LMFDB - Embedded newform 676.2.l.i.19.3

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			19.3
Root			$1.31256 - 0.526485i$ of defining polynomial
Character	$\chi$	$=$	676.19
Dual form			676.2.l.i.427.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.873468	−	1.11223i	0.617635	−	0.786465i
$2$	0.873468	−	1.11223i	0.617635	−	0.786465i
$3$	−2.16981	−	1.25274i	−1.25274	−	0.723270i	−0.281087	−	0.959682i	$-0.590695\pi$
$3$	−2.16981	−	1.25274i	−1.25274	−	0.723270i	−0.971653	+	0.236413i	$0.924028\pi$
$4$	−0.474107	−	1.94299i	−0.237053	−	0.971497i
$5$	2.19962	−	2.19962i	0.983701	−	0.983701i	−0.0161686	−	0.999869i	$-0.505147\pi$
$5$	2.19962	−	2.19962i	0.983701	−	0.983701i	0.999869	+	0.0161686i	$0.00514685\pi$
$6$	−3.28859	+	1.31910i	−1.34256	+	0.538519i
$7$	−0.569525	−	0.152604i	−0.215260	−	0.0576788i	0.149577	−	0.988750i	$-0.452209\pi$
$7$	−0.569525	−	0.152604i	−0.215260	−	0.0576788i	−0.364837	+	0.931071i	$0.618875\pi$
$8$	−2.57517	−	1.16983i	−0.910460	−	0.413596i
$9$	1.63871	+	2.83834i	0.546238	+	0.946112i
$10$	−0.525184	−	4.36778i	−0.166078	−	1.38121i
$11$	−0.764465	−	2.85302i	−0.230495	−	0.860219i	−0.980128	−	0.198365i	$-0.936437\pi$
$11$	−0.764465	−	2.85302i	−0.230495	−	0.860219i	0.749633	−	0.661854i	$-0.230230\pi$
$12$	−1.40534	+	4.80986i	−0.405688	+	1.38849i
$13$		0			0
$13$		0			0
$14$	−0.667192	+	0.500148i	−0.178315	+	0.133670i
$15$	−7.52831	+	2.01721i	−1.94380	+	0.520840i
$16$	−3.55045	+	1.84237i	−0.887611	+	0.460593i
$17$	2.30986	−	1.33360i	0.560222	−	0.323445i	−0.193012	−	0.981196i	$-0.561826\pi$
$17$	2.30986	−	1.33360i	0.560222	−	0.323445i	0.753235	+	0.657752i	$0.228492\pi$
$18$	4.58824	+	0.656570i	1.08146	+	0.154755i
$19$	0.835818	−	3.11932i	0.191750	−	0.715620i	−0.801334	−	0.598217i	$-0.795876\pi$
$19$	0.835818	−	3.11932i	0.191750	−	0.715620i	0.993084	−	0.117404i	$-0.0374571\pi$
$20$	−5.31671	−	3.23099i	−1.18885	−	0.722472i
$21$	1.04459	+	1.04459i	0.227948	+	0.227948i
$22$	−3.84095	−	1.64176i	−0.818894	−	0.350025i
$23$	−1.03076	+	1.78533i	−0.214928	+	0.372266i	−0.953250	−	0.302182i	$-0.902285\pi$
$23$	−1.03076	+	1.78533i	−0.214928	+	0.372266i	0.738322	+	0.674448i	$0.235618\pi$
$24$	4.12214	+	5.76432i	0.841428	+	1.17664i
$25$		−	4.67667i		−	0.935334i
$26$		0			0
$27$		−	0.695088i		−	0.133770i
$28$	−0.0264924	+	1.17893i	−0.00500659	+	0.222798i
$29$	−0.621816	+	1.07702i	−0.115468	+	0.199997i	−0.917967	−	0.396657i	$-0.870170\pi$
$29$	−0.621816	+	1.07702i	−0.115468	+	0.199997i	0.802499	+	0.596654i	$0.203504\pi$
$30$	−4.33215	+	10.1352i	−0.790938	+	1.85042i
$31$	6.34495	+	6.34495i	1.13959	+	1.13959i	0.988524	+	0.151062i	$0.0482694\pi$
$31$	6.34495	+	6.34495i	1.13959	+	1.13959i	0.151062	+	0.988524i	$0.451731\pi$
$32$	−1.05206	+	5.55816i	−0.185980	+	0.982554i
$33$	−1.91535	+	7.14819i	−0.333420	+	1.24434i
$34$	0.534321	−	3.73394i	0.0916354	−	0.640366i
$35$	−1.58841	+	0.917069i	−0.268490	+	0.155013i
$36$	4.73794	−	4.52968i	0.789657	−	0.754947i
$37$	−0.500000	+	0.133975i	−0.0821995	+	0.0220253i	−0.299684	−	0.954038i	$-0.596881\pi$
$37$	−0.500000	+	0.133975i	−0.0821995	+	0.0220253i	0.217485	+	0.976064i	$0.430215\pi$
$38$	−2.73933	−	3.65425i	−0.444379	−	0.592797i
$39$		0			0
$40$	−8.23758	+	3.09122i	−1.30248	+	0.488765i
$41$	1.50000	+	5.59808i	0.234261	+	0.874273i	0.978481	+	0.206338i	$0.0661547\pi$
$41$	1.50000	+	5.59808i	0.234261	+	0.874273i	−0.744220	+	0.667934i	$0.767179\pi$
$42$	2.07423	−	0.249407i	0.320061	−	0.0384843i
$43$	−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
$45$	9.84781	+	2.63871i	1.46803	+	0.393356i
$46$	1.08536	+	2.70587i	0.160027	+	0.398958i
$47$	−3.16813	+	3.16813i	−0.462119	+	0.462119i	−0.899350	−	0.437230i	$-0.855959\pi$
$47$	−3.16813	+	3.16813i	−0.462119	+	0.462119i	0.437230	+	0.899350i	$0.355959\pi$
$48$	10.0118	+	0.450187i	1.44508	+	0.0649789i
$49$	−5.76111	−	3.32618i	−0.823015	−	0.475168i
$50$	−5.20153	−	4.08492i	−0.735607	−	0.577695i
$51$	−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	$0.418742\pi$
$54$	−0.773097	−	0.607137i	−0.105205	−	0.0826209i
$55$	−7.95711	−	4.59404i	−1.07294	−	0.619460i
$56$	1.28810	+	1.05923i	0.172130	+	0.141545i
$57$	−5.72126	+	5.72126i	−0.757799	+	0.757799i
$58$	0.654753	+	1.63234i	0.0859733	+	0.214337i
$59$	6.80816	+	1.82424i	0.886347	+	0.237496i	0.673143	−	0.739512i	$-0.264944\pi$
$59$	6.80816	+	1.82424i	0.886347	+	0.237496i	0.213203	+	0.977008i	$0.431610\pi$
$60$	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	$-0.336729\pi$
$62$	12.5991	−	1.51493i	1.60009	−	0.192396i
$63$	−0.500148	−	1.86658i	−0.0630127	−	0.235167i
$64$	5.26301	+	6.02501i	0.657876	+	0.753126i
$65$		0			0
$66$	6.27743	+	8.37403i	0.772698	+	1.03077i
$67$	7.18077	−	1.92408i	0.877270	−	0.235064i	0.208041	−	0.978120i	$-0.433291\pi$
$67$	7.18077	−	1.92408i	0.877270	−	0.235064i	0.669229	+	0.743056i	$0.266624\pi$
$68$	−3.68629	−	3.85577i	−0.447028	−	0.467581i
$69$	4.47310	−	2.58254i	0.538498	−	0.310902i
$70$	−0.367435	+	2.56771i	−0.0439169	+	0.306900i
$71$	0.530611	−	1.98027i	0.0629719	−	0.235014i	−0.927266	−	0.374404i	$-0.877847\pi$
$71$	0.530611	−	1.98027i	0.0629719	−	0.235014i	0.990238	+	0.139390i	$0.0445140\pi$
$72$	−0.899605	−	9.22621i	−0.106020	−	1.08732i
$73$	−0.0440105	−	0.0440105i	−0.00515104	−	0.00515104i	0.704527	−	0.709678i	$-0.251159\pi$
$73$	−0.0440105	−	0.0440105i	−0.00515104	−	0.00515104i	−0.709678	+	0.704527i	$0.751159\pi$
$74$	−0.287724	+	0.673137i	−0.0334472	+	0.0782506i
$75$	−5.85865	+	10.1475i	−0.676499	+	1.17173i
$76$	−6.45708	−	0.145100i	−0.740678	−	0.0166441i
$77$			1.74153i			0.198466i
$78$		0			0
$79$		−	2.73286i		−	0.307471i	−0.988112	−	0.153735i	$-0.950870\pi$
$79$		−	2.73286i		−	0.307471i	0.988112	−	0.153735i	$-0.0491303\pi$
$80$	−3.75711	+	11.8622i	−0.420058	+	1.32623i
$81$	4.04538	−	7.00680i	0.449486	−	0.778533i
$82$	7.53655	+	3.22140i	0.832272	+	0.355744i
$83$	−10.1844	−	10.1844i	−1.11789	−	1.11789i	−0.992051	−	0.125834i	$-0.959839\pi$
$83$	−10.1844	−	10.1844i	−1.11789	−	1.11789i	−0.125834	−	0.992051i	$-0.540161\pi$
$84$	1.53438	−	2.52487i	0.167415	−	0.275486i
$85$	2.14740	−	8.01422i	0.232919	−	0.869264i
$86$	−10.1009	−	1.44543i	−1.08921	−	0.155864i
$87$	2.69844	−	1.55795i	0.289304	−	0.167029i
$88$	−1.36892	+	8.24131i	−0.145927	+	0.878527i
$89$	8.01501	−	2.14761i	0.849589	−	0.227647i	0.192348	−	0.981327i	$-0.438390\pi$
$89$	8.01501	−	2.14761i	0.849589	−	0.227647i	0.657241	+	0.753680i	$0.271723\pi$
$90$	11.5366	−	8.64819i	1.21606	−	0.911599i
$91$		0			0
$92$	3.95757	+	1.15632i	0.412605	+	0.120555i
$93$	−5.81876	−	21.7159i	−0.603377	−	2.25183i
$94$	0.756425	+	6.29094i	0.0780193	+	0.648861i
$95$	−5.02283	−	8.69980i	−0.515332	−	0.892581i
$96$	9.24570	−	10.7422i	0.943635	−	1.09637i
$97$	−4.58039	−	1.22731i	−0.465068	−	0.124615i	0.0186732	−	0.999826i	$-0.494056\pi$
$97$	−4.58039	−	1.22731i	−0.465068	−	0.124615i	−0.483741	+	0.875211i	$0.660722\pi$
$98$	−8.73161	+	3.50236i	−0.882026	+	0.353792i
$99$	6.84510	−	6.84510i	0.687958	−	0.687958i
$100$	−9.08674	+	2.21724i	−0.908674	+	0.221724i
$101$	−7.77554	−	4.48921i	−0.773695	−	0.446693i	0.0604964	−	0.998168i	$-0.480732\pi$
$101$	−7.77554	−	4.48921i	−0.773695	−	0.446693i	−0.834191	+	0.551476i	$0.814065\pi$
$102$	−5.83703	+	7.43258i	−0.577953	+	0.735935i
$103$	−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
$106$	3.21145	−	4.08930i	0.311924	−	0.397188i
$107$	16.3364	+	9.43183i	1.57930	+	0.911809i	0.994957	+	0.100302i	$0.0319810\pi$
$107$	16.3364	+	9.43183i	1.57930	+	0.911809i	0.584343	+	0.811507i	$0.301352\pi$
$108$	−1.35055	+	0.329546i	−0.129957	+	0.0317106i
$109$	2.95252	−	2.95252i	0.282800	−	0.282800i	−0.551425	−	0.834225i	$-0.685916\pi$
$109$	2.95252	−	2.95252i	0.282800	−	0.282800i	0.834225	+	0.551425i	$0.185916\pi$
$110$	−12.0599	+	4.83738i	−1.14987	+	0.461226i
