LMFDB - Embedded newform 882.2.f.l.589.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(295,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("882.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.f (of order $3$, degree $2$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			589.3
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	882.589
Dual form			882.2.f.l.295.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.64400 - 0.545231i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.84981 + 3.20397i) q^{5} +(-1.29418 - 1.15113i) q^{6} +1.00000 q^{8} +(2.40545 - 1.79272i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.64400 - 0.545231i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.84981 + 3.20397i) q^{5} +(-1.29418 - 1.15113i) q^{6} +1.00000 q^{8} +(2.40545 - 1.79272i) q^{9} +3.69963 q^{10} +(0.738550 + 1.27921i) q^{11} +(-0.349814 + 1.69636i) q^{12} +(-1.34981 + 2.33795i) q^{13} +(-1.29418 + 6.27589i) q^{15} +(-0.500000 - 0.866025i) q^{16} -6.57598 q^{17} +(-2.75526 - 1.18682i) q^{18} +0.888736 q^{19} +(-1.84981 - 3.20397i) q^{20} +(0.738550 - 1.27921i) q^{22} +(-3.14400 + 5.44556i) q^{23} +(1.64400 - 0.545231i) q^{24} +(-4.34362 - 7.52338i) q^{25} +2.69963 q^{26} +(2.97710 - 4.25874i) q^{27} +(1.25526 + 2.17417i) q^{29} +(6.08217 - 2.01715i) q^{30} +(-3.40545 + 5.89841i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.91164 + 1.70033i) q^{33} +(3.28799 + 5.69497i) q^{34} +(0.349814 + 2.97954i) q^{36} +2.77747 q^{37} +(-0.444368 - 0.769668i) q^{38} +(-0.944368 + 4.57954i) q^{39} +(-1.84981 + 3.20397i) q^{40} +(-2.05563 + 3.56046i) q^{41} +(0.00618986 + 0.0107211i) q^{43} -1.47710 q^{44} +(1.29418 + 11.0232i) q^{45} +6.28799 q^{46} +(3.49381 + 6.05146i) q^{47} +(-1.29418 - 1.15113i) q^{48} +(-4.34362 + 7.52338i) q^{50} +(-10.8109 + 3.58543i) q^{51} +(-1.34981 - 2.33795i) q^{52} +3.21015 q^{53} +(-5.17673 - 0.448873i) q^{54} -5.46472 q^{55} +(1.46108 - 0.484566i) q^{57} +(1.25526 - 2.17417i) q^{58} +(-3.45489 + 5.98404i) q^{59} +(-4.78799 - 4.25874i) q^{60} +(2.86652 + 4.96497i) q^{61} +6.81089 q^{62} +1.00000 q^{64} +(-4.99381 - 8.64953i) q^{65} +(0.516710 - 2.50569i) q^{66} +(4.73236 - 8.19669i) q^{67} +(3.28799 - 5.69497i) q^{68} +(-2.19963 + 10.6667i) q^{69} -5.46472 q^{71} +(2.40545 - 1.79272i) q^{72} +12.0655 q^{73} +(-1.38874 - 2.40536i) q^{74} +(-11.2429 - 10.0001i) q^{75} +(-0.444368 + 0.769668i) q^{76} +(4.43818 - 1.47192i) q^{78} +(-5.72617 - 9.91802i) q^{79} +3.69963 q^{80} +(2.57234 - 8.62456i) q^{81} +4.11126 q^{82} +(2.23855 + 3.87728i) q^{83} +(12.1643 - 21.0693i) q^{85} +(0.00618986 - 0.0107211i) q^{86} +(3.24907 + 2.88993i) q^{87} +(0.738550 + 1.27921i) q^{88} +8.87636 q^{89} +(8.89926 - 6.63238i) q^{90} +(-3.14400 - 5.44556i) q^{92} +(-2.38255 + 11.5537i) q^{93} +(3.49381 - 6.05146i) q^{94} +(-1.64400 + 2.84748i) q^{95} +(-0.349814 + 1.69636i) q^{96} +(-6.58836 - 11.4114i) q^{97} +(4.06979 + 1.75305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 5 q^{5} - 2 q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 5 * q^5 - 2 * q^6 + 6 * q^8 + 8 * q^9	$ 6 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 5 q^{5} - 2 q^{6} + 6 q^{8} + 8 q^{9} + 10 q^{10} - q^{11} + 4 q^{12} - 2 q^{13} - 2 q^{15} - 3 q^{16} + 8 q^{17} - 4 q^{18} + 6 q^{19} - 5 q^{20} - q^{22} - 7 q^{23} - 2 q^{24} - 2 q^{25} + 4 q^{26} + 7 q^{27} - 5 q^{29} + 7 q^{30} - 14 q^{31} - 3 q^{32} + 23 q^{33} - 4 q^{34} - 4 q^{36} + 18 q^{37} - 3 q^{38} - 6 q^{39} - 5 q^{40} - 12 q^{41} + 18 q^{43} + 2 q^{44} + 2 q^{45} + 14 q^{46} + 3 q^{47} - 2 q^{48} - 2 q^{50} - 52 q^{51} - 2 q^{52} - 18 q^{53} - 8 q^{54} + 14 q^{55} + 2 q^{57} - 5 q^{58} + 4 q^{59} - 5 q^{60} + 4 q^{61} + 28 q^{62} + 6 q^{64} - 12 q^{65} - 4 q^{66} + 5 q^{67} - 4 q^{68} - q^{69} + 14 q^{71} + 8 q^{72} + 50 q^{73} - 9 q^{74} - 19 q^{75} - 3 q^{76} + 9 q^{78} + 7 q^{79} + 10 q^{80} + 8 q^{81} + 24 q^{82} + 8 q^{83} + 14 q^{85} + 18 q^{86} - 11 q^{87} - q^{88} + 18 q^{89} + 29 q^{90} - 7 q^{92} + 3 q^{93} + 3 q^{94} + 2 q^{95} + 4 q^{96} - 28 q^{97} - 41 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 5 * q^5 - 2 * q^6 + 6 * q^8 + 8 * q^9 + 10 * q^10 - q^11 + 4 * q^12 - 2 * q^13 - 2 * q^15 - 3 * q^16 + 8 * q^17 - 4 * q^18 + 6 * q^19 - 5 * q^20 - q^22 - 7 * q^23 - 2 * q^24 - 2 * q^25 + 4 * q^26 + 7 * q^27 - 5 * q^29 + 7 * q^30 - 14 * q^31 - 3 * q^32 + 23 * q^33 - 4 * q^34 - 4 * q^36 + 18 * q^37 - 3 * q^38 - 6 * q^39 - 5 * q^40 - 12 * q^41 + 18 * q^43 + 2 * q^44 + 2 * q^45 + 14 * q^46 + 3 * q^47 - 2 * q^48 - 2 * q^50 - 52 * q^51 - 2 * q^52 - 18 * q^53 - 8 * q^54 + 14 * q^55 + 2 * q^57 - 5 * q^58 + 4 * q^59 - 5 * q^60 + 4 * q^61 + 28 * q^62 + 6 * q^64 - 12 * q^65 - 4 * q^66 + 5 * q^67 - 4 * q^68 - q^69 + 14 * q^71 + 8 * q^72 + 50 * q^73 - 9 * q^74 - 19 * q^75 - 3 * q^76 + 9 * q^78 + 7 * q^79 + 10 * q^80 + 8 * q^81 + 24 * q^82 + 8 * q^83 + 14 * q^85 + 18 * q^86 - 11 * q^87 - q^88 + 18 * q^89 + 29 * q^90 - 7 * q^92 + 3 * q^93 + 3 * q^94 + 2 * q^95 + 4 * q^96 - 28 * q^97 - 41 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.64400	−	0.545231i	0.949162	−	0.314789i
$3$	1.64400	−	0.545231i	0.949162	−	0.314789i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.84981	+	3.20397i	−0.827262	+	1.43286i	0.0729162	+	0.997338i	$0.476769\pi$
$5$	−1.84981	+	3.20397i	−0.827262	+	1.43286i	−0.900178	+	0.435522i	$0.856564\pi$
$6$	−1.29418	−	1.15113i	−0.528348	−	0.469946i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	2.40545	−	1.79272i	0.801815	−	0.597572i
$10$	3.69963			1.16993
$11$	0.738550	+	1.27921i	0.222681	+	0.385695i	0.955621	−	0.294598i	$-0.0951858\pi$
$11$	0.738550	+	1.27921i	0.222681	+	0.385695i	−0.732940	+	0.680293i	$0.761852\pi$
$12$	−0.349814	+	1.69636i	−0.100983	+	0.489696i
$13$	−1.34981	+	2.33795i	−0.374371	+	0.648430i	−0.990233	−	0.139425i	$-0.955475\pi$
$13$	−1.34981	+	2.33795i	−0.374371	+	0.648430i	0.615862	+	0.787854i	$0.288808\pi$
$14$		0			0
$15$	−1.29418	+	6.27589i	−0.334156	+	1.62043i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.57598			−1.59491			−0.797455	−	0.603378i	$-0.793821\pi$
$17$	−6.57598			−1.59491			−0.797455	+	0.603378i	$0.793821\pi$
$18$	−2.75526	−	1.18682i	−0.649421	−	0.279736i
$19$	0.888736			0.203890			0.101945	−	0.994790i	$-0.467493\pi$
$19$	0.888736			0.203890			0.101945	+	0.994790i	$0.467493\pi$
$20$	−1.84981	−	3.20397i	−0.413631	−	0.716430i
$21$		0			0
$22$	0.738550	−	1.27921i	0.157459	−	0.272728i
$23$	−3.14400	+	5.44556i	−0.655568	+	1.13548i	0.326182	+	0.945307i	$0.394238\pi$
$23$	−3.14400	+	5.44556i	−0.655568	+	1.13548i	−0.981751	+	0.190171i	$0.939096\pi$
$24$	1.64400	−	0.545231i	0.335579	−	0.111295i
$25$	−4.34362	−	7.52338i	−0.868725	−	1.50468i
$26$	2.69963			0.529441
$27$	2.97710	−	4.25874i	0.572943	−	0.819595i
$28$		0			0
$29$	1.25526	+	2.17417i	0.233096	+	0.403734i	0.958718	−	0.284360i	$-0.0917810\pi$
$29$	1.25526	+	2.17417i	0.233096	+	0.403734i	−0.725622	+	0.688094i	$0.758448\pi$
$30$	6.08217	−	2.01715i	1.11045	−	0.368280i
$31$	−3.40545	+	5.89841i	−0.611636	+	1.05938i	0.379329	+	0.925262i	$0.376155\pi$
$31$	−3.40545	+	5.89841i	−0.611636	+	1.05938i	−0.990965	+	0.134123i	$0.957178\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.91164	+	1.70033i	0.332773	+	0.295989i
$34$	3.28799	+	5.69497i	0.563886	+	0.976679i
$35$		0			0
$36$	0.349814	+	2.97954i	0.0583023	+	0.496589i
$37$	2.77747			0.456614			0.228307	−	0.973589i	$-0.426681\pi$
$37$	2.77747			0.456614			0.228307	+	0.973589i	$0.426681\pi$
$38$	−0.444368	−	0.769668i	−0.0720860	−	0.124857i
$39$	−0.944368	+	4.57954i	−0.151220	+	0.733313i
$40$	−1.84981	+	3.20397i	−0.292481	+	0.506592i
$41$	−2.05563	+	3.56046i	−0.321036	+	0.556050i	−0.980702	−	0.195508i	$-0.937364\pi$
$41$	−2.05563	+	3.56046i	−0.321036	+	0.556050i	0.659666	+	0.751559i	$0.270698\pi$
$42$		0			0
$43$	0.00618986	+	0.0107211i	0.000943944	+	0.00163496i	0.866497	−	0.499182i	$-0.166366\pi$
$43$	0.00618986	+	0.0107211i	0.000943944	+	0.00163496i	−0.865553	+	0.500817i	$0.833033\pi$
$44$	−1.47710			−0.222681
$45$	1.29418	+	11.0232i	0.192925	+	1.64324i
$46$	6.28799			0.927114
$47$	3.49381	+	6.05146i	0.509625	+	0.882696i	0.999938	+	0.0111494i	$0.00354904\pi$
$47$	3.49381	+	6.05146i	0.509625	+	0.882696i	−0.490313	+	0.871546i	$0.663118\pi$
$48$	−1.29418	−	1.15113i	−0.186799	−	0.166151i
$49$		0			0
$50$	−4.34362	+	7.52338i	−0.614281	+	1.06397i
$51$	−10.8109	+	3.58543i	−1.51383	+	0.502061i
$52$	−1.34981	−	2.33795i	−0.187186	−	0.324215i
$53$	3.21015			0.440948			0.220474	−	0.975393i	$-0.429240\pi$
$53$	3.21015			0.440948			0.220474	+	0.975393i	$0.429240\pi$
$54$	−5.17673	−	0.448873i	−0.704463	−	0.0610839i
$55$	−5.46472			−0.736863
$56$		0			0
$57$	1.46108	−	0.484566i	0.193525	−	0.0641824i
$58$	1.25526	−	2.17417i	0.164824	−	0.285483i
