^{97} +(-10.6381 + 1.34391i) q^{98} +(-12.5138 - 38.5136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) $ 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{19}{25}\right)$

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 $

$2$	−1.26877	+	1.19146i	−0.897158	+	0.842487i	−0.988170	−	0.153363i	$-0.950990\pi$
$2$	−1.26877	+	1.19146i	−0.897158	+	0.842487i	0.0910125	+	0.995850i	$0.470990\pi$
$3$	−1.66333	−	2.62099i	−0.960324	−	1.51323i	−0.854895	−	0.518801i	$-0.826379\pi$
$3$	−1.66333	−	2.62099i	−0.960324	−	1.51323i	−0.105429	−	0.994427i	$-0.533621\pi$
$4$	0.0646335	−	1.02732i	0.0323168	−	0.513660i
$5$	0.461407	+	2.18795i	0.206347	+	0.978479i
$5$	0.461407	+	2.18795i	0.206347	+	0.978479i
$6$	5.23318	+	1.34365i	2.13644	+	0.548544i
$7$	−0.283105	+	0.871308i	−0.107004	+	0.329323i	−0.990195	−	0.139689i	$-0.955390\pi$
$7$	−0.283105	+	0.871308i	−0.107004	+	0.329323i	0.883192	+	0.469012i	$0.155390\pi$
$8$	−1.07687	−	1.30172i	−0.380733	−	0.460227i
$9$	−2.82557	+	6.00465i	−0.941858	+	2.00155i
$10$	−3.19226	−	2.22626i	−1.00948	−	0.704005i
$11$	−4.44831	+	4.17724i	−1.34122	+	1.25949i	−0.402226	+	0.915540i	$0.631763\pi$
$11$	−4.44831	+	4.17724i	−1.34122	+	1.25949i	−0.938990	+	0.343945i	$0.888237\pi$
$12$	−2.80010	+	1.53937i	−0.808320	+	0.444377i
$13$	−1.21791	+	2.58819i	−0.337788	+	0.717836i	−0.999490	−	0.0319309i	$-0.989834\pi$
$13$	−1.21791	+	2.58819i	−0.337788	+	0.717836i	0.661702	+	0.749767i	$0.269834\pi$
$14$	−0.678930	−	1.44280i	−0.181452	−	0.385604i
$15$	4.96711	−	4.84861i	1.28250	−	1.25191i
$16$	4.95972	+	0.626558i	1.23993	+	0.156640i
$17$	0.114671	+	1.82265i	0.0278119	+	0.442057i	0.987150	+	0.159797i	$0.0510840\pi$
$17$	0.114671	+	1.82265i	0.0278119	+	0.442057i	−0.959338	+	0.282260i	$0.908916\pi$
$18$	−3.56927	−	10.9851i	−0.841285	−	2.58921i
$19$	2.40062	−	3.78277i	0.550740	−	0.867828i	−0.448928	−	0.893568i	$-0.648194\pi$
$19$	2.40062	−	3.78277i	0.550740	−	0.867828i	0.999669	+	0.0257399i	$0.00819417\pi$
$20$	2.27754	−	0.332598i	0.509274	−	0.0743711i
$21$	2.75458	−	0.707257i	0.601100	−	0.154336i
$22$	0.666891	−	10.5999i	0.142182	−	2.25991i
$23$	−0.364380	+	1.91014i	−0.0759784	+	0.398293i	0.923899	+	0.382636i	$0.124984\pi$
$23$	−0.364380	+	1.91014i	−0.0759784	+	0.398293i	−0.999877	+	0.0156563i	$0.995016\pi$
$24$	−1.62059	+	4.98766i	−0.330801	+	1.01810i
$25$	−4.57421	+	2.01906i	−0.914842	+	0.403813i
$26$	−1.53847	−	4.73492i	−0.301718	−	0.928594i
$27$	11.1987	−	1.41473i	2.15519	−	0.272264i
$28$	0.876814	+	0.347155i	0.165702	+	0.0656062i
$29$	−0.541404	−	0.214357i	−0.100536	−	0.0398051i	0.317318	−	0.948319i	$-0.397218\pi$
$29$	−0.541404	−	0.214357i	−0.100536	−	0.0398051i	−0.417854	+	0.908514i	$0.637218\pi$
$30$	−0.525214	+	12.0699i	−0.0958904	+	2.20365i
$31$	−0.408646	−	6.49525i	−0.0733951	−	1.16658i	−0.846530	−	0.532340i	$-0.821313\pi$
$31$	−0.408646	−	6.49525i	−0.0733951	−	1.16658i	0.773135	−	0.634241i	$-0.218687\pi$
$32$	−4.30574	+	3.12830i	−0.761154	+	0.553011i
$33$	18.3475	+	4.71084i	3.19389	+	0.820051i
$34$	−2.31710	−	2.17590i	−0.397379	−	0.373163i
$35$	−2.03700	−	0.217391i	−0.344316	−	0.0367458i
$36$	5.98607	+	3.29087i	0.997679	+	0.548479i
$37$	−7.98303	−	1.00849i	−1.31240	−	0.165795i	−0.562199	−	0.827002i	$-0.690045\pi$
$37$	−7.98303	−	1.00849i	−1.31240	−	0.165795i	−0.750204	+	0.661207i	$0.770045\pi$
$38$	1.46117	+	7.65971i	0.237033	+	1.24257i
$39$	8.80941	−	1.11289i	1.41063	−	0.178205i
$40$	2.35121	−	2.95676i	0.371759	−	0.467505i
$41$	0.198615	+	1.04118i	0.0310185	+	0.162605i	0.994426	−	0.105436i	$-0.0336239\pi$
$41$	0.198615	+	1.04118i	0.0310185	+	0.162605i	−0.963408	+	0.268041i	$0.913624\pi$
$42$	−2.65227	+	4.17932i	−0.409255	+	0.644882i
$43$	0.980592	+	0.712442i	0.149539	+	0.108646i	0.660039	−	0.751231i	$-0.270540\pi$
$43$	0.980592	+	0.712442i	0.149539	+	0.108646i	−0.510500	+	0.859878i	$0.670540\pi$
$44$	4.00386	+	4.83983i	0.603604	+	0.729632i
$45$	−14.4416	−	3.41162i	−2.15282	−	0.508574i
$46$	−1.81354	−	2.85768i	−0.267392	−	0.421342i
$47$	−2.55741	+	3.09138i	−0.373037	+	0.450924i	−0.923307	−	0.384063i	$-0.874525\pi$
$47$	−2.55741	+	3.09138i	−0.373037	+	0.450924i	0.550270	+	0.834987i	$0.314525\pi$
$48$	−6.60744	−	14.0415i	−0.953702	−	2.02672i
$49$	4.98409	+	3.62115i	0.712013	+	0.517308i
$50$	3.39800	−	8.01170i	0.480550	−	1.13303i
$51$	4.58640	−	3.33221i	0.642224	−	0.466603i
$52$	2.58019	+	1.41847i	0.357808	+	0.196706i
$53$	4.55704	−	1.17005i	0.625958	−	0.160719i	0.0776301	−	0.996982i	$-0.475265\pi$
$53$	4.55704	−	1.17005i	0.625958	−	0.160719i	0.548328	+	0.836264i	$0.315265\pi$
$54$	−12.5230	+	15.1378i	−1.70417	+	2.05999i
$55$	−11.1921	−	7.80525i	−1.50914	−	1.05246i
$56$	1.43907	−	0.569766i	0.192303	−	0.0761382i
$57$	−13.9076			−1.84211
$58$	0.942316	−	0.373089i	0.123732	−	0.0489890i
$59$	−2.71744	+	1.49392i	−0.353780	+	0.194492i	−0.648727	−	0.761021i	$-0.724698\pi$
$59$	−2.71744	+	1.49392i	−0.353780	+	0.194492i	0.294946	+	0.955514i	$0.404698\pi$
$60$	−4.66004	−	5.41619i	−0.601609	−	0.699228i
$61$	−0.0312818	+	0.163985i	−0.00400522	+	0.0209961i	−0.984234	−	0.176873i	$-0.943402\pi$
$61$	−0.0312818	+	0.163985i	−0.00400522	+	0.0209961i	0.980229	+	0.197869i	$0.0634020\pi$
$62$	8.25729	+	7.75411i	1.04868	+	0.984773i
$63$	−4.43196	−	4.16189i	−0.558375	−	0.524349i
$64$	−0.137725	+	0.721979i	−0.0172156	+	0.0902474i
$65$	−6.22478	−	1.47051i	−0.772089	−	0.182395i
$66$	−28.8916	+	15.8833i	−3.55630	+	1.95510i
$67$	−1.94939	+	0.771819i	−0.238156	+	0.0942927i	−0.484171	−	0.874973i	$-0.660879\pi$
$67$	−1.94939	+	0.771819i	−0.238156	+	0.0942927i	0.246015	+	0.969266i	$0.420879\pi$
$68$	1.87985			0.227966
$69$	5.61255	−	2.22216i	0.675671	−	0.267517i
$70$	2.84350	−	2.15118i	0.339863	−	0.257115i
$71$	4.40563	−	5.32550i	0.522853	−	0.632020i	−0.441303	−	0.897358i	$-0.645484\pi$
$71$	4.40563	−	5.32550i	0.522853	−	0.632020i	0.964155	+	0.265338i	$0.0854836\pi$
$72$	10.8591	−	2.78816i	1.27976	−	0.328587i
$73$	9.26703	+	5.09459i	1.08462	+	0.596277i	0.920730	−	0.390201i	$-0.127594\pi$
$73$	9.26703	+	5.09459i	1.08462	+	0.596277i	0.163894	+	0.986478i	$0.447594\pi$
$74$	11.3302	−	8.23189i	1.31711	−	0.956938i
$75$	12.9004	+	8.63057i	1.48960	+	0.996573i
$76$	−3.73096	−	2.71070i	−0.427971	−	0.310939i
$77$	−2.38032	−	5.05845i	−0.271263	−	0.576463i
$78$	−9.85118	+	11.9080i	−1.11543	+	1.34832i
$79$	4.14756	+	6.53550i	0.466636	+	0.735301i	0.993399	−	0.114711i	$-0.0365943\pi$
$79$	4.14756	+	6.53550i	0.466636	+	0.735301i	−0.526762	+	0.850013i	$0.676594\pi$
$80$	0.917572	+	11.1407i	0.102588	+	1.24557i
$81$	−9.64484	−	11.6586i	−1.07165	−	1.29540i
$82$	−1.49251	−	1.08438i	−0.164821	−	0.119749i
$83$	−2.01950	+	3.18223i	−0.221669	+	0.349295i	−0.936902	−	0.349591i	$-0.886321\pi$
$83$	−2.01950	+	3.18223i	−0.221669	+	0.349295i	0.715233	+	0.698886i	$0.246321\pi$
$84$	−0.548541	−	2.87555i	−0.0598507	−	0.313749i
$85$	−3.93494	+	1.09188i	−0.426804	+	0.118431i
$86$	−2.09299	+	0.264406i	−0.225693	+	0.0285117i
$87$	0.338706	+	1.77556i	0.0363131	+	0.190360i
$88$	10.2279	+	1.29208i	1.09029	+	0.137736i
$89$	−1.00344	−	0.551644i	−0.106364	−	0.0584741i	0.427684	−	0.903928i	$-0.359330\pi$
$89$	−1.00344	−	0.551644i	−0.106364	−	0.0584741i	−0.534048	+	0.845454i	$0.679330\pi$
$90$	22.3879	−	12.8780i	2.35989	−	1.35746i
$91$	−1.91032	−	1.79391i	−0.200256	−	0.188053i
$92$	1.93878	+	0.497794i	0.202132	+	0.0518986i
$93$	−16.3443	+	11.8748i	−1.69482	+	1.23136i
$94$	−0.438471	−	6.96930i	−0.0452248	−	0.718828i
$95$	9.38416	+	3.50703i	0.962795	+	0.359814i
$96$	15.3611	+	6.08189i	1.56779	+	0.620730i
$97$	14.1417	+	5.59910i	1.43587	+	0.568502i	0.951853	−	0.306554i	$-0.0991761\pi$
$97$	14.1417	+	5.59910i	1.43587	+	0.568502i	0.484020	+	0.875057i	$0.339176\pi$
$98$	−10.6381	+	1.34391i	−1.07461	+	0.135755i
$99$	−12.5138	−	38.5136i	−1.25769	−	3.87077i
$100$	1.77858	+	4.82968i	0.177858	+	0.482968i
$101$	−2.52502	+	7.77122i	−0.251249	+	0.773265i	0.743296	+	0.668962i	$0.233261\pi$
$101$	−2.52502	+	7.77122i	−0.251249	+	0.773265i	−0.994546	+	0.104303i	$0.966739\pi$
$102$	−1.84891	+	9.69231i	−0.183069	+	0.959682i
$103$	−0.951727	+	15.1273i	−0.0937764	+	1.49053i	0.616915	+	0.787030i	$0.288382\pi$
$103$	−0.951727	+	15.1273i	−0.0937764	+	1.49053i	−0.710691	+	0.703504i	$0.751618\pi$
$104$	4.68064	−	1.20178i	0.458974	−	0.117845i
$105$	2.81842	+	5.70055i	0.275050	+	0.556316i
$106$	−4.38778	+	6.91404i	−0.426179	+	0.671551i
$107$	−0.625605	−	1.92541i	−0.0604795	−	0.186137i	0.916252	−	0.400602i	$-0.131199\pi$
$107$	−0.625605	−	1.92541i	−0.0604795	−	0.186137i	−0.976732	+	0.214465i	$0.931199\pi$
$108$	−0.729566	−	11.5961i	−0.0702025	−	1.11584i
$109$	−19.0798	−	2.41034i	−1.82751	−	0.230869i	−0.864937	−	0.501880i	$-0.832642\pi$
$109$	−19.0798	−	2.41034i	−1.82751	−	0.230869i	−0.962576	+	0.271011i	$0.912642\pi$
$110$	23.4998	−	3.43176i	2.24062	−	0.327205i
$111$	10.6352	+	22.6009i	1.00945	+	2.14518i
$112$	−1.95005	+	4.14406i	−0.184262	+	0.391577i
$113$	9.86914	−	5.42560i	0.928410	−	0.510398i	0.0555976	−	0.998453i	$-0.482294\pi$
