LMFDB - Embedded newform 525.2.bg.b.16.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(16,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 10]))

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

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

chi := DirichletCharacter("525.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.4
Character	$\chi$	$=$	525.16
Dual form			525.2.bg.b.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72477 + 0.767919i) q^{2} +(0.669131 - 0.743145i) q^{3} +(1.04689 - 1.16268i) q^{4} +(-2.14015 + 0.647903i) q^{5} +(-0.583424 + 1.79560i) q^{6} +(-2.28147 + 1.33974i) q^{7} +(0.254054 - 0.781898i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(-1.72477 + 0.767919i) q^{2} +(0.669131 - 0.743145i) q^{3} +(1.04689 - 1.16268i) q^{4} +(-2.14015 + 0.647903i) q^{5} +(-0.583424 + 1.79560i) q^{6} +(-2.28147 + 1.33974i) q^{7} +(0.254054 - 0.781898i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(3.19373 - 2.76095i) q^{10} +(0.167256 - 1.59133i) q^{11} +(-0.163540 - 1.55598i) q^{12} +(3.89189 - 2.82763i) q^{13} +(2.90621 - 4.06273i) q^{14} +(-0.950551 + 2.02397i) q^{15} +(0.489328 + 4.65564i) q^{16} +(-3.22875 + 0.686292i) q^{17} +(0.944000 + 1.63506i) q^{18} +(3.70790 + 4.11804i) q^{19} +(-1.48718 + 3.16660i) q^{20} +(-0.530982 + 2.59192i) q^{21} +(0.933535 + 2.87313i) q^{22} +(0.932473 - 0.415164i) q^{23} +(-0.411068 - 0.711991i) q^{24} +(4.16044 - 2.77321i) q^{25} +(-4.54125 + 7.86567i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.830746 + 4.05518i) q^{28} +(1.99139 + 6.12886i) q^{29} +(0.0852403 - 4.22084i) q^{30} +(7.27024 - 1.54534i) q^{31} +(-3.59700 - 6.23019i) q^{32} +(-1.07067 - 1.18910i) q^{33} +(5.04185 - 3.66312i) q^{34} +(4.01466 - 4.34540i) q^{35} +(-1.26574 - 0.919617i) q^{36} +(0.272342 + 2.59116i) q^{37} +(-9.55762 - 4.25533i) q^{38} +(0.502849 - 4.78429i) q^{39} +(-0.0371182 + 1.83798i) q^{40} +(4.00944 - 2.91303i) q^{41} +(-1.07456 - 4.87823i) q^{42} +5.03083 q^{43} +(-1.67512 - 1.86041i) q^{44} +(0.868060 + 2.06070i) q^{45} +(-1.28949 + 1.43213i) q^{46} +(-0.469054 - 0.0997005i) q^{47} +(3.78724 + 2.75159i) q^{48} +(3.41021 - 6.11314i) q^{49} +(-5.04622 + 7.97805i) q^{50} +(-1.65044 + 2.85865i) q^{51} +(0.786731 - 7.48525i) q^{52} +(0.455004 - 0.505333i) q^{53} +(1.84674 + 0.392537i) q^{54} +(0.673077 + 3.51404i) q^{55} +(0.467922 + 2.12424i) q^{56} +5.54138 q^{57} +(-8.14116 - 9.04168i) q^{58} +(10.7592 + 4.79028i) q^{59} +(1.35812 + 3.22406i) q^{60} +(0.339286 - 0.151060i) q^{61} +(-11.3528 + 8.24832i) q^{62} +(1.57088 + 2.12893i) q^{63} +(3.41381 + 2.48028i) q^{64} +(-6.49719 + 8.57310i) q^{65} +(2.75980 + 1.22874i) q^{66} +(1.96150 - 0.416929i) q^{67} +(-2.58219 + 4.47249i) q^{68} +(0.315419 - 0.970761i) q^{69} +(-3.58746 + 10.5778i) q^{70} +(2.50552 + 7.71121i) q^{71} +(-0.804170 - 0.170932i) q^{72} +(-1.41803 + 13.4917i) q^{73} +(-2.45953 - 4.26002i) q^{74} +(0.722979 - 4.94745i) q^{75} +8.66974 q^{76} +(1.75038 + 3.85465i) q^{77} +(2.80665 + 8.63797i) q^{78} +(-5.62389 - 1.19540i) q^{79} +(-4.06364 - 9.64671i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-4.67841 + 8.10324i) q^{82} +(5.35290 - 16.4745i) q^{83} +(2.45771 + 3.33081i) q^{84} +(6.46534 - 3.56068i) q^{85} +(-8.67705 + 3.86327i) q^{86} +(5.88713 + 2.62112i) q^{87} +(-1.20177 - 0.535061i) q^{88} +(8.90600 - 3.96521i) q^{89} +(-3.07966 - 2.88764i) q^{90} +(-5.09096 + 11.6653i) q^{91} +(0.493488 - 1.51880i) q^{92} +(3.71633 - 6.43688i) q^{93} +(0.885574 - 0.188235i) q^{94} +(-10.6035 - 6.41085i) q^{95} +(-7.03679 - 1.49572i) q^{96} +(-5.79068 - 17.8219i) q^{97} +(-1.18744 + 13.1626i) q^{98} -1.60010 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9}+O(q^{10}) $ 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9} - 6 q^{10} + 12 q^{11} + 20 q^{12} + 12 q^{14} + 4 q^{15} + 12 q^{16} - 6 q^{17} - 8 q^{18} + 12 q^{19} - 7 q^{21} + 14 q^{23} - 30 q^{24} - 4 q^{25} - 56 q^{26} - 40 q^{27} - 27 q^{28} - 2 q^{29} + 4 q^{30} + 27 q^{31} - 78 q^{32} - 8 q^{33} + 76 q^{34} + 21 q^{35} - 40 q^{36} + 14 q^{37} - 17 q^{38} + 10 q^{40} - 6 q^{41} - 2 q^{42} + 28 q^{43} - 22 q^{44} + 3 q^{45} - 22 q^{46} + 7 q^{47} - 24 q^{48} + 152 q^{49} - 62 q^{50} + 4 q^{51} + 13 q^{52} - 26 q^{53} + 2 q^{54} + 64 q^{55} - 33 q^{56} + 56 q^{57} + 48 q^{59} + 15 q^{60} + 36 q^{61} - 88 q^{62} - 7 q^{63} - 2 q^{64} + 46 q^{65} + 15 q^{66} + 42 q^{67} - 28 q^{68} - 8 q^{69} - 32 q^{70} + 36 q^{71} + 15 q^{72} + 10 q^{73} - 16 q^{74} + q^{75} - 76 q^{76} + 12 q^{77} - 8 q^{78} - 10 q^{79} + 100 q^{80} + 20 q^{81} + 14 q^{82} - 74 q^{83} - 6 q^{84} + 90 q^{85} + 6 q^{86} - 4 q^{87} + 102 q^{88} + 33 q^{89} - 18 q^{90} - 31 q^{91} - 94 q^{92} - 98 q^{93} - 30 q^{94} - 106 q^{95} + 47 q^{96} - 26 q^{97} + 26 q^{98} + 16 q^{99}+O(q^{100}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9 - 6 * q^10 + 12 * q^11 + 20 * q^12 + 12 * q^14 + 4 * q^15 + 12 * q^16 - 6 * q^17 - 8 * q^18 + 12 * q^19 - 7 * q^21 + 14 * q^23 - 30 * q^24 - 4 * q^25 - 56 * q^26 - 40 * q^27 - 27 * q^28 - 2 * q^29 + 4 * q^30 + 27 * q^31 - 78 * q^32 - 8 * q^33 + 76 * q^34 + 21 * q^35 - 40 * q^36 + 14 * q^37 - 17 * q^38 + 10 * q^40 - 6 * q^41 - 2 * q^42 + 28 * q^43 - 22 * q^44 + 3 * q^45 - 22 * q^46 + 7 * q^47 - 24 * q^48 + 152 * q^49 - 62 * q^50 + 4 * q^51 + 13 * q^52 - 26 * q^53 + 2 * q^54 + 64 * q^55 - 33 * q^56 + 56 * q^57 + 48 * q^59 + 15 * q^60 + 36 * q^61 - 88 * q^62 - 7 * q^63 - 2 * q^64 + 46 * q^65 + 15 * q^66 + 42 * q^67 - 28 * q^68 - 8 * q^69 - 32 * q^70 + 36 * q^71 + 15 * q^72 + 10 * q^73 - 16 * q^74 + q^75 - 76 * q^76 + 12 * q^77 - 8 * q^78 - 10 * q^79 + 100 * q^80 + 20 * q^81 + 14 * q^82 - 74 * q^83 - 6 * q^84 + 90 * q^85 + 6 * q^86 - 4 * q^87 + 102 * q^88 + 33 * q^89 - 18 * q^90 - 31 * q^91 - 94 * q^92 - 98 * q^93 - 30 * q^94 - 106 * q^95 + 47 * q^96 - 26 * q^97 + 26 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.72477	+	0.767919i	−1.21960	+	0.543001i	−0.912657	−	0.408727i	$-0.865973\pi$
$2$	−1.72477	+	0.767919i	−1.21960	+	0.543001i	−0.306943	+	0.951728i	$0.599306\pi$
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$4$	1.04689	−	1.16268i	0.523443	−	0.581342i
$5$	−2.14015	+	0.647903i	−0.957102	+	0.289751i
$5$	−2.14015	+	0.647903i	−0.957102	+	0.289751i
$6$	−0.583424	+	1.79560i	−0.238182	+	0.733049i
$7$	−2.28147	+	1.33974i	−0.862314	+	0.506373i
$7$	−2.28147	+	1.33974i	−0.862314	+	0.506373i
$8$	0.254054	−	0.781898i	0.0898217	−	0.276443i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	3.19373	−	2.76095i	1.00995	−	0.873088i
$11$	0.167256	−	1.59133i	0.0504295	−	0.479804i	−0.939939	−	0.341344i	$-0.889118\pi$
$11$	0.167256	−	1.59133i	0.0504295	−	0.479804i	0.990368	−	0.138460i	$-0.0442154\pi$
$12$	−0.163540	−	1.55598i	−0.0472098	−	0.449172i
$13$	3.89189	−	2.82763i	1.07942	−	0.784242i	0.101836	−	0.994801i	$-0.467528\pi$
$13$	3.89189	−	2.82763i	1.07942	−	0.784242i	0.977581	+	0.210559i	$0.0675284\pi$
$14$	2.90621	−	4.06273i	0.776717	−	1.08581i
$15$	−0.950551	+	2.02397i	−0.245431	+	0.522587i
$16$	0.489328	+	4.65564i	0.122332	+	1.16391i
$17$	−3.22875	+	0.686292i	−0.783087	+	0.166450i	−0.582071	−	0.813138i	$-0.697758\pi$
$17$	−3.22875	+	0.686292i	−0.783087	+	0.166450i	−0.201016	+	0.979588i	$0.564424\pi$
$18$	0.944000	+	1.63506i	0.222503	+	0.385387i
$19$	3.70790	+	4.11804i	0.850652	+	0.944744i	0.999023	−	0.0441874i	$-0.0140699\pi$
$19$	3.70790	+	4.11804i	0.850652	+	0.944744i	−0.148372	+	0.988932i	$0.547403\pi$
$20$	−1.48718	+	3.16660i	−0.332544	+	0.708072i
$21$	−0.530982	+	2.59192i	−0.115870	+	0.565604i
$22$	0.933535	+	2.87313i	0.199030	+	0.612552i
$23$	0.932473	−	0.415164i	0.194434	−	0.0865676i	−0.307210	−	0.951642i	$-0.599395\pi$
$23$	0.932473	−	0.415164i	0.194434	−	0.0865676i	0.501644	+	0.865074i	$0.332729\pi$
$24$	−0.411068	−	0.711991i	−0.0839089	−	0.145335i
$25$	4.16044	−	2.77321i	0.832088	−	0.554643i
$26$	−4.54125	+	7.86567i	−0.890612	+	1.54259i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−0.830746	+	4.05518i	−0.156996	+	0.766357i
$29$	1.99139	+	6.12886i	0.369791	+	1.13810i	0.946926	+	0.321452i	$0.104171\pi$
$29$	1.99139	+	6.12886i	0.369791	+	1.13810i	−0.577134	+	0.816649i	$0.695829\pi$
$30$	0.0852403	−	4.22084i	0.0155627	−	0.770616i
$31$	7.27024	−	1.54534i	1.30577	−	0.277551i	0.498069	−	0.867137i	$-0.334043\pi$
$31$	7.27024	−	1.54534i	1.30577	−	0.277551i	0.807705	+	0.589586i	$0.200709\pi$
$32$	−3.59700	−	6.23019i	−0.635866	−	1.10135i
$33$	−1.07067	−	1.18910i	−0.186380	−	0.206996i
$34$	5.04185	−	3.66312i	0.864670	−	0.628219i
$35$	4.01466	−	4.34540i	0.678601	−	0.734507i
$36$	−1.26574	−	0.919617i	−0.210957	−	0.153270i
$37$	0.272342	+	2.59116i	0.0447727	+	0.425983i	0.993833	+	0.110889i	$0.0353697\pi$
$37$	0.272342	+	2.59116i	0.0447727	+	0.425983i	−0.949060	+	0.315095i	$0.897964\pi$
$38$	−9.55762	−	4.25533i	−1.55045	−	0.690305i
$39$	0.502849	−	4.78429i	0.0805203	−	0.766100i
$40$	−0.0371182	+	1.83798i	−0.00586890	+	0.290610i
$41$	4.00944	−	2.91303i	0.626169	−	0.454939i	−0.228902	−	0.973450i	$-0.573513\pi$
$41$	4.00944	−	2.91303i	0.626169	−	0.454939i	0.855071	+	0.518511i	$0.173513\pi$
$42$	−1.07456	−	4.87823i	−0.165809	−	0.752727i
$43$	5.03083			0.767195			0.383597	−	0.923500i	$-0.374685\pi$
$43$	5.03083			0.767195			0.383597	+	0.923500i	$0.374685\pi$
$44$	−1.67512	−	1.86041i	−0.252534	−	0.280467i
$45$	0.868060	+	2.06070i	0.129403	+	0.307191i
$46$	−1.28949	+	1.43213i	−0.190125	+	0.211156i
$47$	−0.469054	−	0.0997005i	−0.0684185	−	0.0145428i	0.173575	−	0.984821i	$-0.444468\pi$
$47$	−0.469054	−	0.0997005i	−0.0684185	−	0.0145428i	−0.241994	+	0.970278i	$0.577801\pi$
$48$	3.78724	+	2.75159i	0.546641	+	0.397158i
$49$	3.41021	−	6.11314i	0.487172	−	0.873306i
$50$	−5.04622	+	7.97805i	−0.713643	+	1.12827i
$51$	−1.65044	+	2.85865i	−0.231108	+	0.400291i
$52$	0.786731	−	7.48525i	0.109100	−	1.03802i
