LMFDB - Embedded newform 882.2.m.a.587.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(293,882)]

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([5, 3]))

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

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

chi := DirichletCharacter("882.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.m (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			587.6
Root			$1.71298 - 0.256290i$ of defining polynomial
Character	$\chi$	$=$	882.587
Dual form			882.2.m.a.293.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-1.43162 - 0.974922i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.80966 + 3.13442i) q^{5} +(-0.752355 - 1.56012i) q^{6} +1.00000i q^{8} +(1.09905 + 2.79143i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-1.43162 - 0.974922i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.80966 + 3.13442i) q^{5} +(-0.752355 - 1.56012i) q^{6} +1.00000i q^{8} +(1.09905 + 2.79143i) q^{9} +3.61932i q^{10} +(1.73534 + 1.00190i) q^{11} +(0.128499 - 1.72728i) q^{12} +(-2.95206 + 1.70437i) q^{13} +(0.465079 - 6.25156i) q^{15} +(-0.500000 + 0.866025i) q^{16} -6.17418 q^{17} +(-0.443907 + 2.96698i) q^{18} -1.01308i q^{19} +(-1.80966 + 3.13442i) q^{20} +(1.00190 + 1.73534i) q^{22} +(2.62232 - 1.51400i) q^{23} +(0.974922 - 1.43162i) q^{24} +(-4.04972 + 7.01433i) q^{25} -3.40874 q^{26} +(1.14800 - 5.06775i) q^{27} +(5.04560 + 2.91308i) q^{29} +(3.52855 - 5.18147i) q^{30} +(-0.787812 + 0.454844i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.50757 - 3.12615i) q^{33} +(-5.34700 - 3.08709i) q^{34} +(-1.86792 + 2.34752i) q^{36} -7.33650 q^{37} +(0.506540 - 0.877353i) q^{38} +(5.88785 + 0.438020i) q^{39} +(-3.13442 + 1.80966i) q^{40} +(2.85045 + 4.93712i) q^{41} +(-2.39949 + 4.15605i) q^{43} +2.00379i q^{44} +(-6.76060 + 8.49643i) q^{45} +3.02799 q^{46} +(-1.11511 + 1.93143i) q^{47} +(1.56012 - 0.752355i) q^{48} +(-7.01433 + 4.04972i) q^{50} +(8.83906 + 6.01935i) q^{51} +(-2.95206 - 1.70437i) q^{52} -8.75365i q^{53} +(3.52808 - 3.81480i) q^{54} +7.25237i q^{55} +(-0.987674 + 1.45034i) q^{57} +(2.91308 + 5.04560i) q^{58} +(4.49313 + 7.78233i) q^{59} +(5.64655 - 2.72301i) q^{60} +(12.7410 + 7.35603i) q^{61} -0.909687 q^{62} -1.00000 q^{64} +(-10.6844 - 6.16866i) q^{65} +(0.257486 - 3.46111i) q^{66} +(4.15821 + 7.20222i) q^{67} +(-3.08709 - 5.34700i) q^{68} +(-5.23019 - 0.389094i) q^{69} -0.466287i q^{71} +(-2.79143 + 1.09905i) q^{72} -4.21492i q^{73} +(-6.35359 - 3.66825i) q^{74} +(12.6361 - 6.09366i) q^{75} +(0.877353 - 0.506540i) q^{76} +(4.88001 + 3.32326i) q^{78} +(-1.91267 + 3.31284i) q^{79} -3.61932 q^{80} +(-6.58416 + 6.13586i) q^{81} +5.70089i q^{82} +(4.00481 - 6.93654i) q^{83} +(-11.1732 - 19.3525i) q^{85} +(-4.15605 + 2.39949i) q^{86} +(-4.38334 - 9.08948i) q^{87} +(-1.00190 + 1.73534i) q^{88} -4.78647 q^{89} +(-10.1031 + 3.97782i) q^{90} +(2.62232 + 1.51400i) q^{92} +(1.57128 + 0.116894i) q^{93} +(-1.93143 + 1.11511i) q^{94} +(3.17542 - 1.83333i) q^{95} +(1.72728 + 0.128499i) q^{96} +(10.1835 + 5.87944i) q^{97} +(-0.889499 + 5.94521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 6 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 6 * q^9	$ 16 q + 8 q^{4} + 6 q^{9} - 12 q^{11} - 6 q^{13} - 18 q^{15} - 8 q^{16} - 36 q^{17} + 6 q^{23} + 6 q^{24} - 8 q^{25} + 24 q^{26} - 36 q^{27} + 6 q^{29} + 18 q^{30} - 6 q^{31} - 18 q^{33} + 4 q^{37} + 42 q^{39} + 6 q^{41} - 2 q^{43} - 42 q^{45} - 12 q^{46} - 18 q^{47} - 12 q^{50} - 6 q^{51} - 6 q^{52} + 6 q^{57} + 6 q^{58} + 30 q^{59} - 12 q^{60} + 60 q^{61} - 36 q^{62} - 16 q^{64} - 42 q^{65} - 24 q^{66} + 14 q^{67} - 18 q^{68} + 42 q^{69} - 12 q^{72} - 18 q^{74} + 30 q^{75} - 16 q^{79} - 18 q^{81} - 12 q^{85} - 24 q^{86} + 24 q^{87} - 48 q^{89} - 18 q^{90} + 6 q^{92} + 12 q^{93} + 66 q^{95} + 6 q^{96} - 6 q^{97} + 18 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 6 * q^9 - 12 * q^11 - 6 * q^13 - 18 * q^15 - 8 * q^16 - 36 * q^17 + 6 * q^23 + 6 * q^24 - 8 * q^25 + 24 * q^26 - 36 * q^27 + 6 * q^29 + 18 * q^30 - 6 * q^31 - 18 * q^33 + 4 * q^37 + 42 * q^39 + 6 * q^41 - 2 * q^43 - 42 * q^45 - 12 * q^46 - 18 * q^47 - 12 * q^50 - 6 * q^51 - 6 * q^52 + 6 * q^57 + 6 * q^58 + 30 * q^59 - 12 * q^60 + 60 * q^61 - 36 * q^62 - 16 * q^64 - 42 * q^65 - 24 * q^66 + 14 * q^67 - 18 * q^68 + 42 * q^69 - 12 * q^72 - 18 * q^74 + 30 * q^75 - 16 * q^79 - 18 * q^81 - 12 * q^85 - 24 * q^86 + 24 * q^87 - 48 * q^89 - 18 * q^90 + 6 * q^92 + 12 * q^93 + 66 * q^95 + 6 * q^96 - 6 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$785$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−1.43162	−	0.974922i	−0.826544	−	0.562872i
$3$	−1.43162	−	0.974922i	−0.826544	−	0.562872i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.80966	+	3.13442i	0.809304	+	1.40175i	0.913347	+	0.407182i	$0.133489\pi$
$5$	1.80966	+	3.13442i	0.809304	+	1.40175i	−0.104043	+	0.994573i	$0.533178\pi$
$6$	−0.752355	−	1.56012i	−0.307148	−	0.636915i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	1.09905	+	2.79143i	0.366351	+	0.930477i
$10$			3.61932i			1.14453i
$11$	1.73534	+	1.00190i	0.523224	+	0.302083i	0.738253	−	0.674524i	$-0.235651\pi$
$11$	1.73534	+	1.00190i	0.523224	+	0.302083i	−0.215029	+	0.976608i	$0.568985\pi$
$12$	0.128499	−	1.72728i	0.0370945	−	0.498622i
$13$	−2.95206	+	1.70437i	−0.818754	+	0.472708i	−0.849987	−	0.526804i	$-0.823390\pi$
$13$	−2.95206	+	1.70437i	−0.818754	+	0.472708i	0.0312328	+	0.999512i	$0.490057\pi$
$14$		0			0
$15$	0.465079	−	6.25156i	0.120083	−	1.61415i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−6.17418			−1.49746			−0.748730	−	0.662876i	$-0.769336\pi$
$17$	−6.17418			−1.49746			−0.748730	+	0.662876i	$0.769336\pi$
$18$	−0.443907	+	2.96698i	−0.104630	+	0.699323i
$19$		−	1.01308i		−	0.232417i	−0.993225	−	0.116208i	$-0.962926\pi$
$19$		−	1.01308i		−	0.232417i	0.993225	−	0.116208i	$-0.0370740\pi$
$20$	−1.80966	+	3.13442i	−0.404652	+	0.700877i
$21$		0			0
$22$	1.00190	+	1.73534i	0.213605	+	0.369975i
$23$	2.62232	−	1.51400i	0.546791	−	0.315690i	−0.201035	−	0.979584i	$-0.564431\pi$
$23$	2.62232	−	1.51400i	0.546791	−	0.315690i	0.747827	+	0.663894i	$0.231097\pi$
$24$	0.974922	−	1.43162i	0.199005	−	0.292228i
$25$	−4.04972	+	7.01433i	−0.809945	+	1.40287i
$26$	−3.40874			−0.668510
$27$	1.14800	−	5.06775i	0.220934	−	0.975289i
$28$		0			0
$29$	5.04560	+	2.91308i	0.936945	+	0.540945i	0.889001	−	0.457905i	$-0.151400\pi$
$29$	5.04560	+	2.91308i	0.936945	+	0.540945i	0.0479434	+	0.998850i	$0.484733\pi$
$30$	3.52855	−	5.18147i	0.644222	−	0.946003i
$31$	−0.787812	+	0.454844i	−0.141495	+	0.0816923i	−0.569076	−	0.822285i	$-0.692699\pi$
$31$	−0.787812	+	0.454844i	−0.141495	+	0.0816923i	0.427581	+	0.903977i	$0.359366\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−1.50757	−	3.12615i	−0.262434	−	0.544193i
$34$	−5.34700	−	3.08709i	−0.917003	−	0.529432i
$35$		0			0
$36$	−1.86792	+	2.34752i	−0.311320	+	0.391254i
$37$	−7.33650			−1.20611			−0.603056	−	0.797699i	$-0.706051\pi$
$37$	−7.33650			−1.20611			−0.603056	+	0.797699i	$0.706051\pi$
$38$	0.506540	−	0.877353i	0.0821717	−	0.142325i
$39$	5.88785	+	0.438020i	0.942810	+	0.0701394i
$40$	−3.13442	+	1.80966i	−0.495595	+	0.286132i
$41$	2.85045	+	4.93712i	0.445165	+	0.771048i	0.998064	−	0.0622002i	$-0.0198117\pi$
$41$	2.85045	+	4.93712i	0.445165	+	0.771048i	−0.552899	+	0.833248i	$0.686478\pi$
$42$		0			0
$43$	−2.39949	+	4.15605i	−0.365919	+	0.633791i	−0.988923	−	0.148428i	$-0.952579\pi$
$43$	−2.39949	+	4.15605i	−0.365919	+	0.633791i	0.623004	+	0.782219i	$0.285912\pi$
$44$			2.00379i			0.302083i
$45$	−6.76060	+	8.49643i	−1.00781	+	1.26657i
$46$	3.02799			0.446453
$47$	−1.11511	+	1.93143i	−0.162655	+	0.281727i	−0.935820	−	0.352478i	$-0.885339\pi$
$47$	−1.11511	+	1.93143i	−0.162655	+	0.281727i	0.773165	+	0.634205i	$0.218673\pi$
$48$	1.56012	−	0.752355i	0.225183	−	0.108593i
$49$		0			0
$50$	−7.01433	+	4.04972i	−0.991975	+	0.572717i
$51$	8.83906	+	6.01935i	1.23772	+	0.842877i
$52$	−2.95206	−	1.70437i	−0.409377	−	0.236354i
$53$		−	8.75365i		−	1.20241i	−0.799096	−	0.601203i	$-0.794688\pi$
$53$		−	8.75365i		−	1.20241i	0.799096	−	0.601203i	$-0.205312\pi$
$54$	3.52808	−	3.81480i	0.480110	−	0.519128i
$55$			7.25237i			0.977909i
$56$		0			0
$57$	−0.987674	+	1.45034i	−0.130821	+	0.192103i
$58$	2.91308	+	5.04560i	0.382506	+	0.662520i
$59$	4.49313	+	7.78233i	0.584956	+	1.01317i	0.994881	+	0.101054i	$0.0322216\pi$
$59$	4.49313	+	7.78233i	0.584956	+	1.01317i	−0.409925	+	0.912119i	$0.634445\pi$
$60$	5.64655	−	2.72301i	0.728967	−	0.351539i
$61$	12.7410	+	7.35603i	1.63132	+	0.941843i	0.983686	+	0.179892i	$0.0575747\pi$
$61$	12.7410	+	7.35603i	1.63132	+	0.941843i	0.647634	+	0.761952i	$0.275759\pi$