$111$	1.25274	+	0.335671i	0.118905	+	0.0318604i
$112$	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	$0.918843\pi$
$114$	1.36601	+	11.3607i	0.127939	+	1.06403i
$115$	1.65976	+	6.19432i	0.154774	+	0.577623i
$116$	2.38744	+	0.697563i	0.221669	+	0.0647671i
$117$		0			0
$118$	7.97568	−	5.97882i	0.734221	−	0.550395i
$119$	−1.51903	+	0.407024i	−0.139250	+	0.0373118i
$120$	21.7465	+	3.61218i	1.98517	+	0.329745i
$121$	1.97094	−	1.13792i	0.179177	−	0.103448i
$122$	−11.1354	−	1.59345i	−1.00815	−	0.144264i
$123$	3.75822	−	14.0259i	0.338867	−	1.26467i
$124$	9.32001	−	15.3364i	0.836962	−	1.37725i
$125$	0.711203	+	0.711203i	0.0636119	+	0.0636119i
$126$	−2.51292	−	1.07412i	−0.223869	−	0.0956899i
$127$	6.04172	−	10.4646i	0.536116	−	0.928580i	−0.462993	−	0.886362i	$-0.653224\pi$
$127$	6.04172	−	10.4646i	0.536116	−	0.928580i	0.999108	−	0.0422176i	$-0.0134423\pi$
$128$	11.2983	−	0.591017i	0.998635	−	0.0522390i
$129$			18.0775i			1.59163i
$130$		0			0
$131$		−	19.1689i		−	1.67479i	−0.546597	−	0.837396i	$-0.684077\pi$
$131$		−	19.1689i		−	1.67479i	0.546597	−	0.837396i	$-0.315923\pi$
$132$	14.7970	+	0.332510i	1.28791	+	0.0289412i
$133$	−0.952039	+	1.64898i	−0.0825523	+	0.142985i
$134$	4.13215	−	9.66728i	0.356964	−	0.835126i
$135$	−1.52893	−	1.52893i	−0.131589	−	0.131589i
$136$	−7.50835	+	0.732105i	−0.643836	+	0.0627775i
$137$	−1.87840	+	7.01027i	−0.160482	+	0.598927i	0.838091	+	0.545530i	$0.183672\pi$
$137$	−1.87840	+	7.01027i	−0.160482	+	0.598927i	−0.998573	+	0.0533974i	$0.982995\pi$
$138$	1.03473	−	7.23088i	0.0880819	−	0.615533i
$139$	9.61885	−	5.55344i	0.815860	−	0.471037i	−0.0331268	−	0.999451i	$-0.510547\pi$
$139$	9.61885	−	5.55344i	0.815860	−	0.471037i	0.848987	+	0.528414i	$0.177213\pi$
$140$	2.53494	+	2.65148i	0.214241	+	0.224091i
$141$	10.8431	−	2.90539i	0.913152	−	0.244678i
$142$	−1.73904	−	2.31986i	−0.145937	−	0.194678i
$143$		0			0
$144$	−11.0474	−	7.05823i	−0.920620	−	0.588186i
$145$	1.00127	+	3.73679i	0.0831509	+	0.310324i
$146$	−0.0873915	+	0.0105080i	−0.00723257	+	0.000869647i
$147$	8.33367	+	14.4343i	0.687349	+	1.19052i
$148$	0.497365	+	0.907978i	0.0408832	+	0.0746354i
$149$	5.01948	+	1.34497i	0.411212	+	0.110184i	0.458494	−	0.888698i	$-0.348389\pi$
$149$	5.01948	+	1.34497i	0.411212	+	0.110184i	−0.0472817	+	0.998882i	$0.515056\pi$
$150$	6.16898	+	15.3797i	0.503695	+	1.25574i
$151$	3.67697	−	3.67697i	0.299227	−	0.299227i	−0.541484	−	0.840711i	$-0.682137\pi$
$151$	3.67697	−	3.67697i	0.299227	−	0.299227i	0.840711	+	0.541484i	$0.182137\pi$
$152$	−5.80144	+	7.05501i	−0.470559	+	0.572237i
$153$	7.57039	+	4.37076i	0.612029	+	0.353355i
$154$	1.93698	+	1.52117i	0.156086	+	0.122579i
$155$	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	$0.641271\pi$
$158$	−3.03956	−	2.38706i	−0.241815	−	0.189905i
$159$	−7.97767	−	4.60591i	−0.632671	−	0.365272i
$160$	9.91172	+	14.5400i	0.783590	+	1.14949i
$161$	0.859490	−	0.859490i	0.0677373	−	0.0677373i
$162$	−4.25966	−	10.6196i	−0.334670	−	0.834355i
$163$	13.7271	+	3.67817i	1.07519	+	0.288097i	0.752625	−	0.658450i	$-0.228787\pi$
$163$	13.7271	+	3.67817i	1.07519	+	0.288097i	0.322567	+	0.946547i	$0.395454\pi$
$164$	10.1659	−	5.56858i	0.793821	−	0.434833i
$165$	11.5103	+	19.9364i	0.896073	+	1.55204i
$166$	−20.2232	+	2.43164i	−1.56962	+	0.188732i
$167$	−2.41236	−	9.00303i	−0.186674	−	0.696676i	−0.994266	−	0.106935i	$-0.965896\pi$
$167$	−2.41236	−	9.00303i	−0.186674	−	0.696676i	0.807592	−	0.589741i	$-0.200770\pi$
$168$	−1.46800	−	3.91198i	−0.113259	−	0.301816i
$169$		0			0
$170$	−7.03796	−	9.38857i	−0.539787	−	0.720070i
$171$	10.2233	−	2.73933i	0.781798	−	0.209482i
$172$	−10.4305	+	9.97200i	−0.795316	+	0.760358i
$173$	−19.8249	+	11.4459i	−1.50726	+	0.870215i	−0.507292	+	0.861774i	$0.669353\pi$
$173$	−19.8249	+	11.4459i	−1.50726	+	0.870215i	−0.999964	+	0.00844060i	$0.997313\pi$
$174$	0.624210	−	4.36210i	0.0473213	−	0.330690i
$175$	−0.713678	+	2.66348i	−0.0539490	+	0.201340i
$176$	7.97053	+	8.72107i	0.600801	+	0.657376i
$177$	−12.4871	−	12.4871i	−0.938588	−	0.938588i
$178$	4.61221	−	10.7904i	0.345700	−	0.808774i
$179$	−6.60927	+	11.4476i	−0.494000	+	0.855633i	−0.999976	−	0.00691464i	$-0.997799\pi$
$179$	−6.60927	+	11.4476i	−0.494000	+	0.855633i	0.505976	+	0.862547i	$0.331132\pi$
$180$	0.458087	−	20.3853i	0.0341438	−	1.51943i
$181$		−	26.1208i		−	1.94154i	−0.240009	−	0.970771i	$-0.577151\pi$
$181$		−	26.1208i		−	1.94154i	0.240009	−	0.970771i	$-0.422849\pi$
$182$		0			0
$183$			19.9288i			1.47318i
$184$	4.74290	−	3.39171i	0.349651	−	0.250040i
$185$	−0.805117	+	1.39450i	−0.0591934	+	0.102526i
$186$	−29.2355	−	12.4964i	−2.14365	−	0.916277i
$187$	−5.57059	−	5.57059i	−0.407362	−	0.407362i
$188$	7.65768	+	4.65362i	0.558494	+	0.339400i
$189$	−0.106073	+	0.395870i	−0.00771568	+	0.0287953i
$190$	−14.0635	−	2.01246i	−1.02027	−	0.145999i
$191$	−12.2440	+	7.06905i	−0.885942	+	0.511499i	−0.872613	−	0.488412i	$-0.837576\pi$
$191$	−12.2440	+	7.06905i	−0.885942	+	0.511499i	−0.0133290	+	0.999911i	$0.504243\pi$
$192$	−3.87195	−	19.6663i	−0.279434	−	1.41929i
$193$	−22.4082	+	6.00426i	−1.61298	+	0.432196i	−0.948928	−	0.315493i	$-0.897830\pi$
$193$	−22.4082	+	6.00426i	−1.61298	+	0.432196i	−0.664049	+	0.747689i	$0.731163\pi$
$194$	−5.36588	+	4.02243i	−0.385247	+	0.288793i
$195$		0			0
$196$	−3.73136	+	12.7708i	−0.266526	+	0.912197i
$197$	1.60628	+	5.99473i	0.114443	+	0.427107i	0.999245	−	0.0388607i	$-0.0123729\pi$
$197$	1.60628	+	5.99473i	0.114443	+	0.427107i	−0.884802	+	0.465968i	$0.845706\pi$
$198$	−1.63434	−	13.5923i	−0.116148	−	0.965962i
$199$	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
$201$	−17.9913	−	4.82075i	−1.26901	−	0.340029i
$202$	−11.7847	+	4.72700i	−0.829169	+	0.332590i
$203$	0.518497	−	0.518497i	0.0363913	−	0.0363913i
$204$	3.16826	+	12.9842i	0.221823	+	0.909079i
$205$	15.6131	+	9.01422i	1.09046	+	0.629580i
$206$	−8.38678	+	10.6793i	−0.584335	+	0.744062i
$207$	−6.75647			−0.469607
$208$		0			0
$209$	−9.53844			−0.659788
$210$	4.01393	−	5.11113i	0.276988	−	0.352702i
$211$	15.7735	+	9.10682i	1.08589	+	0.626940i	0.932480	−	0.361223i	$-0.117641\pi$
$211$	15.7735	+	9.10682i	1.08589	+	0.626940i	0.153412	+	0.988162i	$0.450974\pi$
$212$	−1.74313	−	7.14375i	−0.119719	−	0.490634i
$213$	−3.63208	+	3.63208i	−0.248866	+	0.248866i
$214$	24.7597	−	9.93142i	1.69254	−	0.678898i
$215$	−21.6797	−	5.80907i	−1.47855	−	0.396175i
$216$	−0.813133	+	1.78997i	−0.0553267	+	0.121792i
$217$	−2.64534	−	4.58187i	−0.179578	−	0.311038i
$218$	−0.704946	−	5.86281i	−0.0477450	−	0.397080i
$219$	0.0403607	+	0.150628i	0.00272732	+	0.0101785i
$220$	−5.15367	+	17.6387i	−0.347460	+	1.18920i
$221$		0			0
$222$	1.46757	−	1.10014i	0.0984969	−	0.0738363i
$223$	3.42992	−	0.919045i	0.229685	−	0.0615438i	−0.142141	−	0.989846i	$-0.545399\pi$
$223$	3.42992	−	0.919045i	0.229685	−	0.0615438i	0.371826	+	0.928303i	$0.378732\pi$
$224$	1.44737	−	3.00496i	0.0967066	−	0.200778i
$225$	13.2740	−	7.66372i	0.884931	−	0.510915i
$226$	−7.89976	−	1.13044i	−0.525484	−	0.0751960i
$227$	−4.51279	+	16.8419i	−0.299524	+	1.11784i	0.638033	+	0.770009i	$0.279748\pi$
$227$	−4.51279	+	16.8419i	−0.299524	+	1.11784i	−0.937557	+	0.347831i	$0.886918\pi$
$228$	13.8289	+	8.40388i	0.915838	+	0.556560i
$229$	14.2869	+	14.2869i	0.944105	+	0.944105i	0.998519	−	0.0544132i	$-0.0173288\pi$
$229$	14.2869	+	14.2869i	0.944105	+	0.944105i	−0.0544132	+	0.998519i	$0.517329\pi$
$230$	8.33925	+	3.56451i	0.549874	+	0.235037i
$231$	2.18168	−	3.77878i	0.143544	−	0.248626i
$232$	2.86121	−	2.04609i	0.187847	−	0.134332i
$233$		−	13.3205i		−	0.872655i	−0.899788	−	0.436328i	$-0.856279\pi$
$233$		−	13.3205i		−	0.872655i	0.899788	−	0.436328i	$-0.143721\pi$
$234$		0			0
$235$			13.9374i			0.909174i
$236$	0.316692	−	14.0931i	0.0206149	−	0.917382i
$237$	−3.42356	+	5.92978i	−0.222384	+	0.385181i