$59$	−3.45489	+	5.98404i	−0.449788	+	0.779056i	−0.998372	−	0.0570397i	$-0.981834\pi$
$59$	−3.45489	+	5.98404i	−0.449788	+	0.779056i	0.548584	+	0.836096i	$0.315167\pi$
$60$	−4.78799	−	4.25874i	−0.618127	−	0.549801i
$61$	2.86652	+	4.96497i	0.367021	+	0.635699i	0.989098	−	0.147257i	$-0.0470444\pi$
$61$	2.86652	+	4.96497i	0.367021	+	0.635699i	−0.622077	+	0.782956i	$0.713711\pi$
$62$	6.81089			0.864984
$63$		0			0
$64$	1.00000			0.125000
$65$	−4.99381	−	8.64953i	−0.619406	−	1.07284i
$66$	0.516710	−	2.50569i	0.0636026	−	0.308429i
$67$	4.73236	−	8.19669i	0.578150	−	1.00138i	−0.417542	−	0.908658i	$-0.637108\pi$
$67$	4.73236	−	8.19669i	0.578150	−	1.00138i	0.995692	−	0.0927271i	$-0.0295584\pi$
$68$	3.28799	−	5.69497i	0.398728	−	0.690616i
$69$	−2.19963	+	10.6667i	−0.264804	+	1.28412i
$70$		0			0
$71$	−5.46472			−0.648543			−0.324271	−	0.945964i	$-0.605119\pi$
$71$	−5.46472			−0.648543			−0.324271	+	0.945964i	$0.605119\pi$
$72$	2.40545	−	1.79272i	0.283485	−	0.211274i
$73$	12.0655			1.41216			0.706078	−	0.708134i	$-0.250463\pi$
$73$	12.0655			1.41216			0.706078	+	0.708134i	$0.250463\pi$
$74$	−1.38874	−	2.40536i	−0.161437	−	0.279618i
$75$	−11.2429	−	10.0001i	−1.29822	−	1.15471i
$76$	−0.444368	+	0.769668i	−0.0509725	+	0.0882870i
$77$		0			0
$78$	4.43818	−	1.47192i	0.502525	−	0.166662i
$79$	−5.72617	−	9.91802i	−0.644244	−	1.11586i	−0.984475	−	0.175522i	$-0.943839\pi$
$79$	−5.72617	−	9.91802i	−0.644244	−	1.11586i	0.340231	−	0.940342i	$-0.389495\pi$
$80$	3.69963			0.413631
$81$	2.57234	−	8.62456i	0.285816	−	0.958285i
$82$	4.11126			0.454013
$83$	2.23855	+	3.87728i	0.245713	+	0.425587i	0.962332	−	0.271878i	$-0.0876447\pi$
$83$	2.23855	+	3.87728i	0.245713	+	0.425587i	−0.716619	+	0.697465i	$0.754311\pi$
$84$		0			0
$85$	12.1643	−	21.0693i	1.31941	−	2.28528i
$86$	0.00618986	−	0.0107211i	0.000667469	−	0.00115609i
$87$	3.24907	+	2.88993i	0.348337	+	0.309833i
$88$	0.738550	+	1.27921i	0.0787297	+	0.136364i
$89$	8.87636			0.940892			0.470446	−	0.882429i	$-0.344093\pi$
$89$	8.87636			0.940892			0.470446	+	0.882429i	$0.344093\pi$
$90$	8.89926	−	6.63238i	0.938064	−	0.699114i
$91$		0			0
$92$	−3.14400	−	5.44556i	−0.327784	−	0.567739i
$93$	−2.38255	+	11.5537i	−0.247059	+	1.19806i
$94$	3.49381	−	6.05146i	0.360359	−	0.624160i
$95$	−1.64400	+	2.84748i	−0.168670	+	0.292146i
$96$	−0.349814	+	1.69636i	−0.0357027	+	0.173134i
$97$	−6.58836	−	11.4114i	−0.668947	−	1.15865i	−0.978199	−	0.207670i	$-0.933412\pi$
$97$	−6.58836	−	11.4114i	−0.668947	−	1.15865i	0.309252	−	0.950980i	$-0.399921\pi$
$98$		0			0
$99$	4.06979	+	1.75305i	0.409030	+	0.176188i
$100$	8.68725			0.868725
$101$	−2.62729	−	4.55059i	−0.261425	−	0.452801i	0.705196	−	0.709012i	$-0.250859\pi$
$101$	−2.62729	−	4.55059i	−0.261425	−	0.452801i	−0.966621	+	0.256212i	$0.917526\pi$
$102$	8.51052	+	7.56979i	0.842667	+	0.749521i
$103$	−0.833104	+	1.44298i	−0.0820882	+	0.142181i	−0.904147	−	0.427222i	$-0.859492\pi$
$103$	−0.833104	+	1.44298i	−0.0820882	+	0.142181i	0.822059	+	0.569403i	$0.192826\pi$
$104$	−1.34981	+	2.33795i	−0.132360	+	0.229255i
$105$		0			0
$106$	−1.60507	−	2.78007i	−0.155899	−	0.270024i
$107$	10.7651			1.04070			0.520350	−	0.853953i	$-0.325801\pi$
$107$	10.7651			1.04070			0.520350	+	0.853953i	$0.325801\pi$
$108$	2.19963	+	4.70761i	0.211659	+	0.452990i
$109$	0.189108			0.0181132			0.00905662	−	0.999959i	$-0.497117\pi$
$109$	0.189108			0.0181132			0.00905662	+	0.999959i	$0.497117\pi$
$110$	2.73236	+	4.73259i	0.260520	+	0.451234i
$111$	4.56615	−	1.51436i	0.433400	−	0.143737i
$112$		0			0
$113$	−6.78180	+	11.7464i	−0.637978	+	1.10501i	0.347897	+	0.937533i	$0.386896\pi$
$113$	−6.78180	+	11.7464i	−0.637978	+	1.10501i	−0.985876	+	0.167478i	$0.946438\pi$
$114$	−1.15019	−	1.02305i	−0.107725	−	0.0958172i
$115$	−11.6316	−	20.1466i	−1.08465	−	1.87868i
$116$	−2.51052			−0.233096
$117$	0.944368	+	8.04364i	0.0873068	+	0.743635i
$118$	6.90978			0.636097
$119$		0			0
$120$	−1.29418	+	6.27589i	−0.118142	+	0.572908i
$121$	4.40909	−	7.63676i	0.400826	−	0.694251i
$122$	2.86652	−	4.96497i	0.259523	−	0.449507i
$123$	−1.43818	+	6.97418i	−0.129676	+	0.628840i
$124$	−3.40545	−	5.89841i	−0.305818	−	0.529692i
$125$	13.6414			1.22013
$126$		0			0
$127$	−2.85669			−0.253490			−0.126745	−	0.991935i	$-0.540453\pi$
$127$	−2.85669			−0.253490			−0.126745	+	0.991935i	$0.540453\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	0.0160216	+	0.0142506i	0.00141062	+	0.00125470i
$130$	−4.99381	+	8.64953i	−0.437986	+	0.758614i
$131$	−0.0778435	+	0.134829i	−0.00680122	+	0.0117801i	−0.869406	−	0.494098i	$-0.835498\pi$
$131$	−0.0778435	+	0.134829i	−0.00680122	+	0.0117801i	0.862605	+	0.505878i	$0.168832\pi$
$132$	−2.42835	+	0.805361i	−0.211360	+	0.0700977i
$133$		0			0
$134$	−9.46472			−0.817627
$135$	8.13781	+	17.4164i	0.700391	+	1.49897i
$136$	−6.57598			−0.563886
$137$	1.70582	+	2.95456i	0.145738	+	0.252425i	0.929648	−	0.368449i	$-0.120111\pi$
$137$	1.70582	+	2.95456i	0.145738	+	0.252425i	−0.783910	+	0.620874i	$0.786778\pi$
$138$	10.3374	−	3.42841i	0.879981	−	0.291846i
$139$	−6.75526	+	11.7005i	−0.572974	+	0.992420i	0.423285	+	0.905997i	$0.360877\pi$
$139$	−6.75526	+	11.7005i	−0.572974	+	0.992420i	−0.996259	+	0.0864229i	$0.972456\pi$
$140$		0			0
$141$	9.04325	+	8.04364i	0.761579	+	0.677396i
$142$	2.73236	+	4.73259i	0.229295	+	0.397150i
$143$	−3.98762			−0.333462
$144$	−2.75526	−	1.18682i	−0.229605	−	0.0989016i
$145$	−9.28799			−0.771326
$146$	−6.03273	−	10.4490i	−0.499272	−	0.864765i
$147$		0			0
$148$	−1.38874	+	2.40536i	−0.114153	+	0.197719i
$149$	−0.166896	+	0.289073i	−0.0136727	+	0.0236818i	−0.872781	−	0.488112i	$-0.837686\pi$
$149$	−0.166896	+	0.289073i	−0.0136727	+	0.0236818i	0.859108	+	0.511794i	$0.171019\pi$
$150$	−3.03892	+	14.7367i	−0.248127	+	1.20325i
$151$	9.95489	+	17.2424i	0.810117	+	1.40316i	0.912781	+	0.408448i	$0.133930\pi$
$151$	9.95489	+	17.2424i	0.810117	+	1.40316i	−0.102664	+	0.994716i	$0.532737\pi$
$152$	0.888736			0.0720860
$153$	−15.8182	+	11.7889i	−1.27882	+	0.953074i
$154$		0			0
$155$	−12.5989	−	21.8219i	−1.01197	−	1.75278i
$156$	−3.49381	−	3.10761i	−0.279729	−	0.248808i
$157$	3.48143	−	6.03001i	0.277848	−	0.481248i	−0.693001	−	0.720936i	$-0.743712\pi$
$157$	3.48143	−	6.03001i	0.277848	−	0.481248i	0.970850	+	0.239689i	$0.0770454\pi$
$158$	−5.72617	+	9.91802i	−0.455550	+	0.789035i
$159$	5.27747	−	1.75027i	0.418531	−	0.138806i
$160$	−1.84981	−	3.20397i	−0.146241	−	0.253296i
$161$		0			0
$162$	−8.75526	+	2.08457i	−0.687878	+	0.163779i
$163$	−8.07413			−0.632414			−0.316207	−	0.948690i	$-0.602409\pi$
$163$	−8.07413			−0.632414			−0.316207	+	0.948690i	$0.602409\pi$
$164$	−2.05563	−	3.56046i	−0.160518	−	0.278025i
$165$	−8.98398	+	2.97954i	−0.699402	+	0.231957i
$166$	2.23855	−	3.87728i	0.173745	−	0.300935i
$167$	9.74288	−	16.8752i	0.753927	−	1.30584i	−0.191979	−	0.981399i	$-0.561491\pi$
$167$	9.74288	−	16.8752i	0.753927	−	1.30584i	0.945906	−	0.324440i	$-0.105176\pi$
$168$		0			0
$169$	2.85600	+	4.94674i	0.219693	+	0.380519i
$170$	−24.3287			−1.86593
$171$	2.13781	−	1.59325i	0.163482	−	0.121839i
$172$	−0.0123797			−0.000943944
$173$	−11.2818	−	19.5407i	−0.857740	−	1.48565i	−0.874080	−	0.485782i	$-0.838535\pi$
$173$	−11.2818	−	19.5407i	−0.857740	−	1.48565i	0.0163405	−	0.999866i	$-0.494798\pi$
$174$	0.878215	−	4.25874i	0.0665773	−	0.322854i
$175$		0			0
$176$	0.738550	−	1.27921i	0.0556703	−	0.0964238i
$177$	−2.41714	+	11.7215i	−0.181683	+	0.881038i
$178$	−4.43818	−	7.68715i	−0.332656	−	0.576176i
$179$	−0.333792			−0.0249488			−0.0124744	−	0.999922i	$-0.503971\pi$
$179$	−0.333792			−0.0249488			−0.0124744	+	0.999922i	$0.503971\pi$
$180$	−10.1934	−	4.39079i	−0.759774	−	0.327270i
$181$	23.2422			1.72758			0.863789	−	0.503853i	$-0.168085\pi$
$181$	23.2422			1.72758			0.863789	+	0.503853i	$0.168085\pi$
$182$		0			0
$183$	7.41961	+	6.59947i	0.548473	+	0.487847i
$184$	−3.14400	+	5.44556i	−0.231778	+	0.401452i
$185$	−5.13781	+	8.89894i	−0.377739	+	0.654263i
$186$	11.1971	−	3.71351i	0.821010	−	0.272288i
$187$	−4.85669	−	8.41204i	−0.355157	−	0.615149i
$188$	−6.98762			−0.509625
$189$		0			0
$190$	3.28799			0.238536
$191$	8.16071	+	14.1348i	0.590488	+	1.02276i	0.994167	+	0.107854i	$0.0343980\pi$
$191$	8.16071	+	14.1348i	0.590488	+	1.02276i	−0.403679	+	0.914901i	$0.632269\pi$
$192$	1.64400	−	0.545231i	0.118645	−	0.0393487i
$193$	7.16071	−	12.4027i	0.515439	−	0.892766i	−0.484400	−	0.874846i	$-0.660962\pi$
$193$	7.16071	−	12.4027i	0.515439	−	0.892766i	0.999839	−	0.0179200i	$-0.00570443\pi$
$194$	−6.58836	+	11.4114i	−0.473017	+	0.819289i
$195$	−12.9258	−	11.4970i	−0.925636	−	0.823319i
$196$		0			0
$197$	2.42402			0.172704			0.0863520	−	0.996265i	$-0.472479\pi$
$197$	2.42402			0.172704			0.0863520	+	0.996265i	$0.472479\pi$
$198$	−0.516710	−	4.40107i	−0.0367210	−	0.312770i
$199$	6.11126			0.433216			0.216608	−	0.976259i	$-0.430501\pi$