$113$	9.86914	−	5.42560i	0.928410	−	0.510398i	0.872813	+	0.488055i	$0.162294\pi$
$114$	17.6456	−	16.5703i	1.65266	−	1.55195i
$115$	−4.34742	+	0.0841108i	−0.405399	+	0.00784337i
$116$	−0.255206	+	0.542341i	−0.0236953	+	0.0503551i
$117$	−12.0999	−	14.6263i	−1.11864	−	1.35220i
$118$	1.66786	−	5.13316i	0.153539	−	0.472546i
$119$	−1.62055	−	0.416087i	−0.148556	−	0.0381426i
$120$	−11.6605	−	1.24442i	−1.06445	−	0.113600i
$121$	1.64742	−	26.1850i	0.149766	−	2.38046i
$122$	−0.155691	−	0.245330i	−0.0140956	−	0.0222112i
$123$	2.39855	−	2.25239i	0.216270	−	0.203091i
$124$	−6.69912			−0.601598
$125$	−6.52817	−	9.07651i	−0.583897	−	0.811827i
$126$	10.5819			0.942708
$127$	−2.77258	+	2.60363i	−0.246027	+	0.231035i	−0.797743	−	0.602997i	$-0.793973\pi$
$127$	−2.77258	+	2.60363i	−0.246027	+	0.231035i	0.551717	+	0.834032i	$0.313973\pi$
$128$	−6.38900	−	10.0675i	−0.564713	−	0.889846i
$129$	0.236254	−	3.75515i	0.0208010	−	0.330622i
$130$	9.64988	−	5.55081i	0.846351	−	0.486838i
$131$	−11.9381	−	3.06518i	−1.04303	−	0.267806i	−0.311954	−	0.950097i	$-0.600984\pi$
$131$	−11.9381	−	3.06518i	−1.04303	−	0.267806i	−0.731080	+	0.682291i	$0.760984\pi$
$132$	6.02540	−	18.5443i	0.524444	−	1.61407i
$133$	2.61633	+	3.16260i	0.226865	+	0.274232i
$134$	1.55375	−	3.30188i	0.134223	−	0.285239i
$135$	8.26251	+	23.8494i	0.711123	+	2.05263i
$136$	2.24908	−	2.11203i	0.192857	−	0.181105i
$137$	7.04471	−	3.87286i	0.601870	−	0.330881i	−0.151521	−	0.988454i	$-0.548417\pi$
$137$	7.04471	−	3.87286i	0.601870	−	0.330881i	0.753391	+	0.657573i	$0.228417\pi$
$138$	−4.47343	+	9.50653i	−0.380804	+	0.809249i
$139$	6.58419	+	13.9921i	0.558464	+	1.18680i	0.962306	+	0.271968i	$0.0876744\pi$
$139$	6.58419	+	13.9921i	0.558464	+	1.18680i	−0.403842	+	0.914829i	$0.632326\pi$
$140$	−0.354989	+	2.07860i	−0.0300020	+	0.175674i
$141$	12.3563	+	1.56096i	1.04059	+	0.131457i
$142$	0.755351	+	12.0060i	0.0633877	+	1.00752i
$143$	−5.39386	−	16.6006i	−0.451057	−	1.38821i
$144$	−17.7763	+	28.0110i	−1.48136	+	2.33425i
$145$	0.219194	−	1.28347i	0.0182031	−	0.106586i
$146$	−17.8277	+	4.57739i	−1.47543	+	0.378827i
$147$	1.20082	−	19.0864i	0.0990416	−	1.57422i
$148$	−1.55202	+	8.13595i	−0.127575	+	0.668771i
$149$	−2.86942	+	8.83117i	−0.235072	+	0.723478i	0.762040	+	0.647530i	$0.224198\pi$
$149$	−2.86942	+	8.83117i	−0.235072	+	0.723478i	−0.997112	+	0.0759473i	$0.975802\pi$
$150$	−26.6506	+	4.41998i	−2.17601	+	0.360890i
$151$	1.52705	+	4.69977i	0.124269	+	0.382462i	0.993767	−	0.111475i	$-0.0355575\pi$
$151$	1.52705	+	4.69977i	0.124269	+	0.382462i	−0.869498	+	0.493937i	$0.835557\pi$
$152$	−7.50927	+	0.948642i	−0.609082	+	0.0769450i
$153$	−11.2684	−	4.46146i	−0.910993	−	0.360688i
$154$	9.04701	+	3.58196i	0.729029	+	0.288643i
$155$	14.0227	−	3.89105i	1.12633	−	0.312536i
$156$	−0.573909	−	9.12202i	−0.0459495	−	0.730346i
$157$	10.6296	−	7.72287i	0.848335	−	0.616352i	−0.0763512	−	0.997081i	$-0.524327\pi$
$157$	10.6296	−	7.72287i	0.848335	−	0.616352i	0.924687	+	0.380729i	$0.124327\pi$
$158$	−13.0491	−	3.35043i	−1.03813	−	0.266546i
$159$	−10.6465	−	9.99777i	−0.844326	−	0.792875i
$160$	−8.83125	−	7.97730i	−0.698171	−	0.630661i
$161$	−1.56117	−	0.858258i	−0.123037	−	0.0676402i
$162$	26.1278	+	3.30071i	2.05280	+	0.259329i
$163$	2.12910	+	11.1611i	0.166764	+	0.874205i	0.963058	+	0.269296i	$0.0867908\pi$
$163$	2.12910	+	11.1611i	0.166764	+	0.874205i	−0.796294	+	0.604910i	$0.793209\pi$
$164$	1.08246	−	0.136746i	0.0845259	−	0.0106781i
$165$	−1.84140	+	42.3169i	−0.143352	+	3.29437i
$166$	−1.22920	−	6.44367i	−0.0954041	−	0.500126i
$167$	−6.16438	+	9.71352i	−0.477014	+	0.751654i	−0.994578	−	0.103990i	$-0.966839\pi$
$167$	−6.16438	+	9.71352i	−0.477014	+	0.751654i	0.517564	+	0.855645i	$0.326839\pi$
$168$	−3.88699	−	2.82406i	−0.299888	−	0.217881i
$169$	3.07107	+	3.71229i	0.236236	+	0.285561i
$170$	3.69162	−	6.07365i	0.283134	−	0.465828i
$171$	15.9311	+	25.1034i	1.21828	+	1.91970i
$172$	0.795285	−	0.961335i	0.0606399	−	0.0733011i
$173$	−2.28043	−	4.84616i	−0.173378	−	0.368446i	0.799186	−	0.601084i	$-0.205264\pi$
$173$	−2.28043	−	4.84616i	−0.173378	−	0.368446i	−0.972563	+	0.232638i	$0.925264\pi$
$174$	−2.54524	−	1.84923i	−0.192954	−	0.140190i
$175$	−0.464245	−	4.55715i	−0.0350937	−	0.344488i
$176$	−24.6796	+	17.9308i	−1.86030	+	1.35159i
$177$	8.43555	+	4.63748i	0.634055	+	0.348575i
$178$	1.93039	−	0.495640i	0.144689	−	0.0371498i
$179$	9.54923	−	11.5430i	0.713743	−	0.862767i	−0.281563	−	0.959543i	$-0.590853\pi$
$179$	9.54923	−	11.5430i	0.713743	−	0.862767i	0.995306	+	0.0967754i	$0.0308528\pi$
$180$	−4.43823	+	14.6156i	−0.330806	+	1.08938i
$181$	7.62755	−	3.01996i	0.566952	−	0.224472i	−0.0671219	−	0.997745i	$-0.521382\pi$
$181$	7.62755	−	3.01996i	0.566952	−	0.224472i	0.634074	+	0.773273i	$0.281382\pi$
$182$	4.56112			0.338093
$183$	0.481834	−	0.190772i	0.0356182	−	0.0141022i
$184$	2.87886	−	1.58267i	0.212232	−	0.116676i
$185$	−1.47690	−	17.9318i	−0.108584	−	1.31837i
$186$	6.58884	−	34.5399i	0.483117	−	2.53259i
$187$	−8.12373	−	7.62869i	−0.594066	−	0.557865i
$188$	3.01054	+	2.82709i	0.219566	+	0.206186i
$189$	−1.93775	+	10.1580i	−0.140951	+	0.738889i
$190$	−16.0848	+	6.73120i	−1.16692	+	0.488333i
$191$	21.6439	−	11.8988i	1.56610	−	0.860970i	0.566788	−	0.823864i	$-0.308186\pi$
$191$	21.6439	−	11.8988i	1.56610	−	0.860970i	0.999311	−	0.0371064i	$-0.0118141\pi$
$192$	2.12138	−	0.839914i	0.153097	−	0.0606155i
$193$	1.00463			0.0723150			0.0361575	−	0.999346i	$-0.488488\pi$
$193$	1.00463			0.0723150			0.0361575	+	0.999346i	$0.488488\pi$
$194$	−24.6137	+	9.74525i	−1.76716	+	0.699668i
$195$	6.49966	+	18.7610i	0.465450	+	1.34350i
$196$	4.04222	−	4.88621i	0.288730	−	0.349015i
$197$	12.2492	−	3.14505i	0.872717	−	0.224076i	0.214335	−	0.976760i	$-0.431241\pi$
$197$	12.2492	−	3.14505i	0.872717	−	0.224076i	0.658381	+	0.752685i	$0.271241\pi$
$198$	61.7645	+	33.9553i	4.38941	+	2.41310i
$199$	−2.34269	+	1.70207i	−0.166069	+	0.120656i	−0.667716	−	0.744416i	$-0.732728\pi$
$199$	−2.34269	+	1.70207i	−0.166069	+	0.120656i	0.501647	+	0.865073i	$0.332728\pi$
$200$	7.55410	+	3.78005i	0.534156	+	0.267290i
$201$	5.26541	+	3.82554i	0.371393	+	0.269833i
$202$	−6.05539	−	12.8684i	−0.426056	−	0.905415i
$203$	0.340045	−	0.411044i	0.0238665	−	0.0288496i
$204$	−3.12682	−	4.92707i	−0.218921	−	0.344964i
$205$	−2.18640	+	0.914965i	−0.152704	+	0.0639039i
$206$	−16.8160	−	20.3270i	−1.17162	−	1.41625i
$207$	−10.4402	−	7.58522i	−0.725642	−	0.527210i
$208$	−7.66215	+	12.0736i	−0.531275	+	0.837155i
$209$	5.12285	+	26.8549i	0.354355	+	1.85759i
$210$	−10.3679	−	3.87467i	−0.715452	−	0.267377i
$211$	−26.4162	+	3.33714i	−1.81856	+	0.229738i	−0.959417	−	0.281991i	$-0.909005\pi$
$211$	−26.4162	+	3.33714i	−1.81856	+	0.229738i	−0.859147	+	0.511729i	$0.829005\pi$
$212$	−0.907478	−	4.75717i	−0.0623258	−	0.326724i
$213$	−21.2861	−	2.68906i	−1.45850	−	0.184251i
$214$	3.08780	+	1.69753i	0.211077	+	0.116041i
$215$	−1.10633	+	2.47421i	−0.0754512	+	0.168740i
$216$	−13.9012	−	13.0541i	−0.945856	−	0.888218i
$217$	5.77505	+	1.48278i	0.392036	+	0.100658i
$218$	27.0797	−	19.6746i	1.83407	−	1.33253i
$219$	−2.06126	−	32.7628i	−0.139287	−	2.21390i
$220$	−8.74188	+	10.9933i	−0.589377	+	0.741171i
$221$	−4.85702	−	1.92303i	−0.326719	−	0.129357i
$222$	−40.4216	−	16.0040i	−2.71292	−	1.07412i
$223$	−14.0640	+	1.77669i	−0.941792	+	0.118976i	−0.581212	−	0.813752i	$-0.697421\pi$
$223$	−14.0640	+	1.77669i	−0.941792	+	0.118976i	−0.360580	+	0.932728i	$0.617421\pi$
$224$	−1.50674	−	4.63726i	−0.100673	−	0.309840i
$225$	0.800986	−	33.1715i	0.0533990	−	2.21144i
$226$	−6.05732	+	18.6425i	−0.402927	+	1.24008i
$227$	−0.633184	+	3.31926i	−0.0420259	+	0.220307i	−0.997104	−	0.0760457i	$-0.975771\pi$
$227$	−0.633184	+	3.31926i	−0.0420259	+	0.220307i	0.955078	+	0.296353i	$0.0957705\pi$
$228$	−0.898899	+	14.2876i	−0.0595310	+	0.946219i
$229$	−13.8526	+	3.55675i	−0.915408	+	0.235037i	−0.676875	−	0.736098i	$-0.736666\pi$
$229$	−13.8526	+	3.55675i	−0.915408	+	0.235037i	−0.238533	+	0.971134i	$0.576666\pi$
$230$	5.41567	−	5.28648i	0.357099	−	0.348580i
$231$	−9.29886	+	14.6527i	−0.611820	+	0.964074i
$232$	0.303992	+	0.935591i	0.0199581	+	0.0614246i
$233$	−1.83396	−	29.1500i	−0.120147	−	1.90968i	−0.350482	−	0.936569i	$-0.613982\pi$
$233$	−1.83396	−	29.1500i	−0.120147	−	1.90968i	0.230335	−	0.973111i	$-0.426018\pi$
$234$	32.7786	+	4.14090i	2.14280	+	0.270699i
$235$	−7.94377	−	4.16909i	−0.518194	−	0.271961i
$236$	1.35910	+	2.88824i	0.0884700	+	0.188008i
$237$	10.2307	−	21.7414i	0.664557	−	1.41225i
$238$	2.55186	−	1.40290i	0.165412	−	0.0909362i
$239$	−18.7627	+	17.6193i	−1.21365	+	1.13970i	−0.227516	+	0.973774i	$0.573061\pi$
$239$	−18.7627	+	17.6193i	−1.21365	+	1.13970i	−0.986139	+	0.165924i	$0.946939\pi$
$240$	27.6734	−	20.9356i	1.78631	−	1.35139i
$241$	−4.61277	+	9.80264i	−0.297135	+	0.631444i	−0.996525	−	0.0832966i	$-0.973455\pi$
$241$	−4.61277	+	9.80264i	−0.297135	+	0.631444i	0.699390	+	0.714740i	$0.253455\pi$
$242$	29.1081	+	35.1857i	1.87114	+	2.26182i
