LMFDB - Embedded newform 882.2.m.a.293.5

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			293.5
Root			$1.27866 - 1.16834i$ of defining polynomial
Character	$\chi$	$=$	882.293
Dual form			882.2.m.a.587.5

$q$-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} +(-1.71170 + 0.264701i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.77612 + 3.07634i) q^{5} +(-1.35003 + 1.08509i) q^{6} -1.00000i q^{8} +(2.85987 - 0.906179i) q^{9} +3.55225i q^{10} +(-2.61745 + 1.51119i) q^{11} +(-0.626615 + 1.61473i) q^{12} +(0.888944 + 0.513232i) q^{13} +(2.22589 - 5.73592i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.61841 q^{17} +(2.02363 - 2.21471i) q^{18} -8.22889i q^{19} +(1.77612 + 3.07634i) q^{20} +(-1.51119 + 2.61745i) q^{22} +(-2.90837 - 1.67915i) q^{23} +(0.264701 + 1.71170i) q^{24} +(-3.80924 - 6.59779i) q^{25} +1.02646 q^{26} +(-4.65538 + 2.30812i) q^{27} +(-3.70319 + 2.13804i) q^{29} +(-0.940283 - 6.08040i) q^{30} +(-5.18382 - 2.99288i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.08029 - 3.27954i) q^{33} +(-1.40158 + 0.809204i) q^{34} +(0.645160 - 2.92981i) q^{36} -5.84647 q^{37} +(-4.11444 - 7.12643i) q^{38} +(-1.65746 - 0.643198i) q^{39} +(3.07634 + 1.77612i) q^{40} +(-0.0472226 + 0.0817920i) q^{41} +(3.05899 + 5.29833i) q^{43} +3.02237i q^{44} +(-2.29177 + 10.4074i) q^{45} -3.35830 q^{46} +(-2.57023 - 4.45176i) q^{47} +(1.08509 + 1.35003i) q^{48} +(-6.59779 - 3.80924i) q^{50} +(2.77024 - 0.428394i) q^{51} +(0.888944 - 0.513232i) q^{52} -3.18968i q^{53} +(-2.87762 + 4.32658i) q^{54} -10.7362i q^{55} +(2.17819 + 14.0854i) q^{57} +(-2.13804 + 3.70319i) q^{58} +(-4.42036 + 7.65628i) q^{59} +(-3.85451 - 4.79564i) q^{60} +(4.06195 - 2.34517i) q^{61} -5.98576 q^{62} -1.00000 q^{64} +(-3.15775 + 1.82313i) q^{65} +(1.89386 - 4.88031i) q^{66} +(0.187838 - 0.325345i) q^{67} +(-0.809204 + 1.40158i) q^{68} +(5.42275 + 2.10436i) q^{69} -13.9868i q^{71} +(-0.906179 - 2.85987i) q^{72} -1.31111i q^{73} +(-5.06319 + 2.92323i) q^{74} +(8.26673 + 10.2852i) q^{75} +(-7.12643 - 4.11444i) q^{76} +(-1.75700 + 0.271706i) q^{78} +(-0.462067 - 0.800324i) q^{79} +3.55225 q^{80} +(7.35768 - 5.18310i) q^{81} +0.0944452i q^{82} +(-5.43209 - 9.40866i) q^{83} +(2.87450 - 4.97877i) q^{85} +(5.29833 + 3.05899i) q^{86} +(5.77283 - 4.63993i) q^{87} +(1.51119 + 2.61745i) q^{88} -4.70989 q^{89} +(3.21897 + 10.1590i) q^{90} +(-2.90837 + 1.67915i) q^{92} +(9.66539 + 3.75077i) q^{93} +(-4.45176 - 2.57023i) q^{94} +(25.3148 + 14.6155i) q^{95} +(1.61473 + 0.626615i) q^{96} +(-13.3330 + 7.69782i) q^{97} +(-6.11615 + 6.69367i) 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
$3$	−1.71170	+	0.264701i	−0.988253	+	0.152825i
$3$	−1.71170	+	0.264701i	−0.988253	+	0.152825i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.77612	+	3.07634i	−0.794307	+	1.37578i	0.128971	+	0.991648i	$0.458833\pi$
$5$	−1.77612	+	3.07634i	−0.794307	+	1.37578i	−0.923278	+	0.384132i	$0.874501\pi$
$6$	−1.35003	+	1.08509i	−0.551147	+	0.442986i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	2.85987	−	0.906179i	0.953289	−	0.302060i
$10$			3.55225i			1.12332i
$11$	−2.61745	+	1.51119i	−0.789191	+	0.455639i	−0.839678	−	0.543085i	$-0.817256\pi$
$11$	−2.61745	+	1.51119i	−0.789191	+	0.455639i	0.0504869	+	0.998725i	$0.483923\pi$
$12$	−0.626615	+	1.61473i	−0.180888	+	0.466132i
$13$	0.888944	+	0.513232i	0.246549	+	0.142345i	0.618183	−	0.786034i	$-0.287869\pi$
$13$	0.888944	+	0.513232i	0.246549	+	0.142345i	−0.371634	+	0.928379i	$0.621202\pi$
$14$		0			0
$15$	2.22589	−	5.73592i	0.574723	−	1.48101i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.61841			−0.392522			−0.196261	−	0.980552i	$-0.562880\pi$
$17$	−1.61841			−0.392522			−0.196261	+	0.980552i	$0.562880\pi$
$18$	2.02363	−	2.21471i	0.476974	−	0.522012i
$19$		−	8.22889i		−	1.88784i	−0.330179	−	0.943918i	$-0.607109\pi$
$19$		−	8.22889i		−	1.88784i	0.330179	−	0.943918i	$-0.392891\pi$
$20$	1.77612	+	3.07634i	0.397154	+	0.687890i
$21$		0			0
$22$	−1.51119	+	2.61745i	−0.322186	+	0.558042i
$23$	−2.90837	−	1.67915i	−0.606438	−	0.350127i	0.165132	−	0.986271i	$-0.447195\pi$
$23$	−2.90837	−	1.67915i	−0.606438	−	0.350127i	−0.771570	+	0.636144i	$0.780528\pi$
$24$	0.264701	+	1.71170i	0.0540318	+	0.349400i
$25$	−3.80924	−	6.59779i	−0.761848	−	1.31956i
$26$	1.02646			0.201306
$27$	−4.65538	+	2.30812i	−0.895929	+	0.444198i
$28$		0			0
$29$	−3.70319	+	2.13804i	−0.687666	+	0.397024i	−0.802737	−	0.596333i	$-0.796624\pi$
$29$	−3.70319	+	2.13804i	−0.687666	+	0.397024i	0.115071	+	0.993357i	$0.463290\pi$
$30$	−0.940283	−	6.08040i	−0.171671	−	1.11012i
$31$	−5.18382	−	2.99288i	−0.931041	−	0.537537i	−0.0439006	−	0.999036i	$-0.513978\pi$
$31$	−5.18382	−	2.99288i	−0.931041	−	0.537537i	−0.887141	+	0.461499i	$0.847312\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	4.08029	−	3.27954i	0.710287	−	0.570895i
$34$	−1.40158	+	0.809204i	−0.240369	+	0.138777i
$35$		0			0
$36$	0.645160	−	2.92981i	0.107527	−	0.488301i
$37$	−5.84647			−0.961154			−0.480577	−	0.876953i	$-0.659573\pi$
$37$	−5.84647			−0.961154			−0.480577	+	0.876953i	$0.659573\pi$
$38$	−4.11444	−	7.12643i	−0.667451	−	1.15606i
$39$	−1.65746	−	0.643198i	−0.265407	−	0.102994i
$40$	3.07634	+	1.77612i	0.486412	+	0.280830i
$41$	−0.0472226	+	0.0817920i	−0.00737493	+	0.0127738i	−0.869689	−	0.493600i	$-0.835681\pi$
$41$	−0.0472226	+	0.0817920i	−0.00737493	+	0.0127738i	0.862314	+	0.506373i	$0.169014\pi$
$42$		0			0
$43$	3.05899	+	5.29833i	0.466492	+	0.807988i	0.999267	−	0.0382684i	$-0.0121842\pi$
$43$	3.05899	+	5.29833i	0.466492	+	0.807988i	−0.532775	+	0.846257i	$0.678851\pi$
$44$			3.02237i			0.455639i
$45$	−2.29177	+	10.4074i	−0.341637	+	1.55144i
$46$	−3.35830			−0.495154
$47$	−2.57023	−	4.45176i	−0.374906	−	0.649356i	0.615407	−	0.788210i	$-0.288992\pi$
$47$	−2.57023	−	4.45176i	−0.374906	−	0.649356i	−0.990313	+	0.138853i	$0.955658\pi$
$48$	1.08509	+	1.35003i	0.156619	+	0.194860i
$49$		0			0
$50$	−6.59779	−	3.80924i	−0.933069	−	0.538708i
$51$	2.77024	−	0.428394i	0.387911	−	0.0599871i
$52$	0.888944	−	0.513232i	0.123274	−	0.0711725i
$53$		−	3.18968i		−	0.438137i	−0.975709	−	0.219068i	$-0.929698\pi$
$53$		−	3.18968i		−	0.438137i	0.975709	−	0.219068i	$-0.0703018\pi$
$54$	−2.87762	+	4.32658i	−0.391594	+	0.588773i
$55$		−	10.7362i		−	1.44767i
$56$		0			0
$57$	2.17819	+	14.0854i	0.288509	+	1.86566i
$58$	−2.13804	+	3.70319i	−0.280738	+	0.486253i
$59$	−4.42036	+	7.65628i	−0.575481	+	0.996763i	0.420508	+	0.907289i	$0.361852\pi$
$59$	−4.42036	+	7.65628i	−0.575481	+	0.996763i	−0.995989	+	0.0894739i	$0.971481\pi$
$60$	−3.85451	−	4.79564i	−0.497615	−	0.619115i
$61$	4.06195	−	2.34517i	0.520080	−	0.300268i	−0.216887	−	0.976197i	$-0.569590\pi$
$61$	4.06195	−	2.34517i	0.520080	−	0.300268i	0.736967	+	0.675928i	$0.236257\pi$
$62$	−5.98576			−0.760192
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.15775	+	1.82313i	−0.391671	+	0.226131i
$66$	1.89386	−	4.88031i	0.233118	−	0.600725i
$67$	0.187838	−	0.325345i	0.0229480	−	0.0397472i	−0.854323	−	0.519742i	$-0.826028\pi$
$67$	0.187838	−	0.325345i	0.0229480	−	0.0397472i	0.877271	+	0.479995i	$0.159361\pi$
$68$	−0.809204	+	1.40158i	−0.0981304	+	0.169967i
$69$	5.42275	+	2.10436i	0.652822	+	0.253335i
$70$		0			0
$71$		−	13.9868i		−	1.65993i	−0.557815	−	0.829966i	$-0.688360\pi$
$71$		−	13.9868i		−	1.65993i	0.557815	−	0.829966i	$-0.311640\pi$
$72$	−0.906179	−	2.85987i	−0.106794	−	0.337039i
$73$		−	1.31111i		−	0.153454i	−0.997052	−	0.0767270i	$-0.975553\pi$
$73$		−	1.31111i		−	0.153454i	0.997052	−	0.0767270i	$-0.0244470\pi$
$74$	−5.06319	+	2.92323i	−0.588584	+	0.339819i
$75$	8.26673	+	10.2852i	0.954560	+	1.18763i
$76$	−7.12643	−	4.11444i	−0.817457	−	0.471959i
$77$		0			0
$78$	−1.75700	+	0.271706i	−0.198942	+	0.0307646i
$79$	−0.462067	−	0.800324i	−0.0519866	−	0.0900434i	0.838861	−	0.544346i	$-0.183222\pi$
$79$	−0.462067	−	0.800324i	−0.0519866	−	0.0900434i	−0.890848	+	0.454302i	$0.849889\pi$
$80$	3.55225			0.397154
$81$	7.35768	−	5.18310i	0.817520	−	0.575900i
$82$			0.0944452i			0.0104297i
$83$	−5.43209	−	9.40866i	−0.596250	−	1.03273i	−0.993369	−	0.114968i	$-0.963323\pi$
$83$	−5.43209	−	9.40866i	−0.596250	−	1.03273i	0.397119	−	0.917767i	$-0.370010\pi$
$84$		0			0
$85$	2.87450	−	4.97877i	0.311783	−	0.540024i
