LMFDB - Embedded newform 52.2.l.b.7.2

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			7.2
Root			$-0.873468 + 1.11223i$ of defining polynomial
Character	$\chi$	$=$	52.7
Dual form			52.2.l.b.15.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.526485 + 1.31256i) q^{2} +(2.16981 + 1.25274i) q^{3} +(-1.44563 - 1.38209i) q^{4} +(-2.19962 - 2.19962i) q^{5} +(-2.78667 + 2.18846i) q^{6} +(-0.152604 + 0.569525i) q^{7} +(2.57517 - 1.16983i) q^{8} +(1.63871 + 2.83834i) q^{9} +O(q^{10})$	\(q+(-0.526485 + 1.31256i) q^{2} +(2.16981 + 1.25274i) q^{3} +(-1.44563 - 1.38209i) q^{4} +(-2.19962 - 2.19962i) q^{5} +(-2.78667 + 2.18846i) q^{6} +(-0.152604 + 0.569525i) q^{7} +(2.57517 - 1.16983i) q^{8} +(1.63871 + 2.83834i) q^{9} +(4.04520 - 1.72907i) 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} +(0.179681 + 3.99596i) q^{16} +(-2.30986 + 1.33360i) q^{17} +(-4.58824 + 0.656570i) q^{18} +(3.11932 + 0.835818i) q^{19} +(0.139770 + 6.21990i) q^{20} +(-1.04459 + 1.04459i) q^{21} +(0.498666 - 4.14724i) q^{22} +(-1.03076 + 1.78533i) q^{23} +(7.05312 + 0.687717i) q^{24} +4.67667i q^{25} +(2.31742 + 4.54198i) q^{26} +0.695088i q^{27} +(1.00774 - 0.612410i) q^{28} +(-0.621816 + 1.07702i) q^{29} +(10.9434 + 1.31584i) q^{30} +(-6.34495 + 6.34495i) q^{31} +(-5.33954 - 1.86797i) q^{32} +(-7.14819 - 1.91535i) q^{33} +(-0.534321 - 3.73394i) q^{34} +(1.58841 - 0.917069i) q^{35} +(1.55385 - 6.36802i) 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} +(-0.821125 - 1.92104i) q^{42} +(-3.60759 - 6.24853i) q^{43} +(5.18097 + 2.83799i) q^{44} +(2.63871 - 9.84781i) q^{45} +(-1.80067 - 2.29288i) q^{46} +(3.16813 + 3.16813i) q^{47} +(-4.61603 + 8.89557i) q^{48} +(5.76111 + 3.32618i) q^{49} +(-6.13841 - 2.46219i) q^{50} -6.68260 q^{51} +(-7.18170 + 0.650478i) q^{52} +3.67667 q^{53} +(-0.912345 - 0.365953i) q^{54} +(7.95711 + 4.59404i) q^{55} +(0.273265 + 1.64514i) q^{56} +(5.72126 + 5.72126i) q^{57} +(-1.08627 - 1.38320i) q^{58} +(1.82424 - 6.80816i) q^{59} +(-7.48864 + 13.6711i) q^{60} +(-3.97705 - 6.88845i) q^{61} +(-4.98761 - 11.6686i) 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} +(5.18234 + 1.26453i) q^{68} +(-4.47310 + 2.58254i) q^{69} +(0.367435 + 2.56771i) q^{70} +(1.98027 + 0.530611i) q^{71} +(7.54033 + 5.39219i) q^{72} +(0.0440105 - 0.0440105i) q^{73} +(0.726816 + 0.0873926i) q^{74} +(-5.85865 + 10.1475i) q^{75} +(-3.35420 - 5.51944i) q^{76} -1.74153i q^{77} +(-0.661547 + 12.7583i) q^{78} +2.73286i q^{79} +(8.39437 - 9.18484i) q^{80} +(4.04538 - 7.00680i) q^{81} +(-0.978460 + 8.13754i) q^{82} +(10.1844 - 10.1844i) q^{83} +(2.95379 - 0.0663761i) q^{84} +(8.01422 + 2.14740i) q^{85} +(10.1009 - 1.44543i) q^{86} +(-2.69844 + 1.55795i) q^{87} +(-6.45273 + 5.30617i) 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} +(-5.82633 + 2.49039i) q^{94} +(-5.02283 - 8.69980i) q^{95} +(-9.24570 - 10.7422i) q^{96} +(-1.22731 + 4.58039i) q^{97} +(-7.39894 + 5.81062i) 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 $

$2$	−0.526485	+	1.31256i	−0.372281	+	0.928120i
$2$	−0.526485	+	1.31256i	−0.372281	+	0.928120i
$3$	2.16981	+	1.25274i	1.25274	+	0.723270i	0.971653	−	0.236413i	$-0.0759717\pi$
$3$	2.16981	+	1.25274i	1.25274	+	0.723270i	0.281087	+	0.959682i	$0.409305\pi$
$4$	−1.44563	−	1.38209i	−0.722814	−	0.691043i
$5$	−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	$0.994853\pi$
$6$	−2.78667	+	2.18846i	−1.13765	+	0.893434i
$7$	−0.152604	+	0.569525i	−0.0576788	+	0.215260i	−0.988750	−	0.149577i	$-0.952209\pi$
$7$	−0.152604	+	0.569525i	−0.0576788	+	0.215260i	0.931071	+	0.364837i	$0.118875\pi$
$8$	2.57517	−	1.16983i	0.910460	−	0.413596i
$9$	1.63871	+	2.83834i	0.546238	+	0.946112i
$10$	4.04520	−	1.72907i	1.27921	−	0.546780i
$11$	−2.85302	+	0.764465i	−0.860219	+	0.230495i	−0.661854	−	0.749633i	$-0.730230\pi$
$11$	−2.85302	+	0.764465i	−0.860219	+	0.230495i	−0.198365	+	0.980128i	$0.563563\pi$
$12$	−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
$16$	0.179681	+	3.99596i	0.0449202	+	0.998991i
$17$	−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	$0.438174\pi$
$18$	−4.58824	+	0.656570i	−1.08146	+	0.154755i
$19$	3.11932	+	0.835818i	0.715620	+	0.191750i	0.598217	−	0.801334i	$-0.295876\pi$
$19$	3.11932	+	0.835818i	0.715620	+	0.191750i	0.117404	+	0.993084i	$0.462543\pi$
$20$	0.139770	+	6.21990i	0.0312536	+	1.39081i
$21$	−1.04459	+	1.04459i	−0.227948	+	0.227948i
$22$	0.498666	−	4.14724i	0.106316	−	0.884195i
$23$	−1.03076	+	1.78533i	−0.214928	+	0.372266i	−0.953250	−	0.302182i	$-0.902285\pi$
$23$	−1.03076	+	1.78533i	−0.214928	+	0.372266i	0.738322	+	0.674448i	$0.235618\pi$
$24$	7.05312	+	0.687717i	1.43971	+	0.140380i
$25$			4.67667i			0.935334i
$26$	2.31742	+	4.54198i	0.454484	+	0.890755i
$27$			0.695088i			0.133770i
$28$	1.00774	−	0.612410i	0.190445	−	0.115735i
$29$	−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	$0.203504\pi$
$30$	10.9434	+	1.31584i	1.99798	+	0.240238i
$31$	−6.34495	+	6.34495i	−1.13959	+	1.13959i	−0.151062	+	0.988524i	$0.548269\pi$
$31$	−6.34495	+	6.34495i	−1.13959	+	1.13959i	−0.988524	+	0.151062i	$0.951731\pi$
$32$	−5.33954	−	1.86797i	−0.943906	−	0.330214i
$33$	−7.14819	−	1.91535i	−1.24434	−	0.333420i
$34$	−0.534321	−	3.73394i	−0.0916354	−	0.640366i
$35$	1.58841	−	0.917069i	0.268490	−	0.155013i
$36$	1.55385	−	6.36802i	0.258975	−	1.06134i
$37$	−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	$0.267179\pi$
$42$	−0.821125	−	1.92104i	−0.126702	−	0.296423i
$43$	−3.60759	−	6.24853i	−0.550152	−	0.952892i	−0.998263	−	0.0589139i	$-0.981236\pi$
$43$	−3.60759	−	6.24853i	−0.550152	−	0.952892i	0.448111	−	0.893978i	$-0.352097\pi$
$44$	5.18097	+	2.83799i	0.781060	+	0.427843i
$45$	2.63871	−	9.84781i	0.393356	−	1.46803i
$46$	−1.80067	−	2.29288i	−0.265494	−	0.338067i
$47$	3.16813	+	3.16813i	0.462119	+	0.462119i	0.899350	−	0.437230i	$-0.144041\pi$
$47$	3.16813	+	3.16813i	0.462119	+	0.462119i	−0.437230	+	0.899350i	$0.644041\pi$
$48$	−4.61603	+	8.89557i	−0.666266	+	1.28396i
$49$	5.76111	+	3.32618i	0.823015	+	0.475168i
$50$	−6.13841	−	2.46219i	−0.868102	−	0.348207i
$51$	−6.68260			−0.935751
$52$	−7.18170	+	0.650478i	−0.995923	+	0.0902051i
$53$	3.67667			0.505030			0.252515	−	0.967593i	$-0.418742\pi$
$53$	3.67667			0.505030			0.252515	+	0.967593i	$0.418742\pi$
$54$	−0.912345	−	0.365953i	−0.124154	−	0.0497999i
$55$	7.95711	+	4.59404i	1.07294	+	0.619460i
$56$	0.273265	+	1.64514i	0.0365166	+	0.219842i
$57$	5.72126	+	5.72126i	0.757799	+	0.757799i
$58$	−1.08627	−	1.38320i	−0.142635	−	0.181624i
$59$	1.82424	−	6.80816i	0.237496	−	0.886347i	−0.739512	−	0.673143i	$-0.764944\pi$
$59$	1.82424	−	6.80816i	0.237496	−	0.886347i	0.977008	−	0.213203i	$-0.0683897\pi$
$60$	−7.48864	+	13.6711i	−0.966779	+	1.76493i
$61$	−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	$-0.336729\pi$
$62$	−4.98761	−	11.6686i	−0.633427	−	1.48192i
$63$	−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	$0.0667088\pi$
$67$	1.92408	+	7.18077i	0.235064	+	0.877270i	−0.743056	+	0.669229i	$0.766624\pi$
$68$	5.18234	+	1.26453i	0.628451	+	0.153347i
$69$	−4.47310	+	2.58254i	−0.538498	+	0.310902i
$70$	0.367435	+	2.56771i	0.0439169	+	0.306900i
$71$	1.98027	+	0.530611i	0.235014	+	0.0629719i	0.374404	−	0.927266i	$-0.377847\pi$
$71$	1.98027	+	0.530611i	0.235014	+	0.0629719i	−0.139390	+	0.990238i	$0.544514\pi$
$72$	7.54033	+	5.39219i	0.888636	+	0.635475i
$73$	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	$0.248841\pi$
$74$	0.726816	+	0.0873926i	0.0844906	+	0.0101592i