$199$	6.11126			0.433216			0.216608	+	0.976259i	$0.430501\pi$
$200$	−4.34362	−	7.52338i	−0.307141	−	0.531983i
$201$	3.31089	−	16.0556i	0.233532	−	1.13247i
$202$	−2.62729	+	4.55059i	−0.184855	+	0.320179i
$203$		0			0
$204$	2.30037	−	11.1552i	0.161058	−	0.781022i
$205$	−7.60507	−	13.1724i	−0.531161	−	0.919999i
$206$	1.66621			0.116090
$207$	2.19963	+	18.7353i	0.152885	+	1.30219i
$208$	2.69963			0.187186
$209$	0.656376	+	1.13688i	0.0454025	+	0.0786394i
$210$		0			0
$211$	5.72253	−	9.91171i	0.393955	−	0.682350i	−0.599012	−	0.800740i	$-0.704440\pi$
$211$	5.72253	−	9.91171i	0.393955	−	0.682350i	0.992967	+	0.118390i	$0.0377732\pi$
$212$	−1.60507	+	2.78007i	−0.110237	+	0.190936i
$213$	−8.98398	+	2.97954i	−0.615572	+	0.204154i
$214$	−5.38255	−	9.32284i	−0.367943	−	0.637296i
$215$	−0.0458003			−0.00312356
$216$	2.97710	−	4.25874i	0.202566	−	0.289771i
$217$		0			0
$218$	−0.0945538	−	0.163772i	−0.00640399	−	0.0110920i
$219$	19.8356	−	6.57847i	1.34036	−	0.444532i
$220$	2.73236	−	4.73259i	0.184216	−	0.319071i
$221$	8.87636	−	15.3743i	0.597088	−	1.03419i
$222$	−3.59455	−	3.19722i	−0.241251	−	0.214584i
$223$	−3.61126	−	6.25489i	−0.241828	−	0.418859i	0.719407	−	0.694589i	$-0.244414\pi$
$223$	−3.61126	−	6.25489i	−0.241828	−	0.418859i	−0.961235	+	0.275730i	$0.911080\pi$
$224$		0			0
$225$	−23.9356	−	10.3102i	−1.59571	−	0.687347i
$226$	13.5636			0.902238
$227$	−6.82760	−	11.8258i	−0.453164	−	0.784903i	0.545417	−	0.838165i	$-0.316371\pi$
$227$	−6.82760	−	11.8258i	−0.453164	−	0.784903i	−0.998581	+	0.0532622i	$0.983038\pi$
$228$	−0.310892	+	1.50761i	−0.0205893	+	0.0998442i
$229$	−8.68725	+	15.0468i	−0.574070	+	0.994318i	0.422073	+	0.906562i	$0.361303\pi$
$229$	−8.68725	+	15.0468i	−0.574070	+	0.994318i	−0.996142	+	0.0877555i	$0.972031\pi$
$230$	−11.6316	+	20.1466i	−0.766966	+	1.32842i
$231$		0			0
$232$	1.25526	+	2.17417i	0.0824119	+	0.142742i
$233$	−15.2422			−0.998549			−0.499275	−	0.866444i	$-0.666400\pi$
$233$	−15.2422			−0.998549			−0.499275	+	0.866444i	$0.666400\pi$
$234$	6.49381	−	4.83967i	0.424514	−	0.316379i
$235$	−25.8516			−1.68637
$236$	−3.45489	−	5.98404i	−0.224894	−	0.389528i
$237$	−14.8214	−	13.1831i	−0.962754	−	0.856334i
$238$		0			0
$239$	9.47524	−	16.4116i	0.612902	−	1.06158i	−0.377846	−	0.925868i	$-0.623335\pi$
$239$	9.47524	−	16.4116i	0.612902	−	1.06158i	0.990749	−	0.135710i	$-0.0433314\pi$
$240$	6.08217	−	2.01715i	0.392603	−	0.130207i
$241$	12.2527	+	21.2223i	0.789267	+	1.36705i	0.926417	+	0.376500i	$0.122872\pi$
$241$	12.2527	+	21.2223i	0.789267	+	1.36705i	−0.137150	+	0.990550i	$0.543794\pi$
$242$	−8.81818			−0.566854
$243$	−0.473458	−	15.5813i	−0.0303723	−	0.999539i
$244$	−5.73305			−0.367021
$245$		0			0
$246$	6.75890	−	2.24159i	0.430932	−	0.142918i
$247$	−1.19963	+	2.07782i	−0.0763305	+	0.132208i
$248$	−3.40545	+	5.89841i	−0.216246	+	0.374549i
$249$	5.79418	+	5.15371i	0.367191	+	0.326603i
$250$	−6.82072	−	11.8138i	−0.431380	−	0.747173i
$251$	−12.1236			−0.765238			−0.382619	−	0.923906i	$-0.624978\pi$
$251$	−12.1236			−0.765238			−0.382619	+	0.923906i	$0.624978\pi$
$252$		0			0
$253$	−9.28799			−0.583931
$254$	1.42835	+	2.47397i	0.0896224	+	0.155231i
$255$	8.51052	−	41.2702i	0.532949	−	2.58444i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.10439	−	7.10900i	0.256025	−	0.443448i	−0.709149	−	0.705059i	$-0.750921\pi$
$257$	4.10439	−	7.10900i	0.256025	−	0.443448i	0.965173	+	0.261611i	$0.0842539\pi$
$258$	0.00433060	−	0.0210004i	0.000269611	−	0.00130743i
$259$		0			0
$260$	9.98762			0.619406
$261$	6.91714	+	2.97954i	0.428160	+	0.184429i
$262$	0.155687			0.00961838
$263$	2.67309	+	4.62992i	0.164830	+	0.285493i	0.936595	−	0.350414i	$-0.113959\pi$
$263$	2.67309	+	4.62992i	0.164830	+	0.285493i	−0.771765	+	0.635908i	$0.780626\pi$
$264$	1.91164	+	1.70033i	0.117653	+	0.104648i
$265$	−5.93818	+	10.2852i	−0.364779	+	0.631816i
$266$		0			0
$267$	14.5927	−	4.83967i	0.893058	−	0.296183i
$268$	4.73236	+	8.19669i	0.289075	+	0.500692i
$269$	−18.4844			−1.12701			−0.563506	−	0.826112i	$-0.690548\pi$
$269$	−18.4844			−1.12701			−0.563506	+	0.826112i	$0.690548\pi$
$270$	11.0142	−	15.7558i	0.670301	−	0.958865i
$271$	7.35483			0.446774			0.223387	−	0.974730i	$-0.428289\pi$
$271$	7.35483			0.446774			0.223387	+	0.974730i	$0.428289\pi$
$272$	3.28799	+	5.69497i	0.199364	+	0.345308i
$273$		0			0
$274$	1.70582	−	2.95456i	0.103052	−	0.178492i
$275$	6.41597	−	11.1128i	0.386897	−	0.670126i
$276$	−8.13781	−	7.23828i	−0.489838	−	0.435693i
$277$	4.54944	+	7.87987i	0.273349	+	0.473455i	0.969717	−	0.244230i	$-0.0785351\pi$
$277$	4.54944	+	7.87987i	0.273349	+	0.473455i	−0.696368	+	0.717685i	$0.745202\pi$
$278$	13.5105			0.810307
$279$	2.38255	+	20.2933i	0.142639	+	1.21493i
$280$		0			0
$281$	6.00433	+	10.3998i	0.358188	+	0.620400i	0.987658	−	0.156624i	$-0.0500612\pi$
$281$	6.00433	+	10.3998i	0.358188	+	0.620400i	−0.629470	+	0.777025i	$0.716728\pi$
$282$	2.44437	−	11.8535i	0.145560	−	0.705866i
$283$	−4.92147	+	8.52423i	−0.292551	+	0.506713i	−0.974412	−	0.224768i	$-0.927837\pi$
$283$	−4.92147	+	8.52423i	−0.292551	+	0.506713i	0.681861	+	0.731481i	$0.261171\pi$
$284$	2.73236	−	4.73259i	0.162136	−	0.280827i
$285$	−1.15019	+	5.57761i	−0.0681311	+	0.330389i
$286$	1.99381	+	3.45338i	0.117896	+	0.204203i
$287$		0			0
$288$	0.349814	+	2.97954i	0.0206130	+	0.175571i
$289$	26.2436			1.54374
$290$	4.64400	+	8.04364i	0.272705	+	0.472339i
$291$	−17.0531	−	15.1681i	−0.999669	−	0.889169i
$292$	−6.03273	+	10.4490i	−0.353039	+	0.611481i
$293$	10.7101	−	18.5505i	0.625694	−	1.08373i	−0.362713	−	0.931901i	$-0.618149\pi$
$293$	10.7101	−	18.5505i	0.625694	−	1.08373i	0.988406	−	0.151832i	$-0.0485173\pi$
$294$		0			0
$295$	−12.7818	−	22.1387i	−0.744185	−	1.28897i
$296$	2.77747			0.161437
$297$	7.64654	+	0.663031i	0.443697	+	0.0384730i
$298$	0.333792			0.0193361
$299$	−8.48762	−	14.7010i	−0.490852	−	0.850180i
$300$	14.2818	−	4.73656i	0.824560	−	0.273465i
$301$		0			0
$302$	9.95489	−	17.2424i	0.572839	−	0.992187i
$303$	−6.80037	−	6.04868i	−0.390671	−	0.347487i
$304$	−0.444368	−	0.769668i	−0.0254862	−	0.0441435i
$305$	−21.2101			−1.21449
$306$	18.1185	+	7.80451i	1.03577	+	0.446154i
$307$	−5.68725			−0.324588			−0.162294	−	0.986742i	$-0.551889\pi$
$307$	−5.68725			−0.324588			−0.162294	+	0.986742i	$0.551889\pi$
$308$		0			0
$309$	−0.582863	+	2.82648i	−0.0331579	+	0.160793i
$310$	−12.5989	+	21.8219i	−0.715569	+	1.23940i
$311$	5.86033	−	10.1504i	0.332309	−	0.575576i	−0.650655	−	0.759373i	$-0.725506\pi$
$311$	5.86033	−	10.1504i	0.332309	−	0.575576i	0.982964	+	0.183797i	$0.0588390\pi$
$312$	−0.944368	+	4.57954i	−0.0534643	+	0.259265i
$313$	13.3869	+	23.1868i	0.756671	+	1.31059i	0.944539	+	0.328398i	$0.106509\pi$
$313$	13.3869	+	23.1868i	0.756671	+	1.31059i	−0.187868	+	0.982194i	$0.560158\pi$
$314$	−6.96286			−0.392937
$315$		0			0
$316$	11.4523			0.644244
$317$	−0.951246	−	1.64761i	−0.0534273	−	0.0925388i	0.838075	−	0.545555i	$-0.183681\pi$
$317$	−0.951246	−	1.64761i	−0.0534273	−	0.0925388i	−0.891502	+	0.453016i	$0.850348\pi$
$318$	−4.15452	−	3.69529i	−0.232974	−	0.207221i
$319$	−1.85414	+	3.21147i	−0.103812	+	0.179808i
$320$	−1.84981	+	3.20397i	−0.103408	+	0.179107i
$321$	17.6978	−	5.86946i	0.987793	−	0.327601i
$322$		0			0
$323$	−5.84431			−0.325186
$324$	6.18292	+	6.53999i	0.343495	+	0.363333i
$325$	23.4523			1.30090
$326$	4.03706	+	6.99240i	0.223592	+	0.387273i
$327$	0.310892	−	0.103107i	0.0171924	−	0.00570185i
$328$	−2.05563	+	3.56046i	−0.113503	+	0.196593i
$329$		0			0
$330$	7.07234	+	6.29059i	0.389320	+	0.346285i
$331$	−2.78366	−	4.82144i	−0.153004	−	0.265010i	0.779327	−	0.626618i	$-0.215561\pi$
$331$	−2.78366	−	4.82144i	−0.153004	−	0.265010i	−0.932330	+	0.361608i	$0.882228\pi$
$332$	−4.47710			−0.245713
$333$	6.68106	−	4.97922i	0.366120	−	0.272859i
$334$	−19.4858			−1.06621
$335$	17.5080	+	30.3247i	0.956563	+	1.65682i
$336$		0			0
$337$	−16.8869	+	29.2489i	−0.919887	+	1.59329i	−0.120302	+	0.992737i	$0.538386\pi$
$337$	−16.8869	+	29.2489i	−0.919887	+	1.59329i	−0.799585	+	0.600553i	$0.794947\pi$
$338$	2.85600	−	4.94674i	0.155346	−	0.269067i
$339$	−4.74474	+	23.0087i	−0.257699	+	1.24966i
$340$	12.1643	+	21.0693i	0.659704	+	1.14264i
$341$	−10.0604			−0.544799
$342$	−2.44870	−	1.05477i	−0.132410	−	0.0570354i
$343$		0			0
$344$	0.00618986	+	0.0107211i	0.000333735	+	0.000578045i
$345$	−30.1069	−	26.7789i	−1.62090	−	1.44173i
$346$	−11.2818	+	19.5407i	−0.606513	+	1.05051i
$347$	15.2033	−	26.3328i	0.816154	−	1.41362i	−0.0923418	−	0.995727i	$-0.529435\pi$
$347$	15.2033	−	26.3328i	0.816154	−	1.41362i	0.908496	−	0.417893i	$-0.137231\pi$
$348$	−4.12729	+	1.36881i	−0.221246	+	0.0733761i
$349$	−6.29782	−	10.9082i	−0.337115	−	0.583900i	0.646774	−	0.762682i	$-0.276118\pi$
$349$	−6.29782	−	10.9082i	−0.337115	−	0.583900i	−0.983889	+	0.178782i	$0.942784\pi$
$350$		0			0
$351$	5.93818	+	12.7088i	0.316956	+	0.678346i