$238$	−0.874123	+	2.04503i	−0.0566610	+	0.132560i
$239$	10.2493	+	10.2493i	0.662972	+	0.662972i	0.956079	−	0.293108i	$-0.0946894\pi$
$239$	10.2493	+	10.2493i	0.662972	+	0.662972i	−0.293108	+	0.956079i	$0.594689\pi$
$240$	23.0124	−	21.0319i	1.48545	−	1.35761i
$241$	3.58474	−	13.3784i	0.230914	−	0.861781i	−0.749035	−	0.662531i	$-0.769482\pi$
$241$	3.58474	−	13.3784i	0.230914	−	0.861781i	0.979949	−	0.199251i	$-0.0638509\pi$
$242$	0.455923	−	3.18608i	0.0293079	−	0.204809i
$243$	−19.3613	+	11.1782i	−1.24203	+	0.717084i
$244$	−11.4987	+	10.9932i	−0.736127	+	0.703770i
$245$	−19.9886	+	5.35593i	−1.27702	+	0.342178i
$246$	−12.3173	−	16.4311i	−0.785322	−	1.04761i
$247$		0			0
$248$	−8.91683	−	23.7618i	−0.566219	−	1.50888i
$249$	9.33982	+	34.8567i	0.591887	+	2.20895i
$250$	1.41223	−	0.169807i	0.0893175	−	0.0107396i
$251$	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
$253$	5.88156	+	1.57596i	0.369770	+	0.0990797i
$254$	−6.36174	−	15.8602i	−0.399171	−	0.995160i
$255$	−14.6992	+	14.6992i	−0.920498	+	0.920498i
$256$	9.21132	−	13.0825i	0.575708	−	0.817656i
$257$	−5.55423	−	3.20673i	−0.346463	−	0.200031i	0.316663	−	0.948538i	$-0.397437\pi$
$257$	−5.55423	−	3.20673i	−0.346463	−	0.200031i	−0.663126	+	0.748507i	$0.730771\pi$
$258$	20.1063	+	15.7901i	1.25176	+	0.983049i
$259$	0.305208			0.0189647
$260$		0			0
$261$	−4.07591			−0.252293
$262$	−21.3202	−	16.7434i	−1.31716	−	1.03441i
$263$	−4.59709	−	2.65413i	−0.283469	−	0.163661i	0.351524	−	0.936179i	$-0.385664\pi$
$263$	−4.59709	−	2.65413i	−0.283469	−	0.163661i	−0.634993	+	0.772518i	$0.718997\pi$
$264$	13.2945	−	16.1672i	0.818220	−	0.995021i
$265$	8.08728	−	8.08728i	0.496798	−	0.496798i
$266$	1.00247	+	2.49922i	0.0614652	+	0.153237i
$267$	−20.0814	−	5.38080i	−1.22896	−	0.329300i
$268$	−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	$0.734715\pi$
$270$	−3.03599	+	0.365049i	−0.184765	+	0.0222162i
$271$	6.60453	+	24.6484i	0.401196	+	1.49729i	0.810964	+	0.585096i	$0.198943\pi$
$271$	6.60453	+	24.6484i	0.401196	+	1.49729i	−0.409768	+	0.912190i	$0.634390\pi$
$272$	−5.74404	+	8.99048i	−0.348283	+	0.545128i
$273$		0			0
$274$	6.15630	+	8.21245i	0.371916	+	0.496132i
$275$	−13.3427	+	3.57515i	−0.804592	+	0.215590i
$276$	−7.13859	−	7.46680i	−0.429693	−	0.449448i
$277$	−0.462736	+	0.267161i	−0.0278031	+	0.0160521i	−0.513837	−	0.857888i	$-0.671776\pi$
$277$	−0.462736	+	0.267161i	−0.0278031	+	0.0160521i	0.486034	+	0.873940i	$0.338443\pi$
$278$	2.22505	−	15.5491i	0.133450	−	0.932574i
$279$	−7.61154	+	28.4066i	−0.455691	+	1.70066i
$280$	5.16324	−	0.503444i	0.308563	−	0.0300865i
$281$	0.275535	+	0.275535i	0.0164370	+	0.0164370i	0.715278	−	0.698840i	$-0.246300\pi$
$281$	0.275535	+	0.275535i	0.0164370	+	0.0164370i	−0.698840	+	0.715278i	$0.746300\pi$
$282$	6.23962	−	14.5978i	0.371564	−	0.869283i
$283$	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	$0.00822935\pi$
$284$	−4.09921	−	0.0921153i	−0.243243	−	0.00546604i
$285$			25.1692i			1.49090i
$286$		0			0
$287$		−	3.41715i		−	0.201708i
$288$	−17.5000	+	6.12214i	−1.03119	+	0.360750i
$289$	−4.94304	+	8.56160i	−0.290767	+	0.503624i
$290$	5.03074	+	2.15033i	0.295415	+	0.126271i
$291$	8.40107	+	8.40107i	0.492479	+	0.492479i
$292$	−0.0646464	+	0.106378i	−0.00378314	+	0.00622529i
$293$	0.530326	−	1.97920i	0.0309820	−	0.115626i	−0.948703	−	0.316168i	$-0.897604\pi$
$293$	0.530326	−	1.97920i	0.0309820	−	0.115626i	0.979685	+	0.200542i	$0.0642703\pi$
$294$	23.3335	+	3.33898i	1.36084	+	0.194734i
$295$	18.9880	−	10.9627i	1.10552	−	0.638275i
$296$	1.44431	+	0.239906i	0.0839490	+	0.0139443i
$297$	−1.98310	+	0.531371i	−0.115071	+	0.0308333i
$298$	5.88027	−	4.40803i	0.340635	−	0.255350i
$299$		0			0
$300$	22.4941	+	6.57233i	1.29870	+	0.379454i
$301$	1.10106	+	4.10923i	0.0634643	+	0.236852i
$302$	−0.877916	−	7.30135i	−0.0505184	−	0.420145i
$303$	11.2476	+	19.4814i	0.646159	+	1.11918i
$304$	2.77942	+	12.6149i	0.159410	+	0.723511i
$305$	−23.9000	−	6.40398i	−1.36851	−	0.366691i
$306$	11.4738	−	4.60228i	0.655912	−	0.263095i
$307$	−11.4337	+	11.4337i	−0.652558	+	0.652558i	−0.953608	−	0.301050i	$-0.902663\pi$
$307$	−11.4337	+	11.4337i	−0.652558	+	0.652558i	0.301050	+	0.953608i	$0.402663\pi$
$308$	3.38378	−	0.825671i	0.192809	−	0.0470470i
$309$	20.8339	+	12.0284i	1.18520	+	0.684274i
$310$	24.3811	−	31.0456i	1.38475	−	1.76327i
$311$	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	$0.195754\pi$
$314$	−9.39894	+	11.9681i	−0.530413	+	0.675400i
$315$	−5.20590	−	3.00563i	−0.293319	−	0.169348i
$316$	−5.30993	+	1.29567i	−0.298707	+	0.0728870i
$317$	−0.0141017	+	0.0141017i	−0.000792031	+	0.000792031i	−0.707503	−	0.706711i	$-0.750178\pi$
$317$	−0.0141017	+	0.0141017i	−0.000792031	+	0.000792031i	0.706711	+	0.707503i	$0.250178\pi$
$318$	−12.0911	+	4.84988i	−0.678034	+	0.271968i
$319$	3.54811	+	0.950714i	0.198656	+	0.0532297i
$320$	24.8294	+	1.67611i	1.38800	+	0.0936976i
$321$	−23.6312	−	40.9305i	−1.31897	−	2.28452i
$322$	−0.205213	−	1.70669i	−0.0114361	−	0.0951100i
$323$	−2.22929	−	8.31982i	−0.124041	−	0.462927i
$324$	−15.5321	−	4.53817i	−0.862894	−	0.252120i
$325$		0			0
$326$	16.0812	−	12.0549i	0.890654	−	0.667662i
$327$	−10.1051	+	2.70767i	−0.558816	+	0.149734i
$328$	2.68603	−	16.1707i	0.148311	−	0.892880i
$329$	2.28780	−	1.32086i	0.126130	−	0.0728214i
$330$	32.2277	+	4.61173i	1.77407	+	0.253867i
$331$	−1.09342	+	4.08070i	−0.0600998	+	0.224295i	−0.989443	−	0.144921i	$-0.953707\pi$
$331$	−1.09342	+	4.08070i	−0.0600998	+	0.224295i	0.929343	+	0.369216i	$0.120374\pi$
$332$	−14.9598	+	24.6168i	−0.821023	+	1.35102i
$333$	−1.19962	−	1.19962i	−0.0657389	−	0.0657389i
$334$	−12.1205	−	5.18077i	−0.663207	−	0.283479i
$335$	11.5627	−	20.0272i	0.631739	−	1.09420i
$336$	−5.63327	−	1.78423i	−0.307320	−	0.0973378i
$337$			9.58550i			0.522155i	0.965318	+	0.261078i	$0.0840778\pi$
$337$			9.58550i			0.522155i	−0.965318	+	0.261078i	$0.915922\pi$
$338$		0			0
$339$			14.1381i			0.767877i
$340$	−16.5897	−	0.372794i	−0.899701	−	0.0202176i
$341$	13.2518	−	22.9528i	0.717625	−	1.24296i
$342$	5.88299	−	13.7634i	0.318116	−	0.744240i
$343$	5.69196	+	5.69196i	0.307337	+	0.307337i
$344$	1.98046	+	20.3113i	0.106779	+	1.09511i
$345$	4.15850	−	15.5197i	0.223886	−	0.835555i
$346$	−4.58593	+	32.0474i	−0.246541	+	1.72288i
$347$	3.56473	−	2.05810i	0.191364	−	0.110484i	−0.401257	−	0.915966i	$-0.631426\pi$
$347$	3.56473	−	2.05810i	0.191364	−	0.110484i	0.592621	+	0.805481i	$0.298093\pi$
$348$	−4.30643	−	4.50442i	−0.230849	−	0.241463i
$349$	28.0634	−	7.51958i	1.50220	−	0.402514i	0.588365	−	0.808595i	$-0.299772\pi$
$349$	28.0634	−	7.51958i	1.50220	−	0.402514i	0.913837	+	0.406082i	$0.133105\pi$
$350$	2.33903	+	3.12024i	0.125026	+	0.166784i
$351$		0			0
$352$	16.6618	−	1.24747i	0.888079	−	0.0664904i
$353$	−6.81469	−	25.4328i	−0.362709	−	1.35365i	−0.870500	−	0.492169i	$-0.836204\pi$
$353$	−6.81469	−	25.4328i	−0.362709	−	1.35365i	0.507790	−	0.861481i	$-0.330463\pi$
$354$	−24.7956	+	2.98143i	−1.31787	+	0.158461i
$355$	−3.18869	−	5.52298i	−0.169238	−	0.293129i
$356$	−7.97277	−	14.5549i	−0.422556	−	0.771408i
$357$	3.80591	+	1.01979i	0.201430	+	0.0539730i
$358$	6.95935	+	17.3501i	0.367813	+	0.916982i
$359$	7.69873	−	7.69873i	0.406324	−	0.406324i	−0.474131	−	0.880454i	$-0.657238\pi$
$359$	7.69873	−	7.69873i	0.406324	−	0.406324i	0.880454	+	0.474131i	$0.157238\pi$
$360$	−22.2730	−	18.3154i	−1.17389	−	0.965305i
$361$	7.42294	+	4.28564i	0.390681	+	0.225560i
$362$	−29.0523	−	22.8157i	−1.52695	−	1.19916i
$363$	−5.70210			−0.299282
$364$		0			0
$365$	−0.193613			−0.0101342
$366$	22.1654	+	17.4072i	1.15861	+	0.909889i
$367$	−1.81711	−	1.04911i	−0.0948522	−	0.0547630i	0.451824	−	0.892107i	$-0.350774\pi$
$367$	−1.81711	−	1.04911i	−0.0948522	−	0.0547630i	−0.546676	+	0.837344i	$0.684107\pi$
$368$	0.370415	−	8.23775i	0.0193092	−	0.429422i