$75$	−5.85865	+	10.1475i	−0.676499	+	1.17173i
$76$	−3.35420	−	5.51944i	−0.384753	−	0.633124i
$77$		−	1.74153i		−	0.198466i
$78$	−0.661547	+	12.7583i	−0.0749055	+	1.44460i
$79$			2.73286i			0.307471i	0.988112	+	0.153735i	$0.0491303\pi$
$79$			2.73286i			0.307471i	−0.988112	+	0.153735i	$0.950870\pi$
$80$	8.39437	−	9.18484i	0.938520	−	1.02690i
$81$	4.04538	−	7.00680i	0.449486	−	0.778533i
$82$	−0.978460	+	8.13754i	−0.108053	+	0.898641i
$83$	10.1844	−	10.1844i	1.11789	−	1.11789i	0.125834	−	0.992051i	$-0.459839\pi$
$83$	10.1844	−	10.1844i	1.11789	−	1.11789i	0.992051	−	0.125834i	$-0.0401606\pi$
$84$	2.95379	−	0.0663761i	0.322285	−	0.00724222i
$85$	8.01422	+	2.14740i	0.869264	+	0.232919i
$86$	10.1009	−	1.44543i	1.08921	−	0.155864i
$87$	−2.69844	+	1.55795i	−0.289304	+	0.167029i
$88$	−6.45273	+	5.30617i	−0.687863	+	0.565640i
$89$	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
$94$	−5.82633	+	2.49039i	−0.600940	+	0.256864i
$95$	−5.02283	−	8.69980i	−0.515332	−	0.892581i
$96$	−9.24570	−	10.7422i	−0.943635	−	1.09637i
$97$	−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	$0.160722\pi$
$98$	−7.39894	+	5.81062i	−0.747406	+	0.586961i
$99$	−6.84510	−	6.84510i	−0.687958	−	0.687958i
$100$	6.46356	−	6.76073i	0.646356	−	0.676073i
$101$	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	$0.519268\pi$
$102$	3.51828	−	8.77131i	0.348362	−	0.868489i
$103$	−9.60170			−0.946084			−0.473042	−	0.881040i	$-0.656844\pi$
$103$	−9.60170			−0.946084			−0.473042	+	0.881040i	$0.656844\pi$
$104$	2.92727	−	9.76889i	0.287042	−	0.957918i
$105$	4.59540			0.448465
$106$	−1.93571	+	4.82585i	−0.188013	+	0.468728i
$107$	−16.3364	−	9.43183i	−1.57930	−	0.911809i	−0.994957	−	0.100302i	$-0.968019\pi$
$107$	−16.3364	−	9.43183i	−1.57930	−	0.911809i	−0.584343	−	0.811507i	$-0.698648\pi$
$108$	0.960671	−	1.00484i	0.0924406	−	0.0966907i
$109$	−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	$0.814084\pi$
$110$	−10.2192	+	8.02549i	−0.974367	+	0.765201i
$111$	0.335671	−	1.25274i	0.0318604	−	0.118905i
$112$	−2.30322	−	0.507466i	−0.217634	−	0.0479510i
$113$	−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	$0.918843\pi$
$114$	−10.5216	+	4.49734i	−0.985443	+	0.421215i
$115$	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
$120$	−14.0015	−	17.0269i	−1.27815	−	1.55434i
$121$	−1.97094	+	1.13792i	−0.179177	+	0.103448i
$122$	11.1354	−	1.59345i	1.00815	−	0.144264i
$123$	14.0259	+	3.75822i	1.26467	+	0.338867i
$124$	17.9417	−	0.403176i	1.61121	−	0.0362063i
$125$	−0.711203	+	0.711203i	−0.0636119	+	0.0636119i
$126$	0.326250	−	2.71331i	0.0290647	−	0.241721i
$127$	6.04172	−	10.4646i	0.536116	−	0.928580i	−0.462993	−	0.886362i	$-0.653224\pi$
$127$	6.04172	−	10.4646i	0.536116	−	0.928580i	0.999108	−	0.0422176i	$-0.0134423\pi$
$128$	5.13729	+	10.0801i	0.454077	+	0.890962i
$129$		−	18.0775i		−	1.59163i
$130$	4.89317	−	15.0881i	0.429160	−	1.32331i
$131$			19.1689i			1.67479i	0.546597	+	0.837396i	$0.315923\pi$
$131$			19.1689i			1.67479i	−0.546597	+	0.837396i	$0.684077\pi$
$132$	7.68645	+	12.6483i	0.669019	+	1.10089i
$133$	−0.952039	+	1.64898i	−0.0825523	+	0.142985i
$134$	−10.4382	−	1.25509i	−0.901722	−	0.108423i
$135$	1.52893	−	1.52893i	0.131589	−	0.131589i
$136$	−4.38820	+	6.13637i	−0.376285	+	0.526189i
$137$	−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	$0.683672\pi$
$138$	−1.03473	−	7.23088i	−0.0880819	−	0.615533i
$139$	−9.61885	+	5.55344i	−0.815860	+	0.471037i	−0.848987	−	0.528414i	$-0.822787\pi$
$139$	−9.61885	+	5.55344i	−0.815860	+	0.471037i	0.0331268	+	0.999451i	$0.489453\pi$
$140$	−3.56372	−	0.869578i	−0.301189	−	0.0734927i
$141$	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
$146$	0.0345956	+	0.0809372i	0.00286315	+	0.00669841i
$147$	8.33367	+	14.4343i	0.687349	+	1.19052i
$148$	−0.497365	+	0.907978i	−0.0408832	+	0.0746354i
$149$	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	$0.0150558\pi$
$150$	−10.2347	−	13.0323i	−0.835659	−	1.06408i
$151$	−3.67697	−	3.67697i	−0.299227	−	0.299227i	0.541484	−	0.840711i	$-0.317863\pi$
$151$	−3.67697	−	3.67697i	−0.299227	−	0.299227i	−0.840711	+	0.541484i	$0.817863\pi$
$152$	9.01054	−	1.49669i	0.730851	−	0.121397i
$153$	−7.57039	−	4.37076i	−0.612029	−	0.353355i
$154$	2.28586	+	0.916888i	0.184200	+	0.0738849i
$155$	27.9130			2.24202
$156$	−16.3978	−	7.58539i	−1.31288	−	0.607318i
$157$	−10.7605			−0.858780			−0.429390	−	0.903119i	$-0.641271\pi$
$157$	−10.7605			−0.858780			−0.429390	+	0.903119i	$0.641271\pi$
$158$	−3.58704	−	1.43881i	−0.285370	−	0.114465i
$159$	7.97767	+	4.60591i	0.632671	+	0.365272i
$160$	7.63614	+	15.8538i	0.603690	+	1.25335i
$161$	−0.859490	−	0.859490i	−0.0677373	−	0.0677373i
$162$	7.06701	+	8.99877i	0.555237	+	0.707010i
$163$	3.67817	−	13.7271i	0.288097	−	1.07519i	−0.658450	−	0.752625i	$-0.728787\pi$
$163$	3.67817	−	13.7271i	0.288097	−	1.07519i	0.946547	−	0.322567i	$-0.104546\pi$
$164$	−10.1659	−	5.56858i	−0.793821	−	0.434833i
$165$	11.5103	+	19.9364i	0.896073	+	1.55204i
$166$	8.00572	+	18.7296i	0.621365	+	1.45370i
$167$	−9.00303	+	2.41236i	−0.696676	+	0.186674i	−0.589741	−	0.807592i	$-0.700770\pi$
$167$	−9.00303	+	2.41236i	−0.696676	+	0.186674i	−0.106935	+	0.994266i	$0.534104\pi$
$168$	−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
$172$	−3.42077	+	14.0191i	−0.260831	+	1.06894i
$173$	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	$-0.00268676\pi$
$174$	−0.624210	−	4.36210i	−0.0473213	−	0.330690i
$175$	−2.66348	−	0.713678i	−0.201340	−	0.0539490i
$176$	−3.56741	−	11.2632i	−0.268904	−	0.848997i
$177$	12.4871	−	12.4871i	0.938588	−	0.938588i
$178$	−11.6509	−	1.40090i	−0.873269	−	0.105002i
$179$	−6.60927	+	11.4476i	−0.494000	+	0.855633i	−0.999976	−	0.00691464i	$-0.997799\pi$
$179$	−6.60927	+	11.4476i	−0.494000	+	0.855633i	0.505976	+	0.862547i	$0.331132\pi$
$180$	−17.4251	+	10.5893i	−1.29879	+	0.789283i
$181$			26.1208i			1.94154i	0.240009	+	0.970771i	$0.422849\pi$
$181$			26.1208i			1.94154i	−0.240009	+	0.970771i	$0.577151\pi$
$182$	−2.94042	+	0.626708i	−0.217958	+	0.0464547i
$183$		−	19.9288i		−	1.47318i
$184$	−0.565856	+	5.80333i	−0.0417155	+	0.427827i
$185$	−0.805117	+	1.39450i	−0.0591934	+	0.102526i
$186$	3.79562	−	31.5669i	0.278308	−	2.31460i
$187$	5.57059	−	5.57059i	0.407362	−	0.407362i
$188$	−0.201312	−	8.95856i	−0.0146822	−	0.653370i
$189$	−0.395870	−	0.106073i	−0.0287953	−	0.00771568i
$190$	14.0635	−	2.01246i	1.02027	−	0.145999i
$191$	12.2440	−	7.06905i	0.885942	−	0.511499i	0.0133290	−	0.999911i	$-0.495757\pi$
$191$	12.2440	−	7.06905i	0.885942	−	0.511499i	0.872613	+	0.488412i	$0.162424\pi$
$192$	18.9675	−	6.47994i	1.36886	−	0.467649i
$193$	−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	$0.345706\pi$
$198$	12.5884	−	5.38076i	0.894621	−	0.382394i
$199$	1.50716	+	2.61048i	0.106840	+	0.185052i	0.914488	−	0.404612i	$-0.132593\pi$
$199$	1.50716	+	2.61048i	0.106840	+	0.185052i	−0.807649	+	0.589664i	$0.799260\pi$
$200$	5.47090	+	12.0432i	0.386851	+	0.851585i
$201$	−4.82075	+	17.9913i	−0.340029	+	1.26901i
$202$	−9.98605	+	7.84236i	−0.702616	+	0.551786i
$203$	−0.518497	−	0.518497i	−0.0363913	−	0.0363913i
$204$	9.66055	+	9.23592i	0.676374	+	0.646644i
$205$	−15.6131	−	9.01422i	−1.09046	−	0.629580i
$206$	5.05515	−	12.6028i	0.352209	−	0.878079i
$207$	−6.75647			−0.469607
$208$	11.2811	+	8.98538i	0.782203	+	0.623024i
$209$	−9.53844			−0.659788
$210$	−2.41940	+	6.03173i	−0.166955	+	0.416229i
$211$	−15.7735	−	9.10682i	−1.08589	−	0.626940i	−0.153412	−	0.988162i	$-0.549026\pi$
