LMFDB - Embedded newform 54.3.f.a.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,3,Mod(5,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	54.f (of order $18$, degree $6$, 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:	$1.47139342755$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.2
Character	$\chi$	$=$	54.29
Dual form			54.3.f.a.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39273 - 0.245576i) q^{2} +(-2.10518 + 2.13733i) q^{3} +(1.87939 + 0.684040i) q^{4} +(-5.37469 - 6.40531i) q^{5} +(3.45683 - 2.45974i) q^{6} +(-8.61655 + 3.13617i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-0.136395 - 8.99897i) q^{9} +O(q^{10})$	\(q+(-1.39273 - 0.245576i) q^{2} +(-2.10518 + 2.13733i) q^{3} +(1.87939 + 0.684040i) q^{4} +(-5.37469 - 6.40531i) q^{5} +(3.45683 - 2.45974i) q^{6} +(-8.61655 + 3.13617i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-0.136395 - 8.99897i) q^{9} +(5.91250 + 10.2407i) q^{10} +(-4.22940 + 5.04040i) q^{11} +(-5.41848 + 2.57684i) q^{12} +(1.04310 + 5.91570i) q^{13} +(12.7707 - 2.25182i) q^{14} +(25.0050 + 1.99684i) q^{15} +(3.06418 + 2.57115i) q^{16} +(-0.880022 + 0.508081i) q^{17} +(-2.01997 + 12.5666i) q^{18} +(10.5593 - 18.2893i) q^{19} +(-5.71963 - 15.7145i) q^{20} +(11.4364 - 25.0187i) q^{21} +(7.12821 - 5.98128i) q^{22} +(-7.33348 + 20.1486i) q^{23} +(8.17928 - 2.25820i) q^{24} +(-7.79945 + 44.2329i) q^{25} -8.49512i q^{26} +(19.5209 + 18.6530i) q^{27} -18.3391 q^{28} +(-47.7181 - 8.41399i) q^{29} +(-34.3348 - 8.92168i) q^{30} +(-6.20863 - 2.25976i) q^{31} +(-3.63616 - 4.33340i) q^{32} +(-1.86936 - 19.6506i) q^{33} +(1.35040 - 0.491507i) q^{34} +(66.3994 + 38.3357i) q^{35} +(5.89932 - 17.0058i) q^{36} +(-33.2994 - 57.6763i) q^{37} +(-19.1977 + 22.8789i) q^{38} +(-14.8397 - 10.2242i) q^{39} +(4.10678 + 23.2907i) q^{40} +(52.2291 - 9.20941i) q^{41} +(-22.0718 + 32.0357i) q^{42} +(-36.3861 - 30.5315i) q^{43} +(-11.3965 + 6.57978i) q^{44} +(-56.9081 + 49.2403i) q^{45} +(15.1616 - 26.2606i) q^{46} +(-2.23172 - 6.13159i) q^{47} +(-11.9461 + 1.13643i) q^{48} +(26.8732 - 22.5493i) q^{49} +(21.7250 - 59.6890i) q^{50} +(0.766670 - 2.95050i) q^{51} +(-2.08619 + 11.8314i) q^{52} +39.7705i q^{53} +(-22.6067 - 30.7724i) q^{54} +55.0170 q^{55} +(25.5414 + 4.50363i) q^{56} +(16.8610 + 61.0711i) q^{57} +(64.3921 + 23.4368i) q^{58} +(-18.0238 - 21.4799i) q^{59} +(45.6281 + 20.8573i) q^{60} +(38.6125 - 14.0538i) q^{61} +(8.09199 + 4.67191i) q^{62} +(29.3975 + 77.1123i) q^{63} +(4.00000 + 6.92820i) q^{64} +(32.2855 - 38.4764i) q^{65} +(-2.22221 + 27.8271i) q^{66} +(-2.57695 - 14.6146i) q^{67} +(-2.00145 + 0.352909i) q^{68} +(-27.6259 - 58.0906i) q^{69} +(-83.0620 - 69.6973i) q^{70} +(-65.6502 + 37.9031i) q^{71} +(-12.3924 + 22.2358i) q^{72} +(-26.5140 + 45.9236i) q^{73} +(32.2131 + 88.5049i) q^{74} +(-78.1212 - 109.788i) q^{75} +(32.3556 - 27.1496i) q^{76} +(20.6353 - 56.6950i) q^{77} +(18.1569 + 17.8838i) q^{78} +(-14.2149 + 80.6166i) q^{79} -33.4461i q^{80} +(-80.9628 + 2.45483i) q^{81} -75.0026 q^{82} +(46.2126 + 8.14852i) q^{83} +(38.6072 - 39.1968i) q^{84} +(7.98426 + 2.90603i) q^{85} +(43.1781 + 51.4577i) q^{86} +(118.439 - 84.2766i) q^{87} +(17.4881 - 6.36514i) q^{88} +(20.2996 + 11.7200i) q^{89} +(91.3497 - 54.6032i) q^{90} +(-27.5405 - 47.7016i) q^{91} +(-27.5649 + 32.8505i) q^{92} +(17.9002 - 8.51271i) q^{93} +(1.60241 + 9.08769i) q^{94} +(-173.902 + 30.6635i) q^{95} +(16.9167 + 1.35093i) q^{96} +(26.8130 + 22.4988i) q^{97} +(-42.9647 + 24.8057i) q^{98} +(45.9353 + 37.3727i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9}+O(q^{10}) $ 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9	$ 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9} - 18 q^{11} - 12 q^{12} - 36 q^{14} - 18 q^{15} - 48 q^{18} - 72 q^{20} - 228 q^{21} + 36 q^{22} - 180 q^{23} + 18 q^{25} + 54 q^{27} + 144 q^{29} + 144 q^{30} - 90 q^{31} + 324 q^{33} - 72 q^{34} + 486 q^{35} + 168 q^{36} + 180 q^{38} + 102 q^{39} - 90 q^{41} + 48 q^{42} + 90 q^{43} - 378 q^{45} - 378 q^{47} - 24 q^{48} + 72 q^{49} - 54 q^{51} - 36 q^{54} - 72 q^{56} + 72 q^{57} + 252 q^{59} + 36 q^{60} - 144 q^{61} + 318 q^{63} + 144 q^{64} + 18 q^{65} - 432 q^{66} - 594 q^{67} - 180 q^{68} - 522 q^{69} - 360 q^{70} - 648 q^{71} - 192 q^{72} + 126 q^{73} - 504 q^{74} - 438 q^{75} - 72 q^{76} - 342 q^{77} - 288 q^{78} - 72 q^{79} + 324 q^{81} + 594 q^{83} + 216 q^{84} + 360 q^{85} + 540 q^{86} + 1062 q^{87} + 144 q^{88} + 648 q^{89} + 720 q^{90} - 198 q^{91} + 396 q^{92} + 462 q^{93} + 504 q^{94} + 252 q^{95} + 96 q^{96} + 702 q^{97} + 648 q^{98} + 126 q^{99}+O(q^{100}) $ 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9 - 18 * q^11 - 12 * q^12 - 36 * q^14 - 18 * q^15 - 48 * q^18 - 72 * q^20 - 228 * q^21 + 36 * q^22 - 180 * q^23 + 18 * q^25 + 54 * q^27 + 144 * q^29 + 144 * q^30 - 90 * q^31 + 324 * q^33 - 72 * q^34 + 486 * q^35 + 168 * q^36 + 180 * q^38 + 102 * q^39 - 90 * q^41 + 48 * q^42 + 90 * q^43 - 378 * q^45 - 378 * q^47 - 24 * q^48 + 72 * q^49 - 54 * q^51 - 36 * q^54 - 72 * q^56 + 72 * q^57 + 252 * q^59 + 36 * q^60 - 144 * q^61 + 318 * q^63 + 144 * q^64 + 18 * q^65 - 432 * q^66 - 594 * q^67 - 180 * q^68 - 522 * q^69 - 360 * q^70 - 648 * q^71 - 192 * q^72 + 126 * q^73 - 504 * q^74 - 438 * q^75 - 72 * q^76 - 342 * q^77 - 288 * q^78 - 72 * q^79 + 324 * q^81 + 594 * q^83 + 216 * q^84 + 360 * q^85 + 540 * q^86 + 1062 * q^87 + 144 * q^88 + 648 * q^89 + 720 * q^90 - 198 * q^91 + 396 * q^92 + 462 * q^93 + 504 * q^94 + 252 * q^95 + 96 * q^96 + 702 * q^97 + 648 * q^98 + 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

Coefficient data

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

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

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

$2$	−1.39273	−	0.245576i	−0.696364	−	0.122788i
$2$	−1.39273	−	0.245576i	−0.696364	−	0.122788i
$3$	−2.10518	+	2.13733i	−0.701728	+	0.712445i
$3$	−2.10518	+	2.13733i	−0.701728	+	0.712445i
$4$	1.87939	+	0.684040i	0.469846	+	0.171010i
$5$	−5.37469	−	6.40531i	−1.07494	−	1.28106i	−0.957641	−	0.287964i	$-0.907022\pi$
$5$	−5.37469	−	6.40531i	−1.07494	−	1.28106i	−0.117297	−	0.993097i	$-0.537423\pi$
$6$	3.45683	−	2.45974i	0.576138	−	0.409957i
$7$	−8.61655	+	3.13617i	−1.23094	+	0.448024i	−0.873918	−	0.486074i	$-0.838429\pi$
$7$	−8.61655	+	3.13617i	−1.23094	+	0.448024i	−0.357018	+	0.934098i	$0.616206\pi$
$8$	−2.44949	−	1.41421i	−0.306186	−	0.176777i
$9$	−0.136395	−	8.99897i	−0.0151550	−	0.999885i
$10$	5.91250	+	10.2407i	0.591250	+	1.02407i
$11$	−4.22940	+	5.04040i	−0.384491	+	0.458218i	−0.923226	−	0.384257i	$-0.874458\pi$
$11$	−4.22940	+	5.04040i	−0.384491	+	0.458218i	0.538735	+	0.842475i	$0.318902\pi$
$12$	−5.41848	+	2.57684i	−0.451540	+	0.214737i
$13$	1.04310	+	5.91570i	0.0802382	+	0.455053i	0.998283	+	0.0585766i	$0.0186562\pi$
$13$	1.04310	+	5.91570i	0.0802382	+	0.455053i	−0.918045	+	0.396477i	$0.870233\pi$
$14$	12.7707	−	2.25182i	0.912192	−	0.160844i
$15$	25.0050	+	1.99684i	1.66700	+	0.133123i
$16$	3.06418	+	2.57115i	0.191511	+	0.160697i
$17$	−0.880022	+	0.508081i	−0.0517660	+	0.0298871i	−0.525660	−	0.850695i	$-0.676181\pi$
$17$	−0.880022	+	0.508081i	−0.0517660	+	0.0298871i	0.473894	+	0.880582i	$0.342848\pi$
$18$	−2.01997	+	12.5666i	−0.112220	+	0.698145i
$19$	10.5593	−	18.2893i	0.555754	−	0.962594i	−0.442091	−	0.896970i	$-0.645763\pi$
$19$	10.5593	−	18.2893i	0.555754	−	0.962594i	0.997844	−	0.0656235i	$-0.0209036\pi$
$20$	−5.71963	−	15.7145i	−0.285981	−	0.785727i
$21$	11.4364	−	25.0187i	0.544590	−	1.19136i
$22$	7.12821	−	5.98128i	0.324009	−	0.271876i
$23$	−7.33348	+	20.1486i	−0.318847	+	0.876025i	0.671941	+	0.740605i	$0.265461\pi$
$23$	−7.33348	+	20.1486i	−0.318847	+	0.876025i	−0.990788	+	0.135421i	$0.956761\pi$
$24$	8.17928	−	2.25820i	0.340803	−	0.0940916i