$352$	−1.47710			−0.0787297
$353$	3.76578	+	6.52252i	0.200432	+	0.347159i	0.948668	−	0.316274i	$-0.102432\pi$
$353$	3.76578	+	6.52252i	0.200432	+	0.347159i	−0.748235	+	0.663433i	$0.769099\pi$
$354$	11.3596	−	3.76742i	0.603758	−	0.200236i
$355$	10.1087	−	17.5088i	0.536515	−	0.929271i
$356$	−4.43818	+	7.68715i	−0.235223	+	0.407418i
$357$		0			0
$358$	0.166896	+	0.289073i	0.00882074	+	0.0152780i
$359$	6.89602			0.363958			0.181979	−	0.983302i	$-0.441750\pi$
$359$	6.89602			0.363958			0.181979	+	0.983302i	$0.441750\pi$
$360$	1.29418	+	11.0232i	0.0682094	+	0.580972i
$361$	−18.2101			−0.958429
$362$	−11.6211	−	20.1283i	−0.610791	−	1.05792i
$363$	3.08472	−	14.9588i	0.161906	−	0.785132i
$364$		0			0
$365$	−22.3189	+	38.6574i	−1.16822	+	2.02342i
$366$	2.00550	−	9.72530i	0.104829	−	0.508350i
$367$	−11.5618	−	20.0257i	−0.603522	−	1.04533i	−0.992283	−	0.123992i	$-0.960430\pi$
$367$	−11.5618	−	20.0257i	−0.603522	−	1.04533i	0.388761	−	0.921339i	$-0.372903\pi$
$368$	6.28799			0.327784
$369$	1.43818	+	12.2497i	0.0748686	+	0.637692i
$370$	10.2756			0.534204
$371$		0			0
$372$	−8.81453	−	7.84020i	−0.457012	−	0.406495i
$373$	−14.5822	+	25.2571i	−0.755036	+	1.30776i	0.190320	+	0.981722i	$0.439047\pi$
$373$	−14.5822	+	25.2571i	−0.755036	+	1.30776i	−0.945356	+	0.326039i	$0.894286\pi$
$374$	−4.85669	+	8.41204i	−0.251134	+	0.434976i
$375$	22.4265	−	7.43774i	1.15810	−	0.384083i
$376$	3.49381	+	6.05146i	0.180180	+	0.312080i
$377$	−6.77747			−0.349058
$378$		0			0
$379$	−13.5622			−0.696645			−0.348322	−	0.937375i	$-0.613249\pi$
$379$	−13.5622			−0.696645			−0.348322	+	0.937375i	$0.613249\pi$
$380$	−1.64400	−	2.84748i	−0.0843352	−	0.146073i
$381$	−4.69639	+	1.55756i	−0.240603	+	0.0797961i
$382$	8.16071	−	14.1348i	0.417538	−	0.723197i
$383$	1.41783	−	2.45575i	0.0724475	−	0.125483i	−0.827526	−	0.561428i	$-0.810252\pi$
$383$	1.41783	−	2.45575i	0.0724475	−	0.125483i	0.899973	+	0.435945i	$0.143586\pi$
$384$	−1.29418	−	1.15113i	−0.0660434	−	0.0587432i
$385$		0			0
$386$	−14.3214			−0.728941
$387$	0.0341093	+	0.0146925i	0.00173387	+	0.000746861i
$388$	13.1767			0.668947
$389$	9.30401	+	16.1150i	0.471732	+	0.817064i	0.999477	−	0.0323388i	$-0.0102956\pi$
$389$	9.30401	+	16.1150i	0.471732	+	0.817064i	−0.527745	+	0.849403i	$0.676962\pi$
$390$	−3.49381	+	16.9426i	−0.176916	+	0.857921i
$391$	20.6749	−	35.8099i	1.04557	−	1.81099i
$392$		0			0
$393$	−0.0544615	+	0.264101i	−0.00274722	+	0.0133221i
$394$	−1.21201	−	2.09926i	−0.0610601	−	0.105759i
$395$	42.3694			2.13184
$396$	−3.55308	+	2.64802i	−0.178549	+	0.133068i
$397$	20.5760			1.03268			0.516340	−	0.856384i	$-0.327294\pi$
$397$	20.5760			1.03268			0.516340	+	0.856384i	$0.327294\pi$
$398$	−3.05563	−	5.29251i	−0.153165	−	0.265290i
$399$		0			0
$400$	−4.34362	+	7.52338i	−0.217181	+	0.376169i
$401$	3.37704	−	5.84921i	0.168642	−	0.292096i	−0.769301	−	0.638887i	$-0.779395\pi$
$401$	3.37704	−	5.84921i	0.168642	−	0.292096i	0.937942	+	0.346791i	$0.112729\pi$
$402$	−15.5600	+	5.16046i	−0.776060	+	0.257380i
$403$	−9.19344	−	15.9235i	−0.457958	−	0.793206i
$404$	5.25457			0.261425
$405$	22.8745	+	24.1955i	1.13664	+	1.20229i
$406$		0			0
$407$	2.05130	+	3.55296i	0.101679	+	0.176114i
$408$	−10.8109	+	3.58543i	−0.535219	+	0.177505i
$409$	−7.66071	+	13.2687i	−0.378798	+	0.656097i	−0.990888	−	0.134691i	$-0.956996\pi$
$409$	−7.66071	+	13.2687i	−0.378798	+	0.656097i	0.612090	+	0.790788i	$0.290329\pi$
$410$	−7.60507	+	13.1724i	−0.375588	+	0.650537i
$411$	4.41528	+	3.92723i	0.217790	+	0.193716i
$412$	−0.833104	−	1.44298i	−0.0410441	−	0.0710904i
$413$		0			0
$414$	15.1254	−	11.2726i	0.743374	−	0.554017i
$415$	−16.5636			−0.813075
$416$	−1.34981	−	2.33795i	−0.0661801	−	0.114627i
$417$	−4.72617	+	22.9187i	−0.231442	+	1.12233i
$418$	0.656376	−	1.13688i	0.0321044	−	0.0556064i
$419$	−4.32141	+	7.48491i	−0.211115	+	0.365662i	−0.952064	−	0.305900i	$-0.901043\pi$
$419$	−4.32141	+	7.48491i	−0.211115	+	0.365662i	0.740949	+	0.671561i	$0.234376\pi$
$420$		0			0
$421$	18.5636	+	32.1531i	0.904735	+	1.56705i	0.821273	+	0.570536i	$0.193264\pi$
$421$	18.5636	+	32.1531i	0.904735	+	1.56705i	0.0834618	+	0.996511i	$0.473402\pi$
$422$	−11.4451			−0.557137
$423$	19.2527	+	8.29305i	0.936099	+	0.403222i
$424$	3.21015			0.155899
$425$	28.5636	+	49.4736i	1.38554	+	2.39982i
$426$	7.07234	+	6.29059i	0.342656	+	0.304780i
$427$		0			0
$428$	−5.38255	+	9.32284i	−0.260175	+	0.450637i
$429$	−6.55563	+	2.17417i	−0.316509	+	0.104970i
$430$	0.0229002	+	0.0396643i	0.00110434	+	0.00191278i
$431$	9.42030			0.453760			0.226880	−	0.973923i	$-0.427148\pi$
$431$	9.42030			0.453760			0.226880	+	0.973923i	$0.427148\pi$
$432$	−5.17673	−	0.448873i	−0.249065	−	0.0215964i
$433$	−0.208771			−0.0100329			−0.00501645	−	0.999987i	$-0.501597\pi$
$433$	−0.208771			−0.0100329			−0.00501645	+	0.999987i	$0.501597\pi$
$434$		0			0
$435$	−15.2694	+	5.06410i	−0.732113	+	0.242805i
$436$	−0.0945538	+	0.163772i	−0.00452831	+	0.00784326i
$437$	−2.79418	+	4.83967i	−0.133664	+	0.231513i
$438$	−15.6149	−	13.8889i	−0.746109	−	0.663636i
$439$	4.98398	+	8.63250i	0.237872	+	0.412007i	0.960104	−	0.279645i	$-0.0902167\pi$
$439$	4.98398	+	8.63250i	0.237872	+	0.412007i	−0.722231	+	0.691652i	$0.756883\pi$
$440$	−5.46472			−0.260520
$441$		0			0
$442$	−17.7527			−0.844410
$443$	7.84981	+	13.5963i	0.372956	+	0.645979i	0.990019	−	0.140935i	$-0.0450109\pi$
$443$	7.84981	+	13.5963i	0.372956	+	0.645979i	−0.617063	+	0.786914i	$0.711678\pi$
$444$	−0.971599	+	4.71159i	−0.0461100	+	0.223602i
$445$	−16.4196	+	28.4396i	−0.778364	+	1.34817i
$446$	−3.61126	+	6.25489i	−0.170998	+	0.296178i
$447$	−0.116765	+	0.566231i	−0.00552281	+	0.0267818i
$448$		0			0
$449$	33.6253			1.58688			0.793439	−	0.608650i	$-0.208288\pi$
$449$	33.6253			1.58688			0.793439	+	0.608650i	$0.208288\pi$
$450$	3.03892	+	25.8840i	0.143256	+	1.22018i
$451$	−6.07275			−0.285955
$452$	−6.78180	−	11.7464i	−0.318989	−	0.552505i
$453$	25.7669	+	22.9187i	1.21063	+	1.07681i
$454$	−6.82760	+	11.8258i	−0.320435	+	0.555010i
$455$		0			0
$456$	1.46108	−	0.484566i	0.0684213	−	0.0226919i
$457$	−16.3541	−	28.3262i	−0.765015	−	1.32504i	−0.940239	−	0.340516i	$-0.889398\pi$
$457$	−16.3541	−	28.3262i	−0.765015	−	1.32504i	0.175224	−	0.984529i	$-0.443935\pi$
$458$	17.3745			0.811857
$459$	−19.5774	+	28.0054i	−0.913793	+	1.30718i
$460$	23.2632			1.08465
$461$	−2.07165	−	3.58821i	−0.0964865	−	0.167120i	0.813742	−	0.581227i	$-0.197427\pi$
$461$	−2.07165	−	3.58821i	−0.0964865	−	0.167120i	−0.910228	+	0.414107i	$0.864094\pi$
$462$		0			0
$463$	−8.34176	+	14.4484i	−0.387675	+	0.671472i	−0.992136	−	0.125162i	$-0.960055\pi$
$463$	−8.34176	+	14.4484i	−0.387675	+	0.671472i	0.604462	+	0.796634i	$0.293388\pi$
$464$	1.25526	−	2.17417i	0.0582740	−	0.100934i
$465$	−32.6105	−	29.0058i	−1.51228	−	1.34511i
$466$	7.62110	+	13.2001i	0.353040	+	0.611484i
$467$	−29.9171			−1.38440			−0.692198	−	0.721707i	$-0.743358\pi$
$467$	−29.9171			−1.38440			−0.692198	+	0.721707i	$0.743358\pi$
$468$	−7.43818	−	3.20397i	−0.343830	−	0.148104i
$469$		0			0
$470$	12.9258	+	22.3881i	0.596223	+	1.03269i
$471$	2.43571	−	11.8115i	0.112231	−	0.544245i
$472$	−3.45489	+	5.98404i	−0.159024	+	0.275438i
$473$	−0.00914304	+	0.0158362i	−0.000420397	+	0.000728149i
$474$	−4.00619	+	19.4273i	−0.184010	+	0.892324i
$475$	−3.86033	−	6.68630i	−0.177124	−	0.306788i
$476$		0			0
$477$	7.72184	−	5.75488i	0.353559	−	0.263498i
$478$	−18.9505			−0.866775
$479$	1.47965	+	2.56283i	0.0676068	+	0.117098i	0.897847	−	0.440307i	$-0.145130\pi$
$479$	1.47965	+	2.56283i	0.0676068	+	0.117098i	−0.830241	+	0.557405i	$0.811797\pi$
$480$	−4.78799	−	4.25874i	−0.218541	−	0.194384i
$481$	−3.74907	+	6.49358i	−0.170943	+	0.296082i
$482$	12.2527	−	21.2223i	0.558096	−	0.966650i
$483$		0			0
$484$	4.40909	+	7.63676i	0.200413	+	0.347126i
$485$	48.7490			2.21358
$486$	−13.2570	+	8.20066i	−0.601352	+	0.371989i
$487$	28.0617			1.27160			0.635800	−	0.771854i	$-0.280671\pi$
$487$	28.0617			1.27160			0.635800	+	0.771854i	$0.280671\pi$
$488$	2.86652	+	4.96497i	0.129761	+	0.224753i
$489$	−13.2738	+	4.40226i	−0.600263	+	0.199077i
$490$		0			0
$491$	17.0734	−	29.5721i	0.770513	−	1.33457i	−0.166769	−	0.985996i	$-0.553333\pi$
$491$	17.0734	−	29.5721i	0.770513	−	1.33457i	0.937282	−	0.348572i	$-0.113333\pi$
$492$	−5.32072	−	4.73259i	−0.239877	−	0.213361i
$493$	−8.25457	−	14.2973i	−0.371767	−	0.643920i
$494$	2.39926			0.107948
$495$	−13.1451	+	9.79669i	−0.590828	+	0.440328i
$496$	6.81089			0.305818
$497$		0			0
$498$	1.56615	−	7.59476i	0.0701810	−	0.340329i
$499$	1.14035	−	1.97515i	0.0510493	−	0.0884199i	−0.839372	−	0.543558i	$-0.817077\pi$
$499$	1.14035	−	1.97515i	0.0510493	−	0.0884199i	0.890421	+	0.455138i	$0.150410\pi$
$500$	−6.82072	+	11.8138i	−0.305032	+	0.528331i
$501$	6.81639	−	33.0548i	0.304534	−	1.47678i
$502$	6.06182	+	10.4994i	0.270552	+	0.468610i
