LMFDB - Embedded newform 54.3.f.a.47.6

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			47.6
Character	$\chi$	$=$	54.47
Dual form			54.3.f.a.23.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.483690 + 1.32893i) q^{2} +(2.82413 + 1.01208i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(0.891042 - 0.157115i) q^{5} +(0.0210163 + 4.24259i) q^{6} +(-5.50064 - 4.61559i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(6.95137 + 5.71650i) q^{9} +O(q^{10})$	\(q+(0.483690 + 1.32893i) q^{2} +(2.82413 + 1.01208i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(0.891042 - 0.157115i) q^{5} +(0.0210163 + 4.24259i) q^{6} +(-5.50064 - 4.61559i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(6.95137 + 5.71650i) q^{9} +(0.639781 + 1.10813i) q^{10} +(7.28314 + 1.28421i) q^{11} +(-5.62792 + 2.08002i) q^{12} +(-18.3634 - 6.68372i) q^{13} +(3.47317 - 9.54246i) q^{14} +(2.67543 + 0.458097i) q^{15} +(0.694593 - 3.93923i) q^{16} +(12.7824 - 7.37992i) q^{17} +(-4.23450 + 12.0029i) q^{18} +(6.58593 - 11.4072i) q^{19} +(-1.16317 + 1.38621i) q^{20} +(-10.8632 - 18.6021i) q^{21} +(1.81615 + 10.2999i) q^{22} +(-15.0696 - 17.9592i) q^{23} +(-5.48637 - 6.47300i) q^{24} +(-22.7230 + 8.27051i) q^{25} -27.6364i q^{26} +(13.8460 + 23.1795i) q^{27} +14.3612 q^{28} +(13.5277 + 37.1670i) q^{29} +(0.685300 + 3.77702i) q^{30} +(-9.20424 + 7.72327i) q^{31} +(5.57091 - 0.982302i) q^{32} +(19.2688 + 10.9979i) q^{33} +(15.9901 + 13.4173i) q^{34} +(-5.62648 - 3.24845i) q^{35} +(-17.9991 + 0.178327i) q^{36} +(33.0149 + 57.1836i) q^{37} +(18.3448 + 3.23469i) q^{38} +(-45.0960 - 37.4609i) q^{39} +(-2.40479 - 0.875273i) q^{40} +(-26.1687 + 71.8979i) q^{41} +(19.4664 - 23.4340i) q^{42} +(9.66961 - 54.8391i) q^{43} +(-12.8094 + 7.39550i) q^{44} +(7.09211 + 4.00148i) q^{45} +(16.5775 - 28.7131i) q^{46} +(-0.204653 + 0.243896i) q^{47} +(5.94845 - 10.4219i) q^{48} +(0.444665 + 2.52182i) q^{49} +(-21.9818 - 26.1969i) q^{50} +(43.5682 - 7.90498i) q^{51} +(36.7267 - 13.3674i) q^{52} -0.264306i q^{53} +(-24.1067 + 29.6120i) q^{54} +6.69135 q^{55} +(6.94634 + 19.0849i) q^{56} +(30.1445 - 25.5498i) q^{57} +(-42.8490 + 35.9545i) q^{58} +(-62.3379 + 10.9919i) q^{59} +(-4.68791 + 2.73762i) q^{60} +(-42.4660 - 35.6332i) q^{61} +(-14.7157 - 8.49608i) q^{62} +(-11.8520 - 63.5291i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-17.4126 - 3.07032i) q^{65} +(-5.29533 + 30.9264i) q^{66} +(58.6251 + 21.3378i) q^{67} +(-10.0963 + 27.7394i) q^{68} +(-24.3822 - 65.9708i) q^{69} +(1.59548 - 9.04842i) q^{70} +(57.0927 - 32.9625i) q^{71} +(-8.94297 - 23.8332i) q^{72} +(22.7040 - 39.3244i) q^{73} +(-60.0237 + 71.5335i) q^{74} +(-72.5432 + 0.359354i) q^{75} +(4.57454 + 25.9435i) q^{76} +(-34.1346 - 40.6800i) q^{77} +(27.9703 - 78.0487i) q^{78} +(22.8997 - 8.33480i) q^{79} -3.61915i q^{80} +(15.6432 + 79.4751i) q^{81} -108.205 q^{82} +(-28.1190 - 77.2563i) q^{83} +(40.5577 + 14.5347i) q^{84} +(10.2302 - 8.58412i) q^{85} +(77.5542 - 13.6749i) q^{86} +(0.587778 + 118.655i) q^{87} +(-16.0238 - 13.4456i) q^{88} +(115.387 + 66.6186i) q^{89} +(-1.88729 + 11.3604i) q^{90} +(70.1610 + 121.522i) q^{91} +(46.1759 + 8.14205i) q^{92} +(-33.8105 + 12.4960i) q^{93} +(-0.423109 - 0.153999i) q^{94} +(4.07611 - 11.1990i) q^{95} +(16.7271 + 2.86408i) q^{96} +(-11.9691 + 67.8800i) q^{97} +(-3.13623 + 1.81071i) q^{98} +(43.2866 + 50.5611i) 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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.483690	+	1.32893i	0.241845	+	0.664463i
$2$	0.483690	+	1.32893i	0.241845	+	0.664463i
$3$	2.82413	+	1.01208i	0.941375	+	0.337361i
$3$	2.82413	+	1.01208i	0.941375	+	0.337361i
$4$	−1.53209	+	1.28558i	−0.383022	+	0.321394i
$5$	0.891042	−	0.157115i	0.178208	−	0.0314229i	−0.0838318	−	0.996480i	$-0.526716\pi$
$5$	0.891042	−	0.157115i	0.178208	−	0.0314229i	0.262040	+	0.965057i	$0.415605\pi$
$6$	0.0210163	+	4.24259i	0.00350272	+	0.707098i
$7$	−5.50064	−	4.61559i	−0.785806	−	0.659370i	0.158897	−	0.987295i	$-0.449206\pi$
$7$	−5.50064	−	4.61559i	−0.785806	−	0.659370i	−0.944704	+	0.327925i	$0.893651\pi$
$8$	−2.44949	−	1.41421i	−0.306186	−	0.176777i
$9$	6.95137	+	5.71650i	0.772375	+	0.635167i
$10$	0.639781	+	1.10813i	0.0639781	+	0.110813i
$11$	7.28314	+	1.28421i	0.662104	+	0.116747i	0.494595	−	0.869124i	$-0.335317\pi$
$11$	7.28314	+	1.28421i	0.662104	+	0.116747i	0.167509	+	0.985871i	$0.446428\pi$
$12$	−5.62792	+	2.08002i	−0.468993	+	0.173335i
$13$	−18.3634	−	6.68372i	−1.41257	−	0.514132i	−0.480684	−	0.876894i	$-0.659612\pi$
$13$	−18.3634	−	6.68372i	−1.41257	−	0.514132i	−0.931882	+	0.362762i	$0.881834\pi$
$14$	3.47317	−	9.54246i	0.248084	−	0.681604i
$15$	2.67543	+	0.458097i	0.178362	+	0.0305398i
$16$	0.694593	−	3.93923i	0.0434120	−	0.246202i
$17$	12.7824	−	7.37992i	0.751906	−	0.434113i	−0.0744762	−	0.997223i	$-0.523728\pi$
$17$	12.7824	−	7.37992i	0.751906	−	0.434113i	0.826382	+	0.563110i	$0.190395\pi$
$18$	−4.23450	+	12.0029i	−0.235250	+	0.666826i
$19$	6.58593	−	11.4072i	0.346628	−	0.600377i	−0.639020	−	0.769190i	$-0.720660\pi$
$19$	6.58593	−	11.4072i	0.346628	−	0.600377i	0.985648	+	0.168813i	$0.0539933\pi$
$20$	−1.16317	+	1.38621i	−0.0581586	+	0.0693107i
$21$	−10.8632	−	18.6021i	−0.517293	−	0.885815i
$22$	1.81615	+	10.2999i	0.0825524	+	0.468178i
$23$	−15.0696	−	17.9592i	−0.655199	−	0.780836i	0.331489	−	0.943459i	$-0.392449\pi$
$23$	−15.0696	−	17.9592i	−0.655199	−	0.780836i	−0.986688	+	0.162623i	$0.948005\pi$
$24$	−5.48637	−	6.47300i	−0.228599	−	0.269709i
$25$	−22.7230	+	8.27051i	−0.908922	+	0.330820i
$26$		−	27.6364i		−	1.06294i
$27$	13.8460	+	23.1795i	0.512814	+	0.858500i
$28$	14.3612			0.512899
$29$	13.5277	+	37.1670i	0.466471	+	1.28162i	0.920538	+	0.390652i	$0.127750\pi$
$29$	13.5277	+	37.1670i	0.466471	+	1.28162i	−0.454067	+	0.890967i	$0.650027\pi$
$30$	0.685300	+	3.77702i	0.0228433	+	0.125901i
$31$	−9.20424	+	7.72327i	−0.296911	+	0.249138i	−0.779057	−	0.626953i	$-0.784302\pi$
$31$	−9.20424	+	7.72327i	−0.296911	+	0.249138i	0.482146	+	0.876091i	$0.339857\pi$
$32$	5.57091	−	0.982302i	0.174091	−	0.0306970i
$33$	19.2688	+	10.9979i	0.583902	+	0.333271i
$34$	15.9901	+	13.4173i	0.470297	+	0.394626i
$35$	−5.62648	−	3.24845i	−0.160757	−	0.0928128i
$36$	−17.9991	+	0.178327i	−0.499975	+	0.00495354i
$37$	33.0149	+	57.1836i	0.892296	+	1.54550i	0.837116	+	0.547025i	$0.184240\pi$
$37$	33.0149	+	57.1836i	0.892296	+	1.54550i	0.0551793	+	0.998476i	$0.482427\pi$
$38$	18.3448	+	3.23469i	0.482758	+	0.0851233i
$39$	−45.0960	−	37.4609i	−1.15631	−	0.960536i
$40$	−2.40479	−	0.875273i	−0.0601198	−	0.0218818i
$41$	−26.1687	+	71.8979i	−0.638261	+	1.75361i	0.0188592	+	0.999822i	$0.493997\pi$
$41$	−26.1687	+	71.8979i	−0.638261	+	1.75361i	−0.657120	+	0.753786i	$0.728226\pi$
$42$	19.4664	−	23.4340i	0.463487	−	0.557952i
$43$	9.66961	−	54.8391i	0.224875	−	1.27533i	−0.638050	−	0.769995i	$-0.720259\pi$
$43$	9.66961	−	54.8391i	0.224875	−	1.27533i	0.862925	−	0.505333i	$-0.168630\pi$
$44$	−12.8094	+	7.39550i	−0.291122	+	0.168079i
$45$	7.09211	+	4.00148i	0.157602	+	0.0889217i
$46$	16.5775	−	28.7131i	0.360380	−	0.624197i
$47$	−0.204653	+	0.243896i	−0.00435432	+	0.00518928i	−0.768217	−	0.640189i	$-0.778856\pi$
$47$	−0.204653	+	0.243896i	−0.00435432	+	0.00518928i	0.763863	+	0.645379i	$0.223300\pi$
$48$	5.94845	−	10.4219i	0.123926	−	0.217123i
