LMFDB - Embedded newform 54.3.f.a.11.1

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			11.1
Character	$\chi$	$=$	54.11
Dual form			54.3.f.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909039 + 1.08335i) q^{2} +(-1.44503 - 2.62905i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(0.696976 - 1.91493i) q^{5} +(4.16177 + 0.824439i) q^{6} +(2.23222 - 12.6596i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-4.82380 + 7.59809i) q^{9} +O(q^{10})$	\(q+(-0.909039 + 1.08335i) q^{2} +(-1.44503 - 2.62905i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(0.696976 - 1.91493i) q^{5} +(4.16177 + 0.824439i) q^{6} +(2.23222 - 12.6596i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-4.82380 + 7.59809i) q^{9} +(1.44096 + 2.49581i) q^{10} +(1.28270 + 3.52418i) q^{11} +(-4.67636 + 3.75920i) q^{12} +(6.69534 - 5.61806i) q^{13} +(11.6856 + 13.9263i) q^{14} +(-6.04158 + 0.934733i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(-20.4462 + 11.8046i) q^{17} +(-3.84637 - 12.1328i) q^{18} +(-2.58391 + 4.47546i) q^{19} +(-4.01373 - 0.707728i) q^{20} +(-36.5082 + 12.4248i) q^{21} +(-4.98394 - 1.81401i) q^{22} +(34.3001 - 6.04803i) q^{23} +(0.178462 - 8.48340i) q^{24} +(15.9699 + 13.4004i) q^{25} +12.3604i q^{26} +(26.9463 + 1.70258i) q^{27} -25.7097 q^{28} +(18.1485 - 21.6285i) q^{29} +(4.47939 - 7.39486i) q^{30} +(-0.600583 - 3.40608i) q^{31} +(1.93476 - 5.31570i) q^{32} +(7.41171 - 8.46479i) q^{33} +(5.79786 - 32.8813i) q^{34} +(-22.6863 - 13.0979i) q^{35} +(16.6406 + 6.86225i) q^{36} +(27.7928 + 48.1386i) q^{37} +(-2.49962 - 6.86765i) q^{38} +(-24.4451 - 9.48415i) q^{39} +(4.41535 - 3.70492i) q^{40} +(-10.1636 - 12.1124i) q^{41} +(19.7270 - 50.8458i) q^{42} +(49.2717 - 17.9334i) q^{43} +(6.49580 - 3.75035i) q^{44} +(11.1877 + 14.5329i) q^{45} +(-24.6280 + 42.6569i) q^{46} +(-53.2114 - 9.38261i) q^{47} +(9.02827 + 7.90508i) q^{48} +(-109.237 - 39.7589i) q^{49} +(-29.0346 + 5.11958i) q^{50} +(60.5802 + 36.6961i) q^{51} +(-13.3907 - 11.2361i) q^{52} +0.286719i q^{53} +(-26.3397 + 27.6445i) q^{54} +7.64255 q^{55} +(23.3711 - 27.8526i) q^{56} +(15.5000 + 0.326068i) q^{57} +(6.93358 + 39.3223i) q^{58} +(3.64869 - 10.0247i) q^{59} +(3.93928 + 11.5750i) q^{60} +(-16.4195 + 93.1195i) q^{61} +(4.23593 + 2.44561i) q^{62} +(85.4206 + 78.0278i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-6.09168 - 16.7367i) q^{65} +(2.43281 + 15.7243i) q^{66} +(16.2682 - 13.6506i) q^{67} +(30.3515 + 36.1715i) q^{68} +(-65.4651 - 81.4371i) q^{69} +(34.8124 - 12.6707i) q^{70} +(-89.4087 + 51.6201i) q^{71} +(-22.5612 + 11.7896i) q^{72} +(11.9742 - 20.7399i) q^{73} +(-77.4157 - 13.6505i) q^{74} +(12.1533 - 61.3497i) q^{75} +(9.71232 + 3.53500i) q^{76} +(47.4778 - 8.37161i) q^{77} +(32.4962 - 17.8611i) q^{78} +(-9.54529 - 8.00945i) q^{79} +8.15129i q^{80} +(-34.4619 - 73.3033i) q^{81} +22.3611 q^{82} +(46.6451 - 55.5895i) q^{83} +(37.1512 + 67.5921i) q^{84} +(8.35446 + 47.3805i) q^{85} +(-25.3617 + 69.6807i) q^{86} +(-83.0873 - 16.4595i) q^{87} +(-1.84199 + 10.4464i) q^{88} +(56.5926 + 32.6737i) q^{89} +(-25.9143 - 1.09078i) q^{90} +(-56.1766 - 97.3008i) q^{91} +(-23.8246 - 65.4576i) q^{92} +(-8.08688 + 6.50083i) q^{93} +(58.5359 - 49.1175i) q^{94} +(6.76926 + 8.06729i) q^{95} +(-16.7710 + 2.59475i) q^{96} +(-31.7241 + 11.5466i) q^{97} +(142.373 - 82.1991i) q^{98} +(-32.9645 - 7.25390i) 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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−0.909039	+	1.08335i	−0.454519	+	0.541675i
$2$	−0.909039	+	1.08335i	−0.454519	+	0.541675i
$3$	−1.44503	−	2.62905i	−0.481675	−	0.876350i
$3$	−1.44503	−	2.62905i	−0.481675	−	0.876350i
$4$	−0.347296	−	1.96962i	−0.0868241	−	0.492404i
$5$	0.696976	−	1.91493i	0.139395	−	0.382985i	−0.850277	−	0.526336i	$-0.823565\pi$
$5$	0.696976	−	1.91493i	0.139395	−	0.382985i	0.989672	+	0.143351i	$0.0457877\pi$
$6$	4.16177	+	0.824439i	0.693628	+	0.137407i
$7$	2.23222	−	12.6596i	0.318889	−	1.80851i	−0.230647	−	0.973037i	$-0.574084\pi$
$7$	2.23222	−	12.6596i	0.318889	−	1.80851i	0.549536	−	0.835470i	$-0.314805\pi$
$8$	2.44949	+	1.41421i	0.306186	+	0.176777i
$9$	−4.82380	+	7.59809i	−0.535978	+	0.844232i
$10$	1.44096	+	2.49581i	0.144096	+	0.249581i
$11$	1.28270	+	3.52418i	0.116609	+	0.320380i	0.984242	−	0.176824i	$-0.0565824\pi$
$11$	1.28270	+	3.52418i	0.116609	+	0.320380i	−0.867634	+	0.497204i	$0.834360\pi$
$12$	−4.67636	+	3.75920i	−0.389697	+	0.313267i
$13$	6.69534	−	5.61806i	0.515026	−	0.432158i	−0.347867	−	0.937544i	$-0.613094\pi$
$13$	6.69534	−	5.61806i	0.515026	−	0.432158i	0.862894	+	0.505385i	$0.168650\pi$
$14$	11.6856	+	13.9263i	0.834683	+	0.994736i
$15$	−6.04158	+	0.934733i	−0.402772	+	0.0623155i
$16$	−3.75877	+	1.36808i	−0.234923	+	0.0855050i
$17$	−20.4462	+	11.8046i	−1.20272	+	0.694390i	−0.961159	−	0.275996i	$-0.910992\pi$
$17$	−20.4462	+	11.8046i	−1.20272	+	0.694390i	−0.241560	+	0.970386i	$0.577659\pi$
$18$	−3.84637	−	12.1328i	−0.213687	−	0.674046i
$19$	−2.58391	+	4.47546i	−0.135995	+	0.235551i	−0.925977	−	0.377579i	$-0.876757\pi$
$19$	−2.58391	+	4.47546i	−0.135995	+	0.235551i	0.789982	+	0.613130i	$0.210090\pi$
$20$	−4.01373	−	0.707728i	−0.200686	−	0.0353864i
$21$	−36.5082	+	12.4248i	−1.73849	+	0.591655i
$22$	−4.98394	−	1.81401i	−0.226543	−	0.0824548i
$23$	34.3001	−	6.04803i	1.49131	−	0.262958i	0.632222	−	0.774787i	$-0.282143\pi$
$23$	34.3001	−	6.04803i	1.49131	−	0.262958i	0.859087	+	0.511829i	$0.171032\pi$
$24$	0.178462	−	8.48340i	0.00743592	−	0.353475i
$25$	15.9699	+	13.4004i	0.638798	+	0.536015i
$26$			12.3604i			0.475401i
$27$	26.9463	+	1.70258i	0.998010	+	0.0630587i
$28$	−25.7097			−0.918203
$29$	18.1485	−	21.6285i	0.625809	−	0.745810i	−0.356249	−	0.934391i	$-0.615944\pi$
$29$	18.1485	−	21.6285i	0.625809	−	0.745810i	0.982058	+	0.188581i	$0.0603889\pi$
$30$	4.47939	−	7.39486i	0.149313	−	0.246495i
$31$	−0.600583	−	3.40608i	−0.0193736	−	0.109873i	0.973587	−	0.228314i	$-0.0733214\pi$
$31$	−0.600583	−	3.40608i	−0.0193736	−	0.109873i	−0.992961	+	0.118441i	$0.962210\pi$
$32$	1.93476	−	5.31570i	0.0604612	−	0.166116i
$33$	7.41171	−	8.46479i	0.224597	−	0.256509i
$34$	5.79786	−	32.8813i	0.170525	−	0.967096i
$35$	−22.6863	−	13.0979i	−0.648180	−	0.374227i
$36$	16.6406	+	6.86225i	0.462239	+	0.190618i
$37$	27.7928	+	48.1386i	0.751158	+	1.30104i	0.947262	+	0.320460i	$0.103838\pi$
$37$	27.7928	+	48.1386i	0.751158	+	1.30104i	−0.196104	+	0.980583i	$0.562829\pi$
$38$	−2.49962	−	6.86765i	−0.0657795	−	0.180728i
$39$	−24.4451	−	9.48415i	−0.626797	−	0.243183i
$40$	4.41535	−	3.70492i	0.110384	−	0.0926230i
$41$	−10.1636	−	12.1124i	−0.247891	−	0.295426i	0.627722	−	0.778437i	$-0.283987\pi$
$41$	−10.1636	−	12.1124i	−0.247891	−	0.295426i	−0.875614	+	0.483012i	$0.839543\pi$
$42$	19.7270	−	50.8458i	0.469691	−	1.21061i
$43$	49.2717	−	17.9334i	1.14585	−	0.417057i	0.301830	−	0.953362i	$-0.402403\pi$
$43$	49.2717	−	17.9334i	1.14585	−	0.417057i	0.844024	+	0.536305i	$0.180180\pi$
$44$	6.49580	−	3.75035i	0.147632	−	0.0852352i
$45$	11.1877	+	14.5329i	0.248616	+	0.322954i
$46$	−24.6280	+	42.6569i	−0.535391	+	0.927325i
$47$	−53.2114	−	9.38261i	−1.13216	−	0.199630i	−0.423985	−	0.905669i	$-0.639369\pi$
$47$	−53.2114	−	9.38261i	−1.13216	−	0.199630i	−0.708173	+	0.706039i	$0.750480\pi$
$48$	9.02827	+	7.90508i	0.188089	+	0.164689i
