LMFDB - Embedded newform 567.2.h.j.298.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(298,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("567.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1767277521.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 $ x^8 - 2x^7 + x^6 - 10x^5 + 38x^4 - 40x^3 + 64x^2 - 38x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			298.4
Root			$0.373419 - 0.0835272i$ of defining polynomial
Character	$\chi$	$=$	567.298
Dual form			567.2.h.j.352.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.37167 q^{2} +3.62484 q^{4} +(0.614373 - 1.06412i) q^{5} +(-0.944883 - 2.47127i) q^{7} +3.85358 q^{8} +O(q^{10})$	\(q+2.37167 q^{2} +3.62484 q^{4} +(0.614373 - 1.06412i) q^{5} +(-0.944883 - 2.47127i) q^{7} +3.85358 q^{8} +(1.45709 - 2.52376i) q^{10} +(1.33051 + 2.30451i) q^{11} +(1.81242 + 3.13920i) q^{13} +(-2.24095 - 5.86106i) q^{14} +1.88977 q^{16} +(3.36579 - 5.82972i) q^{17} +(-1.25730 - 2.17771i) q^{19} +(2.22700 - 3.85728i) q^{20} +(3.15554 + 5.46555i) q^{22} +(-3.99826 + 6.92518i) q^{23} +(1.74509 + 3.02259i) q^{25} +(4.29846 + 7.44516i) q^{26} +(-3.42505 - 8.95796i) q^{28} +(1.12484 - 1.94827i) q^{29} -10.2253 q^{31} -3.22526 q^{32} +(7.98256 - 13.8262i) q^{34} +(-3.21025 - 0.512810i) q^{35} +(1.76951 + 3.06488i) q^{37} +(-2.98191 - 5.16482i) q^{38} +(2.36754 - 4.10069i) q^{40} +(0.932674 + 1.61544i) q^{41} +(-2.56972 + 4.45088i) q^{43} +(4.82288 + 8.35348i) q^{44} +(-9.48256 + 16.4243i) q^{46} +2.14642 q^{47} +(-5.21439 + 4.67013i) q^{49} +(4.13879 + 7.16859i) q^{50} +(6.56972 + 11.3791i) q^{52} +(1.48605 - 2.57391i) q^{53} +3.26972 q^{55} +(-3.64118 - 9.52326i) q^{56} +(2.66774 - 4.62067i) q^{58} +8.72809 q^{59} -15.0048 q^{61} -24.2510 q^{62} -11.4288 q^{64} +4.45400 q^{65} -2.64925 q^{67} +(12.2004 - 21.1318i) q^{68} +(-7.61368 - 1.21622i) q^{70} +10.1150 q^{71} +(-3.64707 + 6.31691i) q^{73} +(4.19670 + 7.26890i) q^{74} +(-4.55751 - 7.89384i) q^{76} +(4.43790 - 5.46555i) q^{77} -0.313764 q^{79} +(1.16102 - 2.01095i) q^{80} +(2.21200 + 3.83129i) q^{82} +(3.84686 - 6.66295i) q^{83} +(-4.13570 - 7.16324i) q^{85} +(-6.09454 + 10.5560i) q^{86} +(5.12723 + 8.88062i) q^{88} +(-3.59628 - 6.22894i) q^{89} +(6.04530 - 7.44516i) q^{91} +(-14.4930 + 25.1026i) q^{92} +5.09060 q^{94} -3.08981 q^{95} +(6.59195 - 11.4176i) q^{97} +(-12.3668 + 11.0760i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 10 q^{4} + 2 q^{5} + q^{7} + 6 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 + 10 * q^4 + 2 * q^5 + q^7 + 6 * q^8	$ 8 q - 2 q^{2} + 10 q^{4} + 2 q^{5} + q^{7} + 6 q^{8} + 7 q^{10} + 5 q^{11} + 5 q^{13} - 16 q^{14} - 2 q^{16} + 6 q^{17} + 8 q^{19} - 8 q^{20} + 7 q^{22} - 12 q^{23} - 8 q^{25} + q^{26} + 5 q^{28} - 10 q^{29} - 36 q^{31} + 20 q^{32} - 23 q^{35} - 20 q^{38} + 18 q^{40} - 5 q^{41} + 7 q^{43} + 13 q^{44} - 12 q^{46} + 42 q^{47} - 19 q^{49} + 38 q^{50} + 25 q^{52} - 12 q^{53} - 52 q^{55} + 6 q^{56} + 7 q^{58} - 12 q^{59} - 40 q^{61} - 36 q^{62} - 46 q^{64} - 16 q^{65} - 10 q^{67} + 51 q^{68} + 29 q^{70} + 18 q^{71} + 6 q^{73} - 5 q^{76} - 53 q^{77} - 20 q^{79} - 2 q^{80} + 35 q^{82} + 9 q^{83} + 9 q^{85} - 22 q^{86} - 18 q^{88} - 22 q^{89} + 13 q^{91} - 36 q^{92} - 30 q^{94} + 32 q^{95} + 9 q^{97} - 11 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 10 * q^4 + 2 * q^5 + q^7 + 6 * q^8 + 7 * q^10 + 5 * q^11 + 5 * q^13 - 16 * q^14 - 2 * q^16 + 6 * q^17 + 8 * q^19 - 8 * q^20 + 7 * q^22 - 12 * q^23 - 8 * q^25 + q^26 + 5 * q^28 - 10 * q^29 - 36 * q^31 + 20 * q^32 - 23 * q^35 - 20 * q^38 + 18 * q^40 - 5 * q^41 + 7 * q^43 + 13 * q^44 - 12 * q^46 + 42 * q^47 - 19 * q^49 + 38 * q^50 + 25 * q^52 - 12 * q^53 - 52 * q^55 + 6 * q^56 + 7 * q^58 - 12 * q^59 - 40 * q^61 - 36 * q^62 - 46 * q^64 - 16 * q^65 - 10 * q^67 + 51 * q^68 + 29 * q^70 + 18 * q^71 + 6 * q^73 - 5 * q^76 - 53 * q^77 - 20 * q^79 - 2 * q^80 + 35 * q^82 + 9 * q^83 + 9 * q^85 - 22 * q^86 - 18 * q^88 - 22 * q^89 + 13 * q^91 - 36 * q^92 - 30 * q^94 + 32 * q^95 + 9 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.37167			1.67703			0.838513	−	0.544881i	$-0.183425\pi$
$2$	2.37167			1.67703			0.838513	+	0.544881i	$0.183425\pi$
$3$		0			0
$3$		0			0
$4$	3.62484			1.81242
$5$	0.614373	−	1.06412i	0.274756	−	0.475891i	−0.695318	−	0.718703i	$-0.744736\pi$
$5$	0.614373	−	1.06412i	0.274756	−	0.475891i	0.970073	+	0.242812i	$0.0780697\pi$
$6$		0			0
$7$	−0.944883	−	2.47127i	−0.357132	−	0.934054i
$7$	−0.944883	−	2.47127i	−0.357132	−	0.934054i
$8$	3.85358			1.36245
$9$		0			0
$10$	1.45709	−	2.52376i	0.460773	−	0.798082i
$11$	1.33051	+	2.30451i	0.401164	+	0.694836i	0.993867	−	0.110585i	$-0.0352724\pi$
$11$	1.33051	+	2.30451i	0.401164	+	0.694836i	−0.592703	+	0.805421i	$0.701939\pi$
$12$		0			0
$13$	1.81242	+	3.13920i	0.502674	+	0.870658i	0.999995	+	0.00309084i	$0.000983846\pi$
$13$	1.81242	+	3.13920i	0.502674	+	0.870658i	−0.497321	+	0.867567i	$0.665683\pi$
$14$	−2.24095	−	5.86106i	−0.598920	−	1.56643i
$15$		0			0
$16$	1.88977			0.472441
$17$	3.36579	−	5.82972i	0.816324	−	1.41391i	−0.0920492	−	0.995754i	$-0.529342\pi$
$17$	3.36579	−	5.82972i	0.816324	−	1.41391i	0.908373	−	0.418160i	$-0.137325\pi$
$18$		0			0
$19$	−1.25730	−	2.17771i	−0.288445	−	0.499601i	0.684994	−	0.728549i	$-0.259805\pi$
$19$	−1.25730	−	2.17771i	−0.288445	−	0.499601i	−0.973439	+	0.228948i	$0.926471\pi$
$20$	2.22700	−	3.85728i	0.497972	−	0.862514i
$21$		0			0
$22$	3.15554	+	5.46555i	0.672763	+	1.16526i
$23$	−3.99826	+	6.92518i	−0.833694	+	1.44400i	0.0613957	+	0.998114i	$0.480445\pi$
$23$	−3.99826	+	6.92518i	−0.833694	+	1.44400i	−0.895089	+	0.445887i	$0.852888\pi$
$24$		0			0
$25$	1.74509	+	3.02259i	0.349018	+	0.604518i
$26$	4.29846	+	7.44516i	0.842998	+	1.46012i
$27$		0			0
$28$	−3.42505	−	8.95796i	−0.647273	−	1.69290i
$29$	1.12484	−	1.94827i	0.208877	−	0.361785i	−0.742484	−	0.669864i	$-0.766353\pi$
$29$	1.12484	−	1.94827i	0.208877	−	0.361785i	0.951361	+	0.308078i	$0.0996859\pi$
$30$		0			0
$31$	−10.2253			−1.83651			−0.918255	−	0.395989i	$-0.870402\pi$
$31$	−10.2253			−1.83651			−0.918255	+	0.395989i	$0.870402\pi$
$32$	−3.22526			−0.570150
$33$		0			0
$34$	7.98256	−	13.8262i	1.36900	−	2.37117i
$35$	−3.21025	−	0.512810i	−0.542632	−	0.0866807i
$36$		0			0
$37$	1.76951	+	3.06488i	0.290906	+	0.503863i	0.974024	−	0.226444i	$-0.0727101\pi$
$37$	1.76951	+	3.06488i	0.290906	+	0.503863i	−0.683119	+	0.730308i	$0.739377\pi$
$38$	−2.98191	−	5.16482i	−0.483729	−	0.837844i
$39$		0			0
$40$	2.36754	−	4.10069i	0.374340	−	0.648376i
$41$	0.932674	+	1.61544i	0.145659	+	0.252289i	0.929619	−	0.368523i	$-0.120136\pi$
$41$	0.932674	+	1.61544i	0.145659	+	0.252289i	−0.783959	+	0.620812i	$0.786803\pi$
$42$		0			0
$43$	−2.56972	+	4.45088i	−0.391879	+	0.678753i	−0.992697	−	0.120632i	$-0.961508\pi$
$43$	−2.56972	+	4.45088i	−0.391879	+	0.678753i	0.600819	+	0.799385i	$0.294841\pi$
$44$	4.82288	+	8.35348i	0.727077	+	1.25933i
$45$		0			0
$46$	−9.48256	+	16.4243i	−1.39813	+	2.42163i
$47$	2.14642			0.313087			0.156544	−	0.987671i	$-0.449965\pi$
$47$	2.14642			0.313087			0.156544	+	0.987671i	$0.449965\pi$
$48$		0			0
$49$	−5.21439	+	4.67013i	−0.744913	+	0.667161i
$50$	4.13879	+	7.16859i	0.585313	+	1.01379i
$51$		0			0
$52$	6.56972	+	11.3791i	0.911056	+	1.57800i
$53$	1.48605	−	2.57391i	0.204124	−	0.353553i	−0.745729	−	0.666249i	$-0.767899\pi$
$53$	1.48605	−	2.57391i	0.204124	−	0.353553i	0.949853	+	0.312696i	$0.101232\pi$
$54$		0			0
$55$	3.26972			0.440888
$56$	−3.64118	−	9.52326i	−0.486574	−	1.27260i
