LMFDB - Embedded newform 882.2.m.b.293.7

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			293.7
Root			$1.71298 + 0.256290i$ of defining polynomial
Character	$\chi$	$=$	882.293
Dual form			882.2.m.b.587.7

$q$-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} +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} - 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}+ \cdots + 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

Character values

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

$n$	$199$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	0.104043	+	0.994573i	$0.466822\pi$
$5$	−1.80966	+	3.13442i	−0.809304	+	1.40175i	−0.913347	+	0.407182i	$0.866511\pi$
$6$	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	−0.215029	−	0.976608i	$-0.568985\pi$
$11$	1.73534	−	1.00190i	0.523224	−	0.302083i	0.738253	+	0.674524i	$0.235651\pi$
$12$	−0.128499	−	1.72728i	−0.0370945	−	0.498622i
$13$	2.95206	+	1.70437i	0.818754	+	0.472708i	0.849987	−	0.526804i	$-0.176610\pi$
$13$	2.95206	+	1.70437i	0.818754	+	0.472708i	−0.0312328	+	0.999512i	$0.509943\pi$
$14$		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	$-0.230664\pi$
$17$	6.17418			1.49746			0.748730	+	0.662876i	$0.230664\pi$
$18$	−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	0.747827	−	0.663894i	$-0.231097\pi$
$23$	2.62232	+	1.51400i	0.546791	+	0.315690i	−0.201035	+	0.979584i	$0.564431\pi$
$24$	−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	0.0479434	−	0.998850i	$-0.484733\pi$
$29$	5.04560	−	2.91308i	0.936945	−	0.540945i	0.889001	+	0.457905i	$0.151400\pi$
$30$	3.52855	+	5.18147i	0.644222	+	0.946003i
$31$	0.787812	+	0.454844i	0.141495	+	0.0816923i	0.569076	−	0.822285i	$-0.307301\pi$
$31$	0.787812	+	0.454844i	0.141495	+	0.0816923i	−0.427581	+	0.903977i	$0.640634\pi$
$32$	−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	$-0.980188\pi$
$41$	−2.85045	+	4.93712i	−0.445165	+	0.771048i	0.552899	+	0.833248i	$0.313522\pi$
$42$		0			0
$43$	−2.39949	−	4.15605i	−0.365919	−	0.633791i	0.623004	−	0.782219i	$-0.285912\pi$
$43$	−2.39949	−	4.15605i	−0.365919	−	0.633791i	−0.988923	+	0.148428i	$0.952579\pi$
$44$		−	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	$-0.114661\pi$
$47$	1.11511	+	1.93143i	0.162655	+	0.281727i	−0.773165	+	0.634205i	$0.781327\pi$
$48$	−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	$0.205312\pi$
$53$			8.75365i			1.20241i	−0.799096	+	0.601203i	$0.794688\pi$
$54$	−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	0.409925	+	0.912119i	$0.365555\pi$
$59$	−4.49313	+	7.78233i	−0.584956	+	1.01317i	−0.994881	+	0.101054i	$0.967778\pi$
$60$	5.64655	+	2.72301i	0.728967	+	0.351539i
$61$	−12.7410	+	7.35603i	−1.63132	+	0.941843i	−0.647634	+	0.761952i	$0.724241\pi$
$61$	−12.7410	+	7.35603i	−1.63132	+	0.941843i	−0.983686	+	0.179892i	$0.942425\pi$
$62$	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	−0.491951	−	0.870623i	$-0.663716\pi$
$67$	4.15821	−	7.20222i	0.508006	−	0.879892i	0.999957	−	0.00926908i	$-0.00295048\pi$
$68$	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	$0.00880846\pi$
$71$			0.466287i			0.0553381i	−0.999617	+	0.0276691i	$0.991192\pi$
$72$	−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	0.738140	−	0.674648i	$-0.235704\pi$
$79$	−1.91267	−	3.31284i	−0.215192	−	0.372723i	−0.953332	+	0.301924i	$0.902371\pi$
$80$	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	$-0.311541\pi$
