LMFDB - Embedded newform 676.2.l.k.319.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(19,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 5]))

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

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

chi := DirichletCharacter("676.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	676.l (of order $12$, degree $4$, not 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:	$5.39788717664$
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:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			319.3
Root			$-0.873468 + 1.11223i$ of defining polynomial
Character	$\chi$	$=$	676.319
Dual form			676.2.l.k.587.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.526485 - 1.31256i) q^{2} +(2.16981 + 1.25274i) q^{3} +(-1.44563 - 1.38209i) q^{4} +(2.19962 + 2.19962i) q^{5} +(2.78667 - 2.18846i) q^{6} +(0.152604 - 0.569525i) q^{7} +(-2.57517 + 1.16983i) q^{8} +(1.63871 + 2.83834i) q^{9} +O(q^{10})$	\(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} +(-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} +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} +(-8.23758 - 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} +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} +(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} +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} +(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} + 8 q^{14} - 2 q^{16} + 12 q^{17} + 6 q^{18} - 2 q^{20} + 28 q^{21} - 10 q^{24} - 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^{53} + 16 q^{54} - 60 q^{56} - 12 q^{57} + 48 q^{58} + 24 q^{60} + 4 q^{61} - 18 q^{62} + 56 q^{66} + 16 q^{68} - 12 q^{69} - 28 q^{70} - 56 q^{72} - 20 q^{73} + 4 q^{74} - 22 q^{76} - 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 + 8 * q^14 - 2 * q^16 + 12 * q^17 + 6 * q^18 - 2 * q^20 + 28 * q^21 - 10 * q^24 - 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^53 + 16 * q^54 - 60 * q^56 - 12 * q^57 + 48 * q^58 + 24 * q^60 + 4 * q^61 - 18 * q^62 + 56 * q^66 + 16 * q^68 - 12 * q^69 - 28 * q^70 - 56 * q^72 - 20 * q^73 + 4 * q^74 - 22 * q^76 - 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 $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

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	0.999869	−	0.0161686i	$-0.00514685\pi$
$5$	2.19962	+	2.19962i	0.983701	+	0.983701i	−0.0161686	+	0.999869i	$0.505147\pi$
$6$	2.78667	−	2.18846i	1.13765	−	0.893434i
$7$	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	$0.0477912\pi$
$8$	−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	0.198365	−	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
$13$		0			0
$13$		0			0
$14$	−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	−0.117404	−	0.993084i	$-0.537457\pi$
$19$	−3.11932	−	0.835818i	−0.715620	−	0.191750i	−0.598217	+	0.801334i	$0.704124\pi$
$20$	−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
$26$		0			0
$27$			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	$-0.451731\pi$
$31$	6.34495	−	6.34495i	1.13959	−	1.13959i	0.988524	−	0.151062i	$-0.0482694\pi$
$32$	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	0.976064	−	0.217485i	$-0.0697853\pi$
$37$	0.133975	+	0.500000i	0.0220253	+	0.0821995i	−0.954038	+	0.299684i	$0.903119\pi$
$38$	−2.73933	+	3.65425i	−0.444379	+	0.592797i
$39$		0			0
$40$	−8.23758	−	3.09122i	−1.30248	−	0.488765i
$41$	−5.59808	+	1.50000i	−0.874273	+	0.234261i	−0.667934	−	0.744220i	$-0.732821\pi$
$41$	−5.59808	+	1.50000i	−0.874273	+	0.234261i	−0.206338	+	0.978481i	$0.566155\pi$
$42$	−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	0.437230	−	0.899350i	$-0.355959\pi$
$47$	−3.16813	−	3.16813i	−0.462119	−	0.462119i	−0.899350	+	0.437230i	$0.855959\pi$