$86$	5.29833	+	3.05899i	0.571334	+	0.329860i
$87$	5.77283	−	4.63993i	0.618913	−	0.497453i
$88$	1.51119	+	2.61745i	0.161093	+	0.279021i
$89$	−4.70989			−0.499247			−0.249624	−	0.968343i	$-0.580307\pi$
$89$	−4.70989			−0.499247			−0.249624	+	0.968343i	$0.580307\pi$
$90$	3.21897	+	10.1590i	0.339310	+	1.07085i
$91$		0			0
$92$	−2.90837	+	1.67915i	−0.303219	+	0.175063i
$93$	9.66539	+	3.75077i	1.00225	+	0.388936i
$94$	−4.45176	−	2.57023i	−0.459164	−	0.265099i
$95$	25.3148	+	14.6155i	2.59725	+	1.49952i
$96$	1.61473	+	0.626615i	0.164803	+	0.0639536i
$97$	−13.3330	+	7.69782i	−1.35376	+	0.781595i	−0.988774	−	0.149417i	$-0.952260\pi$
$97$	−13.3330	+	7.69782i	−1.35376	+	0.781595i	−0.364988	+	0.931012i	$0.618927\pi$
$98$		0			0
$99$	−6.11615	+	6.69367i	−0.614697	+	0.672739i
$100$	−7.61848			−0.761848
$101$	6.85234	+	11.8686i	0.681833	+	1.18097i	0.974421	+	0.224731i	$0.0721503\pi$
$101$	6.85234	+	11.8686i	0.681833	+	1.18097i	−0.292588	+	0.956239i	$0.594516\pi$
$102$	2.18490	−	1.75612i	0.216337	−	0.173882i
$103$	2.64014	+	1.52429i	0.260141	+	0.150192i	0.624399	−	0.781106i	$-0.285344\pi$
$103$	2.64014	+	1.52429i	0.260141	+	0.150192i	−0.364258	+	0.931298i	$0.618677\pi$
$104$	0.513232	−	0.888944i	0.0503266	−	0.0871682i
$105$		0			0
$106$	−1.59484	−	2.76235i	−0.154905	−	0.268303i
$107$			13.1267i			1.26901i	0.772920	+	0.634504i	$0.218796\pi$
$107$			13.1267i			1.26901i	−0.772920	+	0.634504i	$0.781204\pi$
$108$	−0.328801	+	5.18574i	−0.0316389	+	0.498998i
$109$	−10.5715			−1.01256			−0.506282	−	0.862368i	$-0.668980\pi$
$109$	−10.5715			−1.01256			−0.506282	+	0.862368i	$0.668980\pi$
$110$	−5.36811	−	9.29783i	−0.511829	−	0.886514i
$111$	10.0074	−	1.54756i	0.949863	−	0.146888i
$112$		0			0
$113$	10.6520	+	6.14993i	1.00205	+	0.578537i	0.908856	−	0.417111i	$-0.136957\pi$
$113$	10.6520	+	6.14993i	1.00205	+	0.578537i	0.0931992	+	0.995647i	$0.470291\pi$
$114$	8.92908	+	11.1092i	0.836285	+	1.04048i
$115$	10.3313	−	5.96476i	0.963396	−	0.556217i
$116$			4.27608i			0.397024i
$117$	3.00734	+	0.662233i	0.278029	+	0.0612235i
$118$			8.84071i			0.813853i
$119$		0			0
$120$	−5.73592	−	2.22589i	−0.523616	−	0.203195i
$121$	−0.932639	+	1.61538i	−0.0847854	+	0.146853i
$122$	2.34517	−	4.06195i	0.212322	−	0.367752i
$123$	0.0591808	−	0.152504i	0.00533615	−	0.0137508i
$124$	−5.18382	+	2.99288i	−0.465521	+	0.268768i
$125$	9.30148			0.831950
$126$		0			0
$127$	0.287164			0.0254817			0.0127408	−	0.999919i	$-0.495944\pi$
$127$	0.287164			0.0254817			0.0127408	+	0.999919i	$0.495944\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−6.63857	−	8.25947i	−0.584493	−	0.727206i
$130$	−1.82313	+	3.15775i	−0.159899	+	0.276953i
$131$	−0.186474	+	0.322983i	−0.0162923	+	0.0282192i	−0.874057	−	0.485824i	$-0.838520\pi$
$131$	−0.186474	+	0.322983i	−0.0162923	+	0.0282192i	0.857764	+	0.514043i	$0.171853\pi$
$132$	−0.800023	−	5.17341i	−0.0696331	−	0.450287i
$133$		0			0
$134$		−	0.375675i		−	0.0324534i
$135$	1.16798	−	18.4210i	0.100524	−	1.58543i
$136$			1.61841i			0.138777i
$137$	−6.11607	+	3.53111i	−0.522531	+	0.301683i	−0.737969	−	0.674834i	$-0.764215\pi$
$137$	−6.11607	+	3.53111i	−0.522531	+	0.301683i	0.215439	+	0.976517i	$0.430882\pi$
$138$	5.74842	−	0.888944i	0.489338	−	0.0756720i
$139$	12.6320	+	7.29308i	1.07143	+	0.618591i	0.928572	−	0.371152i	$-0.121037\pi$
$139$	12.6320	+	7.29308i	1.07143	+	0.618591i	0.142858	+	0.989743i	$0.454371\pi$
$140$		0			0
$141$	5.57785	+	6.93976i	0.469740	+	0.584434i
$142$	−6.99341	−	12.1129i	−0.586874	−	1.01650i
$143$	−3.10236			−0.259432
$144$	−2.21471	−	2.02363i	−0.184559	−	0.168636i
$145$		−	15.1897i		−	1.26144i
$146$	−0.655556	−	1.13546i	−0.0542542	−	0.0939710i
$147$		0			0
$148$	−2.92323	+	5.06319i	−0.240288	+	0.416192i
$149$	9.26832	+	5.35107i	0.759290	+	0.438376i	0.829041	−	0.559188i	$-0.188887\pi$
$149$	9.26832	+	5.35107i	0.759290	+	0.438376i	−0.0697505	+	0.997564i	$0.522220\pi$
$150$	12.3018	+	4.77385i	1.00444	+	0.389783i
$151$	−8.00065	−	13.8575i	−0.651084	−	1.12771i	−0.982860	−	0.184352i	$-0.940981\pi$
$151$	−8.00065	−	13.8575i	−0.651084	−	1.12771i	0.331777	−	0.943358i	$-0.392352\pi$
$152$	−8.22889			−0.667451
$153$	−4.62843	+	1.46657i	−0.374187	+	0.118565i
$154$		0			0
$155$	18.4142	−	10.6315i	1.47907	−	0.853939i
$156$	−1.38576	+	1.11381i	−0.110949	+	0.0891759i
$157$	9.98239	+	5.76334i	0.796681	+	0.459964i	0.842309	−	0.538994i	$-0.181196\pi$
$157$	9.98239	+	5.76334i	0.796681	+	0.459964i	−0.0456280	+	0.998958i	$0.514529\pi$
$158$	−0.800324	−	0.462067i	−0.0636703	−	0.0367601i
$159$	0.844312	+	5.45980i	0.0669583	+	0.432990i
$160$	3.07634	−	1.77612i	0.243206	−	0.140415i
$161$		0			0
$162$	3.78039	−	8.16754i	0.297015	−	0.641702i
$163$	−2.74773			−0.215219			−0.107609	−	0.994193i	$-0.534320\pi$
$163$	−2.74773			−0.215219			−0.107609	+	0.994193i	$0.534320\pi$
$164$	0.0472226	+	0.0817920i	0.00368747	+	0.00638688i
$165$	2.84188	+	18.3772i	0.221240	+	1.43067i
$166$	−9.40866	−	5.43209i	−0.730254	−	0.421612i
$167$	2.76946	−	4.79685i	0.214307	−	0.371191i	−0.738751	−	0.673979i	$-0.764584\pi$
$167$	2.76946	−	4.79685i	0.214307	−	0.371191i	0.953058	+	0.302788i	$0.0979173\pi$
$168$		0			0
$169$	−5.97319	−	10.3459i	−0.459476	−	0.795835i
$170$		−	5.74899i		−	0.440927i
$171$	−7.45685	−	23.5335i	−0.570239	−	1.79965i
$172$	6.11799			0.466492
$173$	5.60253	+	9.70387i	0.425953	+	0.737772i	0.996509	−	0.0834869i	$-0.0266057\pi$
$173$	5.60253	+	9.70387i	0.425953	+	0.737772i	−0.570556	+	0.821259i	$0.693272\pi$
$174$	2.67945	−	6.90471i	0.203129	−	0.523445i
$175$		0			0
$176$	2.61745	+	1.51119i	0.197298	+	0.113910i
$177$	5.53972	−	14.2754i	0.416391	−	1.07300i
$178$	−4.07888	+	2.35495i	−0.305725	+	0.176511i
$179$		−	2.74178i		−	0.204930i	−0.994737	−	0.102465i	$-0.967327\pi$
$179$		−	2.74178i		−	0.204930i	0.994737	−	0.102465i	$-0.0326730\pi$
$180$	7.86719	+	7.18843i	0.586386	+	0.535794i
$181$		−	22.2899i		−	1.65679i	−0.560142	−	0.828397i	$-0.689253\pi$
$181$		−	22.2899i		−	1.65679i	0.560142	−	0.828397i	$-0.310747\pi$
$182$		0			0
$183$	−6.33210	+	5.08944i	−0.468082	+	0.376222i
$184$	−1.67915	+	2.90837i	−0.123789	+	0.214408i
$185$	10.3841	−	17.9857i	0.763451	−	1.32234i
$186$	10.2459	−	1.58443i	0.751262	−	0.116176i
$187$	4.23610	−	2.44571i	0.309774	−	0.178848i
$188$	−5.14045			−0.374906
$189$		0			0
$190$	29.2311			2.12064
$191$	−4.44499	+	2.56632i	−0.321628	+	0.185692i	−0.652118	−	0.758117i	$-0.726119\pi$
$191$	−4.44499	+	2.56632i	−0.321628	+	0.185692i	0.330490	+	0.943810i	$0.392786\pi$
$192$	1.71170	−	0.264701i	0.123532	−	0.0191031i
$193$	−7.99235	+	13.8432i	−0.575302	+	0.996452i	0.420707	+	0.907197i	$0.361782\pi$
$193$	−7.99235	+	13.8432i	−0.575302	+	0.996452i	−0.996009	+	0.0892557i	$0.971551\pi$
$194$	−7.69782	+	13.3330i	−0.552671	+	0.957254i
$195$	4.92256	−	3.95652i	0.352512	−	0.283332i
$196$		0			0
$197$			4.72572i			0.336694i	0.985728	+	0.168347i	$0.0538428\pi$
$197$			4.72572i			0.336694i	−0.985728	+	0.168347i	$0.946157\pi$
$198$	−1.94991	+	8.85496i	−0.138574	+	0.629295i
$199$		−	2.12095i		−	0.150350i	−0.997170	−	0.0751749i	$-0.976048\pi$
$199$		−	2.12095i		−	0.150350i	0.997170	−	0.0751749i	$-0.0239515\pi$
$200$	−6.59779	+	3.80924i	−0.466534	+	0.269354i
$201$	−0.235404	+	0.606615i	−0.0166041	+	0.0427873i
$202$	11.8686	+	6.85234i	0.835072	+	0.482129i
$203$		0			0
$204$	1.01412	−	2.61329i	0.0710025	−	0.182967i
$205$	−0.167747	−	0.290545i	−0.0117159	−	0.0202926i
$206$	3.04857			0.212404
$207$	−9.83917	−	2.16664i	−0.683870	−	0.150592i
$208$		−	1.02646i		−	0.0711725i
$209$	12.4354	+	21.5387i	0.860173	+	1.48986i
$210$		0			0
$211$	−13.8079	+	23.9160i	−0.950578	+	1.64645i	−0.206399	+	0.978468i	$0.566174\pi$
$211$	−13.8079	+	23.9160i	−0.950578	+	1.64645i	−0.744179	+	0.667981i	$0.767159\pi$
$212$	−2.76235	−	1.59484i	−0.189719	−	0.109534i
$213$	3.70232	+	23.9413i	0.253679	+	1.64043i
$214$	6.56336	+	11.3681i	0.448662	+	0.777105i
$215$	−21.7326			−1.48215
$216$	2.30812	+	4.65538i	0.157048	+	0.316759i
$217$		0			0
$218$	−9.15516	+	5.28574i	−0.620066	+	0.357995i
$219$	0.347052	+	2.24424i	0.0234516	+	0.151651i
$220$	−9.29783	−	5.36811i	−0.626860	−	0.361918i
$221$	−1.43867	−	0.830619i	−0.0967757	−	0.0558735i
$222$	7.89291	−	6.34395i	0.529737	−	0.425778i
$223$	17.6209	−	10.1734i	1.17998	−	0.681264i	0.223973	−	0.974595i	$-0.428097\pi$