$53$	0.455004	−	0.505333i	0.0624995	−	0.0694128i	−0.711084	−	0.703107i	$-0.751796\pi$
$53$	0.455004	−	0.505333i	0.0624995	−	0.0694128i	0.773584	+	0.633694i	$0.218462\pi$
$54$	1.84674	+	0.392537i	0.251310	+	0.0534176i
$55$	0.673077	+	3.51404i	0.0907577	+	0.473834i
$56$	0.467922	+	2.12424i	0.0625287	+	0.283864i
$57$	5.54138			0.733973
$58$	−8.14116	−	9.04168i	−1.06899	−	1.18723i
$59$	10.7592	+	4.79028i	1.40072	+	0.623642i	0.961517	−	0.274745i	$-0.0885935\pi$
$59$	10.7592	+	4.79028i	1.40072	+	0.623642i	0.439205	+	0.898387i	$0.355260\pi$
$60$	1.35812	+	3.22406i	0.175333	+	0.416224i
$61$	0.339286	−	0.151060i	0.0434411	−	0.0193412i	−0.384901	−	0.922958i	$-0.625764\pi$
$61$	0.339286	−	0.151060i	0.0434411	−	0.0193412i	0.428342	+	0.903617i	$0.359098\pi$
$62$	−11.3528	+	8.24832i	−1.44181	+	1.04754i
$63$	1.57088	+	2.12893i	0.197912	+	0.268220i
$64$	3.41381	+	2.48028i	0.426727	+	0.310035i
$65$	−6.49719	+	8.57310i	−0.805877	+	1.06336i
$66$	2.75980	+	1.22874i	0.339708	+	0.151248i
$67$	1.96150	−	0.416929i	0.239635	−	0.0509360i	−0.0865285	−	0.996249i	$-0.527577\pi$
$67$	1.96150	−	0.416929i	0.239635	−	0.0509360i	0.326163	+	0.945313i	$0.394244\pi$
$68$	−2.58219	+	4.47249i	−0.313137	+	0.542369i
$69$	0.315419	−	0.970761i	0.0379720	−	0.116866i
$70$	−3.58746	+	10.5778i	−0.428783	+	1.26429i
$71$	2.50552	+	7.71121i	0.297351	+	0.915152i	0.982422	+	0.186675i	$0.0597712\pi$
$71$	2.50552	+	7.71121i	0.297351	+	0.915152i	−0.685071	+	0.728476i	$0.740229\pi$
$72$	−0.804170	−	0.170932i	−0.0947724	−	0.0201445i
$73$	−1.41803	+	13.4917i	−0.165968	+	1.57908i	0.521746	+	0.853101i	$0.325281\pi$
$73$	−1.41803	+	13.4917i	−0.165968	+	1.57908i	−0.687714	+	0.725981i	$0.741386\pi$
$74$	−2.45953	−	4.26002i	−0.285914	−	0.495218i
$75$	0.722979	−	4.94745i	0.0834824	−	0.571283i
$76$	8.66974			0.994488
$77$	1.75038	+	3.85465i	0.199474	+	0.439278i
$78$	2.80665	+	8.63797i	0.317790	+	0.978057i
$79$	−5.62389	−	1.19540i	−0.632737	−	0.134492i	−0.119632	−	0.992818i	$-0.538172\pi$
$79$	−5.62389	−	1.19540i	−0.632737	−	0.134492i	−0.513105	+	0.858326i	$0.671505\pi$
$80$	−4.06364	−	9.64671i	−0.454329	−	1.07854i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−4.67841	+	8.10324i	−0.516644	+	0.894853i
$83$	5.35290	−	16.4745i	0.587558	−	1.80832i	−0.00119025	−	0.999999i	$-0.500379\pi$
$83$	5.35290	−	16.4745i	0.587558	−	1.80832i	0.588748	−	0.808317i	$-0.299621\pi$
$84$	2.45771	+	3.33081i	0.268158	+	0.363421i
$85$	6.46534	−	3.56068i	0.701265	−	0.386210i
$86$	−8.67705	+	3.86327i	−0.935671	+	0.416587i
$87$	5.88713	+	2.62112i	0.631167	+	0.281013i
$88$	−1.20177	−	0.535061i	−0.128109	−	0.0570377i
$89$	8.90600	−	3.96521i	0.944034	−	0.420311i	0.123780	−	0.992310i	$-0.460498\pi$
$89$	8.90600	−	3.96521i	0.944034	−	0.420311i	0.820255	+	0.571999i	$0.193832\pi$
$90$	−3.07966	−	2.88764i	−0.324624	−	0.304384i
$91$	−5.09096	+	11.6653i	−0.533677	+	1.22285i
$92$	0.493488	−	1.51880i	0.0514497	−	0.158346i
$93$	3.71633	−	6.43688i	0.385366	−	0.667473i
$94$	0.885574	−	0.188235i	0.0913400	−	0.0194149i
$95$	−10.6035	−	6.41085i	−1.08790	−	0.657739i
$96$	−7.03679	−	1.49572i	−0.718190	−	0.152656i
$97$	−5.79068	−	17.8219i	−0.587954	−	1.80954i	−0.587068	−	0.809538i	$-0.699718\pi$
$97$	−5.79068	−	17.8219i	−0.587954	−	1.80954i	−0.000886727	−	1.00000i	$-0.500282\pi$
$98$	−1.18744	+	13.1626i	−0.119949	+	1.32962i
$99$	−1.60010			−0.160816
$100$	1.13113	−	7.74052i	0.113113	−	0.774052i
$101$	2.99108	+	5.18070i	0.297623	+	0.515499i	0.975592	−	0.219592i	$-0.0704727\pi$
$101$	2.99108	+	5.18070i	0.297623	+	0.515499i	−0.677968	+	0.735091i	$0.737139\pi$
$102$	0.651428	−	6.19793i	0.0645010	−	0.613686i
$103$	−11.9239	−	2.53451i	−1.17490	−	0.249733i	−0.421210	−	0.906963i	$-0.638395\pi$
$103$	−11.9239	−	2.53451i	−1.17490	−	0.249733i	−0.753690	+	0.657230i	$0.771728\pi$
$104$	−1.22216	−	3.76143i	−0.119843	−	0.368839i
$105$	−0.542937	−	5.89111i	−0.0529852	−	0.574914i
$106$	−0.396724	+	1.22099i	−0.0385332	+	0.118593i
$107$	3.18477	−	5.51618i	0.307883	−	0.533269i	−0.670016	−	0.742347i	$-0.733713\pi$
$107$	3.18477	−	5.51618i	0.307883	−	0.533269i	0.977899	+	0.209078i	$0.0670461\pi$
$108$	−1.53036	+	0.325288i	−0.147259	+	0.0313008i
$109$	7.73059	+	3.44188i	0.740456	+	0.329672i	0.742066	−	0.670326i	$-0.233846\pi$
$109$	7.73059	+	3.44188i	0.740456	+	0.329672i	−0.00161023	+	0.999999i	$0.500513\pi$
$110$	−3.85941	−	5.54406i	−0.367980	−	0.528606i
$111$	2.10784	+	1.53143i	0.200067	+	0.145357i
$112$	−7.35373	−	9.96614i	−0.694862	−	0.941711i
$113$	−8.56900	+	6.22574i	−0.806104	+	0.585669i	−0.912698	−	0.408634i	$-0.866005\pi$
$113$	−8.56900	+	6.22574i	−0.806104	+	0.585669i	0.106595	+	0.994303i	$0.466005\pi$
$114$	−9.55762	+	4.25533i	−0.895154	+	0.398548i
$115$	−1.72664	+	1.49266i	−0.161010	+	0.139191i
$116$	9.21069	+	4.10086i	0.855191	+	0.380756i
$117$	−3.21895	−	3.57501i	−0.297592	−	0.330509i
$118$	−22.2357			−2.04696
$119$	6.44684	−	5.89143i	0.590981	−	0.540067i
$120$	1.34105	+	1.25743i	0.122420	+	0.114787i
$121$	8.25527	+	1.75471i	0.750479	+	0.159519i
$122$	−0.469190	+	0.521088i	−0.0424785	+	0.0471771i
$123$	0.518037	−	4.92879i	0.0467098	−	0.444414i
$124$	5.81438	−	10.0708i	0.522146	−	0.904384i
$125$	−7.10718	+	8.63065i	−0.635685	+	0.771948i
$126$	−4.34425	−	2.46562i	−0.387017	−	0.219655i
$127$	2.57841	+	1.87333i	0.228797	+	0.166231i	0.696278	−	0.717773i	$-0.254838\pi$
$127$	2.57841	+	1.87333i	0.228797	+	0.166231i	−0.467481	+	0.884003i	$0.654838\pi$
$128$	6.28088	+	1.33504i	0.555156	+	0.118002i
$129$	3.36628	−	3.73864i	0.296385	−	0.329169i
$130$	4.62274	−	19.7760i	0.405441	−	1.73447i
$131$	−11.9462	−	13.2676i	−1.04375	−	1.15920i	−0.986985	−	0.160812i	$-0.948589\pi$
$131$	−11.9462	−	13.2676i	−1.04375	−	1.15920i	−0.0567633	−	0.998388i	$-0.518078\pi$
$132$	−2.50343			−0.217895
$133$	−13.9766	−	4.42757i	−1.21192	−	0.383919i
$134$	−3.06297	+	2.22538i	−0.264600	+	0.192243i
$135$	2.11224	+	0.733781i	0.181793	+	0.0631538i
$136$	−0.283667	+	2.69891i	−0.0243242	+	0.231429i
$137$	19.0600	+	8.48606i	1.62841	+	0.725013i	0.998658	−	0.0517856i	$-0.0164913\pi$
$137$	19.0600	+	8.48606i	1.62841	+	0.725013i	0.629749	+	0.776799i	$0.283158\pi$
$138$	0.201439	+	1.91656i	0.0171476	+	0.163148i
$139$	−11.6184	−	8.44127i	−0.985461	−	0.715979i	−0.0265385	−	0.999648i	$-0.508448\pi$
$139$	−11.6184	−	8.44127i	−0.985461	−	0.715979i	−0.958922	+	0.283669i	$0.908448\pi$
$140$	−0.849450	−	9.21692i	−0.0717916	−	0.778972i
$141$	−0.387950	+	0.281862i	−0.0326713	+	0.0237371i
$142$	−10.2430	−	11.3761i	−0.859577	−	0.954657i
$143$	−3.84875	−	6.66622i	−0.321848	−	0.557458i
$144$	4.57899	−	0.973294i	0.381582	−	0.0811079i
$145$	−8.23277	−	11.8264i	−0.683694	−	0.982131i
$146$	−7.91473	−	24.3590i	−0.655028	−	2.01597i
$147$	−2.26108	−	6.62477i	−0.186490	−	0.546402i
$148$	3.29781	+	2.39600i	0.271078	+	0.196950i
$149$	−2.48602	+	4.30591i	−0.203663	+	0.352754i	−0.949706	−	0.313144i	$-0.898618\pi$
$149$	−2.48602	+	4.30591i	−0.203663	+	0.352754i	0.746043	+	0.665898i	$0.231951\pi$
$150$	2.55227	+	9.08843i	0.208392	+	0.742067i
$151$	−3.29096	−	5.70012i	−0.267815	−	0.463869i	0.700482	−	0.713670i	$-0.252968\pi$
$151$	−3.29096	−	5.70012i	−0.267815	−	0.463869i	−0.968297	+	0.249801i	$0.919635\pi$
$152$	4.16190	−	1.85300i	0.337575	−	0.150298i
$153$	1.02003	+	3.13933i	0.0824644	+	0.253799i
$154$	−5.97907	−	5.30426i	−0.481807	−	0.427429i
$155$	−14.5581	+	8.01766i	−1.16934	+	0.643994i
$156$	−5.03620	−	5.59326i	−0.403218	−	0.447819i
$157$	−3.98558	−	6.90323i	−0.318084	−	0.550938i	0.662004	−	0.749500i	$-0.269706\pi$
$157$	−3.98558	−	6.90323i	−0.318084	−	0.550938i	−0.980088	+	0.198562i	$0.936373\pi$
$158$	10.6179	−	2.25691i	0.844716	−	0.179550i
$159$	−0.0710785	−	0.676267i	−0.00563689	−	0.0536315i
$160$	11.7347	+	11.0030i	0.927707	+	0.869863i
$161$	−1.57120	+	2.19645i	−0.123828	+	0.173105i
$162$	1.52742	−	1.10974i	0.120006	−	0.0871893i
$163$	0.601411	+	5.72204i	0.0471062	+	0.448185i	0.992499	+	0.122252i	$0.0390117\pi$
$163$	0.601411	+	5.72204i	0.0471062	+	0.448185i	−0.945393	+	0.325933i	$0.894322\pi$
$164$	0.810493	−	7.71132i	0.0632888	−	0.602153i
$165$	3.06182	+	1.85116i	0.238362	+	0.144113i
$166$	3.41856	+	32.5255i	0.265332	+	2.52447i
$167$	−1.02515	+	3.15509i	−0.0793286	+	0.244148i	−0.982854	−	0.184387i	$-0.940970\pi$
$167$	−1.02515	+	3.15509i	−0.0793286	+	0.244148i	0.903525	+	0.428535i	$0.140970\pi$
$168$	1.89172	+	1.07366i	0.145949	+	0.0828348i
$169$	3.13414	−	9.64589i	0.241088	−	0.741992i
$170$	−8.41694	+	11.1062i	−0.645550	+	0.851809i
$171$	3.70790	−	4.11804i	0.283551	−	0.314915i
$172$	5.26671	−	5.84927i	0.401583	−	0.446003i
$173$	−3.08557	+	1.37378i	−0.234591	+	0.104447i	−0.520666	−	0.853761i	$-0.674316\pi$
$173$	−3.08557	+	1.37378i	−0.234591	+	0.104447i	0.286074	+	0.958207i	$0.407650\pi$
$174$	−12.1668			−0.922361
$175$	−5.77654	+	11.9009i	−0.436666	+	0.899624i
$176$	7.49051			0.564618
$177$	10.7592	−	4.79028i	0.808707	−	0.360060i
$178$	−12.3159	+	13.6782i	−0.923115	+	1.02522i
$179$	−10.9310	+	12.1401i	−0.817018	+	0.907391i	−0.997088	−	0.0762630i	$-0.975701\pi$
$179$	−10.9310	+	12.1401i	−0.817018	+	0.907391i	0.180069	+	0.983654i	$0.442368\pi$
$180$	3.30470	+	1.14803i	0.246318	+	0.0855694i
$181$	−0.163672	+	0.503729i	−0.0121656	+	0.0374419i	−0.956955	−	0.290236i	$-0.906266\pi$
$181$	−0.163672	+	0.503729i	−0.0121656	+	0.0374419i	0.944789	+	0.327678i	$0.106266\pi$
$182$	−0.177219	−	24.0294i	−0.0131364	−	1.78118i
$183$	0.114767	−	0.353217i	0.00848384	−	0.0261106i
$184$	−0.0877171	−	0.834572i	−0.00646659	−	0.0615255i
$185$	−2.26167	−	5.36900i	−0.166281	−	0.394737i
$186$	−1.46684	+	13.9560i	−0.107554	+	1.02330i
$187$	0.552091	+	5.25279i	0.0403729	+	0.384122i
$188$	−0.606966	+	0.440987i	−0.0442676	+	0.0321623i
$189$	2.63323	+	0.257144i	0.191539	+	0.0187044i
$190$	23.2117	+	2.91460i	1.68396	+	0.211448i
$191$	−1.60623	−	15.2822i	−0.116223	−	1.10578i	−0.884782	−	0.466005i	$-0.845693\pi$
$191$	−1.60623	−	15.2822i	−0.116223	−	1.10578i	0.768560	−	0.639778i	$-0.220974\pi$