$25$	−7.79945	+	44.2329i	−0.311978	+	1.76932i
$26$		−	8.49512i		−	0.326735i
$27$	19.5209	+	18.6530i	0.722998	+	0.690851i
$28$	−18.3391			−0.654967
$29$	−47.7181	−	8.41399i	−1.64545	−	0.290138i	−0.727287	−	0.686334i	$-0.759219\pi$
$29$	−47.7181	−	8.41399i	−1.64545	−	0.290138i	−0.918166	+	0.396196i	$0.870330\pi$
$30$	−34.3348	−	8.92168i	−1.14449	−	0.297389i
$31$	−6.20863	−	2.25976i	−0.200278	−	0.0728954i	0.239933	−	0.970789i	$-0.422874\pi$
$31$	−6.20863	−	2.25976i	−0.200278	−	0.0728954i	−0.440212	+	0.897894i	$0.645097\pi$
$32$	−3.63616	−	4.33340i	−0.113630	−	0.135419i
$33$	−1.86936	−	19.6506i	−0.0566472	−	0.595473i
$34$	1.35040	−	0.491507i	0.0397177	−	0.0144561i
$35$	66.3994	+	38.3357i	1.89713	+	1.09531i
$36$	5.89932	−	17.0058i	0.163870	−	0.472384i
$37$	−33.2994	−	57.6763i	−0.899984	−	1.55882i	−0.827513	−	0.561447i	$-0.810245\pi$
$37$	−33.2994	−	57.6763i	−0.899984	−	1.55882i	−0.0724711	−	0.997371i	$-0.523089\pi$
$38$	−19.1977	+	22.8789i	−0.505202	+	0.602076i
$39$	−14.8397	−	10.2242i	−0.380506	−	0.262159i
$40$	4.10678	+	23.2907i	0.102669	+	0.582267i
$41$	52.2291	−	9.20941i	1.27388	−	0.224620i	0.504501	−	0.863411i	$-0.331676\pi$
$41$	52.2291	−	9.20941i	1.27388	−	0.224620i	0.769380	+	0.638791i	$0.220565\pi$
$42$	−22.0718	+	32.0357i	−0.525518	+	0.762755i
$43$	−36.3861	−	30.5315i	−0.846188	−	0.710036i	0.112759	−	0.993622i	$-0.464031\pi$
$43$	−36.3861	−	30.5315i	−0.846188	−	0.710036i	−0.958947	+	0.283587i	$0.908476\pi$
$44$	−11.3965	+	6.57978i	−0.259012	+	0.149540i
$45$	−56.9081	+	49.2403i	−1.26462	+	1.09423i
$46$	15.1616	−	26.2606i	0.329599	−	0.570882i
$47$	−2.23172	−	6.13159i	−0.0474833	−	0.130459i	0.913684	−	0.406425i	$-0.133225\pi$
$47$	−2.23172	−	6.13159i	−0.0474833	−	0.130459i	−0.961168	+	0.275965i	$0.911002\pi$
$48$	−11.9461	+	1.13643i	−0.248876	+	0.0236755i
$49$	26.8732	−	22.5493i	0.548433	−	0.460190i
$50$	21.7250	−	59.6890i	0.434501	−	1.19378i
$51$	0.766670	−	2.95050i	0.0150327	−	0.0578530i
$52$	−2.08619	+	11.8314i	−0.0401191	+	0.227527i
$53$			39.7705i			0.750386i	0.926947	+	0.375193i	$0.122424\pi$
$53$			39.7705i			0.750386i	−0.926947	+	0.375193i	$0.877576\pi$
$54$	−22.6067	−	30.7724i	−0.418642	−	0.569859i
$55$	55.0170			1.00031
$56$	25.5414	+	4.50363i	0.456096	+	0.0804220i
$57$	16.8610	+	61.0711i	0.295807	+	1.07142i
$58$	64.3921	+	23.4368i	1.11021	+	0.404083i
$59$	−18.0238	−	21.4799i	−0.305488	−	0.364067i	0.591358	−	0.806409i	$-0.298592\pi$
$59$	−18.0238	−	21.4799i	−0.305488	−	0.364067i	−0.896846	+	0.442342i	$0.854148\pi$
$60$	45.6281	+	20.8573i	0.760468	+	0.347621i
$61$	38.6125	−	14.0538i	0.632992	−	0.230390i	−0.00554114	−	0.999985i	$-0.501764\pi$
$61$	38.6125	−	14.0538i	0.632992	−	0.230390i	0.638533	+	0.769594i	$0.279542\pi$
$62$	8.09199	+	4.67191i	0.130516	+	0.0753535i
$63$	29.3975	+	77.1123i	0.466627	+	1.22400i
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	32.2855	−	38.4764i	0.496700	−	0.591944i
$66$	−2.22221	+	27.8271i	−0.0336698	+	0.421622i
$67$	−2.57695	−	14.6146i	−0.0384619	−	0.218128i	0.959519	−	0.281644i	$-0.0908798\pi$
$67$	−2.57695	−	14.6146i	−0.0384619	−	0.218128i	−0.997981	+	0.0635158i	$0.979769\pi$
$68$	−2.00145	+	0.352909i	−0.0294331	+	0.00518984i
$69$	−27.6259	−	58.0906i	−0.400376	−	0.841893i
$70$	−83.0620	−	69.6973i	−1.18660	−	0.995676i
$71$	−65.6502	+	37.9031i	−0.924650	+	0.533847i	−0.885116	−	0.465371i	$-0.845921\pi$
$71$	−65.6502	+	37.9031i	−0.924650	+	0.533847i	−0.0395346	+	0.999218i	$0.512588\pi$
$72$	−12.3924	+	22.2358i	−0.172116	+	0.308830i
$73$	−26.5140	+	45.9236i	−0.363205	+	0.629090i	−0.988486	−	0.151310i	$-0.951651\pi$
$73$	−26.5140	+	45.9236i	−0.363205	+	0.629090i	0.625281	+	0.780400i	$0.284984\pi$
$74$	32.2131	+	88.5049i	0.435313	+	1.19601i
$75$	−78.1212	−	109.788i	−1.04162	−	1.46385i
$76$	32.3556	−	27.1496i	0.425732	−	0.357232i
$77$	20.6353	−	56.6950i	0.267991	−	0.736299i
$78$	18.1569	+	17.8838i	0.232781	+	0.229279i
$79$	−14.2149	+	80.6166i	−0.179935	+	1.02046i	0.752356	+	0.658756i	$0.228917\pi$
$79$	−14.2149	+	80.6166i	−0.179935	+	1.02046i	−0.932292	+	0.361708i	$0.882194\pi$
$80$		−	33.4461i		−	0.418077i
$81$	−80.9628	+	2.45483i	−0.999541	+	0.0303066i
$82$	−75.0026			−0.914666
$83$	46.2126	+	8.14852i	0.556778	+	0.0981749i	0.444955	−	0.895553i	$-0.353220\pi$
$83$	46.2126	+	8.14852i	0.556778	+	0.0981749i	0.111823	+	0.993728i	$0.464331\pi$
$84$	38.6072	−	39.1968i	0.459609	−	0.466628i
$85$	7.98426	+	2.90603i	0.0939324	+	0.0341886i
$86$	43.1781	+	51.4577i	0.502071	+	0.598345i
$87$	118.439	−	84.2766i	1.36137	−	0.968696i
$88$	17.4881	−	6.36514i	0.198728	−	0.0723311i
$89$	20.2996	+	11.7200i	0.228085	+	0.131685i	0.609689	−	0.792641i	$-0.291295\pi$
$89$	20.2996	+	11.7200i	0.228085	+	0.131685i	−0.381603	+	0.924326i	$0.624628\pi$
$90$	91.3497	−	54.6032i	1.01500	−	0.606702i
$91$	−27.5405	−	47.7016i	−0.302643	−	0.524193i
$92$	−27.5649	+	32.8505i	−0.299618	+	0.357071i
$93$	17.9002	−	8.51271i	0.192475	−	0.0915345i
$94$	1.60241	+	9.08769i	0.0170469	+	0.0966776i
$95$	−173.902	+	30.6635i	−1.83054	+	0.322774i
$96$	16.9167	+	1.35093i	0.176216	+	0.0140722i
$97$	26.8130	+	22.4988i	0.276423	+	0.231946i	0.770450	−	0.637500i	$-0.220031\pi$
$97$	26.8130	+	22.4988i	0.276423	+	0.231946i	−0.494028	+	0.869446i	$0.664476\pi$
$98$	−42.9647	+	24.8057i	−0.438415	+	0.253119i
$99$	45.9353	+	37.3727i	0.463993	+	0.377502i
$100$	−44.9152	+	77.7955i	−0.449152	+	0.777955i
$101$	−41.4761	−	113.955i	−0.410655	−	1.12826i	−0.956844	−	0.290603i	$-0.906144\pi$
$101$	−41.4761	−	113.955i	−0.410655	−	1.12826i	0.546189	−	0.837662i	$-0.316078\pi$
$102$	−1.79233	+	3.92098i	−0.0175719	+	0.0384409i
$103$	−144.726	+	121.440i	−1.40511	+	1.17903i	−0.446334	+	0.894866i	$0.647271\pi$
$103$	−144.726	+	121.440i	−1.40511	+	1.17903i	−0.958776	+	0.284161i	$0.908285\pi$
$104$	5.81100	−	15.9656i	0.0558750	−	0.153515i
$105$	−221.719	+	61.2140i	−2.11161	+	0.582990i
$106$	9.76666	−	55.3895i	0.0921383	−	0.522542i
$107$		−	76.4765i		−	0.714733i	−0.933964	−	0.357367i	$-0.883675\pi$
$107$		−	76.4765i		−	0.714733i	0.933964	−	0.357367i	$-0.116325\pi$
$108$	23.9280	+	48.4092i	0.221555	+	0.448233i
$109$	43.7808			0.401659			0.200829	−	0.979626i	$-0.435636\pi$
$109$	43.7808			0.401659			0.200829	+	0.979626i	$0.435636\pi$
$110$	−76.6238	−	13.5108i	−0.696580	−	0.122826i
$111$	193.375	+	50.2472i	1.74212	+	0.452678i
$112$	−34.4662	−	12.5447i	−0.307734	−	0.112006i
$113$	−0.133455	−	0.159046i	−0.00118102	−	0.00140749i	0.765454	−	0.643491i	$-0.222515\pi$
$113$	−0.133455	−	0.159046i	−0.00118102	−	0.00140749i	−0.766635	+	0.642084i	$0.778070\pi$
$114$	−8.48520	−	89.1961i	−0.0744316	−	0.782422i
$115$	168.473	−	61.3192i	1.46498	−	0.533210i
$116$	−83.9252	−	48.4543i	−0.723493	−	0.417709i
$117$	53.0929	−	10.1937i	0.453785	−	0.0871253i
$118$	19.8273	+	34.3419i	0.168028	+	0.291033i
$119$	5.98932	−	7.13780i	0.0503305	−	0.0599815i
$120$	−58.4255	−	40.2537i	−0.486879	−	0.335447i
$121$	13.4936	+	76.5260i	0.111517	+	0.632446i
$122$	−57.2280	+	10.0908i	−0.469082	+	0.0827118i
$123$	−90.2684	+	131.019i	−0.733890	+	1.06519i
$124$	−10.1226	−	8.49390i	−0.0816342	−	0.0684992i
$125$	144.212	−	83.2610i	1.15370	−	0.666088i
$126$	−22.0059	−	114.616i	−0.174650	−	0.909649i
$127$	77.5448	−	134.312i	0.610589	−	1.05757i	−0.380552	−	0.924759i	$-0.624266\pi$
$127$	77.5448	−	134.312i	0.610589	−	1.05757i	0.991141	−	0.132812i	$-0.0424006\pi$
$128$	−3.86952	−	10.6314i	−0.0302306	−	0.0830579i
$129$	141.855	−	13.4947i	1.09965	−	0.104610i
$130$	−54.4138	+	45.6586i	−0.418568	+	0.351220i
$131$	−46.3122	+	127.242i	−0.353529	+	0.971312i	0.627699	+	0.778456i	$0.283997\pi$
$131$	−46.3122	+	127.242i	−0.353529	+	0.971312i	−0.981227	+	0.192855i	$0.938225\pi$
$132$	9.92857	−	38.2098i	0.0752165	−	0.289468i
$133$	−33.6267	+	190.706i	−0.252832	+	1.43388i
$134$			20.9870i			0.156619i
$135$	14.5590	−	225.291i	0.107844	−	1.66883i
$136$	2.87414			0.0211334