$57$		0			0
$58$	2.66774	−	4.62067i	0.350292	−	0.606724i
$59$	8.72809			1.13630			0.568150	−	0.822925i	$-0.307659\pi$
$59$	8.72809			1.13630			0.568150	+	0.822925i	$0.307659\pi$
$60$		0			0
$61$	−15.0048			−1.92117			−0.960583	−	0.277993i	$-0.910331\pi$
$61$	−15.0048			−1.92117			−0.960583	+	0.277993i	$0.910331\pi$
$62$	−24.2510			−3.07988
$63$		0			0
$64$	−11.4288			−1.42860
$65$	4.45400			0.552451
$66$		0			0
$67$	−2.64925			−0.323658			−0.161829	−	0.986819i	$-0.551739\pi$
$67$	−2.64925			−0.323658			−0.161829	+	0.986819i	$0.551739\pi$
$68$	12.2004	−	21.1318i	1.47952	−	2.56260i
$69$		0			0
$70$	−7.61368	−	1.21622i	−0.910008	−	0.145366i
$71$	10.1150			1.20043			0.600216	−	0.799838i	$-0.295081\pi$
$71$	10.1150			1.20043			0.600216	+	0.799838i	$0.295081\pi$
$72$		0			0
$73$	−3.64707	+	6.31691i	−0.426857	+	0.739338i	−0.996592	−	0.0824907i	$-0.973713\pi$
$73$	−3.64707	+	6.31691i	−0.426857	+	0.739338i	0.569735	+	0.821829i	$0.307046\pi$
$74$	4.19670	+	7.26890i	0.487856	+	0.844992i
$75$		0			0
$76$	−4.55751	−	7.89384i	−0.522782	−	0.905486i
$77$	4.43790	−	5.46555i	0.505746	−	0.622857i
$78$		0			0
$79$	−0.313764			−0.0353012			−0.0176506	−	0.999844i	$-0.505619\pi$
$79$	−0.313764			−0.0353012			−0.0176506	+	0.999844i	$0.505619\pi$
$80$	1.16102	−	2.01095i	0.129806	−	0.224831i
$81$		0			0
$82$	2.21200	+	3.83129i	0.244274	+	0.423096i
$83$	3.84686	−	6.66295i	0.422247	−	0.731354i	−0.573912	−	0.818917i	$-0.694575\pi$
$83$	3.84686	−	6.66295i	0.422247	−	0.731354i	0.996159	+	0.0875633i	$0.0279080\pi$
$84$		0			0
$85$	−4.13570	−	7.16324i	−0.448580	−	0.776963i
$86$	−6.09454	+	10.5560i	−0.657191	+	1.13829i
$87$		0			0
$88$	5.12723	+	8.88062i	0.546565	+	0.946678i
$89$	−3.59628	−	6.22894i	−0.381205	−	0.660266i	0.610030	−	0.792378i	$-0.291157\pi$
$89$	−3.59628	−	6.22894i	−0.381205	−	0.660266i	−0.991235	+	0.132112i	$0.957824\pi$
$90$		0			0
$91$	6.04530	−	7.44516i	0.633720	−	0.780465i
$92$	−14.4930	+	25.1026i	−1.51100	+	2.61713i
$93$		0			0
$94$	5.09060			0.525056
$95$	−3.08981			−0.317007
$96$		0			0
$97$	6.59195	−	11.4176i	0.669311	−	1.15928i	−0.308786	−	0.951132i	$-0.599923\pi$
$97$	6.59195	−	11.4176i	0.669311	−	1.15928i	0.978097	−	0.208149i	$-0.0667440\pi$
$98$	−12.3668	+	11.0760i	−1.24924	+	1.11885i
$99$		0			0
$100$	6.32567	+	10.9564i	0.632567	+	1.09564i
$101$	−1.39151	−	2.41017i	−0.138460	−	0.239821i	0.788454	−	0.615094i	$-0.210882\pi$
$101$	−1.39151	−	2.41017i	−0.138460	−	0.239821i	−0.926914	+	0.375274i	$0.877549\pi$
$102$		0			0
$103$	−3.00323	+	5.20175i	−0.295917	+	0.512544i	−0.975198	−	0.221335i	$-0.928959\pi$
$103$	−3.00323	+	5.20175i	−0.295917	+	0.512544i	0.679280	+	0.733879i	$0.262292\pi$
$104$	6.98430	+	12.0972i	0.684867	+	1.18622i
$105$		0			0
$106$	3.52442	−	6.10447i	0.342322	−	0.592919i
$107$	−5.86818	−	10.1640i	−0.567299	−	0.982590i	−0.996832	−	0.0795391i	$-0.974655\pi$
$107$	−5.86818	−	10.1640i	−0.567299	−	0.982590i	0.429533	−	0.903051i	$-0.358678\pi$
$108$		0			0
$109$	3.99237	−	6.91499i	0.382400	−	0.662336i	−0.609005	−	0.793166i	$-0.708431\pi$
$109$	3.99237	−	6.91499i	0.382400	−	0.662336i	0.991405	+	0.130830i	$0.0417644\pi$
$110$	7.75470			0.739382
$111$		0			0
$112$	−1.78561	−	4.67013i	−0.168724	−	0.441286i
$113$	2.32005	+	4.01844i	0.218252	+	0.378023i	0.954274	−	0.298935i	$-0.0966313\pi$
$113$	2.32005	+	4.01844i	0.218252	+	0.378023i	−0.736022	+	0.676958i	$0.763298\pi$
$114$		0			0
$115$	4.91284	+	8.50928i	0.458124	+	0.793495i
$116$	4.07735	−	7.06217i	0.378572	−	0.655706i
$117$		0			0
$118$	20.7002			1.90561
$119$	−17.5871	−	2.80939i	−1.61221	−	0.257536i
$120$		0			0
$121$	1.95949	−	3.39393i	0.178135	−	0.308539i
$122$	−35.5865			−3.22185
$123$		0			0
$124$	−37.0649			−3.32852
$125$	10.4323			0.933091
$126$		0			0
$127$	−3.32633			−0.295164			−0.147582	−	0.989050i	$-0.547149\pi$
$127$	−3.32633			−0.295164			−0.147582	+	0.989050i	$0.547149\pi$
$128$	−20.6548			−1.82565
$129$		0			0
$130$	10.5634			0.926475
$131$	−4.22351	+	7.31533i	−0.369010	+	0.639144i	−0.989411	−	0.145141i	$-0.953636\pi$
$131$	−4.22351	+	7.31533i	−0.369010	+	0.639144i	0.620401	+	0.784285i	$0.286970\pi$
$132$		0			0
$133$	−4.19371	+	5.16482i	−0.363641	+	0.447846i
$134$	−6.28317			−0.542783
$135$		0			0
$136$	12.9703	−	22.4653i	1.11220	−	1.92638i
$137$	6.99826	+	12.1213i	0.597901	+	1.03560i	0.993130	+	0.117013i	$0.0373319\pi$
$137$	6.99826	+	12.1213i	0.597901	+	1.03560i	−0.395229	+	0.918583i	$0.629335\pi$
$138$		0			0
$139$	2.82005	+	4.88446i	0.239193	+	0.414295i	0.960483	−	0.278339i	$-0.0897837\pi$
$139$	2.82005	+	4.88446i	0.239193	+	0.414295i	−0.721290	+	0.692633i	$0.756450\pi$
$140$	−11.6366	−	1.85885i	−0.983476	−	0.157102i
$141$		0			0
$142$	23.9895			2.01316
$143$	−4.82288	+	8.35348i	−0.403310	+	0.698553i
$144$		0			0
$145$	−1.38214	−	2.39393i	−0.114780	−	0.198805i
$146$	−8.64965	+	14.9816i	−0.715850	+	1.23989i
$147$		0			0
$148$	6.41418	+	11.1097i	0.527243	+	0.913211i
$149$	4.38472	−	7.59456i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$149$	4.38472	−	7.59456i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497127\pi$
$150$		0			0
$151$	4.78037	+	8.27985i	0.389021	+	0.673804i	0.992318	−	0.123712i	$-0.0394799\pi$
$151$	4.78037	+	8.27985i	0.389021	+	0.673804i	−0.603297	+	0.797517i	$0.706147\pi$
$152$	−4.84511	−	8.39198i	−0.392991	−	0.680680i
$153$		0			0
$154$	10.5253	−	12.9625i	0.848149	−	1.04455i
$155$	−6.28212	+	10.8809i	−0.504592	+	0.873979i
$156$		0			0
$157$	2.15907			0.172312			0.0861562	−	0.996282i	$-0.472542\pi$
$157$	2.15907			0.172312			0.0861562	+	0.996282i	$0.472542\pi$
$158$	−0.744146			−0.0592011
$159$		0			0
$160$	−1.98151	+	3.43207i	−0.156652	+	0.271329i
$161$	20.8919	+	3.33730i	1.64651	+	0.263016i
$162$		0			0
$163$	−10.4871	−	18.1643i	−0.821416	−	1.42273i	−0.904628	−	0.426202i	$-0.859851\pi$
$163$	−10.4871	−	18.1643i	−0.821416	−	1.42273i	0.0832119	−	0.996532i	$-0.473482\pi$
$164$	3.38079	+	5.85570i	0.263995	+	0.457254i
$165$		0			0
$166$	9.12349	−	15.8023i	0.708120	−	1.22650i
$167$	2.13704	+	3.70147i	0.165370	+	0.286428i	0.936786	−	0.349902i	$-0.113785\pi$
$167$	2.13704	+	3.70147i	0.165370	+	0.286428i	−0.771417	+	0.636330i	$0.780452\pi$
$168$		0			0
$169$	−0.0697192	+	0.120757i	−0.00536302	+	0.00928902i
$170$	−9.80853	−	16.9889i	−0.752280	−	1.30299i
$171$		0			0
$172$	−9.31481	+	16.1337i	−0.710248	+	1.23019i
$173$	−1.81660			−0.138113			−0.0690567	−	0.997613i	$-0.521999\pi$
$173$	−1.81660			−0.138113			−0.0690567	+	0.997613i	$0.521999\pi$
$174$		0			0
$175$	5.82074	−	7.16859i	0.440006	−	0.541895i
$176$	2.51435	+	4.35499i	0.189526	+	0.328269i
$177$		0			0
$178$	−8.52920	−	14.7730i	−0.639291	−	1.10728i
$179$	4.02507	−	6.97162i	0.300848	−	0.521083i	−0.675481	−	0.737378i	$-0.736064\pi$
$179$	4.02507	−	6.97162i	0.300848	−	0.521083i	0.976328	+	0.216295i	$0.0693971\pi$
$180$		0			0
$181$	25.3467			1.88401			0.942004	−	0.335601i	$-0.108939\pi$
$181$	25.3467			1.88401			0.942004	+	0.335601i	$0.108939\pi$
$182$	14.3375	−	17.6575i	1.06277	−	1.30886i
$183$		0			0
$184$	−15.4076	+	26.6868i	−1.13586	+	1.96737i
$185$	4.34855			0.319712
$186$		0			0
$187$	17.9129			1.30992
$188$	7.78042			0.567445
$189$		0			0
$190$	−7.32801			−0.531630
$191$	7.15121			0.517443			0.258722	−	0.965952i	$-0.416699\pi$
$191$	7.15121			0.517443			0.258722	+	0.965952i	$0.416699\pi$
$192$		0			0
$193$	11.3555			0.817389			0.408695	−	0.912671i	$-0.365984\pi$
$193$	11.3555			0.817389			0.408695	+	0.912671i	$0.365984\pi$
$194$	15.6340	−	27.0788i	1.12245	−	1.94414i
