LMFDB - Embedded newform 52.2.l.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,2,Mod(7,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 11]))

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

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

chi := DirichletCharacter("52.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	52.l (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.415222090511$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.102930383934669717504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 5 x^{14} - 2 x^{13} + 5 x^{12} - 8 x^{11} - 12 x^{10} + 32 x^{9} - 36 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 5x^14 - 2x^13 + 5x^12 - 8x^11 - 12x^10 + 32x^9 - 36x^8 + 64x^7 - 48x^6 - 64x^5 + 80x^4 - 64x^3 + 320x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.1
Root			$1.31256 + 0.526485i$ of defining polynomial
Character	$\chi$	$=$	52.7
Dual form			52.2.l.b.15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11223 - 0.873468i) q^{2} +(-2.16981 - 1.25274i) q^{3} +(0.474107 + 1.94299i) q^{4} +(-2.19962 - 2.19962i) q^{5} +(1.31910 + 3.28859i) q^{6} +(0.152604 - 0.569525i) q^{7} +(1.16983 - 2.57517i) q^{8} +(1.63871 + 2.83834i) q^{9} +O(q^{10})$	\(q+(-1.11223 - 0.873468i) q^{2} +(-2.16981 - 1.25274i) q^{3} +(0.474107 + 1.94299i) q^{4} +(-2.19962 - 2.19962i) q^{5} +(1.31910 + 3.28859i) q^{6} +(0.152604 - 0.569525i) q^{7} +(1.16983 - 2.57517i) q^{8} +(1.63871 + 2.83834i) q^{9} +(0.525184 + 4.36778i) q^{10} +(2.85302 - 0.764465i) q^{11} +(1.40534 - 4.80986i) q^{12} +(2.37076 - 2.71652i) q^{13} +(-0.667192 + 0.500148i) q^{14} +(2.01721 + 7.52831i) q^{15} +(-3.55045 + 1.84237i) q^{16} +(-2.30986 + 1.33360i) q^{17} +(0.656570 - 4.58824i) q^{18} +(-3.11932 - 0.835818i) q^{19} +(3.23099 - 5.31671i) q^{20} +(-1.04459 + 1.04459i) q^{21} +(-3.84095 - 1.64176i) q^{22} +(1.03076 - 1.78533i) q^{23} +(-5.76432 + 4.12214i) q^{24} +4.67667i q^{25} +(-5.00963 + 0.950604i) q^{26} -0.695088i q^{27} +(1.17893 + 0.0264924i) q^{28} +(-0.621816 + 1.07702i) q^{29} +(4.33215 - 10.1352i) q^{30} +(6.34495 - 6.34495i) q^{31} +(5.55816 + 1.05206i) q^{32} +(-7.14819 - 1.91535i) q^{33} +(3.73394 + 0.534321i) q^{34} +(-1.58841 + 0.917069i) q^{35} +(-4.73794 + 4.52968i) q^{36} +(-0.133975 - 0.500000i) q^{37} +(2.73933 + 3.65425i) q^{38} +(-8.54720 + 2.92438i) q^{39} +(-8.23758 + 3.09122i) q^{40} +(5.59808 - 1.50000i) q^{41} +(2.07423 - 0.249407i) q^{42} +(3.60759 + 6.24853i) q^{43} +(2.83799 + 5.18097i) q^{44} +(2.63871 - 9.84781i) q^{45} +(-2.70587 + 1.08536i) q^{46} +(-3.16813 - 3.16813i) q^{47} +(10.0118 + 0.450187i) q^{48} +(5.76111 + 3.32618i) q^{49} +(4.08492 - 5.20153i) q^{50} +6.68260 q^{51} +(6.40217 + 3.31846i) q^{52} +3.67667 q^{53} +(-0.607137 + 0.773097i) q^{54} +(-7.95711 - 4.59404i) q^{55} +(-1.28810 - 1.05923i) q^{56} +(5.72126 + 5.72126i) q^{57} +(1.63234 - 0.654753i) q^{58} +(-1.82424 + 6.80816i) q^{59} +(-13.6711 + 7.48864i) q^{60} +(-3.97705 - 6.88845i) q^{61} +(-12.5991 + 1.51493i) q^{62} +(1.86658 - 0.500148i) q^{63} +(-5.26301 - 6.02501i) q^{64} +(-11.1901 + 0.760530i) q^{65} +(6.27743 + 8.37403i) q^{66} +(-1.92408 - 7.18077i) q^{67} +(-3.68629 - 3.85577i) q^{68} +(-4.47310 + 2.58254i) q^{69} +(2.56771 + 0.367435i) q^{70} +(-1.98027 - 0.530611i) q^{71} +(9.22621 - 0.899605i) q^{72} +(0.0440105 - 0.0440105i) q^{73} +(-0.287724 + 0.673137i) q^{74} +(5.85865 - 10.1475i) q^{75} +(0.145100 - 6.45708i) q^{76} -1.74153i q^{77} +(12.0608 + 4.21313i) q^{78} -2.73286i q^{79} +(11.8622 + 3.75711i) q^{80} +(4.04538 - 7.00680i) q^{81} +(-7.53655 - 3.22140i) q^{82} +(-10.1844 + 10.1844i) q^{83} +(-2.52487 - 1.53438i) q^{84} +(8.01422 + 2.14740i) q^{85} +(1.44543 - 10.1009i) q^{86} +(2.69844 - 1.55795i) q^{87} +(1.36892 - 8.24131i) q^{88} +(2.14761 + 8.01501i) q^{89} +(-11.5366 + 8.64819i) q^{90} +(-1.18534 - 1.76476i) q^{91} +(3.95757 + 1.15632i) q^{92} +(-21.7159 + 5.81876i) q^{93} +(0.756425 + 6.29094i) q^{94} +(5.02283 + 8.69980i) q^{95} +(-10.7422 - 9.24570i) q^{96} +(-1.22731 + 4.58039i) q^{97} +(-3.50236 - 8.73161i) q^{98} +(6.84510 + 6.84510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9	$ 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9} - 12 q^{13} + 8 q^{14} - 2 q^{16} + 12 q^{17} - 6 q^{18} + 2 q^{20} - 28 q^{21} + 10 q^{24} + 16 q^{26} + 12 q^{28} - 8 q^{29} + 42 q^{30} + 28 q^{32} - 20 q^{33} + 14 q^{34} - 6 q^{36} - 16 q^{37} - 40 q^{40} + 48 q^{41} - 28 q^{42} - 8 q^{44} + 20 q^{45} - 46 q^{46} - 10 q^{48} + 60 q^{49} + 10 q^{50} - 32 q^{52} - 32 q^{53} - 16 q^{54} - 60 q^{56} + 12 q^{57} - 48 q^{58} - 24 q^{60} + 4 q^{61} - 18 q^{62} - 8 q^{65} + 56 q^{66} + 16 q^{68} - 12 q^{69} + 28 q^{70} + 56 q^{72} + 20 q^{73} + 4 q^{74} + 22 q^{76} + 68 q^{78} + 44 q^{80} + 48 q^{81} + 84 q^{84} + 20 q^{85} + 16 q^{86} + 36 q^{88} - 52 q^{89} - 12 q^{92} - 92 q^{93} - 38 q^{94} - 72 q^{96} - 28 q^{97} - 2 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9 - 12 * q^13 + 8 * q^14 - 2 * q^16 + 12 * q^17 - 6 * q^18 + 2 * q^20 - 28 * q^21 + 10 * q^24 + 16 * q^26 + 12 * q^28 - 8 * q^29 + 42 * q^30 + 28 * q^32 - 20 * q^33 + 14 * q^34 - 6 * q^36 - 16 * q^37 - 40 * q^40 + 48 * q^41 - 28 * q^42 - 8 * q^44 + 20 * q^45 - 46 * q^46 - 10 * q^48 + 60 * q^49 + 10 * q^50 - 32 * q^52 - 32 * q^53 - 16 * q^54 - 60 * q^56 + 12 * q^57 - 48 * q^58 - 24 * q^60 + 4 * q^61 - 18 * q^62 - 8 * q^65 + 56 * q^66 + 16 * q^68 - 12 * q^69 + 28 * q^70 + 56 * q^72 + 20 * q^73 + 4 * q^74 + 22 * q^76 + 68 * q^78 + 44 * q^80 + 48 * q^81 + 84 * q^84 + 20 * q^85 + 16 * q^86 + 36 * q^88 - 52 * q^89 - 12 * q^92 - 92 * q^93 - 38 * q^94 - 72 * q^96 - 28 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−1.11223	−	0.873468i	−0.786465	−	0.617635i
$2$	−1.11223	−	0.873468i	−0.786465	−	0.617635i
$3$	−2.16981	−	1.25274i	−1.25274	−	0.723270i	−0.281087	−	0.959682i	$-0.590695\pi$
$3$	−2.16981	−	1.25274i	−1.25274	−	0.723270i	−0.971653	+	0.236413i	$0.924028\pi$
$4$	0.474107	+	1.94299i	0.237053	+	0.971497i
$5$	−2.19962	−	2.19962i	−0.983701	−	0.983701i	0.0161686	−	0.999869i	$-0.494853\pi$
$5$	−2.19962	−	2.19962i	−0.983701	−	0.983701i	−0.999869	+	0.0161686i	$0.994853\pi$
$6$	1.31910	+	3.28859i	0.538519	+	1.34256i
$7$	0.152604	−	0.569525i	0.0576788	−	0.215260i	−0.931071	−	0.364837i	$-0.881125\pi$
$7$	0.152604	−	0.569525i	0.0576788	−	0.215260i	0.988750	+	0.149577i	$0.0477912\pi$
$8$	1.16983	−	2.57517i	0.413596	−	0.910460i
$9$	1.63871	+	2.83834i	0.546238	+	0.946112i
$10$	0.525184	+	4.36778i	0.166078	+	1.38121i
$11$	2.85302	−	0.764465i	0.860219	−	0.230495i	0.198365	−	0.980128i	$-0.436437\pi$
$11$	2.85302	−	0.764465i	0.860219	−	0.230495i	0.661854	+	0.749633i	$0.269770\pi$
$12$	1.40534	−	4.80986i	0.405688	−	1.38849i
$13$	2.37076	−	2.71652i	0.657532	−	0.753427i
$13$	2.37076	−	2.71652i	0.657532	−	0.753427i
$14$	−0.667192	+	0.500148i	−0.178315	+	0.133670i
$15$	2.01721	+	7.52831i	0.520840	+	1.94380i
$16$	−3.55045	+	1.84237i	−0.887611	+	0.460593i
$17$	−2.30986	+	1.33360i	−0.560222	+	0.323445i	−0.753235	−	0.657752i	$-0.771508\pi$
$17$	−2.30986	+	1.33360i	−0.560222	+	0.323445i	0.193012	+	0.981196i	$0.438174\pi$
$18$	0.656570	−	4.58824i	0.154755	−	1.08146i
$19$	−3.11932	−	0.835818i	−0.715620	−	0.191750i	−0.117404	−	0.993084i	$-0.537457\pi$
$19$	−3.11932	−	0.835818i	−0.715620	−	0.191750i	−0.598217	+	0.801334i	$0.704124\pi$
$20$	3.23099	−	5.31671i	0.722472	−	1.18885i
$21$	−1.04459	+	1.04459i	−0.227948	+	0.227948i
$22$	−3.84095	−	1.64176i	−0.818894	−	0.350025i
$23$	1.03076	−	1.78533i	0.214928	−	0.372266i	−0.738322	−	0.674448i	$-0.764382\pi$
$23$	1.03076	−	1.78533i	0.214928	−	0.372266i	0.953250	+	0.302182i	$0.0977150\pi$
$24$	−5.76432	+	4.12214i	−1.17664	+	0.841428i
$25$			4.67667i			0.935334i
$26$	−5.00963	+	0.950604i	−0.982468	+	0.186429i
$27$		−	0.695088i		−	0.133770i
$28$	1.17893	+	0.0264924i	0.222798	+	0.00500659i
$29$	−0.621816	+	1.07702i	−0.115468	+	0.199997i	−0.917967	−	0.396657i	$-0.870170\pi$
$29$	−0.621816	+	1.07702i	−0.115468	+	0.199997i	0.802499	+	0.596654i	$0.203504\pi$
$30$	4.33215	−	10.1352i	0.790938	−	1.85042i
$31$	6.34495	−	6.34495i	1.13959	−	1.13959i	0.151062	−	0.988524i	$-0.451731\pi$
$31$	6.34495	−	6.34495i	1.13959	−	1.13959i	0.988524	−	0.151062i	$-0.0482694\pi$
$32$	5.55816	+	1.05206i	0.982554	+	0.185980i
$33$	−7.14819	−	1.91535i	−1.24434	−	0.333420i
$34$	3.73394	+	0.534321i	0.640366	+	0.0916354i
$35$	−1.58841	+	0.917069i	−0.268490	+	0.155013i
$36$	−4.73794	+	4.52968i	−0.789657	+	0.754947i
$37$	−0.133975	−	0.500000i	−0.0220253	−	0.0821995i	0.954038	−	0.299684i	$-0.0968814\pi$
$37$	−0.133975	−	0.500000i	−0.0220253	−	0.0821995i	−0.976064	+	0.217485i	$0.930215\pi$
$38$	2.73933	+	3.65425i	0.444379	+	0.592797i
$39$	−8.54720	+	2.92438i	−1.36865	+	0.468275i
$40$	−8.23758	+	3.09122i	−1.30248	+	0.488765i
$41$	5.59808	−	1.50000i	0.874273	−	0.234261i	0.206338	−	0.978481i	$-0.433845\pi$
$41$	5.59808	−	1.50000i	0.874273	−	0.234261i	0.667934	+	0.744220i	$0.267179\pi$
$42$	2.07423	−	0.249407i	0.320061	−	0.0384843i
$43$	3.60759	+	6.24853i	0.550152	+	0.952892i	0.998263	+	0.0589139i	$0.0187638\pi$
$43$	3.60759	+	6.24853i	0.550152	+	0.952892i	−0.448111	+	0.893978i	$0.647903\pi$
$44$	2.83799	+	5.18097i	0.427843	+	0.781060i
$45$	2.63871	−	9.84781i	0.393356	−	1.46803i
$46$	−2.70587	+	1.08536i	−0.398958	+	0.160027i
$47$	−3.16813	−	3.16813i	−0.462119	−	0.462119i	0.437230	−	0.899350i	$-0.355959\pi$
$47$	−3.16813	−	3.16813i	−0.462119	−	0.462119i	−0.899350	+	0.437230i	$0.855959\pi$
$48$	10.0118	+	0.450187i	1.44508	+	0.0649789i
$49$	5.76111	+	3.32618i	0.823015	+	0.475168i
$50$	4.08492	−	5.20153i	0.577695	−	0.735607i
$51$	6.68260			0.935751
$52$	6.40217	+	3.31846i	0.887822	+	0.460187i
$53$	3.67667			0.505030			0.252515	−	0.967593i	$-0.418742\pi$
$53$	3.67667			0.505030			0.252515	+	0.967593i	$0.418742\pi$
$54$	−0.607137	+	0.773097i	−0.0826209	+	0.105205i
