LMFDB - Embedded newform 882.2.h.o.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(67,882)]

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([2, 4]))

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

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

chi := DirichletCharacter("882.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.h (of order $3$, degree $2$, 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:	$7.04280545828$
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			79.3
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	882.79
Dual form			882.2.h.o.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.349814 + 1.69636i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.69963 q^{5} +(1.29418 - 1.15113i) q^{6} +1.00000 q^{8} +(-2.75526 + 1.18682i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.349814 + 1.69636i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.69963 q^{5} +(1.29418 - 1.15113i) q^{6} +1.00000 q^{8} +(-2.75526 + 1.18682i) q^{9} +(1.84981 + 3.20397i) q^{10} -1.47710 q^{11} +(-1.64400 - 0.545231i) q^{12} +(1.34981 + 2.33795i) q^{13} +(-1.29418 - 6.27589i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.28799 - 5.69497i) q^{17} +(2.40545 + 1.79272i) q^{18} +(0.444368 - 0.769668i) q^{19} +(1.84981 - 3.20397i) q^{20} +(0.738550 + 1.27921i) q^{22} +6.28799 q^{23} +(0.349814 + 1.69636i) q^{24} +8.68725 q^{25} +(1.34981 - 2.33795i) q^{26} +(-2.97710 - 4.25874i) q^{27} +(1.25526 - 2.17417i) q^{29} +(-4.78799 + 4.25874i) q^{30} +(3.40545 - 5.89841i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.516710 - 2.50569i) q^{33} +(-3.28799 + 5.69497i) q^{34} +(0.349814 - 2.97954i) q^{36} +(-1.38874 + 2.40536i) q^{37} -0.888736 q^{38} +(-3.49381 + 3.10761i) q^{39} -3.69963 q^{40} +(2.05563 + 3.56046i) q^{41} +(0.00618986 - 0.0107211i) q^{43} +(0.738550 - 1.27921i) q^{44} +(10.1934 - 4.39079i) q^{45} +(-3.14400 - 5.44556i) q^{46} +(-3.49381 - 6.05146i) q^{47} +(1.29418 - 1.15113i) q^{48} +(-4.34362 - 7.52338i) q^{50} +(8.51052 - 7.56979i) q^{51} -2.69963 q^{52} +(-1.60507 - 2.78007i) q^{53} +(-2.19963 + 4.70761i) q^{54} +5.46472 q^{55} +(1.46108 + 0.484566i) q^{57} -2.51052 q^{58} +(3.45489 - 5.98404i) q^{59} +(6.08217 + 2.01715i) q^{60} +(-2.86652 - 4.96497i) q^{61} -6.81089 q^{62} +1.00000 q^{64} +(-4.99381 - 8.64953i) q^{65} +(-1.91164 + 1.70033i) q^{66} +(4.73236 - 8.19669i) q^{67} +6.57598 q^{68} +(2.19963 + 10.6667i) q^{69} -5.46472 q^{71} +(-2.75526 + 1.18682i) q^{72} +(6.03273 + 10.4490i) q^{73} +2.77747 q^{74} +(3.03892 + 14.7367i) q^{75} +(0.444368 + 0.769668i) q^{76} +(4.43818 + 1.47192i) q^{78} +(-5.72617 - 9.91802i) q^{79} +(1.84981 + 3.20397i) q^{80} +(6.18292 - 6.53999i) q^{81} +(2.05563 - 3.56046i) q^{82} +(-2.23855 + 3.87728i) q^{83} +(12.1643 + 21.0693i) q^{85} -0.0123797 q^{86} +(4.12729 + 1.36881i) q^{87} -1.47710 q^{88} +(4.43818 - 7.68715i) q^{89} +(-8.89926 - 6.63238i) q^{90} +(-3.14400 + 5.44556i) q^{92} +(11.1971 + 3.71351i) q^{93} +(-3.49381 + 6.05146i) q^{94} +(-1.64400 + 2.84748i) q^{95} +(-1.64400 - 0.545231i) 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} - 4 q^{3} - 3 q^{4} - 10 q^{5} + 2 q^{6} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 4 * q^3 - 3 * q^4 - 10 * q^5 + 2 * q^6 + 6 * q^8 - 4 * q^9	$ 6 q - 3 q^{2} - 4 q^{3} - 3 q^{4} - 10 q^{5} + 2 q^{6} + 6 q^{8} - 4 q^{9} + 5 q^{10} + 2 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{15} - 3 q^{16} + 4 q^{17} + 8 q^{18} + 3 q^{19} + 5 q^{20} - q^{22} + 14 q^{23} - 4 q^{24} + 4 q^{25} + 2 q^{26} - 7 q^{27} - 5 q^{29} - 5 q^{30} + 14 q^{31} - 3 q^{32} + 4 q^{33} + 4 q^{34} - 4 q^{36} - 9 q^{37} - 6 q^{38} - 3 q^{39} - 10 q^{40} + 12 q^{41} + 18 q^{43} - q^{44} + 31 q^{45} - 7 q^{46} - 3 q^{47} + 2 q^{48} - 2 q^{50} + 26 q^{51} - 4 q^{52} + 9 q^{53} - q^{54} - 14 q^{55} + 2 q^{57} + 10 q^{58} - 4 q^{59} + 7 q^{60} - 4 q^{61} - 28 q^{62} + 6 q^{64} - 12 q^{65} - 23 q^{66} + 5 q^{67} - 8 q^{68} + q^{69} + 14 q^{71} - 4 q^{72} + 25 q^{73} + 18 q^{74} + 25 q^{75} + 3 q^{76} + 9 q^{78} + 7 q^{79} + 5 q^{80} + 32 q^{81} + 12 q^{82} - 8 q^{83} + 14 q^{85} - 36 q^{86} + 20 q^{87} + 2 q^{88} + 9 q^{89} - 29 q^{90} - 7 q^{92} - 3 q^{93} - 3 q^{94} + 2 q^{95} + 2 q^{96} + 28 q^{97} - 41 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 4 * q^3 - 3 * q^4 - 10 * q^5 + 2 * q^6 + 6 * q^8 - 4 * q^9 + 5 * q^10 + 2 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^15 - 3 * q^16 + 4 * q^17 + 8 * q^18 + 3 * q^19 + 5 * q^20 - q^22 + 14 * q^23 - 4 * q^24 + 4 * q^25 + 2 * q^26 - 7 * q^27 - 5 * q^29 - 5 * q^30 + 14 * q^31 - 3 * q^32 + 4 * q^33 + 4 * q^34 - 4 * q^36 - 9 * q^37 - 6 * q^38 - 3 * q^39 - 10 * q^40 + 12 * q^41 + 18 * q^43 - q^44 + 31 * q^45 - 7 * q^46 - 3 * q^47 + 2 * q^48 - 2 * q^50 + 26 * q^51 - 4 * q^52 + 9 * q^53 - q^54 - 14 * q^55 + 2 * q^57 + 10 * q^58 - 4 * q^59 + 7 * q^60 - 4 * q^61 - 28 * q^62 + 6 * q^64 - 12 * q^65 - 23 * q^66 + 5 * q^67 - 8 * q^68 + q^69 + 14 * q^71 - 4 * q^72 + 25 * q^73 + 18 * q^74 + 25 * q^75 + 3 * q^76 + 9 * q^78 + 7 * q^79 + 5 * q^80 + 32 * q^81 + 12 * q^82 - 8 * q^83 + 14 * q^85 - 36 * q^86 + 20 * q^87 + 2 * q^88 + 9 * q^89 - 29 * q^90 - 7 * q^92 - 3 * q^93 - 3 * q^94 + 2 * q^95 + 2 * q^96 + 28 * q^97 - 41 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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
$3$	0.349814	+	1.69636i	0.201965	+	0.979393i
$3$	0.349814	+	1.69636i	0.201965	+	0.979393i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−3.69963			−1.65452			−0.827262	−	0.561816i	$-0.810103\pi$
$5$	−3.69963			−1.65452			−0.827262	+	0.561816i	$0.810103\pi$
$6$	1.29418	−	1.15113i	0.528348	−	0.469946i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−2.75526	+	1.18682i	−0.918420	+	0.395607i
$10$	1.84981	+	3.20397i	0.584963	+	1.01318i
$11$	−1.47710			−0.445362			−0.222681	−	0.974891i	$-0.571481\pi$
$11$	−1.47710			−0.445362			−0.222681	+	0.974891i	$0.571481\pi$
$12$	−1.64400	−	0.545231i	−0.474581	−	0.157395i
$13$	1.34981	+	2.33795i	0.374371	+	0.648430i	0.990233	−	0.139425i	$-0.0445253\pi$
$13$	1.34981	+	2.33795i	0.374371	+	0.648430i	−0.615862	+	0.787854i	$0.711192\pi$
$14$		0			0
$15$	−1.29418	−	6.27589i	−0.334156	−	1.62043i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.28799	−	5.69497i	−0.797455	−	1.38123i	−0.921268	−	0.388927i	$-0.872846\pi$
$17$	−3.28799	−	5.69497i	−0.797455	−	1.38123i	0.123813	−	0.992306i	$-0.460488\pi$
$18$	2.40545	+	1.79272i	0.566969	+	0.422547i
$19$	0.444368	−	0.769668i	0.101945	−	0.176574i	−0.810541	−	0.585682i	$-0.800827\pi$
$19$	0.444368	−	0.769668i	0.101945	−	0.176574i	0.912486	+	0.409108i	$0.134160\pi$
$20$	1.84981	−	3.20397i	0.413631	−	0.716430i
$21$		0			0
$22$	0.738550	+	1.27921i	0.157459	+	0.272728i
$23$	6.28799			1.31114			0.655568	−	0.755136i	$-0.272429\pi$
$23$	6.28799			1.31114			0.655568	+	0.755136i	$0.272429\pi$
$24$	0.349814	+	1.69636i	0.0714055	+	0.346268i
$25$	8.68725			1.73745
$26$	1.34981	−	2.33795i	0.264720	−	0.458509i
$27$	−2.97710	−	4.25874i	−0.572943	−	0.819595i
$28$		0			0
$29$	1.25526	−	2.17417i	0.233096	−	0.403734i	−0.725622	−	0.688094i	$-0.758448\pi$
$29$	1.25526	−	2.17417i	0.233096	−	0.403734i	0.958718	+	0.284360i	$0.0917810\pi$
$30$	−4.78799	+	4.25874i	−0.874164	+	0.777536i
$31$	3.40545	−	5.89841i	0.611636	−	1.05938i	−0.379329	−	0.925262i	$-0.623845\pi$
$31$	3.40545	−	5.89841i	0.611636	−	1.05938i	0.990965	−	0.134123i	$-0.0428217\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.516710	−	2.50569i	−0.0899477	−	0.436185i
$34$	−3.28799	+	5.69497i	−0.563886	+	0.976679i
$35$		0			0
$36$	0.349814	−	2.97954i	0.0583023	−	0.496589i
$37$	−1.38874	+	2.40536i	−0.228307	+	0.395439i	−0.957306	−	0.289075i	$-0.906652\pi$
$37$	−1.38874	+	2.40536i	−0.228307	+	0.395439i	0.729000	+	0.684514i	$0.239986\pi$
$38$	−0.888736			−0.144172
$39$	−3.49381	+	3.10761i	−0.559457	+	0.497617i