$195$		0			0
$196$	−18.9013	+	16.9285i	−1.35009	+	1.20918i
$197$	−20.0998			−1.43205			−0.716024	−	0.698075i	$-0.754040\pi$
$197$	−20.0998			−1.43205			−0.716024	+	0.698075i	$0.754040\pi$
$198$		0			0
$199$	−5.16251	+	8.94173i	−0.365961	+	0.633862i	−0.988930	−	0.148384i	$-0.952593\pi$
$199$	−5.16251	+	8.94173i	−0.365961	+	0.633862i	0.622969	+	0.782246i	$0.285926\pi$
$200$	6.72486	+	11.6478i	0.475519	+	0.823623i
$201$		0			0
$202$	−3.30021	−	5.71613i	−0.232202	−	0.402186i
$203$	−5.87756	−	0.938889i	−0.412524	−	0.0658971i
$204$		0			0
$205$	2.29204			0.160083
$206$	−7.12269	+	12.3369i	−0.496261	+	0.859550i
$207$		0			0
$208$	3.42505	+	5.93235i	0.237484	+	0.411335i
$209$	3.34570	−	5.79493i	0.231427	−	0.400844i
$210$		0			0
$211$	−0.299369	−	0.518522i	−0.0206094	−	0.0356965i	0.855537	−	0.517742i	$-0.173227\pi$
$211$	−0.299369	−	0.518522i	−0.0206094	−	0.0356965i	−0.876146	+	0.482046i	$0.839894\pi$
$212$	5.38668	−	9.32999i	0.369958	−	0.640787i
$213$		0			0
$214$	−13.9174	−	24.1057i	−0.951375	−	1.64783i
$215$	3.15753	+	5.46900i	0.215342	+	0.372983i
$216$		0			0
$217$	9.66167	+	25.2694i	0.655877	+	1.71540i
$218$	9.46860	−	16.4001i	0.641295	−	1.11076i
$219$		0			0
$220$	11.8522			0.799074
$221$	24.4009			1.64138
$222$		0			0
$223$	−1.51002	+	2.61543i	−0.101119	+	0.175142i	−0.912146	−	0.409866i	$-0.865575\pi$
$223$	−1.51002	+	2.61543i	−0.101119	+	0.175142i	0.811027	+	0.585008i	$0.198909\pi$
$224$	3.04749	+	7.97049i	0.203619	+	0.532551i
$225$		0			0
$226$	5.50239	+	9.53043i	0.366014	+	0.633954i
$227$	−10.0540	−	17.4141i	−0.667309	−	1.15581i	−0.978654	−	0.205516i	$-0.934113\pi$
$227$	−10.0540	−	17.4141i	−0.667309	−	1.15581i	0.311345	−	0.950297i	$-0.399221\pi$
$228$		0			0
$229$	10.0032	−	17.3261i	0.661032	−	1.14494i	−0.319312	−	0.947650i	$-0.603452\pi$
$229$	10.0032	−	17.3261i	0.661032	−	1.14494i	0.980345	−	0.197292i	$-0.0632147\pi$
$230$	11.6516	+	20.1812i	0.768287	+	1.33071i
$231$		0			0
$232$	4.33465	−	7.50783i	0.284584	−	0.492913i
$233$	−0.151398	−	0.262229i	−0.00991839	−	0.0171792i	0.861024	−	0.508565i	$-0.169824\pi$
$233$	−0.151398	−	0.262229i	−0.00991839	−	0.0171792i	−0.870942	+	0.491386i	$0.836491\pi$
$234$		0			0
$235$	1.31870	−	2.28406i	0.0860226	−	0.148995i
$236$	31.6379			2.05945
$237$		0			0
$238$	−41.7109	−	6.66295i	−2.70372	−	0.431895i
$239$	1.77340	+	3.07162i	0.114712	+	0.198686i	0.917664	−	0.397356i	$-0.130072\pi$
$239$	1.77340	+	3.07162i	0.114712	+	0.198686i	−0.802953	+	0.596043i	$0.796739\pi$
$240$		0			0
$241$	−3.00323	−	5.20175i	−0.193455	−	0.335074i	0.752938	−	0.658092i	$-0.228636\pi$
$241$	−3.00323	−	5.20175i	−0.193455	−	0.335074i	−0.946393	+	0.323017i	$0.895303\pi$
$242$	4.64726	−	8.04929i	0.298737	−	0.517428i
$243$		0			0
$244$	−54.3899			−3.48196
$245$	1.76602	+	8.41796i	0.112827	+	0.537804i
$246$		0			0
$247$	4.55751	−	7.89384i	0.289987	−	0.502273i
$248$	−39.4039			−2.50215
$249$		0			0
$250$	24.7420			1.56482
$251$	21.0113			1.32622			0.663109	−	0.748523i	$-0.269236\pi$
$251$	21.0113			1.32622			0.663109	+	0.748523i	$0.269236\pi$
$252$		0			0
$253$	−21.2789			−1.33779
$254$	−7.88897			−0.494998
$255$		0			0
$256$	−26.1290			−1.63306
$257$	10.2845	−	17.8133i	0.641530	−	1.11116i	−0.343561	−	0.939130i	$-0.611633\pi$
$257$	10.2845	−	17.8133i	0.641530	−	1.11116i	0.985091	−	0.172033i	$-0.0550334\pi$
$258$		0			0
$259$	5.90218	−	7.26890i	0.366744	−	0.451667i
$260$	16.1450			1.00127
$261$		0			0
$262$	−10.0168	+	17.3496i	−0.618839	+	1.07186i
$263$	−7.10151	−	12.3002i	−0.437898	−	0.758461i	0.559629	−	0.828743i	$-0.310944\pi$
$263$	−7.10151	−	12.3002i	−0.437898	−	0.758461i	−0.997527	+	0.0702817i	$0.977610\pi$
$264$		0			0
$265$	−1.82597	−	3.16268i	−0.112169	−	0.194282i
$266$	−9.94612	+	12.2493i	−0.609836	+	0.751050i
$267$		0			0
$268$	−9.60311			−0.586603
$269$	−15.5662	+	26.9615i	−0.949090	+	1.64387i	−0.201742	+	0.979439i	$0.564660\pi$
$269$	−15.5662	+	26.9615i	−0.949090	+	1.64387i	−0.747348	+	0.664433i	$0.768673\pi$
$270$		0			0
$271$	0.821392	+	1.42269i	0.0498960	+	0.0864225i	0.889895	−	0.456166i	$-0.150778\pi$
$271$	0.821392	+	1.42269i	0.0498960	+	0.0864225i	−0.839999	+	0.542588i	$0.817444\pi$
$272$	6.36056	−	11.0168i	0.385665	−	0.667992i
$273$		0			0
$274$	16.5976	+	28.7478i	1.00270	+	1.73672i
$275$	−4.64373	+	8.04317i	−0.280027	+	0.485021i
$276$		0			0
$277$	11.0475	+	19.1348i	0.663779	+	1.14970i	0.979615	+	0.200885i	$0.0643819\pi$
$277$	11.0475	+	19.1348i	0.663779	+	1.14970i	−0.315835	+	0.948814i	$0.602285\pi$
$278$	6.68823	+	11.5844i	0.401133	+	0.694783i
$279$		0			0
$280$	−12.3710	−	1.97616i	−0.739307	−	0.118098i
$281$	7.74070	−	13.4073i	0.461771	−	0.799811i	−0.537278	−	0.843405i	$-0.680547\pi$
$281$	7.74070	−	13.4073i	0.461771	−	0.799811i	0.999049	+	0.0435938i	$0.0138807\pi$
$282$		0			0
$283$	−26.2348			−1.55950			−0.779749	−	0.626092i	$-0.784654\pi$
$283$	−26.2348			−1.55950			−0.779749	+	0.626092i	$0.784654\pi$
$284$	36.6653			2.17569
$285$		0			0
$286$	−11.4383	+	19.8117i	−0.676361	+	1.17149i
$287$	3.11093	−	3.83129i	0.183632	−	0.226154i
$288$		0			0
$289$	−14.1571	−	24.5208i	−0.832770	−	1.44240i
$290$	−3.27798	−	5.67763i	−0.192490	−	0.333402i
$291$		0			0
$292$	−13.2200	+	22.8977i	−0.773643	+	1.33999i
$293$	−8.45425	−	14.6432i	−0.493903	−	0.855464i	0.506073	−	0.862491i	$-0.331097\pi$
$293$	−8.45425	−	14.6432i	−0.493903	−	0.855464i	−0.999975	+	0.00702646i	$0.997763\pi$
$294$		0			0
$295$	5.36230	−	9.28778i	0.312205	−	0.540755i
$296$	6.81895	+	11.8108i	0.396343	+	0.686487i
$297$		0			0
$298$	10.3991	−	18.0118i	0.602406	−	1.04340i
$299$	−28.9860			−1.67631
$300$		0			0
$301$	13.4274	+	2.14492i	0.773945	+	0.123631i
$302$	11.3375	+	19.6371i	0.652399	+	1.12999i
$303$		0			0
$304$	−2.37600	−	4.11536i	−0.136273	−	0.236032i
$305$	−9.21853	+	15.9670i	−0.527852	+	0.914266i
$306$		0			0
$307$	−14.6835			−0.838034			−0.419017	−	0.907978i	$-0.637625\pi$
$307$	−14.6835			−0.838034			−0.419017	+	0.907978i	$0.637625\pi$
$308$	16.0867	−	19.8117i	0.916623	−	1.12888i
$309$		0			0
$310$	−14.8991	+	25.8061i	−0.846214	+	1.46569i
$311$	−11.8222			−0.670375			−0.335187	−	0.942152i	$-0.608800\pi$
$311$	−11.8222			−0.670375			−0.335187	+	0.942152i	$0.608800\pi$
$312$		0			0
$313$	−0.355120			−0.0200726			−0.0100363	−	0.999950i	$-0.503195\pi$
$313$	−0.355120			−0.0200726			−0.0100363	+	0.999950i	$0.503195\pi$
$314$	5.12061			0.288973
$315$		0			0
$316$	−1.13734			−0.0639805
$317$	10.4497			0.586914			0.293457	−	0.955972i	$-0.405194\pi$
$317$	10.4497			0.586914			0.293457	+	0.955972i	$0.405194\pi$
$318$		0			0
$319$	5.98643			0.335175
$320$	−7.02153	+	12.1617i	−0.392516	+	0.679857i
$321$		0			0
$322$	49.5488	+	7.91499i	2.76125	+	0.441085i
$323$	−16.9272			−0.941857
$324$		0			0
$325$	−6.32567	+	10.9564i	−0.350885	+	0.607751i
$326$	−24.8721	−	43.0797i	−1.37754	−	2.38596i
$327$		0			0
$328$	3.59414	+	6.22523i	0.198453	+	0.343731i
$329$	−2.02811	−	5.30439i	−0.111814	−	0.292440i
$330$		0			0
$331$	14.8670			0.817166			0.408583	−	0.912721i	$-0.366023\pi$
$331$	14.8670			0.817166			0.408583	+	0.912721i	$0.366023\pi$
$332$	13.9442	−	24.1521i	0.765289	−	1.32552i
$333$		0			0
$334$	5.06837	+	8.77868i	0.277329	+	0.480348i
$335$	−1.62763	+	2.81914i	−0.0889269	+	0.154026i
$336$		0			0
$337$	−4.70676	−	8.15235i	−0.256394	−	0.444087i	0.708879	−	0.705330i	$-0.249201\pi$
$337$	−4.70676	−	8.15235i	−0.256394	−	0.444087i	−0.965273	+	0.261243i	$0.915868\pi$
$338$	−0.165351	+	0.286397i	−0.00899392	+	0.0155779i
$339$		0			0
$340$	−14.9912	−	25.9656i	−0.813014	−	1.40818i
