LMFDB - Embedded newform 600.2.b.h.251.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(251,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("600.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.b (of order $2$, degree $1$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.537291533250985984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 14x^{8} - 30x^{6} + 56x^{4} - 80x^{2} + 64 $ x^12 - 5x^10 + 14x^8 - 30x^6 + 56x^4 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.9
Root			$-1.26128 + 0.639662i$ of defining polynomial
Character	$\chi$	$=$	600.251
Dual form			600.2.b.h.251.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26128 - 0.639662i) q^{2} +(1.57067 - 0.730070i) q^{3} +(1.18166 - 1.61359i) q^{4} +(1.51406 - 1.92552i) q^{6} -1.25539i q^{7} +(0.458259 - 2.79106i) q^{8} +(1.93400 - 2.29339i) q^{9} +O(q^{10})$	\(q+(1.26128 - 0.639662i) q^{2} +(1.57067 - 0.730070i) q^{3} +(1.18166 - 1.61359i) q^{4} +(1.51406 - 1.92552i) q^{6} -1.25539i q^{7} +(0.458259 - 2.79106i) q^{8} +(1.93400 - 2.29339i) q^{9} +3.02346i q^{11} +(0.677969 - 3.39711i) q^{12} +5.65509i q^{13} +(-0.803023 - 1.58339i) q^{14} +(-1.20734 - 3.81344i) q^{16} -2.45546i q^{17} +(0.972316 - 4.12972i) q^{18} +1.77801 q^{19} +(-0.916519 - 1.97179i) q^{21} +(1.93400 + 3.81344i) q^{22} -8.84074 q^{23} +(-1.31789 - 4.71839i) q^{24} +(3.61735 + 7.13266i) q^{26} +(1.36333 - 5.01411i) q^{27} +(-2.02568 - 1.48344i) q^{28} -3.79561 q^{29} +5.19897i q^{31} +(-3.96211 - 4.03753i) q^{32} +(2.20734 + 4.74886i) q^{33} +(-1.57067 - 3.09703i) q^{34} +(-1.41526 - 5.83070i) q^{36} -6.45436i q^{37} +(2.24257 - 1.13732i) q^{38} +(4.12861 + 8.88227i) q^{39} +7.57276i q^{41} +(-2.41727 - 1.90072i) q^{42} +4.37266 q^{43} +(4.87863 + 3.57272i) q^{44} +(-11.1507 + 5.65509i) q^{46} +1.83304 q^{47} +(-4.68041 - 5.10821i) q^{48} +5.42401 q^{49} +(-1.79266 - 3.85672i) q^{51} +(9.12499 + 6.68241i) q^{52} +12.0528 q^{53} +(-1.48780 - 7.19628i) q^{54} +(-3.50385 - 0.575292i) q^{56} +(2.79266 - 1.29807i) q^{57} +(-4.78734 + 2.42791i) q^{58} +4.91093i q^{59} +8.16586i q^{61} +(3.32559 + 6.55737i) q^{62} +(-2.87909 - 2.42791i) q^{63} +(-7.58000 - 2.55806i) q^{64} +(5.82174 + 4.57770i) q^{66} -8.50466 q^{67} +(-3.96211 - 2.90153i) q^{68} +(-13.8859 + 6.45436i) q^{69} -7.00770 q^{71} +(-5.51472 - 6.44886i) q^{72} -4.59465 q^{73} +(-4.12861 - 8.14076i) q^{74} +(2.10101 - 2.86897i) q^{76} +3.79561 q^{77} +(10.8890 + 8.56213i) q^{78} +7.36659i q^{79} +(-1.51932 - 8.87083i) q^{81} +(4.84401 + 9.55139i) q^{82} -15.7510i q^{83} +(-4.26468 - 0.851113i) q^{84} +(5.51515 - 2.79702i) q^{86} +(-5.96165 + 2.77106i) q^{87} +(8.43866 + 1.38553i) q^{88} +3.65716i q^{89} +7.09931 q^{91} +(-10.4468 + 14.2653i) q^{92} +(3.79561 + 8.16586i) q^{93} +(2.31198 - 1.17252i) q^{94} +(-9.17084 - 3.44901i) q^{96} -13.8773 q^{97} +(6.84120 - 3.46953i) q^{98} +(6.93400 + 5.84737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} + 10 q^{4} + 7 q^{6} - 2 q^{9}+O(q^{10}) $ 12 * q + 2 * q^3 + 10 * q^4 + 7 * q^6 - 2 * q^9	$ 12 q + 2 q^{3} + 10 q^{4} + 7 q^{6} - 2 q^{9} - 3 q^{12} - 6 q^{16} - 5 q^{18} - 4 q^{19} - 2 q^{22} + 5 q^{24} + 8 q^{27} - 20 q^{28} + 18 q^{33} - 2 q^{34} + 19 q^{36} - 14 q^{42} - 40 q^{43} - 16 q^{46} - 27 q^{48} - 36 q^{49} - 30 q^{51} - 4 q^{52} - 30 q^{54} + 42 q^{57} + 52 q^{58} + 10 q^{64} + 7 q^{66} - 60 q^{67} - 39 q^{72} + 12 q^{73} - 38 q^{76} + 54 q^{78} - 10 q^{81} + 58 q^{82} - 34 q^{84} + 34 q^{88} - 24 q^{91} + 28 q^{94} - 31 q^{96} - 32 q^{97} + 58 q^{99}+O(q^{100}) $ 12 * q + 2 * q^3 + 10 * q^4 + 7 * q^6 - 2 * q^9 - 3 * q^12 - 6 * q^16 - 5 * q^18 - 4 * q^19 - 2 * q^22 + 5 * q^24 + 8 * q^27 - 20 * q^28 + 18 * q^33 - 2 * q^34 + 19 * q^36 - 14 * q^42 - 40 * q^43 - 16 * q^46 - 27 * q^48 - 36 * q^49 - 30 * q^51 - 4 * q^52 - 30 * q^54 + 42 * q^57 + 52 * q^58 + 10 * q^64 + 7 * q^66 - 60 * q^67 - 39 * q^72 + 12 * q^73 - 38 * q^76 + 54 * q^78 - 10 * q^81 + 58 * q^82 - 34 * q^84 + 34 * q^88 - 24 * q^91 + 28 * q^94 - 31 * q^96 - 32 * q^97 + 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	1.26128	−	0.639662i	0.891861	−	0.452310i
$2$	1.26128	−	0.639662i	0.891861	−	0.452310i
$3$	1.57067	−	0.730070i	0.906826	−	0.421506i
$3$	1.57067	−	0.730070i	0.906826	−	0.421506i
$4$	1.18166	−	1.61359i	0.590832	−	0.806795i
$5$		0			0
$5$		0			0
$6$	1.51406	−	1.92552i	0.618111	−	0.786091i
$7$		−	1.25539i		−	0.474491i	−0.971450	−	0.237245i	$-0.923755\pi$
$7$		−	1.25539i		−	0.474491i	0.971450	−	0.237245i	$-0.0762446\pi$
$8$	0.458259	−	2.79106i	0.162019	−	0.986788i
$9$	1.93400	−	2.29339i	0.644665	−	0.764465i
$10$		0			0
$11$			3.02346i			0.911609i	0.890080	+	0.455804i	$0.150648\pi$
$11$			3.02346i			0.911609i	−0.890080	+	0.455804i	$0.849352\pi$
$12$	0.677969	−	3.39711i	0.195713	−	0.980661i
$13$			5.65509i			1.56844i	0.620483	+	0.784220i	$0.286936\pi$
$13$			5.65509i			1.56844i	−0.620483	+	0.784220i	$0.713064\pi$
$14$	−0.803023	−	1.58339i	−0.214617	−	0.423180i
$15$		0			0
$16$	−1.20734	−	3.81344i	−0.301835	−	0.953360i
$17$		−	2.45546i		−	0.595538i	−0.954638	−	0.297769i	$-0.903758\pi$
$17$		−	2.45546i		−	0.595538i	0.954638	−	0.297769i	$-0.0962424\pi$
$18$	0.972316	−	4.12972i	0.229177	−	0.973385i
$19$	1.77801			0.407903			0.203951	−	0.978981i	$-0.434622\pi$
$19$	1.77801			0.407903			0.203951	+	0.978981i	$0.434622\pi$
$20$		0			0
$21$	−0.916519	−	1.97179i	−0.200001	−	0.430281i
$22$	1.93400	+	3.81344i	0.412329	+	0.813028i
$23$	−8.84074			−1.84342			−0.921711	−	0.387878i	$-0.873208\pi$
$23$	−8.84074			−1.84342			−0.921711	+	0.387878i	$0.873208\pi$
$24$	−1.31789	−	4.71839i	−0.269014	−	0.963136i
$25$		0			0
$26$	3.61735	+	7.13266i	0.709420	+	1.39883i
$27$	1.36333	−	5.01411i	0.262373	−	0.964967i
$28$	−2.02568	−	1.48344i	−0.382817	−	0.280344i
$29$	−3.79561			−0.704827			−0.352414	−	0.935844i	$-0.614639\pi$
$29$	−3.79561			−0.704827			−0.352414	+	0.935844i	$0.614639\pi$
$30$		0			0
$31$			5.19897i			0.933763i	0.884320	+	0.466881i	$0.154623\pi$
$31$			5.19897i			0.933763i	−0.884320	+	0.466881i	$0.845377\pi$
$32$	−3.96211	−	4.03753i	−0.700409	−	0.713742i
$33$	2.20734	+	4.74886i	0.384249	+	0.826670i
$34$	−1.57067	−	3.09703i	−0.269367	−	0.531137i
$35$		0			0
$36$	−1.41526	−	5.83070i	−0.235877	−	0.971783i
$37$		−	6.45436i		−	1.06109i	−0.847657	−	0.530545i	$-0.821987\pi$
$37$		−	6.45436i		−	1.06109i	0.847657	−	0.530545i	$-0.178013\pi$
$38$	2.24257	−	1.13732i	0.363793	−	0.184498i
$39$	4.12861	+	8.88227i	0.661107	+	1.42230i
$40$		0			0
$41$			7.57276i			1.18267i	0.806427	+	0.591333i	$0.201398\pi$
$41$			7.57276i			1.18267i	−0.806427	+	0.591333i	$0.798602\pi$
$42$	−2.41727	−	1.90072i	−0.372993	−	0.293288i
$43$	4.37266			0.666824			0.333412	−	0.942781i	$-0.391800\pi$
$43$	4.37266			0.666824			0.333412	+	0.942781i	$0.391800\pi$
$44$	4.87863	+	3.57272i	0.735481	+	0.538608i
$45$		0			0
$46$	−11.1507	+	5.65509i	−1.64408	+	0.833797i
$47$	1.83304			0.267376			0.133688	−	0.991023i	$-0.457318\pi$
$47$	1.83304			0.267376			0.133688	+	0.991023i	$0.457318\pi$
$48$	−4.68041	−	5.10821i	−0.675559	−	0.737306i
$49$	5.42401			0.774858
$50$		0			0
$51$	−1.79266	−	3.85672i	−0.251023	−	0.540049i
$52$	9.12499	+	6.68241i	1.26541	+	0.926684i
$53$	12.0528			1.65558			0.827792	−	0.561035i	$-0.189597\pi$
$53$	12.0528			1.65558			0.827792	+	0.561035i	$0.189597\pi$
$54$	−1.48780	−	7.19628i	−0.202464	−	0.979290i
$55$		0			0
$56$	−3.50385	−	0.575292i	−0.468222	−	0.0768766i
$57$	2.79266	−	1.29807i	0.369897	−	0.171934i
$58$	−4.78734	+	2.42791i	−0.628608	+	0.318800i
$59$			4.91093i			0.639348i	0.947528	+	0.319674i	$0.103573\pi$
$59$			4.91093i			0.639348i	−0.947528	+	0.319674i	$0.896427\pi$
$60$		0			0
$61$			8.16586i			1.04553i	0.852477	+	0.522766i	$0.175100\pi$
$61$			8.16586i			1.04553i	−0.852477	+	0.522766i	$0.824900\pi$