$40$	−3.69963			−0.584963
$41$	2.05563	+	3.56046i	0.321036	+	0.556050i	0.980702	−	0.195508i	$-0.0626357\pi$
$41$	2.05563	+	3.56046i	0.321036	+	0.556050i	−0.659666	+	0.751559i	$0.729302\pi$
$42$		0			0
$43$	0.00618986	−	0.0107211i	0.000943944	−	0.00163496i	−0.865553	−	0.500817i	$-0.833033\pi$
$43$	0.00618986	−	0.0107211i	0.000943944	−	0.00163496i	0.866497	+	0.499182i	$0.166366\pi$
$44$	0.738550	−	1.27921i	0.111341	−	0.192848i
$45$	10.1934	−	4.39079i	1.51955	−	0.654541i
$46$	−3.14400	−	5.44556i	−0.463557	−	0.802904i
$47$	−3.49381	−	6.05146i	−0.509625	−	0.882696i	−0.999938	−	0.0111494i	$-0.996451\pi$
$47$	−3.49381	−	6.05146i	−0.509625	−	0.882696i	0.490313	−	0.871546i	$-0.336882\pi$
$48$	1.29418	−	1.15113i	0.186799	−	0.166151i
$49$		0			0
$50$	−4.34362	−	7.52338i	−0.614281	−	1.06397i
$51$	8.51052	−	7.56979i	1.19171	−	1.05998i
$52$	−2.69963			−0.374371
$53$	−1.60507	−	2.78007i	−0.220474	−	0.381872i	0.734478	−	0.678632i	$-0.237427\pi$
$53$	−1.60507	−	2.78007i	−0.220474	−	0.381872i	−0.954952	+	0.296760i	$0.904094\pi$
$54$	−2.19963	+	4.70761i	−0.299331	+	0.640625i
$55$	5.46472			0.736863
$56$		0			0
$57$	1.46108	+	0.484566i	0.193525	+	0.0641824i
$58$	−2.51052			−0.329647
$59$	3.45489	−	5.98404i	0.449788	−	0.779056i	−0.548584	−	0.836096i	$-0.684833\pi$
$59$	3.45489	−	5.98404i	0.449788	−	0.779056i	0.998372	+	0.0570397i	$0.0181661\pi$
$60$	6.08217	+	2.01715i	0.785205	+	0.260413i
$61$	−2.86652	−	4.96497i	−0.367021	−	0.635699i	0.622077	−	0.782956i	$-0.286289\pi$
$61$	−2.86652	−	4.96497i	−0.367021	−	0.635699i	−0.989098	+	0.147257i	$0.952956\pi$
$62$	−6.81089			−0.864984
$63$		0			0
$64$	1.00000			0.125000
$65$	−4.99381	−	8.64953i	−0.619406	−	1.07284i
$66$	−1.91164	+	1.70033i	−0.235306	+	0.209296i
$67$	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	$-0.0295584\pi$
$68$	6.57598			0.797455
$69$	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	$0.605119\pi$
$72$	−2.75526	+	1.18682i	−0.324711	+	0.139868i
$73$	6.03273	+	10.4490i	0.706078	+	1.22296i	0.966301	+	0.257414i	$0.0828705\pi$
$73$	6.03273	+	10.4490i	0.706078	+	1.22296i	−0.260223	+	0.965548i	$0.583796\pi$
$74$	2.77747			0.322875
$75$	3.03892	+	14.7367i	0.350904	+	1.70165i
$76$	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	$-0.389495\pi$
$80$	1.84981	+	3.20397i	0.206816	+	0.358215i
$81$	6.18292	−	6.53999i	0.686991	−	0.726666i
$82$	2.05563	−	3.56046i	0.227007	−	0.393187i
$83$	−2.23855	+	3.87728i	−0.245713	+	0.425587i	−0.962332	−	0.271878i	$-0.912355\pi$
$83$	−2.23855	+	3.87728i	−0.245713	+	0.425587i	0.716619	+	0.697465i	$0.245689\pi$
$84$		0			0
$85$	12.1643	+	21.0693i	1.31941	+	2.28528i
$86$	−0.0123797			−0.00133494
$87$	4.12729	+	1.36881i	0.442491	+	0.146752i
$88$	−1.47710			−0.157459
$89$	4.43818	−	7.68715i	0.470446	−	0.814836i	−0.528983	−	0.848633i	$-0.677426\pi$
$89$	4.43818	−	7.68715i	0.470446	−	0.814836i	0.999429	+	0.0337963i	$0.0107597\pi$
$90$	−8.89926	−	6.63238i	−0.938064	−	0.699114i
$91$		0			0
$92$	−3.14400	+	5.44556i	−0.327784	+	0.567739i
$93$	11.1971	+	3.71351i	1.16108	+	0.385073i
$94$	−3.49381	+	6.05146i	−0.360359	+	0.624160i
$95$	−1.64400	+	2.84748i	−0.168670	+	0.292146i
$96$	−1.64400	−	0.545231i	−0.167790	−	0.0556474i
$97$	6.58836	−	11.4114i	0.668947	−	1.15865i	−0.309252	−	0.950980i	$-0.600079\pi$
$97$	6.58836	−	11.4114i	0.668947	−	1.15865i	0.978199	−	0.207670i	$-0.0665880\pi$
$98$		0			0
$99$	4.06979	−	1.75305i	0.409030	−	0.176188i
$100$	−4.34362	+	7.52338i	−0.434362	+	0.752338i
$101$	−5.25457			−0.522849			−0.261425	−	0.965224i	$-0.584192\pi$
$101$	−5.25457			−0.522849			−0.261425	+	0.965224i	$0.584192\pi$
$102$	−10.8109	−	3.58543i	−1.07044	−	0.355011i
$103$	−1.66621			−0.164176			−0.0820882	−	0.996625i	$-0.526159\pi$
$103$	−1.66621			−0.164176			−0.0820882	+	0.996625i	$0.526159\pi$
$104$	1.34981	+	2.33795i	0.132360	+	0.229255i
$105$		0			0
$106$	−1.60507	+	2.78007i	−0.155899	+	0.270024i
$107$	−5.38255	+	9.32284i	−0.520350	+	0.901273i	0.479370	+	0.877613i	$0.340865\pi$
$107$	−5.38255	+	9.32284i	−0.520350	+	0.901273i	−0.999720	+	0.0236602i	$0.992468\pi$
$108$	5.17673	−	0.448873i	0.498131	−	0.0431929i
$109$	−0.0945538	−	0.163772i	−0.00905662	−	0.0156865i	0.861462	−	0.507823i	$-0.169550\pi$
$109$	−0.0945538	−	0.163772i	−0.00905662	−	0.0156865i	−0.870518	+	0.492136i	$0.836216\pi$
$110$	−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	−0.985876	−	0.167478i	$-0.946438\pi$
$113$	−6.78180	−	11.7464i	−0.637978	−	1.10501i	0.347897	−	0.937533i	$-0.386896\pi$
$114$	−0.310892	−	1.50761i	−0.0291177	−	0.141201i
$115$	−23.2632			−2.16931
$116$	1.25526	+	2.17417i	0.116548	+	0.201867i
$117$	−6.49381	−	4.83967i	−0.600353	−	0.447427i
$118$	−6.90978			−0.636097
$119$		0			0
$120$	−1.29418	−	6.27589i	−0.118142	−	0.572908i
$121$	−8.81818			−0.801652
$122$	−2.86652	+	4.96497i	−0.259523	+	0.449507i
$123$	−5.32072	+	4.73259i	−0.479754	+	0.426723i
$124$	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
$129$	0.0203522	+	0.00674980i	0.00179191	+	0.000594287i
$130$	−4.99381	+	8.64953i	−0.437986	+	0.758614i
$131$	−0.155687			−0.0136024			−0.00680122	−	0.999977i	$-0.502165\pi$
$131$	−0.155687			−0.0136024			−0.00680122	+	0.999977i	$0.502165\pi$
$132$	2.42835	+	0.805361i	0.211360	+	0.0700977i
$133$		0			0
$134$	−9.46472			−0.817627
$135$	11.0142	+	15.7558i	0.947948	+	1.35604i
$136$	−3.28799	−	5.69497i	−0.281943	−	0.488340i
$137$	−3.41164			−0.291476			−0.145738	−	0.989323i	$-0.546556\pi$
$137$	−3.41164			−0.291476			−0.145738	+	0.989323i	$0.546556\pi$
$138$	8.13781	−	7.23828i	0.692736	−	0.616163i
$139$	6.75526	+	11.7005i	0.572974	+	0.992420i	0.996259	+	0.0864229i	$0.0275436\pi$
$139$	6.75526	+	11.7005i	0.572974	+	0.992420i	−0.423285	+	0.905997i	$0.639123\pi$
$140$		0			0
$141$	9.04325	−	8.04364i	0.761579	−	0.677396i
$142$	2.73236	+	4.73259i	0.229295	+	0.397150i
$143$	−1.99381	−	3.45338i	−0.166731	−	0.288786i
$144$	2.40545	+	1.79272i	0.200454	+	0.149393i
$145$	−4.64400	+	8.04364i	−0.385663	+	0.667988i
$146$	6.03273	−	10.4490i	0.499272	−	0.864765i
$147$		0			0
$148$	−1.38874	−	2.40536i	−0.114153	−	0.197719i
$149$	0.333792			0.0273453			0.0136727	−	0.999907i	$-0.495648\pi$
$149$	0.333792			0.0273453			0.0136727	+	0.999907i	$0.495648\pi$
$150$	11.2429	−	10.0001i	0.917977	−	0.816507i
$151$	−19.9098			−1.62023			−0.810117	−	0.586268i	$-0.800597\pi$
$151$	−19.9098			−1.62023			−0.810117	+	0.586268i	$0.800597\pi$
$152$	0.444368	−	0.769668i	0.0360430	−	0.0624283i
$153$	15.8182	+	11.7889i	1.27882	+	0.953074i
$154$		0			0
$155$	−12.5989	+	21.8219i	−1.01197	+	1.75278i
$156$	−0.944368	−	4.57954i	−0.0756099	−	0.366656i
$157$	−3.48143	+	6.03001i	−0.277848	+	0.481248i	−0.970850	−	0.239689i	$-0.922955\pi$
$157$	−3.48143	+	6.03001i	−0.277848	+	0.481248i	0.693001	+	0.720936i	$0.256288\pi$
$158$	−5.72617	+	9.91802i	−0.455550	+	0.789035i
$159$	4.15452	−	3.69529i	0.329475	−	0.293055i
$160$	1.84981	−	3.20397i	0.146241	−	0.253296i
$161$		0			0
$162$	−8.75526	−	2.08457i	−0.687878	−	0.163779i
$163$	4.03706	−	6.99240i	0.316207	−	0.547687i	−0.663486	−	0.748189i	$-0.730924\pi$
$163$	4.03706	−	6.99240i	0.316207	−	0.547687i	0.979693	+	0.200502i	$0.0642572\pi$
$164$	−4.11126			−0.321036
$165$	1.91164	+	9.27012i	0.148821	+	0.721678i
$166$	4.47710			0.347490
$167$	−9.74288	−	16.8752i	−0.753927	−	1.30584i	−0.945906	−	0.324440i	$-0.894824\pi$
$167$	−9.74288	−	16.8752i	−0.753927	−	1.30584i	0.191979	−	0.981399i	$-0.438509\pi$
$168$		0			0
$169$	2.85600	−	4.94674i	0.219693	−	0.380519i
$170$	12.1643	−	21.0693i	0.932963	−	1.61594i
$171$	−0.310892	+	2.64802i	−0.0237745	+	0.202499i
$172$	0.00618986	+	0.0107211i	0.000471972	+	0.000817480i
$173$	11.2818	+	19.5407i	0.857740	+	1.48565i	0.874080	+	0.485782i	$0.161465\pi$
$173$	11.2818	+	19.5407i	0.857740	+	1.48565i	−0.0163405	+	0.999866i	$0.505202\pi$
$174$	−0.878215	−	4.25874i	−0.0665773	−	0.322854i
$175$		0			0
$176$	0.738550	+	1.27921i	0.0556703	+	0.0964238i
$177$	11.3596	+	3.76742i	0.853843	+	0.283177i