$192$	4.12749	−	0.877326i	0.297876	−	0.0633156i
$193$	−0.798001	−	1.38218i	−0.0574414	−	0.0994914i	0.835875	−	0.548920i	$-0.184961\pi$
$193$	−0.798001	−	1.38218i	−0.0574414	−	0.0994914i	−0.893316	+	0.449429i	$0.851628\pi$
$194$	23.6734	+	26.2919i	1.69965	+	1.88765i
$195$	2.02359	+	10.5649i	0.144912	+	0.756566i
$196$	−3.53756	−	10.3648i	−0.252683	−	0.740340i
$197$	5.60386	+	17.2469i	0.399259	+	1.22879i	0.925595	+	0.378516i	$0.123565\pi$
$197$	5.60386	+	17.2469i	0.399259	+	1.22879i	−0.526336	+	0.850277i	$0.676435\pi$
$198$	2.75980	−	1.22874i	0.196131	−	0.0873231i
$199$	−9.51025	−	16.4722i	−0.674164	−	1.16769i	−0.976713	−	0.214552i	$-0.931171\pi$
$199$	−9.51025	−	16.4722i	−0.674164	−	1.16769i	0.302549	−	0.953134i	$-0.402162\pi$
$200$	−1.11139	−	3.95759i	−0.0785874	−	0.279844i
$201$	1.00266	−	1.73666i	0.0707221	−	0.122494i
$202$	−9.13730	−	6.63863i	−0.642898	−	0.467093i
$203$	−12.7544	−	11.3149i	−0.895180	−	0.794148i
$204$	1.59588	+	4.91162i	0.111734	+	0.343882i
$205$	−6.69342	+	8.83203i	−0.467489	+	0.616856i
$206$	22.5124	−	4.78516i	1.56851	−	0.333398i
$207$	−0.510359	−	0.883968i	−0.0354724	−	0.0614400i
$208$	15.0688	+	16.7356i	1.04483	+	1.16041i
$209$	7.17334	−	5.21174i	0.496190	−	0.360503i
$210$	5.46034	+	9.74391i	0.376799	+	0.672394i
$211$	3.90543	+	2.83746i	0.268861	+	0.195339i	0.714044	−	0.700101i	$-0.246862\pi$
$211$	3.90543	+	2.83746i	0.268861	+	0.195339i	−0.445183	+	0.895439i	$0.646862\pi$
$212$	−0.111206	−	1.05805i	−0.00763764	−	0.0726673i
$213$	7.40707	+	3.29784i	0.507524	+	0.225964i
$214$	−1.25703	+	11.9598i	−0.0859285	+	0.817555i
$215$	−10.7667	+	3.25949i	−0.734284	+	0.222296i
$216$	−0.665122	+	0.483239i	−0.0452558	+	0.0328803i
$217$	−14.5165	+	13.2659i	−0.985444	+	0.900545i
$218$	−15.9766			−1.08207
$219$	9.07743	+	10.0815i	0.613396	+	0.681245i
$220$	4.79036	+	2.89623i	0.322966	+	0.195264i
$221$	−10.6254	+	11.8007i	−0.714740	+	0.793799i
$222$	−4.81156	−	1.02273i	−0.322931	−	0.0686410i
$223$	22.4530	+	16.3131i	1.50356	+	1.09240i	0.968935	+	0.247317i	$0.0795490\pi$
$223$	22.4530	+	16.3131i	1.50356	+	1.09240i	0.534630	+	0.845086i	$0.320451\pi$
$224$	16.5533	+	9.39495i	1.10601	+	0.627726i
$225$	−3.19291	−	3.84777i	−0.212860	−	0.256518i
$226$	9.99873	−	17.3183i	0.665105	−	1.15200i
$227$	−0.654593	+	6.22803i	−0.0434468	+	0.413369i	0.951085	+	0.308931i	$0.0999711\pi$
$227$	−0.654593	+	6.22803i	−0.0434468	+	0.413369i	−0.994531	+	0.104438i	$0.966696\pi$
$228$	5.80119	−	6.44287i	0.384193	−	0.426690i
$229$	−3.97574	−	0.845069i	−0.262724	−	0.0558438i	0.0746661	−	0.997209i	$-0.476211\pi$
$229$	−3.97574	−	0.845069i	−0.262724	−	0.0558438i	−0.337390	+	0.941365i	$0.609544\pi$
$230$	1.83182	−	3.90043i	0.120787	−	0.257187i
$231$	4.03579	+	1.27848i	0.265536	+	0.0841179i
$232$	5.29806			0.347835
$233$	−6.10251	−	6.77752i	−0.399789	−	0.444010i	0.509315	−	0.860580i	$-0.329899\pi$
$233$	−6.10251	−	6.77752i	−0.399789	−	0.444010i	−0.909104	+	0.416570i	$0.863232\pi$
$234$	8.29728	+	3.69419i	0.542410	+	0.241496i
$235$	1.06844	−	0.0905281i	0.0696973	−	0.00590540i
$236$	16.8332	−	7.49462i	1.09575	−	0.487858i
$237$	−4.65147	+	3.37949i	−0.302145	+	0.219522i
$238$	−6.59521	+	15.1120i	−0.427504	+	0.979568i
$239$	6.22689	+	4.52410i	0.402784	+	0.292640i	0.770674	−	0.637230i	$-0.219920\pi$
$239$	6.22689	+	4.52410i	0.402784	+	0.292640i	−0.367890	+	0.929869i	$0.619920\pi$
$240$	−9.88801	−	3.43504i	−0.638268	−	0.221731i
$241$	−4.75293	−	2.11614i	−0.306163	−	0.136313i	0.247904	−	0.968785i	$-0.420258\pi$
$241$	−4.75293	−	2.11614i	−0.306163	−	0.136313i	−0.554067	+	0.832472i	$0.686925\pi$
$242$	−15.5859	+	3.31290i	−1.00190	+	0.212961i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	0.179559	−	0.552625i	0.0114951	−	0.0353782i
$245$	−3.33761	+	15.2925i	−0.213232	+	0.977002i
$246$	2.89142	+	8.89886i	0.184350	+	0.567371i
$247$	26.0751	+	5.54242i	1.65912	+	0.352656i
$248$	0.638738	−	6.07719i	0.0405599	−	0.385902i
$249$	−8.66118	−	15.0016i	−0.548880	−	0.950688i
$250$	5.63064	−	20.3437i	0.356113	−	1.28665i
$251$	28.7609			1.81537			0.907685	−	0.419653i	$-0.137848\pi$
$251$	28.7609			1.81537			0.907685	+	0.419653i	$0.137848\pi$
$252$	4.11980	+	0.402313i	0.259523	+	0.0253433i
$253$	−0.504701	−	1.55331i	−0.0317303	−	0.0976558i
$254$	−5.88574	−	1.25105i	−0.369304	−	0.0784980i
$255$	1.68006	−	7.18725i	0.105209	−	0.450083i
$256$	−20.1133	+	4.27521i	−1.25708	+	0.267201i
$257$	8.16005	−	14.1336i	0.509010	−	0.881631i	−0.490936	−	0.871196i	$-0.663345\pi$
$257$	8.16005	−	14.1336i	0.509010	−	0.881631i	0.999946	−	0.0104349i	$-0.00332160\pi$
$258$	−2.93511	+	9.03334i	−0.182732	+	0.562391i
$259$	−4.09281	−	5.54678i	−0.254315	−	0.344660i
$260$	3.16600	+	16.5292i	0.196347	+	1.02510i
$261$	5.88713	−	2.62112i	0.364404	−	0.162243i
$262$	30.7931	+	13.7100i	1.90240	+	0.847004i
$263$	13.3439	+	5.94107i	0.822817	+	0.366342i	0.774566	−	0.632493i	$-0.217968\pi$
$263$	13.3439	+	5.94107i	0.822817	+	0.366342i	0.0482515	+	0.998835i	$0.484635\pi$
$264$	−1.20177	+	0.535061i	−0.0739636	+	0.0329307i
$265$	−0.646367	+	1.37628i	−0.0397060	+	0.0845444i
$266$	27.5065	−	3.09631i	1.68653	−	0.189847i
$267$	3.01255	−	9.27169i	0.184365	−	0.567418i
$268$	1.56871	−	2.71708i	0.0958240	−	0.165972i
$269$	−13.6529	+	2.90202i	−0.832433	+	0.176939i	−0.604366	−	0.796707i	$-0.706574\pi$
$269$	−13.6529	+	2.90202i	−0.832433	+	0.176939i	−0.228066	+	0.973646i	$0.573240\pi$
$270$	−4.20663	+	0.356424i	−0.256007	+	0.0216913i
$271$	29.9382	+	6.36356i	1.81862	+	0.386559i	0.985926	−	0.167180i	$-0.0534660\pi$
$271$	29.9382	+	6.36356i	1.81862	+	0.386559i	0.832691	+	0.553739i	$0.186799\pi$
$272$	−4.77505	−	14.6961i	−0.289530	−	0.891081i
$273$	5.26246	+	11.5889i	0.318499	+	0.701392i
$274$	−39.3908			−2.37969
$275$	−3.71724	−	7.08447i	−0.224158	−	0.427210i
$276$	−0.798481	−	1.38301i	−0.0480629	−	0.0832474i
$277$	−2.30287	+	21.9103i	−0.138366	+	1.31646i	0.676341	+	0.736589i	$0.263565\pi$
$277$	−2.30287	+	21.9103i	−0.138366	+	1.31646i	−0.814706	+	0.579874i	$0.803102\pi$
$278$	26.5214	+	5.63729i	1.59065	+	0.338102i
$279$	−2.29682	−	7.06889i	−0.137507	−	0.423203i
$280$	−2.37772	−	4.24302i	−0.142096	−	0.253569i
$281$	−5.16922	+	15.9092i	−0.308370	+	0.949065i	0.670028	+	0.742336i	$0.266282\pi$
$281$	−5.16922	+	15.9092i	−0.308370	+	0.949065i	−0.978398	+	0.206729i	$0.933718\pi$
$282$	0.452679	−	0.784063i	0.0269566	−	0.0466903i
$283$	7.66046	−	1.62828i	0.455367	−	0.0967912i	0.0254827	−	0.999675i	$-0.491888\pi$
$283$	7.66046	−	1.62828i	0.455367	−	0.0967912i	0.429884	+	0.902884i	$0.358554\pi$
$284$	11.5887	+	5.15962i	0.687663	+	0.306167i
$285$	−11.8593	+	3.59028i	−0.702487	+	0.212670i
$286$	11.7573	+	8.54221i	0.695226	+	0.505111i
$287$	−5.24472	+	12.0176i	−0.309586	+	0.709375i
$288$	−5.82007	+	4.22853i	−0.342951	+	0.249168i
$289$	−5.57645	+	2.48279i	−0.328026	+	0.146047i
$290$	23.2814	+	14.0758i	1.36713	+	0.826560i
$291$	−17.1190	−	7.62185i	−1.00353	−	0.446801i
$292$	14.2021	+	15.7730i	0.831113	+	0.923044i
$293$	17.8567			1.04320			0.521601	−	0.853190i	$-0.325335\pi$
$293$	17.8567			1.04320			0.521601	+	0.853190i	$0.325335\pi$
$294$	8.98713	+	9.68990i	0.524140	+	0.565127i
$295$	−26.1298	−	3.28101i	−1.52133	−	0.191028i
$296$	2.09521	+	0.445350i	0.121782	+	0.0258855i
$297$	−1.07067	+	1.18910i	−0.0621268	+	0.0689988i
$298$	0.981231	−	9.33579i	0.0568412	−	0.540808i
$299$	2.45516	−	4.25246i	0.141985	−	0.245926i
$300$	−4.99545	−	6.02002i	−0.288413	−	0.347566i
$301$	−11.4777	+	6.74000i	−0.661563	+	0.388487i
$302$	10.0534	+	7.30422i	0.578508	+	0.420311i
$303$	5.85143	+	1.24376i	0.336156	+	0.0714522i
$304$	−17.3578	+	19.2778i	−0.995536	+	1.10565i
$305$	−0.628249	+	0.543114i	−0.0359734	+	0.0310986i
$306$	−4.17007	−	4.63133i	−0.238387	−	0.264755i
$307$	−28.8190			−1.64479			−0.822394	−	0.568919i	$-0.807362\pi$
$307$	−28.8190			−1.64479			−0.822394	+	0.568919i	$0.807362\pi$
$308$	6.31419	+	2.00024i	0.359784	+	0.113974i
$309$	−9.86218	+	7.16529i	−0.561040	+	0.407619i
$310$	18.9526	−	25.0081i	1.07644	−	1.42037i
$311$	2.58374	−	24.5826i	0.146510	−	1.39395i	−0.636179	−	0.771541i	$-0.719486\pi$
$311$	2.58374	−	24.5826i	0.146510	−	1.39395i	0.782690	−	0.622412i	$-0.213847\pi$
$312$	−3.61308	−	1.60865i	−0.204550	−	0.0910716i
$313$	1.19214	+	11.3425i	0.0673839	+	0.641115i	0.975136	+	0.221608i	$0.0711304\pi$
$313$	1.19214	+	11.3425i	0.0673839	+	0.641115i	−0.907752	+	0.419507i	$0.862203\pi$
$314$	12.1754	+	8.84591i	0.687095	+	0.499204i
$315$	−4.74125	−	3.53844i	−0.267139	−	0.199369i
$316$	−7.27744	+	5.28737i	−0.409388	+	0.297438i
$317$	19.3222	+	21.4595i	1.08525	+	1.20529i	0.977462	+	0.211113i	$0.0677088\pi$
$317$	19.3222	+	21.4595i	1.08525	+	1.20529i	0.107784	+	0.994174i	$0.465625\pi$
$318$	0.641913	+	1.11183i	0.0359967	+	0.0623481i
$319$	10.0861	−	2.14387i	0.564714	−	0.120034i
$320$	−8.91304	−	3.09634i	−0.498254	−	0.173091i
$321$	−1.96829	−	6.05779i	−0.109859	−	0.338113i
$322$	1.02326	−	4.99494i	0.0570243	−	0.278357i
$323$	−14.7981	−	10.7514i	−0.823387	−	0.598226i
$324$	−0.782273	+	1.35494i	−0.0434596	+	0.0752743i
$325$	8.35038	−	22.5572i	0.463196	−	1.25125i
$326$	−5.43137	−	9.40740i	−0.300816	−	0.521028i
$327$	7.73059	−	3.44188i	0.427503	−	0.190336i
$328$	−1.25908	−	3.87504i	−0.0695209	−	0.213963i
$329$	1.20370	−	0.400945i	0.0663624	−	0.0221048i
$330$	−6.70249	−	0.841604i	−0.368960	−	0.0463288i
$331$	−21.5064	−	23.8852i	−1.18210	−	1.31285i	−0.939430	−	0.342741i	$-0.888645\pi$
$331$	−21.5064	−	23.8852i	−1.18210	−	1.31285i	−0.242666	−	0.970110i	$-0.578022\pi$
$332$	−13.5508	−	23.4707i	−0.743698	−	1.28812i
$333$	2.54849	−	0.541699i	0.139657	−	0.0296849i
$334$	−0.654700	−	6.22906i	−0.0358236	−	0.340839i
$335$	−3.92776	+	2.16315i	−0.214596	+	0.118185i
$336$	−12.3269	−	1.20376i	−0.672487	−	0.0656706i
$337$	11.2793	−	8.19492i	0.614425	−	0.446406i	−0.236545	−	0.971621i	$-0.576015\pi$