$49$	−109.237	−	39.7589i	−2.22932	−	0.811405i
$50$	−29.0346	+	5.11958i	−0.580692	+	0.102392i
$51$	60.5802	+	36.6961i	1.18785	+	0.719532i
$52$	−13.3907	−	11.2361i	−0.257513	−	0.216079i
$53$			0.286719i			0.00540979i	0.999996	+	0.00270489i	$0.000860996\pi$
$53$			0.286719i			0.00540979i	−0.999996	+	0.00270489i	$0.999139\pi$
$54$	−26.3397	+	27.6445i	−0.487772	+	0.511936i
$55$	7.64255			0.138955
$56$	23.3711	−	27.8526i	0.417341	−	0.497368i
$57$	15.5000	+	0.326068i	0.271930	+	0.00572050i
$58$	6.93358	+	39.3223i	0.119544	+	0.677970i
$59$	3.64869	−	10.0247i	0.0618421	−	0.169910i	−0.904923	−	0.425574i	$-0.860072\pi$
$59$	3.64869	−	10.0247i	0.0618421	−	0.169910i	0.966766	+	0.255665i	$0.0822943\pi$
$60$	3.93928	+	11.5750i	0.0656547	+	0.192916i
$61$	−16.4195	+	93.1195i	−0.269172	+	1.52655i	0.487714	+	0.873003i	$0.337831\pi$
$61$	−16.4195	+	93.1195i	−0.269172	+	1.52655i	−0.756886	+	0.653546i	$0.773280\pi$
$62$	4.23593	+	2.44561i	0.0683214	+	0.0394454i
$63$	85.4206	+	78.0278i	1.35588	+	1.23854i
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	−6.09168	−	16.7367i	−0.0937181	−	0.257488i
$66$	2.43281	+	15.7243i	0.0368607	+	0.238247i
$67$	16.2682	−	13.6506i	0.242809	−	0.203741i	−0.513260	−	0.858233i	$-0.671562\pi$
$67$	16.2682	−	13.6506i	0.242809	−	0.203741i	0.756068	+	0.654493i	$0.227118\pi$
$68$	30.3515	+	36.1715i	0.446345	+	0.531933i
$69$	−65.4651	−	81.4371i	−0.948770	−	1.18025i
$70$	34.8124	−	12.6707i	0.497320	−	0.181010i
$71$	−89.4087	+	51.6201i	−1.25928	+	0.727044i	−0.972934	−	0.231083i	$-0.925773\pi$
$71$	−89.4087	+	51.6201i	−1.25928	+	0.727044i	−0.286343	+	0.958127i	$0.592440\pi$
$72$	−22.5612	+	11.7896i	−0.313350	+	0.163744i
$73$	11.9742	−	20.7399i	0.164030	−	0.284108i	−0.772280	−	0.635282i	$-0.780884\pi$
$73$	11.9742	−	20.7399i	0.164030	−	0.284108i	0.936310	+	0.351174i	$0.114217\pi$
$74$	−77.4157	−	13.6505i	−1.04616	−	0.184466i
$75$	12.1533	−	61.3497i	0.162044	−	0.817995i
$76$	9.71232	+	3.53500i	0.127794	+	0.0465131i
$77$	47.4778	−	8.37161i	0.616594	−	0.108722i
$78$	32.4962	−	17.8611i	0.416618	−	0.228989i
$79$	−9.54529	−	8.00945i	−0.120826	−	0.101385i	0.580372	−	0.814351i	$-0.302907\pi$
$79$	−9.54529	−	8.00945i	−0.120826	−	0.101385i	−0.701199	+	0.712966i	$0.747351\pi$
$80$			8.15129i			0.101891i
$81$	−34.4619	−	73.3033i	−0.425455	−	0.904980i
$82$	22.3611			0.272696
$83$	46.6451	−	55.5895i	0.561990	−	0.669753i	−0.407977	−	0.912992i	$-0.633766\pi$
$83$	46.6451	−	55.5895i	0.561990	−	0.669753i	0.969966	+	0.243239i	$0.0782100\pi$
$84$	37.1512	+	67.5921i	0.442276	+	0.804667i
$85$	8.35446	+	47.3805i	0.0982878	+	0.557418i
$86$	−25.3617	+	69.6807i	−0.294904	+	0.810241i
$87$	−83.0873	−	16.4595i	−0.955027	−	0.189189i
$88$	−1.84199	+	10.4464i	−0.0209317	+	0.118710i
$89$	56.5926	+	32.6737i	0.635871	+	0.367121i	0.783022	−	0.621993i	$-0.213677\pi$
$89$	56.5926	+	32.6737i	0.635871	+	0.367121i	−0.147151	+	0.989114i	$0.547010\pi$
$90$	−25.9143	−	1.09078i	−0.287937	−	0.0121198i
$91$	−56.1766	−	97.3008i	−0.617326	−	1.06924i
$92$	−23.8246	−	65.4576i	−0.258963	−	0.711495i
$93$	−8.08688	+	6.50083i	−0.0869557	+	0.0699014i
$94$	58.5359	−	49.1175i	0.622722	−	0.522526i
$95$	6.76926	+	8.06729i	0.0712553	+	0.0849188i
$96$	−16.7710	+	2.59475i	−0.174698	+	0.0270287i
$97$	−31.7241	+	11.5466i	−0.327053	+	0.119037i	−0.500328	−	0.865836i	$-0.666787\pi$
$97$	−31.7241	+	11.5466i	−0.327053	+	0.119037i	0.173275	+	0.984873i	$0.444565\pi$
$98$	142.373	−	82.1991i	1.45279	−	0.838767i
$99$	−32.9645	−	7.25390i	−0.332974	−	0.0732717i
$100$	20.8473	−	36.1086i	0.208473	−	0.361086i
$101$	120.691	+	21.2810i	1.19496	+	0.210703i	0.735518	−	0.677505i	$-0.236939\pi$
$101$	120.691	+	21.2810i	1.19496	+	0.210703i	0.459440	+	0.888209i	$0.348050\pi$
$102$	−94.8245	+	32.2714i	−0.929652	+	0.316387i
$103$	−117.259	−	42.6789i	−1.13844	−	0.414358i	−0.297090	−	0.954850i	$-0.596016\pi$
$103$	−117.259	−	42.6789i	−1.13844	−	0.414358i	−0.841349	+	0.540492i	$0.818238\pi$
$104$	24.3453	−	4.29273i	0.234090	−	0.0412763i
$105$	−1.65285	+	78.5703i	−0.0157415	+	0.748288i
$106$	−0.310617	−	0.260639i	−0.00293035	−	0.00245885i
$107$			85.6184i			0.800172i	0.916478	+	0.400086i	$0.131020\pi$
$107$			85.6184i			0.800172i	−0.916478	+	0.400086i	$0.868980\pi$
$108$	−6.00490	−	53.6651i	−0.0556009	−	0.496899i
$109$	89.8028			0.823879			0.411940	−	0.911211i	$-0.364851\pi$
$109$	89.8028			0.823879			0.411940	+	0.911211i	$0.364851\pi$
$110$	−6.94737	+	8.27956i	−0.0631579	+	0.0752687i
$111$	86.3974	−	142.630i	0.778355	−	1.28496i
$112$	8.92888	+	50.6382i	0.0797222	+	0.452127i
$113$	18.1968	−	49.9953i	0.161034	−	0.442436i	−0.832766	−	0.553626i	$-0.813244\pi$
$113$	18.1968	−	49.9953i	0.161034	−	0.442436i	0.993799	+	0.111189i	$0.0354660\pi$
$114$	−14.4434	+	16.4956i	−0.126696	+	0.144698i
$115$	12.3248	−	69.8975i	0.107172	−	0.607804i
$116$	−48.9027	−	28.2340i	−0.421575	−	0.243396i
$117$	10.3895	+	77.9722i	0.0887991	+	0.666429i
$118$	7.54345	+	13.0656i	0.0639275	+	0.110726i
$119$	103.801	+	285.190i	0.872276	+	2.39656i
$120$	−16.1207	−	6.25447i	−0.134339	−	0.0521206i
$121$	81.9169	−	68.7364i	0.676999	−	0.568070i
$122$	−85.9551	−	102.437i	−0.704550	−	0.839650i
$123$	−17.1576	+	44.2233i	−0.139493	+	0.359539i
$124$	−6.50008	+	2.36584i	−0.0524200	+	0.0190793i
$125$	80.9115	−	46.7143i	0.647292	−	0.373714i
$126$	−162.182	+	21.6101i	−1.28716	+	0.171509i
$127$	32.5765	−	56.4241i	0.256508	−	0.444284i	−0.708796	−	0.705413i	$-0.750761\pi$
$127$	32.5765	−	56.4241i	0.256508	−	0.444284i	0.965304	+	0.261129i	$0.0840948\pi$
$128$	−11.1418	−	1.96460i	−0.0870455	−	0.0153485i
$129$	−118.347	−	103.624i	−0.917417	−	0.803283i
$130$	23.6693	+	8.61493i	0.182072	+	0.0662687i
$131$	−240.545	+	42.4145i	−1.83622	+	0.323775i	−0.980928	−	0.194372i	$-0.937733\pi$
$131$	−240.545	+	42.4145i	−1.83622	+	0.323775i	−0.855291	+	0.518147i	$0.826622\pi$
$132$	−19.2464	−	11.6584i	−0.145806	−	0.0883214i
$133$	50.8895	+	42.7014i	0.382628	+	0.321063i
$134$			30.0331i			0.224127i
$135$	22.0412	−	50.4135i	0.163268	−	0.373433i
$136$	−66.7770			−0.491008
$137$	−128.507	+	153.149i	−0.938009	+	1.11788i	0.0548401	+	0.998495i	$0.482535\pi$
$137$	−128.507	+	153.149i	−0.938009	+	1.11788i	−0.992849	+	0.119380i	$0.961909\pi$
$138$	147.735	+	3.10785i	1.07055	+	0.0225207i
$139$	30.1070	+	170.745i	0.216597	+	1.22838i	0.878113	+	0.478453i	$0.158802\pi$
$139$	30.1070	+	170.745i	0.216597	+	1.22838i	−0.661516	+	0.749931i	$0.730086\pi$
$140$	−17.9190	+	49.2322i	−0.127993	+	0.351658i
$141$	52.2245	+	153.454i	0.370387	+	1.08832i
$142$	25.3533	−	143.786i	0.178544	−	1.01257i
$143$	28.3871	+	16.3893i	0.198511	+	0.114611i
$144$	7.73677	−	35.1588i	0.0537276	−	0.244158i
$145$	−28.7679	−	49.8275i	−0.198399	−	0.343638i
$146$	11.5836	+	31.8256i	0.0793395	+	0.217984i
$147$	53.3216	+	344.641i	0.362732	+	2.34450i
$148$	85.1622	−	71.4596i	0.575420	−	0.482835i
$149$	51.4192	+	61.2791i	0.345096	+	0.411269i	0.910476	−	0.413561i	$-0.135715\pi$
$149$	51.4192	+	61.2791i	0.345096	+	0.411269i	−0.565381	+	0.824830i	$0.691271\pi$
$150$	55.4154	+	68.9355i	0.369436	+	0.459570i
$151$	−254.454	+	92.6135i	−1.68512	+	0.613335i	−0.993998	−	0.109400i	$-0.965107\pi$
$151$	−254.454	+	92.6135i	−1.68512	+	0.613335i	−0.691125	+	0.722735i	$0.742885\pi$
$152$	−12.6585	+	7.30840i	−0.0832797	+	0.0480816i
$153$	8.93590	−	212.295i	0.0584046	−	1.38755i