$178$	−8.87636			−0.665311
$179$	0.166896	+	0.289073i	0.0124744	+	0.0216063i	0.872195	−	0.489158i	$-0.162696\pi$
$179$	0.166896	+	0.289073i	0.0124744	+	0.0216063i	−0.859721	+	0.510764i	$0.829363\pi$
$180$	−1.29418	+	11.0232i	−0.0964626	+	0.821619i
$181$	−23.2422			−1.72758			−0.863789	−	0.503853i	$-0.831915\pi$
$181$	−23.2422			−1.72758			−0.863789	+	0.503853i	$0.831915\pi$
$182$		0			0
$183$	7.41961	−	6.59947i	0.548473	−	0.487847i
$184$	6.28799			0.463557
$185$	5.13781	−	8.89894i	0.377739	−	0.654263i
$186$	−2.38255	−	11.5537i	−0.174697	−	0.847159i
$187$	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	$0.632269\pi$
$192$	0.349814	+	1.69636i	0.0252457	+	0.122424i
$193$	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	$-0.00570443\pi$
$194$	−13.1767			−0.946034
$195$	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	$0.472479\pi$
$198$	−3.55308	−	2.64802i	−0.252507	−	0.188187i
$199$	3.05563	+	5.29251i	0.216608	+	0.375176i	0.953769	−	0.300541i	$-0.0971673\pi$
$199$	3.05563	+	5.29251i	0.216608	+	0.375176i	−0.737161	+	0.675717i	$0.763834\pi$
$200$	8.68725			0.614281
$201$	15.5600	+	5.16046i	1.09752	+	0.363991i
$202$	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
$206$	0.833104	+	1.44298i	0.0580451	+	0.100537i
$207$	−17.3251	+	7.46271i	−1.20417	+	0.518694i
$208$	1.34981	−	2.33795i	0.0935928	−	0.162107i
$209$	−0.656376	+	1.13688i	−0.0454025	+	0.0786394i
$210$		0			0
$211$	5.72253	+	9.91171i	0.393955	+	0.682350i	0.992967	−	0.118390i	$-0.0377732\pi$
$211$	5.72253	+	9.91171i	0.393955	+	0.682350i	−0.599012	+	0.800740i	$0.704440\pi$
$212$	3.21015			0.220474
$213$	−1.91164	−	9.27012i	−0.130983	−	0.635178i
$214$	10.7651			0.735887
$215$	−0.0229002	+	0.0396643i	−0.00156178	+	0.00270508i
$216$	−2.97710	−	4.25874i	−0.202566	−	0.289771i
$217$		0			0
$218$	−0.0945538	+	0.163772i	−0.00640399	+	0.0110920i
$219$	−15.6149	+	13.8889i	−1.05516	+	0.938523i
$220$	−2.73236	+	4.73259i	−0.184216	+	0.319071i
$221$	8.87636	−	15.3743i	0.597088	−	1.03419i
$222$	0.971599	+	4.71159i	0.0652094	+	0.316221i
$223$	3.61126	−	6.25489i	0.241828	−	0.418859i	−0.719407	−	0.694589i	$-0.755586\pi$
$223$	3.61126	−	6.25489i	0.241828	−	0.418859i	0.961235	+	0.275730i	$0.0889196\pi$
$224$		0			0
$225$	−23.9356	+	10.3102i	−1.59571	+	0.687347i
$226$	−6.78180	+	11.7464i	−0.451119	+	0.781361i
$227$	−13.6552			−0.906328			−0.453164	−	0.891427i	$-0.649705\pi$
$227$	−13.6552			−0.906328			−0.453164	+	0.891427i	$0.649705\pi$
$228$	−1.15019	+	1.02305i	−0.0761729	+	0.0677530i
$229$	−17.3745			−1.14814			−0.574070	−	0.818807i	$-0.694636\pi$
$229$	−17.3745			−1.14814			−0.574070	+	0.818807i	$0.694636\pi$
$230$	11.6316	+	20.1466i	0.766966	+	1.32842i
$231$		0			0
$232$	1.25526	−	2.17417i	0.0824119	−	0.142742i
$233$	7.62110	−	13.2001i	0.499275	−	0.864769i	−0.500725	−	0.865606i	$-0.666933\pi$
$233$	7.62110	−	13.2001i	0.499275	−	0.864769i	1.00000		0.000837426i	$0.000266561\pi$
$234$	−0.944368	+	8.04364i	−0.0617353	+	0.525829i
$235$	12.9258	+	22.3881i	0.843186	+	1.46044i
$236$	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	0.990749	+	0.135710i	$0.0433314\pi$
$239$	9.47524	+	16.4116i	0.612902	+	1.06158i	−0.377846	+	0.925868i	$0.623335\pi$
$240$	−4.78799	+	4.25874i	−0.309064	+	0.274901i
$241$	24.5054			1.57853			0.789267	−	0.614051i	$-0.210461\pi$
$241$	24.5054			1.57853			0.789267	+	0.614051i	$0.210461\pi$
$242$	4.40909	+	7.63676i	0.283427	+	0.490910i
$243$	13.2570	+	8.20066i	0.850440	+	0.526073i
$244$	5.73305			0.367021
$245$		0			0
$246$	6.75890	+	2.24159i	0.430932	+	0.142918i
$247$	2.39926			0.152661
$248$	3.40545	−	5.89841i	0.216246	−	0.374549i
$249$	−7.36033	−	2.44105i	−0.466442	−	0.154696i
$250$	6.82072	+	11.8138i	0.431380	+	0.747173i
$251$	12.1236			0.765238			0.382619	−	0.923906i	$-0.375022\pi$
$251$	12.1236			0.765238			0.382619	+	0.923906i	$0.375022\pi$
$252$		0			0
$253$	−9.28799			−0.583931
$254$	1.42835	+	2.47397i	0.0896224	+	0.155231i
$255$	−31.4858	+	28.0054i	−1.97171	+	1.75377i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.20877			0.512049			0.256025	−	0.966670i	$-0.417587\pi$
$257$	8.20877			0.512049			0.256025	+	0.966670i	$0.417587\pi$
$258$	−0.00433060	−	0.0210004i	−0.000269611	−	0.00130743i
$259$		0			0
$260$	9.98762			0.619406
$261$	−0.878215	+	7.48018i	−0.0543602	+	0.463012i
$262$	0.0778435	+	0.134829i	0.00480919	+	0.00832976i
$263$	−5.34617			−0.329659			−0.164830	−	0.986322i	$-0.552707\pi$
$263$	−5.34617			−0.329659			−0.164830	+	0.986322i	$0.552707\pi$
$264$	−0.516710	−	2.50569i	−0.0318013	−	0.154215i
$265$	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
$269$	−9.24219	−	16.0079i	−0.563506	−	0.976022i	−0.997187	−	0.0749550i	$-0.976119\pi$
$269$	−9.24219	−	16.0079i	−0.563506	−	0.976022i	0.433681	−	0.901067i	$-0.357215\pi$
$270$	8.13781	−	17.4164i	0.495251	−	1.05993i
$271$	3.67742	−	6.36947i	0.223387	−	0.386918i	−0.732447	−	0.680824i	$-0.761622\pi$
$271$	3.67742	−	6.36947i	0.223387	−	0.386918i	0.955834	+	0.293906i	$0.0949552\pi$
$272$	−3.28799	+	5.69497i	−0.199364	+	0.345308i
$273$		0			0
$274$	1.70582	+	2.95456i	0.103052	+	0.178492i
$275$	−12.8319			−0.773795
$276$	−10.3374	−	3.42841i	−0.622240	−	0.206366i
$277$	−9.09888			−0.546699			−0.273349	−	0.961915i	$-0.588132\pi$
$277$	−9.09888			−0.546699			−0.273349	+	0.961915i	$0.588132\pi$
$278$	6.75526	−	11.7005i	0.405154	−	0.701747i
$279$	−2.38255	+	20.2933i	−0.142639	+	1.21493i
$280$		0			0
$281$	6.00433	−	10.3998i	0.358188	−	0.620400i	−0.629470	−	0.777025i	$-0.716728\pi$
$281$	6.00433	−	10.3998i	0.358188	−	0.620400i	0.987658	+	0.156624i	$0.0500612\pi$
$282$	−11.4876	−	3.80987i	−0.684078	−	0.226874i
$283$	4.92147	−	8.52423i	0.292551	−	0.506713i	−0.681861	−	0.731481i	$-0.738829\pi$
$283$	4.92147	−	8.52423i	0.292551	−	0.506713i	0.974412	+	0.224768i	$0.0721626\pi$
$284$	2.73236	−	4.73259i	0.162136	−	0.280827i
$285$	−5.40545	−	1.79272i	−0.320191	−	0.106191i
$286$	−1.99381	+	3.45338i	−0.117896	+	0.204203i
$287$		0			0
$288$	0.349814	−	2.97954i	0.0206130	−	0.175571i
$289$	−13.1218	+	22.7276i	−0.771870	+	1.33692i
$290$	9.28799			0.545410
$291$	21.6625	+	7.18436i	1.26988	+	0.421155i
$292$	−12.0655			−0.706078
$293$	−10.7101	−	18.5505i	−0.625694	−	1.08373i	−0.988406	−	0.151832i	$-0.951483\pi$
$293$	−10.7101	−	18.5505i	−0.625694	−	1.08373i	0.362713	−	0.931901i	$-0.381851\pi$
$294$		0			0
$295$	−12.7818	+	22.1387i	−0.744185	+	1.28897i
$296$	−1.38874	+	2.40536i	−0.0807186	+	0.139809i
$297$	4.39747	+	6.29059i	0.255167	+	0.365017i
$298$	−0.166896	−	0.289073i	−0.00966804	−	0.0167455i
$299$	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
$303$	−1.83812	−	8.91363i	−0.105597	−	0.512075i
$304$	−0.888736			−0.0509725
$305$	10.6051	+	18.3685i	0.607245	+	1.05178i
$306$	2.30037	−	19.5934i	0.131504	−	1.12008i
$307$	5.68725			0.324588			0.162294	−	0.986742i	$-0.448111\pi$
$307$	5.68725			0.324588			0.162294	+	0.986742i	$0.448111\pi$
$308$		0			0
$309$	−0.582863	−	2.82648i	−0.0331579	−	0.160793i
$310$	25.1978			1.43114
$311$	−5.86033	+	10.1504i	−0.332309	+	0.575576i	−0.982964	−	0.183797i	$-0.941161\pi$
$311$	−5.86033	+	10.1504i	−0.332309	+	0.575576i	0.650655	+	0.759373i	$0.274494\pi$
$312$	−3.49381	+	3.10761i	−0.197798	+	0.175934i
$313$	−13.3869	−	23.1868i	−0.756671	−	1.31059i	−0.944539	−	0.328398i	$-0.893491\pi$
$313$	−13.3869	−	23.1868i	−0.756671	−	1.31059i	0.187868	−	0.982194i	$-0.439842\pi$
$314$	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	$0.850348\pi$
$318$	−5.27747	−	1.75027i	−0.295946	−	0.0981504i
$319$	−1.85414	+	3.21147i	−0.103812	+	0.179808i
$320$	−3.69963			−0.206816
$321$	−17.6978	−	5.86946i	−0.987793	−	0.327601i
$322$		0			0
$323$	−5.84431			−0.325186
$324$	2.57234	+	8.62456i	0.142908	+	0.479142i
$325$	11.7262	+	20.3103i	0.650451	+	1.12661i
$326$	−8.07413			−0.447184
$327$	0.244740	−	0.217687i	0.0135341	−	0.0120381i
$328$	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	$0.882228\pi$