$337$	11.2793	−	8.19492i	0.614425	−	0.446406i	0.850970	+	0.525215i	$0.176015\pi$
$338$	2.00158	+	19.0438i	0.108872	+	1.03584i
$339$	−1.10715	+	10.5338i	−0.0601322	+	0.572120i
$340$	2.62853	−	11.2448i	0.142552	−	0.609834i
$341$	−1.24315	−	11.8278i	−0.0673206	−	0.640513i
$342$	−3.23297	+	9.95007i	−0.174819	+	0.538038i
$343$	0.409726	+	18.5157i	0.0221231	+	0.999755i
$344$	1.27810	−	3.93360i	0.0689107	−	0.212085i
$345$	−0.0460839	+	2.28193i	−0.00248107	+	0.122855i
$346$	4.26695	−	4.73893i	0.229393	−	0.254766i
$347$	13.7725	−	15.2959i	0.739347	−	0.821128i	−0.249763	−	0.968307i	$-0.580353\pi$
$347$	13.7725	−	15.2959i	0.739347	−	0.821128i	0.989110	+	0.147179i	$0.0470195\pi$
$348$	9.21069	−	4.10086i	0.493745	−	0.219829i
$349$	−26.2225			−1.40366			−0.701829	−	0.712345i	$-0.747633\pi$
$349$	−26.2225			−1.40366			−0.701829	+	0.712345i	$0.747633\pi$
$350$	0.824299	−	24.9623i	0.0440607	−	1.33429i
$351$	−4.81064			−0.256773
$352$	−10.5159	+	4.68198i	−0.560500	+	0.249551i
$353$	2.44136	−	2.71140i	0.129940	−	0.144313i	−0.674663	−	0.738126i	$-0.735711\pi$
$353$	2.44136	−	2.71140i	0.129940	−	0.144313i	0.804604	+	0.593812i	$0.202378\pi$
$354$	−14.8786	+	16.5243i	−0.790786	+	0.878257i
$355$	−10.3583	−	14.8798i	−0.549761	−	0.789736i
$356$	4.71328	−	14.5060i	0.249803	−	0.768816i
$357$	−0.0644073	−	8.73307i	−0.00340880	−	0.462203i
$358$	9.53086	−	29.3330i	0.503722	−	1.55030i
$359$	2.97723	+	28.3264i	0.157132	+	1.49501i	0.734546	+	0.678559i	$0.237395\pi$
$359$	2.97723	+	28.3264i	0.157132	+	1.49501i	−0.577414	+	0.816452i	$0.695938\pi$
$360$	1.83179	−	0.155206i	0.0965437	−	0.00818008i
$361$	−1.22370	+	11.6427i	−0.0644052	+	0.612775i
$362$	−0.104527	−	0.994506i	−0.00549381	−	0.0522701i
$363$	6.82785	−	4.96073i	0.358369	−	0.260371i
$364$	8.23336	+	18.1314i	0.431546	+	0.950342i
$365$	−5.70651	−	29.7929i	−0.298692	−	1.55943i
$366$	0.0732947	+	0.697352i	0.00383117	+	0.0364512i
$367$	−4.54209	+	0.965451i	−0.237095	+	0.0503962i	−0.324927	−	0.945739i	$-0.605340\pi$
$367$	−4.54209	+	0.965451i	−0.237095	+	0.0503962i	0.0878315	+	0.996135i	$0.472006\pi$
$368$	2.38914	+	4.13811i	0.124542	+	0.215714i
$369$	−3.31617	−	3.68298i	−0.172633	−	0.191728i
$370$	8.02383	+	7.52353i	0.417139	+	0.391130i
$371$	−0.361064	+	1.76249i	−0.0187455	+	0.0915037i
$372$	−3.59348	−	11.0596i	−0.186313	−	0.573414i
$373$	−23.2749	+	10.3627i	−1.20513	+	0.536558i	−0.908279	−	0.418365i	$-0.862603\pi$
$373$	−23.2749	+	10.3627i	−1.20513	+	0.536558i	−0.296851	+	0.954924i	$0.595936\pi$
$374$	−4.98595	−	8.63592i	−0.257817	−	0.446553i
$375$	1.65819	+	11.0567i	0.0856287	+	0.570965i
$376$	−0.197121	+	0.341423i	−0.0101657	+	0.0176075i
$377$	25.0804	+	18.2220i	1.29171	+	0.938479i
$378$	−4.73919	+	1.57859i	−0.243757	+	0.0811939i
$379$	−7.38275	−	22.7218i	−0.379226	−	1.16714i	−0.940583	−	0.339565i	$-0.889720\pi$
$379$	−7.38275	−	22.7218i	−0.379226	−	1.16714i	0.561356	−	0.827574i	$-0.310280\pi$
$380$	−18.5545	+	5.61716i	−0.951826	+	0.288154i
$381$	3.11745	−	0.662634i	0.159712	−	0.0339477i
$382$	14.5059	+	25.1249i	0.742186	+	1.28550i
$383$	−6.37945	−	7.08510i	−0.325975	−	0.362032i	0.557774	−	0.829993i	$-0.311655\pi$
$383$	−6.37945	−	7.08510i	−0.325975	−	0.362032i	−0.883749	+	0.467961i	$0.844989\pi$
$384$	5.19486	−	3.77428i	0.265099	−	0.192606i
$385$	−6.24350	−	7.11544i	−0.318198	−	0.362636i
$386$	2.43777	+	1.77115i	0.124079	+	0.0901490i
$387$	−0.525865	−	5.00327i	−0.0267312	−	0.254331i
$388$	−26.7834	−	11.9247i	−1.35972	−	0.605387i
$389$	−3.48098	+	33.1193i	−0.176493	+	1.67922i	0.444794	+	0.895633i	$0.353277\pi$
$389$	−3.48098	+	33.1193i	−0.176493	+	1.67922i	−0.621286	+	0.783584i	$0.713390\pi$
$390$	−11.6032	−	16.6681i	−0.587551	−	0.844021i
$391$	−2.72580	+	1.98041i	−0.137849	+	0.100154i
$392$	−3.91348	−	4.21950i	−0.197660	−	0.213117i
$393$	−17.8534			−0.900584
$394$	−22.9096	−	25.4437i	−1.15417	−	1.28184i
$395$	12.8104	−	1.08542i	0.644563	−	0.0546134i
$396$	−1.67512	+	1.86041i	−0.0841779	+	0.0934890i
$397$	35.8888	+	7.62839i	1.80121	+	0.382858i	0.981734	−	0.190261i	$-0.0609335\pi$
$397$	35.8888	+	7.62839i	1.80121	+	0.382858i	0.819472	+	0.573119i	$0.194267\pi$
$398$	29.0524	+	21.1078i	1.45626	+	1.05804i
$399$	−12.6425	+	7.42399i	−0.632916	+	0.371664i
$400$	14.9469	+	18.0125i	0.747346	+	0.900626i
$401$	−2.67119	+	4.62664i	−0.133393	+	0.231043i	−0.924982	−	0.380010i	$-0.875921\pi$
$401$	−2.67119	+	4.62664i	−0.133393	+	0.231043i	0.791589	+	0.611053i	$0.209254\pi$
$402$	−0.395749	+	3.76530i	−0.0197382	+	0.187796i
$403$	23.9254	−	26.5718i	1.19181	−	1.32364i
$404$	9.15484	+	1.94592i	0.455470	+	0.0968132i
$405$	1.95867	−	1.07871i	0.0973272	−	0.0536013i
$406$	30.6873	+	9.72129i	1.52299	+	0.482460i
$407$	4.16894			0.206647
$408$	1.81587	+	2.01673i	0.0898989	+	0.0998429i
$409$	20.1868	+	8.98775i	0.998174	+	0.444416i	0.839761	−	0.542957i	$-0.182695\pi$
$409$	20.1868	+	8.98775i	0.998174	+	0.444416i	0.158414	+	0.987373i	$0.449362\pi$
$410$	4.76236	−	20.3733i	0.235196	−	1.00616i
$411$	19.0600	−	8.48606i	0.940161	−	0.418587i
$412$	−15.4298	+	11.2104i	−0.760173	+	0.552298i
$413$	−30.9644	+	3.48556i	−1.52366	+	0.171513i
$414$	1.55907	+	1.13273i	0.0766241	+	0.0556707i
$415$	−0.782078	+	38.7261i	−0.0383907	+	1.90099i
$416$	−31.6158	−	14.0763i	−1.55009	−	0.690145i
$417$	−14.0473	+	2.98585i	−0.687900	+	0.146218i
$418$	−8.37020	+	14.4976i	−0.409400	+	0.709101i
$419$	0.847489	−	2.60830i	0.0414025	−	0.127424i	−0.928219	−	0.372035i	$-0.878660\pi$
$419$	0.847489	−	2.60830i	0.0414025	−	0.127424i	0.969621	+	0.244611i	$0.0786602\pi$
$420$	−7.41790	−	5.53606i	−0.361957	−	0.270132i
$421$	2.79423	+	8.59977i	0.136183	+	0.419127i	0.995772	−	0.0918582i	$-0.0292807\pi$
$421$	2.79423	+	8.59977i	0.136183	+	0.419127i	−0.859589	+	0.510985i	$0.829281\pi$
$422$	−8.91492	−	1.89492i	−0.433972	−	0.0922435i
$423$	−0.0501248	+	0.476906i	−0.00243715	+	0.0231880i
$424$	−0.279523	−	0.484148i	−0.0135748	−	0.0235123i
$425$	−11.5298	+	11.8093i	−0.559277	+	0.572835i
$426$	−15.3080			−0.741675
$427$	−0.571690	+	0.799193i	−0.0276660	+	0.0386756i
$428$	−3.07949	−	9.47769i	−0.148853	−	0.458121i
$429$	−7.52928	−	1.60040i	−0.363517	−	0.0772680i
$430$	16.0671	−	13.8899i	0.774826	−	0.669828i
$431$	−17.3845	+	3.69518i	−0.837381	+	0.177991i	−0.606592	−	0.795013i	$-0.707464\pi$
$431$	−17.3845	+	3.69518i	−0.837381	+	0.177991i	−0.230788	+	0.973004i	$0.574131\pi$
$432$	2.34064	−	4.05411i	0.112614	−	0.195054i
$433$	6.82947	−	21.0190i	0.328203	−	1.01011i	−0.641770	−	0.766897i	$-0.721800\pi$
$433$	6.82947	−	21.0190i	0.328203	−	1.01011i	0.969974	−	0.243209i	$-0.0782002\pi$
$434$	14.8506	−	34.0281i	0.712850	−	1.63340i
$435$	−14.2975	−	1.79528i	−0.685515	−	0.0860773i
$436$	12.0949	−	5.38498i	0.579239	−	0.257894i
$437$	5.16718	+	2.30058i	0.247180	+	0.110052i
$438$	−23.3983	−	10.4176i	−1.11801	−	0.497772i
$439$	37.8035	−	16.8312i	1.80426	−	0.803309i	0.838035	−	0.545616i	$-0.183704\pi$
$439$	37.8035	−	16.8312i	1.80426	−	0.803309i	0.966227	−	0.257693i	$-0.0829624\pi$
$440$	2.91862	+	0.366479i	0.139140	+	0.0174712i
$441$	−6.43612	−	2.75253i	−0.306482	−	0.131073i
$442$	9.26441	−	28.5129i	0.440663	−	1.35622i
$443$	17.1634	−	29.7279i	0.815458	−	1.41241i	−0.0935409	−	0.995615i	$-0.529819\pi$
$443$	17.1634	−	29.7279i	0.815458	−	1.41241i	0.908999	−	0.416799i	$-0.136848\pi$
$444$	3.98724	−	0.847514i	0.189226	−	0.0402212i
$445$	−16.4911	+	14.2563i	−0.781751	+	0.675816i
$446$	−51.2535	−	10.8943i	−2.42692	−	0.515858i
$447$	1.53644	+	4.72869i	0.0726713	+	0.223659i
$448$	−11.1114	−	1.08507i	−0.524966	−	0.0512647i
$449$	−22.0175			−1.03907			−0.519535	−	0.854449i	$-0.673895\pi$
$449$	−22.0175			−1.03907			−0.519535	+	0.854449i	$0.673895\pi$
$450$	8.46182	+	4.18464i	0.398894	+	0.197266i
$451$	−3.96499	−	6.86756i	−0.186704	−	0.323381i
$452$	−1.73219	+	16.4807i	−0.0814754	+	0.775187i
$453$	−6.43810	−	1.36846i	−0.302488	−	0.0642959i
$454$	−3.65360	−	11.2446i	−0.171472	−	0.527736i
$455$	3.33743	−	28.2638i	0.156461	−	1.32503i
$456$	1.40781	−	4.33279i	0.0659267	−	0.202901i
$457$	−13.6220	+	23.5939i	−0.637208	+	1.10368i	0.348834	+	0.937184i	$0.386578\pi$
$457$	−13.6220	+	23.5939i	−0.637208	+	1.10368i	−0.986043	+	0.166493i	$0.946756\pi$
$458$	7.50620	−	1.59549i	0.350742	−	0.0745524i
$459$	3.01551	+	1.34259i	0.140752	+	0.0626667i
$460$	−0.0721004	+	3.57019i	−0.00336170	+	0.166461i
$461$	−6.84581	−	4.97377i	−0.318841	−	0.231652i	0.416840	−	0.908980i	$-0.363138\pi$
$461$	−6.84581	−	4.97377i	−0.318841	−	0.231652i	−0.735681	+	0.677328i	$0.763138\pi$
$462$	−7.94261	+	0.894072i	−0.369523	+	0.0415960i
$463$	3.18870	−	2.31673i	0.148192	−	0.107668i	−0.511219	−	0.859451i	$-0.670806\pi$
$463$	3.18870	−	2.31673i	0.148192	−	0.107668i	0.659411	+	0.751783i	$0.270806\pi$
$464$	−27.5593	+	12.2702i	−1.27941	+	0.569630i
$465$	−3.78302	+	16.1837i	−0.175433	+	0.750500i
$466$	15.7300	+	7.00347i	0.728680	+	0.324429i
$467$	−10.9492	−	12.1603i	−0.506667	−	0.562711i	0.434491	−	0.900676i	$-0.356928\pi$
$467$	−10.9492	−	12.1603i	−0.506667	−	0.562711i	−0.941159	+	0.337965i	$0.890261\pi$
$468$	−7.52648			−0.347912
$469$	−3.91652	+	3.57910i	−0.180848	+	0.165267i
$470$	−1.77330	+	0.976616i	−0.0817962	+	0.0450479i
$471$	−7.79698	−	1.65730i	−0.359266	−	0.0763643i
$472$	6.47892	−	7.19557i	0.298216	−	0.331203i
$473$	0.841435	−	8.00572i	0.0386892	−	0.368103i
$474$	5.42756	−	9.40081i	0.249296	−	0.431794i
$475$	26.8467	+	6.85007i	1.23181	+	0.314303i
$476$	−0.100768	−	13.6633i	−0.00461871	−	0.626256i
$477$	−0.550125	−	0.399689i	−0.0251885	−	0.0183005i
$478$	−14.2141	−	3.02130i	−0.650139	−	0.138191i
$479$	−1.99627	+	2.21709i	−0.0912121	+	0.101301i	−0.787023	−	0.616924i	$-0.788379\pi$
$479$	−1.99627	+	2.21709i	−0.0912121	+	0.101301i	0.695811	+	0.718225i	$0.255045\pi$
$480$	16.0288	−	1.35811i	0.731613	−	0.0619891i
$481$	8.38674	+	9.31442i	0.382403	+	0.424701i
$482$	9.82276			0.447414
$483$	0.580945	+	2.63734i	0.0264339	+	0.120003i
$484$	10.6825	−	7.76129i	0.485568	−	0.352786i
