LMFDB - Embedded newform 567.2.e.e.487.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(163,567)]

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([0, 2]))

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

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

chi := DirichletCharacter("567.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.e (of order $3$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			487.5
Root			$-1.02682 - 1.77851i$ of defining polynomial
Character	$\chi$	$=$	567.487
Dual form			567.2.e.e.163.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02682 + 1.77851i) q^{2} +(-1.10873 + 1.92038i) q^{4} +(-0.0731228 - 0.126652i) q^{5} +(2.25011 + 1.39176i) q^{7} -0.446582 q^{8} +O(q^{10})$	\(q+(1.02682 + 1.77851i) q^{2} +(-1.10873 + 1.92038i) q^{4} +(-0.0731228 - 0.126652i) q^{5} +(2.25011 + 1.39176i) q^{7} -0.446582 q^{8} +(0.150168 - 0.260099i) q^{10} +(0.832020 - 1.44110i) q^{11} -0.199891 q^{13} +(-0.164785 + 5.43093i) q^{14} +(1.75890 + 3.04650i) q^{16} +(-3.13555 + 5.43093i) q^{17} +(3.45879 + 5.99080i) q^{19} +0.324294 q^{20} +3.41735 q^{22} +(-3.09092 - 5.35363i) q^{23} +(2.48931 - 4.31160i) q^{25} +(-0.205252 - 0.355508i) q^{26} +(-5.16746 + 2.77798i) q^{28} -4.93514 q^{29} +(1.25890 - 2.18047i) q^{31} +(-4.05873 + 7.02993i) q^{32} -12.8786 q^{34} +(0.0117348 - 0.386752i) q^{35} +(-3.50023 - 6.06257i) q^{37} +(-7.10312 + 12.3030i) q^{38} +(0.0326554 + 0.0565608i) q^{40} +2.31790 q^{41} +1.88199 q^{43} +(1.84497 + 3.19558i) q^{44} +(6.34765 - 10.9944i) q^{46} +(-0.905887 - 1.56904i) q^{47} +(3.12602 + 6.26322i) q^{49} +10.2243 q^{50} +(0.221625 - 0.383865i) q^{52} +(2.67307 - 4.62989i) q^{53} -0.243359 q^{55} +(-1.00486 - 0.621534i) q^{56} +(-5.06752 - 8.77720i) q^{58} +(-2.28549 + 3.95859i) q^{59} +(0.339138 + 0.587404i) q^{61} +5.17066 q^{62} -9.63481 q^{64} +(0.0146166 + 0.0253167i) q^{65} +(3.09342 - 5.35796i) q^{67} +(-6.95296 - 12.0429i) q^{68} +(0.699891 - 0.376255i) q^{70} -1.27749 q^{71} +(-0.778603 + 1.34858i) q^{73} +(7.18823 - 12.4504i) q^{74} -15.3394 q^{76} +(3.87780 - 2.08467i) q^{77} +(-6.39787 - 11.0814i) q^{79} +(0.257231 - 0.445537i) q^{80} +(2.38008 + 4.12241i) q^{82} +7.51374 q^{83} +0.917122 q^{85} +(1.93247 + 3.34713i) q^{86} +(-0.371566 + 0.643571i) q^{88} +(-4.53394 - 7.85301i) q^{89} +(-0.449777 - 0.278199i) q^{91} +13.7080 q^{92} +(1.86037 - 3.22226i) q^{94} +(0.505833 - 0.876128i) q^{95} +7.97028 q^{97} +(-7.92933 + 11.9909i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 5 q^{7} + 6 q^{8}+O(q^{10}) $ 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 5 * q^7 + 6 * q^8	$ 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 5 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} + 16 q^{13} - 4 q^{14} + 2 q^{16} - 12 q^{17} + q^{19} + 10 q^{20} + 2 q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} + 14 q^{29} - 3 q^{31} + 2 q^{32} - 6 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} + 10 q^{41} + 14 q^{43} + 10 q^{44} + 3 q^{46} - 27 q^{47} - 17 q^{49} + 38 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 27 q^{56} - 10 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} - 27 q^{68} - 11 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} - 10 q^{76} - 20 q^{77} - 4 q^{79} - 20 q^{80} - 5 q^{82} + 18 q^{83} + 12 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} + 54 q^{92} - 3 q^{94} + 14 q^{95} + 24 q^{97} - 59 q^{98}+O(q^{100}) $ 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 5 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 + 16 * q^13 - 4 * q^14 + 2 * q^16 - 12 * q^17 + q^19 + 10 * q^20 + 2 * q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 + 14 * q^29 - 3 * q^31 + 2 * q^32 - 6 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 + 10 * q^41 + 14 * q^43 + 10 * q^44 + 3 * q^46 - 27 * q^47 - 17 * q^49 + 38 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 27 * q^56 - 10 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 27 * q^68 - 11 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 - 10 * q^76 - 20 * q^77 - 4 * q^79 - 20 * q^80 - 5 * q^82 + 18 * q^83 + 12 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 + 54 * q^92 - 3 * q^94 + 14 * q^95 + 24 * q^97 - 59 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.02682	+	1.77851i	0.726073	+	1.25760i	0.958531	+	0.284989i	$0.0919900\pi$
$2$	1.02682	+	1.77851i	0.726073	+	1.25760i	−0.232458	+	0.972607i	$0.574677\pi$
$3$		0			0
$3$		0			0
$4$	−1.10873	+	1.92038i	−0.554365	+	0.960188i
$5$	−0.0731228	−	0.126652i	−0.0327015	−	0.0566407i	0.849211	−	0.528053i	$-0.177078\pi$
$5$	−0.0731228	−	0.126652i	−0.0327015	−	0.0566407i	−0.881913	+	0.471412i	$0.843744\pi$
$6$		0			0
$7$	2.25011	+	1.39176i	0.850463	+	0.526035i
$7$	2.25011	+	1.39176i	0.850463	+	0.526035i
$8$	−0.446582			−0.157891
$9$		0			0
$10$	0.150168	−	0.260099i	0.0474874	−	0.0822506i
$11$	0.832020	−	1.44110i	0.250864	−	0.434508i	−0.712900	−	0.701265i	$-0.752619\pi$
$11$	0.832020	−	1.44110i	0.250864	−	0.434508i	0.963764	+	0.266757i	$0.0859521\pi$
$12$		0			0
$13$	−0.199891			−0.0554397			−0.0277199	−	0.999616i	$-0.508825\pi$
$13$	−0.199891			−0.0554397			−0.0277199	+	0.999616i	$0.508825\pi$
$14$	−0.164785	+	5.43093i	−0.0440406	+	1.45148i
$15$		0			0
$16$	1.75890	+	3.04650i	0.439724	+	0.761625i
$17$	−3.13555	+	5.43093i	−0.760483	+	1.31720i	0.182119	+	0.983277i	$0.441704\pi$
$17$	−3.13555	+	5.43093i	−0.760483	+	1.31720i	−0.942602	+	0.333919i	$0.891629\pi$
$18$		0			0
$19$	3.45879	+	5.99080i	0.793500	+	1.37438i	0.923787	+	0.382907i	$0.125077\pi$
$19$	3.45879	+	5.99080i	0.793500	+	1.37438i	−0.130287	+	0.991476i	$0.541590\pi$
$20$	0.324294			0.0725143
$21$		0			0
$22$	3.41735			0.728581
$23$	−3.09092	−	5.35363i	−0.644501	−	1.11631i	−0.984417	−	0.175852i	$-0.943732\pi$
$23$	−3.09092	−	5.35363i	−0.644501	−	1.11631i	0.339916	−	0.940456i	$-0.389601\pi$
$24$		0			0
$25$	2.48931	−	4.31160i	0.497861	−	0.862321i
$26$	−0.205252	−	0.355508i	−0.0402533	−	0.0697208i
$27$		0			0
$28$	−5.16746	+	2.77798i	−0.976559	+	0.524989i
$29$	−4.93514			−0.916433			−0.458217	−	0.888841i	$-0.651512\pi$
$29$	−4.93514			−0.916433			−0.458217	+	0.888841i	$0.651512\pi$
$30$		0			0
$31$	1.25890	−	2.18047i	0.226105	−	0.391625i	−0.730546	−	0.682864i	$-0.760734\pi$
$31$	1.25890	−	2.18047i	0.226105	−	0.391625i	0.956650	+	0.291239i	$0.0940675\pi$
$32$	−4.05873	+	7.02993i	−0.717490	+	1.24273i
$33$		0			0
$34$	−12.8786			−2.20867
$35$	0.0117348	−	0.386752i	0.00198354	−	0.0653730i
$36$		0			0
$37$	−3.50023	−	6.06257i	−0.575434	−	0.996681i	−0.995994	−	0.0894162i	$-0.971500\pi$
$37$	−3.50023	−	6.06257i	−0.575434	−	0.996681i	0.420560	−	0.907264i	$-0.361833\pi$
$38$	−7.10312	+	12.3030i	−1.15228	+	1.99581i
$39$		0			0
$40$	0.0326554	+	0.0565608i	0.00516327	+	0.00894304i
$41$	2.31790			0.361996			0.180998	−	0.983483i	$-0.442067\pi$
$41$	2.31790			0.361996			0.180998	+	0.983483i	$0.442067\pi$
$42$		0			0
$43$	1.88199			0.287000			0.143500	−	0.989650i	$-0.454164\pi$
$43$	1.88199			0.287000			0.143500	+	0.989650i	$0.454164\pi$
$44$	1.84497	+	3.19558i	0.278140	+	0.481752i
$45$		0			0
$46$	6.34765	−	10.9944i	0.935910	−	1.62104i
$47$	−0.905887	−	1.56904i	−0.132137	−	0.228868i	0.792363	−	0.610050i	$-0.208851\pi$
$47$	−0.905887	−	1.56904i	−0.132137	−	0.228868i	−0.924500	+	0.381181i	$0.875517\pi$
$48$		0			0
$49$	3.12602	+	6.26322i	0.446575	+	0.894746i
$50$	10.2243			1.44593
$51$		0			0
$52$	0.221625	−	0.383865i	0.0307338	−	0.0532325i
$53$	2.67307	−	4.62989i	0.367174	−	0.635964i	−0.621948	−	0.783058i	$-0.713659\pi$
$53$	2.67307	−	4.62989i	0.367174	−	0.635964i	0.989123	+	0.147094i	$0.0469920\pi$
$54$		0			0
$55$	−0.243359			−0.0328145
$56$	−1.00486	−	0.621534i	−0.134280	−	0.0830560i
$57$		0			0
$58$	−5.06752	−	8.77720i	−0.665398	−	1.15250i