$49$	0.444665	+	2.52182i	0.00907480	+	0.0514657i
$50$	−21.9818	−	26.1969i	−0.439636	−	0.523938i
$51$	43.5682	−	7.90498i	0.854279	−	0.155000i
$52$	36.7267	−	13.3674i	0.706283	−	0.257066i
$53$		−	0.264306i		−	0.00498691i	−0.999997	−	0.00249346i	$-0.999206\pi$
$53$		−	0.264306i		−	0.00498691i	0.999997	−	0.00249346i	$-0.000793693\pi$
$54$	−24.1067	+	29.6120i	−0.446420	+	0.548370i
$55$	6.69135			0.121661
$56$	6.94634	+	19.0849i	0.124042	+	0.340802i
$57$	30.1445	−	25.5498i	0.528851	−	0.448241i
$58$	−42.8490	+	35.9545i	−0.738775	+	0.619906i
$59$	−62.3379	+	10.9919i	−1.05657	+	0.186303i	−0.674836	−	0.737968i	$-0.735786\pi$
$59$	−62.3379	+	10.9919i	−1.05657	+	0.186303i	−0.381739	+	0.924270i	$0.624675\pi$
$60$	−4.68791	+	2.73762i	−0.0781318	+	0.0456270i
$61$	−42.4660	−	35.6332i	−0.696164	−	0.584151i	0.224516	−	0.974470i	$-0.427920\pi$
$61$	−42.4660	−	35.6332i	−0.696164	−	0.584151i	−0.920679	+	0.390320i	$0.872364\pi$
$62$	−14.7157	−	8.49608i	−0.237349	−	0.137034i
$63$	−11.8520	−	63.5291i	−0.188127	−	1.00840i
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	−17.4126	−	3.07032i	−0.267887	−	0.0472356i
$66$	−5.29533	+	30.9264i	−0.0802322	+	0.468581i
$67$	58.6251	+	21.3378i	0.875001	+	0.318474i	0.740191	−	0.672397i	$-0.234735\pi$
$67$	58.6251	+	21.3378i	0.875001	+	0.318474i	0.134810	+	0.990871i	$0.456957\pi$
$68$	−10.0963	+	27.7394i	−0.148475	+	0.407933i
$69$	−24.3822	−	65.9708i	−0.353365	−	0.956099i
$70$	1.59548	−	9.04842i	0.0227926	−	0.129263i
$71$	57.0927	−	32.9625i	0.804122	−	0.464260i	−0.0407882	−	0.999168i	$-0.512987\pi$
$71$	57.0927	−	32.9625i	0.804122	−	0.464260i	0.844911	+	0.534908i	$0.179654\pi$
$72$	−8.94297	−	23.8332i	−0.124208	−	0.331017i
$73$	22.7040	−	39.3244i	0.311013	−	0.538691i	−0.667569	−	0.744548i	$-0.732665\pi$
$73$	22.7040	−	39.3244i	0.311013	−	0.538691i	0.978582	+	0.205857i	$0.0659983\pi$
$74$	−60.0237	+	71.5335i	−0.811131	+	0.966669i
$75$	−72.5432	+	0.359354i	−0.967243	+	0.00479139i
$76$	4.57454	+	25.9435i	0.0601913	+	0.341362i
$77$	−34.1346	−	40.6800i	−0.443306	−	0.528311i
$78$	27.9703	−	78.0487i	0.358594	−	1.00062i
$79$	22.8997	−	8.33480i	0.289869	−	0.105504i	−0.192993	−	0.981200i	$-0.561819\pi$
$79$	22.8997	−	8.33480i	0.289869	−	0.105504i	0.482862	+	0.875696i	$0.339597\pi$
$80$		−	3.61915i		−	0.0452394i
$81$	15.6432	+	79.4751i	0.193126	+	0.981174i
$82$	−108.205			−1.31957
$83$	−28.1190	−	77.2563i	−0.338783	−	0.930799i	−0.985740	−	0.168273i	$-0.946181\pi$
$83$	−28.1190	−	77.2563i	−0.338783	−	0.930799i	0.646957	−	0.762526i	$-0.276041\pi$
$84$	40.5577	+	14.5347i	0.482830	+	0.173032i
$85$	10.2302	−	8.58412i	0.120355	−	0.100990i
$86$	77.5542	−	13.6749i	0.901793	−	0.159010i
$87$	0.587778	+	118.655i	0.00675607	+	1.36385i
$88$	−16.0238	−	13.4456i	−0.182089	−	0.152791i
$89$	115.387	+	66.6186i	1.29648	+	0.748523i	0.979794	−	0.200007i	$-0.0640965\pi$
$89$	115.387	+	66.6186i	1.29648	+	0.748523i	0.316686	+	0.948530i	$0.397430\pi$
$90$	−1.88729	+	11.3604i	−0.0209699	+	0.126226i
$91$	70.1610	+	121.522i	0.771000	+	1.33541i
$92$	46.1759	+	8.14205i	0.501912	+	0.0885006i
$93$	−33.8105	+	12.4960i	−0.363554	+	0.134366i
$94$	−0.423109	−	0.153999i	−0.00450115	−	0.00163829i
$95$	4.07611	−	11.1990i	0.0429064	−	0.117884i
$96$	16.7271	+	2.86408i	0.174241	+	0.0298342i
$97$	−11.9691	+	67.8800i	−0.123392	+	0.699794i	0.858857	+	0.512215i	$0.171175\pi$
$97$	−11.9691	+	67.8800i	−0.123392	+	0.699794i	−0.982250	+	0.187578i	$0.939936\pi$
$98$	−3.13623	+	1.81071i	−0.0320024	+	0.0184766i
$99$	43.2866	+	50.5611i	0.437239	+	0.510719i
$100$	24.1814	−	41.8833i	0.241814	−	0.418833i
$101$	114.042	−	135.910i	1.12913	−	1.34564i	0.198316	−	0.980138i	$-0.436453\pi$
$101$	114.042	−	135.910i	1.12913	−	1.34564i	0.930810	−	0.365503i	$-0.119103\pi$
$102$	31.5786	+	54.0754i	0.309594	+	0.530151i
$103$	−2.96634	−	16.8229i	−0.0287994	−	0.163330i	0.967016	−	0.254715i	$-0.0819816\pi$
$103$	−2.96634	−	16.8229i	−0.0287994	−	0.163330i	−0.995816	+	0.0913853i	$0.970871\pi$
$104$	35.5287	+	42.3414i	0.341622	+	0.407129i
$105$	−12.6022	−	14.8685i	−0.120021	−	0.141605i
$106$	0.351244	−	0.127842i	0.00331362	−	0.00120606i
$107$		−	29.1810i		−	0.272719i	−0.990659	−	0.136360i	$-0.956460\pi$
$107$		−	29.1810i		−	0.272719i	0.990659	−	0.136360i	$-0.0435403\pi$
$108$	−51.0123	−	17.7130i	−0.472336	−	0.164009i
$109$	−161.118			−1.47814			−0.739071	−	0.673627i	$-0.764735\pi$
$109$	−161.118			−1.47814			−0.739071	+	0.673627i	$0.764735\pi$
$110$	3.23654	+	8.89231i	0.0294231	+	0.0808392i
$111$	35.3638	+	194.907i	0.318593	+	1.75592i
$112$	−22.0026	+	18.4624i	−0.196452	+	0.164842i
$113$	66.6379	−	11.7501i	0.589716	−	0.103983i	0.129176	−	0.991622i	$-0.458767\pi$
$113$	66.6379	−	11.7501i	0.589716	−	0.103983i	0.460540	+	0.887639i	$0.347656\pi$
$114$	48.5343	+	27.7017i	0.425740	+	0.242997i
$115$	−16.2493	−	13.6348i	−0.141298	−	0.118563i
$116$	−68.5065	−	39.5523i	−0.590573	−	0.340968i
$117$	−89.4431	−	151.435i	−0.764471	−	1.29432i
$118$	−44.7596	−	77.5258i	−0.379318	−	0.656998i
$119$	−104.374	−	18.4040i	−0.877093	−	0.154655i
$120$	−5.90559	−	4.90573i	−0.0492132	−	0.0408811i
$121$	−62.3079	−	22.6782i	−0.514941	−	0.187423i
$122$	26.8135	−	73.6695i	0.219783	−	0.603849i
$123$	−146.670	+	176.564i	−1.19244	+	1.43548i
$124$	4.17286	−	23.6655i	0.0336521	−	0.190851i
$125$	−38.5370	+	22.2493i	−0.308296	+	0.177995i
$126$	78.6928	−	46.4788i	0.624546	−	0.368880i
$127$	26.0758	−	45.1647i	0.205322	−	0.355627i	−0.744914	−	0.667161i	$-0.767509\pi$
$127$	26.0758	−	45.1647i	0.205322	−	0.355627i	0.950235	+	0.311534i	$0.100843\pi$
$128$	−7.27231	+	8.66680i	−0.0568149	+	0.0677094i
$129$	82.8099	−	145.086i	0.641937	−	1.12470i
$130$	−4.34208	−	24.6252i	−0.0334006	−	0.189424i
$131$	25.4225	+	30.2974i	0.194065	+	0.231278i	0.854298	−	0.519783i	$-0.173987\pi$
$131$	25.4225	+	30.2974i	0.194065	+	0.231278i	−0.660233	+	0.751060i	$0.729543\pi$
$132$	−43.6601	+	7.92166i	−0.330759	+	0.0600126i
$133$	−88.8776	+	32.3488i	−0.668253	+	0.243224i
$134$			88.2292i			0.658427i
$135$	15.9792	+	18.4785i	0.118364	+	0.136878i
$136$	−41.7472			−0.306964
$137$	−14.7144	−	40.4275i	−0.107404	−	0.295091i	0.874335	−	0.485323i	$-0.161298\pi$
$137$	−14.7144	−	40.4275i	−0.107404	−	0.295091i	−0.981739	+	0.190232i	$0.939076\pi$
$138$	75.8769	−	64.3115i	0.549833	−	0.466025i
$139$	184.188	−	154.552i	1.32509	−	1.11188i	0.339892	−	0.940465i	$-0.389610\pi$
$139$	184.188	−	154.552i	1.32509	−	1.11188i	0.985198	−	0.171418i	$-0.0548349\pi$
$140$	12.7964	−	2.25635i	0.0914028	−	0.0161168i
$141$	−0.824809	+	0.481667i	−0.00584971	+	0.00341608i
$142$	71.4198	+	59.9284i	0.502957	+	0.422031i
$143$	−125.160	−	72.2609i	−0.875242	−	0.505321i
$144$	27.3470	−	23.4124i	0.189910	−	0.162586i
$145$	17.8932	+	30.9919i	0.123401	+	0.213737i
$146$	63.2409	+	11.1511i	0.433157	+	0.0763773i
$147$	−1.29650	+	7.57198i	−0.00881974	+	0.0515100i
$148$	−124.096	−	45.1671i	−0.838484	−	0.305183i
$149$	−11.4189	+	31.3731i	−0.0766368	+	0.210558i	−0.972095	−	0.234588i	$-0.924626\pi$
$149$	−11.4189	+	31.3731i	−0.0766368	+	0.210558i	0.895458	+	0.445146i	$0.146848\pi$
$150$	−35.5659	−	96.2307i	−0.237106	−	0.641538i
$151$	−24.9315	+	141.394i	−0.165110	+	0.936383i	0.783842	+	0.620960i	$0.213257\pi$
$151$	−24.9315	+	141.394i	−0.165110	+	0.936383i	−0.948951	+	0.315422i	$0.897854\pi$
$152$	−32.2643	+	18.6278i	−0.212265	+	0.122551i