$83$	−4.00481	−	6.93654i	−0.439585	−	0.761384i	−0.997657	+	0.0684084i	$0.978208\pi$
$84$		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	$-0.418358\pi$
$89$	4.78647			0.507365			0.253683	+	0.967288i	$0.418358\pi$
$90$	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	$-0.870294\pi$
$97$	−10.1835	+	5.87944i	−1.03398	+	0.596967i	−0.115856	+	0.993266i	$0.536961\pi$
$98$		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	−0.985118	−	0.171879i	$-0.945016\pi$
$101$	−6.44610	−	11.1650i	−0.641411	−	1.11096i	0.343707	−	0.939077i	$-0.388317\pi$
$102$	4.64518	−	9.63244i	0.459941	−	0.953754i
$103$	−9.31740	−	5.37940i	−0.918070	−	0.530048i	−0.0350515	−	0.999386i	$-0.511160\pi$
$103$	−9.31740	−	5.37940i	−0.918070	−	0.530048i	−0.883019	+	0.469337i	$0.844493\pi$
$104$	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	$0.0407251\pi$
$107$			2.63967i			0.255186i	−0.991827	+	0.127593i	$0.959275\pi$
$108$	−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	0.429551	−	0.903043i	$-0.358672\pi$
$113$	−1.46411	−	0.845306i	−0.137732	−	0.0795197i	−0.567283	+	0.823523i	$0.692005\pi$
$114$	−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	−0.187188	−	0.982324i	$-0.559938\pi$
$131$	8.66567	−	15.0094i	0.757123	−	1.31138i	0.944312	−	0.329052i	$-0.106729\pi$
$132$	−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	−0.500024	−	0.866012i	$-0.666675\pi$
$137$	−0.000558693	0	0.000322562i	−4.77324e−5	0	2.75583e-5i	0.499976	+	0.866039i	$0.333342\pi$
$138$	4.33493	−	2.95206i	0.369013	−	0.251296i
$139$	−8.73273	−	5.04185i	−0.740701	−	0.427644i	0.0816233	−	0.996663i	$-0.473990\pi$
$139$	−8.73273	−	5.04185i	−0.740701	−	0.427644i	−0.822324	+	0.569019i	$0.807323\pi$
$140$		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	0.842766	−	0.538280i	$-0.180926\pi$
$149$	9.74064	+	5.62376i	0.797984	+	0.460716i	−0.0447816	+	0.998997i	$0.514259\pi$
$150$	−13.9900	+	1.04077i	−1.14228	+	0.0849786i
$151$	2.36189	+	4.09092i	0.192208	+	0.332914i	0.945982	−	0.324220i	$-0.105102\pi$
$151$	2.36189	+	4.09092i	0.192208	+	0.332914i	−0.753774	+	0.657134i	$0.771768\pi$
$152$	−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	$-0.294244\pi$
$157$	2.65845	+	1.53486i	0.212168	+	0.122495i	−0.390151	+	0.920751i	$0.627577\pi$
$158$	−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	$-0.815330\pi$
$167$	0.730517	−	1.26529i	0.0565291	−	0.0979113i	0.892905	+	0.450245i	$0.148663\pi$
$168$		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	$-0.129424\pi$
$173$	1.53541	+	2.65940i	0.116735	+	0.202191i	−0.801737	+	0.597677i	$0.796091\pi$
$174$	−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	$0.256776\pi$
$179$			19.3193i			1.44399i	−0.691896	+	0.721997i	$0.743224\pi$
$180$	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	−0.855114	−	0.518441i	$-0.826513\pi$
$191$	−11.5218	+	6.65211i	−0.833688	+	0.481330i	0.0214259	+	0.999770i	$0.493179\pi$
$192$	−1.43162	+	0.974922i	−0.103318	+	0.0703590i
$193$	−3.26786	+	5.66011i	−0.235226	+	0.407423i	−0.959338	−	0.282259i	$-0.908916\pi$
$193$	−3.26786	+	5.66011i	−0.235226	+	0.407423i	0.724112	+	0.689682i	$0.242250\pi$
$194$	−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	$-0.949412\pi$
$197$		−	4.44250i		−	0.316515i	0.987398	−	0.158258i	$-0.0505876\pi$
$198$	−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	−0.155155	−	0.987890i	$-0.549588\pi$
$211$	11.3005	−	19.5731i	0.777961	−	1.34747i	0.933115	−	0.359577i	$-0.117079\pi$