$59$	−2.28549	+	3.95859i	−0.297546	+	0.515364i	−0.975574	−	0.219672i	$-0.929501\pi$
$59$	−2.28549	+	3.95859i	−0.297546	+	0.515364i	0.678028	+	0.735036i	$0.262835\pi$
$60$		0			0
$61$	0.339138	+	0.587404i	0.0434221	+	0.0752094i	0.886920	−	0.461924i	$-0.152841\pi$
$61$	0.339138	+	0.587404i	0.0434221	+	0.0752094i	−0.843498	+	0.537133i	$0.819507\pi$
$62$	5.17066			0.656674
$63$		0			0
$64$	−9.63481			−1.20435
$65$	0.0146166	+	0.0253167i	0.00181296	+	0.00314015i
$66$		0			0
$67$	3.09342	−	5.35796i	0.377921	−	0.654579i	−0.612838	−	0.790208i	$-0.709972\pi$
$67$	3.09342	−	5.35796i	0.377921	−	0.654579i	0.990760	+	0.135630i	$0.0433057\pi$
$68$	−6.95296	−	12.0429i	−0.843170	−	1.46041i
$69$		0			0
$70$	0.699891	−	0.376255i	0.0836530	−	0.0449711i
$71$	−1.27749			−0.151611			−0.0758053	−	0.997123i	$-0.524153\pi$
$71$	−1.27749			−0.151611			−0.0758053	+	0.997123i	$0.524153\pi$
$72$		0			0
$73$	−0.778603	+	1.34858i	−0.0911286	+	0.157839i	−0.907986	−	0.419000i	$-0.862381\pi$
$73$	−0.778603	+	1.34858i	−0.0911286	+	0.157839i	0.816858	+	0.576839i	$0.195714\pi$
$74$	7.18823	−	12.4504i	0.835614	−	1.44733i
$75$		0			0
$76$	−15.3394			−1.75955
$77$	3.87780	−	2.08467i	0.441917	−	0.237570i
$78$		0			0
$79$	−6.39787	−	11.0814i	−0.719817	−	1.24676i	−0.961072	−	0.276298i	$-0.910892\pi$
$79$	−6.39787	−	11.0814i	−0.719817	−	1.24676i	0.241255	−	0.970462i	$-0.422441\pi$
$80$	0.257231	−	0.445537i	0.0287593	−	0.0498126i
$81$		0			0
$82$	2.38008	+	4.12241i	0.262835	+	0.455244i
$83$	7.51374			0.824740			0.412370	−	0.911016i	$-0.364701\pi$
$83$	7.51374			0.824740			0.412370	+	0.911016i	$0.364701\pi$
$84$		0			0
$85$	0.917122			0.0994758
$86$	1.93247	+	3.34713i	0.208383	+	0.360930i
$87$		0			0
$88$	−0.371566	+	0.643571i	−0.0396090	+	0.0686048i
$89$	−4.53394	−	7.85301i	−0.480597	−	0.832418i	0.519155	−	0.854680i	$-0.326247\pi$
$89$	−4.53394	−	7.85301i	−0.480597	−	0.832418i	−0.999752	+	0.0222619i	$0.992913\pi$
$90$		0			0
$91$	−0.449777	−	0.278199i	−0.0471494	−	0.0291632i
$92$	13.7080			1.42915
$93$		0			0
$94$	1.86037	−	3.22226i	0.191883	−	0.332350i
$95$	0.505833	−	0.876128i	0.0518973	−	0.0898888i
$96$		0			0
$97$	7.97028			0.809259			0.404630	−	0.914481i	$-0.367400\pi$
$97$	7.97028			0.809259			0.404630	+	0.914481i	$0.367400\pi$
$98$	−7.92933	+	11.9909i	−0.800983	+	1.21126i
$99$		0			0
$100$	5.51993	+	9.56080i	0.551993	+	0.956080i
$101$	7.42150	−	12.8544i	0.738467	−	1.27906i	−0.214719	−	0.976676i	$-0.568883\pi$
$101$	7.42150	−	12.8544i	0.738467	−	1.27906i	0.953186	−	0.302386i	$-0.0977832\pi$
$102$		0			0
$103$	0.101974	+	0.176624i	0.0100478	+	0.0174033i	0.871006	−	0.491273i	$-0.163468\pi$
$103$	0.101974	+	0.176624i	0.0100478	+	0.0174033i	−0.860958	+	0.508676i	$0.830135\pi$
$104$	0.0892677			0.00875342
$105$		0			0
$106$	10.9791			1.06638
$107$	−3.48444	−	6.03524i	−0.336854	−	0.583448i	0.646985	−	0.762503i	$-0.276030\pi$
$107$	−3.48444	−	6.03524i	−0.336854	−	0.583448i	−0.983839	+	0.179054i	$0.942696\pi$
$108$		0			0
$109$	3.33058	−	5.76874i	0.319012	−	0.552545i	−0.661270	−	0.750148i	$-0.729982\pi$
$109$	3.33058	−	5.76874i	0.319012	−	0.552545i	0.980282	+	0.197603i	$0.0633157\pi$
$110$	−0.249886	−	0.432816i	−0.0238257	−	0.0412674i
$111$		0			0
$112$	−0.282269	+	9.30293i	−0.0266719	+	0.879044i
$113$	−0.0386468			−0.00363558			−0.00181779	−	0.999998i	$-0.500579\pi$
$113$	−0.0386468			−0.00363558			−0.00181779	+	0.999998i	$0.500579\pi$
$114$		0			0
$115$	−0.452033	+	0.782945i	−0.0421523	+	0.0730100i
$116$	5.47174	−	9.47733i	0.508038	−	0.879948i
$117$		0			0
$118$	−9.38718			−0.864160
$119$	−14.6139	+	7.85629i	−1.33965	+	0.720185i
$120$		0			0
$121$	4.11548	+	7.12823i	0.374135	+	0.648021i
$122$	−0.696469	+	1.20632i	−0.0630553	+	0.109215i
$123$		0			0
$124$	2.79155	+	4.83511i	0.250689	+	0.434206i
$125$	−1.45933			−0.130526
$126$		0			0
$127$	13.4788			1.19605			0.598027	−	0.801476i	$-0.295952\pi$
$127$	13.4788			1.19605			0.598027	+	0.801476i	$0.295952\pi$
$128$	−1.77577	−	3.07572i	−0.156957	−	0.271858i
$129$		0			0
$130$	−0.0300173	+	0.0519914i	−0.00263269	+	0.00455995i
$131$	−9.91665	−	17.1761i	−0.866422	−	1.50069i	−0.865628	−	0.500687i	$-0.833081\pi$
$131$	−9.91665	−	17.1761i	−0.866422	−	1.50069i	−0.000793988	−	1.00000i	$-0.500253\pi$
$132$		0			0
$133$	−0.555068	+	18.2938i	−0.0481305	+	1.58627i
$134$	12.7056			1.09759
$135$		0			0
$136$	1.40028	−	2.42536i	0.120073	−	0.207973i
$137$	−3.22255	+	5.58162i	−0.275321	+	0.476870i	−0.970216	−	0.242241i	$-0.922117\pi$
$137$	−3.22255	+	5.58162i	−0.275321	+	0.476870i	0.694895	+	0.719111i	$0.255451\pi$
$138$		0			0
$139$	−12.5305			−1.06283			−0.531413	−	0.847113i	$-0.678339\pi$
$139$	−12.5305			−1.06283			−0.531413	+	0.847113i	$0.678339\pi$
$140$	0.729698	+	0.451338i	0.0616707	+	0.0381450i
$141$		0			0
$142$	−1.31176	−	2.27203i	−0.110080	−	0.190665i
$143$	−0.166313	+	0.288063i	−0.0139078	+	0.0240890i
$144$		0			0
$145$	0.360872	+	0.625048i	0.0299688	+	0.0519074i
$146$	−3.19795			−0.264664
$147$		0			0
$148$	15.5232			1.27600
$149$	8.88364	+	15.3869i	0.727776	+	1.26054i	0.957821	+	0.287365i	$0.0927792\pi$
$149$	8.88364	+	15.3869i	0.727776	+	1.26054i	−0.230045	+	0.973180i	$0.573887\pi$
$150$		0			0
$151$	−4.23300	+	7.33177i	−0.344476	+	0.596651i	−0.985259	−	0.171072i	$-0.945277\pi$
$151$	−4.23300	+	7.33177i	−0.344476	+	0.596651i	0.640782	+	0.767723i	$0.278610\pi$
$152$	−1.54463	−	2.67538i	−0.125286	−	0.217002i
$153$		0			0
$154$	7.68942	+	4.75612i	0.619631	+	0.383259i
$155$	−0.368217			−0.0295759
$156$		0			0
$157$	−2.84968	+	4.93579i	−0.227429	+	0.393919i	−0.957045	−	0.289938i	$-0.906365\pi$
$157$	−2.84968	+	4.93579i	−0.227429	+	0.393919i	0.729616	+	0.683857i	$0.239699\pi$
$158$	13.1390	−	22.7573i	1.04528	−	1.81048i
$159$		0			0
$160$	1.18714			0.0938520
$161$	0.496032	−	16.3481i	0.0390928	−	1.28841i
$162$		0			0
$163$	−1.06267	−	1.84060i	−0.0832349	−	0.144167i	0.821403	−	0.570349i	$-0.193192\pi$
$163$	−1.06267	−	1.84060i	−0.0832349	−	0.144167i	−0.904638	+	0.426181i	$0.859859\pi$
$164$	−2.56993	+	4.45125i	−0.200678	+	0.347584i
$165$		0			0
$166$	7.71528	+	13.3632i	0.598821	+	1.03719i
$167$	−11.5745			−0.895659			−0.447829	−	0.894119i	$-0.647803\pi$
$167$	−11.5745			−0.895659			−0.447829	+	0.894119i	$0.647803\pi$
$168$		0			0
$169$	−12.9600			−0.996926
$170$	0.941721	+	1.63111i	0.0722267	+	0.125100i
$171$		0			0
$172$	−2.08661	+	3.61412i	−0.159103	+	0.275574i
$173$	−7.95546	−	13.7793i	−0.604842	−	1.04762i	−0.992076	−	0.125636i	$-0.959903\pi$
$173$	−7.95546	−	13.7793i	−0.604842	−	1.04762i	0.387234	−	0.921981i	$-0.373430\pi$
$174$		0			0
$175$	11.6019	−	6.23709i	0.877023	−	0.471480i
$176$	5.85375			0.441243
$177$		0			0
$178$	9.31110	−	16.1273i	0.697897	−	1.20879i
$179$	−3.87665	+	6.71456i	−0.289755	+	0.501870i	−0.973751	−	0.227615i	$-0.926907\pi$
$179$	−3.87665	+	6.71456i	−0.289755	+	0.501870i	0.683996	+	0.729485i	$0.260240\pi$
$180$		0			0
$181$	−12.1618			−0.903982			−0.451991	−	0.892022i	$-0.649286\pi$
$181$	−12.1618			−0.903982			−0.451991	+	0.892022i	$0.649286\pi$
$182$	0.0329390	−	1.08559i	0.00244160	−	0.0804696i
$183$		0			0
$184$	1.38035	+	2.39084i	0.101761	+	0.176255i
$185$	−0.511893	+	0.886625i	−0.0376351	+	0.0651860i
$186$		0			0
$187$	5.21769	+	9.03730i	0.381555	+	0.660873i
$188$	4.01754			0.293009
$189$		0			0
$190$	2.07760			0.150725
$191$	−2.48383	−	4.30211i	−0.179723	−	0.311290i	0.762062	−	0.647504i	$-0.224187\pi$
$191$	−2.48383	−	4.30211i	−0.179723	−	0.311290i	−0.941786	+	0.336214i	$0.890854\pi$
$192$		0			0
$193$	7.45221	−	12.9076i	0.536422	−	0.929110i	−0.462671	−	0.886530i	$-0.653109\pi$
$193$	7.45221	−	12.9076i	0.536422	−	0.929110i	0.999093	−	0.0425800i	$-0.0135577\pi$
$194$	8.18406	+	14.1752i	0.587581	+	1.01772i
$195$		0			0
$196$	−15.4937	−	0.941080i	−1.10669	−	0.0672200i
$197$	21.2608			1.51477			0.757386	−	0.652968i	$-0.226476\pi$
$197$	21.2608			1.51477			0.757386	+	0.652968i	$0.226476\pi$