$48$	−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
$52$		0			0
$53$	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	$0.235056\pi$
$59$	−1.82424	+	6.80816i	−0.237496	+	0.886347i	−0.977008	+	0.213203i	$0.931610\pi$
$60$	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
$65$		0			0
$66$	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	$-0.233376\pi$
$68$	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	0.139390	−	0.990238i	$-0.455486\pi$
$71$	−1.98027	−	0.530611i	−0.235014	−	0.0629719i	−0.374404	+	0.927266i	$0.622153\pi$
$72$	−7.54033	−	5.39219i	−0.888636	−	0.635475i
$73$	−0.0440105	+	0.0440105i	−0.00515104	+	0.00515104i	−0.709678	−	0.704527i	$-0.751159\pi$
$73$	−0.0440105	+	0.0440105i	−0.00515104	+	0.00515104i	0.704527	+	0.709678i	$0.251159\pi$
$74$	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			0
$79$			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	$0.540161\pi$
$83$	−10.1844	+	10.1844i	−1.11789	+	1.11789i	−0.992051	+	0.125834i	$0.959839\pi$
$84$	−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	$-0.938390\pi$
$89$	−2.14761	−	8.01501i	−0.227647	−	0.849589i	0.753680	−	0.657241i	$-0.228277\pi$
$90$	11.5366	+	8.64819i	1.21606	+	0.911599i
$91$		0			0
$92$	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	−0.875211	−	0.483741i	$-0.839278\pi$
$97$	1.22731	−	4.58039i	0.124615	−	0.465068i	0.999826	+	0.0186732i	$0.00594421\pi$
$98$	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	$0.656844\pi$
$104$		0			0
$105$	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	0.834225	−	0.551425i	$-0.185916\pi$
$109$	2.95252	+	2.95252i	0.282800	+	0.282800i	−0.551425	+	0.834225i	$0.685916\pi$
$110$	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
$117$		0			0
$118$	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
$130$		0			0
$131$			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	0.545530	−	0.838091i	$-0.316328\pi$
$137$	7.01027	+	1.87840i	0.598927	+	0.160482i	0.0533974	+	0.998573i	$0.482995\pi$
$138$	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
$143$		0			0
$144$	−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	−0.998882	−	0.0472817i	$-0.984944\pi$
$149$	−1.34497	+	5.01948i	−0.110184	+	0.411212i	0.888698	+	0.458494i	$0.151611\pi$
$150$	10.2347	+	13.0323i	0.835659	+	1.06408i
$151$	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	$0.682137\pi$
$152$	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
$156$		0			0
$157$	−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	$0.271213\pi$
$163$	−3.67817	+	13.7271i	−0.288097	+	1.07519i	−0.946547	+	0.322567i	$0.895454\pi$
$164$	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	0.106935	−	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
$169$		0			0
$170$	−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	$0.577151\pi$
$182$		0			0
$183$		−	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	$0.231163\pi$
$193$	6.00426	+	22.4082i	0.432196	+	1.61298i	−0.315493	+	0.948928i	$0.602170\pi$
$194$	−5.36588	−	4.02243i	−0.385247	−	0.288793i
$195$		0			0
$196$	−3.73136	−	12.7708i	−0.266526	−	0.912197i
$197$	−5.99473	+	1.60628i	−0.427107	+	0.114443i	−0.465968	−	0.884802i	$-0.654294\pi$
$197$	−5.99473	+	1.60628i	−0.427107	+	0.114443i	0.0388607	+	0.999245i	$0.487627\pi$
$198$	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
$208$		0			0
$209$	−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
$221$		0			0
$222$	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	$0.954601\pi$
$224$	1.87869	−	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	0.770009	−	0.638033i	$-0.220252\pi$
$227$	16.8419	+	4.51279i	1.11784	+	0.299524i	0.347831	+	0.937557i	$0.386918\pi$