$62$	3.32559	+	6.55737i	0.422350	+	0.832787i
$63$	−2.87909	−	2.42791i	−0.362732	−	0.305888i
$64$	−7.58000	−	2.55806i	−0.947500	−	0.319757i
$65$		0			0
$66$	5.82174	+	4.57770i	0.716607	+	0.563476i
$67$	−8.50466			−1.03901			−0.519505	−	0.854467i	$-0.673884\pi$
$67$	−8.50466			−1.03901			−0.519505	+	0.854467i	$0.673884\pi$
$68$	−3.96211	−	2.90153i	−0.480476	−	0.351863i
$69$	−13.8859	+	6.45436i	−1.67166	+	0.777013i
$70$		0			0
$71$	−7.00770			−0.831661			−0.415831	−	0.909442i	$-0.636509\pi$
$71$	−7.00770			−0.831661			−0.415831	+	0.909442i	$0.636509\pi$
$72$	−5.51472	−	6.44886i	−0.649916	−	0.760006i
$73$	−4.59465			−0.537763			−0.268881	−	0.963173i	$-0.586654\pi$
$73$	−4.59465			−0.537763			−0.268881	+	0.963173i	$0.586654\pi$
$74$	−4.12861	−	8.14076i	−0.479941	−	0.946344i
$75$		0			0
$76$	2.10101	−	2.86897i	0.241002	−	0.329094i
$77$	3.79561			0.432550
$78$	10.8890	+	8.56213i	1.23294	+	0.969470i
$79$			7.36659i			0.828806i	0.910093	+	0.414403i	$0.136010\pi$
$79$			7.36659i			0.828806i	−0.910093	+	0.414403i	$0.863990\pi$
$80$		0			0
$81$	−1.51932	−	8.87083i	−0.168813	−	0.985648i
$82$	4.84401	+	9.55139i	0.534932	+	1.05477i
$83$		−	15.7510i		−	1.72890i	−0.502720	−	0.864449i	$-0.667667\pi$
$83$		−	15.7510i		−	1.72890i	0.502720	−	0.864449i	$-0.332333\pi$
$84$	−4.26468	−	0.851113i	−0.465315	−	0.0928640i
$85$		0			0
$86$	5.51515	−	2.79702i	0.594714	−	0.301611i
$87$	−5.96165	+	2.77106i	−0.639156	+	0.297089i
$88$	8.43866	+	1.38553i	0.899564	+	0.147698i
$89$			3.65716i			0.387658i	0.981035	+	0.193829i	$0.0620907\pi$
$89$			3.65716i			0.387658i	−0.981035	+	0.193829i	$0.937909\pi$
$90$		0			0
$91$	7.09931			0.744210
$92$	−10.4468	+	14.2653i	−1.08915	+	1.48726i
$93$	3.79561	+	8.16586i	0.393587	+	0.846760i
$94$	2.31198	−	1.17252i	0.238462	−	0.120937i
$95$		0			0
$96$	−9.17084	−	3.44901i	−0.935995	−	0.352013i
$97$	−13.8773			−1.40903			−0.704514	−	0.709690i	$-0.748835\pi$
$97$	−13.8773			−1.40903			−0.704514	+	0.709690i	$0.748835\pi$
$98$	6.84120	−	3.46953i	0.691066	−	0.350476i
$99$	6.93400	+	5.84737i	0.696893	+	0.587683i
$100$		0			0
$101$	13.8859			1.38170			0.690848	−	0.723000i	$-0.257237\pi$
$101$	13.8859			1.38170			0.690848	+	0.723000i	$0.257237\pi$
$102$	−4.72805	−	3.71771i	−0.468147	−	0.368108i
$103$		−	7.36659i		−	0.725852i	−0.931818	−	0.362926i	$-0.881778\pi$
$103$		−	7.36659i		−	0.725852i	0.931818	−	0.362926i	$-0.118222\pi$
$104$	15.7837	+	2.59150i	1.54772	+	0.254117i
$105$		0			0
$106$	15.2020	−	7.70974i	1.47655	−	0.748836i
$107$			8.14076i			0.786997i	0.919325	+	0.393499i	$0.128735\pi$
$107$			8.14076i			0.786997i	−0.919325	+	0.393499i	$0.871265\pi$
$108$	−6.47972	−	8.12485i	−0.623512	−	0.781814i
$109$		−	5.65509i		−	0.541659i	−0.962627	−	0.270830i	$-0.912702\pi$
$109$		−	5.65509i		−	0.541659i	0.962627	−	0.270830i	$-0.0872980\pi$
$110$		0			0
$111$	−4.71213	−	10.1377i	−0.447256	−	0.962223i
$112$	−4.78734	+	1.51568i	−0.452361	+	0.143218i
$113$			11.4884i			1.08073i	0.841429	+	0.540367i	$0.181715\pi$
$113$			11.4884i			1.08073i	−0.841429	+	0.540367i	$0.818285\pi$
$114$	2.69201	−	3.42359i	0.252129	−	0.320649i
$115$		0			0
$116$	−4.48514	+	6.12456i	−0.416435	+	0.568651i
$117$	12.9693	+	10.9369i	1.19902	+	1.01112i
$118$	3.14134	+	6.19407i	0.289183	+	0.570210i
$119$	−3.08255			−0.282577
$120$		0			0
$121$	1.85866			0.168969
$122$	5.22339	+	10.2994i	0.472904	+	0.932468i
$123$	5.52865	+	11.8943i	0.498501	+	1.07247i
$124$	8.38900	+	6.14344i	0.753355	+	0.551697i
$125$		0			0
$126$	−5.18439	−	1.22063i	−0.461862	−	0.108742i
$127$		−	21.7081i		−	1.92628i	−0.268993	−	0.963142i	$-0.586691\pi$
$127$		−	21.7081i		−	1.92628i	0.268993	−	0.963142i	$-0.413309\pi$
$128$	−11.1968	+	1.62221i	−0.989667	+	0.143384i
$129$	6.86799	−	3.19234i	0.604693	−	0.281070i
$130$		0			0
$131$		−	12.5212i		−	1.09398i	−0.837139	−	0.546990i	$-0.815773\pi$
$131$		−	12.5212i		−	1.09398i	0.837139	−	0.546990i	$-0.184227\pi$
$132$	10.2710	+	2.04982i	0.893979	+	0.178414i
$133$		−	2.23208i		−	0.193546i
$134$	−10.7268	+	5.44011i	−0.926653	+	0.469954i
$135$		0			0
$136$	−6.85334	−	1.12524i	−0.587669	−	0.0964885i
$137$			18.4649i			1.57757i	0.614672	+	0.788783i	$0.289288\pi$
$137$			18.4649i			1.57757i	−0.614672	+	0.788783i	$0.710712\pi$
$138$	−13.3854	+	17.0230i	−1.13944	+	1.44910i
$139$	−11.6040			−0.984237			−0.492118	−	0.870528i	$-0.663777\pi$
$139$	−11.6040			−0.984237			−0.492118	+	0.870528i	$0.663777\pi$
$140$		0			0
$141$	2.87909	−	1.33825i	0.242463	−	0.112701i
$142$	−8.83869	+	4.48256i	−0.741726	+	0.376168i
$143$	−17.0980			−1.42980
$144$	−11.0807	−	4.60627i	−0.923393	−	0.383856i
$145$		0			0
$146$	−5.79515	+	2.93902i	−0.479610	+	0.243235i
$147$	8.51932	−	3.95990i	0.702661	−	0.326607i
$148$	−10.4147	−	7.62688i	−0.856081	−	0.626926i
$149$	11.9233			0.976794			0.488397	−	0.872621i	$-0.337582\pi$
$149$	11.9233			0.976794			0.488397	+	0.872621i	$0.337582\pi$
$150$		0			0
$151$		−	10.0548i		−	0.818247i	−0.912479	−	0.409124i	$-0.865834\pi$
$151$		−	10.0548i		−	0.818247i	0.912479	−	0.409124i	$-0.134166\pi$
$152$	0.814789	−	4.96252i	0.0660881	−	0.402514i
$153$	−5.63135	−	4.74886i	−0.455268	−	0.383922i
$154$	4.78734	−	2.42791i	0.385775	−	0.195647i
$155$		0			0
$156$	19.2110	+	3.83398i	1.53811	+	0.306964i
$157$			1.71150i			0.136593i	0.997665	+	0.0682964i	$0.0217563\pi$
$157$			1.71150i			0.136593i	−0.997665	+	0.0682964i	$0.978244\pi$
$158$	4.71213	+	9.29135i	0.374877	+	0.739180i
$159$	18.9310	−	8.79941i	1.50133	−	0.697838i
$160$		0			0
$161$			11.0985i			0.874687i
$162$	−7.59062	−	10.2168i	−0.596376	−	0.802705i
$163$	−11.9580			−0.936621			−0.468311	−	0.883564i	$-0.655137\pi$
$163$	−11.9580			−0.936621			−0.468311	+	0.883564i	$0.655137\pi$
$164$	12.2193	+	8.94846i	0.954169	+	0.698758i
$165$		0			0
$166$	−10.0753	−	19.8665i	−0.781997	−	1.54194i
$167$	−0.583522			−0.0451543			−0.0225771	−	0.999745i	$-0.507187\pi$
$167$	−0.583522			−0.0451543			−0.0225771	+	0.999745i	$0.507187\pi$
$168$	−5.92339	+	1.65446i	−0.456999	+	0.127645i
$169$	−18.9800			−1.46000
$170$		0			0
$171$	3.43866	−	4.07767i	0.262961	−	0.311827i
$172$	5.16701	−	7.05567i	0.393981	−	0.537990i
$173$	12.0528			0.916360			0.458180	−	0.888860i	$-0.348502\pi$
$173$	12.0528			0.916360			0.458180	+	0.888860i	$0.348502\pi$
$174$	−5.74677	+	7.30853i	−0.435662	+	0.554058i
$175$		0			0
$176$	11.5298	−	3.65035i	0.869092	−	0.275155i
$177$	3.58532	+	7.71344i	0.269489	+	0.579778i
$178$	2.33935	+	4.61271i	0.175341	+	0.345737i
$179$			0.605490i			0.0452565i	0.999744	+	0.0226282i	$0.00720340\pi$
$179$			0.605490i			0.0452565i	−0.999744	+	0.0226282i	$0.992797\pi$
$180$		0			0
$181$			7.08790i			0.526840i	0.964681	+	0.263420i	$0.0848505\pi$
$181$			7.08790i			0.526840i	−0.964681	+	0.263420i	$0.915150\pi$
$182$	8.95424	−	4.54116i	0.663732	−	0.336613i
$183$	5.96165	+	12.8259i	0.440698	+	0.948114i
$184$	−4.05135	+	24.6750i	−0.298670	+	1.81907i
$185$		0			0
$186$	10.0107	+	7.87154i	0.734022	+	0.577169i
$187$	7.42401			0.542897
$188$	2.16603	−	2.95777i	0.157974	−	0.215717i
$189$	−6.29464	−	1.71150i	−0.457868	−	0.124493i
$190$		0			0
$191$	−18.9310			−1.36980			−0.684899	−	0.728638i	$-0.740154\pi$
$191$	−18.9310			−1.36980			−0.684899	+	0.728638i	$0.740154\pi$
$192$	−13.7732	+	1.51607i	−0.993996	+	0.109413i
$193$	4.27334			0.307602			0.153801	−	0.988102i	$-0.450849\pi$
$193$	4.27334			0.307602			0.153801	+	0.988102i	$0.450849\pi$
$194$	−17.5032	+	8.87680i	−1.25666	+	0.637317i
$195$		0			0
$196$	6.40936	−	8.75212i	0.457811	−	0.625151i
$197$	−10.0903			−0.718901			−0.359450	−	0.933164i	$-0.617036\pi$
$197$	−10.0903			−0.718901			−0.359450	+	0.933164i	$0.617036\pi$
$198$	12.4861	+	2.93976i	0.887346	+	0.208920i
$199$		−	19.0199i		−	1.34829i	−0.738601	−	0.674143i	$-0.764513\pi$
$199$		−	19.0199i		−	1.34829i	0.738601	−	0.674143i	$-0.235487\pi$
$200$		0			0