$153$	131.043	+	21.7700i	0.856488	+	0.142288i
$154$	37.5502	−	65.0388i	0.243832	−	0.422330i
$155$	−6.98792	+	8.32788i	−0.0450834	+	0.0537283i
$156$	117.250	−	0.580816i	0.751602	−	0.00372318i
$157$	−20.8900	−	118.473i	−0.133057	−	0.754606i	−0.976193	−	0.216905i	$-0.930404\pi$
$157$	−20.8900	−	118.473i	−0.133057	−	0.754606i	0.843135	−	0.537701i	$-0.180707\pi$
$158$	22.1527	+	26.4005i	0.140207	+	0.167092i
$159$	0.267500	−	0.746435i	0.00168239	−	0.00469456i
$160$	4.80958	−	1.75055i	0.0300599	−	0.0109409i
$161$			168.342i			1.04560i
$162$	−98.0500	+	59.2300i	−0.605247	+	0.365617i
$163$	−228.535			−1.40205			−0.701027	−	0.713134i	$-0.747275\pi$
$163$	−228.535			−1.40205			−0.701027	+	0.713134i	$0.747275\pi$
$164$	−52.3374	−	143.796i	−0.319131	−	0.876804i
$165$	18.8972	+	6.77221i	0.114529	+	0.0410437i
$166$	89.0671	−	74.7362i	0.536549	−	0.450218i
$167$	191.370	−	33.7438i	1.14593	−	0.202059i	0.431732	−	0.902002i	$-0.357902\pi$
$167$	191.370	−	33.7438i	1.14593	−	0.202059i	0.714199	+	0.699943i	$0.246791\pi$
$168$	0.301819	+	60.9285i	0.00179654	+	0.362670i
$169$	163.079	+	136.840i	0.964967	+	0.809704i
$170$	16.3559	+	9.44308i	0.0962111	+	0.0555475i
$171$	110.990	−	41.6470i	0.649066	−	0.243550i
$172$	55.6851	+	96.4494i	0.323750	+	0.560752i
$173$	−120.900	−	21.3179i	−0.698841	−	0.123225i	−0.187070	−	0.982347i	$-0.559899\pi$
$173$	−120.900	−	21.3179i	−0.698841	−	0.123225i	−0.511771	+	0.859122i	$0.671010\pi$
$174$	−157.400	+	58.1734i	−0.904597	+	0.334330i
$175$	163.165	+	59.3871i	0.932369	+	0.339355i
$176$	10.1176	−	27.7980i	0.0574866	−	0.157943i
$177$	−187.175	−	32.0488i	−1.05748	−	0.181066i
$178$	−32.7198	+	185.563i	−0.183819	+	1.04249i
$179$	−252.003	+	145.494i	−1.40784	+	0.812816i	−0.995180	−	0.0980700i	$-0.968733\pi$
$179$	−252.003	+	145.494i	−1.40784	+	0.812816i	−0.412659	+	0.910886i	$0.635400\pi$
$180$	−16.0099	+	2.98682i	−0.0889442	+	0.0165935i
$181$	111.720	−	193.505i	0.617239	−	1.06909i	−0.372748	−	0.927932i	$-0.621585\pi$
$181$	111.720	−	193.505i	0.617239	−	1.06909i	0.989987	−	0.141157i	$-0.0450821\pi$
$182$	−127.558	+	152.018i	−0.700869	+	0.835263i
$183$	−83.8655	−	143.612i	−0.458281	−	0.784763i
$184$	11.5146	+	65.3026i	0.0625794	+	0.354905i
$185$	38.4021	+	45.7658i	0.207579	+	0.247383i
$186$	−32.9601	−	38.8875i	−0.177205	−	0.209072i
$187$	102.573	−	37.3337i	0.548521	−	0.199645i
$188$		−	0.636768i		−	0.00338706i
$189$	30.8252	−	191.409i	0.163096	−	1.01275i
$190$	16.8542			0.0887064
$191$	100.749	+	276.805i	0.527481	+	1.44924i	0.862027	+	0.506863i	$0.169195\pi$
$191$	100.749	+	276.805i	0.527481	+	1.44924i	−0.334546	+	0.942379i	$0.608583\pi$
$192$	4.28459	+	23.6145i	0.0223155	+	0.122992i
$193$	−43.1317	+	36.1918i	−0.223480	+	0.187522i	−0.747653	−	0.664090i	$-0.768819\pi$
$193$	−43.1317	+	36.1918i	−0.223480	+	0.187522i	0.524172	+	0.851612i	$0.324375\pi$
$194$	−95.9968	+	16.9268i	−0.494829	+	0.0872517i
$195$	−46.0681	−	26.2940i	−0.236246	−	0.134841i
$196$	−3.92326	−	3.29200i	−0.0200166	−	0.0167959i
$197$	146.685	+	84.6884i	0.744592	+	0.429891i	0.823737	−	0.566973i	$-0.191885\pi$
$197$	146.685	+	84.6884i	0.744592	+	0.429891i	−0.0791444	+	0.996863i	$0.525219\pi$
$198$	−46.2547	+	81.9806i	−0.233610	+	0.414044i
$199$	53.4896	+	92.6468i	0.268792	+	0.465562i	0.968550	−	0.248818i	$-0.0800422\pi$
$199$	53.4896	+	92.6468i	0.268792	+	0.465562i	−0.699758	+	0.714380i	$0.746709\pi$
$200$	67.3561	+	11.8767i	0.336781	+	0.0593835i
$201$	143.969	+	119.594i	0.716264	+	0.594995i
$202$	235.775	+	85.8150i	1.16720	+	0.424827i
$203$	97.1365	−	266.880i	0.478505	−	1.31468i
$204$	−56.5879	+	68.1213i	−0.277392	+	0.333928i
$205$	−12.0212	+	68.1755i	−0.0586399	+	0.332564i
$206$	20.9217	−	12.0791i	0.101561	−	0.0586365i
$207$	−2.09036	−	210.987i	−0.0100984	−	1.01926i
$208$	−39.0838	+	67.6951i	−0.187903	+	0.325457i
$209$	62.6155	−	74.6222i	0.299596	−	0.357044i
$210$	13.6636	−	23.9391i	0.0650647	−	0.113996i
$211$	6.11577	+	34.6843i	0.0289847	+	0.164380i	0.995864	−	0.0908522i	$-0.0289591\pi$
$211$	6.11577	+	34.6843i	0.0289847	+	0.164380i	−0.966880	+	0.255233i	$0.917848\pi$
$212$	0.339786	+	0.404941i	0.00160276	+	0.00191010i
$213$	194.598	−	35.3076i	0.913604	−	0.165764i
$214$	38.7793	−	14.1145i	0.181212	−	0.0659557i
$215$		−	50.3832i		−	0.234340i
$216$	−1.13484	−	76.3591i	−0.00525391	−	0.353514i
$217$	86.2767			0.397588
$218$	−77.9309	−	214.113i	−0.357481	−	0.982171i
$219$	103.918	−	88.0788i	0.474514	−	0.402186i
$220$	−10.2517	+	8.60224i	−0.0465989	+	0.0391011i
$221$	−284.053	+	50.0862i	−1.28531	+	0.226635i
$222$	−241.912	+	141.271i	−1.08970	+	0.636354i
$223$	−83.0007	−	69.6459i	−0.372200	−	0.312313i	0.437431	−	0.899252i	$-0.355888\pi$
$223$	−83.0007	−	69.6459i	−0.372200	−	0.312313i	−0.809631	+	0.586939i	$0.800333\pi$
$224$	−35.1775	−	20.3097i	−0.157042	−	0.0906685i
$225$	−205.235	−	72.4049i	−0.912155	−	0.321799i
$226$	47.8470	+	82.8735i	0.211713	+	0.366697i
$227$	−223.383	−	39.3885i	−0.984068	−	0.173518i	−0.341613	−	0.939841i	$-0.610973\pi$
$227$	−223.383	−	39.3885i	−0.984068	−	0.173518i	−0.642455	+	0.766323i	$0.722084\pi$
$228$	−13.3379	+	77.8975i	−0.0584996	+	0.341656i
$229$	−197.382	−	71.8412i	−0.861930	−	0.313717i	−0.127035	−	0.991898i	$-0.540546\pi$
$229$	−197.382	−	71.8412i	−0.861930	−	0.313717i	−0.734895	+	0.678181i	$0.762768\pi$
$230$	10.2600	−	28.1891i	0.0446087	−	0.122561i
$231$	−55.2288	−	149.432i	−0.239086	−	0.646894i
$232$	19.4261	−	110.171i	0.0837334	−	0.474875i
$233$	36.1880	−	20.8932i	0.155313	−	0.0896702i	−0.420329	−	0.907372i	$-0.638085\pi$
$233$	36.1880	−	20.8932i	0.155313	−	0.0896702i	0.575642	+	0.817702i	$0.304752\pi$
$234$	157.983	−	192.111i	0.675143	−	0.820987i
$235$	−0.144035	+	0.249476i	−0.000612914	+	0.00106160i
$236$	81.3764	−	96.9806i	0.344815	−	0.410935i
$237$	73.1070	−	0.362147i	0.308469	−	0.00152805i
$238$	−26.0271	−	147.607i	−0.109358	−	0.620199i
$239$	239.745	+	285.717i	1.00312	+	1.19547i	0.980660	+	0.195722i	$0.0627049\pi$
$239$	239.745	+	285.717i	1.00312	+	1.19547i	0.0224583	+	0.999748i	$0.492851\pi$
$240$	3.66288	−	10.2209i	0.0152620	−	0.0425872i
$241$	−109.123	+	39.7174i	−0.452792	+	0.164803i	−0.558341	−	0.829611i	$-0.688562\pi$
$241$	−109.123	+	39.7174i	−0.452792	+	0.164803i	0.105550	+	0.994414i	$0.466340\pi$
$242$		−	93.7718i		−	0.387487i
$243$	−36.2570	+	240.280i	−0.149206	+	0.988806i
$244$	110.871			0.454388
$245$	0.792430	+	2.17718i	0.00323441	+	0.00888647i
$246$	−305.583	−	109.512i	−1.24221	−	0.445171i
$247$	−197.182	+	165.455i	−0.798308	+	0.669860i
$248$	33.4680	−	5.90132i	0.134952	−	0.0237956i
$249$	−1.22177	−	246.640i	−0.00490672	−	0.990524i
$250$	−48.2077	−	40.4510i	−0.192831	−	0.161804i
$251$	−160.201	−	92.4920i	−0.638251	−	0.368494i	0.145690	−	0.989330i	$-0.453460\pi$
$251$	−160.201	−	92.4920i	−0.638251	−	0.368494i	−0.783940	+	0.620836i	$0.786793\pi$
$252$	99.8298	+	82.0956i	0.396150	+	0.325776i
$253$	−86.6904	−	150.152i	−0.342650	−	0.593487i
$254$	72.6331	+	12.8072i	0.285957	+	0.0504220i
$255$	37.5791	−	13.8889i	0.147369	−	0.0544662i
$256$	−15.0351	−	5.47232i	−0.0587308	−	0.0213763i
$257$	−33.0286	+	90.7454i	−0.128516	+	0.353095i	−0.987217	−	0.159382i	$-0.949050\pi$
$257$	−33.0286	+	90.7454i	−0.128516	+	0.353095i	0.858701	+	0.512477i	$0.171272\pi$
$258$	232.863	+	39.8717i	0.902569	+	0.154541i
$259$	82.3323	−	466.930i	0.317885	−	1.80282i
$260$	30.6248	−	17.6813i	0.117788	−	0.0680048i