$62$	−0.909687			−0.115530
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−10.6844	−	6.16866i	−1.32524	−	0.765128i
$66$	0.257486	−	3.46111i	0.0316943	−	0.426033i
$67$	4.15821	+	7.20222i	0.508006	+	0.879892i	0.999957	+	0.00926908i	$0.00295048\pi$
$67$	4.15821	+	7.20222i	0.508006	+	0.879892i	−0.491951	+	0.870623i	$0.663716\pi$
$68$	−3.08709	−	5.34700i	−0.374365	−	0.648419i
$69$	−5.23019	−	0.389094i	−0.629640	−	0.0468415i
$70$		0			0
$71$		−	0.466287i		−	0.0553381i	−0.999617	−	0.0276691i	$-0.991192\pi$
$71$		−	0.466287i		−	0.0553381i	0.999617	−	0.0276691i	$-0.00880846\pi$
$72$	−2.79143	+	1.09905i	−0.328973	+	0.129525i
$73$		−	4.21492i		−	0.493319i	−0.969102	−	0.246659i	$-0.920667\pi$
$73$		−	4.21492i		−	0.493319i	0.969102	−	0.246659i	$-0.0793329\pi$
$74$	−6.35359	−	3.66825i	−0.738590	−	0.426425i
$75$	12.6361	−	6.09366i	1.45909	−	0.703635i
$76$	0.877353	−	0.506540i	0.100639	−	0.0581041i
$77$		0			0
$78$	4.88001	+	3.32326i	0.552553	+	0.376285i
$79$	−1.91267	+	3.31284i	−0.215192	+	0.372723i	−0.953332	−	0.301924i	$-0.902371\pi$
$79$	−1.91267	+	3.31284i	−0.215192	+	0.372723i	0.738140	+	0.674648i	$0.235704\pi$
$80$	−3.61932			−0.404652
$81$	−6.58416	+	6.13586i	−0.731574	+	0.681762i
$82$			5.70089i			0.629558i
$83$	4.00481	−	6.93654i	0.439585	−	0.761384i	−0.558072	−	0.829792i	$-0.688459\pi$
$83$	4.00481	−	6.93654i	0.439585	−	0.761384i	0.997657	+	0.0684084i	$0.0217921\pi$
$84$		0			0
$85$	−11.1732	−	19.3525i	−1.21190	−	2.09907i
$86$	−4.15605	+	2.39949i	−0.448158	+	0.258744i
$87$	−4.38334	−	9.08948i	−0.469944	−	0.974495i
$88$	−1.00190	+	1.73534i	−0.106803	+	0.184988i
$89$	−4.78647			−0.507365			−0.253683	−	0.967288i	$-0.581642\pi$
$89$	−4.78647			−0.507365			−0.253683	+	0.967288i	$0.581642\pi$
$90$	−10.1031	+	3.97782i	−1.06496	+	0.419299i
$91$		0			0
$92$	2.62232	+	1.51400i	0.273396	+	0.157845i
$93$	1.57128	+	0.116894i	0.162934	+	0.0121213i
$94$	−1.93143	+	1.11511i	−0.199211	+	0.115015i
$95$	3.17542	−	1.83333i	0.325791	−	0.188096i
$96$	1.72728	+	0.128499i	0.176290	+	0.0131149i
$97$	10.1835	+	5.87944i	1.03398	+	0.596967i	0.918121	−	0.396299i	$-0.129706\pi$
$97$	10.1835	+	5.87944i	1.03398	+	0.596967i	0.115856	+	0.993266i	$0.463039\pi$
$98$		0			0
$99$	−0.889499	+	5.94521i	−0.0893980	+	0.597516i
$100$	−8.09945			−0.809945
$101$	6.44610	−	11.1650i	0.641411	−	1.11096i	−0.343707	−	0.939077i	$-0.611683\pi$
$101$	6.44610	−	11.1650i	0.641411	−	1.11096i	0.985118	−	0.171879i	$-0.0549840\pi$
$102$	4.64518	+	9.63244i	0.459941	+	0.953754i
$103$	9.31740	−	5.37940i	0.918070	−	0.530048i	0.0350515	−	0.999386i	$-0.488840\pi$
$103$	9.31740	−	5.37940i	0.918070	−	0.530048i	0.883019	+	0.469337i	$0.155507\pi$
$104$	−1.70437	−	2.95206i	−0.167127	−	0.289473i
$105$		0			0
$106$	4.37683	−	7.58088i	0.425115	−	0.736321i
$107$		−	2.63967i		−	0.255186i	−0.991827	−	0.127593i	$-0.959275\pi$
$107$		−	2.63967i		−	0.255186i	0.991827	−	0.127593i	$-0.0407251\pi$
$108$	4.96280	−	1.53967i	0.477546	−	0.148155i
$109$	−9.03535			−0.865430			−0.432715	−	0.901531i	$-0.642444\pi$
$109$	−9.03535			−0.865430			−0.432715	+	0.901531i	$0.642444\pi$
$110$	−3.62618	+	6.28073i	−0.345743	+	0.598844i
$111$	10.5031	+	7.15251i	0.996905	+	0.678886i
$112$		0			0
$113$	−1.46411	+	0.845306i	−0.137732	+	0.0795197i	−0.567283	−	0.823523i	$-0.692005\pi$
$113$	−1.46411	+	0.845306i	−0.137732	+	0.0795197i	0.429551	+	0.903043i	$0.358672\pi$
$114$	−1.58052	+	0.762196i	−0.148029	+	0.0713862i
$115$	9.49100	+	5.47963i	0.885041	+	0.510978i
$116$			5.82616i			0.540945i
$117$	−8.00210	−	6.36727i	−0.739795	−	0.588654i
$118$			8.98627i			0.827253i
$119$		0			0
$120$	6.25156	+	0.465079i	0.570687	+	0.0424557i
$121$	−3.49240	−	6.04902i	−0.317491	−	0.549911i
$122$	7.35603	+	12.7410i	0.665984	+	1.15352i
$123$	0.732559	−	9.84702i	0.0660526	−	0.887876i
$124$	−0.787812	−	0.454844i	−0.0707476	−	0.0408462i
$125$	−11.2179			−1.00336
$126$		0			0
$127$	17.9292			1.59096			0.795478	−	0.605983i	$-0.207220\pi$
$127$	17.9292			1.59096			0.795478	+	0.605983i	$0.207220\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	7.48698	−	3.61054i	0.659192	−	0.317891i
$130$	−6.16866	−	10.6844i	−0.541027	−	0.937087i
$131$	−8.66567	−	15.0094i	−0.757123	−	1.31138i	−0.944312	−	0.329052i	$-0.893271\pi$
$131$	−8.66567	−	15.0094i	−0.757123	−	1.31138i	0.187188	−	0.982324i	$-0.440062\pi$
$132$	1.95354	−	2.86867i	0.170034	−	0.249685i
$133$		0			0
$134$			8.31641i			0.718429i
$135$	17.9619	−	5.57257i	1.54592	−	0.479610i
$136$		−	6.17418i		−	0.529432i
$137$	−0.000558693	0	0.000322562i	−4.77324e−5	0	2.75583e-5i	0.499976	−	0.866039i	$-0.333342\pi$
$137$	−0.000558693	0	0.000322562i	−4.77324e−5	0	2.75583e-5i	−0.500024	+	0.866012i	$0.666675\pi$
$138$	−4.33493	−	2.95206i	−0.369013	−	0.251296i
$139$	8.73273	−	5.04185i	0.740701	−	0.427644i	−0.0816233	−	0.996663i	$-0.526010\pi$
$139$	8.73273	−	5.04185i	0.740701	−	0.427644i	0.822324	+	0.569019i	$0.192677\pi$
$140$		0			0
$141$	3.47940	−	1.67792i	0.293018	−	0.141306i
$142$	0.233144	−	0.403817i	0.0195650	−	0.0338875i
$143$	−6.83042			−0.571189
$144$	−2.96698	−	0.443907i	−0.247248	−	0.0369923i
$145$			21.0867i			1.75116i
$146$	2.10746	−	3.65022i	0.174414	−	0.302095i
$147$		0			0
$148$	−3.66825	−	6.35359i	−0.301528	−	0.522262i
$149$	9.74064	−	5.62376i	0.797984	−	0.460716i	−0.0447816	−	0.998997i	$-0.514259\pi$
$149$	9.74064	−	5.62376i	0.797984	−	0.460716i	0.842766	+	0.538280i	$0.180926\pi$
$150$	13.9900	+	1.04077i	1.14228	+	0.0849786i
$151$	2.36189	−	4.09092i	0.192208	−	0.332914i	−0.753774	−	0.657134i	$-0.771768\pi$
$151$	2.36189	−	4.09092i	0.192208	−	0.332914i	0.945982	+	0.324220i	$0.105102\pi$
$152$	1.01308			0.0821717
$153$	−6.78575	−	17.2348i	−0.548596	−	1.39335i
$154$		0			0
$155$	−2.85134	−	1.64622i	−0.229025	−	0.132228i
$156$	2.56459	+	5.31804i	0.205331	+	0.425784i
$157$	−2.65845	+	1.53486i	−0.212168	+	0.122495i	−0.602318	−	0.798256i	$-0.705756\pi$
$157$	−2.65845	+	1.53486i	−0.212168	+	0.122495i	0.390151	+	0.920751i	$0.372423\pi$
$158$	−3.31284	+	1.91267i	−0.263555	+	0.152164i
$159$	−8.53413	+	12.5319i	−0.676800	+	0.993842i
$160$	−3.13442	−	1.80966i	−0.247798	−	0.143066i
$161$		0			0
$162$	−8.76998	+	2.02173i	−0.689035	+	0.158842i
$163$	2.87373			0.225088			0.112544	−	0.993647i	$-0.464100\pi$
$163$	2.87373			0.225088			0.112544	+	0.993647i	$0.464100\pi$
$164$	−2.85045	+	4.93712i	−0.222582	+	0.385524i
$165$	7.07049	−	10.3826i	0.550437	−	0.808285i
$166$	6.93654	−	4.00481i	0.538380	−	0.310834i
$167$	−0.730517	−	1.26529i	−0.0565291	−	0.0979113i	0.836376	−	0.548156i	$-0.184670\pi$
$167$	−0.730517	−	1.26529i	−0.0565291	−	0.0979113i	−0.892905	+	0.450245i	$0.851337\pi$
$168$		0			0
$169$	−0.690233	+	1.19552i	−0.0530948	+	0.0919630i
$170$		−	22.3463i		−	1.71388i
$171$	2.82794	−	1.11343i	0.216258	−	0.0851460i
$172$	−4.79899			−0.365919
$173$	−1.53541	+	2.65940i	−0.116735	+	0.202191i	−0.918472	−	0.395486i	$-0.870576\pi$
$173$	−1.53541	+	2.65940i	−0.116735	+	0.202191i	0.801737	+	0.597677i	$0.203909\pi$
$174$	0.748656	−	10.0634i	0.0567554	−	0.762904i
$175$		0			0
$176$	−1.73534	+	1.00190i	−0.130806	+	0.0755209i
$177$	1.15473	−	15.5218i	0.0867946	−	1.16669i
$178$	−4.14521	−	2.39324i	−0.310696	−	0.179381i
$179$		−	19.3193i		−	1.44399i	−0.691896	−	0.721997i	$-0.743224\pi$
$179$		−	19.3193i		−	1.44399i	0.691896	−	0.721997i	$-0.256776\pi$
$180$	−10.7384	−	1.60664i	−0.800395	−	0.119752i
$181$		−	7.89318i		−	0.586695i	−0.956006	−	0.293348i	$-0.905231\pi$
$181$		−	7.89318i		−	0.586695i	0.956006	−	0.293348i	$-0.0947693\pi$
$182$		0			0
$183$	−11.0687	−	22.9525i	−0.818222	−	1.69670i
$184$	1.51400	+	2.62232i	0.111613	+	0.193320i
$185$	−13.2765	−	22.9957i	−0.976111	−	1.69067i
$186$	1.30232	+	0.886874i	0.0954910	+	0.0650288i
$187$	−10.7143	−	6.18590i	−0.783506	−	0.452358i
$188$	−2.23022			−0.162655
$189$		0			0
$190$	3.66666			0.266007
$191$	−11.5218	−	6.65211i	−0.833688	−	0.481330i	0.0214259	−	0.999770i	$-0.493179\pi$
$191$	−11.5218	−	6.65211i	−0.833688	−	0.481330i	−0.855114	+	0.518441i	$0.826513\pi$
$192$	1.43162	+	0.974922i	0.103318	+	0.0703590i
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	0.724112	−	0.689682i	$-0.242250\pi$
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	−0.959338	+	0.282259i	$0.908916\pi$
$194$	5.87944	+	10.1835i	0.422119	+	0.731132i
$195$	9.28205	+	19.2476i	0.664701	+	1.37835i
$196$		0			0
$197$			4.44250i			0.316515i	0.987398	+	0.158258i	$0.0505876\pi$
$197$			4.44250i			0.316515i	−0.987398	+	0.158258i	$0.949412\pi$
$198$	−3.74293	+	4.70395i	−0.265999	+	0.334295i
$199$			11.5108i			0.815982i	0.912986	+	0.407991i	$0.133770\pi$
$199$			11.5108i			0.815982i	−0.912986	+	0.407991i	$0.866230\pi$
$200$	−7.01433	−	4.04972i	−0.495988	−	0.286359i