$223$	17.6209	−	10.1734i	1.17998	−	0.681264i	0.956011	+	0.293331i	$0.0947638\pi$
$224$		0			0
$225$	−16.8727	−	15.4170i	−1.12485	−	1.02780i
$226$	12.2999			0.818174
$227$	2.08000	+	3.60266i	0.138054	+	0.239117i	0.926760	−	0.375654i	$-0.122582\pi$
$227$	2.08000	+	3.60266i	0.138054	+	0.239117i	−0.788706	+	0.614771i	$0.789248\pi$
$228$	13.2874	+	5.15634i	0.879982	+	0.341487i
$229$	−5.16986	−	2.98482i	−0.341634	−	0.197242i	0.319361	−	0.947633i	$-0.396532\pi$
$229$	−5.16986	−	2.98482i	−0.341634	−	0.197242i	−0.660994	+	0.750391i	$0.729865\pi$
$230$	5.96476	−	10.3313i	0.393305	−	0.681224i
$231$		0			0
$232$	2.13804	+	3.70319i	0.140369	+	0.243126i
$233$			4.48720i			0.293966i	0.989139	+	0.146983i	$0.0469563\pi$
$233$			4.48720i			0.293966i	−0.989139	+	0.146983i	$0.953044\pi$
$234$	2.93555	−	0.930160i	0.191903	−	0.0608065i
$235$	18.2602			1.19116
$236$	4.42036	+	7.65628i	0.287741	+	0.498381i
$237$	1.00277	+	1.24761i	0.0651368	+	0.0810409i
$238$		0			0
$239$	−3.02944	−	1.74905i	−0.195958	−	0.113136i	0.398811	−	0.917033i	$-0.369423\pi$
$239$	−3.02944	−	1.74905i	−0.195958	−	0.113136i	−0.594769	+	0.803897i	$0.702756\pi$
$240$	−6.08040	+	0.940283i	−0.392488	+	0.0606950i
$241$	10.0170	−	5.78332i	0.645252	−	0.372537i	−0.141383	−	0.989955i	$-0.545155\pi$
$241$	10.0170	−	5.78332i	0.645252	−	0.372537i	0.786635	+	0.617419i	$0.211821\pi$
$242$			1.86528i			0.119905i
$243$	−11.2222	+	10.8195i	−0.719905	+	0.694073i
$244$		−	4.69034i		−	0.300268i
$245$		0			0
$246$	−0.0249997	−	0.161662i	−0.00159392	−	0.0103072i
$247$	4.22333	−	7.31502i	0.268724	−	0.465444i
$248$	−2.99288	+	5.18382i	−0.190048	+	0.329173i
$249$	11.7886	+	14.6670i	0.747074	+	0.929482i
$250$	8.05532	−	4.65074i	0.509463	−	0.294139i
$251$	−26.7426			−1.68798			−0.843988	−	0.536361i	$-0.819798\pi$
$251$	−26.7426			−1.68798			−0.843988	+	0.536361i	$0.819798\pi$
$252$		0			0
$253$	10.1500			0.638127
$254$	0.248691	−	0.143582i	0.0156043	−	0.00900913i
$255$	−3.60240	+	9.28307i	−0.225591	+	0.581328i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.60614	+	4.51396i	−0.162566	+	0.281573i	−0.935788	−	0.352562i	$-0.885310\pi$
$257$	−2.60614	+	4.51396i	−0.162566	+	0.281573i	0.773222	+	0.634135i	$0.218644\pi$
$258$	−9.87890	−	3.83362i	−0.615034	−	0.238671i
$259$		0			0
$260$			3.64626i			0.226131i
$261$	−8.65319	+	9.47026i	−0.535619	+	0.586194i
$262$			0.372949i			0.0230409i
$263$	13.0228	−	7.51869i	0.803018	−	0.463622i	−0.0415076	−	0.999138i	$-0.513216\pi$
$263$	13.0228	−	7.51869i	0.803018	−	0.463622i	0.844525	+	0.535516i	$0.179883\pi$
$264$	−3.27954	−	4.08029i	−0.201842	−	0.251124i
$265$	9.81255	+	5.66528i	0.602780	+	0.348015i
$266$		0			0
$267$	8.06194	−	1.24671i	0.493383	−	0.0762975i
$268$	−0.187838	−	0.325345i	−0.0114740	−	0.0198736i
$269$	−23.1313			−1.41034			−0.705170	−	0.709038i	$-0.749130\pi$
$269$	−23.1313			−1.41034			−0.705170	+	0.709038i	$0.749130\pi$
$270$	−8.19902	−	16.5371i	−0.498976	−	1.00641i
$271$			9.91496i			0.602291i	0.953578	+	0.301146i	$0.0973690\pi$
$271$			9.91496i			0.602291i	−0.953578	+	0.301146i	$0.902631\pi$
$272$	0.809204	+	1.40158i	0.0490652	+	0.0849834i
$273$		0			0
$274$	−3.53111	+	6.11607i	−0.213322	+	0.369485i
$275$	19.9410	+	11.5129i	1.20249	+	0.694256i
$276$	4.53380	−	3.64406i	0.272903	−	0.219346i
$277$	4.29721	+	7.44299i	0.258195	+	0.447206i	0.965758	−	0.259443i	$-0.0835391\pi$
$277$	4.29721	+	7.44299i	0.258195	+	0.447206i	−0.707564	+	0.706650i	$0.750206\pi$
$278$	14.5862			0.874819
$279$	−17.5371	−	3.86177i	−1.04992	−	0.231198i
$280$		0			0
$281$	−17.9508	+	10.3639i	−1.07085	+	0.618258i	−0.928415	−	0.371545i	$-0.878828\pi$
$281$	−17.9508	+	10.3639i	−1.07085	+	0.618258i	−0.142440	+	0.989803i	$0.545495\pi$
$282$	8.30045	+	3.22108i	0.494284	+	0.191813i
$283$	2.04997	+	1.18355i	0.121858	+	0.0703547i	0.559690	−	0.828702i	$-0.310920\pi$
$283$	2.04997	+	1.18355i	0.121858	+	0.0703547i	−0.437832	+	0.899057i	$0.644254\pi$
$284$	−12.1129	−	6.99341i	−0.718771	−	0.414983i
$285$	−47.2003	−	18.3166i	−2.79590	−	1.08498i
$286$	−2.68672	+	1.55118i	−0.158869	+	0.0917231i
$287$		0			0
$288$	−2.92981	−	0.645160i	−0.172641	−	0.0380164i
$289$	−14.3808			−0.845927
$290$	−7.59485	−	13.1547i	−0.445985	−	0.772468i
$291$	20.7846	−	16.7057i	1.21841	−	0.979303i
$292$	−1.13546	−	0.655556i	−0.0664475	−	0.0383635i
$293$	−8.83774	+	15.3074i	−0.516306	+	0.894268i	0.483515	+	0.875336i	$0.339360\pi$
$293$	−8.83774	+	15.3074i	−0.516306	+	0.894268i	−0.999821	+	0.0189321i	$0.993973\pi$
$294$		0			0
$295$	−15.7022	−	27.1970i	−0.914218	−	1.58347i
$296$			5.84647i			0.339819i
$297$	8.69723	−	13.0765i	0.504665	−	0.758777i
$298$	10.7021			0.619958
$299$	−1.72359	−	2.98534i	−0.0996777	−	0.172647i
$300$	13.0406	−	2.01662i	0.752898	−	0.116429i
$301$		0			0
$302$	−13.8575	−	8.00065i	−0.797411	−	0.460386i
$303$	−14.8708	−	18.5017i	−0.854305	−	1.06290i
$304$	−7.12643	+	4.11444i	−0.408729	+	0.235980i
$305$			16.6613i			0.954021i
$306$	−3.27506	+	3.58430i	−0.187223	+	0.204901i
$307$			1.28155i			0.0731422i	0.999331	+	0.0365711i	$0.0116435\pi$
$307$			1.28155i			0.0731422i	−0.999331	+	0.0365711i	$0.988356\pi$
$308$		0			0
$309$	−4.92262	−	1.91028i	−0.280038	−	0.108672i
$310$	10.6315	−	18.4142i	0.603826	−	1.04586i
$311$	6.26643	−	10.8538i	0.355336	−	0.615461i	−0.631839	−	0.775100i	$-0.717700\pi$
$311$	6.26643	−	10.8538i	0.355336	−	0.615461i	0.987175	+	0.159639i	$0.0510330\pi$
$312$	−0.643198	+	1.65746i	−0.0364139	+	0.0938354i
$313$	−7.58105	+	4.37692i	−0.428507	+	0.247398i	−0.698710	−	0.715405i	$-0.746242\pi$
$313$	−7.58105	+	4.37692i	−0.428507	+	0.247398i	0.270204	+	0.962803i	$0.412909\pi$
$314$	11.5267			0.650488
$315$		0			0
$316$	−0.924134			−0.0519866
$317$	−11.8458	+	6.83920i	−0.665329	+	0.384128i	−0.794304	−	0.607520i	$-0.792164\pi$
$317$	−11.8458	+	6.83920i	−0.665329	+	0.384128i	0.128976	+	0.991648i	$0.458831\pi$
$318$	3.46109	+	4.30617i	0.194089	+	0.241478i
$319$	6.46195	−	11.1924i	0.361799	−	0.626655i
$320$	1.77612	−	3.07634i	0.0992884	−	0.171973i
$321$	−3.47465	−	22.4691i	−0.193936	−	1.25410i
$322$		0			0
$323$			13.3177i			0.741017i
$324$	−0.809858	−	8.96349i	−0.0449921	−	0.497972i
$325$		−	7.82009i		−	0.433781i
$326$	−2.37960	+	1.37386i	−0.131794	+	0.0760912i
$327$	18.0952	−	2.79828i	1.00067	−	0.154745i
$328$	0.0817920	+	0.0472226i	0.00451621	+	0.00260743i
$329$		0			0
$330$	11.6498	+	14.4942i	0.641298	+	0.797880i
$331$	5.44858	+	9.43721i	0.299481	+	0.518716i	0.976017	−	0.217693i	$-0.0698532\pi$
$331$	5.44858	+	9.43721i	0.299481	+	0.518716i	−0.676536	+	0.736409i	$0.736520\pi$
$332$	−10.8642			−0.596250
$333$	−16.7201	+	5.29795i	−0.916257	+	0.290326i
$334$		−	5.53892i		−	0.303076i
$335$	0.667247	+	1.15570i	0.0364556	+	0.0631429i
$336$		0			0
$337$	12.8090	−	22.1858i	0.697749	−	1.20854i	−0.271496	−	0.962440i	$-0.587518\pi$
$337$	12.8090	−	22.1858i	0.697749	−	1.20854i	0.969245	−	0.246098i	$-0.0791484\pi$
$338$	−10.3459	−	5.97319i	−0.562741	−	0.324898i
$339$	−19.8610	−	7.70727i	−1.07870	−	0.418602i
$340$	−2.87450	−	4.97877i	−0.155891	−	0.270012i
$341$	18.0912			0.979692
$342$	−18.2246	−	16.6522i	−0.985473	−	0.900448i
$343$		0			0
$344$	5.29833	−	3.05899i	0.285667	−	0.164930i
$345$	−16.1052	+	12.9446i	−0.867075	+	0.696914i
$346$	9.70387	+	5.60253i	0.521683	+	0.301194i
$347$	−14.5166	−	8.38116i	−0.779291	−	0.449924i	0.0568878	−	0.998381i	$-0.481882\pi$
$347$	−14.5166	−	8.38116i	−0.779291	−	0.449924i	−0.836179	+	0.548457i	$0.815216\pi$
$348$	−1.13188	−	7.31938i	−0.0606752	−	0.392360i
$349$	−14.4455	+	8.34010i	−0.773249	+	0.446435i	−0.834032	−	0.551716i	$-0.813973\pi$
$349$	−14.4455	+	8.34010i	−0.773249	+	0.446435i	0.0607835	+	0.998151i	$0.480640\pi$
$350$		0			0
$351$	−5.32298	−	0.337503i	−0.284119	−	0.0180146i
$352$	3.02237			0.161093
$353$	17.9568	+	31.1021i	0.955746	+	1.65540i	0.732653	+	0.680603i	$0.238282\pi$
$353$	17.9568	+	31.1021i	0.955746	+	1.65540i	0.223093	+	0.974797i	$0.428385\pi$
$354$	−2.34014	−	15.1327i	−0.124377	−	0.804293i
$355$	43.0282	+	24.8424i	2.28370	+	1.31850i
$356$	−2.35495	+	4.07888i	−0.124812	+	0.216180i
$357$		0			0
$358$	−1.37089	−	2.37445i	−0.0724538	−	0.125494i
$359$		−	28.5498i		−	1.50680i	−0.657563	−	0.753399i	$-0.728413\pi$
$359$		−	28.5498i		−	1.50680i	0.657563	−	0.753399i	$-0.271587\pi$
$360$	10.4074	+	2.29177i	0.548518	+	0.120787i