$154$	−34.0897	+	59.0452i	−0.221362	+	0.383410i
$155$	−6.94098	−	1.22388i	−0.0447805	−	0.00789601i
$156$	−10.1904	+	51.4413i	−0.0653233	+	0.329752i
$157$	−1.92768	−	0.701618i	−0.0122782	−	0.00446891i	0.335874	−	0.941907i	$-0.390968\pi$
$157$	−1.92768	−	0.701618i	−0.0122782	−	0.00446891i	−0.348152	+	0.937438i	$0.613191\pi$
$158$	17.3541	−	3.05999i	0.109836	−	0.0193670i
$159$	0.753798	−	0.414316i	0.00474087	−	0.00260576i
$160$	−8.83070	−	7.40984i	−0.0551919	−	0.0463115i
$161$		−	447.725i		−	2.78090i
$162$	110.740	+	29.3013i	0.683583	+	0.180872i
$163$	−37.5034			−0.230082			−0.115041	−	0.993361i	$-0.536700\pi$
$163$	−37.5034			−0.230082			−0.115041	+	0.993361i	$0.536700\pi$
$164$	−20.3271	+	24.2249i	−0.123946	+	0.147713i
$165$	−11.0437	−	20.0926i	−0.0669314	−	0.121774i
$166$	17.8207	+	101.066i	0.107353	+	0.608832i
$167$	51.5277	−	141.571i	0.308549	−	0.847731i	−0.684391	−	0.729115i	$-0.739932\pi$
$167$	51.5277	−	141.571i	0.308549	−	0.847731i	0.992940	−	0.118616i	$-0.0378458\pi$
$168$	−106.998	−	21.1961i	−0.636891	−	0.126167i
$169$	−16.0815	+	91.2028i	−0.0951569	+	0.539662i
$170$	−58.9242	−	34.0199i	−0.346613	−	0.200117i
$171$	−21.5407	−	41.2215i	−0.125969	−	0.241062i
$172$	−52.4339	−	90.8181i	−0.304848	−	0.528012i
$173$	−48.2332	−	132.520i	−0.278805	−	0.766010i	−0.997499	−	0.0706833i	$-0.977482\pi$
$173$	−48.2332	−	132.520i	−0.278805	−	0.766010i	0.718694	−	0.695326i	$-0.244740\pi$
$174$	93.3610	−	75.0504i	0.536557	−	0.431324i
$175$	205.291	−	172.260i	1.17309	−	0.984342i
$176$	−9.64271	−	11.4917i	−0.0547881	−	0.0652940i
$177$	−31.6278	+	4.89335i	−0.178688	+	0.0276460i
$178$	−86.8419	+	31.6079i	−0.487876	+	0.177572i
$179$	−155.945	+	90.0350i	−0.871202	+	0.502989i	−0.867747	−	0.497005i	$-0.834433\pi$
$179$	−155.945	+	90.0350i	−0.871202	+	0.502989i	−0.00345448	+	0.999994i	$0.501100\pi$
$180$	24.7388	−	27.0827i	0.137438	−	0.150459i
$181$	22.7711	−	39.4407i	0.125807	−	0.217905i	−0.796241	−	0.604980i	$-0.793181\pi$
$181$	22.7711	−	39.4407i	0.125807	−	0.217905i	0.922048	+	0.387075i	$0.126515\pi$
$182$	156.478	+	27.5912i	0.859767	+	0.151600i
$183$	268.542	−	91.3925i	1.46744	−	0.499412i
$184$	92.5710	+	33.6931i	0.503103	+	0.183115i
$185$	111.553	−	19.6698i	0.602988	−	0.106323i
$186$	0.308616	−	14.6704i	0.00165923	−	0.0788733i
$187$	−67.8278	−	56.9143i	−0.362716	−	0.304355i
$188$			108.065i			0.574812i
$189$	81.7040	−	337.327i	0.432296	−	1.78480i
$190$	−14.8932			−0.0783854
$191$	28.9138	−	34.4581i	0.151381	−	0.180409i	−0.685024	−	0.728520i	$-0.740208\pi$
$191$	28.9138	−	34.4581i	0.151381	−	0.180409i	0.836406	+	0.548111i	$0.184653\pi$
$192$	12.4345	−	20.5276i	0.0647630	−	0.106915i
$193$	43.6912	+	247.785i	0.226379	+	1.28386i	0.860031	+	0.510242i	$0.170444\pi$
$193$	43.6912	+	247.785i	0.226379	+	1.28386i	−0.633652	+	0.773619i	$0.718445\pi$
$194$	16.3294	−	44.8647i	0.0841722	−	0.231261i
$195$	−35.1991	+	40.2003i	−0.180508	+	0.206156i
$196$	−40.3722	+	228.962i	−0.205981	+	1.16817i
$197$	46.5235	+	26.8604i	0.236160	+	0.136347i	0.613411	−	0.789764i	$-0.289797\pi$
$197$	46.5235	+	26.8604i	0.236160	+	0.136347i	−0.377251	+	0.926111i	$0.623130\pi$
$198$	37.8245	−	29.1180i	0.191033	−	0.147061i
$199$	36.3436	+	62.9489i	0.182631	+	0.316326i	0.942776	−	0.333428i	$-0.108205\pi$
$199$	36.3436	+	62.9489i	0.182631	+	0.316326i	−0.760145	+	0.649754i	$0.774872\pi$
$200$	20.1672	+	55.4090i	0.100836	+	0.277045i
$201$	−59.3961	−	23.0443i	−0.295503	−	0.114648i
$202$	−132.767	+	111.405i	−0.657264	+	0.551510i
$203$	−233.296	−	278.031i	−1.14924	−	1.36961i
$204$	51.2379	−	132.064i	0.251166	−	0.647374i
$205$	−30.2782	+	11.0204i	−0.147699	+	0.0537579i
$206$	152.829	−	88.2361i	0.741890	−	0.428331i
$207$	−119.503	+	289.790i	−0.577311	+	1.39995i
$208$	−17.4803	+	30.2768i	−0.0840399	+	0.145561i
$209$	−19.0867	−	3.36550i	−0.0913239	−	0.0161029i
$210$	−83.6167	−	73.2141i	−0.398175	−	0.348638i
$211$	96.7940	+	35.2301i	0.458739	+	0.166967i	0.561045	−	0.827786i	$-0.310400\pi$
$211$	96.7940	+	35.2301i	0.458739	+	0.166967i	−0.102305	+	0.994753i	$0.532622\pi$
$212$	0.564726	−	0.0995764i	0.00266380	−	0.000469700i
$213$	264.910	+	160.467i	1.24371	+	0.753368i
$214$	−92.7547	−	77.8304i	−0.433433	−	0.363694i
$215$		−	106.851i		−	0.496981i
$216$	63.5968	+	42.2782i	0.294430	+	0.195733i
$217$	−44.4600			−0.204885
$218$	−81.6343	+	97.2879i	−0.374469	+	0.446275i
$219$	−71.8292	−	1.51104i	−0.327987	−	0.00689974i
$220$	−2.65423	−	15.0529i	−0.0120647	−	0.0684222i
$221$	−70.5753	+	193.904i	−0.319345	+	0.877394i
$222$	75.9799	+	223.255i	0.342252	+	1.00565i
$223$	7.39155	−	41.9196i	0.0331460	−	0.187980i	−0.963739	−	0.266846i	$-0.914019\pi$
$223$	7.39155	−	41.9196i	0.0331460	−	0.187980i	0.996885	+	0.0788655i	$0.0251298\pi$
$224$	−62.9756	−	36.3590i	−0.281141	−	0.162317i
$225$	−178.853	+	56.7003i	−0.794903	+	0.252001i
$226$	37.6208	+	65.1612i	0.166464	+	0.288324i
$227$	−76.0581	−	208.968i	−0.335058	−	0.920563i	−0.986774	−	0.162101i	$-0.948173\pi$
$227$	−76.0581	−	208.968i	−0.335058	−	0.920563i	0.651716	−	0.758463i	$-0.274049\pi$
$228$	−4.74087	−	30.6423i	−0.0207933	−	0.134396i
$229$	−84.5044	+	70.9076i	−0.369015	+	0.309640i	−0.808372	−	0.588672i	$-0.799651\pi$
$229$	−84.5044	+	70.9076i	−0.369015	+	0.309640i	0.439357	+	0.898313i	$0.355206\pi$
$230$	64.5198	+	76.8917i	0.280521	+	0.334312i
$231$	−90.6160	−	112.724i	−0.392277	−	0.487983i
$232$	75.0417	−	27.3130i	0.323456	−	0.117728i
$233$	30.0900	−	17.3725i	0.129142	−	0.0745600i	−0.434037	−	0.900895i	$-0.642911\pi$
$233$	30.0900	−	17.3725i	0.129142	−	0.0745600i	0.563179	+	0.826335i	$0.309578\pi$
$234$	−93.9157	−	59.6243i	−0.401349	−	0.254805i
$235$	−55.0541	+	95.3565i	−0.234273	+	0.405772i
$236$	−21.0119	−	3.70497i	−0.0890337	−	0.0156990i
$237$	−7.26405	+	36.6689i	−0.0306500	+	0.154721i
$238$	−403.320	−	146.797i	−1.69462	−	0.616792i
$239$	−43.8258	+	7.72767i	−0.183371	+	0.0323333i	−0.264580	−	0.964364i	$-0.585233\pi$
$239$	−43.8258	+	7.72767i	−0.183371	+	0.0323333i	0.0812083	+	0.996697i	$0.474122\pi$
$240$	21.4301	−	11.7788i	0.0892922	−	0.0490784i
$241$	−29.2796	−	24.5685i	−0.121492	−	0.101944i	0.580017	−	0.814604i	$-0.303046\pi$
$241$	−29.2796	−	24.5685i	−0.121492	−	0.101944i	−0.701509	+	0.712660i	$0.747490\pi$
$242$			151.229i			0.624912i
$243$	−142.920	+	196.527i	−0.588148	+	0.808754i
$244$	189.112			0.775050
$245$	−152.271	+	181.469i	−0.621512	+	0.740690i
$246$	−32.3123	−	58.7884i	−0.131351	−	0.238977i
$247$	7.84326	+	44.4813i	0.0317541	+	0.180086i
$248$	3.34580	−	9.19250i	0.0134911	−	0.0370665i
$249$	−213.551	−	42.3041i	−0.857634	−	0.169896i
$250$	−22.9438	+	130.121i	−0.0917751	+	0.520483i
$251$	246.971	+	142.589i	0.983946	+	0.568082i	0.903459	−	0.428674i	$-0.141019\pi$
$251$	246.971	+	142.589i	0.983946	+	0.568082i	0.0804871	+	0.996756i	$0.474352\pi$
$252$	124.018	−	195.345i	0.492137	−	0.775177i
$253$	65.3109	+	113.122i	0.258146	+	0.447122i
$254$	31.5138	+	86.5834i	0.124070	+	0.340880i
$255$	112.493	−	90.4304i	0.441150	−	0.354629i
$256$	12.2567	−	10.2846i	0.0478778	−	0.0401742i
$257$	57.4488	+	68.4649i	0.223536	+	0.266400i	0.866143	−	0.499796i	$-0.166592\pi$
$257$	57.4488	+	68.4649i	0.223536	+	0.266400i	−0.642607	+	0.766196i	$0.722147\pi$
$258$	219.842	−	34.0132i	0.852102	−	0.131834i
$259$	671.453	−	244.389i	2.59248	−	0.943586i
$260$	−30.8493	+	17.8109i	−0.118651	+	0.0685033i