$201$	1.06865	−	14.3648i	0.0753768	−	1.01321i
$202$	11.1650	−	6.44610i	0.785565	−	0.453546i
$203$		0			0
$204$	−0.793376	+	10.6645i	−0.0555475	+	0.746666i
$205$	−10.3167	+	17.8690i	−0.720547	+	1.24802i
$206$	10.7588			0.749601
$207$	7.10829	+	5.65606i	0.494060	+	0.393123i
$208$		−	3.40874i		−	0.236354i
$209$	1.01500	−	1.75804i	0.0702092	−	0.121606i
$210$		0			0
$211$	11.3005	+	19.5731i	0.777961	+	1.34747i	0.933115	+	0.359577i	$0.117079\pi$
$211$	11.3005	+	19.5731i	0.777961	+	1.34747i	−0.155155	+	0.987890i	$0.549588\pi$
$212$	7.58088	−	4.37683i	0.520657	−	0.300602i
$213$	−0.454594	+	0.667545i	−0.0311483	+	0.0457394i
$214$	1.31983	−	2.28602i	0.0902219	−	0.156269i
$215$	−17.3691			−1.18456
$216$	5.06775	+	1.14800i	0.344817	+	0.0781118i
$217$		0			0
$218$	−7.82484	−	4.51768i	−0.529965	−	0.305976i
$219$	−4.10922	+	6.03414i	−0.277675	+	0.407750i
$220$	−6.28073	+	3.62618i	−0.423447	+	0.244477i
$221$	18.2265	−	10.5231i	1.22605	−	0.707860i
$222$	5.51965	+	11.4458i	0.370455	+	0.768191i
$223$	−16.2994	−	9.41045i	−1.09149	−	0.630170i	−0.157515	−	0.987517i	$-0.550348\pi$
$223$	−16.2994	−	9.41045i	−1.09149	−	0.630170i	−0.933972	+	0.357346i	$0.883682\pi$
$224$		0			0
$225$	−24.0309	−	3.59540i	−1.60206	−	0.239693i
$226$	−1.69061			−0.112458
$227$	7.30665	−	12.6555i	0.484960	−	0.839975i	−0.514891	−	0.857256i	$-0.672168\pi$
$227$	7.30665	−	12.6555i	0.484960	−	0.839975i	0.999851	+	0.0172809i	$0.00550095\pi$
$228$	−1.74987	−	0.130180i	−0.115888	−	0.00862137i
$229$	2.06044	−	1.18959i	0.136158	−	0.0786106i	−0.430374	−	0.902651i	$-0.641618\pi$
$229$	2.06044	−	1.18959i	0.136158	−	0.0786106i	0.566531	+	0.824040i	$0.308285\pi$
$230$	5.47963	+	9.49100i	0.361316	+	0.625818i
$231$		0			0
$232$	−2.91308	+	5.04560i	−0.191253	+	0.331260i
$233$			10.4324i			0.683448i	0.939800	+	0.341724i	$0.111011\pi$
$233$			10.4324i			0.683448i	−0.939800	+	0.341724i	$0.888989\pi$
$234$	−3.74639	−	9.51527i	−0.244909	−	0.622033i
$235$	−8.07186			−0.526550
$236$	−4.49313	+	7.78233i	−0.292478	+	0.506587i
$237$	5.96796	−	2.87801i	0.387661	−	0.186947i
$238$		0			0
$239$	20.5971	−	11.8917i	1.33232	−	0.769213i	0.346662	−	0.937990i	$-0.387315\pi$
$239$	20.5971	−	11.8917i	1.33232	−	0.769213i	0.985654	+	0.168777i	$0.0539818\pi$
$240$	5.18147	+	3.52855i	0.334463	+	0.227767i
$241$	24.8105	+	14.3243i	1.59818	+	0.922712i	0.991837	+	0.127513i	$0.0406994\pi$
$241$	24.8105	+	14.3243i	1.59818	+	0.922712i	0.606348	+	0.795200i	$0.292634\pi$
$242$		−	6.98481i		−	0.449000i
$243$	15.4080	−	2.36515i	0.988423	−	0.151725i
$244$			14.7121i			0.941843i
$245$		0			0
$246$	5.55793	−	8.16149i	0.354360	−	0.520358i
$247$	1.72667	+	2.99067i	0.109865	+	0.190292i
$248$	−0.454844	−	0.787812i	−0.0288826	−	0.0500261i
$249$	−12.4959	+	6.02608i	−0.791898	+	0.381888i
$250$	−9.71496	−	5.60894i	−0.614428	−	0.354740i
$251$	11.0301			0.696216			0.348108	−	0.937454i	$-0.386824\pi$
$251$	11.0301			0.696216			0.348108	+	0.937454i	$0.386824\pi$
$252$		0			0
$253$	6.06748			0.381459
$254$	15.5271	+	8.96458i	0.974257	+	0.562488i
$255$	−2.87148	+	38.5983i	−0.179819	+	2.41712i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.54890	+	13.0751i	0.470888	+	0.815601i	0.999446	−	0.0332960i	$-0.0106004\pi$
$257$	7.54890	+	13.0751i	0.470888	+	0.815601i	−0.528558	+	0.848897i	$0.677267\pi$
$258$	8.28919	+	0.616665i	0.516062	+	0.0383919i
$259$		0			0
$260$		−	12.3373i		−	0.765128i
$261$	−2.58627	+	17.2861i	−0.160086	+	1.06998i
$262$		−	17.3313i		−	1.07073i
$263$	−17.0075	−	9.81926i	−1.04873	−	0.605482i	−0.126433	−	0.991975i	$-0.540353\pi$
$263$	−17.0075	−	9.81926i	−1.04873	−	0.605482i	−0.922292	+	0.386493i	$0.873686\pi$
$264$	3.12615	−	1.50757i	0.192401	−	0.0927843i
$265$	27.4376	−	15.8411i	1.68548	−	0.973112i
$266$		0			0
$267$	6.85240	+	4.66644i	0.419360	+	0.285581i
$268$	−4.15821	+	7.20222i	−0.254003	+	0.439946i
$269$	0.491005			0.0299371			0.0149686	−	0.999888i	$-0.495235\pi$
$269$	0.491005			0.0299371			0.0149686	+	0.999888i	$0.495235\pi$
$270$	18.3418	+	4.15499i	1.11625	+	0.252865i
$271$			14.0789i			0.855232i	0.903960	+	0.427616i	$0.140647\pi$
$271$			14.0789i			0.855232i	−0.903960	+	0.427616i	$0.859353\pi$
$272$	3.08709	−	5.34700i	0.187182	−	0.324209i
$273$		0			0
$274$	−0.000322562	0	0.000558693i	−1.94867e−5	0	3.37519e-5i
$275$	−14.0553	+	8.11481i	−0.847565	+	0.489342i
$276$	−2.27813	−	4.72402i	−0.137127	−	0.284353i
$277$	−15.3600	+	26.6043i	−0.922894	+	1.59850i	−0.127981	+	0.991777i	$0.540850\pi$
$277$	−15.3600	+	26.6043i	−0.922894	+	1.59850i	−0.794913	+	0.606723i	$0.792484\pi$
$278$	10.0837			0.604780
$279$	−2.13551	−	1.69923i	−0.127850	−	0.101730i
$280$		0			0
$281$	6.86286	+	3.96227i	0.409404	+	0.236369i	0.690534	−	0.723300i	$-0.257376\pi$
$281$	6.86286	+	3.96227i	0.409404	+	0.236369i	−0.281130	+	0.959670i	$0.590709\pi$
$282$	3.85221	+	0.286581i	0.229395	+	0.0170656i
$283$	9.97303	−	5.75793i	0.592835	−	0.342273i	−0.173383	−	0.984855i	$-0.555470\pi$
$283$	9.97303	−	5.75793i	0.592835	−	0.342273i	0.766218	+	0.642581i	$0.222136\pi$
$284$	0.403817	−	0.233144i	0.0239621	−	0.0138345i
$285$	−6.33333	−	0.471162i	−0.375154	−	0.0279092i
$286$	−5.91532	−	3.41521i	−0.349780	−	0.201946i
$287$		0			0
$288$	−2.34752	−	1.86792i	−0.138329	−	0.110068i
$289$	21.1205			1.24238
$290$	−10.5434	+	18.2616i	−0.619127	+	1.07236i
$291$	−8.84686	−	18.3452i	−0.518612	−	1.07542i
$292$	3.65022	−	2.10746i	0.213613	−	0.123330i
$293$	2.50937	+	4.34636i	0.146599	+	0.253917i	0.929968	−	0.367639i	$-0.119834\pi$
$293$	2.50937	+	4.34636i	0.146599	+	0.253917i	−0.783369	+	0.621557i	$0.786501\pi$
$294$		0			0
$295$	−16.2621	+	28.1667i	−0.946814	+	1.63993i
$296$		−	7.33650i		−	0.426425i
$297$	7.06954	−	7.64407i	0.410216	−	0.443554i
$298$	11.2475			0.651551
$299$	−5.16083	+	8.93882i	−0.298458	+	0.516945i
$300$	11.5953	+	7.89633i	0.669455	+	0.455895i
$301$		0			0
$302$	4.09092	−	2.36189i	0.235406	−	0.135912i
$303$	−20.1133	+	9.69952i	−1.15548	+	0.557223i
$304$	0.877353	+	0.506540i	0.0503197	+	0.0290521i
$305$			53.2476i			3.04895i
$306$	2.74076	−	18.3186i	0.156679	−	1.04721i
$307$			17.5309i			1.00054i	0.865869	+	0.500271i	$0.166766\pi$
$307$			17.5309i			1.00054i	−0.865869	+	0.500271i	$0.833234\pi$
$308$		0			0
$309$	−18.5834	−	1.38250i	−1.05717	−	0.0786474i
$310$	−1.64622	−	2.85134i	−0.0934992	−	0.161945i
$311$	8.64759	+	14.9781i	0.490360	+	0.849328i	0.999938	−	0.0110959i	$-0.00353200\pi$
$311$	8.64759	+	14.9781i	0.490360	+	0.849328i	−0.509579	+	0.860424i	$0.670199\pi$
$312$	−0.438020	+	5.88785i	−0.0247980	+	0.333334i
$313$	−7.78988	−	4.49749i	−0.440310	−	0.254213i	0.263419	−	0.964681i	$-0.415150\pi$
$313$	−7.78988	−	4.49749i	−0.440310	−	0.254213i	−0.703729	+	0.710468i	$0.748483\pi$
$314$	−3.06972			−0.173234
$315$		0			0
$316$	−3.82533			−0.215192
$317$	5.82002	+	3.36019i	0.326885	+	0.188727i	0.654457	−	0.756099i	$-0.272897\pi$
$317$	5.82002	+	3.36019i	0.326885	+	0.188727i	−0.327572	+	0.944826i	$0.606230\pi$
$318$	−13.6567	+	6.58586i	−0.765830	+	0.369316i
$319$	5.83721	+	10.1103i	0.326821	+	0.566071i
$320$	−1.80966	−	3.13442i	−0.101163	−	0.175219i
$321$	−2.57347	+	3.77899i	−0.143637	+	0.210923i
$322$		0			0
$323$			6.25494i			0.348034i
$324$	−8.60589	−	2.63412i	−0.478105	−	0.146340i
$325$		−	27.6089i		−	1.53147i
$326$	2.48873	+	1.43687i	0.137838	+	0.0795807i
$327$	12.9352	+	8.80877i	0.715316	+	0.487126i
$328$	−4.93712	+	2.85045i	−0.272607	+	0.157390i
$329$		0			0
$330$	11.3145	−	5.45636i	0.622844	−	0.300363i
$331$	9.38725	−	16.2592i	0.515970	−	0.893686i	−0.483858	−	0.875146i	$-0.660765\pi$
$331$	9.38725	−	16.2592i	0.515970	−	0.893686i	0.999828	−	0.0185396i	$-0.00590167\pi$
$332$	8.00963			0.439585
$333$	−8.06320	−	20.4793i	−0.441861	−	1.12226i
$334$		−	1.46103i		−	0.0799443i
$335$	−15.0499	+	26.0671i	−0.822262	+	1.42420i
$336$		0			0
$337$	2.42287	+	4.19654i	0.131982	+	0.228600i	0.924441	−	0.381326i	$-0.124532\pi$
$337$	2.42287	+	4.19654i	0.131982	+	0.228600i	−0.792458	+	0.609926i	$0.791199\pi$
$338$	−1.19552	+	0.690233i	−0.0650276	+	0.0375437i
$339$	2.92016	+	0.217242i	0.158601	+	0.0117990i
$340$	11.1732	−	19.3525i	0.605949	−	1.04954i
$341$	−1.82283			−0.0987116
$342$	3.00578	+	0.449713i	0.162534	+	0.0243177i
$343$		0			0
$344$	−4.15605	−	2.39949i	−0.224079	−	0.129372i
$345$	−8.24526	−	17.0977i	−0.443910	−	0.920511i
$346$	−2.65940	+	1.53541i	−0.142970	+	0.0825440i
$347$	15.1305	−	8.73559i	0.812247	−	0.468951i	−0.0354887	−	0.999370i	$-0.511299\pi$
$347$	15.1305	−	8.73559i	0.812247	−	0.468951i	0.847736	+	0.530419i	$0.177965\pi$
$348$	5.68005	−	8.34083i	0.304483	−	0.447115i
$349$	−20.6338	−	11.9129i	−1.10450	−	0.637683i	−0.167101	−	0.985940i	$-0.553440\pi$
$349$	−20.6338	−	11.9129i	−1.10450	−	0.637683i	−0.937399	+	0.348257i	$0.886774\pi$
$350$		0			0
