LMFDB - Embedded newform 54.3.f.a.41.2

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			41.2
Character	$\chi$	$=$	54.41
Dual form			54.3.f.a.29.2

$q$-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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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	−0.117297	+	0.993097i	$0.537423\pi$
$5$	−5.37469	+	6.40531i	−1.07494	+	1.28106i	−0.957641	+	0.287964i	$0.907022\pi$
$6$	3.45683	+	2.45974i	0.576138	+	0.409957i
$7$	−8.61655	−	3.13617i	−1.23094	−	0.448024i	−0.357018	−	0.934098i	$-0.616206\pi$
$7$	−8.61655	−	3.13617i	−1.23094	−	0.448024i	−0.873918	+	0.486074i	$0.838429\pi$
$8$	−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	0.538735	−	0.842475i	$-0.318902\pi$
$11$	−4.22940	−	5.04040i	−0.384491	−	0.458218i	−0.923226	+	0.384257i	$0.874458\pi$
$12$	−5.41848	−	2.57684i	−0.451540	−	0.214737i
$13$	1.04310	−	5.91570i	0.0802382	−	0.455053i	−0.918045	−	0.396477i	$-0.870233\pi$
$13$	1.04310	−	5.91570i	0.0802382	−	0.455053i	0.998283	−	0.0585766i	$-0.0186562\pi$
$14$	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	0.473894	−	0.880582i	$-0.342848\pi$
$17$	−0.880022	−	0.508081i	−0.0517660	−	0.0298871i	−0.525660	+	0.850695i	$0.676181\pi$
$18$	−2.01997	−	12.5666i	−0.112220	−	0.698145i
$19$	10.5593	+	18.2893i	0.555754	+	0.962594i	0.997844	+	0.0656235i	$0.0209036\pi$
$19$	10.5593	+	18.2893i	0.555754	+	0.962594i	−0.442091	+	0.896970i	$0.645763\pi$
$20$	−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	−0.990788	−	0.135421i	$-0.956761\pi$
$23$	−7.33348	−	20.1486i	−0.318847	−	0.876025i	0.671941	−	0.740605i	$-0.265461\pi$
$24$	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	−0.918166	−	0.396196i	$-0.870330\pi$
$29$	−47.7181	+	8.41399i	−1.64545	+	0.290138i	−0.727287	+	0.686334i	$0.759219\pi$
$30$	−34.3348	+	8.92168i	−1.14449	+	0.297389i
$31$	−6.20863	+	2.25976i	−0.200278	+	0.0728954i	−0.440212	−	0.897894i	$-0.645097\pi$
$31$	−6.20863	+	2.25976i	−0.200278	+	0.0728954i	0.239933	+	0.970789i	$0.422874\pi$
$32$	−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	−0.0724711	+	0.997371i	$0.523089\pi$
$37$	−33.2994	+	57.6763i	−0.899984	+	1.55882i	−0.827513	+	0.561447i	$0.810245\pi$
$38$	−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	0.769380	−	0.638791i	$-0.220565\pi$
$41$	52.2291	+	9.20941i	1.27388	+	0.224620i	0.504501	+	0.863411i	$0.331676\pi$
$42$	−22.0718	−	32.0357i	−0.525518	−	0.762755i
$43$	−36.3861	+	30.5315i	−0.846188	+	0.710036i	−0.958947	−	0.283587i	$-0.908476\pi$
$43$	−36.3861	+	30.5315i	−0.846188	+	0.710036i	0.112759	+	0.993622i	$0.464031\pi$
$44$	−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	−0.961168	−	0.275965i	$-0.911002\pi$
$47$	−2.23172	+	6.13159i	−0.0474833	+	0.130459i	0.913684	+	0.406425i	$0.133225\pi$
$48$	−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	$-0.877576\pi$
$53$		−	39.7705i		−	0.750386i	0.926947	−	0.375193i	$-0.122424\pi$
$54$	−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	−0.896846	−	0.442342i	$-0.854148\pi$
$59$	−18.0238	+	21.4799i	−0.305488	+	0.364067i	0.591358	+	0.806409i	$0.298592\pi$
$60$	45.6281	−	20.8573i	0.760468	−	0.347621i
$61$	38.6125	+	14.0538i	0.632992	+	0.230390i	0.638533	−	0.769594i	$-0.279542\pi$
$61$	38.6125	+	14.0538i	0.632992	+	0.230390i	−0.00554114	+	0.999985i	$0.501764\pi$
$62$	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	−0.997981	−	0.0635158i	$-0.979769\pi$