$261$	76.7906	+	242.225i	0.294217	+	0.928065i
$262$	172.715	−	299.151i	0.659216	−	1.14180i
$263$	287.776	+	50.7427i	1.09421	+	0.192938i	0.691489	−	0.722387i	$-0.256955\pi$
$263$	287.776	+	50.7427i	1.09421	+	0.192938i	0.402717	+	0.915325i	$0.368066\pi$
$264$	30.1259	−	10.2527i	0.114113	−	0.0388359i
$265$	0.549045	+	0.199836i	0.00207187	+	0.000754099i
$266$	−92.5211	+	16.3140i	−0.347824	+	0.0613307i
$267$	4.12316	−	195.999i	0.0154425	−	0.734079i
$268$	−32.5363	−	27.3012i	−0.121404	−	0.101870i
$269$			269.220i			1.00082i	0.865790	+	0.500408i	$0.166817\pi$
$269$			269.220i			1.00082i	−0.865790	+	0.500408i	$0.833183\pi$
$270$	34.5791	+	69.7062i	0.128071	+	0.258171i
$271$	−196.043			−0.723407			−0.361704	−	0.932293i	$-0.617805\pi$
$271$	−196.043			−0.723407			−0.361704	+	0.932293i	$0.617805\pi$
$272$	60.7029	−	72.3429i	0.223173	−	0.265967i
$273$	−174.632	+	288.293i	−0.639677	+	1.05602i
$274$	−49.0959	−	278.437i	−0.179182	−	1.01619i
$275$	−26.7407	+	73.4695i	−0.0972389	+	0.267162i
$276$	−137.664	+	157.224i	−0.498783	+	0.569652i
$277$	5.99182	−	33.9813i	0.0216311	−	0.122676i	−0.972080	−	0.234649i	$-0.924606\pi$
$277$	5.99182	−	33.9813i	0.0216311	−	0.122676i	0.993711	+	0.111973i	$0.0357170\pi$
$278$	−212.346	−	122.598i	−0.763833	−	0.440999i
$279$	28.7768	+	11.8670i	0.103142	+	0.0425339i
$280$	−37.0466	−	64.1666i	−0.132309	−	0.229166i
$281$	−144.516	−	397.056i	−0.514294	−	1.41301i	−0.876722	−	0.480998i	$-0.840274\pi$
$281$	−144.516	−	397.056i	−0.514294	−	1.41301i	0.362428	−	0.932012i	$-0.381948\pi$
$282$	−213.718	−	82.9178i	−0.757866	−	0.294035i
$283$	28.7015	−	24.0834i	0.101419	−	0.0851004i	−0.590668	−	0.806914i	$-0.701136\pi$
$283$	28.7015	−	24.0834i	0.101419	−	0.0851004i	0.692087	+	0.721814i	$0.256691\pi$
$284$	132.723	+	158.173i	0.467335	+	0.556948i
$285$	11.4275	−	29.4541i	0.0400967	−	0.103348i
$286$	−43.5604	+	15.8547i	−0.152309	+	0.0554359i
$287$	−176.025	+	101.628i	−0.613329	+	0.354106i
$288$	31.0563	+	40.3424i	0.107834	+	0.140078i
$289$	134.198	−	232.438i	0.464354	−	0.804285i
$290$	80.1318	+	14.1294i	0.276317	+	0.0487221i
$291$	76.1988	+	66.7191i	0.261852	+	0.229275i
$292$	−45.0082	−	16.3816i	−0.154138	−	0.0561015i
$293$	144.314	−	25.4465i	0.492540	−	0.0868481i	0.0781389	−	0.996942i	$-0.475102\pi$
$293$	144.314	−	25.4465i	0.492540	−	0.0868481i	0.414401	+	0.910094i	$0.363991\pi$
$294$	−421.838	−	255.526i	−1.43482	−	0.869136i
$295$	−16.6535	−	13.9739i	−0.0564525	−	0.0473693i
$296$			157.220i			0.531149i
$297$	28.5636	+	97.1473i	0.0961739	+	0.327095i
$298$	−113.129			−0.379627
$299$	195.673	−	233.194i	0.654424	−	0.779912i
$300$	−125.056	−	2.63076i	−0.416853	−	0.00876919i
$301$	−117.044	−	663.789i	−0.388850	−	2.20528i
$302$	130.975	−	359.852i	0.433693	−	1.19156i
$303$	−118.452	−	348.054i	−0.390932	−	1.14869i
$304$	3.58953	−	20.3572i	0.0118077	−	0.0669646i
$305$	166.873	+	96.3442i	0.547125	+	0.315883i
$306$	221.867	+	202.665i	0.725056	+	0.662305i
$307$	−44.2657	−	76.6704i	−0.144188	−	0.249741i	0.784882	−	0.619646i	$-0.212724\pi$
$307$	−44.2657	−	76.6704i	−0.144188	−	0.249741i	−0.929070	+	0.369905i	$0.879390\pi$
$308$	−32.9777	−	90.6055i	−0.107070	−	0.294174i
$309$	57.2377	+	369.952i	0.185235	+	1.19726i
$310$	7.63551	−	6.40695i	0.0246307	−	0.0206676i
$311$	347.817	+	414.512i	1.11838	+	1.33284i	0.936962	+	0.349432i	$0.113625\pi$
$311$	347.817	+	414.512i	1.11838	+	1.33284i	0.181421	+	0.983405i	$0.441930\pi$
$312$	−46.4654	−	57.8019i	−0.148928	−	0.185263i
$313$	−195.682	+	71.2223i	−0.625181	+	0.227547i	−0.635132	−	0.772403i	$-0.719055\pi$
$313$	−195.682	+	71.2223i	−0.625181	+	0.227547i	0.00995150	+	0.999950i	$0.496832\pi$
$314$	2.51244	−	1.45056i	0.00800139	−	0.00461960i
$315$	208.954	−	109.191i	0.663345	−	0.346637i
$316$	−12.4605	+	21.5822i	−0.0394319	+	0.0682981i
$317$	−472.889	−	83.3831i	−1.49176	−	0.263038i	−0.632496	−	0.774564i	$-0.717969\pi$
$317$	−472.889	−	83.3831i	−1.49176	−	0.263038i	−0.859268	+	0.511526i	$0.829080\pi$
$318$	−0.236382	+	1.19326i	−0.000743340	+	0.00375238i
$319$	99.5015	+	36.2156i	0.311917	+	0.113529i
$320$	16.0549	−	2.83091i	0.0501716	−	0.00884660i
$321$	225.095	−	123.721i	0.701230	−	0.385423i
$322$	485.043	+	406.999i	1.50634	+	1.26397i
$323$		−	122.008i		−	0.377735i
$324$	−132.411	+	93.3346i	−0.408676	+	0.288070i
$325$	182.208			0.560641
$326$	34.0920	−	40.6293i	0.104577	−	0.124630i
$327$	−129.767	−	236.096i	−0.396842	−	0.722006i
$328$	−7.76593	−	44.0428i	−0.0236766	−	0.134277i
$329$	−237.559	+	652.689i	−0.722065	+	1.98386i
$330$	31.8065	+	6.30082i	0.0963833	+	0.0190934i
$331$	65.1675	−	369.583i	0.196881	−	1.11657i	−0.712834	−	0.701333i	$-0.752589\pi$
$331$	65.1675	−	369.583i	0.196881	−	1.11657i	0.909715	−	0.415234i	$-0.136300\pi$
$332$	−125.690	−	72.5669i	−0.378583	−	0.218575i
$333$	−499.828	−	21.0387i	−1.50099	−	0.0631793i
$334$	106.530	+	184.516i	0.318953	+	0.552444i
$335$	−14.8014	−	40.6665i	−0.0441833	−	0.121393i
$336$	120.228	−	96.6480i	0.357821	−	0.287643i
$337$	−93.3224	+	78.3068i	−0.276921	+	0.232364i	−0.770661	−	0.637245i	$-0.780074\pi$
$337$	−93.3224	+	78.3068i	−0.276921	+	0.232364i	0.493740	+	0.869610i	$0.335629\pi$
$338$	−84.1859	−	100.329i	−0.249071	−	0.296831i
$339$	−157.735	+	24.4042i	−0.465295	+	0.0719888i
$340$	90.4199	−	32.9102i	0.265941	−	0.0967946i
$341$	11.2332	−	6.48552i	0.0329421	−	0.0190191i
$342$	64.2387	+	14.1359i	0.187832	+	0.0413329i
$343$	−432.226	+	748.637i	−1.26013	+	2.18261i
$344$	146.052	+	25.7530i	0.424571	+	0.0748633i
$345$	−201.574	+	68.6011i	−0.584272	+	0.198844i
$346$	187.411	+	68.2121i	0.541651	+	0.197145i
$347$	208.683	−	36.7964i	0.601392	−	0.106042i	0.135340	−	0.990799i	$-0.456787\pi$
$347$	208.683	−	36.7964i	0.601392	−	0.106042i	0.466051	+	0.884758i	$0.345676\pi$
$348$	−3.56290	+	169.366i	−0.0102382	+	0.486685i
$349$	108.035	+	90.6521i	0.309556	+	0.259748i	0.784308	−	0.620371i	$-0.213018\pi$
$349$	108.035	+	90.6521i	0.309556	+	0.259748i	−0.474753	+	0.880119i	$0.657462\pi$
$350$			378.993i			1.08284i
$351$	189.980	−	139.986i	0.541253	−	0.398821i
$352$	21.2152			0.0602704
$353$	49.0352	−	58.4379i	0.138910	−	0.165546i	−0.692104	−	0.721797i	$-0.743316\pi$
$353$	49.0352	−	58.4379i	0.138910	−	0.165546i	0.831014	+	0.556251i	$0.187761\pi$
$354$	23.4497	−	38.7123i	0.0662422	−	0.109357i
$355$	36.5330	+	207.189i	0.102910	+	0.583631i
$356$	44.7003	−	122.813i	0.125563	−	0.344980i
$357$	599.785	−	685.005i	1.68007	−	1.91878i
$358$	44.2208	−	250.789i	0.123522	−	0.700527i
$359$	144.922	+	83.6709i	0.403683	+	0.233067i	0.688072	−	0.725642i	$-0.258457\pi$
$359$	144.922	+	83.6709i	0.403683	+	0.233067i	−0.284389	+	0.958709i	$0.591791\pi$
$360$	6.85152	+	51.4200i	0.0190320	+	0.142833i
$361$	167.147	+	289.507i	0.463011	+	0.801958i
$362$	22.0283	+	60.5223i	0.0608517	+	0.167189i
$363$	−299.083	−	116.038i	−0.823921	−	0.319663i
$364$	−172.135	+	144.439i	−0.472899	+	0.396809i
$365$	−31.3696	−	37.3849i	−0.0859442	−	0.102424i
$366$	−145.105	+	374.005i	−0.396463	+	1.02187i
$367$	−93.9774	+	34.2050i	−0.256069	+	0.0932016i	−0.466865	−	0.884329i	$-0.654617\pi$
$367$	−93.9774	+	34.2050i	−0.256069	+	0.0932016i	0.210796	+	0.977530i	$0.432394\pi$
$368$	−120.652	+	69.6585i	−0.327859	+	0.189289i
$369$	141.058	−	18.7955i	0.382272	−	0.0509363i
$370$	−80.0966	+	138.731i	−0.216477	+	0.374950i
$371$	3.62973	+	0.640020i	0.00978365	+	0.00172512i