$503$	13.9890			0.623739			0.311869	−	0.950125i	$-0.399045\pi$
$503$	13.9890			0.623739			0.311869	+	0.950125i	$0.399045\pi$
$504$		0			0
$505$	19.4400			0.865067
$506$	4.64400	+	8.04364i	0.206451	+	0.357583i
$507$	7.39238	+	6.57525i	0.328307	+	0.292017i
$508$	1.42835	−	2.47397i	0.0633726	−	0.109765i
$509$	−12.8090	+	22.1859i	−0.567750	+	0.983373i	0.429038	+	0.903287i	$0.358853\pi$
$509$	−12.8090	+	22.1859i	−0.567750	+	0.983373i	−0.996788	+	0.0800859i	$0.974481\pi$
$510$	−39.9963	+	13.2648i	−1.77107	+	0.587374i
$511$		0			0
$512$	1.00000			0.0441942
$513$	2.64586	−	3.78490i	0.116817	−	0.167107i
$514$	−8.20877			−0.362073
$515$	−3.08217	−	5.33848i	−0.135817	−	0.235242i
$516$	−0.0203522	+	0.00674980i	−0.000895956	+	0.000297144i
$517$	−5.16071	+	8.93861i	−0.226968	+	0.393119i
$518$		0			0
$519$	−29.2014	−	25.9736i	−1.28180	−	1.14011i
$520$	−4.99381	−	8.64953i	−0.218993	−	0.379307i
$521$	41.8255			1.83241			0.916203	−	0.400714i	$-0.131238\pi$
$521$	41.8255			1.83241			0.916203	+	0.400714i	$0.131238\pi$
$522$	−0.878215	−	7.48018i	−0.0384384	−	0.327399i
$523$	−15.7665			−0.689420			−0.344710	−	0.938709i	$-0.612023\pi$
$523$	−15.7665			−0.689420			−0.344710	+	0.938709i	$0.612023\pi$
$524$	−0.0778435	−	0.134829i	−0.00340061	−	0.00589003i
$525$		0			0
$526$	2.67309	−	4.62992i	0.116552	−	0.201874i
$527$	22.3942	−	38.7878i	0.975505	−	1.68962i
$528$	0.516710	−	2.50569i	0.0224869	−	0.109046i
$529$	−8.26942	−	14.3231i	−0.359540	−	0.622742i
$530$	11.8764			0.515876
$531$	2.41714	+	20.5879i	0.104895	+	0.893440i
$532$		0			0
$533$	−5.54944	−	9.61192i	−0.240373	−	0.416338i
$534$	−11.4876	−	10.2178i	−0.497118	−	0.442168i
$535$	−19.9134	+	34.4911i	−0.860932	+	1.49118i
$536$	4.73236	−	8.19669i	0.204407	−	0.354043i
$537$	−0.548754	+	0.181994i	−0.0236805	+	0.00785362i
$538$	9.24219	+	16.0079i	0.398459	+	0.690152i
$539$		0			0
$540$	−19.1520	−	1.66066i	−0.824170	−	0.0714636i
$541$	42.1927			1.81400			0.907002	−	0.421126i	$-0.138365\pi$
$541$	42.1927			1.81400			0.907002	+	0.421126i	$0.138365\pi$
$542$	−3.67742	−	6.36947i	−0.157959	−	0.273592i
$543$	38.2101	−	12.6724i	1.63975	−	0.543823i
$544$	3.28799	−	5.69497i	0.140971	−	0.244170i
$545$	−0.349814	+	0.605896i	−0.0149844	+	0.0259537i
$546$		0			0
$547$	20.3356	+	35.2222i	0.869486	+	1.50599i	0.862522	+	0.506019i	$0.168883\pi$
$547$	20.3356	+	35.2222i	0.869486	+	1.50599i	0.00696400	+	0.999976i	$0.497783\pi$
$548$	−3.41164			−0.145738
$549$	15.7960	+	6.80410i	0.674159	+	0.290392i
$550$	−12.8319			−0.547155
$551$	1.11559	+	1.93227i	0.0475259	+	0.0823173i
$552$	−2.19963	+	10.6667i	−0.0936224	+	0.454004i
$553$		0			0
$554$	4.54944	−	7.87987i	0.193287	−	0.334783i
$555$	−3.59455	+	17.4311i	−0.152580	+	0.739910i
$556$	−6.75526	−	11.7005i	−0.286487	−	0.496210i
$557$	−13.3759			−0.566754			−0.283377	−	0.959009i	$-0.591455\pi$
$557$	−13.3759			−0.566754			−0.283377	+	0.959009i	$0.591455\pi$
$558$	16.3832	−	12.2100i	0.693558	−	0.516890i
$559$	−0.0334206			−0.00141354
$560$		0			0
$561$	−12.5709	−	11.1813i	−0.530743	−	0.472076i
$562$	6.00433	−	10.3998i	0.253277	−	0.438689i
$563$	16.3807	−	28.3722i	0.690364	−	1.19574i	−0.281355	−	0.959604i	$-0.590784\pi$
$563$	16.3807	−	28.3722i	0.690364	−	1.19574i	0.971719	−	0.236141i	$-0.0758828\pi$
$564$	−11.4876	+	3.80987i	−0.483716	+	0.160424i
$565$	−25.0901	−	43.4574i	−1.05555	−	1.82827i
$566$	9.84294			0.413729
$567$		0			0
$568$	−5.46472			−0.229295
$569$	8.36398	+	14.4868i	0.350636	+	0.607320i	0.986361	−	0.164596i	$-0.0526321\pi$
$569$	8.36398	+	14.4868i	0.350636	+	0.607320i	−0.635725	+	0.771916i	$0.719299\pi$
$570$	5.40545	−	1.79272i	0.226409	−	0.0750886i
$571$	13.7367	−	23.7926i	0.574863	−	0.995691i	−0.421194	−	0.906971i	$-0.638389\pi$
$571$	13.7367	−	23.7926i	0.574863	−	0.995691i	0.996057	−	0.0887207i	$-0.0282778\pi$
$572$	1.99381	−	3.45338i	0.0833654	−	0.144393i
$573$	21.1229	+	18.7880i	0.882421	+	0.784881i
$574$		0			0
$575$	54.6253			2.27803
$576$	2.40545	−	1.79272i	0.100227	−	0.0746965i
$577$	−2.83427			−0.117992			−0.0589962	−	0.998258i	$-0.518790\pi$
$577$	−2.83427			−0.117992			−0.0589962	+	0.998258i	$0.518790\pi$
$578$	−13.1218	−	22.7276i	−0.545794	−	0.945343i
$579$	5.00983	−	24.2942i	0.208202	−	1.00963i
$580$	4.64400	−	8.04364i	0.192831	−	0.333994i
$581$		0			0
$582$	−4.60940	+	22.3524i	−0.191066	+	0.926539i
$583$	2.37085	+	4.10644i	0.0981908	+	0.170071i
$584$	12.0655			0.499272
$585$	−27.5185	−	11.8535i	−1.13775	−	0.490082i
$586$	−21.4203			−0.884864
$587$	−2.34795	−	4.06678i	−0.0969105	−	0.167854i	0.813494	−	0.581573i	$-0.197563\pi$
$587$	−2.34795	−	4.06678i	−0.0969105	−	0.167854i	−0.910404	+	0.413720i	$0.864229\pi$
$588$		0			0
$589$	−3.02654	+	5.24212i	−0.124706	+	0.215998i
$590$	−12.7818	+	22.1387i	−0.526218	+	0.911437i
$591$	3.98507	−	1.32165i	0.163924	−	0.0543654i
$592$	−1.38874	−	2.40536i	−0.0570767	−	0.0988597i
$593$	−1.27205			−0.0522367			−0.0261184	−	0.999659i	$-0.508315\pi$
$593$	−1.27205			−0.0522367			−0.0261184	+	0.999659i	$0.508315\pi$
$594$	−3.24907	−	6.95362i	−0.133311	−	0.285310i
$595$		0			0
$596$	−0.166896	−	0.289073i	−0.00683634	−	0.0118409i
$597$	10.0469	−	3.33205i	0.411192	−	0.136372i
$598$	−8.48762	+	14.7010i	−0.347085	+	0.601168i
$599$	−21.9258	+	37.9766i	−0.895864	+	1.55168i	−0.0631320	+	0.998005i	$0.520109\pi$
$599$	−21.9258	+	37.9766i	−0.895864	+	1.55168i	−0.832732	+	0.553676i	$0.813224\pi$
$600$	−11.2429	−	10.0001i	−0.458989	−	0.408253i
$601$	−6.71634	−	11.6330i	−0.273965	−	0.474522i	0.695908	−	0.718131i	$-0.255002\pi$
$601$	−6.71634	−	11.6330i	−0.273965	−	0.474522i	−0.969874	+	0.243609i	$0.921669\pi$
$602$		0			0
$603$	−3.31089	−	28.2005i	−0.134830	−	1.14841i
$604$	−19.9098			−0.810117
$605$	16.3120	+	28.2532i	0.663177	+	1.14866i
$606$	−1.83812	+	8.91363i	−0.0746686	+	0.362092i
$607$	2.29232	−	3.97042i	0.0930425	−	0.161154i	−0.815747	−	0.578408i	$-0.803674\pi$
$607$	2.29232	−	3.97042i	0.0930425	−	0.161154i	0.908790	+	0.417254i	$0.137007\pi$
$608$	−0.444368	+	0.769668i	−0.0180215	+	0.0312142i
$609$		0			0
$610$	10.6051	+	18.3685i	0.429387	+	0.743720i
$611$	−18.8640			−0.763155
$612$	−2.30037	−	19.5934i	−0.0929870	−	0.792015i
$613$	22.1075			0.892915			0.446458	−	0.894805i	$-0.352685\pi$
$613$	22.1075			0.892915			0.446458	+	0.894805i	$0.352685\pi$
$614$	2.84362	+	4.92530i	0.114759	+	0.198769i
$615$	−19.6847	−	17.5088i	−0.793764	−	0.706023i
$616$		0			0
$617$	6.00433	−	10.3998i	0.241725	−	0.418680i	−0.719481	−	0.694513i	$-0.755620\pi$
$617$	6.00433	−	10.3998i	0.241725	−	0.418680i	0.961206	+	0.275832i	$0.0889534\pi$
$618$	2.73924	−	0.908468i	0.110188	−	0.0365439i
$619$	8.78180	+	15.2105i	0.352970	+	0.611363i	0.986768	−	0.162136i	$-0.0518383\pi$
$619$	8.78180	+	15.2105i	0.352970	+	0.611363i	−0.633798	+	0.773499i	$0.718505\pi$
$620$	25.1978			1.01197
$621$	13.8312	+	29.6014i	0.555029	+	1.18787i
$622$	−11.7207			−0.469956
$623$		0			0
$624$	4.43818	−	1.47192i	0.177669	−	0.0589240i
$625$	−3.51602	+	6.08993i	−0.140641	+	0.243597i
$626$	13.3869	−	23.1868i	0.535047	−	0.926729i
$627$	1.69894	+	1.51114i	0.0678491	+	0.0603493i
$628$	3.48143	+	6.03001i	0.138924	+	0.240624i
$629$	−18.2646			−0.728258
$630$		0			0
$631$	−44.9381			−1.78896			−0.894479	−	0.447110i	$-0.852453\pi$
$631$	−44.9381			−1.78896			−0.894479	+	0.447110i	$0.852453\pi$
$632$	−5.72617	−	9.91802i	−0.227775	−	0.394518i
$633$	4.00364	−	19.4149i	0.159130	−	0.771673i
$634$	−0.951246	+	1.64761i	−0.0377788	+	0.0654348i
$635$	5.28435	−	9.15276i	0.209703	−	0.363216i
$636$	−1.12296	+	5.44556i	−0.0445281	+	0.215931i
$637$		0			0
$638$	3.70829			0.146813
$639$	−13.1451	+	9.79669i	−0.520012	+	0.387551i
$640$	3.69963			0.146241
$641$	14.4920	+	25.1008i	0.572398	+	0.991422i	0.996319	+	0.0857228i	$0.0273199\pi$
$641$	14.4920	+	25.1008i	0.572398	+	0.991422i	−0.423921	+	0.905699i	$0.639347\pi$
$642$	−13.9320	−	12.3920i	−0.549852	−	0.489073i
$643$	6.03087	−	10.4458i	0.237834	−	0.411941i	−0.722258	−	0.691623i	$-0.756896\pi$
$643$	6.03087	−	10.4458i	0.237834	−	0.411941i	0.960093	+	0.279682i	$0.0902291\pi$
$644$		0			0
$645$	−0.0752956	+	0.0249718i	−0.00296476	+	0.000983262i
$646$	2.92216	+	5.06132i	0.114971	+	0.199135i
$647$	−37.7651			−1.48470			−0.742349	−	0.670013i	$-0.766289\pi$
$647$	−37.7651			−1.48470			−0.742349	+	0.670013i	$0.766289\pi$
$648$	2.57234	−	8.62456i	0.101051	−	0.338805i
$649$	−10.2064			−0.400637
$650$	−11.7262	−	20.3103i	−0.459938	−	0.796636i
$651$		0			0
$652$	4.03706	−	6.99240i	0.158104	−	0.273843i
$653$	−18.7040	+	32.3962i	−0.731942	+	1.26776i	0.224109	+	0.974564i	$0.428053\pi$
$653$	−18.7040	+	32.3962i	−0.731942	+	1.26776i	−0.956052	+	0.293198i	$0.905281\pi$
$654$	−0.244740	−	0.217687i	−0.00957008	−	0.00851223i
$655$	−0.287992	−	0.498817i	−0.0112528	−	0.0194904i
$656$	4.11126			0.160518
$657$	29.0228	−	21.6299i	1.13229	−	0.843864i
$658$		0			0