$67$	−2.57695	+	14.6146i	−0.0384619	+	0.218128i	0.959519	+	0.281644i	$0.0908798\pi$
$68$	−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	−0.0395346	−	0.999218i	$-0.512588\pi$
$71$	−65.6502	−	37.9031i	−0.924650	−	0.533847i	−0.885116	+	0.465371i	$0.845921\pi$
$72$	−12.3924	−	22.2358i	−0.172116	−	0.308830i
$73$	−26.5140	−	45.9236i	−0.363205	−	0.629090i	0.625281	−	0.780400i	$-0.284984\pi$
$73$	−26.5140	−	45.9236i	−0.363205	−	0.629090i	−0.988486	+	0.151310i	$0.951651\pi$
$74$	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	−0.932292	−	0.361708i	$-0.882194\pi$
$79$	−14.2149	−	80.6166i	−0.179935	−	1.02046i	0.752356	−	0.658756i	$-0.228917\pi$
$80$			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	0.111823	−	0.993728i	$-0.464331\pi$
$83$	46.2126	−	8.14852i	0.556778	−	0.0981749i	0.444955	+	0.895553i	$0.353220\pi$
$84$	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	−0.381603	−	0.924326i	$-0.624628\pi$
$89$	20.2996	−	11.7200i	0.228085	−	0.131685i	0.609689	+	0.792641i	$0.291295\pi$
$90$	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	−0.494028	−	0.869446i	$-0.664476\pi$
$97$	26.8130	−	22.4988i	0.276423	−	0.231946i	0.770450	+	0.637500i	$0.220031\pi$
$98$	−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	0.546189	+	0.837662i	$0.316078\pi$
$101$	−41.4761	+	113.955i	−0.410655	+	1.12826i	−0.956844	+	0.290603i	$0.906144\pi$
$102$	−1.79233	−	3.92098i	−0.0175719	−	0.0384409i
$103$	−144.726	−	121.440i	−1.40511	−	1.17903i	−0.958776	−	0.284161i	$-0.908285\pi$
$103$	−144.726	−	121.440i	−1.40511	−	1.17903i	−0.446334	−	0.894866i	$-0.647271\pi$
$104$	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	$0.116325\pi$
$107$			76.4765i			0.714733i	−0.933964	+	0.357367i	$0.883675\pi$
$108$	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	−0.766635	−	0.642084i	$-0.778070\pi$
$113$	−0.133455	+	0.159046i	−0.00118102	+	0.00140749i	0.765454	+	0.643491i	$0.222515\pi$
$114$	−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	0.991141	+	0.132812i	$0.0424006\pi$
$127$	77.5448	+	134.312i	0.610589	+	1.05757i	−0.380552	+	0.924759i	$0.624266\pi$
$128$	−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	−0.981227	−	0.192855i	$-0.938225\pi$
$131$	−46.3122	−	127.242i	−0.353529	−	0.971312i	0.627699	−	0.778456i	$-0.283997\pi$
$132$	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	−0.00211111	−	0.999998i	$-0.500672\pi$
$137$	46.2957	−	8.16317i	0.337924	−	0.0595852i	0.340036	+	0.940413i	$0.389561\pi$
$138$	24.2098	−	87.6887i	0.175433	−	0.635425i
$139$	−45.5216	+	16.5685i	−0.327494	+	0.119198i	−0.500534	−	0.865717i	$-0.666863\pi$
$139$	−45.5216	+	16.5685i	−0.327494	+	0.119198i	0.173040	+	0.984915i	$0.444641\pi$
$140$	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	0.443951	−	0.896051i	$-0.353577\pi$
$149$	82.6444	+	14.5724i	0.554660	+	0.0978015i	0.110710	+	0.993853i	$0.464688\pi$
$150$	81.8402	−	172.090i	0.545601	−	1.14727i
$151$	−98.8811	+	82.9711i	−0.654842	+	0.549477i	−0.908536	−	0.417807i	$-0.862799\pi$
$151$	−98.8811	+	82.9711i	−0.654842	+	0.549477i	0.253694	+	0.967284i	$0.418354\pi$
$152$	−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	0.988743	−	0.149625i	$-0.0478066\pi$
$157$	159.054	+	133.462i	1.01308	+	0.850079i	0.0243416	+	0.999704i	$0.492251\pi$
$158$	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	−0.978780	−	0.204914i	$-0.934308\pi$