$198$		0			0
$199$	−9.97208	+	17.2722i	−0.706902	+	1.22439i	0.259098	+	0.965851i	$0.416575\pi$
$199$	−9.97208	+	17.2722i	−0.706902	+	1.22439i	−0.966001	+	0.258540i	$0.916759\pi$
$200$	−1.11168	+	1.92549i	−0.0786077	+	0.136152i
$201$		0			0
$202$	30.4823			2.14472
$203$	−11.1046	−	6.86852i	−0.779393	−	0.482076i
$204$		0			0
$205$	−0.169492	−	0.293568i	−0.0118378	−	0.0205037i
$206$	−0.209419	+	0.362724i	−0.0145909	+	0.0252722i
$207$		0			0
$208$	−0.351587	−	0.608967i	−0.0243782	−	0.0422243i
$209$	11.5111			0.796241
$210$		0			0
$211$	−23.5139			−1.61876			−0.809381	−	0.587284i	$-0.800197\pi$
$211$	−23.5139			−1.61876			−0.809381	+	0.587284i	$0.800197\pi$
$212$	5.92742	+	10.2666i	0.407097	+	0.705112i
$213$		0			0
$214$	7.15581	−	12.3942i	0.489161	−	0.847252i
$215$	−0.137616	−	0.238358i	−0.00938535	−	0.0162559i
$216$		0			0
$217$	5.86735	−	3.15424i	0.398302	−	0.214123i
$218$	13.6797			0.926504
$219$		0			0
$220$	0.269819	−	0.467340i	0.0181912	−	0.0315081i
$221$	0.626768	−	1.08559i	0.0421610	−	0.0730250i
$222$		0			0
$223$	−4.06104			−0.271947			−0.135974	−	0.990712i	$-0.543416\pi$
$223$	−4.06104			−0.271947			−0.135974	+	0.990712i	$0.543416\pi$
$224$	−18.9166	+	10.1694i	−1.26392	+	0.679470i
$225$		0			0
$226$	−0.0396834	−	0.0687336i	−0.00263970	−	0.00457209i
$227$	−1.92643	+	3.33667i	−0.127861	+	0.221462i	−0.922848	−	0.385165i	$-0.874145\pi$
$227$	−1.92643	+	3.33667i	−0.127861	+	0.221462i	0.794986	+	0.606627i	$0.207478\pi$
$228$		0			0
$229$	−6.55812	−	11.3590i	−0.433373	−	0.750624i	0.563788	−	0.825919i	$-0.309343\pi$
$229$	−6.55812	−	11.3590i	−0.433373	−	0.750624i	−0.997161	+	0.0752952i	$0.976010\pi$
$230$	−1.85663			−0.122423
$231$		0			0
$232$	2.20395			0.144696
$233$	8.75115	+	15.1574i	0.573307	+	0.992997i	0.996223	+	0.0868284i	$0.0276732\pi$
$233$	8.75115	+	15.1574i	0.573307	+	0.992997i	−0.422916	+	0.906169i	$0.638993\pi$
$234$		0			0
$235$	−0.132482	+	0.229466i	−0.00864218	+	0.0149687i
$236$	−5.06798	−	8.77801i	−0.329898	−	0.571400i
$237$		0			0
$238$	−28.9784	−	17.9239i	−1.87839	−	1.16183i
$239$	7.31714			0.473306			0.236653	−	0.971594i	$-0.423949\pi$
$239$	7.31714			0.473306			0.236653	+	0.971594i	$0.423949\pi$
$240$		0			0
$241$	−3.11553	+	5.39626i	−0.200689	+	0.347604i	−0.948751	−	0.316026i	$-0.897651\pi$
$241$	−3.11553	+	5.39626i	−0.200689	+	0.347604i	0.748062	+	0.663629i	$0.230985\pi$
$242$	−8.45174	+	14.6389i	−0.543299	+	0.941021i
$243$		0			0
$244$	−1.50405			−0.0962868
$245$	0.564669	−	0.853903i	0.0360754	−	0.0545539i
$246$		0			0
$247$	−0.691380	−	1.19751i	−0.0439915	−	0.0761954i
$248$	−0.562201	+	0.973761i	−0.0356998	+	0.0618339i
$249$		0			0
$250$	−1.49847	−	2.59543i	−0.0947717	−	0.164149i
$251$	−5.65283			−0.356803			−0.178402	−	0.983958i	$-0.557093\pi$
$251$	−5.65283			−0.356803			−0.178402	+	0.983958i	$0.557093\pi$
$252$		0			0
$253$	−10.2868			−0.646727
$254$	13.8404	+	23.9722i	0.868422	+	1.50415i
$255$		0			0
$256$	−5.98801	+	10.3715i	−0.374250	+	0.648221i
$257$	5.90082	+	10.2205i	0.368083	+	0.637539i	0.989266	−	0.146127i	$-0.0466808\pi$
$257$	5.90082	+	10.2205i	0.368083	+	0.637539i	−0.621183	+	0.783666i	$0.713347\pi$
$258$		0			0
$259$	0.561718	−	18.5129i	0.0349035	−	1.15034i
$260$	−0.0648233			−0.00402017
$261$		0			0
$262$	20.3653	−	35.2737i	1.25817	−	2.17922i
$263$	−11.1200	+	19.2605i	−0.685691	+	1.18765i	0.287528	+	0.957772i	$0.407166\pi$
$263$	−11.1200	+	19.2605i	−0.685691	+	1.18765i	−0.973219	+	0.229879i	$0.926167\pi$
$264$		0			0
$265$	−0.781849			−0.0480286
$266$	−33.1056	+	17.7973i	−2.02983	+	1.09122i
$267$		0			0
$268$	6.85953	+	11.8810i	0.419012	+	0.725750i
$269$	1.19442	−	2.06880i	0.0728251	−	0.126137i	−0.827313	−	0.561741i	$-0.810132\pi$
$269$	1.19442	−	2.06880i	0.0728251	−	0.126137i	0.900138	+	0.435604i	$0.143465\pi$
$270$		0			0
$271$	−11.6129	−	20.1142i	−0.705435	−	1.22185i	−0.966534	−	0.256537i	$-0.917419\pi$
$271$	−11.6129	−	20.1142i	−0.705435	−	1.22185i	0.261100	−	0.965312i	$-0.415915\pi$
$272$	−22.0605			−1.33761
$273$		0			0
$274$	−13.2359			−0.799612
$275$	−4.14231	−	7.17469i	−0.249790	−	0.432650i
$276$		0			0
$277$	2.30900	−	3.99931i	0.138734	−	0.240295i	−0.788283	−	0.615312i	$-0.789030\pi$
$277$	2.30900	−	3.99931i	0.138734	−	0.240295i	0.927018	+	0.375017i	$0.122363\pi$
$278$	−12.8666	−	22.2857i	−0.771690	−	1.33661i
$279$		0			0
$280$	−0.00524055	+	0.172716i	−0.000313183	+	0.0103218i
$281$	11.8168			0.704933			0.352466	−	0.935825i	$-0.385343\pi$
$281$	11.8168			0.704933			0.352466	+	0.935825i	$0.385343\pi$
$282$		0			0
$283$	−7.92483	+	13.7262i	−0.471082	+	0.815939i	−0.999453	−	0.0330753i	$-0.989470\pi$
$283$	−7.92483	+	13.7262i	−0.471082	+	0.815939i	0.528370	+	0.849014i	$0.322803\pi$
$284$	1.41639	−	2.45327i	0.0840475	−	0.145575i
$285$		0			0
$286$	−0.683097			−0.0403924
$287$	5.21555	+	3.22596i	0.307864	+	0.190422i
$288$		0			0
$289$	−11.1634	−	19.3355i	−0.656669	−	1.13738i
$290$	−0.741102	+	1.28363i	−0.0435190	+	0.0753772i
$291$		0			0
$292$	−1.72652	−	2.99042i	−0.101037	−	0.175001i
$293$	14.0961			0.823502			0.411751	−	0.911296i	$-0.364917\pi$
$293$	14.0961			0.823502			0.411751	+	0.911296i	$0.364917\pi$
$294$		0			0
$295$	0.668487			0.0389208
$296$	1.56314	+	2.70744i	0.0908557	+	0.157367i
$297$		0			0
$298$	−18.2438	+	31.5993i	−1.05684	+	1.83050i
$299$	0.617846	+	1.07014i	0.0357310	+	0.0618878i
$300$		0			0
$301$	4.23468	+	2.61927i	0.244083	+	0.150972i
$302$	−17.3861			−1.00046
$303$		0			0
$304$	−12.1673	+	21.0744i	−0.697843	+	1.20870i
$305$	0.0495974	−	0.0859053i	0.00283994	−	0.00491892i
$306$		0			0
$307$	27.3916			1.56332			0.781660	−	0.623704i	$-0.214373\pi$
$307$	27.3916			1.56332			0.781660	+	0.623704i	$0.214373\pi$
$308$	−0.296082	+	9.75818i	−0.0168708	+	0.556024i
$309$		0			0
$310$	−0.378093	−	0.654877i	−0.0214742	−	0.0371945i
$311$	−7.02785	+	12.1726i	−0.398513	+	0.690244i	−0.993543	−	0.113459i	$-0.963807\pi$
$311$	−7.02785	+	12.1726i	−0.398513	+	0.690244i	0.595030	+	0.803704i	$0.297140\pi$
$312$		0			0
$313$	−10.8723	−	18.8314i	−0.614540	−	1.06441i	−0.990465	−	0.137764i	$-0.956008\pi$
$313$	−10.8723	−	18.8314i	−0.614540	−	1.06441i	0.375925	−	0.926650i	$-0.377325\pi$
$314$	−11.7045			−0.660520
$315$		0			0
$316$	28.3740			1.59616
$317$	4.28148	+	7.41575i	0.240472	+	0.416510i	0.960849	−	0.277073i	$-0.0893644\pi$
$317$	4.28148	+	7.41575i	0.240472	+	0.416510i	−0.720377	+	0.693583i	$0.756031\pi$
$318$		0			0
$319$	−4.10614	+	7.11204i	−0.229900	+	0.398198i
$320$	0.704524	+	1.22027i	0.0393841	+	0.0682153i
$321$		0			0
$322$	29.5845	−	15.9044i	1.64868	−	0.886316i
$323$	−43.3808			−2.41377
$324$		0			0
$325$	−0.497589	+	0.861850i	−0.0276013	+	0.0478068i
$326$	2.18235	−	3.77995i	0.120869	−	0.209352i
$327$		0			0
$328$	−1.03514			−0.0571558
$329$	0.145377	−	4.79130i	0.00801490	−	0.264153i
$330$		0			0
$331$	−5.42360	−	9.39396i	−0.298108	−	0.516339i	0.677595	−	0.735435i	$-0.263022\pi$
$331$	−5.42360	−	9.39396i	−0.298108	−	0.516339i	−0.975703	+	0.219097i	$0.929689\pi$
$332$	−8.33070	+	14.4292i	−0.457207	+	0.791905i
$333$		0			0
$334$	−11.8849	−	20.5853i	−0.650314	−	1.12638i
$335$	−0.904798			−0.0494344
$336$		0			0
$337$	−3.34822			−0.182389			−0.0911945	−	0.995833i	$-0.529069\pi$
$337$	−3.34822			−0.182389			−0.0911945	+	0.995833i	$0.529069\pi$
$338$	−13.3077	−	23.0496i	−0.723842	−	1.25373i
$339$		0			0
$340$	−1.01684	+	1.76122i	−0.0551459	+	0.0955154i
$341$	−2.09486	−	3.62840i	−0.113443	−	0.196489i
$342$		0			0
$343$	−1.68298	+	18.4436i	−0.0908723	+	0.995863i
$344$	−0.840462			−0.0453147
$345$		0			0
$346$	16.3377	−	28.2977i	0.878319	−	1.52129i
$347$	−5.76652	+	9.98790i	−0.309563	+	0.536178i	−0.978267	−	0.207350i	$-0.933516\pi$
$347$	−5.76652	+	9.98790i	−0.309563	+	0.536178i	0.668704	+	0.743529i	$0.266849\pi$
$348$		0			0
$349$	8.89834			0.476317			0.238159	−	0.971226i	$-0.423456\pi$