$201$	−13.3580	+	6.20900i	−0.942201	+	0.437949i
$202$	17.5140	−	8.88227i	1.23228	−	0.624954i
$203$			4.76495i			0.334434i
$204$	−8.34148	−	1.66473i	−0.584021	−	0.116554i
$205$		0			0
$206$	−4.71213	−	9.29135i	−0.328310	−	0.647359i
$207$	−17.0980	+	20.2753i	−1.18839	+	1.40923i
$208$	21.5653	−	6.82761i	1.49529	−	0.473410i
$209$			5.37574i			0.371848i
$210$		0			0
$211$	5.49534			0.378315			0.189157	−	0.981947i	$-0.439424\pi$
$211$	5.49534			0.378315			0.189157	+	0.981947i	$0.439424\pi$
$212$	14.2424	−	19.4483i	0.978172	−	1.33572i
$213$	−11.0068	+	5.11611i	−0.754172	+	0.350550i
$214$	5.20734	+	10.2678i	0.355966	+	0.701892i
$215$		0			0
$216$	−13.3699	−	6.10289i	−0.909708	−	0.415249i
$217$	6.52671			0.443062
$218$	−3.61735	−	7.13266i	−0.244998	−	0.483085i
$219$	−7.21667	+	3.35441i	−0.487657	+	0.226670i
$220$		0			0
$221$	13.8859			0.934065
$222$	−12.4280	−	9.77226i	−0.834113	−	0.655871i
$223$		−	7.70974i		−	0.516282i	−0.966107	−	0.258141i	$-0.916890\pi$
$223$		−	7.70974i		−	0.516282i	0.966107	−	0.258141i	$-0.0831100\pi$
$224$	−5.06866	+	4.97397i	−0.338664	+	0.332338i
$225$		0			0
$226$	7.34868	+	14.4901i	0.488827	+	0.963865i
$227$		−	7.40388i		−	0.491413i	−0.969344	−	0.245706i	$-0.920980\pi$
$227$		−	7.40388i		−	0.491413i	0.969344	−	0.245706i	$-0.0790199\pi$
$228$	1.20544	−	6.04009i	0.0798319	−	0.400015i
$229$		−	17.1310i		−	1.13205i	−0.824389	−	0.566024i	$-0.808481\pi$
$229$		−	17.1310i		−	1.13205i	0.824389	−	0.566024i	$-0.191519\pi$
$230$		0			0
$231$	5.96165	−	2.77106i	0.392248	−	0.182322i
$232$	−1.73937	+	10.5938i	−0.114196	+	0.695515i
$233$			1.40807i			0.0922454i	0.998936	+	0.0461227i	$0.0146865\pi$
$233$			1.40807i			0.0922454i	−0.998936	+	0.0461227i	$0.985313\pi$
$234$	23.3539	+	5.49854i	1.52669	+	0.359450i
$235$		0			0
$236$	7.92422	+	5.80307i	0.515823	+	0.377748i
$237$	5.37812	+	11.5705i	0.349347	+	0.751583i
$238$	−3.88797	+	1.97179i	−0.252020	+	0.127812i
$239$	−9.50673			−0.614939			−0.307470	−	0.951558i	$-0.599482\pi$
$239$	−9.50673			−0.614939			−0.307470	+	0.951558i	$0.599482\pi$
$240$		0			0
$241$	2.27334			0.146439			0.0732195	−	0.997316i	$-0.476673\pi$
$241$	2.27334			0.146439			0.0732195	+	0.997316i	$0.476673\pi$
$242$	2.34430	−	1.18892i	0.150697	−	0.0764265i
$243$	−8.86267	−	12.8239i	−0.568540	−	0.822655i
$244$	13.1763	+	9.64930i	0.843529	+	0.617733i
$245$		0			0
$246$	14.5815	+	11.4656i	0.929683	+	0.731020i
$247$			10.0548i			0.639771i
$248$	14.5106	+	2.38248i	0.921426	+	0.151287i
$249$	−11.4993	−	24.7396i	−0.728741	−	1.56781i
$250$		0			0
$251$			9.49772i			0.599491i	0.954019	+	0.299745i	$0.0969017\pi$
$251$			9.49772i			0.599491i	−0.954019	+	0.299745i	$0.903098\pi$
$252$	−7.31977	+	1.77670i	−0.461102	+	0.111922i
$253$		−	26.7297i		−	1.68048i
$254$	−13.8859	−	27.3801i	−0.871277	−	1.71798i
$255$		0			0
$256$	−13.0847	+	9.20824i	−0.817791	+	0.575515i
$257$		−	27.3144i		−	1.70382i	−0.523686	−	0.851912i	$-0.675443\pi$
$257$		−	27.3144i		−	1.70382i	0.523686	−	0.851912i	$-0.324557\pi$
$258$	6.62045	−	8.41964i	0.412171	−	0.524184i
$259$	−8.10270			−0.503477
$260$		0			0
$261$	−7.34070	+	8.70484i	−0.454378	+	0.538816i
$262$	−8.00933	−	15.7927i	−0.494818	−	0.975679i
$263$	−1.24952			−0.0770484			−0.0385242	−	0.999258i	$-0.512266\pi$
$263$	−1.24952			−0.0770484			−0.0385242	+	0.999258i	$0.512266\pi$
$264$	14.2659	−	3.98460i	0.878004	−	0.245235i
$265$		0			0
$266$	−1.42778	−	2.81529i	−0.0875428	−	0.172616i
$267$	2.66998	+	5.74418i	0.163400	+	0.351538i
$268$	−10.0497	+	13.7230i	−0.613880	+	0.838268i
$269$	15.7189			0.958399			0.479199	−	0.877706i	$-0.340927\pi$
$269$	15.7189			0.958399			0.479199	+	0.877706i	$0.340927\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	−9.36377	+	2.96458i	−0.567762	+	0.179754i
$273$	11.1507	−	5.18299i	0.674869	−	0.313689i
$274$	11.8113	+	23.2895i	0.713548	+	1.40697i
$275$		0			0
$276$	−5.99375	+	30.0330i	−0.360781	+	1.80777i
$277$			0.633548i			0.0380662i	0.999819	+	0.0190331i	$0.00605879\pi$
$277$			0.633548i			0.0380662i	−0.999819	+	0.0190331i	$0.993941\pi$
$278$	−14.6359	+	7.42263i	−0.877802	+	0.445180i
$279$	11.9233	+	10.0548i	0.713829	+	0.601965i
$280$		0			0
$281$		−	20.9204i		−	1.24801i	−0.781422	−	0.624003i	$-0.785505\pi$
$281$		−	20.9204i		−	1.24801i	0.781422	−	0.624003i	$-0.214495\pi$
$282$	2.77532	−	3.52955i	0.165268	−	0.210182i
$283$	14.6846			0.872911			0.436455	−	0.899726i	$-0.356234\pi$
$283$	14.6846			0.872911			0.436455	+	0.899726i	$0.356234\pi$
$284$	−8.28075	+	11.3076i	−0.491372	+	0.670980i
$285$		0			0
$286$	−21.5653	+	10.9369i	−1.27519	+	0.646714i
$287$	9.50673			0.561165
$288$	−16.9224	+	1.27811i	−0.997160	+	0.0753131i
$289$	10.9707			0.645335
$290$		0			0
$291$	−21.7967	+	10.1314i	−1.27774	+	0.593914i
$292$	−5.42933	+	7.41388i	−0.317728	+	0.433864i
$293$	5.49911			0.321262			0.160631	−	0.987015i	$-0.448647\pi$
$293$	5.49911			0.321262			0.160631	+	0.987015i	$0.448647\pi$
$294$	8.21226	−	10.4440i	0.478949	−	0.609109i
$295$		0			0
$296$	−18.0145	−	2.95777i	−1.04707	−	0.171917i
$297$	15.1600	+	4.12197i	0.879672	+	0.239181i
$298$	15.0386	−	7.62688i	0.871165	−	0.441813i
$299$		−	49.9952i		−	2.89129i
$300$		0			0
$301$		−	5.48937i		−	0.316402i
$302$	−6.43167	−	12.6819i	−0.370101	−	0.729763i
$303$	21.8101	−	10.1377i	1.25296	−	0.582393i
$304$	−2.14666	−	6.78033i	−0.123119	−	0.388878i
$305$		0			0
$306$	−10.1404	−	2.38749i	−0.579687	−	0.136484i
$307$	−6.11929			−0.349246			−0.174623	−	0.984635i	$-0.555871\pi$
$307$	−6.11929			−0.349246			−0.174623	+	0.984635i	$0.555871\pi$
$308$	4.48514	−	6.12456i	0.255564	−	0.348979i
$309$	−5.37812	−	11.5705i	−0.305951	−	0.658221i
$310$		0			0
$311$	5.75819			0.326517			0.163258	−	0.986583i	$-0.447800\pi$
$311$	5.75819			0.326517			0.163258	+	0.986583i	$0.447800\pi$
$312$	26.6829	−	7.45280i	1.51062	−	0.421932i
$313$	−21.9800			−1.24238			−0.621192	−	0.783658i	$-0.713351\pi$
$313$	−21.9800			−1.24238			−0.621192	+	0.783658i	$0.713351\pi$
$314$	1.09478	+	2.15869i	0.0617822	+	0.121822i
$315$		0			0
$316$	11.8867	+	8.70484i	0.668676	+	0.489685i
$317$	−17.6815			−0.993091			−0.496545	−	0.868011i	$-0.665398\pi$
$317$	−17.6815			−0.993091			−0.496545	+	0.868011i	$0.665398\pi$
$318$	18.2487	−	23.2080i	1.02333	−	1.30144i
$319$		−	11.4759i		−	0.642527i
$320$		0			0
$321$	5.94333	+	12.7864i	0.331724	+	0.713669i
$322$	7.09931	+	13.9984i	0.395629	+	0.780099i
$323$		−	4.36583i		−	0.242922i
$324$	−16.1092	−	8.03079i	−0.894956	−	0.446155i
$325$		0			0
$326$	−15.0824	+	7.64907i	−0.835336	+	0.423643i
$327$	−4.12861	−	8.88227i	−0.228313	−	0.491190i
$328$	21.1360	+	3.47029i	1.16704	+	0.191615i
$329$		−	2.30117i		−	0.126867i
$330$		0			0
$331$	−7.14134			−0.392523			−0.196262	−	0.980552i	$-0.562880\pi$
$331$	−7.14134			−0.392523			−0.196262	+	0.980552i	$0.562880\pi$
$332$	−25.4157	−	18.6124i	−1.39487	−	1.02149i
$333$	−14.8024	−	12.4827i	−0.811166	−	0.684048i
$334$	−0.735985	+	0.373257i	−0.0402713	+	0.0204237i
$335$		0			0
$336$	−6.41277	+	5.87571i	−0.349845	+	0.320546i
$337$	1.90663			0.103861			0.0519303	−	0.998651i	$-0.483463\pi$
$337$	1.90663			0.103861			0.0519303	+	0.998651i	$0.483463\pi$
$338$	−23.9392	+	12.1408i	−1.30212	+	0.660373i
$339$	8.38731	+	18.0444i	0.455536	+	0.980038i
$340$		0			0
$341$	−15.7189			−0.851226
$342$	1.72879	−	7.34268i	0.0934821	−	0.397047i
$343$		−	15.5969i		−	0.842154i
$344$	2.00381	−	12.2043i	0.108038	−	0.658014i
$345$		0			0
$346$	15.2020	−	7.70974i	0.817265	−	0.414478i
$347$		−	0.530510i		−	0.0284793i	−0.999899	−	0.0142396i	$-0.995467\pi$
$347$		−	0.530510i		−	0.0284793i	0.999899	−	0.0142396i	$-0.00453277\pi$
$348$	−2.57331	+	12.8941i	−0.137944	+	0.691197i
$349$			7.36659i			0.394325i	0.980371	+	0.197162i	$0.0631726\pi$
$349$			7.36659i			0.394325i	−0.980371	+	0.197162i	$0.936827\pi$
$350$		0			0
$351$	28.3553	+	7.70974i	1.51349	+	0.411516i