$369$	−13.4311	+	13.4311i	−0.699198	+	0.699198i
$370$	0.847764	+	2.11353i	0.0440731	+	0.109877i
$371$	−2.09396	−	0.561074i	−0.108713	−	0.0291295i
$372$	−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	$0.571555\pi$
$374$	−11.0615	+	1.33004i	−0.571976	+	0.0687746i
$375$	−0.652222	−	2.43413i	−0.0336806	−	0.125698i
$376$	11.8646	−	4.45231i	0.611872	−	0.229610i
$377$		0			0
$378$	0.347647	+	0.463757i	0.0178810	+	0.0238531i
$379$	27.9257	−	7.48268i	1.43445	−	0.384360i	0.543863	−	0.839174i	$-0.316961\pi$
$379$	27.9257	−	7.48268i	1.43445	−	0.384360i	0.890586	+	0.454814i	$0.150294\pi$
$380$	−14.5223	+	13.8840i	−0.744978	+	0.712232i
$381$	−26.2187	+	15.1374i	−1.34323	+	0.775512i
$382$	−2.83230	+	19.7927i	−0.144913	+	1.01268i
$383$	−3.91754	+	14.6205i	−0.200177	+	0.747070i	0.790689	+	0.612218i	$0.209723\pi$
$383$	−3.91754	+	14.6205i	−0.200177	+	0.747070i	−0.990866	+	0.134852i	$0.956944\pi$
$384$	−25.2555	−	12.8714i	−1.28881	−	0.656840i
$385$	3.83070	+	3.83070i	0.195231	+	0.195231i
$386$	−12.8947	+	30.1676i	−0.656325	+	1.53549i
$387$	11.8236	−	20.4791i	0.601028	−	1.04101i
$388$	−0.213064	+	9.48154i	−0.0108167	+	0.481352i
$389$			30.3695i			1.53979i	0.638168	+	0.769897i	$0.279692\pi$
$389$			30.3695i			1.53979i	−0.638168	+	0.769897i	$0.720308\pi$
$390$		0			0
$391$			5.49846i			0.278069i
$392$	10.9448	+	15.3050i	0.552795	+	0.773018i
$393$	−24.0136	+	41.5928i	−1.21133	+	2.09808i
$394$	8.07056	+	3.44965i	0.406589	+	0.173791i
$395$	−6.01125	−	6.01125i	−0.302459	−	0.302459i
$396$	−16.5453	−	10.0547i	−0.831432	−	0.505266i
$397$	−4.14218	+	15.4588i	−0.207890	+	0.775857i	0.780659	+	0.624957i	$0.214884\pi$
$397$	−4.14218	+	15.4588i	−0.207890	+	0.775857i	−0.988549	+	0.150899i	$0.951783\pi$
$398$	4.21990	+	0.603862i	0.211525	+	0.0302689i
$399$	4.13149	−	2.38531i	0.206833	−	0.119415i
$400$	8.61617	+	16.6043i	0.430809	+	0.830213i
$401$	13.2993	−	3.56354i	0.664137	−	0.177955i	0.0890245	−	0.996029i	$-0.471625\pi$
$401$	13.2993	−	3.56354i	0.664137	−	0.177955i	0.575112	+	0.818075i	$0.304958\pi$
$402$	−21.0766	+	15.7996i	−1.05120	+	0.788014i
$403$		0			0
$404$	−5.03606	+	17.2362i	−0.250554	+	0.857532i
$405$	−6.51401	−	24.3106i	−0.323684	−	1.20800i
$406$	−0.123797	−	1.02958i	−0.00614393	−	0.0510971i
$407$	0.764465	+	1.32409i	0.0378931	+	0.0656328i
$408$	17.2088	+	7.81748i	0.851964	+	0.387023i
$409$	0.564858	+	0.151353i	0.0279305	+	0.00748394i	0.272757	−	0.962083i	$-0.412064\pi$
$409$	0.564858	+	0.151353i	0.0279305	+	0.00748394i	−0.244827	+	0.969567i	$0.578731\pi$
$410$	23.6634	−	9.49169i	1.16865	−	0.468761i
$411$	12.8578	−	12.8578i	0.634228	−	0.634228i
$412$	4.55223	+	18.6560i	0.224272	+	0.919117i
$413$	−3.59903	−	2.07790i	−0.177097	−	0.102247i
$414$	−5.90156	+	7.51475i	−0.290046	+	0.369330i
$415$	−44.8037			−2.19933
$416$		0			0
$417$	−27.8281			−1.36275
$418$	−8.33152	+	10.6089i	−0.407508	+	0.518900i
$419$	−31.9541	−	18.4487i	−1.56106	−	0.901278i	−0.997150	−	0.0754420i	$-0.975963\pi$
$419$	−31.9541	−	18.4487i	−1.56106	−	0.901278i	−0.563910	−	0.825836i	$-0.690703\pi$
$420$	−2.17871	−	8.92882i	−0.106310	−	0.435682i
$421$	22.1875	−	22.1875i	1.08135	−	1.08135i	0.0849697	−	0.996384i	$-0.472921\pi$
$421$	22.1875	−	22.1875i	1.08135	−	1.08135i	0.996384	−	0.0849697i	$-0.0270794\pi$
$422$	23.9065	−	9.58920i	1.16375	−	0.466795i
$423$	−14.1839	−	3.80056i	−0.689643	−	0.184789i
$424$	−9.46805	−	4.30107i	−0.459809	−	0.208878i
$425$	−6.23679	−	10.8024i	−0.302529	−	0.523995i
$426$	0.867199	+	7.21222i	0.0420159	+	0.349433i
$427$	1.21383	+	4.53006i	0.0587411	+	0.219225i
$428$	10.5808	−	36.2132i	0.511441	−	1.75043i
$429$		0			0
$430$	−25.3976	+	19.0388i	−1.22478	+	0.918132i
$431$	−30.0439	+	8.05023i	−1.44716	+	0.387766i	−0.895036	−	0.445994i	$-0.852850\pi$
$431$	−30.0439	+	8.05023i	−1.44716	+	0.387766i	−0.552127	+	0.833760i	$0.686183\pi$
$432$	1.28061	+	2.46787i	0.0616134	+	0.118736i
$433$	−9.34712	+	5.39656i	−0.449194	+	0.259342i	−0.707490	−	0.706724i	$-0.750172\pi$
$433$	−9.34712	+	5.39656i	−0.449194	+	0.259342i	0.258296	+	0.966066i	$0.416839\pi$
$434$	−7.40671	−	1.05989i	−0.355534	−	0.0508763i
$435$	2.50866	−	9.36245i	0.120281	−	0.448895i
$436$	−7.13654	−	4.33692i	−0.341778	−	0.207701i
$437$	4.70747	+	4.70747i	0.225189	+	0.225189i
$438$	0.202787	+	0.0866785i	0.00968952	+	0.00414166i
$439$	6.48316	−	11.2292i	0.309424	−	0.535938i	−0.668812	−	0.743431i	$-0.733197\pi$
$439$	6.48316	−	11.2292i	0.309424	−	0.535938i	0.978237	+	0.207493i	$0.0665304\pi$
$440$	15.1167	+	21.1389i	0.720659	+	1.00776i
$441$		−	21.8026i		−	1.03822i
$442$		0			0
$443$			15.6512i			0.743611i	0.928311	+	0.371805i	$0.121261\pi$
$443$			15.6512i			0.743611i	−0.928311	+	0.371805i	$0.878739\pi$
$444$	0.0582732	−	2.59321i	0.00276552	−	0.123068i
$445$	12.9060	−	22.3539i	0.611805	−	1.05968i
$446$	1.97374	−	4.61762i	0.0934593	−	0.218650i
$447$	−9.20642	−	9.20642i	−0.435449	−	0.435449i
$448$	−2.07798	−	4.23455i	−0.0981751	−	0.200064i
$449$	2.89994	−	10.8227i	0.136856	−	0.510755i	−0.863127	−	0.504987i	$-0.831497\pi$
$449$	2.89994	−	10.8227i	0.136856	−	0.510755i	0.999983	−	0.00576812i	$-0.00183606\pi$
$450$	3.07056	−	21.4577i	0.144748	−	1.01153i
$451$	14.8247	−	8.55907i	0.698070	−	0.403031i
$452$	−8.15750	+	7.79893i	−0.383696	+	0.366831i
$453$	−12.5846	+	3.37203i	−0.591276	+	0.158432i
$454$	14.7903	+	19.7302i	0.694145	+	0.925982i
$455$		0			0
$456$	21.4261	−	8.04033i	1.00337	−	0.376523i
$457$	4.97316	+	18.5601i	0.232634	+	0.868204i	0.979201	+	0.202893i	$0.0650343\pi$
$457$	4.97316	+	18.5601i	0.232634	+	0.868204i	−0.746566	+	0.665311i	$0.768299\pi$
$458$	28.3695	−	3.41115i	1.32562	−	0.159393i
$459$	−0.926967	−	1.60555i	−0.0432671	−	0.0749408i
$460$	11.2486	−	6.16168i	0.524470	−	0.287290i
$461$	23.6892	+	6.34751i	1.10332	+	0.295633i	0.764114	−	0.645081i	$-0.223176\pi$
$461$	23.6892	+	6.34751i	1.10332	+	0.295633i	0.339202	+	0.940713i	$0.389843\pi$
$462$	−2.29724	−	5.72718i	−0.106877	−	0.266452i
$463$	13.2027	−	13.2027i	0.613581	−	0.613581i	−0.330296	−	0.943877i	$-0.607149\pi$
$463$	13.2027	−	13.2027i	0.613581	−	0.613581i	0.943877	+	0.330296i	$0.107149\pi$
$464$	0.223457	−	4.96951i	0.0103737	−	0.230704i
$465$	−60.5658	−	34.9677i	−2.80867	−	1.62159i
$466$	−14.8155	−	11.6350i	−0.686313	−	0.538983i
$467$	−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
$470$	15.5015	+	12.1738i	0.715033	+	0.561538i
$471$	23.3482	+	13.4801i	1.07583	+	0.621130i
$472$	−15.3981	−	12.6621i	−0.708756	−	0.582820i
$473$	−15.0693	+	15.0693i	−0.692888	+	0.692888i
$474$	3.60490	+	8.98726i	0.165579	+	0.412798i
$475$	−14.5880	−	3.90885i	−0.669344	−	0.179350i
$476$	1.51103	+	2.75850i	0.0692579	+	0.126436i
$477$	6.02501	+	10.4356i	0.275866	+	0.477814i
$478$	20.3520	−	2.44713i	0.930879	−	0.111929i
$479$	0.840559	+	3.13701i	0.0384061	+	0.143334i	0.982467	−	0.186439i	$-0.0596946\pi$
$479$	0.840559	+	3.13701i	0.0384061	+	0.143334i	−0.944060	+	0.329772i	$0.893028\pi$
$480$	−3.29172	−	43.9658i	−0.150246	−	2.00676i
$481$		0			0
$482$	−11.7487	−	15.6727i	−0.535140	−	0.713872i
$483$	−2.94165	+	0.788212i	−0.133850	+	0.0358649i
$484$	−3.14542	−	3.29003i	−0.142974	−	0.149547i
$485$	−12.7747	+	7.37550i	−0.580071	+	0.334904i
$486$	−4.47870	+	31.2980i	−0.203158	+	1.41971i
$487$	11.1003	−	41.4268i	0.503002	−	1.87723i	0.0234304	−	0.999725i	$-0.492541\pi$
$487$	11.1003	−	41.4268i	0.503002	−	1.87723i	0.479571	−	0.877503i	$-0.340792\pi$
$488$	2.18328	+	22.3914i	0.0988326	+	1.01361i
$489$	−25.1775	−	25.1775i	−1.13856	−	1.13856i
$490$	−11.5024	+	26.9101i	−0.519624	+	1.21568i
$491$	−0.796904	+	1.38028i	−0.0359638	+	0.0622911i	−0.883447	−	0.468531i	$-0.844783\pi$
$491$	−0.796904	+	1.38028i	−0.0359638	+	0.0622911i	0.847483	+	0.530822i	$0.178117\pi$
$492$	−29.0340	−	0.652435i	−1.30895	−	0.0294141i
$493$			3.31701i			0.149390i