$351$	5.24835	+	16.9169i	0.280136	+	0.902958i
$352$	−2.00379			−0.106803
$353$	−5.02061	+	8.69596i	−0.267220	+	0.462839i	−0.968143	−	0.250398i	$-0.919438\pi$
$353$	−5.02061	+	8.69596i	−0.267220	+	0.462839i	0.700923	+	0.713237i	$0.252772\pi$
$354$	8.76091	−	12.8649i	0.465637	−	0.683761i
$355$	1.46154	−	0.843820i	0.0775705	−	0.0447853i
$356$	−2.39324	−	4.14521i	−0.126841	−	0.219696i
$357$		0			0
$358$	9.65966	−	16.7310i	0.510529	−	0.884262i
$359$		−	12.1651i		−	0.642048i	−0.947071	−	0.321024i	$-0.895973\pi$
$359$		−	12.1651i		−	0.642048i	0.947071	−	0.321024i	$-0.104027\pi$
$360$	−8.49643	−	6.76060i	−0.447801	−	0.356315i
$361$	17.9737			0.945983
$362$	3.94659	−	6.83569i	0.207428	−	0.359276i
$363$	−0.897541	+	12.0647i	−0.0471087	+	0.633233i
$364$		0			0
$365$	13.2113	−	7.62756i	0.691512	−	0.399245i
$366$	1.89049	−	25.4118i	0.0988173	−	1.32830i
$367$	3.14420	+	1.81531i	0.164126	+	0.0947582i	0.579813	−	0.814749i	$-0.303126\pi$
$367$	3.14420	+	1.81531i	0.164126	+	0.0947582i	−0.415687	+	0.909508i	$0.636459\pi$
$368$			3.02799i			0.157845i
$369$	−10.6488	+	13.3830i	−0.554356	+	0.696690i
$370$		−	26.5531i		−	1.38043i
$371$		0			0
$372$	0.684408	+	1.41922i	0.0354849	+	0.0735830i
$373$	−2.74616	−	4.75648i	−0.142191	−	0.246281i	0.786131	−	0.618060i	$-0.212081\pi$
$373$	−2.74616	−	4.75648i	−0.142191	−	0.246281i	−0.928321	+	0.371779i	$0.878748\pi$
$374$	−6.18590	−	10.7143i	−0.319865	−	0.554023i
$375$	16.0597	+	10.9366i	0.829319	+	0.564761i
$376$	−1.93143	−	1.11511i	−0.0996057	−	0.0575074i
$377$	−19.8599			−1.02284
$378$		0			0
$379$	−15.5960			−0.801112			−0.400556	−	0.916272i	$-0.631183\pi$
$379$	−15.5960			−0.801112			−0.400556	+	0.916272i	$0.631183\pi$
$380$	3.17542	+	1.83333i	0.162896	+	0.0940478i
$381$	−25.6677	−	17.4795i	−1.31500	−	0.895504i
$382$	−6.65211	−	11.5218i	−0.340352	−	0.589506i
$383$	−4.71534	−	8.16720i	−0.240942	−	0.417324i	0.720041	−	0.693932i	$-0.244123\pi$
$383$	−4.71534	−	8.16720i	−0.240942	−	0.417324i	−0.960983	+	0.276607i	$0.910790\pi$
$384$	0.752355	+	1.56012i	0.0383935	+	0.0796143i
$385$		0			0
$386$		−	6.53573i		−	0.332660i
$387$	−14.2385	−	2.13030i	−0.723783	−	0.108289i
$388$			11.7589i			0.596967i
$389$	−5.56142	−	3.21089i	−0.281975	−	0.162798i	0.352342	−	0.935871i	$-0.385385\pi$
$389$	−5.56142	−	3.21089i	−0.281975	−	0.162798i	−0.634317	+	0.773073i	$0.718719\pi$
$390$	−1.58533	+	21.3100i	−0.0802765	+	1.07907i
$391$	−16.1907	+	9.34769i	−0.818798	+	0.472733i
$392$		0			0
$393$	−2.22706	+	29.9360i	−0.112340	+	1.51007i
$394$	−2.22125	+	3.84732i	−0.111905	+	0.193825i
$395$	−13.8451			−0.696622
$396$	−5.59345	+	2.20228i	−0.281082	+	0.110669i
$397$		−	6.92531i		−	0.347572i	−0.984783	−	0.173786i	$-0.944400\pi$
$397$		−	6.92531i		−	0.347572i	0.984783	−	0.173786i	$-0.0556000\pi$
$398$	−5.75542	+	9.96868i	−0.288493	+	0.499685i
$399$		0			0
$400$	−4.04972	−	7.01433i	−0.202486	−	0.350716i
$401$	9.16848	−	5.29343i	0.457852	−	0.264341i	−0.253289	−	0.967391i	$-0.581512\pi$
$401$	9.16848	−	5.29343i	0.457852	−	0.264341i	0.711141	+	0.703050i	$0.248179\pi$
$402$	8.10786	−	11.9059i	0.404383	−	0.593813i
$403$	1.55045	−	2.68545i	0.0772332	−	0.133772i
$404$	12.8922			0.641411
$405$	−31.1474	−	9.53372i	−1.54773	−	0.473735i
$406$		0			0
$407$	−12.7313	−	7.35042i	−0.631067	−	0.364347i
$408$	−6.01935	+	8.83906i	−0.298002	+	0.437599i
$409$	−7.72792	+	4.46172i	−0.382121	+	0.220618i	−0.678741	−	0.734378i	$-0.737474\pi$
$409$	−7.72792	+	4.46172i	−0.382121	+	0.220618i	0.296620	+	0.954996i	$0.404141\pi$
$410$	−17.8690	+	10.3167i	−0.882486	+	0.509504i
$411$	0.000485362		0.00100647i	2.39411e−5		4.96454e-5i
$412$	9.31740	+	5.37940i	0.459035	+	0.265024i
$413$		0			0
$414$	3.32793	+	8.45243i	0.163559	+	0.415414i
$415$	28.9894			1.42303
$416$	1.70437	−	2.95206i	0.0835637	−	0.144737i
$417$	−17.4173	−	1.29574i	−0.852931	−	0.0634529i
$418$	1.75804	−	1.01500i	0.0859883	−	0.0496454i
$419$	−17.1924	−	29.7781i	−0.839903	−	1.45475i	−0.889975	−	0.456009i	$-0.849279\pi$
$419$	−17.1924	−	29.7781i	−0.839903	−	1.45475i	0.0500724	−	0.998746i	$-0.484055\pi$
$420$		0			0
$421$	−17.7840	+	30.8028i	−0.866739	+	1.50124i	−0.00142877	+	0.999999i	$0.500455\pi$
$421$	−17.7840	+	30.8028i	−0.866739	+	1.50124i	−0.865310	+	0.501237i	$0.832879\pi$
$422$			22.6011i			1.10020i
$423$	−6.61700	−	0.990009i	−0.321730	−	0.0481359i
$424$	8.75365			0.425115
$425$	25.0037	−	43.3077i	1.21286	−	2.10073i
$426$	−0.727462	+	0.350814i	−0.0352457	+	0.0169970i
$427$		0			0
$428$	2.28602	−	1.31983i	0.110499	−	0.0637965i
$429$	9.77855	+	6.65913i	0.472113	+	0.321506i
$430$	−15.0420	−	8.68453i	−0.725392	−	0.418805i
$431$			30.8695i			1.48693i	0.668774	+	0.743466i	$0.266820\pi$
$431$			30.8695i			1.48693i	−0.668774	+	0.743466i	$0.733180\pi$
$432$	3.81480	+	3.52808i	0.183540	+	0.169745i
$433$			23.2463i			1.11715i	0.829455	+	0.558574i	$0.188651\pi$
$433$			23.2463i			1.11715i	−0.829455	+	0.558574i	$0.811349\pi$
$434$		0			0
$435$	20.5579	−	30.1881i	0.985676	−	1.44741i
$436$	−4.51768	−	7.82484i	−0.216357	−	0.374742i
$437$	−1.53380	−	2.65662i	−0.0733716	−	0.127083i
$438$	−6.57576	+	3.17111i	−0.314202	+	0.151522i
$439$	−19.2887	−	11.1364i	−0.920601	−	0.531509i	−0.0367744	−	0.999324i	$-0.511708\pi$
$439$	−19.2887	−	11.1364i	−0.920601	−	0.531509i	−0.883827	+	0.467814i	$0.845042\pi$
$440$	−7.25237			−0.345743
$441$		0			0
$442$	21.0462			1.00107
$443$	−15.5756	−	8.99259i	−0.740020	−	0.427251i	0.0820566	−	0.996628i	$-0.473851\pi$
$443$	−15.5756	−	8.99259i	−0.740020	−	0.427251i	−0.822077	+	0.569377i	$0.807185\pi$
$444$	−0.942733	+	12.6722i	−0.0447401	+	0.601394i
$445$	−8.66188	−	15.0028i	−0.410612	−	0.711202i
$446$	−9.41045	−	16.2994i	−0.445598	−	0.771798i
$447$	−19.4276	−	1.44530i	−0.918894	−	0.0683601i
$448$		0			0
$449$		−	9.44363i		−	0.445673i	−0.974856	−	0.222836i	$-0.928468\pi$
$449$		−	9.44363i		−	0.445673i	0.974856	−	0.222836i	$-0.0715315\pi$
$450$	−19.0136	−	15.1291i	−0.896311	−	0.713194i
$451$			11.4234i			0.537908i
$452$	−1.46411	−	0.845306i	−0.0688661	−	0.0397599i
$453$	−7.36966	+	3.55397i	−0.346257	+	0.166980i
$454$	12.6555	−	7.30665i	0.593952	−	0.342918i
$455$		0			0
$456$	−1.45034	−	0.987674i	−0.0679185	−	0.0462521i
$457$	0.922251	−	1.59739i	0.0431411	−	0.0747225i	−0.843649	−	0.536896i	$-0.819597\pi$
$457$	0.922251	−	1.59739i	0.0431411	−	0.0747225i	0.886790	+	0.462173i	$0.152930\pi$
$458$	2.37919			0.111172
$459$	−7.08799	+	31.2892i	−0.330839	+	1.46046i
$460$			10.9593i			0.510978i
$461$	18.1869	−	31.5007i	0.847050	−	1.46713i	−0.0367790	−	0.999323i	$-0.511710\pi$
$461$	18.1869	−	31.5007i	0.847050	−	1.46713i	0.883829	−	0.467810i	$-0.154957\pi$
$462$		0			0
$463$	−15.9830	−	27.6834i	−0.742794	−	1.28656i	−0.951219	−	0.308518i	$-0.900167\pi$
$463$	−15.9830	−	27.6834i	−0.742794	−	1.28656i	0.208425	−	0.978038i	$-0.433166\pi$
$464$	−5.04560	+	2.91308i	−0.234236	+	0.135236i
$465$	2.47709	+	5.13660i	0.114872	+	0.238204i
$466$	−5.21619	+	9.03470i	−0.241635	+	0.418525i
$467$	24.4411			1.13100			0.565500	−	0.824748i	$-0.308683\pi$
$467$	24.4411			1.13100			0.565500	+	0.824748i	$0.308683\pi$
$468$	1.51317	−	10.1137i	0.0699461	−	0.467504i
$469$		0			0
$470$	−6.99044	−	4.03593i	−0.322445	−	0.186164i
$471$	5.30225	+	0.394456i	0.244315	+	0.0181756i
$472$	−7.78233	+	4.49313i	−0.358211	+	0.206813i
$473$	−8.32786	+	4.80809i	−0.382916	+	0.221076i
$474$	6.60741	+	0.491552i	0.303489	+	0.0225777i
$475$	7.10607	+	4.10269i	0.326049	+	0.188245i
$476$		0			0
$477$	24.4352	−	9.62073i	1.11881	−	0.440503i
$478$	23.7835			1.08783
$479$	−5.48032	+	9.49220i	−0.250402	+	0.433710i	−0.963637	−	0.267216i	$-0.913896\pi$
$479$	−5.48032	+	9.49220i	−0.250402	+	0.433710i	0.713234	+	0.700926i	$0.247230\pi$
$480$	2.72301	+	5.64655i	0.124288	+	0.257729i
$481$	21.6578	−	12.5041i	0.987509	−	0.570139i
$482$	14.3243	+	24.8105i	0.652456	+	1.13009i
$483$		0			0
$484$	3.49240	−	6.04902i	0.158746	−	0.274955i
$485$			42.5591i			1.93251i
$486$	14.5263	+	5.65571i	0.658926	+	0.256548i
$487$	33.6175			1.52335			0.761677	−	0.647957i	$-0.224376\pi$
$487$	33.6175			1.52335			0.761677	+	0.647957i	$0.224376\pi$
$488$	−7.35603	+	12.7410i	−0.332992	+	0.576759i
$489$	−4.11408	−	2.80167i	−0.186045	−	0.126696i
$490$		0			0
$491$	−19.6893	+	11.3676i	−0.888568	+	0.513015i	−0.873474	−	0.486871i	$-0.838138\pi$
$491$	−19.6893	+	11.3676i	−0.888568	+	0.513015i	−0.0150939	+	0.999886i	$0.504805\pi$
$492$	8.89405	−	4.28910i	0.400975	−	0.193367i
$493$	−31.1525	−	17.9859i	−1.40304	−	0.810043i
$494$			3.45333i			0.155373i
$495$	−20.2445	+	7.97074i	−0.909921	+	0.358258i
$496$		−	0.909687i		−	0.0408462i
$497$		0			0
$498$	−13.8348	−	1.02923i	−0.619954	−	0.0461209i
$499$	−9.76175	−	16.9079i	−0.436996	−	0.756899i	0.560460	−	0.828181i	$-0.310624\pi$