$372$	15.6127	+	13.6703i	0.0419696	+	0.0367482i
$373$	−481.489	−	175.248i	−1.29086	−	0.469833i	−0.396848	−	0.917884i	$-0.629896\pi$
$373$	−481.489	−	175.248i	−1.29086	−	0.469833i	−0.894008	+	0.448051i	$0.852118\pi$
$374$	123.316	−	21.7440i	0.329723	−	0.0581390i
$375$	−239.733	−	145.217i	−0.639289	−	0.387246i
$376$	−117.072	−	98.2349i	−0.311361	−	0.261263i
$377$		−	246.769i		−	0.654560i
$378$	291.171	+	395.158i	0.770295	+	1.04539i
$379$	−207.305			−0.546979			−0.273489	−	0.961875i	$-0.588178\pi$
$379$	−207.305			−0.546979			−0.273489	+	0.961875i	$0.588178\pi$
$380$	13.5385	−	16.1346i	0.0356277	−	0.0424594i
$381$	−195.416	−	4.11088i	−0.512902	−	0.0107897i
$382$	11.0465	+	62.6476i	0.0289174	+	0.163999i
$383$	206.290	−	566.776i	0.538615	−	1.47983i	−0.309956	−	0.950751i	$-0.600314\pi$
$383$	206.290	−	566.776i	0.538615	−	1.47983i	0.848571	−	0.529082i	$-0.177463\pi$
$384$	10.9352	+	32.1313i	0.0284770	+	0.0836753i
$385$	17.0599	−	96.7512i	0.0443113	−	0.251302i
$386$	−308.155	−	177.913i	−0.798329	−	0.460916i
$387$	−101.417	+	460.878i	−0.262060	+	1.19090i
$388$	33.7601	+	58.4742i	0.0870105	+	0.150707i
$389$	14.8087	+	40.6865i	0.0380686	+	0.104593i	0.957271	−	0.289194i	$-0.0933872\pi$
$389$	14.8087	+	40.6865i	0.0380686	+	0.104593i	−0.919202	+	0.393786i	$0.871165\pi$
$390$	−11.5537	−	74.6766i	−0.0296249	−	0.191479i
$391$	−629.912	+	528.559i	−1.61103	+	1.35181i
$392$	−211.346	−	251.873i	−0.539149	−	0.642532i
$393$	459.103	+	571.114i	1.16820	+	1.45322i
$394$	−71.3909	+	25.9842i	−0.181195	+	0.0659497i
$395$	−21.9904	+	12.6961i	−0.0556718	+	0.0321421i
$396$	−2.83895	+	67.4466i	−0.00716907	+	0.170320i
$397$	−65.2019	+	112.933i	−0.164236	+	0.284466i	−0.936384	−	0.350978i	$-0.885849\pi$
$397$	−65.2019	+	112.933i	−0.164236	+	0.284466i	0.772147	+	0.635443i	$0.219183\pi$
$398$	−101.233	−	17.8502i	−0.254355	−	0.0448497i
$399$	38.7274	−	195.496i	0.0970611	−	0.489964i
$400$	−78.3601	−	28.5208i	−0.195900	−	0.0713019i
$401$	65.9004	−	11.6200i	0.164340	−	0.0289776i	−0.0908725	−	0.995863i	$-0.528966\pi$
$401$	65.9004	−	11.6200i	0.164340	−	0.0289776i	0.255213	+	0.966885i	$0.417854\pi$
$402$	78.9584	−	43.3986i	0.196414	−	0.107957i
$403$	−23.1566	−	19.4307i	−0.0574607	−	0.0482152i
$404$		−	245.105i		−	0.606696i
$405$	−164.390	+	14.9012i	−0.405900	+	0.0367932i
$406$	513.280			1.26424
$407$	−133.999	+	159.694i	−0.329236	+	0.392369i
$408$	96.4945	+	175.560i	0.236506	+	0.430294i
$409$	−95.6784	−	542.619i	−0.233933	−	1.32670i	−0.844850	−	0.535003i	$-0.820310\pi$
$409$	−95.6784	−	542.619i	−0.233933	−	1.32670i	0.610917	−	0.791694i	$-0.290801\pi$
$410$	15.5851	−	42.8198i	0.0380126	−	0.104439i
$411$	588.332	+	116.548i	1.43146	+	0.283571i
$412$	−43.3373	+	245.778i	−0.105188	+	0.596548i
$413$	−118.763	−	68.5680i	−0.287563	−	0.166024i
$414$	−205.311	−	392.894i	−0.495919	−	0.949020i
$415$	−73.9393	−	128.067i	−0.178167	−	0.308594i
$416$	−16.9101	−	46.4600i	−0.0406492	−	0.111683i
$417$	405.393	−	325.884i	0.972165	−	0.781498i
$418$	20.9966	−	17.6182i	0.0502310	−	0.0421488i
$419$	−38.0213	−	45.3120i	−0.0907430	−	0.108143i	0.718762	−	0.695256i	$-0.244709\pi$
$419$	−38.0213	−	45.3120i	−0.0907430	−	0.108143i	−0.809505	+	0.587113i	$0.800265\pi$
$420$	155.327	−	24.0317i	0.369827	−	0.0572183i
$421$	−124.731	+	45.3982i	−0.296272	+	0.107834i	−0.485880	−	0.874026i	$-0.661501\pi$
$421$	−124.731	+	45.3982i	−0.296272	+	0.107834i	0.189608	+	0.981860i	$0.439278\pi$
$422$	−126.156	+	72.8363i	−0.298948	+	0.172598i
$423$	327.971	−	359.045i	0.775346	−	0.848806i
$424$	−0.405482	+	0.702315i	−0.000956325	+	0.00165640i
$425$	−484.711	−	85.4677i	−1.14050	−	0.201100i
$426$	−414.656	+	141.119i	−0.973370	+	0.331265i
$427$	1142.20	+	415.727i	2.67494	+	0.973599i
$428$	168.635	−	29.7349i	0.394008	−	0.0694742i
$429$	2.06820	−	98.3141i	0.00482097	−	0.229170i
$430$	115.757	+	97.1316i	0.269202	+	0.225887i
$431$			225.339i			0.522829i	0.965227	+	0.261415i	$0.0841890\pi$
$431$			225.339i			0.522829i	−0.965227	+	0.261415i	$0.915811\pi$
$432$	−103.614	+	30.4650i	−0.239847	+	0.0705209i
$433$	−136.913			−0.316196			−0.158098	−	0.987423i	$-0.550536\pi$
$433$	−136.913			−0.316196			−0.158098	+	0.987423i	$0.550536\pi$
$434$	40.4159	−	48.1658i	0.0931242	−	0.110981i
$435$	−89.4286	+	147.634i	−0.205583	+	0.339389i
$436$	−31.1882	−	176.877i	−0.0715326	−	0.405681i
$437$	−61.5606	+	169.136i	−0.140871	+	0.387040i
$438$	66.9325	−	76.4426i	0.152814	−	0.174526i
$439$	57.0136	−	323.340i	0.129872	−	0.736538i	−0.848423	−	0.529319i	$-0.822447\pi$
$439$	57.0136	−	323.340i	0.129872	−	0.736538i	0.978294	−	0.207219i	$-0.0664414\pi$
$440$	18.7203	+	10.8082i	0.0425462	+	0.0245641i
$441$	829.027	−	638.200i	1.87988	−	1.44717i
$442$	−145.910	−	252.724i	−0.330114	−	0.571774i
$443$	−38.7141	−	106.366i	−0.0873907	−	0.240104i	0.888297	−	0.459270i	$-0.151889\pi$
$443$	−38.7141	−	106.366i	−0.0873907	−	0.240104i	−0.975688	+	0.219165i	$0.929667\pi$
$444$	−310.932	−	120.635i	−0.700298	−	0.271700i
$445$	102.011	−	85.5978i	0.229239	−	0.192355i
$446$	38.6944	+	46.1141i	0.0867587	+	0.103395i
$447$	86.8036	−	223.734i	0.194191	−	0.500522i
$448$	96.6368	−	35.1729i	0.215707	−	0.0785110i
$449$	−450.020	+	259.819i	−1.00227	+	0.578661i	−0.908919	−	0.416972i	$-0.863091\pi$
$449$	−450.020	+	259.819i	−1.00227	+	0.578661i	−0.0933515	+	0.995633i	$0.529758\pi$
$450$	101.158	−	245.303i	0.224796	−	0.545118i
$451$	29.6497	−	51.3547i	0.0657421	−	0.113869i
$452$	−104.791	−	18.4775i	−0.231839	−	0.0408795i
$453$	611.177	+	535.142i	1.34918	+	1.18133i
$454$	295.525	+	107.562i	0.650937	+	0.236922i
$455$	−225.478	+	39.7578i	−0.495555	+	0.0873798i
$456$	37.5060	+	22.7191i	0.0822501	+	0.0498225i
$457$	−203.183	−	170.491i	−0.444601	−	0.373065i	0.392827	−	0.919613i	$-0.371497\pi$
$457$	−203.183	−	170.491i	−0.444601	−	0.373065i	−0.837428	+	0.546548i	$0.815942\pi$
$458$		−	156.006i		−	0.340624i
$459$	−571.047	+	283.279i	−1.24411	+	0.617166i
$460$	−141.952			−0.308590
$461$	425.520	−	507.115i	0.923037	−	1.10003i	−0.0716856	−	0.997427i	$-0.522838\pi$
$461$	425.520	−	507.115i	0.923037	−	1.10003i	0.994722	−	0.102605i	$-0.0327177\pi$
$462$	204.493	+	4.30185i	0.442626	+	0.00931136i
$463$	40.8741	+	231.808i	0.0882810	+	0.500666i	0.996600	+	0.0823887i	$0.0262549\pi$
$463$	40.8741	+	231.808i	0.0882810	+	0.500666i	−0.908319	+	0.418277i	$0.862634\pi$
$464$	−38.6264	+	106.125i	−0.0832465	+	0.228718i
$465$	6.81224	+	20.0167i	0.0146500	+	0.0430467i
$466$	−8.53252	+	48.3903i	−0.0183101	+	0.103842i
$467$	−444.948	−	256.891i	−0.952780	−	0.550088i	−0.0588364	−	0.998268i	$-0.518739\pi$
$467$	−444.948	−	256.891i	−0.952780	−	0.550088i	−0.893943	+	0.448180i	$0.852072\pi$
$468$	149.967	−	47.5428i	0.320442	−	0.101587i
$469$	−136.497	−	236.419i	−0.291037	−	0.504092i
$470$	−53.2582	−	146.326i	−0.113315	−	0.311331i
$471$	0.940958	+	6.08182i	0.00199779	+	0.0129126i
$472$	23.1145	−	19.3953i	0.0489713	−	0.0410918i
$473$	126.401	+	150.639i	0.267233	+	0.318476i
$474$	−33.1220	−	41.2030i	−0.0698776	−	0.0869261i
$475$	−101.238	+	36.8475i	−0.213132	+	0.0775738i
$476$	525.666	−	303.493i	1.10434	−	0.637591i
$477$	−2.17851	−	1.38307i	−0.00456712	−	0.00289953i
$478$	31.4676	−	54.5034i	0.0658317	−	0.114024i
$479$	476.222	+	83.9707i	0.994200	+	0.175304i	0.647003	−	0.762488i	$-0.276022\pi$
$479$	476.222	+	83.9707i	0.994200	+	0.175304i	0.347197	+	0.937792i	$0.387133\pi$