$361$	−48.7146			−2.56393
$362$	−11.1449	−	19.3036i	−0.585765	−	1.01457i
$363$	1.16881	−	3.01192i	0.0613467	−	0.158085i
$364$		0			0
$365$	4.03342	+	2.32870i	0.211119	+	0.121890i
$366$	−2.93904	+	7.57364i	−0.153626	+	0.395880i
$367$	0.310665	−	0.179362i	0.0162166	−	0.00936264i	−0.491870	−	0.870669i	$-0.663686\pi$
$367$	0.310665	−	0.179362i	0.0162166	−	0.00936264i	0.508086	+	0.861306i	$0.330353\pi$
$368$			3.35830i			0.175063i
$369$	−0.0609323	+	0.276706i	−0.00317201	+	0.0144048i
$370$		−	20.7681i		−	1.07968i
$371$		0			0
$372$	8.08095	−	6.49509i	0.418978	−	0.336755i
$373$	−12.6854	+	21.9718i	−0.656826	+	1.13766i	0.324606	+	0.945849i	$0.394768\pi$
$373$	−12.6854	+	21.9718i	−0.656826	+	1.13766i	−0.981433	+	0.191807i	$0.938565\pi$
$374$	2.44571	−	4.23610i	0.126465	−	0.219044i
$375$	−15.9214	+	2.46211i	−0.822177	+	0.127143i
$376$	−4.45176	+	2.57023i	−0.229582	+	0.132549i
$377$	−4.38924			−0.226057
$378$		0			0
$379$	26.9063			1.38209			0.691043	−	0.722814i	$-0.257152\pi$
$379$	26.9063			1.38209			0.691043	+	0.722814i	$0.257152\pi$
$380$	25.3148	−	14.6155i	1.29862	−	0.749761i
$381$	−0.491540	+	0.0760125i	−0.0251823	+	0.00389424i
$382$	−2.56632	+	4.44499i	−0.131304	+	0.227426i
$383$	6.28586	−	10.8874i	0.321192	−	0.556322i	−0.659542	−	0.751668i	$-0.729250\pi$
$383$	6.28586	−	10.8874i	0.321192	−	0.556322i	0.980734	+	0.195346i	$0.0625830\pi$
$384$	1.35003	−	1.08509i	0.0688934	−	0.0553733i
$385$		0			0
$386$			15.9847i			0.813600i
$387$	13.5496	+	12.3805i	0.688763	+	0.629338i
$388$			15.3956i			0.781595i
$389$	14.0805	−	8.12937i	0.713909	−	0.412175i	−0.0985980	−	0.995127i	$-0.531436\pi$
$389$	14.0805	−	8.12937i	0.713909	−	0.412175i	0.812507	+	0.582952i	$0.198102\pi$
$390$	2.28480	−	5.88772i	0.115695	−	0.298136i
$391$	4.70694	+	2.71755i	0.238040	+	0.137432i
$392$		0			0
$393$	0.233695	−	0.602212i	0.0117884	−	0.0303776i
$394$	2.36286	+	4.09259i	0.119039	+	0.206182i
$395$	3.28275			0.165173
$396$	2.73881	+	8.64358i	0.137630	+	0.434356i
$397$		−	14.6938i		−	0.737463i	−0.929536	−	0.368732i	$-0.879792\pi$
$397$		−	14.6938i		−	0.737463i	0.929536	−	0.368732i	$-0.120208\pi$
$398$	−1.06047	−	1.83679i	−0.0531567	−	0.0920701i
$399$		0			0
$400$	−3.80924	+	6.59779i	−0.190462	+	0.329890i
$401$	−14.4162	−	8.32318i	−0.719909	−	0.415640i	0.0948099	−	0.995495i	$-0.469776\pi$
$401$	−14.4162	−	8.32318i	−0.719909	−	0.415640i	−0.814719	+	0.579855i	$0.803109\pi$
$402$	0.0994416	+	0.643046i	0.00495969	+	0.0320722i
$403$	−3.07208	−	5.32101i	−0.153031	−	0.265058i
$404$	13.7047			0.681833
$405$	2.87682	+	31.8405i	0.142950	+	1.58217i
$406$		0			0
$407$	15.3028	−	8.83510i	0.758534	−	0.437940i
$408$	−0.428394	−	2.77024i	−0.0212087	−	0.137147i
$409$	2.43254	+	1.40443i	0.120282	+	0.0694446i	0.558934	−	0.829212i	$-0.311211\pi$
$409$	2.43254	+	1.40443i	0.120282	+	0.0694446i	−0.438652	+	0.898657i	$0.644544\pi$
$410$	−0.290545	−	0.167747i	−0.0143490	−	0.00828441i
$411$	9.53421	−	7.66315i	0.470288	−	0.377995i
$412$	2.64014	−	1.52429i	0.130070	−	0.0750962i
$413$		0			0
$414$	−9.60429	+	3.04322i	−0.472025	+	0.149566i
$415$	38.5923			1.89442
$416$	−0.513232	−	0.888944i	−0.0251633	−	0.0435841i
$417$	−23.5527	−	9.13990i	−1.15338	−	0.447583i
$418$	21.5387	+	12.4354i	1.05349	+	0.608234i
$419$	−7.47362	+	12.9447i	−0.365110	+	0.632390i	−0.988794	−	0.149287i	$-0.952302\pi$
$419$	−7.47362	+	12.9447i	−0.365110	+	0.632390i	0.623684	+	0.781677i	$0.285635\pi$
$420$		0			0
$421$	−7.80336	−	13.5158i	−0.380312	−	0.658720i	0.610794	−	0.791789i	$-0.290850\pi$
$421$	−7.80336	−	13.5158i	−0.380312	−	0.658720i	−0.991107	+	0.133069i	$0.957517\pi$
$422$			27.6159i			1.34432i
$423$	−11.3846	−	10.4024i	−0.553538	−	0.505780i
$424$	−3.18968			−0.154905
$425$	6.16490	+	10.6779i	0.299042	+	0.517955i
$426$	15.1770	+	18.8826i	0.735326	+	0.914867i
$427$		0			0
$428$	11.3681	+	6.56336i	0.549496	+	0.317252i
$429$	5.31032	−	0.821196i	0.256385	−	0.0396477i
$430$	−18.8210	+	10.8663i	−0.907629	+	0.524020i
$431$		−	16.1758i		−	0.779163i	−0.920992	−	0.389581i	$-0.872620\pi$
$431$		−	16.1758i		−	0.779163i	0.920992	−	0.389581i	$-0.127380\pi$
$432$	4.32658	+	2.87762i	0.208163	+	0.138450i
$433$			27.2499i			1.30955i	0.755824	+	0.654774i	$0.227236\pi$
$433$			27.2499i			1.30955i	−0.755824	+	0.654774i	$0.772764\pi$
$434$		0			0
$435$	4.02072	+	26.0003i	0.192779	+	1.24662i
$436$	−5.28574	+	9.15516i	−0.253141	+	0.438453i
$437$	−13.8175	+	23.9327i	−0.660983	+	1.14486i
$438$	1.42267	+	1.77004i	0.0679780	+	0.0845757i
$439$	−28.6955	+	16.5674i	−1.36956	+	0.790717i	−0.990872	−	0.134806i	$-0.956959\pi$
$439$	−28.6955	+	16.5674i	−1.36956	+	0.790717i	−0.378690	+	0.925523i	$0.623625\pi$
$440$	−10.7362			−0.511829
$441$		0			0
$442$	−1.66124			−0.0790171
$443$	−19.2808	+	11.1318i	−0.916060	+	0.528887i	−0.882376	−	0.470545i	$-0.844057\pi$
$443$	−19.2808	+	11.1318i	−0.916060	+	0.528887i	−0.0336837	+	0.999433i	$0.510724\pi$
$444$	3.66349	−	9.44047i	0.173861	−	0.448025i
$445$	8.36535	−	14.4892i	0.396556	−	0.686855i
$446$	10.1734	−	17.6209i	0.481727	−	0.834375i
$447$	−17.2811	−	6.70612i	−0.817366	−	0.317188i
$448$		0			0
$449$		−	6.80819i		−	0.321298i	−0.987012	−	0.160649i	$-0.948641\pi$
$449$		−	6.80819i		−	0.321298i	0.987012	−	0.160649i	$-0.0513588\pi$
$450$	−22.3207	−	4.91513i	−1.05221	−	0.231702i
$451$		−	0.285448i		−	0.0134412i
$452$	10.6520	−	6.14993i	0.501027	−	0.289268i
$453$	17.3628	+	21.6022i	0.815778	+	1.01496i
$454$	3.60266	+	2.08000i	0.169081	+	0.0976192i
$455$		0			0
$456$	14.0854	−	2.17819i	0.659611	−	0.102003i
$457$	−7.61298	−	13.1861i	−0.356120	−	0.616818i	0.631189	−	0.775629i	$-0.282567\pi$
$457$	−7.61298	−	13.1861i	−0.356120	−	0.616818i	−0.987309	+	0.158811i	$0.949234\pi$
$458$	−5.96964			−0.278943
$459$	7.53431	−	3.73548i	0.351671	−	0.174357i
$460$		−	11.9295i		−	0.556217i
$461$	−0.103381	−	0.179060i	−0.00481492	−	0.00833968i	0.863608	−	0.504164i	$-0.168199\pi$
$461$	−0.103381	−	0.179060i	−0.00481492	−	0.00833968i	−0.868423	+	0.495824i	$0.834866\pi$
$462$		0			0
$463$	−7.60217	+	13.1673i	−0.353303	+	0.611938i	−0.986826	−	0.161785i	$-0.948275\pi$
$463$	−7.60217	+	13.1673i	−0.353303	+	0.611938i	0.633523	+	0.773724i	$0.281608\pi$
$464$	3.70319	+	2.13804i	0.171916	+	0.0992560i
$465$	−28.7056	+	23.0722i	−1.33119	+	1.06995i
$466$	2.24360	+	3.88603i	0.103933	+	0.180017i
$467$	2.30849			0.106824			0.0534120	−	0.998573i	$-0.482990\pi$
$467$	2.30849			0.106824			0.0534120	+	0.998573i	$0.482990\pi$
$468$	2.07718	−	2.27332i	0.0960178	−	0.105084i
$469$		0			0
$470$	15.8138	−	9.13009i	0.729435	−	0.421139i
$471$	−18.6125	−	7.22278i	−0.857617	−	0.332808i
$472$	7.65628	+	4.42036i	0.352409	+	0.203463i
$473$	−16.0135	−	9.24541i	−0.736303	−	0.425105i
$474$	1.49223	+	0.579076i	0.0685403	+	0.0265978i
$475$	−54.2925	+	31.3458i	−2.49111	+	1.43824i
$476$		0			0
$477$	−2.89042	−	9.12207i	−0.132343	−	0.417671i
$478$	−3.49809			−0.159999
$479$	−6.21659	−	10.7674i	−0.284043	−	0.491977i	0.688334	−	0.725394i	$-0.258343\pi$
$479$	−6.21659	−	10.7674i	−0.284043	−	0.491977i	−0.972377	+	0.233417i	$0.925009\pi$
$480$	−4.79564	+	3.85451i	−0.218890	+	0.175934i
$481$	−5.19719	−	3.00060i	−0.236971	−	0.136815i
$482$	5.78332	−	10.0170i	0.263423	−	0.456262i
$483$		0			0
$484$	0.932639	+	1.61538i	0.0423927	+	0.0734263i
$485$		−	54.6891i		−	2.48331i
$486$	−4.30895	+	14.9811i	−0.195458	+	0.679556i
$487$	37.3007			1.69026			0.845128	−	0.534565i	$-0.179524\pi$
$487$	37.3007			1.69026			0.845128	+	0.534565i	$0.179524\pi$
$488$	−2.34517	−	4.06195i	−0.106161	−	0.183876i
$489$	4.70330	−	0.727325i	0.212690	−	0.0328908i
$490$		0			0
$491$	−11.8191	−	6.82377i	−0.533389	−	0.307952i	0.209006	−	0.977914i	$-0.432977\pi$
$491$	−11.8191	−	6.82377i	−0.533389	−	0.307952i	−0.742396	+	0.669962i	$0.766310\pi$
$492$	−0.102482	−	0.127504i	−0.00462023	−	0.00574832i
$493$	5.99328	−	3.46022i	0.269924	−	0.155840i
$494$		−	8.44666i		−	0.380033i
$495$	−9.72893	−	30.7041i	−0.437283	−	1.38005i
$496$			5.98576i			0.268768i
$497$		0			0
$498$	17.5427	+	6.80766i	0.786109	+	0.305059i
$499$	10.5010	−	18.1882i	0.470088	−	0.814216i	−0.529327	−	0.848418i	$-0.677556\pi$
$499$	10.5010	−	18.1882i	0.470088	−	0.814216i	0.999415	+	0.0342021i	$0.0108890\pi$
$500$	4.65074	−	8.05532i	0.207987	−	0.360245i
$501$	−3.47077	+	8.94386i	−0.155063	+	0.399582i