$261$	−118.429	+	335.692i	−0.453751	+	1.28618i
$262$	−27.9664	+	48.4392i	−0.106742	+	0.184882i
$263$	8.89610	−	10.6020i	0.0338255	−	0.0403116i	−0.748866	−	0.662721i	$-0.769402\pi$
$263$	8.89610	−	10.6020i	0.0338255	−	0.0403116i	0.782692	+	0.622409i	$0.213846\pi$
$264$	−31.6453	−	54.1895i	−0.119868	−	0.205263i
$265$	−0.0415264	−	0.235508i	−0.000156704	−	0.000888710i
$266$	−85.9783	−	102.465i	−0.323227	−	0.385207i
$267$	258.443	+	304.920i	0.967952	+	1.14202i
$268$	−117.250	+	42.6756i	−0.437501	+	0.159237i
$269$			52.5454i			0.195336i	0.995219	+	0.0976680i	$0.0311383\pi$
$269$			52.5454i			0.195336i	−0.995219	+	0.0976680i	$0.968862\pi$
$270$	−16.8276	+	30.1730i	−0.0623244	+	0.111752i
$271$	−282.779			−1.04346			−0.521732	−	0.853109i	$-0.674714\pi$
$271$	−282.779			−1.04346			−0.521732	+	0.853109i	$0.674714\pi$
$272$	−20.1927	−	55.4789i	−0.0742377	−	0.203966i
$273$	75.1527	+	414.203i	0.275285	+	1.51723i
$274$	46.6079	−	39.1087i	0.170102	−	0.142732i
$275$	−176.116	+	31.0540i	−0.640423	+	0.112924i
$276$	122.166	+	69.7280i	0.442631	+	0.252638i
$277$	62.3862	+	52.3482i	0.225221	+	0.188983i	0.748415	−	0.663231i	$-0.230815\pi$
$277$	62.3862	+	52.3482i	0.225221	+	0.188983i	−0.523194	+	0.852214i	$0.675260\pi$
$278$	294.477	+	170.017i	1.05927	+	0.611570i
$279$	−108.132	+	1.07133i	−0.387571	+	0.00383988i
$280$	9.18800	+	15.9141i	0.0328143	+	0.0568360i
$281$	206.646	+	36.4372i	0.735393	+	0.129670i	0.528787	−	0.848754i	$-0.322647\pi$
$281$	206.646	+	36.4372i	0.735393	+	0.129670i	0.206606	+	0.978424i	$0.433758\pi$
$282$	−1.03905	−	0.863133i	−0.00368458	−	0.00306076i
$283$	60.4622	+	22.0064i	0.213647	+	0.0777612i	0.446627	−	0.894720i	$-0.352625\pi$
$283$	60.4622	+	22.0064i	0.213647	+	0.0777612i	−0.232979	+	0.972482i	$0.574847\pi$
$284$	−45.0953	+	123.898i	−0.158786	+	0.436262i
$285$	22.8458	−	27.5020i	0.0801606	−	0.0964984i
$286$	35.4911	−	201.280i	0.124095	−	0.703775i
$287$	475.796	−	274.701i	1.65783	−	0.957146i
$288$	44.3408	+	25.0178i	0.153961	+	0.0868673i
$289$	−35.5735	+	61.6150i	−0.123092	+	0.213201i
$290$	−32.5312	+	38.7692i	−0.112177	+	0.133687i
$291$	−102.502	+	179.588i	−0.352242	+	0.617141i
$292$	15.7700	+	89.4362i	0.0540069	+	0.306288i
$293$	−88.2641	−	105.189i	−0.301243	−	0.359007i	0.594095	−	0.804395i	$-0.297510\pi$
$293$	−88.2641	−	105.189i	−0.301243	−	0.359007i	−0.895338	+	0.445388i	$0.853066\pi$
$294$	−10.6897	+	1.93953i	−0.0363595	+	0.00659704i
$295$	−53.8187	+	19.5884i	−0.182436	+	0.0664014i
$296$		−	186.761i		−	0.630948i
$297$	71.0748	+	186.601i	0.239309	+	0.628285i
$298$	−47.2158			−0.158442
$299$	156.694	+	430.513i	0.524060	+	1.43984i
$300$	110.681	−	93.8103i	0.368935	−	0.312701i
$301$	−306.304	+	257.019i	−1.01762	+	0.853885i
$302$	−199.961	+	35.2585i	−0.662123	+	0.116750i
$303$	459.620	−	268.406i	1.51690	−	0.885830i
$304$	−40.3609	−	33.8668i	−0.132766	−	0.111404i
$305$	−43.4375	−	25.0786i	−0.142418	−	0.0822250i
$306$	34.4532	+	184.676i	0.112592	+	0.603516i
$307$	−181.401	−	314.195i	−0.590882	−	1.02344i	−0.994114	−	0.108340i	$-0.965447\pi$
$307$	−181.401	−	314.195i	−0.590882	−	1.02344i	0.403232	−	0.915098i	$-0.367887\pi$
$308$	104.594	+	18.4428i	0.339592	+	0.0598792i
$309$	8.64891	−	50.5123i	0.0279900	−	0.163470i
$310$	−14.4471	−	5.25832i	−0.0466036	−	0.0169623i
$311$	75.3296	−	206.966i	0.242217	−	0.665487i	−0.757700	−	0.652603i	$-0.773677\pi$
$311$	75.3296	−	206.966i	0.242217	−	0.665487i	0.999917	−	0.0128834i	$-0.00410102\pi$
$312$	57.4844	+	155.535i	0.184245	+	0.498511i
$313$	−7.54061	+	42.7650i	−0.0240914	+	0.136629i	−0.994481	−	0.104915i	$-0.966543\pi$
$313$	−7.54061	+	42.7650i	−0.0240914	+	0.136629i	0.970390	+	0.241544i	$0.0776540\pi$
$314$	147.338	−	85.0655i	0.469228	−	0.270909i
$315$	−20.5420	−	54.7450i	−0.0652127	−	0.173794i
$316$	−24.3693	+	42.2089i	−0.0771181	+	0.133572i
$317$	78.0234	−	92.9846i	0.246131	−	0.293327i	−0.628808	−	0.777560i	$-0.716457\pi$
$317$	78.0234	−	92.9846i	0.246131	−	0.293327i	0.874939	+	0.484233i	$0.160901\pi$
$318$	1.12134	−	0.00555475i	0.00352624	−	1.74678e-5i
$319$	50.7936	+	288.065i	0.159228	+	0.903024i
$320$	4.65269	+	5.54486i	0.0145397	+	0.0173277i
$321$	29.5336	−	82.4107i	0.0920049	−	0.256731i
$322$	−223.714	+	81.4254i	−0.694765	+	0.252874i
$323$		−	194.415i		−	0.601903i
$324$	−126.138	−	101.652i	−0.389315	−	0.313742i
$325$	472.549			1.45400
$326$	−110.540	−	303.706i	−0.339080	−	0.931613i
$327$	−455.016	−	163.064i	−1.39149	−	0.498668i
$328$	165.779	−	139.105i	0.505424	−	0.424101i
$329$	2.25145	−	0.396991i	0.00684331	−	0.00120666i
$330$	0.140628	+	28.3887i	0.000426145	+	0.0860262i
$331$	−106.552	−	89.4075i	−0.321908	−	0.270113i	0.467485	−	0.884001i	$-0.345160\pi$
$331$	−106.552	−	89.4075i	−0.321908	−	0.270113i	−0.789393	+	0.613888i	$0.789605\pi$
$332$	142.400	+	82.2145i	0.428915	+	0.247634i
$333$	−97.3906	+	586.234i	−0.292464	+	1.76046i
$334$	137.407	+	237.996i	0.411398	+	0.712562i
$335$	55.5899	+	9.80199i	0.165940	+	0.0292597i
$336$	−80.8235	+	29.8716i	−0.240546	+	0.0889035i
$337$	−22.7816	−	8.29181i	−0.0676010	−	0.0246048i	0.307998	−	0.951387i	$-0.400341\pi$
$337$	−22.7816	−	8.29181i	−0.0676010	−	0.0246048i	−0.375599	+	0.926782i	$0.622563\pi$
$338$	−102.970	+	282.909i	−0.304646	+	0.837008i
$339$	200.086	+	34.2595i	0.590224	+	0.101060i
$340$	−4.63798	+	26.3033i	−0.0136411	+	0.0773626i
$341$	−76.9541	+	44.4295i	−0.225672	+	0.130292i
$342$	109.031	+	127.354i	0.318803	+	0.372379i
$343$	−166.730	+	288.786i	−0.486095	+	0.841941i
$344$	−101.240	+	120.653i	−0.294302	+	0.350735i
$345$	−32.0905	−	54.9519i	−0.0930160	−	0.159281i
$346$	−30.1480	−	170.978i	−0.0871329	−	0.494155i
$347$	−163.919	−	195.352i	−0.472390	−	0.562973i	0.476258	−	0.879306i	$-0.341993\pi$
$347$	−163.919	−	195.352i	−0.472390	−	0.562973i	−0.948648	+	0.316333i	$0.897548\pi$
$348$	−153.441	−	181.035i	−0.440922	−	0.520215i
$349$	588.280	−	214.116i	1.68562	−	0.613514i	0.691554	−	0.722325i	$-0.256926\pi$
$349$	588.280	−	214.116i	1.68562	−	0.613514i	0.994062	+	0.108811i	$0.0347042\pi$
$350$			245.559i			0.701596i
$351$	−99.3336	−	518.196i	−0.283002	−	1.47634i
$352$	41.8352			0.118850
$353$	45.8606	+	126.001i	0.129917	+	0.356944i	0.987547	−	0.157323i	$-0.0502864\pi$
$353$	45.8606	+	126.001i	0.129917	+	0.356944i	−0.857630	+	0.514267i	$0.828064\pi$
$354$	−47.9440	−	264.243i	−0.135435	−	0.746449i
$355$	45.6931	−	38.3410i	0.128713	−	0.108003i
$356$	−262.426	+	46.2728i	−0.737152	+	0.129980i
$357$	−276.139	−	157.610i	−0.773499	−	0.441486i
$358$	−315.242	−	264.519i	−0.880564	−	0.738881i
$359$	−480.602	−	277.476i	−1.33872	−	0.772913i	−0.352107	−	0.935960i	$-0.614535\pi$
$359$	−480.602	−	277.476i	−1.33872	−	0.772913i	−0.986618	+	0.163047i	$0.947868\pi$
$360$	−11.7131	−	19.8313i	−0.0325364	−	0.0550871i
$361$	93.7511	+	162.382i	0.259698	+	0.449811i
$362$	311.192	+	54.8715i	0.859646	+	0.151579i
$363$	−153.013	−	127.107i	−0.421523	−	0.350157i
$364$	−263.719	−	95.9859i	−0.724503	−	0.263698i
$365$	14.0517	−	38.6068i	0.0384979	−	0.105772i
$366$	150.284	−	180.915i	0.410613	−	0.494302i
$367$	31.4908	−	178.593i	0.0858061	−	0.486630i	−0.911374	−	0.411580i	$-0.864977\pi$
$367$	31.4908	−	178.593i	0.0858061	−	0.486630i	0.997180	−	0.0750505i	$-0.0239118\pi$
$368$	−81.2128	+	46.8882i	−0.220687	+	0.127414i
$369$	−592.913	+	350.196i	−1.60681	+	0.949041i
$370$	−42.2447	+	73.1699i	−0.114175	+	0.197757i