$228$	0.363545	+	16.1781i	0.0240764	+	1.07142i
$229$	14.2869	−	14.2869i	0.944105	−	0.944105i	−0.0544132	−	0.998519i	$-0.517329\pi$
$229$	14.2869	−	14.2869i	0.944105	−	0.944105i	0.998519	+	0.0544132i	$0.0173288\pi$
$230$	−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	$0.856279\pi$
$234$		0			0
$235$		−	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	−0.293108	−	0.956079i	$-0.594689\pi$
$239$	10.2493	−	10.2493i	0.662972	−	0.662972i	0.956079	+	0.293108i	$0.0946894\pi$
$240$	−29.7204	+	9.41337i	−1.91844	+	0.607630i
$241$	−13.3784	−	3.58474i	−0.861781	−	0.230914i	−0.199251	−	0.979949i	$-0.563851\pi$
$241$	−13.3784	−	3.58474i	−0.861781	−	0.230914i	−0.662531	+	0.749035i	$0.730518\pi$
$242$	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
$247$		0			0
$248$	−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
$260$		0			0
$261$	−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	−0.912190	−	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			0
$274$	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	−0.698840	−	0.715278i	$-0.746300\pi$
$281$	0.275535	−	0.275535i	0.0164370	−	0.0164370i	0.715278	+	0.698840i	$0.246300\pi$
$282$	−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
$286$		0			0
$287$			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	0.200542	−	0.979685i	$-0.435730\pi$
$293$	−1.97920	−	0.530326i	−0.115626	−	0.0309820i	−0.316168	+	0.948703i	$0.602396\pi$
$294$	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
$299$		0			0
$300$	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	0.301050	−	0.953608i	$-0.402663\pi$
$307$	−11.4337	−	11.4337i	−0.652558	−	0.652558i	−0.953608	+	0.301050i	$0.902663\pi$
$308$	−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	$0.261483\pi$
$312$		0			0
$313$	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	0.706711	−	0.707503i	$-0.250178\pi$
$317$	−0.0141017	−	0.0141017i	−0.000792031	−	0.000792031i	−0.707503	+	0.706711i	$0.750178\pi$
$318$	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
$325$		0			0
$326$	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	0.369216	−	0.929343i	$-0.379626\pi$
$331$	4.08070	+	1.09342i	0.224295	+	0.0600998i	−0.144921	+	0.989443i	$0.546293\pi$
$332$	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	$-0.0840778\pi$
$338$		0			0
$339$		−	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	$-0.799772\pi$
$349$	−7.51958	−	28.0634i	−0.402514	−	1.50220i	0.406082	−	0.913837i	$-0.366895\pi$
$350$	2.33903	−	3.12024i	0.125026	−	0.166784i
$351$		0			0
$352$	16.6618	+	1.24747i	0.888079	+	0.0664904i
$353$	25.4328	−	6.81469i	1.35365	−	0.362709i	0.492169	−	0.870500i	$-0.336204\pi$
$353$	25.4328	−	6.81469i	1.35365	−	0.362709i	0.861481	+	0.507790i	$0.169537\pi$
$354$	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	0.880454	−	0.474131i	$-0.157238\pi$
$359$	7.69873	+	7.69873i	0.406324	+	0.406324i	−0.474131	+	0.880454i	$0.657238\pi$
$360$	−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			0
$365$	−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
$377$		0			0
$378$	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	$-0.349706\pi$
$380$	−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	0.612218	−	0.790689i	$-0.290277\pi$
$383$	14.6205	+	3.91754i	0.747070	+	0.200177i	0.134852	+	0.990866i	$0.456944\pi$
$384$	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	$-0.279692\pi$
$390$		0			0
$391$		−	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	0.624957	−	0.780659i	$-0.285116\pi$
$397$	15.4588	+	4.14218i	0.775857	+	0.207890i	0.150899	+	0.988549i	$0.451783\pi$
$398$	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	$-0.971625\pi$
$401$	−3.56354	−	13.2993i	−0.177955	−	0.664137i	0.818075	−	0.575112i	$-0.195042\pi$