$137$	46.2957	+	8.16317i	0.337924	+	0.0595852i	0.340036	−	0.940413i	$-0.389561\pi$
$137$	46.2957	+	8.16317i	0.337924	+	0.0595852i	−0.00211111	+	0.999998i	$0.500672\pi$
$138$	24.2098	+	87.6887i	0.175433	+	0.635425i
$139$	−45.5216	−	16.5685i	−0.327494	−	0.119198i	0.173040	−	0.984915i	$-0.444641\pi$
$139$	−45.5216	−	16.5685i	−0.327494	−	0.119198i	−0.500534	+	0.865717i	$0.666863\pi$
$140$	98.5669	+	117.467i	0.704049	+	0.839053i
$141$	17.8034	+	8.13820i	0.126265	+	0.0577177i
$142$	100.741	−	36.6667i	0.709443	−	0.258216i
$143$	−34.2292	−	19.7622i	−0.239365	−	0.138197i
$144$	22.7198	−	27.9251i	0.157776	−	0.193924i
$145$	202.576	+	350.872i	1.39708	+	2.41981i
$146$	48.2045	−	57.4479i	0.330168	−	0.393479i
$147$	−8.37768	+	104.908i	−0.0569910	+	0.713657i
$148$	−23.1295	−	131.174i	−0.156281	−	0.886311i
$149$	82.6444	−	14.5724i	0.554660	−	0.0978015i	0.110710	−	0.993853i	$-0.464688\pi$
$149$	82.6444	−	14.5724i	0.554660	−	0.0978015i	0.443951	+	0.896051i	$0.353577\pi$
$150$	81.8402	+	172.090i	0.545601	+	1.14727i
$151$	−98.8811	−	82.9711i	−0.654842	−	0.549477i	0.253694	−	0.967284i	$-0.418354\pi$
$151$	−98.8811	−	82.9711i	−0.654842	−	0.549477i	−0.908536	+	0.417807i	$0.862799\pi$
$152$	−51.7299	+	29.8663i	−0.340328	+	0.196489i
$153$	4.69223	+	7.84999i	0.0306682	+	0.0513071i
$154$	−42.6623	+	73.8932i	−0.277028	+	0.479826i
$155$	18.8950	+	51.9137i	0.121903	+	0.334927i
$156$	−20.8958	−	29.3662i	−0.133948	−	0.188245i
$157$	159.054	−	133.462i	1.01308	−	0.850079i	0.0243416	−	0.999704i	$-0.492251\pi$
$157$	159.054	−	133.462i	1.01308	−	0.850079i	0.988743	+	0.149625i	$0.0478066\pi$
$158$	39.5950	−	108.786i	0.250601	−	0.688521i
$159$	−85.0028	−	83.7242i	−0.534609	−	0.526567i
$160$	−8.21355	+	46.5814i	−0.0513347	+	0.291134i
$161$		−	196.610i		−	1.22118i
$162$	113.362	+	16.4636i	0.699766	+	0.101627i
$163$	−171.033			−1.04928			−0.524641	−	0.851324i	$-0.675800\pi$
$163$	−171.033			−1.04928			−0.524641	+	0.851324i	$0.675800\pi$
$164$	104.458	+	18.4188i	0.636941	+	0.112310i
$165$	−115.821	+	117.590i	−0.701946	+	0.712666i
$166$	−62.3605	−	22.6974i	−0.375665	−	0.136731i
$167$	−101.372	−	120.810i	−0.607015	−	0.723413i	0.371765	−	0.928327i	$-0.378753\pi$
$167$	−101.372	−	120.810i	−0.607015	−	0.723413i	−0.978780	+	0.204914i	$0.934308\pi$
$168$	−63.3951	+	45.1095i	−0.377352	+	0.268509i
$169$	124.901	−	45.4601i	0.739057	−	0.268995i
$170$	−10.4063	−	6.00805i	−0.0612132	−	0.0353415i
$171$	−166.025	−	92.5284i	−0.970906	−	0.541102i
$172$	−47.4986	−	82.2700i	−0.276155	−	0.478314i
$173$	−10.7700	+	12.8352i	−0.0622543	+	0.0741918i	−0.796273	−	0.604938i	$-0.793198\pi$
$173$	−10.7700	+	12.8352i	−0.0622543	+	0.0741918i	0.734019	+	0.679129i	$0.237642\pi$
$174$	−185.650	+	88.2887i	−1.06695	+	0.507406i
$175$	−71.5174	−	405.595i	−0.408671	−	2.31769i
$176$	−25.9193	+	4.57027i	−0.147269	+	0.0259674i
$177$	83.8532	+	6.69633i	0.473747	+	0.0378324i
$178$	−25.3937	−	21.3078i	−0.142661	−	0.119707i
$179$	−94.2561	+	54.4188i	−0.526570	+	0.304016i	−0.739619	−	0.673026i	$-0.764994\pi$
$179$	−94.2561	+	54.4188i	−0.526570	+	0.304016i	0.213048	+	0.977042i	$0.431661\pi$
$180$	−140.635	+	53.6141i	−0.781303	+	0.297856i
$181$	−18.5784	+	32.1787i	−0.102643	+	0.177783i	−0.912773	−	0.408468i	$-0.866063\pi$
$181$	−18.5784	+	32.1787i	−0.102643	+	0.177783i	0.810130	+	0.586251i	$0.199397\pi$
$182$	26.6421	+	73.1986i	0.146385	+	0.402190i
$183$	−51.2488	+	112.114i	−0.280048	+	0.612643i
$184$	46.4577	−	38.9826i	0.252487	−	0.211862i
$185$	−190.460	+	523.285i	−1.02951	+	2.82857i
$186$	−27.0206	+	7.46005i	−0.145272	+	0.0401078i
$187$	1.16103	−	6.58454i	0.00620873	−	0.0352115i
$188$		−	13.0502i		−	0.0694160i
$189$	−226.702	−	99.5033i	−1.19948	−	0.526472i
$190$	249.728			1.31436
$191$	211.469	+	37.2877i	1.10717	+	0.195223i	0.697200	−	0.716877i	$-0.254429\pi$
$191$	211.469	+	37.2877i	1.10717	+	0.195223i	0.409967	+	0.912100i	$0.365540\pi$
$192$	−23.2286	−	6.03581i	−0.120982	−	0.0314365i
$193$	−266.703	−	97.0720i	−1.38188	−	0.502964i	−0.459134	−	0.888367i	$-0.651840\pi$
$193$	−266.703	−	97.0720i	−1.38188	−	0.502964i	−0.922748	+	0.385403i	$0.874062\pi$
$194$	−31.8181	−	37.9193i	−0.164011	−	0.195460i
$195$	14.2699	+	150.005i	0.0731790	+	0.769256i
$196$	65.9298	−	23.9965i	0.336376	−	0.122431i
$197$	−154.203	−	89.0292i	−0.782756	−	0.451925i	0.0546498	−	0.998506i	$-0.482596\pi$
$197$	−154.203	−	89.0292i	−0.782756	−	0.451925i	−0.837406	+	0.546581i	$0.815929\pi$
$198$	−54.7976	−	63.3307i	−0.276755	−	0.319852i
$199$	−72.8436	−	126.169i	−0.366048	−	0.634014i	0.622896	−	0.782305i	$-0.285956\pi$
$199$	−72.8436	−	126.169i	−0.366048	−	0.634014i	−0.988944	+	0.148291i	$0.952623\pi$
$200$	81.6594	−	97.3179i	0.408297	−	0.486590i
$201$	36.6612	+	25.2586i	0.182394	+	0.125665i
$202$	29.7805	+	168.894i	0.147428	+	0.836107i
$203$	437.553	−	77.1525i	2.15544	−	0.380061i
$204$	3.45913	−	5.02070i	0.0169565	−	0.0246113i
$205$	−339.705	−	285.046i	−1.65710	−	1.39047i
$206$	231.387	−	133.591i	1.12324	−	0.648502i
$207$	182.317	+	63.2456i	0.880757	+	0.305534i
$208$	−12.0139	+	20.8087i	−0.0577592	+	0.100042i
$209$	47.5258	+	130.576i	0.227396	+	0.624765i
$210$	323.827	−	30.8056i	1.54204	−	0.146693i
$211$	−227.718	+	191.078i	−1.07923	+	0.905584i	−0.995857	−	0.0909345i	$-0.971015\pi$
$211$	−227.718	+	191.078i	−1.07923	+	0.905584i	−0.0833757	+	0.996518i	$0.526570\pi$
$212$	−27.2046	+	74.7440i	−0.128324	+	0.352566i
$213$	57.1940	−	220.109i	0.268517	−	1.03338i
$214$	−18.7808	+	106.511i	−0.0877605	+	0.497715i
$215$			397.161i			1.84726i
$216$	−21.4371	−	73.2970i	−0.0992456	−	0.339338i
$217$	60.5839			0.279189
$218$	−60.9748	−	10.7515i	−0.279701	−	0.0493188i
$219$	−42.3372	−	153.347i	−0.193320	−	0.700214i
$220$	103.398	+	37.6339i	0.469992	+	0.171063i
$221$	−3.92360	−	4.67596i	−0.0177538	−	0.0211582i
$222$	−256.979	−	117.469i	−1.15756	−	0.529139i
$223$	198.549	−	72.2658i	0.890352	−	0.324062i	0.143972	−	0.989582i	$-0.454012\pi$
$223$	198.549	−	72.2658i	0.890352	−	0.324062i	0.746380	+	0.665520i	$0.231790\pi$
$224$	44.9214	+	25.9354i	0.200542	+	0.115783i
$225$	399.114	+	64.1538i	1.77384	+	0.285128i
$226$	0.146809	+	0.254281i	0.000649599	+	0.00112514i
$227$	10.3430	−	12.3263i	0.0455638	−	0.0543008i	−0.742781	−	0.669534i	$-0.766494\pi$
$227$	10.3430	−	12.3263i	0.0455638	−	0.0543008i	0.788345	+	0.615233i	$0.210938\pi$
$228$	−10.0868	+	126.310i	−0.0442404	+	0.553990i
$229$	45.3854	+	257.394i	0.198190	+	1.12399i	0.907803	+	0.419398i	$0.137759\pi$
$229$	45.3854	+	257.394i	0.198190	+	1.12399i	−0.709613	+	0.704592i	$0.751130\pi$
$230$	−249.696	+	44.0281i	−1.08563	+	0.191426i
$231$	77.7351	+	163.458i	0.336515	+	0.707610i
$232$	104.986	+	88.0936i	0.452525	+	0.379714i
$233$	278.614	−	160.858i	1.19577	−	0.690377i	0.236159	−	0.971715i	$-0.424111\pi$
$233$	278.614	−	160.858i	1.19577	−	0.690377i	0.959609	+	0.281338i	$0.0907782\pi$
$234$	−76.4473	+	1.15869i	−0.326698	+	0.00495168i
$235$	−27.2799	+	47.2502i	−0.116085	+	0.201065i
$236$	−19.1805	−	52.6981i	−0.0812735	−	0.223297i
$237$	−142.380	−	200.095i	−0.600758	−	0.844282i
$238$	−10.0944	+	8.47018i	−0.0424133	+	0.0355890i
$239$	26.9782	−	74.1219i	0.112879	−	0.310133i	−0.870370	−	0.492398i	$-0.836121\pi$
$239$	26.9782	−	74.1219i	0.112879	−	0.310133i	0.983250	+	0.182265i	$0.0583427\pi$
$240$	71.4856	+	70.4103i	0.297857	+	0.293376i
$241$	52.6081	−	298.355i	0.218291	−	1.23799i	−0.656813	−	0.754053i	$-0.728096\pi$
$241$	52.6081	−	298.355i	0.218291	−	1.23799i	0.875104	−	0.483935i	$-0.160793\pi$
$242$		−	109.894i		−	0.454106i
$243$	165.195	−	178.212i	0.679814	−	0.733384i
$244$	82.1811			0.336808
$245$	−288.870	−	50.9357i	−1.17906	−	0.207901i
$246$	157.894	−	160.306i	0.641847	−	0.651649i
$247$	119.208	+	43.3882i	0.482624	+	0.175661i
$248$	12.0122	+	14.3156i	0.0484363	+	0.0577241i
$249$	−114.702	+	81.6175i	−0.460651	+	0.327781i
$250$	−221.295	+	80.5449i	−0.885182	+	0.322180i