$349$	8.89834			0.476317			0.238159	+	0.971226i	$0.423456\pi$
$350$	23.0058	+	14.2297i	1.22971	+	0.760612i
$351$		0			0
$352$	6.75390	+	11.6981i	0.359984	+	0.623511i
$353$	−1.32349	+	2.29236i	−0.0704424	+	0.122010i	−0.899095	−	0.437753i	$-0.855774\pi$
$353$	−1.32349	+	2.29236i	−0.0704424	+	0.122010i	0.828653	+	0.559763i	$0.189108\pi$
$354$		0			0
$355$	0.0934139	+	0.161798i	0.00495790	+	0.00858733i
$356$	20.1076			1.06570
$357$		0			0
$358$	−15.9225			−0.841533
$359$	12.9835	+	22.4882i	0.685245	+	1.18688i	0.973360	+	0.229284i	$0.0736384\pi$
$359$	12.9835	+	22.4882i	0.685245	+	1.18688i	−0.288114	+	0.957596i	$0.593028\pi$
$360$		0			0
$361$	−14.4264	+	24.9873i	−0.759286	+	1.31512i
$362$	−12.4880	−	21.6299i	−0.656357	−	1.13684i
$363$		0			0
$364$	1.03293	−	0.555293i	0.0541402	−	0.0291053i
$365$	0.227735			0.0119202
$366$		0			0
$367$	−8.79371	+	15.2312i	−0.459028	+	0.795060i	−0.998910	−	0.0466808i	$-0.985136\pi$
$367$	−8.79371	+	15.2312i	−0.459028	+	0.795060i	0.539882	+	0.841741i	$0.318469\pi$
$368$	10.8732	−	18.8330i	0.566806	−	0.981736i
$369$		0			0
$370$	−2.10249			−0.109303
$371$	12.4584	−	6.69752i	0.646807	−	0.347718i
$372$		0			0
$373$	−0.407538	−	0.705876i	−0.0211015	−	0.0365489i	0.855282	−	0.518163i	$-0.173384\pi$
$373$	−0.407538	−	0.705876i	−0.0211015	−	0.0365489i	−0.876383	+	0.481614i	$0.840051\pi$
$374$	−10.7153	+	18.5594i	−0.554074	+	0.959684i
$375$		0			0
$376$	0.404553	+	0.700707i	0.0208632	+	0.0361362i
$377$	0.986490			0.0508068
$378$		0			0
$379$	−20.4312			−1.04948			−0.524741	−	0.851262i	$-0.675838\pi$
$379$	−20.4312			−1.04948			−0.524741	+	0.851262i	$0.675838\pi$
$380$	1.12166	+	1.94278i	0.0575401	+	0.0996624i
$381$		0			0
$382$	5.10090	−	8.83501i	0.260985	−	0.452039i
$383$	8.94638	+	15.4956i	0.457139	+	0.791788i	0.998808	−	0.0488039i	$-0.0155409\pi$
$383$	8.94638	+	15.4956i	0.457139	+	0.791788i	−0.541670	+	0.840591i	$0.682208\pi$
$384$		0			0
$385$	−0.547585	−	0.338696i	−0.0279075	−	0.0172616i
$386$	30.6084			1.55793
$387$		0			0
$388$	−8.83688	+	15.3059i	−0.448625	+	0.777041i
$389$	7.81392	−	13.5341i	0.396181	−	0.686206i	−0.597070	−	0.802189i	$-0.703669\pi$
$389$	7.81392	−	13.5341i	0.396181	−	0.686206i	0.993251	+	0.115983i	$0.0370018\pi$
$390$		0			0
$391$	38.7669			1.96053
$392$	−1.39603	−	2.79705i	−0.0705100	−	0.141272i
$393$		0			0
$394$	21.8311	+	37.8126i	1.09984	+	1.90497i
$395$	−0.935661	+	1.62061i	−0.0470782	+	0.0815419i
$396$		0			0
$397$	9.63064	+	16.6808i	0.483348	+	0.837183i	0.999817	−	0.0191225i	$-0.00608724\pi$
$397$	9.63064	+	16.6808i	0.483348	+	0.837183i	−0.516469	+	0.856306i	$0.672754\pi$
$398$	−40.9582			−2.05305
$399$		0			0
$400$	17.5137			0.875687
$401$	7.15064	+	12.3853i	0.357086	+	0.618491i	0.987473	−	0.157790i	$-0.0504370\pi$
$401$	7.15064	+	12.3853i	0.357086	+	0.618491i	−0.630387	+	0.776281i	$0.717104\pi$
$402$		0			0
$403$	−0.251642	+	0.435857i	−0.0125352	+	0.0217116i
$404$	16.4569	+	28.5041i	0.818760	+	1.41813i
$405$		0			0
$406$	0.813237	−	26.8024i	0.0403603	−	1.33018i
$407$	−11.6490			−0.577422
$408$		0			0
$409$	−15.9305	+	27.5924i	−0.787712	+	1.36436i	0.139654	+	0.990200i	$0.455401\pi$
$409$	−15.9305	+	27.5924i	−0.787712	+	1.36436i	−0.927366	+	0.374156i	$0.877932\pi$
$410$	0.348076	−	0.602885i	0.0171902	−	0.0297744i
$411$		0			0
$412$	−0.452247			−0.0222806
$413$	−10.6520	+	5.72643i	−0.524151	+	0.281779i
$414$		0			0
$415$	−0.549426	−	0.951633i	−0.0269702	−	0.0467138i
$416$	0.811304	−	1.40522i	0.0397774	−	0.0688965i
$417$		0			0
$418$	11.8199	+	20.4726i	0.578130	+	1.00135i
$419$	23.8960			1.16739			0.583697	−	0.811971i	$-0.301605\pi$
$419$	23.8960			1.16739			0.583697	+	0.811971i	$0.301605\pi$
$420$		0			0
$421$	2.44501			0.119163			0.0595813	−	0.998223i	$-0.481023\pi$
$421$	2.44501			0.119163			0.0595813	+	0.998223i	$0.481023\pi$
$422$	−24.1446	−	41.8197i	−1.17534	−	2.03575i
$423$		0			0
$424$	−1.19375	+	2.06763i	−0.0579734	+	0.100413i
$425$	15.6107	+	27.0385i	0.757230	+	1.31156i
$426$		0			0
$427$	−0.0544250	+	1.79372i	−0.00263381	+	0.0868043i
$428$	15.4532			0.746960
$429$		0			0
$430$	0.282615	−	0.489503i	0.0136289	−	0.0236059i
$431$	−2.46382	+	4.26746i	−0.118678	+	0.205556i	−0.919244	−	0.393688i	$-0.871199\pi$
$431$	−2.46382	+	4.26746i	−0.118678	+	0.205556i	0.800566	+	0.599244i	$0.204532\pi$
$432$		0			0
$433$	30.8539			1.48274			0.741371	−	0.671095i	$-0.234176\pi$
$433$	30.8539			1.48274			0.741371	+	0.671095i	$0.234176\pi$
$434$	11.6346	+	7.19630i	0.558477	+	0.345433i
$435$		0			0
$436$	7.38543	+	12.7919i	0.353698	+	0.612622i
$437$	21.3817	−	37.0341i	1.02282	−	1.77158i
$438$		0			0
$439$	−1.22411	−	2.12022i	−0.0584235	−	0.101192i	0.835334	−	0.549742i	$-0.185274\pi$
$439$	−1.22411	−	2.12022i	−0.0584235	−	0.101192i	−0.893758	+	0.448550i	$0.851941\pi$
$440$	0.108680			0.00518110
$441$		0			0
$442$	2.57432			0.122448
$443$	−13.1475	−	22.7722i	−0.624657	−	1.08194i	−0.988607	−	0.150520i	$-0.951905\pi$
$443$	−13.1475	−	22.7722i	−0.624657	−	1.08194i	0.363950	−	0.931419i	$-0.381428\pi$
$444$		0			0
$445$	−0.663069	+	1.14847i	−0.0314325	+	0.0544427i
$446$	−4.16996	−	7.22259i	−0.197453	−	0.341999i
$447$		0			0
$448$	−21.6794	−	13.4093i	−1.02426	−	0.633530i
$449$	38.7077			1.82673			0.913365	−	0.407141i	$-0.133474\pi$
$449$	38.7077			1.82673			0.913365	+	0.407141i	$0.133474\pi$
$450$		0			0
$451$	1.92854	−	3.34034i	0.0908116	−	0.157290i
$452$	0.0428488	−	0.0742163i	0.00201544	−	0.00349084i
$453$		0			0
$454$	−7.91239			−0.371347
$455$	−0.00234568	+	0.0773081i	−0.000109967	+	0.00362426i
$456$		0			0
$457$	4.57756	+	7.92856i	0.214129	+	0.370882i	0.953003	−	0.302961i	$-0.0979754\pi$
$457$	4.57756	+	7.92856i	0.214129	+	0.370882i	−0.738874	+	0.673844i	$0.764642\pi$
$458$	13.4681	−	23.3274i	0.629321	−	1.09002i
$459$		0			0
$460$	−1.00237	−	1.73615i	−0.0467355	−	0.0809483i
$461$	29.2304			1.36140			0.680698	−	0.732564i	$-0.261676\pi$
$461$	29.2304			1.36140			0.680698	+	0.732564i	$0.261676\pi$
$462$		0			0
$463$	16.4206			0.763131			0.381565	−	0.924342i	$-0.375385\pi$
$463$	16.4206			0.763131			0.381565	+	0.924342i	$0.375385\pi$
$464$	−8.68041	−	15.0349i	−0.402978	−	0.697978i
$465$		0			0
$466$	−17.9718	+	31.1280i	−0.832526	+	1.44198i
$467$	−7.68632	−	13.3131i	−0.355680	−	0.616057i	0.631554	−	0.775332i	$-0.282418\pi$
$467$	−7.68632	−	13.3131i	−0.355680	−	0.616057i	−0.987234	+	0.159276i	$0.949084\pi$
$468$		0			0
$469$	14.4175	−	7.75073i	0.665739	−	0.357895i
$470$	−0.544142			−0.0250994
$471$		0			0
$472$	1.02066	−	1.76784i	0.0469797	−	0.0813713i
$473$	1.56585	−	2.71213i	0.0719979	−	0.124704i
$474$		0			0
$475$	34.4399			1.58021
$476$	1.11581	−	36.7747i	0.0511432	−	1.68556i
$477$		0			0
$478$	7.51341	+	13.0136i	0.343655	+	0.595228i
$479$	−18.9646	+	32.8476i	−0.866513	+	1.50084i	−0.000975329		1.00000i	$0.500310\pi$
$479$	−18.9646	+	32.8476i	−0.866513	+	1.50084i	−0.865537	+	0.500844i	$0.833023\pi$
$480$		0			0
$481$	0.699663	+	1.21185i	0.0319019	+	0.0552557i
$482$	−12.7964			−0.582860
$483$		0			0
$484$	−18.2518			−0.829629
$485$	−0.582809	−	1.00946i	−0.0264640	−	0.0458370i
$486$		0			0
$487$	2.30247	−	3.98800i	0.104335	−	0.180714i	−0.809131	−	0.587628i	$-0.800062\pi$
$487$	2.30247	−	3.98800i	0.104335	−	0.180714i	0.913466	+	0.406914i	$0.133395\pi$
$488$	−0.151453	−	0.262324i	−0.00685595	−	0.0118749i
$489$		0			0
$490$	2.09849	+	0.127462i	0.0948001	+	0.00575813i
$491$	−30.3751			−1.37081			−0.685405	−	0.728162i	$-0.740375\pi$
$491$	−30.3751			−1.37081			−0.685405	+	0.728162i	$0.740375\pi$
$492$		0			0
$493$	15.4744	−	26.8024i	0.696932	−	1.20712i
$494$	1.41985	−	2.45925i	0.0638820	−	0.110647i
$495$		0			0
$496$	8.85709			0.397695
$497$	−2.87450	−	1.77796i	−0.128939	−	0.0797524i
$498$		0			0
$499$	−4.63436	−	8.02694i	−0.207462	−	0.359335i	0.743452	−	0.668789i	$-0.233187\pi$
$499$	−4.63436	−	8.02694i	−0.207462	−	0.359335i	−0.950914	+	0.309454i	$0.899854\pi$