$402$	−21.0766	−	15.7996i	−1.05120	−	0.788014i
$403$		0			0
$404$	−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	−0.969567	−	0.244827i	$-0.921269\pi$
$409$	−0.151353	+	0.564858i	−0.00748394	+	0.0279305i	0.962083	+	0.272757i	$0.0879356\pi$
$410$	−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
$416$		0			0
$417$	−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	$0.0270794\pi$
$421$	22.1875	+	22.1875i	1.08135	+	1.08135i	0.0849697	+	0.996384i	$0.472921\pi$
$422$	−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
$429$		0			0
$430$	−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	$0.647150\pi$
$432$	−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
$442$		0			0
$443$		−	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	−0.00576812	−	0.999983i	$-0.501836\pi$
$449$	−10.8227	−	2.89994i	−0.510755	−	0.136856i	−0.504987	+	0.863127i	$0.668503\pi$
$450$	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
$455$		0			0
$456$	21.4261	+	8.04033i	1.00337	+	0.376523i
$457$	−18.5601	+	4.97316i	−0.868204	+	0.232634i	−0.665311	−	0.746566i	$-0.731701\pi$
$457$	−18.5601	+	4.97316i	−0.868204	+	0.232634i	−0.202893	+	0.979201i	$0.565034\pi$
$458$	−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	$0.276824\pi$
$461$	−6.34751	+	23.6892i	−0.295633	+	1.10332i	−0.940713	+	0.339202i	$0.889843\pi$
$462$	−3.81126	−	4.85306i	−0.177316	−	0.225785i
$463$	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	$0.607149\pi$
$464$	−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	$0.675625\pi$
$468$		0			0
$469$	−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	−0.329772	−	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
$481$		0			0
$482$	−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	$-0.992541\pi$
$487$	−41.4268	−	11.1003i	−1.87723	−	0.503002i	−0.877503	−	0.479571i	$-0.840792\pi$
$488$	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
$494$		0			0
$495$			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	−0.639278	−	0.768975i	$-0.720767\pi$
$499$	2.89721	−	2.89721i	0.129697	−	0.129697i	0.768975	+	0.639278i	$0.220767\pi$
$500$	−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
$507$		0			0
$508$	−23.1970	+	6.77770i	−1.02920	+	0.300712i
$509$	24.1589	−	6.47337i	1.07083	−	0.286927i	0.319994	−	0.947420i	$-0.396319\pi$
$509$	24.1589	−	6.47337i	1.07083	−	0.286927i	0.750832	+	0.660493i	$0.229653\pi$
$510$	−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
$520$		0			0
$521$	−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
$533$		0			0
$534$	−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	−0.943739	−	0.330692i	$-0.892718\pi$
$541$	−14.2591	+	14.2591i	−0.613047	+	0.613047i	0.330692	+	0.943739i	$0.392718\pi$
$542$	−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
$546$		0			0
$547$			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	$-0.863246\pi$
$557$	−7.78980	−	29.0719i	−0.330064	−	1.23182i	0.579058	−	0.815287i	$-0.303421\pi$
$558$	24.9463	−	33.2781i	1.05606	−	1.40877i
$559$		0			0
$560$	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	$0.514510\pi$
$572$		0			0
$573$	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	0.295104	−	0.955465i	$-0.404646\pi$
$577$	−15.8624	−	15.8624i	−0.660361	−	0.660361i	−0.955465	+	0.295104i	$0.904646\pi$
$578$	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
$585$		0			0
$586$	−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	$0.768921\pi$
$588$	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	−0.724510	−	0.689264i	$-0.757934\pi$
$593$	−0.858298	+	0.858298i	−0.0352461	+	0.0352461i	0.689264	+	0.724510i	$0.257934\pi$
$594$	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
$598$		0			0