$332$	−2.23855	−	3.87728i	−0.122856	−	0.212794i
$333$	0.971599	−	8.27557i	0.0532433	−	0.453499i
$334$	−9.74288	+	16.8752i	−0.533107	+	0.923368i
$335$	−17.5080	+	30.3247i	−0.956563	+	1.65682i
$336$		0			0
$337$	−16.8869	−	29.2489i	−0.919887	−	1.59329i	−0.799585	−	0.600553i	$-0.794947\pi$
$337$	−16.8869	−	29.2489i	−0.919887	−	1.59329i	−0.120302	−	0.992737i	$-0.538386\pi$
$338$	−5.71201			−0.310692
$339$	17.5538	−	15.6134i	0.953390	−	0.848005i
$340$	−24.3287			−1.31941
$341$	−5.03018	+	8.71253i	−0.272400	+	0.471810i
$342$	2.44870	−	1.05477i	0.132410	−	0.0570354i
$343$		0			0
$344$	0.00618986	−	0.0107211i	0.000333735	−	0.000578045i
$345$	−8.13781	−	39.4628i	−0.438125	−	2.12460i
$346$	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	$-0.137231\pi$
$348$	−3.24907	+	2.88993i	−0.174168	+	0.154916i
$349$	6.29782	−	10.9082i	0.337115	−	0.583900i	−0.646774	−	0.762682i	$-0.723882\pi$
$349$	6.29782	−	10.9082i	0.337115	−	0.583900i	0.983889	+	0.178782i	$0.0572156\pi$
$350$		0			0
$351$	5.93818	−	12.7088i	0.316956	−	0.678346i
$352$	0.738550	−	1.27921i	0.0393648	−	0.0681819i
$353$	7.53156			0.400865			0.200432	−	0.979708i	$-0.435765\pi$
$353$	7.53156			0.400865			0.200432	+	0.979708i	$0.435765\pi$
$354$	−2.41714	−	11.7215i	−0.128469	−	0.622988i
$355$	20.2174			1.07303
$356$	4.43818	+	7.68715i	0.235223	+	0.407418i
$357$		0			0
$358$	0.166896	−	0.289073i	0.00882074	−	0.0152780i
$359$	−3.44801	+	5.97213i	−0.181979	+	0.315197i	−0.942554	−	0.334053i	$-0.891584\pi$
$359$	−3.44801	+	5.97213i	−0.181979	+	0.315197i	0.760575	+	0.649250i	$0.224917\pi$
$360$	10.1934	−	4.39079i	0.537241	−	0.231415i
$361$	9.10507	+	15.7705i	0.479214	+	0.830024i
$362$	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
$366$	−9.42511	−	3.12584i	−0.492658	−	0.163390i
$367$	−23.1236			−1.20704			−0.603522	−	0.797346i	$-0.706237\pi$
$367$	−23.1236			−1.20704			−0.603522	+	0.797346i	$0.706237\pi$
$368$	−3.14400	−	5.44556i	−0.163892	−	0.283869i
$369$	−9.88942	−	7.37033i	−0.514823	−	0.383684i
$370$	−10.2756			−0.534204
$371$		0			0
$372$	−8.81453	+	7.84020i	−0.457012	+	0.406495i
$373$	29.1643			1.51007			0.755036	−	0.655683i	$-0.227619\pi$
$373$	29.1643			1.51007			0.755036	+	0.655683i	$0.227619\pi$
$374$	4.85669	−	8.41204i	0.251134	−	0.434976i
$375$	−4.77197	−	23.1408i	−0.246423	−	1.19498i
$376$	−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
$381$	−0.999311	−	4.84597i	−0.0511963	−	0.248267i
$382$	8.16071	−	14.1348i	0.417538	−	0.723197i
$383$	2.83565			0.144895			0.0724475	−	0.997372i	$-0.476919\pi$
$383$	2.83565			0.144895			0.0724475	+	0.997372i	$0.476919\pi$
$384$	1.29418	−	1.15113i	0.0660434	−	0.0587432i
$385$		0			0
$386$	−14.3214			−0.728941
$387$	−0.00433060	+	0.0368858i	−0.000220137	+	0.00187501i
$388$	6.58836	+	11.4114i	0.334474	+	0.579325i
$389$	−18.6080			−0.943464			−0.471732	−	0.881742i	$-0.656371\pi$
$389$	−18.6080			−0.943464			−0.471732	+	0.881742i	$0.656371\pi$
$390$	−16.4196	−	5.44556i	−0.831439	−	0.275747i
$391$	−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
$395$	21.1847	+	36.6930i	1.06592	+	1.84622i
$396$	−0.516710	+	4.40107i	−0.0259657	+	0.221162i
$397$	10.2880	−	17.8193i	0.516340	−	0.894326i	−0.483481	−	0.875355i	$-0.660628\pi$
$397$	10.2880	−	17.8193i	0.516340	−	0.894326i	0.999820	−	0.0189712i	$-0.00603907\pi$
$398$	3.05563	−	5.29251i	0.153165	−	0.265290i
$399$		0			0
$400$	−4.34362	−	7.52338i	−0.217181	−	0.376169i
$401$	−6.75409			−0.337283			−0.168642	−	0.985677i	$-0.553938\pi$
$401$	−6.75409			−0.337283			−0.168642	+	0.985677i	$0.553938\pi$
$402$	−3.31089	−	16.0556i	−0.165132	−	0.800778i
$403$	18.3869			0.915916
$404$	2.62729	−	4.55059i	0.130712	−	0.226400i
$405$	−22.8745	+	24.1955i	−1.13664	+	1.20229i
$406$		0			0
$407$	2.05130	−	3.55296i	0.101679	−	0.176114i
$408$	8.51052	−	7.56979i	0.421334	−	0.374761i
$409$	7.66071	−	13.2687i	0.378798	−	0.656097i	−0.612090	−	0.790788i	$-0.709671\pi$
$409$	7.66071	−	13.2687i	0.378798	−	0.656097i	0.990888	+	0.134691i	$0.0430043\pi$
$410$	−7.60507	+	13.1724i	−0.375588	+	0.650537i
$411$	−1.19344	−	5.78736i	−0.0588680	−	0.285469i
$412$	0.833104	−	1.44298i	0.0410441	−	0.0710904i
$413$		0			0
$414$	15.1254	+	11.2726i	0.743374	+	0.554017i
$415$	8.28180	−	14.3445i	0.406538	−	0.704144i
$416$	−2.69963			−0.132360
$417$	−17.4851	+	15.5523i	−0.856248	+	0.761601i
$418$	1.31275			0.0642088
$419$	4.32141	+	7.48491i	0.211115	+	0.365662i	0.952064	−	0.305900i	$-0.0989573\pi$
$419$	4.32141	+	7.48491i	0.211115	+	0.365662i	−0.740949	+	0.671561i	$0.765624\pi$
$420$		0			0
$421$	18.5636	−	32.1531i	0.904735	−	1.56705i	0.0834618	−	0.996511i	$-0.473402\pi$
$421$	18.5636	−	32.1531i	0.904735	−	1.56705i	0.821273	−	0.570536i	$-0.193264\pi$
$422$	5.72253	−	9.91171i	0.278568	−	0.482494i
$423$	16.8083	+	12.5268i	0.817250	+	0.609075i
$424$	−1.60507	−	2.78007i	−0.0779493	−	0.135012i
$425$	−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
$429$	5.16071	−	4.59026i	0.249161	−	0.221620i
$430$	0.0458003			0.00220869
$431$	−4.71015	−	8.15822i	−0.226880	−	0.392967i	0.730002	−	0.683445i	$-0.239519\pi$
$431$	−4.71015	−	8.15822i	−0.226880	−	0.392967i	−0.956882	+	0.290478i	$0.906186\pi$
$432$	−2.19963	+	4.70761i	−0.105830	+	0.226495i
$433$	0.208771			0.0100329			0.00501645	−	0.999987i	$-0.498403\pi$
$433$	0.208771			0.0100329			0.00501645	+	0.999987i	$0.498403\pi$
$434$		0			0
$435$	−15.2694	−	5.06410i	−0.732113	−	0.242805i
$436$	0.189108			0.00905662
$437$	2.79418	−	4.83967i	0.133664	−	0.231513i
$438$	19.8356	+	6.57847i	0.947780	+	0.314331i
$439$	−4.98398	−	8.63250i	−0.237872	−	0.412007i	0.722231	−	0.691652i	$-0.243117\pi$
$439$	−4.98398	−	8.63250i	−0.237872	−	0.412007i	−0.960104	+	0.279645i	$0.909783\pi$
$440$	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	$0.711678\pi$
$444$	3.59455	−	3.19722i	0.170590	−	0.151733i
$445$	−16.4196	+	28.4396i	−0.778364	+	1.34817i
$446$	−7.22253			−0.341997
$447$	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	$0.208288\pi$
$450$	20.8967	+	15.5738i	0.985080	+	0.734154i
$451$	−3.03637	−	5.25915i	−0.142977	−	0.247644i
$452$	13.5636			0.637978
$453$	−6.96472	−	33.7741i	−0.327231	−	1.58685i
$454$	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	$-0.443935\pi$
$458$	8.68725	+	15.0468i	0.405928	+	0.703089i
$459$	−14.4647	+	30.9572i	−0.675155	+	1.44496i
$460$	11.6316	−	20.1466i	0.542327	−	0.939338i
$461$	2.07165	−	3.58821i	0.0964865	−	0.167120i	−0.813742	−	0.581227i	$-0.802573\pi$
$461$	2.07165	−	3.58821i	0.0964865	−	0.167120i	0.910228	+	0.414107i	$0.135906\pi$
$462$		0			0
$463$	−8.34176	−	14.4484i	−0.387675	−	0.671472i	0.604462	−	0.796634i	$-0.293388\pi$
$463$	−8.34176	−	14.4484i	−0.387675	−	0.671472i	−0.992136	+	0.125162i	$0.960055\pi$
$464$	−2.51052			−0.116548
$465$	−41.4250	−	13.7386i	−1.92104	−	0.637113i
$466$	−15.2422			−0.706081
$467$	−14.9585	+	25.9089i	−0.692198	+	1.19892i	0.278918	+	0.960315i	$0.410024\pi$
$467$	−14.9585	+	25.9089i	−0.692198	+	1.19892i	−0.971116	+	0.238608i	$0.923309\pi$
$468$	7.43818	−	3.20397i	0.343830	−	0.148104i
$469$		0			0
$470$	12.9258	−	22.3881i	0.596223	−	1.03269i
$471$	−11.4469	−	3.79637i	−0.527446	−	0.174927i
$472$	3.45489	−	5.98404i	0.159024	−	0.275438i
$473$	−0.00914304	+	0.0158362i	−0.000420397	+	0.000728149i
$474$	−18.8276	−	6.24417i	−0.864780	−	0.286804i
$475$	3.86033	−	6.68630i	0.177124	−	0.306788i
$476$		0			0
$477$	7.72184	+	5.75488i	0.353559	+	0.263498i
$478$	9.47524	−	16.4116i	0.433387	−	0.750649i
$479$	2.95930			0.135214			0.0676068	−	0.997712i	$-0.478464\pi$
$479$	2.95930			0.135214			0.0676068	+	0.997712i	$0.478464\pi$
$480$	6.08217	+	2.01715i	0.277612	+	0.0920700i
$481$	−7.49814			−0.341886
$482$	−12.2527	−	21.2223i	−0.558096	−	0.966650i
$483$		0			0
$484$	4.40909	−	7.63676i	0.200413	−	0.347126i
$485$	−24.3745	+	42.2179i	−1.10679	+	1.91701i
$486$	0.473458	−	15.5813i	0.0214765	−	0.706781i