$211$	−15.7735	−	9.10682i	−1.08589	−	0.626940i	−0.932480	+	0.361223i	$0.882359\pi$
$212$	−5.31510	−	5.08147i	−0.365042	−	0.348997i
$213$	3.63208	+	3.63208i	0.248866	+	0.248866i
$214$	20.9807	−	16.4768i	1.43421	−	1.12633i
$215$	−5.80907	+	21.6797i	−0.396175	+	1.47855i
$216$	0.813133	+	1.78997i	0.0553267	+	0.121792i
$217$	−2.64534	−	4.58187i	−0.179578	−	0.311038i
$218$	5.42982	−	2.32090i	0.367754	−	0.157191i
$219$	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	0.989846	−	0.142141i	$-0.0453986\pi$
$223$	0.919045	+	3.42992i	0.0615438	+	0.229685i	−0.928303	+	0.371826i	$0.878732\pi$
$224$	1.87869	−	2.75594i	0.125525	−	0.184139i
$225$	−13.2740	+	7.66372i	−0.884931	+	0.510915i
$226$	7.89976	−	1.13044i	0.525484	−	0.0751960i
$227$	−16.8419	−	4.51279i	−1.11784	−	0.299524i	−0.347831	−	0.937557i	$-0.613082\pi$
$227$	−16.8419	−	4.51279i	−1.11784	−	0.299524i	−0.770009	+	0.638033i	$0.779748\pi$
$228$	−0.363545	−	16.1781i	−0.0240764	−	1.07142i
$229$	−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	$0.482671\pi$
$230$	−1.08268	+	9.00426i	−0.0713895	+	0.593723i
$231$	2.18168	−	3.77878i	0.143544	−	0.248626i
$232$	−0.341359	+	3.50092i	−0.0224113	+	0.229847i
$233$			13.3205i			0.872655i	0.899788	+	0.436328i	$0.143721\pi$
$233$			13.3205i			0.872655i	−0.899788	+	0.436328i	$0.856279\pi$
$234$	−9.09406	+	14.0206i	−0.594497	+	0.916557i
$235$		−	13.9374i		−	0.909174i
$236$	−12.0466	+	7.32081i	−0.784169	+	0.476544i
$237$	−3.42356	+	5.92978i	−0.222384	+	0.385181i
$238$	2.20811	+	0.265504i	0.143131	+	0.0172101i
$239$	−10.2493	+	10.2493i	−0.662972	+	0.662972i	−0.956079	−	0.293108i	$-0.905311\pi$
$239$	−10.2493	+	10.2493i	−0.662972	+	0.662972i	0.293108	+	0.956079i	$0.405311\pi$
$240$	29.7204	−	9.41337i	1.91844	−	0.607630i
$241$	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	$0.436149\pi$
$242$	−0.455923	−	3.18608i	−0.0293079	−	0.204809i
$243$	19.3613	−	11.1782i	1.24203	−	0.717084i
$244$	−3.77109	+	15.4548i	−0.241419	+	0.989389i
$245$	−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
$250$	−0.559059	−	1.30793i	−0.0353580	−	0.0827210i
$251$	1.25814	+	2.17916i	0.0794129	+	0.137547i	0.902997	−	0.429647i	$-0.141362\pi$
$251$	1.25814	+	2.17916i	0.0794129	+	0.137547i	−0.823584	+	0.567195i	$0.808029\pi$
$252$	3.38962	+	1.85674i	0.213526	+	0.116964i
$253$	1.57596	−	5.88156i	0.0990797	−	0.369770i
$254$	10.5545	+	13.4395i	0.662248	+	0.843272i
$255$	14.6992	+	14.6992i	0.920498	+	0.920498i
$256$	−15.9354	+	1.43600i	−0.995964	+	0.0897498i
$257$	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	$0.602563\pi$
$258$	23.7278	+	9.51752i	1.47723	+	0.592535i
$259$	0.305208			0.0189647
$260$	17.2278	+	14.3662i	1.06843	+	0.890956i
$261$	−4.07591			−0.252293
$262$	−25.1603	−	10.0921i	−1.55441	−	0.623493i
$263$	4.59709	+	2.65413i	0.283469	+	0.163661i	0.634993	−	0.772518i	$-0.281003\pi$
$263$	4.59709	+	2.65413i	0.283469	+	0.163661i	−0.351524	+	0.936179i	$0.614336\pi$
$264$	−20.6484	+	3.42979i	−1.27082	+	0.211089i
$265$	−8.08728	−	8.08728i	−0.496798	−	0.496798i
$266$	−1.66315	−	2.11777i	−0.101974	−	0.129849i
$267$	−5.38080	+	20.0814i	−0.329300	+	1.22896i
$268$	7.14293	−	13.0400i	0.436324	−	0.796543i
$269$	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	$0.734715\pi$
$270$	1.20186	+	2.81177i	0.0731426	+	0.171119i
$271$	24.6484	−	6.60453i	1.49729	−	0.401196i	0.585096	−	0.810964i	$-0.301057\pi$
$271$	24.6484	−	6.60453i	1.49729	−	0.401196i	0.912190	+	0.409768i	$0.134390\pi$
$272$	−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
$276$	10.0357	+	2.44880i	0.604080	+	0.147401i
$277$	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	$0.328224\pi$
$278$	−2.22505	−	15.5491i	−0.133450	−	0.932574i
$279$	−28.4066	−	7.61154i	−1.70066	−	0.455691i
$280$	3.01762	−	4.21978i	0.180337	−	0.252180i
$281$	−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	$0.253700\pi$
$282$	−15.7618	−	1.89521i	−0.938603	−	0.112858i
$283$	8.03188	−	13.9116i	0.477446	−	0.826960i	−0.522220	−	0.852811i	$-0.674896\pi$
$283$	8.03188	−	13.9116i	0.477446	−	0.826960i	0.999666	+	0.0258504i	$0.00822935\pi$
$284$	−2.12938	−	3.50396i	−0.126355	−	0.207922i
$285$		−	25.1692i		−	1.49090i
$286$	−10.0838	−	11.1868i	−0.596270	−	0.661488i
$287$			3.41715i			0.201708i
$288$	−3.44805	−	18.2165i	−0.203178	−	1.07342i
$289$	−4.94304	+	8.56160i	−0.290767	+	0.503624i
$290$	−0.653135	+	5.43191i	−0.0383534	+	0.318973i
$291$	−8.40107	+	8.40107i	−0.492479	+	0.492479i
$292$	−0.124449	+	0.00279655i	−0.00728283	+	0.000163656i
$293$	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	$0.564270\pi$
$294$	−23.3335	+	3.33898i	−1.36084	+	0.194734i
$295$	−18.9880	+	10.9627i	−1.10552	+	0.638275i
$296$	−0.929921	−	1.13086i	−0.0540506	−	0.0657298i
$297$	−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
$302$	6.76211	−	2.89038i	0.389116	−	0.166322i
$303$	11.2476	+	19.4814i	0.646159	+	1.11918i
$304$	−2.77942	+	12.6149i	−0.159410	+	0.723511i
$305$	−6.40398	+	23.9000i	−0.366691	+	1.36851i
$306$	9.72258	−	7.63545i	0.555803	−	0.436489i
$307$	11.4337	+	11.4337i	0.652558	+	0.652558i	0.953608	−	0.301050i	$-0.0973372\pi$
$307$	11.4337	+	11.4337i	0.652558	+	0.652558i	−0.301050	+	0.953608i	$0.597337\pi$
$308$	−2.40694	+	2.51760i	−0.137148	+	0.143454i
$309$	−20.8339	−	12.0284i	−1.18520	−	0.684274i
$310$	−14.6957	+	36.6375i	−0.834663	+	2.08087i
$311$	24.0242			1.36229			0.681143	−	0.732151i	$-0.261483\pi$
$311$	24.0242			1.36229			0.681143	+	0.732151i	$0.261483\pi$
$312$	18.5895	−	17.5295i	1.05242	−	0.992413i
$313$	28.9008			1.63357			0.816786	−	0.576941i	$-0.195754\pi$
$313$	28.9008			1.63357			0.816786	+	0.576941i	$0.195754\pi$
$314$	5.66523	−	14.1238i	0.319707	−	0.797051i
$315$	5.20590	+	3.00563i	0.293319	+	0.169348i
$316$	3.77704	−	3.95070i	0.212475	−	0.222244i
$317$	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	$0.749822\pi$
$318$	−10.2457	+	8.04623i	−0.574548	+	0.451210i
$319$	0.950714	−	3.54811i	0.0532297	−	0.198656i
$320$	−24.8294	+	1.67611i	−1.38800	+	0.0936976i
$321$	−23.6312	−	40.9305i	−1.31897	−	2.28452i
$322$	1.58064	−	0.675624i	0.0880857	−	0.0376511i
$323$	−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
$328$	12.6613	−	10.4115i	0.699101	−	0.574881i
$329$	−2.28780	+	1.32086i	−0.126130	+	0.0728214i
$330$	−32.2277	+	4.61173i	−1.77407	+	0.253867i
$331$	−4.08070	−	1.09342i	−0.224295	−	0.0600998i	0.144921	−	0.989443i	$-0.453707\pi$
$331$	−4.08070	−	1.09342i	−0.224295	−	0.0600998i	−0.369216	+	0.929343i	$0.620374\pi$
$332$	−28.7986	+	0.647147i	−1.58053	+	0.0355168i
$333$	1.19962	−	1.19962i	0.0657389	−	0.0657389i
$334$	1.57360	−	13.0871i	0.0861033	−	0.716094i
$335$	11.5627	−	20.0272i	0.631739	−	1.09420i
$336$	−4.36183	−	3.98644i	−0.237957	−	0.217478i
$337$		−	9.58550i		−	0.522155i	−0.965318	−	0.261078i	$-0.915922\pi$
$337$		−	9.58550i		−	0.522155i	0.965318	−	0.261078i	$-0.0840778\pi$
$338$	17.8324	+	4.47263i	0.969956	+	0.243279i
$339$		−	14.1381i		−	0.767877i
$340$	−8.61768	−	14.1807i	−0.467359	−	0.769055i
$341$	13.2518	−	22.9528i	0.717625	−	1.24296i
$342$	−14.8610	−	1.78689i	−0.803588	−	0.0966238i
$343$	−5.69196	+	5.69196i	−0.307337	+	0.307337i
$344$	−16.5999	−	11.8708i	−0.895005	−	0.640029i
$345$	15.5197	+	4.15850i	0.835555	+	0.223886i
$346$	4.58593	+	32.0474i	0.246541	+	1.72288i
$347$	−3.56473	+	2.05810i	−0.191364	+	0.110484i	−0.592621	−	0.805481i	$-0.701907\pi$
$347$	−3.56473	+	2.05810i	−0.191364	+	0.110484i	0.401257	+	0.915966i	$0.368574\pi$
$348$	6.05416	+	1.47727i	0.324537	+	0.0791898i
$349$	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	$0.663796\pi$