$55$	−7.95711	−	4.59404i	−1.07294	−	0.619460i
$56$	−1.28810	−	1.05923i	−0.172130	−	0.141545i
$57$	5.72126	+	5.72126i	0.757799	+	0.757799i
$58$	1.63234	−	0.654753i	0.214337	−	0.0859733i
$59$	−1.82424	+	6.80816i	−0.237496	+	0.886347i	0.739512	+	0.673143i	$0.235056\pi$
$59$	−1.82424	+	6.80816i	−0.237496	+	0.886347i	−0.977008	+	0.213203i	$0.931610\pi$
$60$	−13.6711	+	7.48864i	−1.76493	+	0.966779i
$61$	−3.97705	−	6.88845i	−0.509209	−	0.881976i	−0.999943	−	0.0106664i	$-0.996605\pi$
$61$	−3.97705	−	6.88845i	−0.509209	−	0.881976i	0.490734	−	0.871309i	$-0.336729\pi$
$62$	−12.5991	+	1.51493i	−1.60009	+	0.192396i
$63$	1.86658	−	0.500148i	0.235167	−	0.0630127i
$64$	−5.26301	−	6.02501i	−0.657876	−	0.753126i
$65$	−11.1901	+	0.760530i	−1.38796	+	0.0943321i
$66$	6.27743	+	8.37403i	0.772698	+	1.03077i
$67$	−1.92408	−	7.18077i	−0.235064	−	0.877270i	−0.978120	−	0.208041i	$-0.933291\pi$
$67$	−1.92408	−	7.18077i	−0.235064	−	0.877270i	0.743056	−	0.669229i	$-0.233376\pi$
$68$	−3.68629	−	3.85577i	−0.447028	−	0.467581i
$69$	−4.47310	+	2.58254i	−0.538498	+	0.310902i
$70$	2.56771	+	0.367435i	0.306900	+	0.0439169i
$71$	−1.98027	−	0.530611i	−0.235014	−	0.0629719i	0.139390	−	0.990238i	$-0.455486\pi$
$71$	−1.98027	−	0.530611i	−0.235014	−	0.0629719i	−0.374404	+	0.927266i	$0.622153\pi$
$72$	9.22621	−	0.899605i	1.08732	−	0.106020i
$73$	0.0440105	−	0.0440105i	0.00515104	−	0.00515104i	−0.704527	−	0.709678i	$-0.748841\pi$
$73$	0.0440105	−	0.0440105i	0.00515104	−	0.00515104i	0.709678	+	0.704527i	$0.248841\pi$
$74$	−0.287724	+	0.673137i	−0.0334472	+	0.0782506i
$75$	5.85865	−	10.1475i	0.676499	−	1.17173i
$76$	0.145100	−	6.45708i	0.0166441	−	0.740678i
$77$		−	1.74153i		−	0.198466i
$78$	12.0608	+	4.21313i	1.36562	+	0.477043i
$79$		−	2.73286i		−	0.307471i	−0.988112	−	0.153735i	$-0.950870\pi$
$79$		−	2.73286i		−	0.307471i	0.988112	−	0.153735i	$-0.0491303\pi$
$80$	11.8622	+	3.75711i	1.32623	+	0.420058i
$81$	4.04538	−	7.00680i	0.449486	−	0.778533i
$82$	−7.53655	−	3.22140i	−0.832272	−	0.355744i
$83$	−10.1844	+	10.1844i	−1.11789	+	1.11789i	−0.125834	+	0.992051i	$0.540161\pi$
$83$	−10.1844	+	10.1844i	−1.11789	+	1.11789i	−0.992051	+	0.125834i	$0.959839\pi$
$84$	−2.52487	−	1.53438i	−0.275486	−	0.167415i
$85$	8.01422	+	2.14740i	0.869264	+	0.232919i
$86$	1.44543	−	10.1009i	0.155864	−	1.08921i
$87$	2.69844	−	1.55795i	0.289304	−	0.167029i
$88$	1.36892	−	8.24131i	0.145927	−	0.878527i
$89$	2.14761	+	8.01501i	0.227647	+	0.849589i	0.981327	+	0.192348i	$0.0616101\pi$
$89$	2.14761	+	8.01501i	0.227647	+	0.849589i	−0.753680	+	0.657241i	$0.771723\pi$
$90$	−11.5366	+	8.64819i	−1.21606	+	0.911599i
$91$	−1.18534	−	1.76476i	−0.124257	−	0.184997i
$92$	3.95757	+	1.15632i	0.412605	+	0.120555i
$93$	−21.7159	+	5.81876i	−2.25183	+	0.603377i
$94$	0.756425	+	6.29094i	0.0780193	+	0.648861i
$95$	5.02283	+	8.69980i	0.515332	+	0.892581i
$96$	−10.7422	−	9.24570i	−1.09637	−	0.943635i
$97$	−1.22731	+	4.58039i	−0.124615	+	0.465068i	−0.999826	−	0.0186732i	$-0.994056\pi$
$97$	−1.22731	+	4.58039i	−0.124615	+	0.465068i	0.875211	+	0.483741i	$0.160722\pi$
$98$	−3.50236	−	8.73161i	−0.353792	−	0.882026i
$99$	6.84510	+	6.84510i	0.687958	+	0.687958i
$100$	−9.08674	+	2.21724i	−0.908674	+	0.221724i
$101$	7.77554	+	4.48921i	0.773695	+	0.446693i	0.834191	−	0.551476i	$-0.185935\pi$
$101$	7.77554	+	4.48921i	0.773695	+	0.446693i	−0.0604964	+	0.998168i	$0.519268\pi$
$102$	−7.43258	−	5.83703i	−0.735935	−	0.577953i
$103$	9.60170			0.946084			0.473042	−	0.881040i	$-0.343156\pi$
$103$	9.60170			0.946084			0.473042	+	0.881040i	$0.343156\pi$
$104$	−4.22212	−	9.28298i	−0.414013	−	0.910271i
$105$	4.59540			0.448465
$106$	−4.08930	−	3.21145i	−0.397188	−	0.311924i
$107$	16.3364	+	9.43183i	1.57930	+	0.911809i	0.994957	+	0.100302i	$0.0319810\pi$
$107$	16.3364	+	9.43183i	1.57930	+	0.911809i	0.584343	+	0.811507i	$0.301352\pi$
$108$	1.35055	−	0.329546i	0.129957	−	0.0317106i
$109$	−2.95252	−	2.95252i	−0.282800	−	0.282800i	0.551425	−	0.834225i	$-0.314084\pi$
$109$	−2.95252	−	2.95252i	−0.282800	−	0.282800i	−0.834225	+	0.551425i	$0.814084\pi$
$110$	4.83738	+	12.0599i	0.461226	+	1.14987i
$111$	−0.335671	+	1.25274i	−0.0318604	+	0.118905i
$112$	0.507466	+	2.30322i	0.0479510	+	0.217634i
$113$	−2.82144	−	4.88687i	−0.265419	−	0.459718i	0.702255	−	0.711926i	$-0.252177\pi$
$113$	−2.82144	−	4.88687i	−0.265419	−	0.459718i	−0.967673	+	0.252207i	$0.918843\pi$
$114$	−1.36601	−	11.3607i	−0.127939	−	1.06403i
$115$	−6.19432	+	1.65976i	−0.577623	+	0.154774i
$116$	−2.38744	−	0.697563i	−0.221669	−	0.0647671i
$117$	11.5954	+	2.27743i	1.07199	+	0.210548i
$118$	7.97568	−	5.97882i	0.734221	−	0.550395i
$119$	0.407024	+	1.51903i	0.0373118	+	0.139250i
$120$	21.7465	+	3.61218i	1.98517	+	0.329745i
$121$	−1.97094	+	1.13792i	−0.179177	+	0.103448i
$122$	−1.59345	+	11.1354i	−0.144264	+	1.00815i
$123$	−14.0259	−	3.75822i	−1.26467	−	0.338867i
$124$	15.3364	+	9.32001i	1.37725	+	0.836962i
$125$	−0.711203	+	0.711203i	−0.0636119	+	0.0636119i
$126$	−2.51292	−	1.07412i	−0.223869	−	0.0956899i
$127$	−6.04172	+	10.4646i	−0.536116	+	0.928580i	0.462993	+	0.886362i	$0.346776\pi$
$127$	−6.04172	+	10.4646i	−0.536116	+	0.928580i	−0.999108	+	0.0422176i	$0.986558\pi$
$128$	0.591017	+	11.2983i	0.0522390	+	0.998635i
$129$		−	18.0775i		−	1.59163i
$130$	13.1103	+	8.92831i	1.14985	+	0.783065i
$131$		−	19.1689i		−	1.67479i	−0.546597	−	0.837396i	$-0.684077\pi$
$131$		−	19.1689i		−	1.67479i	0.546597	−	0.837396i	$-0.315923\pi$
$132$	0.332510	−	14.7970i	0.0289412	−	1.28791i
$133$	−0.952039	+	1.64898i	−0.0825523	+	0.142985i
$134$	−4.13215	+	9.66728i	−0.356964	+	0.835126i
$135$	−1.52893	+	1.52893i	−0.131589	+	0.131589i
$136$	0.732105	+	7.50835i	0.0627775	+	0.643836i
$137$	−7.01027	−	1.87840i	−0.598927	−	0.160482i	−0.0533974	−	0.998573i	$-0.517005\pi$
$137$	−7.01027	−	1.87840i	−0.598927	−	0.160482i	−0.545530	+	0.838091i	$0.683672\pi$
$138$	7.23088	+	1.03473i	0.615533	+	0.0880819i
$139$	9.61885	−	5.55344i	0.815860	−	0.471037i	−0.0331268	−	0.999451i	$-0.510547\pi$
$139$	9.61885	−	5.55344i	0.815860	−	0.471037i	0.848987	+	0.528414i	$0.177213\pi$
$140$	−2.53494	−	2.65148i	−0.214241	−	0.224091i
$141$	2.90539	+	10.8431i	0.244678	+	0.913152i
$142$	1.73904	+	2.31986i	0.145937	+	0.194678i
$143$	4.68716	−	9.56266i	0.391960	−	0.799670i
$144$	−11.0474	−	7.05823i	−0.920620	−	0.588186i
$145$	3.73679	−	1.00127i	0.310324	−	0.0831509i
$146$	−0.0873915	+	0.0105080i	−0.00723257	+	0.000869647i
$147$	−8.33367	−	14.4343i	−0.687349	−	1.19052i
$148$	0.907978	−	0.497365i	0.0746354	−	0.0408832i
$149$	1.34497	−	5.01948i	0.110184	−	0.411212i	−0.888698	−	0.458494i	$-0.848389\pi$
$149$	1.34497	−	5.01948i	0.110184	−	0.411212i	0.998882	+	0.0472817i	$0.0150558\pi$
$150$	−15.3797	+	6.16898i	−1.25574	+	0.503695i
$151$	3.67697	+	3.67697i	0.299227	+	0.299227i	0.840711	−	0.541484i	$-0.182137\pi$
$151$	3.67697	+	3.67697i	0.299227	+	0.299227i	−0.541484	+	0.840711i	$0.682137\pi$
$152$	−5.80144	+	7.05501i	−0.470559	+	0.572237i
$153$	−7.57039	−	4.37076i	−0.612029	−	0.353355i
$154$	−1.52117	+	1.93698i	−0.122579	+	0.156086i
$155$	−27.9130			−2.24202
$156$	−9.73433	−	15.2207i	−0.779370	−	1.21863i
$157$	−10.7605			−0.858780			−0.429390	−	0.903119i	$-0.641271\pi$
$157$	−10.7605			−0.858780			−0.429390	+	0.903119i	$0.641271\pi$
$158$	−2.38706	+	3.03956i	−0.189905	+	0.241815i
$159$	−7.97767	−	4.60591i	−0.632671	−	0.365272i
$160$	−9.91172	−	14.5400i	−0.783590	−	1.14949i
$161$	−0.859490	−	0.859490i	−0.0677373	−	0.0677373i
$162$	−10.6196	+	4.25966i	−0.834355	+	0.334670i
$163$	−3.67817	+	13.7271i	−0.288097	+	1.07519i	0.658450	+	0.752625i	$0.271213\pi$
$163$	−3.67817	+	13.7271i	−0.288097	+	1.07519i	−0.946547	+	0.322567i	$0.895454\pi$
$164$	5.56858	+	10.1659i	0.434833	+	0.793821i
$165$	11.5103	+	19.9364i	0.896073	+	1.55204i
$166$	20.2232	−	2.43164i	1.56962	−	0.188732i
$167$	9.00303	−	2.41236i	0.696676	−	0.186674i	0.106935	−	0.994266i	$-0.465896\pi$
$167$	9.00303	−	2.41236i	0.696676	−	0.186674i	0.589741	+	0.807592i	$0.299230\pi$
$168$	1.46800	+	3.91198i	0.113259	+	0.301816i
$169$	−1.75895	−	12.8805i	−0.135304	−	0.990804i
$170$	−7.03796	−	9.38857i	−0.539787	−	0.720070i
$171$	−2.73933	−	10.2233i	−0.209482	−	0.781798i
$172$	−10.4305	+	9.97200i	−0.795316	+	0.760358i
$173$	19.8249	−	11.4459i	1.50726	−	0.870215i	0.507292	−	0.861774i	$-0.330647\pi$
$173$	19.8249	−	11.4459i	1.50726	−	0.870215i	0.999964	−	0.00844060i	$-0.00268676\pi$
$174$	−4.36210	−	0.624210i	−0.330690	−	0.0473213i
$175$	2.66348	+	0.713678i	0.201340	+	0.0539490i
$176$	−8.72107	+	7.97053i	−0.657376	+	0.600801i
$177$	12.4871	−	12.4871i	0.938588	−	0.938588i
$178$	4.61221	−	10.7904i	0.345700	−	0.808774i
$179$	6.60927	−	11.4476i	0.494000	−	0.855633i	−0.505976	−	0.862547i	$-0.668868\pi$
$179$	6.60927	−	11.4476i	0.494000	−	0.855633i	0.999976	+	0.00691464i	$0.00220102\pi$
$180$	20.3853	+	0.458087i	1.51943	+	0.0341438i
$181$			26.1208i			1.94154i	0.240009	+	0.970771i	$0.422849\pi$
$181$			26.1208i			1.94154i	−0.240009	+	0.970771i	$0.577151\pi$
$182$	−0.223095	+	2.99817i	−0.0165369	+	0.222239i
$183$			19.9288i			1.47318i
$184$	−3.39171	−	4.74290i	−0.250040	−	0.349651i
$185$	−0.805117	+	1.39450i	−0.0591934	+	0.102526i
$186$	29.2355	+	12.4964i	2.14365	+	0.916277i
$187$	−5.57059	+	5.57059i	−0.407362	+	0.407362i
$188$	4.65362	−	7.65768i	0.339400	−	0.558494i
$189$	−0.395870	−	0.106073i	−0.0287953	−	0.00771568i
$190$	2.01246	−	14.0635i	0.145999	−	1.02027i
$191$	−12.2440	+	7.06905i	−0.885942	+	0.511499i	−0.872613	−	0.488412i	$-0.837576\pi$
$191$	−12.2440	+	7.06905i	−0.885942	+	0.511499i	−0.0133290	+	0.999911i	$0.504243\pi$
$192$	3.87195	+	19.6663i	0.279434	+	1.41929i
$193$	−6.00426	−	22.4082i	−0.432196	−	1.61298i	−0.747689	−	0.664049i	$-0.768837\pi$
$193$	−6.00426	−	22.4082i	−0.432196	−	1.61298i	0.315493	−	0.948928i	$-0.397830\pi$
$194$	5.36588	−	4.02243i	0.385247	−	0.288793i
$195$	25.2331	+	12.3681i	1.80698	+	0.885696i
$196$	−3.73136	+	12.7708i	−0.266526	+	0.912197i