$485$	23.9397	+	34.3896i	1.08705	+	1.56155i
$486$	0.197350	−	1.87766i	0.00895197	−	0.0851723i
$487$	−0.404457	−	0.180076i	−0.0183277	−	0.00816002i	0.397552	−	0.917580i	$-0.369860\pi$
$487$	−0.404457	−	0.180076i	−0.0183277	−	0.00816002i	−0.415880	+	0.909419i	$0.636526\pi$
$488$	−0.0319164	−	0.303664i	−0.00144479	−	0.0137462i
$489$	4.65473	+	3.38186i	0.210494	+	0.152933i
$490$	−5.98677	−	28.9391i	−0.270455	−	1.30734i
$491$	7.08426	−	5.14702i	0.319708	−	0.232282i	−0.416343	−	0.909208i	$-0.636688\pi$
$491$	7.08426	−	5.14702i	0.319708	−	0.232282i	0.736051	+	0.676926i	$0.236688\pi$
$492$	−5.18830	−	5.76220i	−0.233907	−	0.259780i
$493$	−10.6359	−	18.4219i	−0.479016	−	0.829680i
$494$	−49.2297	+	10.4641i	−2.21495	+	0.470802i
$495$	3.42444	−	1.03671i	0.153917	−	0.0465965i
$496$	10.7521	+	33.0915i	0.482782	+	1.48585i
$497$	−16.0473	−	14.2361i	−0.719818	−	0.638578i
$498$	26.4586	+	19.2233i	1.18564	+	0.861417i
$499$	19.7438	−	34.1972i	0.883852	−	1.53088i	0.0368286	−	0.999322i	$-0.488274\pi$
$499$	19.7438	−	34.1972i	0.883852	−	1.53088i	0.847024	−	0.531555i	$-0.178392\pi$
$500$	2.59432	+	17.2987i	0.116021	+	0.773622i
$501$	1.65873	+	2.87301i	0.0741066	+	0.128356i
$502$	−49.6060	+	22.0860i	−2.21402	+	0.985747i
$503$	11.2906	+	34.7489i	0.503423	+	1.54938i	0.803406	+	0.595432i	$0.203019\pi$
$503$	11.2906	+	34.7489i	0.503423	+	1.54938i	−0.299983	+	0.953945i	$0.596981\pi$
$504$	2.06369	−	0.687402i	0.0919242	−	0.0306193i
$505$	−9.75794	−	9.14952i	−0.434222	−	0.407148i
$506$	2.06331	+	2.29154i	0.0917254	+	0.101871i
$507$	−5.07115	−	8.78348i	−0.225218	−	0.390088i
$508$	4.87739	−	1.03672i	0.216399	−	0.0459971i
$509$	−1.64813	−	15.6810i	−0.0730523	−	0.695046i	−0.968353	−	0.249584i	$-0.919706\pi$
$509$	−1.64813	−	15.6810i	−0.0730523	−	0.695046i	0.895301	−	0.445462i	$-0.146961\pi$
$510$	2.62151	+	13.6865i	0.116082	+	0.606050i
$511$	−14.8401	−	32.6807i	−0.656488	−	1.44571i
$512$	21.0182	−	15.2706i	0.928880	−	0.674871i
$513$	−0.579232	−	5.51102i	−0.0255737	−	0.243317i
$514$	−3.22077	+	30.6436i	−0.142062	+	1.35163i
$515$	27.1611	−	2.30134i	1.19686	−	0.101409i
$516$	−0.822741	−	7.82786i	−0.0362191	−	0.344602i
$517$	−0.237108	+	0.729744i	−0.0104280	+	0.0320941i
$518$	11.3186	+	6.42400i	0.497313	+	0.282254i
$519$	−1.04373	+	3.21226i	−0.0458145	+	0.141003i
$520$	5.05265	+	7.25817i	0.221573	+	0.318292i
$521$	−6.27352	+	6.96745i	−0.274848	+	0.305250i	−0.864727	−	0.502242i	$-0.832509\pi$
$521$	−6.27352	+	6.96745i	−0.274848	+	0.305250i	0.589879	+	0.807491i	$0.299175\pi$
$522$	−8.14116	+	9.04168i	−0.356329	+	0.395744i
$523$	12.0181	−	5.35078i	0.525513	−	0.233973i	−0.126793	−	0.991929i	$-0.540468\pi$
$523$	12.0181	−	5.35078i	0.525513	−	0.233973i	0.652306	+	0.757956i	$0.273802\pi$
$524$	−27.9325			−1.22023
$525$	4.97884	+	12.2561i	0.217294	+	0.534899i
$526$	−27.5774			−1.20243
$527$	−22.4132	+	9.97902i	−0.976336	+	0.434693i
$528$	5.01213	−	5.56653i	0.218125	−	0.242252i
$529$	−14.6929	+	16.3181i	−0.638820	+	0.709481i
$530$	0.0579628	−	2.87014i	0.00251774	−	0.124671i
$531$	3.63940	−	11.2009i	0.157937	−	0.486079i
$532$	−19.7798	+	11.6152i	−0.857561	+	0.503582i
$533$	7.36735	−	22.6744i	0.319116	−	0.982137i
$534$	1.92393	+	18.3050i	0.0832566	+	0.792134i
$535$	−3.24191	+	13.8688i	−0.140160	+	0.599602i
$536$	0.172330	−	1.63961i	0.00744353	−	0.0708204i
$537$	1.70758	+	16.2466i	0.0736877	+	0.701091i
$538$	21.3197	−	15.4897i	0.919157	−	0.667806i
$539$	−9.15765	−	6.44922i	−0.394448	−	0.277788i
$540$	3.06443	−	1.68769i	0.131872	−	0.0726265i
$541$	−0.817307	−	7.77616i	−0.0351388	−	0.334323i	−0.997942	−	0.0641202i	$-0.979576\pi$
$541$	−0.817307	−	7.77616i	−0.0351388	−	0.334323i	0.962803	−	0.270203i	$-0.0870908\pi$
$542$	−56.5234	+	12.0144i	−2.42789	+	0.516063i
$543$	0.264826	+	0.458692i	0.0113648	+	0.0196844i
$544$	15.8895	+	17.6471i	0.681258	+	0.756614i
$545$	−18.7746	−	2.35745i	−0.804215	−	0.100982i
$546$	−17.9759	−	15.9471i	−0.769297	−	0.682473i
$547$	8.75720	+	26.9519i	0.374431	+	1.15238i	0.943862	+	0.330341i	$0.107164\pi$
$547$	8.75720	+	26.9519i	0.374431	+	1.15238i	−0.569431	+	0.822039i	$0.692836\pi$
$548$	29.8203	−	13.2768i	1.27386	−	0.567159i
$549$	−0.185697	−	0.321637i	−0.00792537	−	0.0137271i
$550$	11.8517	+	9.36458i	0.505359	+	0.399307i
$551$	−17.8551	+	30.9259i	−0.760651	+	1.31749i
$552$	−0.678902	−	0.493251i	−0.0288960	−	0.0209942i
$553$	14.4323	−	4.80728i	0.613722	−	0.204426i
$554$	−12.8534	−	39.5587i	−0.546089	−	1.68069i
$555$	−5.50330	−	1.91181i	−0.233602	−	0.0811520i
$556$	−21.9777	+	4.67150i	−0.932062	+	0.198116i
$557$	13.8693	+	24.0223i	0.587661	+	1.01786i	0.994538	+	0.104376i	$0.0332846\pi$
$557$	13.8693	+	24.0223i	0.587661	+	1.01786i	−0.406877	+	0.913483i	$0.633382\pi$
$558$	9.38983	+	10.4285i	0.397503	+	0.441472i
$559$	19.5795	−	14.2253i	0.828123	−	0.601667i
$560$	22.1951	+	16.5645i	0.937916	+	0.699977i
$561$	4.27301	+	3.10452i	0.180407	+	0.131073i
$562$	−3.30126	−	31.4094i	−0.139255	−	1.32492i
$563$	−10.7299	−	4.77726i	−0.452211	−	0.201337i	0.167976	−	0.985791i	$-0.446277\pi$
$563$	−10.7299	−	4.77726i	−0.452211	−	0.201337i	−0.620187	+	0.784454i	$0.712943\pi$
$564$	−0.0784226	+	0.746141i	−0.00330219	+	0.0314182i
$565$	14.3052	−	18.8759i	0.601825	−	0.794114i
$566$	−11.9622	+	8.69103i	−0.502808	+	0.365311i
$567$	1.95307	−	1.78481i	0.0820211	−	0.0749548i
$568$	6.66591			0.279696
$569$	19.5197	+	21.6788i	0.818307	+	0.908822i	0.997180	−	0.0750502i	$-0.0239117\pi$
$569$	19.5197	+	21.6788i	0.818307	+	0.908822i	−0.178873	+	0.983872i	$0.557245\pi$
$570$	17.6977	−	15.2994i	0.741273	−	0.640823i
$571$	−4.06300	+	4.51242i	−0.170031	+	0.188839i	−0.822138	−	0.569288i	$-0.807219\pi$
$571$	−4.06300	+	4.51242i	−0.170031	+	0.188839i	0.652107	+	0.758127i	$0.273885\pi$
$572$	−11.7799	−	2.50390i	−0.492543	−	0.104693i
$573$	−12.4317	−	9.03215i	−0.519341	−	0.377323i
$574$	−0.182572	−	24.7551i	−0.00762040	−	1.03326i
$575$	2.72816	−	4.31321i	0.113772	−	0.179873i
$576$	2.10985	−	3.65437i	0.0879105	−	0.152265i
$577$	−2.94100	+	27.9818i	−0.122436	+	1.16490i	0.744901	+	0.667175i	$0.232497\pi$
$577$	−2.94100	+	27.9818i	−0.122436	+	1.16490i	−0.867337	+	0.497722i	$0.834170\pi$
$578$	7.71153	−	8.56452i	0.320757	−	0.356237i
$579$	−1.56113	−	0.331828i	−0.0648782	−	0.0137903i
$580$	−22.3692	−	2.80881i	−0.928830	−	0.116629i
$581$	9.85908	+	44.7577i	0.409024	+	1.85686i
$582$	35.3793			1.46652
$583$	−0.728049	−	0.808581i	−0.0301527	−	0.0334880i
$584$	10.1889	+	4.53637i	0.421618	+	0.187716i
$585$	9.20528	+	5.56546i	0.380591	+	0.230104i
$586$	−30.7988	+	13.7125i	−1.27229	+	0.566459i
$587$	10.3595	−	7.52663i	0.427583	−	0.310657i	−0.353099	−	0.935586i	$-0.614872\pi$
$587$	10.3595	−	7.52663i	0.427583	−	0.310657i	0.780682	+	0.624929i	$0.214872\pi$
$588$	−10.0696	−	4.30646i	−0.415264	−	0.177595i
$589$	33.3211	+	24.2092i	1.37297	+	0.997524i
$590$	47.5875	−	14.4066i	1.95915	−	0.593109i
$591$	16.5667	+	7.37596i	0.681462	+	0.303406i
$592$	−11.9302	+	2.53585i	−0.490330	+	0.104223i
$593$	−4.87764	+	8.44831i	−0.200301	+	0.346931i	−0.948625	−	0.316402i	$-0.897525\pi$
$593$	−4.87764	+	8.44831i	−0.200301	+	0.346931i	0.748325	+	0.663333i	$0.230859\pi$
$594$	0.933535	−	2.87313i	0.0383034	−	0.117886i
$595$	−9.98010	+	16.7854i	−0.409144	+	0.688136i
$596$	2.40384	+	7.39826i	0.0984651	+	0.303044i
$597$	−18.6049	−	3.95458i	−0.761446	−	0.161850i
$598$	−0.969049	+	9.21989i	−0.0396274	+	0.377029i
$599$	−9.35923	−	16.2107i	−0.382408	−	0.662350i	0.608998	−	0.793172i	$-0.291572\pi$
$599$	−9.35923	−	16.2107i	−0.382408	−	0.662350i	−0.991406	+	0.130822i	$0.958238\pi$
$600$	−3.68473	−	1.82222i	−0.150428	−	0.0743917i
$601$	6.91394			0.282026			0.141013	−	0.990008i	$-0.454964\pi$
$601$	6.91394			0.282026			0.141013	+	0.990008i	$0.454964\pi$
$602$	14.6207	−	20.4389i	0.595894	−	0.833028i
$603$	−0.619677	−	1.90717i	−0.0252352	−	0.0776660i
$604$	−10.0727	−	2.14102i	−0.409853	−	0.0871168i
$605$	−18.8043	+	1.59328i	−0.764505	+	0.0647760i
$606$	−11.0475	+	2.34822i	−0.448774	+	0.0953900i
$607$	−15.6455	+	27.0988i	−0.635032	+	1.09991i	0.351476	+	0.936197i	$0.385680\pi$
$607$	−15.6455	+	27.0988i	−0.635032	+	1.09991i	−0.986508	+	0.163711i	$0.947653\pi$
$608$	12.3189	−	37.9135i	0.499596	−	1.53760i
$609$	−16.9429	+	1.90721i	−0.686562	+	0.0772839i
$610$	0.666520	−	1.41919i	0.0269866	−	0.0574615i
$611$	−2.10742	+	0.938285i	−0.0852572	+	0.0379589i
$612$	4.71790	+	2.10054i	0.190710	+	0.0849095i
$613$	−10.6497	−	4.74157i	−0.430139	−	0.191510i	0.180235	−	0.983624i	$-0.442314\pi$
$613$	−10.6497	−	4.74157i	−0.430139	−	0.191510i	−0.610374	+	0.792113i	$0.708981\pi$
$614$	49.7063	−	22.1307i	2.00598	−	0.893121i
$615$	2.08471	+	10.8840i	0.0840635	+	0.438884i
$616$	3.45863	−	0.389327i	0.139352	−	0.0156864i
$617$	0.925871	−	2.84954i	0.0372742	−	0.114718i	−0.930688	−	0.365813i	$-0.880791\pi$
$617$	0.925871	−	2.84954i	0.0372742	−	0.114718i	0.967962	+	0.251095i	$0.0807908\pi$
$618$	11.5077	−	19.9319i	0.462906	−	0.801777i
$619$	15.9855	−	3.39782i	0.642511	−	0.136570i	0.124877	−	0.992172i	$-0.460146\pi$
$619$	15.9855	−	3.39782i	0.642511	−	0.136570i	0.517634	+	0.855602i	$0.326813\pi$
$620$	−5.91871	+	25.3201i	−0.237701	+	1.01688i
$621$	−0.998413	−	0.212219i	−0.0400649	−	0.00851607i
$622$	14.4211	+	44.3836i	0.578234	+	1.77962i
$623$	−15.0064	+	20.9782i	−0.601220	+	0.840474i
$624$	22.5200			0.901522
$625$	9.61856	−	23.0756i	0.384742	−	0.923024i
$626$	−10.7663	−	18.6477i	−0.430307	−	0.745314i
$627$	0.926826	−	8.81816i	0.0370139	−	0.352163i
$628$	−12.1987	−	2.59292i	−0.486783	−	0.103469i
$629$	−2.65761	−	8.17929i	−0.105966	−	0.326130i
$630$	10.8948	+	2.46212i	0.434060	+	0.0980934i
$631$	8.92475	−	27.4676i	0.355289	−	1.09347i	−0.600553	−	0.799585i	$-0.705053\pi$
$631$	8.92475	−	27.4676i	0.355289	−	1.09347i	0.955842	−	0.293882i	$-0.0949472\pi$
$632$	−2.36345	+	4.09361i	−0.0940130	+	0.162835i
$633$	4.72188	−	1.00367i	0.187678	−	0.0398922i
$634$	−49.8057	−	22.1749i	−1.97804	−	0.880679i