$659$	14.9356	+	25.8693i	0.581810	+	1.00772i	0.995265	+	0.0971993i	$0.0309884\pi$
$659$	14.9356	+	25.8693i	0.581810	+	1.00772i	−0.413455	+	0.910524i	$0.635678\pi$
$660$	1.91164	−	9.27012i	0.0744103	−	0.360839i
$661$	−2.80401	+	4.85669i	−0.109063	+	0.188904i	−0.915391	−	0.402566i	$-0.868119\pi$
$661$	−2.80401	+	4.85669i	−0.109063	+	0.188904i	0.806328	+	0.591469i	$0.201452\pi$
$662$	−2.78366	+	4.82144i	−0.108190	+	0.187391i
$663$	6.21015	−	30.1150i	0.241182	−	1.16957i
$664$	2.23855	+	3.87728i	0.0868726	+	0.150468i
$665$		0			0
$666$	−7.65266	−	3.29636i	−0.296534	−	0.127731i
$667$	−15.7861			−0.611242
$668$	9.74288	+	16.8752i	0.376963	+	0.652920i
$669$	−9.34727	−	8.31405i	−0.361386	−	0.321440i
$670$	17.5080	−	30.3247i	0.676392	−	1.17155i
$671$	−4.23414	+	7.33375i	−0.163457	+	0.283116i
$672$		0			0
$673$	−4.72253	−	8.17966i	−0.182040	−	0.315303i	0.760535	−	0.649297i	$-0.224937\pi$
$673$	−4.72253	−	8.17966i	−0.182040	−	0.315303i	−0.942575	+	0.333994i	$0.891603\pi$
$674$	33.7738			1.30092
$675$	−44.9715	−	3.89948i	−1.73095	−	0.150091i
$676$	−5.71201			−0.219693
$677$	−5.53087	−	9.57975i	−0.212569	−	0.368180i	0.739949	−	0.672663i	$-0.234850\pi$
$677$	−5.53087	−	9.57975i	−0.212569	−	0.368180i	−0.952518	+	0.304483i	$0.901516\pi$
$678$	22.2985	−	7.39530i	0.856369	−	0.284015i
$679$		0			0
$680$	12.1643	−	21.0693i	0.466481	−	0.807970i
$681$	−17.6723	−	15.7189i	−0.677205	−	0.602349i
$682$	5.03018	+	8.71253i	0.192616	+	0.333620i
$683$	8.83922			0.338223			0.169112	−	0.985597i	$-0.445910\pi$
$683$	8.83922			0.338223			0.169112	+	0.985597i	$0.445910\pi$
$684$	0.310892	+	2.64802i	0.0118873	+	0.101250i
$685$	−12.6218			−0.482254
$686$		0			0
$687$	−6.07784	+	29.4734i	−0.231884	+	1.12448i
$688$	0.00618986	−	0.0107211i	0.000235986	−	0.000408740i
$689$	−4.33310	+	7.50516i	−0.165078	+	0.285924i
$690$	−8.13781	+	39.4628i	−0.309801	+	1.50232i
$691$	−12.5309	−	21.7041i	−0.476697	−	0.825663i	0.522947	−	0.852365i	$-0.324833\pi$
$691$	−12.5309	−	21.7041i	−0.476697	−	0.825663i	−0.999643	+	0.0267023i	$0.991499\pi$
$692$	22.5636			0.857740
$693$		0			0
$694$	−30.4065			−1.15422
$695$	−24.9920	−	43.2873i	−0.947999	−	1.64198i
$696$	3.24907	+	2.88993i	0.123156	+	0.109542i
$697$	13.5178	−	23.4135i	0.512023	−	0.886850i
$698$	−6.29782	+	10.9082i	−0.238376	+	0.412880i
$699$	−25.0581	+	8.31052i	−0.947785	+	0.314333i
$700$		0			0
$701$	−43.4858			−1.64243			−0.821217	−	0.570616i	$-0.806705\pi$
$701$	−43.4858			−1.64243			−0.821217	+	0.570616i	$0.806705\pi$
$702$	8.03706	−	11.4970i	0.303339	−	0.433927i
$703$	2.46844			0.0930989
$704$	0.738550	+	1.27921i	0.0278351	+	0.0482119i
$705$	−42.4999	+	14.0951i	−1.60064	+	0.530852i
$706$	3.76578	−	6.52252i	0.141727	−	0.245478i
$707$		0			0
$708$	−8.94251	−	7.95403i	−0.336080	−	0.298931i
$709$	11.3702	+	19.6937i	0.427016	+	0.739613i	0.996606	−	0.0823158i	$-0.0262316\pi$
$709$	11.3702	+	19.6937i	0.427016	+	0.739613i	−0.569591	+	0.821928i	$0.692898\pi$
$710$	−20.2174			−0.758747
$711$	−31.5542	−	13.5919i	−1.18337	−	0.509735i
$712$	8.87636			0.332656
$713$	−21.4134	−	37.0891i	−0.801939	−	1.38900i
$714$		0			0
$715$	7.37636	−	12.7762i	0.275860	−	0.477804i
$716$	0.166896	−	0.289073i	0.00623721	−	0.0108032i
$717$	6.62915	−	32.1468i	0.247570	−	1.20054i
$718$	−3.44801	−	5.97213i	−0.128679	−	0.222878i
$719$	−12.1236			−0.452136			−0.226068	−	0.974112i	$-0.572587\pi$
$719$	−12.1236			−0.452136			−0.226068	+	0.974112i	$0.572587\pi$
$720$	8.89926	−	6.63238i	0.331656	−	0.247174i
$721$		0			0
$722$	9.10507	+	15.7705i	0.338856	+	0.586915i
$723$	31.7145	+	28.2089i	1.17947	+	1.04910i
$724$	−11.6211	+	20.1283i	−0.431895	+	0.748063i
$725$	10.9048	−	18.8876i	0.404993	−	0.701468i
$726$	−14.4970	+	4.80794i	−0.538036	+	0.178440i
$727$	23.0908	+	39.9945i	0.856392	+	1.48331i	0.875348	+	0.483494i	$0.160632\pi$
$727$	23.0908	+	39.9945i	0.856392	+	1.48331i	−0.0189562	+	0.999820i	$0.506034\pi$
$728$		0			0
$729$	−9.27375	−	25.3574i	−0.343472	−	0.939163i
$730$	44.6377			1.65212
$731$	−0.0407044	−	0.0705021i	−0.00150551	−	0.00260761i
$732$	−9.42511	+	3.12584i	−0.348362	+	0.115534i
$733$	18.0149	−	31.2026i	0.665394	−	1.15250i	−0.313785	−	0.949494i	$-0.601597\pi$
$733$	18.0149	−	31.2026i	0.665394	−	1.15250i	0.979178	−	0.203002i	$-0.0650696\pi$
$734$	−11.5618	+	20.0257i	−0.426755	+	0.739161i
$735$		0			0
$736$	−3.14400	−	5.44556i	−0.115889	−	0.200726i
$737$	13.9803			0.514972
$738$	9.88942	−	7.37033i	0.364035	−	0.271305i
$739$	−46.4239			−1.70773			−0.853865	−	0.520495i	$-0.825747\pi$
$739$	−46.4239			−1.70773			−0.853865	+	0.520495i	$0.825747\pi$
$740$	−5.13781	−	8.89894i	−0.188870	−	0.327132i
$741$	−0.839294	+	4.07000i	−0.0308322	+	0.149515i
$742$		0			0
$743$	0.598884	−	1.03730i	0.0219709	−	0.0380548i	−0.854831	−	0.518907i	$-0.826339\pi$
$743$	0.598884	−	1.03730i	0.0219709	−	0.0380548i	0.876802	+	0.480852i	$0.159673\pi$
$744$	−2.38255	+	11.5537i	−0.0873484	+	0.423580i
$745$	−0.617454	−	1.06946i	−0.0226218	−	0.0391820i
$746$	29.1643			1.06778
$747$	12.3356	+	5.31351i	0.451335	+	0.194411i
$748$	9.71339			0.355157
$749$		0			0
$750$	−17.6545	−	15.7030i	−0.644652	−	0.573394i
$751$	−24.0600	+	41.6731i	−0.877961	+	1.52067i	−0.0243853	+	0.999703i	$0.507763\pi$
$751$	−24.0600	+	41.6731i	−0.877961	+	1.52067i	−0.853575	+	0.520970i	$0.825570\pi$
$752$	3.49381	−	6.05146i	0.127406	−	0.220674i
$753$	−19.9312	+	6.61019i	−0.726334	+	0.240889i
$754$	3.38874	+	5.86946i	0.123410	+	0.213753i
$755$	−73.6588			−2.68072
$756$		0			0
$757$	49.6006			1.80276			0.901382	−	0.433025i	$-0.142554\pi$
$757$	49.6006			1.80276			0.901382	+	0.433025i	$0.142554\pi$
$758$	6.78111	+	11.7452i	0.246301	+	0.426606i
$759$	−15.2694	+	5.06410i	−0.554245	+	0.183815i
$760$	−1.64400	+	2.84748i	−0.0596340	+	0.103289i
$761$	18.7701	−	32.5108i	0.680416	−	1.17852i	−0.294438	−	0.955671i	$-0.595132\pi$
$761$	18.7701	−	32.5108i	0.680416	−	1.17852i	0.974854	−	0.222845i	$-0.0715342\pi$
$762$	3.69708	+	3.28842i	0.133931	+	0.119127i
$763$		0			0
$764$	−16.3214			−0.590488
$765$	−8.51052	−	72.4882i	−0.307699	−	2.62082i
$766$	−2.83565			−0.102456
$767$	−9.32691	−	16.1547i	−0.336775	−	0.583312i
$768$	−0.349814	+	1.69636i	−0.0126228	+	0.0612120i
$769$	−13.4592	+	23.3121i	−0.485352	+	0.840654i	−0.999858	−	0.0168324i	$-0.994642\pi$
$769$	−13.4592	+	23.3121i	−0.485352	+	0.840654i	0.514506	+	0.857486i	$0.327975\pi$
$770$		0			0
$771$	2.87154	−	13.9250i	0.103416	−	0.501497i
$772$	7.16071	+	12.4027i	0.257719	+	0.446383i
$773$	−50.2261			−1.80651			−0.903254	−	0.429107i	$-0.858828\pi$
$773$	−50.2261			−1.80651			−0.903254	+	0.429107i	$0.858828\pi$
$774$	−0.00433060	−	0.0368858i	−0.000155660	−	0.00132583i
$775$	59.1679			2.12537
$776$	−6.58836	−	11.4114i	−0.236508	−	0.409645i
$777$		0			0
$778$	9.30401	−	16.1150i	0.333565	−	0.577752i
$779$	−1.82691	+	3.16431i	−0.0654560	+	0.113373i
$780$	16.4196	−	5.44556i	0.587916	−	0.194982i
$781$	−4.03597	−	6.99050i	−0.144418	−	0.250140i
$782$	−41.3497			−1.47866
$783$	12.9963	+	1.12691i	0.464449	+	0.0402723i
$784$		0			0
$785$	12.8800	+	22.3088i	0.459707	+	0.796236i
$786$	0.255949	−	0.0848854i	0.00912940	−	0.00302776i
$787$	0.829462	−	1.43667i	0.0295671	−	0.0512118i	−0.850863	−	0.525387i	$-0.823920\pi$
$787$	0.829462	−	1.43667i	0.0295671	−	0.0512118i	0.880430	+	0.474176i	$0.157254\pi$
$788$	−1.21201	+	2.09926i	−0.0431760	+	0.0747830i
$789$	6.91892	+	6.15412i	0.246320	+	0.219093i
$790$	−21.1847	−	36.6930i	−0.753718	−	1.30548i
$791$		0			0
$792$	4.06979	+	1.75305i	0.144614	+	0.0622920i
$793$	−15.4771			−0.549608
$794$	−10.2880	−	17.8193i	−0.365107	−	0.632384i
$795$	−4.15452	+	20.1466i	−0.147346	+	0.714525i
$796$	−3.05563	+	5.29251i	−0.108304	+	0.187588i
$797$	−15.3702	+	26.6219i	−0.544439	+	0.942996i	0.454203	+	0.890898i	$0.349924\pi$
$797$	−15.3702	+	26.6219i	−0.544439	+	0.942996i	−0.998642	+	0.0520981i	$0.983409\pi$
$798$		0			0
$799$	−22.9752	−	39.7943i	−0.812806	−	1.40782i
$800$	8.68725			0.307141
$801$	21.3516	−	15.9128i	0.754422	−	0.562250i
$802$	−6.75409			−0.238495
$803$	8.91095	+	15.4342i	0.314461	+	0.544662i
$804$	12.2491	+	10.8951i	0.431991	+	0.384240i
$805$		0			0
$806$	−9.19344	+	15.9235i	−0.323825	+	0.560881i
$807$	−30.3883	+	10.0783i	−1.06972	+	0.354772i
$808$	−2.62729	−	4.55059i	−0.0924276	−	0.160089i
$809$	2.88502			0.101432			0.0507159	−	0.998713i	$-0.483850\pi$
$809$	2.88502			0.101432			0.0507159	+	0.998713i	$0.483850\pi$
$810$	9.51671	−	31.9077i	0.334383	−	1.12112i
$811$	28.5461			1.00239			0.501195	−	0.865334i	$-0.332894\pi$
$811$	28.5461			1.00239			0.501195	+	0.865334i	$0.332894\pi$
$812$		0			0
$813$	12.0913	−	4.01008i	0.424061	−	0.140640i
$814$	2.05130	−	3.55296i	0.0718981	−	0.124531i
$815$	14.9356	−	25.8693i	0.523172	−	0.906161i
$816$	8.51052	+	7.56979i	0.297928	+	0.264996i
$817$	0.00550115	+	0.00952827i	0.000192461	+	0.000333352i
$818$	15.3214			0.535701
$819$		0			0