$197$	5.99473	−	1.60628i	0.427107	−	0.114443i	−0.0388607	−	0.999245i	$-0.512373\pi$
$197$	5.99473	−	1.60628i	0.427107	−	0.114443i	0.465968	+	0.884802i	$0.345706\pi$
$198$	−1.63434	−	13.5923i	−0.116148	−	0.965962i
$199$	−1.50716	−	2.61048i	−0.106840	−	0.185052i	0.807649	−	0.589664i	$-0.200740\pi$
$199$	−1.50716	−	2.61048i	−0.106840	−	0.185052i	−0.914488	+	0.404612i	$0.867407\pi$
$200$	12.0432	+	5.47090i	0.851585	+	0.386851i
$201$	−4.82075	+	17.9913i	−0.340029	+	1.26901i
$202$	−4.72700	−	11.7847i	−0.332590	−	0.829169i
$203$	0.518497	+	0.518497i	0.0363913	+	0.0363913i
$204$	3.16826	+	12.9842i	0.221823	+	0.909079i
$205$	−15.6131	−	9.01422i	−1.09046	−	0.629580i
$206$	−10.6793	−	8.38678i	−0.744062	−	0.584335i
$207$	6.75647			0.469607
$208$	−3.41243	+	14.0127i	−0.236609	+	0.971605i
$209$	−9.53844			−0.659788
$210$	−5.11113	−	4.01393i	−0.352702	−	0.276988i
$211$	15.7735	+	9.10682i	1.08589	+	0.626940i	0.932480	−	0.361223i	$-0.117641\pi$
$211$	15.7735	+	9.10682i	1.08589	+	0.626940i	0.153412	+	0.988162i	$0.450974\pi$
$212$	1.74313	+	7.14375i	0.119719	+	0.490634i
$213$	3.63208	+	3.63208i	0.248866	+	0.248866i
$214$	−9.93142	−	24.7597i	−0.678898	−	1.69254i
$215$	5.80907	−	21.6797i	0.396175	−	1.47855i
$216$	−1.78997	−	0.813133i	−0.121792	−	0.0553267i
$217$	−2.64534	−	4.58187i	−0.179578	−	0.311038i
$218$	0.704946	+	5.86281i	0.0477450	+	0.397080i
$219$	−0.150628	+	0.0403607i	−0.0101785	+	0.00272732i
$220$	5.15367	−	17.6387i	0.347460	−	1.18920i
$221$	−1.85339	+	9.43641i	−0.124672	+	0.634762i
$222$	1.46757	−	1.10014i	0.0984969	−	0.0738363i
$223$	−0.919045	−	3.42992i	−0.0615438	−	0.229685i	0.928303	−	0.371826i	$-0.121268\pi$
$223$	−0.919045	−	3.42992i	−0.0615438	−	0.229685i	−0.989846	+	0.142141i	$0.954601\pi$
$224$	1.44737	−	3.00496i	0.0967066	−	0.200778i
$225$	−13.2740	+	7.66372i	−0.884931	+	0.510915i
$226$	−1.13044	+	7.89976i	−0.0751960	+	0.525484i
$227$	16.8419	+	4.51279i	1.11784	+	0.299524i	0.770009	−	0.638033i	$-0.220252\pi$
$227$	16.8419	+	4.51279i	1.11784	+	0.299524i	0.347831	+	0.937557i	$0.386918\pi$
$228$	−8.40388	+	13.8289i	−0.556560	+	0.915838i
$229$	−14.2869	+	14.2869i	−0.944105	+	0.944105i	−0.998519	−	0.0544132i	$-0.982671\pi$
$229$	−14.2869	+	14.2869i	−0.944105	+	0.944105i	0.0544132	+	0.998519i	$0.482671\pi$
$230$	8.33925	+	3.56451i	0.549874	+	0.235037i
$231$	−2.18168	+	3.77878i	−0.143544	+	0.248626i
$232$	2.04609	+	2.86121i	0.134332	+	0.187847i
$233$			13.3205i			0.872655i	0.899788	+	0.436328i	$0.143721\pi$
$233$			13.3205i			0.872655i	−0.899788	+	0.436328i	$0.856279\pi$
$234$	−10.9075	−	12.6612i	−0.713044	−	0.827690i
$235$			13.9374i			0.909174i
$236$	−14.0931	−	0.316692i	−0.917382	−	0.0206149i
$237$	−3.42356	+	5.92978i	−0.222384	+	0.385181i
$238$	0.874123	−	2.04503i	0.0566610	−	0.132560i
$239$	10.2493	−	10.2493i	0.662972	−	0.662972i	−0.293108	−	0.956079i	$-0.594689\pi$
$239$	10.2493	−	10.2493i	0.662972	−	0.662972i	0.956079	+	0.293108i	$0.0946894\pi$
$240$	−21.0319	−	23.0124i	−1.35761	−	1.48545i
$241$	13.3784	+	3.58474i	0.861781	+	0.230914i	0.662531	−	0.749035i	$-0.269482\pi$
$241$	13.3784	+	3.58474i	0.861781	+	0.230914i	0.199251	+	0.979949i	$0.436149\pi$
$242$	3.18608	+	0.455923i	0.204809	+	0.0293079i
$243$	−19.3613	+	11.1782i	−1.24203	+	0.717084i
$244$	11.4987	−	10.9932i	0.736127	−	0.703770i
$245$	−5.35593	−	19.9886i	−0.342178	−	1.27702i
$246$	12.3173	+	16.4311i	0.785322	+	1.04761i
$247$	−9.66568	+	6.49216i	−0.615013	+	0.413086i
$248$	−8.91683	−	23.7618i	−0.566219	−	1.50888i
$249$	34.8567	−	9.33982i	2.20895	−	0.591887i
$250$	1.41223	−	0.169807i	0.0893175	−	0.0107396i
$251$	−1.25814	−	2.17916i	−0.0794129	−	0.137547i	0.823584	−	0.567195i	$-0.191971\pi$
$251$	−1.25814	−	2.17916i	−0.0794129	−	0.137547i	−0.902997	+	0.429647i	$0.858638\pi$
$252$	1.85674	+	3.38962i	0.116964	+	0.213526i
$253$	1.57596	−	5.88156i	0.0990797	−	0.369770i
$254$	15.8602	−	6.36174i	0.995160	−	0.399171i
$255$	−14.6992	−	14.6992i	−0.920498	−	0.920498i
$256$	9.21132	−	13.0825i	0.575708	−	0.817656i
$257$	5.55423	+	3.20673i	0.346463	+	0.200031i	0.663126	−	0.748507i	$-0.269229\pi$
$257$	5.55423	+	3.20673i	0.346463	+	0.200031i	−0.316663	+	0.948538i	$0.602563\pi$
$258$	−15.7901	+	20.1063i	−0.983049	+	1.25176i
$259$	−0.305208			−0.0189647
$260$	−6.78301	−	21.3817i	−0.420664	−	1.32604i
$261$	−4.07591			−0.252293
$262$	−16.7434	+	21.3202i	−1.03441	+	1.31716i
$263$	−4.59709	−	2.65413i	−0.283469	−	0.163661i	0.351524	−	0.936179i	$-0.385664\pi$
$263$	−4.59709	−	2.65413i	−0.283469	−	0.163661i	−0.634993	+	0.772518i	$0.718997\pi$
$264$	−13.2945	+	16.1672i	−0.818220	+	0.995021i
$265$	−8.08728	−	8.08728i	−0.496798	−	0.496798i
$266$	2.49922	−	1.00247i	0.153237	−	0.0614652i
$267$	5.38080	−	20.0814i	0.329300	−	1.22896i
$268$	13.0400	−	7.14293i	0.796543	−	0.436324i
$269$	5.00048	+	8.66109i	0.304885	+	0.528076i	0.977236	−	0.212157i	$-0.0680487\pi$
$269$	5.00048	+	8.66109i	0.304885	+	0.528076i	−0.672351	+	0.740233i	$0.734715\pi$
$270$	3.03599	−	0.365049i	0.184765	−	0.0222162i
$271$	−24.6484	+	6.60453i	−1.49729	+	0.401196i	−0.912190	−	0.409768i	$-0.865610\pi$
$271$	−24.6484	+	6.60453i	−1.49729	+	0.401196i	−0.585096	+	0.810964i	$0.698943\pi$
$272$	5.74404	−	8.99048i	0.348283	−	0.545128i
$273$	0.361171	+	5.31411i	0.0218591	+	0.321625i
$274$	6.15630	+	8.21245i	0.371916	+	0.496132i
$275$	3.57515	+	13.3427i	0.215590	+	0.804592i
$276$	−7.13859	−	7.46680i	−0.429693	−	0.449448i
$277$	0.462736	−	0.267161i	0.0278031	−	0.0160521i	−0.486034	−	0.873940i	$-0.661557\pi$
$277$	0.462736	−	0.267161i	0.0278031	−	0.0160521i	0.513837	+	0.857888i	$0.328224\pi$
$278$	−15.5491	−	2.22505i	−0.932574	−	0.133450i
$279$	28.4066	+	7.61154i	1.70066	+	0.455691i
$280$	0.503444	+	5.16324i	0.0300865	+	0.308563i
$281$	−0.275535	+	0.275535i	−0.0164370	+	0.0164370i	−0.715278	−	0.698840i	$-0.753700\pi$
$281$	−0.275535	+	0.275535i	−0.0164370	+	0.0164370i	0.698840	+	0.715278i	$0.253700\pi$
$282$	6.23962	−	14.5978i	0.371564	−	0.869283i
$283$	−8.03188	+	13.9116i	−0.477446	+	0.826960i	−0.999666	−	0.0258504i	$-0.991771\pi$
$283$	−8.03188	+	13.9116i	−0.477446	+	0.826960i	0.522220	+	0.852811i	$0.325104\pi$
$284$	0.0921153	−	4.09921i	0.00546604	−	0.243243i
$285$		−	25.1692i		−	1.49090i
$286$	−13.5659	+	6.54178i	−0.802167	+	0.386824i
$287$		−	3.41715i		−	0.201708i
$288$	6.12214	+	17.5000i	0.360750	+	1.03119i
$289$	−4.94304	+	8.56160i	−0.290767	+	0.503624i
$290$	−5.03074	−	2.15033i	−0.295415	−	0.126271i
$291$	8.40107	−	8.40107i	0.492479	−	0.492479i
$292$	0.106378	+	0.0646464i	0.00622529	+	0.00378314i
$293$	1.97920	+	0.530326i	0.115626	+	0.0309820i	0.316168	−	0.948703i	$-0.397604\pi$
$293$	1.97920	+	0.530326i	0.115626	+	0.0309820i	−0.200542	+	0.979685i	$0.564270\pi$
$294$	−3.33898	+	23.3335i	−0.194734	+	1.36084i
$295$	18.9880	−	10.9627i	1.10552	−	0.638275i
$296$	−1.44431	−	0.239906i	−0.0839490	−	0.0139443i
$297$	−0.531371	−	1.98310i	−0.0308333	−	0.115071i
$298$	−5.88027	+	4.40803i	−0.340635	+	0.255350i
$299$	−2.40619	−	7.03266i	−0.139153	−	0.406709i
$300$	22.4941	+	6.57233i	1.29870	+	0.379454i
$301$	4.10923	−	1.10106i	0.236852	−	0.0634643i
$302$	−0.877916	−	7.30135i	−0.0505184	−	0.420145i
$303$	−11.2476	−	19.4814i	−0.646159	−	1.11918i
$304$	12.6149	−	2.77942i	0.723511	−	0.159410i
$305$	−6.40398	+	23.9000i	−0.366691	+	1.36851i
$306$	4.60228	+	11.4738i	0.263095	+	0.655912i
$307$	−11.4337	−	11.4337i	−0.652558	−	0.652558i	0.301050	−	0.953608i	$-0.402663\pi$
$307$	−11.4337	−	11.4337i	−0.652558	−	0.652558i	−0.953608	+	0.301050i	$0.902663\pi$
$308$	3.38378	−	0.825671i	0.192809	−	0.0470470i
$309$	−20.8339	−	12.0284i	−1.18520	−	0.684274i
$310$	31.0456	+	24.3811i	1.76327	+	1.38475i
$311$	−24.0242			−1.36229			−0.681143	−	0.732151i	$-0.738517\pi$
$311$	−24.0242			−1.36229			−0.681143	+	0.732151i	$0.738517\pi$
$312$	−2.46797	+	25.4315i	−0.139722	+	1.43978i
$313$	28.9008			1.63357			0.816786	−	0.576941i	$-0.195754\pi$
$313$	28.9008			1.63357			0.816786	+	0.576941i	$0.195754\pi$
$314$	11.9681	+	9.39894i	0.675400	+	0.530413i
$315$	−5.20590	−	3.00563i	−0.293319	−	0.169348i
$316$	5.30993	−	1.29567i	0.298707	−	0.0728870i
$317$	0.0141017	+	0.0141017i	0.000792031	+	0.000792031i	0.707503	−	0.706711i	$-0.249822\pi$
$317$	0.0141017	+	0.0141017i	0.000792031	+	0.000792031i	−0.706711	+	0.707503i	$0.749822\pi$
$318$	4.84988	+	12.0911i	0.271968	+	0.678034i
$319$	−0.950714	+	3.54811i	−0.0532297	+	0.198656i
$320$	−1.67611	+	24.8294i	−0.0936976	+	1.38800i
$321$	−23.6312	−	40.9305i	−1.31897	−	2.28452i
$322$	0.205213	+	1.70669i	0.0114361	+	0.0951100i
$323$	8.31982	−	2.22929i	0.462927	−	0.124041i
$324$	15.5321	+	4.53817i	0.862894	+	0.252120i
$325$	12.7043	+	11.0873i	0.704706	+	0.615012i
$326$	16.0812	−	12.0549i	0.890654	−	0.667662i
$327$	2.70767	+	10.1051i	0.149734	+	0.558816i
$328$	2.68603	−	16.1707i	0.148311	−	0.892880i
$329$	−2.28780	+	1.32086i	−0.126130	+	0.0728214i
$330$	4.61173	−	32.2277i	0.253867	−	1.77407i
$331$	4.08070	+	1.09342i	0.224295	+	0.0600998i	0.369216	−	0.929343i	$-0.379626\pi$
$331$	4.08070	+	1.09342i	0.224295	+	0.0600998i	−0.144921	+	0.989443i	$0.546293\pi$
$332$	−24.6168	−	14.9598i	−1.35102	−	0.821023i
$333$	1.19962	−	1.19962i	0.0657389	−	0.0657389i
$334$	−12.1205	−	5.18077i	−0.663207	−	0.283479i
$335$	−11.5627	+	20.0272i	−0.631739	+	1.09420i
$336$	1.78423	−	5.63327i	0.0973378	−	0.307320i
$337$		−	9.58550i		−	0.522155i	−0.965318	−	0.261078i	$-0.915922\pi$
$337$		−	9.58550i		−	0.522155i	0.965318	−	0.261078i	$-0.0840778\pi$
$338$	−9.29431	+	15.8624i	−0.505544	+	0.862801i
$339$			14.1381i			0.767877i
$340$	−0.372794	+	16.5897i	−0.0202176	+	0.899701i
$341$	13.2518	−	22.9528i	0.717625	−	1.24296i
$342$	−5.88299	+	13.7634i	−0.318116	+	0.744240i
$343$	5.69196	−	5.69196i	0.307337	−	0.307337i
$344$	20.3113	−	1.98046i	1.09511	−	0.106779i
$345$	15.5197	+	4.15850i	0.835555	+	0.223886i
$346$	−32.0474	−	4.58593i	−1.72288	−	0.246541i