$499$	−9.76175	−	16.9079i	−0.436996	−	0.756899i	−0.997456	+	0.0712820i	$0.977291\pi$
$500$	−5.60894	−	9.71496i	−0.250839	−	0.434466i
$501$	−0.187742	+	2.52361i	−0.00838768	+	0.112747i
$502$	9.55238	+	5.51507i	0.426343	+	0.246149i
$503$	13.6867			0.610262			0.305131	−	0.952310i	$-0.401300\pi$
$503$	13.6867			0.610262			0.305131	+	0.952310i	$0.401300\pi$
$504$		0			0
$505$	46.6609			2.07638
$506$	5.25459	+	3.03374i	0.233595	+	0.134866i
$507$	2.15369	−	1.03860i	0.0956486	−	0.0461259i
$508$	8.96458	+	15.5271i	0.397739	+	0.688904i
$509$	1.14583	+	1.98464i	0.0507881	+	0.0879675i	0.890302	−	0.455371i	$-0.150493\pi$
$509$	1.14583	+	1.98464i	0.0507881	+	0.0879675i	−0.839514	+	0.543338i	$0.817160\pi$
$510$	−21.7859	+	31.9914i	−0.964697	+	1.41660i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−5.13404	−	1.16302i	−0.226673	−	0.0513486i
$514$			15.0978i			0.665936i
$515$	33.7226	+	19.4698i	1.48600	+	0.857940i
$516$	6.87031	+	4.67864i	0.302449	+	0.205966i
$517$	−3.87018	+	2.23445i	−0.170210	+	0.0982710i
$518$		0			0
$519$	4.79082	−	2.31034i	0.210294	−	0.101413i
$520$	6.16866	−	10.6844i	0.270514	−	0.468543i
$521$	17.0820			0.748377			0.374189	−	0.927353i	$-0.377921\pi$
$521$	17.0820			0.748377			0.374189	+	0.927353i	$0.377921\pi$
$522$	−10.8828	+	13.6770i	−0.476328	+	0.598628i
$523$		−	41.2762i		−	1.80488i	−0.430815	−	0.902440i	$-0.641774\pi$
$523$		−	41.2762i		−	1.80488i	0.430815	−	0.902440i	$-0.358226\pi$
$524$	8.66567	−	15.0094i	0.378562	−	0.655688i
$525$		0			0
$526$	−9.81926	−	17.0075i	−0.428140	−	0.741561i
$527$	4.86410	−	2.80829i	0.211883	−	0.122331i
$528$	3.46111	+	0.257486i	0.150625	+	0.0112056i
$529$	−6.91563	+	11.9782i	−0.300679	+	0.520792i
$530$	31.6822			1.37619
$531$	−16.7857	+	21.0955i	−0.728435	+	0.915465i
$532$		0			0
$533$	−16.8294	−	9.71644i	−0.728961	−	0.420866i
$534$	3.60113	+	7.46745i	0.155836	+	0.323148i
$535$	8.27382	−	4.77689i	0.357708	−	0.206523i
$536$	−7.20222	+	4.15821i	−0.311089	+	0.179607i
$537$	−18.8348	+	27.6579i	−0.812783	+	1.19352i
$538$	0.425223	+	0.245503i	0.0183327	+	0.0105844i
$539$		0			0
$540$	13.8070	+	12.7692i	0.594157	+	0.549500i
$541$	−45.4393			−1.95359			−0.976795	−	0.214177i	$-0.931293\pi$
$541$	−45.4393			−1.95359			−0.976795	+	0.214177i	$0.931293\pi$
$542$	−7.03945	+	12.1927i	−0.302370	+	0.523721i
$543$	−7.69523	+	11.3000i	−0.330234	+	0.484929i
$544$	5.34700	−	3.08709i	0.229251	−	0.132358i
$545$	−16.3509	−	28.3206i	−0.700395	−	1.21312i
$546$		0			0
$547$	15.1095	−	26.1705i	0.646037	−	1.11897i	−0.338024	−	0.941138i	$-0.609758\pi$
$547$	15.1095	−	26.1705i	0.646037	−	1.11897i	0.984061	−	0.177832i	$-0.0569082\pi$
$548$		0	0.000645123i		0	2.75583e-5i
$549$	−6.53079	+	43.6503i	−0.278727	+	1.86295i
$550$	−16.2296			−0.692034
$551$	2.95118	−	5.11160i	0.125725	−	0.217761i
$552$	0.389094	−	5.23019i	0.0165610	−	0.222612i
$553$		0			0
$554$	−26.6043	+	15.3600i	−1.13031	+	0.652585i
$555$	−3.41205	+	45.8646i	−0.144833	+	1.94684i
$556$	8.73273	+	5.04185i	0.370350	+	0.213822i
$557$		−	25.4212i		−	1.07713i	−0.842584	−	0.538565i	$-0.818967\pi$
$557$		−	25.4212i		−	1.07713i	0.842584	−	0.538565i	$-0.181033\pi$
$558$	−0.999795	−	2.53933i	−0.0423247	−	0.107498i
$559$		−	16.3585i		−	0.691892i
$560$		0			0
$561$	9.30799	+	19.3014i	0.392983	+	0.814907i
$562$	3.96227	+	6.86286i	0.167138	+	0.289492i
$563$	1.44346	+	2.50015i	0.0608346	+	0.105369i	0.894839	−	0.446390i	$-0.147290\pi$
$563$	1.44346	+	2.50015i	0.0608346	+	0.105369i	−0.834004	+	0.551758i	$0.813957\pi$
$564$	3.19282	+	2.17429i	0.134442	+	0.0915541i
$565$	−5.29909	−	3.05943i	−0.222934	−	0.128711i
$566$	11.5159			0.484048
$567$		0			0
$568$	0.466287			0.0195650
$569$	38.5945	+	22.2826i	1.61797	+	0.934134i	0.987445	+	0.157963i	$0.0504927\pi$
$569$	38.5945	+	22.2826i	1.61797	+	0.934134i	0.630523	+	0.776171i	$0.282841\pi$
$570$	−5.24925	−	3.57471i	−0.219867	−	0.149728i
$571$	3.26470	+	5.65462i	0.136623	+	0.236638i	0.926216	−	0.376992i	$-0.123042\pi$
$571$	3.26470	+	5.65462i	0.136623	+	0.236638i	−0.789593	+	0.613631i	$0.789708\pi$
$572$	−3.41521	−	5.91532i	−0.142797	−	0.247332i
$573$	10.0095	+	20.7561i	0.418153	+	0.867100i
$574$		0			0
$575$			24.5251i			1.02277i
$576$	−1.09905	−	2.79143i	−0.0457939	−	0.116310i
$577$			1.35932i			0.0565891i	0.999600	+	0.0282945i	$0.00900764\pi$
$577$			1.35932i			0.0565891i	−0.999600	+	0.0282945i	$0.990992\pi$
$578$	18.2909	+	10.5603i	0.760802	+	0.439249i
$579$	−0.839835	+	11.2890i	−0.0349024	+	0.469156i
$580$	−18.2616	+	10.5434i	−0.758273	+	0.437789i
$581$		0			0
$582$	1.51101	−	20.3109i	0.0626332	−	0.841912i
$583$	8.77026	−	15.1905i	0.363227	−	0.629128i
$584$	4.21492			0.174414
$585$	5.47662	−	36.6045i	0.226431	−	1.51341i
$586$			5.01875i			0.207323i
$587$	−22.2025	+	38.4559i	−0.916397	+	1.58725i	−0.111555	+	0.993758i	$0.535583\pi$
$587$	−22.2025	+	38.4559i	−0.916397	+	1.58725i	−0.804843	+	0.593488i	$0.797750\pi$
$588$		0			0
$589$	0.460793	+	0.798117i	0.0189866	+	0.0328858i
$590$	−28.1667	+	16.2621i	−1.15961	+	0.669499i
$591$	4.33109	−	6.35996i	0.178157	−	0.261614i
$592$	3.66825	−	6.35359i	0.150764	−	0.261131i
$593$	14.3513			0.589336			0.294668	−	0.955600i	$-0.404791\pi$
$593$	14.3513			0.589336			0.294668	+	0.955600i	$0.404791\pi$
$594$	9.94444	−	3.08519i	0.408025	−	0.126587i
$595$		0			0
$596$	9.74064	+	5.62376i	0.398992	+	0.230358i
$597$	11.2222	−	16.4791i	0.459293	−	0.674445i
$598$	−8.93882	+	5.16083i	−0.365535	+	0.211042i
$599$	3.03349	−	1.75139i	0.123945	−	0.0715597i	−0.436746	−	0.899585i	$-0.643869\pi$
$599$	3.03349	−	1.75139i	0.123945	−	0.0715597i	0.560691	+	0.828025i	$0.310536\pi$
$600$	6.09366	+	12.6361i	0.248773	+	0.515866i
$601$	−15.1846	−	8.76685i	−0.619394	−	0.357607i	0.157239	−	0.987561i	$-0.449741\pi$
$601$	−15.1846	−	8.76685i	−0.619394	−	0.357607i	−0.776633	+	0.629953i	$0.783074\pi$
$602$		0			0
$603$	−15.5344	+	19.5230i	−0.632610	+	0.795037i
$604$	4.72379			0.192208
$605$	12.6401	−	21.8933i	0.513894	−	0.890090i
$606$	−22.2684	−	1.65664i	−0.904592	−	0.0672962i
$607$	0.0755923	−	0.0436432i	0.00306820	−	0.00177142i	−0.498465	−	0.866910i	$-0.666103\pi$
$607$	0.0755923	−	0.0436432i	0.00306820	−	0.00177142i	0.501533	+	0.865138i	$0.332769\pi$
$608$	0.506540	+	0.877353i	0.0205429	+	0.0355814i
$609$		0			0
$610$	−26.6238	+	46.1138i	−1.07797	+	1.86709i
$611$		−	7.60224i		−	0.307554i
$612$	11.5329	−	14.4940i	0.466190	−	0.585887i
$613$	−25.0704			−1.01258			−0.506292	−	0.862362i	$-0.668984\pi$
$613$	−25.0704			−1.01258			−0.506292	+	0.862362i	$0.668984\pi$
$614$	−8.76545	+	15.1822i	−0.353745	+	0.612704i
$615$	32.1904	−	15.5236i	1.29804	−	0.625972i
$616$		0			0
$617$	−10.6365	+	6.14101i	−0.428211	+	0.247228i	−0.698584	−	0.715528i	$-0.746186\pi$
$617$	−10.6365	+	6.14101i	−0.428211	+	0.247228i	0.270373	+	0.962756i	$0.412853\pi$
$618$	−15.4025	−	10.4890i	−0.619579	−	0.421929i
$619$	−17.5869	−	10.1538i	−0.706875	−	0.408115i	0.103028	−	0.994678i	$-0.467147\pi$
$619$	−17.5869	−	10.1538i	−0.706875	−	0.408115i	−0.809903	+	0.586564i	$0.800480\pi$
$620$		−	3.29245i		−	0.132228i
$621$	−4.66212	−	15.0273i	−0.187085	−	0.603026i
$622$			17.2952i			0.693474i
$623$		0			0
$624$	−3.32326	+	4.88001i	−0.133037	+	0.195357i
$625$	−0.0518970	−	0.0898882i	−0.00207588	−	0.00359553i
$626$	−4.49749	−	7.78988i	−0.179756	−	0.311346i
$627$	−3.16704	+	1.52729i	−0.126479	+	0.0609939i
$628$	−2.65845	−	1.53486i	−0.106084	−	0.0612475i
$629$	45.2969			1.80610
$630$		0			0
$631$	−45.9665			−1.82990			−0.914950	−	0.403568i	$-0.867770\pi$
$631$	−45.9665			−1.82990			−0.914950	+	0.403568i	$0.867770\pi$
$632$	−3.31284	−	1.91267i	−0.131778	−	0.0760818i
$633$	2.90422	−	39.0383i	0.115432	−	1.55163i
$634$	3.36019	+	5.82002i	0.133450	+	0.231143i
$635$	32.4456	+	56.1975i	1.28757	+	2.23013i
$636$	−15.1200	−	1.12484i	−0.599546	−	0.0446026i
$637$		0			0
$638$			11.6744i			0.462195i
$639$	1.30161	−	0.512475i	0.0514908	−	0.0202732i
$640$		−	3.61932i		−	0.143066i
$641$	27.4104	+	15.8254i	1.08265	+	0.625067i	0.931609	−	0.363461i	$-0.118405\pi$
$641$	27.4104	+	15.8254i	1.08265	+	0.625067i	0.151038	+	0.988528i	$0.451738\pi$
$642$	−4.11818	+	1.98597i	−0.162532	+	0.0783799i
$643$	10.0106	−	5.77960i	0.394778	−	0.227925i	−0.289450	−	0.957193i	$-0.593472\pi$
$643$	10.0106	−	5.77960i	0.394778	−	0.227925i	0.684228	+	0.729268i	$0.260139\pi$
$644$		0			0
$645$	24.8658	+	16.9335i	0.979091	+	0.666755i
$646$	−3.12747	+	5.41694i	−0.123049	+	0.213127i
$647$	−26.0730			−1.02504			−0.512519	−	0.858676i	$-0.671287\pi$
$647$	−26.0730			−1.02504			−0.512519	+	0.858676i	$0.671287\pi$
$648$	−6.13586	−	6.58416i	−0.241039	−	0.258650i
$649$			18.0066i			0.706822i
$650$	13.8045	−	23.9100i	0.541456	−	0.937829i
$651$		0			0
$652$	1.43687	+	2.48873i	0.0562720	+	0.0974660i