$371$	−1.21993	+	1.45386i	−0.00328822	+	0.00391875i
$372$	35.7361	−	62.6110i	0.0960648	−	0.168309i
$373$	61.7520	+	350.213i	0.165555	+	0.938909i	0.948490	+	0.316806i	$0.102610\pi$
$373$	61.7520	+	350.213i	0.165555	+	0.938909i	−0.782935	+	0.622103i	$0.786278\pi$
$374$	99.2274	+	118.255i	0.265314	+	0.316189i
$375$	−131.352	+	23.8323i	−0.350271	+	0.0635528i
$376$	0.846217	−	0.307998i	0.00225058	−	0.000819143i
$377$		−	772.925i		−	2.05020i
$378$	269.279	−	51.6184i	0.712378	−	0.136557i
$379$	571.606			1.50819			0.754097	−	0.656763i	$-0.228075\pi$
$379$	571.606			1.50819			0.754097	+	0.656763i	$0.228075\pi$
$380$	8.15221	+	22.3980i	0.0214532	+	0.0589421i
$381$	119.352	−	101.160i	0.313259	−	0.265511i
$382$	−319.123	+	267.776i	−0.835399	+	0.700983i
$383$	410.213	−	72.3315i	1.07105	−	0.188855i	0.389796	−	0.920901i	$-0.372546\pi$
$383$	410.213	−	72.3315i	1.07105	−	0.188855i	0.681255	+	0.732046i	$0.261434\pi$
$384$	−29.3095	+	17.1160i	−0.0763267	+	0.0445728i
$385$	−36.8067	−	30.8845i	−0.0956019	−	0.0802195i
$386$	−68.9586	−	39.8133i	−0.178649	−	0.103143i
$387$	380.705	−	325.931i	0.983733	−	0.842198i
$388$	−68.9271	−	119.385i	−0.177647	−	0.307694i
$389$	−181.375	−	31.9812i	−0.466259	−	0.0822140i	−0.0644168	−	0.997923i	$-0.520519\pi$
$389$	−181.375	−	31.9812i	−0.466259	−	0.0822140i	−0.401842	+	0.915709i	$0.631630\pi$
$390$	12.6601	−	73.9392i	0.0324619	−	0.189588i
$391$	−325.163	−	118.350i	−0.831620	−	0.302685i
$392$	2.47719	−	6.80602i	0.00631936	−	0.0173623i
$393$	41.1329	+	111.293i	0.104664	+	0.283189i
$394$	−41.5948	+	235.896i	−0.105571	+	0.598721i
$395$	19.0950	−	11.0245i	0.0483419	−	0.0279102i
$396$	−131.319	−	21.8159i	−0.331614	−	0.0550908i
$397$	145.068	−	251.265i	0.365411	−	0.632910i	−0.623431	−	0.781878i	$-0.714262\pi$
$397$	145.068	−	251.265i	0.365411	−	0.632910i	0.988842	+	0.148968i	$0.0475952\pi$
$398$	−97.2483	+	115.896i	−0.244343	+	0.291196i
$399$	−283.741	+	1.40556i	−0.711131	+	0.00352270i
$400$	16.7962	+	95.2560i	0.0419905	+	0.238140i
$401$	−290.603	−	346.328i	−0.724697	−	0.863660i	0.270381	−	0.962753i	$-0.412850\pi$
$401$	−290.603	−	346.328i	−0.724697	−	0.863660i	−0.995078	+	0.0990934i	$0.968406\pi$
$402$	−89.2953	+	249.171i	−0.222128	+	0.619827i
$403$	220.641	−	80.3067i	0.547496	−	0.199272i
$404$			354.835i			0.878305i
$405$	26.4255	+	68.3578i	0.0652481	+	0.168785i
$406$	401.648			0.989281
$407$	167.017	+	458.874i	0.410360	+	1.12745i
$408$	−117.899	−	42.2516i	−0.288969	−	0.103558i
$409$	226.326	−	189.910i	0.553363	−	0.464327i	−0.322715	−	0.946496i	$-0.604595\pi$
$409$	226.326	−	189.910i	0.553363	−	0.464327i	0.876078	+	0.482169i	$0.160151\pi$
$410$	−96.4148	+	17.0005i	−0.235158	+	0.0414647i
$411$	−0.639341	−	129.064i	−0.00155557	−	0.314025i
$412$	26.1719	+	21.9608i	0.0635239	+	0.0533029i
$413$	393.632	+	227.264i	0.953105	+	0.550276i
$414$	279.375	−	104.830i	0.674818	−	0.253212i
$415$	−37.1933	−	64.4207i	−0.0896225	−	0.155231i
$416$	−108.866	−	19.1960i	−0.261697	−	0.0461443i
$417$	676.588	−	250.060i	1.62251	−	0.599665i
$418$	129.454	+	47.1174i	0.309698	+	0.112721i
$419$	−184.754	+	507.608i	−0.440941	+	1.21147i	0.497934	+	0.867215i	$0.334092\pi$
$419$	−184.754	+	507.608i	−0.440941	+	1.21147i	−0.938875	+	0.344259i	$0.888130\pi$
$420$	38.4222	+	6.57880i	0.0914815	+	0.0156638i
$421$	−58.5712	+	332.174i	−0.139124	+	0.789011i	0.832775	+	0.553612i	$0.186751\pi$
$421$	−58.5712	+	332.174i	−0.139124	+	0.789011i	−0.971899	+	0.235399i	$0.924360\pi$
$422$	−43.1347	+	24.9038i	−0.102215	+	0.0590138i
$423$	−2.81685	+	0.525513i	−0.00665923	+	0.00124235i
$424$	−0.373786	+	0.647416i	−0.000881570	+	0.00152692i
$425$	−229.419	+	273.411i	−0.539810	+	0.643321i
$426$	141.046	+	241.528i	0.331094	+	0.566967i
$427$	69.1221	+	392.011i	0.161878	+	0.918058i
$428$	37.5143	+	44.7078i	0.0876503	+	0.104458i
$429$	−280.332	−	330.746i	−0.653456	−	0.770970i
$430$	66.9555	−	24.3698i	0.155710	−	0.0566740i
$431$			625.633i			1.45158i	0.687914	+	0.725792i	$0.258527\pi$
$431$			625.633i			1.45158i	−0.687914	+	0.725792i	$0.741473\pi$
$432$	100.927	−	38.4422i	0.233627	−	0.0889866i
$433$	754.656			1.74286			0.871428	−	0.490524i	$-0.163195\pi$
$433$	754.656			1.74286			0.871428	+	0.490524i	$0.163195\pi$
$434$	41.7311	+	114.655i	0.0961546	+	0.264183i
$435$	19.1662	+	105.634i	0.0440603	+	0.242838i
$436$	246.846	−	207.129i	0.566161	−	0.475066i
$437$	−304.111	+	53.6230i	−0.695906	+	0.122707i
$438$	167.315	+	95.4972i	0.381997	+	0.218030i
$439$	130.229	+	109.276i	0.296650	+	0.248919i	0.778948	−	0.627088i	$-0.215753\pi$
$439$	130.229	+	109.276i	0.296650	+	0.248919i	−0.482298	+	0.876007i	$0.660198\pi$
$440$	−16.3904	−	9.46300i	−0.0372509	−	0.0215068i
$441$	−11.3250	+	20.0720i	−0.0256802	+	0.0455148i
$442$	−203.954	−	353.260i	−0.461435	−	0.799230i
$443$	16.3964	+	2.89112i	0.0370121	+	0.00652623i	0.192124	−	0.981371i	$-0.438463\pi$
$443$	16.3964	+	2.89112i	0.0370121	+	0.00652623i	−0.155111	+	0.987897i	$0.549574\pi$
$444$	−304.749	−	253.153i	−0.686371	−	0.570164i
$445$	113.281	+	41.2310i	0.254564	+	0.0926539i
$446$	52.4076	−	143.989i	0.117506	−	0.322845i
$447$	−64.0006	+	77.0448i	−0.143178	+	0.172360i
$448$	9.97516	−	56.5719i	0.0222660	−	0.126277i
$449$	−584.655	+	337.551i	−1.30213	+	0.751784i	−0.980769	−	0.195174i	$-0.937473\pi$
$449$	−584.655	+	337.551i	−1.30213	+	0.751784i	−0.321359	+	0.946958i	$0.604140\pi$
$450$	−3.04918	−	307.763i	−0.00677596	−	0.683919i
$451$	−282.923	+	490.037i	−0.627323	+	1.08656i
$452$	−86.9896	+	103.670i	−0.192455	+	0.229359i
$453$	−213.512	+	374.081i	−0.471329	+	0.825786i
$454$	−55.7038	−	315.912i	−0.122696	−	0.695841i
$455$	81.6094	+	97.2583i	0.179361	+	0.213754i
$456$	−109.971	+	19.9531i	−0.241165	+	0.0437568i
$457$	−504.675	+	183.687i	−1.10432	+	0.401940i	−0.828908	−	0.559385i	$-0.811037\pi$
$457$	−504.675	+	183.687i	−1.10432	+	0.401940i	−0.275414	+	0.961326i	$0.588815\pi$
$458$		−	297.055i		−	0.648591i
$459$	348.048	+	194.107i	0.758274	+	0.422892i
$460$	42.4239			0.0922258
$461$	−111.541	−	306.457i	−0.241955	−	0.664765i	−0.999922	−	0.0124727i	$-0.996030\pi$
$461$	−111.541	−	306.457i	−0.241955	−	0.664765i	0.757968	−	0.652292i	$-0.226192\pi$
$462$	171.871	−	145.674i	0.372015	−	0.315311i
$463$	−170.249	+	142.856i	−0.367708	+	0.308544i	−0.807854	−	0.589382i	$-0.799371\pi$
$463$	−170.249	+	142.856i	−0.367708	+	0.308544i	0.440146	+	0.897926i	$0.354927\pi$
$464$	155.805	−	27.4727i	0.335788	−	0.0592084i
$465$	−28.1633	+	16.4466i	−0.0605662	+	0.0353691i
$466$	45.2692	+	37.9854i	0.0971443	+	0.0815137i
$467$	−80.9832	−	46.7556i	−0.173411	−	0.100119i	0.410782	−	0.911734i	$-0.365256\pi$
$467$	−80.9832	−	46.7556i	−0.173411	−	0.100119i	−0.584193	+	0.811614i	$0.698589\pi$
$468$	331.716	+	117.026i	0.708795	+	0.250056i
$469$	−223.989	−	387.961i	−0.477589	−	0.827208i
$470$	−0.401203	−	0.0707429i	−0.000853623	−	0.000150517i
$471$	60.9086	−	355.725i	0.129318	−	0.755256i
$472$	168.241	+	61.2347i	0.356443	+	0.129734i
$473$	140.850	−	386.983i	0.297781	−	0.818146i
$474$	35.8424	+	96.9787i	0.0756168	+	0.204596i
$475$	−55.3093	+	313.675i	−0.116441	+	0.660367i
$476$	183.570	−	105.984i	0.385652	−	0.222656i
$477$	1.51091	−	1.83729i	0.00316752	−	0.00385177i
$478$	−263.735	+	456.802i	−0.551746	+	0.955653i
$479$	−7.97154	+	9.50011i	−0.0166420	+	0.0198332i	−0.774301	−	0.632817i	$-0.781898\pi$