$347$	3.56473	−	2.05810i	0.191364	−	0.110484i	−0.401257	−	0.915966i	$-0.631426\pi$
$347$	3.56473	−	2.05810i	0.191364	−	0.110484i	0.592621	+	0.805481i	$0.298093\pi$
$348$	4.30643	+	4.50442i	0.230849	+	0.241463i
$349$	7.51958	+	28.0634i	0.402514	+	1.50220i	0.808595	+	0.588365i	$0.200228\pi$
$349$	7.51958	+	28.0634i	0.402514	+	1.50220i	−0.406082	+	0.913837i	$0.633105\pi$
$350$	−2.33903	−	3.12024i	−0.125026	−	0.166784i
$351$	−1.88822	−	1.64789i	−0.100786	−	0.0879579i
$352$	16.6618	−	1.24747i	0.888079	−	0.0664904i
$353$	−25.4328	+	6.81469i	−1.35365	+	0.362709i	−0.861481	−	0.507790i	$-0.830463\pi$
$353$	−25.4328	+	6.81469i	−1.35365	+	0.362709i	−0.492169	+	0.870500i	$0.663796\pi$
$354$	−24.7956	+	2.98143i	−1.31787	+	0.158461i
$355$	3.18869	+	5.52298i	0.169238	+	0.293129i
$356$	−14.5549	+	7.97277i	−0.771408	+	0.422556i
$357$	1.01979	−	3.80591i	0.0539730	−	0.201430i
$358$	−17.3501	+	6.95935i	−0.916982	+	0.367813i
$359$	7.69873	+	7.69873i	0.406324	+	0.406324i	0.880454	−	0.474131i	$-0.157238\pi$
$359$	7.69873	+	7.69873i	0.406324	+	0.406324i	−0.474131	+	0.880454i	$0.657238\pi$
$360$	−22.2730	−	18.3154i	−1.17389	−	0.965305i
$361$	−7.42294	−	4.28564i	−0.390681	−	0.225560i
$362$	22.8157	−	29.0523i	1.19916	−	1.52695i
$363$	5.70210			0.299282
$364$	2.86694	−	3.13979i	0.150269	−	0.164570i
$365$	−0.193613			−0.0101342
$366$	17.4072	−	22.1654i	0.909889	−	1.15861i
$367$	−1.81711	−	1.04911i	−0.0948522	−	0.0547630i	0.451824	−	0.892107i	$-0.350774\pi$
$367$	−1.81711	−	1.04911i	−0.0948522	−	0.0547630i	−0.546676	+	0.837344i	$0.684107\pi$
$368$	−0.370415	+	8.23775i	−0.0193092	+	0.429422i
$369$	13.4311	+	13.4311i	0.699198	+	0.699198i
$370$	2.11353	−	0.847764i	0.109877	−	0.0440731i
$371$	0.561074	−	2.09396i	0.0291295	−	0.108713i
$372$	−21.6015	−	39.4351i	−1.11998	−	2.04462i
$373$	14.1524	+	24.5126i	0.732781	+	1.26921i	0.955690	+	0.294375i	$0.0951114\pi$
$373$	14.1524	+	24.5126i	0.732781	+	1.26921i	−0.222909	+	0.974839i	$0.571555\pi$
$374$	11.0615	−	1.33004i	0.571976	−	0.0687746i
$375$	2.43413	−	0.652222i	0.125698	−	0.0336806i
$376$	−11.8646	+	4.45231i	−0.611872	+	0.229610i
$377$	1.45156	+	4.24253i	0.0747590	+	0.218501i
$378$	0.347647	+	0.463757i	0.0178810	+	0.0238531i
$379$	−7.48268	−	27.9257i	−0.384360	−	1.43445i	−0.839174	−	0.543863i	$-0.816961\pi$
$379$	−7.48268	−	27.9257i	−0.384360	−	1.43445i	0.454814	−	0.890586i	$-0.349706\pi$
$380$	−14.5223	+	13.8840i	−0.744978	+	0.712232i
$381$	26.2187	−	15.1374i	1.34323	−	0.775512i
$382$	19.7927	+	2.83230i	1.01268	+	0.144913i
$383$	14.6205	+	3.91754i	0.747070	+	0.200177i	0.612218	−	0.790689i	$-0.290277\pi$
$383$	14.6205	+	3.91754i	0.747070	+	0.200177i	0.134852	+	0.990866i	$0.456944\pi$
$384$	12.8714	−	25.2555i	0.656840	−	1.28881i
$385$	−3.83070	+	3.83070i	−0.195231	+	0.195231i
$386$	−12.8947	+	30.1676i	−0.656325	+	1.53549i
$387$	−11.8236	+	20.4791i	−0.601028	+	1.04101i
$388$	−9.48154	−	0.213064i	−0.481352	−	0.0108167i
$389$		−	30.3695i		−	1.53979i	−0.638168	−	0.769897i	$-0.720308\pi$
$389$		−	30.3695i		−	1.53979i	0.638168	−	0.769897i	$-0.279692\pi$
$390$	−17.2619	−	35.7965i	−0.874090	−	1.81262i
$391$			5.49846i			0.278069i
$392$	15.3050	−	10.9448i	0.773018	−	0.552795i
$393$	−24.0136	+	41.5928i	−1.21133	+	2.09808i
$394$	−8.07056	−	3.44965i	−0.406589	−	0.173791i
$395$	−6.01125	+	6.01125i	−0.302459	+	0.302459i
$396$	−10.0547	+	16.5453i	−0.505266	+	0.831432i
$397$	−15.4588	−	4.14218i	−0.775857	−	0.207890i	−0.150899	−	0.988549i	$-0.548217\pi$
$397$	−15.4588	−	4.14218i	−0.775857	−	0.207890i	−0.624957	+	0.780659i	$0.714884\pi$
$398$	−0.603862	+	4.21990i	−0.0302689	+	0.211525i
$399$	4.13149	−	2.38531i	0.206833	−	0.119415i
$400$	−8.61617	−	16.6043i	−0.430809	−	0.830213i
$401$	3.56354	+	13.2993i	0.177955	+	0.664137i	0.996029	+	0.0890245i	$0.0283749\pi$
$401$	3.56354	+	13.2993i	0.177955	+	0.664137i	−0.818075	+	0.575112i	$0.804958\pi$
$402$	21.0766	−	15.7996i	1.05120	−	0.788014i
$403$	−2.19380	−	32.2786i	−0.109281	−	1.60791i
$404$	−5.03606	+	17.2362i	−0.250554	+	0.857532i
$405$	−24.3106	+	6.51401i	−1.20800	+	0.323684i
$406$	−0.123797	−	1.02958i	−0.00614393	−	0.0510971i
$407$	−0.764465	−	1.32409i	−0.0378931	−	0.0656328i
$408$	7.81748	−	17.2088i	0.387023	−	0.851964i
$409$	0.151353	−	0.564858i	0.00748394	−	0.0279305i	−0.962083	−	0.272757i	$-0.912064\pi$
$409$	0.151353	−	0.564858i	0.00748394	−	0.0279305i	0.969567	+	0.244827i	$0.0787311\pi$
$410$	9.49169	+	23.6634i	0.468761	+	1.16865i
$411$	12.8578	+	12.8578i	0.634228	+	0.634228i
$412$	4.55223	+	18.6560i	0.224272	+	0.919117i
$413$	3.59903	+	2.07790i	0.177097	+	0.102247i
$414$	−7.51475	−	5.90156i	−0.369330	−	0.290046i
$415$	44.8037			2.19933
$416$	16.0350	−	12.6047i	0.786182	−	0.617995i
$417$	−27.8281			−1.36275
$418$	10.6089	+	8.33152i	0.518900	+	0.407508i
$419$	−31.9541	−	18.4487i	−1.56106	−	0.901278i	−0.997150	−	0.0754420i	$-0.975963\pi$
$419$	−31.9541	−	18.4487i	−1.56106	−	0.901278i	−0.563910	−	0.825836i	$-0.690703\pi$
$420$	2.17871	+	8.92882i	0.106310	+	0.435682i
$421$	−22.1875	−	22.1875i	−1.08135	−	1.08135i	−0.996384	−	0.0849697i	$-0.972921\pi$
$421$	−22.1875	−	22.1875i	−1.08135	−	1.08135i	−0.0849697	−	0.996384i	$-0.527079\pi$
$422$	−9.58920	−	23.9065i	−0.466795	−	1.16375i
$423$	3.80056	−	14.1839i	0.184789	−	0.689643i
$424$	4.30107	−	9.46805i	0.208878	−	0.459809i
$425$	−6.23679	−	10.8024i	−0.302529	−	0.523995i
$426$	−0.867199	−	7.21222i	−0.0420159	−	0.349433i
$427$	−4.53006	+	1.21383i	−0.219225	+	0.0587411i
$428$	−10.5808	+	36.2132i	−0.511441	+	1.75043i
$429$	−22.1498	+	14.8774i	−1.06940	+	0.718285i
$430$	−25.3976	+	19.0388i	−1.22478	+	0.918132i
$431$	8.05023	+	30.0439i	0.387766	+	1.44716i	0.833760	+	0.552127i	$0.186183\pi$
$431$	8.05023	+	30.0439i	0.387766	+	1.44716i	−0.445994	+	0.895036i	$0.647150\pi$
$432$	1.28061	+	2.46787i	0.0616134	+	0.118736i
$433$	9.34712	−	5.39656i	0.449194	−	0.259342i	−0.258296	−	0.966066i	$-0.583161\pi$
$433$	9.34712	−	5.39656i	0.449194	−	0.259342i	0.707490	+	0.706724i	$0.249828\pi$
$434$	−1.05989	+	7.40671i	−0.0508763	+	0.355534i
$435$	−9.36245	−	2.50866i	−0.448895	−	0.120281i
$436$	4.33692	−	7.13654i	0.207701	−	0.341778i
$437$	−4.70747	+	4.70747i	−0.225189	+	0.225189i
$438$	0.202787	+	0.0866785i	0.00968952	+	0.00414166i
$439$	−6.48316	+	11.2292i	−0.309424	+	0.535938i	−0.978237	−	0.207493i	$-0.933470\pi$
$439$	−6.48316	+	11.2292i	−0.309424	+	0.535938i	0.668812	+	0.743431i	$0.266803\pi$
$440$	−21.1389	+	15.1167i	−1.00776	+	0.720659i
$441$			21.8026i			1.03822i
$442$	10.3038	−	8.87658i	0.490101	−	0.422216i
$443$			15.6512i			0.743611i	0.928311	+	0.371805i	$0.121261\pi$
$443$			15.6512i			0.743611i	−0.928311	+	0.371805i	$0.878739\pi$
$444$	−2.59321	−	0.0582732i	−0.123068	−	0.00276552i
$445$	12.9060	−	22.3539i	0.611805	−	1.05968i
$446$	−1.97374	+	4.61762i	−0.0934593	+	0.218650i
$447$	−9.20642	+	9.20642i	−0.435449	+	0.435449i
$448$	−4.23455	+	2.07798i	−0.200064	+	0.0981751i
$449$	10.8227	+	2.89994i	0.510755	+	0.136856i	0.504987	−	0.863127i	$-0.331497\pi$
$449$	10.8227	+	2.89994i	0.510755	+	0.136856i	0.00576812	+	0.999983i	$0.498164\pi$
$450$	21.4577	+	3.07056i	1.01153	+	0.144748i
$451$	14.8247	−	8.55907i	0.698070	−	0.403031i
$452$	8.15750	−	7.79893i	0.383696	−	0.366831i
$453$	−3.37203	−	12.5846i	−0.158432	−	0.591276i
$454$	−14.7903	−	19.7302i	−0.694145	−	0.925982i
$455$	−1.27451	+	6.48910i	−0.0597500	+	0.304214i
$456$	21.4261	−	8.04033i	1.00337	−	0.376523i
$457$	18.5601	−	4.97316i	0.868204	−	0.232634i	0.202893	−	0.979201i	$-0.434966\pi$
$457$	18.5601	−	4.97316i	0.868204	−	0.232634i	0.665311	+	0.746566i	$0.268299\pi$
$458$	28.3695	−	3.41115i	1.32562	−	0.159393i
$459$	0.926967	+	1.60555i	0.0432671	+	0.0749408i
$460$	−6.16168	−	11.2486i	−0.287290	−	0.524470i
$461$	6.34751	−	23.6892i	0.295633	−	1.10332i	−0.645081	−	0.764114i	$-0.723176\pi$
$461$	6.34751	−	23.6892i	0.295633	−	1.10332i	0.940713	−	0.339202i	$-0.110157\pi$
$462$	5.72718	−	2.29724i	0.266452	−	0.106877i
$463$	13.2027	+	13.2027i	0.613581	+	0.613581i	0.943877	−	0.330296i	$-0.107149\pi$
$463$	13.2027	+	13.2027i	0.613581	+	0.613581i	−0.330296	+	0.943877i	$0.607149\pi$
$464$	0.223457	−	4.96951i	0.0103737	−	0.230704i
$465$	60.5658	+	34.9677i	2.80867	+	1.62159i
$466$	11.6350	−	14.8155i	0.538983	−	0.686313i
$467$	22.6548			1.04834			0.524171	−	0.851613i	$-0.324375\pi$
$467$	22.6548			1.04834			0.524171	+	0.851613i	$0.324375\pi$
$468$	1.07243	+	23.6095i	0.0495731	+	1.09135i
$469$	−4.38325			−0.202400
$470$	12.1738	−	15.5015i	0.561538	−	0.715033i
$471$	23.3482	+	13.4801i	1.07583	+	0.621130i
$472$	15.3981	+	12.6621i	0.708756	+	0.582820i
$473$	15.0693	+	15.0693i	0.692888	+	0.692888i
$474$	8.98726	−	3.60490i	0.412798	−	0.165579i
$475$	3.90885	−	14.5880i	0.179350	−	0.669344i
$476$	−2.75850	+	1.51103i	−0.126436	+	0.0692579i
$477$	6.02501	+	10.4356i	0.275866	+	0.477814i
$478$	−20.3520	+	2.44713i	−0.930879	+	0.111929i
$479$	−3.13701	+	0.840559i	−0.143334	+	0.0384061i	−0.329772	−	0.944060i	$-0.606972\pi$
$479$	−3.13701	+	0.840559i	−0.143334	+	0.0384061i	0.186439	+	0.982467i	$0.440305\pi$
$480$	3.29172	+	43.9658i	0.150246	+	2.00676i
$481$	−1.67588	−	0.821438i	−0.0764136	−	0.0374543i
$482$	−11.7487	−	15.6727i	−0.535140	−	0.713872i
$483$	0.788212	+	2.94165i	0.0358649	+	0.133850i
$484$	−3.14542	−	3.29003i	−0.142974	−	0.149547i
$485$	12.7747	−	7.37550i	0.580071	−	0.334904i
$486$	31.2980	+	4.47870i	1.41971	+	0.203158i
$487$	−41.4268	−	11.1003i	−1.87723	−	0.503002i	−0.999725	−	0.0234304i	$-0.992541\pi$
$487$	−41.4268	−	11.1003i	−1.87723	−	0.503002i	−0.877503	−	0.479571i	$-0.840792\pi$
$488$	−22.3914	+	2.18328i	−1.01361	+	0.0988326i
$489$	25.1775	−	25.1775i	1.13856	−	1.13856i
$490$	−11.5024	+	26.9101i	−0.519624	+	1.21568i
$491$	0.796904	−	1.38028i	0.0359638	−	0.0622911i	−0.847483	−	0.530822i	$-0.821883\pi$
$491$	0.796904	−	1.38028i	0.0359638	−	0.0622911i	0.883447	+	0.468531i	$0.155217\pi$
$492$	0.652435	−	29.0340i	0.0294141	−	1.30895i
$493$		−	3.31701i		−	0.149390i