$251$	−71.3813	−	41.2120i	−0.284387	−	0.164191i	0.351021	−	0.936368i	$-0.385835\pi$
$251$	−71.3813	−	41.2120i	−0.284387	−	0.164191i	−0.635408	+	0.772177i	$0.719168\pi$
$252$	2.50136	+	165.033i	0.00992605	+	0.654892i
$253$	−70.5407	−	122.180i	−0.278817	−	0.482925i
$254$	−140.982	+	168.016i	−0.555049	+	0.661482i
$255$	−23.0195	+	10.9473i	−0.0902725	+	0.0429306i
$256$	2.77837	+	15.7569i	0.0108530	+	0.0615505i
$257$	−21.2643	+	3.74948i	−0.0827406	+	0.0145894i	−0.214865	−	0.976644i	$-0.568931\pi$
$257$	−21.2643	+	3.74948i	−0.0827406	+	0.0145894i	0.132125	+	0.991233i	$0.457820\pi$
$258$	−200.880	−	16.0418i	−0.778605	−	0.0621777i
$259$	467.808	+	392.538i	1.80621	+	1.51559i
$260$	86.9963	−	50.2274i	0.334601	−	0.193182i
$261$	−69.2087	+	430.561i	−0.265167	+	1.64966i
$262$	95.7479	−	165.840i	0.365450	−	0.632978i
$263$	−17.1583	−	47.1420i	−0.0652407	−	0.179247i	0.902789	−	0.430085i	$-0.141516\pi$
$263$	−17.1583	−	47.1420i	−0.0652407	−	0.179247i	−0.968029	+	0.250837i	$0.919294\pi$
$264$	−23.2112	+	50.7777i	−0.0879212	+	0.192340i
$265$	254.742	−	213.754i	0.961291	−	0.806619i
$266$	93.6657	−	257.344i	0.352127	−	0.967460i
$267$	−67.7839	+	18.7143i	−0.253872	+	0.0700911i
$268$	5.15390	−	29.2292i	0.0192310	−	0.109064i
$269$			119.776i			0.445263i	0.974903	+	0.222632i	$0.0714648\pi$
$269$			119.776i			0.445263i	−0.974903	+	0.222632i	$0.928535\pi$
$270$	−75.6028	+	310.195i	−0.280010	+	1.14887i
$271$	−146.752			−0.541522			−0.270761	−	0.962647i	$-0.587275\pi$
$271$	−146.752			−0.541522			−0.270761	+	0.962647i	$0.587275\pi$
$272$	−4.00289	−	0.705818i	−0.0147165	−	0.00259492i
$273$	159.932	+	41.5573i	0.585832	+	0.152225i
$274$	−62.4726	−	22.7382i	−0.228002	−	0.0829860i
$275$	−189.965	−	226.391i	−0.690780	−	0.823240i
$276$	−12.1834	−	128.072i	−0.0441429	−	0.464028i
$277$	−306.464	+	111.544i	−1.10637	+	0.402685i	−0.829659	−	0.558270i	$-0.811465\pi$
$277$	−306.464	+	111.544i	−1.10637	+	0.402685i	−0.276707	+	0.960954i	$0.589243\pi$
$278$	59.3305	+	34.2545i	0.213419	+	0.123217i
$279$	−19.4886	+	56.1795i	−0.0698518	+	0.201360i
$280$	−108.430	−	187.806i	−0.387249	−	0.670735i
$281$	−8.78420	+	10.4686i	−0.0312605	+	0.0372548i	−0.781448	−	0.623970i	$-0.785519\pi$
$281$	−8.78420	+	10.4686i	−0.0312605	+	0.0372548i	0.750188	+	0.661225i	$0.229963\pi$
$282$	−22.7968	−	15.7064i	−0.0808397	−	0.0556964i
$283$	79.1142	+	448.679i	0.279555	+	1.58544i	0.724109	+	0.689685i	$0.242251\pi$
$283$	79.1142	+	448.679i	0.279555	+	1.58544i	−0.444554	+	0.895752i	$0.646638\pi$
$284$	−149.309	+	26.3272i	−0.525737	+	0.0927016i
$285$	300.557	−	436.238i	1.05458	−	1.53066i
$286$	42.8188	+	35.9293i	0.149716	+	0.125627i
$287$	−421.153	+	243.153i	−1.46743	+	0.847222i
$288$	−38.5002	+	33.3127i	−0.133681	+	0.115669i
$289$	−143.984	+	249.387i	−0.498214	+	0.862931i
$290$	−195.968	−	538.417i	−0.675751	−	1.85661i
$291$	−104.534	+	9.94426i	−0.359222	+	0.0341727i
$292$	−81.2436	+	68.1715i	−0.278231	+	0.233464i
$293$	166.845	−	458.404i	0.569438	−	1.56452i	−0.235946	−	0.971766i	$-0.575819\pi$
$293$	166.845	−	458.404i	0.569438	−	1.56452i	0.805384	−	0.592753i	$-0.201959\pi$
$294$	37.4306	−	144.050i	0.127315	−	0.489967i
$295$	−40.7132	+	230.896i	−0.138011	+	0.782698i
$296$			188.370i			0.636385i
$297$	−176.580	+	19.5025i	−0.594547	+	0.0656651i
$298$	−118.680			−0.398254
$299$	−126.842	−	22.3657i	−0.424222	−	0.0748018i
$300$	−71.7201	−	259.773i	−0.239067	−	0.865909i
$301$	409.274	+	148.964i	1.35972	+	0.494896i
$302$	117.339	+	139.839i	0.388539	+	0.463043i
$303$	330.874	+	151.247i	1.09199	+	0.499166i
$304$	79.3801	−	28.8920i	0.261119	−	0.0950395i
$305$	−297.549	−	171.790i	−0.975571	−	0.563246i
$306$	−4.60724	−	12.0852i	−0.0150563	−	0.0394941i
$307$	4.37352	+	7.57515i	0.0142460	+	0.0246748i	0.873061	−	0.487612i	$-0.162132\pi$
$307$	4.37352	+	7.57515i	0.0142460	+	0.0246748i	−0.858815	+	0.512287i	$0.828799\pi$
$308$	77.5633	−	92.4364i	0.251829	−	0.300118i
$309$	45.1182	−	564.982i	0.146014	−	1.82842i
$310$	−13.5669	−	76.9418i	−0.0437642	−	0.248199i
$311$	51.0927	−	9.00901i	0.164285	−	0.0289679i	−0.0909005	−	0.995860i	$-0.528975\pi$
$311$	51.0927	−	9.00901i	0.164285	−	0.0289679i	0.255186	+	0.966892i	$0.417863\pi$
$312$	21.8906	+	46.0306i	0.0701621	+	0.147534i
$313$	−279.972	−	234.925i	−0.894481	−	0.750558i	0.0746231	−	0.997212i	$-0.476225\pi$
$313$	−279.972	−	234.925i	−0.894481	−	0.750558i	−0.969104	+	0.246653i	$0.920669\pi$
$314$	−254.294	+	146.817i	−0.809855	+	0.467570i
$315$	335.925	−	602.755i	1.06643	−	1.91351i
$316$	−81.8603	+	141.786i	−0.259052	+	0.448690i
$317$	156.797	+	430.796i	0.494627	+	1.35898i	0.896403	+	0.443239i	$0.146171\pi$
$317$	156.797	+	430.796i	0.494627	+	1.35898i	−0.401776	+	0.915738i	$0.631607\pi$
$318$	97.8252	+	137.480i	0.307626	+	0.432326i
$319$	244.229	−	204.932i	0.765608	−	0.642421i
$320$	22.8785	−	62.8582i	0.0714953	−	0.196432i
$321$	163.456	+	160.997i	0.509208	+	0.501548i
$322$	−48.2827	+	273.825i	−0.149946	+	0.850387i
$323$			21.4600i			0.0664395i
$324$	−153.839	−	50.7682i	−0.474813	−	0.156692i
$325$	−269.804			−0.830166
$326$	238.202	+	42.0015i	0.730682	+	0.128839i
$327$	−92.1667	+	93.5742i	−0.281855	+	0.286160i
$328$	−140.959	−	51.3048i	−0.429753	−	0.156417i
$329$	38.4594	+	45.8341i	0.116898	+	0.139313i
$330$	190.184	−	135.328i	0.576317	−	0.410084i
$331$	−417.551	+	151.976i	−1.26148	+	0.459143i	−0.884267	−	0.466982i	$-0.845341\pi$
$331$	−417.551	+	151.976i	−1.26148	+	0.459143i	−0.377218	+	0.926125i	$0.623119\pi$
$332$	81.2773	+	46.9255i	0.244811	+	0.141342i
$333$	−514.485	+	307.527i	−1.54500	+	0.923504i
$334$	111.515	+	193.150i	0.333877	+	0.578293i
$335$	−79.7607	+	95.0551i	−0.238092	+	0.283747i
$336$	99.3699	−	47.2569i	0.295744	−	0.140646i
$337$	−15.6199	−	88.5848i	−0.0463498	−	0.262863i	0.952823	−	0.303526i	$-0.0981640\pi$
$337$	−15.6199	−	88.5848i	−0.0463498	−	0.262863i	−0.999173	+	0.0406634i	$0.987053\pi$
$338$	−185.117	+	32.6410i	−0.547682	+	0.0965712i
$339$	0.620883	+	0.0495823i	0.00183151	+	0.000146261i
$340$	13.0177	+	10.9231i	0.0382872	+	0.0321268i
$341$	37.6489	−	21.7366i	0.110407	−	0.0637436i
$342$	208.505	+	169.639i	0.609663	+	0.496019i
$343$	63.8177	−	110.536i	0.186058	−	0.322261i
$344$	45.9492	+	126.244i	0.133573	+	0.366989i
$345$	−223.607	+	489.171i	−0.648137	+	1.41789i
$346$	18.1517	−	15.2311i	0.0524615	−	0.0440204i
$347$	169.850	−	466.660i	0.489483	−	1.34484i	−0.411667	−	0.911334i	$-0.635053\pi$
$347$	169.850	−	466.660i	0.489483	−	1.34484i	0.901150	−	0.433508i	$-0.142724\pi$
$348$	280.241	−	77.3711i	0.805290	−	0.222331i
$349$	58.8946	−	334.008i	0.168752	−	0.957042i	−0.776358	−	0.630292i	$-0.782935\pi$
$349$	58.8946	−	334.008i	0.168752	−	0.957042i	0.945111	−	0.326750i	$-0.105954\pi$
$350$			582.447i			1.66413i
$351$	−89.9830	+	134.937i	−0.256362	+	0.384435i
$352$	37.2209			0.105741
$353$	−217.451	−	38.3425i	−0.616008	−	0.108619i	−0.143067	−	0.989713i	$-0.545696\pi$
$353$	−217.451	−	38.3425i	−0.616008	−	0.108619i	−0.472941	+	0.881094i	$0.656808\pi$
$354$	−115.140	−	29.9185i	−0.325255	−	0.0845155i
$355$	595.631	+	216.792i	1.67783	+	0.610681i
$356$	30.1338	+	35.9121i	0.0846456	+	0.100877i
$357$	2.64723	+	27.8276i	0.00741521	+	0.0779484i
$358$	144.637	−	52.6436i	0.404014	−	0.147049i
$359$	494.204	+	285.329i	1.37661	+	0.794788i	0.991750	−	0.128185i	$-0.0409152\pi$
$359$	494.204	+	285.329i	1.37661	+	0.794788i	0.384864	+	0.922973i	$0.374249\pi$
$360$	209.032	−	40.1335i	0.580644	−	0.111482i
$361$	−42.4986	−	73.6098i	−0.117725	−	0.203905i
$362$	33.7770	−	40.2539i	0.0933066	−	0.111198i
$363$	−191.968	−	132.261i	−0.528838	−	0.364355i
$364$	−19.1294	−	108.488i	−0.0525534	−	0.298045i
$365$	436.659	−	76.9948i	1.19633	−	0.210945i
$366$	98.9080	−	143.558i	0.270240	−	0.392236i
$367$	−161.979	−	135.917i	−0.441360	−	0.370345i	0.394858	−	0.918742i	$-0.370794\pi$
$367$	−161.979	−	135.917i	−0.441360	−	0.370345i	−0.836218	+	0.548397i	$0.815238\pi$