$341$	−13.6048	−	23.5642i	−0.736742	−	1.27607i
$342$		0			0
$343$	16.4682	+	8.47347i	0.889197	+	0.457524i
$344$	−9.90262	+	17.1518i	−0.533914	+	0.924766i
$345$		0			0
$346$	−4.30838			−0.231620
$347$	−26.5865			−1.42724			−0.713618	−	0.700535i	$-0.752945\pi$
$347$	−26.5865			−1.42724			−0.713618	+	0.700535i	$0.752945\pi$
$348$		0			0
$349$	−4.77648	+	8.27311i	−0.255679	+	0.442850i	−0.965080	−	0.261956i	$-0.915632\pi$
$349$	−4.77648	+	8.27311i	−0.255679	+	0.442850i	0.709401	+	0.704806i	$0.248966\pi$
$350$	13.8049	−	17.0016i	0.737902	−	0.908772i
$351$		0			0
$352$	−4.29124	−	7.43264i	−0.228724	−	0.396161i
$353$	8.53643	+	14.7855i	0.454349	+	0.786955i	0.998650	−	0.0519347i	$-0.0165388\pi$
$353$	8.53643	+	14.7855i	0.454349	+	0.786955i	−0.544302	+	0.838889i	$0.683205\pi$
$354$		0			0
$355$	6.21439	−	10.7636i	0.329826	−	0.571275i
$356$	−13.0359	−	22.5789i	−0.690903	−	1.19668i
$357$		0			0
$358$	9.54614	−	16.5344i	0.504529	−	0.873870i
$359$	12.8333	+	22.2280i	0.677318	+	1.17315i	0.975786	+	0.218730i	$0.0701912\pi$
$359$	12.8333	+	22.2280i	0.677318	+	1.17315i	−0.298467	+	0.954420i	$0.596475\pi$
$360$		0			0
$361$	6.33839	−	10.9784i	0.333599	−	0.577811i
$362$	60.1142			3.15953
$363$		0			0
$364$	21.9132	−	26.9875i	1.14857	−	1.41453i
$365$	4.48132	+	7.76187i	0.234563	+	0.406275i
$366$		0			0
$367$	5.18758	+	8.98516i	0.270790	+	0.469021i	0.969064	−	0.246809i	$-0.0793819\pi$
$367$	5.18758	+	8.98516i	0.270790	+	0.469021i	−0.698275	+	0.715830i	$0.746049\pi$
$368$	−7.55577	+	13.0870i	−0.393872	+	0.682205i
$369$		0			0
$370$	10.3134			0.536166
$371$	−7.76497	−	1.24039i	−0.403137	−	0.0643977i
$372$		0			0
$373$	9.90760	−	17.1605i	0.512996	−	0.888535i	−0.486890	−	0.873463i	$-0.661869\pi$
$373$	9.90760	−	17.1605i	0.512996	−	0.888535i	0.999886	−	0.0150723i	$-0.00479785\pi$
$374$	42.4835			2.19677
$375$		0			0
$376$	8.27140			0.426565
$377$	8.15470			0.419988
$378$		0			0
$379$	14.1716			0.727948			0.363974	−	0.931409i	$-0.381420\pi$
$379$	14.1716			0.727948			0.363974	+	0.931409i	$0.381420\pi$
$380$	−11.2000			−0.574550
$381$		0			0
$382$	16.9603			0.867766
$383$	−6.72435	+	11.6469i	−0.343598	+	0.595130i	−0.985098	−	0.171993i	$-0.944979\pi$
$383$	−6.72435	+	11.6469i	−0.343598	+	0.595130i	0.641500	+	0.767123i	$0.278313\pi$
$384$		0			0
$385$	−3.08950	−	8.08037i	−0.157455	−	0.411814i
$386$	26.9316			1.37078
$387$		0			0
$388$	23.8947	−	41.3869i	1.21307	−	2.10110i
$389$	10.4649	+	18.1257i	0.530590	+	0.919008i	0.999363	+	0.0356897i	$0.0113628\pi$
$389$	10.4649	+	18.1257i	0.530590	+	0.919008i	−0.468773	+	0.883319i	$0.655304\pi$
$390$		0			0
$391$	26.9146	+	46.6174i	1.36113	+	2.35754i
$392$	−20.0941	+	17.9967i	−1.01490	+	0.908972i
$393$		0			0
$394$	−47.6701			−2.40158
$395$	−0.192768	+	0.333884i	−0.00969921	+	0.0167995i
$396$		0			0
$397$	12.5708	+	21.7732i	0.630909	+	1.09277i	0.987366	+	0.158454i	$0.0506511\pi$
$397$	12.5708	+	21.7732i	0.630909	+	1.09277i	−0.356458	+	0.934312i	$0.616016\pi$
$398$	−12.2438	+	21.2069i	−0.613726	+	1.06300i
$399$		0			0
$400$	3.29782	+	5.71198i	0.164891	+	0.285599i
$401$	10.5801	−	18.3253i	0.528347	−	0.915124i	−0.471107	−	0.882076i	$-0.656145\pi$
$401$	10.5801	−	18.3253i	0.528347	−	0.915124i	0.999454	−	0.0330477i	$-0.0105213\pi$
$402$		0			0
$403$	−18.5324	−	32.0991i	−0.923167	−	1.59897i
$404$	−5.04400	−	8.73646i	−0.250948	−	0.434655i
$405$		0			0
$406$	−13.9396	−	2.22674i	−0.691813	−	0.110511i
$407$	−4.70870	+	8.15571i	−0.233402	+	0.404264i
$408$		0			0
$409$	0.543806			0.0268895			0.0134447	−	0.999910i	$-0.495720\pi$
$409$	0.543806			0.0268895			0.0134447	+	0.999910i	$0.495720\pi$
$410$	5.43597			0.268463
$411$		0			0
$412$	−10.8862	+	18.8555i	−0.536326	+	0.928944i
$413$	−8.24702	−	21.5695i	−0.405810	−	1.06137i
$414$		0			0
$415$	−4.72681	−	8.18707i	−0.232030	−	0.401888i
$416$	−5.84551	−	10.1247i	−0.286600	−	0.496405i
$417$		0			0
$418$	7.93492	−	13.7437i	0.388110	−	0.672225i
$419$	−11.9044	−	20.6190i	−0.581566	−	1.00730i	−0.995294	−	0.0969018i	$-0.969107\pi$
$419$	−11.9044	−	20.6190i	−0.581566	−	1.00730i	0.413728	−	0.910401i	$-0.364227\pi$
$420$		0			0
$421$	1.45490	−	2.51997i	0.0709077	−	0.122816i	−0.828392	−	0.560149i	$-0.810744\pi$
$421$	1.45490	−	2.51997i	0.0709077	−	0.122816i	0.899299	+	0.437334i	$0.144077\pi$
$422$	−0.710005	−	1.22976i	−0.0345625	−	0.0598640i
$423$		0			0
$424$	5.72660	−	9.91876i	0.278108	−	0.481698i
$425$	23.4945			1.13965
$426$		0			0
$427$	14.1778	+	37.0809i	0.686110	+	1.79447i
$428$	−21.2712	−	36.8428i	−1.02818	−	1.78086i
$429$		0			0
$430$	7.48863	+	12.9707i	0.361134	+	0.625502i
$431$	−15.6897	+	27.1754i	−0.755747	+	1.30899i	0.189255	+	0.981928i	$0.439393\pi$
$431$	−15.6897	+	27.1754i	−0.755747	+	1.30899i	−0.945002	+	0.327065i	$0.893941\pi$
$432$		0			0
$433$	−26.9281			−1.29408			−0.647042	−	0.762455i	$-0.723994\pi$
$433$	−26.9281			−1.29408			−0.647042	+	0.762455i	$0.723994\pi$
$434$	22.9143	+	59.9308i	1.09992	+	2.87677i
$435$		0			0
$436$	14.4717	−	25.0657i	0.693068	−	1.20043i
$437$	20.1080			0.961898
$438$		0			0
$439$	−25.3294			−1.20891			−0.604453	−	0.796641i	$-0.706608\pi$
$439$	−25.3294			−1.20891			−0.604453	+	0.796641i	$0.706608\pi$
$440$	12.6001			0.600687
$441$		0			0
$442$	57.8709			2.75264
$443$	13.0314			0.619140			0.309570	−	0.950877i	$-0.399815\pi$
$443$	13.0314			0.619140			0.309570	+	0.950877i	$0.399815\pi$
$444$		0			0
$445$	−8.83783			−0.418953
$446$	−3.58128	+	6.20296i	−0.169578	+	0.293719i
$447$		0			0
$448$	10.7989	+	28.2437i	0.510198	+	1.33439i
$449$	19.4353			0.917206			0.458603	−	0.888641i	$-0.348350\pi$
$449$	19.4353			0.917206			0.458603	+	0.888641i	$0.348350\pi$
$450$		0			0
$451$	−2.48187	+	4.29872i	−0.116866	+	0.202419i
$452$	8.40979	+	14.5662i	0.395563	+	0.685136i
$453$		0			0
$454$	−23.8449	−	41.3005i	−1.11909	−	1.93833i
$455$	−4.20851	−	11.0071i	−0.197298	−	0.516019i
$456$		0			0
$457$	−28.6975			−1.34241			−0.671206	−	0.741271i	$-0.734223\pi$
$457$	−28.6975			−1.34241			−0.671206	+	0.741271i	$0.734223\pi$
$458$	23.7244	−	41.0919i	1.10857	−	1.92010i
$459$		0			0
$460$	17.8082	+	30.8448i	0.830313	+	1.43814i
$461$	−11.5240	+	19.9601i	−0.536725	+	0.929635i	0.462353	+	0.886696i	$0.347005\pi$
$461$	−11.5240	+	19.9601i	−0.536725	+	0.929635i	−0.999078	+	0.0429386i	$0.986328\pi$
$462$		0			0
$463$	−14.6074	−	25.3007i	−0.678863	−	1.17583i	−0.975324	−	0.220780i	$-0.929140\pi$
$463$	−14.6074	−	25.3007i	−0.678863	−	1.17583i	0.296460	−	0.955045i	$-0.404194\pi$
$464$	2.12568	−	3.68178i	0.0986821	−	0.170922i
$465$		0			0
$466$	−0.359066	−	0.621920i	−0.0166334	−	0.0288099i
$467$	2.18254	+	3.78027i	0.100996	+	0.174930i	0.912095	−	0.409978i	$-0.134464\pi$
$467$	2.18254	+	3.78027i	0.100996	+	0.174930i	−0.811099	+	0.584908i	$0.801130\pi$
$468$		0			0
$469$	2.50323	+	6.54703i	0.115589	+	0.302314i
$470$	3.12753	−	5.41704i	0.144262	−	0.249869i
$471$		0			0
$472$	33.6344			1.54815
$473$	−13.6762			−0.628830
$474$		0			0
$475$	4.38821	−	7.60061i	0.201345	−	0.348740i
$476$	−63.7504	−	10.1836i	−2.92200	−	0.466763i
$477$		0			0
$478$	4.20592	+	7.28487i	0.192374	+	0.333202i
$479$	−7.96144	−	13.7896i	−0.363767	−	0.630064i	0.624810	−	0.780777i	$-0.285176\pi$
$479$	−7.96144	−	13.7896i	−0.363767	−	0.630064i	−0.988578	+	0.150713i	$0.951843\pi$
$480$		0			0
$481$	−6.41418	+	11.1097i	−0.292462	+	0.506558i
$482$	−7.12269	−	12.3369i	−0.324430	−	0.561929i
$483$		0			0
$484$	7.10281	−	12.3024i	0.322855	−	0.559201i
$485$	−8.09983	−	14.0293i	−0.367794	−	0.637038i
$486$		0			0