$479$	−7.97154	+	9.50011i	−0.0166420	+	0.0198332i	0.757659	+	0.652650i	$0.226343\pi$
$480$	15.3546	−	0.0760613i	0.0319887	−	0.000158461i
$481$	−224.067	−	1270.74i	−0.465835	−	2.64188i
$482$	−105.563	−	125.805i	−0.219011	−	0.261007i
$483$	−170.376	+	475.420i	−0.352746	+	0.984306i
$484$	124.616	−	45.3564i	0.257471	−	0.0937116i
$485$			62.3644i			0.128586i
$486$	−336.851	+	68.0381i	−0.693110	+	0.139996i
$487$	−551.768			−1.13299			−0.566497	−	0.824064i	$-0.691702\pi$
$487$	−551.768			−1.13299			−0.566497	+	0.824064i	$0.691702\pi$
$488$	53.6270	+	147.339i	0.109891	+	0.301924i
$489$	−645.411	−	231.296i	−1.31986	−	0.472999i
$490$	−2.51003	+	2.10616i	−0.00512250	+	0.00429829i
$491$	803.339	−	141.650i	1.63613	−	0.288494i	0.721387	−	0.692532i	$-0.243505\pi$
$491$	803.339	−	141.650i	1.63613	−	0.288494i	0.914742	+	0.404038i	$0.132394\pi$
$492$	−2.27406	−	459.067i	−0.00462208	−	0.933064i
$493$	447.205	+	375.250i	0.907110	+	0.761156i
$494$	−315.253	−	182.011i	−0.638164	−	0.368444i
$495$	46.5141	+	38.2511i	0.0939679	+	0.0772750i
$496$	24.0306	+	41.6221i	0.0484487	+	0.0839156i
$497$	−466.188	−	82.2015i	−0.938003	−	0.165395i
$498$	327.176	−	120.921i	0.656980	−	0.242813i
$499$	270.216	+	98.3506i	0.541515	+	0.197095i	0.598273	−	0.801293i	$-0.295854\pi$
$499$	270.216	+	98.3506i	0.541515	+	0.197095i	−0.0567575	+	0.998388i	$0.518076\pi$
$500$	30.4389	−	83.6302i	0.0608778	−	0.167260i
$501$	574.606	+	98.3862i	1.14692	+	0.196380i
$502$	45.4276	−	257.633i	0.0904932	−	0.513212i
$503$	−22.2054	+	12.8203i	−0.0441459	+	0.0254877i	−0.521911	−	0.853000i	$-0.674781\pi$
$503$	−22.2054	+	12.8203i	−0.0441459	+	0.0254877i	0.477765	+	0.878488i	$0.341447\pi$
$504$	−60.8123	+	172.375i	−0.120659	+	0.342014i
$505$	80.2626	−	139.019i	0.158936	−	0.275285i
$506$	157.610	−	187.832i	0.311482	−	0.371210i
$507$	322.064	+	551.503i	0.635234	+	1.08778i
$508$	18.1121	+	102.719i	0.0356537	+	0.202202i
$509$	80.2854	+	95.6804i	0.157732	+	0.187977i	0.839123	−	0.543942i	$-0.183069\pi$
$509$	80.2854	+	95.6804i	0.157732	+	0.187977i	−0.681391	+	0.731920i	$0.738625\pi$
$510$	36.6339	+	43.2220i	0.0718312	+	0.0847489i
$511$	−306.392	+	111.517i	−0.599593	+	0.218234i
$512$		−	22.6274i		−	0.0441942i
$513$	355.601	−	5.28492i	0.693179	−	0.0103020i
$514$	−136.570			−0.265699
$515$	−5.28627	−	14.5239i	−0.0102646	−	0.0282017i
$516$	59.6469	+	328.743i	0.115595	+	0.637099i
$517$	−1.80373	+	1.51351i	−0.00348884	+	0.00292749i
$518$	660.338	−	116.435i	1.27478	−	0.224779i
$519$	−319.860	−	182.565i	−0.616301	−	0.351762i
$520$	38.3100	+	32.1459i	0.0736730	+	0.0618190i
$521$	23.1236	+	13.3504i	0.0443831	+	0.0256246i	0.522027	−	0.852929i	$-0.325176\pi$
$521$	23.1236	+	13.3504i	0.0443831	+	0.0256246i	−0.477644	+	0.878553i	$0.658509\pi$
$522$	−503.393	+	4.98740i	−0.964355	+	0.00955441i
$523$	−361.405	−	625.972i	−0.691023	−	1.19689i	−0.971503	−	0.237027i	$-0.923827\pi$
$523$	−361.405	−	625.972i	−0.691023	−	1.19689i	0.280480	−	0.959860i	$-0.409506\pi$
$524$	−77.8991	−	13.7357i	−0.148662	−	0.0262132i
$525$	400.693	+	332.853i	0.763224	+	0.634005i
$526$	18.3922	+	6.69420i	0.0349661	+	0.0127266i
$527$	−60.6551	+	166.649i	−0.115095	+	0.316221i
$528$	56.7073	−	68.2651i	0.107400	−	0.129290i
$529$	−3.58173	+	20.3130i	−0.00677075	+	0.0383988i
$530$	0.292887	−	0.169098i	0.000552617	−	0.000319053i
$531$	−496.169	−	279.946i	−0.934405	−	0.527206i
$532$	94.5816	−	163.820i	0.177785	−	0.307933i
$533$	961.091	−	1145.38i	1.80317	−	2.14894i
$534$	−280.210	+	490.939i	−0.524738	+	0.919361i
$535$	−4.58476	−	26.0015i	−0.00856964	−	0.0486009i
$536$	−113.425	−	135.175i	−0.211614	−	0.252192i
$537$	−858.940	+	155.845i	−1.59952	+	0.290215i
$538$	−69.8289	+	25.4157i	−0.129794	+	0.0472410i
$539$			18.9378i			0.0351351i
$540$	−48.2370	−	7.76824i	−0.0893278	−	0.0143856i
$541$	−181.539			−0.335562			−0.167781	−	0.985824i	$-0.553660\pi$
$541$	−181.539			−0.335562			−0.167781	+	0.985824i	$0.553660\pi$
$542$	−136.777	−	375.792i	−0.252356	−	0.693343i
$543$	511.355	−	433.413i	0.941723	−	0.798182i
$544$	63.9603	−	53.6691i	0.117574	−	0.0986564i
$545$	−143.562	+	25.3139i	−0.263417	+	0.0464476i
$546$	−514.095	+	300.218i	−0.941566	+	0.549850i
$547$	−584.502	−	490.456i	−1.06856	−	0.896628i	−0.0736388	−	0.997285i	$-0.523461\pi$
$547$	−584.502	−	490.456i	−1.06856	−	0.896628i	−0.994921	+	0.100657i	$0.967906\pi$
$548$	74.5163	+	43.0220i	0.135979	+	0.0785073i
$549$	−91.4998	−	490.456i	−0.166666	−	0.893363i
$550$	−126.454	−	219.025i	−0.229917	−	0.398227i
$551$	513.062	+	90.4667i	0.931147	+	0.164186i
$552$	−33.5729	+	196.076i	−0.0608205	+	0.355211i
$553$	−164.433	−	59.8487i	−0.297347	−	0.108225i
$554$	−39.3914	+	108.227i	−0.0711036	+	0.195356i
$555$	62.1335	+	168.114i	0.111952	+	0.302909i
$556$	−83.5038	+	473.574i	−0.150187	+	0.851752i
$557$	154.424	−	89.1568i	0.277243	−	0.160066i	−0.354932	−	0.934892i	$-0.615496\pi$
$557$	154.424	−	89.1568i	0.277243	−	0.160066i	0.632174	+	0.774826i	$0.282163\pi$
$558$	−53.7261	−	143.182i	−0.0962834	−	0.256598i
$559$	−544.096	+	942.401i	−0.973337	+	1.68587i
$560$	−16.7045	+	19.9077i	−0.0298295	+	0.0355494i
$561$	327.465	−	1.62215i	0.583717	−	0.00289153i
$562$	51.5300	+	292.241i	0.0916903	+	0.520002i
$563$	−83.6205	−	99.6550i	−0.148527	−	0.177007i	0.686651	−	0.726987i	$-0.259080\pi$
$563$	−83.6205	−	99.6550i	−0.148527	−	0.177007i	−0.835178	+	0.549980i	$0.814635\pi$
$564$	0.644462	−	1.79831i	0.00114266	−	0.00318850i
$565$	57.5311	−	20.9396i	0.101825	−	0.0370612i
$566$			90.9940i			0.160767i
$567$	280.776	−	509.367i	0.495197	−	0.898354i
$568$	−186.464			−0.328282
$569$	−334.788	−	919.824i	−0.588380	−	1.61656i	−0.773465	−	0.633839i	$-0.781478\pi$
$569$	−334.788	−	919.824i	−0.588380	−	1.61656i	0.185084	−	0.982723i	$-0.440744\pi$
$570$	47.5984	+	17.0579i	0.0835060	+	0.0299261i
$571$	353.588	−	296.696i	0.619244	−	0.519607i	−0.278322	−	0.960488i	$-0.589778\pi$
$571$	353.588	−	296.696i	0.619244	−	0.519607i	0.897566	+	0.440880i	$0.145334\pi$
$572$	284.653	−	50.1919i	0.497644	−	0.0877481i
$573$	4.37754	+	883.699i	0.00763969	+	1.54223i
$574$	595.195	+	499.428i	1.03692	+	0.870083i
$575$	490.959	+	283.455i	0.853842	+	0.492966i
$576$	−11.7996	+	71.0265i	−0.0204854	+	0.123310i
$577$	−192.832	−	333.994i	−0.334197	−	0.578846i	0.649133	−	0.760675i	$-0.275132\pi$
$577$	−192.832	−	333.994i	−0.334197	−	0.578846i	−0.983330	+	0.181829i	$0.941798\pi$
$578$	−99.0883	−	17.4719i	−0.171433	−	0.0302283i
$579$	−158.439	+	58.5573i	−0.273642	+	0.101135i
$580$	−67.2564	−	24.4793i	−0.115959	−	0.0422057i
$581$	−201.911	+	554.745i	−0.347523	+	0.954811i
$582$	−288.238	−	49.3533i	−0.495255	−	0.0847994i
$583$	0.339426	−	1.92498i	0.000582206	−	0.00330185i
$584$	−111.226	+	64.2165i	−0.190456	+	0.109960i
$585$	−103.490	−	120.882i	−0.176906	−	0.206636i
$586$	97.0961	−	168.175i	0.165693	−	0.286989i
$587$	−633.940	+	755.500i	−1.07997	+	1.28705i	−0.124414	+	0.992230i	$0.539705\pi$
$587$	−633.940	+	755.500i	−1.07997	+	1.28705i	−0.955552	+	0.294823i	$0.904739\pi$
$588$	−7.74799	−	13.2677i	−0.0131769	−	0.0225641i
$589$	27.4822	+	155.859i	0.0466590	+	0.264617i
$590$	−52.0631	−	62.0464i	−0.0882425	−	0.105163i
$591$	328.544	+	387.628i	0.555912	+	0.655885i
$592$	248.191	−	90.3342i	0.419242	−	0.152592i
$593$			216.884i			0.365741i	0.983137	+	0.182870i	$0.0585388\pi$
$593$			216.884i			0.365741i	−0.983137	+	0.182870i	$0.941461\pi$