$368$	−74.2761	+	42.8833i	−0.201837	+	0.116531i
$369$	−89.9990	−	468.752i	−0.243900	−	1.27033i
$370$	393.765	−	682.021i	1.06423	−	1.84330i
$371$	−124.727	−	342.684i	−0.336191	−	0.923677i
$372$	39.4643	−	3.75423i	0.106087	−	0.0100920i
$373$	−53.2124	+	44.6505i	−0.142661	+	0.119706i	−0.711325	−	0.702863i	$-0.751905\pi$
$373$	−53.2124	+	44.6505i	−0.142661	+	0.119706i	0.568665	+	0.822569i	$0.307460\pi$
$374$	−3.23401	+	8.88536i	−0.00864707	+	0.0237576i
$375$	−125.637	+	483.510i	−0.335032	+	1.28936i
$376$	−3.20481	+	18.1754i	−0.00852343	+	0.0483388i
$377$		−	291.063i		−	0.772049i
$378$	291.299	+	194.254i	0.770632	+	0.513898i
$379$	390.211			1.02958			0.514791	−	0.857316i	$-0.327870\pi$
$379$	390.211			1.02958			0.514791	+	0.857316i	$0.327870\pi$
$380$	−347.803	−	61.3271i	−0.915271	−	0.161387i
$381$	123.823	+	448.490i	0.324994	+	1.17714i
$382$	−285.362	−	103.863i	−0.747020	−	0.271893i
$383$	−116.563	−	138.915i	−0.304342	−	0.362701i	0.592098	−	0.805866i	$-0.298300\pi$
$383$	−116.563	−	138.915i	−0.304342	−	0.362701i	−0.896440	+	0.443165i	$0.853856\pi$
$384$	30.8689	+	14.1106i	0.0803878	+	0.0367464i
$385$	−474.057	+	172.543i	−1.23132	+	0.448163i
$386$	347.607	+	200.691i	0.900535	+	0.519924i
$387$	−269.789	+	331.601i	−0.697130	+	0.856851i
$388$	35.0019	+	60.6250i	0.0902110	+	0.156250i
$389$	−432.550	+	515.493i	−1.11195	+	1.32518i	−0.171527	+	0.985179i	$0.554870\pi$
$389$	−432.550	+	515.493i	−1.11195	+	1.32518i	−0.940427	+	0.339996i	$0.889574\pi$
$390$	16.9634	−	212.420i	0.0434959	−	0.544668i
$391$	−3.78348	−	21.4572i	−0.00967642	−	0.0548777i
$392$	−97.7152	+	17.2298i	−0.249274	+	0.0439536i
$393$	−174.463	−	366.852i	−0.443925	−	0.933467i
$394$	192.900	+	161.862i	0.489593	+	0.410817i
$395$	592.775	−	342.239i	1.50070	−	0.866427i
$396$	60.7656	+	101.659i	0.153449	+	0.256716i
$397$	226.822	−	392.867i	0.571340	−	0.989590i	−0.425089	−	0.905152i	$-0.639757\pi$
$397$	226.822	−	392.867i	0.571340	−	0.989590i	0.996429	−	0.0844384i	$-0.0269096\pi$
$398$	70.4674	+	193.608i	0.177054	+	0.486451i
$399$	−336.813	−	473.344i	−0.844143	−	1.18632i
$400$	−137.628	+	115.484i	−0.344071	+	0.288710i
$401$	−107.387	+	295.043i	−0.267798	+	0.735769i	0.730788	+	0.682605i	$0.239153\pi$
$401$	−107.387	+	295.043i	−0.267798	+	0.735769i	−0.998586	+	0.0531643i	$0.983069\pi$
$402$	−44.8563	−	44.1815i	−0.111583	−	0.109904i
$403$	6.89183	−	39.0855i	0.0171013	−	0.0969864i
$404$		−	242.536i		−	0.600337i
$405$	450.874	+	505.398i	1.11327	+	1.24790i
$406$	−628.340			−1.54763
$407$	431.548	+	76.0936i	1.06031	+	0.186962i
$408$	−6.05059	+	6.14300i	−0.0148299	+	0.0150564i
$409$	−1.59923	−	0.582072i	−0.00391009	−	0.00142316i	0.340064	−	0.940402i	$-0.389551\pi$
$409$	−1.59923	−	0.582072i	−0.00391009	−	0.00142316i	−0.343974	+	0.938979i	$0.611773\pi$
$410$	403.116	+	480.415i	0.983209	+	1.17174i
$411$	−114.908	+	81.7643i	−0.279582	+	0.198940i
$412$	−355.066	+	129.234i	−0.861812	+	0.313674i
$413$	222.668	+	128.557i	0.539147	+	0.311277i
$414$	−238.386	−	132.856i	−0.575812	−	0.320909i
$415$	−196.184	−	339.801i	−0.472733	−	0.818798i
$416$	21.8422	−	26.0305i	0.0525053	−	0.0625734i
$417$	131.244	−	62.4152i	0.314734	−	0.149677i
$418$	−34.1242	−	193.528i	−0.0816369	−	0.462986i
$419$	−98.5462	+	17.3764i	−0.235194	+	0.0414710i	−0.290003	−	0.957026i	$-0.593656\pi$
$419$	−98.5462	+	17.3764i	−0.235194	+	0.0414710i	0.0548088	+	0.998497i	$0.482545\pi$
$420$	−458.569	−	36.6203i	−1.09183	−	0.0871911i
$421$	486.614	+	408.318i	1.15585	+	0.969876i	0.999840	−	0.0178796i	$-0.00569155\pi$
$421$	486.614	+	408.318i	1.15585	+	0.969876i	0.156012	+	0.987755i	$0.450136\pi$
$422$	364.074	−	210.198i	0.862734	−	0.498099i
$423$	−54.8736	+	20.9195i	−0.129725	+	0.0494550i
$424$	56.2439	−	97.4173i	0.132651	−	0.229758i
$425$	−15.6102	−	42.8886i	−0.0367299	−	0.100914i
$426$	−133.709	+	292.507i	−0.313872	+	0.686637i
$427$	−288.632	+	242.191i	−0.675952	+	0.567191i
$428$	52.3130	−	143.729i	0.122227	−	0.335815i
$429$	114.297	−	31.5560i	0.266427	−	0.0735572i
$430$	97.5332	−	553.138i	0.226821	−	1.28637i
$431$		−	180.242i		−	0.418195i	−0.977895	−	0.209098i	$-0.932947\pi$
$431$		−	180.242i		−	0.418195i	0.977895	−	0.209098i	$-0.0670526\pi$
$432$	11.8560	+	107.347i	0.0274445	+	0.248489i
$433$	161.992			0.374115			0.187058	−	0.982349i	$-0.440105\pi$
$433$	161.992			0.374115			0.187058	+	0.982349i	$0.440105\pi$
$434$	−84.3770	−	14.8779i	−0.194417	−	0.0342810i
$435$	−1176.39	−	305.677i	−2.70435	−	0.702707i
$436$	82.2810	+	29.9478i	0.188718	+	0.0686877i
$437$	291.066	+	346.880i	0.666056	+	0.793775i
$438$	21.3060	+	223.968i	0.0486437	+	0.511341i
$439$	302.339	−	110.043i	0.688700	−	0.250666i	0.0261216	−	0.999659i	$-0.491684\pi$
$439$	302.339	−	110.043i	0.688700	−	0.250666i	0.662579	+	0.748992i	$0.269462\pi$
$440$	−134.764	−	77.8059i	−0.306281	−	0.176831i
$441$	−206.586	−	238.756i	−0.468449	−	0.541396i
$442$	4.31621	+	7.47589i	0.00976517	+	0.0169138i
$443$	325.041	−	387.368i	0.733726	−	0.874421i	−0.262161	−	0.965024i	$-0.584435\pi$
$443$	325.041	−	387.368i	0.733726	−	0.874421i	0.995887	+	0.0906036i	$0.0288796\pi$
$444$	329.055	+	226.710i	0.741114	+	0.510608i
$445$	−34.0340	−	193.016i	−0.0764809	−	0.433745i
$446$	−294.271	+	51.8879i	−0.659800	+	0.116341i
$447$	−142.835	+	207.316i	−0.319542	+	0.463795i
$448$	−56.1942	−	47.1525i	−0.125434	−	0.105251i
$449$	−621.494	+	358.820i	−1.38417	+	0.799153i	−0.992651	−	0.121015i	$-0.961385\pi$
$449$	−621.494	+	358.820i	−1.38417	+	0.799153i	−0.391524	+	0.920168i	$0.628052\pi$
$450$	−540.103	−	187.362i	−1.20023	−	0.416359i
$451$	−174.479	+	302.206i	−0.386871	+	0.670080i
$452$	−0.142020	−	0.390198i	−0.000314204	−	0.000863269i
$453$	385.500	−	36.6725i	0.850993	−	0.0809547i
$454$	−17.4320	+	14.6272i	−0.0383965	+	0.0322185i
$455$	−157.521	+	432.787i	−0.346201	+	0.951179i
$456$	45.0668	−	173.438i	0.0988307	−	0.380347i
$457$	72.4920	−	411.123i	0.158626	−	0.899612i	−0.796770	−	0.604283i	$-0.793460\pi$
$457$	72.4920	−	411.123i	0.158626	−	0.899612i	0.955396	−	0.295329i	$-0.0954292\pi$
$458$		−	369.625i		−	0.807041i
$459$	−26.6561	−	6.49680i	−0.0580742	−	0.0141542i
$460$	358.570			0.779501
$461$	−807.492	−	142.383i	−1.75161	−	0.308856i	−0.796397	−	0.604774i	$-0.793263\pi$
$461$	−807.492	−	142.383i	−1.75161	−	0.308856i	−0.955213	+	0.295918i	$0.904374\pi$
$462$	−68.1226	−	246.742i	−0.147451	−	0.534074i
$463$	−800.359	−	291.307i	−1.72864	−	0.629173i	−0.730105	−	0.683335i	$-0.760529\pi$
$463$	−800.359	−	291.307i	−1.72864	−	0.629173i	−0.998532	+	0.0541620i	$0.982751\pi$
$464$	−124.583	−	148.472i	−0.268498	−	0.319984i
$465$	−150.734	−	68.9029i	−0.324160	−	0.148178i
$466$	−427.536	+	155.610i	−0.917460	+	0.333928i
$467$	−557.001	−	321.585i	−1.19272	−	0.688619i	−0.233800	−	0.972285i	$-0.575116\pi$
$467$	−557.001	−	321.585i	−1.19272	−	0.688619i	−0.958923	+	0.283666i	$0.908449\pi$
$468$	106.755	+	17.1598i	0.228109	+	0.0366663i
$469$	68.0383	+	117.846i	0.145071	+	0.251270i
$470$	49.5970	−	59.1074i	0.105526	−	0.125760i
$471$	−49.5849	+	620.915i	−0.105276	+	1.31829i
$472$	13.7719	+	78.1044i	0.0291778	+	0.165475i
$473$	307.782	−	54.2704i	0.650703	−	0.114736i
$474$	149.158	+	313.643i	0.314679	+	0.661694i
$475$	726.631	+	609.716i	1.52975	+	1.28361i
$476$	16.1388	−	9.31774i	0.0339050	−	0.0195751i
$477$	357.893	−	5.42450i	0.750300	−	0.0113721i
$478$	−55.7758	+	96.6065i	−0.116686	+	0.202106i
$479$	−103.396	−	284.077i	−0.215857	−	0.593062i	0.783751	−	0.621076i	$-0.213304\pi$
$479$	−103.396	−	284.077i	−0.215857	−	0.593062i	−0.999608	+	0.0280135i	$0.991082\pi$
$480$	−82.2689	−	115.618i	−0.171394	−	0.240870i
$481$	306.461	−	257.151i	0.637132	−	0.534617i
$482$	−146.538	+	402.609i	−0.304020	+	0.835288i
$483$	420.222	+	413.901i	0.870025	+	0.856938i
$484$	−26.9872	+	153.052i	−0.0557586	+	0.316223i
$485$		−	292.669i		−	0.603442i
$486$	−273.836	+	207.634i	−0.563449	+	0.427230i