$653$	−16.3952	+	9.46576i	−0.641593	+	0.370424i	−0.785228	−	0.619207i	$-0.787454\pi$
$653$	−16.3952	+	9.46576i	−0.641593	+	0.370424i	0.143635	+	0.989631i	$0.454121\pi$
$654$	6.79780	+	14.0962i	0.265815	+	0.551205i
$655$	31.3638	−	54.3237i	1.22549	−	2.12260i
$656$	−5.70089			−0.222582
$657$	11.7656	−	4.63242i	0.459021	−	0.180728i
$658$		0			0
$659$	23.3508	+	13.4816i	0.909618	+	0.525168i	0.880308	−	0.474402i	$-0.157336\pi$
$659$	23.3508	+	13.4816i	0.909618	+	0.525168i	0.0293098	+	0.999570i	$0.490669\pi$
$660$	12.5268	+	0.931922i	0.487607	+	0.0362750i
$661$	−22.3201	+	12.8865i	−0.868151	+	0.501227i	−0.866733	−	0.498772i	$-0.833785\pi$
$661$	−22.3201	+	12.8865i	−0.868151	+	0.501227i	−0.00141768	+	0.999999i	$0.500451\pi$
$662$	16.2592	−	9.38725i	0.631931	−	0.364846i
$663$	−36.3526	−	2.70442i	−1.41182	−	0.105031i
$664$	6.93654	+	4.00481i	0.269190	+	0.155417i
$665$		0			0
$666$	3.25672	−	21.7672i	0.126195	−	0.843462i
$667$	17.6416			0.683084
$668$	0.730517	−	1.26529i	0.0282646	−	0.0489557i
$669$	14.1600	+	29.3628i	0.547457	+	1.13523i
$670$	−26.0671	+	15.0499i	−1.00706	+	0.581427i
$671$	14.7400	+	25.5304i	0.569030	+	0.985590i
$672$		0			0
$673$	−12.9608	+	22.4487i	−0.499601	+	0.865335i	−1.00000		0.000460130i	$-0.999854\pi$
$673$	−12.9608	+	22.4487i	−0.499601	+	0.865335i	0.500398	+	0.865795i	$0.333187\pi$
$674$			4.84575i			0.186651i
$675$	30.8977	+	28.5755i	1.18925	+	1.09987i
$676$	−1.38047			−0.0530948
$677$	6.55382	−	11.3515i	0.251884	−	0.436275i	−0.712161	−	0.702016i	$-0.752283\pi$
$677$	6.55382	−	11.3515i	0.251884	−	0.436275i	0.964044	+	0.265741i	$0.0856166\pi$
$678$	2.42031	+	1.64822i	0.0929514	+	0.0632993i
$679$		0			0
$680$	19.3525	−	11.1732i	0.742134	−	0.428471i
$681$	−22.7985	+	10.9944i	−0.873639	+	0.421306i
$682$	−1.57861	−	0.911413i	−0.0604483	−	0.0348998i
$683$		−	29.6654i		−	1.13511i	−0.823334	−	0.567557i	$-0.807888\pi$
$683$		−	29.6654i		−	1.13511i	0.823334	−	0.567557i	$-0.192112\pi$
$684$	2.37823	+	1.89236i	0.0909339	+	0.0723560i
$685$		−	0.00233490i		−	8.92121e-5i
$686$		0			0
$687$	−4.10952	−	0.305723i	−0.156788	−	0.0116641i
$688$	−2.39949	−	4.15605i	−0.0914799	−	0.158448i
$689$	14.9195	+	25.8413i	0.568387	+	0.984475i
$690$	1.40826	−	18.9297i	0.0536114	−	0.720641i
$691$	−40.9767	−	23.6579i	−1.55883	−	0.899990i	−0.997369	−	0.0724857i	$-0.976907\pi$
$691$	−40.9767	−	23.6579i	−1.55883	−	0.899990i	−0.561459	−	0.827504i	$-0.689760\pi$
$692$	−3.07081			−0.116735
$693$		0			0
$694$	17.4712			0.663197
$695$	31.6065	+	18.2480i	1.19890	+	0.692187i
$696$	9.08948	−	4.38334i	0.344536	−	0.166150i
$697$	−17.5992	−	30.4827i	−0.666616	−	1.15461i
$698$	−11.9129	−	20.6338i	−0.450910	−	0.780999i
$699$	10.1708	−	14.9352i	0.384693	−	0.564900i
$700$		0			0
$701$		−	13.7742i		−	0.520244i	−0.965576	−	0.260122i	$-0.916237\pi$
$701$		−	13.7742i		−	0.520244i	0.965576	−	0.260122i	$-0.0837627\pi$
$702$	−3.91325	+	17.2747i	−0.147696	+	0.651990i
$703$			7.43246i			0.280320i
$704$	−1.73534	−	1.00190i	−0.0654030	−	0.0377604i
$705$	11.5558	+	7.86944i	0.435217	+	0.296380i
$706$	−8.69596	+	5.02061i	−0.327277	+	0.188953i
$707$		0			0
$708$	14.0196	−	6.76087i	0.526889	−	0.254089i
$709$	21.9691	−	38.0517i	0.825069	−	1.42906i	−0.0767981	−	0.997047i	$-0.524470\pi$
$709$	21.9691	−	38.0517i	0.825069	−	1.42906i	0.901867	−	0.432014i	$-0.142197\pi$
$710$	1.68764			0.0633360
$711$	−11.3497	−	1.69809i	−0.425646	−	0.0636835i
$712$		−	4.78647i		−	0.179381i
$713$	−1.37726	+	2.38549i	−0.0515789	+	0.0893373i
$714$		0			0
$715$	−12.3607	−	21.4094i	−0.462265	−	0.800667i
$716$	16.7310	−	9.65966i	0.625268	−	0.360998i
$717$	−41.0807	−	3.05616i	−1.53419	−	0.114134i
$718$	6.08254	−	10.5353i	0.226998	−	0.393173i
$719$	−29.5860			−1.10337			−0.551687	−	0.834051i	$-0.686016\pi$
$719$	−29.5860			−1.10337			−0.551687	+	0.834051i	$0.686016\pi$
$720$	−3.97782	−	10.1031i	−0.148245	−	0.376519i
$721$		0			0
$722$	15.5657	+	8.98683i	0.579294	+	0.334455i
$723$	−21.5540	−	44.6953i	−0.801602	−	1.66224i
$724$	6.83569	−	3.94659i	0.254046	−	0.146674i
$725$	−40.8666	+	23.5943i	−1.51775	+	0.876271i
$726$	−6.80964	+	9.99957i	−0.252730	+	0.371119i
$727$	−10.1244	−	5.84534i	−0.375494	−	0.216792i	0.300362	−	0.953825i	$-0.402893\pi$
$727$	−10.1244	−	5.84534i	−0.375494	−	0.216792i	−0.675856	+	0.737034i	$0.736226\pi$
$728$		0			0
$729$	−24.3642	−	11.6356i	−0.902377	−	0.430948i
$730$	15.2551			0.564617
$731$	14.8149	−	25.6602i	0.547949	−	0.949076i
$732$	14.3431	−	21.0620i	0.530137	−	0.778475i
$733$	−28.6423	+	16.5366i	−1.05793	+	0.610795i	−0.924858	−	0.380312i	$-0.875817\pi$
$733$	−28.6423	+	16.5366i	−1.05793	+	0.610795i	−0.133070	+	0.991107i	$0.542483\pi$
$734$	1.81531	+	3.14420i	0.0670042	+	0.116055i
$735$		0			0
$736$	−1.51400	+	2.62232i	−0.0558067	+	0.0966600i
$737$			16.6644i			0.613841i
$738$	−15.9136	+	6.26558i	−0.585789	+	0.230639i
$739$	43.5056			1.60038			0.800190	−	0.599747i	$-0.204732\pi$
$739$	43.5056			1.60038			0.800190	+	0.599747i	$0.204732\pi$
$740$	13.2765	−	22.9957i	0.488056	−	0.845337i
$741$	0.443750	−	5.96486i	0.0163016	−	0.219125i
$742$		0			0
$743$	18.0206	−	10.4042i	0.661112	−	0.381693i	−0.131589	−	0.991304i	$-0.542008\pi$
$743$	18.0206	−	10.4042i	0.661112	−	0.381693i	0.792701	+	0.609611i	$0.208674\pi$
$744$	−0.116894	+	1.57128i	−0.00428554	+	0.0576060i
$745$	35.2544	+	20.3542i	1.29162	+	0.745719i
$746$		−	5.49231i		−	0.201088i
$747$	23.7644	+	3.55553i	0.869493	+	0.130090i
$748$		−	12.3718i		−	0.452358i
$749$		0			0
$750$	8.43983	+	17.5012i	0.308179	+	0.639053i
$751$	19.9492	+	34.5531i	0.727957	+	1.26086i	0.957745	+	0.287618i	$0.0928634\pi$
$751$	19.9492	+	34.5531i	0.727957	+	1.26086i	−0.229788	+	0.973241i	$0.573803\pi$
$752$	−1.11511	−	1.93143i	−0.0406638	−	0.0704318i
$753$	−15.7909	−	10.7535i	−0.575453	−	0.391880i
$754$	−17.1992	−	9.92994i	−0.626357	−	0.361627i
$755$	17.0969			0.622219
$756$		0			0
$757$	7.45545			0.270973			0.135486	−	0.990779i	$-0.456740\pi$
$757$	7.45545			0.270973			0.135486	+	0.990779i	$0.456740\pi$
$758$	−13.5065	−	7.79800i	−0.490579	−	0.283236i
$759$	−8.68630	−	5.91532i	−0.315293	−	0.214713i
$760$	1.83333	+	3.17542i	0.0665018	+	0.115185i
$761$	4.32462	+	7.49046i	0.156767	+	0.271529i	0.933701	−	0.358053i	$-0.116559\pi$
$761$	4.32462	+	7.49046i	0.156767	+	0.271529i	−0.776934	+	0.629582i	$0.783226\pi$
$762$	−13.4891	−	27.9716i	−0.488658	−	1.01330i
$763$		0			0
$764$		−	13.3042i		−	0.481330i
$765$	41.7412	−	52.4585i	1.50916	−	1.89664i
$766$		−	9.43067i		−	0.340744i
$767$	−26.5280	−	15.3159i	−0.957870	−	0.553026i
$768$	−0.128499	+	1.72728i	−0.00463681	+	0.0623278i
$769$	−20.4818	+	11.8252i	−0.738592	+	0.426426i	−0.821557	−	0.570126i	$-0.806894\pi$
$769$	−20.4818	+	11.8252i	−0.738592	+	0.426426i	0.0829652	+	0.996552i	$0.473561\pi$
$770$		0			0
$771$	1.94005	−	26.0781i	0.0698693	−	0.939180i
$772$	3.26786	−	5.66011i	0.117613	−	0.203712i
$773$	46.5699			1.67500			0.837501	−	0.546436i	$-0.184016\pi$
$773$	46.5699			1.67500			0.837501	+	0.546436i	$0.184016\pi$
$774$	−11.2657	−	8.96414i	−0.404939	−	0.322209i
$775$		−	7.36796i		−	0.264665i
$776$	−5.87944	+	10.1835i	−0.211060	+	0.365566i
$777$		0			0
$778$	−3.21089	−	5.56142i	−0.115116	−	0.199387i
$779$	5.00170	−	2.88773i	0.179204	−	0.103464i
$780$	−12.0279	+	17.6623i	−0.430669	+	0.632412i
$781$	0.467172	−	0.809166i	0.0167167	−	0.0289542i
$782$	−18.6954			−0.668546
$783$	20.5551	−	22.2256i	0.734580	−	0.794279i
$784$		0			0
$785$	−9.62178	−	5.55513i	−0.343416	−	0.198271i
$786$	−16.8967	+	24.8118i	−0.602686	+	0.885009i
$787$	21.1657	−	12.2200i	0.754474	−	0.435596i	−0.0728341	−	0.997344i	$-0.523204\pi$
$787$	21.1657	−	12.2200i	0.754474	−	0.435596i	0.827308	+	0.561748i	$0.189871\pi$
$788$	−3.84732	+	2.22125i	−0.137055	+	0.0791288i
$789$	14.7752	+	30.6384i	0.526009	+	1.09076i
$790$	−11.9902	−	6.92255i	−0.426592	−	0.246293i
$791$		0			0
$792$	−5.94521	−	0.889499i	−0.211254	−	0.0316070i
$793$	−50.1496			−1.78087
$794$	3.46266	−	5.99750i	0.122885	−	0.212843i
$795$	−54.7240	−	4.07114i	−1.94086	−	0.144388i
$796$	−9.96868	+	5.75542i	−0.353330	+	0.203995i
$797$	24.9202	+	43.1631i	0.882719	+	1.52891i	0.848306	+	0.529506i	$0.177623\pi$
$797$	24.9202	+	43.1631i	0.882719	+	1.52891i	0.0344128	+	0.999408i	$0.489044\pi$
$798$		0			0
$799$	6.88489	−	11.9250i	0.243570	−	0.421875i
$800$		−	8.09945i		−	0.286359i
$801$	−5.26059	−	13.3611i	−0.185874	−	0.472091i
$802$	10.5869			0.373835
$803$	4.22291	−	7.31430i	0.149023	−	0.258116i
$804$	12.9746	−	6.25690i	0.457578	−	0.220664i
$805$		0			0
$806$	2.68545	−	1.55045i	0.0945910	−	0.0546121i
$807$	−0.702931	−	0.478692i	−0.0247444	−	0.0168508i
$808$	11.1650	+	6.44610i	0.392782	+	0.226773i
$809$			12.3247i			0.433315i	0.976248	+	0.216657i	$0.0695154\pi$
$809$			12.3247i			0.433315i	−0.976248	+	0.216657i	$0.930485\pi$