$502$	−23.1598	+	13.3713i	−1.03367	+	0.596790i
$503$	22.3018			0.994388			0.497194	−	0.867639i	$-0.334364\pi$
$503$	22.3018			0.994388			0.497194	+	0.867639i	$0.334364\pi$
$504$		0			0
$505$	−48.6824			−2.16634
$506$	8.79018	−	5.07501i	0.390771	−	0.225612i
$507$	12.9629	+	16.1280i	0.575702	+	0.716268i
$508$	0.143582	−	0.248691i	0.00637042	−	0.0110339i
$509$	10.9589	−	18.9814i	0.485746	−	0.841337i	−0.514120	−	0.857719i	$-0.671881\pi$
$509$	10.9589	−	18.9814i	0.485746	−	0.841337i	0.999866	+	0.0163813i	$0.00521458\pi$
$510$	1.52176	+	9.84057i	0.0673847	+	0.435748i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	18.9933	+	38.3086i	0.838573	+	1.69137i
$514$			5.21227i			0.229904i
$515$	−9.37844	+	5.41465i	−0.413264	+	0.238598i
$516$	−10.4722	+	1.61944i	−0.461013	+	0.0712917i
$517$	13.4549	+	7.76818i	0.591745	+	0.341644i
$518$		0			0
$519$	−12.1585	−	15.1272i	−0.533699	−	0.664009i
$520$	1.82313	+	3.15775i	0.0799495	+	0.138477i
$521$	26.7678			1.17272			0.586358	−	0.810052i	$-0.300561\pi$
$521$	26.7678			1.17272			0.586358	+	0.810052i	$0.300561\pi$
$522$	−2.75875	+	12.5281i	−0.120747	+	0.548339i
$523$			17.1561i			0.750184i	0.926988	+	0.375092i	$0.122389\pi$
$523$			17.1561i			0.750184i	−0.926988	+	0.375092i	$0.877611\pi$
$524$	0.186474	+	0.322983i	0.00814617	+	0.0141096i
$525$		0			0
$526$	7.51869	−	13.0228i	0.327831	−	0.567819i
$527$	8.38954	+	4.84370i	0.365454	+	0.210995i
$528$	−4.88031	−	1.89386i	−0.212388	−	0.0824198i
$529$	−5.86091	−	10.1514i	−0.254822	−	0.441365i
$530$	11.3306			0.492168
$531$	−5.70367	+	25.9016i	−0.247518	+	1.12403i
$532$		0			0
$533$	−0.0839566	+	0.0484723i	−0.00363656	+	0.00209957i
$534$	6.35849	−	5.11065i	0.275159	−	0.221160i
$535$	−40.3822	−	23.3147i	−1.74588	−	1.00798i
$536$	−0.325345	−	0.187838i	−0.0140527	−	0.00811336i
$537$	0.725752	+	4.69312i	0.0313185	+	0.202523i
$538$	−20.0323	+	11.5657i	−0.863654	+	0.498631i
$539$		0			0
$540$	−15.3691	−	10.2220i	−0.661381	−	0.439886i
$541$	28.8182			1.23899			0.619496	−	0.785000i	$-0.287337\pi$
$541$	28.8182			1.23899			0.619496	+	0.785000i	$0.287337\pi$
$542$	4.95748	+	8.58661i	0.212942	+	0.368827i
$543$	5.90015	+	38.1537i	0.253199	+	1.63733i
$544$	1.40158	+	0.809204i	0.0600924	+	0.0346943i
$545$	18.7763	−	32.5214i	0.804286	−	1.39306i
$546$		0			0
$547$	−16.4045	−	28.4135i	−0.701407	−	1.21487i	−0.967972	−	0.251056i	$-0.919222\pi$
$547$	−16.4045	−	28.4135i	−0.701407	−	1.21487i	0.266565	−	0.963817i	$-0.414111\pi$
$548$			7.06222i			0.301683i
$549$	9.49151	−	10.3877i	0.405088	−	0.443338i
$550$	23.0259			0.981826
$551$	17.5937	+	30.4732i	0.749516	+	1.29820i
$552$	2.10436	−	5.42275i	0.0895676	−	0.230808i
$553$		0			0
$554$	7.44299	+	4.29721i	0.316223	+	0.182571i
$555$	−13.0136	+	33.5349i	−0.552397	+	1.42348i
$556$	12.6320	−	7.29308i	0.535715	−	0.309295i
$557$		−	46.2508i		−	1.95971i	−0.199708	−	0.979855i	$-0.563999\pi$
$557$		−	46.2508i		−	1.95971i	0.199708	−	0.979855i	$-0.436001\pi$
$558$	−17.1185	+	5.42417i	−0.724683	+	0.229623i
$559$			6.27990i			0.265611i
$560$		0			0
$561$	−6.60357	+	5.30764i	−0.278803	+	0.224089i
$562$	−10.3639	+	17.9508i	−0.437174	+	0.757208i
$563$	0.988637	−	1.71237i	0.0416661	−	0.0721678i	−0.844440	−	0.535650i	$-0.820067\pi$
$563$	0.988637	−	1.71237i	0.0416661	−	0.0721678i	0.886106	+	0.463482i	$0.153400\pi$
$564$	8.79894	−	1.36068i	0.370502	−	0.0572950i
$565$	−37.8385	+	21.8461i	−1.59188	+	0.919071i
$566$	2.36710			0.0994966
$567$		0			0
$568$	−13.9868			−0.586874
$569$	28.5702	−	16.4950i	1.19773	−	0.691508i	0.237679	−	0.971344i	$-0.423613\pi$
$569$	28.5702	−	16.4950i	1.19773	−	0.691508i	0.960048	+	0.279836i	$0.0902800\pi$
$570$	−50.0350	+	7.73748i	−2.09573	+	0.324087i
$571$	−7.40326	+	12.8228i	−0.309817	+	0.536618i	−0.978322	−	0.207089i	$-0.933601\pi$
$571$	−7.40326	+	12.8228i	−0.309817	+	0.536618i	0.668505	+	0.743707i	$0.266934\pi$
$572$	−1.55118	+	2.68672i	−0.0648580	+	0.112337i
$573$	6.92921	−	5.56937i	0.289472	−	0.232664i
$574$		0			0
$575$			25.5851i			1.06697i
$576$	−2.85987	+	0.906179i	−0.119161	+	0.0377575i
$577$			18.4180i			0.766752i	0.923592	+	0.383376i	$0.125239\pi$
$577$			18.4180i			0.766752i	−0.923592	+	0.383376i	$0.874761\pi$
$578$	−12.4541	+	7.19038i	−0.518022	+	0.299080i
$579$	10.0163	−	25.8110i	0.416261	−	1.07267i
$580$	−13.1547	−	7.59485i	−0.546218	−	0.315359i
$581$		0			0
$582$	9.64714	−	24.8598i	0.399887	−	1.03047i
$583$	4.82020	+	8.34884i	0.199632	+	0.345774i
$584$	−1.31111			−0.0542542
$585$	−7.37867	+	8.07539i	−0.305070	+	0.333876i
$586$			17.6755i			0.730167i
$587$	−23.1065	−	40.0216i	−0.953707	−	1.65187i	−0.737301	−	0.675565i	$-0.763900\pi$
$587$	−23.1065	−	40.0216i	−0.953707	−	1.65187i	−0.216406	−	0.976304i	$-0.569433\pi$
$588$		0			0
$589$	−24.6281	+	42.6571i	−1.01478	+	1.75765i
$590$	−27.1970	−	15.7022i	−1.11968	−	0.646450i
$591$	−1.25090	−	8.08904i	−0.0514552	−	0.332738i
$592$	2.92323	+	5.06319i	0.120144	+	0.208096i
$593$	13.6093			0.558867			0.279434	−	0.960165i	$-0.409853\pi$
$593$	13.6093			0.558867			0.279434	+	0.960165i	$0.409853\pi$
$594$	0.993759	−	15.6732i	0.0407744	−	0.643080i
$595$		0			0
$596$	9.26832	−	5.35107i	0.379645	−	0.219188i
$597$	0.561416	+	3.63043i	0.0229772	+	0.148584i
$598$	−2.98534	−	1.72359i	−0.122080	−	0.0704827i
$599$	−20.4214	−	11.7903i	−0.834396	−	0.481739i	0.0209595	−	0.999780i	$-0.493328\pi$
$599$	−20.4214	−	11.7903i	−0.834396	−	0.481739i	−0.855355	+	0.518042i	$0.826661\pi$
$600$	10.2852	−	8.26673i	0.419890	−	0.337488i
$601$	31.0765	−	17.9420i	1.26764	−	0.731871i	0.293097	−	0.956083i	$-0.405314\pi$
$601$	31.0765	−	17.9420i	1.26764	−	0.731871i	0.974540	+	0.224212i	$0.0719808\pi$
$602$		0			0
$603$	0.242371	−	1.10066i	0.00987010	−	0.0448222i
$604$	−16.0013			−0.651084
$605$	−3.31297	−	5.73823i	−0.134691	−	0.233292i
$606$	−22.1294	−	8.58755i	−0.898943	−	0.348846i
$607$	−16.8502	−	9.72845i	−0.683928	−	0.394866i	0.117406	−	0.993084i	$-0.462542\pi$
$607$	−16.8502	−	9.72845i	−0.683928	−	0.394866i	−0.801333	+	0.598218i	$0.795876\pi$
$608$	−4.11444	+	7.12643i	−0.166863	+	0.289015i
$609$		0			0
$610$	8.33063	+	14.4291i	0.337297	+	0.584216i
$611$		−	5.27649i		−	0.213464i
$612$	−1.04413	+	4.74162i	−0.0422065	+	0.191669i
$613$	42.2421			1.70614			0.853071	−	0.521795i	$-0.174738\pi$
$613$	42.2421			1.70614			0.853071	+	0.521795i	$0.174738\pi$
$614$	0.640777	+	1.10986i	0.0258597	+	0.0447902i
$615$	0.364040	+	0.452926i	0.0146795	+	0.0182637i
$616$		0			0
$617$	9.63660	+	5.56369i	0.387955	+	0.223986i	0.681274	−	0.732029i	$-0.261426\pi$
$617$	9.63660	+	5.56369i	0.387955	+	0.223986i	−0.293319	+	0.956015i	$0.594760\pi$
$618$	−5.21826	+	0.806960i	−0.209909	+	0.0324607i
$619$	8.71387	−	5.03096i	0.350240	−	0.202211i	−0.314551	−	0.949241i	$-0.601854\pi$
$619$	8.71387	−	5.03096i	0.350240	−	0.202211i	0.664791	+	0.747029i	$0.268521\pi$
$620$		−	21.2629i		−	0.853939i
$621$	17.4153	+	1.10421i	0.698851	+	0.0443105i
$622$		−	12.5329i		−	0.502522i
$623$		0			0
$624$	0.271706	+	1.75700i	0.0108769	+	0.0703365i
$625$	2.52560	−	4.37447i	0.101024	−	0.174979i
$626$	−4.37692	+	7.58105i	−0.174937	+	0.303000i
$627$	−26.9870	−	33.5762i	−1.07776	−	1.34091i
$628$	9.98239	−	5.76334i	0.398341	−	0.229982i
$629$	9.46198			0.377274
$630$		0			0
$631$	10.3528			0.412139			0.206070	−	0.978537i	$-0.433933\pi$
$631$	10.3528			0.412139			0.206070	+	0.978537i	$0.433933\pi$
$632$	−0.800324	+	0.462067i	−0.0318352	+	0.0183800i
$633$	17.3045	−	44.5922i	0.687793	−	1.77238i
$634$	−6.83920	+	11.8458i	−0.271619	+	0.470459i
$635$	−0.510039	+	0.883413i	−0.0202403	+	0.0350572i
$636$	5.15048	+	1.99870i	0.204230	+	0.0792538i
$637$		0			0
$638$		−	12.9239i		−	0.511662i
$639$	−12.6746	−	40.0005i	−0.501398	−	1.58239i
$640$		−	3.55225i		−	0.140415i
$641$	23.0678	−	13.3182i	0.911123	−	0.526037i	0.0303310	−	0.999540i	$-0.490344\pi$
$641$	23.0678	−	13.3182i	0.911123	−	0.526037i	0.880792	+	0.473503i	$0.157011\pi$
$642$	−14.2437	−	17.7215i	−0.562153	−	0.699410i
$643$	−40.0493	−	23.1225i	−1.57939	−	0.911861i	−0.994944	−	0.100429i	$-0.967979\pi$
$643$	−40.0493	−	23.1225i	−1.57939	−	0.911861i	−0.584446	−	0.811433i	$-0.698688\pi$
$644$		0			0
$645$	37.1998	−	5.75264i	1.46474	−	0.226510i
$646$	6.65885	+	11.5335i	0.261989	+	0.453778i
$647$	−31.4063			−1.23471			−0.617355	−	0.786684i	$-0.711796\pi$