$352$	12.2073	−	11.9793i	0.650653	−	0.638499i
$353$		−	11.2299i		−	0.597708i	−0.954299	−	0.298854i	$-0.903396\pi$
$353$		−	11.2299i		−	0.597708i	0.954299	−	0.298854i	$-0.0966044\pi$
$354$	9.45610	+	7.43543i	0.502586	+	0.395188i
$355$		0			0
$356$	5.90115	+	4.32153i	0.312760	+	0.229041i
$357$	−4.84167	+	2.25048i	−0.256248	+	0.119108i
$358$	0.387309	+	0.763694i	0.0204699	+	0.0403625i
$359$	−17.0980			−0.902396			−0.451198	−	0.892424i	$-0.649003\pi$
$359$	−17.0980			−0.902396			−0.451198	+	0.892424i	$0.649003\pi$
$360$		0			0
$361$	−15.8387			−0.833615
$362$	4.53387	+	8.93985i	0.238295	+	0.469868i
$363$	2.91934	−	1.35695i	0.153226	−	0.0712216i
$364$	8.38900	−	11.4554i	0.439703	−	0.600425i
$365$		0			0
$366$	15.7235	+	12.3636i	0.821882	+	0.646254i
$367$			13.9984i			0.730709i	0.930868	+	0.365355i	$0.119052\pi$
$367$			13.9984i			0.730709i	−0.930868	+	0.365355i	$0.880948\pi$
$368$	10.6738	+	33.7136i	0.556409	+	1.75744i
$369$	17.3673	+	14.6457i	0.904107	+	0.762424i
$370$		0			0
$371$		−	15.1309i		−	0.785559i
$372$	17.6615	+	3.52474i	0.915705	+	0.182749i
$373$			21.5952i			1.11815i	0.829116	+	0.559077i	$0.188845\pi$
$373$			21.5952i			1.11815i	−0.829116	+	0.559077i	$0.811155\pi$
$374$	9.36377	−	4.74886i	0.484189	−	0.245558i
$375$		0			0
$376$	0.840006	−	5.11611i	0.0433200	−	0.263843i
$377$		−	21.4645i		−	1.10548i
$378$	−9.03410	+	1.86776i	−0.464664	+	0.0960672i
$379$	11.7780			0.604996			0.302498	−	0.953150i	$-0.402180\pi$
$379$	11.7780			0.604996			0.302498	+	0.953150i	$0.402180\pi$
$380$		0			0
$381$	−15.8484	−	34.0963i	−0.811940	−	1.74680i
$382$	−23.8773	+	12.1094i	−1.22167	+	0.619573i
$383$	15.8484			0.809818			0.404909	−	0.914357i	$-0.367303\pi$
$383$	15.8484			0.809818			0.404909	+	0.914357i	$0.367303\pi$
$384$	−16.4021	+	10.7224i	−0.837018	+	0.547175i
$385$		0			0
$386$	5.38989	−	2.73350i	0.274338	−	0.139131i
$387$	8.45670	−	10.0282i	0.429878	−	0.509763i
$388$	−16.3983	+	22.3923i	−0.832499	+	1.13680i
$389$	18.4770			0.936822			0.468411	−	0.883511i	$-0.344827\pi$
$389$	18.4770			0.936822			0.468411	+	0.883511i	$0.344827\pi$
$390$		0			0
$391$			21.7081i			1.09783i
$392$	2.48560	−	15.1387i	0.125542	−	0.764621i
$393$	−9.14134	−	19.6666i	−0.461119	−	0.992050i
$394$	−12.7267	+	6.45436i	−0.641160	+	0.325166i
$395$		0			0
$396$	17.6289	−	4.27900i	0.885886	−	0.215028i
$397$		−	18.3981i		−	0.923373i	−0.887043	−	0.461687i	$-0.847244\pi$
$397$		−	18.3981i		−	0.923373i	0.887043	−	0.461687i	$-0.152756\pi$
$398$	−12.1663	−	23.9895i	−0.609843	−	1.20248i
$399$	−1.62958	−	3.50586i	−0.0815809	−	0.175513i
$400$		0			0
$401$			0.183464i			0.00916176i	0.999990	+	0.00458088i	$0.00145814\pi$
$401$			0.183464i			0.00916176i	−0.999990	+	0.00458088i	$0.998542\pi$
$402$	−12.8765	+	16.3759i	−0.642224	+	0.816756i
$403$	−29.4006			−1.46455
$404$	16.4084	−	22.4061i	0.816350	−	1.11474i
$405$		0			0
$406$	3.04796	+	6.00995i	0.151268	+	0.298269i
$407$	19.5145			0.967299
$408$	−11.5858	+	3.23604i	−0.573584	+	0.160208i
$409$	−30.5933			−1.51274			−0.756371	−	0.654142i	$-0.773030\pi$
$409$	−30.5933			−1.51274			−0.756371	+	0.654142i	$0.773030\pi$
$410$		0			0
$411$	13.4807	+	29.0023i	0.664953	+	1.43058i
$412$	−11.8867	−	8.70484i	−0.585613	−	0.428856i
$413$	6.16511			0.303365
$414$	−8.59600	+	36.5098i	−0.422470	+	1.79436i
$415$		0			0
$416$	22.8326	−	22.4061i	1.11946	−	1.09855i
$417$	−18.2260	+	8.47171i	−0.892531	+	0.414862i
$418$	3.43866	+	6.78033i	0.168190	+	0.331637i
$419$			13.9813i			0.683032i	0.939876	+	0.341516i	$0.110940\pi$
$419$			13.9813i			0.683032i	−0.939876	+	0.341516i	$0.889060\pi$
$420$		0			0
$421$		−	26.7297i		−	1.30272i	−0.758767	−	0.651362i	$-0.774198\pi$
$421$		−	26.7297i		−	1.30272i	0.758767	−	0.651362i	$-0.225802\pi$
$422$	6.93117	−	3.51516i	0.337404	−	0.171115i
$423$	3.54509	−	4.20388i	0.172368	−	0.204400i
$424$	5.52332	−	33.6401i	0.268236	−	1.63371i
$425$		0			0
$426$	−10.6101	+	13.4935i	−0.514059	+	0.653761i
$427$	10.2513			0.496095
$428$	13.1358	+	9.61965i	0.634945	+	0.464983i
$429$	−26.8552	+	12.4827i	−1.29658	+	0.602671i
$430$		0			0
$431$	34.7794			1.67527			0.837633	−	0.546233i	$-0.183939\pi$
$431$	34.7794			1.67527			0.837633	+	0.546233i	$0.183939\pi$
$432$	−20.7670	+	0.854768i	−0.999154	+	0.0411250i
$433$	19.8667			0.954731			0.477366	−	0.878705i	$-0.341592\pi$
$433$	19.8667			0.954731			0.477366	+	0.878705i	$0.341592\pi$
$434$	8.23202	−	4.17489i	0.395150	−	0.200401i
$435$		0			0
$436$	−9.12499	−	6.68241i	−0.437008	−	0.320030i
$437$	−15.7189			−0.751937
$438$	−6.95656	+	8.84709i	−0.332397	+	0.422730i
$439$			2.85392i			0.136210i	0.997678	+	0.0681051i	$0.0216953\pi$
$439$			2.85392i			0.136210i	−0.997678	+	0.0681051i	$0.978305\pi$
$440$		0			0
$441$	10.4900	−	12.4394i	0.499524	−	0.592352i
$442$	17.5140	−	8.88227i	0.833056	−	0.422486i
$443$			13.6854i			0.650212i	0.945678	+	0.325106i	$0.105400\pi$
$443$			13.6854i			0.650212i	−0.945678	+	0.325106i	$0.894600\pi$
$444$	−21.9262	−	4.37586i	−1.04057	−	0.207669i
$445$		0			0
$446$	−4.93163	−	9.72416i	−0.233520	−	0.460452i
$447$	18.7275	−	8.70484i	0.885782	−	0.411725i
$448$	−3.21134	+	9.51581i	−0.151722	+	0.449580i
$449$			19.1132i			0.902008i	0.892522	+	0.451004i	$0.148934\pi$
$449$			19.1132i			0.902008i	−0.892522	+	0.451004i	$0.851066\pi$
$450$		0			0
$451$	−22.8960			−1.07813
$452$	18.5375	+	13.5754i	0.871931	+	0.638533i
$453$	−7.34070	−	15.7927i	−0.344896	−	0.742008i
$454$	−4.73599	−	9.33838i	−0.222271	−	0.438272i
$455$		0			0
$456$	−2.34322	−	8.38933i	−0.109732	−	0.392866i
$457$	22.6133			1.05781			0.528903	−	0.848682i	$-0.322604\pi$
$457$	22.6133			1.05781			0.528903	+	0.848682i	$0.322604\pi$
$458$	−10.9580	−	21.6070i	−0.512036	−	1.00963i
$459$	−12.3120	−	3.34760i	−0.574674	−	0.156253i
$460$		0			0
$461$	−13.2199			−0.615711			−0.307855	−	0.951433i	$-0.599611\pi$
$461$	−13.2199			−0.615711			−0.307855	+	0.951433i	$0.599611\pi$
$462$	5.74677	−	7.30853i	0.267364	−	0.340024i
$463$			40.5506i			1.88455i	0.334845	+	0.942273i	$0.391316\pi$
$463$			40.5506i			1.88455i	−0.334845	+	0.942273i	$0.608684\pi$
$464$	4.58259	+	14.4743i	0.212742	+	0.671954i
$465$		0			0
$466$	0.900687	+	1.77597i	0.0417235	+	0.0822701i
$467$			10.2492i			0.474276i	0.971476	+	0.237138i	$0.0762093\pi$
$467$			10.2492i			0.474276i	−0.971476	+	0.237138i	$0.923791\pi$
$468$	32.9731	−	8.00343i	1.52418	−	0.369959i
$469$			10.6766i			0.493001i
$470$		0			0
$471$	1.24952	+	2.68820i	0.0575746	+	0.123866i
$472$	13.7067	+	2.25048i	0.630901	+	0.103587i
$473$			13.2206i			0.607883i
$474$	14.1845	+	11.1534i	0.651517	+	0.512294i
$475$		0			0
$476$	−3.64254	+	4.97397i	−0.166956	+	0.227982i
$477$	23.3101	−	27.6419i	1.06730	−	1.26564i
$478$	−11.9907	+	6.08110i	−0.548441	+	0.278143i
$479$	−31.4378			−1.43643			−0.718215	−	0.695821i	$-0.755041\pi$
$479$	−31.4378			−1.43643			−0.718215	+	0.695821i	$0.755041\pi$
$480$		0			0
$481$	36.5000			1.66425
$482$	2.86733	−	1.45417i	0.130603	−	0.0662357i
$483$	8.10270	+	17.4321i	0.368686	+	0.793188i
$484$	2.19632	−	2.99912i	0.0998326	−	0.136324i
$485$		0			0
$486$	−19.3813	−	10.5055i	−0.879154	−	0.476538i
$487$		−	0.177431i		−	0.00804018i	−0.999992	−	0.00402009i	$-0.998720\pi$
$487$		−	0.177431i		−	0.00804018i	0.999992	−	0.00402009i	$-0.00127964\pi$
$488$	22.7914	+	3.74208i	1.03172	+	0.169396i
$489$	−18.7820	+	8.73016i	−0.849352	+	0.394791i
$490$		0			0
$491$		−	7.75623i		−	0.350034i	−0.984565	−	0.175017i	$-0.944002\pi$
$491$		−	7.75623i		−	0.350034i	0.984565	−	0.175017i	$-0.0559980\pi$
$492$	25.7255	+	5.13410i	1.15980	+	0.231463i
$493$			9.31999i			0.419751i
$494$	6.43167	+	12.6819i	0.289375	+	0.570587i
$495$		0			0
$496$	19.8260	−	6.27693i	0.890212	−	0.281842i
$497$			8.79736i			0.394616i
$498$	−30.3289	−	23.8479i	−1.35907	−	1.06865i
$499$	5.22067			0.233709			0.116855	−	0.993149i	$-0.462719\pi$