$500$	1.61800	−	2.80246i	0.0723592	−	0.125330i
$501$		0			0
$502$	−5.80445	−	10.0536i	−0.259065	−	0.448715i
$503$	22.4230			0.999791			0.499896	−	0.866086i	$-0.333372\pi$
$503$	22.4230			0.999791			0.499896	+	0.866086i	$0.333372\pi$
$504$		0			0
$505$	−2.17072			−0.0965960
$506$	−10.5627	−	18.2952i	−0.469571	−	0.813321i
$507$		0			0
$508$	−14.9444	+	25.8844i	−0.663050	+	1.14844i
$509$	−18.8207	−	32.5984i	−0.834213	−	1.44490i	−0.894670	−	0.446728i	$-0.852589\pi$
$509$	−18.8207	−	32.5984i	−0.834213	−	1.44490i	0.0604572	−	0.998171i	$-0.480744\pi$
$510$		0			0
$511$	−3.62884	+	1.95083i	−0.160530	+	0.0862997i
$512$	−31.6976			−1.40085
$513$		0			0
$514$	−12.1182	+	20.9893i	−0.534511	+	0.925800i
$515$	0.0149133	−	0.0258306i	0.000657158	−	0.00113823i
$516$		0			0
$517$	−3.01487			−0.132594
$518$	33.5022	−	18.0105i	1.47200	−	0.791335i
$519$		0			0
$520$	−0.00652751	−	0.0113060i	−0.000286250	−	0.000495800i
$521$	−17.4641	+	30.2488i	−0.765117	+	1.32522i	0.175067	+	0.984556i	$0.443986\pi$
$521$	−17.4641	+	30.2488i	−0.765117	+	1.32522i	−0.940185	+	0.340666i	$0.889348\pi$
$522$		0			0
$523$	−11.8735	−	20.5656i	−0.519194	−	0.899270i	−0.999751	−	0.0223069i	$-0.992899\pi$
$523$	−11.8735	−	20.5656i	−0.519194	−	0.899270i	0.480557	−	0.876963i	$-0.340434\pi$
$524$	43.9795			1.92126
$525$		0			0
$526$	−45.6732			−1.99145
$527$	7.89468	+	13.6740i	0.343898	+	0.595648i
$528$		0			0
$529$	−7.60755	+	13.1767i	−0.330763	+	0.572898i
$530$	−0.802820	−	1.39053i	−0.0348723	−	0.0604006i
$531$		0			0
$532$	−34.5155	−	21.3488i	−1.49644	−	0.925587i
$533$	−0.463328			−0.0200690
$534$		0			0
$535$	−0.509585	+	0.882627i	−0.0220313	+	0.0381593i
$536$	−1.38147	+	2.39277i	−0.0596702	+	0.103352i
$537$		0			0
$538$	4.90583			0.211505
$539$	11.6269	+	0.706212i	0.500804	+	0.0304187i
$540$		0			0
$541$	8.58542	+	14.8704i	0.369116	+	0.639328i	0.989428	−	0.145028i	$-0.0463271\pi$
$541$	8.58542	+	14.8704i	0.369116	+	0.639328i	−0.620311	+	0.784356i	$0.712994\pi$
$542$	23.8488	−	41.3074i	1.02439	−	1.77430i
$543$		0			0
$544$	−25.4527	−	44.0854i	−1.09128	−	1.89015i
$545$	−0.974166			−0.0417287
$546$		0			0
$547$	20.0091			0.855529			0.427765	−	0.903890i	$-0.359301\pi$
$547$	20.0091			0.855529			0.427765	+	0.903890i	$0.359301\pi$
$548$	−7.14586	−	12.3770i	−0.305256	−	0.528719i
$549$		0			0
$550$	8.50683	−	14.7343i	0.362732	−	0.628271i
$551$	−17.0696	−	29.5654i	−0.727190	−	1.25953i
$552$		0			0
$553$	1.02673	−	33.8388i	0.0436611	−	1.43897i
$554$	9.48374			0.402926
$555$		0			0
$556$	13.8930	−	24.0633i	0.589193	−	1.02051i
$557$	0.122740	−	0.212593i	0.00520068	−	0.00900784i	−0.863413	−	0.504497i	$-0.831678\pi$
$557$	0.122740	−	0.212593i	0.00520068	−	0.00900784i	0.868614	+	0.495489i	$0.165011\pi$
$558$		0			0
$559$	−0.376192			−0.0159112
$560$	1.19888	−	0.644507i	0.0506619	−	0.0272354i
$561$		0			0
$562$	12.1338	+	21.0163i	0.511833	+	0.886520i
$563$	−22.1255	+	38.3224i	−0.932477	+	1.61510i	−0.153404	+	0.988164i	$0.549024\pi$
$563$	−22.1255	+	38.3224i	−0.932477	+	1.61510i	−0.779073	+	0.626934i	$0.784310\pi$
$564$		0			0
$565$	0.00282596	+	0.00489471i	0.000118889	+	0.000205922i
$566$	−32.5496			−1.36816
$567$		0			0
$568$	0.570506			0.0239379
$569$	−2.76767	−	4.79374i	−0.116027	−	0.200964i	0.802163	−	0.597105i	$-0.203682\pi$
$569$	−2.76767	−	4.79374i	−0.116027	−	0.200964i	−0.918190	+	0.396141i	$0.870349\pi$
$570$		0			0
$571$	2.05191	−	3.55400i	0.0858696	−	0.148730i	−0.819892	−	0.572518i	$-0.805966\pi$
$571$	2.05191	−	3.55400i	0.0858696	−	0.148730i	0.905761	+	0.423788i	$0.139300\pi$
$572$	−0.368793	−	0.638768i	−0.0154200	−	0.0267082i
$573$		0			0
$574$	−0.381956	+	12.5884i	−0.0159425	+	0.525429i
$575$	−30.7770			−1.28349
$576$		0			0
$577$	−2.82275	+	4.88915i	−0.117513	+	0.203538i	−0.918781	−	0.394767i	$-0.870825\pi$
$577$	−2.82275	+	4.88915i	−0.117513	+	0.203538i	0.801269	+	0.598305i	$0.204159\pi$
$578$	22.9256	−	39.7083i	0.953579	−	1.65165i
$579$		0			0
$580$	−1.60044			−0.0664545
$581$	16.9068	+	10.4573i	0.701411	+	0.433842i
$582$		0			0
$583$	−4.44809	−	7.70433i	−0.184221	−	0.319081i
$584$	0.347710	−	0.602252i	0.0143884	−	0.0249214i
$585$		0			0
$586$	14.4742	+	25.0700i	0.597923	+	1.03563i
$587$	18.7329			0.773189			0.386595	−	0.922250i	$-0.373651\pi$
$587$	18.7329			0.773189			0.386595	+	0.922250i	$0.373651\pi$
$588$		0			0
$589$	17.4170			0.717657
$590$	0.686417	+	1.18891i	0.0282594	+	0.0489466i
$591$		0			0
$592$	12.3131	−	21.3269i	0.506065	−	0.876530i
$593$	9.43516	+	16.3422i	0.387456	+	0.671093i	0.992107	−	0.125398i	$-0.0400207\pi$
$593$	9.43516	+	16.3422i	0.387456	+	0.671093i	−0.604651	+	0.796491i	$0.706687\pi$
$594$		0			0
$595$	2.06363	+	1.27641i	0.0846005	+	0.0523277i
$596$	−39.3982			−1.61381
$597$		0			0
$598$	−1.26884	+	2.19769i	−0.0518866	+	0.0898702i
$599$	1.33726	−	2.31620i	0.0546388	−	0.0946372i	−0.837412	−	0.546572i	$-0.815933\pi$
$599$	1.33726	−	2.31620i	0.0546388	−	0.0946372i	0.892051	+	0.451934i	$0.149266\pi$
$600$		0			0
$601$	13.2143			0.539023			0.269511	−	0.962997i	$-0.413138\pi$
$601$	13.2143			0.539023			0.269511	+	0.962997i	$0.413138\pi$
$602$	−0.310123	+	10.2209i	−0.0126397	+	0.416575i
$603$		0			0
$604$	−9.38650	−	16.2579i	−0.381931	−	0.661524i
$605$	0.601872	−	1.04247i	0.0244696	−	0.0423825i
$606$		0			0
$607$	−12.9026	−	22.3480i	−0.523701	−	0.907076i	−0.999619	−	0.0275869i	$-0.991218\pi$
$607$	−12.9026	−	22.3480i	−0.523701	−	0.907076i	0.475919	−	0.879489i	$-0.342116\pi$
$608$	−56.1532			−2.27731
$609$		0			0
$610$	0.203711			0.00824802
$611$	0.181079	+	0.313637i	0.00732565	+	0.0126884i
$612$		0			0
$613$	13.4766	−	23.3422i	0.544316	−	0.942784i	−0.454333	−	0.890832i	$-0.650122\pi$
$613$	13.4766	−	23.3422i	0.544316	−	0.942784i	0.998650	−	0.0519519i	$-0.0165443\pi$
$614$	28.1263	+	48.7162i	1.13509	+	1.96603i
$615$		0			0
$616$	−1.73176	+	0.930978i	−0.0697746	+	0.0375102i
$617$	−9.53175			−0.383734			−0.191867	−	0.981421i	$-0.561454\pi$
$617$	−9.53175			−0.383734			−0.191867	+	0.981421i	$0.561454\pi$
$618$		0			0
$619$	−17.3536	+	30.0573i	−0.697499	+	1.20810i	0.271832	+	0.962345i	$0.412370\pi$
$619$	−17.3536	+	30.0573i	−0.697499	+	1.20810i	−0.969331	+	0.245759i	$0.920963\pi$
$620$	0.408253	−	0.707114i	0.0163958	−	0.0283984i
$621$		0			0
$622$	−28.8654			−1.15740
$623$	0.727609	−	23.9803i	0.0291510	−	0.960751i
$624$		0			0
$625$	−12.3398	−	21.3732i	−0.493593	−	0.854928i
$626$	22.3279	−	38.6730i	0.892402	−	1.54568i
$627$		0			0
$628$	−6.31904	−	10.9449i	−0.252157	−	0.436749i
$629$	43.9006			1.75043
$630$		0			0
$631$	−36.7963			−1.46484			−0.732419	−	0.680854i	$-0.761609\pi$
$631$	−36.7963			−1.46484			−0.732419	+	0.680854i	$0.761609\pi$
$632$	2.85718	+	4.94877i	0.113652	+	0.196852i
$633$		0			0
$634$	−8.79265	+	15.2293i	−0.349201	+	0.604833i
$635$	−0.985611	−	1.70713i	−0.0391128	−	0.0677453i
$636$		0			0
$637$	−0.624863	−	1.25196i	−0.0247580	−	0.0496045i
$638$	−16.8651			−0.667696
$639$		0			0
$640$	−0.259699	+	0.449811i	−0.0102655	+	0.0177804i
$641$	−22.0922	+	38.2648i	−0.872590	+	1.51137i	−0.0132813	+	0.999912i	$0.504228\pi$
$641$	−22.0922	+	38.2648i	−0.872590	+	1.51137i	−0.859308	+	0.511458i	$0.829106\pi$
$642$		0			0
$643$	−14.4813			−0.571087			−0.285543	−	0.958366i	$-0.592174\pi$
$643$	−14.4813			−0.571087			−0.285543	+	0.958366i	$0.592174\pi$
$644$	30.8445	+	19.0782i	1.21544	+	0.751785i
$645$		0			0
$646$	−44.5444	−	77.1532i	−1.75258	−	3.03555i
$647$	16.6536	−	28.8448i	0.654719	−	1.13401i	−0.327245	−	0.944940i	$-0.606120\pi$
$647$	16.6536	−	28.8448i	0.654719	−	1.13401i	0.981964	−	0.189068i	$-0.0605465\pi$
$648$		0			0
$649$	3.80315	+	6.58725i	0.149287	+	0.258572i
$650$	−2.04374			−0.0801622
$651$		0			0
$652$	4.71286			0.184570
$653$	−4.53322	−	7.85176i	−0.177398	−	0.307263i	0.763590	−	0.645701i	$-0.223435\pi$