$647$	−31.4063			−1.23471			−0.617355	+	0.786684i	$0.711796\pi$
$648$	−5.18310	−	7.35768i	−0.203611	−	0.289037i
$649$		−	26.7199i		−	1.04885i
$650$	−3.91005	−	6.77240i	−0.153365	−	0.265635i
$651$		0			0
$652$	−1.37386	+	2.37960i	−0.0538046	+	0.0931923i
$653$	−39.9639	−	23.0732i	−1.56391	−	0.902924i	−0.996855	−	0.0792429i	$-0.974750\pi$
$653$	−39.9639	−	23.0732i	−1.56391	−	0.902924i	−0.567054	−	0.823681i	$-0.691917\pi$
$654$	14.2718	−	11.4710i	0.558072	−	0.448552i
$655$	−0.662404	−	1.14732i	−0.0258823	−	0.0448294i
$656$	0.0944452			0.00368747
$657$	−1.18810	−	3.74960i	−0.0463522	−	0.146286i
$658$		0			0
$659$	1.18052	−	0.681575i	0.0459867	−	0.0265504i	−0.476830	−	0.878995i	$-0.658214\pi$
$659$	1.18052	−	0.681575i	0.0459867	−	0.0265504i	0.522817	+	0.852445i	$0.324881\pi$
$660$	17.3361	+	6.72747i	0.674806	+	0.261866i
$661$	−6.23888	−	3.60202i	−0.242664	−	0.140102i	0.373736	−	0.927535i	$-0.378076\pi$
$661$	−6.23888	−	3.60202i	−0.242664	−	0.140102i	−0.616401	+	0.787433i	$0.711410\pi$
$662$	9.43721	+	5.44858i	0.366788	+	0.211765i
$663$	2.68245	+	1.04096i	0.104178	+	0.0404274i
$664$	−9.40866	+	5.43209i	−0.365127	+	0.210806i
$665$		0			0
$666$	−11.8311	+	12.9482i	−0.458445	+	0.501733i
$667$	14.3604			0.556035
$668$	−2.76946	−	4.79685i	−0.107154	−	0.185596i
$669$	−27.4689	+	22.0782i	−1.06201	+	0.853593i
$670$	1.15570	+	0.667247i	0.0446488	+	0.0257780i
$671$	−7.08797	+	12.2767i	−0.273628	+	0.473938i
$672$		0			0
$673$	19.4709	+	33.7246i	0.750548	+	1.29999i	0.947558	+	0.319585i	$0.103544\pi$
$673$	19.4709	+	33.7246i	0.750548	+	1.29999i	−0.197010	+	0.980402i	$0.563123\pi$
$674$		−	25.6180i		−	0.986767i
$675$	32.9620	+	21.9231i	1.26871	+	0.843820i
$676$	−11.9464			−0.459476
$677$	1.20505	+	2.08722i	0.0463140	+	0.0802182i	0.888253	−	0.459354i	$-0.151919\pi$
$677$	1.20505	+	2.08722i	0.0463140	+	0.0802182i	−0.841939	+	0.539573i	$0.818586\pi$
$678$	−21.0537	+	3.25578i	−0.808563	+	0.125037i
$679$		0			0
$680$	−4.97877	−	2.87450i	−0.190927	−	0.110232i
$681$	−4.51397	−	5.61612i	−0.172976	−	0.215210i
$682$	15.6674	−	9.04559i	0.599937	−	0.346374i
$683$			28.3251i			1.08383i	0.840433	+	0.541915i	$0.182300\pi$
$683$			28.3251i			1.08383i	−0.840433	+	0.541915i	$0.817700\pi$
$684$	−24.1091	−	5.30895i	−0.921833	−	0.202993i
$685$		−	25.0868i		−	0.958517i
$686$		0			0
$687$	9.63935	+	3.74066i	0.367764	+	0.142715i
$688$	3.05899	−	5.29833i	0.116623	−	0.201997i
$689$	1.63705	−	2.83545i	0.0623666	−	0.108022i
$690$	−7.47522	+	19.2630i	−0.284577	+	0.733328i
$691$	2.95334	−	1.70511i	0.112350	−	0.0648655i	−0.442772	−	0.896634i	$-0.646005\pi$
$691$	2.95334	−	1.70511i	0.112350	−	0.0648655i	0.555122	+	0.831769i	$0.312672\pi$
$692$	11.2051			0.425953
$693$		0			0
$694$	−16.7623			−0.636289
$695$	−44.8719	+	25.9068i	−1.70209	+	0.982702i
$696$	−4.63993	−	5.77283i	−0.175876	−	0.218819i
$697$	0.0764255	−	0.132373i	0.00289482	−	0.00501398i
$698$	−8.34010	+	14.4455i	−0.315678	+	0.546769i
$699$	−1.18776	−	7.68076i	−0.0449254	−	0.290513i
$700$		0			0
$701$		−	51.4943i		−	1.94491i	−0.233087	−	0.972456i	$-0.574883\pi$
$701$		−	51.4943i		−	1.94491i	0.233087	−	0.972456i	$-0.425117\pi$
$702$	−4.77858	+	2.36920i	−0.180356	+	0.0894198i
$703$			48.1099i			1.81450i
$704$	2.61745	−	1.51119i	0.0986488	−	0.0569549i
$705$	−31.2560	+	4.83348i	−1.17717	+	0.182039i
$706$	31.1021	+	17.9568i	1.17054	+	0.675814i
$707$		0			0
$708$	−9.59297	−	11.9352i	−0.360526	−	0.448553i
$709$	−5.04218	−	8.73331i	−0.189363	−	0.327986i	0.755675	−	0.654947i	$-0.227309\pi$
$709$	−5.04218	−	8.73331i	−0.189363	−	0.327986i	−0.945038	+	0.326960i	$0.893976\pi$
$710$	49.6847			1.86463
$711$	−2.04669	−	1.87010i	−0.0767567	−	0.0701344i
$712$			4.70989i			0.176511i
$713$	10.0510	+	17.4088i	0.376412	+	0.651965i
$714$		0			0
$715$	5.51017	−	9.54389i	0.206069	−	0.356921i
$716$	−2.37445	−	1.37089i	−0.0887375	−	0.0512326i
$717$	5.64848	+	2.19196i	0.210946	+	0.0818602i
$718$	−14.2749	−	24.7248i	−0.532734	−	0.922722i
$719$	−31.9168			−1.19030			−0.595148	−	0.803616i	$-0.702907\pi$
$719$	−31.9168			−1.19030			−0.595148	+	0.803616i	$0.702907\pi$
$720$	10.1590	−	3.21897i	0.378602	−	0.119964i
$721$		0			0
$722$	−42.1881	+	24.3573i	−1.57008	+	0.906485i
$723$	−15.6153	+	12.5508i	−0.580740	+	0.466771i
$724$	−19.3036	−	11.1449i	−0.717413	−	0.414198i
$725$	28.2127	+	16.2886i	1.04779	+	0.604943i
$726$	−0.493741	−	3.19281i	−0.0183244	−	0.118496i
$727$	17.9336	−	10.3540i	0.665120	−	0.384007i	−0.129105	−	0.991631i	$-0.541210\pi$
$727$	17.9336	−	10.3540i	0.665120	−	0.384007i	0.794225	+	0.607624i	$0.207877\pi$
$728$		0			0
$729$	16.3452	−	21.4904i	0.605377	−	0.795939i
$730$	4.65739			0.172378
$731$	−4.95070	−	8.57487i	−0.183108	−	0.317153i
$732$	1.24154	+	8.02848i	0.0458885	+	0.296741i
$733$	7.69996	+	4.44558i	0.284405	+	0.164201i	0.635416	−	0.772170i	$-0.280829\pi$
$733$	7.69996	+	4.44558i	0.284405	+	0.164201i	−0.351011	+	0.936371i	$0.614162\pi$
$734$	0.179362	−	0.310665i	0.00662038	−	0.0114668i
$735$		0			0
$736$	1.67915	+	2.90837i	0.0618943	+	0.107204i
$737$			1.13543i			0.0418241i
$738$	0.0855843	+	0.270101i	0.00315040	+	0.00994255i
$739$	32.7763			1.20570			0.602848	−	0.797856i	$-0.294032\pi$
$739$	32.7763			1.20570			0.602848	+	0.797856i	$0.294032\pi$
$740$	−10.3841	−	17.9857i	−0.381726	−	0.661168i
$741$	−5.29280	+	13.6391i	−0.194436	+	0.501044i
$742$		0			0
$743$	−6.68055	−	3.85702i	−0.245086	−	0.141500i	0.372426	−	0.928062i	$-0.378526\pi$
$743$	−6.68055	−	3.85702i	−0.245086	−	0.141500i	−0.617512	+	0.786562i	$0.711859\pi$
$744$	3.75077	−	9.66539i	0.137510	−	0.354350i
$745$	−32.9234	+	19.0083i	−1.20622	+	0.696411i
$746$			25.3708i			0.928893i
$747$	−24.0610	−	21.9851i	−0.880346	−	0.804392i
$748$		−	4.89143i		−	0.178848i
$749$		0			0
$750$	−12.5573	+	10.0929i	−0.458527	+	0.368542i
$751$	−15.3804	+	26.6397i	−0.561239	+	0.972095i	0.436149	+	0.899874i	$0.356342\pi$
$751$	−15.3804	+	26.6397i	−0.561239	+	0.972095i	−0.997389	+	0.0722207i	$0.976991\pi$
$752$	−2.57023	+	4.45176i	−0.0937265	+	0.162339i
$753$	45.7754	−	7.07878i	1.66815	−	0.257965i
$754$	−3.80120	+	2.19462i	−0.138431	+	0.0799234i
$755$	56.8406			2.06864
$756$		0			0
$757$	46.4611			1.68866			0.844328	−	0.535827i	$-0.180000\pi$
$757$	46.4611			1.68866			0.844328	+	0.535827i	$0.180000\pi$
$758$	23.3016	−	13.4532i	0.846351	−	0.488641i
$759$	−17.3738	+	2.68672i	−0.630631	+	0.0975217i
$760$	14.6155	−	25.3148i	0.530161	−	0.918266i
$761$	18.5959	−	32.2090i	0.674099	−	1.16757i	−0.302632	−	0.953107i	$-0.597865\pi$
$761$	18.5959	−	32.2090i	0.674099	−	1.16757i	0.976731	−	0.214467i	$-0.0688013\pi$
$762$	−0.387680	+	0.311599i	−0.0140442	+	0.0112880i
$763$		0			0
$764$			5.13264i			0.185692i
$765$	3.70902	−	16.8434i	0.134100	−	0.608976i
$766$		−	12.5717i		−	0.454235i
$767$	−7.85890	+	4.53734i	−0.283768	+	0.163834i
$768$	0.626615	−	1.61473i	0.0226110	−	0.0582666i
$769$	12.2312	+	7.06166i	0.441067	+	0.254650i	0.704050	−	0.710150i	$-0.251373\pi$
$769$	12.2312	+	7.06166i	0.441067	+	0.254650i	−0.262983	+	0.964800i	$0.584706\pi$
$770$		0			0
$771$	3.26609	−	8.41642i	0.117625	−	0.303110i
$772$	7.99235	+	13.8432i	0.287651	+	0.498226i
$773$	30.9455			1.11303			0.556517	−	0.830836i	$-0.312138\pi$
$773$	30.9455			1.11303			0.556517	+	0.830836i	$0.312138\pi$
$774$	17.9245	+	3.94708i	0.644284	+	0.141875i
$775$			45.6024i			1.63809i
$776$	7.69782	+	13.3330i	0.276336	+	0.478627i
$777$		0			0
$778$	8.12937	−	14.0805i	0.291452	−	0.504810i
$779$	0.673057	+	0.388590i	0.0241148	+	0.0139227i
$780$	−0.965167	−	6.24132i	−0.0345585	−	0.223475i
$781$	21.1367	+	36.6098i	0.756330	+	1.31000i
$782$	5.43510			0.194359
$783$	12.3049	−	18.5008i	0.439742	−	0.661165i
$784$		0			0
$785$	−35.4599	+	20.4728i	−1.26562	+	0.730706i
$786$	−0.0987198	−	0.638378i	−0.00352122	−	0.0227702i
$787$	15.8704	+	9.16280i	0.565720	+	0.326619i	0.755438	−	0.655220i	$-0.227424\pi$
$787$	15.8704	+	9.16280i	0.565720	+	0.326619i	−0.189718	+	0.981839i	$0.560757\pi$
$788$	4.09259	+	2.36286i	0.145793	+	0.0841734i
$789$	−20.3009	+	16.3169i	−0.722732	+	0.580898i
$790$	2.84295	−	1.64138i	0.101148	−	0.0583976i
$791$		0			0
$792$	6.69367	+	6.11615i	0.237849	+	0.217328i
$793$	4.81447			0.170967
$794$	−7.34692	−	12.7252i	−0.260733	−	0.451602i
$795$	−18.2958	−	7.09990i	−0.648885	−	0.251807i