$487$	19.1329	−	33.1391i	0.866993	−	1.50168i	0.00193753	−	0.999998i	$-0.499383\pi$
$487$	19.1329	−	33.1391i	0.866993	−	1.50168i	0.865055	−	0.501677i	$-0.167283\pi$
$488$	−57.8222			−2.61749
$489$		0			0
$490$	4.18842	+	19.9647i	0.189214	+	0.901912i
$491$	6.69540	+	11.5968i	0.302159	+	0.523355i	0.976625	−	0.214951i	$-0.0689593\pi$
$491$	6.69540	+	11.5968i	0.302159	+	0.523355i	−0.674466	+	0.738306i	$0.735626\pi$
$492$		0			0
$493$	−7.57193	−	13.1150i	−0.341022	−	0.590668i
$494$	10.8089	−	18.7216i	0.486317	−	0.842325i
$495$		0			0
$496$	−19.3233			−0.867643
$497$	−9.55751	−	24.9970i	−0.428713	−	1.12127i
$498$		0			0
$499$	−2.70353	+	4.68265i	−0.121027	+	0.209624i	−0.920173	−	0.391513i	$-0.871952\pi$
$499$	−2.70353	+	4.68265i	−0.121027	+	0.209624i	0.799146	+	0.601137i	$0.205285\pi$
$500$	37.8153			1.69115
$501$		0			0
$502$	49.8318			2.22410
$503$	−9.49157			−0.423208			−0.211604	−	0.977355i	$-0.567869\pi$
$503$	−9.49157			−0.423208			−0.211604	+	0.977355i	$0.567869\pi$
$504$		0			0
$505$	−3.41962			−0.152171
$506$	−50.4666			−2.24351
$507$		0			0
$508$	−12.0574			−0.534961
$509$	−18.6148	+	32.2418i	−0.825088	+	1.42909i	0.0767644	+	0.997049i	$0.475541\pi$
$509$	−18.6148	+	32.2418i	−0.825088	+	1.42909i	−0.901852	+	0.432045i	$0.857792\pi$
$510$		0			0
$511$	19.0569	+	3.04417i	0.843026	+	0.134666i
$512$	−20.6597			−0.913039
$513$		0			0
$514$	24.3915	−	42.2473i	1.07586	−	1.86345i
$515$	3.69021	+	6.39163i	0.162610	+	0.281649i
$516$		0			0
$517$	2.85583	+	4.94645i	0.125599	+	0.217544i
$518$	13.9980	−	17.2395i	0.615039	−	0.757458i
$519$		0			0
$520$	17.1639			0.752685
$521$	−7.60082	+	13.1650i	−0.332998	+	0.576769i	−0.983098	−	0.183079i	$-0.941394\pi$
$521$	−7.60082	+	13.1650i	−0.332998	+	0.576769i	0.650100	+	0.759848i	$0.274727\pi$
$522$		0			0
$523$	−2.39824	−	4.15387i	−0.104867	−	0.181636i	0.808817	−	0.588061i	$-0.200109\pi$
$523$	−2.39824	−	4.15387i	−0.104867	−	0.181636i	−0.913684	+	0.406425i	$0.866775\pi$
$524$	−15.3095	+	26.5169i	−0.668800	+	1.15840i
$525$		0			0
$526$	−16.8425	−	29.1720i	−0.734366	−	1.27196i
$527$	−34.4161	+	59.6104i	−1.49919	+	2.59667i
$528$		0			0
$529$	−20.4721	−	35.4587i	−0.890091	−	1.54168i
$530$	−4.33061	−	7.50084i	−0.188110	−	0.325816i
$531$		0			0
$532$	−15.2015	+	18.7216i	−0.659070	+	0.811685i
$533$	−3.38079	+	5.85570i	−0.146438	+	0.253639i
$534$		0			0
$535$	−14.4210			−0.623475
$536$	−10.2091			−0.440967
$537$		0			0
$538$	−36.9180	+	63.9439i	−1.59165	+	2.75682i
$539$	−17.7002	−	5.80297i	−0.762400	−	0.249952i
$540$		0			0
$541$	3.22660	+	5.58864i	0.138722	+	0.240274i	0.927013	−	0.375029i	$-0.122367\pi$
$541$	3.22660	+	5.58864i	0.138722	+	0.240274i	−0.788291	+	0.615303i	$0.789034\pi$
$542$	1.94807	+	3.37416i	0.0836770	+	0.144933i
$543$		0			0
$544$	−10.8555	+	18.8023i	−0.465427	+	0.806143i
$545$	−4.90561	−	8.49676i	−0.210133	−	0.363961i
$546$		0			0
$547$	−13.1281	+	22.7385i	−0.561316	+	0.972227i	0.436066	+	0.899915i	$0.356371\pi$
$547$	−13.1281	+	22.7385i	−0.561316	+	0.972227i	−0.997382	+	0.0723129i	$0.976962\pi$
$548$	25.3675	+	43.9378i	1.08365	+	1.87693i
$549$		0			0
$550$	−11.0134	+	19.0758i	−0.469613	+	0.813394i
$551$	−5.65703			−0.240998
$552$		0			0
$553$	0.296470	+	0.775397i	0.0126072	+	0.0329732i
$554$	26.2010	+	45.3815i	1.11318	+	1.92808i
$555$		0			0
$556$	10.2222	+	17.7054i	0.433518	+	0.750875i
$557$	−0.00716610	+	0.0124121i	−0.000303638	+	0.000525916i	−0.866177	−	0.499737i	$-0.833430\pi$
$557$	−0.00716610	+	0.0124121i	−0.000303638	+	0.000525916i	0.865874	+	0.500263i	$0.166763\pi$
$558$		0			0
$559$	−18.6296			−0.787949
$560$	−6.06663	−	0.969091i	−0.256362	−	0.0409516i
$561$		0			0
$562$	18.3584	−	31.7977i	0.774403	−	1.34131i
$563$	17.1826			0.724160			0.362080	−	0.932147i	$-0.382067\pi$
$563$	17.1826			0.724160			0.362080	+	0.932147i	$0.382067\pi$
$564$		0			0
$565$	5.70149			0.239864
$566$	−62.2205			−2.61532
$567$		0			0
$568$	38.9791			1.63553
$569$	29.4779			1.23578			0.617889	−	0.786265i	$-0.287988\pi$
$569$	29.4779			1.23578			0.617889	+	0.786265i	$0.287988\pi$
$570$		0			0
$571$	−32.8321			−1.37398			−0.686991	−	0.726666i	$-0.741069\pi$
$571$	−32.8321			−1.37398			−0.686991	+	0.726666i	$0.741069\pi$
$572$	−17.4822	+	30.2800i	−0.730966	+	1.26607i
$573$		0			0
$574$	7.37810	−	9.08658i	0.307956	−	0.379267i
$575$	−27.9093			−1.16390
$576$		0			0
$577$	−15.9787	+	27.6759i	−0.665201	+	1.15216i	0.314030	+	0.949413i	$0.398321\pi$
$577$	−15.9787	+	27.6759i	−0.665201	+	1.15216i	−0.979231	+	0.202748i	$0.935013\pi$
$578$	−33.5760	−	58.1553i	−1.39658	−	2.41894i
$579$		0			0
$580$	−5.01002	−	8.67761i	−0.208030	−	0.360318i
$581$	−20.1008	−	3.21093i	−0.833922	−	0.133212i
$582$		0			0
$583$	7.90880			0.327549
$584$	−14.0543	+	24.3427i	−0.581570	+	1.00731i
$585$		0			0
$586$	−20.0507	−	34.7289i	−0.828288	−	1.43464i
$587$	−2.37316	+	4.11044i	−0.0979509	+	0.169656i	−0.910836	−	0.412768i	$-0.864562\pi$
$587$	−2.37316	+	4.11044i	−0.0979509	+	0.169656i	0.812885	+	0.582424i	$0.197895\pi$
$588$		0			0
$589$	12.8562	+	22.2676i	0.529732	+	0.917522i
$590$	12.7176	−	22.0276i	0.523576	−	0.906861i
$591$		0			0
$592$	3.34396	+	5.79191i	0.137436	+	0.238046i
$593$	−0.970397	−	1.68078i	−0.0398494	−	0.0690212i	0.845413	−	0.534113i	$-0.179354\pi$
$593$	−0.970397	−	1.68078i	−0.0398494	−	0.0690212i	−0.885262	+	0.465092i	$0.846021\pi$
$594$		0			0
$595$	−13.7946	+	16.9889i	−0.565523	+	0.696476i
$596$	15.8939	−	27.5290i	0.651040	−	1.12763i
$597$		0			0
$598$	−68.7454			−2.81121
$599$	8.80134			0.359613			0.179807	−	0.983702i	$-0.442453\pi$
$599$	8.80134			0.359613			0.179807	+	0.983702i	$0.442453\pi$
$600$		0			0
$601$	7.48016	−	12.9560i	0.305122	−	0.528487i	−0.672166	−	0.740400i	$-0.734636\pi$
$601$	7.48016	−	12.9560i	0.305122	−	0.528487i	0.977289	+	0.211913i	$0.0679694\pi$
$602$	31.8455	+	5.08704i	1.29793	+	0.207332i
$603$		0			0
$604$	17.3281	+	30.0131i	0.705069	+	1.22122i
$605$	−2.40771	−	4.17027i	−0.0978873	−	0.169546i
$606$		0			0
$607$	−1.39569	+	2.41741i	−0.0566494	+	0.0981196i	−0.892959	−	0.450137i	$-0.851375\pi$
$607$	−1.39569	+	2.41741i	−0.0566494	+	0.0981196i	0.836310	+	0.548257i	$0.184708\pi$
$608$	4.05512	+	7.02367i	0.164457	+	0.284847i
$609$		0			0
$610$	−21.8633	+	37.8684i	−0.885221	+	1.53325i
$611$	3.89021	+	6.73804i	0.157381	+	0.272592i
$612$		0			0
$613$	−13.3218	+	23.0740i	−0.538062	+	0.931950i	0.460947	+	0.887428i	$0.347510\pi$
$613$	−13.3218	+	23.0740i	−0.538062	+	0.931950i	−0.999008	+	0.0445225i	$0.985823\pi$
$614$	−34.8246			−1.40541
$615$		0			0
$616$	17.1018	−	21.0619i	0.689052	−	0.848610i
$617$	−19.0560	−	33.0060i	−0.767166	−	1.32877i	−0.939094	−	0.343661i	$-0.888333\pi$
$617$	−19.0560	−	33.0060i	−0.767166	−	1.32877i	0.171927	−	0.985110i	$-0.445001\pi$
$618$		0			0
$619$	11.9658	+	20.7253i	0.480945	+	0.833021i	0.999761	−	0.0218650i	$-0.00696041\pi$
$619$	11.9658	+	20.7253i	0.480945	+	0.833021i	−0.518816	+	0.854886i	$0.673627\pi$
$620$	−22.7716	+	39.4417i	−0.914531	+	1.58401i
$621$		0			0
$622$	−28.0384			−1.12424
$623$	−11.9954	+	14.7730i	−0.480584	+	0.591868i
$624$		0			0
$625$	−2.31616	+	4.01170i	−0.0926463	+	0.160468i
$626$	−0.842228			−0.0336622
$627$		0			0
$628$	7.82627			0.312302
$629$	23.8232			0.949893
$630$		0			0
$631$	−16.6748			−0.663812			−0.331906	−	0.943313i	$-0.607692\pi$
$631$	−16.6748			−0.663812			−0.331906	+	0.943313i	$0.607692\pi$
$632$	−1.20912			−0.0480960
$633$		0			0
$634$	24.7833			0.984271
$635$	−2.04361	+	3.53963i	−0.0810980	+	0.140466i
$636$		0			0