$494$		0			0
$495$		−	30.1132i		−	1.35349i
$496$	−34.2172	−	10.8376i	−1.53640	−	0.486624i
$497$	−0.604392	+	1.04684i	−0.0271107	+	0.0469571i
$498$	46.9266	+	20.0582i	2.10283	+	0.898828i
$499$	2.89721	+	2.89721i	0.129697	+	0.129697i	0.768975	−	0.639278i	$-0.220767\pi$
$499$	2.89721	+	2.89721i	0.129697	+	0.129697i	−0.639278	+	0.768975i	$0.720767\pi$
$500$	1.04468	−	1.71905i	0.0467193	−	0.0768782i
$501$	−6.04411	+	22.5569i	−0.270031	+	1.00777i
$502$	3.52267	+	0.504088i	0.157224	+	0.0224986i
$503$	−13.0990	+	7.56273i	−0.584057	+	0.337205i	−0.762744	−	0.646701i	$-0.776148\pi$
$503$	−13.0990	+	7.56273i	−0.584057	+	0.337205i	0.178687	+	0.983906i	$0.442815\pi$
$504$	−0.895607	+	5.39184i	−0.0398935	+	0.240172i
$505$	−26.9778	+	7.22868i	−1.20050	+	0.321672i
$506$	6.89018	−	5.16509i	0.306306	−	0.229616i
$507$		0			0
$508$	−23.1970	−	6.77770i	−1.02920	−	0.300712i
$509$	−6.47337	−	24.1589i	−0.286927	−	1.07083i	−0.947420	−	0.319994i	$-0.896319\pi$
$509$	−6.47337	−	24.1589i	−0.286927	−	1.07083i	0.660493	−	0.750832i	$-0.270347\pi$
$510$	3.50959	+	29.1881i	0.155407	+	1.29247i
$511$	0.0183489	+	0.0317812i	0.000811708	+	0.00140592i
$512$	−6.50493	−	21.6722i	−0.287480	−	0.957787i
$513$	−2.16820	−	0.580967i	−0.0957284	−	0.0256503i
$514$	−8.41806	+	3.37659i	−0.371305	+	0.148935i
$515$	−21.1201	+	21.1201i	−0.930663	+	0.930663i
$516$	35.1244	−	8.57066i	1.54627	−	0.377302i
$517$	11.4607	+	6.61682i	0.504040	+	0.291007i
$518$	0.266589	−	0.339461i	0.0117133	−	0.0149150i
$519$	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	$0.856927\pi$
$522$	−3.56018	+	4.53335i	−0.155825	+	0.198419i
$523$	2.27834	+	1.31540i	0.0996249	+	0.0575185i	0.548985	−	0.835832i	$-0.315015\pi$
$523$	2.27834	+	1.31540i	0.0996249	+	0.0575185i	−0.449360	+	0.893351i	$0.648348\pi$
$524$	−37.2450	+	9.08809i	−1.62705	+	0.397015i
$525$	4.88519	−	4.88519i	0.213207	−	0.213207i
$526$	−6.96741	+	2.79472i	−0.303794	+	0.121856i
$527$	23.1175	+	6.19432i	1.00702	+	0.269829i
$528$	−6.36928	−	28.9081i	−0.277187	−	1.25806i
$529$	9.37507	+	16.2381i	0.407612	+	0.706004i
$530$	−1.93093	−	16.0589i	−0.0838741	−	0.697554i
$531$	5.97882	+	22.3132i	0.259459	+	0.968312i
$532$	3.65533	+	1.06801i	0.158478	+	0.0463042i
$533$		0			0
$534$	−23.5252	+	17.6352i	−1.01803	+	0.763149i
$535$	56.6804	−	15.1875i	2.45051	−	0.656611i
$536$	−20.7425	−	3.44542i	−0.895941	−	0.148820i
$537$	28.6817	−	16.5594i	1.23771	−	0.714590i
$538$	14.0009	+	2.00350i	0.603621	+	0.0863772i
$539$	−5.08549	+	18.9793i	−0.219048	+	0.817497i
$540$	−2.24583	+	3.69558i	−0.0966449	+	0.159032i
$541$	−14.2591	−	14.2591i	−0.613047	−	0.613047i	0.330692	−	0.943739i	$-0.392718\pi$
$541$	−14.2591	−	14.2591i	−0.613047	−	0.613047i	−0.943739	+	0.330692i	$0.892718\pi$
$542$	33.1835	+	14.1839i	1.42536	+	0.609249i
$543$	−32.7225	+	56.6771i	−1.40426	+	2.43225i
$544$	4.98224	+	14.2416i	0.213612	+	0.610603i
$545$		−	12.9889i		−	0.556381i
$546$		0			0
$547$		−	40.9532i		−	1.75103i	−0.483190	−	0.875515i	$-0.660522\pi$
$547$		−	40.9532i		−	1.75103i	0.483190	−	0.875515i	$-0.339478\pi$
$548$	14.5115	+	0.326094i	0.619899	+	0.0139300i
$549$	13.0345	−	22.5764i	0.556298	−	0.963537i
$550$	−7.67799	+	17.9629i	−0.327391	+	0.765939i
$551$	2.83983	+	2.83983i	0.120981	+	0.120981i
$552$	−14.5401	+	1.41774i	−0.618869	+	0.0603431i
$553$	−0.417045	+	1.55643i	−0.0177345	+	0.0661862i
$554$	−0.107041	+	0.748024i	−0.00454774	+	0.0317805i
$555$	3.49390	−	2.01721i	0.148308	−	0.0856256i
$556$	−15.3507	−	16.0564i	−0.651013	−	0.680944i
$557$	29.0719	−	7.78980i	1.23182	−	0.330064i	0.416530	−	0.909122i	$-0.363246\pi$
$557$	29.0719	−	7.78980i	1.23182	−	0.330064i	0.815287	+	0.579058i	$0.196579\pi$
$558$	24.9463	+	33.2781i	1.05606	+	1.40877i
$559$		0			0
$560$	3.94998	−	6.18245i	0.166917	−	0.261256i
$561$	5.10861	+	19.0656i	0.215686	+	0.804950i
$562$	0.547129	−	0.0657870i	0.0230793	−	0.00277506i
$563$	−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
$565$	−16.9554	−	4.54318i	−0.713318	−	0.191133i
$566$	−8.45732	−	21.0847i	−0.355488	−	0.886254i
$567$	−3.37321	+	3.37321i	−0.141661	+	0.141661i
$568$	−3.68298	+	4.47880i	−0.154535	+	0.187926i
$569$	19.5646	+	11.2956i	0.820192	+	0.473538i	0.850483	−	0.526003i	$-0.176310\pi$
$569$	19.5646	+	11.2956i	0.820192	+	0.473538i	−0.0302909	+	0.999541i	$0.509643\pi$
$570$	27.9939	+	21.9845i	1.17254	+	0.920829i
$571$	−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
$574$	−3.80065	−	2.98477i	−0.158636	−	0.124582i
$575$	8.34938	+	4.82052i	0.348193	+	0.201030i
$576$	−8.47643	+	24.8114i	−0.353185	+	1.03381i
$577$	−15.8624	+	15.8624i	−0.660361	+	0.660361i	−0.955465	−	0.295104i	$-0.904646\pi$
$577$	−15.8624	+	15.8624i	−0.660361	+	0.660361i	0.295104	+	0.955465i	$0.404646\pi$
$578$	5.20487	+	12.9761i	0.216494	+	0.539734i
$579$	56.1433	+	15.0435i	2.33323	+	0.625188i
$580$	6.78585	−	3.71710i	0.281767	−	0.154344i
$581$	4.24610	+	7.35446i	0.176158	+	0.305115i
$582$	16.6820	−	2.00585i	0.691490	−	0.0831450i
$583$	−2.81069	−	10.4896i	−0.116407	−	0.434436i
$584$	0.0618498	+	0.164819i	0.00255936	+	0.00682027i
$585$		0			0
$586$	−1.73810	−	2.31861i	−0.0718004	−	0.0957811i
$587$	−20.9531	+	5.61437i	−0.864827	+	0.231730i	−0.663850	−	0.747866i	$-0.731079\pi$
$587$	−20.9531	+	5.61437i	−0.864827	+	0.231730i	−0.200978	+	0.979596i	$0.564412\pi$
$588$	24.0948	−	23.0357i	0.993651	−	0.949975i
$589$	25.0951	−	14.4887i	1.03403	−	0.596996i
$590$	4.39235	−	30.6946i	0.180830	−	1.26368i
$591$	4.02451	−	15.0197i	0.165546	−	0.617827i
$592$	1.52839	−	1.39686i	0.0628165	−	0.0574104i
$593$	−0.858298	−	0.858298i	−0.0352461	−	0.0352461i	0.689264	−	0.724510i	$-0.257934\pi$
$593$	−0.858298	−	0.858298i	−0.0352461	−	0.0352461i	−0.724510	+	0.689264i	$0.757934\pi$
$594$	−1.14117	+	2.66980i	−0.0468228	+	0.109543i
$595$	−2.44600	+	4.23660i	−0.100276	+	0.173683i
$596$	0.233489	−	10.3905i	0.00956409	−	0.425611i
$597$		−	7.55231i		−	0.309096i
$598$		0			0
$599$			7.16374i			0.292702i	0.989233	+	0.146351i	$0.0467529\pi$
$599$			7.16374i			0.292702i	−0.989233	+	0.146351i	$0.953247\pi$
$600$	26.9578	−	19.2779i	1.10055	−	0.787016i
$601$	−8.02549	+	13.9006i	−0.327367	+	0.567016i	−0.981988	−	0.188941i	$-0.939495\pi$
$601$	−8.02549	+	13.9006i	−0.327367	+	0.567016i	0.654622	+	0.755956i	$0.272828\pi$
$602$	5.53215	+	2.36464i	0.225473	+	0.0963757i
$603$	17.2284	+	17.2284i	0.701595	+	0.701595i
$604$	−8.88760	−	5.40105i	−0.361631	−	0.219766i
$605$	1.83233	−	6.83834i	0.0744947	−	0.278018i
$606$	31.4923	+	4.50649i	1.27929	+	0.183064i
$607$	−30.3120	+	17.5006i	−1.23033	+	0.710329i	−0.967098	−	0.254404i	$-0.918121\pi$
$607$	−30.3120	+	17.5006i	−1.23033	+	0.710329i	−0.263229	+	0.964734i	$0.584787\pi$
$608$	16.4583	+	7.92732i	0.667474	+	0.321495i
$609$	−1.77458	+	0.475497i	−0.0719096	+	0.0192681i
$610$	−27.9986	+	20.9886i	−1.13363	+	0.849803i
$611$		0			0
$612$	4.90319	−	16.7814i	0.198200	−	0.678349i
$613$	5.31448	+	19.8339i	0.214650	+	0.801084i	0.986290	+	0.165024i	$0.0527702\pi$
$613$	5.31448	+	19.8339i	0.214650	+	0.801084i	−0.771640	+	0.636060i	$0.780563\pi$
$614$	2.72993	+	22.7039i	0.110171	+	0.916256i
$615$	−22.5849	−	39.1183i	−0.910712	−	1.57740i
$616$	2.03729	−	4.48473i	0.0820847	−	0.180695i
$617$	18.1886	+	4.87361i	0.732244	+	0.196204i	0.605628	−	0.795748i	$-0.292922\pi$
$617$	18.1886	+	4.87361i	0.732244	+	0.196204i	0.126616	+	0.991952i	$0.459588\pi$
$618$	31.5761	−	12.6656i	1.27018	−	0.509484i
$619$	28.1707	−	28.1707i	1.13228	−	1.13228i	0.142478	−	0.989798i	$-0.454493\pi$
$619$	28.1707	−	28.1707i	1.13228	−	1.13228i	0.989798	−	0.142478i	$-0.0455069\pi$
$620$	−13.2337	−	54.2347i	−0.531480	−	2.17812i
$621$	1.24096	+	0.716468i	0.0497980	+	0.0287509i
$622$	20.9843	−	26.7204i	0.841395	−	1.07139i
$623$	−4.89248			−0.196013
$624$		0			0
$625$	26.5121			1.06048
$626$	25.2440	−	32.1443i	1.00895	−	1.28475i