$354$	9.81581	+	22.9643i	0.521704	+	1.22054i
$355$	−3.18869	−	5.52298i	−0.169238	−	0.293129i
$356$	7.97277	−	14.5549i	0.422556	−	0.771408i
$357$	1.01979	−	3.80591i	0.0539730	−	0.201430i
$358$	−11.5460	−	14.7020i	−0.610223	−	0.777027i
$359$	−7.69873	−	7.69873i	−0.406324	−	0.406324i	0.474131	−	0.880454i	$-0.342762\pi$
$359$	−7.69873	−	7.69873i	−0.406324	−	0.406324i	−0.880454	+	0.474131i	$0.842762\pi$
$360$	−4.72510	−	28.4466i	−0.249035	−	1.49927i
$361$	−7.42294	−	4.28564i	−0.390681	−	0.225560i
$362$	−34.2851	−	13.7522i	−1.80198	−	0.722798i
$363$	−5.70210			−0.299282
$364$	0.725492	−	4.18943i	0.0380261	−	0.219586i
$365$	−0.193613			−0.0101342
$366$	26.1578	+	10.4922i	1.36729	+	0.548437i
$367$	1.81711	+	1.04911i	0.0948522	+	0.0547630i	0.546676	−	0.837344i	$-0.315893\pi$
$367$	1.81711	+	1.04911i	0.0948522	+	0.0547630i	−0.451824	+	0.892107i	$0.649226\pi$
$368$	−7.31930	−	3.79808i	−0.381545	−	0.197989i
$369$	13.4311	+	13.4311i	0.699198	+	0.699198i
$370$	−1.40649	−	1.79095i	−0.0731199	−	0.0931071i
$371$	−0.561074	+	2.09396i	−0.0291295	+	0.108713i
$372$	39.4351	+	21.6015i	2.04462	+	1.11998i
$373$	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	$0.571555\pi$
$374$	4.37890	+	10.2446i	0.226428	+	0.529733i
$375$	−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	$0.183039\pi$
$379$	7.48268	+	27.9257i	0.384360	+	1.43445i	−0.454814	+	0.890586i	$0.650294\pi$
$380$	−4.76272	+	19.5187i	−0.244322	+	1.00129i
$381$	26.2187	−	15.1374i	1.34323	−	0.775512i
$382$	2.83230	+	19.7927i	0.144913	+	1.01268i
$383$	−14.6205	−	3.91754i	−0.747070	−	0.200177i	−0.134852	−	0.990866i	$-0.543056\pi$
$383$	−14.6205	−	3.91754i	−0.747070	−	0.200177i	−0.612218	+	0.790689i	$0.709723\pi$
$384$	−1.48078	+	28.3076i	−0.0755658	+	1.44456i
$385$	−3.83070	+	3.83070i	−0.195231	+	0.195231i
$386$	32.5733	+	3.91662i	1.65793	+	0.199351i
$387$	11.8236	−	20.4791i	0.601028	−	1.04101i
$388$	8.10473	−	4.92529i	0.411455	−	0.250044i
$389$		−	30.3695i		−	1.53979i	−0.638168	−	0.769897i	$-0.720308\pi$
$389$		−	30.3695i		−	1.53979i	0.638168	−	0.769897i	$-0.279692\pi$
$390$	29.5187	−	26.6084i	1.49474	−	1.34737i
$391$		−	5.49846i		−	0.278069i
$392$	18.7269	+	1.82597i	0.945851	+	0.0922256i
$393$	−24.0136	+	41.5928i	−1.21133	+	2.09808i
$394$	−1.04779	+	8.71413i	−0.0527869	+	0.439012i
$395$	6.01125	−	6.01125i	0.302459	−	0.302459i
$396$	0.434957	+	19.3560i	0.0218574	+	0.972674i
$397$	−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	$0.714884\pi$
$398$	−4.21990	+	0.603862i	−0.211525	+	0.0302689i
$399$	−4.13149	+	2.38531i	−0.206833	+	0.119415i
$400$	−18.6878	+	0.840309i	−0.934390	+	0.0420154i
$401$	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
$406$	0.953539	−	0.407578i	0.0473233	−	0.0202277i
$407$	0.764465	+	1.32409i	0.0378931	+	0.0656328i
$408$	−17.2088	+	7.81748i	−0.851964	+	0.387023i
$409$	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	$0.0787311\pi$
$410$	20.0517	−	15.7473i	0.990285	−	0.777702i
$411$	−12.8578	−	12.8578i	−0.634228	−	0.634228i
$412$	13.8805	+	13.2704i	0.683843	+	0.653784i
$413$	3.59903	+	2.07790i	0.177097	+	0.102247i
$414$	3.55718	−	8.86828i	0.174826	−	0.435852i
$415$	−44.8037			−2.19933
$416$	−17.7332	+	10.0764i	−0.869440	+	0.494038i
$417$	−27.8281			−1.36275
$418$	5.02184	−	12.5198i	0.245626	−	0.612362i
$419$	31.9541	+	18.4487i	1.56106	+	0.901278i	0.997150	+	0.0754420i	$0.0240368\pi$
$419$	31.9541	+	18.4487i	1.56106	+	0.901278i	0.563910	+	0.825836i	$0.309297\pi$
$420$	−6.64323	−	6.35123i	−0.324157	−	0.309908i
$421$	−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	$-0.527079\pi$
$422$	20.2577	−	15.9090i	0.986132	−	0.774440i
$423$	−3.80056	+	14.1839i	−0.184789	+	0.689643i
$424$	9.46805	−	4.30107i	0.459809	−	0.208878i
$425$	−6.23679	−	10.8024i	−0.302529	−	0.523995i
$426$	−6.67956	+	2.85509i	−0.323626	+	0.138330i
$427$	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	$-0.813817\pi$
$431$	−8.05023	−	30.0439i	−0.387766	−	1.44716i	0.445994	−	0.895036i	$-0.352850\pi$
$432$	−2.77755	+	0.124894i	−0.133635	+	0.00600897i
$433$	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	$0.249828\pi$
$434$	7.40671	−	1.05989i	0.355534	−	0.0508763i
$435$	9.36245	+	2.50866i	0.448895	+	0.120281i
$436$	0.187612	+	8.34888i	0.00898496	+	0.399839i
$437$	−4.70747	+	4.70747i	−0.225189	+	0.225189i
$438$	−0.0263275	+	0.218958i	−0.00125798	+	0.0104622i
$439$	6.48316	−	11.2292i	0.309424	−	0.535938i	−0.668812	−	0.743431i	$-0.733197\pi$
$439$	6.48316	−	11.2292i	0.309424	−	0.535938i	0.978237	+	0.207493i	$0.0665304\pi$
$440$	25.8651	+	2.52199i	1.23307	+	0.120231i
$441$			21.8026i			1.03822i
$442$	−11.4101	−	7.40080i	−0.542722	−	0.352020i
$443$		−	15.6512i		−	0.743611i	−0.928311	−	0.371805i	$-0.878739\pi$
$443$		−	15.6512i		−	0.743611i	0.928311	−	0.371805i	$-0.121261\pi$
$444$	−2.21665	+	1.34707i	−0.105197	+	0.0639291i
$445$	12.9060	−	22.3539i	0.611805	−	1.05968i
$446$	−4.98584	−	0.599499i	−0.236086	−	0.0283871i
$447$	9.20642	−	9.20642i	0.435449	−	0.435449i
$448$	2.62824	+	3.91685i	0.124173	+	0.185054i
$449$	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	$0.498164\pi$
$450$	−3.07056	−	21.4577i	−0.144748	−	1.01153i
$451$	−14.8247	+	8.55907i	−0.698070	+	0.403031i
$452$	−2.67533	+	10.9641i	−0.125837	+	0.515706i
$453$	−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	$0.268299\pi$
$458$	−11.2306	−	26.2743i	−0.524771	−	1.22772i
$459$	−0.926967	−	1.60555i	−0.0432671	−	0.0749408i
$460$	−11.2486	−	6.16168i	−0.524470	−	0.287290i
$461$	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	$-0.110157\pi$
$462$	3.81126	+	4.85306i	0.177316	+	0.225785i
$463$	−13.2027	−	13.2027i	−0.613581	−	0.613581i	0.330296	−	0.943877i	$-0.392851\pi$
$463$	−13.2027	−	13.2027i	−0.613581	−	0.613581i	−0.943877	+	0.330296i	$0.892851\pi$
$464$	−4.41545	−	2.29123i	−0.204982	−	0.106368i
$465$	60.5658	+	34.9677i	2.80867	+	1.62159i
$466$	−17.4840	−	7.01304i	−0.809929	−	0.324873i
$467$	−22.6548			−1.04834			−0.524171	−	0.851613i	$-0.675625\pi$
$467$	−22.6548			−1.04834			−0.524171	+	0.851613i	$0.675625\pi$
$468$	−13.6150	−	19.3181i	−0.629355	−	0.892981i
$469$	−4.38325			−0.202400
$470$	18.2936	+	7.33781i	0.843822	+	0.338468i
$471$	−23.3482	−	13.4801i	−1.07583	−	0.621130i
$472$	−3.26664	−	19.6662i	−0.150359	−	0.905211i
$473$	15.0693	+	15.0693i	0.692888	+	0.692888i
$474$	−5.98074	−	7.61557i	−0.274705	−	0.349795i
$475$	−3.90885	+	14.5880i	−0.179350	+	0.669344i
$476$	−1.51103	+	2.75850i	−0.0692579	+	0.126436i
$477$	6.02501	+	10.4356i	0.275866	+	0.477814i
$478$	−8.05672	−	18.8489i	−0.368506	−	0.862129i
$479$	3.13701	−	0.840559i	0.143334	−	0.0384061i	−0.186439	−	0.982467i	$-0.559695\pi$
$479$	3.13701	−	0.840559i	0.143334	−	0.0384061i	0.329772	+	0.944060i	$0.393028\pi$
$480$	−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
$484$	4.42196	+	1.07900i	0.200998	+	0.0490453i
$485$	12.7747	−	7.37550i	0.580071	−	0.334904i
$486$	4.47870	+	31.2980i	0.203158	+	1.41971i
$487$	41.4268	+	11.1003i	1.87723	+	0.503002i	0.999725	+	0.0234304i	$0.00745882\pi$
$487$	41.4268	+	11.1003i	1.87723	+	0.503002i	0.877503	+	0.479571i	$0.159208\pi$
$488$	−18.2999	−	13.0865i	−0.828396	−	0.592397i
$489$	25.1775	−	25.1775i	1.13856	−	1.13856i
$490$	29.0560	+	3.49371i	1.31262	+	0.157830i
$491$	−0.796904	+	1.38028i	−0.0359638	+	0.0622911i	−0.883447	−	0.468531i	$-0.844783\pi$
$491$	−0.796904	+	1.38028i	−0.0359638	+	0.0622911i	0.847483	+	0.530822i	$0.178117\pi$
$492$	−15.0820	−	24.8179i	−0.679949	−	1.11888i
$493$		−	3.31701i		−	0.149390i