$653$	−4.53322	−	7.85176i	−0.177398	−	0.307263i	−0.940989	+	0.338438i	$0.890101\pi$
$654$		0			0
$655$	−1.45027	+	2.51194i	−0.0566666	+	0.0981495i
$656$	4.07696	+	7.06150i	0.159178	+	0.275705i
$657$		0			0
$658$	8.67065	−	4.66126i	0.338017	−	0.181715i
$659$	32.3611			1.26061			0.630305	−	0.776348i	$-0.282930\pi$
$659$	32.3611			1.26061			0.630305	+	0.776348i	$0.282930\pi$
$660$		0			0
$661$	4.32958	−	7.49905i	0.168401	−	0.291679i	−0.769457	−	0.638699i	$-0.779473\pi$
$661$	4.32958	−	7.49905i	0.168401	−	0.291679i	0.937858	+	0.347020i	$0.112806\pi$
$662$	11.1382	−	19.2919i	0.432897	−	0.749799i
$663$		0			0
$664$	−3.35550			−0.130219
$665$	2.35754	−	1.26739i	0.0914214	−	0.0491473i
$666$		0			0
$667$	15.2541	+	26.4209i	0.590642	+	1.02302i
$668$	12.8329	−	22.2273i	0.496522	−	0.860001i
$669$		0			0
$670$	−0.929067	−	1.60919i	−0.0358930	−	0.0621685i
$671$	1.12868			0.0435721
$672$		0			0
$673$	−14.4968			−0.558812			−0.279406	−	0.960173i	$-0.590138\pi$
$673$	−14.4968			−0.558812			−0.279406	+	0.960173i	$0.590138\pi$
$674$	−3.43803	−	5.95484i	−0.132428	−	0.229372i
$675$		0			0
$676$	14.3692	−	24.8881i	0.552661	−	0.957236i
$677$	19.1657	+	33.1960i	0.736600	+	1.27583i	0.954018	+	0.299749i	$0.0969030\pi$
$677$	19.1657	+	33.1960i	0.736600	+	1.27583i	−0.217418	+	0.976078i	$0.569764\pi$
$678$		0			0
$679$	17.9340	+	11.0927i	0.688245	+	0.425699i
$680$	−0.409570			−0.0157063
$681$		0			0
$682$	4.30209	−	7.45144i	0.164736	−	0.285330i
$683$	3.31659	−	5.74450i	0.126906	−	0.219807i	−0.795570	−	0.605861i	$-0.792829\pi$
$683$	3.31659	−	5.74450i	0.126906	−	0.219807i	0.922476	+	0.386054i	$0.126162\pi$
$684$		0			0
$685$	0.942567			0.0360136
$686$	−34.5303	+	15.9451i	−1.31837	+	0.608789i
$687$		0			0
$688$	3.31022	+	5.73347i	0.126201	+	0.218587i
$689$	−0.534322	+	0.925472i	−0.0203560	+	0.0352577i
$690$		0			0
$691$	11.6938	+	20.2542i	0.444852	+	0.770506i	0.998042	−	0.0625490i	$-0.0199230\pi$
$691$	11.6938	+	20.2542i	0.444852	+	0.770506i	−0.553190	+	0.833055i	$0.686590\pi$
$692$	35.2818			1.34121
$693$		0			0
$694$	−23.6848			−0.899061
$695$	0.916269	+	1.58702i	0.0347561	+	0.0601992i
$696$		0			0
$697$	−7.26791	+	12.5884i	−0.275292	+	0.476819i
$698$	9.13702	+	15.8258i	0.345841	+	0.599015i
$699$		0			0
$700$	−0.885841	+	29.1953i	−0.0334816	+	1.10348i
$701$	−9.26736			−0.350023			−0.175012	−	0.984566i	$-0.555996\pi$
$701$	−9.26736			−0.350023			−0.175012	+	0.984566i	$0.555996\pi$
$702$		0			0
$703$	24.2131	−	41.9383i	0.913214	−	1.58173i
$704$	−8.01636	+	13.8847i	−0.302128	+	0.523301i
$705$		0			0
$706$	−5.43597			−0.204585
$707$	34.5894	−	18.5950i	1.30087	−	0.699336i
$708$		0			0
$709$	−7.11775	−	12.3283i	−0.267313	−	0.462999i	0.700854	−	0.713305i	$-0.252802\pi$
$709$	−7.11775	−	12.3283i	−0.267313	−	0.462999i	−0.968167	+	0.250305i	$0.919469\pi$
$710$	−0.191839	+	0.332275i	−0.00719959	+	0.0124701i
$711$		0			0
$712$	2.02478	+	3.50702i	0.0758817	+	0.131431i
$713$	−15.5646			−0.582899
$714$		0			0
$715$	0.0486452			0.00181923
$716$	−8.59632	−	14.8893i	−0.321260	−	0.556438i
$717$		0			0
$718$	−26.6636	+	46.1827i	−0.995077	+	1.72352i
$719$	−6.92848	−	12.0005i	−0.258389	−	0.447542i	0.707422	−	0.706792i	$-0.249858\pi$
$719$	−6.92848	−	12.0005i	−0.258389	−	0.447542i	−0.965810	+	0.259249i	$0.916525\pi$
$720$		0			0
$721$	−0.0163649	+	0.539348i	−0.000609459	+	0.0200864i
$722$	−59.2536			−2.20519
$723$		0			0
$724$	13.4842	−	23.3553i	0.501136	−	0.867993i
$725$	−12.2851	+	21.2784i	−0.456257	+	0.790260i
$726$		0			0
$727$	−31.4000			−1.16456			−0.582280	−	0.812988i	$-0.697839\pi$
$727$	−31.4000			−1.16456			−0.582280	+	0.812988i	$0.697839\pi$
$728$	0.200862	+	0.124239i	0.00744446	+	0.00460460i
$729$		0			0
$730$	0.233843	+	0.405028i	0.00865492	+	0.0149908i
$731$	−5.90107	+	10.2209i	−0.218259	+	0.378035i
$732$		0			0
$733$	13.3003	+	23.0368i	0.491257	+	0.850883i	0.999949	−	0.0100658i	$-0.00320409\pi$
$733$	13.3003	+	23.0368i	0.491257	+	0.850883i	−0.508692	+	0.860949i	$0.669871\pi$
$734$	−36.1183			−1.33315
$735$		0			0
$736$	50.1809			1.84969
$737$	−5.14757	−	8.91586i	−0.189613	−	0.328420i
$738$		0			0
$739$	16.5019	−	28.5822i	0.607034	−	1.05141i	−0.384693	−	0.923045i	$-0.625693\pi$
$739$	16.5019	−	28.5822i	0.607034	−	1.05141i	0.991727	−	0.128368i	$-0.0409740\pi$
$740$	−1.13510	−	1.96605i	−0.0417272	−	0.0722736i
$741$		0			0
$742$	24.7042	+	15.2802i	0.906918	+	0.560954i
$743$	38.6015			1.41615			0.708076	−	0.706136i	$-0.249563\pi$
$743$	38.6015			1.41615			0.708076	+	0.706136i	$0.249563\pi$
$744$		0			0
$745$	1.29919	−	2.25027i	0.0475988	−	0.0824435i
$746$	0.836938	−	1.44962i	0.0306425	−	0.0530743i
$747$		0			0
$748$	−23.1400			−0.846082
$749$	0.559185	−	18.4295i	0.0204322	−	0.673398i
$750$		0			0
$751$	18.9498	+	32.8220i	0.691487	+	1.19769i	0.971351	+	0.237651i	$0.0763776\pi$
$751$	18.9498	+	32.8220i	0.691487	+	1.19769i	−0.279863	+	0.960040i	$0.590289\pi$
$752$	3.18673	−	5.51957i	0.116208	−	0.201278i
$753$		0			0
$754$	1.01295	+	1.75448i	0.0368895	+	0.0638944i
$755$	1.23811			0.0450596
$756$		0			0
$757$	22.5927			0.821147			0.410573	−	0.911828i	$-0.365329\pi$
$757$	22.5927			0.821147			0.410573	+	0.911828i	$0.365329\pi$
$758$	−20.9793	−	36.3371i	−0.762001	−	1.31982i
$759$		0			0
$760$	−0.225896	+	0.391263i	−0.00819411	+	0.0141926i
$761$	13.8735	+	24.0296i	0.502913	+	0.871072i	0.999994	+	0.00336738i	$0.00107187\pi$
$761$	13.8735	+	24.0296i	0.502913	+	0.871072i	−0.497081	+	0.867704i	$0.665595\pi$
$762$		0			0
$763$	15.5229	−	8.34495i	0.561966	−	0.302108i
$764$	11.0156			0.398529
$765$		0			0
$766$	−18.3727	+	31.8224i	−0.663832	+	1.14979i
$767$	0.456849	−	0.791286i	0.0164959	−	0.0285717i
$768$		0			0
$769$	12.1534			0.438262			0.219131	−	0.975695i	$-0.429678\pi$
$769$	12.1534			0.438262			0.219131	+	0.975695i	$0.429678\pi$
$770$	0.0401019	−	1.32167i	0.00144517	−	0.0476295i
$771$		0			0
$772$	16.5250	+	28.6221i	0.594747	+	1.03013i
$773$	20.7795	−	35.9912i	0.747388	−	1.29451i	−0.201682	−	0.979451i	$-0.564641\pi$
$773$	20.7795	−	35.9912i	0.747388	−	1.29451i	0.949071	−	0.315063i	$-0.102026\pi$
$774$		0			0
$775$	−6.26756	−	10.8557i	−0.225137	−	0.389950i
$776$	−3.55939			−0.127775
$777$		0			0
$778$	32.0940			1.15063
$779$	8.01714	+	13.8861i	0.287244	+	0.497521i
$780$		0			0
$781$	−1.06290	+	1.84100i	−0.0380336	+	0.0658761i
$782$	39.8068	+	68.9473i	1.42349	+	2.46555i
$783$		0			0
$784$	−13.5826	+	20.5398i	−0.485091	+	0.733564i
$785$	0.833506			0.0297491
$786$		0			0
$787$	10.4484	−	18.0972i	0.372446	−	0.645096i	−0.617495	−	0.786575i	$-0.711852\pi$
$787$	10.4484	−	18.0972i	0.372446	−	0.645096i	0.989941	+	0.141479i	$0.0451857\pi$
$788$	−23.5725	+	40.8288i	−0.839736	+	1.45447i
$789$		0			0
$790$	−3.84303			−0.136729
$791$	−0.0869596	−	0.0537869i	−0.00309193	−	0.00191244i
$792$		0			0
$793$	−0.0677905	−	0.117417i	−0.00240731	−	0.00416959i
$794$	−19.7779	+	34.2564i	−0.701892	+	1.21571i
$795$		0			0
$796$	−22.1127	−	38.3003i	−0.783763	−	1.35752i
$797$	−0.638766			−0.0226263			−0.0113131	−	0.999936i	$-0.503601\pi$
$797$	−0.638766			−0.0226263			−0.0113131	+	0.999936i	$0.503601\pi$
$798$		0			0
$799$	11.3618			0.401953
$800$	20.2069	+	34.9993i	0.714420	+	1.23741i
$801$		0			0
$802$	−14.6849	+	25.4350i	−0.518541	+	0.898139i
$803$	1.29563	+	2.24409i	0.0457217	+	0.0791923i
$804$		0			0
$805$	−2.10680	+	1.13259i	−0.0742548	+	0.0399187i
$806$	−1.03357			−0.0364058
$807$		0			0
$808$	−3.31431	+	5.74055i	−0.116597	+	0.201952i
$809$	−25.2796	+	43.7856i	−0.888783	+	1.53942i	−0.0474686	+	0.998873i	$0.515115\pi$
$809$	−25.2796	+	43.7856i	−0.888783	+	1.53942i	−0.841315	+	0.540545i	$0.818218\pi$
$810$		0			0
$811$	−0.784071			−0.0275325			−0.0137662	−	0.999905i	$-0.504382\pi$
$811$	−0.784071			−0.0275325			−0.0137662	+	0.999905i	$0.504382\pi$
$812$	25.5022	−	13.7097i	0.894951	−	0.481117i
$813$		0			0
$814$	−11.9615	−	20.7179i	−0.419250	−	0.726163i