$243$	−4.05023	+	12.4653i	−0.259822	+	0.799651i
$244$	0.166443	+	0.0427353i	0.0106554	+	0.00273585i
$245$	−5.62319	+	12.5757i	−0.359253	+	0.803435i
$246$	−0.359591	+	5.71553i	−0.0229267	+	0.364409i
$247$	6.86681	+	10.8204i	0.436925	+	0.688483i
$248$	−8.01492	+	7.52651i	−0.508948	+	0.477934i
$249$	11.6997			0.741437
$250$	19.0970	+	3.73799i	1.20780	+	0.236411i
$251$	8.89468			0.561427			0.280714	−	0.959792i	$-0.409429\pi$
$251$	8.89468			0.561427			0.280714	+	0.959792i	$0.409429\pi$
$252$	−4.56205	+	4.28405i	−0.287382	+	0.269870i
$253$	−6.35826	−	10.0190i	−0.399740	−	0.629890i
$254$	0.415666	−	6.60682i	0.0260812	−	0.414549i
$255$	9.40689	+	8.49728i	0.589083	+	0.532120i
$256$	18.6773	+	4.79552i	1.16733	+	0.299720i
$257$	−3.61350	+	11.1212i	−0.225404	+	0.693722i	0.772846	+	0.634593i	$0.218832\pi$
$257$	−3.61350	+	11.1212i	−0.225404	+	0.693722i	−0.998250	+	0.0591291i	$0.981168\pi$
$258$	4.17434	+	5.04591i	0.259883	+	0.314145i
$259$	3.13874	−	6.67017i	0.195032	−	0.414464i
$260$	−1.91302	+	6.29980i	−0.118640	+	0.390697i
$261$	2.81692	−	2.64526i	0.174363	−	0.163738i
$262$	18.7987	−	10.3347i	1.16139	−	0.638479i
$263$	5.62844	−	11.9610i	0.347064	−	0.737549i	−0.652735	−	0.757586i	$-0.726378\pi$
$263$	5.62844	−	11.9610i	0.347064	−	0.737549i	0.999799	+	0.0200371i	$0.00637844\pi$
$264$	−13.6258	−	28.9562i	−0.838608	−	1.78213i
$265$	4.66265	+	9.43069i	0.286424	+	0.579323i
$266$	−7.08763	−	0.895376i	−0.434571	−	0.0548990i
$267$	0.223193	+	3.54756i	0.0136592	+	0.217107i
$268$	0.666910	+	2.05254i	0.0407380	+	0.125379i
$269$	−4.96658	+	7.82607i	−0.302818	+	0.477164i	−0.961327	−	0.275408i	$-0.911187\pi$
$269$	−4.96658	+	7.82607i	−0.302818	+	0.477164i	0.658510	+	0.752572i	$0.271187\pi$
$270$	−38.8988	−	20.4151i	−2.36730	−	1.24242i
$271$	7.80752	−	2.00463i	0.474273	−	0.121773i	−0.00398491	−	0.999992i	$-0.501268\pi$
$271$	7.80752	−	2.00463i	0.474273	−	0.121773i	0.478258	+	0.878219i	$0.341268\pi$
$272$	−0.573257	+	9.11166i	−0.0347588	+	0.552476i
$273$	−1.52432	+	7.99077i	−0.0922562	+	0.483624i
$274$	−4.32379	+	13.3072i	−0.261209	+	0.803920i
$275$	11.9134	−	28.0890i	0.718403	−	1.69383i
$276$	−1.92012	−	5.90951i	−0.115577	−	0.355711i
$277$	−7.38492	+	0.932933i	−0.443717	+	0.0560545i	−0.344018	−	0.938963i	$-0.611788\pi$
$277$	−7.38492	+	0.932933i	−0.443717	+	0.0560545i	−0.0996992	+	0.995018i	$0.531788\pi$
$278$	−25.0248	−	9.90804i	−1.50089	−	0.594245i
$279$	40.1564	+	15.8990i	2.40410	+	0.951850i
$280$	1.91061	+	2.88570i	0.114181	+	0.172454i
$281$	1.53267	+	24.3611i	0.0914314	+	1.45326i	0.729869	+	0.683587i	$0.239581\pi$
$281$	1.53267	+	24.3611i	0.0914314	+	1.45326i	−0.638438	+	0.769674i	$0.720419\pi$
$282$	−17.5371	+	12.7415i	−1.04432	+	0.758743i
$283$	−4.27295	−	1.09711i	−0.254001	−	0.0652163i	0.119542	−	0.992829i	$-0.461857\pi$
$283$	−4.27295	−	1.09711i	−0.254001	−	0.0652163i	−0.373543	+	0.927613i	$0.621857\pi$
$284$	−5.18624	−	4.87020i	−0.307747	−	0.288993i
$285$	−6.41707	−	30.4291i	−0.380114	−	1.80247i
$286$	26.6225	+	14.6358i	1.57422	+	0.865435i
$287$	−0.963415	−	0.121708i	−0.0568686	−	0.00718417i
$288$	−6.61818	−	34.6937i	−0.389980	−	2.04435i
$289$	13.5571	−	1.71265i	0.797474	−	0.100744i
$290$	1.25109	+	1.88959i	0.0734665	+	0.110961i
$291$	−8.84715	−	46.3784i	−0.518629	−	2.71875i
$292$	5.83274	−	9.19093i	0.341335	−	0.537858i
$293$	12.6342	+	9.17925i	0.738095	+	0.536258i	0.892114	−	0.451810i	$-0.149222\pi$
$293$	12.6342	+	9.17925i	0.738095	+	0.536258i	−0.154019	+	0.988068i	$0.549222\pi$
$294$	21.2171	+	25.6470i	1.23740	+	1.49576i
$295$	−4.52247	−	5.25630i	−0.263308	−	0.306034i
$296$	7.28396	+	11.4777i	0.423371	+	0.667126i
$297$	−43.9057	+	53.0729i	−2.54767	+	3.07960i
$298$	−6.88131	−	14.6235i	−0.398624	−	0.847119i
$299$	−4.50004	−	3.26947i	−0.260244	−	0.189078i
$300$	9.70016	−	12.6950i	0.560039	−	0.732945i
$301$	−0.898367	+	0.652702i	−0.0517810	+	0.0376211i
$302$	−7.53704	−	4.14353i	−0.433708	−	0.238433i
$303$	24.5682	−	6.30804i	1.41141	−	0.362388i
$304$	14.2765	−	17.2574i	0.818815	−	0.989778i
$305$	−0.373223	+	0.00722086i	−0.0213707	+	0.000413465i
$306$	19.6126	−	7.76519i	1.12118	−	0.443906i
$307$	−8.79133			−0.501748			−0.250874	−	0.968020i	$-0.580718\pi$
$307$	−8.79133			−0.501748			−0.250874	+	0.968020i	$0.580718\pi$
$308$	−5.35049	+	2.11841i	−0.304873	+	0.120708i
$309$	41.2314	−	22.6672i	2.34557	−	1.28949i
$310$	−13.1556	+	21.6443i	−0.747188	+	1.22931i
$311$	3.58259	−	18.7806i	0.203150	−	1.06495i	−0.723870	−	0.689937i	$-0.757638\pi$
$311$	3.58259	−	18.7806i	0.203150	−	1.06495i	0.927020	−	0.375012i	$-0.122362\pi$
$312$	−10.9353	−	10.2689i	−0.619089	−	0.581364i
$313$	14.6930	+	13.7976i	0.830495	+	0.779887i	0.977874	−	0.209193i	$-0.0670838\pi$
$313$	14.6930	+	13.7976i	0.830495	+	0.779887i	−0.147379	+	0.989080i	$0.547084\pi$
$314$	−4.28510	+	22.4633i	−0.241822	+	1.26768i
$315$	7.06105	−	11.6172i	0.397845	−	0.654556i
$316$	6.98213	−	3.83846i	0.392775	−	0.215930i
$317$	−12.7553	+	5.05017i	−0.716407	+	0.283646i	−0.697912	−	0.716183i	$-0.745887\pi$
$317$	−12.7553	+	5.05017i	−0.716407	+	0.283646i	−0.0184948	+	0.999829i	$0.505887\pi$
$318$	25.4200			1.42548
$319$	3.30375	−	1.30805i	0.184975	−	0.0732367i
$320$	−1.64320	+	0.0317914i	−0.0918575	+	0.00177719i
$321$	−4.00590	+	4.84230i	−0.223587	+	0.270271i
$322$	3.00334	−	0.771127i	0.167370	−	0.0429732i
$323$	7.16994	+	3.94171i	0.398946	+	0.219323i
$324$	−12.6005	+	9.15481i	−0.700028	+	0.508600i
$325$	0.345250	−	14.2980i	0.0191510	−	0.793109i
$326$	−15.9993	−	11.6242i	−0.886120	−	0.643804i
$327$	25.4185	+	54.0171i	1.40565	+	2.98715i
$328$	1.14143	−	1.37976i	0.0630252	−	0.0761844i
$329$	−1.96953	−	3.10348i	−0.108583	−	0.171100i
$330$	−48.0825	−	55.8845i	−2.64685	−	3.07634i
$331$	6.65197	+	8.04085i	0.365625	+	0.441965i	0.920957	−	0.389664i	$-0.127409\pi$
$331$	6.65197	+	8.04085i	0.365625	+	0.441965i	−0.555332	+	0.831629i	$0.687409\pi$
$332$	3.13864	+	2.28036i	0.172255	+	0.125151i
$333$	28.6123	−	45.0858i	1.56794	−	2.47068i
$334$	−3.75203	−	19.6688i	−0.205302	−	1.07623i
$335$	−2.58816	−	3.90904i	−0.141406	−	0.213574i
$336$	14.1051	−	1.78189i	0.769496	−	0.0972100i
$337$	3.68421	+	19.3133i	0.200692	+	1.05206i	0.929912	+	0.367783i	$0.119883\pi$
$337$	3.68421	+	19.3133i	0.200692	+	1.05206i	−0.729220	+	0.684279i	$0.760117\pi$
$338$	−8.31952	−	1.05100i	−0.452522	−	0.0571669i
$339$	−30.6361	−	16.8423i	−1.66392	−	0.914749i
$340$	0.867377	+	4.11302i	0.0470401	+	0.223060i
$341$	28.9500	+	27.1859i	1.56773	+	1.47220i
$342$	−50.1225	−	12.8693i	−2.71032	−	0.695891i
$343$	−9.75441	+	7.08700i	−0.526689	+	0.382662i
$344$	−0.128576	−	2.04366i	−0.00693238	−	0.110187i
$345$	7.45164	+	11.2546i	0.401183	+	0.605929i
$346$	8.66733	+	3.43164i	0.465958	+	0.184486i
$347$	−32.9857	−	13.0599i	−1.77076	−	0.701095i	−0.997775	−	0.0666747i	$-0.978761\pi$
$347$	−32.9857	−	13.0599i	−1.77076	−	0.701095i	−0.772988	−	0.634420i	$-0.781239\pi$
$348$	1.84596	−	0.233199i	0.0989539	−	0.0125008i
$349$	7.09939	+	21.8497i	0.380022	+	1.16959i	0.940028	+	0.341098i	$0.110799\pi$
$349$	7.09939	+	21.8497i	0.380022	+	1.16959i	−0.560006	+	0.828488i	$0.689201\pi$
$350$	6.01867	+	5.22886i	0.321711	+	0.279494i
$351$	−9.97746	+	30.7075i	−0.532557	+	1.63904i
$352$	6.08558	−	31.9018i	0.324363	−	1.70037i
$353$	−0.324140	+	5.15206i	−0.0172523	+	0.274217i	0.979938	+	0.199304i	$0.0638680\pi$
$353$	−0.324140	+	5.15206i	−0.0172523	+	0.274217i	−0.997190	+	0.0749132i	$0.976132\pi$
$354$	−16.2282	+	4.16668i	−0.862517	+	0.221457i
$355$	13.6847	+	7.18207i	0.726308	+	0.381184i
$356$	−0.631571	+	0.995196i	−0.0334732	+	0.0527453i
$357$	1.60495	+	4.93953i	0.0849430	+	0.261428i
$358$	1.63723	+	26.0230i	0.0865302	+	1.37536i
$359$	−9.85927	−	1.24552i	−0.520353	−	0.0657358i	−0.139230	−	0.990260i	$-0.544463\pi$
$359$	−9.85927	−	1.24552i	−0.520353	−	0.0657358i	−0.381123	+	0.924524i	$0.624463\pi$
$360$	11.1108	+	22.4727i	0.585591	+	1.18442i
$361$	−0.456589	−	0.970301i	−0.0240310	−	0.0510685i
$362$	−6.07948	+	12.9195i	−0.319530	+	0.679036i
$363$	−71.3708	+	39.2364i	−3.74600	+	2.05938i
$364$	−1.96639	+	1.84656i	−0.103067	+	0.0967861i
$365$	−6.87082	+	22.6264i	−0.359635	+	1.18432i
$366$	−0.384042	+	0.816130i	−0.0200742	+	0.0426598i
$367$	−18.7573	−	22.6737i	−0.979125	−	1.18356i	−0.983007	−	0.183566i	$-0.941236\pi$
$367$	−18.7573	−	22.6737i	−0.979125	−	1.18356i	0.00388289	−	0.999992i	$-0.498764\pi$
$368$	−3.00404	+	9.24547i	−0.156596	+	0.481954i
$369$	−6.81310	−	1.74931i	−0.354676	−	0.0910653i
$370$	23.2388	+	20.9917i	1.20813	+	1.09130i
$371$	−0.270648	+	4.30183i	−0.0140514	+	0.223340i
$372$	11.1428	+	17.5583i	0.577729	+	0.910355i
$373$	24.4670	−	22.9760i	1.26685	−	1.18965i	0.294626	−	0.955613i	$-0.404805\pi$
$373$	24.4670	−	22.9760i	1.26685	−	1.18965i	0.972227	−	0.234041i	$-0.0751950\pi$
$374$	19.3964			1.00296
$375$	−12.9309	+	32.2075i	−0.667749	+	1.66319i
$376$	6.77811			0.349554
$377$	1.21418	−	1.14019i	0.0625335	−	0.0587228i
$378$	−9.64431	−	15.1970i	−0.496050	−	0.781649i