$494$	3.43251	+	16.1048i	0.154436	+	0.724590i
$495$			30.1132i			1.35349i
$496$	−26.4942	−	24.2141i	−1.18963	−	1.08725i
$497$	−0.604392	+	1.04684i	−0.0271107	+	0.0469571i
$498$	−6.09243	+	50.6687i	−0.273008	+	2.27052i
$499$	−2.89721	+	2.89721i	−0.129697	+	0.129697i	−0.768975	−	0.639278i	$-0.779233\pi$
$499$	−2.89721	+	2.89721i	−0.129697	+	0.129697i	0.639278	+	0.768975i	$0.279233\pi$
$500$	2.01108	−	0.0451919i	0.0899381	−	0.00202104i
$501$	−22.5569	−	6.04411i	−1.00777	−	0.270031i
$502$	−3.52267	+	0.504088i	−0.157224	+	0.0224986i
$503$	13.0990	−	7.56273i	0.584057	−	0.337205i	−0.178687	−	0.983906i	$-0.557185\pi$
$503$	13.0990	−	7.56273i	0.584057	−	0.337205i	0.762744	+	0.646701i	$0.223852\pi$
$504$	−4.22167	+	3.47154i	−0.188048	+	0.154635i
$505$	−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	$0.603681\pi$
$510$	−27.0325	+	11.5547i	−1.19702	+	0.511649i
$511$	0.0183489	+	0.0317812i	0.000811708	+	0.00140592i
$512$	6.50493	−	21.6722i	0.287480	−	0.957787i
$513$	−0.580967	+	2.16820i	−0.0256503	+	0.0957284i
$514$	−7.13324	+	5.60196i	−0.314634	+	0.247092i
$515$	21.1201	+	21.1201i	0.930663	+	0.930663i
$516$	−24.9846	+	26.1333i	−1.09989	+	1.15046i
$517$	−11.4607	−	6.61682i	−0.504040	−	0.291007i
$518$	−0.160687	+	0.400603i	−0.00706018	+	0.0176015i
$519$	57.3549			2.51760
$520$	−27.9267	+	15.0490i	−1.22467	+	0.659941i
$521$	−41.1166			−1.80135			−0.900675	−	0.434494i	$-0.856927\pi$
$521$	−41.1166			−1.80135			−0.900675	+	0.434494i	$0.856927\pi$
$522$	2.14591	−	5.34988i	0.0939237	−	0.234158i
$523$	−2.27834	−	1.31540i	−0.0996249	−	0.0575185i	0.449360	−	0.893351i	$-0.351652\pi$
$523$	−2.27834	−	1.31540i	−0.0996249	−	0.0575185i	−0.548985	+	0.835832i	$0.684985\pi$
$524$	26.4930	−	27.7110i	1.15735	−	1.21056i
$525$	−4.88519	−	4.88519i	−0.213207	−	0.213207i
$526$	−5.90400	+	4.63660i	−0.257427	+	0.202165i
$527$	6.19432	−	23.1175i	0.269829	−	1.00702i
$528$	6.36928	−	28.9081i	0.277187	−	1.25806i
$529$	9.37507	+	16.2381i	0.407612	+	0.706004i
$530$	14.8729	−	6.35722i	0.646036	−	0.276140i
$531$	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
$536$	13.3551	+	16.2409i	0.576852	+	0.701498i
$537$	−28.6817	+	16.5594i	−1.23771	+	0.714590i
$538$	−14.0009	+	2.00350i	−0.603621	+	0.0863772i
$539$	−18.9793	−	5.08549i	−0.817497	−	0.219048i
$540$	−4.32338	+	0.0971526i	−0.186049	+	0.00418078i
$541$	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	$0.107282\pi$
$542$	−4.30818	+	35.8297i	−0.185052	+	1.53902i
$543$	−32.7225	+	56.6771i	−1.40426	+	2.43225i
$544$	14.8247	−	2.80605i	0.635603	−	0.120308i
$545$			12.9889i			0.556381i
$546$	−7.16525	−	2.32374i	−0.306644	−	0.0994469i
$547$			40.9532i			1.75103i	0.483190	+	0.875515i	$0.339478\pi$
$547$			40.9532i			1.75103i	−0.483190	+	0.875515i	$0.660522\pi$
$548$	7.53814	+	12.4042i	0.322013	+	0.529883i
$549$	13.0345	−	22.5764i	0.556298	−	0.963537i
$550$	19.3953	+	2.33210i	0.827018	+	0.0994409i
$551$	−2.83983	+	2.83983i	−0.120981	+	0.120981i
$552$	−8.49786	+	11.8832i	−0.361693	+	0.505785i
$553$	−1.55643	−	0.417045i	−0.0661862	−	0.0177345i
$554$	0.107041	+	0.748024i	0.00454774	+	0.0317805i
$555$	−3.49390	+	2.01721i	−0.148308	+	0.0856256i
$556$	21.5806	+	5.26585i	0.915221	+	0.223322i
$557$	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
$562$	−0.216591	−	0.506721i	−0.00913636	−	0.0213748i
$563$	−7.94721	−	13.7650i	−0.334935	−	0.580124i	0.648537	−	0.761183i	$-0.275381\pi$
$563$	−7.94721	−	13.7650i	−0.334935	−	0.580124i	−0.983472	+	0.181058i	$0.942048\pi$
$564$	10.7859	−	19.6906i	0.454170	−	0.829122i
$565$	−4.54318	+	16.9554i	−0.191133	+	0.713318i
$566$	14.0312	+	17.8666i	0.589775	+	0.750989i
$567$	3.37321	+	3.37321i	0.141661	+	0.141661i
$568$	5.72025	−	0.950156i	0.240016	−	0.0398677i
$569$	−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	$0.823690\pi$
$570$	33.0361	+	13.2512i	1.38373	+	0.555032i
$571$	−2.17784			−0.0911398			−0.0455699	−	0.998961i	$-0.514510\pi$
$571$	−2.17784			−0.0911398			−0.0455699	+	0.998961i	$0.514510\pi$
$572$	19.9923	−	7.34599i	0.835920	−	0.307151i
$573$	35.4227			1.47981
$574$	−4.48522	−	1.79908i	−0.187209	−	0.0750920i
$575$	−8.34938	−	4.82052i	−0.348193	−	0.201030i
$576$	25.7256	+	5.06492i	1.07190	+	0.211038i
$577$	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	$0.595354\pi$
$578$	−8.63518	−	10.9956i	−0.359176	−	0.457356i
$579$	15.0435	−	56.1433i	0.625188	−	2.33323i
$580$	−6.78585	−	3.71710i	−0.281767	−	0.154344i
$581$	4.24610	+	7.35446i	0.176158	+	0.305115i
$582$	−6.60387	−	15.4499i	−0.273739	−	0.640421i
$583$	−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	$-0.935588\pi$
$587$	−5.61437	−	20.9531i	−0.231730	−	0.864827i	0.747866	−	0.663850i	$-0.231079\pi$
$588$	7.90210	−	32.3845i	0.325877	−	1.33551i
$589$	−25.0951	+	14.4887i	−1.03403	+	0.596996i
$590$	−4.39235	−	30.6946i	−0.180830	−	1.26368i
$591$	15.0197	+	4.02451i	0.617827	+	0.165546i
$592$	1.97391	−	0.625198i	0.0811271	−	0.0256955i
$593$	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	$0.242066\pi$
$594$	2.88270	+	0.346617i	0.118279	+	0.0142219i
$595$	−2.44600	+	4.23660i	−0.100276	+	0.173683i
$596$	−8.88167	+	5.39745i	−0.363807	+	0.221088i
$597$			7.55231i			0.309096i
$598$	−10.4976	−	0.544323i	−0.429279	−	0.0222590i
$599$		−	7.16374i		−	0.292702i	−0.989233	−	0.146351i	$-0.953247\pi$
$599$		−	7.16374i		−	0.292702i	0.989233	−	0.146351i	$-0.0467529\pi$
$600$	−3.21623	+	32.9851i	−0.131302	+	1.34661i
$601$	−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	$0.272828\pi$
$602$	−0.718232	+	5.97330i	−0.0292729	+	0.243454i
$603$	−17.2284	+	17.2284i	−0.701595	+	0.701595i
$604$	0.233645	+	10.3974i	0.00950688	+	0.423065i
$605$	6.83834	+	1.83233i	0.278018	+	0.0744947i
$606$	−31.4923	+	4.50649i	−1.27929	+	0.183064i
$607$	30.3120	−	17.5006i	1.23033	−	0.710329i	0.263229	−	0.964734i	$-0.415213\pi$
$607$	30.3120	−	17.5006i	1.23033	−	0.710329i	0.967098	+	0.254404i	$0.0818793\pi$
$608$	−15.0944	−	10.2897i	−0.612160	−	0.417301i
$609$	−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	$0.280563\pi$
$614$	−21.0272	+	8.98778i	−0.848587	+	0.362717i
$615$	−22.5849	−	39.1183i	−0.910712	−	1.57740i
$616$	−2.03729	−	4.48473i	−0.0820847	−	0.180695i
$617$	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	$-0.0404115\pi$
$618$	26.7567	−	21.0129i	1.07631	−	0.845263i
$619$	−28.1707	−	28.1707i	−1.13228	−	1.13228i	−0.989798	−	0.142478i	$-0.954493\pi$
$619$	−28.1707	−	28.1707i	−1.13228	−	1.13228i	−0.142478	−	0.989798i	$-0.545507\pi$
$620$	−40.3518	−	38.5781i	−1.62057	−	1.54933i
$621$	−1.24096	−	0.716468i	−0.0497980	−	0.0287509i
$622$	−12.6484	+	31.5332i	−0.507153	+	1.26436i
$623$	−4.89248			−0.196013
$624$	13.2215	+	33.6288i	0.529282	+	1.34623i
$625$	26.5121			1.06048
$626$	−15.2158	+	37.9341i	−0.608147	+	1.51615i
$627$	−20.6966	−	11.9492i	−0.826542	−	0.477204i
$628$	15.5557	+	14.8719i	0.620738	+	0.593454i
$629$	0.976260	+	0.976260i	0.0389260	+	0.0389260i
$630$	−6.68589	+	5.25064i	−0.266372	+	0.209190i
$631$	3.23895	−	12.0879i	0.128941	−	0.481213i	−0.871009	−	0.491267i	$-0.836534\pi$
$631$	3.23895	−	12.0879i	0.128941	−	0.481213i	0.999949	+	0.0100543i	$0.00320045\pi$
$632$	3.19697	+	7.03758i	0.127169	+	0.279940i
$633$	−22.8170	−	39.5201i	−0.906893	−	1.57078i
$634$	−0.0259337	+	0.0110850i	−0.00102996	+	0.000440242i
$635$	−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
$640$	10.8723	−	33.4725i	0.429765	−	1.32312i
$641$	−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	$0.506470\pi$
$642$	66.1653	−	9.46815i	2.61133	−	0.373678i