$487$	584.450			1.20010			0.600052	−	0.799961i	$-0.295147\pi$
$487$	584.450			1.20010			0.600052	+	0.799961i	$0.295147\pi$
$488$	−114.456	−	20.1817i	−0.234541	−	0.0413559i
$489$	360.056	−	365.555i	0.736311	−	0.747555i
$490$	389.810	+	141.879i	0.795530	+	0.289549i
$491$	−177.012	−	210.954i	−0.360513	−	0.429643i	0.555050	−	0.831817i	$-0.312699\pi$
$491$	−177.012	−	210.954i	−0.360513	−	0.429643i	−0.915563	+	0.402174i	$0.868255\pi$
$492$	−259.271	+	184.487i	−0.526974	+	0.374974i
$493$	46.2680	−	16.8402i	0.0938498	−	0.0341586i
$494$	−155.370	−	89.7027i	−0.314513	−	0.181584i
$495$	−7.50406	−	495.097i	−0.0151597	−	1.00020i
$496$	−13.2142	−	22.8876i	−0.0266415	−	0.0461444i
$497$	446.807	−	532.484i	0.899009	−	1.07140i
$498$	179.792	−	85.5030i	0.361028	−	0.171693i
$499$	−29.6099	−	167.926i	−0.0593384	−	0.336525i	0.940658	−	0.339357i	$-0.110210\pi$
$499$	−29.6099	−	167.926i	−0.0593384	−	0.336525i	−0.999996	+	0.00283231i	$0.999098\pi$
$500$	327.984	−	57.8325i	0.655969	−	0.115665i
$501$	471.617	+	37.6623i	0.941351	+	0.0751742i
$502$	89.2941	+	74.9266i	0.177877	+	0.149256i
$503$	−13.2176	+	7.63121i	−0.0262776	+	0.0151714i	−0.513081	−	0.858340i	$-0.671496\pi$
$503$	−13.2176	+	7.63121i	−0.0262776	+	0.0151714i	0.486804	+	0.873511i	$0.338163\pi$
$504$	37.0443	−	230.460i	0.0735006	−	0.457262i
$505$	−506.994	+	878.139i	−1.00395	+	1.73889i
$506$	68.2396	+	187.487i	0.134861	+	0.370527i
$507$	−165.775	+	362.656i	−0.326973	+	0.715299i
$508$	237.611	−	199.379i	0.467738	−	0.392479i
$509$	−177.011	+	486.334i	−0.347762	+	0.955470i	0.635311	+	0.772257i	$0.280872\pi$
$509$	−177.011	+	486.334i	−0.347762	+	0.955470i	−0.983073	+	0.183213i	$0.941350\pi$
$510$	34.7483	−	9.59358i	0.0681339	−	0.0188109i
$511$	84.4351	−	478.855i	0.165235	−	0.937094i
$512$		−	22.6274i		−	0.0441942i
$513$	547.277	−	160.061i	1.06682	−	0.312010i
$514$	30.5362			0.0594090
$515$	1555.72	+	274.315i	3.02081	+	0.532651i
$516$	275.832	+	71.6732i	0.534558	+	0.138902i
$517$	40.3445	+	14.6842i	0.0780358	+	0.0284027i
$518$	−555.132	−	661.581i	−1.07168	−	1.27718i
$519$	−4.76024	−	50.0395i	−0.00917195	−	0.0964152i
$520$	−133.497	+	48.5889i	−0.256725	+	0.0934402i
$521$	843.550	+	487.024i	1.61910	+	0.934786i	0.987154	+	0.159771i	$0.0510757\pi$
$521$	843.550	+	487.024i	1.61910	+	0.934786i	0.631943	+	0.775015i	$0.282258\pi$
$522$	202.124	−	582.659i	0.387211	−	1.11621i
$523$	159.545	+	276.340i	0.305058	+	0.528375i	0.977274	−	0.211979i	$-0.0679909\pi$
$523$	159.545	+	276.340i	0.305058	+	0.528375i	−0.672217	+	0.740355i	$0.734658\pi$
$524$	−174.077	+	207.457i	−0.332208	+	0.395910i
$525$	1017.45	+	700.996i	1.93800	+	1.33523i
$526$	12.3199	+	69.8697i	0.0234219	+	0.132832i
$527$	6.61187	−	1.16585i	0.0125462	−	0.00221224i
$528$	44.7967	−	65.0194i	0.0848422	−	0.123143i
$529$	53.0522	+	44.5161i	0.100288	+	0.0841514i
$530$	−407.279	+	235.143i	−0.768451	+	0.443666i
$531$	−190.839	+	165.125i	−0.359395	+	0.310971i
$532$	−193.648	+	335.409i	−0.364001	+	0.630468i
$533$	108.960	+	299.365i	0.204428	+	0.561661i
$534$	99.0004	−	9.41788i	0.185394	−	0.0176365i
$535$	−489.855	+	411.037i	−0.915617	+	0.768294i
$536$	−14.3560	+	39.4427i	−0.0267835	+	0.0735871i
$537$	82.1153	−	316.018i	0.152915	−	0.588489i
$538$	29.4140	−	166.815i	0.0546729	−	0.310066i
$539$			230.822i			0.428241i
$540$	181.470	−	413.451i	0.336056	−	0.765649i
$541$	−604.682			−1.11771			−0.558856	−	0.829265i	$-0.688759\pi$
$541$	−604.682			−1.11771			−0.558856	+	0.829265i	$0.688759\pi$
$542$	204.386	+	36.0388i	0.377096	+	0.0664922i
$543$	−29.6658	−	107.450i	−0.0546331	−	0.197883i
$544$	5.40161	+	1.96603i	0.00992944	+	0.00361402i
$545$	−235.308	−	280.430i	−0.431758	−	0.514550i
$546$	−212.536	−	97.1535i	−0.389261	−	0.177937i
$547$	−789.301	+	287.282i	−1.44296	+	0.525196i	−0.940617	−	0.339470i	$-0.889752\pi$
$547$	−789.301	+	287.282i	−1.44296	+	0.525196i	−0.502347	+	0.864666i	$0.667530\pi$
$548$	81.4234	+	47.0098i	0.148583	+	0.0857844i
$549$	−131.736	−	345.556i	−0.239957	−	0.629428i
$550$	208.973	+	361.952i	0.379951	+	0.658094i
$551$	−657.757	+	783.884i	−1.19375	+	1.42266i
$552$	−14.4831	+	181.361i	−0.0262375	+	0.328553i
$553$	−130.344	−	739.218i	−0.235703	−	1.33674i
$554$	454.213	−	80.0900i	0.819879	−	0.144567i
$555$	−717.481	−	1508.69i	−1.29276	−	2.71836i
$556$	−74.2192	−	62.2773i	−0.133488	−	0.112009i
$557$	−785.853	+	453.713i	−1.41087	+	0.814565i	−0.995470	−	0.0950749i	$-0.969691\pi$
$557$	−785.853	+	453.713i	−1.41087	+	0.814565i	−0.415398	+	0.909640i	$0.636358\pi$
$558$	40.9387	−	73.4568i	0.0733668	−	0.131643i
$559$	142.661	−	247.096i	0.255208	−	0.442033i
$560$	104.893	+	288.190i	0.187308	+	0.514626i
$561$	11.6292	+	16.3432i	0.0207294	+	0.0291322i
$562$	14.8048	−	12.4227i	0.0263431	−	0.0221045i
$563$	23.4667	−	64.4741i	0.0416815	−	0.114519i	−0.917106	−	0.398644i	$-0.869481\pi$
$563$	23.4667	−	64.4741i	0.0416815	−	0.114519i	0.958787	+	0.284125i	$0.0917031\pi$
$564$	27.8926	+	27.4731i	0.0494550	+	0.0487111i
$565$	−0.301457	+	1.70965i	−0.000533552	+	0.00302592i
$566$		−	644.316i		−	1.13837i
$567$	689.921	−	275.065i	1.21679	−	0.485124i
$568$	214.413			0.377487
$569$	−459.085	−	80.9491i	−0.806828	−	0.142265i	−0.245004	−	0.969522i	$-0.578789\pi$
$569$	−459.085	−	80.9491i	−0.806828	−	0.142265i	−0.561824	+	0.827257i	$0.689900\pi$
$570$	−525.723	+	533.752i	−0.922322	+	0.936407i
$571$	−496.079	−	180.558i	−0.868789	−	0.316213i	−0.131113	−	0.991367i	$-0.541855\pi$
$571$	−496.079	−	180.558i	−0.868789	−	0.316213i	−0.737677	+	0.675154i	$0.764077\pi$
$572$	−50.8116	−	60.5549i	−0.0888315	−	0.105865i
$573$	−524.877	+	373.482i	−0.916016	+	0.651801i
$574$	646.264	−	235.221i	1.12590	−	0.409792i
$575$	−834.033	−	481.529i	−1.45049	−	0.837442i
$576$	61.8011	−	36.9408i	0.107294	−	0.0641334i
$577$	171.837	+	297.630i	0.297811	+	0.515824i	0.975635	−	0.219401i	$-0.0704101\pi$
$577$	171.837	+	297.630i	0.297811	+	0.515824i	−0.677824	+	0.735224i	$0.737077\pi$
$578$	261.774	−	311.970i	0.452895	−	0.539740i
$579$	768.935	−	365.679i	1.32804	−	0.631571i
$580$	140.708	+	797.993i	0.242600	+	1.37585i
$581$	−423.748	+	74.7182i	−0.729342	+	0.128603i
$582$	148.029	+	11.8213i	0.254346	+	0.0203115i
$583$	−200.459	−	168.205i	−0.343841	−	0.288517i
$584$	129.891	−	74.9929i	0.222417	−	0.128412i
$585$	−350.651	−	285.288i	−0.599404	−	0.487672i
$586$	−344.943	+	597.459i	−0.588640	+	1.01956i
$587$	−56.2267	−	154.482i	−0.0957866	−	0.263172i	0.882541	−	0.470236i	$-0.155831\pi$
$587$	−56.2267	−	154.482i	−0.0957866	−	0.263172i	−0.978327	+	0.207064i	$0.933609\pi$
$588$	−87.5059	+	191.431i	−0.148819	+	0.325563i
$589$	−106.888	+	89.6899i	−0.181474	+	0.152275i
$590$	113.405	−	311.577i	0.192212	−	0.528097i
$591$	514.911	−	142.161i	0.871254	−	0.240542i
$592$	46.2590	−	262.348i	0.0781403	−	0.443155i
$593$		−	349.285i		−	0.589014i	−0.955649	−	0.294507i	$-0.904845\pi$
$593$		−	349.285i		−	0.589014i	0.955649	−	0.294507i	$-0.0951555\pi$
$594$	250.718	+	16.2021i	0.422084	+	0.0272762i
$595$	−77.9106			−0.130942
$596$	165.289	+	29.1449i	0.277330	+	0.0489008i
$597$	423.014	+	109.918i	0.708566	+	0.184116i
$598$	171.165	+	62.2988i	0.286228	+	0.104179i
$599$	−387.503	−	461.808i	−0.646917	−	0.770965i	0.338529	−	0.940956i	$-0.390071\pi$
$599$	−387.503	−	461.808i	−0.646917	−	0.770965i	−0.985446	+	0.169991i	$0.945626\pi$
$600$	36.0927	+	379.406i	0.0601546	+	0.632343i
$601$	37.6412	−	13.7003i	0.0626310	−	0.0227958i	−0.310515	−	0.950569i	$-0.600501\pi$
$601$	37.6412	−	13.7003i	0.0626310	−	0.0227958i	0.373146	+	0.927773i	$0.378279\pi$
$602$	−533.426	−	307.974i	−0.886090	−	0.511584i
$603$	−131.165	+	25.1832i	−0.217520	+	0.0417632i
$604$	−129.080	−	223.573i	−0.213709	−	0.370154i
$605$	417.648	−	497.734i	0.690328	−	0.822701i
$606$	−423.675	−	291.901i	−0.699134	−	0.481685i
$607$	173.949	+	986.513i	0.286572	+	1.62523i	0.699617	+	0.714518i	$0.253354\pi$