$212$	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	$-0.449652\pi$
$223$	16.2994	−	9.41045i	1.09149	−	0.630170i	0.933972	+	0.357346i	$0.116318\pi$
$224$		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	$-0.327832\pi$
$227$	−7.30665	−	12.6555i	−0.484960	−	0.839975i	−0.999851	+	0.0172809i	$0.994499\pi$
$228$	−1.74987	+	0.130180i	−0.115888	+	0.00862137i
$229$	−2.06044	−	1.18959i	−0.136158	−	0.0786106i	0.430374	−	0.902651i	$-0.358382\pi$
$229$	−2.06044	−	1.18959i	−0.136158	−	0.0786106i	−0.566531	+	0.824040i	$0.691715\pi$
$230$	−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	$-0.888989\pi$
$233$		−	10.4324i		−	0.683448i	0.939800	−	0.341724i	$-0.111011\pi$
$234$	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	0.985654	−	0.168777i	$-0.0539818\pi$
$239$	20.5971	+	11.8917i	1.33232	+	0.769213i	0.346662	+	0.937990i	$0.387315\pi$
$240$	5.18147	−	3.52855i	0.334463	−	0.227767i
$241$	−24.8105	+	14.3243i	−1.59818	+	0.922712i	−0.606348	+	0.795200i	$0.707366\pi$
$241$	−24.8105	+	14.3243i	−1.59818	+	0.922712i	−0.991837	+	0.127513i	$0.959301\pi$
$242$			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	$-0.613176\pi$
$251$	−11.0301			−0.696216			−0.348108	+	0.937454i	$0.613176\pi$
$252$		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	$-0.989400\pi$
$257$	−7.54890	+	13.0751i	−0.470888	+	0.815601i	0.528558	+	0.848897i	$0.322733\pi$
$258$	−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	−0.922292	−	0.386493i	$-0.873686\pi$
$263$	−17.0075	+	9.81926i	−1.04873	+	0.605482i	−0.126433	+	0.991975i	$0.540353\pi$
$264$	−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	$-0.504765\pi$
$269$	−0.491005			−0.0299371			−0.0149686	+	0.999888i	$0.504765\pi$
$270$	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	−0.794913	−	0.606723i	$-0.792484\pi$
$277$	−15.3600	−	26.6043i	−0.922894	−	1.59850i	−0.127981	−	0.991777i	$-0.540850\pi$
$278$	−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	−0.281130	−	0.959670i	$-0.590709\pi$
$281$	6.86286	−	3.96227i	0.409404	−	0.236369i	0.690534	+	0.723300i	$0.257376\pi$
$282$	3.85221	−	0.286581i	0.229395	−	0.0170656i
$283$	−9.97303	−	5.75793i	−0.592835	−	0.342273i	0.173383	−	0.984855i	$-0.444530\pi$
$283$	−9.97303	−	5.75793i	−0.592835	−	0.342273i	−0.766218	+	0.642581i	$0.777864\pi$
$284$	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	$-0.880166\pi$
$293$	−2.50937	+	4.34636i	−0.146599	+	0.253917i	0.783369	+	0.621557i	$0.213499\pi$
$294$		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	$-0.996468\pi$
$311$	−8.64759	+	14.9781i	−0.490360	+	0.849328i	0.509579	+	0.860424i	$0.329801\pi$
$312$	−0.438020	−	5.88785i	−0.0247980	−	0.333334i
$313$	7.78988	−	4.49749i	0.440310	−	0.254213i	−0.263419	−	0.964681i	$-0.584850\pi$
$313$	7.78988	−	4.49749i	0.440310	−	0.254213i	0.703729	+	0.710468i	$0.251517\pi$
$314$	3.06972			0.173234
$315$		0			0
$316$	−3.82533			−0.215192
$317$	5.82002	−	3.36019i	0.326885	−	0.188727i	−0.327572	−	0.944826i	$-0.606230\pi$
$317$	5.82002	−	3.36019i	0.326885	−	0.188727i	0.654457	+	0.756099i	$0.272897\pi$
$318$	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	0.999828	+	0.0185396i	$0.00590167\pi$
$331$	9.38725	+	16.2592i	0.515970	+	0.893686i	−0.483858	+	0.875146i	$0.660765\pi$
$332$	−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	−0.792458	−	0.609926i	$-0.791199\pi$
$337$	2.42287	−	4.19654i	0.131982	−	0.228600i	0.924441	+	0.381326i	$0.124532\pi$