$810$	−22.2076	−	23.8302i	−0.780296	−	0.837307i
$811$			24.8017i			0.870906i	0.900212	+	0.435453i	$0.143412\pi$
$811$			24.8017i			0.870906i	−0.900212	+	0.435453i	$0.856588\pi$
$812$		0			0
$813$	13.7258	−	20.1556i	0.481386	−	0.706888i
$814$	−7.35042	−	12.7313i	−0.257632	−	0.446232i
$815$	5.20047	+	9.00748i	0.182165	+	0.315518i
$816$	−9.63244	+	4.64518i	−0.337203	+	0.162614i
$817$	4.21041	+	2.43088i	0.147304	+	0.0850457i
$818$	−8.92343			−0.312000
$819$		0			0
$820$	−20.6333			−0.720547
$821$	−31.3573	−	18.1041i	−1.09438	−	0.631839i	−0.159639	−	0.987175i	$-0.551033\pi$
$821$	−31.3573	−	18.1041i	−1.09438	−	0.631839i	−0.934738	+	0.355336i	$0.884366\pi$
$822$	−8.28977e−5		0.00111431i	−2.89139e−6		3.88659e-5i
$823$	9.54093	+	16.5254i	0.332576	+	0.576038i	0.983016	−	0.183519i	$-0.0587489\pi$
$823$	9.54093	+	16.5254i	0.332576	+	0.576038i	−0.650440	+	0.759557i	$0.725416\pi$
$824$	5.37940	+	9.31740i	0.187400	+	0.324587i
$825$	28.0331	+	2.08549i	0.975986	+	0.0726075i
$826$		0			0
$827$		−	31.9013i		−	1.10932i	−0.832079	−	0.554658i	$-0.812849\pi$
$827$		−	31.9013i		−	1.10932i	0.832079	−	0.554658i	$-0.187151\pi$
$828$	−1.34415	+	8.98399i	−0.0467124	+	0.312215i
$829$			15.0856i			0.523943i	0.965076	+	0.261971i	$0.0843726\pi$
$829$			15.0856i			0.523943i	−0.965076	+	0.261971i	$0.915627\pi$
$830$	25.1055	+	14.4947i	0.871425	+	0.503118i
$831$	47.9268	−	23.1124i	1.66256	−	0.801760i
$832$	2.95206	−	1.70437i	0.102344	−	0.0590885i
$833$		0			0
$834$	−14.4360	−	9.83082i	−0.499877	−	0.340413i
$835$	2.64397	−	4.57950i	0.0914985	−	0.158480i
$836$	2.03000			0.0702092
$837$	1.40062	+	4.51460i	0.0484126	+	0.156047i
$838$		−	34.3848i		−	1.18780i
$839$	8.19860	−	14.2004i	0.283047	−	0.490252i	−0.689087	−	0.724679i	$-0.741988\pi$
$839$	8.19860	−	14.2004i	0.283047	−	0.490252i	0.972134	+	0.234427i	$0.0753214\pi$
$840$		0			0
$841$	2.47206	+	4.28173i	0.0852434	+	0.147646i
$842$	−30.8028	+	17.7840i	−1.06153	+	0.612877i
$843$	−5.96208	−	12.3632i	−0.205345	−	0.425812i
$844$	−11.3005	+	19.5731i	−0.388980	+	0.673734i
$845$	−4.99634			−0.171879
$846$	−5.23549	−	4.16587i	−0.180000	−	0.143226i
$847$		0			0
$848$	7.58088	+	4.37683i	0.260329	+	0.150301i
$849$	−19.8911	−	1.47978i	−0.682660	−	0.0507858i
$850$	43.3077	−	25.0037i	1.48544	−	0.857621i
$851$	−19.2386	+	11.1074i	−0.659492	+	0.380758i
$852$	−0.805408	−	0.0599175i	−0.0275928	−	0.00205274i
$853$	−16.5936	−	9.58030i	−0.568153	−	0.328023i	0.188258	−	0.982120i	$-0.439716\pi$
$853$	−16.5936	−	9.58030i	−0.568153	−	0.328023i	−0.756411	+	0.654096i	$0.773049\pi$
$854$		0			0
$855$	8.60756	+	6.84903i	0.294372	+	0.234232i
$856$	2.63967			0.0902219
$857$	−8.05723	+	13.9555i	−0.275230	+	0.476712i	−0.970193	−	0.242333i	$-0.922087\pi$
$857$	−8.05723	+	13.9555i	−0.275230	+	0.476712i	0.694963	+	0.719045i	$0.255421\pi$
$858$	5.13891	+	10.6563i	0.175439	+	0.363798i
$859$	10.4830	−	6.05238i	0.357677	−	0.206505i	−0.310384	−	0.950611i	$-0.600458\pi$
$859$	10.4830	−	6.05238i	0.357677	−	0.206505i	0.668061	+	0.744106i	$0.267124\pi$
$860$	−8.68453	−	15.0420i	−0.296140	−	0.512929i
$861$		0			0
$862$	−15.4348	+	26.7338i	−0.525710	+	0.910556i
$863$			37.2655i			1.26853i	0.773115	+	0.634265i	$0.218697\pi$
$863$			37.2655i			1.26853i	−0.773115	+	0.634265i	$0.781303\pi$
$864$	1.53967	+	4.96280i	0.0523808	+	0.168838i
$865$	−11.1142			−0.377896
$866$	−11.6232	+	20.1319i	−0.394971	+	0.684110i
$867$	−30.2365	−	20.5909i	−1.02689	−	0.699303i
$868$		0			0
$869$	−6.63824	+	3.83259i	−0.225187	+	0.130012i
$870$	32.8977	−	15.8647i	1.11534	−	0.537864i
$871$	−24.5505	−	14.1743i	−0.831863	−	0.480276i
$872$		−	9.03535i		−	0.305976i
$873$	−5.21985	+	34.8883i	−0.176665	+	1.18079i
$874$		−	3.06760i		−	0.103763i
$875$		0			0
$876$	−7.28033	−	0.541613i	−0.245980	−	0.0182994i
$877$	4.85474	+	8.40866i	0.163933	+	0.283940i	0.936276	−	0.351266i	$-0.114249\pi$
$877$	4.85474	+	8.40866i	0.163933	+	0.283940i	−0.772343	+	0.635206i	$0.780915\pi$
$878$	−11.1364	−	19.2887i	−0.375834	−	0.650963i
$879$	0.644905	−	8.66877i	0.0217521	−	0.292390i
$880$	−6.28073	−	3.62618i	−0.211723	−	0.122239i
$881$	2.63241			0.0886881			0.0443440	−	0.999016i	$-0.485880\pi$
$881$	2.63241			0.0886881			0.0443440	+	0.999016i	$0.485880\pi$
$882$		0			0
$883$	−36.3181			−1.22220			−0.611101	−	0.791553i	$-0.709273\pi$
$883$	−36.3181			−1.22220			−0.611101	+	0.791553i	$0.709273\pi$
$884$	18.2265	+	10.5231i	0.613025	+	0.353930i
$885$	50.7414	−	24.4697i	1.70565	−	0.822540i
$886$	−8.99259	−	15.5756i	−0.302112	−	0.523273i
$887$	8.18209	+	14.1718i	0.274728	+	0.475842i	0.970066	−	0.242840i	$-0.0780790\pi$
$887$	8.18209	+	14.1718i	0.274728	+	0.475842i	−0.695339	+	0.718682i	$0.744746\pi$
$888$	−7.15251	+	10.5031i	−0.240023	+	0.352459i
$889$		0			0
$890$		−	17.3238i		−	0.580694i
$891$	−17.5732	+	4.05113i	−0.588726	+	0.135718i
$892$		−	18.8209i		−	0.630170i
$893$	1.95669	+	1.12969i	0.0654781	+	0.0378038i
$894$	−16.1021	−	10.9655i	−0.538536	−	0.366740i
$895$	60.5549	−	34.9614i	2.02413	−	1.16863i
$896$		0			0
$897$	16.1030	−	7.76555i	0.537663	−	0.259284i
$898$	4.72182	−	8.17843i	0.157569	−	0.272918i
$899$	−5.29998			−0.176764
$900$	−8.90172	−	22.6090i	−0.296724	−	0.753635i
$901$			54.0466i			1.80055i
$902$	−5.71171	+	9.89297i	−0.190179	+	0.329400i
$903$		0			0
$904$	−0.845306	−	1.46411i	−0.0281145	−	0.0486957i
$905$	24.7405	−	14.2839i	0.822403	−	0.474814i
$906$	−8.15930	−	0.607002i	−0.271074	−	0.0201663i
$907$	−5.41666	+	9.38192i	−0.179857	+	0.311522i	−0.941831	−	0.336086i	$-0.890897\pi$
$907$	−5.41666	+	9.38192i	−0.179857	+	0.311522i	0.761974	+	0.647607i	$0.224230\pi$
$908$	14.6133			0.484960
$909$	38.2509	+	5.72294i	1.26870	+	0.189818i
$910$		0			0
$911$	36.8512	+	21.2760i	1.22093	+	0.704907i	0.965117	−	0.261818i	$-0.0843221\pi$
$911$	36.8512	+	21.2760i	1.22093	+	0.704907i	0.255817	+	0.966725i	$0.417655\pi$
$912$	−0.762196	−	1.58052i	−0.0252388	−	0.0523363i
$913$	13.8994	−	8.02482i	0.460003	−	0.265583i
$914$	1.59739	−	0.922251i	0.0528368	−	0.0305053i
$915$	51.9123	−	76.2301i	1.71617	−	2.52009i
$916$	2.06044	+	1.18959i	0.0680788	+	0.0393053i
$917$		0			0
$918$	−21.7830	+	23.5533i	−0.718946	+	0.777373i
$919$	25.9393			0.855659			0.427829	−	0.903860i	$-0.359278\pi$
$919$	25.9393			0.855659			0.427829	+	0.903860i	$0.359278\pi$
$920$	−5.47963	+	9.49100i	−0.180658	+	0.312909i
$921$	17.0913	−	25.0975i	0.563177	−	0.826992i
$922$	31.5007	−	18.1869i	1.03742	−	0.598955i
$923$	0.794727	+	1.37651i	0.0261588	+	0.0453083i
$924$		0			0
$925$	29.7108	−	51.4606i	0.976884	−	1.69201i
$926$		−	31.9660i		−	1.05047i
$927$	25.2565	+	20.0966i	0.829534	+	0.660059i
$928$	−5.82616			−0.191253
$929$	23.4456	−	40.6089i	0.769224	−	1.33234i	−0.168760	−	0.985657i	$-0.553976\pi$
$929$	23.4456	−	40.6089i	0.769224	−	1.33234i	0.937984	−	0.346678i	$-0.112690\pi$
$930$	−0.423076	+	5.68697i	−0.0138732	+	0.186483i
$931$		0			0
$932$	−9.03470	+	5.21619i	−0.295942	+	0.170862i
$933$	2.22241	−	29.8736i	0.0727586	−	0.978017i
$934$	21.1666	+	12.2206i	0.692593	+	0.399869i
$935$		−	44.7774i		−	1.46438i
$936$	6.36727	−	8.00210i	0.208121	−	0.261557i
$937$			0.209357i			0.00683939i	0.999994	+	0.00341969i	$0.00108852\pi$
$937$			0.209357i			0.00683939i	−0.999994	+	0.00341969i	$0.998911\pi$
$938$		0			0
$939$	6.76742	+	14.0332i	0.220846	+	0.457956i
$940$	−4.03593	−	6.99044i	−0.131638	−	0.228003i
$941$	−0.388565	−	0.673014i	−0.0126669	−	0.0219396i	0.859622	−	0.510930i	$-0.170699\pi$
$941$	−0.388565	−	0.673014i	−0.0126669	−	0.0219396i	−0.872289	+	0.488990i	$0.837365\pi$
$942$	4.39466	+	2.99273i	0.143186	+	0.0975085i
$943$	14.9496	+	8.63113i	0.486825	+	0.281068i
$944$	−8.98627			−0.292478
$945$		0			0
$946$	−9.61619			−0.312649
$947$	−43.1233	−	24.8972i	−1.40132	−	0.809052i	−0.406791	−	0.913521i	$-0.633352\pi$
$947$	−43.1233	−	24.8972i	−1.40132	−	0.809052i	−0.994528	+	0.104470i	$0.966686\pi$
$948$	5.47641	+	3.72940i	0.177866	+	0.121125i
$949$	7.18378	+	12.4427i	0.233196	+	0.403906i
$950$	4.10269	+	7.10607i	0.133109	+	0.230552i
$951$	−5.05612	−	10.4846i	−0.163956	−	0.339986i
$952$		0			0
$953$		−	41.4104i		−	1.34141i	−0.741722	−	0.670707i	$-0.765991\pi$
$953$		−	41.4104i		−	1.34141i	0.741722	−	0.670707i	$-0.234009\pi$
$954$	25.9719	+	3.88581i	0.840870	+	0.125808i
$955$		−	48.1522i		−	1.55817i
$956$	20.5971	+	11.8917i	0.666158	+	0.384607i
$957$	1.50015	−	20.1650i	0.0484930	−	0.651841i
$958$	−9.49220	+	5.48032i	−0.306679	+	0.177061i
$959$		0			0
$960$	−0.465079	+	6.25156i	−0.0150103	+	0.201768i
$961$	−15.0862	+	26.1301i	−0.486653	+	0.842907i
$962$	25.0082			0.806298
$963$	7.36844	−	2.90113i	0.237445	−	0.0934877i
$964$			28.6487i			0.922712i
$965$	11.8274	−	20.4857i	0.380739	−	0.659459i
$966$		0			0