$607$	173.949	+	986.513i	0.286572	+	1.62523i	−0.413046	+	0.910710i	$0.635535\pi$
$608$	−117.650	+	20.7449i	−0.193504	+	0.0341199i
$609$	−756.230	+	1097.62i	−1.24176	+	1.80233i
$610$	372.218	+	312.328i	0.610193	+	0.512013i
$611$	33.9447	−	19.5980i	0.0555560	−	0.0320753i
$612$	3.44881	+	17.9628i	0.00563530	+	0.0293510i
$613$	−45.2825	+	78.4316i	−0.0738704	+	0.127947i	−0.900594	−	0.434660i	$-0.856868\pi$
$613$	−45.2825	+	78.4316i	−0.0738704	+	0.127947i	0.826724	+	0.562608i	$0.190202\pi$
$614$	−4.23085	−	11.6242i	−0.00689063	−	0.0189319i
$615$	1324.38	−	125.988i	2.15346	−	0.204858i
$616$	−130.725	+	109.691i	−0.212216	+	0.178070i
$617$	−337.332	+	926.812i	−0.546729	+	1.50213i	0.291371	+	0.956610i	$0.405889\pi$
$617$	−337.332	+	926.812i	−0.546729	+	1.50213i	−0.838100	+	0.545516i	$0.816334\pi$
$618$	−201.583	+	775.787i	−0.326186	+	1.25532i
$619$	169.172	−	959.420i	0.273298	−	1.54995i	−0.471017	−	0.882124i	$-0.656113\pi$
$619$	169.172	−	959.420i	0.273298	−	1.54995i	0.744316	−	0.667828i	$-0.232776\pi$
$620$			110.491i			0.178211i
$621$	−518.987	+	256.528i	−0.835728	+	0.413088i
$622$	−73.3706			−0.117959
$623$	−211.668	−	37.3228i	−0.339757	−	0.0599083i
$624$	−19.1837	−	69.4839i	−0.0307430	−	0.111352i
$625$	−253.245	−	92.1738i	−0.405193	−	0.147478i
$626$	332.234	+	395.941i	0.530725	+	0.632493i
$627$	−379.135	−	173.308i	−0.604681	−	0.276408i
$628$	390.218	−	142.028i	0.621366	−	0.226159i
$629$	58.6084	+	33.8376i	0.0931771	+	0.0537958i
$630$	−615.875	+	756.979i	−0.977579	+	1.20155i
$631$	5.01746	+	8.69050i	0.00795160	+	0.0137726i	0.869974	−	0.493098i	$-0.164136\pi$
$631$	5.01746	+	8.69050i	0.00795160	+	0.0137726i	−0.862022	+	0.506870i	$0.830802\pi$
$632$	148.828	−	177.367i	0.235488	−	0.280644i
$633$	70.9907	−	888.964i	0.112150	−	1.40437i
$634$	−112.582	−	638.487i	−0.177575	−	1.00708i
$635$	−1277.09	+	225.185i	−2.01116	+	0.354622i
$636$	−102.482	−	215.495i	−0.161136	−	0.338829i
$637$	161.426	+	135.453i	0.253416	+	0.212642i
$638$	−390.471	+	225.439i	−0.612024	+	0.353352i
$639$	350.043	+	585.614i	0.547799	+	0.916454i
$640$	−47.3000	+	81.9260i	−0.0739062	+	0.128009i
$641$	−80.7353	−	221.818i	−0.125952	−	0.346050i	0.860650	−	0.509197i	$-0.170058\pi$
$641$	−80.7353	−	221.818i	−0.125952	−	0.346050i	−0.986602	+	0.163147i	$0.947835\pi$
$642$	−188.113	−	264.366i	−0.293010	−	0.411785i
$643$	−21.9909	+	18.4526i	−0.0342005	+	0.0286976i	−0.659728	−	0.751505i	$-0.729328\pi$
$643$	−21.9909	+	18.4526i	−0.0342005	+	0.0286976i	0.625527	+	0.780202i	$0.284884\pi$
$644$	134.489	−	369.506i	0.208834	−	0.573768i
$645$	−848.867	−	836.098i	−1.31607	−	1.29628i
$646$	5.27004	−	29.8879i	0.00815796	−	0.0462661i
$647$		−	230.995i		−	0.357024i	−0.983938	−	0.178512i	$-0.942872\pi$
$647$		−	230.995i		−	0.357024i	0.983938	−	0.178512i	$-0.0571284\pi$
$648$	201.789	+	108.486i	0.311403	+	0.167416i
$649$	184.497			0.284280
$650$	375.763	+	66.2572i	0.578098	+	0.101934i
$651$	−127.540	+	129.488i	−0.195915	+	0.198907i
$652$	−321.437	−	116.993i	−0.493001	−	0.179438i
$653$	704.150	+	839.173i	1.07833	+	1.28510i	0.956239	+	0.292586i	$0.0945157\pi$
$653$	704.150	+	839.173i	1.07833	+	1.28510i	0.122092	+	0.992519i	$0.461040\pi$
$654$	151.343	−	107.690i	0.231411	−	0.164663i
$655$	1063.94	−	387.241i	1.62433	−	0.591208i
$656$	183.718	+	106.070i	0.280058	+	0.161692i
$657$	416.881	+	232.335i	0.634522	+	0.353630i
$658$	−42.3077	−	73.2791i	−0.0642975	−	0.111366i
$659$	231.520	−	275.915i	0.351321	−	0.418688i	−0.561224	−	0.827664i	$-0.689670\pi$
$659$	231.520	−	275.915i	0.351321	−	0.418688i	0.912545	+	0.408976i	$0.134114\pi$
$660$	−298.109	+	141.770i	−0.451680	+	0.214803i
$661$	−27.1592	−	154.027i	−0.0410880	−	0.233022i	0.957347	−	0.288940i	$-0.0933027\pi$
$661$	−27.1592	−	154.027i	−0.0410880	−	0.233022i	−0.998435	+	0.0559177i	$0.982192\pi$
$662$	618.857	−	109.121i	0.934830	−	0.164836i
$663$	18.2540	+	1.45772i	0.0275324	+	0.00219868i
$664$	−101.673	−	85.3141i	−0.153123	−	0.128485i
$665$	1402.27	−	809.598i	2.10867	−	1.21744i
$666$	792.059	−	301.957i	1.18928	−	0.453388i
$667$	519.470	−	899.749i	0.778816	−	1.34895i
$668$	−107.877	−	296.391i	−0.161493	−	0.443698i
$669$	−263.525	+	576.498i	−0.393909	+	0.861730i
$670$	134.428	−	112.799i	0.200639	−	0.168356i
$671$	−92.4709	+	254.062i	−0.137811	+	0.378632i
$672$	−150.000	+	41.4133i	−0.223215	+	0.0616269i
$673$	−131.778	+	747.351i	−0.195807	+	1.11048i	0.715458	+	0.698656i	$0.246218\pi$
$673$	−131.778	+	747.351i	−0.195807	+	1.11048i	−0.911265	+	0.411821i	$0.864893\pi$
$674$			127.210i			0.188739i
$675$	−977.327	+	717.984i	−1.44789	+	1.06368i
$676$	265.833			0.393244
$677$	1043.94	+	184.074i	1.54200	+	0.271897i	0.879038	−	0.476752i	$-0.158186\pi$
$677$	1043.94	+	184.074i	1.54200	+	0.271897i	0.662966	+	0.748649i	$0.269297\pi$
$678$	−0.852545	−	0.221528i	−0.00125744	−	0.000326738i
$679$	−301.595	−	109.772i	−0.444176	−	0.161667i
$680$	−15.4476	−	18.4097i	−0.0227171	−	0.0270731i
$681$	4.57151	+	48.0555i	0.00671293	+	0.0705661i
$682$	−57.7726	+	21.0275i	−0.0847106	+	0.0308321i
$683$	927.527	+	535.508i	1.35802	+	0.784053i	0.989357	−	0.145511i	$-0.0464825\pi$
$683$	927.527	+	535.508i	1.35802	+	0.784053i	0.368663	+	0.929563i	$0.379816\pi$
$684$	−248.732	−	287.464i	−0.363643	−	0.420269i
$685$	−196.537	−	340.412i	−0.286916	−	0.496952i
$686$	−116.026	+	138.274i	−0.169134	+	0.201565i
$687$	−645.681	−	444.857i	−0.939856	−	0.647536i
$688$	−32.9922	−	187.108i	−0.0479538	−	0.271959i
$689$	−235.270	+	41.4844i	−0.341466	+	0.0602096i
$690$	431.553	−	626.370i	0.625439	−	0.907783i
$691$	338.945	+	284.409i	0.490514	+	0.411590i	0.854211	−	0.519927i	$-0.174041\pi$
$691$	338.945	+	284.409i	0.490514	+	0.411590i	−0.363696	+	0.931518i	$0.618485\pi$
$692$	−29.0207	+	16.7551i	−0.0419375	+	0.0242126i
$693$	−513.011	−	177.963i	−0.740276	−	0.256801i
$694$	−351.156	+	608.220i	−0.505988	+	0.876398i
$695$	138.538	+	380.631i	0.199336	+	0.547670i
$696$	−409.300	+	38.9366i	−0.588075	+	0.0559434i
$697$	−41.2837	+	34.6411i	−0.0592305	+	0.0497003i
$698$	−164.048	+	450.719i	−0.235026	+	0.645729i
$699$	−242.727	+	934.126i	−0.347249	+	1.33638i
$700$	143.035	−	811.191i	0.204335	−	1.15884i
$701$			77.6184i			0.110725i	0.998466	+	0.0553626i	$0.0176315\pi$
$701$			77.6184i			0.110725i	−0.998466	+	0.0553626i	$0.982369\pi$
$702$	158.459	−	165.833i	0.225725	−	0.236229i
$703$	−1406.48			−2.00068
$704$	−51.8385	−	9.14053i	−0.0736343	−	0.0129837i
$705$	−43.5602	−	157.777i	−0.0617875	−	0.223797i
$706$	293.434	+	106.801i	0.415629	+	0.151277i
$707$	714.763	+	851.821i	1.01098	+	1.20484i
$708$	153.012	+	69.9440i	0.216119	+	0.0987909i
$709$	−139.805	+	50.8850i	−0.197187	+	0.0717700i	−0.438726	−	0.898621i	$-0.644570\pi$
$709$	−139.805	+	50.8850i	−0.197187	+	0.0717700i	0.241539	+	0.970391i	$0.422348\pi$
$710$	−776.313	−	448.204i	−1.09340	−	0.631274i
$711$	727.405	+	116.924i	1.02307	+	0.164449i
$712$	−33.1491	−	57.4159i	−0.0465577	−	0.0806404i
$713$	91.0618	−	108.523i	0.127716	−	0.152206i
$714$	3.14690	−	39.4064i	0.00440743	−	0.0551910i
$715$	57.3881	+	325.464i	0.0802631	+	0.455195i
$716$	−214.368	+	37.7989i	−0.299397	+	0.0527917i
$717$	101.629	+	213.702i	0.141742	+	0.298050i
$718$	−618.223	−	518.750i	−0.861034	−	0.722494i
$719$	−22.6129	+	13.0556i	−0.0314505	+	0.0181580i	−0.515643	−	0.856804i	$-0.672447\pi$
$719$	−22.6129	+	13.0556i	−0.0314505	+	0.0181580i	0.484192	+	0.874962i	$0.339114\pi$
$720$	−300.981	+	4.56189i	−0.418029	+	0.00633596i
$721$	866.187	−	1500.28i	1.20137	−	2.08083i
$722$	41.1123	+	112.955i	0.0569422	+	0.156447i
$723$	526.935	+	740.534i	0.728818	+	1.02425i
$724$	−56.9275	+	47.7679i	−0.0786292	+	0.0659777i
$725$	744.350	−	2045.09i	1.02669	−	2.82081i
$726$	234.879	+	231.346i	0.323525	+	0.318659i
$727$	−159.723	+	905.834i	−0.219701	+	1.24599i	0.652858	+	0.757480i	$0.273570\pi$
$727$	−159.723	+	905.834i	−0.219701	+	1.24599i	−0.872559	+	0.488508i	$0.837541\pi$