$796$	−1.83679	−	1.06047i	−0.0651034	−	0.0375875i
$797$	1.07681	−	1.86508i	0.0381424	−	0.0660646i	−0.846324	−	0.532668i	$-0.821189\pi$
$797$	1.07681	−	1.86508i	0.0381424	−	0.0660646i	0.884466	+	0.466604i	$0.154523\pi$
$798$		0			0
$799$	4.15968	+	7.20477i	0.147159	+	0.254886i
$800$			7.61848i			0.269354i
$801$	−13.4697	+	4.26800i	−0.475927	+	0.150802i
$802$	−16.6464			−0.587804
$803$	1.98133	+	3.43177i	0.0699197	+	0.121104i
$804$	0.407642	+	0.507173i	0.0143764	+	0.0178866i
$805$		0			0
$806$	−5.32101	−	3.07208i	−0.187424	−	0.108210i
$807$	39.5940	−	6.12287i	1.39377	−	0.215535i
$808$	11.8686	−	6.85234i	0.417536	−	0.241064i
$809$			19.6468i			0.690746i	0.938465	+	0.345373i	$0.112248\pi$
$809$			19.6468i			0.690746i	−0.938465	+	0.345373i	$0.887752\pi$
$810$	18.4117	+	26.1363i	0.646920	+	0.918336i
$811$		−	12.3340i		−	0.433105i	−0.976271	−	0.216552i	$-0.930519\pi$
$811$		−	12.3340i		−	0.433105i	0.976271	−	0.216552i	$-0.0694812\pi$
$812$		0			0
$813$	−2.62450	−	16.9715i	−0.0920452	−	0.595216i
$814$	8.83510	−	15.3028i	0.309670	−	0.536364i
$815$	4.88030	−	8.45293i	0.170950	−	0.296093i
$816$	−1.75612	−	2.18490i	−0.0614765	−	0.0764868i
$817$	43.5994	−	25.1721i	1.52535	−	0.880661i
$818$	2.80886			0.0982095
$819$		0			0
$820$	−0.335493			−0.0117159
$821$	19.3763	−	11.1869i	0.676238	−	0.390426i	−0.122198	−	0.992506i	$-0.538994\pi$
$821$	19.3763	−	11.1869i	0.676238	−	0.390426i	0.798436	+	0.602079i	$0.205661\pi$
$822$	4.42529	−	11.4036i	0.154350	−	0.397746i
$823$	−13.5033	+	23.3883i	−0.470694	+	0.815266i	−0.999438	−	0.0335154i	$-0.989330\pi$
$823$	−13.5033	+	23.3883i	−0.470694	+	0.815266i	0.528744	+	0.848781i	$0.322663\pi$
$824$	1.52429	−	2.64014i	0.0531010	−	0.0919737i
$825$	−37.1805	−	14.4283i	−1.29446	−	0.502330i
$826$		0			0
$827$			26.3189i			0.915196i	0.889159	+	0.457598i	$0.151290\pi$
$827$			26.3189i			0.915196i	−0.889159	+	0.457598i	$0.848710\pi$
$828$	−6.79595	+	7.43765i	−0.236176	+	0.258476i
$829$		−	33.3351i		−	1.15778i	−0.815407	−	0.578888i	$-0.803487\pi$
$829$		−	33.3351i		−	1.15778i	0.815407	−	0.578888i	$-0.196513\pi$
$830$	33.4219	−	19.2962i	1.16009	−	0.669779i
$831$	−9.32573	−	11.6027i	−0.323506	−	0.402494i
$832$	−0.888944	−	0.513232i	−0.0308186	−	0.0177931i
$833$		0			0
$834$	−24.9672	+	3.86096i	−0.864543	+	0.133694i
$835$	9.83781	+	17.0396i	0.340452	+	0.589679i
$836$	24.8707			0.860173
$837$	31.0406	+	1.96812i	1.07292	+	0.0680283i
$838$			14.9472i			0.516344i
$839$	18.6896	+	32.3713i	0.645236	+	1.11758i	0.984247	+	0.176799i	$0.0565743\pi$
$839$	18.6896	+	32.3713i	0.645236	+	1.11758i	−0.339011	+	0.940782i	$0.610092\pi$
$840$		0			0
$841$	−5.35758	+	9.27960i	−0.184744	+	0.319986i
$842$	−13.5158	−	7.80336i	−0.465786	−	0.268922i
$843$	27.9831	−	22.4915i	0.963790	−	0.774649i
$844$	13.8079	+	23.9160i	0.475289	+	0.823224i
$845$	42.4365			1.45986
$846$	−15.0605	−	3.31641i	−0.517792	−	0.114021i
$847$		0			0
$848$	−2.76235	+	1.59484i	−0.0948594	+	0.0547671i
$849$	−3.82223	−	1.48326i	−0.131178	−	0.0509053i
$850$	10.6779	+	6.16490i	0.366250	+	0.211454i
$851$	17.0037	+	9.81710i	0.582880	+	0.336526i
$852$	22.5850	+	8.76436i	0.773748	+	0.300262i
$853$	4.65798	−	2.68929i	0.159486	−	0.0920795i	−0.418133	−	0.908386i	$-0.637315\pi$
$853$	4.65798	−	2.68929i	0.159486	−	0.0920795i	0.577619	+	0.816306i	$0.303982\pi$
$854$		0			0
$855$	85.6414	+	18.8587i	2.92887	+	0.644954i
$856$	13.1267			0.448662
$857$	−22.7000	−	39.3176i	−0.775418	−	1.34306i	−0.934559	−	0.355807i	$-0.884206\pi$
$857$	−22.7000	−	39.3176i	−0.775418	−	1.34306i	0.159142	−	0.987256i	$-0.449127\pi$
$858$	4.18827	−	3.36633i	0.142985	−	0.114925i
$859$	3.36261	+	1.94141i	0.114731	+	0.0662399i	0.556267	−	0.831003i	$-0.312233\pi$
$859$	3.36261	+	1.94141i	0.114731	+	0.0662399i	−0.441536	+	0.897243i	$0.645566\pi$
$860$	−10.8663	+	18.8210i	−0.370538	+	0.641791i
$861$		0			0
$862$	−8.08792	−	14.0087i	−0.275476	−	0.477138i
$863$			23.4788i			0.799228i	0.916684	+	0.399614i	$0.130856\pi$
$863$			23.4788i			0.799228i	−0.916684	+	0.399614i	$0.869144\pi$
$864$	5.18574	+	0.328801i	0.176422	+	0.0111860i
$865$	−39.8032			−1.35335
$866$	13.6250	+	23.5991i	0.462995	+	0.801931i
$867$	24.6156	−	3.80660i	0.835990	−	0.129279i
$868$		0			0
$869$	2.41887	+	1.39654i	0.0820547	+	0.0473743i
$870$	16.4822	+	20.5065i	0.558798	+	0.695237i
$871$	0.333955	−	0.192809i	0.0113156	−	0.00653308i
$872$			10.5715i			0.357995i
$873$	−31.1550	+	34.0968i	−1.05444	+	1.15400i
$874$			27.6351i			0.934770i
$875$		0			0
$876$	2.11709	+	0.821562i	0.0715299	+	0.0277580i
$877$	−16.4796	+	28.5434i	−0.556475	+	0.963843i	0.441312	+	0.897354i	$0.354513\pi$
$877$	−16.4796	+	28.5434i	−0.556475	+	0.963843i	−0.997787	+	0.0664896i	$0.978820\pi$
$878$	−16.5674	+	28.6955i	−0.559121	+	0.968427i
$879$	11.0757	−	28.5411i	0.373575	−	0.962668i
$880$	−9.29783	+	5.36811i	−0.313430	+	0.180959i
$881$	−7.44403			−0.250796			−0.125398	−	0.992107i	$-0.540021\pi$
$881$	−7.44403			−0.250796			−0.125398	+	0.992107i	$0.540021\pi$
$882$		0			0
$883$	−28.2839			−0.951828			−0.475914	−	0.879492i	$-0.657883\pi$
$883$	−28.2839			−0.951828			−0.475914	+	0.879492i	$0.657883\pi$
$884$	−1.43867	+	0.830619i	−0.0483879	+	0.0279368i
$885$	34.0766	+	42.3969i	1.14547	+	1.42516i
$886$	−11.1318	+	19.2808i	−0.373980	+	0.647752i
$887$	−6.06377	+	10.5028i	−0.203602	+	0.352648i	−0.949686	−	0.313203i	$-0.898598\pi$
$887$	−6.06377	+	10.5028i	−0.203602	+	0.352648i	0.746085	+	0.665851i	$0.231931\pi$
$888$	−1.54756	−	10.0074i	−0.0519329	−	0.335827i
$889$		0			0
$890$		−	16.7307i		−	0.560814i
$891$	−11.4257	+	24.6853i	−0.382776	+	0.826989i
$892$		−	20.3469i		−	0.681264i
$893$	−36.6331	+	21.1501i	−1.22588	+	0.707761i
$894$	−18.3189	+	2.83286i	−0.612676	+	0.0947451i
$895$	8.43465	+	4.86975i	0.281939	+	0.162778i
$896$		0			0
$897$	3.74050	+	4.65379i	0.124892	+	0.155385i
$898$	−3.40409	−	5.89606i	−0.113596	−	0.196754i
$899$	25.5956			0.853660
$900$	−21.7878	+	6.90370i	−0.726261	+	0.230123i
$901$			5.16221i			0.171978i
$902$	−0.142724	−	0.247206i	−0.00475220	−	0.00823105i
$903$		0			0
$904$	6.14993	−	10.6520i	0.204544	−	0.354280i
$905$	68.5712	+	39.5896i	2.27938	+	1.31600i
$906$	25.8378	+	10.0267i	0.858403	+	0.333113i
$907$	23.0890	+	39.9913i	0.766657	+	1.32789i	0.939366	+	0.342916i	$0.111415\pi$
$907$	23.0890	+	39.9913i	0.766657	+	1.32789i	−0.172709	+	0.984973i	$0.555252\pi$
$908$	4.16000			0.138054
$909$	30.3518	+	27.7332i	1.00671	+	0.919851i
$910$		0			0
$911$	−12.7284	+	7.34874i	−0.421710	+	0.243475i	−0.695809	−	0.718227i	$-0.744954\pi$
$911$	−12.7284	+	7.34874i	−0.421710	+	0.243475i	0.274098	+	0.961702i	$0.411621\pi$
$912$	11.1092	−	8.92908i	0.367864	−	0.295672i
$913$	28.4365	+	16.4178i	0.941110	+	0.543350i
$914$	−13.1861	−	7.61298i	−0.436156	−	0.251815i
$915$	−4.41025	−	28.5192i	−0.145798	−	0.942814i
$916$	−5.16986	+	2.98482i	−0.170817	+	0.0986212i
$917$		0			0
$918$	4.65716	−	7.00218i	0.153709	−	0.231106i
$919$	25.8691			0.853342			0.426671	−	0.904407i	$-0.359686\pi$
$919$	25.8691			0.853342			0.426671	+	0.904407i	$0.359686\pi$
$920$	−5.96476	−	10.3313i	−0.196652	−	0.340612i
$921$	−0.339228	−	2.19364i	−0.0111780	−	0.0722830i
$922$	−0.179060	−	0.103381i	−0.00589704	−	0.00340466i
$923$	7.17849	−	12.4335i	0.236283	−	0.409254i
$924$		0			0
$925$	22.2706	+	38.5738i	0.732253	+	1.26830i
$926$			15.2043i			0.499645i
$927$	8.93173	+	1.96682i	0.293357	+	0.0645987i
$928$	4.27608			0.140369
$929$	6.59673	+	11.4259i	0.216432	+	0.374870i	0.953714	−	0.300714i	$-0.0972248\pi$
$929$	6.59673	+	11.4259i	0.216432	+	0.374870i	−0.737283	+	0.675584i	$0.763892\pi$
$930$	−13.3237	+	34.3339i	−0.436900	+	1.12585i
$931$		0			0
$932$	3.88603	+	2.24360i	0.127291	+	0.0734915i
$933$	−7.85327	+	20.2372i	−0.257105	+	0.662535i
$934$	1.99921	−	1.15424i	0.0654161	−	0.0377680i
$935$			17.3756i			0.568242i
$936$	0.662233	−	3.00734i	0.0216458	−	0.0982981i
$937$		−	8.86021i		−	0.289451i	−0.989472	−	0.144725i	$-0.953770\pi$
$937$		−	8.86021i		−	0.289451i	0.989472	−	0.144725i	$-0.0462298\pi$
$938$		0			0
$939$	11.8180	−	9.49871i	0.385664	−	0.309979i
$940$	9.13009	−	15.8138i	0.297791	−	0.515788i
$941$	−2.05919	+	3.56663i	−0.0671278	+	0.116269i	−0.897636	−	0.440738i	$-0.854717\pi$
$941$	−2.05919	+	3.56663i	−0.0671278	+	0.116269i	0.830508	+	0.557007i	$0.188050\pi$