$379$	1.40267	−	22.2949i	0.0720505	−	1.14521i	−0.781398	−	0.624033i	$-0.785493\pi$
$379$	1.40267	−	22.2949i	0.0720505	−	1.14521i	0.853449	−	0.521177i	$-0.174507\pi$
$380$	4.20938	−	9.41387i	0.215936	−	0.482922i
$381$	11.4358	+	2.93621i	0.585873	+	0.150427i
$382$	−13.2842	+	40.8847i	−0.679681	+	2.09184i
$383$	−2.05793	−	2.48761i	−0.105155	−	0.127111i	0.715310	−	0.698807i	$-0.246286\pi$
$383$	−2.05793	−	2.48761i	−0.105155	−	0.127111i	−0.820465	+	0.571696i	$0.806286\pi$
$384$	−15.7597	+	33.4910i	−0.804232	+	1.70908i
$385$	9.96930	−	7.54202i	0.508083	−	0.384377i
$386$	−1.27465	+	1.19698i	−0.0648780	+	0.0609245i
$387$	−7.04870	+	3.87506i	−0.358306	+	0.196980i
$388$	6.66610	−	14.1662i	0.338420	−	0.719179i
$389$	4.43938	+	9.43416i	0.225085	+	0.478331i	0.985189	−	0.171471i	$-0.0548519\pi$
$389$	4.43938	+	9.43416i	0.225085	+	0.478331i	−0.760104	+	0.649802i	$0.774852\pi$
$390$	−30.5995	−	16.0594i	−1.54947	−	0.813199i
$391$	−3.52330	−	0.445097i	−0.178181	−	0.0225095i
$392$	−0.653520	−	10.3874i	−0.0330078	−	0.524643i
$393$	11.8232	+	36.3880i	0.596400	+	1.83553i
$394$	−11.7942	+	18.5847i	−0.594184	+	0.936284i
$395$	−12.3856	+	12.0901i	−0.623188	+	0.608321i
$396$	−40.3747	+	10.3665i	−2.02890	+	0.520934i
$397$	0.722274	−	11.4802i	0.0362499	−	0.576175i	−0.937418	−	0.348205i	$-0.886791\pi$
$397$	0.722274	−	11.4802i	0.0362499	−	0.576175i	0.973668	−	0.227970i	$-0.0732088\pi$
$398$	0.944406	−	4.95075i	0.0473388	−	0.248159i
$399$	3.93732	−	12.1178i	0.197113	−	0.606650i
$400$	−23.9518	+	7.14799i	−1.19759	+	0.357399i
$401$	−8.41676	−	25.9041i	−0.420313	−	1.29359i	−0.907411	−	0.420243i	$-0.861945\pi$
$401$	−8.41676	−	25.9041i	−0.420313	−	1.29359i	0.487098	−	0.873347i	$-0.338055\pi$
$402$	−11.2386	+	1.41976i	−0.560529	+	0.0708113i
$403$	17.3087	+	6.85298i	0.862206	+	0.341371i
$404$	7.82033	+	3.09629i	0.389076	+	0.154046i
$405$	21.0582	−	26.4817i	1.04639	−	1.31589i
$406$	0.0583012	+	0.926671i	0.00289344	+	0.0459899i
$407$	39.7237	−	28.8610i	1.96903	−	1.43059i
$408$	−9.27658	−	2.38182i	−0.459259	−	0.117918i
$409$	−20.6821	−	19.4218i	−1.02266	−	0.960346i	−0.0234405	−	0.999725i	$-0.507462\pi$
$409$	−20.6821	−	19.4218i	−1.02266	−	0.960346i	−0.999224	+	0.0393790i	$0.987462\pi$
$410$	1.68390	−	3.76588i	0.0831618	−	0.185983i
$411$	−21.8684	−	12.0223i	−1.07869	−	0.593014i
$412$	15.4790	+	1.95546i	0.762597	+	0.0963384i
$413$	−0.532347	−	2.79066i	−0.0261951	−	0.137320i
$414$	22.2837	−	2.81508i	1.09518	−	0.138354i
$415$	−7.89435	−	2.95026i	−0.387519	−	0.144823i
$416$	−2.85264	−	14.9541i	−0.139862	−	0.733184i
$417$	25.7215	−	40.5306i	1.25959	−	1.98479i
$418$	−38.4962	−	27.9691i	−1.88291	−	1.36801i
$419$	2.47599	+	2.99296i	0.120960	+	0.146216i	0.827517	−	0.561440i	$-0.189753\pi$
$419$	2.47599	+	2.99296i	0.120960	+	0.146216i	−0.706557	+	0.707656i	$0.749753\pi$
$420$	6.03845	−	2.52698i	0.294646	−	0.123304i
$421$	−13.0049	−	20.4925i	−0.633821	−	0.998741i	−0.997732	−	0.0673079i	$-0.978559\pi$
$421$	−13.0049	−	20.4925i	−0.633821	−	0.998741i	0.363912	−	0.931433i	$-0.381441\pi$
$422$	29.5400	−	35.7078i	1.43799	−	1.73823i
$423$	−11.3365	−	24.0913i	−0.551199	−	1.17136i
$424$	−6.43044	−	4.67198i	−0.312290	−	0.226892i
$425$	−4.20457	−	8.10564i	−0.203952	−	0.393181i
$426$	30.2111	−	21.9496i	1.46373	−	1.06346i
$427$	−0.134025	−	0.0736810i	−0.00648594	−	0.00356567i
$428$	−2.01845	+	0.518250i	−0.0975655	+	0.0250506i
$429$	−34.5382	+	41.7495i	−1.66752	+	2.01569i
$430$	−1.54423	−	4.45735i	−0.0744692	−	0.214953i
$431$	−21.3331	+	8.44635i	−1.02758	+	0.406847i	−0.820602	−	0.571500i	$-0.806362\pi$
$431$	−21.3331	+	8.44635i	−1.02758	+	0.406847i	−0.206975	+	0.978346i	$0.566362\pi$
$432$	56.4289			2.71494
$433$	−20.4860	+	8.11098i	−0.984495	+	0.389789i	−0.804548	−	0.593887i	$-0.797592\pi$
$433$	−20.4860	+	8.11098i	−0.984495	+	0.389789i	−0.179946	+	0.983676i	$0.557592\pi$
$434$	−9.09390	+	4.99941i	−0.436521	+	0.239979i
$435$	−3.72855	+	1.56033i	−0.178770	+	0.0748119i
$436$	−3.70939	+	19.4453i	−0.177647	+	0.931260i
$437$	6.35091	+	5.96390i	0.303805	+	0.285292i
$438$	41.6507	+	39.1126i	1.99015	+	1.86887i
$439$	0.355194	−	1.86199i	0.0169525	−	0.0888680i	−0.972806	−	0.231624i	$-0.925596\pi$
$439$	0.355194	−	1.86199i	0.0169525	−	0.0888680i	0.989758	+	0.142755i	$0.0455963\pi$
$440$	1.89220	+	22.9742i	0.0902073	+	1.09525i
$441$	−35.8267	+	19.6959i	−1.70603	+	0.937899i
$442$	8.45366	−	3.34704i	0.402100	−	0.159203i
$443$	7.76788			0.369063			0.184532	−	0.982827i	$-0.440923\pi$
$443$	7.76788			0.369063			0.184532	+	0.982827i	$0.440923\pi$
$444$	23.9057	−	9.46496i	1.13452	−	0.449187i
$445$	0.743974	−	2.45000i	0.0352678	−	0.116141i
$446$	15.7271	−	19.0108i	0.744700	−	0.900188i
$447$	27.9192	−	7.16843i	1.32053	−	0.339055i
$448$	−0.590075	−	0.324397i	−0.0278784	−	0.0153263i
$449$	−9.10245	+	6.61332i	−0.429571	+	0.312102i	−0.781477	−	0.623934i	$-0.785534\pi$
$449$	−9.10245	+	6.61332i	−0.429571	+	0.312102i	0.351906	+	0.936035i	$0.385534\pi$
$450$	38.5062	+	43.0415i	1.81520	+	2.02899i
$451$	−5.23275	−	3.80181i	−0.246400	−	0.179020i
$452$	−4.93596	−	10.4894i	−0.232168	−	0.493382i
$453$	9.77805	−	11.8196i	0.459413	−	0.555335i
$454$	−3.15139	−	4.96580i	−0.147902	−	0.233057i
$455$	3.04354	−	5.00739i	0.142683	−	0.234750i
$456$	14.9768	+	18.1038i	0.701352	+	0.847788i
$457$	−26.7155	−	19.4099i	−1.24970	−	0.907958i	−0.251493	−	0.967859i	$-0.580921\pi$
$457$	−26.7155	−	19.4099i	−1.24970	−	0.907958i	−0.998204	+	0.0599013i	$0.980921\pi$
$458$	13.3381	−	21.0175i	0.623250	−	0.982085i
$459$	3.86272	+	20.2491i	0.180296	+	0.945146i
$460$	−0.194580	+	4.47163i	−0.00907235	+	0.208491i
$461$	32.1468	−	4.06109i	1.49723	−	0.189144i	0.666366	−	0.745624i	$-0.267849\pi$
$461$	32.1468	−	4.06109i	1.49723	−	0.189144i	0.830861	+	0.556481i	$0.187849\pi$
$462$	−5.65987	−	29.6701i	−0.263321	−	1.38038i
$463$	13.5498	+	1.71173i	0.629711	+	0.0795509i	0.433710	−	0.901053i	$-0.357204\pi$
$463$	13.5498	+	1.71173i	0.629711	+	0.0795509i	0.196001	+	0.980604i	$0.437204\pi$
$464$	−2.55091	−	1.40237i	−0.118423	−	0.0651035i
$465$	−33.5228	−	30.2812i	−1.55458	−	1.40426i
$466$	37.0579	+	34.7996i	1.71667	+	1.61206i
$467$	29.3775	+	7.54287i	1.35943	+	0.349043i	0.856885	−	0.515508i	$-0.172397\pi$
$467$	29.3775	+	7.54287i	1.35943	+	0.349043i	0.502546	+	0.864550i	$0.332397\pi$
$468$	−15.8079	+	11.4851i	−0.730722	+	0.530900i
$469$	−0.120609	−	1.91703i	−0.00556921	−	0.0885201i
$470$	15.0461	−	4.17503i	0.694026	−	0.192580i
$471$	−37.9221	−	15.0144i	−1.74736	−	0.691828i
$472$	4.87101	+	1.92857i	0.224206	+	0.0887696i
$473$	−7.33802	+	0.927007i	−0.337402	+	0.0426238i
$474$	12.9235	+	39.7743i	0.593594	+	1.82690i
$475$	−3.34328	+	22.1502i	−0.153400	+	1.01632i
$476$	−0.532196	+	1.63793i	−0.0243932	+	0.0750745i
$477$	−5.85052	+	30.6695i	−0.267877	+	1.40426i
$478$	2.81290	−	44.7098i	0.128659	−	2.04498i
$479$	2.28887	−	0.587682i	0.104581	−	0.0268519i	−0.196037	−	0.980597i	$-0.562807\pi$
$479$	2.28887	−	0.587682i	0.104581	−	0.0268519i	0.300618	+	0.953745i	$0.402807\pi$
$480$	−6.21913	+	36.4155i	−0.283863	+	1.66213i
$481$	12.3328	−	19.4334i	0.562327	−	0.886086i
$482$	−5.82686	−	17.9332i	−0.265406	−	0.816837i
$483$	0.347249	+	5.51936i	0.0158004	+	0.251140i
$484$	−26.7939	−	3.38486i	−1.21791	−	0.153857i
$485$	−5.72544	+	33.5248i	−0.259979	+	1.52228i
$486$	−9.71307	−	20.6413i	−0.440594	−	0.936310i
$487$	−13.2020	+	28.0556i	−0.598238	+	1.27132i	0.344813	+	0.938672i	$0.387942\pi$
$487$	−13.2020	+	28.0556i	−0.598238	+	1.27132i	−0.943051	+	0.332649i	$0.892058\pi$
$488$	0.247149	−	0.135871i	0.0111879	−	0.00615059i
$489$	25.7117	−	24.1449i	1.16272	−	1.09187i
$490$	−7.84890	−	22.6555i	−0.354577	−	1.02347i
$491$	−3.73200	+	7.93090i	−0.168423	+	0.357916i	−0.971165	−	0.238410i	$-0.923374\pi$
$491$	−3.73200	+	7.93090i	−0.168423	+	0.357916i	0.802742	+	0.596327i	$0.203374\pi$
$492$	−2.15890	−	2.60966i	−0.0973306	−	0.117653i
$493$	0.328614	−	1.01137i	0.0148000	−	0.0455498i
$494$	−21.6044	−	5.54707i	−0.972028	−	0.249574i
$495$	78.4918	−	45.1500i	3.52794	−	2.02934i
$496$	2.04288	−	32.4707i	0.0917280	−	1.45798i
$497$	3.39289	+	5.34634i	0.152192	+	0.239816i
$498$	−14.8442	+	13.9397i	−0.665186	+	0.624651i
$499$	32.3758			1.44934			0.724669	−	0.689097i	$-0.241993\pi$
$499$	32.3758			1.44934			0.724669	+	0.689097i	$0.241993\pi$
$500$	−9.74642	+	6.11988i	−0.435873	+	0.273689i
$501$	35.7124			1.59551
$502$	−11.2853	+	10.5976i	−0.503689	+	0.472995i
$503$	14.6638	+	23.1065i	0.653827	+	1.03027i	0.995888	+	0.0905886i	$0.0288748\pi$
$503$	14.6638	+	23.1065i	0.653827	+	1.03027i	−0.342062	+	0.939678i	$0.611125\pi$
$504$	−0.644938	+	10.2510i	−0.0287278	+	0.456616i
$505$	−18.1681	−	1.93892i	−0.808468	−	0.0862807i
$506$	20.0044	+	5.13626i	0.889304	+	0.228334i
$507$	4.62166	−	14.2240i	0.205255	−	0.631710i
$508$	2.49556	+	3.01661i	0.110723	+	0.133841i
$509$	0.224454	−	0.476990i	0.00994877	−	0.0211422i	−0.899791	−	0.436321i	$-0.856281\pi$
$509$	0.224454	−	0.476990i	0.00994877	−	0.0211422i	0.909740	+	0.415179i	$0.136281\pi$