$635$	−6.73191	−	2.33863i	−0.267148	−	0.0928056i
$636$	−0.860697	−	0.625333i	−0.0341288	−	0.0247961i
$637$	−4.01352	−	33.4345i	−0.159021	−	1.32472i
$638$	−15.7500	+	11.4430i	−0.623547	+	0.453033i
$639$	7.40707	−	3.29784i	0.293019	−	0.130460i
$640$	−14.3070	+	1.21222i	−0.565533	+	0.0479172i
$641$	−27.9165	−	12.4292i	−1.10264	−	0.490926i	−0.227000	−	0.973895i	$-0.572892\pi$
$641$	−27.9165	−	12.4292i	−1.10264	−	0.490926i	−0.875637	+	0.482969i	$0.839558\pi$
$642$	8.04675	+	8.93682i	0.317580	+	0.352708i
$643$	−3.42518			−0.135076			−0.0675380	−	0.997717i	$-0.521514\pi$
$643$	−3.42518			−0.135076			−0.0675380	+	0.997717i	$0.521514\pi$
$644$	0.908916	+	4.12624i	0.0358163	+	0.162597i
$645$	−4.78206	+	10.1823i	−0.188293	+	0.400926i
$646$	33.7796	+	7.18007i	1.32904	+	0.282496i
$647$	1.68652	−	1.87307i	0.0663040	−	0.0736380i	−0.709080	−	0.705128i	$-0.750890\pi$
$647$	1.68652	−	1.87307i	0.0663040	−	0.0736380i	0.775384	+	0.631490i	$0.217556\pi$
$648$	−0.0859366	+	0.817632i	−0.00337591	+	0.0321196i
$649$	9.42245	−	16.3202i	0.369864	−	0.640622i
$650$	2.91960	+	45.3185i	0.114516	+	1.77754i
$651$	0.145027	+	19.6645i	0.00568407	+	0.770711i
$652$	7.28254	+	5.29108i	0.285206	+	0.207215i
$653$	−24.6661	−	5.24294i	−0.965258	−	0.205172i	−0.301788	−	0.953375i	$-0.597584\pi$
$653$	−24.6661	−	5.24294i	−0.965258	−	0.205172i	−0.663470	+	0.748203i	$0.730917\pi$
$654$	−10.6904	+	11.8729i	−0.418029	+	0.464268i
$655$	34.1629	+	20.6547i	1.33485	+	0.807045i
$656$	15.5239	+	17.2411i	0.606108	+	0.673151i
$657$	13.5660			0.529260
$658$	−1.76822	+	1.61589i	−0.0689326	+	0.0629939i
$659$	−0.492861	+	0.358084i	−0.0191991	+	0.0139490i	−0.597343	−	0.801986i	$-0.703777\pi$
$659$	−0.492861	+	0.358084i	−0.0191991	+	0.0139490i	0.578144	+	0.815935i	$0.303777\pi$
$660$	5.35769	−	1.62198i	0.208548	−	0.0631354i
$661$	−1.19339	+	11.3544i	−0.0464176	+	0.441634i	0.946489	+	0.322736i	$0.104603\pi$
$661$	−1.19339	+	11.3544i	−0.0464176	+	0.441634i	−0.992907	+	0.118897i	$0.962064\pi$
$662$	55.4355	+	24.6815i	2.15456	+	0.959273i
$663$	1.65985	+	15.7924i	0.0644631	+	0.613325i
$664$	−11.5215	−	8.37085i	−0.447120	−	0.324852i
$665$	32.7805	+	0.420184i	1.27117	+	0.0162941i
$666$	−3.97960	+	2.89135i	−0.154206	+	0.112037i
$667$	4.40139	+	4.88824i	0.170423	+	0.189274i
$668$	2.59516	+	4.49495i	0.100410	+	0.173915i
$669$	27.1470	−	5.77027i	1.04956	−	0.223091i
$670$	5.11337	−	6.74714i	0.197547	−	0.260665i
$671$	−0.183639	−	0.565182i	−0.00708929	−	0.0218186i
$672$	18.0581	−	6.01503i	0.696606	−	0.232035i
$673$	−10.4607	−	7.60014i	−0.403230	−	0.292964i	0.367625	−	0.929974i	$-0.380171\pi$
$673$	−10.4607	−	7.60014i	−0.403230	−	0.292964i	−0.770855	+	0.637010i	$0.780171\pi$
$674$	−13.1613	+	22.7960i	−0.506954	+	0.878070i
$675$	−4.99592	−	0.201869i	−0.192293	−	0.00776994i
$676$	−7.93405	−	13.7422i	−0.305156	−	0.528545i
$677$	−34.4965	+	15.3588i	−1.32581	+	0.590288i	−0.942770	−	0.333445i	$-0.891789\pi$
$677$	−34.4965	+	15.3588i	−1.32581	+	0.590288i	−0.383038	+	0.923732i	$0.625122\pi$
$678$	−6.17955	−	19.0187i	−0.237324	−	0.730409i
$679$	37.0879	+	32.9021i	1.42330	+	1.26267i
$680$	−1.14154	−	5.95984i	−0.0437762	−	0.228550i
$681$	4.19032	+	4.65382i	0.160574	+	0.178335i
$682$	11.2270	+	19.4457i	0.429903	+	0.744614i
$683$	−37.6198	+	7.99634i	−1.43948	+	0.305971i	−0.860534	−	0.509393i	$-0.829870\pi$
$683$	−37.6198	+	7.99634i	−1.43948	+	0.305971i	−0.578948	+	0.815364i	$0.696537\pi$
$684$	−0.906235	−	8.62225i	−0.0346508	−	0.329680i
$685$	−46.2893	−	5.81236i	−1.76862	−	0.222079i
$686$	−14.9253	−	31.6208i	−0.569849	−	1.20729i
$687$	−3.28830	+	2.38909i	−0.125456	+	0.0911494i
$688$	2.46173	+	23.4218i	0.0938524	+	0.892946i
$689$	0.341934	−	3.25328i	0.0130266	−	0.123940i
$690$	−1.67285	−	3.97120i	−0.0636844	−	0.151181i
$691$	−4.45883	−	42.4229i	−0.169622	−	1.61384i	−0.666146	−	0.745821i	$-0.732057\pi$
$691$	−4.45883	−	42.4229i	−0.169622	−	1.61384i	0.496524	−	0.868023i	$-0.334609\pi$
$692$	−1.63296	+	5.02573i	−0.0620758	+	0.191050i
$693$	3.65057	−	2.14371i	0.138674	−	0.0814328i
$694$	−12.0084	+	36.9582i	−0.455834	+	1.40291i
$695$	30.3342	+	10.5379i	1.15064	+	0.399727i
$696$	3.54510	−	3.93723i	0.134377	−	0.149240i
$697$	−10.9463	+	12.1571i	−0.414620	+	0.460482i
$698$	45.2279	−	20.1368i	1.71190	−	0.762188i
$699$	−9.12006			−0.344952
$700$	7.78962	+	19.1752i	0.294420	+	0.724754i
$701$	−7.99605			−0.302007			−0.151003	−	0.988533i	$-0.548250\pi$
$701$	−7.99605			−0.302007			−0.151003	+	0.988533i	$0.548250\pi$
$702$	8.29728	−	3.69419i	0.313160	−	0.139428i
$703$	−9.66068	+	10.7293i	−0.364360	+	0.404662i
$704$	4.51793	−	5.01766i	0.170276	−	0.189110i
$705$	0.647650	−	0.854580i	0.0243919	−	0.0321854i
$706$	−2.12866	+	6.55133i	−0.0801130	+	0.246562i
$707$	−13.7648	−	7.81235i	−0.517680	−	0.293814i
$708$	5.69402	−	17.5244i	0.213994	−	0.658607i
$709$	−5.37003	−	51.0924i	−0.201676	−	1.91882i	−0.362774	−	0.931877i	$-0.618170\pi$
$709$	−5.37003	−	51.0924i	−0.201676	−	1.91882i	0.161098	−	0.986938i	$-0.448496\pi$
$710$	29.2922	+	17.7099i	1.09932	+	0.664641i
$711$	−0.600990	+	5.71804i	−0.0225389	+	0.214443i
$712$	−0.837782	−	7.97096i	−0.0313972	−	0.298724i
$713$	6.13774	−	4.45933i	0.229860	−	0.167003i
$714$	6.81738	+	15.0131i	0.255134	+	0.561852i
$715$	12.5559	+	11.7731i	0.469566	+	0.440288i
$716$	2.67159	+	25.4185i	0.0998422	+	0.949935i
$717$	7.52866	−	1.60027i	0.281163	−	0.0597630i
$718$	−26.8874	−	46.5704i	−1.00343	−	1.73799i
$719$	−14.4701	−	16.0706i	−0.539643	−	0.599334i	0.410226	−	0.911984i	$-0.365450\pi$
$719$	−14.4701	−	16.0706i	−0.539643	−	0.599334i	−0.949868	+	0.312650i	$0.898783\pi$
$720$	−9.16910	+	5.04973i	−0.341712	+	0.188192i
$721$	30.5997	−	10.1925i	1.13959	−	0.379590i
$722$	−6.83006	−	21.0208i	−0.254189	−	0.782312i
$723$	−4.75293	+	2.11614i	−0.176763	+	0.0787001i
$724$	0.414333	+	0.717646i	0.0153986	+	0.0266711i
$725$	25.2817	+	19.9762i	0.938939	+	0.741899i
$726$	−7.96707	+	13.7994i	−0.295686	+	0.512143i
$727$	−26.0904	−	18.9558i	−0.967639	−	0.703031i	−0.0127266	−	0.999919i	$-0.504051\pi$
$727$	−26.0904	−	18.9558i	−0.967639	−	0.703031i	−0.954912	+	0.296888i	$0.904051\pi$
$728$	7.82766	+	6.94421i	0.290112	+	0.257370i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	32.7210	+	47.0039i	1.21106	+	1.73969i
$731$	−16.2433	+	3.45262i	−0.600780	+	0.127700i
$732$	−0.290532	−	0.503216i	−0.0107384	−	0.0185994i
$733$	−27.6809	−	30.7428i	−1.02242	−	1.13551i	−0.990707	−	0.136013i	$-0.956571\pi$
$733$	−27.6809	−	30.7428i	−1.02242	−	1.13551i	−0.0317113	−	0.999497i	$-0.510096\pi$
$734$	7.09270	−	5.15315i	0.261796	−	0.190206i
$735$	9.13124	+	12.7130i	0.336811	+	0.468926i
$736$	−5.94065	−	4.31614i	−0.218975	−	0.159095i
$737$	−0.335400	−	3.19112i	−0.0123546	−	0.117546i
$738$	8.54788	+	3.80576i	0.314652	+	0.140092i
$739$	2.60854	−	24.8186i	0.0959567	−	0.912967i	−0.835592	−	0.549351i	$-0.814875\pi$
$739$	2.60854	−	24.8186i	0.0959567	−	0.912967i	0.931549	−	0.363617i	$-0.118458\pi$
$740$	−8.61016	−	2.99112i	−0.316516	−	0.109956i
$741$	21.5664	−	15.6689i	0.792263	−	0.575613i
$742$	−0.730694	−	3.31716i	−0.0268246	−	0.121777i
$743$	−29.9489			−1.09872			−0.549359	−	0.835587i	$-0.685128\pi$
$743$	−29.9489			−1.09872			−0.549359	+	0.835587i	$0.685128\pi$
$744$	−4.08883	−	4.54111i	−0.149904	−	0.166485i
$745$	2.53063	−	10.8260i	0.0927150	−	0.396633i
$746$	32.1863	−	35.7465i	1.17842	−	1.30877i
$747$	−16.9438	−	3.60152i	−0.619942	−	0.131773i
$748$	6.68532	+	4.85717i	0.244440	+	0.177596i
$749$	0.124283	+	16.8517i	0.00454121	+	0.615749i
$750$	−11.3507	−	17.7969i	−0.414467	−	0.649852i
$751$	−9.53058	+	16.5075i	−0.347776	+	0.602365i	−0.985854	−	0.167606i	$-0.946396\pi$
$751$	−9.53058	+	16.5075i	−0.347776	+	0.602365i	0.638078	+	0.769972i	$0.279730\pi$
$752$	0.234649	−	2.23253i	0.00855676	−	0.0814121i
$753$	19.2448	−	21.3735i	0.701318	−	0.778893i
$754$	−57.2510	−	12.1691i	−2.08496	−	0.443172i
$755$	10.7363	+	10.0669i	0.390733	+	0.366370i
$756$	3.05566	−	2.79241i	0.111133	−	0.101559i
$757$	−0.618596			−0.0224833			−0.0112416	−	0.999937i	$-0.503578\pi$
$757$	−0.618596			−0.0224833			−0.0112416	+	0.999937i	$0.503578\pi$
$758$	30.1821	+	33.5206i	1.09626	+	1.21752i
$759$	−1.49205	−	0.664302i	−0.0541578	−	0.0241126i
$760$	−7.70650	+	6.66219i	−0.279544	+	0.241663i
$761$	−35.5721	+	15.8377i	−1.28949	+	0.574117i	−0.932897	−	0.360144i	$-0.882728\pi$
$761$	−35.5721	+	15.8377i	−1.28949	+	0.574117i	−0.356591	+	0.934261i	$0.616061\pi$
$762$	−4.86804	+	3.53684i	−0.176351	+	0.128126i
$763$	−22.2483	+	2.50442i	−0.805443	+	0.0906660i
$764$	−19.4500	−	14.1312i	−0.703675	−	0.511249i
$765$	−4.21699	−	6.05773i	−0.152466	−	0.219018i
$766$	16.4439	+	7.32130i	0.594142	+	0.264529i
$767$	55.4186	−	11.7796i	2.00105	−	0.425336i
$768$	−10.2813	+	17.8078i	−0.370995	+	0.642582i
$769$	−3.94623	+	12.1452i	−0.142305	+	0.437968i	−0.996655	−	0.0817297i	$-0.973956\pi$
$769$	−3.94623	+	12.1452i	−0.142305	+	0.437968i	0.854350	+	0.519698i	$0.173956\pi$
$770$	16.2327	+	7.47802i	0.584986	+	0.269489i
$771$	−5.04319	−	15.5213i	−0.181626	−	0.558987i
$772$	−2.44246	−	0.519160i	−0.0879059	−	0.0186850i
$773$	4.47349	−	42.5625i	0.160900	−	1.53086i	−0.554520	−	0.832171i	$-0.687098\pi$
$773$	4.47349	−	42.5625i	0.160900	−	1.53086i	0.715420	−	0.698694i	$-0.246235\pi$
$774$	4.74911	+	8.22570i	0.170703	+	0.295667i
$775$	25.9619	−	26.5912i	0.932578	−	0.955185i
$776$	−15.4060			−0.553044
$777$	−6.86068	−	0.669969i	−0.246126	−	0.0240350i
$778$	−19.4291	−	59.7965i	−0.696565	−	2.14381i
$779$	26.8626	+	5.70982i	0.962452	+	0.204576i
$780$	14.4021	+	8.70742i	0.515677	+	0.311776i
$781$	12.6901	−	2.69737i	0.454089	−	0.0965196i
$782$	3.18059	−	5.50895i	0.113738	−	0.197000i
$783$	1.99139	−	6.12886i	0.0711664	−	0.219028i
$784$	30.1293	+	12.8854i	1.07605	+	0.460192i
$785$	13.0024	+	12.1916i	0.464074	+	0.435139i
$786$	30.7931	−	13.7100i	1.09835	−	0.489018i