$487$	−14.0309	−	24.3022i	−0.635800	−	1.10124i	−0.986345	−	0.164691i	$-0.947337\pi$
$487$	−14.0309	−	24.3022i	−0.635800	−	1.10124i	0.350546	−	0.936546i	$-0.385996\pi$
$488$	−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	0.937282	+	0.348572i	$0.113333\pi$
$491$	17.0734	+	29.5721i	0.770513	+	1.33457i	−0.166769	+	0.985996i	$0.553333\pi$
$492$	−1.43818	−	6.97418i	−0.0648381	−	0.314420i
$493$	−16.5091			−0.743534
$494$	−1.19963	−	2.07782i	−0.0539738	−	0.0934854i
$495$	−15.0567	+	6.48564i	−0.676750	+	0.291508i
$496$	−6.81089			−0.305818
$497$		0			0
$498$	1.56615	+	7.59476i	0.0701810	+	0.340329i
$499$	−2.28071			−0.102099			−0.0510493	−	0.998696i	$-0.516257\pi$
$499$	−2.28071			−0.102099			−0.0510493	+	0.998696i	$0.516257\pi$
$500$	6.82072	−	11.8138i	0.305032	−	0.528331i
$501$	25.2181	−	22.4306i	1.12666	−	1.00212i
$502$	−6.06182	−	10.4994i	−0.270552	−	0.468610i
$503$	−13.9890			−0.623739			−0.311869	−	0.950125i	$-0.600955\pi$
$503$	−13.9890			−0.623739			−0.311869	+	0.950125i	$0.600955\pi$
$504$		0			0
$505$	19.4400			0.865067
$506$	4.64400	+	8.04364i	0.206451	+	0.357583i
$507$	9.39052	+	3.11436i	0.417048	+	0.138314i
$508$	1.42835	−	2.47397i	0.0633726	−	0.109765i
$509$	−25.6181			−1.13550			−0.567750	−	0.823201i	$-0.692186\pi$
$509$	−25.6181			−1.13550			−0.567750	+	0.823201i	$0.692186\pi$
$510$	39.9963	+	13.2648i	1.77107	+	0.587374i
$511$		0			0
$512$	1.00000			0.0441942
$513$	−4.60074	+	0.398930i	−0.203128	+	0.0176132i
$514$	−4.10439	−	7.10900i	−0.181037	−	0.313565i
$515$	6.16435			0.271634
$516$	−0.0160216	+	0.0142506i	−0.000705312	+	0.000627349i
$517$	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
$521$	20.9127	+	36.2219i	0.916203	+	1.58691i	0.805130	+	0.593099i	$0.202096\pi$
$521$	20.9127	+	36.2219i	0.916203	+	1.58691i	0.111073	+	0.993812i	$0.464571\pi$
$522$	6.91714	−	2.97954i	0.302755	−	0.130411i
$523$	−7.88323	+	13.6542i	−0.344710	+	0.597055i	−0.985301	−	0.170827i	$-0.945356\pi$
$523$	−7.88323	+	13.6542i	−0.344710	+	0.597055i	0.640591	+	0.767882i	$0.278689\pi$
$524$	0.0778435	−	0.134829i	0.00340061	−	0.00589003i
$525$		0			0
$526$	2.67309	+	4.62992i	0.116552	+	0.201874i
$527$	−44.7883			−1.95101
$528$	−1.91164	+	1.70033i	−0.0831933	+	0.0739973i
$529$	16.5388			0.719080
$530$	5.93818	−	10.2852i	0.257938	−	0.446762i
$531$	−2.41714	+	20.5879i	−0.104895	+	0.893440i
$532$		0			0
$533$	−5.54944	+	9.61192i	−0.240373	+	0.416338i
$534$	−3.10507	−	15.0575i	−0.134370	−	0.651601i
$535$	19.9134	−	34.4911i	0.860932	−	1.49118i
$536$	4.73236	−	8.19669i	0.204407	−	0.354043i
$537$	−0.431988	+	0.384237i	−0.0186417	+	0.0165811i
$538$	−9.24219	+	16.0079i	−0.398459	+	0.690152i
$539$		0			0
$540$	−19.1520	+	1.66066i	−0.824170	+	0.0714636i
$541$	−21.0963	+	36.5399i	−0.907002	+	1.57097i	−0.0887957	+	0.996050i	$0.528302\pi$
$541$	−21.0963	+	36.5399i	−0.907002	+	1.57097i	−0.818207	+	0.574924i	$0.805031\pi$
$542$	−7.35483			−0.315917
$543$	−8.13045	−	39.4271i	−0.348911	−	1.69198i
$544$	6.57598			0.281943
$545$	0.349814	+	0.605896i	0.0149844	+	0.0259537i
$546$		0			0
$547$	20.3356	−	35.2222i	0.869486	−	1.50599i	0.00696400	−	0.999976i	$-0.497783\pi$
$547$	20.3356	−	35.2222i	0.869486	−	1.50599i	0.862522	−	0.506019i	$-0.168883\pi$
$548$	1.70582	−	2.95456i	0.0728689	−	0.126213i
$549$	13.7905	+	10.2777i	0.588566	+	0.438643i
$550$	6.41597	+	11.1128i	0.273578	+	0.473851i
$551$	−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
$555$	16.8931	+	5.60258i	0.717071	+	0.237816i
$556$	−13.5105			−0.572974
$557$	6.68794	+	11.5838i	0.283377	+	0.490823i	0.972214	−	0.234093i	$-0.0752119\pi$
$557$	6.68794	+	11.5838i	0.283377	+	0.490823i	−0.688837	+	0.724916i	$0.741879\pi$
$558$	18.7658	−	8.08330i	0.794419	−	0.342193i
$559$	0.0334206			0.00141354
$560$		0			0
$561$	−12.5709	+	11.1813i	−0.530743	+	0.472076i
$562$	−12.0087			−0.506555
$563$	−16.3807	+	28.3722i	−0.690364	+	1.19574i	0.281355	+	0.959604i	$0.409216\pi$
$563$	−16.3807	+	28.3722i	−0.690364	+	1.19574i	−0.971719	+	0.236141i	$0.924117\pi$
$564$	2.44437	+	11.8535i	0.102926	+	0.499123i
$565$	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	$0.719299\pi$
$570$	1.15019	+	5.57761i	0.0481760	+	0.233620i
$571$	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	$-0.0282778\pi$
$572$	3.98762			0.166731
$573$	−21.1229	+	18.7880i	−0.882421	+	0.784881i
$574$		0			0
$575$	54.6253			2.27803
$576$	−2.75526	+	1.18682i	−0.114803	+	0.0494508i
$577$	−1.41714	−	2.45455i	−0.0589962	−	0.102184i	0.835019	−	0.550221i	$-0.185457\pi$
$577$	−1.41714	−	2.45455i	−0.0589962	−	0.102184i	−0.894015	+	0.448037i	$0.852123\pi$
$578$	26.2436			1.09159
$579$	23.5443	+	7.80848i	0.978470	+	0.324509i
$580$	−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
$584$	6.03273	+	10.4490i	0.249636	+	0.432383i
$585$	24.0247	+	17.9050i	0.993298	+	0.740279i
$586$	−10.7101	+	18.5505i	−0.442432	+	0.766315i
$587$	2.34795	−	4.06678i	0.0969105	−	0.167854i	−0.813494	−	0.581573i	$-0.802437\pi$
$587$	2.34795	−	4.06678i	0.0969105	−	0.167854i	0.910404	+	0.413720i	$0.135771\pi$
$588$		0			0
$589$	−3.02654	−	5.24212i	−0.124706	−	0.215998i
$590$	25.5636			1.05244
$591$	0.847955	+	4.11200i	0.0348802	+	0.169145i
$592$	2.77747			0.114153
$593$	−0.636024	+	1.10163i	−0.0261184	+	0.0452383i	−0.878789	−	0.477210i	$-0.841648\pi$
$593$	−0.636024	+	1.10163i	−0.0261184	+	0.0452383i	0.852671	+	0.522449i	$0.174981\pi$
$594$	3.24907	−	6.95362i	0.133311	−	0.285310i
$595$		0			0
$596$	−0.166896	+	0.289073i	−0.00683634	+	0.0118409i
$597$	−7.90909	+	7.03484i	−0.323697	+	0.287917i
$598$	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	$0.813224\pi$
$600$	3.03892	+	14.7367i	0.124063	+	0.601623i
$601$	6.71634	−	11.6330i	0.273965	−	0.474522i	−0.695908	−	0.718131i	$-0.744998\pi$
$601$	6.71634	−	11.6330i	0.273965	−	0.474522i	0.969874	+	0.243609i	$0.0783314\pi$
$602$		0			0
$603$	−3.31089	+	28.2005i	−0.134830	+	1.14841i
$604$	9.95489	−	17.2424i	0.405059	−	0.701582i
$605$	32.6240			1.32635
$606$	−6.80037	+	6.04868i	−0.276246	+	0.245711i
$607$	4.58465			0.186085			0.0930425	−	0.995662i	$-0.470341\pi$
$607$	4.58465			0.186085			0.0930425	+	0.995662i	$0.470341\pi$
$608$	0.444368	+	0.769668i	0.0180215	+	0.0312142i
$609$		0			0
$610$	10.6051	−	18.3685i	0.429387	−	0.743720i
$611$	9.43199	−	16.3367i	0.381577	−	0.660911i
$612$	−18.1185	+	7.80451i	−0.732399	+	0.315479i
$613$	−11.0538	−	19.1457i	−0.446458	−	0.773287i	0.551695	−	0.834046i	$-0.313981\pi$
$613$	−11.0538	−	19.1457i	−0.446458	−	0.773287i	−0.998152	+	0.0607587i	$0.980648\pi$
$614$	−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	0.961206	−	0.275832i	$-0.0889534\pi$
$617$	6.00433	+	10.3998i	0.241725	+	0.418680i	−0.719481	+	0.694513i	$0.755620\pi$
$618$	−2.15638	+	1.91802i	−0.0867422	+	0.0771539i
$619$	17.5636			0.705941			0.352970	−	0.935634i	$-0.385172\pi$
$619$	17.5636			0.705941			0.352970	+	0.935634i	$0.385172\pi$
$620$	−12.5989	−	21.8219i	−0.505983	−	0.876389i
$621$	−18.7200	−	26.7789i	−0.751207	−	1.07460i
$622$	11.7207			0.469956
$623$		0			0
$624$	4.43818	+	1.47192i	0.177669	+	0.0589240i
$625$	7.03204			0.281282
$626$	−13.3869	+	23.1868i	−0.535047	+	0.926729i
$627$	−2.15816	−	0.715753i	−0.0861885	−	0.0285844i
$628$	−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
$633$	−14.8120	+	13.1747i	−0.588724	+	0.523648i
$634$	−0.951246	+	1.64761i	−0.0377788	+	0.0654348i
$635$	10.5687			0.419406
$636$	1.12296	+	5.44556i	0.0445281	+	0.215931i
$637$		0			0
$638$	3.70829			0.146813
$639$	15.0567	−	6.48564i	0.595635	−	0.256568i
$640$	1.84981	+	3.20397i	0.0731203	+	0.126648i
$641$	−28.9839			−1.14480			−0.572398	−	0.819976i	$-0.693987\pi$
$641$	−28.9839			−1.14480			−0.572398	+	0.819976i	$0.693987\pi$
$642$	3.76578	+	18.2614i	0.148624	+	0.720722i
$643$	−6.03087	−	10.4458i	−0.237834	−	0.411941i	0.722258	−	0.691623i	$-0.243104\pi$
$643$	−6.03087	−	10.4458i	−0.237834	−	0.411941i	−0.960093	+	0.279682i	$0.909771\pi$
$644$		0			0