$167$	−101.372	+	120.810i	−0.607015	+	0.723413i	0.371765	+	0.928327i	$0.378753\pi$
$168$	−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	0.734019	−	0.679129i	$-0.237642\pi$
$173$	−10.7700	−	12.8352i	−0.0622543	−	0.0741918i	−0.796273	+	0.604938i	$0.793198\pi$
$174$	−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	0.213048	−	0.977042i	$-0.431661\pi$
$179$	−94.2561	−	54.4188i	−0.526570	−	0.304016i	−0.739619	+	0.673026i	$0.764994\pi$
$180$	−140.635	−	53.6141i	−0.781303	−	0.297856i
$181$	−18.5784	−	32.1787i	−0.102643	−	0.177783i	0.810130	−	0.586251i	$-0.199397\pi$
$181$	−18.5784	−	32.1787i	−0.102643	−	0.177783i	−0.912773	+	0.408468i	$0.866063\pi$
$182$	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	0.409967	−	0.912100i	$-0.365540\pi$
$191$	211.469	−	37.2877i	1.10717	−	0.195223i	0.697200	+	0.716877i	$0.254429\pi$
$192$	−23.2286	+	6.03581i	−0.120982	+	0.0314365i
$193$	−266.703	+	97.0720i	−1.38188	+	0.502964i	−0.922748	−	0.385403i	$-0.874062\pi$
$193$	−266.703	+	97.0720i	−1.38188	+	0.502964i	−0.459134	+	0.888367i	$0.651840\pi$
$194$	−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	−0.837406	−	0.546581i	$-0.815929\pi$
$197$	−154.203	+	89.0292i	−0.782756	+	0.451925i	0.0546498	+	0.998506i	$0.482596\pi$
$198$	−54.7976	+	63.3307i	−0.276755	+	0.319852i
$199$	−72.8436	+	126.169i	−0.366048	+	0.634014i	−0.988944	−	0.148291i	$-0.952623\pi$
$199$	−72.8436	+	126.169i	−0.366048	+	0.634014i	0.622896	+	0.782305i	$0.285956\pi$
$200$	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	−0.0833757	−	0.996518i	$-0.526570\pi$
$211$	−227.718	−	191.078i	−1.07923	−	0.905584i	−0.995857	+	0.0909345i	$0.971015\pi$
$212$	−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	0.746380	−	0.665520i	$-0.231790\pi$
$223$	198.549	+	72.2658i	0.890352	+	0.324062i	0.143972	+	0.989582i	$0.454012\pi$
$224$	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	0.788345	−	0.615233i	$-0.210938\pi$
$227$	10.3430	+	12.3263i	0.0455638	+	0.0543008i	−0.742781	+	0.669534i	$0.766494\pi$
$228$	−10.0868	−	126.310i	−0.0442404	−	0.553990i
$229$	45.3854	−	257.394i	0.198190	−	1.12399i	−0.709613	−	0.704592i	$-0.751130\pi$
$229$	45.3854	−	257.394i	0.198190	−	1.12399i	0.907803	−	0.419398i	$-0.137759\pi$
$230$	−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	0.959609	−	0.281338i	$-0.0907782\pi$
$233$	278.614	+	160.858i	1.19577	+	0.690377i	0.236159	+	0.971715i	$0.424111\pi$
$234$	−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	0.983250	−	0.182265i	$-0.0583427\pi$
$239$	26.9782	+	74.1219i	0.112879	+	0.310133i	−0.870370	+	0.492398i	$0.836121\pi$
$240$	71.4856	−	70.4103i	0.297857	−	0.293376i
$241$	52.6081	+	298.355i	0.218291	+	1.23799i	0.875104	+	0.483935i	$0.160793\pi$
$241$	52.6081	+	298.355i	0.218291	+	1.23799i	−0.656813	+	0.754053i	$0.728096\pi$
$242$			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	−0.635408	−	0.772177i	$-0.719168\pi$
$251$	−71.3813	+	41.2120i	−0.284387	+	0.164191i	0.351021	+	0.936368i	$0.385835\pi$
$252$	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	0.132125	−	0.991233i	$-0.457820\pi$
$257$	−21.2643	−	3.74948i	−0.0827406	−	0.0145894i	−0.214865	+	0.976644i	$0.568931\pi$
$258$	−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	−0.968029	−	0.250837i	$-0.919294\pi$
$263$	−17.1583	+	47.1420i	−0.0652407	+	0.179247i	0.902789	+	0.430085i	$0.141516\pi$
$264$	−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	$-0.928535\pi$