$499$	5.22067			0.233709			0.116855	+	0.993149i	$0.462719\pi$
$500$		0			0
$501$	−0.916519	+	0.426011i	−0.0409470	+	0.0190328i
$502$	6.07533	+	11.9793i	0.271155	+	0.534662i
$503$	6.34171			0.282763			0.141381	−	0.989955i	$-0.454846\pi$
$503$	6.34171			0.282763			0.141381	+	0.989955i	$0.454846\pi$
$504$	−8.09581	+	6.92310i	−0.360616	+	0.308379i
$505$		0			0
$506$	−17.0980	−	33.7136i	−0.760097	−	1.49875i
$507$	−29.8113	+	13.8567i	−1.32397	+	0.615399i
$508$	−35.0280	−	25.6517i	−1.55412	−	1.13811i
$509$	34.1959			1.51571			0.757854	−	0.652425i	$-0.226248\pi$
$509$	34.1959			1.51571			0.757854	+	0.652425i	$0.226248\pi$
$510$		0			0
$511$			5.76805i			0.255164i
$512$	−10.6133	+	19.9839i	−0.469045	+	0.883174i
$513$	2.42401	−	8.91513i	0.107023	−	0.393613i
$514$	−17.4720	−	34.4511i	−0.770656	−	1.51957i
$515$		0			0
$516$	2.96453	−	14.8544i	0.130506	−	0.653928i
$517$			5.54212i			0.243742i
$518$	−10.2198	+	5.18299i	−0.449032	+	0.227728i
$519$	18.9310	−	8.79941i	0.830978	−	0.386251i
$520$		0			0
$521$		−	32.6151i		−	1.42889i	−0.699689	−	0.714447i	$-0.746678\pi$
$521$		−	32.6151i		−	1.42889i	0.699689	−	0.714447i	$-0.253322\pi$
$522$	−3.69054	+	15.6748i	−0.161530	+	0.686068i
$523$	14.6074			0.638736			0.319368	−	0.947631i	$-0.396529\pi$
$523$	14.6074			0.638736			0.319368	+	0.947631i	$0.396529\pi$
$524$	−20.2040	−	14.7958i	−0.882618	−	0.646359i
$525$		0			0
$526$	−1.57599	+	0.799268i	−0.0687165	+	0.0348498i
$527$	12.7659			0.556091
$528$	15.4445	−	14.1510i	0.672135	−	0.615845i
$529$	55.1587			2.39820
$530$		0			0
$531$	11.2627	+	9.49772i	0.488759	+	0.412166i
$532$	−3.60167	−	2.63757i	−0.156152	−	0.114353i
$533$	−42.8246			−1.85494
$534$	7.04194	+	5.53715i	0.304734	+	0.239616i
$535$		0			0
$536$	−3.89734	+	23.7370i	−0.168340	+	1.02528i
$537$	0.442050	+	0.951024i	0.0190759	+	0.0410397i
$538$	19.8260	−	10.0548i	0.854758	−	0.433493i
$539$			16.3993i			0.706368i
$540$		0			0
$541$			13.0217i			0.559846i	0.960023	+	0.279923i	$0.0903089\pi$
$541$			13.0217i			0.559846i	−0.960023	+	0.279923i	$0.909691\pi$
$542$		0			0
$543$	5.17466	+	11.1327i	0.222066	+	0.477752i
$544$	−9.91402	+	9.72882i	−0.425060	+	0.417120i
$545$		0			0
$546$	10.7488	−	13.6699i	0.460005	−	0.585017i
$547$	−37.8280			−1.61741			−0.808705	−	0.588214i	$-0.799831\pi$
$547$	−37.8280			−1.61741			−0.808705	+	0.588214i	$0.799831\pi$
$548$	29.7948	+	21.8193i	1.27277	+	0.932076i
$549$	18.7275	+	15.7927i	0.799272	+	0.674018i
$550$		0			0
$551$	−6.74863			−0.287501
$552$	11.6511	+	41.7140i	0.495906	+	1.77547i
$553$	9.24791			0.393261
$554$	0.405257	+	0.799083i	0.0172177	+	0.0339498i
$555$		0			0
$556$	−13.7120	+	18.7241i	−0.581519	+	0.794077i
$557$	−22.0135			−0.932744			−0.466372	−	0.884589i	$-0.654439\pi$
$557$	−22.0135			−0.932744			−0.466372	+	0.884589i	$0.654439\pi$
$558$	21.4703	+	5.05505i	0.908910	+	0.213997i
$559$			24.7278i			1.04587i
$560$		0			0
$561$	11.6607	−	5.42004i	0.492313	−	0.228834i
$562$	−13.3820	−	26.3865i	−0.564485	−	1.11305i
$563$			9.80727i			0.413327i	0.978412	+	0.206664i	$0.0662606\pi$
$563$			9.80727i			0.413327i	−0.978412	+	0.206664i	$0.933739\pi$
$564$	1.24274	−	6.22703i	0.0523289	−	0.262205i
$565$		0			0
$566$	18.5215	−	9.39321i	0.778515	−	0.394826i
$567$	−11.1363	+	1.90733i	−0.467681	+	0.0801002i
$568$	−3.21134	+	19.5589i	−0.134745	+	0.820673i
$569$		−	22.4555i		−	0.941384i	−0.882298	−	0.470692i	$-0.844004\pi$
$569$		−	22.4555i		−	0.941384i	0.882298	−	0.470692i	$-0.155996\pi$
$570$		0			0
$571$	5.92867			0.248107			0.124054	−	0.992276i	$-0.460411\pi$
$571$	5.92867			0.248107			0.124054	+	0.992276i	$0.460411\pi$
$572$	−20.2040	+	27.5891i	−0.844773	+	1.15356i
$573$	−29.7343	+	13.8209i	−1.24217	+	0.577378i
$574$	11.9907	−	6.08110i	0.500481	−	0.253820i
$575$		0			0
$576$	−20.5263	+	12.4367i	−0.855263	+	0.518194i
$577$	−39.1587			−1.63020			−0.815098	−	0.579322i	$-0.803317\pi$
$577$	−39.1587			−1.63020			−0.815098	+	0.579322i	$0.803317\pi$
$578$	13.8371	−	7.01754i	0.575549	−	0.291891i
$579$	6.71200	−	3.11984i	0.278941	−	0.129656i
$580$		0			0
$581$	−19.7736			−0.820347
$582$	−21.0111	+	26.7211i	−0.870936	+	1.10762i
$583$			36.4413i			1.50924i
$584$	−2.10554	+	12.8239i	−0.0871279	+	0.530658i
$585$		0			0
$586$	6.93593	−	3.51757i	0.286521	−	0.145310i
$587$			29.3332i			1.21071i	0.795955	+	0.605356i	$0.206969\pi$
$587$			29.3332i			1.21071i	−0.795955	+	0.605356i	$0.793031\pi$
$588$	3.67731	−	18.4260i	0.151650	−	0.759874i
$589$			9.24381i			0.380885i
$590$		0			0
$591$	−15.8484	+	7.36659i	−0.651918	+	0.303021i
$592$	−24.6133	+	7.79260i	−1.01160	+	0.320274i
$593$			24.6525i			1.01236i	0.862428	+	0.506179i	$0.168942\pi$
$593$			24.6525i			1.01236i	−0.862428	+	0.506179i	$0.831058\pi$
$594$	21.7577	−	4.49831i	0.892729	−	0.184568i
$595$		0			0
$596$	14.0893	−	19.2393i	0.577121	−	0.788072i
$597$	−13.8859	−	29.8740i	−0.568311	−	1.22266i
$598$	−31.9800	−	63.0580i	−1.30776	−	2.57863i
$599$	−29.8638			−1.22020			−0.610102	−	0.792323i	$-0.708871\pi$
$599$	−29.8638			−1.22020			−0.610102	+	0.792323i	$0.708871\pi$
$600$		0			0
$601$	−17.7267			−0.723085			−0.361543	−	0.932356i	$-0.617750\pi$
$601$	−17.7267			−0.723085			−0.361543	+	0.932356i	$0.617750\pi$
$602$	−3.51134	−	6.92364i	−0.143112	−	0.282187i
$603$	−16.4480	+	19.5046i	−0.669814	+	0.794287i
$604$	−16.2243	−	11.8814i	−0.660158	−	0.483447i
$605$		0			0
$606$	21.0240	−	26.7375i	0.854041	−	1.08614i
$607$			25.8174i			1.04790i	0.851750	+	0.523949i	$0.175542\pi$
$607$			25.8174i			1.04790i	−0.851750	+	0.523949i	$0.824458\pi$
$608$	−7.04466	−	7.17877i	−0.285699	−	0.291137i
$609$	3.47875	+	7.48416i	0.140966	+	0.303274i
$610$		0			0
$611$			10.3660i			0.419363i
$612$	−14.3171	+	3.47513i	−0.578733	+	0.140474i
$613$		−	16.6866i		−	0.673965i	−0.941511	−	0.336982i	$-0.890594\pi$
$613$		−	16.6866i		−	0.673965i	0.941511	−	0.336982i	$-0.109406\pi$
$614$	−7.71815	+	3.91428i	−0.311479	+	0.157967i
$615$		0			0
$616$	1.73937	−	10.5938i	0.0700814	−	0.426835i
$617$			8.69514i			0.350053i	0.984564	+	0.175027i	$0.0560012\pi$
$617$			8.69514i			0.350053i	−0.984564	+	0.175027i	$0.943999\pi$
$618$	−14.1845	−	11.1534i	−0.570585	−	0.448657i
$619$	20.3727			0.818846			0.409423	−	0.912345i	$-0.365730\pi$
$619$	20.3727			0.818846			0.409423	+	0.912345i	$0.365730\pi$
$620$		0			0
$621$	−12.0528	+	44.3285i	−0.483663	+	1.77884i
$622$	7.26270	−	3.68330i	0.291208	−	0.147687i
$623$	4.59114			0.183940
$624$	28.8874	−	26.4681i	1.15642	−	1.05957i
$625$		0			0
$626$	−27.7230	+	14.0598i	−1.10803	+	0.561942i
$627$	3.92467	+	8.44351i	0.156736	+	0.337201i
$628$	2.76166	+	2.02242i	0.110202	+	0.0807034i
$629$	−15.8484			−0.631919
$630$		0			0
$631$			4.51267i			0.179647i	0.995958	+	0.0898233i	$0.0286302\pi$
$631$			4.51267i			0.179647i	−0.995958	+	0.0898233i	$0.971370\pi$
$632$	20.5606	+	3.37581i	0.817856	+	0.134282i
$633$	8.63135	−	4.01198i	0.343065	−	0.159462i
$634$	−22.3013	+	11.3102i	−0.885699	+	0.449184i
$635$		0			0
$636$	8.17145	−	40.9448i	0.324019	−	1.62357i
$637$			30.6732i			1.21532i
$638$	−7.34070	−	14.4743i	−0.290621	−	0.573045i
$639$	−13.5529	+	16.0714i	−0.536143	+	0.635776i
$640$		0			0
$641$			25.0424i			0.989114i	0.869145	+	0.494557i	$0.164670\pi$
$641$			25.0424i			0.989114i	−0.869145	+	0.494557i	$0.835330\pi$
$642$	15.6752	+	12.3256i	0.618651	+	0.486452i
$643$	21.7360			0.857184			0.428592	−	0.903498i	$-0.359010\pi$
$643$	21.7360			0.857184			0.428592	+	0.903498i	$0.359010\pi$
$644$	17.9085	+	13.1147i	0.705693	+	0.516793i
$645$		0			0
$646$	−2.79266	−	5.50655i	−0.109876	−	0.216652i
$647$	21.3476			0.839259			0.419629	−	0.907695i	$-0.362160\pi$
$647$	21.3476			0.839259			0.419629	+	0.907695i	$0.362160\pi$
$648$	−25.4552	+	0.175357i	−0.999976	+	0.00688868i
$649$	−14.8480			−0.582836
$650$		0			0
$651$	10.2513	−	4.76495i	0.401780	−	0.186753i