$594$	−213.600	+	184.710i	−0.359597	+	0.310960i
$595$	−95.8932			−0.161165
$596$	−22.8378	−	62.7463i	−0.0383184	−	0.105279i
$597$	57.2952	+	315.782i	0.0959719	+	0.528948i
$598$	−496.328	+	416.469i	−0.829981	+	0.696436i
$599$	641.044	−	113.033i	1.07019	−	0.188703i	0.389316	−	0.921104i	$-0.372711\pi$
$599$	641.044	−	113.033i	1.07019	−	0.188703i	0.680874	+	0.732401i	$0.261600\pi$
$600$	178.202	+	101.711i	0.297003	+	0.169519i
$601$	−165.422	−	138.806i	−0.275245	−	0.230958i	0.494707	−	0.869060i	$-0.335275\pi$
$601$	−165.422	−	138.806i	−0.275245	−	0.230958i	−0.769952	+	0.638102i	$0.779720\pi$
$602$	−489.716	−	282.737i	−0.813481	−	0.469663i
$603$	285.547	+	483.457i	0.473545	+	0.801753i
$604$	−143.575	−	248.679i	−0.237707	−	0.411721i
$605$	−59.0820	−	10.4177i	−0.0976562	−	0.0172194i
$606$	579.006	+	480.976i	0.955455	+	0.793690i
$607$	611.890	+	222.710i	1.00806	+	0.366902i	0.792686	−	0.609630i	$-0.208682\pi$
$607$	611.890	+	222.710i	1.00806	+	0.366902i	0.215370	+	0.976532i	$0.430904\pi$
$608$	25.4844	−	70.0177i	0.0419151	−	0.115161i
$609$	544.431	−	655.393i	0.893975	−	1.07618i
$610$	12.3174	−	69.8554i	0.0201925	−	0.114517i
$611$	5.38825	−	3.11091i	0.00881874	−	0.00509150i
$612$	−228.756	+	135.112i	−0.373784	+	0.220771i
$613$	−428.616	+	742.385i	−0.699211	+	1.21107i	0.269529	+	0.962992i	$0.413132\pi$
$613$	−428.616	+	742.385i	−0.699211	+	1.21107i	−0.968740	+	0.248077i	$0.920201\pi$
$614$	329.801	−	393.041i	0.537135	−	0.640132i
$615$	−102.949	+	180.370i	−0.167396	+	0.293284i
$616$	26.0821	+	147.919i	0.0423410	+	0.240128i
$617$	633.317	+	754.757i	1.02645	+	1.22327i	0.974446	+	0.224623i	$0.0721149\pi$
$617$	633.317	+	754.757i	1.02645	+	1.22327i	0.0519994	+	0.998647i	$0.483441\pi$
$618$	71.3105	−	12.9385i	0.115389	−	0.0209361i
$619$	83.7604	−	30.4863i	0.135316	−	0.0492509i	−0.273475	−	0.961879i	$-0.588173\pi$
$619$	83.7604	−	30.4863i	0.135316	−	0.0492509i	0.408790	+	0.912628i	$0.365951\pi$
$620$		−	21.7425i		−	0.0350686i
$621$	207.633	−	597.968i	0.334352	−	0.962912i
$622$	311.479			0.500770
$623$	−327.217	−	899.023i	−0.525229	−	1.44305i
$624$	−178.891	+	151.623i	−0.286684	+	0.242986i
$625$	432.258	−	362.707i	0.691612	−	0.580331i
$626$	−60.4788	+	10.6640i	−0.0966115	+	0.0170352i
$627$	252.358	−	147.371i	0.402485	−	0.235041i
$628$	184.311	+	154.656i	0.293490	+	0.246267i
$629$	844.020	+	487.295i	1.34184	+	0.774715i
$630$	62.8161	−	53.7784i	0.0997080	−	0.0853625i
$631$	71.5623	+	123.950i	0.113411	+	0.196433i	0.917143	−	0.398557i	$-0.130489\pi$
$631$	71.5623	+	123.950i	0.113411	+	0.196433i	−0.803733	+	0.594991i	$0.797156\pi$
$632$	−67.8797	−	11.9690i	−0.107405	−	0.0189383i
$633$	−17.8316	+	104.142i	−0.0281701	+	0.164522i
$634$	161.309	+	58.7116i	0.254430	+	0.0926050i
$635$	16.1386	−	44.3405i	0.0254152	−	0.0698276i
$636$	0.549764	+	1.48750i	0.000864409	+	0.00233883i
$637$	8.68959	−	49.2811i	0.0136414	−	0.0773644i
$638$	−358.248	+	206.835i	−0.561518	+	0.324192i
$639$	585.303	+	97.2359i	0.915967	+	0.152169i
$640$	−5.11825	+	8.86507i	−0.00799727	+	0.0138517i
$641$	−176.476	+	210.316i	−0.275314	+	0.328106i	−0.885929	−	0.463821i	$-0.846478\pi$
$641$	−176.476	+	210.316i	−0.275314	+	0.328106i	0.610615	+	0.791928i	$0.290922\pi$
$642$	123.803	−	0.613277i	0.192839	−	0.000955260i
$643$	−157.474	−	893.080i	−0.244905	−	1.38893i	−0.820713	−	0.571341i	$-0.806423\pi$
$643$	−157.474	−	893.080i	−0.244905	−	1.38893i	0.575807	−	0.817585i	$-0.304688\pi$
$644$	−216.417	−	257.915i	−0.336051	−	0.400490i
$645$	50.9920	−	142.288i	0.0790573	−	0.220602i
$646$	258.363	−	94.0363i	0.399942	−	0.145567i
$647$			766.329i			1.18443i	0.805779	+	0.592217i	$0.201747\pi$
$647$			766.329i			1.18443i	−0.805779	+	0.592217i	$0.798253\pi$
$648$	74.0768	−	216.796i	0.114316	−	0.334562i
$649$	−468.132			−0.721312
$650$	228.567	+	627.983i	0.351642	+	0.966128i
$651$	243.656	+	87.3192i	0.374280	+	0.134131i
$652$	350.136	−	293.799i	0.537018	−	0.450612i
$653$	−491.110	+	86.5959i	−0.752082	+	0.132612i	−0.536532	−	0.843880i	$-0.680266\pi$
$653$	−491.110	+	86.5959i	−0.752082	+	0.132612i	−0.215551	+	0.976493i	$0.569155\pi$
$654$	−3.38610	−	683.555i	−0.00517752	−	1.04519i
$655$	27.4127	+	23.0020i	0.0418514	+	0.0351175i
$656$	265.046	+	153.024i	0.404033	+	0.233269i
$657$	382.622	−	143.572i	0.582377	−	0.218526i
$658$	1.61657	+	2.79999i	0.00245680	+	0.00425530i
$659$	−987.874	−	174.189i	−1.49905	−	0.264323i	−0.636888	−	0.770956i	$-0.719779\pi$
$659$	−987.874	−	174.189i	−1.49905	−	0.264323i	−0.862162	+	0.506633i	$0.830890\pi$
$660$	−37.6584	+	13.9182i	−0.0570582	+	0.0210882i
$661$	−40.4553	−	14.7245i	−0.0612032	−	0.0222761i	0.311237	−	0.950332i	$-0.399257\pi$
$661$	−40.4553	−	14.7245i	−0.0612032	−	0.0222761i	−0.372440	+	0.928056i	$0.621479\pi$
$662$	67.2780	−	184.845i	0.101628	−	0.279222i
$663$	−852.893	−	146.036i	−1.28642	−	0.220265i
$664$	−40.3797	+	229.005i	−0.0608129	+	0.344887i
$665$	−74.1112	+	42.7881i	−0.111445	+	0.0643430i
$666$	−826.169	+	154.130i	−1.24049	+	0.231427i
$667$	463.634	−	803.037i	0.695103	−	1.20395i
$668$	−249.816	+	297.720i	−0.373977	+	0.445688i
$669$	−163.917	−	280.692i	−0.245018	−	0.419570i
$670$	13.8621	+	78.6159i	0.0206897	+	0.117337i
$671$	−263.525	−	314.057i	−0.392735	−	0.468043i
$672$	−78.7906	−	92.9599i	−0.117248	−	0.138333i
$673$	−254.900	+	92.7760i	−0.378752	+	0.137854i	−0.524379	−	0.851485i	$-0.675702\pi$
$673$	−254.900	+	92.7760i	−0.378752	+	0.137854i	0.145627	+	0.989340i	$0.453480\pi$
$674$		−	34.2857i		−	0.0508689i
$675$	−506.329	−	412.195i	−0.750117	−	0.610660i
$676$	−425.770			−0.629838
$677$	332.978	+	914.850i	0.491844	+	1.35133i	0.898991	+	0.437967i	$0.144301\pi$
$677$	332.978	+	914.850i	0.491844	+	1.35133i	−0.407147	+	0.913362i	$0.633476\pi$
$678$	51.2512	+	282.470i	0.0755917	+	0.416623i
$679$	379.144	−	318.139i	0.558385	−	0.468541i
$680$	−37.1985	+	6.55909i	−0.0547036	+	0.00964572i
$681$	−590.999	−	337.321i	−0.867839	−	0.495332i
$682$	−96.2654	−	80.7762i	−0.141152	−	0.118440i
$683$	−1043.61	−	602.531i	−1.52799	−	0.882183i	−0.999446	−	0.0332748i	$-0.989406\pi$
$683$	−1043.61	−	602.531i	−1.52799	−	0.882183i	−0.528540	−	0.848908i	$-0.677260\pi$
$684$	−116.507	+	206.493i	−0.170331	+	0.301891i
$685$	−19.4629	−	33.7107i	−0.0284130	−	0.0492127i
$686$	−464.421	−	81.8899i	−0.676998	−	0.119373i
$687$	−484.722	−	402.656i	−0.705564	−	0.586107i
$688$	−209.307	−	76.1817i	−0.304226	−	0.110729i
$689$	−1.76655	+	4.85355i	−0.00256393	+	0.00704435i
$690$	57.5052	−	69.2256i	0.0833409	−	0.100327i
$691$	44.6727	−	253.352i	0.0646494	−	0.366645i	−0.935270	−	0.353935i	$-0.884843\pi$
$691$	44.6727	−	253.352i	0.0646494	−	0.366645i	0.999919	−	0.0127094i	$-0.00404563\pi$
$692$	212.635	−	122.765i	0.307275	−	0.177406i
$693$	−4.73494	−	477.912i	−0.00683253	−	0.689628i
$694$	180.322	−	312.326i	0.259829	−	0.450038i
$695$	139.836	−	166.651i	0.201204	−	0.239785i
$696$	166.364	−	291.476i	0.239029	−	0.418788i
$697$	196.102	+	1112.15i	0.281352	+	1.59563i
$698$	569.090	+	678.215i	0.815315	+	0.971655i
$699$	123.345	−	22.3796i	0.176459	−	0.0320166i
$700$	−326.329	+	118.774i	−0.466185	+	0.169677i
$701$			357.086i			0.509395i	0.967021	+	0.254697i	$0.0819759\pi$
$701$			357.086i			0.509395i	−0.967021	+	0.254697i	$0.918024\pi$
$702$	640.597	−	382.653i	0.912532	−	0.545090i
$703$	869.736			1.23718
$704$	20.2353	+	55.5959i	0.0287433	+	0.0789715i