$494$	16.4211	+	1.22190i	0.738822	+	0.0549759i
$495$		−	30.1132i		−	1.35349i
$496$	−10.8376	+	34.2172i	−0.486624	+	1.53640i
$497$	−0.604392	+	1.04684i	−0.0271107	+	0.0469571i
$498$	−46.9266	−	20.0582i	−2.10283	−	0.898828i
$499$	2.89721	−	2.89721i	0.129697	−	0.129697i	−0.639278	−	0.768975i	$-0.720767\pi$
$499$	2.89721	−	2.89721i	0.129697	−	0.129697i	0.768975	+	0.639278i	$0.220767\pi$
$500$	−1.71905	−	1.04468i	−0.0768782	−	0.0467193i
$501$	−22.5569	−	6.04411i	−1.00777	−	0.270031i
$502$	−0.504088	+	3.52267i	−0.0224986	+	0.157224i
$503$	−13.0990	+	7.56273i	−0.584057	+	0.337205i	−0.762744	−	0.646701i	$-0.776148\pi$
$503$	−13.0990	+	7.56273i	−0.584057	+	0.337205i	0.178687	+	0.983906i	$0.442815\pi$
$504$	0.895607	−	5.39184i	0.0398935	−	0.240172i
$505$	−7.22868	−	26.9778i	−0.321672	−	1.20050i
$506$	−6.89018	+	5.16509i	−0.306306	+	0.229616i
$507$	−12.3193	+	30.1516i	−0.547118	+	1.33908i
$508$	−23.1970	−	6.77770i	−1.02920	−	0.300712i
$509$	−24.1589	+	6.47337i	−1.07083	+	0.286927i	−0.750832	−	0.660493i	$-0.770347\pi$
$509$	−24.1589	+	6.47337i	−1.07083	+	0.286927i	−0.319994	+	0.947420i	$0.603681\pi$
$510$	3.50959	+	29.1881i	0.155407	+	1.29247i
$511$	−0.0183489	−	0.0317812i	−0.000811708	−	0.00140592i
$512$	−21.6722	+	6.50493i	−0.957787	+	0.287480i
$513$	−0.580967	+	2.16820i	−0.0256503	+	0.0957284i
$514$	−3.37659	−	8.41806i	−0.148935	−	0.371305i
$515$	−21.1201	−	21.1201i	−0.930663	−	0.930663i
$516$	35.1244	−	8.57066i	1.54627	−	0.377302i
$517$	−11.4607	−	6.61682i	−0.504040	−	0.291007i
$518$	0.339461	+	0.266589i	0.0149150	+	0.0117133i
$519$	−57.3549			−2.51760
$520$	−11.1320	+	29.7061i	−0.488170	+	1.30270i
$521$	−41.1166			−1.80135			−0.900675	−	0.434494i	$-0.856927\pi$
$521$	−41.1166			−1.80135			−0.900675	+	0.434494i	$0.856927\pi$
$522$	4.53335	+	3.56018i	0.198419	+	0.155825i
$523$	2.27834	+	1.31540i	0.0996249	+	0.0575185i	0.548985	−	0.835832i	$-0.315015\pi$
$523$	2.27834	+	1.31540i	0.0996249	+	0.0575185i	−0.449360	+	0.893351i	$0.648348\pi$
$524$	37.2450	−	9.08809i	1.62705	−	0.397015i
$525$	−4.88519	−	4.88519i	−0.213207	−	0.213207i
$526$	2.79472	+	6.96741i	0.121856	+	0.303794i
$527$	−6.19432	+	23.1175i	−0.269829	+	1.00702i
$528$	28.9081	−	6.36928i	1.25806	−	0.277187i
$529$	9.37507	+	16.2381i	0.407612	+	0.706004i
$530$	1.93093	+	16.0589i	0.0838741	+	0.697554i
$531$	−22.3132	+	5.97882i	−0.968312	+	0.259459i
$532$	−3.65533	−	1.06801i	−0.158478	−	0.0463042i
$533$	9.19694	−	18.7634i	0.398364	−	0.812734i
$534$	−23.5252	+	17.6352i	−1.01803	+	0.763149i
$535$	−15.1875	−	56.6804i	−0.656611	−	2.45051i
$536$	−20.7425	−	3.44542i	−0.895941	−	0.148820i
$537$	−28.6817	+	16.5594i	−1.23771	+	0.714590i
$538$	2.00350	−	14.0009i	0.0863772	−	0.603621i
$539$	18.9793	+	5.08549i	0.817497	+	0.219048i
$540$	−3.69558	−	2.24583i	−0.159032	−	0.0966449i
$541$	14.2591	−	14.2591i	0.613047	−	0.613047i	−0.330692	−	0.943739i	$-0.607282\pi$
$541$	14.2591	−	14.2591i	0.613047	−	0.613047i	0.943739	+	0.330692i	$0.107282\pi$
$542$	33.1835	+	14.1839i	1.42536	+	0.609249i
$543$	32.7225	−	56.6771i	1.40426	−	2.43225i
$544$	−14.2416	+	4.98224i	−0.610603	+	0.213612i
$545$			12.9889i			0.556381i
$546$	4.24000	−	6.22598i	0.181455	−	0.266447i
$547$		−	40.9532i		−	1.75103i	−0.483190	−	0.875515i	$-0.660522\pi$
$547$		−	40.9532i		−	1.75103i	0.483190	−	0.875515i	$-0.339478\pi$
$548$	0.326094	−	14.5115i	0.0139300	−	0.619899i
$549$	13.0345	−	22.5764i	0.556298	−	0.963537i
$550$	7.67799	−	17.9629i	0.327391	−	0.765939i
$551$	2.83983	−	2.83983i	0.120981	−	0.120981i
$552$	1.41774	+	14.5401i	0.0603431	+	0.618869i
$553$	−1.55643	−	0.417045i	−0.0661862	−	0.0177345i
$554$	−0.748024	−	0.107041i	−0.0317805	−	0.00454774i
$555$	3.49390	−	2.01721i	0.148308	−	0.0856256i
$556$	15.3507	+	16.0564i	0.651013	+	0.680944i
$557$	7.78980	+	29.0719i	0.330064	+	1.23182i	0.909122	+	0.416530i	$0.136754\pi$
$557$	7.78980	+	29.0719i	0.330064	+	1.23182i	−0.579058	+	0.815287i	$0.696579\pi$
$558$	−24.9463	−	33.2781i	−1.05606	−	1.40877i
$559$	25.5270	+	5.01370i	1.07968	+	0.212057i
$560$	3.94998	−	6.18245i	0.166917	−	0.261256i
$561$	19.0656	−	5.10861i	0.804950	−	0.215686i
$562$	0.547129	−	0.0657870i	0.0230793	−	0.00277506i
$563$	7.94721	+	13.7650i	0.334935	+	0.580124i	0.983472	−	0.181058i	$-0.0579523\pi$
$563$	7.94721	+	13.7650i	0.334935	+	0.580124i	−0.648537	+	0.761183i	$0.724619\pi$
$564$	−19.6906	+	10.7859i	−0.829122	+	0.454170i
$565$	−4.54318	+	16.9554i	−0.191133	+	0.713318i
$566$	21.0847	−	8.45732i	0.886254	−	0.355488i
$567$	−3.37321	−	3.37321i	−0.141661	−	0.141661i
$568$	−3.68298	+	4.47880i	−0.154535	+	0.187926i
$569$	−19.5646	−	11.2956i	−0.820192	−	0.473538i	0.0302909	−	0.999541i	$-0.490357\pi$
$569$	−19.5646	−	11.2956i	−0.820192	−	0.473538i	−0.850483	+	0.526003i	$0.823690\pi$
$570$	−21.9845	+	27.9939i	−0.920829	+	1.17254i
$571$	2.17784			0.0911398			0.0455699	−	0.998961i	$-0.485490\pi$
$571$	2.17784			0.0911398			0.0455699	+	0.998961i	$0.485490\pi$
$572$	20.8024	+	4.57340i	0.869792	+	0.191223i
$573$	35.4227			1.47981
$574$	−2.98477	+	3.80065i	−0.124582	+	0.158636i
$575$	8.34938	+	4.82052i	0.348193	+	0.201030i
$576$	8.47643	−	24.8114i	0.353185	−	1.03381i
$577$	15.8624	+	15.8624i	0.660361	+	0.660361i	0.955465	−	0.295104i	$-0.0953543\pi$
$577$	15.8624	+	15.8624i	0.660361	+	0.660361i	−0.295104	+	0.955465i	$0.595354\pi$
$578$	12.9761	−	5.20487i	0.539734	−	0.216494i
$579$	−15.0435	+	56.1433i	−0.625188	+	2.33323i
$580$	3.71710	+	6.78585i	0.154344	+	0.281767i
$581$	4.24610	+	7.35446i	0.176158	+	0.305115i
$582$	−16.6820	+	2.00585i	−0.691490	+	0.0831450i
$583$	10.4896	−	2.81069i	0.434436	−	0.116407i
$584$	−0.0618498	−	0.164819i	−0.00255936	−	0.00682027i
$585$	−20.4960	−	30.5150i	−0.847406	−	1.26164i
$586$	−1.73810	−	2.31861i	−0.0718004	−	0.0957811i
$587$	5.61437	+	20.9531i	0.231730	+	0.864827i	0.979596	+	0.200978i	$0.0644119\pi$
$587$	5.61437	+	20.9531i	0.231730	+	0.864827i	−0.747866	+	0.663850i	$0.768921\pi$
$588$	24.0948	−	23.0357i	0.993651	−	0.949975i
$589$	−25.0951	+	14.4887i	−1.03403	+	0.596996i
$590$	−30.6946	−	4.39235i	−1.26368	−	0.180830i
$591$	−15.0197	−	4.02451i	−0.617827	−	0.165546i
$592$	1.39686	+	1.52839i	0.0574104	+	0.0628165i
$593$	0.858298	−	0.858298i	0.0352461	−	0.0352461i	−0.689264	−	0.724510i	$-0.742066\pi$
$593$	0.858298	−	0.858298i	0.0352461	−	0.0352461i	0.724510	+	0.689264i	$0.242066\pi$
$594$	−1.14117	+	2.66980i	−0.0468228	+	0.109543i
$595$	2.44600	−	4.23660i	0.100276	−	0.173683i
$596$	10.3905	+	0.233489i	0.425611	+	0.00956409i
$597$			7.55231i			0.309096i
$598$	−3.46658	+	9.92366i	−0.141759	+	0.405809i
$599$			7.16374i			0.292702i	0.989233	+	0.146351i	$0.0467529\pi$
$599$			7.16374i			0.292702i	−0.989233	+	0.146351i	$0.953247\pi$
$600$	−19.2779	−	26.9578i	−0.787016	−	1.10055i
$601$	−8.02549	+	13.9006i	−0.327367	+	0.567016i	−0.981988	−	0.188941i	$-0.939495\pi$
$601$	−8.02549	+	13.9006i	−0.327367	+	0.567016i	0.654622	+	0.755956i	$0.272828\pi$
$602$	−5.53215	−	2.36464i	−0.225473	−	0.0963757i
$603$	17.2284	−	17.2284i	0.701595	−	0.701595i
$604$	−5.40105	+	8.88760i	−0.219766	+	0.361631i
$605$	6.83834	+	1.83233i	0.278018	+	0.0744947i
$606$	−4.50649	+	31.4923i	−0.183064	+	1.27929i
$607$	−30.3120	+	17.5006i	−1.23033	+	0.710329i	−0.967098	−	0.254404i	$-0.918121\pi$
$607$	−30.3120	+	17.5006i	−1.23033	+	0.710329i	−0.263229	+	0.964734i	$0.584787\pi$
$608$	−16.4583	−	7.92732i	−0.667474	−	0.321495i
$609$	−0.475497	−	1.77458i	−0.0192681	−	0.0719096i
$610$	27.9986	−	20.9886i	1.13363	−	0.849803i
$611$	−16.1172	+	1.09540i	−0.652031	+	0.0443150i
$612$	4.90319	−	16.7814i	0.198200	−	0.678349i
$613$	19.8339	−	5.31448i	0.801084	−	0.214650i	0.165024	−	0.986290i	$-0.447230\pi$
$613$	19.8339	−	5.31448i	0.801084	−	0.214650i	0.636060	+	0.771640i	$0.280563\pi$
$614$	2.72993	+	22.7039i	0.110171	+	0.916256i
$615$	22.5849	+	39.1183i	0.910712	+	1.57740i
$616$	−4.48473	−	2.03729i	−0.180695	−	0.0820847i
$617$	4.87361	−	18.1886i	0.196204	−	0.732244i	−0.795748	−	0.605628i	$-0.792922\pi$
$617$	4.87361	−	18.1886i	0.196204	−	0.732244i	0.991952	−	0.126616i	$-0.0404115\pi$
$618$	12.6656	+	31.5761i	0.509484	+	1.27018i
$619$	28.1707	+	28.1707i	1.13228	+	1.13228i	0.989798	+	0.142478i	$0.0455069\pi$
$619$	28.1707	+	28.1707i	1.13228	+	1.13228i	0.142478	+	0.989798i	$0.454493\pi$
$620$	−13.2337	−	54.2347i	−0.531480	−	2.17812i
$621$	−1.24096	−	0.716468i	−0.0497980	−	0.0287509i
$622$	26.7204	+	20.9843i	1.07139	+	0.841395i
$623$	4.89248			0.196013
$624$	24.9586	−	26.1300i	0.999142	−	1.04604i
$625$	26.5121			1.06048
$626$	−32.1443	−	25.2440i	−1.28475	−	1.00895i
$627$	20.6966	+	11.9492i	0.826542	+	0.477204i
$628$	−5.10162	−	20.9075i	−0.203577	−	0.834302i
$629$	0.976260	+	0.976260i	0.0389260	+	0.0389260i
$630$	3.16483	+	7.89013i	0.126090	+	0.314350i
$631$	−3.23895	+	12.0879i	−0.128941	+	0.481213i	−0.999949	−	0.0100543i	$-0.996800\pi$
$631$	−3.23895	+	12.0879i	−0.128941	+	0.481213i	0.871009	+	0.491267i	$0.163466\pi$
$632$	−7.03758	−	3.19697i	−0.279940	−	0.127169i
$633$	−22.8170	−	39.5201i	−0.906893	−	1.57078i
$634$	−0.00336694	−	0.0280017i	−0.000133718	−	0.00111209i
$635$	36.3076	−	9.72858i	1.44082	−	0.386067i
$636$	5.16698	−	17.6843i	0.204884	−	0.701226i
$637$	22.6938	−	7.76458i	0.899163	−	0.307644i
$638$	4.15657	−	3.11589i	0.164560	−	0.123359i
$639$	−1.73904	−	6.49018i	−0.0687953	−	0.256748i
$640$	23.5519	−	26.1519i	0.930970	−	1.03375i
$641$	−22.6933	+	13.1020i	−0.896331	+	0.517497i	−0.876008	−	0.482296i	$-0.839803\pi$
$641$	−22.6933	+	13.1020i	−0.896331	+	0.517497i	−0.0203232	+	0.999793i	$0.506470\pi$
$642$	−9.46815	+	66.1653i	−0.373678	+	2.61133i
$643$	−0.362291	−	0.0970757i	−0.0142874	−	0.00382829i	0.251668	−	0.967814i	$-0.419021\pi$
$643$	−0.362291	−	0.0970757i	−0.0142874	−	0.00382829i	−0.265956	+	0.963985i	$0.585687\pi$
$644$	1.26249	−	2.07747i	0.0497492	−	0.0818640i
$645$	−39.7636	+	39.7636i	−1.56569	+	1.56569i
$646$	−11.2008	−	4.78762i	−0.440688	−	0.188366i