$338$	−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	0.847736	−	0.530419i	$-0.177965\pi$
$347$	15.1305	+	8.73559i	0.812247	+	0.468951i	−0.0354887	+	0.999370i	$0.511299\pi$
$348$	−5.68005	−	8.34083i	−0.304483	−	0.447115i
$349$	20.6338	−	11.9129i	1.10450	−	0.637683i	0.167101	−	0.985940i	$-0.446560\pi$
$349$	20.6338	−	11.9129i	1.10450	−	0.637683i	0.937399	+	0.348257i	$0.113226\pi$
$350$		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	$-0.0805615\pi$
$353$	5.02061	+	8.69596i	0.267220	+	0.462839i	−0.700923	+	0.713237i	$0.747228\pi$
$354$	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	$0.104027\pi$
$359$			12.1651i			0.642048i	−0.947071	+	0.321024i	$0.895973\pi$
$360$	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	$-0.696874\pi$
$367$	−3.14420	+	1.81531i	−0.164126	+	0.0947582i	0.415687	+	0.909508i	$0.363541\pi$
$368$		−	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	−0.928321	−	0.371779i	$-0.878748\pi$
$373$	−2.74616	+	4.75648i	−0.142191	+	0.246281i	0.786131	+	0.618060i	$0.212081\pi$
$374$	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	$-0.755877\pi$
$383$	4.71534	−	8.16720i	0.240942	−	0.417324i	0.960983	+	0.276607i	$0.0892102\pi$
$384$	−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	−0.634317	−	0.773073i	$-0.718719\pi$
$389$	−5.56142	+	3.21089i	−0.281975	+	0.162798i	0.352342	+	0.935871i	$0.385385\pi$
$390$	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	0.711141	−	0.703050i	$-0.248179\pi$
$401$	9.16848	+	5.29343i	0.457852	+	0.264341i	−0.253289	+	0.967391i	$0.581512\pi$
$402$	−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	$-0.262526\pi$
$409$	7.72792	+	4.46172i	0.382121	+	0.220618i	−0.296620	+	0.954996i	$0.595859\pi$
$410$	−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	−0.0500724	−	0.998746i	$-0.515945\pi$
$419$	17.1924	−	29.7781i	0.839903	−	1.45475i	0.889975	−	0.456009i	$-0.150721\pi$
$420$		0			0
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.865310	−	0.501237i	$-0.832879\pi$
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.00142877	−	0.999999i	$-0.500455\pi$
$422$		−	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	$-0.733180\pi$
$431$		−	30.8695i		−	1.48693i	0.668774	−	0.743466i	$-0.266820\pi$
$432$	−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	$-0.488292\pi$
$439$	19.2887	−	11.1364i	0.920601	−	0.531509i	0.883827	+	0.467814i	$0.154958\pi$
$440$	7.25237			0.345743
$441$		0			0
$442$	21.0462			1.00107
$443$	−15.5756	+	8.99259i	−0.740020	+	0.427251i	−0.822077	−	0.569377i	$-0.807185\pi$
$443$	−15.5756	+	8.99259i	−0.740020	+	0.427251i	0.0820566	+	0.996628i	$0.473851\pi$
$444$	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	$0.0715315\pi$
$449$			9.44363i			0.445673i	−0.974856	+	0.222836i	$0.928468\pi$
$450$	−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	0.886790	−	0.462173i	$-0.152930\pi$
$457$	0.922251	+	1.59739i	0.0431411	+	0.0747225i	−0.843649	+	0.536896i	$0.819597\pi$
$458$	−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	−0.883829	−	0.467810i	$-0.845043\pi$
$461$	−18.1869	−	31.5007i	−0.847050	−	1.46713i	0.0367790	−	0.999323i	$-0.488290\pi$
$462$		0			0
$463$	−15.9830	+	27.6834i	−0.742794	+	1.28656i	0.208425	+	0.978038i	$0.433166\pi$
$463$	−15.9830	+	27.6834i	−0.742794	+	1.28656i	−0.951219	+	0.308518i	$0.900167\pi$
$464$	−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	$-0.691317\pi$
$467$	−24.4411			−1.13100			−0.565500	+	0.824748i	$0.691317\pi$