$269$		−	119.776i		−	0.445263i	0.974903	−	0.222632i	$-0.0714648\pi$
$270$	−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	−0.276707	−	0.960954i	$-0.589243\pi$
$277$	−306.464	−	111.544i	−1.10637	−	0.402685i	−0.829659	+	0.558270i	$0.811465\pi$
$278$	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	0.750188	−	0.661225i	$-0.229963\pi$
$281$	−8.78420	−	10.4686i	−0.0312605	−	0.0372548i	−0.781448	+	0.623970i	$0.785519\pi$
$282$	−22.7968	+	15.7064i	−0.0808397	+	0.0556964i
$283$	79.1142	−	448.679i	0.279555	−	1.58544i	−0.444554	−	0.895752i	$-0.646638\pi$
$283$	79.1142	−	448.679i	0.279555	−	1.58544i	0.724109	−	0.689685i	$-0.242251\pi$
$284$	−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	0.805384	+	0.592753i	$0.201959\pi$
$293$	166.845	+	458.404i	0.569438	+	1.56452i	−0.235946	+	0.971766i	$0.575819\pi$
$294$	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	−0.858815	−	0.512287i	$-0.828799\pi$
$307$	4.37352	−	7.57515i	0.0142460	−	0.0246748i	0.873061	+	0.487612i	$0.162132\pi$
$308$	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	0.255186	−	0.966892i	$-0.417863\pi$
$311$	51.0927	+	9.00901i	0.164285	+	0.0289679i	−0.0909005	+	0.995860i	$0.528975\pi$
$312$	21.8906	−	46.0306i	0.0701621	−	0.147534i
$313$	−279.972	+	234.925i	−0.894481	+	0.750558i	−0.969104	−	0.246653i	$-0.920669\pi$
$313$	−279.972	+	234.925i	−0.894481	+	0.750558i	0.0746231	+	0.997212i	$0.476225\pi$
$314$	−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	−0.401776	−	0.915738i	$-0.631607\pi$
$317$	156.797	−	430.796i	0.494627	−	1.35898i	0.896403	−	0.443239i	$-0.146171\pi$
$318$	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	−0.377218	−	0.926125i	$-0.623119\pi$
$331$	−417.551	−	151.976i	−1.26148	−	0.459143i	−0.884267	+	0.466982i	$0.845341\pi$
$332$	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	−0.999173	−	0.0406634i	$-0.987053\pi$
$337$	−15.6199	+	88.5848i	−0.0463498	+	0.262863i	0.952823	+	0.303526i	$0.0981640\pi$
$338$	−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	0.901150	+	0.433508i	$0.142724\pi$
$347$	169.850	+	466.660i	0.489483	+	1.34484i	−0.411667	+	0.911334i	$0.635053\pi$
$348$	280.241	+	77.3711i	0.805290	+	0.222331i
$349$	58.8946	+	334.008i	0.168752	+	0.957042i	0.945111	+	0.326750i	$0.105954\pi$
$349$	58.8946	+	334.008i	0.168752	+	0.957042i	−0.776358	+	0.630292i	$0.782935\pi$
$350$		−	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	−0.472941	−	0.881094i	$-0.656808\pi$
$353$	−217.451	+	38.3425i	−0.616008	+	0.108619i	−0.143067	+	0.989713i	$0.545696\pi$
$354$	−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	0.384864	−	0.922973i	$-0.374249\pi$
$359$	494.204	−	285.329i	1.37661	−	0.794788i	0.991750	+	0.128185i	$0.0409152\pi$
$360$	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	−0.836218	−	0.548397i	$-0.815238\pi$
$367$	−161.979	+	135.917i	−0.441360	+	0.370345i	0.394858	+	0.918742i	$0.370794\pi$
$368$	−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	0.568665	−	0.822569i	$-0.307460\pi$
$373$	−53.2124	−	44.6505i	−0.142661	−	0.119706i	−0.711325	+	0.702863i	$0.751905\pi$
$374$	−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	−0.896440	−	0.443165i	$-0.853856\pi$
$383$	−116.563	+	138.915i	−0.304342	+	0.362701i	0.592098	+	0.805866i	$0.298300\pi$
$384$	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	−0.940427	−	0.339996i	$-0.889574\pi$