$647$	17.6527	−	30.5754i	0.693999	−	1.20204i	−0.276517	−	0.961009i	$-0.589180\pi$
$647$	17.6527	−	30.5754i	0.693999	−	1.20204i	0.970517	−	0.241033i	$-0.0774863\pi$
$648$	−13.3113	−	18.6143i	−0.522918	−	0.731238i
$649$			20.8184i			0.817194i
$650$	−4.44566	−	23.4284i	−0.174373	−	0.918936i
$651$			13.2557i			0.519532i
$652$	−28.4156	−	0.638539i	−1.11284	−	0.0250071i
$653$	−16.0606	+	27.8178i	−0.628500	+	1.08859i	0.359353	+	0.933202i	$0.382997\pi$
$653$	−16.0606	+	27.8178i	−0.628500	+	1.08859i	−0.987853	+	0.155392i	$0.950336\pi$
$654$	5.81498	−	13.6043i	0.227384	−	0.531970i
$655$	−42.1642	+	42.1642i	−1.64749	+	1.64749i
$656$	−17.1121	+	15.6394i	−0.668115	+	0.610616i
$657$	0.197037	+	0.0527959i	0.00768715	+	0.00205977i
$658$	3.69828	+	0.529219i	0.144174	+	0.0206311i
$659$	−9.20996	+	5.31737i	−0.358769	+	0.207135i	−0.668541	−	0.743676i	$-0.733081\pi$
$659$	−9.20996	+	5.31737i	−0.358769	+	0.207135i	0.309772	+	0.950811i	$0.399747\pi$
$660$	−33.2791	+	31.8163i	−1.29539	+	1.23845i
$661$	2.08438	+	7.77900i	0.0810729	+	0.302568i	0.994542	−	0.104341i	$-0.0332733\pi$
$661$	2.08438	+	7.77900i	0.0810729	+	0.302568i	−0.913469	+	0.406909i	$0.866607\pi$
$662$	−3.58360	−	4.78049i	−0.139281	−	0.185799i
$663$	15.8429	−	18.1534i	0.615286	−	0.705020i
$664$	14.3126	+	38.1406i	0.555437	+	1.48014i
$665$	5.72126	−	1.53301i	0.221861	−	0.0594474i
$666$	−2.38209	+	0.286423i	−0.0923039	+	0.0110987i
$667$	1.28188	+	2.22029i	0.0496348	+	0.0859699i
$668$	8.95559	+	16.3491i	0.346502	+	0.632566i
$669$	−2.30265	+	8.59360i	−0.0890255	+	0.332248i
$670$	30.3535	−	12.1752i	1.17266	−	0.470369i
$671$	−16.6126	−	16.6126i	−0.641322	−	0.641322i
$672$	−6.90496	+	4.70702i	−0.266365	+	0.181577i
$673$	1.15151	+	0.664827i	0.0443876	+	0.0256272i	0.522030	−	0.852927i	$-0.325175\pi$
$673$	1.15151	+	0.664827i	0.0443876	+	0.0256272i	−0.477642	+	0.878555i	$0.658508\pi$
$674$	−8.37262	+	10.6613i	−0.322501	+	0.410657i
$675$	3.25070			0.125119
$676$	24.1927	−	9.52434i	0.930489	−	0.366321i
$677$	33.7816			1.29833			0.649167	−	0.760646i	$-0.275118\pi$
$677$	33.7816			1.29833			0.649167	+	0.760646i	$0.275118\pi$
$678$	12.3492	−	15.7248i	0.474268	−	0.603908i
$679$	2.42135	+	1.39797i	0.0929231	+	0.0536492i
$680$	14.9052	−	18.1259i	0.571587	−	0.695096i
$681$	−30.8905	−	30.8905i	−1.18373	−	1.18373i
$682$	−34.7876	+	13.9537i	−1.33208	+	0.534316i
$683$	11.4324	−	42.6664i	0.437449	−	1.63258i	−0.297687	−	0.954664i	$-0.596215\pi$
$683$	11.4324	−	42.6664i	0.437449	−	1.63258i	0.735136	−	0.677920i	$-0.237118\pi$
$684$	18.5651	−	10.1695i	0.709856	−	0.388839i
$685$	11.2882	+	19.5517i	0.431299	+	0.747032i
$686$	−11.3025	+	1.35902i	−0.431532	+	0.0518875i
$687$	48.8976	−	13.1021i	1.86556	−	0.499876i
$688$	−24.3207	−	15.5385i	−0.927217	−	0.592401i
$689$	8.71652	−	9.98775i	0.332073	−	0.380503i
$690$	−13.6292	−	18.1812i	−0.518854	−	0.692147i
$691$	10.7564	+	40.1436i	0.409195	+	1.52714i	0.796186	+	0.605052i	$0.206848\pi$
$691$	10.7564	+	40.1436i	0.409195	+	1.52714i	−0.386991	+	0.922083i	$0.626486\pi$
$692$	31.6384	+	33.0930i	1.20271	+	1.25801i
$693$	4.94304	−	2.85387i	0.187771	−	0.108409i
$694$	−5.76247	−	0.824601i	−0.218740	−	0.0313014i
$695$	−33.3733	−	8.94235i	−1.26592	−	0.339203i
$696$	−0.855267	−	8.77148i	−0.0324188	−	0.332482i
$697$	−10.9304	+	10.9304i	−0.414017	+	0.414017i
$698$	16.1490	−	37.7811i	0.611250	−	1.43004i
$699$	16.6871	−	28.9030i	0.631165	−	1.09321i
$700$	−0.123896	+	5.51349i	−0.00468283	+	0.208390i
$701$			17.2912i			0.653080i	0.945183	+	0.326540i	$0.105883\pi$
$701$			17.2912i			0.653080i	−0.945183	+	0.326540i	$0.894117\pi$
$702$	0.660754	+	3.48213i	0.0249385	+	0.131425i
$703$			1.67164i			0.0630470i
$704$	−19.6214	−	13.1661i	−0.739509	−	0.496216i
$705$	17.4599	−	30.2414i	0.657578	−	1.13896i
$706$	34.2395	+	14.6352i	1.28862	+	0.550804i
$707$	3.74329	−	3.74329i	0.140781	−	0.140781i
$708$	30.1826	+	18.3421i	1.13433	+	0.689340i
$709$	−40.4498	−	10.8385i	−1.51913	−	0.407048i	−0.599672	−	0.800246i	$-0.704702\pi$
$709$	−40.4498	−	10.8385i	−1.51913	−	0.407048i	−0.919454	+	0.393198i	$0.871369\pi$
$710$	1.27759	−	8.92804i	0.0479471	−	0.335063i
$711$	7.75677	−	4.47837i	0.290902	−	0.167952i
$712$	23.1523	+	3.84570i	0.867671	+	0.144124i
$713$	−4.78769	−	17.8679i	−0.179301	−	0.669159i
$714$	−4.45858	+	3.34229i	−0.166858	+	0.125082i
$715$	−31.3442	+	10.7243i	−1.17221	+	0.401064i
$716$	25.3761	+	7.41438i	0.948349	+	0.277088i
$717$	−35.0787	+	9.39931i	−1.31004	+	0.351024i
$718$	−1.83816	−	15.2874i	−0.0685994	−	0.570519i
$719$	−17.2567	−	29.8894i	−0.643565	−	1.11469i	−0.984631	−	0.174647i	$-0.944121\pi$
$719$	−17.2567	−	29.8894i	−0.643565	−	1.11469i	0.341066	−	0.940039i	$-0.389212\pi$
$720$	8.77474	+	39.8256i	0.327015	+	1.48421i
$721$	1.46526	−	5.46841i	0.0545690	−	0.203654i
$722$	4.51264	+	11.2503i	0.167943	+	0.418693i
$723$	−24.5379	−	24.5379i	−0.912575	−	0.912575i
$724$	−50.7525	+	12.3840i	−1.88620	+	0.460249i
$725$	−5.03685	−	2.90803i	−0.187064	−	0.108001i
$726$	−6.34204	−	4.98060i	−0.235375	−	0.184847i
$727$	−3.77644			−0.140060			−0.0700302	−	0.997545i	$-0.522310\pi$
$727$	−3.77644			−0.140060			−0.0700302	+	0.997545i	$0.522310\pi$
$728$	−5.93120	+	0.987983i	−0.219825	+	0.0366171i
$729$	31.7414			1.17561
$730$	0.215342	+	0.169115i	0.00797016	+	0.00625921i
$731$	−16.6660	−	9.62214i	−0.616416	−	0.355888i
$732$	−38.7216	+	9.44839i	−1.43119	+	0.349223i
$733$	4.25026	+	4.25026i	0.156987	+	0.156987i	0.781230	−	0.624243i	$-0.214593\pi$
$733$	4.25026	+	4.25026i	0.156987	+	0.156987i	−0.624243	+	0.781230i	$0.714593\pi$
$734$	1.10468	+	2.75403i	0.0407744	+	0.101653i
$735$	−13.4192	+	50.0810i	−0.494973	+	1.84727i
$736$	7.60739	−	8.83871i	0.280412	−	0.325799i
$737$	−10.9789	−	19.0160i	−0.404413	−	0.700464i
$738$	−3.20683	−	26.6702i	−0.118045	−	0.981743i
$739$	−17.4311	+	4.67066i	−0.641215	+	0.171813i	−0.564754	−	0.825260i	$-0.691029\pi$
$739$	−17.4311	+	4.67066i	−0.641215	+	0.171813i	−0.0764613	+	0.997073i	$0.524362\pi$
$740$	−3.09122	−	0.903194i	−0.113636	−	0.0332021i
$741$	29.1057	−	1.97815i	1.06922	−	0.0726692i
$742$	−2.45305	+	1.83888i	−0.0900542	+	0.0675074i
$743$	−3.46818	−	12.9434i	−0.127235	−	0.474848i	0.872674	−	0.488303i	$-0.162384\pi$
$743$	−3.46818	−	12.9434i	−0.127235	−	0.474848i	−0.999909	+	0.0134546i	$0.995717\pi$
$744$	−10.4196	+	62.7291i	−0.381999	+	2.29976i
$745$	−13.9994	+	8.08254i	−0.512898	+	0.296122i
$746$	5.67031	−	39.6252i	0.207605	−	1.45078i
$747$	−45.5961	−	12.2174i	−1.66828	−	0.447013i
$748$	−13.4647	−	8.18256i	−0.492317	−	0.299184i
$749$	7.86466	−	7.86466i	0.287368	−	0.287368i
$750$	−3.27700	−	1.40071i	−0.119659	−	0.0511467i
$751$	12.5103	−	21.6684i	0.456506	−	0.790691i	−0.542268	−	0.840206i	$-0.682434\pi$
$751$	12.5103	−	21.6684i	0.456506	−	0.790691i	0.998773	+	0.0495148i	$0.0157675\pi$
$752$	17.0851	+	5.41139i	0.623031	+	0.197333i
$753$			6.30448i			0.229748i
$754$	2.09125	−	5.98655i	0.0761588	−	0.218017i
$755$		−	16.1759i		−	0.588700i
$756$	0.0184145	−	0.819463i	0.000669730	−	0.0298036i
$757$	19.6123	−	33.9695i	0.712821	−	1.23464i	−0.250973	−	0.967994i	$-0.580751\pi$
$757$	19.6123	−	33.9695i	0.712821	−	1.23464i	0.963794	−	0.266648i	$-0.0859161\pi$
$758$	−16.0698	+	37.5957i	−0.583681	+	1.36554i
$759$	−10.7876	+	10.7876i	−0.391565	+	0.391565i
$760$	28.2793	−	2.75739i	1.02580	−	0.100021i
$761$	13.7578	+	3.68640i	0.498722	+	0.133632i	0.499407	−	0.866368i	$-0.333551\pi$
$761$	13.7578	+	3.68640i	0.498722	+	0.133632i	−0.000685009		1.00000i	$0.500218\pi$
$762$	−42.3833	−	6.06498i	−1.53538	−	0.219711i
$763$	−2.13210	+	1.23097i	−0.0771872	+	0.0445641i
$764$	−19.5401	−	20.4384i	−0.706935	−	0.739437i
$765$	7.03796	+	26.2660i	0.254458	+	0.949650i
$766$	−12.8394	−	17.1277i	−0.463908	−	0.618849i
$767$	14.1696	+	21.0961i	0.511636	+	0.761737i
$768$	−36.3758	+	16.8471i	−1.31260	+	0.607918i
$769$	19.3143	−	5.17525i	0.696491	−	0.186624i	0.106833	−	0.994277i	$-0.465929\pi$
$769$	19.3143	−	5.17525i	0.696491	−	0.186624i	0.589658	+	0.807653i	$0.299262\pi$
$770$	7.60662	−	0.914622i	0.274124	−	0.0329607i
$771$	−8.03441	−	13.9160i	−0.289352	−	0.501172i
$772$	40.6923	−	22.2901i	1.46455	−	0.802239i
$773$	7.82826	−	29.2155i	0.281563	−	1.05081i	−0.669751	−	0.742585i	$-0.733599\pi$
$773$	7.82826	−	29.2155i	0.281563	−	1.05081i	0.951314	−	0.308222i	$-0.0997340\pi$
$774$	31.0384	−	12.4499i	1.11565	−	0.447503i
$775$	29.6732	+	29.6732i	1.06589	+	1.06589i
$776$	10.3595	+	8.51880i	0.371886	+	0.305807i
$777$	0.662242	+	0.382346i	0.0237578	+	0.0137166i
$778$	−26.5268	+	33.7778i	−0.951031	+	1.21099i
$779$	−18.7159			−0.670567
$780$	−12.0679	+	54.8916i	−0.432100	+	1.96543i
$781$	−6.05538			−0.216679
$782$	4.80273	−	6.11555i	0.171745	−	0.218692i
$783$	0.748622	+	0.432217i	0.0267536	+	0.0154462i
$784$	−26.5826	−	1.19530i	−0.949377	−	0.0426893i
$785$	23.6690	+	23.6690i	0.844783	+	0.844783i
$786$	63.0386	−	25.2856i	2.24851	−	0.901907i
$787$	2.42897	−	9.06504i	0.0865834	−	0.323134i	−0.909026	−	0.416740i	$-0.863173\pi$
$787$	2.42897	−	9.06504i	0.0865834	−	0.323134i	0.995609	+	0.0936059i	$0.0298394\pi$
$788$	5.96314	+	10.8862i	0.212428	+	0.387804i
$789$	6.64987	+	11.5179i	0.236742	+	0.410049i
$790$	11.9365	−	1.43525i	0.424683	−	0.0510640i
$791$	−3.21376	+	0.861124i	−0.114268	+	0.0306181i
$792$	25.6349	−	9.61971i	0.910896	−	0.341822i
$793$	−28.1413	−	5.52716i	−0.999325	−	0.196275i
$794$	13.5757	+	18.1099i	0.481784	+	0.642695i
$795$	7.41660	+	27.6791i	0.263040	+	0.981677i
$796$	4.35758	−	4.16605i	0.154450	−	0.147662i
$797$	−10.0960	+	5.82891i	−0.357617	+	0.206471i	−0.668035	−	0.744130i	$-0.732864\pi$
$797$	−10.0960	+	5.82891i	−0.357617	+	0.206471i	0.310418	+	0.950600i	$0.399531\pi$
$798$	−6.67865	−	0.955705i	−0.236422	−	0.0338316i
$799$	11.5429	+	3.09292i	0.408359	+	0.109420i
$800$	−4.92014	+	25.9937i	−0.173953	+	0.919016i
$801$	−19.2299	+	19.2299i	−0.679457	+	0.679457i
$802$	7.65306	−	17.9045i	0.270239	−	0.632231i
$803$	0.0919184	−	0.159207i	0.00324373	−	0.00561831i