$468$	−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	$-0.0861037\pi$
$479$	5.48032	+	9.49220i	0.250402	+	0.433710i	−0.713234	+	0.700926i	$0.752770\pi$
$480$	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	−0.0150939	−	0.999886i	$-0.504805\pi$
$491$	−19.6893	−	11.3676i	−0.888568	−	0.513015i	−0.873474	+	0.486871i	$0.838138\pi$
$492$	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	−0.997456	−	0.0712820i	$-0.977291\pi$
$499$	−9.76175	+	16.9079i	−0.436996	+	0.756899i	0.560460	+	0.828181i	$0.310624\pi$
$500$	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	$-0.598700\pi$
$503$	−13.6867			−0.610262			−0.305131	+	0.952310i	$0.598700\pi$
$504$		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	$-0.849507\pi$
$509$	−1.14583	+	1.98464i	−0.0507881	+	0.0879675i	0.839514	+	0.543338i	$0.182840\pi$
$510$	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	$-0.622079\pi$
$521$	−17.0820			−0.748377			−0.374189	+	0.927353i	$0.622079\pi$
$522$	−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	0.984061	+	0.177832i	$0.0569082\pi$
$547$	15.1095	+	26.1705i	0.646037	+	1.11897i	−0.338024	+	0.941138i	$0.609758\pi$
$548$		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	$0.181033\pi$
$557$			25.4212i			1.07713i	−0.842584	+	0.538565i	$0.818967\pi$
$558$	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	$-0.852710\pi$
$563$	−1.44346	+	2.50015i	−0.0608346	+	0.105369i	0.834004	+	0.551758i	$0.186043\pi$
$564$	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	0.630523	−	0.776171i	$-0.282841\pi$
$569$	38.5945	−	22.2826i	1.61797	−	0.934134i	0.987445	−	0.157963i	$-0.0504927\pi$
$570$	5.24925	−	3.57471i	0.219867	−	0.149728i
$571$	3.26470	−	5.65462i	0.136623	−	0.236638i	−0.789593	−	0.613631i	$-0.789708\pi$
$571$	3.26470	−	5.65462i	0.136623	−	0.236638i	0.926216	+	0.376992i	$0.123042\pi$
$572$	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	0.804843	+	0.593488i	$0.202250\pi$
$587$	22.2025	+	38.4559i	0.916397	+	1.58725i	0.111555	+	0.993758i	$0.464417\pi$
$588$		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	$-0.595209\pi$
$593$	−14.3513			−0.589336			−0.294668	+	0.955600i	$0.595209\pi$
$594$	−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	0.560691	−	0.828025i	$-0.310536\pi$
$599$	3.03349	+	1.75139i	0.123945	+	0.0715597i	−0.436746	+	0.899585i	$0.643869\pi$
$600$	−6.09366	+	12.6361i	−0.248773	+	0.515866i
$601$	15.1846	−	8.76685i	0.619394	−	0.357607i	−0.157239	−	0.987561i	$-0.550259\pi$
$601$	15.1846	−	8.76685i	0.619394	−	0.357607i	0.776633	+	0.629953i	$0.216926\pi$
$602$		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	$-0.333897\pi$
$607$	−0.0755923	−	0.0436432i	−0.00306820	−	0.00177142i	−0.501533	+	0.865138i	$0.667231\pi$
$608$	−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	0.270373	−	0.962756i	$-0.412853\pi$
$617$	−10.6365	−	6.14101i	−0.428211	−	0.247228i	−0.698584	+	0.715528i	$0.746186\pi$
$618$	−15.4025	+	10.4890i	−0.619579	+	0.421929i
$619$	17.5869	−	10.1538i	0.706875	−	0.408115i	−0.103028	−	0.994678i	$-0.532853\pi$
$619$	17.5869	−	10.1538i	0.706875	−	0.408115i	0.809903	+	0.586564i	$0.199520\pi$
$620$			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	0.151038	−	0.988528i	$-0.451738\pi$
$641$	27.4104	−	15.8254i	1.08265	−	0.625067i	0.931609	+	0.363461i	$0.118405\pi$
$642$	4.11818	+	1.98597i	0.162532	+	0.0783799i
$643$	−10.0106	−	5.77960i	−0.394778	−	0.227925i	0.289450	−	0.957193i	$-0.406528\pi$