$510$	−22.0593	+	0.426789i	−0.976804	+	0.0188985i
$511$	−7.06250	+	6.63213i	−0.312427	+	0.293388i
$512$	−8.51339	+	4.68028i	−0.376242	+	0.206841i
$513$	21.5323	−	45.7584i	0.950674	−	2.02028i
$514$	−8.66573	−	18.4156i	−0.382229	−	0.812278i
$515$	−33.5368	+	4.89749i	−1.47781	+	0.215809i
$516$	−3.84247	−	0.485417i	−0.169155	−	0.0213693i
$517$	−1.53728	−	24.4343i	−0.0676094	−	1.07462i
$518$	3.96487	+	12.2026i	0.174206	+	0.536152i
$519$	−8.90861	+	14.0377i	−0.391045	+	0.616188i
$520$	4.78911	+	9.68646i	0.210016	+	0.424780i
$521$	9.50124	−	2.43950i	0.416257	−	0.106877i	−0.0347521	−	0.999396i	$-0.511064\pi$
$521$	9.50124	−	2.43950i	0.416257	−	0.106877i	0.451009	+	0.892519i	$0.351064\pi$
$522$	−0.422313	+	6.71247i	−0.0184841	+	0.293797i
$523$	−0.586785	+	3.07603i	−0.0256583	+	0.134506i	−0.992811	−	0.119689i	$-0.961810\pi$
$523$	−0.586785	+	3.07603i	−0.0256583	+	0.134506i	0.967153	+	0.254194i	$0.0818103\pi$
$524$	−3.92052	+	12.0661i	−0.171269	+	0.527111i
$525$	−11.1720	+	8.79682i	−0.487588	+	0.383925i
$526$	7.10985	+	21.8819i	0.310004	+	0.954095i
$527$	11.7917	−	1.48964i	0.513654	−	0.0648896i
$528$	88.0468	+	34.8602i	3.83175	+	1.51710i
$529$	17.8690	+	7.07483i	0.776912	+	0.307601i
$530$	−17.1521	−	6.41005i	−0.745040	−	0.278435i
$531$	−1.29217	−	20.5385i	−0.0560754	−	0.891293i
$532$	3.41811	−	2.48340i	0.148194	−	0.107669i
$533$	−2.93666	−	0.754007i	−0.127201	−	0.0326597i
$534$	−4.50994	−	4.23512i	−0.195164	−	0.183272i
$535$	3.92404	−	2.25719i	0.169651	−	0.0975867i
$536$	3.10394	+	1.70641i	0.134070	+	0.0737055i
$537$	−46.1377	−	5.82855i	−1.99099	−	0.251520i
$538$	−3.02297	−	15.8470i	−0.130330	−	0.683211i
$539$	−37.2972	+	4.71173i	−1.60650	+	0.202949i
$540$	25.0350	−	6.94677i	1.07734	−	0.298941i
$541$	−1.85486	−	9.72350i	−0.0797465	−	0.418046i	−0.999664	−	0.0259331i	$-0.991744\pi$
$541$	−1.85486	−	9.72350i	−0.0797465	−	0.418046i	0.919917	−	0.392113i	$-0.128256\pi$
$542$	−7.51753	+	11.8457i	−0.322906	+	0.508818i
$543$	−20.6024	−	14.9685i	−0.884134	−	0.642361i
$544$	−6.19553	−	7.48911i	−0.265631	−	0.321093i
$545$	−3.52986	−	42.8577i	−0.151202	−	1.83582i
$546$	−7.58664	−	11.9546i	−0.324678	−	0.511611i
$547$	9.91408	−	11.9841i	0.423896	−	0.512402i	−0.514724	−	0.857356i	$-0.672106\pi$
$547$	9.91408	−	11.9841i	0.423896	−	0.512402i	0.938619	+	0.344954i	$0.112106\pi$
$548$	−3.52335	−	7.48749i	−0.150510	−	0.319850i
$549$	−0.896282	−	0.651187i	−0.0382524	−	0.0277920i
$550$	18.3515	+	49.8328i	0.782509	+	2.12488i
$551$	−2.11057	+	1.53342i	−0.0899134	+	0.0653259i
$552$	−8.93664	−	4.91296i	−0.380369	−	0.209109i
$553$	−6.86863	+	1.76356i	−0.292084	+	0.0749944i
$554$	8.25824	−	9.98249i	0.350859	−	0.424115i
$555$	−44.5424	+	33.6974i	−1.89072	+	1.43037i
$556$	14.8000	−	5.85972i	0.627658	−	0.248507i
$557$	10.9186			0.462638			0.231319	−	0.972878i	$-0.425696\pi$
$557$	10.9186			0.462638			0.231319	+	0.972878i	$0.425696\pi$
$558$	−69.8923	+	27.6723i	−2.95878	+	1.17146i
$559$	−3.03821	+	1.67027i	−0.128503	+	0.0706450i
$560$	−9.96674	−	2.35450i	−0.421172	−	0.0994957i
$561$	−6.48226	+	33.9812i	−0.273681	+	1.43469i
$562$	−30.9698	−	29.0826i	−1.30638	−	1.22677i
$563$	3.06738	+	2.88046i	0.129275	+	0.121397i	0.746488	−	0.665399i	$-0.231738\pi$
$563$	3.06738	+	2.88046i	0.129275	+	0.121397i	−0.617213	+	0.786796i	$0.711738\pi$
$564$	2.40224	−	12.5930i	0.101152	−	0.530260i
$565$	16.4246	+	19.0897i	0.690988	+	0.803111i
$566$	6.72856	−	3.69906i	0.282822	−	0.155483i
$567$	12.8887	−	5.10301i	0.541276	−	0.214306i
$568$	−11.6766			−0.489940
$569$	15.4019	−	6.09804i	0.645681	−	0.255643i	−0.0223802	−	0.999750i	$-0.507124\pi$
$569$	15.4019	−	6.09804i	0.645681	−	0.255643i	0.668061	+	0.744106i	$0.267124\pi$
$570$	44.3968	+	30.9620i	1.85958	+	1.29685i
$571$	−25.5990	+	30.9439i	−1.07129	+	1.29496i	−0.117960	+	0.993018i	$0.537635\pi$
$571$	−25.5990	+	30.9439i	−1.07129	+	1.29496i	−0.953326	+	0.301943i	$0.902365\pi$
$572$	−17.4028	+	4.46827i	−0.727646	+	0.186828i
$573$	−67.1877	−	36.9367i	−2.80681	−	1.54305i
$574$	1.36736	−	0.993447i	0.0570726	−	0.0414657i
$575$	−2.18996	−	9.47310i	−0.0913275	−	0.395056i
$576$	−3.94608	−	2.86699i	−0.164420	−	0.119458i
$577$	−2.99943	−	6.37412i	−0.124868	−	0.265358i	0.832613	−	0.553856i	$-0.186844\pi$
$577$	−2.99943	−	6.37412i	−0.124868	−	0.265358i	−0.957481	+	0.288498i	$0.906844\pi$
$578$	−15.1603	+	18.3256i	−0.630584	+	0.762245i
$579$	−1.67104	−	2.63313i	−0.0694458	−	0.109429i
$580$	−1.30437	−	0.308138i	−0.0541609	−	0.0127947i
$581$	−2.20097	−	2.66051i	−0.0913116	−	0.110377i
$582$	66.4829	+	48.3026i	2.75580	+	2.00221i
$583$	−15.3836	+	24.2406i	−0.637122	+	1.00394i
$584$	−3.34771	−	17.5493i	−0.138529	−	0.726195i
$585$	26.4185	−	33.2226i	1.09227	−	1.37358i
$586$	−26.9665	+	3.40667i	−1.11398	+	0.140728i
$587$	4.69237	+	24.5983i	0.193675	+	1.01528i	0.937783	+	0.347221i	$0.112875\pi$
$587$	4.69237	+	24.5983i	0.193675	+	1.01528i	−0.744108	+	0.668059i	$0.767125\pi$
$588$	−19.5302	−	2.46724i	−0.805414	−	0.101747i
$589$	−25.5511	−	14.0468i	−1.05281	−	0.578789i
$590$	12.0006	+	1.28072i	0.494058	+	0.0527265i
$591$	−28.6175	−	26.8737i	−1.17717	−	1.10543i
$592$	−38.9617	−	10.0037i	−1.60132	−	0.411148i
$593$	9.88538	−	7.18215i	0.405944	−	0.294936i	−0.366014	−	0.930609i	$-0.619278\pi$
$593$	9.88538	−	7.18215i	0.405944	−	0.294936i	0.771958	+	0.635674i	$0.219278\pi$
$594$	−7.52769	−	119.649i	−0.308865	−	4.90926i
$595$	0.162642	−	3.73766i	0.00666767	−	0.153229i
$596$	8.88698	+	3.51860i	0.364025	+	0.144128i
$597$	8.35776	+	3.30907i	0.342060	+	0.135431i
$598$	9.60496	−	1.21339i	0.392776	−	0.0496192i
$599$	−2.20543	−	6.78763i	−0.0901116	−	0.277335i	0.895837	−	0.444382i	$-0.146577\pi$
$599$	−2.20543	−	6.78763i	−0.0901116	−	0.277335i	−0.985949	+	0.167047i	$0.946577\pi$
$600$	−2.65750	−	26.0867i	−0.108492	−	1.06498i
$601$	0.656755	−	2.02128i	0.0267896	−	0.0824499i	−0.936768	−	0.349951i	$-0.886198\pi$
$601$	0.656755	−	2.02128i	0.0267896	−	0.0824499i	0.963557	+	0.267502i	$0.0861981\pi$
$602$	0.362157	−	1.89849i	0.0147604	−	0.0773769i
$603$	0.873649	−	13.8863i	0.0355777	−	0.565492i
$604$	4.92687	−	1.26500i	0.200471	−	0.0514723i
$605$	58.0515	−	8.47747i	2.36013	−	0.344658i
$606$	−23.6557	+	37.2754i	−0.960947	+	1.51421i
$607$	13.0359	+	40.1205i	0.529112	+	1.62844i	0.756037	+	0.654528i	$0.227133\pi$
$607$	13.0359	+	40.1205i	0.529112	+	1.62844i	−0.226925	+	0.973912i	$0.572867\pi$
$608$	1.49721	+	23.7975i	0.0607200	+	0.965116i
$609$	−1.64295	−	0.207553i	−0.0665757	−	0.00841046i
$610$	0.464932	−	0.453841i	0.0188246	−	0.0183755i
$611$	−4.88639	−	10.3841i	−0.197682	−	0.420096i
$612$	−5.31167	+	11.2879i	−0.214711	+	0.456285i
$613$	−14.9638	+	8.22645i	−0.604384	+	0.332263i	−0.754394	−	0.656421i	$-0.772069\pi$
$613$	−14.9638	+	8.22645i	−0.604384	+	0.332263i	0.150010	+	0.988684i	$0.452069\pi$
$614$	11.1542	−	10.4745i	0.450147	−	0.422716i
$615$	6.03481	+	4.20863i	0.243347	+	0.169708i
$616$	−4.02136	+	8.54582i	−0.162025	+	0.344321i
$617$	17.0526	+	20.6130i	0.686511	+	0.829850i	0.992508	−	0.122183i	$-0.0389895\pi$
$617$	17.0526	+	20.6130i	0.686511	+	0.829850i	−0.305996	+	0.952033i	$0.598990\pi$
$618$	−25.3063	+	77.8849i	−1.01797	+	3.13299i
$619$	6.85421	+	1.75986i	0.275494	+	0.0707348i	0.383909	−	0.923371i	$-0.374578\pi$
$619$	6.85421	+	1.75986i	0.275494	+	0.0707348i	−0.108415	+	0.994106i	$0.534578\pi$
$620$	−3.09102	−	14.6573i	−0.124138	−	0.588651i
$621$	−1.37825	+	21.9067i	−0.0553073	+	0.879084i
$622$	17.8308	+	28.0968i	0.714948	+	1.12658i
$623$	0.764729	−	0.718129i	0.0306382	−	0.0287712i
$624$	44.3895			1.77700
$625$	16.8468	−	18.4712i	0.673870	−	0.738850i
$626$	−35.0813			−1.40213
$627$	61.8654	−	58.0955i	2.47067	−	2.32011i
$628$	−7.24683	−	11.4192i	−0.289180	−	0.455675i
$629$	0.922700	−	14.6659i	0.0367905	−	0.584768i
$630$	4.88254	+	23.1525i	0.194525	+	0.922419i
$631$	−29.3688	−	7.54064i	−1.16916	−	0.300188i	−0.386289	−	0.922378i	$-0.626243\pi$
$631$	−29.3688	−	7.54064i	−1.16916	−	0.300188i	−0.782866	+	0.622190i	$0.786243\pi$
$632$	4.04098	−	12.4369i	0.160742	−	0.494712i
$633$	52.6854	+	63.6857i	2.09406	+	2.53128i
$634$	10.1665	−	21.6049i	0.403762	−	0.858038i
$635$	−6.97588	−	4.86493i	−0.276829	−	0.193059i
$636$	−10.9590	+	10.2912i	−0.434554	+	0.408074i
$637$	−15.4424	+	8.48955i	−0.611851	+	0.336368i
$638$	−2.63323	+	5.59590i	−0.104251	+	0.221544i
$639$	19.5293	+	41.5019i	0.772567	+	1.64179i
$640$	19.0791	−	18.6240i	0.754168	−	0.736177i
$641$	−19.0322	−	2.40433i	−0.751727	−	0.0949652i	−0.259873	−	0.965643i	$-0.583681\pi$
$641$	−19.0322	−	2.40433i	−0.751727	−	0.0949652i	−0.491854	+	0.870678i	$0.663681\pi$
$642$	−0.686816	−	10.9166i	−0.0271065	−	0.430845i
$643$	−7.10768	−	21.8752i	−0.280300	−	0.862673i	−0.987768	−	0.155929i	$-0.950163\pi$
$643$	−7.10768	−	21.8752i	−0.280300	−	0.862673i	0.707469	−	0.706745i	$-0.249837\pi$
$644$	−0.982610	+	1.54835i	−0.0387203	+	0.0610134i
$645$	8.32506	−	1.21574i	0.327799	−	0.0478697i
$646$	−13.7934	+	3.54154i	−0.542694	+	0.139340i
$647$	1.23250	−	19.5900i	0.0484546	−	0.770163i	−0.896517	−	0.443010i	$-0.853911\pi$