$804$	−37.2425	−	0.836892i	−1.31344	−	0.0295149i
$805$			3.78111i			0.133267i
$806$	−25.7543	+	37.8174i	−0.907156	+	1.33206i
$807$		−	25.0572i		−	0.882055i
$808$	20.6565	−	14.7717i	0.726693	−	0.519668i
$809$	15.5430	−	26.9212i	0.546461	−	0.946499i	−0.452052	−	0.891992i	$-0.649308\pi$
$809$	15.5430	−	26.9212i	0.546461	−	0.946499i	0.998513	−	0.0545072i	$-0.0173588\pi$
$810$	32.7287	+	13.9895i	1.14997	+	0.491540i
$811$	−0.110267	+	0.110267i	−0.00387201	+	0.00387201i	−0.709040	−	0.705168i	$-0.750872\pi$
$811$	−0.110267	+	0.110267i	−0.00387201	+	0.00387201i	0.705168	+	0.709040i	$0.250872\pi$
$812$	−0.761613	+	1.25326i	−0.0267274	+	0.0439807i
$813$	61.7561	+	16.5475i	2.16588	+	0.580346i
$814$	−0.306292	+	2.14043i	−0.0107355	+	0.0750221i
$815$	38.2851	−	22.1039i	1.34107	−	0.774266i
$816$	−23.7262	+	12.3118i	−0.830583	+	0.431000i
$817$	−6.03058	−	22.5064i	−0.210983	−	0.787401i
$818$	−0.661725	+	0.496050i	−0.0231367	+	0.0173440i
$819$	3.06655	−	6.25632i	0.107154	−	0.218614i
$820$	10.1123	−	34.6098i	0.353137	−	1.20863i
$821$	−17.4699	+	4.68104i	−0.609703	+	0.163370i	−0.550443	−	0.834873i	$-0.685541\pi$
$821$	−17.4699	+	4.68104i	−0.609703	+	0.163370i	−0.0592608	+	0.998243i	$0.518874\pi$
$822$	−3.06994	−	25.5317i	−0.107076	−	0.890520i
$823$	13.0969	+	22.6845i	0.456530	+	0.790733i	0.998775	−	0.0494874i	$-0.0157588\pi$
$823$	13.0969	+	22.6845i	0.456530	+	0.790733i	−0.542245	+	0.840221i	$0.682425\pi$
$824$	11.2323	−	24.7260i	0.391297	−	0.861372i
$825$	8.95747	−	33.4297i	0.311859	−	1.16387i
$826$	−2.18797	−	5.45474i	−0.0761291	−	0.189795i
$827$	11.7822	+	11.7822i	0.409707	+	0.409707i	0.881636	−	0.471930i	$-0.156442\pi$
$827$	11.7822	+	11.7822i	0.409707	+	0.409707i	−0.471930	+	0.881636i	$0.656442\pi$
$828$	3.20329	+	13.1278i	0.111322	+	0.456222i
$829$	−11.3492	−	6.55249i	−0.394176	−	0.227577i	0.289792	−	0.957090i	$-0.406414\pi$
$829$	−11.3492	−	6.55249i	−0.394176	−	0.227577i	−0.683968	+	0.729512i	$0.739747\pi$
$830$	−49.8320	−	39.1346i	−1.72969	−	1.35838i
$831$	−1.33873			−0.0464401
$832$	−28.8444	+	0.0131852i	−1.00000	+	0.000457113i
$833$	−17.7431			−0.614762
$834$	30.9512	+	24.3069i	1.07175	+	0.841680i
$835$	−25.1095	−	14.4970i	−0.868951	−	0.501689i
$836$	−4.52224	−	18.5331i	−0.156405	−	0.640981i
$837$	−4.41030	−	4.41030i	−0.152442	−	0.152442i
$838$	19.4259	+	48.4301i	0.671057	+	1.67299i
$839$	−6.19456	+	23.1184i	−0.213860	+	0.798136i	0.772705	+	0.634766i	$0.218903\pi$
$839$	−6.19456	+	23.1184i	−0.213860	+	0.798136i	−0.986565	+	0.163371i	$0.947763\pi$
$840$	5.37582	−	11.8339i	0.185483	−	0.408309i
$841$	13.7267	+	23.7753i	0.473334	+	0.819839i
$842$	5.29751	+	44.0577i	0.182564	+	1.51833i
$843$	0.943032	−	0.252685i	0.0324798	−	0.00870293i
$844$	−10.2162	+	34.9654i	−0.351655	+	1.20356i
$845$	−24.4631	+	32.2012i	−0.841556	+	1.10775i
$846$	−16.6162	+	12.4560i	−0.571278	+	0.428248i
$847$	0.347303	+	1.29615i	0.0119335	+	0.0445364i
$848$	−13.0538	+	6.77380i	−0.448270	+	0.232613i
$849$	34.8553	−	20.1237i	1.19623	−	0.690644i
$850$	−2.49885	+	17.4624i	−0.0857097	+	0.598956i
$851$	−1.03076	−	0.276191i	−0.0353340	−	0.00946770i
$852$	−5.33512	+	8.77911i	−0.182778	+	0.300767i
$853$	−12.1913	+	12.1913i	−0.417422	+	0.417422i	−0.884314	−	0.466892i	$-0.845374\pi$
$853$	−12.1913	+	12.1913i	−0.417422	+	0.417422i	0.466892	+	0.884314i	$0.345374\pi$
$854$	6.09870	+	2.60681i	0.208693	+	0.0892032i
$855$	−16.4620	+	28.5130i	−0.562987	+	0.975123i
$856$	43.3993	−	31.0354i	1.48336	−	1.06077i
$857$		−	20.1694i		−	0.688974i	−0.938791	−	0.344487i	$-0.888053\pi$
$857$		−	20.1694i		−	0.688974i	0.938791	−	0.344487i	$-0.111947\pi$
$858$	37.6305	+	2.80010i	1.28468	+	0.0955937i
$859$		−	10.5286i		−	0.359231i	−0.983737	−	0.179616i	$-0.942515\pi$
$859$		−	10.5286i		−	0.359231i	0.983737	−	0.179616i	$-0.0574854\pi$
$860$	44.8777	+	1.00847i	1.53032	+	0.0343885i
$861$	−4.28080	+	7.41456i	−0.145889	+	0.252688i
$862$	17.2887	−	40.4473i	0.588854	−	1.37764i
$863$	−0.357134	+	0.357134i	−0.0121570	+	0.0121570i	−0.713159	−	0.701002i	$-0.752736\pi$
$863$	−0.357134	+	0.357134i	−0.0121570	+	0.0121570i	0.701002	+	0.713159i	$0.252736\pi$
$864$	0.731274	−	3.86341i	0.0248785	−	0.131436i
$865$	−68.7838	−	18.4306i	−2.33872	−	0.626658i
$866$	−15.1099	−	2.16220i	−0.513454	−	0.0734745i
$867$	21.4509	−	12.3847i	0.728511	−	0.420606i
$868$	7.64837	−	7.31218i	0.259603	−	0.248192i
$869$	−2.08918	−	7.79691i	−0.0708704	−	0.264492i
$870$	8.22195	+	10.9680i	0.278750	+	0.371850i
$871$	−24.0682	−	11.7971i	−0.815521	−	0.399730i
$872$	−11.0572	+	4.14931i	−0.374443	+	0.140513i
$873$	−15.0119	+	4.02243i	−0.508076	+	0.136138i
$874$	9.34761	−	1.12396i	0.316188	−	0.0380185i
$875$	0.296516	+	0.513580i	0.0100241	+	0.0173622i
$876$	−0.149834	−	0.273534i	−0.00506243	−	0.00924186i
$877$	8.27012	−	30.8645i	0.279262	−	1.04222i	−0.673669	−	0.739033i	$-0.735283\pi$
$877$	8.27012	−	30.8645i	0.279262	−	1.04222i	0.952931	−	0.303187i	$-0.0980508\pi$
$878$	17.0191	−	6.82656i	0.574366	−	0.230385i
$879$	−3.63013	−	3.63013i	−0.122441	−	0.122441i
$880$	36.7152	+	1.65092i	1.23767	+	0.0556526i
$881$	26.4430	+	15.2668i	0.890886	+	0.514353i	0.874232	−	0.485508i	$-0.161365\pi$
$881$	26.4430	+	15.2668i	0.890886	+	0.514353i	0.0166536	+	0.999861i	$0.494699\pi$
$882$	19.0439	−	24.2495i	0.641241	−	0.816523i
$883$	49.7844			1.67538			0.837689	−	0.546148i	$-0.183906\pi$
$883$	49.7844			1.67538			0.837689	+	0.546148i	$0.183906\pi$
$884$	−19.2136	+	0.872752i	−0.646223	+	0.0293538i
$885$	−54.9338			−1.84658
$886$	13.6708	−	17.4077i	0.459280	−	0.584824i
$887$	21.7002	+	12.5286i	0.728621	+	0.420669i	0.817917	−	0.575336i	$-0.195129\pi$
$887$	21.7002	+	12.5286i	0.728621	+	0.420669i	−0.0892967	+	0.996005i	$0.528462\pi$
$888$	2.83334	+	2.32990i	0.0950807	+	0.0781863i
$889$	5.03784	+	5.03784i	0.168964	+	0.168964i
$890$	−33.8799	+	13.5897i	−1.13566	+	0.455526i
$891$	6.18510	−	23.0831i	0.207209	−	0.773313i
$892$	6.22859	−	3.41185i	0.208549	−	0.114237i
$893$	7.23442	+	12.5304i	0.242091	+	0.419313i
$894$	18.2812	−	2.19813i	0.611414	−	0.0735166i
$895$	−39.7182	+	10.6425i	−1.32763	+	0.355739i
$896$	6.52483	+	1.38756i	0.217979	+	0.0463551i
$897$	−3.58913	+	18.2739i	−0.119838	+	0.610146i
$898$	−9.50433	−	12.6787i	−0.317164	−	0.423093i
$899$	2.88823	+	10.7790i	0.0963278	+	0.359500i
$900$	−21.1838	−	22.1578i	−0.706128	−	0.738593i
$901$	−8.49258	+	4.90319i	−0.282929	+	0.163349i
$902$	−23.9646	−	3.42930i	−0.797933	−	0.114183i
$903$	−10.2956	−	2.75869i	−0.342616	−	0.0918036i
$904$	−15.8851	+	1.54889i	−0.528331	+	0.0515152i
$905$	57.4558	−	57.4558i	1.90990	−	1.90990i
$906$	−7.24178	+	16.9423i	−0.240592	+	0.562871i
$907$	−25.1973	+	43.6429i	−0.836661	+	1.44914i	0.0560094	+	0.998430i	$0.482162\pi$
$907$	−25.1973	+	43.6429i	−0.836661	+	1.44914i	−0.892671	+	0.450710i	$0.851171\pi$
$908$	−0.783430	+	34.8633i	−0.0259990	+	1.15698i
$909$			29.4261i			0.976002i
$910$	7.08557	−	6.10412i	0.234884	−	0.202350i
$911$			7.50959i			0.248804i	0.992232	+	0.124402i	$0.0397012\pi$
$911$			7.50959i			0.248804i	−0.992232	+	0.124402i	$0.960299\pi$
$912$	−30.8537	−	9.77232i	−1.02167	−	0.323594i
$913$	−21.2708	+	36.8420i	−0.703959	+	1.21929i
$914$	−24.9869	−	10.6803i	−0.826495	−	0.353274i
$915$	43.8359	−	43.8359i	1.44917	−	1.44917i
$916$	−34.5329	−	20.9858i	−1.14100	−	0.693392i
$917$	−10.9171	−	2.92524i	−0.360516	−	0.0966000i
$918$	0.371400	−	2.59542i	0.0122580	−	0.0856616i
$919$	24.3508	−	14.0590i	0.803260	−	0.463762i	−0.0413499	−	0.999145i	$-0.513166\pi$
$919$	24.3508	−	14.0590i	0.803260	−	0.463762i	0.844610	+	0.535382i	$0.179832\pi$
$920$	−2.97211	+	17.8931i	−0.0979876	+	0.589917i
$921$	10.4855	+	39.1325i	0.345510	+	1.28946i
$922$	−27.7517	+	20.8035i	−0.913952	+	0.685126i
$923$	−6.13616	+	4.12148i	−0.201974	+	0.135660i
$924$	−8.37650	−	2.44745i	−0.275567	−	0.0805151i
$925$	2.33834	−	0.626555i	0.0768840	−	0.0206010i
$926$	−3.15229	−	26.2165i	−0.103591	−	0.861529i
$927$	15.7344	+	27.2528i	0.516787	+	0.895101i
$928$	−4.58924	+	5.33205i	−0.150649	+	0.175033i
$929$	−11.1025	+	41.4351i	−0.364261	+	1.35944i	0.504159	+	0.863611i	$0.331802\pi$
$929$	−11.1025	+	41.4351i	−0.364261	+	1.35944i	−0.868420	+	0.495829i	$0.834864\pi$
$930$	−36.8199	−	91.7944i	−1.20737	−	3.01006i
$931$	−15.1906	−	15.1906i	−0.497853	−	0.497853i
$932$	−25.8817	+	6.31534i	−0.847782	+	0.206866i
$933$	52.1278	+	30.0960i	1.70659	+	0.985300i
$934$	−25.1974	−	19.7883i	−0.824483	−	0.647492i
$935$	24.5064			0.801444
$936$	19.4294	−	27.1959i	0.635069	−	0.888927i
$937$	−0.397858			−0.0129975			−0.00649873	−	0.999979i	$-0.502069\pi$
$937$	−0.397858			−0.0129975			−0.00649873	+	0.999979i	$0.502069\pi$
$938$	4.87518	+	3.82863i	0.159180	+	0.125009i
$939$	−62.7093	−	36.2052i	−2.04644	−	1.18151i
$940$	−27.0802	+	6.60780i	−0.883259	+	0.215523i
$941$	−4.33123	−	4.33123i	−0.141194	−	0.141194i	0.632977	−	0.774171i	$-0.281833\pi$
$941$	−4.33123	−	4.33123i	−0.141194	−	0.141194i	−0.774171	+	0.632977i	$0.781833\pi$
$942$	−14.1941	−	35.3868i	−0.462469	−	1.15297i
$943$	3.09228	−	11.5405i	0.100698	−	0.375811i
$944$	−6.06630	−	27.5329i	−0.197441	−	0.896120i
$945$	0.637444	+	1.10409i	0.0207360	+	0.0359159i
$946$	−3.59797	−	29.9231i	−0.116980	−	0.972885i
$947$	7.47663	−	2.00336i	0.242958	−	0.0651003i	−0.135285	−	0.990807i	$-0.543195\pi$
$947$	7.47663	−	2.00336i	0.242958	−	0.0651003i	0.378243	+	0.925706i	$0.376528\pi$
$948$	−13.1447	−	3.84060i	−0.426919	−	0.124737i
$949$	−0.0152168	−	0.223894i	−0.000493959	−	0.00726790i
$950$	−17.0897	+	12.8110i	−0.554463	+	0.415642i
$951$	−0.0129322	−	0.0482638i	−0.000419357	−	0.00156506i
$952$	4.38792	+	0.728851i	0.142213	+	0.0236222i
$953$	−12.6528	+	7.30512i	−0.409866	+	0.236636i	−0.690732	−	0.723111i	$-0.742712\pi$
$953$	−12.6528	+	7.30512i	−0.409866	+	0.236636i	0.280866	+	0.959747i	$0.409378\pi$
$954$	2.41399	−	16.8695i	0.0781559	−	0.546169i
$955$	42.4813	+	11.3828i	1.37466	+	0.368340i
$956$	24.7736	+	15.0551i	0.801235	+	0.486915i