$645$	−0.0752956	−	0.0249718i	−0.00296476	−	0.000983262i
$646$	2.92216	+	5.06132i	0.114971	+	0.199135i
$647$	−18.8825	−	32.7055i	−0.742349	−	1.28579i	−0.951423	−	0.307887i	$-0.900378\pi$
$647$	−18.8825	−	32.7055i	−0.742349	−	1.28579i	0.209073	−	0.977900i	$-0.432955\pi$
$648$	6.18292	−	6.53999i	0.242888	−	0.256915i
$649$	−5.10322	+	8.83903i	−0.200319	+	0.346962i
$650$	11.7262	−	20.3103i	0.459938	−	0.796636i
$651$		0			0
$652$	4.03706	+	6.99240i	0.158104	+	0.273843i
$653$	37.4079			1.46388			0.731942	−	0.681366i	$-0.238614\pi$
$653$	37.4079			1.46388			0.731942	+	0.681366i	$0.238614\pi$
$654$	−0.310892	−	0.103107i	−0.0121569	−	0.00403182i
$655$	0.575984			0.0225056
$656$	2.05563	−	3.56046i	0.0802589	−	0.139013i
$657$	−29.0228	−	21.6299i	−1.13229	−	0.843864i
$658$		0			0
$659$	14.9356	−	25.8693i	0.581810	−	1.00772i	−0.413455	−	0.910524i	$-0.635678\pi$
$659$	14.9356	−	25.8693i	0.581810	−	1.00772i	0.995265	−	0.0971993i	$-0.0309884\pi$
$660$	−8.98398	−	2.97954i	−0.349701	−	0.115978i
$661$	2.80401	−	4.85669i	0.109063	−	0.188904i	−0.806328	−	0.591469i	$-0.798548\pi$
$661$	2.80401	−	4.85669i	0.109063	−	0.188904i	0.915391	+	0.402566i	$0.131881\pi$
$662$	−2.78366	+	4.82144i	−0.108190	+	0.187391i
$663$	29.1854	+	9.67933i	1.13347	+	0.375914i
$664$	−2.23855	+	3.87728i	−0.0868726	+	0.150468i
$665$		0			0
$666$	−7.65266	+	3.29636i	−0.296534	+	0.127731i
$667$	7.89307	−	13.6712i	0.305621	−	0.529351i
$668$	19.4858			0.753927
$669$	11.8738	+	3.93795i	0.459068	+	0.152250i
$670$	35.0159			1.35278
$671$	4.23414	+	7.33375i	0.163457	+	0.283116i
$672$		0			0
$673$	−4.72253	+	8.17966i	−0.182040	+	0.315303i	−0.942575	−	0.333994i	$-0.891603\pi$
$673$	−4.72253	+	8.17966i	−0.182040	+	0.315303i	0.760535	+	0.649297i	$0.224937\pi$
$674$	−16.8869	+	29.2489i	−0.650458	+	1.12663i
$675$	−25.8628	−	36.9967i	−0.995460	−	1.42401i
$676$	2.85600	+	4.94674i	0.109846	+	0.190259i
$677$	5.53087	+	9.57975i	0.212569	+	0.368180i	0.952518	−	0.304483i	$-0.0984837\pi$
$677$	5.53087	+	9.57975i	0.212569	+	0.368180i	−0.739949	+	0.672663i	$0.765150\pi$
$678$	−22.2985	−	7.39530i	−0.856369	−	0.284015i
$679$		0			0
$680$	12.1643	+	21.0693i	0.466481	+	0.807970i
$681$	−4.77678	−	23.1641i	−0.183047	−	0.887651i
$682$	10.0604			0.385231
$683$	−4.41961	−	7.65499i	−0.169112	−	0.292910i	0.768996	−	0.639253i	$-0.220757\pi$
$683$	−4.41961	−	7.65499i	−0.169112	−	0.292910i	−0.938108	+	0.346343i	$0.887423\pi$
$684$	−2.13781	−	1.59325i	−0.0817411	−	0.0609195i
$685$	12.6218			0.482254
$686$		0			0
$687$	−6.07784	−	29.4734i	−0.231884	−	1.12448i
$688$	−0.0123797			−0.000471972
$689$	4.33310	−	7.50516i	0.165078	−	0.285924i
$690$	−30.1069	+	26.7789i	−1.14615	+	1.01946i
$691$	12.5309	+	21.7041i	0.476697	+	0.825663i	0.999643	−	0.0267023i	$-0.00850061\pi$
$691$	12.5309	+	21.7041i	0.476697	+	0.825663i	−0.522947	+	0.852365i	$0.675167\pi$
$692$	−22.5636			−0.857740
$693$		0			0
$694$	−30.4065			−1.15422
$695$	−24.9920	−	43.2873i	−0.947999	−	1.64198i
$696$	4.12729	+	1.36881i	0.156444	+	0.0518848i
$697$	13.5178	−	23.4135i	0.512023	−	0.886850i
$698$	−12.5956			−0.476752
$699$	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	$0.806705\pi$
$702$	−13.9752	+	1.21179i	−0.527461	+	0.0457361i
$703$	1.23422	+	2.13773i	0.0465495	+	0.0806260i
$704$	−1.47710			−0.0556703
$705$	−33.4567	+	29.7585i	−1.26005	+	1.12077i
$706$	−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	$0.692898\pi$
$710$	−10.1087	−	17.5088i	−0.379373	−	0.657094i
$711$	27.5480	+	20.5308i	1.03313	+	0.769965i
$712$	4.43818	−	7.68715i	0.166328	−	0.288088i
$713$	21.4134	−	37.0891i	0.801939	−	1.38900i
$714$		0			0
$715$	7.37636	+	12.7762i	0.275860	+	0.477804i
$716$	−0.333792			−0.0124744
$717$	−24.5254	+	21.8144i	−0.915917	+	0.814674i
$718$	6.89602			0.257357
$719$	−6.06182	+	10.4994i	−0.226068	+	0.391561i	−0.956639	−	0.291275i	$-0.905920\pi$
$719$	−6.06182	+	10.4994i	−0.226068	+	0.391561i	0.730571	+	0.682836i	$0.239254\pi$
$720$	−8.89926	−	6.63238i	−0.331656	−	0.247174i
$721$		0			0
$722$	9.10507	−	15.7705i	0.338856	−	0.586915i
$723$	8.57234	+	41.5700i	0.318809	+	1.54600i
$724$	11.6211	−	20.1283i	0.431895	−	0.748063i
$725$	10.9048	−	18.8876i	0.404993	−	0.701468i
$726$	−11.4123	+	10.1508i	−0.423551	+	0.376733i
$727$	−23.0908	+	39.9945i	−0.856392	+	1.48331i	0.0189562	+	0.999820i	$0.493966\pi$
$727$	−23.0908	+	39.9945i	−0.856392	+	1.48331i	−0.875348	+	0.483494i	$0.839368\pi$
$728$		0			0
$729$	−9.27375	+	25.3574i	−0.343472	+	0.939163i
$730$	−22.3189	+	38.6574i	−0.826058	+	1.43077i
$731$	−0.0814088			−0.00301101
$732$	2.00550	+	9.72530i	0.0741255	+	0.359458i
$733$	36.0297			1.33079			0.665394	−	0.746493i	$-0.268264\pi$
$733$	36.0297			1.33079			0.665394	+	0.746493i	$0.268264\pi$
$734$	11.5618	+	20.0257i	0.426755	+	0.739161i
$735$		0			0
$736$	−3.14400	+	5.44556i	−0.115889	+	0.200726i
$737$	−6.99017	+	12.1073i	−0.257486	+	0.445979i
$738$	−1.43818	+	12.2497i	−0.0529401	+	0.450916i
$739$	23.2119	+	40.2042i	0.853865	+	1.47894i	0.877694	+	0.479221i	$0.159081\pi$
$739$	23.2119	+	40.2042i	0.853865	+	1.47894i	−0.0238296	+	0.999716i	$0.507586\pi$
$740$	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	0.876802	−	0.480852i	$-0.159673\pi$
$743$	0.598884	+	1.03730i	0.0219709	+	0.0380548i	−0.854831	+	0.518907i	$0.826339\pi$
$744$	11.1971	+	3.71351i	0.410505	+	0.136144i
$745$	−1.23491			−0.0452435
$746$	−14.5822	−	25.2571i	−0.533891	−	0.924727i
$747$	1.56615	−	13.3397i	0.0573025	−	0.488073i
$748$	−9.71339			−0.355157
$749$		0			0
$750$	−17.6545	+	15.7030i	−0.644652	+	0.573394i
$751$	48.1199			1.75592			0.877961	−	0.478733i	$-0.158904\pi$
$751$	48.1199			1.75592			0.877961	+	0.478733i	$0.158904\pi$
$752$	−3.49381	+	6.05146i	−0.127406	+	0.220674i
$753$	4.24102	+	20.5660i	0.154551	+	0.749468i
$754$	−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
$759$	−3.24907	−	15.7558i	−0.117934	−	0.571898i
$760$	−1.64400	+	2.84748i	−0.0596340	+	0.103289i
$761$	37.5402			1.36083			0.680416	−	0.732826i	$-0.261799\pi$
$761$	37.5402			1.36083			0.680416	+	0.732826i	$0.261799\pi$
$762$	−3.69708	+	3.28842i	−0.133931	+	0.119127i
$763$		0			0
$764$	−16.3214			−0.590488
$765$	−58.5214	−	43.6144i	−2.11584	−	1.57688i
$766$	−1.41783	−	2.45575i	−0.0512281	−	0.0887297i
$767$	18.6538			0.673551
$768$	−1.64400	−	0.545231i	−0.0593226	−	0.0196743i
$769$	13.4592	+	23.3121i	0.485352	+	0.840654i	0.999858	−	0.0168324i	$-0.00535818\pi$
$769$	13.4592	+	23.3121i	0.485352	+	0.840654i	−0.514506	+	0.857486i	$0.672025\pi$
$770$		0			0
$771$	2.87154	+	13.9250i	0.103416	+	0.501497i
$772$	7.16071	+	12.4027i	0.257719	+	0.446383i
$773$	−25.1130	−	43.4971i	−0.903254	−	1.56448i	−0.823245	−	0.567687i	$-0.807838\pi$
$773$	−25.1130	−	43.4971i	−0.903254	−	1.56448i	−0.0800089	−	0.996794i	$-0.525495\pi$
$774$	0.0341093	−	0.0146925i	0.00122603	−	0.000528111i
$775$	29.5840	−	51.2409i	1.06269	−	1.84063i
$776$	6.58836	−	11.4114i	0.236508	−	0.409645i
$777$		0			0
$778$	9.30401	+	16.1150i	0.333565	+	0.577752i
$779$	3.65383			0.130912
$780$	3.49381	+	16.9426i	0.125098	+	0.606642i
$781$	8.07194			0.288837
$782$	−20.6749	+	35.8099i	−0.739332	+	1.28056i
$783$	−12.9963	+	1.12691i	−0.464449	+	0.0402723i
$784$		0			0
$785$	12.8800	−	22.3088i	0.459707	−	0.796236i
$786$	−0.201487	+	0.179216i	−0.00718682	+	0.00639241i
$787$	−0.829462	+	1.43667i	−0.0295671	+	0.0512118i	−0.880430	−	0.474176i	$-0.842746\pi$
$787$	−0.829462	+	1.43667i	−0.0295671	+	0.0512118i	0.850863	+	0.525387i	$0.176080\pi$
$788$	−1.21201	+	2.09926i	−0.0431760	+	0.0747830i
$789$	−1.87017	−	9.06902i	−0.0665797	−	0.322866i
$790$	21.1847	−	36.6930i	0.753718	−	1.30548i
$791$		0			0
$792$	4.06979	−	1.75305i	0.144614	−	0.0622920i
$793$	7.73855	−	13.4036i	0.274804	−	0.475974i
$794$	−20.5760			−0.730214
$795$	−15.3702	+	13.6712i	−0.545124	+	0.484867i
$796$	−6.11126			−0.216608
$797$	15.3702	+	26.6219i	0.544439	+	0.942996i	0.998642	+	0.0520981i	$0.0165908\pi$
$797$	15.3702	+	26.6219i	0.544439	+	0.942996i	−0.454203	+	0.890898i	$0.650076\pi$