$787$	−38.3835	−	17.0894i	−1.36822	−	0.609172i	−0.414553	−	0.910025i	$-0.636062\pi$
$787$	−38.3835	−	17.0894i	−1.36822	−	0.609172i	−0.953671	+	0.300853i	$0.902729\pi$
$788$	25.9193	+	11.5400i	0.923338	+	0.411097i
$789$	13.3439	−	5.94107i	0.475054	−	0.211508i
$790$	−21.2616	+	11.7095i	−0.756454	+	0.416605i
$791$	11.2091	−	25.6841i	0.398548	−	0.913220i
$792$	−0.406511	+	1.25111i	−0.0144447	+	0.0444563i
$793$	0.893324	−	1.54728i	0.0317229	−	0.0549456i
$794$	−67.7580	+	14.4024i	−2.40464	+	0.511122i
$795$	0.590274	+	1.40126i	0.0209349	+	0.0496975i
$796$	−29.1082	−	6.18713i	−1.03171	−	0.219297i
$797$	−11.6399	−	35.8240i	−0.412308	−	1.26895i	−0.914637	−	0.404276i	$-0.867523\pi$
$797$	−11.6399	−	35.8240i	−0.412308	−	1.26895i	0.502329	−	0.864677i	$-0.332477\pi$
$798$	16.1044	−	22.5131i	0.570090	−	0.796955i
$799$	1.58288			0.0559983
$800$	−32.2428	−	15.9451i	−1.13995	−	0.563744i
$801$	−4.87442	−	8.44274i	−0.172229	−	0.298309i
$802$	1.05432	−	10.0312i	0.0372293	−	0.354213i
$803$	21.2326	+	4.51312i	0.749281	+	0.159265i
$804$	−0.969514	−	2.98386i	−0.0341921	−	0.105232i
$805$	1.93950	−	5.71871i	0.0683585	−	0.201558i
$806$	−20.8609	+	64.2031i	−0.734793	+	2.26146i
$807$	−6.97896	+	12.0879i	−0.245671	+	0.425515i
$808$	4.81067	−	1.02254i	0.169239	−	0.0359728i
$809$	−15.4332	−	6.87130i	−0.542602	−	0.241582i	0.117086	−	0.993122i	$-0.462645\pi$
$809$	−15.4332	−	6.87130i	−0.542602	−	0.241582i	−0.659688	+	0.751540i	$0.729311\pi$
$810$	−2.54991	+	3.36463i	−0.0895946	+	0.118221i
$811$	−15.7910	−	11.4729i	−0.554499	−	0.402867i	0.274943	−	0.961461i	$-0.411341\pi$
$811$	−15.7910	−	11.4729i	−0.554499	−	0.402867i	−0.829441	+	0.558594i	$0.811341\pi$
$812$	−26.5080	+	2.98391i	−0.930248	+	0.104715i
$813$	24.7616	−	17.9904i	0.868428	−	0.630950i
$814$	−7.19048	+	3.20141i	−0.252026	+	0.112209i
$815$	−4.99444	−	11.8563i	−0.174948	−	0.415310i
$816$	−14.1164	−	6.28505i	−0.494174	−	0.220021i
$817$	18.6538	+	20.7172i	0.652616	+	0.724803i
$818$	−41.7196			−1.45869
$819$	12.1335	+	3.84372i	0.423979	+	0.134310i
$820$	3.26162	+	17.0285i	0.113901	+	0.594660i
$821$	27.9018	+	5.93072i	0.973781	+	0.206984i	0.667214	−	0.744866i	$-0.267486\pi$
$821$	27.9018	+	5.93072i	0.973781	+	0.206984i	0.306567	+	0.951849i	$0.400820\pi$
$822$	−26.3576	+	29.2731i	−0.919327	+	1.02102i
$823$	−2.52516	+	24.0253i	−0.0880217	+	0.837470i	0.858062	+	0.513547i	$0.171669\pi$
$823$	−2.52516	+	24.0253i	−0.0880217	+	0.837470i	−0.946083	+	0.323923i	$0.894998\pi$
$824$	−5.01105	+	8.67940i	−0.174568	+	0.302361i
$825$	−7.75211	−	1.97799i	−0.269894	−	0.0688647i
$826$	50.7300	−	29.7899i	1.76512	−	1.03652i
$827$	−22.5325	−	16.3708i	−0.783531	−	0.569268i	0.122506	−	0.992468i	$-0.460907\pi$
$827$	−22.5325	−	16.3708i	−0.783531	−	0.569268i	−0.906037	+	0.423199i	$0.860907\pi$
$828$	−1.56206	−	0.332027i	−0.0542855	−	0.0115387i
$829$	−18.3503	+	20.3801i	−0.637333	+	0.707830i	−0.972125	−	0.234462i	$-0.924667\pi$
$829$	−18.3503	+	20.3801i	−0.637333	+	0.707830i	0.334792	+	0.942292i	$0.391334\pi$
$830$	−28.3896	−	67.3943i	−0.985417	−	2.33929i
$831$	14.7416	+	16.3722i	0.511381	+	0.567946i
$832$	20.2995			0.703758
$833$	−6.81530	+	22.0782i	−0.236136	+	0.764964i
$834$	21.9356	−	15.9371i	0.759567	−	0.551858i
$835$	0.149778	−	7.41656i	0.00518329	−	0.256661i
$836$	1.45006	−	13.7964i	0.0501515	−	0.477159i
$837$	−6.79008	−	3.02314i	−0.234699	−	0.104495i
$838$	0.541238	+	5.14953i	0.0186968	+	0.177888i
$839$	−12.1186	−	8.80464i	−0.418379	−	0.303970i	0.358606	−	0.933489i	$-0.383252\pi$
$839$	−12.1186	−	8.80464i	−0.418379	−	0.303970i	−0.776985	+	0.629519i	$0.783252\pi$
$840$	−4.74418	−	1.07214i	−0.163690	−	0.0369923i
$841$	−10.1358	+	7.36411i	−0.349511	+	0.253935i
$842$	−11.4234	−	12.6869i	−0.393675	−	0.437220i
$843$	8.36397	+	14.4868i	0.288071	+	0.498953i
$844$	7.38761	−	1.57028i	0.254292	−	0.0540514i
$845$	−0.457909	+	22.6742i	−0.0157525	+	0.780017i
$846$	−0.279771	−	0.861047i	−0.00961873	−	0.0296034i
$847$	−21.1850	+	7.05657i	−0.727925	+	0.242467i
$848$	2.57529	+	1.87106i	0.0884360	+	0.0642525i
$849$	3.91580	−	6.78236i	0.134390	−	0.232770i
$850$	10.8177	−	29.2223i	0.371044	−	1.00232i
$851$	1.32970	+	2.30312i	0.0455817	+	0.0789498i
$852$	11.5887	−	5.15962i	0.397022	−	0.176766i
$853$	15.2577	+	46.9583i	0.522413	+	1.60782i	0.769376	+	0.638797i	$0.220567\pi$
$853$	15.2577	+	46.9583i	0.522413	+	1.60782i	−0.246963	+	0.969025i	$0.579433\pi$
$854$	0.372321	−	1.81744i	0.0127406	−	0.0621915i
$855$	−5.26736	+	11.2156i	−0.180140	+	0.383565i
$856$	−3.50398	−	3.89157i	−0.119764	−	0.133011i
$857$	−16.6156	−	28.7791i	−0.567579	−	0.983076i	−0.996805	−	0.0798787i	$-0.974547\pi$
$857$	−16.6156	−	28.7791i	−0.567579	−	0.983076i	0.429225	−	0.903197i	$-0.358787\pi$
$858$	14.2153	−	3.02155i	0.485302	−	0.103154i
$859$	2.16769	+	20.6242i	0.0739607	+	0.703689i	0.967184	+	0.254076i	$0.0817715\pi$
$859$	2.16769	+	20.6242i	0.0739607	+	0.703689i	−0.893223	+	0.449613i	$0.851562\pi$
$860$	−7.48176	+	15.9306i	−0.255126	+	0.543229i
$861$	5.42140	+	11.9389i	0.184761	+	0.406877i
$862$	27.1467	−	19.7232i	0.924620	−	0.671776i
$863$	−1.08543	−	10.3271i	−0.0369483	−	0.351540i	−0.997340	−	0.0728870i	$-0.976779\pi$
$863$	−1.08543	−	10.3271i	−0.0369483	−	0.351540i	0.960392	−	0.278653i	$-0.0898879\pi$
$864$	−0.751978	+	7.15459i	−0.0255828	+	0.243404i
$865$	5.71348	−	4.93924i	0.194264	−	0.167939i
$866$	4.36156	+	41.4974i	0.148212	+	1.41014i
$867$	−1.88630	+	5.80542i	−0.0640619	+	0.197162i
$868$	0.226902	+	30.7660i	0.00770156	+	1.04426i
$869$	−2.84290	+	8.74953i	−0.0964386	+	0.296808i
$870$	26.0387	−	7.88290i	0.882794	−	0.267255i
$871$	6.45501	−	7.16902i	0.218720	−	0.242913i
$872$	4.65519	−	5.17011i	0.157644	−	0.175082i
$873$	−17.1190	+	7.62185i	−0.579389	+	0.257961i
$874$	−10.6789			−0.361219
$875$	4.65200	−	29.2123i	0.157266	−	0.987556i
$876$	21.2246			0.717114
$877$	19.9832	−	8.89709i	0.674785	−	0.300434i	−0.0405886	−	0.999176i	$-0.512923\pi$
$877$	19.9832	−	8.89709i	0.674785	−	0.300434i	0.715373	+	0.698742i	$0.246257\pi$
$878$	−52.2775	+	58.0600i	−1.76428	+	1.95943i
$879$	11.9485	−	13.2701i	0.403013	−	0.447591i
$880$	−16.0308	+	4.85313i	−0.540397	+	0.163599i
$881$	5.44064	−	16.7446i	0.183300	−	0.564139i	−0.816615	−	0.577183i	$-0.804152\pi$
$881$	5.44064	−	16.7446i	0.183300	−	0.564139i	0.999915	+	0.0130439i	$0.00415212\pi$
$882$	13.2146	−	0.194928i	0.444958	−	0.00656357i
$883$	10.8746	−	33.4685i	0.365958	−	1.12630i	−0.583420	−	0.812170i	$-0.698286\pi$
$883$	10.8746	−	33.4685i	0.365958	−	1.12630i	0.949379	−	0.314134i	$-0.101714\pi$
$884$	2.59691	+	24.7079i	0.0873434	+	0.831017i
$885$	−19.9225	+	17.2228i	−0.669688	+	0.578938i
$886$	−6.77439	+	64.4540i	−0.227590	+	2.16537i
$887$	2.12323	+	20.2012i	0.0712910	+	0.678289i	0.970555	+	0.240882i	$0.0774365\pi$
$887$	2.12323	+	20.2012i	0.0712910	+	0.678289i	−0.899263	+	0.437407i	$0.855897\pi$
$888$	1.73293	−	1.25905i	0.0581533	−	0.0422508i
$889$	−8.39233	−	0.819540i	−0.281470	−	0.0274865i
$890$	17.4956	−	37.2528i	0.586455	−	1.24872i
$891$	0.167256	+	1.59133i	0.00560327	+	0.0533116i
$892$	42.4727	−	9.02785i	1.42209	−	0.302275i
$893$	−1.32864	−	2.30126i	−0.0444611	−	0.0770089i
$894$	−6.28127	−	6.97606i	−0.210077	−	0.233314i
$895$	15.5283	−	33.0637i	0.519052	−	1.10520i
$896$	−16.1182	+	5.36887i	−0.538472	+	0.179361i
$897$	−1.51737	−	4.66998i	−0.0506635	−	0.155926i
$898$	37.9752	−	16.9076i	1.26725	−	0.564215i
$899$	23.9490	+	41.4810i	0.798745	+	1.38347i
$900$	−7.81636	−	0.315833i	−0.260545	−	0.0105278i
$901$	−1.12229	+	1.94386i	−0.0373888	+	0.0647593i
$902$	12.1124	+	8.80021i	0.403300	+	0.293015i
$903$	−2.67128	+	13.0395i	−0.0888947	+	0.433928i
$904$	2.69091	+	8.28176i	0.0894982	+	0.275447i
$905$	0.0239130	−	1.18410i	0.000794895	−	0.0393607i
$906$	12.1551	−	2.58365i	0.403827	−	0.0858361i
$907$	−9.49041	−	16.4379i	−0.315124	−	0.545810i	0.664340	−	0.747430i	$-0.268713\pi$
$907$	−9.49041	−	16.4379i	−0.315124	−	0.545810i	−0.979464	+	0.201620i	$0.935379\pi$
$908$	6.55596	+	7.28113i	0.217567	+	0.241633i
$909$	4.83967	−	3.51622i	0.160522	−	0.116626i
$910$	15.9480	+	51.3115i	0.528671	+	1.70096i
$911$	33.3917	+	24.2605i	1.10632	+	0.803786i	0.982079	−	0.188467i	$-0.0603519\pi$
$911$	33.3917	+	24.2605i	1.10632	+	0.803786i	0.124236	+	0.992253i	$0.460352\pi$
$912$	2.71155	+	25.7987i	0.0897884	+	0.854279i
$913$	−25.3211	−	11.2737i	−0.838007	−	0.373105i
$914$	5.37658	−	51.1548i	0.177842	−	1.69205i
$915$	−0.0167679	+	0.830294i	−0.000554330	+	0.0274487i
$916$	−5.14470	+	3.73784i	−0.169986	+	0.123502i
$917$	45.0302	+	14.2649i	1.48703	+	0.471069i
$918$	−6.23207			−0.205689
$919$	9.31935	+	10.3502i	0.307417	+	0.341421i	0.876980	−	0.480526i	$-0.159554\pi$
$919$	9.31935	+	10.3502i	0.307417	+	0.341421i	−0.569563	+	0.821947i	$0.692888\pi$
$920$	0.728450	+	1.72927i	0.0240163	+	0.0570125i
$921$	−19.2837	+	21.4167i	−0.635419	+	0.705704i
$922$	15.6269	+	3.32161i	0.514645	+	0.109391i
$923$	31.5556	+	22.9265i	1.03867	+	0.754635i
$924$	5.71149	−	3.35393i	0.187894	−	0.110336i
$925$	8.31889	+	10.0251i	0.273524	+	0.329623i
$926$	−3.72074	+	6.44450i	−0.122271	+	0.211780i
$927$	−1.27424	+	12.1235i	−0.0418514	+	0.398189i
$928$	31.0209	−	34.4522i	1.01831	−	1.13095i
$929$	54.6862	+	11.6239i	1.79420	+	0.381368i	0.979965	−	0.199171i	$-0.0638250\pi$
$929$	54.6862	+	11.6239i	1.79420	+	0.381368i	0.814232	+	0.580540i	$0.197158\pi$
$930$	−5.90290	−	30.8182i	−0.193564	−	1.01057i
$931$	37.8189	−	8.62356i	1.23946	−	0.282626i
$932$	−14.2688			−0.467389
$933$	−16.5396	−	18.3691i	−0.541482	−	0.601377i
$934$	28.2230	+	12.5657i	0.923484	+	0.411162i
$935$	−4.58486	−	10.8840i	−0.149941	−	0.355946i
$936$	−3.61308	+	1.60865i	−0.118097	+	0.0525802i
$937$	−8.35730	+	6.07193i	−0.273021	+	0.198361i	−0.715868	−	0.698236i	$-0.753969\pi$
$937$	−8.35730	+	6.07193i	−0.273021	+	0.198361i	0.442847	+	0.896597i	$0.353969\pi$
$938$	4.00665	−	9.18071i	0.130822	−	0.299761i
$939$	9.22680	+	6.70366i	0.301105	+	0.218766i