$820$	15.2101			0.531161
$821$	−3.98329	−	6.89926i	−0.139018	−	0.240786i	0.788107	−	0.615538i	$-0.211061\pi$
$821$	−3.98329	−	6.89926i	−0.139018	−	0.240786i	−0.927125	+	0.374752i	$0.877728\pi$
$822$	1.19344	−	5.78736i	0.0416259	−	0.201857i
$823$	−20.2731	+	35.1140i	−0.706675	+	1.22400i	0.259409	+	0.965768i	$0.416472\pi$
$823$	−20.2731	+	35.1140i	−0.706675	+	1.22400i	−0.966084	+	0.258229i	$0.916861\pi$
$824$	−0.833104	+	1.44298i	−0.0290225	+	0.0502685i
$825$	4.48879	−	21.7676i	0.156280	−	0.757849i
$826$		0			0
$827$	1.22115			0.0424636			0.0212318	−	0.999775i	$-0.493241\pi$
$827$	1.22115			0.0424636			0.0212318	+	0.999775i	$0.493241\pi$
$828$	−17.3251	−	7.46271i	−0.602087	−	0.259347i
$829$	14.1506			0.491470			0.245735	−	0.969337i	$-0.420971\pi$
$829$	14.1506			0.491470			0.245735	+	0.969337i	$0.420971\pi$
$830$	8.28180	+	14.3445i	0.287466	+	0.497905i
$831$	11.7756	+	10.4740i	0.408491	+	0.363338i
$832$	−1.34981	+	2.33795i	−0.0467964	+	0.0810537i
$833$		0			0
$834$	22.2112	−	7.36636i	0.769112	−	0.255076i
$835$	36.0450	+	62.4318i	1.24739	+	2.16054i
$836$	−1.31275			−0.0454025
$837$	14.9814	+	32.0631i	0.517834	+	1.10826i
$838$	8.64283			0.298561
$839$	1.19599	+	2.07151i	0.0412900	+	0.0715164i	0.885932	−	0.463815i	$-0.153520\pi$
$839$	1.19599	+	2.07151i	0.0412900	+	0.0715164i	−0.844642	+	0.535332i	$0.820187\pi$
$840$		0			0
$841$	11.3486	−	19.6564i	0.391333	−	0.677808i
$842$	18.5636	−	32.1531i	0.639744	−	1.10807i
$843$	15.5414	+	13.8235i	0.535274	+	0.476106i
$844$	5.72253	+	9.91171i	0.196978	+	0.341175i
$845$	−21.1323			−0.726973
$846$	−2.44437	−	20.8199i	−0.0840391	−	0.715802i
$847$		0			0
$848$	−1.60507	−	2.78007i	−0.0551185	−	0.0954680i
$849$	−3.44320	+	16.6971i	−0.118170	+	0.573044i
$850$	28.5636	−	49.4736i	0.979724	−	1.69693i
$851$	−8.73236	+	15.1249i	−0.299341	+	0.518475i
$852$	1.91164	−	9.27012i	0.0654916	−	0.317589i
$853$	−8.33998	−	14.4453i	−0.285556	−	0.494597i	0.687188	−	0.726479i	$-0.258845\pi$
$853$	−8.33998	−	14.4453i	−0.285556	−	0.494597i	−0.972744	+	0.231883i	$0.925511\pi$
$854$		0			0
$855$	1.15019	+	9.79669i	0.0393355	+	0.335040i
$856$	10.7651			0.367943
$857$	6.92580	+	11.9958i	0.236581	+	0.409770i	0.959731	−	0.280921i	$-0.0906399\pi$
$857$	6.92580	+	11.9958i	0.236581	+	0.409770i	−0.723150	+	0.690691i	$0.757307\pi$
$858$	5.16071	+	4.59026i	0.176184	+	0.156709i
$859$	−24.2472	+	41.9974i	−0.827304	+	1.43293i	0.0728414	+	0.997344i	$0.476793\pi$
$859$	−24.2472	+	41.9974i	−0.827304	+	1.43293i	−0.900146	+	0.435589i	$0.856540\pi$
$860$	0.0229002	−	0.0396643i	0.000780889	−	0.00135254i
$861$		0			0
$862$	−4.71015	−	8.15822i	−0.160428	−	0.277870i
$863$	−5.93082			−0.201887			−0.100944	−	0.994892i	$-0.532186\pi$
$863$	−5.93082			−0.201887			−0.100944	+	0.994892i	$0.532186\pi$
$864$	2.19963	+	4.70761i	0.0748329	+	0.160156i
$865$	83.4769			2.83830
$866$	0.104386	+	0.180801i	0.00354717	+	0.00614387i
$867$	43.1443	−	14.3088i	1.46526	−	0.485953i
$868$		0			0
$869$	8.45813	−	14.6499i	0.286922	−	0.496964i
$870$	12.0204	+	10.6917i	0.407528	+	0.362481i
$871$	12.7756	+	22.1280i	0.432885	+	0.749779i
$872$	0.189108			0.00640399
$873$	−36.3053	−	15.6384i	−1.22875	−	0.529280i
$874$	5.58836			0.189029
$875$		0			0
$876$	−4.22067	+	20.4673i	−0.142603	+	0.691527i
$877$	−1.96472	+	3.40300i	−0.0663439	+	0.114911i	−0.897289	−	0.441443i	$-0.854467\pi$
$877$	−1.96472	+	3.40300i	−0.0663439	+	0.114911i	0.830945	+	0.556354i	$0.187800\pi$
$878$	4.98398	−	8.63250i	0.168201	−	0.291333i
$879$	7.49312	−	36.3365i	0.252737	−	1.22560i
$880$	2.73236	+	4.73259i	0.0921078	+	0.159535i
$881$	37.6552			1.26864			0.634318	−	0.773072i	$-0.281281\pi$
$881$	37.6552			1.26864			0.634318	+	0.773072i	$0.281281\pi$
$882$		0			0
$883$	−53.2334			−1.79145			−0.895723	−	0.444613i	$-0.853341\pi$
$883$	−53.2334			−1.79145			−0.895723	+	0.444613i	$0.853341\pi$
$884$	8.87636	+	15.3743i	0.298544	+	0.517094i
$885$	−33.0840	−	29.4270i	−1.11211	−	0.989176i
$886$	7.84981	−	13.5963i	0.263720	−	0.456776i
$887$	18.4938	−	32.0322i	0.620961	−	1.07554i	−0.368346	−	0.929689i	$-0.620076\pi$
$887$	18.4938	−	32.0322i	0.620961	−	1.07554i	0.989307	−	0.145848i	$-0.0465910\pi$
$888$	4.56615	−	1.51436i	0.153230	−	0.0508187i
$889$		0			0
$890$	32.8392			1.10077
$891$	12.9324	−	3.07911i	0.433251	−	0.103154i
$892$	7.22253			0.241828
$893$	3.10507	+	5.37815i	0.103907	+	0.179973i
$894$	0.548754	−	0.181994i	0.0183531	−	0.00608679i
$895$	0.617454	−	1.06946i	0.0206392	−	0.0357482i
$896$		0			0
$897$	−21.9691	−	19.5407i	−0.733525	−	0.652443i
$898$	−16.8127	−	29.1204i	−0.561046	−	0.971761i
$899$	−17.0989			−0.570280
$900$	20.8967	−	15.5738i	0.696557	−	0.519125i
$901$	−21.1099			−0.703272
$902$	3.03637	+	5.25915i	0.101100	+	0.175111i
$903$		0			0
$904$	−6.78180	+	11.7464i	−0.225559	+	0.390680i
$905$	−42.9937	+	74.4673i	−1.42916	+	2.47538i
$906$	6.96472	−	33.7741i	0.231387	−	1.12207i
$907$	19.5080	+	33.7888i	0.647752	+	1.12194i	0.983659	+	0.180044i	$0.0576239\pi$
$907$	19.5080	+	33.7888i	0.647752	+	1.12194i	−0.335907	+	0.941895i	$0.609043\pi$
$908$	13.6552			0.453164
$909$	−14.4777	−	6.23623i	−0.480195	−	0.206843i
$910$		0			0
$911$	−12.8090	−	22.1859i	−0.424382	−	0.735052i	0.571980	−	0.820267i	$-0.306175\pi$
$911$	−12.8090	−	22.1859i	−0.424382	−	0.735052i	−0.996363	+	0.0852158i	$0.972842\pi$
$912$	−1.15019	−	1.02305i	−0.0380865	−	0.0338765i
$913$	−3.30656	+	5.72713i	−0.109431	+	0.189540i
$914$	−16.3541	+	28.3262i	−0.540947	+	0.936948i
$915$	−34.8694	+	11.5644i	−1.15275	+	0.382308i
$916$	−8.68725	−	15.0468i	−0.287035	−	0.497159i
$917$		0			0
$918$	34.0421	+	2.95178i	1.12356	+	0.0974234i
$919$	−20.6735			−0.681956			−0.340978	−	0.940071i	$-0.610758\pi$
$919$	−20.6735			−0.681956			−0.340978	+	0.940071i	$0.610758\pi$
$920$	−11.6316	−	20.1466i	−0.383483	−	0.664212i
$921$	−9.34981	+	3.10086i	−0.308087	+	0.102177i
$922$	−2.07165	+	3.58821i	−0.0682263	+	0.118171i
$923$	7.37636	−	12.7762i	0.242796	−	0.420535i
$924$		0			0
$925$	−12.0643	−	20.8960i	−0.396672	−	0.687055i
$926$	16.6835			0.548255
$927$	0.582863	+	4.96452i	0.0191437	+	0.163056i
$928$	−2.51052			−0.0824119
$929$	1.87017	+	3.23922i	0.0613582	+	0.106275i	0.895073	−	0.445920i	$-0.147123\pi$
$929$	1.87017	+	3.23922i	0.0613582	+	0.106275i	−0.833715	+	0.552196i	$0.813790\pi$
$930$	−8.81453	+	42.7444i	−0.289040	+	1.40165i
$931$		0			0
$932$	7.62110	−	13.2001i	0.249637	−	0.432384i
$933$	4.10005	−	19.8824i	0.134230	−	0.650922i
$934$	14.9585	+	25.9089i	0.489458	+	0.847766i
$935$	35.9359			1.17523
$936$	0.944368	+	8.04364i	0.0308676	+	0.262915i
$937$	−27.1345			−0.886445			−0.443223	−	0.896412i	$-0.646165\pi$
$937$	−27.1345			−0.886445			−0.443223	+	0.896412i	$0.646165\pi$
$938$		0			0
$939$	34.6501	+	30.8200i	1.13076	+	1.00577i
$940$	12.9258	−	22.3881i	0.421593	−	0.730221i
$941$	−3.16435	+	5.48081i	−0.103155	+	0.178669i	−0.912983	−	0.407998i	$-0.866227\pi$
$941$	−3.16435	+	5.48081i	−0.103155	+	0.178669i	0.809828	+	0.586667i	$0.199560\pi$
$942$	−11.4469	+	3.79637i	−0.372961	+	0.123692i
$943$	−12.9258	−	22.3881i	−0.420922	−	0.729058i
$944$	6.90978			0.224894
$945$		0			0
$946$	0.0182861			0.000594531
$947$	−15.6396	−	27.0886i	−0.508218	−	0.880260i	−0.999955	−	0.00951587i	$-0.996971\pi$
$947$	−15.6396	−	27.0886i	−0.508218	−	0.880260i	0.491736	−	0.870744i	$-0.336362\pi$
$948$	18.8276	−	6.24417i	0.611492	−	0.202801i
$949$	−16.2861	+	28.2084i	−0.528670	+	0.915684i
$950$	−3.86033	+	6.68630i	−0.125246	+	0.216932i
$951$	−2.46217	−	2.19001i	−0.0798414	−	0.0710160i
$952$		0			0
$953$	4.28937			0.138946			0.0694732	−	0.997584i	$-0.477868\pi$
$953$	4.28937			0.138946			0.0694732	+	0.997584i	$0.477868\pi$
$954$	−8.84479	−	3.80987i	−0.286361	−	0.123349i
$955$	−60.3832			−1.95395
$956$	9.47524	+	16.4116i	0.306451	+	0.530789i
$957$	−1.29721	+	6.29059i	−0.0419329	+	0.203346i
$958$	1.47965	−	2.56283i	0.0478053	−	0.0828011i
$959$		0			0
$960$	−1.29418	+	6.27589i	−0.0417695	+	0.202554i
$961$	−7.69413	−	13.3266i	−0.248198	−	0.429891i
$962$	7.49814			0.241750
$963$	25.8948	−	19.2987i	0.834450	−	0.621893i
$964$	−24.5054			−0.789267
$965$	26.4920	+	45.8854i	0.852806	+	1.47710i
$966$		0			0
$967$	−7.59201	+	13.1497i	−0.244142	+	0.422867i	−0.961890	−	0.273436i	$-0.911840\pi$
$967$	−7.59201	+	13.1497i	−0.244142	+	0.422867i	0.717748	+	0.696303i	$0.245173\pi$
$968$	4.40909	−	7.63676i	0.141713	−	0.245455i
$969$	−9.60803	+	3.18650i	−0.308654	+	0.102365i
$970$	−24.3745	−	42.2179i	−0.782618	−	1.35553i
$971$	−3.24729			−0.104210			−0.0521052	−	0.998642i	$-0.516593\pi$
$971$	−3.24729			−0.104210			−0.0521052	+	0.998642i	$0.516593\pi$
$972$	13.7305	+	7.38061i	0.440406	+	0.236733i
$973$		0			0
$974$	−14.0309	−	24.3022i	−0.449578	−	0.778692i
$975$	38.5556	−	12.7869i	1.23477	−	0.409510i
$976$	2.86652	−	4.96497i	0.0917552	−	0.158925i
$977$	−7.77197	+	13.4614i	−0.248647	+	0.430670i	−0.963151	−	0.268962i	$-0.913319\pi$