$798$		0			0
$799$	−22.9752	+	39.7943i	−0.812806	+	1.40782i
$800$	−4.34362	+	7.52338i	−0.153570	+	0.265992i
$801$	−3.10507	+	26.4474i	−0.109712	+	0.934473i
$802$	3.37704	+	5.84921i	0.119248	+	0.206543i
$803$	−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
$807$	23.9222	−	21.2779i	0.842100	−	0.749016i
$808$	−5.25457			−0.184855
$809$	−1.44251	−	2.49850i	−0.0507159	−	0.0878425i	0.839553	−	0.543278i	$-0.182817\pi$
$809$	−1.44251	−	2.49850i	−0.0507159	−	0.0878425i	−0.890269	+	0.455435i	$0.849484\pi$
$810$	32.3912	+	7.71212i	1.13811	+	0.270976i
$811$	−28.5461			−1.00239			−0.501195	−	0.865334i	$-0.667106\pi$
$811$	−28.5461			−1.00239			−0.501195	+	0.865334i	$0.667106\pi$
$812$		0			0
$813$	12.0913	+	4.01008i	0.424061	+	0.140640i
$814$	−4.10260			−0.143796
$815$	−14.9356	+	25.8693i	−0.523172	+	0.906161i
$816$	−10.8109	−	3.58543i	−0.378457	−	0.125515i
$817$	−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	$0.877728\pi$
$822$	−4.41528	+	3.92723i	−0.154001	+	0.136978i
$823$	−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	$0.916861\pi$
$824$	−1.66621			−0.0580451
$825$	−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	$0.493241\pi$
$828$	2.19963	−	18.7353i	0.0764424	−	0.651096i
$829$	7.07530	+	12.2548i	0.245735	+	0.425626i	0.962338	−	0.271856i	$-0.0876373\pi$
$829$	7.07530	+	12.2548i	0.245735	+	0.425626i	−0.716603	+	0.697481i	$0.754304\pi$
$830$	−16.5636			−0.574931
$831$	−3.18292	−	15.4350i	−0.110414	−	0.535433i
$832$	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
$836$	−0.656376	−	1.13688i	−0.0227012	−	0.0393197i
$837$	−35.2581	+	3.05723i	−1.21870	+	0.105673i
$838$	4.32141	−	7.48491i	0.149281	−	0.258562i
$839$	−1.19599	+	2.07151i	−0.0412900	+	0.0715164i	−0.885932	−	0.463815i	$-0.846480\pi$
$839$	−1.19599	+	2.07151i	−0.0412900	+	0.0715164i	0.844642	+	0.535332i	$0.179813\pi$
$840$		0			0
$841$	11.3486	+	19.6564i	0.391333	+	0.677808i
$842$	−37.1272			−1.27949
$843$	19.7422	+	6.54750i	0.679957	+	0.225508i
$844$	−11.4451			−0.393955
$845$	−10.5662	+	18.3011i	−0.363487	+	0.629577i
$846$	2.44437	−	20.8199i	0.0840391	−	0.715802i
$847$		0			0
$848$	−1.60507	+	2.78007i	−0.0551185	+	0.0954680i
$849$	16.1817	+	5.36667i	0.555356	+	0.184184i
$850$	−28.5636	+	49.4736i	−0.979724	+	1.69693i
$851$	−8.73236	+	15.1249i	−0.299341	+	0.518475i
$852$	8.98398	+	2.97954i	0.307786	+	0.102077i
$853$	8.33998	−	14.4453i	0.285556	−	0.494597i	−0.687188	−	0.726479i	$-0.741155\pi$
$853$	8.33998	−	14.4453i	0.285556	−	0.494597i	0.972744	+	0.231883i	$0.0744886\pi$
$854$		0			0
$855$	1.15019	−	9.79669i	0.0393355	−	0.335040i
$856$	−5.38255	+	9.32284i	−0.183972	+	0.318648i
$857$	13.8516			0.473162			0.236581	−	0.971612i	$-0.423973\pi$
$857$	13.8516			0.473162			0.236581	+	0.971612i	$0.423973\pi$
$858$	−6.55563	−	2.17417i	−0.223806	−	0.0742251i
$859$	−48.4944			−1.65461			−0.827304	−	0.561754i	$-0.810127\pi$
$859$	−48.4944			−1.65461			−0.827304	+	0.561754i	$0.810127\pi$
$860$	−0.0229002	−	0.0396643i	−0.000780889	−	0.00135254i
$861$		0			0
$862$	−4.71015	+	8.15822i	−0.160428	+	0.277870i
$863$	2.96541	−	5.13624i	0.100944	−	0.174840i	−0.811130	−	0.584866i	$-0.801147\pi$
$863$	2.96541	−	5.13624i	0.100944	−	0.174840i	0.912074	+	0.410026i	$0.134480\pi$
$864$	5.17673	−	0.448873i	0.176116	−	0.0152710i
$865$	−41.7385	−	72.2932i	−1.41915	−	2.45804i
$866$	−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
$870$	3.24907	+	15.7558i	0.110154	+	0.534170i
$871$	25.5512			0.865770
$872$	−0.0945538	−	0.163772i	−0.00320200	−	0.00554602i
$873$	−4.60940	+	39.2605i	−0.156005	+	1.32877i
$874$	−5.58836			−0.189029
$875$		0			0
$876$	−4.22067	−	20.4673i	−0.142603	−	0.691527i
$877$	3.92944			0.132688			0.0663439	−	0.997797i	$-0.478867\pi$
$877$	3.92944			0.132688			0.0663439	+	0.997797i	$0.478867\pi$
$878$	−4.98398	+	8.63250i	−0.168201	+	0.291333i
$879$	27.7218	−	24.6575i	0.935032	−	0.831676i
$880$	−2.73236	−	4.73259i	−0.0921078	−	0.159535i
$881$	−37.6552			−1.26864			−0.634318	−	0.773072i	$-0.718719\pi$
$881$	−37.6552			−1.26864			−0.634318	+	0.773072i	$0.718719\pi$
$882$		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
$885$	−42.0265	−	13.9381i	−1.41270	−	0.468523i
$886$	7.84981	−	13.5963i	0.263720	−	0.456776i
$887$	36.9876			1.24192			0.620961	−	0.783841i	$-0.286742\pi$
$887$	36.9876			1.24192			0.620961	+	0.783841i	$0.286742\pi$
$888$	−4.56615	−	1.51436i	−0.153230	−	0.0508187i
$889$		0			0
$890$	32.8392			1.10077
$891$	−9.13279	+	9.66022i	−0.305960	+	0.323630i
$892$	3.61126	+	6.25489i	0.120914	+	0.209429i
$893$	−6.21015			−0.207815
$894$	0.431988	−	0.384237i	0.0144478	−	0.0128508i
$895$	−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
$899$	−8.54944	−	14.8081i	−0.285140	−	0.493877i
$900$	3.03892	−	25.8840i	0.101297	−	0.862799i
$901$	−10.5549	+	18.2817i	−0.351636	+	0.609052i
$902$	−3.03637	+	5.25915i	−0.101100	+	0.175111i
$903$		0			0
$904$	−6.78180	−	11.7464i	−0.225559	−	0.390680i
$905$	85.9875			2.85832
$906$	−25.7669	+	22.9187i	−0.856047	+	0.761422i
$907$	−39.0159			−1.29550			−0.647752	−	0.761852i	$-0.724291\pi$
$907$	−39.0159			−1.29550			−0.647752	+	0.761852i	$0.724291\pi$
$908$	6.82760	−	11.8258i	0.226582	−	0.392451i
$909$	14.4777	−	6.23623i	0.480195	−	0.206843i
$910$		0			0
$911$	−12.8090	+	22.1859i	−0.424382	+	0.735052i	−0.996363	−	0.0852158i	$-0.972842\pi$
$911$	−12.8090	+	22.1859i	−0.424382	+	0.735052i	0.571980	+	0.820267i	$0.306175\pi$
$912$	−0.310892	−	1.50761i	−0.0102947	−	0.0499221i
$913$	3.30656	−	5.72713i	0.109431	−	0.189540i
$914$	−16.3541	+	28.3262i	−0.540947	+	0.936948i
$915$	−27.4498	+	24.4156i	−0.907462	+	0.807154i
$916$	8.68725	−	15.0468i	0.287035	−	0.497159i
$917$		0			0
$918$	34.0421	−	2.95178i	1.12356	−	0.0974234i
$919$	10.3367	−	17.9038i	0.340978	−	0.590591i	−0.643637	−	0.765331i	$-0.722575\pi$
$919$	10.3367	−	17.9038i	0.340978	−	0.590591i	0.984615	+	0.174740i	$0.0559086\pi$
$920$	−23.2632			−0.766966
$921$	1.98948	+	9.64761i	0.0655556	+	0.317900i
$922$	−4.14331			−0.136453
$923$	−7.37636	−	12.7762i	−0.242796	−	0.420535i
$924$		0			0
$925$	−12.0643	+	20.8960i	−0.396672	+	0.687055i
$926$	−8.34176	+	14.4484i	−0.274127	+	0.474803i
$927$	4.59084	−	1.97749i	0.150783	−	0.0649492i
$928$	1.25526	+	2.17417i	0.0412059	+	0.0713708i
$929$	−1.87017	−	3.23922i	−0.0613582	−	0.106275i	0.833715	−	0.552196i	$-0.186210\pi$
$929$	−1.87017	−	3.23922i	−0.0613582	−	0.106275i	−0.895073	+	0.445920i	$0.852877\pi$
$930$	8.81453	+	42.7444i	0.289040	+	1.40165i
$931$		0			0
$932$	7.62110	+	13.2001i	0.249637	+	0.432384i
$933$	−19.2687	−	6.39047i	−0.630830	−	0.209215i
$934$	29.9171			0.978916
$935$	−17.9680	−	31.1214i	−0.587615	−	1.01778i
$936$	−6.49381	−	4.83967i	−0.212257	−	0.158189i
$937$	27.1345			0.886445			0.443223	−	0.896412i	$-0.353835\pi$
$937$	27.1345			0.886445			0.443223	+	0.896412i	$0.353835\pi$
$938$		0			0
$939$	34.6501	−	30.8200i	1.13076	−	1.00577i
$940$	−25.8516			−0.843186
$941$	3.16435	−	5.48081i	0.103155	−	0.178669i	−0.809828	−	0.586667i	$-0.800440\pi$
$941$	3.16435	−	5.48081i	0.103155	−	0.178669i	0.912983	+	0.407998i	$0.133773\pi$
$942$	2.43571	+	11.8115i	0.0793596	+	0.384840i
$943$	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	$-0.336362\pi$
$948$	4.00619	+	19.4273i	0.130115	+	0.630968i
$949$	−16.2861	+	28.2084i	−0.528670	+	0.915684i
$950$	−7.72067			−0.250492
$951$	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	$0.477868\pi$
$954$	1.12296	−	9.56475i	0.0363570	−	0.309670i
$955$	−30.1916	−	52.2933i	−0.976977	−	1.69217i
$956$	−18.9505			−0.612902
$957$	−6.09641	−	2.02187i	−0.197069	−	0.0653579i
$958$	−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
$962$	3.74907	+	6.49358i	0.120875	+	0.209361i
$963$	3.76578	−	32.0750i	0.121351	−	1.03360i
$964$	−12.2527	+	21.2223i	−0.394633	+	0.683525i
$965$	−26.4920	+	45.8854i	−0.852806	+	1.47710i
$966$		0			0