$967$	22.8028	+	39.4956i	0.733289	+	1.27009i	0.955470	+	0.295088i	$0.0953491\pi$
$967$	22.8028	+	39.4956i	0.733289	+	1.27009i	−0.222181	+	0.975005i	$0.571318\pi$
$968$	6.04902	−	3.49240i	0.194423	−	0.112250i
$969$	6.09808	−	8.95468i	0.195899	−	0.287666i
$970$	−21.2796	+	36.8573i	−0.683245	+	1.18342i
$971$	−8.73466			−0.280309			−0.140154	−	0.990130i	$-0.544760\pi$
$971$	−8.73466			−0.280309			−0.140154	+	0.990130i	$0.544760\pi$
$972$	9.75228	+	12.1611i	0.312804	+	0.390068i
$973$		0			0
$974$	29.1136	+	16.8087i	0.932860	+	0.538587i
$975$	−26.9166	+	39.5254i	−0.862020	+	1.26583i
$976$	−12.7410	+	7.35603i	−0.407830	+	0.235461i
$977$	12.9058	−	7.45114i	0.412892	−	0.238383i	−0.279140	−	0.960250i	$-0.590049\pi$
$977$	12.9058	−	7.45114i	0.412892	−	0.238383i	0.692031	+	0.721867i	$0.256716\pi$
$978$	−2.16207	−	4.48336i	−0.0691353	−	0.143362i
$979$	−8.30615	−	4.79556i	−0.265466	−	0.153267i
$980$		0			0
$981$	−9.93033	−	25.2216i	−0.317051	−	0.805262i
$982$	−22.7353			−0.725512
$983$	1.53458	−	2.65798i	0.0489456	−	0.0847763i	−0.840515	−	0.541789i	$-0.817747\pi$
$983$	1.53458	−	2.65798i	0.0489456	−	0.0847763i	0.889460	+	0.457013i	$0.151081\pi$
$984$	9.84702	+	0.732559i	0.313912	+	0.0233531i
$985$	−13.9247	+	8.03941i	−0.443677	+	0.256157i
$986$	−17.9859	−	31.1525i	−0.572787	−	0.992096i
$987$		0			0
$988$	−1.72667	+	2.99067i	−0.0549325	+	0.0951460i
$989$			14.5313i			0.462069i
$990$	−21.5176	−	3.21938i	−0.683874	−	0.102318i
$991$	−55.8150			−1.77302			−0.886510	−	0.462709i	$-0.846878\pi$
$991$	−55.8150			−1.77302			−0.886510	+	0.462709i	$0.846878\pi$
$992$	0.454844	−	0.787812i	0.0144413	−	0.0250131i
$993$	−29.2904	+	14.1251i	−0.929502	+	0.448246i
$994$		0			0
$995$	−36.0798	+	20.8307i	−1.14381	+	0.660377i
$996$	−11.4667	−	7.80876i	−0.363337	−	0.247430i
$997$	5.30607	+	3.06346i	0.168045	+	0.0970208i	0.581664	−	0.813429i	$-0.302402\pi$
$997$	5.30607	+	3.06346i	0.168045	+	0.0970208i	−0.413619	+	0.910450i	$0.635735\pi$
$998$		−	19.5235i		−	0.618006i
$999$	−8.42233	+	37.1795i	−0.266471	+	1.17631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.m.a.587.6		16
3.2	odd	2		2646.2.m.a.1763.1		16
7.2	even	3		882.2.l.b.227.4		16
7.3	odd	6		882.2.t.a.803.3		16
7.4	even	3		126.2.t.a.47.2	yes	16
7.5	odd	6		126.2.l.a.101.1	yes	16
7.6	odd	2		882.2.m.b.587.7		16
9.4	even	3		2646.2.m.b.881.4		16
9.5	odd	6		882.2.m.b.293.7		16
21.2	odd	6		2646.2.l.a.521.5		16
21.5	even	6		378.2.l.a.143.8		16
21.11	odd	6		378.2.t.a.89.8		16
21.17	even	6		2646.2.t.b.1979.5		16
21.20	even	2		2646.2.m.b.1763.4		16
28.11	odd	6		1008.2.df.c.929.5		16
28.19	even	6		1008.2.ca.c.353.8		16
63.4	even	3		378.2.l.a.341.4		16
63.5	even	6		126.2.t.a.59.2	yes	16
63.11	odd	6		1134.2.k.a.971.1		16
63.13	odd	6		2646.2.m.a.881.1		16
63.23	odd	6		882.2.t.a.815.3		16
63.25	even	3		1134.2.k.b.971.8		16
63.31	odd	6		2646.2.l.a.1097.1		16
63.32	odd	6		126.2.l.a.5.5	✓	16
63.40	odd	6		378.2.t.a.17.8		16
63.41	even	6	inner	882.2.m.a.293.6		16
63.47	even	6		1134.2.k.b.647.8		16
63.58	even	3		2646.2.t.b.2285.5		16
63.59	even	6		882.2.l.b.509.8		16
63.61	odd	6		1134.2.k.a.647.1		16
84.11	even	6		3024.2.df.c.1601.7		16
84.47	odd	6		3024.2.ca.c.2033.7		16
252.67	odd	6		3024.2.ca.c.2609.7		16
252.95	even	6		1008.2.ca.c.257.8		16
252.103	even	6		3024.2.df.c.17.7		16
252.131	odd	6		1008.2.df.c.689.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.5	✓	16	63.32	odd	6
126.2.l.a.101.1	yes	16	7.5	odd	6
126.2.t.a.47.2	yes	16	7.4	even	3
126.2.t.a.59.2	yes	16	63.5	even	6
378.2.l.a.143.8		16	21.5	even	6
378.2.l.a.341.4		16	63.4	even	3
378.2.t.a.17.8		16	63.40	odd	6
378.2.t.a.89.8		16	21.11	odd	6
882.2.l.b.227.4		16	7.2	even	3
882.2.l.b.509.8		16	63.59	even	6
882.2.m.a.293.6		16	63.41	even	6	inner
882.2.m.a.587.6		16	1.1	even	1	trivial
882.2.m.b.293.7		16	9.5	odd	6
882.2.m.b.587.7		16	7.6	odd	2
882.2.t.a.803.3		16	7.3	odd	6
882.2.t.a.815.3		16	63.23	odd	6
1008.2.ca.c.257.8		16	252.95	even	6
1008.2.ca.c.353.8		16	28.19	even	6
1008.2.df.c.689.5		16	252.131	odd	6
1008.2.df.c.929.5		16	28.11	odd	6
1134.2.k.a.647.1		16	63.61	odd	6
1134.2.k.a.971.1		16	63.11	odd	6
1134.2.k.b.647.8		16	63.47	even	6
1134.2.k.b.971.8		16	63.25	even	3
2646.2.l.a.521.5		16	21.2	odd	6
2646.2.l.a.1097.1		16	63.31	odd	6
2646.2.m.a.881.1		16	63.13	odd	6
2646.2.m.a.1763.1		16	3.2	odd	2
2646.2.m.b.881.4		16	9.4	even	3
2646.2.m.b.1763.4		16	21.20	even	2
2646.2.t.b.1979.5		16	21.17	even	6
2646.2.t.b.2285.5		16	63.58	even	3
3024.2.ca.c.2033.7		16	84.47	odd	6
3024.2.ca.c.2609.7		16	252.67	odd	6
3024.2.df.c.17.7		16	252.103	even	6
3024.2.df.c.1601.7		16	84.11	even	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.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.43162 - 0.974922i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.80966 + 3.13442i) q^{5} +(-0.752355 - 1.56012i) q^{6} +1.00000i q^{8} +(1.09905 + 2.79143i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.43162 - 0.974922i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.80966 + 3.13442i) q^{5} +(-0.752355 - 1.56012i) q^{6} +1.00000i q^{8} +(1.09905 + 2.79143i) q^{9} +3.61932i q^{10} +(1.73534 + 1.00190i) q^{11} +(0.128499 - 1.72728i) q^{12} +(-2.95206 + 1.70437i) q^{13} +(0.465079 - 6.25156i) q^{15} +(-0.500000 + 0.866025i) q^{16} -6.17418 q^{17} +(-0.443907 + 2.96698i) q^{18} -1.01308i q^{19} +(-1.80966 + 3.13442i) q^{20} +(1.00190 + 1.73534i) q^{22} +(2.62232 - 1.51400i) q^{23} +(0.974922 - 1.43162i) q^{24} +(-4.04972 + 7.01433i) q^{25} -3.40874 q^{26} +(1.14800 - 5.06775i) q^{27} +(5.04560 + 2.91308i) q^{29} +(3.52855 - 5.18147i) q^{30} +(-0.787812 + 0.454844i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.50757 - 3.12615i) q^{33} +(-5.34700 - 3.08709i) q^{34} +(-1.86792 + 2.34752i) q^{36} -7.33650 q^{37} +(0.506540 - 0.877353i) q^{38} +(5.88785 + 0.438020i) q^{39} +(-3.13442 + 1.80966i) q^{40} +(2.85045 + 4.93712i) q^{41} +(-2.39949 + 4.15605i) q^{43} +2.00379i q^{44} +(-6.76060 + 8.49643i) q^{45} +3.02799 q^{46} +(-1.11511 + 1.93143i) q^{47} +(1.56012 - 0.752355i) q^{48} +(-7.01433 + 4.04972i) q^{50} +(8.83906 + 6.01935i) q^{51} +(-2.95206 - 1.70437i) q^{52} -8.75365i q^{53} +(3.52808 - 3.81480i) q^{54} +7.25237i q^{55} +(-0.987674 + 1.45034i) q^{57} +(2.91308 + 5.04560i) q^{58} +(4.49313 + 7.78233i) q^{59} +(5.64655 - 2.72301i) q^{60} +(12.7410 + 7.35603i) q^{61} -0.909687 q^{62} -1.00000 q^{64} +(-10.6844 - 6.16866i) q^{65} +(0.257486 - 3.46111i) q^{66} +(4.15821 + 7.20222i) q^{67} +(-3.08709 - 5.34700i) q^{68} +(-5.23019 - 0.389094i) q^{69} -0.466287i q^{71} +(-2.79143 + 1.09905i) q^{72} -4.21492i q^{73} +(-6.35359 - 3.66825i) q^{74} +(12.6361 - 6.09366i) q^{75} +(0.877353 - 0.506540i) q^{76} +(4.88001 + 3.32326i) q^{78} +(-1.91267 + 3.31284i) q^{79} -3.61932 q^{80} +(-6.58416 + 6.13586i) q^{81} +5.70089i q^{82} +(4.00481 - 6.93654i) q^{83} +(-11.1732 - 19.3525i) q^{85} +(-4.15605 + 2.39949i) q^{86} +(-4.38334 - 9.08948i) q^{87} +(-1.00190 + 1.73534i) q^{88} -4.78647 q^{89} +(-10.1031 + 3.97782i) q^{90} +(2.62232 + 1.51400i) q^{92} +(1.57128 + 0.116894i) q^{93} +(-1.93143 + 1.11511i) q^{94} +(3.17542 - 1.83333i) q^{95} +(1.72728 + 0.128499i) q^{96} +(10.1835 + 5.87944i) q^{97} +(-0.889499 + 5.94521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 6 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 6 * q^9	\( 16 q + 8 q^{4} + 6 q^{9} - 12 q^{11} - 6 q^{13} - 18 q^{15} - 8 q^{16} - 36 q^{17} + 6 q^{23} + 6 q^{24} - 8 q^{25} + 24 q^{26} - 36 q^{27} + 6 q^{29} + 18 q^{30} - 6 q^{31} - 18 q^{33} + 4 q^{37} + 42 q^{39} + 6 q^{41} - 2 q^{43} - 42 q^{45} - 12 q^{46} - 18 q^{47} - 12 q^{50} - 6 q^{51} - 6 q^{52} + 6 q^{57} + 6 q^{58} + 30 q^{59} - 12 q^{60} + 60 q^{61} - 36 q^{62} - 16 q^{64} - 42 q^{65} - 24 q^{66} + 14 q^{67} - 18 q^{68} + 42 q^{69} - 12 q^{72} - 18 q^{74} + 30 q^{75} - 16 q^{79} - 18 q^{81} - 12 q^{85} - 24 q^{86} + 24 q^{87} - 48 q^{89} - 18 q^{90} + 6 q^{92} + 12 q^{93} + 66 q^{95} + 6 q^{96} - 6 q^{97} + 18 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 6 * q^9 - 12 * q^11 - 6 * q^13 - 18 * q^15 - 8 * q^16 - 36 * q^17 + 6 * q^23 + 6 * q^24 - 8 * q^25 + 24 * q^26 - 36 * q^27 + 6 * q^29 + 18 * q^30 - 6 * q^31 - 18 * q^33 + 4 * q^37 + 42 * q^39 + 6 * q^41 - 2 * q^43 - 42 * q^45 - 12 * q^46 - 18 * q^47 - 12 * q^50 - 6 * q^51 - 6 * q^52 + 6 * q^57 + 6 * q^58 + 30 * q^59 - 12 * q^60 + 60 * q^61 - 36 * q^62 - 16 * q^64 - 42 * q^65 - 24 * q^66 + 14 * q^67 - 18 * q^68 + 42 * q^69 - 12 * q^72 - 18 * q^74 + 30 * q^75 - 16 * q^79 - 18 * q^81 - 12 * q^85 - 24 * q^86 + 24 * q^87 - 48 * q^89 - 18 * q^90 + 6 * q^92 + 12 * q^93 + 66 * q^95 + 6 * q^96 - 6 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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