$643$	0.362291	+	0.0970757i	0.0142874	+	0.00382829i	0.265956	−	0.963985i	$-0.414313\pi$
$643$	0.362291	+	0.0970757i	0.0142874	+	0.00382829i	−0.251668	+	0.967814i	$0.580979\pi$
$644$	0.0546145	+	2.43039i	0.00215211	+	0.0957709i
$645$	−39.7636	+	39.7636i	−1.56569	+	1.56569i
$646$	1.45418	−	12.0939i	0.0572140	−	0.475830i
$647$	−17.6527	+	30.5754i	−0.693999	+	1.20204i	0.276517	+	0.961009i	$0.410820\pi$
$647$	−17.6527	+	30.5754i	−0.693999	+	1.20204i	−0.970517	+	0.241033i	$0.922514\pi$
$648$	2.22079	−	22.7761i	0.0872410	−	0.894729i
$649$			20.8184i			0.817194i
$650$	−21.2413	+	10.8378i	−0.833153	+	0.425095i
$651$		−	13.2557i		−	0.519532i
$652$	−24.2893	+	14.7608i	−0.951244	+	0.578077i
$653$	−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	$0.950336\pi$
$654$	14.6892	+	1.76623i	0.574391	+	0.0690650i
$655$	42.1642	−	42.1642i	1.64749	−	1.64749i
$656$	6.99981	+	22.1002i	0.273297	+	0.862867i
$657$	0.197037	+	0.0527959i	0.00768715	+	0.00205977i
$658$	−0.529219	−	3.69828i	−0.0206311	−	0.144174i
$659$	9.20996	−	5.31737i	0.358769	−	0.207135i	−0.309772	−	0.950811i	$-0.600253\pi$
$659$	9.20996	−	5.31737i	0.358769	−	0.207135i	0.668541	+	0.743676i	$0.266919\pi$
$660$	10.9142	−	44.7287i	0.424834	−	1.74106i
$661$	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
$666$	0.942993	+	2.20616i	0.0365402	+	0.0854869i
$667$	−1.28188	−	2.22029i	−0.0496348	−	0.0859699i
$668$	16.3491	+	8.95559i	0.632566	+	0.346502i
$669$	−2.30265	+	8.59360i	−0.0890255	+	0.332248i
$670$	20.1993	+	25.7208i	0.780369	+	0.993681i
$671$	16.6126	+	16.6126i	0.641322	+	0.641322i
$672$	7.52888	−	3.62636i	0.290433	−	0.139890i
$673$	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	$0.658508\pi$
$674$	12.5815	+	5.04661i	0.484623	+	0.194388i
$675$	−3.25070			−0.125119
$676$	−15.2591	+	21.0514i	−0.586888	+	0.809668i
$677$	33.7816			1.29833			0.649167	−	0.760646i	$-0.275118\pi$
$677$	33.7816			1.29833			0.649167	+	0.760646i	$0.275118\pi$
$678$	18.5571	+	7.44350i	0.712682	+	0.285866i
$679$	−2.42135	−	1.39797i	−0.0929231	−	0.0536492i
$680$	23.1501	−	3.84532i	0.887765	−	0.147461i
$681$	−30.8905	−	30.8905i	−1.18373	−	1.18373i
$682$	23.1500	+	29.4781i	0.886461	+	1.12877i
$683$	−11.4324	+	42.6664i	−0.437449	+	1.63258i	0.297687	+	0.954664i	$0.403785\pi$
$683$	−11.4324	+	42.6664i	−0.437449	+	1.63258i	−0.735136	+	0.677920i	$0.762882\pi$
$684$	10.1695	−	18.5651i	0.388839	−	0.709856i
$685$	11.2882	+	19.5517i	0.431299	+	0.747032i
$686$	−4.47431	−	10.4678i	−0.170830	−	0.399661i
$687$	−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	$-0.793152\pi$
$691$	−10.7564	−	40.1436i	−0.409195	−	1.52714i	0.386991	−	0.922083i	$-0.373514\pi$
$692$	−44.4786	−	10.8531i	−1.69082	−	0.412575i
$693$	4.94304	−	2.85387i	0.187771	−	0.108409i
$694$	−0.824601	−	5.76247i	−0.0313014	−	0.218740i
$695$	33.3733	+	8.94235i	1.26592	+	0.339203i
$696$	−5.12642	+	7.16869i	−0.194317	+	0.271729i
$697$	−10.9304	+	10.9304i	−0.414017	+	0.414017i
$698$	−40.7939	−	4.90507i	−1.54407	−	0.185660i
$699$	−16.6871	+	28.9030i	−0.631165	+	1.09321i
$700$	2.86404	+	4.71287i	0.108251	+	0.178130i
$701$			17.2912i			0.653080i	0.945183	+	0.326540i	$0.105883\pi$
$701$			17.2912i			0.653080i	−0.945183	+	0.326540i	$0.894117\pi$
$702$	−3.15707	+	1.61081i	−0.119156	+	0.0607962i
$703$		−	1.67164i		−	0.0630470i
$704$	−10.4096	+	21.2129i	−0.392326	+	0.799491i
$705$	17.4599	−	30.2414i	0.657578	−	1.13896i
$706$	4.44527	−	36.9699i	0.167300	−	1.39138i
$707$	−3.74329	+	3.74329i	−0.140781	+	0.140781i
$708$	−35.3099	+	0.793466i	−1.32703	+	0.0298203i
$709$	−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	$0.871369\pi$
$710$	8.92804	−	1.27759i	0.335063	−	0.0479471i
$711$	−7.75677	+	4.47837i	−0.290902	+	0.167952i
$712$	14.9066	+	18.1277i	0.558650	+	0.679363i
$713$	−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
$718$	14.1583	−	6.05179i	0.528384	−	0.225851i
$719$	17.2567	+	29.8894i	0.643565	+	1.11469i	0.984631	+	0.174647i	$0.0558786\pi$
$719$	17.2567	+	29.8894i	0.643565	+	1.11469i	−0.341066	+	0.940039i	$0.610788\pi$
$720$	39.8256	+	8.77474i	1.48421	+	0.327015i
$721$	1.46526	−	5.46841i	0.0545690	−	0.203654i
$722$	9.53322	−	7.48673i	0.354790	−	0.278627i
$723$	24.5379	+	24.5379i	0.912575	+	0.912575i
$724$	36.1011	−	37.7609i	1.34169	−	1.40337i
$725$	−5.03685	−	2.90803i	−0.187064	−	0.108001i
$726$	3.00207	−	7.48434i	0.111417	−	0.277770i
$727$	3.77644			0.140060			0.0700302	−	0.997545i	$-0.477690\pi$
$727$	3.77644			0.140060			0.0700302	+	0.997545i	$0.477690\pi$
$728$	5.11691	+	3.15792i	0.189645	+	0.117040i
$729$	31.7414			1.17561
$730$	0.101934	−	0.254128i	0.00377275	−	0.00940572i
$731$	16.6660	+	9.62214i	0.616416	+	0.355888i
$732$	−27.5433	+	28.8097i	−1.01803	+	1.06484i
$733$	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	$0.714593\pi$
$734$	−2.33370	+	1.83272i	−0.0861383	+	0.0676471i
$735$	13.4192	−	50.0810i	0.494973	−	1.84727i
$736$	8.83871	−	7.60739i	0.325799	−	0.280412i
$737$	−10.9789	−	19.0160i	−0.404413	−	0.700464i
$738$	−24.7005	+	10.5579i	−0.909237	+	0.388642i
$739$	17.4311	−	4.67066i	0.641215	−	0.171813i	0.0764613	−	0.997073i	$-0.475638\pi$
$739$	17.4311	−	4.67066i	0.641215	−	0.171813i	0.564754	+	0.825260i	$0.308971\pi$
$740$	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	0.999909	−	0.0134546i	$-0.00428288\pi$
$743$	3.46818	+	12.9434i	0.127235	+	0.474848i	−0.872674	+	0.488303i	$0.837616\pi$
$744$	−49.1152	+	40.3881i	−1.80065	+	1.48070i
$745$	−13.9994	+	8.08254i	−0.512898	+	0.296122i
$746$	−39.6252	+	5.67031i	−1.45078	+	0.207605i
$747$	45.5961	+	12.2174i	1.66828	+	0.447013i
$748$	−15.7520	+	0.353971i	−0.575951	+	0.0129425i
$749$	7.86466	−	7.86466i	0.287368	−	0.287368i
$750$	0.425449	−	3.53832i	0.0155352	−	0.129201i
$751$	−12.5103	+	21.6684i	−0.456506	+	0.790691i	−0.998773	−	0.0495148i	$-0.984233\pi$
$751$	−12.5103	+	21.6684i	−0.456506	+	0.790691i	0.542268	+	0.840206i	$0.317566\pi$
$752$	−12.0905	+	13.2290i	−0.440894	+	0.482411i
$753$			6.30448i			0.229748i
$754$	−6.33280	−	0.328369i	−0.230627	−	0.0119585i
$755$			16.1759i			0.588700i
$756$	0.425679	+	0.700468i	0.0154818	+	0.0254758i
$757$	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	$-0.0859161\pi$
$758$	−40.5937	−	4.88100i	−1.47443	−	0.177286i
$759$	10.7876	−	10.7876i	0.391565	−	0.391565i
$760$	−23.1119	−	16.5276i	−0.838357	−	0.599520i
$761$	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	$0.500218\pi$
$762$	6.06498	+	42.3833i	0.219711	+	1.53538i
$763$	2.13210	−	1.23097i	0.0771872	−	0.0445641i
$764$	−27.4702	−	6.70297i	−0.993839	−	0.242505i
$765$	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	$0.299262\pi$
$770$	−3.01122	−	7.04484i	−0.108517	−	0.253878i
$771$	8.03441	+	13.9160i	0.289352	+	0.501172i
$772$	−22.2901	+	40.6923i	−0.802239	+	1.46455i
$773$	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	$-0.0997340\pi$
$774$	20.6551	+	26.3011i	0.742432	+	0.945375i
$775$	−29.6732	−	29.6732i	−1.06589	−	1.06589i
$776$	2.19773	+	13.2310i	0.0788938	+	0.474966i
$777$	0.662242	+	0.382346i	0.0237578	+	0.0137166i
$778$	39.8618	+	15.9891i	1.42911	+	0.573236i
$779$	18.7159			0.670567
$780$	19.3840	+	52.7540i	0.694057	+	1.88889i
$781$	−6.05538			−0.216679
$782$	7.21706	+	2.89486i	0.258082	+	0.103520i
$783$	−0.748622	−	0.432217i	−0.0267536	−	0.0154462i
$784$	−12.2561	+	23.6188i	−0.437718	+	0.843529i
$785$	23.6690	+	23.6690i	0.844783	+	0.844783i
$786$	−41.9502	−	53.4172i	−1.49631	−	1.90533i
$787$	−2.42897	+	9.06504i	−0.0865834	+	0.323134i	−0.995609	−	0.0936059i	$-0.970161\pi$