$728$			155.793i			0.214001i
$729$	33.1339	+	728.247i	0.0454512	+	0.998967i
$730$	−627.056			−0.858980
$731$	47.5330	+	8.38135i	0.0650246	+	0.0114656i
$732$	−173.006	+	175.649i	−0.236348	+	0.239957i
$733$	332.814	+	121.134i	0.454044	+	0.165258i	0.558911	−	0.829228i	$-0.311219\pi$
$733$	332.814	+	121.134i	0.454044	+	0.165258i	−0.104867	+	0.994486i	$0.533442\pi$
$734$	192.215	+	229.073i	0.261874	+	0.312089i
$735$	716.992	−	510.184i	0.975500	−	0.694128i
$736$	113.978	−	41.4844i	0.154861	−	0.0563647i
$737$	84.5624	+	48.8222i	0.114739	+	0.0662444i
$738$	10.2300	+	674.946i	0.0138618	+	0.914561i
$739$	410.346	+	710.740i	0.555272	+	0.961760i	0.997882	+	0.0650455i	$0.0207192\pi$
$739$	410.346	+	710.740i	0.555272	+	0.961760i	−0.442610	+	0.896714i	$0.645947\pi$
$740$	−715.896	+	853.171i	−0.967427	+	1.15293i
$741$	−343.691	+	163.448i	−0.463820	+	0.220577i
$742$	89.5558	+	507.896i	0.120695	+	0.684496i
$743$	−132.906	+	23.4348i	−0.178877	+	0.0315408i	−0.262369	−	0.964968i	$-0.584504\pi$
$743$	−132.906	+	23.4348i	−0.178877	+	0.0315408i	0.0834921	+	0.996508i	$0.473393\pi$
$744$	−55.8851	−	4.46286i	−0.0751143	−	0.00599846i
$745$	−537.529	−	451.040i	−0.721515	−	0.605423i
$746$	85.0755	−	49.1184i	0.114042	−	0.0658423i
$747$	67.0251	−	416.977i	0.0897257	−	0.558202i
$748$	6.68612	−	11.5807i	0.00893866	−	0.0154822i
$749$	239.843	+	658.963i	0.320218	+	0.879791i
$750$	293.716	−	642.544i	0.391622	−	0.856726i
$751$	938.326	−	787.349i	1.24944	−	1.04840i	0.252710	−	0.967542i	$-0.418678\pi$
$751$	938.326	−	787.349i	1.24944	−	1.04840i	0.996726	−	0.0808587i	$-0.0257663\pi$
$752$	8.92686	−	24.5264i	0.0118708	−	0.0326148i
$753$	238.355	−	65.8068i	0.316540	−	0.0873928i
$754$	−71.4779	+	405.371i	−0.0947982	+	0.537627i
$755$			1079.31i			1.42955i
$756$	−357.996	−	342.078i	−0.473540	−	0.452484i
$757$	915.003			1.20872			0.604361	−	0.796710i	$-0.293428\pi$
$757$	915.003			1.20872			0.604361	+	0.796710i	$0.293428\pi$
$758$	−543.458	−	95.8264i	−0.716964	−	0.126420i
$759$	409.641	+	106.443i	0.539711	+	0.140241i
$760$	469.335	+	170.824i	0.617546	+	0.224768i
$761$	−482.010	−	574.437i	−0.633391	−	0.754846i	0.349920	−	0.936780i	$-0.386209\pi$
$761$	−482.010	−	574.437i	−0.633391	−	0.754846i	−0.983311	+	0.181934i	$0.941764\pi$
$762$	−62.3130	−	655.032i	−0.0817756	−	0.859622i
$763$	−377.240	+	137.304i	−0.494416	+	0.179953i
$764$	371.925	+	214.731i	0.486813	+	0.281062i
$765$	25.0623	−	72.2464i	0.0327611	−	0.0944398i
$766$	128.227	+	222.095i	0.167398	+	0.289942i

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	54.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39273 - 0.245576i) q^{2} +(-2.10518 + 2.13733i) q^{3} +(1.87939 + 0.684040i) q^{4} +(-5.37469 - 6.40531i) q^{5} +(3.45683 - 2.45974i) q^{6} +(-8.61655 + 3.13617i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-0.136395 - 8.99897i) q^{9} +O(q^{10})\)	\(q+(-1.39273 - 0.245576i) q^{2} +(-2.10518 + 2.13733i) q^{3} +(1.87939 + 0.684040i) q^{4} +(-5.37469 - 6.40531i) q^{5} +(3.45683 - 2.45974i) q^{6} +(-8.61655 + 3.13617i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-0.136395 - 8.99897i) q^{9} +(5.91250 + 10.2407i) q^{10} +(-4.22940 + 5.04040i) q^{11} +(-5.41848 + 2.57684i) q^{12} +(1.04310 + 5.91570i) q^{13} +(12.7707 - 2.25182i) q^{14} +(25.0050 + 1.99684i) q^{15} +(3.06418 + 2.57115i) q^{16} +(-0.880022 + 0.508081i) q^{17} +(-2.01997 + 12.5666i) q^{18} +(10.5593 - 18.2893i) q^{19} +(-5.71963 - 15.7145i) q^{20} +(11.4364 - 25.0187i) q^{21} +(7.12821 - 5.98128i) q^{22} +(-7.33348 + 20.1486i) q^{23} +(8.17928 - 2.25820i) q^{24} +(-7.79945 + 44.2329i) q^{25} -8.49512i q^{26} +(19.5209 + 18.6530i) q^{27} -18.3391 q^{28} +(-47.7181 - 8.41399i) q^{29} +(-34.3348 - 8.92168i) q^{30} +(-6.20863 - 2.25976i) q^{31} +(-3.63616 - 4.33340i) q^{32} +(-1.86936 - 19.6506i) q^{33} +(1.35040 - 0.491507i) q^{34} +(66.3994 + 38.3357i) q^{35} +(5.89932 - 17.0058i) q^{36} +(-33.2994 - 57.6763i) q^{37} +(-19.1977 + 22.8789i) q^{38} +(-14.8397 - 10.2242i) q^{39} +(4.10678 + 23.2907i) q^{40} +(52.2291 - 9.20941i) q^{41} +(-22.0718 + 32.0357i) q^{42} +(-36.3861 - 30.5315i) q^{43} +(-11.3965 + 6.57978i) q^{44} +(-56.9081 + 49.2403i) q^{45} +(15.1616 - 26.2606i) q^{46} +(-2.23172 - 6.13159i) q^{47} +(-11.9461 + 1.13643i) q^{48} +(26.8732 - 22.5493i) q^{49} +(21.7250 - 59.6890i) q^{50} +(0.766670 - 2.95050i) q^{51} +(-2.08619 + 11.8314i) q^{52} +39.7705i q^{53} +(-22.6067 - 30.7724i) q^{54} +55.0170 q^{55} +(25.5414 + 4.50363i) q^{56} +(16.8610 + 61.0711i) q^{57} +(64.3921 + 23.4368i) q^{58} +(-18.0238 - 21.4799i) q^{59} +(45.6281 + 20.8573i) q^{60} +(38.6125 - 14.0538i) q^{61} +(8.09199 + 4.67191i) q^{62} +(29.3975 + 77.1123i) q^{63} +(4.00000 + 6.92820i) q^{64} +(32.2855 - 38.4764i) q^{65} +(-2.22221 + 27.8271i) q^{66} +(-2.57695 - 14.6146i) q^{67} +(-2.00145 + 0.352909i) q^{68} +(-27.6259 - 58.0906i) q^{69} +(-83.0620 - 69.6973i) q^{70} +(-65.6502 + 37.9031i) q^{71} +(-12.3924 + 22.2358i) q^{72} +(-26.5140 + 45.9236i) q^{73} +(32.2131 + 88.5049i) q^{74} +(-78.1212 - 109.788i) q^{75} +(32.3556 - 27.1496i) q^{76} +(20.6353 - 56.6950i) q^{77} +(18.1569 + 17.8838i) q^{78} +(-14.2149 + 80.6166i) q^{79} -33.4461i q^{80} +(-80.9628 + 2.45483i) q^{81} -75.0026 q^{82} +(46.2126 + 8.14852i) q^{83} +(38.6072 - 39.1968i) q^{84} +(7.98426 + 2.90603i) q^{85} +(43.1781 + 51.4577i) q^{86} +(118.439 - 84.2766i) q^{87} +(17.4881 - 6.36514i) q^{88} +(20.2996 + 11.7200i) q^{89} +(91.3497 - 54.6032i) q^{90} +(-27.5405 - 47.7016i) q^{91} +(-27.5649 + 32.8505i) q^{92} +(17.9002 - 8.51271i) q^{93} +(1.60241 + 9.08769i) q^{94} +(-173.902 + 30.6635i) q^{95} +(16.9167 + 1.35093i) q^{96} +(26.8130 + 22.4988i) q^{97} +(-42.9647 + 24.8057i) q^{98} +(45.9353 + 37.3727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9}+O(q^{10}) \) 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9	\( 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9} - 18 q^{11} - 12 q^{12} - 36 q^{14} - 18 q^{15} - 48 q^{18} - 72 q^{20} - 228 q^{21} + 36 q^{22} - 180 q^{23} + 18 q^{25} + 54 q^{27} + 144 q^{29} + 144 q^{30} - 90 q^{31} + 324 q^{33} - 72 q^{34} + 486 q^{35} + 168 q^{36} + 180 q^{38} + 102 q^{39} - 90 q^{41} + 48 q^{42} + 90 q^{43} - 378 q^{45} - 378 q^{47} - 24 q^{48} + 72 q^{49} - 54 q^{51} - 36 q^{54} - 72 q^{56} + 72 q^{57} + 252 q^{59} + 36 q^{60} - 144 q^{61} + 318 q^{63} + 144 q^{64} + 18 q^{65} - 432 q^{66} - 594 q^{67} - 180 q^{68} - 522 q^{69} - 360 q^{70} - 648 q^{71} - 192 q^{72} + 126 q^{73} - 504 q^{74} - 438 q^{75} - 72 q^{76} - 342 q^{77} - 288 q^{78} - 72 q^{79} + 324 q^{81} + 594 q^{83} + 216 q^{84} + 360 q^{85} + 540 q^{86} + 1062 q^{87} + 144 q^{88} + 648 q^{89} + 720 q^{90} - 198 q^{91} + 396 q^{92} + 462 q^{93} + 504 q^{94} + 252 q^{95} + 96 q^{96} + 702 q^{97} + 648 q^{98} + 126 q^{99}+O(q^{100}) \) 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9 - 18 * q^11 - 12 * q^12 - 36 * q^14 - 18 * q^15 - 48 * q^18 - 72 * q^20 - 228 * q^21 + 36 * q^22 - 180 * q^23 + 18 * q^25 + 54 * q^27 + 144 * q^29 + 144 * q^30 - 90 * q^31 + 324 * q^33 - 72 * q^34 + 486 * q^35 + 168 * q^36 + 180 * q^38 + 102 * q^39 - 90 * q^41 + 48 * q^42 + 90 * q^43 - 378 * q^45 - 378 * q^47 - 24 * q^48 + 72 * q^49 - 54 * q^51 - 36 * q^54 - 72 * q^56 + 72 * q^57 + 252 * q^59 + 36 * q^60 - 144 * q^61 + 318 * q^63 + 144 * q^64 + 18 * q^65 - 432 * q^66 - 594 * q^67 - 180 * q^68 - 522 * q^69 - 360 * q^70 - 648 * q^71 - 192 * q^72 + 126 * q^73 - 504 * q^74 - 438 * q^75 - 72 * q^76 - 342 * q^77 - 288 * q^78 - 72 * q^79 + 324 * q^81 + 594 * q^83 + 216 * q^84 + 360 * q^85 + 540 * q^86 + 1062 * q^87 + 144 * q^88 + 648 * q^89 + 720 * q^90 - 198 * q^91 + 396 * q^92 + 462 * q^93 + 504 * q^94 + 252 * q^95 + 96 * q^96 + 702 * q^97 + 648 * q^98 + 126 * q^99

Introduction

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