$705$	−0.659263	+	0.558775i	−0.000935124	+	0.000792589i
$706$	−145.264	+	121.891i	−0.205756	+	0.172650i
$707$	−1254.61	+	221.221i	−1.77455	+	0.312901i
$708$	327.969	−	191.526i	0.463234	−	0.270516i
$709$	137.566	+	115.432i	0.194029	+	0.162809i	0.734626	−	0.678472i	$-0.237357\pi$
$709$	137.566	+	115.432i	0.194029	+	0.162809i	−0.540598	+	0.841281i	$0.681802\pi$
$710$	73.0537	+	42.1776i	0.102893	+	0.0594050i
$711$	206.830	+	72.9677i	0.290900	+	0.102627i
$712$	−188.426	−	326.363i	−0.264643	−	0.458375i
$713$	277.408	+	48.9145i	0.389072	+	0.0686038i
$714$	75.8869	−	443.203i	0.106284	−	0.620733i
$715$	−122.876	−	44.7231i	−0.171854	−	0.0625498i
$716$	199.048	−	546.879i	0.277999	−	0.763797i
$717$	387.901	+	1049.54i	0.541006	+	1.46380i
$718$	136.283	−	772.897i	0.189809	−	1.07646i
$719$	768.741	−	443.833i	1.06918	−	0.617292i	0.141223	−	0.989978i	$-0.454897\pi$
$719$	768.741	−	443.833i	1.06918	−	0.617292i	0.927957	+	0.372686i	$0.121563\pi$
$720$	20.6889	−	25.1581i	0.0287346	−	0.0349418i
$721$	−61.3310	+	106.228i	−0.0850638	+	0.147335i
$722$	−170.447	+	203.131i	−0.236076	+	0.281344i
$723$	−348.374	+	1.72572i	−0.481845	+	0.00238689i
$724$	77.6001	+	440.092i	0.107182	+	0.607862i
$725$	−614.780	−	732.666i	−0.847972	−	1.01057i
$726$	94.9048	−	264.823i	0.130723	−	0.364770i
$727$	−822.255	+	299.276i	−1.13103	+	0.411659i	−0.838664	−	0.544649i	$-0.816663\pi$
$727$	−822.255	+	299.276i	−1.13103	+	0.411659i	−0.292361	+	0.956308i	$0.594441\pi$
$728$		−	396.891i		−	0.545179i
$729$	−345.577	+	641.886i	−0.474043	+	0.880502i
$730$	58.1023			0.0795922
$731$	−281.107	−	772.336i	−0.384552	−	1.05655i
$732$	313.113	+	112.210i	0.427750	+	0.153293i
$733$	22.5932	−	18.9579i	0.0308229	−	0.0258634i	−0.627246	−	0.778821i	$-0.715818\pi$
$733$	22.5932	−	18.9579i	0.0308229	−	0.0258634i	0.658069	+	0.752958i	$0.271374\pi$
$734$	252.569	−	44.5348i	0.344100	−	0.0606741i
$735$	0.0344311	+	6.95065i	4.68451e−5	+	0.00945666i
$736$	−101.593	−	85.2464i	−0.138034	−	0.115824i
$737$	399.572	+	230.693i	0.542161	+	0.313017i
$738$	−752.170	−	618.551i	−1.01920	−	0.838146i
$739$	589.760	+	1021.50i	0.798052	+	1.38227i	0.920883	+	0.389839i	$0.127469\pi$
$739$	589.760	+	1021.50i	0.798052	+	1.38227i	−0.122831	+	0.992428i	$0.539197\pi$
$740$	−117.671	−	20.7485i	−0.159015	−	0.0280386i
$741$	−724.322	+	267.702i	−0.977492	+	0.361272i
$742$	−2.52213	−	0.917982i	−0.00339910	−	0.00123717i
$743$	−178.261	+	489.768i	−0.239921	+	0.659176i	0.760036	+	0.649881i	$0.225181\pi$
$743$	−178.261	+	489.768i	−0.239921	+	0.659176i	−0.999957	+	0.00929571i	$0.997041\pi$
$744$	100.491	+	17.2064i	0.135068	+	0.0231268i
$745$	−5.24553	+	29.7489i	−0.00704097	+	0.0399313i
$746$	−435.539	+	251.458i	−0.583832	+	0.337076i
$747$	246.170	−	697.780i	0.329545	−	0.934110i
$748$	−109.156	+	189.064i	−0.145931	+	0.252760i
$749$	−134.687	+	160.514i	−0.179823	+	0.214305i
$750$	−95.2047	−	163.029i	−0.126940	−	0.217372i
$751$	11.9742	+	67.9089i	0.0159443	+	0.0904246i	0.991742	−	0.128253i	$-0.0409369\pi$
$751$	11.9742	+	67.9089i	0.0159443	+	0.0904246i	−0.975797	+	0.218677i	$0.929826\pi$
$752$	0.818613	+	0.975585i	0.00108858	+	0.00129732i
$753$	−358.818	−	423.346i	−0.476518	−	0.562212i
$754$	1027.16	−	373.856i	1.36228	−	0.495830i
$755$			129.905i			0.172059i
$756$	198.844	+	332.884i	0.263022	+	0.440323i
$757$	376.111			0.496845			0.248422	−	0.968652i	$-0.420088\pi$
$757$	376.111			0.496845			0.248422	+	0.968652i	$0.420088\pi$
$758$	276.480	+	759.622i	0.364749	+	1.00214i
$759$	−92.8581	−	511.787i	−0.122343	−	0.674291i
$760$	−25.8222	+	21.6674i	−0.0339765	+	0.0285097i
$761$	−21.1240	+	3.72472i	−0.0277582	+	0.00489451i	−0.187510	−	0.982263i	$-0.560042\pi$
$761$	−21.1240	+	3.72472i	−0.0277582	+	0.00489451i	0.159752	+	0.987157i	$0.448931\pi$
$762$	192.163	+	109.680i	0.252183	+	0.143937i
$763$	886.250	+	743.652i	1.16153	+	0.974642i
$764$	−510.210	−	294.570i	−0.667814	−	0.385563i
$765$	120.185	−	1.19074i	0.157104	−	0.00155652i
$766$	294.539	+	510.156i

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)

\(f(q)\)	\(=\)	\(q+(0.483690 + 1.32893i) q^{2} +(2.82413 + 1.01208i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(0.891042 - 0.157115i) q^{5} +(0.0210163 + 4.24259i) q^{6} +(-5.50064 - 4.61559i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(6.95137 + 5.71650i) q^{9} +O(q^{10})\)	\(q+(0.483690 + 1.32893i) q^{2} +(2.82413 + 1.01208i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(0.891042 - 0.157115i) q^{5} +(0.0210163 + 4.24259i) q^{6} +(-5.50064 - 4.61559i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(6.95137 + 5.71650i) q^{9} +(0.639781 + 1.10813i) q^{10} +(7.28314 + 1.28421i) q^{11} +(-5.62792 + 2.08002i) q^{12} +(-18.3634 - 6.68372i) q^{13} +(3.47317 - 9.54246i) q^{14} +(2.67543 + 0.458097i) q^{15} +(0.694593 - 3.93923i) q^{16} +(12.7824 - 7.37992i) q^{17} +(-4.23450 + 12.0029i) q^{18} +(6.58593 - 11.4072i) q^{19} +(-1.16317 + 1.38621i) q^{20} +(-10.8632 - 18.6021i) q^{21} +(1.81615 + 10.2999i) q^{22} +(-15.0696 - 17.9592i) q^{23} +(-5.48637 - 6.47300i) q^{24} +(-22.7230 + 8.27051i) q^{25} -27.6364i q^{26} +(13.8460 + 23.1795i) q^{27} +14.3612 q^{28} +(13.5277 + 37.1670i) q^{29} +(0.685300 + 3.77702i) q^{30} +(-9.20424 + 7.72327i) q^{31} +(5.57091 - 0.982302i) q^{32} +(19.2688 + 10.9979i) q^{33} +(15.9901 + 13.4173i) q^{34} +(-5.62648 - 3.24845i) q^{35} +(-17.9991 + 0.178327i) q^{36} +(33.0149 + 57.1836i) q^{37} +(18.3448 + 3.23469i) q^{38} +(-45.0960 - 37.4609i) q^{39} +(-2.40479 - 0.875273i) q^{40} +(-26.1687 + 71.8979i) q^{41} +(19.4664 - 23.4340i) q^{42} +(9.66961 - 54.8391i) q^{43} +(-12.8094 + 7.39550i) q^{44} +(7.09211 + 4.00148i) q^{45} +(16.5775 - 28.7131i) q^{46} +(-0.204653 + 0.243896i) q^{47} +(5.94845 - 10.4219i) q^{48} +(0.444665 + 2.52182i) q^{49} +(-21.9818 - 26.1969i) q^{50} +(43.5682 - 7.90498i) q^{51} +(36.7267 - 13.3674i) q^{52} -0.264306i q^{53} +(-24.1067 + 29.6120i) q^{54} +6.69135 q^{55} +(6.94634 + 19.0849i) q^{56} +(30.1445 - 25.5498i) q^{57} +(-42.8490 + 35.9545i) q^{58} +(-62.3379 + 10.9919i) q^{59} +(-4.68791 + 2.73762i) q^{60} +(-42.4660 - 35.6332i) q^{61} +(-14.7157 - 8.49608i) q^{62} +(-11.8520 - 63.5291i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-17.4126 - 3.07032i) q^{65} +(-5.29533 + 30.9264i) q^{66} +(58.6251 + 21.3378i) q^{67} +(-10.0963 + 27.7394i) q^{68} +(-24.3822 - 65.9708i) q^{69} +(1.59548 - 9.04842i) q^{70} +(57.0927 - 32.9625i) q^{71} +(-8.94297 - 23.8332i) q^{72} +(22.7040 - 39.3244i) q^{73} +(-60.0237 + 71.5335i) q^{74} +(-72.5432 + 0.359354i) q^{75} +(4.57454 + 25.9435i) q^{76} +(-34.1346 - 40.6800i) q^{77} +(27.9703 - 78.0487i) q^{78} +(22.8997 - 8.33480i) q^{79} -3.61915i q^{80} +(15.6432 + 79.4751i) q^{81} -108.205 q^{82} +(-28.1190 - 77.2563i) q^{83} +(40.5577 + 14.5347i) q^{84} +(10.2302 - 8.58412i) q^{85} +(77.5542 - 13.6749i) q^{86} +(0.587778 + 118.655i) q^{87} +(-16.0238 - 13.4456i) q^{88} +(115.387 + 66.6186i) q^{89} +(-1.88729 + 11.3604i) q^{90} +(70.1610 + 121.522i) q^{91} +(46.1759 + 8.14205i) q^{92} +(-33.8105 + 12.4960i) q^{93} +(-0.423109 - 0.153999i) q^{94} +(4.07611 - 11.1990i) q^{95} +(16.7271 + 2.86408i) q^{96} +(-11.9691 + 67.8800i) q^{97} +(-3.13623 + 1.81071i) q^{98} +(43.2866 + 50.5611i) 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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