$787$	−2.42897	+	9.06504i	−0.0865834	+	0.323134i	0.909026	+	0.416740i	$0.136827\pi$
$788$	−10.8862	−	5.96314i	−0.387804	−	0.212428i
$789$	6.64987	+	11.5179i	0.236742	+	0.410049i
$790$	4.72530	+	11.0550i	0.168119	+	0.393318i
$791$	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
$796$	1.42911	−	5.85680i	0.0506534	−	0.207589i
$797$	−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	$0.399531\pi$
$798$	−0.955705	−	6.67865i	−0.0338316	−	0.236422i
$799$	−11.5429	−	3.09292i	−0.408359	−	0.109420i
$800$	8.73588	−	24.9713i	0.308860	−	0.882868i
$801$	−19.2299	+	19.2299i	−0.679457	+	0.679457i
$802$	−19.3323	−	2.32452i	−0.682648	−	0.0820818i
$803$	−0.0919184	+	0.159207i	−0.00324373	+	0.00561831i
$804$	31.8345	−	19.3460i	1.12272	−	0.682281i
$805$			3.78111i			0.133267i
$806$	−43.5225	−	14.1147i	−1.53302	−	0.497168i
$807$			25.0572i			0.882055i
$808$	25.2749	+	2.46444i	0.889169	+	0.0866988i
$809$	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	$-0.0173588\pi$
$810$	4.24913	−	35.3386i	0.149299	−	1.24167i
$811$	0.110267	−	0.110267i	0.00387201	−	0.00387201i	−0.705168	−	0.709040i	$-0.749128\pi$
$811$	0.110267	−	0.110267i	0.00387201	−	0.00387201i	0.709040	+	0.705168i	$0.249128\pi$
$812$	0.0329468	+	1.46616i	0.00115620	+	0.0514521i
$813$	61.7561	+	16.5475i	2.16588	+	0.580346i
$814$	−2.14043	+	0.306292i	−0.0750221	+	0.0107355i
$815$	−38.2851	+	22.1039i	−1.34107	+	0.774266i
$816$	−1.20074	−	26.7034i	−0.0420341	−	0.934806i
$817$	−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	$0.518874\pi$
$822$	23.6461	−	10.1072i	0.824751	−	0.352529i
$823$	−13.0969	−	22.6845i	−0.456530	−	0.790733i	0.542245	−	0.840221i	$-0.317575\pi$
$823$	−13.0969	−	22.6845i	−0.456530	−	0.790733i	−0.998775	+	0.0494874i	$0.984241\pi$
$824$	−24.7260	+	11.2323i	−0.861372	+	0.391297i
$825$	8.95747	−	33.4297i	0.311859	−	1.16387i
$826$	−4.62221	+	3.62996i	−0.160827	+	0.126303i
$827$	−11.7822	−	11.7822i	−0.409707	−	0.409707i	0.471930	−	0.881636i	$-0.343558\pi$
$827$	−11.7822	−	11.7822i	−0.409707	−	0.409707i	−0.881636	+	0.471930i	$0.843558\pi$
$828$	9.76735	+	9.33802i	0.339439	+	0.324519i
$829$	−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	$0.739747\pi$
$830$	23.5885	−	58.8076i	0.818768	−	2.04124i
$831$	1.33873			0.0464401
$832$	−3.88970	−	28.5809i	−0.134851	−	0.990866i
$833$	−17.7431			−0.614762
$834$	14.6511	−	36.5260i	0.507324	−	1.26479i
$835$	25.1095	+	14.4970i	0.868951	+	0.501689i
$836$	13.7890	+	13.1829i	0.476904	+	0.455941i
$837$	−4.41030	−	4.41030i	−0.152442	−	0.152442i
$838$	−41.0384	+	32.2287i	−1.41765	+	1.11332i
$839$	6.19456	−	23.1184i	0.213860	−	0.798136i	−0.772705	−	0.634766i	$-0.781097\pi$
$839$	6.19456	−	23.1184i	0.213860	−	0.798136i	0.986565	−	0.163371i	$-0.0522367\pi$
$840$	11.8339	−	5.37582i	0.408309	−	0.185483i
$841$	13.7267	+	23.7753i	0.473334	+	0.819839i
$842$	40.8038	−	17.4411i	1.40619	−	0.601059i
$843$	−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
$848$	0.660628	+	14.6918i	0.0226860	+	0.504520i
$849$	34.8553	−	20.1237i	1.19623	−	0.690644i
$850$	17.4624	−	2.49885i	0.598956	−	0.0857097i
$851$	1.03076	+	0.276191i	0.0353340	+	0.00946770i
$852$	−0.230793	−	10.2705i	−0.00790683	−	0.351861i
$853$	−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	$0.345374\pi$
$854$	−0.791787	+	6.58503i	−0.0270944	+	0.225335i
$855$	16.4620	−	28.5130i	0.562987	−	0.975123i
$856$	−53.1026	−	5.17780i	−1.81501	−	0.176973i
$857$		−	20.1694i		−	0.688974i	−0.938791	−	0.344487i	$-0.888053\pi$
$857$		−	20.1694i		−	0.688974i	0.938791	−	0.344487i	$-0.111947\pi$
$858$	−7.86591	−	36.9056i	−0.268538	−	1.25994i
$859$			10.5286i			0.359231i	0.983737	+	0.179616i	$0.0574854\pi$
$859$			10.5286i			0.359231i	−0.983737	+	0.179616i	$0.942515\pi$
$860$	38.3610	−	23.3122i	1.30810	−	0.794940i
$861$	−4.28080	+	7.41456i	−0.145889	+	0.252688i
$862$	43.6727	+	5.25122i	1.48750	+	0.178857i
$863$	0.357134	−	0.357134i	0.0121570	−	0.0121570i	−0.701002	−	0.713159i	$-0.747264\pi$
$863$	0.357134	−	0.357134i	0.0121570	−	0.0121570i	0.713159	+	0.701002i	$0.247264\pi$
$864$	1.29840	−	3.71145i	0.0441726	−	0.126266i
$865$	−68.7838	−	18.4306i	−2.33872	−	0.626658i
$866$	2.16220	+	15.1099i	0.0734745	+	0.513454i
$867$	−21.4509	+	12.3847i	−0.728511	+	0.420606i
$868$	−2.50835	+	10.2798i	−0.0851390	+	0.348918i
$869$	−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
$874$	−3.70043	−	8.65725i	−0.125169	−	0.292836i
$875$	−0.296516	−	0.513580i	−0.0100241	−	0.0173622i
$876$	−0.273534	−	0.149834i	−0.00924186	−	0.00506243i
$877$	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	$-0.0980508\pi$
$878$	11.3257	+	14.4215i	0.382223	+	0.486702i
$879$	3.63013	+	3.63013i	0.122441	+	0.122441i
$880$	−16.9279	+	32.6218i	−0.570638	+	1.09968i
$881$	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	$0.494699\pi$
$882$	−28.6172	−	11.4787i	−0.963592	−	0.386509i
$883$	−49.7844			−1.67538			−0.837689	−	0.546148i	$-0.816094\pi$
$883$	−49.7844			−1.67538			−0.837689	+	0.546148i	$0.816094\pi$
$884$	15.7212	−	11.0800i	0.528762	−	0.372661i
$885$	−54.9338			−1.84658
$886$	20.5431	+	8.24011i	0.690160	+	0.276832i
$887$	−21.7002	−	12.5286i	−0.728621	−	0.420669i	0.0892967	−	0.996005i	$-0.471538\pi$
$887$	−21.7002	−	12.5286i	−0.728621	−	0.420669i	−0.817917	+	0.575336i	$0.804871\pi$
$888$	−0.601080	−	3.61870i	−0.0201709	−	0.121435i
$889$	5.03784	+	5.03784i	0.168964	+	0.168964i
$890$	22.5460	+	28.7089i	0.755745	+	0.962326i
$891$	−6.18510	+	23.0831i	−0.207209	+	0.773313i
$892$	3.41185	−	6.22859i	0.114237	−	0.208549i
$893$	7.23442	+	12.5304i	0.242091	+	0.419313i
$894$	7.23694	+	16.9310i	0.242040	+	0.566258i
$895$	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
$900$	29.7811	+	7.26685i	0.992704	+	0.242228i
$901$	−8.49258	+	4.90319i	−0.282929	+	0.163349i
$902$	−3.42930	−	23.9646i	−0.114183	−	0.797933i
$903$	10.2956	+	2.75869i	0.342616	+	0.0918036i
$904$	−12.9825	−	9.28394i	−0.431791	−	0.308779i
$905$	57.4558	−	57.4558i	1.90990	−	1.90990i
$906$	18.2934	+	2.19960i	0.607757	+	0.0730769i
$907$	25.1973	−	43.6429i	0.836661	−	1.44914i	−0.0560094	−	0.998430i	$-0.517838\pi$
$907$	25.1973	−	43.6429i	0.836661	−	1.44914i	0.892671	−	0.450710i	$-0.148829\pi$
$908$	18.1101	+	29.8008i	0.601006	+	0.988975i
$909$			29.4261i			0.976002i
$910$	7.84633	+	5.08928i	0.260103	+	0.168708i
$911$		−	7.50959i		−	0.248804i	−0.992232	−	0.124402i	$-0.960299\pi$
$911$		−	7.50959i		−	0.248804i	0.992232	−	0.124402i	$-0.0397012\pi$
$912$	−21.8339	+	23.8899i	−0.722994	+	0.791075i
$913$	−21.2708	+	36.8420i	−0.703959	+	1.21929i
$914$	−3.24402	+	26.9795i	−0.107303	+	0.892403i
$915$	−43.8359	+	43.8359i	−1.44917	+	1.44917i
$916$	40.3993	−	0.907831i	1.33483	−	0.0299956i
$917$	−10.9171	−	2.92524i	−0.360516	−	0.0966000i
$918$	2.59542	−	0.371400i	0.0856616	−	0.0122580i
$919$	−24.3508	+	14.0590i	−0.803260	+	0.463762i	−0.844610	−	0.535382i	$-0.820168\pi$
$919$	−24.3508	+	14.0590i	−0.803260	+	0.463762i	0.0413499	+	0.999145i	$0.486834\pi$
$920$	14.0098	−	11.5205i	0.461889	−	0.379818i
$921$	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
$926$	24.2803	−	10.3783i	0.797901	−	0.341052i
$927$	−15.7344	−	27.2528i	−0.516787	−	0.895101i
$928$	5.33205	−	4.58924i	0.175033	−	0.150649i
$929$	−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	$0.834864\pi$
$930$	−77.7842	+	61.0863i	−2.55064	+	2.00310i
$931$	15.1906	+	15.1906i	0.497853	+	0.497853i
$932$	18.4101	−	19.2565i	0.603042	−	0.630768i
$933$	52.1278	+	30.0960i	1.70659	+	0.985300i
$934$	11.9274	−	29.7358i	0.390277	−	0.972986i