$389$	−432.550	−	515.493i	−1.11195	−	1.32518i	−0.171527	−	0.985179i	$-0.554870\pi$
$390$	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	0.996429	+	0.0844384i	$0.0269096\pi$
$397$	226.822	+	392.867i	0.571340	+	0.989590i	−0.425089	+	0.905152i	$0.639757\pi$
$398$	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	−0.998586	−	0.0531643i	$-0.983069\pi$
$401$	−107.387	−	295.043i	−0.267798	−	0.735769i	0.730788	−	0.682605i	$-0.239153\pi$
$402$	−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	−0.343974	−	0.938979i	$-0.611773\pi$
$409$	−1.59923	+	0.582072i	−0.00391009	+	0.00142316i	0.340064	+	0.940402i	$0.389551\pi$
$410$	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	0.0548088	−	0.998497i	$-0.482545\pi$
$419$	−98.5462	−	17.3764i	−0.235194	−	0.0414710i	−0.290003	+	0.957026i	$0.593656\pi$
$420$	−458.569	+	36.6203i	−1.09183	+	0.0871911i
$421$	486.614	−	408.318i	1.15585	−	0.969876i	0.156012	−	0.987755i	$-0.450136\pi$
$421$	486.614	−	408.318i	1.15585	−	0.969876i	0.999840	+	0.0178796i	$0.00569155\pi$
$422$	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	$0.0670526\pi$
$431$			180.242i			0.418195i	−0.977895	+	0.209098i	$0.932947\pi$
$432$	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	0.662579	−	0.748992i	$-0.269462\pi$
$439$	302.339	+	110.043i	0.688700	+	0.250666i	0.0261216	+	0.999659i	$0.491684\pi$
$440$	−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	0.995887	−	0.0906036i	$-0.0288796\pi$
$443$	325.041	+	387.368i	0.733726	+	0.874421i	−0.262161	+	0.965024i	$0.584435\pi$
$444$	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	−0.391524	−	0.920168i	$-0.628052\pi$
$449$	−621.494	−	358.820i	−1.38417	−	0.799153i	−0.992651	+	0.121015i	$0.961385\pi$
$450$	−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	0.955396	+	0.295329i	$0.0954292\pi$
$457$	72.4920	+	411.123i	0.158626	+	0.899612i	−0.796770	+	0.604283i	$0.793460\pi$
$458$			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	−0.955213	−	0.295918i	$-0.904374\pi$
$461$	−807.492	+	142.383i	−1.75161	+	0.308856i	−0.796397	+	0.604774i	$0.793263\pi$
$462$	−68.1226	+	246.742i	−0.147451	+	0.534074i
$463$	−800.359	+	291.307i	−1.72864	+	0.629173i	−0.998532	−	0.0541620i	$-0.982751\pi$
$463$	−800.359	+	291.307i	−1.72864	+	0.629173i	−0.730105	+	0.683335i	$0.760529\pi$
$464$	−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	−0.958923	−	0.283666i	$-0.908449\pi$
$467$	−557.001	+	321.585i	−1.19272	+	0.688619i	−0.233800	+	0.972285i	$0.575116\pi$
$468$	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	−0.999608	−	0.0280135i	$-0.991082\pi$
$479$	−103.396	+	284.077i	−0.215857	+	0.593062i	0.783751	+	0.621076i	$0.213304\pi$
$480$	−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	−0.915563	−	0.402174i	$-0.868255\pi$
$491$	−177.012	+	210.954i	−0.360513	+	0.429643i	0.555050	+	0.831817i	$0.312699\pi$
$492$	−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	−0.999996	−	0.00283231i	$-0.999098\pi$
$499$	−29.6099	+	167.926i	−0.0593384	+	0.336525i	0.940658	+	0.339357i	$0.110210\pi$
$500$	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	0.486804	−	0.873511i	$-0.338163\pi$
$503$	−13.2176	−	7.63121i	−0.0262776	−	0.0151714i	−0.513081	+	0.858340i	$0.671496\pi$
$504$	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	−0.983073	−	0.183213i	$-0.941350\pi$
$509$	−177.011	−	486.334i	−0.347762	−	0.955470i	0.635311	−	0.772257i	$-0.280872\pi$