$627$	20.6966	+	11.9492i	0.826542	+	0.477204i
$628$	5.10162	+	20.9075i	0.203577	+	0.834302i
$629$	−0.976260	+	0.976260i	−0.0389260	+	0.0389260i
$630$	−7.89013	+	3.16483i	−0.314350	+	0.126090i
$631$	12.0879	+	3.23895i	0.481213	+	0.128941i	0.491267	−	0.871009i	$-0.336534\pi$
$631$	12.0879	+	3.23895i	0.481213	+	0.128941i	−0.0100543	+	0.999949i	$0.503200\pi$
$632$	−3.19697	+	7.03758i	−0.127169	+	0.279940i
$633$	−22.8170	−	39.5201i	−0.906893	−	1.57078i
$634$	0.00336694	+	0.0280017i	0.000133718	+	0.00111209i
$635$	−9.72858	−	36.3076i	−0.386067	−	1.44082i
$636$	−5.16698	+	17.6843i	−0.204884	+	0.701226i
$637$		0			0
$638$	4.15657	−	3.11589i	0.164560	−	0.123359i
$639$	6.49018	−	1.73904i	0.256748	−	0.0687953i
$640$	23.5519	−	26.1519i	0.930970	−	1.03375i
$641$	22.6933	−	13.1020i	0.896331	−	0.517497i	0.0203232	−	0.999793i	$-0.493530\pi$
$641$	22.6933	−	13.1020i	0.896331	−	0.517497i	0.876008	+	0.482296i	$0.160197\pi$
$642$	−66.1653	−	9.46815i	−2.61133	−	0.373678i
$643$	0.0970757	−	0.362291i	0.00382829	−	0.0142874i	−0.963985	−	0.265956i	$-0.914313\pi$
$643$	0.0970757	−	0.362291i	0.00382829	−	0.0142874i	0.967814	+	0.251668i	$0.0809792\pi$
$644$	−2.07747	−	1.26249i	−0.0818640	−	0.0497492i
$645$	39.7636	+	39.7636i	1.56569	+	1.56569i
$646$	−11.2008	−	4.78762i	−0.440688	−	0.188366i
$647$	−17.6527	+	30.5754i	−0.693999	+	1.20204i	0.276517	+	0.961009i	$0.410820\pi$
$647$	−17.6527	+	30.5754i	−0.693999	+	1.20204i	−0.970517	+	0.241033i	$0.922514\pi$
$648$	−18.6143	+	13.3113i	−0.731238	+	0.522918i
$649$		−	20.8184i		−	0.817194i
$650$		0			0
$651$			13.2557i			0.519532i
$652$	0.638539	−	28.4156i	0.0250071	−	1.11284i
$653$	−16.0606	+	27.8178i	−0.628500	+	1.08859i	0.359353	+	0.933202i	$0.382997\pi$
$653$	−16.0606	+	27.8178i	−0.628500	+	1.08859i	−0.987853	+	0.155392i	$0.950336\pi$
$654$	−5.81498	+	13.6043i	−0.227384	+	0.531970i
$655$	−42.1642	−	42.1642i	−1.64749	−	1.64749i
$656$	−15.6394	−	17.1121i	−0.610616	−	0.668115i
$657$	0.0527959	−	0.197037i	0.00205977	−	0.00768715i
$658$	0.529219	−	3.69828i	0.0206311	−	0.144174i
$659$	−9.20996	+	5.31737i	−0.358769	+	0.207135i	−0.668541	−	0.743676i	$-0.733081\pi$
$659$	−9.20996	+	5.31737i	−0.358769	+	0.207135i	0.309772	+	0.950811i	$0.399747\pi$
$660$	33.2791	−	31.8163i	1.29539	−	1.23845i
$661$	7.77900	−	2.08438i	0.302568	−	0.0810729i	−0.104341	−	0.994542i	$-0.533273\pi$
$661$	7.77900	−	2.08438i	0.302568	−	0.0810729i	0.406909	+	0.913469i	$0.366607\pi$
$662$	3.58360	+	4.78049i	0.139281	+	0.185799i
$663$		0			0
$664$	14.3126	+	38.1406i	0.555437	+	1.48014i
$665$	1.53301	+	5.72126i	0.0594474	+	0.221861i
$666$	−2.38209	+	0.286423i	−0.0923039	+	0.0110987i
$667$	−1.28188	−	2.22029i	−0.0496348	−	0.0859699i
$668$	−16.3491	+	8.95559i	−0.632566	+	0.346502i
$669$	−8.59360	−	2.30265i	−0.332248	−	0.0890255i
$670$	−12.1752	−	30.3535i	−0.470369	−	1.17266i
$671$	−16.6126	+	16.6126i	−0.641322	+	0.641322i
$672$	−6.90496	+	4.70702i	−0.266365	+	0.181577i
$673$	−1.15151	−	0.664827i	−0.0443876	−	0.0256272i	0.477642	−	0.878555i	$-0.341492\pi$
$673$	−1.15151	−	0.664827i	−0.0443876	−	0.0256272i	−0.522030	+	0.852927i	$0.674825\pi$
$674$	10.6613	+	8.37262i	0.410657	+	0.322501i
$675$	−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	$0.275118\pi$
$678$	15.7248	+	12.3492i	0.603908	+	0.474268i
$679$	2.42135	+	1.39797i	0.0929231	+	0.0536492i
$680$	−14.9052	+	18.1259i	−0.571587	+	0.695096i
$681$	30.8905	−	30.8905i	1.18373	−	1.18373i
$682$	−13.9537	−	34.7876i	−0.534316	−	1.33208i
$683$	−42.6664	−	11.4324i	−1.63258	−	0.437449i	−0.677920	−	0.735136i	$-0.737118\pi$
$683$	−42.6664	−	11.4324i	−1.63258	−	0.437449i	−0.954664	+	0.297687i	$0.903785\pi$
$684$	−10.1695	−	18.5651i	−0.388839	−	0.709856i
$685$	11.2882	+	19.5517i	0.431299	+	0.747032i
$686$	11.3025	−	1.35902i	0.431532	−	0.0518875i
$687$	−13.1021	−	48.8976i	−0.499876	−	1.86556i
$688$	24.3207	+	15.5385i	0.927217	+	0.592401i
$689$		0			0
$690$	−13.6292	−	18.1812i	−0.518854	−	0.692147i
$691$	−40.1436	+	10.7564i	−1.52714	+	0.409195i	−0.922083	−	0.386991i	$-0.873514\pi$
$691$	−40.1436	+	10.7564i	−1.52714	+	0.409195i	−0.605052	+	0.796186i	$0.706848\pi$
$692$	31.6384	+	33.0930i	1.20271	+	1.25801i
$693$	−4.94304	+	2.85387i	−0.187771	+	0.108409i
$694$	0.824601	−	5.76247i	0.0313014	−	0.218740i
$695$	8.94235	−	33.3733i	0.339203	−	1.26592i
$696$	−8.77148	+	0.855267i	−0.332482	+	0.0324188i
$697$	10.9304	+	10.9304i	0.414017	+	0.414017i
$698$	16.1490	−	37.7811i	0.611250	−	1.43004i
$699$	−16.6871	+	28.9030i	−0.631165	+	1.09321i
$700$	5.51349	+	0.123896i	0.208390	+	0.00468283i
$701$		−	17.2912i		−	0.653080i	−0.945183	−	0.326540i	$-0.894117\pi$
$701$		−	17.2912i		−	0.653080i	0.945183	−	0.326540i	$-0.105883\pi$
$702$		0			0
$703$			1.67164i			0.0630470i
$704$	13.1661	−	19.6214i	0.496216	−	0.739509i
$705$	17.4599	−	30.2414i	0.657578	−	1.13896i
$706$	−34.2395	−	14.6352i	−1.28862	−	0.550804i
$707$	3.74329	+	3.74329i	0.140781	+	0.140781i
$708$	−18.3421	+	30.1826i	−0.689340	+	1.13433i
$709$	−10.8385	+	40.4498i	−0.407048	+	1.51913i	0.393198	+	0.919454i	$0.371369\pi$
$709$	−10.8385	+	40.4498i	−0.407048	+	1.51913i	−0.800246	+	0.599672i	$0.795298\pi$
$710$	−8.92804	−	1.27759i	−0.335063	−	0.0479471i
$711$	7.75677	−	4.47837i	0.290902	−	0.167952i
$712$	−23.1523	−	3.84570i	−0.867671	−	0.144124i
$713$	−17.8679	+	4.78769i	−0.669159	+	0.179301i
$714$	4.45858	−	3.34229i	0.166858	−	0.125082i
$715$		0			0
$716$	25.3761	+	7.41438i	0.948349	+	0.277088i
$717$	−9.39931	−	35.0787i	−0.351024	−	1.31004i
$718$	−1.83816	−	15.2874i	−0.0685994	−	0.570519i
$719$	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
$721$	5.46841	+	1.46526i	0.203654	+	0.0545690i
$722$	11.2503	−	4.51264i	0.418693	−	0.167943i
$723$	−24.5379	+	24.5379i	−0.912575	+	0.912575i
$724$	−50.7525	+	12.3840i	−1.88620	+	0.460249i
$725$	5.03685	+	2.90803i	0.187064	+	0.108001i
$726$	−4.98060	+	6.34204i	−0.184847	+	0.235375i
$727$	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
$730$	−0.169115	+	0.215342i	−0.00625921	+	0.00797016i
$731$	−16.6660	−	9.62214i	−0.616416	−	0.355888i
$732$	38.7216	−	9.44839i	1.43119	−	0.349223i
$733$	−4.25026	+	4.25026i	−0.156987	+	0.156987i	−0.781230	−	0.624243i	$-0.785407\pi$
$733$	−4.25026	+	4.25026i	−0.156987	+	0.156987i	0.624243	+	0.781230i	$0.285407\pi$
$734$	−2.75403	+	1.10468i	−0.101653	+	0.0407744i
$735$	50.0810	+	13.4192i	1.84727	+	0.494973i
$736$	−8.83871	−	7.60739i	−0.325799	−	0.280412i
$737$	−10.9789	−	19.0160i	−0.404413	−	0.700464i
$738$	3.20683	+	26.6702i	0.118045	+	0.981743i
$739$	4.67066	+	17.4311i	0.171813	+	0.641215i	0.997073	+	0.0764613i	$0.0243622\pi$
$739$	4.67066	+	17.4311i	0.171813	+	0.641215i	−0.825260	+	0.564754i	$0.808971\pi$
$740$	3.09122	+	0.903194i	0.113636	+	0.0332021i
$741$		0			0
$742$	−2.45305	+	1.83888i	−0.0900542	+	0.0675074i
$743$	12.9434	−	3.46818i	0.474848	−	0.127235i	−0.0134546	−	0.999909i	$-0.504283\pi$
$743$	12.9434	−	3.46818i	0.474848	−	0.127235i	0.488303	+	0.872674i	$0.337616\pi$
$744$	−10.4196	+	62.7291i	−0.381999	+	2.29976i
$745$	13.9994	−	8.08254i	0.512898	−	0.296122i
$746$	39.6252	+	5.67031i	1.45078	+	0.207605i
$747$	12.2174	−	45.5961i	0.447013	−	1.66828i
$748$	−8.18256	+	13.4647i	−0.299184	+	0.492317i
$749$	−7.86466	−	7.86466i	−0.287368	−	0.287368i
$750$	−3.27700	−	1.40071i	−0.119659	−	0.0511467i
$751$	−12.5103	+	21.6684i	−0.456506	+	0.790691i	−0.998773	−	0.0495148i	$-0.984233\pi$
$751$	−12.5103	+	21.6684i	−0.456506	+	0.790691i	0.542268	+	0.840206i	$0.317566\pi$
$752$	5.41139	−	17.0851i	0.197333	−	0.623031i
$753$		−	6.30448i		−	0.229748i
$754$		0			0
$755$		−	16.1759i		−	0.588700i
$756$	0.819463	+	0.0184145i	0.0298036	+	0.000669730i
$757$	19.6123	−	33.9695i	0.712821	−	1.23464i	−0.250973	−	0.967994i	$-0.580751\pi$