$977$	−7.77197	+	13.4614i	−0.248647	+	0.430670i	0.714503	+	0.699632i	$0.246653\pi$
$978$	10.4494	+	9.29434i	0.334135	+	0.297200i
$979$	6.55563	+	11.3547i	0.209519	+	0.362897i
$980$		0			0
$981$	0.454888	−	0.339016i	0.0145235	−	0.0108240i
$982$	−34.1469			−1.08967
$983$	−6.19158	−	10.7241i	−0.197481	−	0.342047i	0.750230	−	0.661177i	$-0.229943\pi$
$983$	−6.19158	−	10.7241i	−0.197481	−	0.342047i	−0.947711	+	0.319130i	$0.896609\pi$
$984$	−1.43818	+	6.97418i	−0.0458474	+	0.222329i
$985$	−4.48398	+	7.76648i	−0.142871	+	0.247461i
$986$	−8.25457	+	14.2973i	−0.262879	+	0.455320i
$987$		0			0
$988$	−1.19963	−	2.07782i	−0.0381653	−	0.0661042i
$989$	−0.0778435			−0.00247528
$990$	15.0567	+	6.48564i	0.478534	+	0.206127i
$991$	6.65521			0.211410			0.105705	−	0.994398i	$-0.466290\pi$
$991$	6.65521			0.211410			0.105705	+	0.994398i	$0.466290\pi$
$992$	−3.40545	−	5.89841i	−0.108123	−	0.187275i
$993$	−7.20513	−	6.40869i	−0.228648	−	0.203374i
$994$		0			0
$995$	−11.3047	+	19.5803i	−0.358383	+	0.620738i
$996$	−7.36033	+	2.44105i	−0.233221	+	0.0773478i
$997$	−2.40104	−	4.15872i	−0.0760417	−	0.131708i	0.825497	−	0.564406i	$-0.190895\pi$
$997$	−2.40104	−	4.15872i	−0.0760417	−	0.131708i	−0.901539	+	0.432698i	$0.857562\pi$
$998$	−2.28071			−0.0721946
$999$	8.26881	−	11.8285i	0.261614	−	0.374238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.f.l.589.3		6
3.2	odd	2		2646.2.f.o.1765.3		6
7.2	even	3		126.2.h.c.67.1	yes	6
7.3	odd	6		882.2.e.p.373.3		6
7.4	even	3		126.2.e.d.121.1	yes	6
7.5	odd	6		882.2.h.o.67.3		6
7.6	odd	2		882.2.f.m.589.1		6
9.2	odd	6		2646.2.f.o.883.3		6
9.4	even	3		7938.2.a.cb.1.3		3
9.5	odd	6		7938.2.a.bu.1.1		3
9.7	even	3	inner	882.2.f.l.295.3		6
21.2	odd	6		378.2.h.d.361.1		6
21.5	even	6		2646.2.h.p.361.3		6
21.11	odd	6		378.2.e.c.37.3		6
21.17	even	6		2646.2.e.o.1549.1		6
21.20	even	2		2646.2.f.n.1765.1		6
28.11	odd	6		1008.2.q.h.625.3		6
28.23	odd	6		1008.2.t.g.193.3		6
63.2	odd	6		378.2.e.c.235.3		6
63.4	even	3		1134.2.g.k.163.1		6
63.11	odd	6		378.2.h.d.289.1		6
63.13	odd	6		7938.2.a.by.1.1		3
63.16	even	3		126.2.e.d.25.1	✓	6
63.20	even	6		2646.2.f.n.883.1		6
63.23	odd	6		1134.2.g.n.487.3		6
63.25	even	3		126.2.h.c.79.1	yes	6
63.32	odd	6		1134.2.g.n.163.3		6
63.34	odd	6		882.2.f.m.295.1		6
63.38	even	6		2646.2.h.p.667.3		6
63.41	even	6		7938.2.a.bx.1.3		3
63.47	even	6		2646.2.e.o.2125.1		6
63.52	odd	6		882.2.h.o.79.3		6
63.58	even	3		1134.2.g.k.487.1		6
63.61	odd	6		882.2.e.p.655.3		6
84.11	even	6		3024.2.q.h.2305.3		6
84.23	even	6		3024.2.t.g.1873.1		6
252.11	even	6		3024.2.t.g.289.1		6
252.79	odd	6		1008.2.q.h.529.3		6
252.151	odd	6		1008.2.t.g.961.3		6
252.191	even	6		3024.2.q.h.2881.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.1	✓	6	63.16	even	3
126.2.e.d.121.1	yes	6	7.4	even	3
126.2.h.c.67.1	yes	6	7.2	even	3
126.2.h.c.79.1	yes	6	63.25	even	3
378.2.e.c.37.3		6	21.11	odd	6
378.2.e.c.235.3		6	63.2	odd	6
378.2.h.d.289.1		6	63.11	odd	6
378.2.h.d.361.1		6	21.2	odd	6
882.2.e.p.373.3		6	7.3	odd	6
882.2.e.p.655.3		6	63.61	odd	6
882.2.f.l.295.3		6	9.7	even	3	inner
882.2.f.l.589.3		6	1.1	even	1	trivial
882.2.f.m.295.1		6	63.34	odd	6
882.2.f.m.589.1		6	7.6	odd	2
882.2.h.o.67.3		6	7.5	odd	6
882.2.h.o.79.3		6	63.52	odd	6
1008.2.q.h.529.3		6	252.79	odd	6
1008.2.q.h.625.3		6	28.11	odd	6
1008.2.t.g.193.3		6	28.23	odd	6
1008.2.t.g.961.3		6	252.151	odd	6
1134.2.g.k.163.1		6	63.4	even	3
1134.2.g.k.487.1		6	63.58	even	3
1134.2.g.n.163.3		6	63.32	odd	6
1134.2.g.n.487.3		6	63.23	odd	6
2646.2.e.o.1549.1		6	21.17	even	6
2646.2.e.o.2125.1		6	63.47	even	6
2646.2.f.n.883.1		6	63.20	even	6
2646.2.f.n.1765.1		6	21.20	even	2
2646.2.f.o.883.3		6	9.2	odd	6
2646.2.f.o.1765.3		6	3.2	odd	2
2646.2.h.p.361.3		6	21.5	even	6
2646.2.h.p.667.3		6	63.38	even	6
3024.2.q.h.2305.3		6	84.11	even	6
3024.2.q.h.2881.3		6	252.191	even	6
3024.2.t.g.289.1		6	252.11	even	6
3024.2.t.g.1873.1		6	84.23	even	6
7938.2.a.bu.1.1		3	9.5	odd	6
7938.2.a.bx.1.3		3	63.41	even	6
7938.2.a.by.1.1		3	63.13	odd	6
7938.2.a.cb.1.3		3	9.4	even	3

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.64400 - 0.545231i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.84981 + 3.20397i) q^{5} +(-1.29418 - 1.15113i) q^{6} +1.00000 q^{8} +(2.40545 - 1.79272i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.64400 - 0.545231i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.84981 + 3.20397i) q^{5} +(-1.29418 - 1.15113i) q^{6} +1.00000 q^{8} +(2.40545 - 1.79272i) q^{9} +3.69963 q^{10} +(0.738550 + 1.27921i) q^{11} +(-0.349814 + 1.69636i) q^{12} +(-1.34981 + 2.33795i) q^{13} +(-1.29418 + 6.27589i) q^{15} +(-0.500000 - 0.866025i) q^{16} -6.57598 q^{17} +(-2.75526 - 1.18682i) q^{18} +0.888736 q^{19} +(-1.84981 - 3.20397i) q^{20} +(0.738550 - 1.27921i) q^{22} +(-3.14400 + 5.44556i) q^{23} +(1.64400 - 0.545231i) q^{24} +(-4.34362 - 7.52338i) q^{25} +2.69963 q^{26} +(2.97710 - 4.25874i) q^{27} +(1.25526 + 2.17417i) q^{29} +(6.08217 - 2.01715i) q^{30} +(-3.40545 + 5.89841i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.91164 + 1.70033i) q^{33} +(3.28799 + 5.69497i) q^{34} +(0.349814 + 2.97954i) q^{36} +2.77747 q^{37} +(-0.444368 - 0.769668i) q^{38} +(-0.944368 + 4.57954i) q^{39} +(-1.84981 + 3.20397i) q^{40} +(-2.05563 + 3.56046i) q^{41} +(0.00618986 + 0.0107211i) q^{43} -1.47710 q^{44} +(1.29418 + 11.0232i) q^{45} +6.28799 q^{46} +(3.49381 + 6.05146i) q^{47} +(-1.29418 - 1.15113i) q^{48} +(-4.34362 + 7.52338i) q^{50} +(-10.8109 + 3.58543i) q^{51} +(-1.34981 - 2.33795i) q^{52} +3.21015 q^{53} +(-5.17673 - 0.448873i) q^{54} -5.46472 q^{55} +(1.46108 - 0.484566i) q^{57} +(1.25526 - 2.17417i) q^{58} +(-3.45489 + 5.98404i) q^{59} +(-4.78799 - 4.25874i) q^{60} +(2.86652 + 4.96497i) q^{61} +6.81089 q^{62} +1.00000 q^{64} +(-4.99381 - 8.64953i) q^{65} +(0.516710 - 2.50569i) q^{66} +(4.73236 - 8.19669i) q^{67} +(3.28799 - 5.69497i) q^{68} +(-2.19963 + 10.6667i) q^{69} -5.46472 q^{71} +(2.40545 - 1.79272i) q^{72} +12.0655 q^{73} +(-1.38874 - 2.40536i) q^{74} +(-11.2429 - 10.0001i) q^{75} +(-0.444368 + 0.769668i) q^{76} +(4.43818 - 1.47192i) q^{78} +(-5.72617 - 9.91802i) q^{79} +3.69963 q^{80} +(2.57234 - 8.62456i) q^{81} +4.11126 q^{82} +(2.23855 + 3.87728i) q^{83} +(12.1643 - 21.0693i) q^{85} +(0.00618986 - 0.0107211i) q^{86} +(3.24907 + 2.88993i) q^{87} +(0.738550 + 1.27921i) q^{88} +8.87636 q^{89} +(8.89926 - 6.63238i) q^{90} +(-3.14400 - 5.44556i) q^{92} +(-2.38255 + 11.5537i) q^{93} +(3.49381 - 6.05146i) q^{94} +(-1.64400 + 2.84748i) q^{95} +(-0.349814 + 1.69636i) q^{96} +(-6.58836 - 11.4114i) q^{97} +(4.06979 + 1.75305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 5 q^{5} - 2 q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 5 * q^5 - 2 * q^6 + 6 * q^8 + 8 * q^9	\( 6 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 5 q^{5} - 2 q^{6} + 6 q^{8} + 8 q^{9} + 10 q^{10} - q^{11} + 4 q^{12} - 2 q^{13} - 2 q^{15} - 3 q^{16} + 8 q^{17} - 4 q^{18} + 6 q^{19} - 5 q^{20} - q^{22} - 7 q^{23} - 2 q^{24} - 2 q^{25} + 4 q^{26} + 7 q^{27} - 5 q^{29} + 7 q^{30} - 14 q^{31} - 3 q^{32} + 23 q^{33} - 4 q^{34} - 4 q^{36} + 18 q^{37} - 3 q^{38} - 6 q^{39} - 5 q^{40} - 12 q^{41} + 18 q^{43} + 2 q^{44} + 2 q^{45} + 14 q^{46} + 3 q^{47} - 2 q^{48} - 2 q^{50} - 52 q^{51} - 2 q^{52} - 18 q^{53} - 8 q^{54} + 14 q^{55} + 2 q^{57} - 5 q^{58} + 4 q^{59} - 5 q^{60} + 4 q^{61} + 28 q^{62} + 6 q^{64} - 12 q^{65} - 4 q^{66} + 5 q^{67} - 4 q^{68} - q^{69} + 14 q^{71} + 8 q^{72} + 50 q^{73} - 9 q^{74} - 19 q^{75} - 3 q^{76} + 9 q^{78} + 7 q^{79} + 10 q^{80} + 8 q^{81} + 24 q^{82} + 8 q^{83} + 14 q^{85} + 18 q^{86} - 11 q^{87} - q^{88} + 18 q^{89} + 29 q^{90} - 7 q^{92} + 3 q^{93} + 3 q^{94} + 2 q^{95} + 4 q^{96} - 28 q^{97} - 41 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 5 * q^5 - 2 * q^6 + 6 * q^8 + 8 * q^9 + 10 * q^10 - q^11 + 4 * q^12 - 2 * q^13 - 2 * q^15 - 3 * q^16 + 8 * q^17 - 4 * q^18 + 6 * q^19 - 5 * q^20 - q^22 - 7 * q^23 - 2 * q^24 - 2 * q^25 + 4 * q^26 + 7 * q^27 - 5 * q^29 + 7 * q^30 - 14 * q^31 - 3 * q^32 + 23 * q^33 - 4 * q^34 - 4 * q^36 + 18 * q^37 - 3 * q^38 - 6 * q^39 - 5 * q^40 - 12 * q^41 + 18 * q^43 + 2 * q^44 + 2 * q^45 + 14 * q^46 + 3 * q^47 - 2 * q^48 - 2 * q^50 - 52 * q^51 - 2 * q^52 - 18 * q^53 - 8 * q^54 + 14 * q^55 + 2 * q^57 - 5 * q^58 + 4 * q^59 - 5 * q^60 + 4 * q^61 + 28 * q^62 + 6 * q^64 - 12 * q^65 - 4 * q^66 + 5 * q^67 - 4 * q^68 - q^69 + 14 * q^71 + 8 * q^72 + 50 * q^73 - 9 * q^74 - 19 * q^75 - 3 * q^76 + 9 * q^78 + 7 * q^79 + 10 * q^80 + 8 * q^81 + 24 * q^82 + 8 * q^83 + 14 * q^85 + 18 * q^86 - 11 * q^87 - q^88 + 18 * q^89 + 29 * q^90 - 7 * q^92 + 3 * q^93 + 3 * q^94 + 2 * q^95 + 4 * q^96 - 28 * q^97 - 41 * q^99

Introduction

L-functions

Modular forms

Varieties

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