$599$		−	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
$611$		0			0
$612$	4.90319	+	16.7814i	0.198200	+	0.678349i
$613$	−19.8339	+	5.31448i	−0.801084	+	0.214650i	−0.636060	−	0.771640i	$-0.719437\pi$
$613$	−19.8339	+	5.31448i	−0.801084	+	0.214650i	−0.165024	+	0.986290i	$0.552770\pi$
$614$	−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	$0.207078\pi$
$617$	−4.87361	+	18.1886i	−0.196204	+	0.732244i	−0.991952	+	0.126616i	$0.959588\pi$
$618$	−26.7567	+	21.0129i	−1.07631	+	0.845263i
$619$	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	$0.454493\pi$
$620$	−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
$624$		0			0
$625$	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	−0.999949	−	0.0100543i	$-0.996800\pi$
$631$	−3.23895	+	12.0879i	−0.128941	+	0.481213i	0.871009	+	0.491267i	$0.163466\pi$
$632$	−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
$637$		0			0
$638$	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	0.251668	−	0.967814i	$-0.419021\pi$
$643$	−0.362291	−	0.0970757i	−0.0142874	−	0.00382829i	−0.265956	+	0.963985i	$0.585687\pi$
$644$	−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
$650$		0			0
$651$		−	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	0.913469	−	0.406909i	$-0.133393\pi$
$661$	−2.08438	−	7.77900i	−0.0810729	−	0.302568i	−0.994542	+	0.104341i	$0.966727\pi$
$662$	3.58360	−	4.78049i	0.139281	−	0.185799i
$663$		0			0
$664$	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
$676$		0			0
$677$	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	$-0.596215\pi$
$683$	11.4324	−	42.6664i	0.437449	−	1.63258i	0.735136	−	0.677920i	$-0.237118\pi$
$684$	−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
$689$		0			0
$690$	−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	$0.626486\pi$
$692$	−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	$0.894117\pi$
$702$		0			0
$703$		−	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	0.919454	−	0.393198i	$-0.128631\pi$
$709$	40.4498	+	10.8385i	1.51913	+	0.407048i	0.599672	+	0.800246i	$0.295298\pi$
$710$	−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
$715$		0			0
$716$	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	$0.477690\pi$
$728$		0			0
$729$	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	0.624243	−	0.781230i	$-0.285407\pi$
$733$	−4.25026	−	4.25026i	−0.156987	−	0.156987i	−0.781230	+	0.624243i	$0.785407\pi$
$734$	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	−0.564754	−	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
$741$		0			0
$742$	−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	$0.995717\pi$
$744$	−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
$754$		0			0
$755$			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	0.000685009	−	1.00000i	$-0.499782\pi$
$761$	−13.7578	−	3.68640i	−0.498722	−	0.133632i	−0.499407	+	0.866368i	$0.666449\pi$
$762$	−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
$767$		0			0
$768$	−36.3758	−	16.8471i	−1.31260	−	0.607918i
$769$	−19.3143	+	5.17525i	−0.696491	+	0.186624i	−0.589658	−	0.807653i	$-0.700738\pi$
$769$	−19.3143	+	5.17525i	−0.696491	+	0.186624i	−0.106833	+	0.994277i	$0.534071\pi$
$770$	−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	$0.266401\pi$
$773$	−7.82826	+	29.2155i	−0.281563	+	1.05081i	−0.951314	+	0.308222i	$0.900266\pi$
$774$	−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
$780$		0			0
$781$	−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	−0.909026	−	0.416740i	$-0.863173\pi$
$787$	2.42897	−	9.06504i	0.0865834	−	0.323134i	0.995609	+	0.0936059i	$0.0298394\pi$
$788$	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
$793$		0			0
$794$	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