$757$	19.6123	−	33.9695i	0.712821	−	1.23464i	0.963794	−	0.266648i	$-0.0859161\pi$
$758$	16.0698	−	37.5957i	0.583681	−	1.36554i
$759$	−10.7876	−	10.7876i	−0.391565	−	0.391565i
$760$	2.75739	+	28.2793i	0.100021	+	1.02580i
$761$	3.68640	−	13.7578i	0.133632	−	0.498722i	−0.866368	−	0.499407i	$-0.833551\pi$
$761$	3.68640	−	13.7578i	0.133632	−	0.498722i	1.00000		0.000685009i	$0.000218045\pi$
$762$	−6.06498	+	42.3833i	−0.219711	+	1.53538i
$763$	−2.13210	+	1.23097i	−0.0771872	+	0.0445641i
$764$	19.5401	+	20.4384i	0.706935	+	0.739437i
$765$	26.2660	−	7.03796i	0.949650	−	0.254458i
$766$	12.8394	+	17.1277i	0.463908	+	0.618849i
$767$		0			0
$768$	−36.3758	+	16.8471i	−1.31260	+	0.607918i
$769$	5.17525	+	19.3143i	0.186624	+	0.696491i	0.994277	+	0.106833i	$0.0340709\pi$
$769$	5.17525	+	19.3143i	0.186624	+	0.696491i	−0.807653	+	0.589658i	$0.799262\pi$
$770$	7.60662	−	0.914622i	0.274124	−	0.0329607i
$771$	8.03441	+	13.9160i	0.289352	+	0.501172i
$772$	22.2901	+	40.6923i	0.802239	+	1.46455i
$773$	29.2155	+	7.82826i	1.05081	+	0.281563i	0.742585	−	0.669751i	$-0.233599\pi$
$773$	29.2155	+	7.82826i	1.05081	+	0.281563i	0.308222	+	0.951314i	$0.400266\pi$
$774$	−12.4499	−	31.0384i	−0.447503	−	1.11565i
$775$	29.6732	−	29.6732i	1.06589	−	1.06589i
$776$	10.3595	+	8.51880i	0.371886	+	0.305807i
$777$	−0.662242	−	0.382346i	−0.0237578	−	0.0137166i
$778$	33.7778	+	26.5268i	1.21099	+	0.951031i
$779$	18.7159			0.670567
$780$		0			0
$781$	−6.05538			−0.216679
$782$	6.11555	+	4.80273i	0.218692	+	0.171745i
$783$	0.748622	+	0.432217i	0.0267536	+	0.0154462i
$784$	26.5826	+	1.19530i	0.949377	+	0.0426893i
$785$	−23.6690	+	23.6690i	−0.844783	+	0.844783i
$786$	25.2856	+	63.0386i	0.901907	+	2.24851i
$787$	−9.06504	−	2.42897i	−0.323134	−	0.0865834i	0.0936059	−	0.995609i	$-0.470161\pi$
$787$	−9.06504	−	2.42897i	−0.323134	−	0.0865834i	−0.416740	+	0.909026i	$0.636827\pi$
$788$	10.8862	−	5.96314i	0.387804	−	0.212428i
$789$	6.64987	+	11.5179i	0.236742	+	0.410049i
$790$	−11.9365	+	1.43525i	−0.424683	+	0.0510640i
$791$	0.861124	+	3.21376i	0.0306181	+	0.114268i
$792$	−25.6349	+	9.61971i	−0.910896	+	0.341822i
$793$		0			0
$794$	13.5757	+	18.1099i	0.481784	+	0.642695i
$795$	−27.6791	+	7.41660i	−0.981677	+	0.263040i
$796$	4.35758	−	4.16605i	0.154450	−	0.147662i
$797$	10.0960	−	5.82891i	0.357617	−	0.206471i	−0.310418	−	0.950600i	$-0.600469\pi$
$797$	10.0960	−	5.82891i	0.357617	−	0.206471i	0.668035	+	0.744130i	$0.267136\pi$
$798$	0.955705	−	6.67865i	0.0338316	−	0.236422i
$799$	−3.09292	+	11.5429i	−0.109420	+	0.408359i
$800$	25.9937	+	4.92014i	0.919016	+	0.173953i
$801$	19.2299	+	19.2299i	0.679457	+	0.679457i
$802$	7.65306	−	17.9045i	0.270239	−	0.632231i
$803$	−0.0919184	+	0.159207i	−0.00324373	+	0.00561831i
$804$	−0.836892	+	37.2425i	−0.0295149	+	1.31344i
$805$		−	3.78111i		−	0.133267i
$806$		0			0
$807$		−	25.0572i		−	0.882055i
$808$	14.7717	+	20.6565i	0.519668	+	0.726693i
$809$	15.5430	−	26.9212i	0.546461	−	0.946499i	−0.452052	−	0.891992i	$-0.649308\pi$
$809$	15.5430	−	26.9212i	0.546461	−	0.946499i	0.998513	−	0.0545072i	$-0.0173588\pi$
$810$	−32.7287	−	13.9895i	−1.14997	−	0.491540i
$811$	−0.110267	−	0.110267i	−0.00387201	−	0.00387201i	0.705168	−	0.709040i	$-0.250872\pi$
$811$	−0.110267	−	0.110267i	−0.00387201	−	0.00387201i	−0.709040	+	0.705168i	$0.750872\pi$
$812$	−1.25326	−	0.761613i	−0.0439807	−	0.0267274i
$813$	16.5475	−	61.7561i	0.580346	−	2.16588i
$814$	2.14043	+	0.306292i	0.0750221	+	0.0107355i
$815$	38.2851	−	22.1039i	1.34107	−	0.774266i
$816$	23.7262	−	12.3118i	0.830583	−	0.431000i
$817$	−22.5064	+	6.03058i	−0.787401	+	0.210983i
$818$	0.661725	−	0.496050i	0.0231367	−	0.0173440i
$819$		0			0
$820$	10.1123	−	34.6098i	0.353137	−	1.20863i
$821$	−4.68104	−	17.4699i	−0.163370	−	0.609703i	−0.998243	−	0.0592608i	$-0.981126\pi$
$821$	−4.68104	−	17.4699i	−0.163370	−	0.609703i	0.834873	−	0.550443i	$-0.185541\pi$
$822$	−3.06994	−	25.5317i	−0.107076	−	0.890520i
$823$	−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
$825$	33.4297	+	8.95747i	1.16387	+	0.311859i
$826$	−5.45474	+	2.18797i	−0.189795	+	0.0761291i
$827$	11.7822	−	11.7822i	0.409707	−	0.409707i	−0.471930	−	0.881636i	$-0.656442\pi$
$827$	11.7822	−	11.7822i	0.409707	−	0.409707i	0.881636	+	0.471930i	$0.156442\pi$
$828$	3.20329	+	13.1278i	0.111322	+	0.456222i
$829$	11.3492	+	6.55249i	0.394176	+	0.227577i	0.683968	−	0.729512i	$-0.260253\pi$
$829$	11.3492	+	6.55249i	0.394176	+	0.227577i	−0.289792	+	0.957090i	$0.593586\pi$
$830$	−39.1346	+	49.8320i	−1.35838	+	1.72969i
$831$	1.33873			0.0464401
$832$		0			0
$833$	−17.7431			−0.614762
$834$	−24.3069	+	30.9512i	−0.841680	+	1.07175i
$835$	−25.1095	−	14.4970i	−0.868951	−	0.501689i
$836$	4.52224	+	18.5331i	0.156405	+	0.640981i
$837$	4.41030	−	4.41030i	0.152442	−	0.152442i
$838$	−48.4301	+	19.4259i	−1.67299	+	0.671057i
$839$	23.1184	+	6.19456i	0.798136	+	0.213860i	0.634766	−	0.772705i	$-0.281097\pi$
$839$	23.1184	+	6.19456i	0.798136	+	0.213860i	0.163371	+	0.986565i	$0.447763\pi$
$840$	−11.8339	−	5.37582i	−0.408309	−	0.185483i
$841$	13.7267	+	23.7753i	0.473334	+	0.819839i
$842$	−5.29751	−	44.0577i	−0.182564	−	1.51833i
$843$	−0.252685	−	0.943032i	−0.00870293	−	0.0324798i
$844$	10.2162	−	34.9654i	0.351655	−	1.20356i
$845$		0			0
$846$	−16.6162	+	12.4560i	−0.571278	+	0.428248i
$847$	−1.29615	+	0.347303i	−0.0445364	+	0.0119335i
$848$	−13.0538	+	6.77380i	−0.448270	+	0.232613i
$849$	−34.8553	+	20.1237i	−1.19623	+	0.690644i
$850$	−17.4624	−	2.49885i	−0.598956	−	0.0857097i
$851$	0.276191	−	1.03076i	0.00946770	−	0.0353340i
$852$	8.77911	+	5.33512i	0.300767	+	0.182778i
$853$	12.1913	+	12.1913i	0.417422	+	0.417422i	0.884314	−	0.466892i	$-0.154626\pi$
$853$	12.1913	+	12.1913i	0.417422	+	0.417422i	−0.466892	+	0.884314i	$0.654626\pi$
$854$	6.09870	+	2.60681i	0.208693	+	0.0892032i
$855$	16.4620	−	28.5130i	0.562987	−	0.975123i
$856$	−31.0354	−	43.3993i	−1.06077	−	1.48336i
$857$			20.1694i			0.688974i	0.938791	+	0.344487i	$0.111947\pi$
$857$			20.1694i			0.688974i	−0.938791	+	0.344487i	$0.888053\pi$
$858$		0			0
$859$		−	10.5286i		−	0.359231i	−0.983737	−	0.179616i	$-0.942515\pi$
$859$		−	10.5286i		−	0.359231i	0.983737	−	0.179616i	$-0.0574854\pi$
$860$	−1.00847	+	44.8777i	−0.0343885	+	1.53032i
$861$	−4.28080	+	7.41456i	−0.145889	+	0.252688i
$862$	−17.2887	+	40.4473i	−0.588854	+	1.37764i
$863$	−0.357134	−	0.357134i	−0.0121570	−	0.0121570i	0.701002	−	0.713159i	$-0.252736\pi$
$863$	−0.357134	−	0.357134i	−0.0121570	−	0.0121570i	−0.713159	+	0.701002i	$0.752736\pi$
$864$	3.86341	+	0.731274i	0.131436	+	0.0248785i
$865$	−18.4306	+	68.7838i	−0.626658	+	2.33872i
$866$	−2.16220	+	15.1099i	−0.0734745	+	0.513454i
$867$	21.4509	−	12.3847i	0.728511	−	0.420606i
$868$	−7.64837	+	7.31218i	−0.259603	+	0.248192i
$869$	−7.79691	+	2.08918i	−0.264492	+	0.0708704i
$870$	−8.22195	−	10.9680i	−0.278750	−	0.371850i
$871$		0			0
$872$	−11.0572	+	4.14931i	−0.374443	+	0.140513i
$873$	−4.02243	−	15.0119i	−0.136138	−	0.508076i
$874$	9.34761	−	1.12396i	0.316188	−	0.0380185i
$875$	−0.296516	−	0.513580i	−0.0100241	−	0.0173622i
$876$	0.273534	−	0.149834i	0.00924186	−	0.00506243i
$877$	30.8645	+	8.27012i	1.04222	+	0.279262i	0.739033	−	0.673669i	$-0.235283\pi$
$877$	30.8645	+	8.27012i	1.04222	+	0.279262i	0.303187	+	0.952931i	$0.401949\pi$
$878$	−6.82656	−	17.0191i	−0.230385	−	0.574366i
$879$	−3.63013	+	3.63013i	−0.122441	+	0.122441i
$880$	36.7152	+	1.65092i	1.23767	+	0.0556526i
$881$	−26.4430	−	15.2668i	−0.890886	−	0.514353i	−0.0166536	−	0.999861i	$-0.505301\pi$
$881$	−26.4430	−	15.2668i	−0.890886	−	0.514353i	−0.874232	+	0.485508i	$0.838635\pi$
$882$	−24.2495	−	19.0439i	−0.816523	−	0.641241i
$883$	−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
$886$	17.4077	+	13.6708i	0.584824	+	0.459280i
$887$	21.7002	+	12.5286i	0.728621	+	0.420669i	0.817917	−	0.575336i	$-0.195129\pi$