$643$	−10.0106	−	5.77960i	−0.394778	−	0.227925i	−0.684228	+	0.729268i	$0.739861\pi$
$644$		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	$-0.328713\pi$
$647$	26.0730			1.02504			0.512519	+	0.858676i	$0.328713\pi$
$648$	−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	0.143635	−	0.989631i	$-0.454121\pi$
$653$	−16.3952	−	9.46576i	−0.641593	−	0.370424i	−0.785228	+	0.619207i	$0.787454\pi$
$654$	−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	0.0293098	−	0.999570i	$-0.490669\pi$
$659$	23.3508	−	13.4816i	0.909618	−	0.525168i	0.880308	+	0.474402i	$0.157336\pi$
$660$	12.5268	−	0.931922i	0.487607	−	0.0362750i
$661$	22.3201	+	12.8865i	0.868151	+	0.501227i	0.866733	−	0.498772i	$-0.166215\pi$
$661$	22.3201	+	12.8865i	0.868151	+	0.501227i	0.00141768	+	0.999999i	$0.499549\pi$
$662$	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	0.500398	−	0.865795i	$-0.333187\pi$
$673$	−12.9608	−	22.4487i	−0.499601	−	0.865335i	−1.00000		0.000460130i	$0.999854\pi$
$674$		−	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	$-0.247717\pi$
$677$	−6.55382	−	11.3515i	−0.251884	−	0.436275i	−0.964044	+	0.265741i	$0.914383\pi$
$678$	−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	$0.192112\pi$
$683$			29.6654i			1.13511i	−0.823334	+	0.567557i	$0.807888\pi$
$684$	−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	0.561459	−	0.827504i	$-0.310240\pi$
$691$	40.9767	−	23.6579i	1.55883	−	0.899990i	0.997369	−	0.0724857i	$-0.0230932\pi$
$692$	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	$0.0837627\pi$
$701$			13.7742i			0.520244i	−0.965576	+	0.260122i	$0.916237\pi$
$702$	−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	0.901867	+	0.432014i	$0.142197\pi$
$709$	21.9691	+	38.0517i	0.825069	+	1.42906i	−0.0767981	+	0.997047i	$0.524470\pi$
$710$	−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	$-0.313984\pi$
$719$	29.5860			1.10337			0.551687	+	0.834051i	$0.313984\pi$
$720$	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	$-0.597107\pi$
$727$	10.1244	−	5.84534i	0.375494	−	0.216792i	0.675856	+	0.737034i	$0.263774\pi$
$728$		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	$-0.124183\pi$
$733$	28.6423	+	16.5366i	1.05793	+	0.610795i	0.133070	+	0.991107i	$0.457517\pi$
$734$	−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	0.792701	−	0.609611i	$-0.208674\pi$
$743$	18.0206	+	10.4042i	0.661112	+	0.381693i	−0.131589	+	0.991304i	$0.542008\pi$
$744$	−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	−0.229788	−	0.973241i	$-0.573803\pi$
$751$	19.9492	−	34.5531i	0.727957	−	1.26086i	0.957745	−	0.287618i	$-0.0928634\pi$
$752$	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	$-0.883441\pi$
$761$	−4.32462	+	7.49046i	−0.156767	+	0.271529i	0.776934	+	0.629582i	$0.216774\pi$
$762$	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	$-0.193106\pi$
$769$	20.4818	+	11.8252i	0.738592	+	0.426426i	−0.0829652	+	0.996552i	$0.526439\pi$
$770$		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	$-0.815984\pi$
$773$	−46.5699			−1.67500			−0.837501	+	0.546436i	$0.815984\pi$
$774$	−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	$-0.476796\pi$
$787$	−21.1657	−	12.2200i	−0.754474	−	0.435596i	−0.827308	+	0.561748i	$0.810129\pi$
$788$	−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	−0.0344128	+	0.999408i	$0.510956\pi$
$797$	−24.9202	+	43.1631i	−0.882719	+	1.52891i	−0.848306	+	0.529506i	$0.822377\pi$
$798$		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	$-0.930485\pi$