$647$	1.23250	−	19.5900i	0.0484546	−	0.770163i	0.944971	−	0.327153i	$-0.106089\pi$
$648$	−4.78994	+	25.1097i	−0.188166	+	0.986403i
$649$	5.84752	−	17.9968i	0.229535	−	0.706437i
$650$	16.5974	+	18.5522i	0.651003	+	0.727678i
$651$	−5.71946	−	17.6027i	−0.224163	−	0.689904i
$652$	11.6036	−	1.46588i	0.454434	−	0.0574083i
$653$	−18.9838	−	7.51622i	−0.742894	−	0.294133i	−0.0339753	−	0.999423i	$-0.510817\pi$
$653$	−18.9838	−	7.51622i	−0.742894	−	0.294133i	−0.708919	+	0.705290i	$0.750817\pi$
$654$	−96.6094	−	38.2504i	−3.77773	−	1.49571i
$655$	1.19813	−	27.5342i	0.0468149	−	1.07585i
$656$	0.332717	+	5.28839i	0.0129904	+	0.206477i
$657$	−56.7759	+	41.2501i	−2.21504	+	1.60932i
$658$	6.19654	+	1.59100i	0.241566	+	0.0620236i
$659$	30.2633	+	28.4191i	1.17889	+	1.10705i	0.992203	+	0.124633i	$0.0397753\pi$
$659$	30.2633	+	28.4191i	1.17889	+	1.10705i	0.186688	+	0.982419i	$0.440225\pi$
$660$	43.3540	+	4.62680i	1.68755	+	0.180098i
$661$	28.0945	+	15.4451i	1.09275	+	0.600744i	0.923022	−	0.384747i	$-0.125711\pi$
$661$	28.0945	+	15.4451i	1.09275	+	0.600744i	0.169727	+	0.985491i	$0.445711\pi$
$662$	−18.0202	−	2.27647i	−0.700373	−	0.0884777i
$663$	3.03859	+	15.9288i	0.118009	+	0.618624i
$664$	6.31711	−	0.798037i	0.245152	−	0.0309698i
$665$	−5.71241	+	7.18364i	−0.221518	+	0.278570i
$666$	17.4152	+	91.2939i	0.674827	+	3.53757i
$667$	0.606730	−	0.956053i	0.0234927	−	0.0370185i
$668$	9.58047	+	6.96062i	0.370679	+	0.269314i
$669$	28.0497	+	33.9062i	1.08446	+	1.31089i
$670$	7.94124	+	1.87600i	0.306797	+	0.0724763i
$671$	−0.545853	−	0.860127i	−0.0210724	−	0.0332048i
$672$	−9.64800	+	11.6624i	−0.372180	+	0.449888i
$673$	−8.15953	−	17.3399i	−0.314527	−	0.668404i	0.683582	−	0.729874i	$-0.260421\pi$
$673$	−8.15953	−	17.3399i	−0.314527	−	0.668404i	−0.998109	+	0.0614701i	$0.980421\pi$
$674$	−27.6854	−	20.1146i	−1.06640	−	0.774785i
$675$	−48.3688	+	29.0822i	−1.86172	+	1.11937i
$676$	4.01220	−	2.91504i	0.154316	−	0.112117i
$677$	0.0329787	+	0.0181302i	0.00126747	+	0.000696800i	0.482387	−	0.875958i	$-0.339770\pi$
$677$	0.0329787	+	0.0181302i	0.00126747	+	0.000696800i	−0.481120	+	0.876655i	$0.659770\pi$
$678$	58.9371	−	15.1325i	2.26346	−	0.581159i
$679$	−8.88213	+	10.7367i	−0.340865	+	0.412035i
$680$	5.65875	+	3.94637i	0.217003	+	0.151336i
$681$	9.75294	−	3.86146i	0.373734	−	0.147972i
$682$	−69.1217			−2.64681
$683$	27.9669	−	11.0729i	1.07012	−	0.423692i	0.234002	−	0.972236i	$-0.424818\pi$
$683$	27.9669	−	11.0729i	1.07012	−	0.423692i	0.836121	+	0.548545i	$0.184818\pi$
$684$	26.8189	−	14.7438i	1.02545	−	0.563744i
$685$	11.7241	+	13.6265i	0.447954	+	0.520641i
$686$	3.93228	−	20.6137i	0.150135	−	0.787036i
$687$	32.3637	+	30.3915i	1.23475	+	1.15951i
$688$	4.41707	+	4.14791i	0.168399	+	0.158138i
$689$	−2.52176	+	13.2195i	−0.0960714	+	0.503624i
$690$	−22.8638	−	5.40125i	−0.870411	−	0.205622i
$691$	30.5297	−	16.7839i	1.16141	−	0.638488i	0.219912	−	0.975520i	$-0.429423\pi$
$691$	30.5297	−	16.7839i	1.16141	−	0.638488i	0.941493	+	0.337032i	$0.109423\pi$
$692$	−5.12595	+	2.02951i	−0.194859	+	0.0771503i
$693$	37.1000			1.40931
$694$	57.4117	−	22.7309i	2.17932	−	0.862853i
$695$	−27.5760	+	20.8619i	−1.04602	+	0.791337i
$696$	1.94653	−	2.35296i	0.0737832	−	0.0891886i
$697$	−1.87492	+	0.481398i	−0.0710177	+	0.0182343i
$698$	−35.0404	−	19.2636i	−1.32630	−	0.729140i
$699$	−73.3513	+	53.2929i	−2.77440	+	2.01572i
$700$	−4.71166	+	0.182384i	−0.178084	+	0.00689347i
$701$	13.1514	+	9.55508i	0.496723	+	0.360890i	0.807764	−	0.589506i	$-0.200678\pi$
$701$	13.1514	+	9.55508i	0.496723	+	0.360890i	−0.311041	+	0.950397i	$0.600678\pi$
$702$	−23.9275	−	50.8485i	−0.903085	−	1.91915i
$703$	−22.9791	+	27.7770i	−0.866675	+	1.04763i
$704$	−2.40324	−	3.78690i	−0.0905754	−	0.142724i
$705$	2.28597	+	27.7551i	0.0860947	+	1.04532i
$706$	−5.72720	−	6.92300i	−0.215546	−	0.260550i
$707$	−6.05628	−	4.40014i	−0.227770	−	0.165484i
$708$	5.30940	−	8.36628i	0.199540	−	0.314424i
$709$	−4.58970	−	24.0600i	−0.172370	−	0.903594i	−0.958405	−	0.285412i	$-0.907870\pi$
$709$	−4.58970	−	24.0600i	−0.172370	−	0.903594i	0.786035	−	0.618182i	$-0.212130\pi$
$710$	−25.9199	+	7.19230i	−0.972755	+	0.269922i
$711$	−50.9626	+	6.43808i	−1.91125	+	0.241447i
$712$	0.362490	+	1.90024i	0.0135849	+	0.0712146i
$713$	12.5558	+	1.58616i	0.470217	+	0.0594022i
$714$	−7.92155	−	4.35491i	−0.296457	−	0.162978i
$715$	33.8324	−	19.4611i	1.26526	−	0.727804i
$716$	−11.2412	−	10.5562i	−0.420103	−	0.394503i
$717$	77.3884	+	19.8700i	2.89012	+	0.742058i
$718$	13.9932	−	10.1666i	0.522220	−	0.379415i
$719$	0.811196	+	12.8936i	0.0302525	+	0.480850i	0.983761	+	0.179484i	$0.0574427\pi$
$719$	0.811196	+	12.8936i	0.0302525	+	0.480850i	−0.953508	+	0.301366i	$0.902557\pi$
$720$	−69.4886	−	25.9691i	−2.58969	−	0.967813i
$721$	−12.9111	−	5.11185i	−0.480833	−	0.190375i
$722$	1.73538	+	0.687085i	0.0645841	+	0.0255707i
$723$	33.3652	−	4.21500i	1.24086	−	0.156758i
$724$	−2.60947	−	8.03113i	−0.0969803	−	0.298475i
$725$	2.90930	−	0.112616i	0.108049	−	0.00418246i
$726$	43.8048	−	134.817i	1.62575	−	5.00354i
$727$	7.73453	−	40.5458i	0.286858	−	1.50376i	−0.488682	−	0.872462i	$-0.662522\pi$
$727$	7.73453	−	40.5458i	0.286858	−	1.50376i	0.775540	−	0.631299i	$-0.217478\pi$
$728$	−0.277989	+	4.41851i	−0.0103030	+	0.163761i
$729$	−4.55847	+	1.17042i	−0.168832	+	0.0433488i
$730$	−18.2409	−	36.8941i	−0.675126	−	1.36551i
$731$	−1.18608	+	1.86897i	−0.0438689	+	0.0691263i
$732$	−0.164841	−	0.507328i	−0.00609270	−	0.0187514i
$733$	−0.913523	−	14.5200i	−0.0337418	−	0.536310i	−0.978198	−	0.207673i	$-0.933411\pi$
$733$	−0.913523	−	14.5200i	−0.0337418	−	0.536310i	0.944456	−	0.328637i	$-0.106589\pi$
$734$	50.8135	+	6.41924i	1.87556	+	0.236938i
$735$	42.3141	−	6.17928i	1.56078	−	0.227926i
$736$	−4.40658	−	9.36447i	−0.162429	−	0.345179i
$737$	5.44743	−	11.5764i	0.200659	−	0.426421i
$738$	10.7285	−	5.89804i	0.394922	−	0.217110i
$739$	−3.58412	+	3.36571i	−0.131844	+	0.123810i	−0.747664	−	0.664077i	$-0.768825\pi$
$739$	−3.58412	+	3.36571i	−0.131844	+	0.123810i	0.615820	+	0.787887i	$0.288825\pi$
$740$	−18.5171	+	0.358256i	−0.680703	+	0.0131698i
$741$	16.9383	−	35.9956i	0.622243	−	1.32233i
$742$	−4.78206	−	5.78051i	−0.175555	−	0.212209i
$743$	−7.21731	+	22.2126i	−0.264777	+	0.814901i	0.726967	+	0.686672i	$0.240929\pi$
$743$	−7.21731	+	22.2126i	−0.264777	+	0.814901i	−0.991745	+	0.128229i	$0.959071\pi$
$744$	33.0583	+	8.48794i	1.21198	+	0.311183i
$745$	−20.6461	−	2.20338i	−0.756414	−	0.0807254i
$746$	−3.66809	+	58.3027i	−0.134298	+	2.13461i
$747$	−13.4019	−	21.1180i	−0.490350	−	0.772668i
$748$	−8.36217	+	7.85260i	−0.305751	+	0.287120i
$749$	1.85474			0.0677707
$750$	−21.9674	−	56.2706i	−0.802137	−	2.05471i
$751$	−18.1277			−0.661491			−0.330745	−	0.943720i	$-0.607300\pi$
$751$	−18.1277			−0.661491			−0.330745	+	0.943720i	$0.607300\pi$
$752$	−14.6210	+	13.7300i	−0.533172	+	0.500682i
$753$	−14.7948	−	23.3128i	−0.539152	−	0.849567i
$754$	−0.182030	+	2.89329i	−0.00662915	+	0.105367i
$755$	−9.57824	+	5.50960i	−0.348588	+	0.200515i
$756$	10.3103	+	2.64724i	0.374983	+	0.0962793i
$757$	−8.19764	+	25.2297i	−0.297948	+	0.916991i	0.684267	+	0.729232i	$0.260122\pi$
$757$	−8.19764	+	25.2297i	−0.297948	+	0.916991i	−0.982215	+	0.187759i	$0.939878\pi$
$758$	24.7837	+	29.9583i	0.900184	+	1.08814i
$759$	−15.6838	+	33.3298i	−0.569287	+	1.20980i
$760$	−5.54040	−	15.9922i	−0.200972	−	0.580097i
$761$	16.1679	−	15.1827i	0.586086	−	0.550371i	−0.333757	−	0.942659i	$-0.608316\pi$
$761$	16.1679	−	15.1827i	0.586086	−	0.550371i	0.919842	+	0.392288i	$0.128316\pi$
$762$	−18.0078	+	9.89986i	−0.652353	+	0.358634i
$763$	7.50174	−	15.9420i	0.271581	−	0.577139i
$764$	−10.8250	−	23.0043i	−0.391635	−	0.832267i
$765$	4.56214	−	26.7131i	0.164944	−	0.965815i
$766$	5.57493	+	0.704278i	0.201430	+	0.0254466i
$767$	−0.556966	−	8.85273i	−0.0201109	−	0.319653i
$768$	−18.4975	−	56.9295i	−0.667472	−	2.05427i
$769$	25.5397	−	40.2441i	0.920983	−	1.45124i	0.0287893	−	0.999586i	$-0.490835\pi$
$769$	25.5397	−	40.2441i	0.920983	−	1.45124i	0.892194	−	0.451652i	$-0.149165\pi$
$770$	−3.66279	+	21.4471i	−0.131998	+	0.772900i
$771$	35.1590	−	9.02730i	1.26622	−	0.325110i
$772$	0.0649330	−	1.03208i	0.00233699	−	0.0371454i
$773$	1.21208	−	6.35393i	0.0435954	−	0.228535i	−0.953821	−	0.300377i	$-0.902888\pi$
$773$	1.21208	−	6.35393i	0.0435954	−	0.228535i	0.997416	+	0.0718416i	$0.0228876\pi$
$774$	4.32623	−	13.3148i	0.155503	−	0.478590i
$775$	14.9836	+	28.8855i	0.538225	+	1.03760i
$776$	−7.94040	−	24.4380i	−0.285044	−	0.877275i
$777$	−22.7032	+	2.86808i	−0.814473	+	0.102892i
$778$	−16.8730	−	6.68048i	−0.604925	−	0.239507i
$779$	4.41534	+	1.74816i	0.158196	+	0.0626342i
$780$	19.6937	−	5.46464i	0.705147	−	0.195666i
$781$	2.64826	+	42.0928i	0.0947621	+	1.50620i
$782$	5.00058	−	3.63313i	0.178820	−	0.129921i
$783$	−6.36629	−	1.63459i	−0.227513	−	0.0584153i
$784$	22.4508	+	21.0827i	0.801815	+	0.752954i
$785$	21.8018	+	19.6936i	0.778139	+	0.702896i
$786$	−58.3556	−	32.0812i	−2.08147	−	1.14430i