$637$	−24.1111	−	7.90480i	−0.955318	−	0.313199i
$638$	14.1978			0.562098
$639$		0			0
$640$	−12.6898	+	21.9793i	−0.501607	+	0.868809i
$641$	16.0107	+	27.7313i	0.632383	+	1.09532i	0.987063	+	0.160332i	$0.0512566\pi$
$641$	16.0107	+	27.7313i	0.632383	+	1.09532i	−0.354680	+	0.934988i	$0.615410\pi$
$642$		0			0
$643$	1.75969	+	3.04788i	0.0693956	+	0.120197i	0.898635	−	0.438696i	$-0.144560\pi$
$643$	1.75969	+	3.04788i	0.0693956	+	0.120197i	−0.829240	+	0.558893i	$0.811226\pi$
$644$	75.7297	+	12.0972i	2.98417	+	0.476695i
$645$		0			0
$646$	−40.1459			−1.57952
$647$	20.7773	−	35.9873i	0.816839	−	1.41481i	−0.0911605	−	0.995836i	$-0.529058\pi$
$647$	20.7773	−	35.9873i	0.816839	−	1.41481i	0.908000	−	0.418971i	$-0.137609\pi$
$648$		0			0
$649$	11.6128	+	20.1140i	0.455843	+	0.789543i
$650$	−15.0024	+	25.9850i	−0.588444	+	1.01921i
$651$		0			0
$652$	−38.0142	−	65.8424i	−1.48875	−	2.57859i
$653$	5.14289	−	8.90774i	0.201257	−	0.348587i	−0.747677	−	0.664063i	$-0.768831\pi$
$653$	5.14289	−	8.90774i	0.201257	−	0.348587i	0.948934	+	0.315476i	$0.102164\pi$
$654$		0			0
$655$	5.18962	+	8.98868i	0.202775	+	0.351217i
$656$	1.76254	+	3.05280i	0.0688155	+	0.119192i
$657$		0			0
$658$	−4.81002	−	12.5803i	−0.187514	−	0.490430i
$659$	10.1776	−	17.6281i	0.396461	−	0.686691i	−0.596825	−	0.802371i	$-0.703571\pi$
$659$	10.1776	−	17.6281i	0.396461	−	0.686691i	0.993287	+	0.115680i	$0.0369047\pi$
$660$		0			0
$661$	−16.6527			−0.647716			−0.323858	−	0.946106i	$-0.604980\pi$
$661$	−16.6527			−0.647716			−0.323858	+	0.946106i	$0.604980\pi$
$662$	35.2597			1.37041
$663$		0			0
$664$	14.8242	−	25.6762i	0.575290	−	0.996431i
$665$	2.91950	+	7.63576i	0.113214	+	0.296102i
$666$		0			0
$667$	8.99477	+	15.5794i	0.348279	+	0.603236i
$668$	7.74644	+	13.4172i	0.299719	+	0.519128i
$669$		0			0
$670$	−3.86020	+	6.68607i	−0.149133	+	0.258305i
$671$	−19.9640	−	34.5787i	−0.770703	−	1.33490i
$672$		0			0
$673$	−5.10939	+	8.84973i	−0.196953	+	0.341132i	−0.947539	−	0.319641i	$-0.896438\pi$
$673$	−5.10939	+	8.84973i	−0.196953	+	0.341132i	0.750586	+	0.660772i	$0.229771\pi$
$674$	−11.1629	−	19.3347i	−0.429979	−	0.744746i
$675$		0			0
$676$	−0.252721	+	0.437725i	−0.00972003	+	0.0168356i
$677$	−6.38685			−0.245466			−0.122733	−	0.992440i	$-0.539166\pi$
$677$	−6.38685			−0.245466			−0.122733	+	0.992440i	$0.539166\pi$
$678$		0			0
$679$	−34.4446	−	5.50223i	−1.32186	−	0.211156i
$680$	−15.9373	−	27.6041i	−0.611166	−	1.05857i
$681$		0			0
$682$	−32.2662	−	55.8866i	−1.23554	−	2.14001i
$683$	−15.4061	+	26.6842i	−0.589499	+	1.02104i	0.404800	+	0.914405i	$0.367341\pi$
$683$	−15.4061	+	26.6842i	−0.589499	+	1.02104i	−0.994298	+	0.106636i	$0.965992\pi$
$684$		0			0
$685$	17.1981			0.657107
$686$	39.0571	+	20.0963i	1.49121	+	0.767280i
$687$		0			0
$688$	−4.85617	+	8.41113i	−0.185140	+	0.320671i
$689$	10.7734			0.410432
$690$		0			0
$691$	−4.86804			−0.185189			−0.0925945	−	0.995704i	$-0.529516\pi$
$691$	−4.86804			−0.185189			−0.0925945	+	0.995704i	$0.529516\pi$
$692$	−6.58487			−0.250319
$693$		0			0
$694$	−63.0544			−2.39351
$695$	6.93024			0.262879
$696$		0			0
$697$	12.5567			0.475621
$698$	−11.3283	+	19.6211i	−0.428781	+	0.742670i
$699$		0			0
$700$	21.0992	−	25.9850i	0.797476	−	0.982140i
$701$	−44.4038			−1.67711			−0.838554	−	0.544819i	$-0.816598\pi$
$701$	−44.4038			−1.67711			−0.838554	+	0.544819i	$0.816598\pi$
$702$		0			0
$703$	4.44961	−	7.70696i	0.167820	−	0.290673i
$704$	−15.2061	−	26.3378i	−0.573102	−	0.992642i
$705$		0			0
$706$	20.2456	+	35.0665i	0.761955	+	1.31974i
$707$	−4.64137	+	5.71613i	−0.174557	+	0.214977i
$708$		0			0
$709$	−26.5768			−0.998112			−0.499056	−	0.866570i	$-0.666320\pi$
$709$	−26.5768			−0.998112			−0.499056	+	0.866570i	$0.666320\pi$
$710$	14.7385	−	25.5279i	0.553126	−	0.958043i
$711$		0			0
$712$	−13.8586	−	24.0037i	−0.519372	−	0.899578i
$713$	40.8832	−	70.8117i	1.53109	−	2.65192i
$714$		0			0
$715$	5.92609	+	10.2643i	0.221623	+	0.383863i
$716$	14.5902	−	25.2710i	0.545262	−	0.944421i
$717$		0			0
$718$	30.4365	+	52.7176i	1.13588	+	1.96740i
$719$	−16.9462	−	29.3517i	−0.631987	−	1.09463i	−0.987145	−	0.159828i	$-0.948906\pi$
$719$	−16.9462	−	29.3517i	−0.631987	−	1.09463i	0.355157	−	0.934807i	$-0.384427\pi$
$720$		0			0
$721$	15.6927	+	2.50677i	0.584425	+	0.0933569i
$722$	15.0326	−	26.0372i	0.559455	−	0.969005i
$723$		0			0
$724$	91.8778			3.41461
$725$	7.85177			0.291608
$726$		0			0
$727$	11.9709	−	20.7341i	0.443974	−	0.768986i	−0.554006	−	0.832513i	$-0.686901\pi$
$727$	11.9709	−	20.7341i	0.443974	−	0.768986i	0.997980	+	0.0635267i	$0.0202348\pi$
$728$	23.2961	−	28.6905i	0.863410	−	1.06334i
$729$		0			0
$730$	10.6282	+	18.4086i	0.393368	+	0.681334i
$731$	17.2983	+	29.9615i	0.639800	+	1.10817i
$732$		0			0
$733$	18.7852	−	32.5369i	0.693846	−	1.20178i	−0.276723	−	0.960950i	$-0.589248\pi$
$733$	18.7852	−	32.5369i	0.693846	−	1.20178i	0.970568	−	0.240826i	$-0.0774184\pi$
$734$	12.3033	+	21.3099i	0.454121	+	0.786561i
$735$		0			0
$736$	12.8954	−	22.3355i	0.475331	−	0.823297i
$737$	−3.52486	−	6.10523i	−0.129840	−	0.224889i
$738$		0			0
$739$	2.82055	−	4.88534i	0.103756	−	0.179710i	−0.809473	−	0.587156i	$-0.800247\pi$
$739$	2.82055	−	4.88534i	0.103756	−	0.179710i	0.913229	+	0.407446i	$0.133581\pi$
$740$	15.7628			0.579452
$741$		0			0
$742$	−18.4160	−	2.94179i	−0.676072	−	0.107997i
$743$	7.58516	+	13.1379i	0.278273	+	0.481982i	0.970956	−	0.239260i	$-0.0769048\pi$
$743$	7.58516	+	13.1379i	0.278273	+	0.481982i	−0.692683	+	0.721242i	$0.743571\pi$
$744$		0			0
$745$	−5.38771	−	9.33178i	−0.197390	−	0.341890i
$746$	23.4976	−	40.6990i	0.860308	−	1.49010i
$747$		0			0
$748$	64.9312			2.37412
$749$	−19.5733	+	24.1057i	−0.715192	+	0.880802i
$750$		0			0
$751$	−12.9468	+	22.4245i	−0.472434	+	0.818280i	−0.999502	−	0.0315427i	$-0.989958\pi$
$751$	−12.9468	+	22.4245i	−0.472434	+	0.818280i	0.527068	+	0.849823i	$0.323291\pi$
$752$	4.05623			0.147915
$753$		0			0
$754$	19.3403			0.704331
$755$	11.7477			0.427543
$756$		0			0
$757$	36.9054			1.34135			0.670675	−	0.741752i	$-0.266005\pi$
$757$	36.9054			1.34135			0.670675	+	0.741752i	$0.266005\pi$
$758$	33.6105			1.22079
$759$		0			0
$760$	−11.9068			−0.431906
$761$	14.2004	−	24.5959i	0.514765	−	0.891600i	−0.485088	−	0.874465i	$-0.661212\pi$
$761$	14.2004	−	24.5959i	0.514765	−	0.891600i	0.999853	−	0.0171342i	$-0.00545427\pi$
$762$		0			0
$763$	−20.8612	−	3.33239i	−0.755225	−	0.120641i
$764$	25.9219			0.937823
$765$		0			0
$766$	−15.9480	+	27.6227i	−0.576223	+	0.998048i
$767$	15.8190	+	27.3992i	0.571189	+	0.989329i
$768$		0			0
$769$	2.63076	+	4.55661i	0.0948677	+	0.164316i	0.909553	−	0.415587i	$-0.136424\pi$
$769$	2.63076	+	4.55661i	0.0948677	+	0.164316i	−0.814686	+	0.579903i	$0.803091\pi$
$770$	−7.32728	−	19.1640i	−0.264057	−	0.690622i
$771$		0			0
$772$	41.1620			1.48145
$773$	−20.6873	+	35.8315i	−0.744071	+	1.28877i	0.206556	+	0.978435i	$0.433774\pi$
$773$	−20.6873	+	35.8315i	−0.744071	+	1.28877i	−0.950627	+	0.310335i	$0.899559\pi$
$774$		0			0
$775$	−17.8440	−	30.9067i	−0.640976	−	1.11020i
$776$	25.4026	−	43.9986i	0.911901	−	1.57946i
$777$		0			0
$778$	24.8192	+	42.9882i	0.889813	+	1.54120i
$779$	2.34530	−	4.06219i	0.0840293	−	0.145543i
$780$		0			0
$781$	13.4581	+	23.3102i	0.481570	+	0.834104i
$782$	63.8326	+	110.561i	2.28265	+	3.95366i
$783$		0			0
$784$	−9.85398	+	8.82545i	−0.351928	+	0.315195i
$785$	1.32647	−	2.29752i	0.0473438	−	0.0820019i
$786$		0			0
$787$	5.36129			0.191109			0.0955547	−	0.995424i	$-0.469538\pi$
$787$	5.36129			0.191109			0.0955547	+	0.995424i	$0.469538\pi$