$967$	−7.59201	−	13.1497i	−0.244142	−	0.422867i	0.717748	−	0.696303i	$-0.245173\pi$
$967$	−7.59201	−	13.1497i	−0.244142	−	0.422867i	−0.961890	+	0.273436i	$0.911840\pi$
$968$	−8.81818			−0.283427
$969$	−2.04442	−	9.91405i	−0.0656763	−	0.318485i
$970$	48.7490			1.56524
$971$	−1.62364	+	2.81223i	−0.0521052	+	0.0902489i	−0.890902	−	0.454196i	$-0.849926\pi$
$971$	−1.62364	+	2.81223i	−0.0521052	+	0.0902489i	0.838796	+	0.544445i	$0.183260\pi$
$972$	−13.7305	+	7.38061i	−0.440406	+	0.236733i
$973$		0			0
$974$	−14.0309	+	24.3022i	−0.449578	+	0.778692i
$975$	−30.3516	+	26.9966i	−0.972029	+	0.864584i
$976$	−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	$0.246653\pi$
$978$	−2.82444	−	13.6966i	−0.0903157	−	0.437969i
$979$	−6.55563	+	11.3547i	−0.209519	+	0.362897i
$980$		0			0
$981$	0.454888	+	0.339016i	0.0145235	+	0.0108240i
$982$	17.0734	−	29.5721i	0.544835	−	0.943682i
$983$	−12.3832			−0.394961			−0.197481	−	0.980307i	$-0.563276\pi$
$983$	−12.3832			−0.394961			−0.197481	+	0.980307i	$0.563276\pi$
$984$	−5.32072	+	4.73259i	−0.169618	+	0.150869i
$985$	−8.96796			−0.285743
$986$	8.25457	+	14.2973i	0.262879	+	0.455320i
$987$		0			0
$988$	−1.19963	+	2.07782i	−0.0381653	+	0.0661042i
$989$	0.0389218	−	0.0674145i	0.00123764	−	0.00214366i
$990$	13.1451	+	9.79669i	0.417778	+	0.311359i
$991$	−3.32760	−	5.76358i	−0.105705	−	0.183086i	0.808321	−	0.588742i	$-0.200377\pi$
$991$	−3.32760	−	5.76358i	−0.105705	−	0.183086i	−0.914026	+	0.405656i	$0.867043\pi$
$992$	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
$996$	5.79418	−	5.15371i	0.183596	−	0.163302i
$997$	−4.80208			−0.152083			−0.0760417	−	0.997105i	$-0.524228\pi$
$997$	−4.80208			−0.152083			−0.0760417	+	0.997105i	$0.524228\pi$
$998$	1.14035	+	1.97515i	0.0360973	+	0.0625223i
$999$	14.3782	−	1.24673i	0.454907	−	0.0394449i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.1	✓	6	7.3	odd	6
126.2.e.d.121.1	yes	6	63.13	odd	6
126.2.h.c.67.1	yes	6	63.31	odd	6
126.2.h.c.79.1	yes	6	7.6	odd	2
378.2.e.c.37.3		6	63.41	even	6
378.2.e.c.235.3		6	21.17	even	6
378.2.h.d.289.1		6	21.20	even	2
378.2.h.d.361.1		6	63.59	even	6
882.2.e.p.373.3		6	9.4	even	3
882.2.e.p.655.3		6	7.4	even	3
882.2.f.l.295.3		6	7.5	odd	6
882.2.f.l.589.3		6	63.40	odd	6
882.2.f.m.295.1		6	7.2	even	3
882.2.f.m.589.1		6	63.58	even	3
882.2.h.o.67.3		6	63.4	even	3	inner
882.2.h.o.79.3		6	1.1	even	1	trivial
1008.2.q.h.529.3		6	28.3	even	6
1008.2.q.h.625.3		6	252.139	even	6
1008.2.t.g.193.3		6	252.31	even	6
1008.2.t.g.961.3		6	28.27	even	2
1134.2.g.k.163.1		6	63.34	odd	6
1134.2.g.k.487.1		6	63.52	odd	6
1134.2.g.n.163.3		6	63.20	even	6
1134.2.g.n.487.3		6	63.38	even	6
2646.2.e.o.1549.1		6	9.5	odd	6
2646.2.e.o.2125.1		6	21.11	odd	6
2646.2.f.n.883.1		6	21.2	odd	6
2646.2.f.n.1765.1		6	63.23	odd	6
2646.2.f.o.883.3		6	21.5	even	6
2646.2.f.o.1765.3		6	63.5	even	6
2646.2.h.p.361.3		6	63.32	odd	6
2646.2.h.p.667.3		6	3.2	odd	2
3024.2.q.h.2305.3		6	252.167	odd	6
3024.2.q.h.2881.3		6	84.59	odd	6
3024.2.t.g.289.1		6	84.83	odd	2
3024.2.t.g.1873.1		6	252.59	odd	6
7938.2.a.bu.1.1		3	63.47	even	6
7938.2.a.bx.1.3		3	63.2	odd	6
7938.2.a.by.1.1		3	63.16	even	3
7938.2.a.cb.1.3		3	63.61	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.349814 + 1.69636i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.69963 q^{5} +(1.29418 - 1.15113i) q^{6} +1.00000 q^{8} +(-2.75526 + 1.18682i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.349814 + 1.69636i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.69963 q^{5} +(1.29418 - 1.15113i) q^{6} +1.00000 q^{8} +(-2.75526 + 1.18682i) q^{9} +(1.84981 + 3.20397i) q^{10} -1.47710 q^{11} +(-1.64400 - 0.545231i) q^{12} +(1.34981 + 2.33795i) q^{13} +(-1.29418 - 6.27589i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.28799 - 5.69497i) q^{17} +(2.40545 + 1.79272i) q^{18} +(0.444368 - 0.769668i) q^{19} +(1.84981 - 3.20397i) q^{20} +(0.738550 + 1.27921i) q^{22} +6.28799 q^{23} +(0.349814 + 1.69636i) q^{24} +8.68725 q^{25} +(1.34981 - 2.33795i) q^{26} +(-2.97710 - 4.25874i) q^{27} +(1.25526 - 2.17417i) q^{29} +(-4.78799 + 4.25874i) q^{30} +(3.40545 - 5.89841i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.516710 - 2.50569i) q^{33} +(-3.28799 + 5.69497i) q^{34} +(0.349814 - 2.97954i) q^{36} +(-1.38874 + 2.40536i) q^{37} -0.888736 q^{38} +(-3.49381 + 3.10761i) q^{39} -3.69963 q^{40} +(2.05563 + 3.56046i) q^{41} +(0.00618986 - 0.0107211i) q^{43} +(0.738550 - 1.27921i) q^{44} +(10.1934 - 4.39079i) q^{45} +(-3.14400 - 5.44556i) q^{46} +(-3.49381 - 6.05146i) q^{47} +(1.29418 - 1.15113i) q^{48} +(-4.34362 - 7.52338i) q^{50} +(8.51052 - 7.56979i) q^{51} -2.69963 q^{52} +(-1.60507 - 2.78007i) q^{53} +(-2.19963 + 4.70761i) q^{54} +5.46472 q^{55} +(1.46108 + 0.484566i) q^{57} -2.51052 q^{58} +(3.45489 - 5.98404i) q^{59} +(6.08217 + 2.01715i) q^{60} +(-2.86652 - 4.96497i) q^{61} -6.81089 q^{62} +1.00000 q^{64} +(-4.99381 - 8.64953i) q^{65} +(-1.91164 + 1.70033i) q^{66} +(4.73236 - 8.19669i) q^{67} +6.57598 q^{68} +(2.19963 + 10.6667i) q^{69} -5.46472 q^{71} +(-2.75526 + 1.18682i) q^{72} +(6.03273 + 10.4490i) q^{73} +2.77747 q^{74} +(3.03892 + 14.7367i) q^{75} +(0.444368 + 0.769668i) q^{76} +(4.43818 + 1.47192i) q^{78} +(-5.72617 - 9.91802i) q^{79} +(1.84981 + 3.20397i) q^{80} +(6.18292 - 6.53999i) q^{81} +(2.05563 - 3.56046i) q^{82} +(-2.23855 + 3.87728i) q^{83} +(12.1643 + 21.0693i) q^{85} -0.0123797 q^{86} +(4.12729 + 1.36881i) q^{87} -1.47710 q^{88} +(4.43818 - 7.68715i) q^{89} +(-8.89926 - 6.63238i) q^{90} +(-3.14400 + 5.44556i) q^{92} +(11.1971 + 3.71351i) q^{93} +(-3.49381 + 6.05146i) q^{94} +(-1.64400 + 2.84748i) q^{95} +(-1.64400 - 0.545231i) q^{96} +(6.58836 - 11.4114i) q^{97} +(4.06979 - 1.75305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 4 q^{3} - 3 q^{4} - 10 q^{5} + 2 q^{6} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 4 * q^3 - 3 * q^4 - 10 * q^5 + 2 * q^6 + 6 * q^8 - 4 * q^9	\( 6 q - 3 q^{2} - 4 q^{3} - 3 q^{4} - 10 q^{5} + 2 q^{6} + 6 q^{8} - 4 q^{9} + 5 q^{10} + 2 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{15} - 3 q^{16} + 4 q^{17} + 8 q^{18} + 3 q^{19} + 5 q^{20} - q^{22} + 14 q^{23} - 4 q^{24} + 4 q^{25} + 2 q^{26} - 7 q^{27} - 5 q^{29} - 5 q^{30} + 14 q^{31} - 3 q^{32} + 4 q^{33} + 4 q^{34} - 4 q^{36} - 9 q^{37} - 6 q^{38} - 3 q^{39} - 10 q^{40} + 12 q^{41} + 18 q^{43} - q^{44} + 31 q^{45} - 7 q^{46} - 3 q^{47} + 2 q^{48} - 2 q^{50} + 26 q^{51} - 4 q^{52} + 9 q^{53} - q^{54} - 14 q^{55} + 2 q^{57} + 10 q^{58} - 4 q^{59} + 7 q^{60} - 4 q^{61} - 28 q^{62} + 6 q^{64} - 12 q^{65} - 23 q^{66} + 5 q^{67} - 8 q^{68} + q^{69} + 14 q^{71} - 4 q^{72} + 25 q^{73} + 18 q^{74} + 25 q^{75} + 3 q^{76} + 9 q^{78} + 7 q^{79} + 5 q^{80} + 32 q^{81} + 12 q^{82} - 8 q^{83} + 14 q^{85} - 36 q^{86} + 20 q^{87} + 2 q^{88} + 9 q^{89} - 29 q^{90} - 7 q^{92} - 3 q^{93} - 3 q^{94} + 2 q^{95} + 2 q^{96} + 28 q^{97} - 41 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 4 * q^3 - 3 * q^4 - 10 * q^5 + 2 * q^6 + 6 * q^8 - 4 * q^9 + 5 * q^10 + 2 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^15 - 3 * q^16 + 4 * q^17 + 8 * q^18 + 3 * q^19 + 5 * q^20 - q^22 + 14 * q^23 - 4 * q^24 + 4 * q^25 + 2 * q^26 - 7 * q^27 - 5 * q^29 - 5 * q^30 + 14 * q^31 - 3 * q^32 + 4 * q^33 + 4 * q^34 - 4 * q^36 - 9 * q^37 - 6 * q^38 - 3 * q^39 - 10 * q^40 + 12 * q^41 + 18 * q^43 - q^44 + 31 * q^45 - 7 * q^46 - 3 * q^47 + 2 * q^48 - 2 * q^50 + 26 * q^51 - 4 * q^52 + 9 * q^53 - q^54 - 14 * q^55 + 2 * q^57 + 10 * q^58 - 4 * q^59 + 7 * q^60 - 4 * q^61 - 28 * q^62 + 6 * q^64 - 12 * q^65 - 23 * q^66 + 5 * q^67 - 8 * q^68 + q^69 + 14 * q^71 - 4 * q^72 + 25 * q^73 + 18 * q^74 + 25 * q^75 + 3 * q^76 + 9 * q^78 + 7 * q^79 + 5 * q^80 + 32 * q^81 + 12 * q^82 - 8 * q^83 + 14 * q^85 - 36 * q^86 + 20 * q^87 + 2 * q^88 + 9 * q^89 - 29 * q^90 - 7 * q^92 - 3 * q^93 - 3 * q^94 + 2 * q^95 + 2 * q^96 + 28 * q^97 - 41 * q^99

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