$480$	−6.72024	+	33.9238i	−0.0140005	+	0.0706745i
$481$	456.528	+	166.163i	0.949123	+	0.345452i
$482$	53.2326	−	9.38634i	0.110441	−	0.0194737i
$483$	−1177.09	+	646.973i	−2.43704	+	1.33949i
$484$	−163.834	−	137.473i	−0.338499	−	0.284035i
$485$			68.7970i			0.141850i
$486$	−82.9881	−	333.483i	−0.170757	−	0.686179i
$487$	−420.969			−0.864413			−0.432206	−	0.901775i	$-0.642265\pi$
$487$	−420.969			−0.864413			−0.432206	+	0.901775i	$0.642265\pi$
$488$	−171.910	+	204.875i	−0.352275	+	0.419825i
$489$	54.1933	+	98.5982i	0.110825	+	0.201632i
$490$	−58.1746	−	329.925i	−0.118724	−	0.673316i
$491$	231.119	−	634.994i	0.470711	−	1.29327i	−0.446471	−	0.894798i	$-0.647319\pi$
$491$	231.119	−	634.994i	0.470711	−	1.29327i	0.917182	−	0.398469i	$-0.130458\pi$
$492$	93.0616	+	18.4354i	0.189150	+	0.0374702i
$493$	−115.751	+	656.456i	−0.234789	+	1.33155i
$494$	−55.3187	−	31.9383i	−0.111981	−	0.0646523i
$495$	−36.8661	+	58.0687i	−0.0744770	+	0.117311i
$496$	6.91724	+	11.9810i	0.0139460	+	0.0241553i
$497$	453.908	+	1247.10i	0.913296	+	2.50926i
$498$	239.956	−	192.894i	0.481840	−	0.387338i
$499$	−4.02772	+	3.37966i	−0.00807159	+	0.00677287i	−0.646814	−	0.762647i	$-0.723899\pi$
$499$	−4.02772	+	3.37966i	−0.00807159	+	0.00677287i	0.638743	+	0.769420i	$0.279455\pi$
$500$	−120.109	−	143.141i	−0.240219	−	0.286282i
$501$	−446.656	+	69.1051i	−0.891529	+	0.137934i
$502$	−378.979	+	137.937i	−0.754939	+	0.274775i
$503$	99.8385	−	57.6418i	0.198486	−	0.114596i	−0.397463	−	0.917618i	$-0.630109\pi$
$503$	99.8385	−	57.6418i	0.198486	−	0.114596i	0.595949	+	0.803022i	$0.296776\pi$
$504$	98.8889	+	311.931i	0.196208	+	0.618911i
$505$	124.870	−	216.282i	0.247268	−	0.428280i
$506$	−181.921	−	32.0775i	−0.359527	−	0.0633943i
$507$	263.015	−	89.5113i	0.518767	−	0.176551i
$508$	−122.447	−	44.5672i	−0.241038	−	0.0877308i
$509$	−283.458	+	49.9813i	−0.556893	+	0.0981952i	−0.445009	−	0.895526i	$-0.646799\pi$
$509$	−283.458	+	49.9813i	−0.556893	+	0.0981952i	−0.111884	+	0.993721i	$0.535688\pi$
$510$	−4.29304	+	204.074i	−0.00841772	+	0.400146i
$511$	−235.829	−	197.884i	−0.461504	−	0.387248i
$512$			22.6274i			0.0441942i
$513$	−77.2466	+	116.198i	−0.150578	+	0.226506i
$514$	−126.395			−0.245904
$515$	−163.454	+	194.797i	−0.317386	+	0.378246i
$516$	−162.997	+	269.086i	−0.315886	+	0.521484i
$517$	−35.1881	−	199.561i	−0.0680620	−	0.385999i
$518$	−345.618	+	949.578i	−0.667216	+	1.83316i
$519$	−278.703	+	318.302i	−0.536999	+	0.613298i
$520$	8.74783	−	49.6114i	0.0168227	−	0.0954066i
$521$	620.496	+	358.243i	1.19097	+	0.687607i	0.958527	−	0.285003i	$-0.0919945\pi$
$521$	620.496	+	358.243i	1.19097	+	0.687607i	0.232444	+	0.972610i	$0.425328\pi$
$522$	−332.220	−	137.001i	−0.636437	−	0.262454i
$523$	181.209	+	313.864i	0.346480	+	0.600122i	0.985622	−	0.168968i	$-0.0540434\pi$
$523$	181.209	+	313.864i	0.346480	+	0.600122i	−0.639141	+	0.769089i	$0.720710\pi$
$524$	167.081	+	459.050i	0.318856	+	0.876050i
$525$	−749.530	−	290.801i	−1.42768	−	0.553907i
$526$	−316.572	+	265.635i	−0.601848	+	0.505010i
$527$	52.4871	+	62.5517i	0.0995960	+	0.118694i
$528$	−16.2784	+	41.9570i	−0.0308303	+	0.0794641i
$529$	642.821	−	233.968i	1.21516	−	0.442283i
$530$	−0.715596	+	0.413150i	−0.00135018	+	0.000779528i
$531$	58.5679	+	76.0801i	0.110297	+	0.143277i
$532$	66.4315	−	115.063i	0.124871	−	0.216283i
$533$	−136.097	−	23.9976i	−0.255341	−	0.0450236i
$534$	208.588	+	182.638i	0.390613	+	0.342018i
$535$	163.953	+	59.6740i	0.306454	+	0.111540i
$536$	59.1536	−	10.4304i	0.110361	−	0.0194597i
$537$	462.051	+	279.885i	0.860430	+	0.521201i
$538$	−291.659	−	244.731i	−0.542118	−	0.454891i
$539$		−	435.967i		−	0.808845i
$540$	−106.950	−	25.9043i	−0.198055	−	0.0479710i
$541$	955.760			1.76665			0.883327	−	0.468757i	$-0.155298\pi$
$541$	955.760			1.76665			0.883327	+	0.468757i	$0.155298\pi$
$542$	178.211	−	212.384i	0.328803	−	0.391852i
$543$	−136.596	−	2.87353i	−0.251559	−	0.00529195i
$544$	23.1914	+	131.525i	0.0426313	+	0.241774i
$545$	62.5904	−	171.966i	0.114845	−	0.315534i
$546$	−153.575	−	451.257i	−0.281274	−	0.826479i
$547$	−140.379	+	796.129i	−0.256635	+	1.45545i	0.535207	+	0.844721i	$0.320233\pi$
$547$	−140.379	+	796.129i	−0.256635	+	1.45545i	−0.791842	+	0.610726i	$0.790878\pi$
$548$	346.274	+	199.922i	0.631888	+	0.364821i
$549$	−628.326	−	573.947i	−1.14449	−	1.04544i
$550$	−55.2849	−	95.7562i	−0.100518	−	0.174102i
$551$	49.9035	+	137.109i	0.0905690	+	0.248836i
$552$	−45.1867	−	292.061i	−0.0818599	−	0.529096i
$553$	−122.703	+	102.960i	−0.221887	+	0.186185i
$554$	31.3669	+	37.3816i	0.0566189	+	0.0674758i
$555$	−212.909	−	264.855i	−0.383621	−	0.477215i
$556$	325.847	−	118.599i	0.586056	−	0.213307i
$557$	905.625	−	522.863i	1.62590	−	0.938713i	0.640599	−	0.767876i	$-0.278686\pi$
$557$	905.625	−	522.863i	1.62590	−	0.938713i	0.985299	−	0.170837i	$-0.0546472\pi$
$558$	−39.0153	+	20.3878i	−0.0699198	+	0.0365373i
$559$	229.140	−	396.882i	0.409910	−	0.709986i
$560$	103.192	+	18.1955i	0.184271	+	0.0324919i
$561$	−51.6176	+	260.565i	−0.0920100	+	0.464466i
$562$	561.522	+	204.377i	0.999149	+	0.363660i
$563$	−794.540	+	140.099i	−1.41126	+	0.248843i	−0.826762	−	0.562552i	$-0.809820\pi$
$563$	−794.540	+	140.099i	−1.41126	+	0.248843i	−0.584498	+	0.811395i	$0.698709\pi$
$564$	284.107	−	156.156i	0.503736	−	0.276872i
$565$	−83.0546	−	69.6911i	−0.146999	−	0.123347i
$566$			52.9865i			0.0936157i
$567$	−1004.91	+	272.643i	−1.77234	+	0.480851i
$568$	−292.008			−0.514098
$569$	−449.679	+	535.906i	−0.790296	+	0.941838i	−0.999349	−	0.0360660i	$-0.988517\pi$
$569$	−449.679	+	535.906i	−0.790296	+	0.941838i	0.209053	+	0.977904i	$0.432962\pi$
$570$	21.5211	+	39.1550i	0.0377563	+	0.0686930i
$571$	−165.128	−	936.488i	−0.289191	−	1.64008i	−0.689919	−	0.723886i	$-0.742354\pi$
$571$	−165.128	−	936.488i	−0.289191	−	1.64008i	0.400728	−	0.916197i	$-0.368757\pi$
$572$	22.4219	−	61.6037i	0.0391991	−	0.107699i
$573$	−132.373	−	26.2230i	−0.231018	−	0.0457643i
$574$	49.9149	−	283.081i	0.0869597	−	0.493173i
$575$	628.817	+	363.048i	1.09359	+	0.631387i
$576$	−71.9363	−	3.02793i	−0.124889	−	0.00525683i
$577$	−493.211	−	854.266i	−0.854785	−	1.48053i	−0.876845	−	0.480774i	$-0.840356\pi$
$577$	−493.211	−	854.266i	−0.854785	−	1.48053i	0.0220601	−	0.999757i	$-0.492977\pi$
$578$	129.821	+	356.679i	0.224603	+	0.617092i
$579$	588.304	−	472.922i	1.01607	−	0.816791i
$580$	−88.1500	+	73.9666i	−0.151983	+	0.127529i
$581$	−599.616	−	714.595i	−1.03204	−	1.22994i
$582$	−141.548	+	21.8998i	−0.243209	+	0.0376285i
$583$	−1.01045	+	0.367773i	−0.00173319	+	0.000630828i
$584$	58.6613	−	33.8681i	0.100447	−	0.0579933i
$585$	156.552	+	34.4496i	0.267611	+	0.0588883i
$586$	−103.620	+	179.475i	−0.176826	+	0.306271i
$587$	401.070	+	70.7195i	0.683254	+	0.120476i	0.504492	−	0.863416i	$-0.331680\pi$
$587$	401.070	+	70.7195i	0.683254	+	0.120476i	0.178762	+	0.983892i	$0.442791\pi$
$588$	660.292	−	224.716i	1.12294	−	0.382169i
$589$	16.7956	+	6.11310i	0.0285155	+	0.0103788i
$590$	30.2773	−	5.33871i	0.0513175	−	0.00904866i
$591$	3.38956	−	161.127i	0.00573530	−	0.272634i
$592$	−170.324	−	142.919i	−0.287710	−	0.241417i
$593$		−	1081.76i		−	1.82421i	−0.409956	−	0.912105i	$-0.634456\pi$
$593$		−	1081.76i		−	1.82421i	0.409956	−	0.912105i	$-0.365544\pi$
$594$	−131.210	−	57.3662i	−0.220892	−	0.0965762i