$652$	−14.1303	+	19.2953i	−0.553386	+	0.755661i
$653$	−25.9387			−1.01506			−0.507530	−	0.861634i	$-0.669441\pi$
$653$	−25.9387			−1.01506			−0.507530	+	0.861634i	$0.669441\pi$
$654$	−10.8890	−	8.56213i	−0.425793	−	0.334806i
$655$		0			0
$656$	28.8783	−	9.14290i	1.12751	−	0.356970i
$657$	−8.88603	+	10.5373i	−0.346677	+	0.411101i
$658$	−1.47197	−	2.90242i	−0.0573834	−	0.113148i
$659$		−	20.6474i		−	0.804307i	−0.915572	−	0.402153i	$-0.868262\pi$
$659$		−	20.6474i		−	0.804307i	0.915572	−	0.402153i	$-0.131738\pi$
$660$		0			0
$661$			9.31999i			0.362506i	0.983437	+	0.181253i	$0.0580152\pi$
$661$			9.31999i			0.362506i	−0.983437	+	0.181253i	$0.941985\pi$
$662$	−9.00724	+	4.56804i	−0.350076	+	0.177542i
$663$	21.8101	−	10.1377i	0.847034	−	0.393714i
$664$	−43.9620	−	7.21805i	−1.70606	−	0.280115i
$665$		0			0
$666$	−26.6547	−	6.27568i	−1.03285	−	0.243178i
$667$	33.5560			1.29929
$668$	−0.689526	+	0.941564i	−0.0266786	+	0.0364302i
$669$	−5.62865	−	12.1094i	−0.217616	−	0.468178i
$670$		0			0
$671$	−24.6892			−0.953115
$672$	−4.32983	+	11.5129i	−0.167027	+	0.444121i
$673$	37.2520			1.43596			0.717980	−	0.696063i	$-0.245067\pi$
$673$	37.2520			1.43596			0.717980	+	0.696063i	$0.245067\pi$
$674$	2.40479	−	1.21960i	0.0926292	−	0.0469771i
$675$		0			0
$676$	−22.4280	+	30.6260i	−0.862616	+	1.17792i
$677$	37.0665			1.42458			0.712290	−	0.701885i	$-0.247658\pi$
$677$	37.0665			1.42458			0.712290	+	0.701885i	$0.247658\pi$
$678$	22.1211	+	17.3940i	0.849555	+	0.668014i
$679$			17.4214i			0.668571i
$680$		0			0
$681$	−5.40535	−	11.6290i	−0.207133	−	0.445626i
$682$	−19.8260	+	10.0548i	−0.759176	+	0.385018i
$683$			26.0898i			0.998297i	0.866516	+	0.499149i	$0.166354\pi$
$683$			26.0898i			0.998297i	−0.866516	+	0.499149i	$0.833646\pi$
$684$	−2.51635	−	10.3670i	−0.0962150	−	0.396393i
$685$		0			0
$686$	−9.97676	−	19.6721i	−0.380914	−	0.751085i
$687$	−12.5068	−	26.9071i	−0.477165	−	1.02657i
$688$	−5.27928	−	16.6749i	−0.201271	−	0.635723i
$689$			68.1598i			2.59668i
$690$		0			0
$691$	34.8187			1.32457			0.662283	−	0.749254i	$-0.269588\pi$
$691$	34.8187			1.32457			0.662283	+	0.749254i	$0.269588\pi$
$692$	14.2424	−	19.4483i	0.541415	−	0.739314i
$693$	7.34070	−	8.70484i	0.278850	−	0.330669i
$694$	−0.339347	−	0.669123i	−0.0128814	−	0.0253995i
$695$		0			0
$696$	5.00221	+	17.9092i	0.189608	+	0.678845i
$697$	18.5946			0.704323
$698$	4.71213	+	9.29135i	0.178357	+	0.351683i
$699$	1.02799	+	2.21160i	0.0388820	+	0.0836505i
$700$		0			0
$701$	−12.7188			−0.480383			−0.240192	−	0.970725i	$-0.577210\pi$
$701$	−12.7188			−0.480383			−0.240192	+	0.970725i	$0.577210\pi$
$702$	40.6956	−	8.41363i	1.53596	−	0.317552i
$703$		−	11.4759i		−	0.432822i
$704$	7.73419	−	22.9178i	0.291493	−	0.863749i
$705$		0			0
$706$	−7.18336	−	14.1641i	−0.270349	−	0.533073i
$707$		−	17.4321i		−	0.655602i
$708$	16.6830	+	3.32946i	0.626984	+	0.125129i
$709$			46.7263i			1.75484i	0.479721	+	0.877421i	$0.340738\pi$
$709$			46.7263i			1.75484i	−0.479721	+	0.877421i	$0.659262\pi$
$710$		0			0
$711$	16.8945	+	14.2470i	0.633593	+	0.534303i
$712$	10.2073	+	1.67593i	0.382536	+	0.0628080i
$713$		−	45.9628i		−	1.72132i
$714$	−4.66716	+	5.93552i	−0.174664	+	0.222131i
$715$		0			0
$716$	0.977012	+	0.715486i	0.0365127	+	0.0267390i
$717$	−14.9319	+	6.94058i	−0.557643	+	0.259201i
$718$	−21.5653	+	10.9369i	−0.804812	+	0.408162i
$719$	9.50673			0.354541			0.177271	−	0.984162i	$-0.443273\pi$
$719$	9.50673			0.354541			0.177271	+	0.984162i	$0.443273\pi$
$720$		0			0
$721$	−9.24791			−0.344410
$722$	−19.9771	+	10.1314i	−0.743469	+	0.377052i
$723$	3.57067	−	1.65970i	0.132795	−	0.0617249i
$724$	11.4370	+	8.37552i	0.425051	+	0.311274i
$725$		0			0
$726$	2.81412	−	3.57890i	0.104442	−	0.132825i
$727$		−	31.7629i		−	1.17802i	−0.808125	−	0.589011i	$-0.799518\pi$
$727$		−	31.7629i		−	1.17802i	0.808125	−	0.589011i	$-0.200482\pi$
$728$	3.25333	−	19.8146i	0.120576	−	0.734377i
$729$	−23.2827	−	13.6718i	−0.862321	−	0.506362i
$730$		0			0
$731$		−	10.7369i		−	0.397119i
$732$	27.7403	+	5.53620i	1.02531	+	0.204624i
$733$			15.5852i			0.575653i	0.957683	+	0.287826i	$0.0929326\pi$
$733$			15.5852i			0.575653i	−0.957683	+	0.287826i	$0.907067\pi$
$734$	8.95424	+	17.6559i	0.330507	+	0.651691i
$735$		0			0
$736$	35.0280	+	35.6948i	1.29115	+	1.31573i
$737$		−	25.7135i		−	0.947171i
$738$	31.2734	+	7.36312i	1.15119	+	0.271040i
$739$	4.17997			0.153763			0.0768813	−	0.997040i	$-0.475504\pi$
$739$	4.17997			0.153763			0.0768813	+	0.997040i	$0.475504\pi$
$740$		0			0
$741$	7.34070	+	15.7927i	0.269667	+	0.580161i
$742$	−9.67869	−	19.0844i	−0.355316	−	0.700610i
$743$	20.1805			0.740351			0.370176	−	0.928962i	$-0.379298\pi$
$743$	20.1805			0.740351			0.370176	+	0.928962i	$0.379298\pi$
$744$	24.5307	−	6.85169i	0.899341	−	0.251195i
$745$		0			0
$746$	13.8136	+	27.2376i	0.505752	+	0.997239i
$747$	−36.1233	−	30.4624i	−1.32168	−	1.11456i
$748$	8.77268	−	11.9793i	0.320761	−	0.438007i
$749$	10.2198			0.373423
$750$		0			0
$751$		−	19.0316i		−	0.694474i	−0.937777	−	0.347237i	$-0.887120\pi$
$751$		−	19.0316i		−	0.694474i	0.937777	−	0.347237i	$-0.112880\pi$
$752$	−2.21310	−	6.99018i	−0.0807034	−	0.254906i
$753$	6.93400	+	14.9178i	0.252689	+	0.543633i
$754$	−13.7300	−	27.0728i	−0.500019	−	0.985934i
$755$		0			0
$756$	−10.1998	+	8.13455i	−0.370964	+	0.295851i
$757$		−	4.22227i		−	0.153461i	−0.997052	−	0.0767305i	$-0.975552\pi$
$757$		−	4.22227i		−	0.153461i	0.997052	−	0.0767305i	$-0.0244481\pi$
$758$	14.8554	−	7.53395i	0.539572	−	0.273645i
$759$	−19.5145	−	41.9834i	−0.708332	−	1.52390i
$760$		0			0
$761$			38.0795i			1.38038i	0.723628	+	0.690190i	$0.242473\pi$
$761$			38.0795i			1.38038i	−0.723628	+	0.690190i	$0.757527\pi$
$762$	−41.7994	−	32.8673i	−1.51423	−	1.19066i
$763$	−7.09931			−0.257012
$764$	−22.3701	+	30.5468i	−0.809321	+	1.10515i
$765$		0			0
$766$	19.9894	−	10.1377i	0.722245	−	0.366288i
$767$	−27.7717			−1.00278
$768$	−13.8290	+	24.0158i	−0.499011	+	0.866596i
$769$	16.9600			0.611595			0.305797	−	0.952097i	$-0.401077\pi$
$769$	16.9600			0.611595			0.305797	+	0.952097i	$0.401077\pi$
$770$		0			0
$771$	−19.9414	−	42.9018i	−0.718172	−	1.54507i
$772$	5.04966	−	6.89542i	0.181741	−	0.248172i
$773$	16.3849			0.589324			0.294662	−	0.955602i	$-0.404793\pi$
$773$	16.3849			0.589324			0.294662	+	0.955602i	$0.404793\pi$
$774$	4.25161	−	18.0579i	0.152821	−	0.649076i
$775$		0			0
$776$	−6.35941	+	38.7324i	−0.228290	+	1.39041i
$777$	−12.7267	+	5.91554i	−0.456566	+	0.212219i
$778$	23.3047	−	11.8190i	0.835515	−	0.423733i
$779$			13.4644i			0.482413i
$780$		0			0
$781$		−	21.1875i		−	0.758150i
$782$	13.8859	+	27.3801i	0.496558	+	0.979109i
$783$	−5.17466	+	19.0316i	−0.184927	+	0.680135i
$784$	−6.54862	−	20.6841i	−0.233879	−	0.738719i
$785$		0			0
$786$	−24.1098	−	18.9578i	−0.859968	−	0.676202i
$787$	25.6833			0.915511			0.457756	−	0.889078i	$-0.348653\pi$
$787$	25.6833			0.915511			0.457756	+	0.889078i	$0.348653\pi$
$788$	−11.9233	+	16.2815i	−0.424750	+	0.580005i
$789$	−1.96257	+	0.912234i	−0.0698695	+	0.0324764i
$790$		0			0
$791$	14.4223			0.512799
$792$	19.4979	−	16.6736i	0.692828	−	0.592469i
$793$	−46.1787			−1.63985
$794$	−11.7686	−	23.2052i	−0.417651	−	0.823521i
$795$		0			0
$796$	−30.6903	−	22.4752i	−1.08779	−	0.796611i
$797$	13.7563			0.487274			0.243637	−	0.969866i	$-0.421659\pi$
$797$	13.7563			0.487274			0.243637	+	0.969866i	$0.421659\pi$
$798$	−4.29793	−	3.37950i	−0.152145	−	0.119633i
$799$		−	4.50096i		−	0.159232i
$800$		0			0
$801$	8.38731	+	7.07293i	0.296351	+	0.249910i
$802$	0.117355	+	0.231400i	0.00414395	+	0.00817102i
$803$		−	13.8918i		−	0.490229i
$804$	−5.76590	+	28.8913i	−0.203348	+	1.01892i
$805$		0			0
$806$	−37.0825	+	18.8065i	−1.30618	+	0.662430i
$807$	24.6892	−	11.4759i	0.869100	−	0.403971i
$808$	6.36333	−	38.7562i	0.223861	−	1.36344i