$887$	21.7002	+	12.5286i	0.728621	+	0.420669i	−0.0892967	+	0.996005i	$0.528462\pi$
$888$	−2.83334	−	2.32990i	−0.0950807	−	0.0781863i
$889$	−5.03784	+	5.03784i	−0.168964	+	0.168964i
$890$	−13.5897	−	33.8799i	−0.455526	−	1.13566i
$891$	−23.0831	−	6.18510i	−0.773313	−	0.207209i
$892$	−3.41185	−	6.22859i	−0.114237	−	0.208549i
$893$	7.23442	+	12.5304i	0.242091	+	0.419313i
$894$	−18.2812	+	2.19813i	−0.611414	+	0.0735166i
$895$	10.6425	+	39.7182i	0.355739	+	1.32763i
$896$	−6.52483	−	1.38756i	−0.217979	−	0.0463551i
$897$		0			0
$898$	−9.50433	−	12.6787i	−0.317164	−	0.423093i
$899$	−10.7790	+	2.88823i	−0.359500	+	0.0963278i
$900$	−21.1838	−	22.1578i	−0.706128	−	0.738593i
$901$	8.49258	−	4.90319i	0.282929	−	0.163349i
$902$	3.42930	−	23.9646i	0.114183	−	0.797933i
$903$	2.75869	−	10.2956i	0.0918036	−	0.342616i
$904$	1.54889	+	15.8851i	0.0515152	+	0.528331i
$905$	−57.4558	−	57.4558i	−1.90990	−	1.90990i
$906$	−7.24178	+	16.9423i	−0.240592	+	0.562871i
$907$	25.1973	−	43.6429i	0.836661	−	1.44914i	−0.0560094	−	0.998430i	$-0.517838\pi$
$907$	25.1973	−	43.6429i	0.836661	−	1.44914i	0.892671	−	0.450710i	$-0.148829\pi$
$908$	34.8633	+	0.783430i	1.15698	+	0.0259990i
$909$		−	29.4261i		−	0.976002i
$910$		0			0
$911$			7.50959i			0.248804i	0.992232	+	0.124402i	$0.0397012\pi$
$911$			7.50959i			0.248804i	−0.992232	+	0.124402i	$0.960299\pi$
$912$	9.77232	−	30.8537i	0.323594	−	1.02167i
$913$	−21.2708	+	36.8420i	−0.703959	+	1.21929i
$914$	24.9869	+	10.6803i	0.826495	+	0.353274i
$915$	43.8359	+	43.8359i	1.44917	+	1.44917i
$916$	20.9858	−	34.5329i	0.693392	−	1.14100i
$917$	−2.92524	+	10.9171i	−0.0966000	+	0.360516i
$918$	−2.59542	−	0.371400i	−0.0856616	−	0.0122580i
$919$	24.3508	−	14.0590i	0.803260	−	0.463762i	−0.0413499	−	0.999145i	$-0.513166\pi$
$919$	24.3508	−	14.0590i	0.803260	−	0.463762i	0.844610	+	0.535382i	$0.179832\pi$
$920$	2.97211	−	17.8931i	0.0979876	−	0.589917i
$921$	39.1325	−	10.4855i	1.28946	−	0.345510i
$922$	27.7517	−	20.8035i	0.913952	−	0.685126i
$923$		0			0
$924$	−8.37650	−	2.44745i	−0.275567	−	0.0805151i
$925$	0.626555	+	2.33834i	0.0206010	+	0.0768840i
$926$	−3.15229	−	26.2165i	−0.103591	−	0.861529i
$927$	−15.7344	−	27.2528i	−0.516787	−	0.895101i
$928$	−5.33205	−	4.58924i	−0.175033	−	0.150649i
$929$	−41.4351	−	11.1025i	−1.35944	−	0.364261i	−0.495829	−	0.868420i	$-0.665136\pi$
$929$	−41.4351	−	11.1025i	−1.35944	−	0.364261i	−0.863611	+	0.504159i	$0.831802\pi$
$930$	−91.7944	+	36.8199i	−3.01006	+	1.20737i
$931$	−15.1906	+	15.1906i	−0.497853	+	0.497853i
$932$	−25.8817	+	6.31534i	−0.847782	+	0.206866i
$933$	−52.1278	−	30.0960i	−1.70659	−	0.985300i
$934$	−19.7883	+	25.1974i	−0.647492	+	0.824483i
$935$	−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	$0.502069\pi$
$938$	−3.82863	+	4.87518i	−0.125009	+	0.159180i
$939$	−62.7093	−	36.2052i	−2.04644	−	1.18151i
$940$	27.0802	−	6.60780i	0.883259	−	0.215523i
$941$	4.33123	−	4.33123i	0.141194	−	0.141194i	−0.632977	−	0.774171i	$-0.718167\pi$
$941$	4.33123	−	4.33123i	0.141194	−	0.141194i	0.774171	+	0.632977i	$0.218167\pi$
$942$	35.3868	−	14.1941i	1.15297	−	0.462469i
$943$	−11.5405	−	3.09228i	−0.375811	−	0.100698i
$944$	−27.5329	+	6.06630i	−0.896120	+	0.197441i
$945$	0.637444	+	1.10409i	0.0207360	+	0.0359159i
$946$	3.59797	+	29.9231i	0.116980	+	0.972885i
$947$	−2.00336	−	7.47663i	−0.0651003	−	0.242958i	0.925706	−	0.378243i	$-0.123472\pi$
$947$	−2.00336	−	7.47663i	−0.0651003	−	0.242958i	−0.990807	+	0.135285i	$0.956805\pi$
$948$	13.1447	+	3.84060i	0.426919	+	0.124737i
$949$		0			0
$950$	−17.0897	+	12.8110i	−0.554463	+	0.415642i
$951$	0.0482638	−	0.0129322i	0.00156506	−	0.000419357i
$952$	4.38792	+	0.728851i	0.142213	+	0.0236222i
$953$	12.6528	−	7.30512i	0.409866	−	0.236636i	−0.280866	−	0.959747i	$-0.590622\pi$
$953$	12.6528	−	7.30512i	0.409866	−	0.236636i	0.690732	+	0.723111i	$0.257288\pi$
$954$	16.8695	+	2.41399i	0.546169	+	0.0781559i
$955$	−11.3828	+	42.4813i	−0.368340	+	1.37466i
$956$	15.0551	−	24.7736i	0.486915	−	0.801235i
$957$	−6.50773	−	6.50773i	−0.210365	−	0.210365i
$958$	4.22327	+	1.80518i	0.136448	+	0.0583228i
$959$	2.13959	−	3.70587i	0.0690909	−	0.119669i
$960$	−51.7752	−	34.7416i	−1.67104	−	1.12128i
$961$			49.5168i			1.59731i
$962$		0			0
$963$			61.8243i			1.99226i
$964$	−27.6938	−	0.622320i	−0.891957	−	0.0200436i
$965$	−36.0825	+	62.4966i	−1.16154	+	2.01184i
$966$	−1.69276	+	3.96026i	−0.0544638	+	0.127419i
$967$	6.52725	+	6.52725i	0.209902	+	0.209902i	0.804226	−	0.594324i	$-0.202580\pi$
$967$	6.52725	+	6.52725i	0.209902	+	0.209902i	−0.594324	+	0.804226i	$0.702580\pi$
$968$	−6.40669	+	0.624687i	−0.205919	+	0.0200782i
$969$	−5.58544	+	20.8451i	−0.179430	+	0.669642i
$970$	−2.95508	+	20.6507i	−0.0948821	+	0.663054i
$971$	−33.9607	+	19.6072i	−1.08985	+	0.629226i	−0.933537	−	0.358481i	$-0.883295\pi$
$971$	−33.9607	+	19.6072i	−1.08985	+	0.629226i	−0.156315	+	0.987707i	$0.549962\pi$
$972$	30.8986	+	32.3192i	0.991072	+	1.03664i
$973$	−6.32565	+	1.69495i	−0.202791	+	0.0543377i
$974$	−36.3804	−	48.5311i	−1.16570	−	1.55504i
$975$		0			0
$976$	26.8114	+	17.1299i	0.858212	+	0.548313i
$977$	3.04098	+	11.3491i	0.0972895	+	0.363089i	0.997357	−	0.0726619i	$-0.0231494\pi$
$977$	3.04098	+	11.3491i	0.0972895	+	0.363089i	−0.900067	+	0.435751i	$0.856483\pi$
$978$	−49.9948	+	6.01139i	−1.59866	+	0.192223i
$979$	−12.2544	−	21.2252i	−0.391652	−	0.678361i
$980$	19.8833	+	36.2984i	0.635147	+	1.15951i
$981$	13.2186	+	3.54191i	0.422037	+	0.113084i
$982$	0.839115	+	2.09197i	0.0267772	+	0.0667574i
$983$	17.0818	−	17.0818i	0.544823	−	0.544823i	−0.380116	−	0.924939i	$-0.624116\pi$
$983$	17.0818	−	17.0818i	0.544823	−	0.544823i	0.924939	+	0.380116i	$0.124116\pi$
$984$	−26.0859	+	31.7225i	−0.831588	+	1.01128i
$985$	16.7194	+	9.65293i	0.532723	+	0.307568i
$986$	3.68927	+	2.89730i	0.117490	+	0.0922688i
$987$	−6.61878			−0.210678
$988$		0			0
$989$	14.8742			0.472973
$990$	−33.4928	−	26.3030i	−1.06447	−	0.835963i
$991$	24.9439	+	14.4013i	0.792368	+	0.457474i	0.840796	−	0.541353i	$-0.182088\pi$
$991$	24.9439	+	14.4013i	0.792368	+	0.457474i	−0.0484275	+	0.998827i	$0.515421\pi$
$992$	−41.9415	+	28.5910i	−1.33164	+	0.907765i
$993$	7.48456	−	7.48456i	0.237515	−	0.237515i
$994$	0.636406	+	1.58660i	0.0201856	+	0.0503240i
$995$	9.05724	+	2.42688i	0.287134	+	0.0769373i
$996$	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	$-0.492508\pi$
$998$	5.75298	−	0.691740i	0.182107	−	0.0218966i
$999$	0.0931241	+	0.347544i	0.00294632	+	0.0109958i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.7.1	✓	16	13.5	odd	4
52.2.l.b.7.2	yes	16	52.31	even	4
52.2.l.b.15.1	yes	16	52.23	odd	6
52.2.l.b.15.2	yes	16	13.10	even	6
468.2.cb.f.163.3		16	156.83	odd	4
468.2.cb.f.163.4		16	39.5	even	4
468.2.cb.f.379.3		16	39.23	odd	6
468.2.cb.f.379.4		16	156.23	even	6
676.2.f.h.99.5		16	13.6	odd	12
676.2.f.h.99.8		16	52.19	even	12
676.2.f.h.239.5		16	52.43	odd	6
676.2.f.h.239.8		16	13.4	even	6
676.2.f.i.99.1		16	52.7	even	12
676.2.f.i.99.4		16	13.7	odd	12
676.2.f.i.239.1		16	13.9	even	3
676.2.f.i.239.4		16	52.35	odd	6
676.2.l.i.19.1		16	4.3	odd	2	inner
676.2.l.i.19.3		16	1.1	even	1	trivial
676.2.l.i.427.1		16	13.11	odd	12	inner
676.2.l.i.427.3		16	52.11	even	12	inner
676.2.l.k.319.3		16	52.47	even	4
676.2.l.k.319.4		16	13.8	odd	4
676.2.l.k.587.3		16	13.3	even	3
676.2.l.k.587.4		16	52.3	odd	6
676.2.l.m.19.2		16	13.12	even	2
676.2.l.m.19.4		16	52.51	odd	2
676.2.l.m.427.2		16	52.15	even	12
676.2.l.m.427.4		16	13.2	odd	12
832.2.bu.n.319.1		16	104.83	even	4
832.2.bu.n.319.4		16	104.5	odd	4
832.2.bu.n.639.1		16	104.101	even	6
832.2.bu.n.639.4		16	104.75	odd	6

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)

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

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