$815$	−0.155411	+	0.269180i	−0.00544382	+	0.00942897i
$816$		0			0
$817$	6.50939	+	11.2746i	0.227735	+	0.394448i
$818$	−65.4311			−2.28775
$819$		0			0
$820$	0.751682			0.0262499
$821$	21.7207	+	37.6213i	0.758056	+	1.31299i	0.943841	+	0.330401i	$0.107184\pi$
$821$	21.7207	+	37.6213i	0.758056	+	1.31299i	−0.185784	+	0.982591i	$0.559483\pi$
$822$		0			0
$823$	−1.98273	+	3.43419i	−0.0691136	+	0.119708i	−0.898511	−	0.438950i	$-0.855350\pi$
$823$	−1.98273	+	3.43419i	−0.0691136	+	0.119708i	0.829398	+	0.558659i	$0.188684\pi$
$824$	−0.0455399	−	0.0788774i	−0.00158646	−	0.00274782i
$825$		0			0
$826$	−21.1222	−	13.0647i	−0.734936	−	0.454578i
$827$	−29.3159			−1.01941			−0.509707	−	0.860348i	$-0.670246\pi$
$827$	−29.3159			−1.01941			−0.509707	+	0.860348i	$0.670246\pi$
$828$		0			0
$829$	−17.5213	+	30.3478i	−0.608541	+	1.05402i	0.382940	+	0.923773i	$0.374912\pi$
$829$	−17.5213	+	30.3478i	−0.608541	+	1.05402i	−0.991481	+	0.130251i	$0.958422\pi$
$830$	1.12833	−	1.95432i	0.0391648	−	0.0678353i
$831$		0			0
$832$	1.92591			0.0667689
$833$	−43.8170	−	2.66143i	−1.51817	−	0.0922131i
$834$		0			0
$835$	0.846358	+	1.46593i	0.0292894	+	0.0507308i
$836$	−12.7627	+	22.1057i	−0.441408	+	0.764541i
$837$		0			0
$838$	24.5369	+	42.4992i	0.847614	+	1.46811i
$839$	−37.5843			−1.29755			−0.648777	−	0.760979i	$-0.724719\pi$
$839$	−37.5843			−1.29755			−0.648777	+	0.760979i	$0.724719\pi$
$840$		0			0
$841$	−4.64435			−0.160150
$842$	2.51060	+	4.34848i	0.0865208	+	0.149858i
$843$		0			0
$844$	26.0705	−	45.1555i	0.897385	−	1.55432i
$845$	0.947675	+	1.64142i	0.0326010	+	0.0564666i
$846$		0			0
$847$	−0.660455	+	21.7671i	−0.0226935	+	0.747926i
$848$	18.8066			0.645822
$849$		0			0
$850$	−32.0588	+	55.5275i	−1.09961	+	1.90458i
$851$	−21.6378	+	37.4778i	−0.741735	+	1.28472i
$852$		0			0
$853$	−32.7699			−1.12202			−0.561009	−	0.827810i	$-0.689587\pi$
$853$	−32.7699			−1.12202			−0.561009	+	0.827810i	$0.689587\pi$
$854$	−3.24604	+	1.74504i	−0.111077	+	0.0597140i
$855$		0			0
$856$	1.55609	+	2.69523i	0.0531861	+	0.0921211i
$857$	13.7673	−	23.8457i	0.470283	−	0.814554i	−0.529139	−	0.848535i	$-0.677485\pi$
$857$	13.7673	−	23.8457i	0.470283	−	0.814554i	0.999422	+	0.0339808i	$0.0108185\pi$
$858$		0			0
$859$	23.2550	+	40.2789i	0.793451	+	1.37430i	0.923818	+	0.382832i	$0.125051\pi$
$859$	23.2550	+	40.2789i	0.793451	+	1.37430i	−0.130366	+	0.991466i	$0.541615\pi$
$860$	0.610316			0.0208116
$861$		0			0
$862$	−10.1196			−0.344675
$863$	−2.44007	−	4.22633i	−0.0830610	−	0.143866i	0.821502	−	0.570205i	$-0.193136\pi$
$863$	−2.44007	−	4.22633i	−0.0830610	−	0.143866i	−0.904563	+	0.426339i	$0.859803\pi$
$864$		0			0
$865$	−1.16345	+	2.01516i	−0.0395585	+	0.0685174i
$866$	31.6814	+	54.8739i	1.07658	+	1.86469i
$867$		0			0
$868$	−0.447990	+	14.7647i	−0.0152058	+	0.501147i
$869$	−21.2926			−0.722303
$870$		0			0
$871$	−0.618346	+	1.07101i	−0.0209518	+	0.0362897i
$872$	−1.48738	+	2.57622i	−0.0503690	+	0.0872417i
$873$		0			0
$874$	87.8207			2.97058
$875$	−3.28366	−	2.03103i	−0.111008	−	0.0686614i
$876$		0			0
$877$	−19.6446	−	34.0255i	−0.663352	−	1.14896i	−0.979729	−	0.200326i	$-0.935800\pi$
$877$	−19.6446	−	34.0255i	−0.663352	−	1.14896i	0.316378	−	0.948633i	$-0.397533\pi$
$878$	2.51388	−	4.35418i	0.0848395	−	0.146946i
$879$		0			0
$880$	−0.428043	−	0.741392i	−0.0144293	−	0.0249923i
$881$	−47.3713			−1.59598			−0.797990	−	0.602670i	$-0.794103\pi$
$881$	−47.3713			−1.59598			−0.797990	+	0.602670i	$0.794103\pi$
$882$		0			0
$883$	−2.67206			−0.0899221			−0.0449610	−	0.998989i	$-0.514316\pi$
$883$	−2.67206			−0.0899221			−0.0449610	+	0.998989i	$0.514316\pi$
$884$	1.38983	+	2.40726i	0.0467451	+	0.0809649i
$885$		0			0
$886$	27.0003	−	46.7659i	0.907094	−	1.57113i
$887$	−11.4800	−	19.8840i	−0.385461	−	0.667638i	0.606372	−	0.795181i	$-0.292624\pi$
$887$	−11.4800	−	19.8840i	−0.385461	−	0.667638i	−0.991833	+	0.127543i	$0.959291\pi$
$888$		0			0
$889$	30.3289	+	18.7593i	1.01720	+	0.629166i
$890$	−2.72342			−0.0912891
$891$		0			0
$892$	4.50259	−	7.79871i	0.150758	−	0.261120i
$893$	6.26655	−	10.8540i	0.209702	−	0.363214i
$894$		0			0
$895$	1.13389			0.0379017
$896$	0.284976	−	9.39217i	0.00952039	−	0.313770i
$897$		0			0
$898$	39.7460	+	68.8420i	1.32634	+	2.29729i
$899$	−6.21284	+	10.7610i	−0.207210	+	0.358898i
$900$		0			0
$901$	16.7631	+	29.0345i	0.558459	+	0.967280i
$902$	7.92109			0.263743
$903$		0			0
$904$	0.0172590			0.000574024
$905$	0.889308	+	1.54033i	0.0295616	+	0.0512022i
$906$		0			0
$907$	13.9491	−	24.1606i	0.463173	−	0.802238i	−0.535944	−	0.844253i	$-0.680044\pi$
$907$	13.9491	−	24.1606i	0.463173	−	0.802238i	0.999117	+	0.0420148i	$0.0133777\pi$
$908$	−4.27177	−	7.39892i	−0.141764	−	0.245542i
$909$		0			0
$910$	−0.139902	+	0.0752099i	−0.00463770	+	0.00249318i
$911$	−37.4762			−1.24164			−0.620820	−	0.783953i	$-0.713200\pi$
$911$	−37.4762			−1.24164			−0.620820	+	0.783953i	$0.713200\pi$
$912$		0			0
$913$	6.25158	−	10.8281i	0.206897	−	0.358356i
$914$	−9.40068	+	16.2825i	−0.310947	+	0.538576i
$915$		0			0
$916$	29.0847			0.960987
$917$	1.59143	−	52.4499i	0.0525536	−	1.73205i
$918$		0			0
$919$	−15.1073	−	26.1667i	−0.498345	−	0.863160i	0.501653	−	0.865069i	$-0.332726\pi$
$919$	−15.1073	−	26.1667i	−0.498345	−	0.863160i	−0.999998	+	0.00190951i	$0.999392\pi$
$920$	0.201870	−	0.349649i	0.00665546	−	0.0115276i
$921$		0			0
$922$	30.0145	+	51.9866i	0.988474	+	1.71209i
$923$	0.255359			0.00840525
$924$		0			0
$925$	−34.8526			−1.14594
$926$	16.8611	+	29.2042i	0.554089	+	0.959710i
$927$		0			0
$928$	20.0304	−	34.6937i	0.657531	−	1.13888i
$929$	−22.9675	−	39.7809i	−0.753540	−	1.30517i	−0.946097	−	0.323884i	$-0.895011\pi$
$929$	−22.9675	−	39.7809i	−0.753540	−	1.30517i	0.192556	−	0.981286i	$-0.438322\pi$
$930$		0			0
$931$	−26.7095	+	40.3905i	−0.875367	+	1.32375i
$932$	−38.8106			−1.27128
$933$		0			0
$934$	15.7850	−	27.3404i	0.516500	−	0.894604i
$935$	0.763064	−	1.32167i	0.0249549	−	0.0432231i
$936$		0			0
$937$	−45.3797			−1.48249			−0.741245	−	0.671235i	$-0.765764\pi$
$937$	−45.3797			−1.48249			−0.741245	+	0.671235i	$0.765764\pi$
$938$	28.5890	+	17.6831i	0.933463	+	0.577372i
$939$		0			0
$940$	−0.293774	−	0.508831i	−0.00958184	−	0.0165962i
$941$	24.7002	−	42.7819i	0.805202	−	1.39465i	−0.110952	−	0.993826i	$-0.535390\pi$
$941$	24.7002	−	42.7819i	0.805202	−	1.39465i	0.916154	−	0.400825i	$-0.131277\pi$
$942$		0			0
$943$	−7.16445	−	12.4092i	−0.233307	−	0.404099i
$944$	−16.0798			−0.523353
$945$		0			0
$946$	6.43141			0.209103
$947$	15.8253	+	27.4102i	0.514252	+	0.890711i	0.999863	+	0.0165357i	$0.00526371\pi$
$947$	15.8253	+	27.4102i	0.514252	+	0.890711i	−0.485611	+	0.874175i	$0.661403\pi$
$948$		0			0
$949$	0.155636	−	0.269569i	0.00505214	−	0.00875057i
$950$	35.3637	+	61.2517i	1.14735	+	1.98727i
$951$		0			0
$952$	6.52631	−	3.50848i	0.211519	−	0.113711i
$953$	19.1237			0.619477			0.309739	−	0.950822i	$-0.399758\pi$
$953$	19.1237			0.619477			0.309739	+	0.950822i	$0.399758\pi$
$954$		0			0
$955$	−0.363249	+	0.629165i	−0.0117545	+	0.0203593i
$956$	−8.11273	+	14.0517i	−0.262384	+	0.454463i
$957$		0			0
$958$	−77.8929			−2.51661
$959$	−15.0194	+	8.07427i	−0.485000	+	0.260732i
$960$		0			0
$961$	12.3304	+	21.3568i	0.397753	+	0.688929i
$962$	−1.43686	+	2.48871i	−0.0463262	+	0.0802394i
$963$		0			0
$964$	−6.90857	−	11.9660i	−0.222510	−	0.385399i
$965$	−2.17971			−0.0701673
$966$		0			0
$967$	−9.97050			−0.320630			−0.160315	−	0.987066i	$-0.551251\pi$
$967$	−9.97050			−0.320630			−0.160315	+	0.987066i	$0.551251\pi$
$968$	−1.83790	−	3.18334i	−0.0590724	−	0.102316i
$969$		0			0
$970$	1.19688	−	2.07306i	0.0384296	−	0.0665621i
$971$	−0.522554	−	0.905090i	−0.0167695	−	0.0290457i	0.857519	−	0.514453i	$-0.172005\pi$
$971$	−0.522554	−	0.905090i	−0.0167695	−	0.0290457i	−0.874288	+	0.485407i	$0.838671\pi$
$972$		0			0
$973$	−28.1951	−	17.4395i	−0.903895	−	0.559084i