$809$		−	6.42314i		−	0.225826i	−0.993605	−	0.112913i	$-0.963982\pi$
$809$		−	6.42314i		−	0.225826i	0.993605	−	0.112913i	$-0.0360181\pi$
$810$		0			0
$811$	−40.8353			−1.43392			−0.716961	−	0.697114i	$-0.754467\pi$
$811$	−40.8353			−1.43392			−0.716961	+	0.697114i	$0.754467\pi$
$812$	7.68868	+	5.63058i	0.269820	+	0.197594i
$813$		0			0
$814$	24.6133	−	12.4827i	0.862696	−	0.437518i
$815$		0			0
$816$	−12.5430	+	11.4926i	−0.439094	+	0.402321i
$817$	7.77462			0.271999
$818$	−38.5868	+	19.5694i	−1.34916	+	0.684228i
$819$	13.7300	−	16.2815i	0.479767	−	0.568923i
$820$		0			0
$821$	51.8774			1.81053			0.905267	−	0.424844i	$-0.139671\pi$
$821$	51.8774			1.81053			0.905267	+	0.424844i	$0.139671\pi$
$822$	35.5546	+	27.9570i	1.24011	+	0.975111i
$823$			36.0379i			1.25620i	0.778131	+	0.628102i	$0.216168\pi$
$823$			36.0379i			1.25620i	−0.778131	+	0.628102i	$0.783832\pi$
$824$	−20.5606	−	3.37581i	−0.716261	−	0.117602i
$825$		0			0
$826$	7.77594	−	3.94359i	0.270559	−	0.137215i
$827$		−	29.8501i		−	1.03799i	−0.854777	−	0.518995i	$-0.826306\pi$
$827$		−	29.8501i		−	1.03799i	0.854777	−	0.518995i	$-0.173694\pi$
$828$	12.5120	+	51.5477i	0.434821	+	1.79141i
$829$			22.2287i			0.772035i	0.922492	+	0.386017i	$0.126150\pi$
$829$			22.2287i			0.772035i	−0.922492	+	0.386017i	$0.873850\pi$
$830$		0			0
$831$	0.462534	+	0.995094i	0.0160451	+	0.0345194i
$832$	14.4660	−	42.8656i	0.501519	−	1.48610i
$833$		−	13.3185i		−	0.461457i
$834$	−17.5691	+	22.3437i	−0.608368	+	0.773699i
$835$		0			0
$836$	8.67424	+	6.35232i	0.300005	+	0.219700i
$837$	26.0682	+	7.08790i	0.901050	+	0.244994i
$838$	8.94333	+	17.6344i	0.308942	+	0.609170i
$839$	5.17466			0.178649			0.0893246	−	0.996003i	$-0.471529\pi$
$839$	5.17466			0.178649			0.0893246	+	0.996003i	$0.471529\pi$
$840$		0			0
$841$	−14.5933			−0.503218
$842$	−17.0980	−	33.7136i	−0.589235	−	1.16185i
$843$	−15.2733	−	32.8590i	−0.526042	−	1.13172i
$844$	6.49364	−	8.86721i	0.223520	−	0.305222i
$845$		0			0
$846$	1.78229	−	7.56993i	0.0612765	−	0.260260i
$847$		−	2.33334i		−	0.0801745i
$848$	−14.5519	−	45.9628i	−0.499713	−	1.57837i
$849$	23.0647	−	10.7208i	0.791578	−	0.367937i
$850$		0			0
$851$			57.0613i			1.95604i
$852$	−4.75101	+	23.8059i	−0.162767	+	0.815578i
$853$		−	36.3283i		−	1.24386i	−0.783073	−	0.621929i	$-0.786349\pi$
$853$		−	36.3283i		−	1.24386i	0.783073	−	0.621929i	$-0.213651\pi$
$854$	12.9298	−	6.55737i	0.442448	−	0.224389i
$855$		0			0
$856$	22.7213	+	3.73058i	0.776599	+	0.127509i
$857$			9.42274i			0.321875i	0.986965	+	0.160937i	$0.0514517\pi$
$857$			9.42274i			0.321875i	−0.986965	+	0.160937i	$0.948548\pi$
$858$	−25.8873	+	32.9225i	−0.883777	+	1.12395i
$859$	18.0480			0.615789			0.307894	−	0.951421i	$-0.400376\pi$
$859$	18.0480			0.615789			0.307894	+	0.951421i	$0.400376\pi$
$860$		0			0
$861$	14.9319	−	6.94058i	0.508879	−	0.236534i
$862$	43.8667	−	22.2471i	1.49410	−	0.757739i
$863$	−18.3475			−0.624555			−0.312278	−	0.949991i	$-0.601092\pi$
$863$	−18.3475			−0.624555			−0.312278	+	0.949991i	$0.601092\pi$
$864$	−25.6463	+	14.3620i	−0.872505	+	0.488605i
$865$		0			0
$866$	25.0575	−	12.7080i	0.851488	−	0.431834i
$867$	17.2313	−	8.00937i	0.585206	−	0.272013i
$868$	7.71238	−	10.5314i	0.261775	−	0.357460i
$869$	−22.2726			−0.755547
$870$		0			0
$871$		−	48.0946i		−	1.62962i
$872$	−15.7837	−	2.59150i	−0.534503	−	0.0877592i
$873$	−26.8387	+	31.8262i	−0.908352	+	1.07715i
$874$	−19.8260	+	10.0548i	−0.670623	+	0.340108i
$875$		0			0
$876$	−3.11503	+	15.6085i	−0.105247	+	0.527363i
$877$			16.5736i			0.559651i	0.960051	+	0.279826i	$0.0902766\pi$
$877$			16.5736i			0.559651i	−0.960051	+	0.279826i	$0.909723\pi$
$878$	1.82555	+	3.59960i	0.0616092	+	0.121481i
$879$	8.63728	−	4.01474i	0.291328	−	0.135414i
$880$		0			0
$881$		−	25.5865i		−	0.862031i	−0.902345	−	0.431015i	$-0.858155\pi$
$881$		−	25.5865i		−	0.862031i	0.902345	−	0.431015i	$-0.141845\pi$
$882$	5.27385	−	22.3996i	0.177580	−	0.754235i
$883$	−21.2127			−0.713863			−0.356931	−	0.934131i	$-0.616177\pi$
$883$	−21.2127			−0.713863			−0.356931	+	0.934131i	$0.616177\pi$
$884$	16.4084	−	22.4061i	0.551875	−	0.753598i
$885$		0			0
$886$	8.75403	+	17.2611i	0.294097	+	0.579899i
$887$	−25.2727			−0.848574			−0.424287	−	0.905528i	$-0.639475\pi$
$887$	−25.2727			−0.848574			−0.424287	+	0.905528i	$0.639475\pi$
$888$	−30.4541	+	8.50615i	−1.02197	+	0.285448i
$889$	−27.2520			−0.914004
$890$		0			0
$891$	26.8206	−	4.59360i	0.898525	−	0.153891i
$892$	−12.4404	−	9.11033i	−0.416534	−	0.305036i
$893$	3.25915			0.109063
$894$	18.0525	−	22.9586i	0.603767	−	0.767849i
$895$		0			0
$896$	2.03650	+	14.0563i	0.0680346	+	0.469588i
$897$	−36.5000	−	78.5258i	−1.21870	−	2.62190i
$898$	12.2260	+	24.1071i	0.407987	+	0.804466i
$899$		−	19.7333i		−	0.658142i
$900$		0			0
$901$		−	29.5953i		−	0.985962i
$902$	−28.8783	+	14.6457i	−0.961542	+	0.487648i
$903$	−4.00762	−	8.62198i	−0.133365	−	0.286921i
$904$	32.0647	+	5.26465i	1.06646	+	0.175100i
$905$		0			0
$906$	−19.3607	−	15.2235i	−0.643217	−	0.505768i
$907$	22.7267			0.754626			0.377313	−	0.926086i	$-0.376848\pi$
$907$	22.7267			0.754626			0.377313	+	0.926086i	$0.376848\pi$
$908$	−11.9468	−	8.74890i	−0.396469	−	0.290343i
$909$	26.8552	−	31.8458i	0.890731	−	1.05626i
$910$		0			0
$911$	−8.92321			−0.295639			−0.147820	−	0.989014i	$-0.547226\pi$
$911$	−8.92321			−0.295639			−0.147820	+	0.989014i	$0.547226\pi$
$912$	−8.32180	−	9.08243i	−0.275562	−	0.300749i
$913$	47.6226			1.57608
$914$	28.5218	−	14.4649i	0.943416	−	0.478456i
$915$		0			0
$916$	−27.6424	−	20.2431i	−0.913330	−	0.668850i
$917$	−15.7189			−0.519084
$918$	−17.6702	+	3.65324i	−0.583204	+	0.120575i
$919$			33.7531i			1.11341i	0.830710	+	0.556706i	$0.187935\pi$
$919$			33.7531i			1.11341i	−0.830710	+	0.556706i	$0.812065\pi$
$920$		0			0
$921$	−9.61137	+	4.46751i	−0.316705	+	0.147209i
$922$	−16.6740	+	8.45626i	−0.549129	+	0.278492i
$923$		−	39.6292i		−	1.30441i
$924$	2.57331	−	12.8941i	0.0846556	−	0.424185i
$925$		0			0
$926$	25.9387	+	51.1457i	0.852398	+	1.68075i
$927$	−16.8945	−	14.2470i	−0.554888	−	0.467932i
$928$	15.0386	+	15.3249i	0.493667	+	0.503065i
$929$		−	51.1823i		−	1.67924i	−0.543177	−	0.839618i	$-0.682779\pi$
$929$		−	51.1823i		−	1.67924i	0.543177	−	0.839618i	$-0.317221\pi$
$930$		0			0
$931$	9.64393			0.316067
$932$	2.27204	+	1.66386i	0.0744231	+	0.0545016i
$933$	9.04420	−	4.20388i	0.296094	−	0.137629i
$934$	6.55602	+	12.9271i	0.214519	+	0.422988i
$935$		0			0
$936$	36.4689	−	31.1862i	1.19202	−	1.01935i
$937$	56.9974			1.86202			0.931011	−	0.364990i	$-0.118928\pi$
$937$	56.9974			1.86202			0.931011	+	0.364990i	$0.118928\pi$
$938$	6.82944	+	13.4662i	0.222989	+	0.439688i
$939$	−34.5233	+	16.0470i	−1.12663	+	0.523672i
$940$		0			0
$941$	37.1960			1.21255			0.606277	−	0.795253i	$-0.292662\pi$
$941$	37.1960			1.21255			0.606277	+	0.795253i	$0.292662\pi$
$942$	3.29553	+	2.59131i	0.107374	+	0.0844295i
$943$		−	66.9488i		−	2.18015i
$944$	18.7275	−	5.92916i	0.609529	−	0.192978i
$945$		0			0
$946$	8.45670	+	16.6749i	0.274951	+	0.542147i
$947$			36.5775i			1.18861i	0.804240	+	0.594305i	$0.202573\pi$
$947$			36.5775i			1.18861i	−0.804240	+	0.594305i	$0.797427\pi$
$948$	25.0251	+	4.99432i	0.812778	+	0.162208i
$949$		−	25.9831i		−	0.843449i
$950$		0			0
$951$	−27.7717	+	12.9087i	−0.900560	+	0.418594i
$952$	−1.41261	+	8.60358i	−0.0457829	+	0.278844i
$953$		−	30.3524i		−	0.983211i	−0.870818	−	0.491606i	$-0.836410\pi$
$953$		−	30.3524i		−	0.983211i	0.870818	−	0.491606i	$-0.163590\pi$
$954$	11.7192	−	49.7748i	0.379422	−	1.61152i
$955$		0			0
$956$	−11.2338	+	15.3400i	−0.363326	+	0.496130i
$957$	−8.37821	−	18.0248i	−0.270829	−	0.582660i
$958$	−39.6519	+	20.1096i	−1.28110	+	0.649711i
$959$	23.1806			0.748540
$960$		0			0
$961$	3.97070			0.128087
$962$	46.0367	−	23.3476i	1.48428	−	0.752758i
$963$	18.6700	+	15.7442i	0.601632	+	0.507350i