$940$	1.01328	−	1.33703i	0.0330495	−	0.0436091i
$941$	−23.8927	−	10.6377i	−0.778878	−	0.346779i	−0.0215114	−	0.999769i	$-0.506848\pi$
$941$	−23.8927	−	10.6377i	−0.778878	−	0.346779i	−0.757367	+	0.652990i	$0.773514\pi$
$942$	14.7207	−	3.12898i	0.479626	−	0.101948i
$943$	2.52931	−	4.38089i	0.0823656	−	0.142661i
$944$	−17.0371	+	52.4348i	−0.554510	+	1.70661i
$945$	−5.80209	+	1.15575i	−0.188742	+	0.0375966i
$946$	4.69646	+	14.4542i	0.152695	+	0.469947i
$947$	−39.6104	−	8.41946i	−1.28717	−	0.273596i	−0.487015	−	0.873394i	$-0.661914\pi$
$947$	−39.6104	−	8.41946i	−1.28717	−	0.273596i	−0.800151	+	0.599798i	$0.795247\pi$
$948$	−0.940277	+	8.94613i	−0.0305388	+	0.290557i
$949$	32.6306	+	56.5179i	1.05923	+	1.83465i
$950$	−51.5649	+	8.80129i	−1.67299	+	0.285552i
$951$	28.8766			0.936389
$952$	−2.96865	−	6.53751i	−0.0962146	−	0.211882i
$953$	4.29374	+	13.2148i	0.139088	+	0.428068i	0.996203	−	0.0870557i	$-0.0277458\pi$
$953$	4.29374	+	13.2148i	0.139088	+	0.428068i	−0.857116	+	0.515124i	$0.827746\pi$
$954$	1.25577	+	0.266922i	0.0406571	+	0.00864193i
$955$	13.3390	+	31.6655i	0.431639	+	1.02467i
$956$	11.7789	−	2.50369i	0.380958	−	0.0809752i
$957$	5.15572	−	8.92997i	0.166661	−	0.288665i
$958$	1.74058	−	5.35695i	0.0562356	−	0.173075i
$959$	−54.8539	+	6.17472i	−1.77133	+	0.199392i
$960$	−8.26501	+	4.55182i	−0.266752	+	0.146909i
$961$	22.1485	−	9.86113i	0.714467	−	0.318101i
$962$	−21.6180	−	9.62494i	−0.696991	−	0.310320i
$963$	−5.81886	−	2.59072i	−0.187510	−	0.0834849i
$964$	−7.43618	+	3.31080i	−0.239503	+	0.106634i
$965$	2.60336	+	2.44104i	0.0838050	+	0.0785797i
$966$	−3.02726	−	4.10270i	−0.0974006	−	0.132002i
$967$	−9.35905	+	28.8042i	−0.300967	+	0.926281i	0.680185	+	0.733041i	$0.261900\pi$
$967$	−9.35905	+	28.8042i	−0.300967	+	0.926281i	−0.981152	+	0.193240i	$0.938100\pi$
$968$	3.46929	−	6.00898i	0.111507	−	0.193136i
$969$	−17.8917	+	3.80300i	−0.574765	+	0.122170i
$970$	−67.6991	−	40.9305i	−2.17369	−	1.31420i
$971$	−13.5225	−	2.87430i	−0.433958	−	0.0922407i	−0.0142473	−	0.999899i	$-0.504535\pi$
$971$	−13.5225	−	2.87430i	−0.433958	−	0.0922407i	−0.419711	+	0.907658i	$0.637869\pi$
$972$	0.483472	+	1.48797i	0.0155074	+	0.0477267i
$973$	37.8161	+	3.69288i	1.21233	+	0.118388i
$974$	0.835881			0.0267834
$975$	−11.1758	−	21.2993i	−0.357912	−	0.682123i
$976$	0.869303	+	1.50568i	0.0278257	+	0.0481955i
$977$	−1.05583	+	10.0455i	−0.0337790	+	0.321385i	0.964564	+	0.263848i	$0.0849916\pi$
$977$	−1.05583	+	10.0455i	−0.0337790	+	0.321385i	−0.998343	+	0.0575377i	$0.981675\pi$
$978$	−10.6254	−	2.25849i	−0.339761	−	0.0722185i
$979$	−4.82038	−	14.8356i	−0.154060	−	0.474148i
$980$	14.2863	+	19.8901i	0.456358	+	0.635366i
$981$	2.61496	−	8.04802i	0.0834892	−	0.256953i
$982$	−8.26626	+	14.3176i	−0.263787	+	0.456893i
$983$	24.0379	−	5.10942i	0.766691	−	0.162965i	0.192066	−	0.981382i	$-0.438481\pi$
$983$	24.0379	−	5.10942i	0.766691	−	0.162965i	0.574625	+	0.818417i	$0.305148\pi$
$984$	−3.72220	−	1.65723i	−0.118659	−	0.0528306i
$985$	−23.1674	−	33.2802i	−0.738175	−	1.06039i
$986$	32.4910	+	23.6061i	1.03472	+	0.751771i
$987$	0.507475	−	1.16281i	0.0161531	−	0.0370127i
$988$	33.7417	−	24.5148i	1.07347	−	0.779919i
$989$	4.69111	−	2.08862i	0.149169	−	0.0664142i
$990$	−5.11028	+	4.41778i	−0.162415	+	0.140406i
$991$	−23.1633	−	10.3129i	−0.735805	−	0.327602i	0.00439300	−	0.999990i	$-0.498602\pi$
$991$	−23.1633	−	10.3129i	−0.735805	−	0.327602i	−0.740198	+	0.672389i	$0.765268\pi$
$992$	−35.7788	−	39.7364i	−1.13598	−	1.26163i
$993$	−32.1407			−1.01996
$994$	38.6101	+	12.2311i	1.22464	+	0.387948i
$995$	31.0257	+	29.0913i	0.983582	+	0.922255i
$996$	−26.5094	−	5.63475i	−0.839983	−	0.178544i
$997$	10.2020	−	11.3305i	0.323102	−	0.358841i	−0.559609	−	0.828756i	$-0.689049\pi$
$997$	10.2020	−	11.3305i	0.323102	−	0.358841i	0.882712	+	0.469915i	$0.155716\pi$
$998$	−7.79286	+	74.1441i	−0.246679	+	2.34699i
$999$	1.30271	−	2.25637i	0.0412161	−	0.0713883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bg.b.16.4	✓	160
7.4	even	3	inner	525.2.bg.b.466.17	yes	160
25.11	even	5	inner	525.2.bg.b.436.17	yes	160
175.11	even	15	inner	525.2.bg.b.361.4	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.b.16.4	✓	160	1.1	even	1	trivial
525.2.bg.b.361.4	yes	160	175.11	even	15	inner
525.2.bg.b.436.17	yes	160	25.11	even	5	inner
525.2.bg.b.466.17	yes	160	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72477 + 0.767919i) q^{2} +(0.669131 - 0.743145i) q^{3} +(1.04689 - 1.16268i) q^{4} +(-2.14015 + 0.647903i) q^{5} +(-0.583424 + 1.79560i) q^{6} +(-2.28147 + 1.33974i) q^{7} +(0.254054 - 0.781898i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(-1.72477 + 0.767919i) q^{2} +(0.669131 - 0.743145i) q^{3} +(1.04689 - 1.16268i) q^{4} +(-2.14015 + 0.647903i) q^{5} +(-0.583424 + 1.79560i) q^{6} +(-2.28147 + 1.33974i) q^{7} +(0.254054 - 0.781898i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(3.19373 - 2.76095i) q^{10} +(0.167256 - 1.59133i) q^{11} +(-0.163540 - 1.55598i) q^{12} +(3.89189 - 2.82763i) q^{13} +(2.90621 - 4.06273i) q^{14} +(-0.950551 + 2.02397i) q^{15} +(0.489328 + 4.65564i) q^{16} +(-3.22875 + 0.686292i) q^{17} +(0.944000 + 1.63506i) q^{18} +(3.70790 + 4.11804i) q^{19} +(-1.48718 + 3.16660i) q^{20} +(-0.530982 + 2.59192i) q^{21} +(0.933535 + 2.87313i) q^{22} +(0.932473 - 0.415164i) q^{23} +(-0.411068 - 0.711991i) q^{24} +(4.16044 - 2.77321i) q^{25} +(-4.54125 + 7.86567i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.830746 + 4.05518i) q^{28} +(1.99139 + 6.12886i) q^{29} +(0.0852403 - 4.22084i) q^{30} +(7.27024 - 1.54534i) q^{31} +(-3.59700 - 6.23019i) q^{32} +(-1.07067 - 1.18910i) q^{33} +(5.04185 - 3.66312i) q^{34} +(4.01466 - 4.34540i) q^{35} +(-1.26574 - 0.919617i) q^{36} +(0.272342 + 2.59116i) q^{37} +(-9.55762 - 4.25533i) q^{38} +(0.502849 - 4.78429i) q^{39} +(-0.0371182 + 1.83798i) q^{40} +(4.00944 - 2.91303i) q^{41} +(-1.07456 - 4.87823i) q^{42} +5.03083 q^{43} +(-1.67512 - 1.86041i) q^{44} +(0.868060 + 2.06070i) q^{45} +(-1.28949 + 1.43213i) q^{46} +(-0.469054 - 0.0997005i) q^{47} +(3.78724 + 2.75159i) q^{48} +(3.41021 - 6.11314i) q^{49} +(-5.04622 + 7.97805i) q^{50} +(-1.65044 + 2.85865i) q^{51} +(0.786731 - 7.48525i) q^{52} +(0.455004 - 0.505333i) q^{53} +(1.84674 + 0.392537i) q^{54} +(0.673077 + 3.51404i) q^{55} +(0.467922 + 2.12424i) q^{56} +5.54138 q^{57} +(-8.14116 - 9.04168i) q^{58} +(10.7592 + 4.79028i) q^{59} +(1.35812 + 3.22406i) q^{60} +(0.339286 - 0.151060i) q^{61} +(-11.3528 + 8.24832i) q^{62} +(1.57088 + 2.12893i) q^{63} +(3.41381 + 2.48028i) q^{64} +(-6.49719 + 8.57310i) q^{65} +(2.75980 + 1.22874i) q^{66} +(1.96150 - 0.416929i) q^{67} +(-2.58219 + 4.47249i) q^{68} +(0.315419 - 0.970761i) q^{69} +(-3.58746 + 10.5778i) q^{70} +(2.50552 + 7.71121i) q^{71} +(-0.804170 - 0.170932i) q^{72} +(-1.41803 + 13.4917i) q^{73} +(-2.45953 - 4.26002i) q^{74} +(0.722979 - 4.94745i) q^{75} +8.66974 q^{76} +(1.75038 + 3.85465i) q^{77} +(2.80665 + 8.63797i) q^{78} +(-5.62389 - 1.19540i) q^{79} +(-4.06364 - 9.64671i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-4.67841 + 8.10324i) q^{82} +(5.35290 - 16.4745i) q^{83} +(2.45771 + 3.33081i) q^{84} +(6.46534 - 3.56068i) q^{85} +(-8.67705 + 3.86327i) q^{86} +(5.88713 + 2.62112i) q^{87} +(-1.20177 - 0.535061i) q^{88} +(8.90600 - 3.96521i) q^{89} +(-3.07966 - 2.88764i) q^{90} +(-5.09096 + 11.6653i) q^{91} +(0.493488 - 1.51880i) q^{92} +(3.71633 - 6.43688i) q^{93} +(0.885574 - 0.188235i) q^{94} +(-10.6035 - 6.41085i) q^{95} +(-7.03679 - 1.49572i) q^{96} +(-5.79068 - 17.8219i) q^{97} +(-1.18744 + 13.1626i) q^{98} -1.60010 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9}+O(q^{10}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9} - 6 q^{10} + 12 q^{11} + 20 q^{12} + 12 q^{14} + 4 q^{15} + 12 q^{16} - 6 q^{17} - 8 q^{18} + 12 q^{19} - 7 q^{21} + 14 q^{23} - 30 q^{24} - 4 q^{25} - 56 q^{26} - 40 q^{27} - 27 q^{28} - 2 q^{29} + 4 q^{30} + 27 q^{31} - 78 q^{32} - 8 q^{33} + 76 q^{34} + 21 q^{35} - 40 q^{36} + 14 q^{37} - 17 q^{38} + 10 q^{40} - 6 q^{41} - 2 q^{42} + 28 q^{43} - 22 q^{44} + 3 q^{45} - 22 q^{46} + 7 q^{47} - 24 q^{48} + 152 q^{49} - 62 q^{50} + 4 q^{51} + 13 q^{52} - 26 q^{53} + 2 q^{54} + 64 q^{55} - 33 q^{56} + 56 q^{57} + 48 q^{59} + 15 q^{60} + 36 q^{61} - 88 q^{62} - 7 q^{63} - 2 q^{64} + 46 q^{65} + 15 q^{66} + 42 q^{67} - 28 q^{68} - 8 q^{69} - 32 q^{70} + 36 q^{71} + 15 q^{72} + 10 q^{73} - 16 q^{74} + q^{75} - 76 q^{76} + 12 q^{77} - 8 q^{78} - 10 q^{79} + 100 q^{80} + 20 q^{81} + 14 q^{82} - 74 q^{83} - 6 q^{84} + 90 q^{85} + 6 q^{86} - 4 q^{87} + 102 q^{88} + 33 q^{89} - 18 q^{90} - 31 q^{91} - 94 q^{92} - 98 q^{93} - 30 q^{94} - 106 q^{95} + 47 q^{96} - 26 q^{97} + 26 q^{98} + 16 q^{99}+O(q^{100}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9 - 6 * q^10 + 12 * q^11 + 20 * q^12 + 12 * q^14 + 4 * q^15 + 12 * q^16 - 6 * q^17 - 8 * q^18 + 12 * q^19 - 7 * q^21 + 14 * q^23 - 30 * q^24 - 4 * q^25 - 56 * q^26 - 40 * q^27 - 27 * q^28 - 2 * q^29 + 4 * q^30 + 27 * q^31 - 78 * q^32 - 8 * q^33 + 76 * q^34 + 21 * q^35 - 40 * q^36 + 14 * q^37 - 17 * q^38 + 10 * q^40 - 6 * q^41 - 2 * q^42 + 28 * q^43 - 22 * q^44 + 3 * q^45 - 22 * q^46 + 7 * q^47 - 24 * q^48 + 152 * q^49 - 62 * q^50 + 4 * q^51 + 13 * q^52 - 26 * q^53 + 2 * q^54 + 64 * q^55 - 33 * q^56 + 56 * q^57 + 48 * q^59 + 15 * q^60 + 36 * q^61 - 88 * q^62 - 7 * q^63 - 2 * q^64 + 46 * q^65 + 15 * q^66 + 42 * q^67 - 28 * q^68 - 8 * q^69 - 32 * q^70 + 36 * q^71 + 15 * q^72 + 10 * q^73 - 16 * q^74 + q^75 - 76 * q^76 + 12 * q^77 - 8 * q^78 - 10 * q^79 + 100 * q^80 + 20 * q^81 + 14 * q^82 - 74 * q^83 - 6 * q^84 + 90 * q^85 + 6 * q^86 - 4 * q^87 + 102 * q^88 + 33 * q^89 - 18 * q^90 - 31 * q^91 - 94 * q^92 - 98 * q^93 - 30 * q^94 - 106 * q^95 + 47 * q^96 - 26 * q^97 + 26 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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