$957$	6.50773	−	6.50773i	0.210365	−	0.210365i
$958$	4.22327	+	1.80518i	0.136448	+	0.0583228i
$959$	−2.13959	+	3.70587i	−0.0690909	+	0.119669i
$960$	34.7416	−	51.7752i	1.12128	−	1.67104i
$961$		−	49.5168i		−	1.59731i
$962$	1.14646	+	2.37746i	0.0369635	+	0.0766523i
$963$			61.8243i			1.99226i
$964$	−0.622320	+	27.6938i	−0.0200436	+	0.891957i
$965$	−36.0825	+	62.4966i	−1.16154	+	2.01184i
$966$	1.69276	−	3.96026i	0.0544638	−	0.127419i
$967$	6.52725	−	6.52725i	0.209902	−	0.209902i	−0.594324	−	0.804226i	$-0.702580\pi$
$967$	6.52725	−	6.52725i	0.209902	−	0.209902i	0.804226	+	0.594324i	$0.202580\pi$
$968$	0.624687	+	6.40669i	0.0200782	+	0.205919i
$969$	−20.8451	−	5.58544i	−0.669642	−	0.179430i
$970$	−20.6507	−	2.95508i	−0.663054	−	0.0948821i
$971$	−33.9607	+	19.6072i	−1.08985	+	0.629226i	−0.933537	−	0.358481i	$-0.883295\pi$
$971$	−33.9607	+	19.6072i	−1.08985	+	0.629226i	−0.156315	+	0.987707i	$0.549962\pi$
$972$	−30.8986	−	32.3192i	−0.991072	−	1.03664i
$973$	−1.69495	−	6.32565i	−0.0543377	−	0.202791i
$974$	36.3804	+	48.5311i	1.16570	+	1.55504i
$975$	−13.6763	−	39.9724i	−0.437994	−	1.28014i
$976$	26.8114	+	17.1299i	0.858212	+	0.548313i
$977$	11.3491	−	3.04098i	0.363089	−	0.0972895i	−0.0726619	−	0.997357i	$-0.523149\pi$
$977$	11.3491	−	3.04098i	0.363089	−	0.0972895i	0.435751	+	0.900067i	$0.356483\pi$
$978$	−49.9948	+	6.01139i	−1.59866	+	0.192223i
$979$	12.2544	+	21.2252i	0.391652	+	0.678361i
$980$	36.2984	−	19.8833i	1.15951	−	0.635147i
$981$	3.54191	−	13.2186i	0.113084	−	0.422037i
$982$	−2.09197	+	0.839115i	−0.0667574	+	0.0267772i
$983$	17.0818	+	17.0818i	0.544823	+	0.544823i	0.924939	−	0.380116i	$-0.124116\pi$
$983$	17.0818	+	17.0818i	0.544823	+	0.544823i	−0.380116	+	0.924939i	$0.624116\pi$
$984$	−26.0859	+	31.7225i	−0.831588	+	1.01128i
$985$	−16.7194	−	9.65293i	−0.532723	−	0.307568i
$986$	−2.89730	+	3.68927i	−0.0922688	+	0.117490i
$987$	6.61878			0.210678
$988$	−17.1968	−	15.7024i	−0.547102	−	0.499559i
$989$	14.8742			0.472973
$990$	−26.3030	+	33.4928i	−0.835963	+	1.06447i
$991$	24.9439	+	14.4013i	0.792368	+	0.457474i	0.840796	−	0.541353i	$-0.182088\pi$
$991$	24.9439	+	14.4013i	0.792368	+	0.457474i	−0.0484275	+	0.998827i	$0.515421\pi$
$992$	41.9415	−	28.5910i	1.33164	−	0.907765i
$993$	−7.48456	−	7.48456i	−0.237515	−	0.237515i
$994$	1.58660	−	0.636406i	0.0503240	−	0.0201856i
$995$	−2.42688	+	9.05724i	−0.0769373	+	0.287134i
$996$	34.6730	+	63.2982i	1.09866	+	2.00568i
$997$	−26.9659	−	46.7063i	−0.854019	−	1.47920i	−0.877552	−	0.479481i	$-0.840825\pi$
$997$	−26.9659	−	46.7063i	−0.854019	−	1.47920i	0.0235336	−	0.999723i	$-0.492508\pi$
$998$	−5.75298	+	0.691740i	−0.182107	+	0.0218966i
$999$	−0.347544	+	0.0931241i	−0.0109958	+	0.00294632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.2.l.b.7.1	✓	16
3.2	odd	2		468.2.cb.f.163.4		16
4.3	odd	2	inner	52.2.l.b.7.2	yes	16
8.3	odd	2		832.2.bu.n.319.1		16
8.5	even	2		832.2.bu.n.319.4		16
12.11	even	2		468.2.cb.f.163.3		16
13.2	odd	12	inner	52.2.l.b.15.2	yes	16
13.3	even	3		676.2.l.m.427.4		16
13.4	even	6		676.2.f.i.99.4		16
13.5	odd	4		676.2.l.m.19.2		16
13.6	odd	12		676.2.f.h.239.8		16
13.7	odd	12		676.2.f.i.239.1		16
13.8	odd	4		676.2.l.i.19.3		16
13.9	even	3		676.2.f.h.99.5		16
13.10	even	6		676.2.l.i.427.1		16
13.11	odd	12		676.2.l.k.587.3		16
13.12	even	2		676.2.l.k.319.4		16
39.2	even	12		468.2.cb.f.379.3		16
52.3	odd	6		676.2.l.m.427.2		16
52.7	even	12		676.2.f.i.239.4		16
52.11	even	12		676.2.l.k.587.4		16
52.15	even	12	inner	52.2.l.b.15.1	yes	16
52.19	even	12		676.2.f.h.239.5		16
52.23	odd	6		676.2.l.i.427.3		16
52.31	even	4		676.2.l.m.19.4		16
52.35	odd	6		676.2.f.h.99.8		16
52.43	odd	6		676.2.f.i.99.1		16
52.47	even	4		676.2.l.i.19.1		16
52.51	odd	2		676.2.l.k.319.3		16
104.67	even	12		832.2.bu.n.639.4		16
104.93	odd	12		832.2.bu.n.639.1		16
156.119	odd	12		468.2.cb.f.379.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.7.1	✓	16	1.1	even	1	trivial
52.2.l.b.7.2	yes	16	4.3	odd	2	inner
52.2.l.b.15.1	yes	16	52.15	even	12	inner
52.2.l.b.15.2	yes	16	13.2	odd	12	inner
468.2.cb.f.163.3		16	12.11	even	2
468.2.cb.f.163.4		16	3.2	odd	2
468.2.cb.f.379.3		16	39.2	even	12
468.2.cb.f.379.4		16	156.119	odd	12
676.2.f.h.99.5		16	13.9	even	3
676.2.f.h.99.8		16	52.35	odd	6
676.2.f.h.239.5		16	52.19	even	12
676.2.f.h.239.8		16	13.6	odd	12
676.2.f.i.99.1		16	52.43	odd	6
676.2.f.i.99.4		16	13.4	even	6
676.2.f.i.239.1		16	13.7	odd	12
676.2.f.i.239.4		16	52.7	even	12
676.2.l.i.19.1		16	52.47	even	4
676.2.l.i.19.3		16	13.8	odd	4
676.2.l.i.427.1		16	13.10	even	6
676.2.l.i.427.3		16	52.23	odd	6
676.2.l.k.319.3		16	52.51	odd	2
676.2.l.k.319.4		16	13.12	even	2
676.2.l.k.587.3		16	13.11	odd	12
676.2.l.k.587.4		16	52.11	even	12
676.2.l.m.19.2		16	13.5	odd	4
676.2.l.m.19.4		16	52.31	even	4
676.2.l.m.427.2		16	52.3	odd	6
676.2.l.m.427.4		16	13.3	even	3
832.2.bu.n.319.1		16	8.3	odd	2
832.2.bu.n.319.4		16	8.5	even	2
832.2.bu.n.639.1		16	104.93	odd	12
832.2.bu.n.639.4		16	104.67	even	12

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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	52.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11223 - 0.873468i) q^{2} +(-2.16981 - 1.25274i) q^{3} +(0.474107 + 1.94299i) q^{4} +(-2.19962 - 2.19962i) q^{5} +(1.31910 + 3.28859i) q^{6} +(0.152604 - 0.569525i) q^{7} +(1.16983 - 2.57517i) q^{8} +(1.63871 + 2.83834i) q^{9} +O(q^{10})\)	\(q+(-1.11223 - 0.873468i) q^{2} +(-2.16981 - 1.25274i) q^{3} +(0.474107 + 1.94299i) q^{4} +(-2.19962 - 2.19962i) q^{5} +(1.31910 + 3.28859i) q^{6} +(0.152604 - 0.569525i) q^{7} +(1.16983 - 2.57517i) q^{8} +(1.63871 + 2.83834i) q^{9} +(0.525184 + 4.36778i) q^{10} +(2.85302 - 0.764465i) q^{11} +(1.40534 - 4.80986i) q^{12} +(2.37076 - 2.71652i) q^{13} +(-0.667192 + 0.500148i) q^{14} +(2.01721 + 7.52831i) q^{15} +(-3.55045 + 1.84237i) q^{16} +(-2.30986 + 1.33360i) q^{17} +(0.656570 - 4.58824i) q^{18} +(-3.11932 - 0.835818i) q^{19} +(3.23099 - 5.31671i) q^{20} +(-1.04459 + 1.04459i) q^{21} +(-3.84095 - 1.64176i) q^{22} +(1.03076 - 1.78533i) q^{23} +(-5.76432 + 4.12214i) q^{24} +4.67667i q^{25} +(-5.00963 + 0.950604i) q^{26} -0.695088i q^{27} +(1.17893 + 0.0264924i) q^{28} +(-0.621816 + 1.07702i) q^{29} +(4.33215 - 10.1352i) q^{30} +(6.34495 - 6.34495i) q^{31} +(5.55816 + 1.05206i) q^{32} +(-7.14819 - 1.91535i) q^{33} +(3.73394 + 0.534321i) q^{34} +(-1.58841 + 0.917069i) q^{35} +(-4.73794 + 4.52968i) q^{36} +(-0.133975 - 0.500000i) q^{37} +(2.73933 + 3.65425i) q^{38} +(-8.54720 + 2.92438i) q^{39} +(-8.23758 + 3.09122i) q^{40} +(5.59808 - 1.50000i) q^{41} +(2.07423 - 0.249407i) q^{42} +(3.60759 + 6.24853i) q^{43} +(2.83799 + 5.18097i) q^{44} +(2.63871 - 9.84781i) q^{45} +(-2.70587 + 1.08536i) q^{46} +(-3.16813 - 3.16813i) q^{47} +(10.0118 + 0.450187i) q^{48} +(5.76111 + 3.32618i) q^{49} +(4.08492 - 5.20153i) q^{50} +6.68260 q^{51} +(6.40217 + 3.31846i) q^{52} +3.67667 q^{53} +(-0.607137 + 0.773097i) q^{54} +(-7.95711 - 4.59404i) q^{55} +(-1.28810 - 1.05923i) q^{56} +(5.72126 + 5.72126i) q^{57} +(1.63234 - 0.654753i) q^{58} +(-1.82424 + 6.80816i) q^{59} +(-13.6711 + 7.48864i) q^{60} +(-3.97705 - 6.88845i) q^{61} +(-12.5991 + 1.51493i) q^{62} +(1.86658 - 0.500148i) q^{63} +(-5.26301 - 6.02501i) q^{64} +(-11.1901 + 0.760530i) q^{65} +(6.27743 + 8.37403i) q^{66} +(-1.92408 - 7.18077i) q^{67} +(-3.68629 - 3.85577i) q^{68} +(-4.47310 + 2.58254i) q^{69} +(2.56771 + 0.367435i) q^{70} +(-1.98027 - 0.530611i) q^{71} +(9.22621 - 0.899605i) q^{72} +(0.0440105 - 0.0440105i) q^{73} +(-0.287724 + 0.673137i) q^{74} +(5.85865 - 10.1475i) q^{75} +(0.145100 - 6.45708i) q^{76} -1.74153i q^{77} +(12.0608 + 4.21313i) q^{78} -2.73286i q^{79} +(11.8622 + 3.75711i) q^{80} +(4.04538 - 7.00680i) q^{81} +(-7.53655 - 3.22140i) q^{82} +(-10.1844 + 10.1844i) q^{83} +(-2.52487 - 1.53438i) q^{84} +(8.01422 + 2.14740i) q^{85} +(1.44543 - 10.1009i) q^{86} +(2.69844 - 1.55795i) q^{87} +(1.36892 - 8.24131i) q^{88} +(2.14761 + 8.01501i) q^{89} +(-11.5366 + 8.64819i) q^{90} +(-1.18534 - 1.76476i) q^{91} +(3.95757 + 1.15632i) q^{92} +(-21.7159 + 5.81876i) q^{93} +(0.756425 + 6.29094i) q^{94} +(5.02283 + 8.69980i) q^{95} +(-10.7422 - 9.24570i) q^{96} +(-1.22731 + 4.58039i) q^{97} +(-3.50236 - 8.73161i) q^{98} +(6.84510 + 6.84510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9	\( 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9} - 12 q^{13} + 8 q^{14} - 2 q^{16} + 12 q^{17} - 6 q^{18} + 2 q^{20} - 28 q^{21} + 10 q^{24} + 16 q^{26} + 12 q^{28} - 8 q^{29} + 42 q^{30} + 28 q^{32} - 20 q^{33} + 14 q^{34} - 6 q^{36} - 16 q^{37} - 40 q^{40} + 48 q^{41} - 28 q^{42} - 8 q^{44} + 20 q^{45} - 46 q^{46} - 10 q^{48} + 60 q^{49} + 10 q^{50} - 32 q^{52} - 32 q^{53} - 16 q^{54} - 60 q^{56} + 12 q^{57} - 48 q^{58} - 24 q^{60} + 4 q^{61} - 18 q^{62} - 8 q^{65} + 56 q^{66} + 16 q^{68} - 12 q^{69} + 28 q^{70} + 56 q^{72} + 20 q^{73} + 4 q^{74} + 22 q^{76} + 68 q^{78} + 44 q^{80} + 48 q^{81} + 84 q^{84} + 20 q^{85} + 16 q^{86} + 36 q^{88} - 52 q^{89} - 12 q^{92} - 92 q^{93} - 38 q^{94} - 72 q^{96} - 28 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9 - 12 * q^13 + 8 * q^14 - 2 * q^16 + 12 * q^17 - 6 * q^18 + 2 * q^20 - 28 * q^21 + 10 * q^24 + 16 * q^26 + 12 * q^28 - 8 * q^29 + 42 * q^30 + 28 * q^32 - 20 * q^33 + 14 * q^34 - 6 * q^36 - 16 * q^37 - 40 * q^40 + 48 * q^41 - 28 * q^42 - 8 * q^44 + 20 * q^45 - 46 * q^46 - 10 * q^48 + 60 * q^49 + 10 * q^50 - 32 * q^52 - 32 * q^53 - 16 * q^54 - 60 * q^56 + 12 * q^57 - 48 * q^58 - 24 * q^60 + 4 * q^61 - 18 * q^62 - 8 * q^65 + 56 * q^66 + 16 * q^68 - 12 * q^69 + 28 * q^70 + 56 * q^72 + 20 * q^73 + 4 * q^74 + 22 * q^76 + 68 * q^78 + 44 * q^80 + 48 * q^81 + 84 * q^84 + 20 * q^85 + 16 * q^86 + 36 * q^88 - 52 * q^89 - 12 * q^92 - 92 * q^93 - 38 * q^94 - 72 * q^96 - 28 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

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