$510$	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	0.631943	−	0.775015i	$-0.282258\pi$
$521$	843.550	−	487.024i	1.61910	−	0.934786i	0.987154	−	0.159771i	$-0.0510757\pi$
$522$	202.124	+	582.659i	0.387211	+	1.11621i
$523$	159.545	−	276.340i	0.305058	−	0.528375i	−0.672217	−	0.740355i	$-0.734658\pi$
$523$	159.545	−	276.340i	0.305058	−	0.528375i	0.977274	+	0.211979i	$0.0679909\pi$
$524$	−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	−0.502347	−	0.864666i	$-0.667530\pi$
$547$	−789.301	−	287.282i	−1.44296	−	0.525196i	−0.940617	+	0.339470i	$0.889752\pi$
$548$	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	−0.415398	−	0.909640i	$-0.636358\pi$
$557$	−785.853	−	453.713i	−1.41087	−	0.814565i	−0.995470	+	0.0950749i	$0.969691\pi$
$558$	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	0.958787	−	0.284125i	$-0.0917031\pi$
$563$	23.4667	+	64.4741i	0.0416815	+	0.114519i	−0.917106	+	0.398644i	$0.869481\pi$
$564$	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	−0.561824	−	0.827257i	$-0.689900\pi$
$569$	−459.085	+	80.9491i	−0.806828	+	0.142265i	−0.245004	+	0.969522i	$0.578789\pi$
$570$	−525.723	−	533.752i	−0.922322	−	0.936407i
$571$	−496.079	+	180.558i	−0.868789	+	0.316213i	−0.737677	−	0.675154i	$-0.764077\pi$
$571$	−496.079	+	180.558i	−0.868789	+	0.316213i	−0.131113	+	0.991367i	$0.541855\pi$
$572$	−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	−0.677824	−	0.735224i	$-0.737077\pi$
$577$	171.837	−	297.630i	0.297811	−	0.515824i	0.975635	+	0.219401i	$0.0704101\pi$
$578$	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	−0.978327	−	0.207064i	$-0.933609\pi$
$587$	−56.2267	+	154.482i	−0.0957866	+	0.263172i	0.882541	+	0.470236i	$0.155831\pi$
$588$	−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	$0.0951555\pi$
$593$			349.285i			0.589014i	−0.955649	+	0.294507i	$0.904845\pi$
$594$	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	−0.985446	−	0.169991i	$-0.945626\pi$
$599$	−387.503	+	461.808i	−0.646917	+	0.770965i	0.338529	+	0.940956i	$0.390071\pi$
$600$	36.0927	−	379.406i	0.0601546	−	0.632343i
$601$	37.6412	+	13.7003i	0.0626310	+	0.0227958i	0.373146	−	0.927773i	$-0.378279\pi$
$601$	37.6412	+	13.7003i	0.0626310	+	0.0227958i	−0.310515	+	0.950569i	$0.600501\pi$
$602$	−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	−0.413046	−	0.910710i	$-0.635535\pi$
$607$	173.949	−	986.513i	0.286572	−	1.62523i	0.699617	−	0.714518i	$-0.253354\pi$
$608$	−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	0.826724	−	0.562608i	$-0.190202\pi$
$613$	−45.2825	−	78.4316i	−0.0738704	−	0.127947i	−0.900594	+	0.434660i	$0.856868\pi$
$614$	−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	−0.838100	−	0.545516i	$-0.816334\pi$
$617$	−337.332	−	926.812i	−0.546729	−	1.50213i	0.291371	−	0.956610i	$-0.405889\pi$
$618$	−201.583	−	775.787i	−0.326186	−	1.25532i
$619$	169.172	+	959.420i	0.273298	+	1.54995i	0.744316	+	0.667828i	$0.232776\pi$
$619$	169.172	+	959.420i	0.273298	+	1.54995i	−0.471017	+	0.882124i	$0.656113\pi$
$620$		−	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	−0.862022	−	0.506870i	$-0.830802\pi$
$631$	5.01746	−	8.69050i	0.00795160	−	0.0137726i	0.869974	+	0.493098i	$0.164136\pi$
$632$	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	−0.986602	−	0.163147i	$-0.947835\pi$
$641$	−80.7353	+	221.818i	−0.125952	+	0.346050i	0.860650	+	0.509197i	$0.170058\pi$
$642$	−188.113	+	264.366i	−0.293010	+	0.411785i