$935$	−24.5064			−0.801444
$936$	32.5243	−	7.69985i	1.06309	−	0.251677i
$937$	−0.397858			−0.0129975			−0.00649873	−	0.999979i	$-0.502069\pi$
$937$	−0.397858			−0.0129975			−0.00649873	+	0.999979i	$0.502069\pi$
$938$	2.30771	−	5.75328i	0.0753495	−	0.187851i
$939$	62.7093	+	36.2052i	2.04644	+	1.18151i
$940$	−19.2626	+	20.1483i	−0.628278	+	0.657163i
$941$	−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	$0.781833\pi$
$942$	29.9859	−	23.5489i	0.976993	−	0.767263i
$943$	−3.09228	+	11.5405i	−0.100698	+	0.375811i
$944$	27.5329	+	6.06630i	0.896120	+	0.197441i
$945$	0.637444	+	1.10409i	0.0207360	+	0.0359159i
$946$	−27.7132	+	11.8456i	−0.901033	+	0.385135i
$947$	−7.47663	+	2.00336i	−0.242958	+	0.0651003i	−0.378243	−	0.925706i	$-0.623472\pi$
$947$	−7.47663	+	2.00336i	−0.242958	+	0.0651003i	0.135285	+	0.990807i	$0.456805\pi$
$948$	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
$952$	−2.82516	−	3.43562i	−0.0915640	−	0.111349i
$953$	−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	$0.409378\pi$
$954$	−16.8695	+	2.41399i	−0.546169	+	0.0781559i
$955$	−42.4813	−	11.3828i	−1.37466	−	0.368340i
$956$	28.9821	−	0.651270i	0.937347	−	0.0210636i
$957$	6.50773	−	6.50773i	0.210365	−	0.210365i
$958$	−0.548302	+	4.56005i	−0.0177148	+	0.147329i
$959$	2.13959	−	3.70587i	0.0690909	−	0.119669i
$960$	−55.9747	−	27.4679i	−1.80658	−	0.886522i
$961$		−	49.5168i		−	1.59731i
$962$	1.96051	−	1.76722i	0.0632094	−	0.0569775i
$963$		−	61.8243i		−	1.99226i
$964$	−14.3858	−	23.6724i	−0.463337	−	0.762435i
$965$	−36.0825	+	62.4966i	−1.16154	+	2.01184i
$966$	4.27607	+	0.514156i	0.137580	+	0.0165427i
$967$	−6.52725	+	6.52725i	−0.209902	+	0.209902i	−0.804226	−	0.594324i	$-0.797420\pi$
$967$	−6.52725	+	6.52725i	−0.209902	+	0.209902i	0.594324	+	0.804226i	$0.297420\pi$
$968$	−3.74434	+	5.23601i	−0.120348	+	0.168292i
$969$	−20.8451	−	5.58544i	−0.669642	−	0.179430i
$970$	2.95508	+	20.6507i	0.0948821	+	0.663054i
$971$	33.9607	−	19.6072i	1.08985	−	0.629226i	0.156315	−	0.987707i	$-0.450038\pi$
$971$	33.9607	−	19.6072i	1.08985	−	0.629226i	0.933537	+	0.358481i	$0.116705\pi$
$972$	−43.4385	−	10.5994i	−1.39329	−	0.339975i
$973$	−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	$0.356483\pi$
$978$	19.7914	+	46.3025i	0.632859	+	1.48059i
$979$	−12.2544	−	21.2252i	−0.391652	−	0.678361i
$980$	−19.8833	+	36.2984i	−0.635147	+	1.15951i
$981$	3.54191	−	13.2186i	0.113084	−	0.422037i
$982$	−1.39214	−	1.77268i	−0.0444250	−	0.0565685i
$983$	−17.0818	−	17.0818i	−0.544823	−	0.544823i	0.380116	−	0.924939i	$-0.375884\pi$
$983$	−17.0818	−	17.0818i	−0.544823	−	0.544823i	−0.924939	+	0.380116i	$0.875884\pi$
$984$	40.5155	−	6.72978i	1.29159	−	0.214538i
$985$	−16.7194	−	9.65293i	−0.532723	−	0.307568i
$986$	4.35377	+	1.74635i	0.138652	+	0.0556152i
$987$	−6.61878			−0.210678
$988$	−22.9457	−	3.97355i	−0.730000	−	0.126416i
$989$	14.8742			0.472973
$990$	−39.5254	−	15.8542i	−1.25620	−	0.503878i
$991$	−24.9439	−	14.4013i	−0.792368	−	0.457474i	0.0484275	−	0.998827i	$-0.484579\pi$
$991$	−24.9439	−	14.4013i	−0.792368	−	0.457474i	−0.840796	+	0.541353i	$0.817912\pi$
$992$	45.7313	−	22.0269i	1.45197	−	0.699356i
$993$	−7.48456	−	7.48456i	−0.237515	−	0.237515i
$994$	−1.05583	−	1.34445i	−0.0334891	−	0.0426432i
$995$	2.42688	−	9.05724i	0.0769373	−	0.287134i
$996$	−63.2982	−	34.6730i	−2.00568	−	1.09866i
$997$	−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	$-0.492508\pi$
$998$	−2.27742	−	5.32809i	−0.0720906	−	0.168658i
$999$	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.7.2	yes	16
3.2	odd	2		468.2.cb.f.163.3		16
4.3	odd	2	inner	52.2.l.b.7.1	✓	16
8.3	odd	2		832.2.bu.n.319.4		16
8.5	even	2		832.2.bu.n.319.1		16
12.11	even	2		468.2.cb.f.163.4		16
13.2	odd	12	inner	52.2.l.b.15.1	yes	16
13.3	even	3		676.2.l.m.427.2		16
13.4	even	6		676.2.f.i.99.1		16
13.5	odd	4		676.2.l.m.19.4		16
13.6	odd	12		676.2.f.h.239.5		16
13.7	odd	12		676.2.f.i.239.4		16
13.8	odd	4		676.2.l.i.19.1		16
13.9	even	3		676.2.f.h.99.8		16
13.10	even	6		676.2.l.i.427.3		16
13.11	odd	12		676.2.l.k.587.4		16
13.12	even	2		676.2.l.k.319.3		16
39.2	even	12		468.2.cb.f.379.4		16
52.3	odd	6		676.2.l.m.427.4		16
52.7	even	12		676.2.f.i.239.1		16
52.11	even	12		676.2.l.k.587.3		16
52.15	even	12	inner	52.2.l.b.15.2	yes	16
52.19	even	12		676.2.f.h.239.8		16
52.23	odd	6		676.2.l.i.427.1		16
52.31	even	4		676.2.l.m.19.2		16
52.35	odd	6		676.2.f.h.99.5		16
52.43	odd	6		676.2.f.i.99.4		16
52.47	even	4		676.2.l.i.19.3		16
52.51	odd	2		676.2.l.k.319.4		16
104.67	even	12		832.2.bu.n.639.1		16
104.93	odd	12		832.2.bu.n.639.4		16
156.119	odd	12		468.2.cb.f.379.3		16

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

\(f(q)\)	\(=\)	\(q+(-0.526485 + 1.31256i) q^{2} +(2.16981 + 1.25274i) q^{3} +(-1.44563 - 1.38209i) q^{4} +(-2.19962 - 2.19962i) q^{5} +(-2.78667 + 2.18846i) q^{6} +(-0.152604 + 0.569525i) q^{7} +(2.57517 - 1.16983i) q^{8} +(1.63871 + 2.83834i) q^{9} +O(q^{10})\)	\(q+(-0.526485 + 1.31256i) q^{2} +(2.16981 + 1.25274i) q^{3} +(-1.44563 - 1.38209i) q^{4} +(-2.19962 - 2.19962i) q^{5} +(-2.78667 + 2.18846i) q^{6} +(-0.152604 + 0.569525i) q^{7} +(2.57517 - 1.16983i) q^{8} +(1.63871 + 2.83834i) q^{9} +(4.04520 - 1.72907i) 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} +(0.179681 + 3.99596i) q^{16} +(-2.30986 + 1.33360i) q^{17} +(-4.58824 + 0.656570i) q^{18} +(3.11932 + 0.835818i) q^{19} +(0.139770 + 6.21990i) q^{20} +(-1.04459 + 1.04459i) q^{21} +(0.498666 - 4.14724i) q^{22} +(-1.03076 + 1.78533i) q^{23} +(7.05312 + 0.687717i) q^{24} +4.67667i q^{25} +(2.31742 + 4.54198i) q^{26} +0.695088i q^{27} +(1.00774 - 0.612410i) q^{28} +(-0.621816 + 1.07702i) q^{29} +(10.9434 + 1.31584i) q^{30} +(-6.34495 + 6.34495i) q^{31} +(-5.33954 - 1.86797i) q^{32} +(-7.14819 - 1.91535i) q^{33} +(-0.534321 - 3.73394i) q^{34} +(1.58841 - 0.917069i) q^{35} +(1.55385 - 6.36802i) 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} +(-0.821125 - 1.92104i) q^{42} +(-3.60759 - 6.24853i) q^{43} +(5.18097 + 2.83799i) q^{44} +(2.63871 - 9.84781i) q^{45} +(-1.80067 - 2.29288i) q^{46} +(3.16813 + 3.16813i) q^{47} +(-4.61603 + 8.89557i) q^{48} +(5.76111 + 3.32618i) q^{49} +(-6.13841 - 2.46219i) q^{50} -6.68260 q^{51} +(-7.18170 + 0.650478i) q^{52} +3.67667 q^{53} +(-0.912345 - 0.365953i) q^{54} +(7.95711 + 4.59404i) q^{55} +(0.273265 + 1.64514i) q^{56} +(5.72126 + 5.72126i) q^{57} +(-1.08627 - 1.38320i) q^{58} +(1.82424 - 6.80816i) q^{59} +(-7.48864 + 13.6711i) q^{60} +(-3.97705 - 6.88845i) q^{61} +(-4.98761 - 11.6686i) 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} +(5.18234 + 1.26453i) q^{68} +(-4.47310 + 2.58254i) q^{69} +(0.367435 + 2.56771i) q^{70} +(1.98027 + 0.530611i) q^{71} +(7.54033 + 5.39219i) q^{72} +(0.0440105 - 0.0440105i) q^{73} +(0.726816 + 0.0873926i) q^{74} +(-5.85865 + 10.1475i) q^{75} +(-3.35420 - 5.51944i) q^{76} -1.74153i q^{77} +(-0.661547 + 12.7583i) q^{78} +2.73286i q^{79} +(8.39437 - 9.18484i) q^{80} +(4.04538 - 7.00680i) q^{81} +(-0.978460 + 8.13754i) q^{82} +(10.1844 - 10.1844i) q^{83} +(2.95379 - 0.0663761i) q^{84} +(8.01422 + 2.14740i) q^{85} +(10.1009 - 1.44543i) q^{86} +(-2.69844 + 1.55795i) q^{87} +(-6.45273 + 5.30617i) 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} +(-5.82633 + 2.49039i) q^{94} +(-5.02283 - 8.69980i) q^{95} +(-9.24570 - 10.7422i) q^{96} +(-1.22731 + 4.58039i) q^{97} +(-7.39894 + 5.81062i) 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

Varieties

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