$787$	30.3051	+	3.82843i	1.08026	+	0.136469i	0.645262	−	0.763962i	$-0.276748\pi$
$787$	30.3051	+	3.82843i	1.08026	+	0.136469i	0.435000	+	0.900430i	$0.356748\pi$
$788$	−2.43927	−	12.7871i	−0.0868953	−	0.455521i
$789$	−40.7117	+	5.14308i	−1.44937	+	0.183099i
$790$	1.30963	−	30.0966i	0.0465947	−	1.07079i
$791$	1.93337	+	10.1351i	0.0687427	+	0.360362i
$792$	−36.6581	+	57.7639i	−1.30259	+	2.05255i
$793$	−0.386326	−	0.280682i	−0.0137188	−	0.00996732i
$794$	12.7618	+	15.4263i	0.452898	+	0.547460i
$795$	16.9622	−	27.9071i	0.601587	−	0.989763i
$796$	1.59715	+	2.51671i	0.0566095	+	0.0892023i
$797$	−26.9951	+	32.6314i	−0.956214	+	1.15586i	0.0314858	+	0.999504i	$0.489976\pi$
$797$	−26.9951	+	32.6314i	−0.956214	+	1.15586i	−0.987700	+	0.156360i	$0.950024\pi$
$798$	9.44230	+	20.0659i	0.334254	+	0.710325i
$799$	−5.92775	−	4.30676i	−0.209709	−	0.152362i
$800$	13.3791	−	23.0031i	0.473022	−	0.813281i
$801$	6.14771	−	4.46657i	0.217219	−	0.157819i
$802$	41.5426	+	22.8382i	1.46692	+	0.806446i
$803$	−62.5040	+	16.0483i	−2.20572	+	0.566332i
$804$	4.27038	−	5.16201i	0.150605	−	0.182050i
$805$	1.15749	−	3.81175i	0.0407962	−	0.134347i
$806$	−30.1258	+	11.9276i	−1.06114	+	0.420133i
$807$	28.7731			1.01286
$808$	12.8351	−	5.08176i	0.451536	−	0.178776i
$809$	−10.8312	+	5.95450i	−0.380804	+	0.209349i	−0.660647	−	0.750697i	$-0.729718\pi$
$809$	−10.8312	+	5.95450i	−0.380804	+	0.209349i	0.279842	+	0.960046i	$0.409718\pi$
$810$	4.83378	+	58.6892i	0.169842	+	2.06213i
$811$	−3.66160	+	19.1948i	−0.128576	+	0.674020i	0.858378	+	0.513018i	$0.171473\pi$
$811$	−3.66160	+	19.1948i	−0.128576	+	0.674020i	−0.986954	+	0.161002i	$0.948527\pi$
$812$	−0.400296	−	0.375903i	−0.0140476	−	0.0131916i
$813$	−18.2406	−	17.1290i	−0.639725	−	0.600742i
$814$	−16.0138	+	83.9471i	−0.561282	+	2.94234i
$815$	−23.4375	+	9.80815i	−0.820980	+	0.343565i
$816$	24.8351	−	13.6532i	0.869401	−	0.477957i
$817$	5.04904	−	1.99906i	0.176643	−	0.0699381i
$818$	49.3811			1.72657
$819$	16.1695	−	6.40197i	0.565009	−	0.223703i
$820$	0.798648	+	2.30527i	0.0278900	+	0.0805034i
$821$	−19.8065	+	23.9419i	−0.691251	+	0.835579i	−0.993038	−	0.117797i	$-0.962417\pi$
$821$	−19.8065	+	23.9419i	−0.691251	+	0.835579i	0.301787	+	0.953375i	$0.402417\pi$
$822$	42.0700	−	10.8017i	1.46736	−	0.376754i
$823$	36.0786	+	19.8344i	1.25762	+	0.691383i	0.964346	−	0.264645i	$-0.0852548\pi$
$823$	36.0786	+	19.8344i	1.25762	+	0.691383i	0.293275	+	0.956028i	$0.405255\pi$
$824$	20.7163	−	15.0513i	0.721687	−	0.524336i
$825$	−93.4368	+	15.4964i	−3.25305	+	0.539517i
$826$	4.00038	+	2.90645i	0.139191	+	0.101128i
$827$	−9.44207	−	20.0654i	−0.328333	−	0.697743i	0.670699	−	0.741730i	$-0.265994\pi$
$827$	−9.44207	−	20.0654i	−0.328333	−	0.697743i	−0.999032	+	0.0439863i	$0.985994\pi$
$828$	−8.46724	+	10.2351i	−0.294257	+	0.355696i
$829$	22.5055	+	35.4629i	0.781647	+	1.23168i	0.968432	+	0.249278i	$0.0801933\pi$
$829$	22.5055	+	35.4629i	0.781647	+	1.23168i	−0.186785	+	0.982401i	$0.559807\pi$
$830$	13.5312	−	5.66257i	0.469676	−	0.196551i
$831$	14.7288	+	17.8040i	0.510935	+	0.617614i
$832$	−1.70088	−	1.23577i	−0.0589676	−	0.0428425i
$833$	−6.02855	+	9.49948i	−0.208877	+	0.329137i
$834$	15.6557	+	82.0701i	0.542113	+	2.84186i
$835$	−24.0969	−	9.00546i	−0.833909	−	0.311647i
$836$	27.9197	−	3.52708i	0.965624	−	0.121987i
$837$	−13.7653	−	72.1603i	−0.475799	−	2.49423i
$838$	−6.70746	−	0.847349i	−0.231705	−	0.0292712i
$839$	0.698953	+	0.384253i	0.0241305	+	0.0132659i	0.493773	−	0.869591i	$-0.335617\pi$
$839$	0.698953	+	0.384253i	0.0241305	+	0.0132659i	−0.469643	+	0.882857i	$0.655617\pi$
$840$	4.38541	−	9.80756i	0.151311	−	0.338393i
$841$	−20.8929	−	19.6198i	−0.720446	−	0.676543i
$842$	40.9161	+	10.5055i	1.41006	+	0.362043i
$843$	61.3008	−	44.5376i	2.11131	−	1.53396i
$844$	1.72094	+	27.3536i	0.0592372	+	0.941548i
$845$	−6.70527	+	8.43221i	−0.230668	+	0.290077i
$846$	43.0871	+	17.0594i	1.48137	+	0.586514i
$847$	22.3488	+	8.84852i	0.767915	+	0.304039i
$848$	23.3347	−	2.94786i	0.801318	−	0.101230i
$849$	4.23182	+	13.0242i	0.145236	+	0.446990i
$850$	14.9922	+	5.27464i	0.514227	+	0.180919i
$851$	4.83522	−	14.8813i	0.165749	−	0.510124i
$852$	−4.13832	+	21.6938i	−0.141776	+	0.743218i
$853$	0.517248	−	8.22142i	0.0177102	−	0.281496i	−0.979197	−	0.202911i	$-0.934960\pi$
$853$	0.517248	−	8.22142i	0.0177102	−	0.281496i	0.996907	−	0.0785851i	$-0.0250402\pi$
$854$	0.257835	−	0.0662008i	0.00882294	−	0.00226535i
$855$	−47.5741	+	46.4392i	−1.62700	+	1.58819i
$856$	−1.83265	+	2.88779i	−0.0626386	+	0.0987026i
$857$	−8.83501	−	27.1914i	−0.301798	−	0.928839i	−0.980853	−	0.194751i	$-0.937610\pi$
$857$	−8.83501	−	27.1914i	−0.301798	−	0.928839i	0.679055	−	0.734088i	$-0.262390\pi$
$858$	−5.92161	−	94.1214i	−0.202161	−	3.21325i
$859$	43.2101	+	5.45870i	1.47431	+	0.186249i	0.821037	−	0.570875i	$-0.193396\pi$
$859$	43.2101	+	5.45870i	1.47431	+	0.186249i	0.653272	+	0.757123i	$0.273396\pi$
$860$	2.47030	+	1.29647i	0.0842365	+	0.0442094i
$861$	1.28348	+	2.72754i	0.0437409	+	0.0929542i
$862$	17.0033	−	36.1339i	0.579136	−	1.23073i
$863$	21.2870	−	11.7026i	0.724617	−	0.398361i	−0.0763416	−	0.997082i	$-0.524324\pi$
$863$	21.2870	−	11.7026i	0.724617	−	0.398361i	0.800958	+	0.598720i	$0.204324\pi$
$864$	−43.7930	+	41.1244i	−1.48987	+	1.39908i
$865$	9.55092	−	7.22550i	0.324741	−	0.245674i
$866$	16.3282	−	34.6992i	0.554855	−	1.17913i
$867$	−27.0387	−	32.6842i	−0.918282	−	1.11001i
$868$	1.89655	−	5.83699i	0.0643732	−	0.198120i
$869$	−45.7500	−	11.7466i	−1.55196	−	0.398476i
$870$	2.87162	−	6.42210i	0.0973569	−	0.217730i
$871$	0.376570	−	5.98541i	0.0127596	−	0.202808i
$872$	17.4090	+	27.4322i	0.589542	+	0.928970i
$873$	−73.5791	+	69.0954i	−2.49027	+	2.33852i
$874$	−15.1636			−0.512916
$875$	9.75659	−	3.11844i	0.329833	−	0.105423i
$876$	−33.7911			−1.14169
$877$	−6.11334	+	5.74080i	−0.206433	+	0.193853i	−0.780867	−	0.624698i	$-0.785222\pi$
$877$	−6.11334	+	5.74080i	−0.206433	+	0.193853i	0.574434	+	0.818551i	$0.305222\pi$
$878$	1.76782	+	2.78564i	0.0596611	+	0.0940109i
$879$	3.04394	−	48.3821i	0.102670	−	1.63189i
$880$	−50.6190	−	45.7243i	−1.70637	−	1.54137i
$881$	−28.6656	−	7.36007i	−0.965768	−	0.247967i	−0.267304	−	0.963612i	$-0.586133\pi$
$881$	−28.6656	−	7.36007i	−0.965768	−	0.247967i	−0.698464	+	0.715645i	$0.746133\pi$
$882$	21.9891	−	67.6755i	0.740412	−	2.27875i
$883$	26.2998	+	31.7910i	0.885059	+	1.06985i	0.997096	+	0.0761485i	$0.0242623\pi$
$883$	26.2998	+	31.7910i	0.885059	+	1.06985i	−0.112038	+	0.993704i	$0.535738\pi$
$884$	−2.28950	+	4.86543i	−0.0770041	+	0.163642i
$885$	−6.25434	+	20.5963i	−0.210237	+	0.692337i
$886$	−9.85567	+	9.25509i	−0.331108	+	0.310931i
$887$	3.68697	−	2.02693i	0.123797	−	0.0680577i	−0.418652	−	0.908147i	$-0.637497\pi$
$887$	3.68697	−	2.02693i	0.123797	−	0.0680577i	0.542449	+	0.840089i	$0.317497\pi$
$888$	17.9672	−	38.1823i	0.602941	−	1.28131i
$889$	−1.48363	−	3.15287i	−0.0497593	−	0.105744i
$890$	1.97513	+	3.99490i	0.0662065	+	0.133909i
$891$	91.6041	+	11.5723i	3.06885	+	0.387686i
$892$	0.916228	+	14.5630i	0.0306776	+	0.487606i
$893$	5.55461	+	17.0953i	0.185878	+	0.572073i
$894$	−26.8822	+	42.3596i	−0.899076	+	1.41672i
$895$	29.6616	+	15.5672i	0.991479	+	0.520353i
$896$	10.5806	−	2.71664i	0.353474	−	0.0907566i
$897$	−1.08419	+	17.2328i	−0.0362002	+	0.575385i
$898$	3.66946	−	19.2360i	0.122451	−	0.641912i
$899$	−1.17106	+	3.60415i	−0.0390570	+	0.120205i
$900$	−34.0260	−	2.96686i	−1.13420	−	0.0988954i
$901$	2.65515	+	8.17170i	0.0884558	+	0.272239i
$902$	11.1689	−	1.41096i	0.371882	−	0.0469797i
$903$	3.20500	+	1.26895i	0.106656	+	0.0422280i
$904$	−17.6904	−	7.00414i	−0.588375	−	0.232954i
$905$	10.1269	+	15.2952i	0.336630	+	0.508431i
$906$	1.67646	+	26.6465i	0.0556966	+	0.885272i
$907$	4.67700	−	3.39804i	0.155297	−	0.112830i	−0.507423	−	0.861697i	$-0.669402\pi$
$907$	4.67700	−	3.39804i	0.155297	−	0.112830i	0.662720	+	0.748867i	$0.269402\pi$
$908$	3.36902	+	0.865018i	0.111805	+	0.0287066i
$909$	−39.5288	−	37.1200i	−1.31109	−	1.23119i
$910$	2.10453	+	9.97948i	0.0697645	+	0.330816i
$911$	−30.9196	−	16.9982i	−1.02441	−	0.563175i	−0.121315	−	0.992614i	$-0.538711\pi$
$911$	−30.9196	−	16.9982i	−1.02441	−	0.563175i	−0.903096	+	0.429440i	$0.858711\pi$
$912$	−68.9779	−	8.71394i	−2.28409	−	0.288547i
$913$	−4.30956	−	22.5915i	−0.142626	−	0.747669i
$914$	57.0219	−	7.20354i	1.88612	−	0.238272i
$915$	0.639719	+	0.966203i	0.0211485	+	0.0319417i
$916$	2.75858	+	14.4610i	0.0911461	+	0.477804i
$917$	6.05044	−	9.53397i	0.199803	−	0.314840i
$918$	−29.0268	−	21.0892i	−0.958027	−	0.696048i
$919$	−1.77334	−	2.14360i	−0.0584970	−	0.0707107i	0.740453	−	0.672108i	$-0.234611\pi$
$919$	−1.77334	−	2.14360i	−0.0584970	−	0.0707107i	−0.798950	+	0.601397i	$0.794611\pi$
$920$	4.79111	+	5.56853i	0.157958	+	0.183589i
$921$	14.6229	+	23.0420i	0.481840	+	0.759259i
$922$	−35.9484	+	43.4541i	−1.18390	+	1.43109i
$923$	8.41775	+	17.8886i	0.277073	+	0.588811i
$924$	14.4520	+	10.5000i	0.475435	+	0.345423i