$806$		0			0
$807$			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	−0.709040	−	0.705168i	$-0.750872\pi$
$811$	−0.110267	+	0.110267i	−0.00387201	+	0.00387201i	0.705168	+	0.709040i	$0.250872\pi$
$812$	−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
$819$		0			0
$820$	10.1123	+	34.6098i	0.353137	+	1.20863i
$821$	17.4699	−	4.68104i	0.609703	−	0.163370i	0.0592608	−	0.998243i	$-0.481126\pi$
$821$	17.4699	−	4.68104i	0.609703	−	0.163370i	0.550443	+	0.834873i	$0.314459\pi$
$822$	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	0.881636	−	0.471930i	$-0.156442\pi$
$827$	11.7822	+	11.7822i	0.409707	+	0.409707i	−0.471930	+	0.881636i	$0.656442\pi$
$828$	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
$832$		0			0
$833$	−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	$0.218903\pi$
$839$	−6.19456	+	23.1184i	−0.213860	+	0.798136i	−0.986565	+	0.163371i	$0.947763\pi$
$840$	−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
$845$		0			0
$846$	−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	−0.466892	−	0.884314i	$-0.654626\pi$
$853$	12.1913	−	12.1913i	0.417422	−	0.417422i	0.884314	+	0.466892i	$0.154626\pi$
$854$	−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	$-0.111947\pi$
$858$		0			0
$859$			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	−0.713159	−	0.701002i	$-0.752736\pi$
$863$	−0.357134	+	0.357134i	−0.0121570	+	0.0121570i	0.701002	+	0.713159i	$0.252736\pi$
$864$	−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
$871$		0			0
$872$	−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	$0.264717\pi$
$877$	−8.27012	+	30.8645i	−0.279262	+	1.04222i	−0.952931	+	0.303187i	$0.901949\pi$
$878$	−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	$0.816094\pi$
$884$		0			0
$885$	−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
$897$		0			0
$898$	−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
$910$		0			0
$911$		−	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
$923$		0			0
$924$	−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	$-0.668198\pi$
$929$	11.1025	−	41.4351i	0.364261	−	1.35944i	0.868420	−	0.495829i	$-0.165136\pi$
$930$	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
$936$		0			0
$937$	−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	0.774171	−	0.632977i	$-0.218167\pi$
$941$	4.33123	+	4.33123i	0.141194	+	0.141194i	−0.632977	+	0.774171i	$0.718167\pi$
$942$	−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	−0.135285	−	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			0
$950$	−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
$962$		0			0
$963$		−	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	−0.594324	−	0.804226i	$-0.702580\pi$
$967$	6.52725	−	6.52725i	0.209902	−	0.209902i	0.804226	+	0.594324i	$0.202580\pi$
$968$	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
$975$		0			0
$976$	26.8114	−	17.1299i	0.858212	−	0.548313i
$977$	−11.3491	+	3.04098i	−0.363089	+	0.0972895i	−0.435751	−	0.900067i	$-0.643517\pi$
$977$	−11.3491	+	3.04098i	−0.363089	+	0.0972895i	0.0726619	+	0.997357i	$0.476851\pi$
$978$	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	0.924939	−	0.380116i	$-0.124116\pi$
$983$	17.0818	+	17.0818i	0.544823	+	0.544823i	−0.380116	+	0.924939i	$0.624116\pi$
$984$	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
$988$		0			0
$989$	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	676.2.l.k.319.3		16
4.3	odd	2	inner	676.2.l.k.319.4		16
13.2	odd	12	inner	676.2.l.k.587.4		16
13.3	even	3		676.2.l.i.427.3		16
13.4	even	6		676.2.f.h.99.8		16
13.5	odd	4		676.2.l.i.19.1		16
13.6	odd	12		676.2.f.i.239.4		16
13.7	odd	12		676.2.f.h.239.5		16
13.8	odd	4		676.2.l.m.19.4		16
13.9	even	3		676.2.f.i.99.1		16