$809$		−	12.3247i		−	0.433315i	0.976248	−	0.216657i	$-0.0695154\pi$
$810$	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	−0.934738	−	0.355336i	$-0.884366\pi$
$821$	−31.3573	+	18.1041i	−1.09438	+	0.631839i	−0.159639	+	0.987175i	$0.551033\pi$
$822$	8.28977e−5		0.00111431i	2.89139e−6		3.88659e-5i
$823$	9.54093	−	16.5254i	0.332576	−	0.576038i	−0.650440	−	0.759557i	$-0.725416\pi$
$823$	9.54093	−	16.5254i	0.332576	−	0.576038i	0.983016	+	0.183519i	$0.0587489\pi$
$824$	−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	$0.187151\pi$
$827$			31.9013i			1.10932i	−0.832079	+	0.554658i	$0.812849\pi$
$828$	−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	$-0.258012\pi$
$839$	−8.19860	−	14.2004i	−0.283047	−	0.490252i	−0.972134	+	0.234427i	$0.924679\pi$
$840$		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	$-0.560284\pi$
$853$	16.5936	−	9.58030i	0.568153	−	0.328023i	0.756411	+	0.654096i	$0.226951\pi$
$854$		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	$-0.0779127\pi$
$857$	8.05723	+	13.9555i	0.275230	+	0.476712i	−0.694963	+	0.719045i	$0.744579\pi$
$858$	5.13891	−	10.6563i	0.175439	−	0.363798i
$859$	−10.4830	−	6.05238i	−0.357677	−	0.206505i	0.310384	−	0.950611i	$-0.399542\pi$
$859$	−10.4830	−	6.05238i	−0.357677	−	0.206505i	−0.668061	+	0.744106i	$0.732876\pi$
$860$	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	$-0.781303\pi$
$863$		−	37.2655i		−	1.26853i	0.773115	−	0.634265i	$-0.218697\pi$
$864$	−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	−0.772343	−	0.635206i	$-0.780915\pi$
$877$	4.85474	−	8.40866i	0.163933	−	0.283940i	0.936276	+	0.351266i	$0.114249\pi$
$878$	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	$-0.514120\pi$
$881$	−2.63241			−0.0886881			−0.0443440	+	0.999016i	$0.514120\pi$
$882$		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	$-0.921921\pi$
$887$	−8.18209	+	14.1718i	−0.274728	+	0.475842i	0.695339	+	0.718682i	$0.255254\pi$
$888$	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	0.761974	−	0.647607i	$-0.224230\pi$
$907$	−5.41666	−	9.38192i	−0.179857	−	0.311522i	−0.941831	+	0.336086i	$0.890897\pi$
$908$	−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	0.255817	−	0.966725i	$-0.417655\pi$
$911$	36.8512	−	21.2760i	1.22093	−	0.704907i	0.965117	+	0.261818i	$0.0843221\pi$
$912$	−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	−0.937984	−	0.346678i	$-0.887310\pi$
$929$	−23.4456	−	40.6089i	−0.769224	−	1.33234i	0.168760	−	0.985657i	$-0.446024\pi$
$930$	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	$-0.829301\pi$
$941$	0.388565	−	0.673014i	0.0126669	−	0.0219396i	0.872289	+	0.488990i	$0.162635\pi$
$942$	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	−0.994528	−	0.104470i	$-0.966686\pi$
$947$	−43.1233	+	24.8972i	−1.40132	+	0.809052i	−0.406791	+	0.913521i	$0.633352\pi$
$948$	−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	$0.234009\pi$
$953$			41.4104i			1.34141i	−0.741722	+	0.670707i	$0.765991\pi$
$954$	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	−0.222181	−	0.975005i	$-0.571318\pi$
$967$	22.8028	−	39.4956i	0.733289	−	1.27009i	0.955470	−	0.295088i	$-0.0953491\pi$
$968$	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	$-0.455240\pi$
$971$	8.73466			0.280309			0.140154	+	0.990130i	$0.455240\pi$
$972$	−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	0.692031	−	0.721867i	$-0.256716\pi$
$977$	12.9058	+	7.45114i	0.412892	+	0.238383i	−0.279140	+	0.960250i	$0.590049\pi$