$595$	618.465			1.03944
$596$	102.838	−	122.558i	0.172548	−	0.205634i
$597$	112.978	−	186.512i	0.189244	−	0.312415i
$598$	74.7564	+	423.964i	0.125011	+	0.708970i
$599$	−164.606	+	452.252i	−0.274802	+	0.755012i	0.723129	+	0.690713i	$0.242703\pi$
$599$	−164.606	+	452.252i	−0.274802	+	0.755012i	−0.997931	+	0.0642990i	$0.979519\pi$
$600$	116.531	−	133.088i	0.194218	−	0.221813i
$601$	37.6355	−	213.442i	0.0626215	−	0.355144i	−0.937356	−	0.348374i	$-0.886734\pi$
$601$	37.6355	−	213.442i	0.0626215	−	0.355144i	0.999977	−	0.00676998i	$-0.00215497\pi$
$602$	825.514	+	476.611i	1.37129	+	0.791712i
$603$	25.2441	+	189.455i	0.0418642	+	0.314187i
$604$	270.784	+	469.011i	0.448318	+	0.776509i
$605$	−74.5311	−	204.772i	−0.123192	−	0.338467i
$606$	484.742	+	188.069i	0.799904	+	0.310345i
$607$	−266.484	+	223.607i	−0.439019	+	0.368381i	−0.835342	−	0.549730i	$-0.814730\pi$
$607$	−266.484	+	223.607i	−0.439019	+	0.368381i	0.396323	+	0.918111i	$0.370286\pi$
$608$	18.7910	+	22.3942i	0.0309062	+	0.0368326i
$609$	−393.839	+	1015.11i	−0.646698	+	1.66684i
$610$	−256.069	+	93.2014i	−0.419785	+	0.152789i
$611$	−408.981	+	236.125i	−0.669363	+	0.386457i
$612$	−421.243	+	56.1291i	−0.688306	+	0.0917142i
$613$	552.987	−	957.801i	0.902099	−	1.56248i	0.0773349	−	0.997005i	$-0.475359\pi$
$613$	552.987	−	957.801i	0.902099	−	1.56248i	0.824764	−	0.565477i	$-0.191308\pi$
$614$	123.300	+	21.7411i	0.200815	+	0.0354090i
$615$	72.7259	+	63.6782i	0.118253	+	0.103542i
$616$	128.136	+	46.6375i	0.208012	+	0.0757103i
$617$	564.719	−	99.5753i	0.915266	−	0.161386i	0.303873	−	0.952713i	$-0.401720\pi$
$617$	564.719	−	99.5753i	0.915266	−	0.161386i	0.611394	+	0.791327i	$0.290609\pi$
$618$	−452.819	−	274.293i	−0.732718	−	0.443839i
$619$	382.711	+	321.132i	0.618273	+	0.518792i	0.897260	−	0.441502i	$-0.145554\pi$
$619$	382.711	+	321.132i	0.618273	+	0.518792i	−0.278987	+	0.960295i	$0.589999\pi$
$620$			14.0961i			0.0227357i
$621$	934.557	−	104.573i	1.50492	−	0.168395i
$622$	−765.241			−1.23029
$623$	539.962	−	643.502i	0.866713	−	1.03291i
$624$	104.859	+	2.20587i	0.168043	+	0.00353505i
$625$	57.4413	+	325.766i	0.0919061	+	0.521225i
$626$	100.724	−	276.736i	0.160900	−	0.442070i
$627$	18.7327	+	55.0431i	0.0298767	+	0.0877880i
$628$	−0.712442	+	4.04046i	−0.00113446	+	0.00643385i
$629$	−1136.52	−	656.168i	−1.80686	−	1.04319i
$630$	−71.6552	+	325.629i	−0.113738	+	0.516871i
$631$	−50.5825	−	87.6115i	−0.0801625	−	0.138846i	0.823157	−	0.567814i	$-0.192211\pi$
$631$	−50.5825	−	87.6115i	−0.0801625	−	0.138846i	−0.903320	+	0.428968i	$0.858877\pi$
$632$	−12.0540	−	33.1182i	−0.0190728	−	0.0524021i
$633$	−47.2480	−	305.385i	−0.0746415	−	0.482440i
$634$	520.208	−	436.506i	0.820517	−	0.688495i
$635$	−85.3430	−	101.708i	−0.134398	−	0.160170i
$636$	−1.07783	−	1.34080i	−0.00169471	−	0.00210818i
$637$	−954.744	+	347.498i	−1.49881	+	0.545523i
$638$	−129.685	+	74.8736i	−0.203268	+	0.117357i
$639$	39.0756	−	928.340i	0.0611511	−	1.45280i
$640$	−11.5277	+	19.9665i	−0.0180120	+	0.0311977i
$641$	−653.181	−	115.173i	−1.01900	−	0.179678i	−0.360899	−	0.932605i	$-0.617530\pi$
$641$	−653.181	−	115.173i	−1.01900	−	0.179678i	−0.658104	+	0.752927i	$0.728641\pi$
$642$	−70.5872	+	356.324i	−0.109949	+	0.555021i
$643$	−363.283	−	132.224i	−0.564981	−	0.205636i	0.0437094	−	0.999044i	$-0.486082\pi$
$643$	−363.283	−	132.224i	−0.564981	−	0.205636i	−0.608690	+	0.793408i	$0.708305\pi$
$644$	−881.845	+	155.493i	−1.36933	+	0.241449i
$645$	−280.916	+	154.402i	−0.435529	+	0.239383i
$646$	132.178	+	110.910i	0.204610	+	0.171688i
$647$			1077.93i			1.66604i	0.553245	+	0.833018i	$0.313389\pi$
$647$			1077.93i			1.66604i	−0.553245	+	0.833018i	$0.686611\pi$
$648$	19.2526	−	228.292i	0.0297108	−	0.352303i
$649$	40.0089			0.0616470
$650$	−165.634	+	197.396i	−0.254822	+	0.303685i
$651$	64.2459	+	116.888i	0.0986880	+	0.179551i
$652$	13.0248	+	73.8672i	0.0199767	+	0.113293i
$653$	−145.722	+	400.367i	−0.223157	+	0.613120i	−0.999860	−	0.0167481i	$-0.994669\pi$
$653$	−145.722	+	400.367i	−0.223157	+	0.613120i	0.776702	+	0.629868i	$0.216891\pi$
$654$	373.738	+	74.0370i	0.571465	+	0.113206i
$655$	−86.4332	+	490.187i	−0.131959	+	0.748378i
$656$	54.7733	+	31.6234i	0.0834958	+	0.0482063i
$657$	99.8224	+	191.026i	0.151937	+	0.290755i
$658$	−491.140	−	850.679i	−0.746413	−	1.29283i
$659$	19.8338	+	54.4930i	0.0300969	+	0.0826904i	0.953831	−	0.300344i	$-0.0971014\pi$
$659$	19.8338	+	54.4930i	0.0300969	+	0.0826904i	−0.923734	+	0.383034i	$0.874879\pi$
$660$	−35.7393	+	28.7299i	−0.0541505	+	0.0435301i
$661$	−124.607	+	104.558i	−0.188514	+	0.158182i	−0.732160	−	0.681133i	$-0.761488\pi$
$661$	−124.607	+	104.558i	−0.188514	+	0.158182i	0.543646	+	0.839314i	$0.317043\pi$
$662$	341.149	+	406.565i	0.515330	+	0.614147i
$663$	611.766	−	94.6503i	0.922725	−	0.142761i
$664$	192.872	−	70.1997i	0.290470	−	0.105722i
$665$	117.239	−	67.6878i	0.176299	−	0.101786i
$666$	477.156	−	522.364i	0.716450	−	0.784331i
$667$	491.684	−	851.622i	0.737158	−	1.27679i
$668$	−296.736	−	52.3226i	−0.444216	−	0.0783272i
$669$	−120.890	+	41.1421i	−0.180702	+	0.0614979i
$670$	57.5111	+	20.9323i	0.0858375	+	0.0312423i
$671$	−349.231	+	61.5788i	−0.520463	+	0.0917717i
$672$	−4.58821	+	218.106i	−0.00682769	+	0.324562i
$673$	846.960	+	710.683i	1.25848	+	1.05599i	0.995842	+	0.0910998i	$0.0290382\pi$
$673$	846.960	+	710.683i	1.25848	+	1.05599i	0.262642	+	0.964893i	$0.415406\pi$
$674$		−	172.285i		−	0.255615i
$675$	407.515	+	388.280i	0.603726	+	0.575230i
$676$	185.220			0.273993
$677$	228.197	−	271.955i	0.337071	−	0.401706i	−0.570709	−	0.821153i	$-0.693331\pi$
$677$	228.197	−	271.955i	0.337071	−	0.401706i	0.907780	+	0.419447i	$0.137776\pi$
$678$	116.949	−	193.067i	0.172491	−	0.284759i
$679$	75.3600	+	427.388i	0.110987	+	0.629437i
$680$	−46.5420	+	127.873i	−0.0684441	+	0.188049i
$681$	−439.481	+	501.924i	−0.645347	+	0.737040i
$682$	−3.18537	+	18.0651i	−0.00467063	+	0.0264885i
$683$	−698.995	−	403.565i	−1.02342	−	0.590871i	−0.108326	−	0.994115i	$-0.534549\pi$
$683$	−698.995	−	403.565i	−1.02342	−	0.590871i	−0.915092	+	0.403244i	$0.867882\pi$
$684$	−73.7095	+	56.7430i	−0.107762	+	0.0829575i
$685$	203.702	+	352.823i	0.297376	+	0.515070i
$686$	−418.126	−	1148.79i	−0.609513	−	1.67462i
$687$	308.531	+	119.703i	0.449099	+	0.174240i
$688$	−160.667	+	134.815i	−0.233527	+	0.195953i
$689$	1.61080	+	1.91968i	0.00233789	+	0.00278618i
$690$	108.919	−	280.736i	0.157854	−	0.406864i
$691$	−1157.65	+	421.352i	−1.67533	+	0.609771i	−0.992658	−	0.120953i	$-0.961405\pi$
$691$	−1157.65	+	421.352i	−1.67533	+	0.609771i	−0.682673	+	0.730724i	$0.739183\pi$
$692$	−244.262	+	141.024i	−0.352979	+	0.203793i
$693$	−165.415	+	401.123i	−0.238694	+	0.578821i
$694$	−149.837	+	259.526i	−0.215904	+	0.373957i
$695$	347.949	+	61.3528i	0.500646	+	0.0882774i
$696$	−180.244	−	157.821i	−0.258972	−	0.226754i
$697$	350.789	+	127.677i	0.503284	+	0.183180i
$698$	−196.416	+	34.6334i	−0.281398	+	0.0496181i
$699$	−89.1540	−	54.0045i	−0.127545	−	0.0772597i
$700$	−410.582	−	344.520i	−0.586546	−	0.492171i
$701$			912.288i			1.30141i	0.759331	+	0.650705i	$0.225526\pi$
$701$			912.288i			1.30141i	−0.759331	+	0.650705i	$0.774474\pi$
$702$	−21.0447	+	333.068i	−0.0299782	+	0.474455i
$703$	−287.257			−0.408615
$704$	−19.2854	+	22.9835i	−0.0273941	+	0.0326470i
$705$	330.251	+	6.94737i	0.468442	+	0.00985443i