$942$	−19.7303	+	3.05112i	−0.642847	+	0.0994108i
$943$	0.274682	−	0.158588i	0.00894488	−	0.00516433i
$944$	8.84071			0.287741
$945$		0			0
$946$	−18.4908			−0.601189
$947$	21.4498	−	12.3840i	0.697024	−	0.402427i	−0.109214	−	0.994018i	$-0.534833\pi$
$947$	21.4498	−	12.3840i	0.697024	−	0.402427i	0.806238	+	0.591591i	$0.201500\pi$
$948$	1.58184	−	0.244619i	0.0513759	−	0.00794485i
$949$	0.672905	−	1.16550i	0.0218434	−	0.0378339i
$950$	−31.3458	+	54.2925i	−1.01699	+	1.76148i
$951$	18.4662	−	14.8423i	0.598809	−	0.481294i
$952$		0			0
$953$		−	9.62625i		−	0.311825i	−0.987771	−	0.155912i	$-0.950168\pi$
$953$		−	9.62625i		−	0.311825i	0.987771	−	0.155912i	$-0.0498317\pi$
$954$	−7.06422	−	6.45474i	−0.228713	−	0.208980i
$955$		−	18.2324i		−	0.589987i
$956$	−3.02944	+	1.74905i	−0.0979790	+	0.0565682i
$957$	−8.09830	+	20.8686i	−0.261781	+	0.674586i
$958$	−10.7674	−	6.21659i	−0.347880	−	0.200849i
$959$		0			0
$960$	−2.22589	+	5.73592i	−0.0718404	+	0.185126i
$961$	2.41465	+	4.18230i	0.0778920	+	0.134913i
$962$	−6.00119			−0.193486
$963$	11.8952	+	37.5407i	0.383316	+	1.20973i
$964$		−	11.5666i		−	0.372537i
$965$	−28.3908	−	49.1744i	−0.913933	−	1.58298i
$966$		0			0
$967$	5.05558	−	8.75652i	0.162576	−	0.281591i	−0.773216	−	0.634143i	$-0.781353\pi$
$967$	5.05558	−	8.75652i	0.162576	−	0.281591i	0.935792	+	0.352553i	$0.114686\pi$
$968$	1.61538	+	0.932639i	0.0519202	+	0.0299762i
$969$	−3.52520	−	22.7960i	−0.113246	−	0.732312i
$970$	−27.3446	−	47.3622i	−0.877981	−	1.52071i
$971$	−25.3149			−0.812392			−0.406196	−	0.913786i	$-0.633145\pi$
$971$	−25.3149			−0.812392			−0.406196	+	0.913786i	$0.633145\pi$
$972$	3.75888	+	15.1285i	0.120566	+	0.485246i
$973$		0			0
$974$	32.3033	−	18.6503i	1.03507	−	0.597595i
$975$	2.06998	+	13.3857i	0.0662926	+	0.428685i
$976$	−4.06195	−	2.34517i	−0.130020	−	0.0750671i
$977$	−7.84008	−	4.52647i	−0.250826	−	0.144815i	0.369316	−	0.929304i	$-0.379592\pi$
$977$	−7.84008	−	4.52647i	−0.250826	−	0.144815i	−0.620143	+	0.784489i	$0.712925\pi$
$978$	3.70951	−	2.98153i	0.118617	−	0.0953388i
$979$	12.3279	−	7.11752i	0.394001	−	0.227477i
$980$		0			0
$981$	−30.2330	+	9.57964i	−0.965266	+	0.305855i
$982$	−13.6475			−0.435511
$983$	3.19651	+	5.53653i	0.101953	+	0.176588i	0.912489	−	0.409101i	$-0.134158\pi$
$983$	3.19651	+	5.53653i	0.101953	+	0.176588i	−0.810536	+	0.585688i	$0.800824\pi$
$984$	−0.152504	−	0.0591808i	−0.00486164	−	0.00188661i
$985$	−14.5379	−	8.39347i	−0.463216	−	0.267438i
$986$	3.46022	−	5.99328i	0.110196	−	0.190865i
$987$		0			0
$988$	−4.22333	−	7.31502i	−0.134362	−	0.232722i
$989$		−	20.5460i		−	0.653326i
$990$	−23.7776	−	21.7261i	−0.755701	−	0.690501i
$991$	−13.8446			−0.439788			−0.219894	−	0.975524i	$-0.570571\pi$
$991$	−13.8446			−0.439788			−0.219894	+	0.975524i	$0.570571\pi$
$992$	2.99288	+	5.18382i	0.0950240	+	0.164586i
$993$	−11.8244	−	14.7115i	−0.375236	−	0.466855i
$994$		0			0
$995$	6.52475	+	3.76706i	0.206848	+	0.119424i
$996$	18.5963	−	2.87576i	0.589246	−	0.0911219i
$997$	−5.99391	+	3.46059i	−0.189829	+	0.109598i	−0.591903	−	0.806010i	$-0.701623\pi$
$997$	−5.99391	+	3.46059i	−0.189829	+	0.109598i	0.402073	+	0.915607i	$0.368290\pi$
$998$		−	21.0019i		−	0.664804i
$999$	27.2176	−	13.4944i	0.861125	−	0.426942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.m.a.293.5		16
3.2	odd	2		2646.2.m.a.881.4		16
7.2	even	3		126.2.t.a.59.4	yes	16
7.3	odd	6		126.2.l.a.5.6	✓	16
7.4	even	3		882.2.l.b.509.7		16
7.5	odd	6		882.2.t.a.815.1		16
7.6	odd	2		882.2.m.b.293.8		16
9.2	odd	6		882.2.m.b.587.8		16
9.7	even	3		2646.2.m.b.1763.1		16
21.2	odd	6		378.2.t.a.17.5		16
21.5	even	6		2646.2.t.b.2285.8		16
21.11	odd	6		2646.2.l.a.1097.4		16
21.17	even	6		378.2.l.a.341.1		16
21.20	even	2		2646.2.m.b.881.1		16
28.3	even	6		1008.2.ca.c.257.7		16
28.23	odd	6		1008.2.df.c.689.3		16
63.2	odd	6		126.2.l.a.101.2	yes	16
63.11	odd	6		882.2.t.a.803.1		16
63.16	even	3		378.2.l.a.143.5		16
63.20	even	6	inner	882.2.m.a.587.5		16
63.23	odd	6		1134.2.k.a.647.4		16
63.25	even	3		2646.2.t.b.1979.8		16
63.31	odd	6		1134.2.k.a.971.4		16
63.34	odd	6		2646.2.m.a.1763.4		16
63.38	even	6		126.2.t.a.47.4	yes	16
63.47	even	6		882.2.l.b.227.3		16
63.52	odd	6		378.2.t.a.89.5		16
63.58	even	3		1134.2.k.b.647.5		16
63.59	even	6		1134.2.k.b.971.5		16
63.61	odd	6		2646.2.l.a.521.8		16
84.23	even	6		3024.2.df.c.17.1		16
84.59	odd	6		3024.2.ca.c.2609.1		16
252.79	odd	6		3024.2.ca.c.2033.1		16
252.115	even	6		3024.2.df.c.1601.1		16
252.191	even	6		1008.2.ca.c.353.7		16
252.227	odd	6		1008.2.df.c.929.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.6	✓	16	7.3	odd	6
126.2.l.a.101.2	yes	16	63.2	odd	6
126.2.t.a.47.4	yes	16	63.38	even	6
126.2.t.a.59.4	yes	16	7.2	even	3
378.2.l.a.143.5		16	63.16	even	3
378.2.l.a.341.1		16	21.17	even	6
378.2.t.a.17.5		16	21.2	odd	6
378.2.t.a.89.5		16	63.52	odd	6
882.2.l.b.227.3		16	63.47	even	6
882.2.l.b.509.7		16	7.4	even	3
882.2.m.a.293.5		16	1.1	even	1	trivial
882.2.m.a.587.5		16	63.20	even	6	inner
882.2.m.b.293.8		16	7.6	odd	2
882.2.m.b.587.8		16	9.2	odd	6
882.2.t.a.803.1		16	63.11	odd	6
882.2.t.a.815.1		16	7.5	odd	6
1008.2.ca.c.257.7		16	28.3	even	6
1008.2.ca.c.353.7		16	252.191	even	6
1008.2.df.c.689.3		16	28.23	odd	6
1008.2.df.c.929.3		16	252.227	odd	6
1134.2.k.a.647.4		16	63.23	odd	6
1134.2.k.a.971.4		16	63.31	odd	6
1134.2.k.b.647.5		16	63.58	even	3
1134.2.k.b.971.5		16	63.59	even	6
2646.2.l.a.521.8		16	63.61	odd	6
2646.2.l.a.1097.4		16	21.11	odd	6
2646.2.m.a.881.4		16	3.2	odd	2
2646.2.m.a.1763.4		16	63.34	odd	6
2646.2.m.b.881.1		16	21.20	even	2
2646.2.m.b.1763.1		16	9.7	even	3
2646.2.t.b.1979.8		16	63.25	even	3
2646.2.t.b.2285.8		16	21.5	even	6
3024.2.ca.c.2033.1		16	252.79	odd	6
3024.2.ca.c.2609.1		16	84.59	odd	6
3024.2.df.c.17.1		16	84.23	even	6
3024.2.df.c.1601.1		16	252.115	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} +(-1.71170 + 0.264701i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.77612 + 3.07634i) q^{5} +(-1.35003 + 1.08509i) q^{6} -1.00000i q^{8} +(2.85987 - 0.906179i) q^{9} +3.55225i q^{10} +(-2.61745 + 1.51119i) q^{11} +(-0.626615 + 1.61473i) q^{12} +(0.888944 + 0.513232i) q^{13} +(2.22589 - 5.73592i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.61841 q^{17} +(2.02363 - 2.21471i) q^{18} -8.22889i q^{19} +(1.77612 + 3.07634i) q^{20} +(-1.51119 + 2.61745i) q^{22} +(-2.90837 - 1.67915i) q^{23} +(0.264701 + 1.71170i) q^{24} +(-3.80924 - 6.59779i) q^{25} +1.02646 q^{26} +(-4.65538 + 2.30812i) q^{27} +(-3.70319 + 2.13804i) q^{29} +(-0.940283 - 6.08040i) q^{30} +(-5.18382 - 2.99288i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.08029 - 3.27954i) q^{33} +(-1.40158 + 0.809204i) q^{34} +(0.645160 - 2.92981i) q^{36} -5.84647 q^{37} +(-4.11444 - 7.12643i) q^{38} +(-1.65746 - 0.643198i) q^{39} +(3.07634 + 1.77612i) q^{40} +(-0.0472226 + 0.0817920i) q^{41} +(3.05899 + 5.29833i) q^{43} +3.02237i q^{44} +(-2.29177 + 10.4074i) q^{45} -3.35830 q^{46} +(-2.57023 - 4.45176i) q^{47} +(1.08509 + 1.35003i) q^{48} +(-6.59779 - 3.80924i) q^{50} +(2.77024 - 0.428394i) q^{51} +(0.888944 - 0.513232i) q^{52} -3.18968i q^{53} +(-2.87762 + 4.32658i) q^{54} -10.7362i q^{55} +(2.17819 + 14.0854i) q^{57} +(-2.13804 + 3.70319i) q^{58} +(-4.42036 + 7.65628i) q^{59} +(-3.85451 - 4.79564i) q^{60} +(4.06195 - 2.34517i) q^{61} -5.98576 q^{62} -1.00000 q^{64} +(-3.15775 + 1.82313i) q^{65} +(1.89386 - 4.88031i) q^{66} +(0.187838 - 0.325345i) q^{67} +(-0.809204 + 1.40158i) q^{68} +(5.42275 + 2.10436i) q^{69} -13.9868i q^{71} +(-0.906179 - 2.85987i) q^{72} -1.31111i q^{73} +(-5.06319 + 2.92323i) q^{74} +(8.26673 + 10.2852i) q^{75} +(-7.12643 - 4.11444i) q^{76} +(-1.75700 + 0.271706i) q^{78} +(-0.462067 - 0.800324i) q^{79} +3.55225 q^{80} +(7.35768 - 5.18310i) q^{81} +0.0944452i q^{82} +(-5.43209 - 9.40866i) q^{83} +(2.87450 - 4.97877i) q^{85} +(5.29833 + 3.05899i) q^{86} +(5.77283 - 4.63993i) q^{87} +(1.51119 + 2.61745i) q^{88} -4.70989 q^{89} +(3.21897 + 10.1590i) q^{90} +(-2.90837 + 1.67915i) q^{92} +(9.66539 + 3.75077i) q^{93} +(-4.45176 - 2.57023i) q^{94} +(25.3148 + 14.6155i) q^{95} +(1.61473 + 0.626615i) q^{96} +(-13.3330 + 7.69782i) q^{97} +(-6.11615 + 6.69367i) 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

L-functions

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