$788$	−72.8584			−2.59547
$789$		0			0
$790$	−0.457183	+	0.791864i	−0.0162658	+	0.0281733i
$791$	7.73849	−	9.53043i	0.275149	−	0.338863i
$792$		0			0
$793$	−27.1949	−	47.1030i	−0.965721	−	1.67268i
$794$	29.8138	+	51.6389i	1.05805	+	1.83260i
$795$		0			0
$796$	−18.7133	+	32.4123i	−0.663274	+	1.14882i
$797$	15.2102	+	26.3448i	0.538773	+	0.933182i	0.998970	+	0.0453658i	$0.0144453\pi$
$797$	15.2102	+	26.3448i	0.538773	+	0.933182i	−0.460197	+	0.887817i	$0.652221\pi$
$798$		0			0
$799$	7.22439	−	12.5130i	0.255581	−	0.442679i
$800$	−5.62837	−	9.74862i	−0.198993	−	0.344666i
$801$		0			0
$802$	25.0926	−	43.4617i	0.886052	−	1.53469i
$803$	−19.4098			−0.684958
$804$		0			0
$805$	16.3867	−	20.1812i	0.577556	−	0.711295i
$806$	−43.9529	−	76.1287i	−1.54817	−	2.68152i
$807$		0			0
$808$	−5.36230	−	9.28778i	−0.188645	−	0.326743i
$809$	21.7729	−	37.7117i	0.765494	−	1.32587i	−0.174491	−	0.984659i	$-0.555828\pi$
$809$	21.7729	−	37.7117i	0.765494	−	1.32587i	0.939985	−	0.341216i	$-0.110839\pi$
$810$		0			0
$811$	17.4078			0.611272			0.305636	−	0.952148i	$-0.401131\pi$
$811$	17.4078			0.611272			0.305636	+	0.952148i	$0.401131\pi$
$812$	−21.3052	−	3.40332i	−0.747665	−	0.119433i
$813$		0			0
$814$	−11.1675	+	19.3427i	−0.391421	+	0.677961i
$815$	−25.7720			−0.902755
$816$		0			0
$817$	12.9236			0.452141
$818$	1.28973			0.0450944
$819$		0			0
$820$	8.30826			0.290137
$821$	−23.0636			−0.804925			−0.402462	−	0.915437i	$-0.631846\pi$
$821$	−23.0636			−0.804925			−0.402462	+	0.915437i	$0.631846\pi$
$822$		0			0
$823$	10.0780			0.351298			0.175649	−	0.984453i	$-0.443798\pi$
$823$	10.0780			0.351298			0.175649	+	0.984453i	$0.443798\pi$
$824$	−11.5732	+	20.0454i	−0.403172	+	0.698314i
$825$		0			0
$826$	−19.5592	−	51.1558i	−0.680553	−	1.77994i
$827$	28.4954			0.990882			0.495441	−	0.868642i	$-0.335007\pi$
$827$	28.4954			0.990882			0.495441	+	0.868642i	$0.335007\pi$
$828$		0			0
$829$	0.907602	−	1.57201i	0.0315223	−	0.0545983i	−0.849834	−	0.527051i	$-0.823298\pi$
$829$	0.907602	−	1.57201i	0.0315223	−	0.0545983i	0.881356	+	0.472452i	$0.156631\pi$
$830$	−11.2104	−	19.4171i	−0.389120	−	0.673976i
$831$		0			0
$832$	−20.7137	−	35.8772i	−0.718120	−	1.24382i
$833$	9.67499	+	46.1171i	0.335219	+	1.59786i
$834$		0			0
$835$	5.25177			0.181745
$836$	12.1276	−	21.0057i	0.419443	−	0.726496i
$837$		0			0
$838$	−28.2333	−	48.9015i	−0.975302	−	1.68927i
$839$	3.43860	−	5.95583i	0.118714	−	0.205618i	−0.800544	−	0.599273i	$-0.795456\pi$
$839$	3.43860	−	5.95583i	0.118714	−	0.205618i	0.919258	+	0.393655i	$0.128790\pi$
$840$		0			0
$841$	11.9695	+	20.7318i	0.412741	+	0.714888i
$842$	3.45056	−	5.97654i	0.118914	−	0.205965i
$843$		0			0
$844$	−1.08516	−	1.87956i	−0.0373528	−	0.0646970i
$845$	0.0856672	+	0.148380i	0.00294704	+	0.00510442i
$846$		0			0
$847$	−10.2388	−	1.63556i	−0.351810	−	0.0561985i
$848$	2.80828	−	4.86408i	0.0964367	−	0.167033i
$849$		0			0
$850$	55.7212			1.91122
$851$	−28.2998			−0.970105
$852$		0			0
$853$	1.34635	−	2.33195i	0.0460982	−	0.0798445i	−0.842056	−	0.539391i	$-0.818655\pi$
$853$	1.34635	−	2.33195i	0.0460982	−	0.0798445i	0.888154	+	0.459546i	$0.151988\pi$
$854$	33.6250	+	87.9439i	1.15063	+	3.00938i
$855$		0			0
$856$	−22.6135	−	39.1678i	−0.772914	−	1.33873i
$857$	−11.8361	−	20.5007i	−0.404313	−	0.700290i	0.589929	−	0.807455i	$-0.299156\pi$
$857$	−11.8361	−	20.5007i	−0.404313	−	0.700290i	−0.994241	+	0.107165i	$0.965823\pi$
$858$		0			0
$859$	6.51374	−	11.2821i	0.222246	−	0.384941i	−0.733244	−	0.679966i	$-0.761995\pi$
$859$	6.51374	−	11.2821i	0.222246	−	0.384941i	0.955490	+	0.295025i	$0.0953279\pi$
$860$	11.4455	+	19.8242i	0.390289	+	0.676001i
$861$		0			0
$862$	−37.2109	+	64.4512i	−1.26741	+	2.19522i
$863$	9.87796	+	17.1091i	0.336250	+	0.582401i	0.983724	−	0.179686i	$-0.0575081\pi$
$863$	9.87796	+	17.1091i	0.336250	+	0.582401i	−0.647475	+	0.762087i	$0.724175\pi$
$864$		0			0
$865$	−1.11607	+	1.93309i	−0.0379475	+	0.0657270i
$866$	−63.8647			−2.17021
$867$		0			0
$868$	35.0220	+	91.5975i	1.18872	+	3.10902i
$869$	−0.417466	−	0.723073i	−0.0141616	−	0.0245286i
$870$		0			0
$871$	−4.80156	−	8.31654i	−0.162694	−	0.281795i
$872$	15.3849	−	26.6475i	0.520999	−	0.902398i
$873$		0			0
$874$	47.6897			1.61313
$875$	−9.85728	−	25.7810i	−0.333237	−	0.871557i
$876$		0			0
$877$	−6.34072	+	10.9825i	−0.214111	+	0.370851i	−0.952997	−	0.302979i	$-0.902019\pi$
$877$	−6.34072	+	10.9825i	−0.214111	+	0.370851i	0.738886	+	0.673830i	$0.235352\pi$
$878$	−60.0731			−2.02737
$879$		0			0
$880$	6.17900			0.208294
$881$	43.7202			1.47297			0.736485	−	0.676454i	$-0.236484\pi$
$881$	43.7202			1.47297			0.736485	+	0.676454i	$0.236484\pi$
$882$		0			0
$883$	−1.03795			−0.0349298			−0.0174649	−	0.999847i	$-0.505560\pi$
$883$	−1.03795			−0.0349298			−0.0174649	+	0.999847i	$0.505560\pi$
$884$	88.4492			2.97487
$885$		0			0
$886$	30.9062			1.03831
$887$	−3.19128	+	5.52746i	−0.107153	+	0.185594i	−0.914616	−	0.404324i	$-0.867507\pi$
$887$	−3.19128	+	5.52746i	−0.107153	+	0.185594i	0.807463	+	0.589918i	$0.200840\pi$
$888$		0			0
$889$	3.14299	+	8.22027i	0.105413	+	0.275699i
$890$	−20.9604			−0.702596
$891$		0			0
$892$	−5.47358	+	9.48052i	−0.183269	+	0.317431i
$893$	−2.69869	−	4.67428i	−0.0903084	−	0.156419i
$894$		0			0
$895$	−4.94578	−	8.56634i	−0.165319	−	0.286341i
$896$	19.5164	+	51.0438i	0.651997	+	1.70525i
$897$		0			0
$898$	46.0941			1.53818
$899$	−11.5017	+	19.9216i	−0.383604	+	0.664422i
$900$		0			0
$901$	−10.0034	−	17.3265i	−0.333263	−	0.577228i
$902$	−5.88617	+	10.1952i	−0.195988	+	0.339461i
$903$		0			0
$904$	8.94049	+	15.4854i	0.297356	+	0.515036i
$905$	15.5723	−	26.9721i	0.517642	−	0.896583i
$906$		0			0
$907$	22.7131	+	39.3402i	0.754176	+	1.30627i	0.945783	+	0.324800i	$0.105297\pi$
$907$	22.7131	+	39.3402i	0.754176	+	1.30627i	−0.191607	+	0.981472i	$0.561370\pi$
$908$	−36.4442	−	63.1232i	−1.20944	−	2.09482i
$909$		0			0
$910$	−9.98121	−	26.1051i	−0.330874	−	0.865377i
$911$	2.24354	−	3.88592i	0.0743318	−	0.128746i	−0.826464	−	0.562990i	$-0.809651\pi$
$911$	2.24354	−	3.88592i	0.0743318	−	0.128746i	0.900795	+	0.434244i	$0.142984\pi$
$912$		0			0
$913$	20.4731			0.677562
$914$	−68.0611			−2.25126
$915$		0			0
$916$	36.2601	−	62.8043i	1.19807	−	2.07511i
$917$	22.0689	+	3.52532i	0.728780	+	0.116416i
$918$		0			0
$919$	17.3189	+	29.9972i	0.571298	+	0.989517i	0.996433	+	0.0843873i	$0.0268933\pi$
$919$	17.3189	+	29.9972i	0.571298	+	0.989517i	−0.425135	+	0.905130i	$0.639773\pi$
$920$	18.9320	+	32.7912i	0.624170	+	1.08109i
$921$		0			0
$922$	−27.3311	+	47.3388i	−0.900102	+	1.55902i
$923$	18.3326	+	31.7531i	0.603426	+	1.04517i
$924$		0			0
$925$	−6.17592	+	10.6970i	−0.203063	+	0.351715i
$926$	−34.6440	−	60.0051i	−1.13847	−	1.97189i
$927$		0			0
$928$	−3.62788	+	6.28368i	−0.119091	+	0.206272i
$929$	−15.2728			−0.501084			−0.250542	−	0.968106i	$-0.580609\pi$
$929$	−15.2728			−0.501084			−0.250542	+	0.968106i	$0.580609\pi$
$930$		0			0
$931$	16.7262	+	5.48367i	0.548181	+	0.179720i
$932$	−0.548792	−	0.950535i	−0.0179763	−	0.0311358i
$933$		0			0
$934$	5.17627	+	8.96556i	0.169373	+	0.293362i
$935$	11.0052	−	19.0615i	0.359908	−	0.623379i
$936$		0			0
$937$	16.6920			0.545305			0.272652	−	0.962113i	$-0.412099\pi$
$937$	16.6920			0.545305			0.272652	+	0.962113i	$0.412099\pi$
$938$	5.93686	+	15.5274i	0.193845	+	0.506988i
$939$		0			0
$940$	4.78007	−	8.27933i	0.155909	−	0.270042i
$941$	−21.2479			−0.692661			−0.346330	−	0.938113i	$-0.612572\pi$