$643$	−21.9909	−	18.4526i	−0.0342005	−	0.0286976i	0.625527	−	0.780202i	$-0.284884\pi$
$643$	−21.9909	−	18.4526i	−0.0342005	−	0.0286976i	−0.659728	+	0.751505i	$0.729328\pi$
$644$	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	$0.0571284\pi$
$647$			230.995i			0.357024i	−0.983938	+	0.178512i	$0.942872\pi$
$648$	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	0.122092	−	0.992519i	$-0.461040\pi$
$653$	704.150	−	839.173i	1.07833	−	1.28510i	0.956239	−	0.292586i	$-0.0945157\pi$
$654$	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	0.912545	−	0.408976i	$-0.134114\pi$
$659$	231.520	+	275.915i	0.351321	+	0.418688i	−0.561224	+	0.827664i	$0.689670\pi$
$660$	−298.109	−	141.770i	−0.451680	−	0.214803i
$661$	−27.1592	+	154.027i	−0.0410880	+	0.233022i	−0.998435	−	0.0559177i	$-0.982192\pi$
$661$	−27.1592	+	154.027i	−0.0410880	+	0.233022i	0.957347	+	0.288940i	$0.0933027\pi$
$662$	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	−0.911265	−	0.411821i	$-0.864893\pi$
$673$	−131.778	−	747.351i	−0.195807	−	1.11048i	0.715458	−	0.698656i	$-0.246218\pi$
$674$		−	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	0.662966	−	0.748649i	$-0.269297\pi$
$677$	1043.94	−	184.074i	1.54200	−	0.271897i	0.879038	+	0.476752i	$0.158186\pi$
$678$	−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	0.368663	−	0.929563i	$-0.379816\pi$
$683$	927.527	−	535.508i	1.35802	−	0.784053i	0.989357	+	0.145511i	$0.0464825\pi$
$684$	−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	−0.363696	−	0.931518i	$-0.618485\pi$
$691$	338.945	−	284.409i	0.490514	−	0.411590i	0.854211	+	0.519927i	$0.174041\pi$
$692$	−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	$-0.982369\pi$
$701$		−	77.6184i		−	0.110725i	0.998466	−	0.0553626i	$-0.0176315\pi$
$702$	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	0.241539	−	0.970391i	$-0.422348\pi$
$709$	−139.805	−	50.8850i	−0.197187	−	0.0717700i	−0.438726	+	0.898621i	$0.644570\pi$
$710$	−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	0.484192	−	0.874962i	$-0.339114\pi$
$719$	−22.6129	−	13.0556i	−0.0314505	−	0.0181580i	−0.515643	+	0.856804i	$0.672447\pi$
$720$	−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	−0.872559	−	0.488508i	$-0.837541\pi$
$727$	−159.723	−	905.834i	−0.219701	−	1.24599i	0.652858	−	0.757480i	$-0.273570\pi$
$728$		−	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	−0.104867	−	0.994486i	$-0.533442\pi$
$733$	332.814	−	121.134i	0.454044	−	0.165258i	0.558911	+	0.829228i	$0.311219\pi$
$734$	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	−0.442610	−	0.896714i	$-0.645947\pi$
$739$	410.346	−	710.740i	0.555272	−	0.961760i	0.997882	−	0.0650455i	$-0.0207192\pi$
$740$	−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	0.0834921	−	0.996508i	$-0.473393\pi$
$743$	−132.906	−	23.4348i	−0.178877	−	0.0315408i	−0.262369	+	0.964968i	$0.584504\pi$
$744$	−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	0.996726	+	0.0808587i	$0.0257663\pi$
$751$	938.326	+	787.349i	1.24944	+	1.04840i	0.252710	+	0.967542i	$0.418678\pi$
$752$	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	−0.983311	−	0.181934i	$-0.941764\pi$
$761$	−482.010	+	574.437i	−0.633391	+	0.754846i	0.349920	+	0.936780i	$0.386209\pi$
$762$	−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

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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