13.10	even	6		676.2.l.m.427.2		16
13.11	odd	12		52.2.l.b.15.1	yes	16
13.12	even	2		52.2.l.b.7.2	yes	16
39.11	even	12		468.2.cb.f.379.4		16
39.38	odd	2		468.2.cb.f.163.3		16
52.3	odd	6		676.2.l.i.427.1		16
52.7	even	12		676.2.f.h.239.8		16
52.11	even	12		52.2.l.b.15.2	yes	16
52.15	even	12	inner	676.2.l.k.587.3		16
52.19	even	12		676.2.f.i.239.1		16
52.23	odd	6		676.2.l.m.427.4		16
52.31	even	4		676.2.l.i.19.3		16
52.35	odd	6		676.2.f.i.99.4		16
52.43	odd	6		676.2.f.h.99.5		16
52.47	even	4		676.2.l.m.19.2		16
52.51	odd	2		52.2.l.b.7.1	✓	16
104.11	even	12		832.2.bu.n.639.1		16
104.37	odd	12		832.2.bu.n.639.4		16
104.51	odd	2		832.2.bu.n.319.4		16
104.77	even	2		832.2.bu.n.319.1		16
156.11	odd	12		468.2.cb.f.379.3		16
156.155	even	2		468.2.cb.f.163.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.7.1	✓	16	52.51	odd	2
52.2.l.b.7.2	yes	16	13.12	even	2
52.2.l.b.15.1	yes	16	13.11	odd	12
52.2.l.b.15.2	yes	16	52.11	even	12
468.2.cb.f.163.3		16	39.38	odd	2
468.2.cb.f.163.4		16	156.155	even	2
468.2.cb.f.379.3		16	156.11	odd	12
468.2.cb.f.379.4		16	39.11	even	12
676.2.f.h.99.5		16	52.43	odd	6
676.2.f.h.99.8		16	13.4	even	6
676.2.f.h.239.5		16	13.7	odd	12
676.2.f.h.239.8		16	52.7	even	12
676.2.f.i.99.1		16	13.9	even	3
676.2.f.i.99.4		16	52.35	odd	6
676.2.f.i.239.1		16	52.19	even	12
676.2.f.i.239.4		16	13.6	odd	12
676.2.l.i.19.1		16	13.5	odd	4
676.2.l.i.19.3		16	52.31	even	4
676.2.l.i.427.1		16	52.3	odd	6
676.2.l.i.427.3		16	13.3	even	3
676.2.l.k.319.3		16	1.1	even	1	trivial
676.2.l.k.319.4		16	4.3	odd	2	inner
676.2.l.k.587.3		16	52.15	even	12	inner
676.2.l.k.587.4		16	13.2	odd	12	inner
676.2.l.m.19.2		16	52.47	even	4
676.2.l.m.19.4		16	13.8	odd	4
676.2.l.m.427.2		16	13.10	even	6
676.2.l.m.427.4		16	52.23	odd	6
832.2.bu.n.319.1		16	104.77	even	2
832.2.bu.n.319.4		16	104.51	odd	2
832.2.bu.n.639.1		16	104.11	even	12
832.2.bu.n.639.4		16	104.37	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:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.l (of order \(12\), degree \(4\), not 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} +(-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} +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} +(-8.23758 - 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} +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} +(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} +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} +(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	\( 16 q + 2 q^{2} - 6 q^{4} + 12 q^{5} + 14 q^{6} - 10 q^{8} + 4 q^{9} + 8 q^{14} - 2 q^{16} + 12 q^{17} + 6 q^{18} - 2 q^{20} + 28 q^{21} - 10 q^{24} - 12 q^{28} - 8 q^{29} + 42 q^{30} - 28 q^{32} + 20 q^{33} - 14 q^{34} - 6 q^{36} + 16 q^{37} - 40 q^{40} - 48 q^{41} - 28 q^{42} + 8 q^{44} - 20 q^{45} + 46 q^{46} - 10 q^{48} + 60 q^{49} - 10 q^{50} - 32 q^{53} + 16 q^{54} - 60 q^{56} - 12 q^{57} + 48 q^{58} + 24 q^{60} + 4 q^{61} - 18 q^{62} + 56 q^{66} + 16 q^{68} - 12 q^{69} - 28 q^{70} - 56 q^{72} - 20 q^{73} + 4 q^{74} - 22 q^{76} - 44 q^{80} + 48 q^{81} - 84 q^{84} - 20 q^{85} - 16 q^{86} + 36 q^{88} + 52 q^{89} - 12 q^{92} + 92 q^{93} - 38 q^{94} + 72 q^{96} + 28 q^{97} + 2 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 6 * q^4 + 12 * q^5 + 14 * q^6 - 10 * q^8 + 4 * q^9 + 8 * q^14 - 2 * q^16 + 12 * q^17 + 6 * q^18 - 2 * q^20 + 28 * q^21 - 10 * q^24 - 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^53 + 16 * q^54 - 60 * q^56 - 12 * q^57 + 48 * q^58 + 24 * q^60 + 4 * q^61 - 18 * q^62 + 56 * q^66 + 16 * q^68 - 12 * q^69 - 28 * q^70 - 56 * q^72 - 20 * q^73 + 4 * q^74 - 22 * q^76 - 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

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