$925$	38.5523	−	11.5052i	1.26759	−	0.378289i
$926$	−19.2310	+	13.9721i	−0.631970	+	0.459153i
$927$	−88.1447	−	48.4580i	−2.89505	−	1.59157i
$928$	3.00172	−	0.770710i	0.0985362	−	0.0252998i
$929$	−12.0573	+	14.5748i	−0.395589	+	0.478184i	−0.930273	−	0.366867i	$-0.880430\pi$
$929$	−12.0573	+	14.5748i	−0.395589	+	0.478184i	0.534685	+	0.845052i	$0.320430\pi$
$930$	78.6115	−	1.52092i	2.57777	−	0.0498729i
$931$	25.6629	−	10.1607i	0.841068	−	0.333002i
$932$	−30.0649			−0.984810
$933$	−55.1827	+	21.8484i	−1.80660	+	0.715284i
$934$	−46.2604	+	25.4319i	−1.51369	+	0.832157i
$935$	12.9428	−	21.2942i	0.423275	−	0.696395i
$936$	−6.00920	+	31.5013i	−0.196417	+	1.02965i
$937$	31.7207	+	29.7878i	1.03627	+	0.973124i	0.999657	−	0.0262057i	$-0.00834247\pi$
$937$	31.7207	+	29.7878i	1.03627	+	0.973124i	0.0366150	+	0.999329i	$0.488342\pi$
$938$	2.43708	+	2.28857i	0.0795735	+	0.0747245i
$939$	11.7241	−	61.4600i	0.382602	−	2.00567i
$940$	−4.79643	+	7.89134i	−0.156442	+	0.257387i
$941$	6.38243	−	3.50877i	0.208061	−	0.114383i	−0.374316	−	0.927301i	$-0.622123\pi$
$941$	6.38243	−	3.50877i	0.208061	−	0.114383i	0.582377	+	0.812918i	$0.302123\pi$
$942$	66.0035	−	26.1326i	2.15051	−	0.851447i
$943$	−2.06117			−0.0671209
$944$	−14.4138	+	5.70681i	−0.469128	+	0.185741i
$945$	−23.1193	+	0.447297i	−0.752072	+	0.0145506i
$946$	8.20579	−	9.91909i	0.266793	−	0.322497i
$947$	−56.9301	+	14.6172i	−1.84998	+	0.474994i	−0.998759	−	0.0498126i	$-0.984138\pi$
$947$	−56.9301	+	14.6172i	−1.84998	+	0.474994i	−0.851221	+	0.524807i	$0.824138\pi$
$948$	−21.6741	−	11.9154i	−0.703943	−	0.386996i
$949$	−24.4722	+	17.7801i	−0.794402	+	0.577167i
$950$	−22.1491	−	32.0869i	−0.718613	−	1.04104i
$951$	34.4526	+	25.0313i	1.11720	+	0.811696i
$952$	1.20350	+	2.55757i	0.0390057	+	0.0828914i
$953$	−1.06488	+	1.28722i	−0.0344949	+	0.0416972i	−0.787479	−	0.616342i	$-0.788614\pi$
$953$	−1.06488	+	1.28722i	−0.0344949	+	0.0416972i	0.752984	+	0.658039i	$0.228614\pi$
$954$	−29.1184	−	45.8832i	−0.942743	−	1.48553i
$955$	36.0207	+	41.8655i	1.16560	+	1.35474i
$956$	16.8880	+	20.4141i	0.546196	+	0.660238i
$957$	−8.92361	−	6.48338i	−0.288459	−	0.209578i
$958$	−2.20386	+	3.47272i	−0.0712034	+	0.112199i
$959$	1.38006	+	7.23454i	0.0445645	+	0.233615i
$960$	2.81650	+	4.25392i	0.0909023	+	0.137295i
$961$	−11.2657	+	1.42319i	−0.363410	+	0.0459094i
$962$	7.50652	+	39.3505i	0.242020	+	1.26871i
$963$	13.3291	+	1.68386i	0.429525	+	0.0542616i
$964$	9.77232	+	5.37238i	0.314745	+	0.173033i
$965$	0.463544	+	2.19808i	0.0149220	+	0.0707587i
$966$	−7.01666	−	6.58908i	−0.225757	−	0.212000i
$967$	−1.30143	−	0.334150i	−0.0418511	−	0.0107455i	0.227706	−	0.973730i	$-0.426877\pi$
$967$	−1.30143	−	0.334150i	−0.0418511	−	0.0107455i	−0.269557	+	0.962984i	$0.586877\pi$
$968$	−35.8596	+	26.0535i	−1.15257	+	0.837391i
$969$	−1.59480	−	25.3487i	−0.0512325	−	0.814317i
$970$	−32.6790	−	49.3569i	−1.04926	−	1.58475i
$971$	35.4756	+	14.0458i	1.13846	+	0.450750i	0.860303	−	0.509784i	$-0.170275\pi$
$971$	35.4756	+	14.0458i	1.13846	+	0.450750i	0.278162	+	0.960534i	$0.410275\pi$
$972$	12.5441	+	4.96656i	0.402352	+	0.159303i
$973$	−14.0555	+	1.77562i	−0.450597	+	0.0569237i
$974$	−16.6767	−	51.3257i	−0.534357	−	1.64458i
$975$	−38.0491	+	22.8774i	−1.21855	+	0.732662i
$976$	−0.257895	+	0.793719i	−0.00825501	+	0.0254063i
$977$	7.30023	−	38.2692i	0.233555	−	1.22434i	−0.651426	−	0.758712i	$-0.725829\pi$
$977$	7.30023	−	38.2692i	0.233555	−	1.22434i	0.884981	−	0.465627i	$-0.154171\pi$
$978$	−3.85471	+	61.2688i	−0.123260	+	1.95916i
$979$	6.76794	−	1.73771i	0.216304	−	0.0555375i
$980$	12.5559	+	6.58964i	0.401083	+	0.210498i
$981$	68.3846	−	107.757i	2.18335	−	3.44041i
$982$	−4.71426	−	14.5090i	−0.150438	−	0.463001i
$983$	0.194762	+	3.09565i	0.00621194	+	0.0987360i	0.999911	−	0.0133456i	$-0.00424818\pi$
$983$	0.194762	+	3.09565i	0.00621194	+	0.0987360i	−0.993699	+	0.112082i	$0.964248\pi$
$984$	−5.51491	−	0.696695i	−0.175809	−	0.0222098i
$985$	12.5330	+	25.3494i	0.399336	+	0.807697i
$986$	0.788066	+	1.67473i	0.0250971	+	0.0533342i
$987$	−4.85820	+	10.3242i	−0.154638	+	0.328623i
$988$	11.5598	−	6.35506i	0.367766	−	0.202181i
$989$	−1.71817	+	1.61347i	−0.0546348	+	0.0513055i
$990$	−45.7939	+	150.805i	−1.45542	+	4.79289i
$991$	−11.1803	+	23.7593i	−0.355154	+	0.754740i	−0.999954	−	0.00961117i	$-0.996941\pi$
$991$	−11.1803	+	23.7593i	−0.355154	+	0.754740i	0.644800	+	0.764351i	$0.276941\pi$
$992$	22.0786	+	26.6885i	0.700997	+	0.847360i
$993$	10.0105	−	30.8093i	0.317675	−	0.977704i
$994$	−10.6747	−	2.74081i	−0.338582	−	0.0869331i
$995$	−4.80496	−	4.34034i	−0.152327	−	0.137598i
$996$	0.756192	−	12.0193i	0.0239608	−	0.380847i
$997$	−1.97092	−	3.10567i	−0.0624196	−	0.0983575i	0.811685	−	0.584096i	$-0.198551\pi$
$997$	−1.97092	−	3.10567i	−0.0624196	−	0.0983575i	−0.874104	+	0.485738i	$0.838551\pi$
$998$	−41.0775	+	38.5743i	−1.30028	+	1.22105i
$999$	−90.8265			−2.87362

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.g.a.11.3	✓	220
5.2	odd	4		625.2.h.b.199.5		440
5.3	odd	4		625.2.h.b.199.18		440
5.4	even	2		625.2.g.a.426.9		220
125.34	even	50		625.2.g.a.201.9		220
125.62	odd	100		625.2.h.b.424.18		440
125.63	odd	100		625.2.h.b.424.5		440
125.91	even	25	inner	125.2.g.a.91.3	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.11.3	✓	220	1.1	even	1	trivial
125.2.g.a.91.3	yes	220	125.91	even	25	inner
625.2.g.a.201.9		220	125.34	even	50
625.2.g.a.426.9		220	5.4	even	2
625.2.h.b.199.5		440	5.2	odd	4
625.2.h.b.199.18		440	5.3	odd	4
625.2.h.b.424.5		440	125.63	odd	100
625.2.h.b.424.18		440	125.62	odd	100

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.g (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26877 + 1.19146i) q^{2} +(-1.66333 - 2.62099i) q^{3} +(0.0646335 - 1.02732i) q^{4} +(0.461407 + 2.18795i) q^{5} +(5.23318 + 1.34365i) q^{6} +(-0.283105 + 0.871308i) q^{7} +(-1.07687 - 1.30172i) q^{8} +(-2.82557 + 6.00465i) q^{9} +O(q^{10})\)	\(q+(-1.26877 + 1.19146i) q^{2} +(-1.66333 - 2.62099i) q^{3} +(0.0646335 - 1.02732i) q^{4} +(0.461407 + 2.18795i) q^{5} +(5.23318 + 1.34365i) q^{6} +(-0.283105 + 0.871308i) q^{7} +(-1.07687 - 1.30172i) q^{8} +(-2.82557 + 6.00465i) q^{9} +(-3.19226 - 2.22626i) q^{10} +(-4.44831 + 4.17724i) q^{11} +(-2.80010 + 1.53937i) q^{12} +(-1.21791 + 2.58819i) q^{13} +(-0.678930 - 1.44280i) q^{14} +(4.96711 - 4.84861i) q^{15} +(4.95972 + 0.626558i) q^{16} +(0.114671 + 1.82265i) q^{17} +(-3.56927 - 10.9851i) q^{18} +(2.40062 - 3.78277i) q^{19} +(2.27754 - 0.332598i) q^{20} +(2.75458 - 0.707257i) q^{21} +(0.666891 - 10.5999i) q^{22} +(-0.364380 + 1.91014i) q^{23} +(-1.62059 + 4.98766i) q^{24} +(-4.57421 + 2.01906i) q^{25} +(-1.53847 - 4.73492i) q^{26} +(11.1987 - 1.41473i) q^{27} +(0.876814 + 0.347155i) q^{28} +(-0.541404 - 0.214357i) q^{29} +(-0.525214 + 12.0699i) q^{30} +(-0.408646 - 6.49525i) q^{31} +(-4.30574 + 3.12830i) q^{32} +(18.3475 + 4.71084i) q^{33} +(-2.31710 - 2.17590i) q^{34} +(-2.03700 - 0.217391i) q^{35} +(5.98607 + 3.29087i) q^{36} +(-7.98303 - 1.00849i) q^{37} +(1.46117 + 7.65971i) q^{38} +(8.80941 - 1.11289i) q^{39} +(2.35121 - 2.95676i) q^{40} +(0.198615 + 1.04118i) q^{41} +(-2.65227 + 4.17932i) q^{42} +(0.980592 + 0.712442i) q^{43} +(4.00386 + 4.83983i) q^{44} +(-14.4416 - 3.41162i) q^{45} +(-1.81354 - 2.85768i) q^{46} +(-2.55741 + 3.09138i) q^{47} +(-6.60744 - 14.0415i) q^{48} +(4.98409 + 3.62115i) q^{49} +(3.39800 - 8.01170i) q^{50} +(4.58640 - 3.33221i) q^{51} +(2.58019 + 1.41847i) q^{52} +(4.55704 - 1.17005i) q^{53} +(-12.5230 + 15.1378i) q^{54} +(-11.1921 - 7.80525i) q^{55} +(1.43907 - 0.569766i) q^{56} -13.9076 q^{57} +(0.942316 - 0.373089i) q^{58} +(-2.71744 + 1.49392i) q^{59} +(-4.66004 - 5.41619i) q^{60} +(-0.0312818 + 0.163985i) q^{61} +(8.25729 + 7.75411i) q^{62} +(-4.43196 - 4.16189i) q^{63} +(-0.137725 + 0.721979i) q^{64} +(-6.22478 - 1.47051i) q^{65} +(-28.8916 + 15.8833i) q^{66} +(-1.94939 + 0.771819i) q^{67} +1.87985 q^{68} +(5.61255 - 2.22216i) q^{69} +(2.84350 - 2.15118i) q^{70} +(4.40563 - 5.32550i) q^{71} +(10.8591 - 2.78816i) q^{72} +(9.26703 + 5.09459i) q^{73} +(11.3302 - 8.23189i) q^{74} +(12.9004 + 8.63057i) q^{75} +(-3.73096 - 2.71070i) q^{76} +(-2.38032 - 5.05845i) q^{77} +(-9.85118 + 11.9080i) q^{78} +(4.14756 + 6.53550i) q^{79} +(0.917572 + 11.1407i) q^{80} +(-9.64484 - 11.6586i) q^{81} +(-1.49251 - 1.08438i) q^{82} +(-2.01950 + 3.18223i) q^{83} +(-0.548541 - 2.87555i) q^{84} +(-3.93494 + 1.09188i) q^{85} +(-2.09299 + 0.264406i) q^{86} +(0.338706 + 1.77556i) q^{87} +(10.2279 + 1.29208i) q^{88} +(-1.00344 - 0.551644i) q^{89} +(22.3879 - 12.8780i) q^{90} +(-1.91032 - 1.79391i) q^{91} +(1.93878 + 0.497794i) q^{92} +(-16.3443 + 11.8748i) q^{93} +(-0.438471 - 6.96930i) q^{94} +(9.38416 + 3.50703i) q^{95} +(15.3611 + 6.08189i) q^{96} +(14.1417 + 5.59910i) q^{97} +(-10.6381 + 1.34391i) q^{98} +(-12.5138 - 38.5136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

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