$974$	9.45693			0.303020
$975$		0			0
$976$	−1.19302	+	2.06637i	−0.0381875	+	0.0661428i
$977$	−9.44308	+	16.3559i	−0.302111	+	0.523272i	−0.976614	−	0.215001i	$-0.931025\pi$
$977$	−9.44308	+	16.3559i	−0.302111	+	0.523272i	0.674503	+	0.738272i	$0.264358\pi$
$978$		0			0
$979$	−15.0893			−0.482257
$980$	1.01375	+	2.03112i	0.0323830	+	0.0648819i
$981$		0			0
$982$	−31.1899	−	54.0224i	−0.995309	−	1.72393i
$983$	1.14446	−	1.98226i	0.0365025	−	0.0632242i	−0.847197	−	0.531279i	$-0.821712\pi$
$983$	1.14446	−	1.98226i	0.0365025	−	0.0632242i	0.883700	+	0.468055i	$0.155045\pi$
$984$		0			0
$985$	−1.55465	−	2.69274i	−0.0495353	−	0.0857977i
$986$	63.5579			2.02409
$987$		0			0
$988$	3.06621			0.0975492
$989$	−5.81707	−	10.0755i	−0.184972	−	0.320381i
$990$		0			0
$991$	−9.53491	+	16.5150i	−0.302886	+	0.524615i	−0.976789	−	0.214206i	$-0.931284\pi$
$991$	−9.53491	+	16.5150i	−0.302886	+	0.524615i	0.673902	+	0.738821i	$0.264617\pi$
$992$	10.2191	+	17.6999i	0.324455	+	0.561973i
$993$		0			0
$994$	0.210512	−	6.93798i	0.00667702	−	0.220059i
$995$	2.91675			0.0924671
$996$		0			0
$997$	−18.5075	+	32.0560i	−0.586139	+	1.01522i	0.408593	+	0.912717i	$0.366020\pi$
$997$	−18.5075	+	32.0560i	−0.586139	+	1.01522i	−0.994732	+	0.102507i	$0.967314\pi$
$998$	9.51732	−	16.4845i	0.301266	−	0.521807i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.e.e.487.5		10
3.2	odd	2		567.2.e.f.487.1		10
7.2	even	3	inner	567.2.e.e.163.5		10
7.3	odd	6		3969.2.a.bb.1.1		5
7.4	even	3		3969.2.a.bc.1.1		5
9.2	odd	6		63.2.g.b.4.1	✓	10
9.4	even	3		189.2.h.b.46.1		10
9.5	odd	6		63.2.h.b.25.5	yes	10
9.7	even	3		189.2.g.b.172.5		10
21.2	odd	6		567.2.e.f.163.1		10
21.11	odd	6		3969.2.a.z.1.5		5
21.17	even	6		3969.2.a.ba.1.5		5
36.7	odd	6		3024.2.t.i.1873.3		10
36.11	even	6		1008.2.t.i.193.2		10
36.23	even	6		1008.2.q.i.529.5		10
36.31	odd	6		3024.2.q.i.2881.3		10
63.2	odd	6		63.2.h.b.58.5	yes	10
63.4	even	3		1323.2.f.e.883.5		10
63.5	even	6		441.2.g.f.79.1		10
63.11	odd	6		441.2.f.e.148.1		10
63.13	odd	6		1323.2.h.f.802.1		10
63.16	even	3		189.2.h.b.37.1		10
63.20	even	6		441.2.g.f.67.1		10
63.23	odd	6		63.2.g.b.16.1	yes	10
63.25	even	3		1323.2.f.e.442.5		10
63.31	odd	6		1323.2.f.f.883.5		10
63.32	odd	6		441.2.f.e.295.1		10
63.34	odd	6		1323.2.g.f.361.5		10
63.38	even	6		441.2.f.f.148.1		10
63.40	odd	6		1323.2.g.f.667.5		10
63.41	even	6		441.2.h.f.214.5		10
63.47	even	6		441.2.h.f.373.5		10
63.52	odd	6		1323.2.f.f.442.5		10
63.58	even	3		189.2.g.b.100.5		10
63.59	even	6		441.2.f.f.295.1		10
63.61	odd	6		1323.2.h.f.226.1		10
252.23	even	6		1008.2.t.i.961.2		10
252.79	odd	6		3024.2.q.i.2305.3		10
252.191	even	6		1008.2.q.i.625.5		10
252.247	odd	6		3024.2.t.i.289.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.1	✓	10	9.2	odd	6
63.2.g.b.16.1	yes	10	63.23	odd	6
63.2.h.b.25.5	yes	10	9.5	odd	6
63.2.h.b.58.5	yes	10	63.2	odd	6
189.2.g.b.100.5		10	63.58	even	3
189.2.g.b.172.5		10	9.7	even	3
189.2.h.b.37.1		10	63.16	even	3
189.2.h.b.46.1		10	9.4	even	3
441.2.f.e.148.1		10	63.11	odd	6
441.2.f.e.295.1		10	63.32	odd	6
441.2.f.f.148.1		10	63.38	even	6
441.2.f.f.295.1		10	63.59	even	6
441.2.g.f.67.1		10	63.20	even	6
441.2.g.f.79.1		10	63.5	even	6
441.2.h.f.214.5		10	63.41	even	6
441.2.h.f.373.5		10	63.47	even	6
567.2.e.e.163.5		10	7.2	even	3	inner
567.2.e.e.487.5		10	1.1	even	1	trivial
567.2.e.f.163.1		10	21.2	odd	6
567.2.e.f.487.1		10	3.2	odd	2
1008.2.q.i.529.5		10	36.23	even	6
1008.2.q.i.625.5		10	252.191	even	6
1008.2.t.i.193.2		10	36.11	even	6
1008.2.t.i.961.2		10	252.23	even	6
1323.2.f.e.442.5		10	63.25	even	3
1323.2.f.e.883.5		10	63.4	even	3
1323.2.f.f.442.5		10	63.52	odd	6
1323.2.f.f.883.5		10	63.31	odd	6
1323.2.g.f.361.5		10	63.34	odd	6
1323.2.g.f.667.5		10	63.40	odd	6
1323.2.h.f.226.1		10	63.61	odd	6
1323.2.h.f.802.1		10	63.13	odd	6
3024.2.q.i.2305.3		10	252.79	odd	6
3024.2.q.i.2881.3		10	36.31	odd	6
3024.2.t.i.289.3		10	252.247	odd	6
3024.2.t.i.1873.3		10	36.7	odd	6
3969.2.a.z.1.5		5	21.11	odd	6
3969.2.a.ba.1.5		5	21.17	even	6
3969.2.a.bb.1.1		5	7.3	odd	6
3969.2.a.bc.1.1		5	7.4	even	3

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02682 + 1.77851i) q^{2} +(-1.10873 + 1.92038i) q^{4} +(-0.0731228 - 0.126652i) q^{5} +(2.25011 + 1.39176i) q^{7} -0.446582 q^{8} +O(q^{10})\)	\(q+(1.02682 + 1.77851i) q^{2} +(-1.10873 + 1.92038i) q^{4} +(-0.0731228 - 0.126652i) q^{5} +(2.25011 + 1.39176i) q^{7} -0.446582 q^{8} +(0.150168 - 0.260099i) q^{10} +(0.832020 - 1.44110i) q^{11} -0.199891 q^{13} +(-0.164785 + 5.43093i) q^{14} +(1.75890 + 3.04650i) q^{16} +(-3.13555 + 5.43093i) q^{17} +(3.45879 + 5.99080i) q^{19} +0.324294 q^{20} +3.41735 q^{22} +(-3.09092 - 5.35363i) q^{23} +(2.48931 - 4.31160i) q^{25} +(-0.205252 - 0.355508i) q^{26} +(-5.16746 + 2.77798i) q^{28} -4.93514 q^{29} +(1.25890 - 2.18047i) q^{31} +(-4.05873 + 7.02993i) q^{32} -12.8786 q^{34} +(0.0117348 - 0.386752i) q^{35} +(-3.50023 - 6.06257i) q^{37} +(-7.10312 + 12.3030i) q^{38} +(0.0326554 + 0.0565608i) q^{40} +2.31790 q^{41} +1.88199 q^{43} +(1.84497 + 3.19558i) q^{44} +(6.34765 - 10.9944i) q^{46} +(-0.905887 - 1.56904i) q^{47} +(3.12602 + 6.26322i) q^{49} +10.2243 q^{50} +(0.221625 - 0.383865i) q^{52} +(2.67307 - 4.62989i) q^{53} -0.243359 q^{55} +(-1.00486 - 0.621534i) q^{56} +(-5.06752 - 8.77720i) q^{58} +(-2.28549 + 3.95859i) q^{59} +(0.339138 + 0.587404i) q^{61} +5.17066 q^{62} -9.63481 q^{64} +(0.0146166 + 0.0253167i) q^{65} +(3.09342 - 5.35796i) q^{67} +(-6.95296 - 12.0429i) q^{68} +(0.699891 - 0.376255i) q^{70} -1.27749 q^{71} +(-0.778603 + 1.34858i) q^{73} +(7.18823 - 12.4504i) q^{74} -15.3394 q^{76} +(3.87780 - 2.08467i) q^{77} +(-6.39787 - 11.0814i) q^{79} +(0.257231 - 0.445537i) q^{80} +(2.38008 + 4.12241i) q^{82} +7.51374 q^{83} +0.917122 q^{85} +(1.93247 + 3.34713i) q^{86} +(-0.371566 + 0.643571i) q^{88} +(-4.53394 - 7.85301i) q^{89} +(-0.449777 - 0.278199i) q^{91} +13.7080 q^{92} +(1.86037 - 3.22226i) q^{94} +(0.505833 - 0.876128i) q^{95} +7.97028 q^{97} +(-7.92933 + 11.9909i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 5 q^{7} + 6 q^{8}+O(q^{10}) \) 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 5 * q^7 + 6 * q^8	\( 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 5 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} + 16 q^{13} - 4 q^{14} + 2 q^{16} - 12 q^{17} + q^{19} + 10 q^{20} + 2 q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} + 14 q^{29} - 3 q^{31} + 2 q^{32} - 6 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} + 10 q^{41} + 14 q^{43} + 10 q^{44} + 3 q^{46} - 27 q^{47} - 17 q^{49} + 38 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 27 q^{56} - 10 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} - 27 q^{68} - 11 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} - 10 q^{76} - 20 q^{77} - 4 q^{79} - 20 q^{80} - 5 q^{82} + 18 q^{83} + 12 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} + 54 q^{92} - 3 q^{94} + 14 q^{95} + 24 q^{97} - 59 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 5 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 + 16 * q^13 - 4 * q^14 + 2 * q^16 - 12 * q^17 + q^19 + 10 * q^20 + 2 * q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 + 14 * q^29 - 3 * q^31 + 2 * q^32 - 6 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 + 10 * q^41 + 14 * q^43 + 10 * q^44 + 3 * q^46 - 27 * q^47 - 17 * q^49 + 38 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 27 * q^56 - 10 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 27 * q^68 - 11 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 - 10 * q^76 - 20 * q^77 - 4 * q^79 - 20 * q^80 - 5 * q^82 + 18 * q^83 + 12 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 + 54 * q^92 - 3 * q^94 + 14 * q^95 + 24 * q^97 - 59 * q^98

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