$964$	2.68633	−	3.66824i	0.0865208	−	0.118146i
$965$		0			0
$966$	21.3705	+	16.8038i	0.687583	+	0.540654i
$967$			25.8174i			0.830232i	0.909768	+	0.415116i	$0.136259\pi$
$967$			25.8174i			0.830232i	−0.909768	+	0.415116i	$0.863741\pi$
$968$	0.851750	−	5.18764i	0.0273763	−	0.166737i
$969$	−3.18736	−	6.85728i	−0.102393	−	0.220287i
$970$		0			0
$971$			22.9904i			0.737796i	0.929470	+	0.368898i	$0.120265\pi$
$971$			22.9904i			0.737796i	−0.929470	+	0.368898i	$0.879735\pi$
$972$	−31.1652	−	0.852868i	−0.999626	−	0.0273557i
$973$			14.5675i			0.467011i
$974$	−0.113496	−	0.223791i	−0.00363665	−	0.00717072i
$975$		0			0
$976$	31.1400	−	9.85897i	0.996768	−	0.315578i
$977$			36.2952i			1.16119i	0.814194	+	0.580593i	$0.197179\pi$
$977$			36.2952i			1.16119i	−0.814194	+	0.580593i	$0.802821\pi$
$978$	−18.1051	+	23.0253i	−0.578936	+	0.736269i
$979$	−11.0573			−0.353393
$980$		0			0
$981$	−12.9693	−	10.9369i	−0.414079	−	0.349189i
$982$	−4.96137	−	9.78279i	−0.158324	−	0.312181i
$983$	−6.92523			−0.220881			−0.110440	−	0.993883i	$-0.535226\pi$
$983$	−6.92523			−0.220881			−0.110440	+	0.993883i	$0.535226\pi$
$984$	35.7312	−	9.98009i	1.13907	−	0.318154i
$985$		0			0
$986$	5.96165	+	11.7551i	0.189857	+	0.374360i
$987$	−1.68001	−	3.61437i	−0.0534754	−	0.115047i
$988$	16.2243	+	11.8814i	0.516164	+	0.377997i
$989$	−38.6575			−1.22924
$990$		0			0
$991$		−	42.7182i		−	1.35699i	−0.734605	−	0.678495i	$-0.762633\pi$
$991$		−	42.7182i		−	1.35699i	0.734605	−	0.678495i	$-0.237367\pi$
$992$	20.9910	−	20.5989i	0.666466	−	0.654016i
$993$	−11.2167	+	5.21367i	−0.355950	+	0.165451i
$994$	5.62734	+	11.0960i	0.178488	+	0.351942i
$995$		0			0
$996$	−53.5079	−	10.6787i	−1.69546	−	0.338368i
$997$		−	15.7743i		−	0.499579i	−0.968300	−	0.249789i	$-0.919639\pi$
$997$		−	15.7743i		−	0.499579i	0.968300	−	0.249789i	$-0.0803613\pi$
$998$	6.58474	−	3.33947i	0.208436	−	0.105709i
$999$	−32.3629	−	8.79941i	−1.02392	−	0.278401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.b.h.251.9	yes	12
3.2	odd	2	inner	600.2.b.h.251.4	yes	12
4.3	odd	2		2400.2.b.g.2351.4		12
5.2	odd	4		600.2.m.e.299.19		24
5.3	odd	4		600.2.m.e.299.6		24
5.4	even	2		600.2.b.g.251.4	yes	12
8.3	odd	2	inner	600.2.b.h.251.3	yes	12
8.5	even	2		2400.2.b.g.2351.3		12
12.11	even	2		2400.2.b.g.2351.2		12
15.2	even	4		600.2.m.e.299.5		24
15.8	even	4		600.2.m.e.299.20		24
15.14	odd	2		600.2.b.g.251.9	yes	12
20.3	even	4		2400.2.m.e.1199.10		24
20.7	even	4		2400.2.m.e.1199.15		24
20.19	odd	2		2400.2.b.h.2351.9		12
24.5	odd	2		2400.2.b.g.2351.1		12
24.11	even	2	inner	600.2.b.h.251.10	yes	12
40.3	even	4		600.2.m.e.299.8		24
40.13	odd	4		2400.2.m.e.1199.9		24
40.19	odd	2		600.2.b.g.251.10	yes	12
40.27	even	4		600.2.m.e.299.17		24
40.29	even	2		2400.2.b.h.2351.10		12
40.37	odd	4		2400.2.m.e.1199.16		24
60.23	odd	4		2400.2.m.e.1199.14		24
60.47	odd	4		2400.2.m.e.1199.11		24
60.59	even	2		2400.2.b.h.2351.11		12
120.29	odd	2		2400.2.b.h.2351.12		12
120.53	even	4		2400.2.m.e.1199.13		24
120.59	even	2		600.2.b.g.251.3	✓	12
120.77	even	4		2400.2.m.e.1199.12		24
120.83	odd	4		600.2.m.e.299.18		24
120.107	odd	4		600.2.m.e.299.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.b.g.251.3	✓	12	120.59	even	2
600.2.b.g.251.4	yes	12	5.4	even	2
600.2.b.g.251.9	yes	12	15.14	odd	2
600.2.b.g.251.10	yes	12	40.19	odd	2
600.2.b.h.251.3	yes	12	8.3	odd	2	inner
600.2.b.h.251.4	yes	12	3.2	odd	2	inner
600.2.b.h.251.9	yes	12	1.1	even	1	trivial
600.2.b.h.251.10	yes	12	24.11	even	2	inner
600.2.m.e.299.5		24	15.2	even	4
600.2.m.e.299.6		24	5.3	odd	4
600.2.m.e.299.7		24	120.107	odd	4
600.2.m.e.299.8		24	40.3	even	4
600.2.m.e.299.17		24	40.27	even	4
600.2.m.e.299.18		24	120.83	odd	4
600.2.m.e.299.19		24	5.2	odd	4
600.2.m.e.299.20		24	15.8	even	4
2400.2.b.g.2351.1		12	24.5	odd	2
2400.2.b.g.2351.2		12	12.11	even	2
2400.2.b.g.2351.3		12	8.5	even	2
2400.2.b.g.2351.4		12	4.3	odd	2
2400.2.b.h.2351.9		12	20.19	odd	2
2400.2.b.h.2351.10		12	40.29	even	2
2400.2.b.h.2351.11		12	60.59	even	2
2400.2.b.h.2351.12		12	120.29	odd	2
2400.2.m.e.1199.9		24	40.13	odd	4
2400.2.m.e.1199.10		24	20.3	even	4
2400.2.m.e.1199.11		24	60.47	odd	4
2400.2.m.e.1199.12		24	120.77	even	4
2400.2.m.e.1199.13		24	120.53	even	4
2400.2.m.e.1199.14		24	60.23	odd	4
2400.2.m.e.1199.15		24	20.7	even	4
2400.2.m.e.1199.16		24	40.37	odd	4

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26128 - 0.639662i) q^{2} +(1.57067 - 0.730070i) q^{3} +(1.18166 - 1.61359i) q^{4} +(1.51406 - 1.92552i) q^{6} -1.25539i q^{7} +(0.458259 - 2.79106i) q^{8} +(1.93400 - 2.29339i) q^{9} +O(q^{10})\)	\(q+(1.26128 - 0.639662i) q^{2} +(1.57067 - 0.730070i) q^{3} +(1.18166 - 1.61359i) q^{4} +(1.51406 - 1.92552i) q^{6} -1.25539i q^{7} +(0.458259 - 2.79106i) q^{8} +(1.93400 - 2.29339i) q^{9} +3.02346i q^{11} +(0.677969 - 3.39711i) q^{12} +5.65509i q^{13} +(-0.803023 - 1.58339i) q^{14} +(-1.20734 - 3.81344i) q^{16} -2.45546i q^{17} +(0.972316 - 4.12972i) q^{18} +1.77801 q^{19} +(-0.916519 - 1.97179i) q^{21} +(1.93400 + 3.81344i) q^{22} -8.84074 q^{23} +(-1.31789 - 4.71839i) q^{24} +(3.61735 + 7.13266i) q^{26} +(1.36333 - 5.01411i) q^{27} +(-2.02568 - 1.48344i) q^{28} -3.79561 q^{29} +5.19897i q^{31} +(-3.96211 - 4.03753i) q^{32} +(2.20734 + 4.74886i) q^{33} +(-1.57067 - 3.09703i) q^{34} +(-1.41526 - 5.83070i) q^{36} -6.45436i q^{37} +(2.24257 - 1.13732i) q^{38} +(4.12861 + 8.88227i) q^{39} +7.57276i q^{41} +(-2.41727 - 1.90072i) q^{42} +4.37266 q^{43} +(4.87863 + 3.57272i) q^{44} +(-11.1507 + 5.65509i) q^{46} +1.83304 q^{47} +(-4.68041 - 5.10821i) q^{48} +5.42401 q^{49} +(-1.79266 - 3.85672i) q^{51} +(9.12499 + 6.68241i) q^{52} +12.0528 q^{53} +(-1.48780 - 7.19628i) q^{54} +(-3.50385 - 0.575292i) q^{56} +(2.79266 - 1.29807i) q^{57} +(-4.78734 + 2.42791i) q^{58} +4.91093i q^{59} +8.16586i q^{61} +(3.32559 + 6.55737i) q^{62} +(-2.87909 - 2.42791i) q^{63} +(-7.58000 - 2.55806i) q^{64} +(5.82174 + 4.57770i) q^{66} -8.50466 q^{67} +(-3.96211 - 2.90153i) q^{68} +(-13.8859 + 6.45436i) q^{69} -7.00770 q^{71} +(-5.51472 - 6.44886i) q^{72} -4.59465 q^{73} +(-4.12861 - 8.14076i) q^{74} +(2.10101 - 2.86897i) q^{76} +3.79561 q^{77} +(10.8890 + 8.56213i) q^{78} +7.36659i q^{79} +(-1.51932 - 8.87083i) q^{81} +(4.84401 + 9.55139i) q^{82} -15.7510i q^{83} +(-4.26468 - 0.851113i) q^{84} +(5.51515 - 2.79702i) q^{86} +(-5.96165 + 2.77106i) q^{87} +(8.43866 + 1.38553i) q^{88} +3.65716i q^{89} +7.09931 q^{91} +(-10.4468 + 14.2653i) q^{92} +(3.79561 + 8.16586i) q^{93} +(2.31198 - 1.17252i) q^{94} +(-9.17084 - 3.44901i) q^{96} -13.8773 q^{97} +(6.84120 - 3.46953i) q^{98} +(6.93400 + 5.84737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} + 10 q^{4} + 7 q^{6} - 2 q^{9}+O(q^{10}) \) 12 * q + 2 * q^3 + 10 * q^4 + 7 * q^6 - 2 * q^9	\( 12 q + 2 q^{3} + 10 q^{4} + 7 q^{6} - 2 q^{9} - 3 q^{12} - 6 q^{16} - 5 q^{18} - 4 q^{19} - 2 q^{22} + 5 q^{24} + 8 q^{27} - 20 q^{28} + 18 q^{33} - 2 q^{34} + 19 q^{36} - 14 q^{42} - 40 q^{43} - 16 q^{46} - 27 q^{48} - 36 q^{49} - 30 q^{51} - 4 q^{52} - 30 q^{54} + 42 q^{57} + 52 q^{58} + 10 q^{64} + 7 q^{66} - 60 q^{67} - 39 q^{72} + 12 q^{73} - 38 q^{76} + 54 q^{78} - 10 q^{81} + 58 q^{82} - 34 q^{84} + 34 q^{88} - 24 q^{91} + 28 q^{94} - 31 q^{96} - 32 q^{97} + 58 q^{99}+O(q^{100}) \) 12 * q + 2 * q^3 + 10 * q^4 + 7 * q^6 - 2 * q^9 - 3 * q^12 - 6 * q^16 - 5 * q^18 - 4 * q^19 - 2 * q^22 + 5 * q^24 + 8 * q^27 - 20 * q^28 + 18 * q^33 - 2 * q^34 + 19 * q^36 - 14 * q^42 - 40 * q^43 - 16 * q^46 - 27 * q^48 - 36 * q^49 - 30 * q^51 - 4 * q^52 - 30 * q^54 + 42 * q^57 + 52 * q^58 + 10 * q^64 + 7 * q^66 - 60 * q^67 - 39 * q^72 + 12 * q^73 - 38 * q^76 + 54 * q^78 - 10 * q^81 + 58 * q^82 - 34 * q^84 + 34 * q^88 - 24 * q^91 + 28 * q^94 - 31 * q^96 - 32 * q^97 + 58 * q^99

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