$978$	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	$-0.182253\pi$
$983$	−1.53458	−	2.65798i	−0.0489456	−	0.0847763i	−0.889460	+	0.457013i	$0.848919\pi$
$984$	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	$-0.697598\pi$
$997$	−5.30607	+	3.06346i	−0.168045	+	0.0970208i	0.413619	+	0.910450i	$0.364265\pi$
$998$			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.b.293.7		16
3.2	odd	2		2646.2.m.b.881.4		16
7.2	even	3		882.2.t.a.815.3		16
7.3	odd	6		882.2.l.b.509.8		16
7.4	even	3		126.2.l.a.5.5	✓	16
7.5	odd	6		126.2.t.a.59.2	yes	16
7.6	odd	2		882.2.m.a.293.6		16
9.2	odd	6		882.2.m.a.587.6		16
9.7	even	3		2646.2.m.a.1763.1		16
21.2	odd	6		2646.2.t.b.2285.5		16
21.5	even	6		378.2.t.a.17.8		16
21.11	odd	6		378.2.l.a.341.4		16
21.17	even	6		2646.2.l.a.1097.1		16
21.20	even	2		2646.2.m.a.881.1		16
28.11	odd	6		1008.2.ca.c.257.8		16
28.19	even	6		1008.2.df.c.689.5		16
63.2	odd	6		882.2.l.b.227.4		16
63.4	even	3		1134.2.k.a.971.1		16
63.5	even	6		1134.2.k.a.647.1		16
63.11	odd	6		126.2.t.a.47.2	yes	16
63.16	even	3		2646.2.l.a.521.5		16
63.20	even	6	inner	882.2.m.b.587.7		16
63.25	even	3		378.2.t.a.89.8		16
63.32	odd	6		1134.2.k.b.971.8		16
63.34	odd	6		2646.2.m.b.1763.4		16
63.38	even	6		882.2.t.a.803.3		16
63.40	odd	6		1134.2.k.b.647.8		16
63.47	even	6		126.2.l.a.101.1	yes	16
63.52	odd	6		2646.2.t.b.1979.5		16
63.61	odd	6		378.2.l.a.143.8		16
84.11	even	6		3024.2.ca.c.2609.7		16
84.47	odd	6		3024.2.df.c.17.7		16
252.11	even	6		1008.2.df.c.929.5		16
252.47	odd	6		1008.2.ca.c.353.8		16
252.151	odd	6		3024.2.df.c.1601.7		16
252.187	even	6		3024.2.ca.c.2033.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.5	✓	16	7.4	even	3
126.2.l.a.101.1	yes	16	63.47	even	6
126.2.t.a.47.2	yes	16	63.11	odd	6
126.2.t.a.59.2	yes	16	7.5	odd	6
378.2.l.a.143.8		16	63.61	odd	6
378.2.l.a.341.4		16	21.11	odd	6
378.2.t.a.17.8		16	21.5	even	6
378.2.t.a.89.8		16	63.25	even	3
882.2.l.b.227.4		16	63.2	odd	6
882.2.l.b.509.8		16	7.3	odd	6
882.2.m.a.293.6		16	7.6	odd	2
882.2.m.a.587.6		16	9.2	odd	6
882.2.m.b.293.7		16	1.1	even	1	trivial
882.2.m.b.587.7		16	63.20	even	6	inner
882.2.t.a.803.3		16	63.38	even	6
882.2.t.a.815.3		16	7.2	even	3
1008.2.ca.c.257.8		16	28.11	odd	6
1008.2.ca.c.353.8		16	252.47	odd	6
1008.2.df.c.689.5		16	28.19	even	6
1008.2.df.c.929.5		16	252.11	even	6
1134.2.k.a.647.1		16	63.5	even	6
1134.2.k.a.971.1		16	63.4	even	3
1134.2.k.b.647.8		16	63.40	odd	6
1134.2.k.b.971.8		16	63.32	odd	6
2646.2.l.a.521.5		16	63.16	even	3
2646.2.l.a.1097.1		16	21.17	even	6
2646.2.m.a.881.1		16	21.20	even	2
2646.2.m.a.1763.1		16	9.7	even	3
2646.2.m.b.881.4		16	3.2	odd	2
2646.2.m.b.1763.4		16	63.34	odd	6
2646.2.t.b.1979.5		16	63.52	odd	6
2646.2.t.b.2285.5		16	21.2	odd	6
3024.2.ca.c.2033.7		16	252.187	even	6
3024.2.ca.c.2609.7		16	84.11	even	6
3024.2.df.c.17.7		16	84.47	odd	6
3024.2.df.c.1601.7		16	252.151	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.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} +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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 6 q^{9} - 12 q^{11} + 6 q^{13} - 18 q^{15} - 8 q^{16} + 36 q^{17} + 6 q^{23} - 6 q^{24} - 8 q^{25} - 24 q^{26} + 36 q^{27} + 6 q^{29} + 18 q^{30} + 6 q^{31} + 18 q^{33} + 4 q^{37} + 42 q^{39}+ \cdots + 18 q^{99}+O(q^{100}) \) 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

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