$706$	18.7338	+	106.245i	0.0265351	+	0.150488i
$707$	538.817	−	1480.39i	0.762117	−	2.09390i
$708$	20.6222	+	60.5952i	0.0291275	+	0.0855865i
$709$	48.7199	−	276.304i	0.0687163	−	0.389710i	−0.930980	−	0.365070i	$-0.881045\pi$
$709$	48.7199	−	276.304i	0.0687163	−	0.389710i	0.999696	−	0.0246396i	$-0.00784383\pi$
$710$	−257.668	−	148.765i	−0.362913	−	0.209528i
$711$	106.901	−	33.8900i	0.150353	−	0.0476652i
$712$	92.4153	+	160.068i	0.129797	+	0.224815i
$713$	−41.2001	−	113.196i	−0.0577842	−	0.158761i
$714$	196.873	+	1272.47i	0.275732	+	1.78218i
$715$	51.1695	−	42.9363i	0.0715657	−	0.0600507i
$716$	231.493	+	275.883i	0.323315	+	0.385312i
$717$	83.6458	+	104.053i	0.116661	+	0.145123i
$718$	−222.385	+	80.9415i	−0.309728	+	0.112732i
$719$	575.407	−	332.211i	0.800287	−	0.462046i	−0.0432843	−	0.999063i	$-0.513782\pi$
$719$	575.407	−	332.211i	0.800287	−	0.462046i	0.843572	+	0.537017i	$0.180449\pi$
$720$	−61.9342	−	39.3202i	−0.0860197	−	0.0546114i
$721$	−802.044	+	1389.18i	−1.11241	+	1.92674i
$722$	−465.580	−	82.0944i	−0.644848	−	0.113704i
$723$	−22.2820	+	112.480i	−0.0308188	+	0.155573i
$724$	−85.5914	−	31.1527i	−0.118220	−	0.0430286i
$725$	579.660	−	102.210i	0.799530	−	0.140979i
$726$	397.588	−	218.529i	0.547642	−	0.301005i
$727$	182.224	+	152.904i	0.250652	+	0.210322i	0.759453	−	0.650562i	$-0.225467\pi$
$727$	182.224	+	152.904i	0.250652	+	0.210322i	−0.508801	+	0.860884i	$0.669911\pi$
$728$		−	317.783i		−	0.436515i
$729$	723.202	+	91.7566i	0.992047	+	0.125866i
$730$	69.0171			0.0945440
$731$	−795.722	+	948.305i	−1.08854	+	1.29727i
$732$	−273.272	−	497.185i	−0.373322	−	0.679215i
$733$	39.7563	+	225.469i	0.0542378	+	0.307598i	0.999843	−	0.0177186i	$-0.00564029\pi$
$733$	39.7563	+	225.469i	0.0542378	+	0.307598i	−0.945605	+	0.325316i	$0.894529\pi$
$734$	48.3731	−	132.904i	0.0659035	−	0.181068i
$735$	697.126	+	138.100i	0.948470	+	0.187890i
$736$	34.2128	−	194.031i	0.0464848	−	0.263629i
$737$	68.9743	+	39.8223i	0.0935879	+	0.0540330i
$738$	−107.865	+	169.902i	−0.146159	+	0.230219i
$739$	409.364	+	709.039i	0.553943	+	0.959457i	0.997985	+	0.0634509i	$0.0202106\pi$
$739$	409.364	+	709.039i	0.553943	+	0.959457i	−0.444042	+	0.896006i	$0.646456\pi$
$740$	−77.4838	−	212.885i	−0.104708	−	0.287682i
$741$	105.610	−	84.8969i	0.142523	−	0.114571i
$742$	−3.99293	+	3.35047i	−0.00538131	+	0.00451546i
$743$	−376.831	−	449.090i	−0.507175	−	0.604428i	0.450323	−	0.892866i	$-0.351309\pi$
$743$	−376.831	−	449.090i	−0.507175	−	0.604428i	−0.957499	+	0.288437i	$0.906864\pi$
$744$	−29.0023	+	4.48713i	−0.0389816	+	0.00603109i
$745$	153.183	−	55.7540i	0.205615	−	0.0748376i
$746$	627.547	−	362.314i	0.841216	−	0.485676i
$747$	197.367	+	622.567i	0.264213	+	0.833422i
$748$	−88.5429	+	153.361i	−0.118373	+	0.205028i
$749$	1083.89	+	191.119i	1.44712	+	0.255166i
$750$	375.248	−	127.707i	0.500331	−	0.170276i
$751$	−565.095	−	205.678i	−0.752456	−	0.273872i	−0.0628174	−	0.998025i	$-0.520009\pi$
$751$	−565.095	−	205.678i	−0.752456	−	0.273872i	−0.689639	+	0.724153i	$0.742231\pi$
$752$	212.846	−	37.5304i	0.283039	−	0.0499075i
$753$	17.9935	−	855.342i	0.0238958	−	1.13591i
$754$	267.338	+	224.323i	0.354559	+	0.297510i
$755$			551.809i			0.730873i
$756$	−692.780	−	43.7729i	−0.916376	−	0.0579007i
$757$	−1129.66			−1.49229			−0.746143	−	0.665785i	$-0.768097\pi$
$757$	−1129.66			−1.49229			−0.746143	+	0.665785i	$0.768097\pi$
$758$	188.448	−	224.584i	0.248612	−	0.296285i
$759$	203.027	−	335.170i	0.267493	−	0.441594i
$760$	5.17236	+	29.3339i	0.00680574	+	0.0385973i
$761$	−341.118	+	937.215i	−0.448250	+	1.23156i	0.485691	+	0.874131i	$0.338568\pi$
$761$	−341.118	+	937.215i	−0.448250	+	1.23156i	−0.933941	+	0.357427i	$0.883654\pi$
$762$	182.094	−	207.967i	0.238968	−	0.272922i
$763$	200.460	−	1136.86i	0.262726	−	1.48999i
$764$	−77.9110	−	44.9819i	−0.101978	−	0.0588769i
$765$	−400.302	−	165.076i	−0.523270	−	0.215786i
$766$	426.492	+	738.705i	0.556778	+	0

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)

\(f(q)\)	\(=\)	\(q+(-0.909039 + 1.08335i) q^{2} +(-1.44503 - 2.62905i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(0.696976 - 1.91493i) q^{5} +(4.16177 + 0.824439i) q^{6} +(2.23222 - 12.6596i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-4.82380 + 7.59809i) q^{9} +O(q^{10})\)	\(q+(-0.909039 + 1.08335i) q^{2} +(-1.44503 - 2.62905i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(0.696976 - 1.91493i) q^{5} +(4.16177 + 0.824439i) q^{6} +(2.23222 - 12.6596i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-4.82380 + 7.59809i) q^{9} +(1.44096 + 2.49581i) q^{10} +(1.28270 + 3.52418i) q^{11} +(-4.67636 + 3.75920i) q^{12} +(6.69534 - 5.61806i) q^{13} +(11.6856 + 13.9263i) q^{14} +(-6.04158 + 0.934733i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(-20.4462 + 11.8046i) q^{17} +(-3.84637 - 12.1328i) q^{18} +(-2.58391 + 4.47546i) q^{19} +(-4.01373 - 0.707728i) q^{20} +(-36.5082 + 12.4248i) q^{21} +(-4.98394 - 1.81401i) q^{22} +(34.3001 - 6.04803i) q^{23} +(0.178462 - 8.48340i) q^{24} +(15.9699 + 13.4004i) q^{25} +12.3604i q^{26} +(26.9463 + 1.70258i) q^{27} -25.7097 q^{28} +(18.1485 - 21.6285i) q^{29} +(4.47939 - 7.39486i) q^{30} +(-0.600583 - 3.40608i) q^{31} +(1.93476 - 5.31570i) q^{32} +(7.41171 - 8.46479i) q^{33} +(5.79786 - 32.8813i) q^{34} +(-22.6863 - 13.0979i) q^{35} +(16.6406 + 6.86225i) q^{36} +(27.7928 + 48.1386i) q^{37} +(-2.49962 - 6.86765i) q^{38} +(-24.4451 - 9.48415i) q^{39} +(4.41535 - 3.70492i) q^{40} +(-10.1636 - 12.1124i) q^{41} +(19.7270 - 50.8458i) q^{42} +(49.2717 - 17.9334i) q^{43} +(6.49580 - 3.75035i) q^{44} +(11.1877 + 14.5329i) q^{45} +(-24.6280 + 42.6569i) q^{46} +(-53.2114 - 9.38261i) q^{47} +(9.02827 + 7.90508i) q^{48} +(-109.237 - 39.7589i) q^{49} +(-29.0346 + 5.11958i) q^{50} +(60.5802 + 36.6961i) q^{51} +(-13.3907 - 11.2361i) q^{52} +0.286719i q^{53} +(-26.3397 + 27.6445i) q^{54} +7.64255 q^{55} +(23.3711 - 27.8526i) q^{56} +(15.5000 + 0.326068i) q^{57} +(6.93358 + 39.3223i) q^{58} +(3.64869 - 10.0247i) q^{59} +(3.93928 + 11.5750i) q^{60} +(-16.4195 + 93.1195i) q^{61} +(4.23593 + 2.44561i) q^{62} +(85.4206 + 78.0278i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-6.09168 - 16.7367i) q^{65} +(2.43281 + 15.7243i) q^{66} +(16.2682 - 13.6506i) q^{67} +(30.3515 + 36.1715i) q^{68} +(-65.4651 - 81.4371i) q^{69} +(34.8124 - 12.6707i) q^{70} +(-89.4087 + 51.6201i) q^{71} +(-22.5612 + 11.7896i) q^{72} +(11.9742 - 20.7399i) q^{73} +(-77.4157 - 13.6505i) q^{74} +(12.1533 - 61.3497i) q^{75} +(9.71232 + 3.53500i) q^{76} +(47.4778 - 8.37161i) q^{77} +(32.4962 - 17.8611i) q^{78} +(-9.54529 - 8.00945i) q^{79} +8.15129i q^{80} +(-34.4619 - 73.3033i) q^{81} +22.3611 q^{82} +(46.6451 - 55.5895i) q^{83} +(37.1512 + 67.5921i) q^{84} +(8.35446 + 47.3805i) q^{85} +(-25.3617 + 69.6807i) q^{86} +(-83.0873 - 16.4595i) q^{87} +(-1.84199 + 10.4464i) q^{88} +(56.5926 + 32.6737i) q^{89} +(-25.9143 - 1.09078i) q^{90} +(-56.1766 - 97.3008i) q^{91} +(-23.8246 - 65.4576i) q^{92} +(-8.08688 + 6.50083i) q^{93} +(58.5359 - 49.1175i) q^{94} +(6.76926 + 8.06729i) q^{95} +(-16.7710 + 2.59475i) q^{96} +(-31.7241 + 11.5466i) q^{97} +(142.373 - 82.1991i) q^{98} +(-32.9645 - 7.25390i) 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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