$941$	−21.2479			−0.692661			−0.346330	+	0.938113i	$0.612572\pi$
$942$		0			0
$943$	−14.9163			−0.485741
$944$	16.4940			0.536836
$945$		0			0
$946$	−32.4354			−1.05456
$947$	−39.3146			−1.27755			−0.638777	−	0.769392i	$-0.720559\pi$
$947$	−39.3146			−1.27755			−0.638777	+	0.769392i	$0.720559\pi$
$948$		0			0
$949$	−26.4400			−0.858280
$950$	10.4074	−	18.0262i	0.337661	−	0.584846i
$951$		0			0
$952$	−67.7734	−	10.8262i	−2.19655	−	0.350879i
$953$	15.1311			0.490143			0.245072	−	0.969505i	$-0.421189\pi$
$953$	15.1311			0.490143			0.245072	+	0.969505i	$0.421189\pi$
$954$		0			0
$955$	4.39351	−	7.60977i	0.142170	−	0.246247i
$956$	6.42828	+	11.1341i	0.207905	+	0.360103i
$957$		0			0
$958$	−18.8819	−	32.7045i	−0.610047	−	1.05663i
$959$	23.3426	−	28.7478i	0.753772	−	0.928316i
$960$		0			0
$961$	73.5558			2.37277
$962$	−15.2123	+	26.3486i	−0.490466	+	0.849512i
$963$		0			0
$964$	−10.8862	−	18.8555i	−0.350622	−	0.607295i
$965$	6.97653	−	12.0837i	0.224582	−	0.388988i
$966$		0			0
$967$	−15.6941	−	27.1829i	−0.504687	−	0.874143i	−0.999985	−	0.00542015i	$-0.998275\pi$
$967$	−15.6941	−	27.1829i	−0.504687	−	0.874143i	0.495299	−	0.868723i	$-0.335059\pi$
$968$	7.55104	−	13.0788i	0.242699	−	0.420368i
$969$		0			0
$970$	−19.2101	−	33.2730i	−0.616801	−	1.06833i
$971$	17.4760	+	30.2694i	0.560833	+	0.971391i	0.997424	+	0.0717309i	$0.0228523\pi$
$971$	17.4760	+	30.2694i	0.560833	+	0.971391i	−0.436591	+	0.899660i	$0.643814\pi$
$972$		0			0
$973$	9.40624	−	11.5844i	0.301550	−	0.371377i
$974$	45.3769	−	78.5951i	1.45397	−	2.51835i
$975$		0			0
$976$	−28.3555			−0.907639
$977$	7.68632			0.245907			0.122954	−	0.992412i	$-0.460763\pi$
$977$	7.68632			0.245907			0.122954	+	0.992412i	$0.460763\pi$
$978$		0			0
$979$	9.56978	−	16.5753i	0.305851	−	0.529750i
$980$	6.40153	+	30.5137i	0.204489	+	0.974726i
$981$		0			0
$982$	15.8793	+	27.5037i	0.506729	+	0.877680i
$983$	1.09035	+	1.88855i	0.0347769	+	0.0602354i	0.882890	−	0.469580i	$-0.155595\pi$
$983$	1.09035	+	1.88855i	0.0347769	+	0.0602354i	−0.848113	+	0.529815i	$0.822261\pi$
$984$		0			0
$985$	−12.3487	+	21.3887i	−0.393464	+	0.681499i
$986$	−17.9581	−	31.1044i	−0.571904	−	0.990566i
$987$		0			0
$988$	16.5202	−	28.6139i	0.525579	−	0.910329i
$989$	−20.5488	−	35.5915i	−0.653413	−	1.13175i
$990$		0			0
$991$	2.85159	−	4.93909i	0.0905837	−	0.156895i	−0.817173	−	0.576392i	$-0.804460\pi$
$991$	2.85159	−	4.93909i	0.0905837	−	0.156895i	0.907757	+	0.419497i	$0.137793\pi$
$992$	32.9791			1.04709
$993$		0			0
$994$	−22.6673	−	59.2847i	−0.718963	−	1.88040i
$995$	6.34341	+	10.9871i	0.201100	+	0.348315i
$996$		0			0
$997$	−15.6898	−	27.1756i	−0.496902	−	0.860659i	0.503092	−	0.864233i	$-0.332196\pi$
$997$	−15.6898	−	27.1756i	−0.496902	−	0.860659i	−0.999994	+	0.00357385i	$0.998862\pi$
$998$	−6.41189	+	11.1057i	−0.202965	+	0.351545i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.h.j.298.4		8
3.2	odd	2		567.2.h.k.298.1		8
7.2	even	3		567.2.g.k.541.1		8
9.2	odd	6		567.2.e.c.487.4	yes	8
9.4	even	3		567.2.g.k.109.1		8
9.5	odd	6		567.2.g.j.109.4		8
9.7	even	3		567.2.e.d.487.1	yes	8
21.2	odd	6		567.2.g.j.541.4		8
63.2	odd	6		567.2.e.c.163.4	✓	8
63.11	odd	6		3969.2.a.x.1.1		4
63.16	even	3		567.2.e.d.163.1	yes	8
63.23	odd	6		567.2.h.k.352.1		8
63.25	even	3		3969.2.a.s.1.4		4
63.38	even	6		3969.2.a.w.1.1		4
63.52	odd	6		3969.2.a.t.1.4		4
63.58	even	3	inner	567.2.h.j.352.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.c.163.4	✓	8	63.2	odd	6
567.2.e.c.487.4	yes	8	9.2	odd	6
567.2.e.d.163.1	yes	8	63.16	even	3
567.2.e.d.487.1	yes	8	9.7	even	3
567.2.g.j.109.4		8	9.5	odd	6
567.2.g.j.541.4		8	21.2	odd	6
567.2.g.k.109.1		8	9.4	even	3
567.2.g.k.541.1		8	7.2	even	3
567.2.h.j.298.4		8	1.1	even	1	trivial
567.2.h.j.352.4		8	63.58	even	3	inner
567.2.h.k.298.1		8	3.2	odd	2
567.2.h.k.352.1		8	63.23	odd	6
3969.2.a.s.1.4		4	63.25	even	3
3969.2.a.t.1.4		4	63.52	odd	6
3969.2.a.w.1.1		4	63.38	even	6
3969.2.a.x.1.1		4	63.11	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.37167 q^{2} +3.62484 q^{4} +(0.614373 - 1.06412i) q^{5} +(-0.944883 - 2.47127i) q^{7} +3.85358 q^{8} +O(q^{10})\)	\(q+2.37167 q^{2} +3.62484 q^{4} +(0.614373 - 1.06412i) q^{5} +(-0.944883 - 2.47127i) q^{7} +3.85358 q^{8} +(1.45709 - 2.52376i) q^{10} +(1.33051 + 2.30451i) q^{11} +(1.81242 + 3.13920i) q^{13} +(-2.24095 - 5.86106i) q^{14} +1.88977 q^{16} +(3.36579 - 5.82972i) q^{17} +(-1.25730 - 2.17771i) q^{19} +(2.22700 - 3.85728i) q^{20} +(3.15554 + 5.46555i) q^{22} +(-3.99826 + 6.92518i) q^{23} +(1.74509 + 3.02259i) q^{25} +(4.29846 + 7.44516i) q^{26} +(-3.42505 - 8.95796i) q^{28} +(1.12484 - 1.94827i) q^{29} -10.2253 q^{31} -3.22526 q^{32} +(7.98256 - 13.8262i) q^{34} +(-3.21025 - 0.512810i) q^{35} +(1.76951 + 3.06488i) q^{37} +(-2.98191 - 5.16482i) q^{38} +(2.36754 - 4.10069i) q^{40} +(0.932674 + 1.61544i) q^{41} +(-2.56972 + 4.45088i) q^{43} +(4.82288 + 8.35348i) q^{44} +(-9.48256 + 16.4243i) q^{46} +2.14642 q^{47} +(-5.21439 + 4.67013i) q^{49} +(4.13879 + 7.16859i) q^{50} +(6.56972 + 11.3791i) q^{52} +(1.48605 - 2.57391i) q^{53} +3.26972 q^{55} +(-3.64118 - 9.52326i) q^{56} +(2.66774 - 4.62067i) q^{58} +8.72809 q^{59} -15.0048 q^{61} -24.2510 q^{62} -11.4288 q^{64} +4.45400 q^{65} -2.64925 q^{67} +(12.2004 - 21.1318i) q^{68} +(-7.61368 - 1.21622i) q^{70} +10.1150 q^{71} +(-3.64707 + 6.31691i) q^{73} +(4.19670 + 7.26890i) q^{74} +(-4.55751 - 7.89384i) q^{76} +(4.43790 - 5.46555i) q^{77} -0.313764 q^{79} +(1.16102 - 2.01095i) q^{80} +(2.21200 + 3.83129i) q^{82} +(3.84686 - 6.66295i) q^{83} +(-4.13570 - 7.16324i) q^{85} +(-6.09454 + 10.5560i) q^{86} +(5.12723 + 8.88062i) q^{88} +(-3.59628 - 6.22894i) q^{89} +(6.04530 - 7.44516i) q^{91} +(-14.4930 + 25.1026i) q^{92} +5.09060 q^{94} -3.08981 q^{95} +(6.59195 - 11.4176i) q^{97} +(-12.3668 + 11.0760i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 10 q^{4} + 2 q^{5} + q^{7} + 6 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 + 10 * q^4 + 2 * q^5 + q^7 + 6 * q^8	\( 8 q - 2 q^{2} + 10 q^{4} + 2 q^{5} + q^{7} + 6 q^{8} + 7 q^{10} + 5 q^{11} + 5 q^{13} - 16 q^{14} - 2 q^{16} + 6 q^{17} + 8 q^{19} - 8 q^{20} + 7 q^{22} - 12 q^{23} - 8 q^{25} + q^{26} + 5 q^{28} - 10 q^{29} - 36 q^{31} + 20 q^{32} - 23 q^{35} - 20 q^{38} + 18 q^{40} - 5 q^{41} + 7 q^{43} + 13 q^{44} - 12 q^{46} + 42 q^{47} - 19 q^{49} + 38 q^{50} + 25 q^{52} - 12 q^{53} - 52 q^{55} + 6 q^{56} + 7 q^{58} - 12 q^{59} - 40 q^{61} - 36 q^{62} - 46 q^{64} - 16 q^{65} - 10 q^{67} + 51 q^{68} + 29 q^{70} + 18 q^{71} + 6 q^{73} - 5 q^{76} - 53 q^{77} - 20 q^{79} - 2 q^{80} + 35 q^{82} + 9 q^{83} + 9 q^{85} - 22 q^{86} - 18 q^{88} - 22 q^{89} + 13 q^{91} - 36 q^{92} - 30 q^{94} + 32 q^{95} + 9 q^{97} - 11 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 10 * q^4 + 2 * q^5 + q^7 + 6 * q^8 + 7 * q^10 + 5 * q^11 + 5 * q^13 - 16 * q^14 - 2 * q^16 + 6 * q^17 + 8 * q^19 - 8 * q^20 + 7 * q^22 - 12 * q^23 - 8 * q^25 + q^26 + 5 * q^28 - 10 * q^29 - 36 * q^31 + 20 * q^32 - 23 * q^35 - 20 * q^38 + 18 * q^40 - 5 * q^41 + 7 * q^43 + 13 * q^44 - 12 * q^46 + 42 * q^47 - 19 * q^49 + 38 * q^50 + 25 * q^52 - 12 * q^53 - 52 * q^55 + 6 * q^56 + 7 * q^58 - 12 * q^59 - 40 * q^61 - 36 * q^62 - 46 * q^64 - 16 * q^65 - 10 * q^67 + 51 * q^68 + 29 * q^70 + 18 * q^71 + 6 * q^73 - 5 * q^76 - 53 * q^77 - 20 * q^79 - 2 * q^80 + 35 * q^82 + 9 * q^83 + 9 * q^85 - 22 * q^86 - 18 * q^88 - 22 * q^89 + 13 * q^91 - 36 * q^92 - 30 * q^94 + 32 * q^95 + 9 * q^97 - 11 * q^98

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