LMFDB - Embedded newform 54.3.f.a.41.1

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			41.1
Character	$\chi$	$=$	54.41
Dual form			54.3.f.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39273 + 0.245576i) q^{2} +(-2.97067 + 0.418457i) q^{3} +(1.87939 - 0.684040i) q^{4} +(5.54906 - 6.61311i) q^{5} +(4.03458 - 1.31232i) q^{6} +(7.83131 + 2.85036i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(8.64979 - 2.48620i) q^{9} +O(q^{10})$	\(q+(-1.39273 + 0.245576i) q^{2} +(-2.97067 + 0.418457i) q^{3} +(1.87939 - 0.684040i) q^{4} +(5.54906 - 6.61311i) q^{5} +(4.03458 - 1.31232i) q^{6} +(7.83131 + 2.85036i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(8.64979 - 2.48620i) q^{9} +(-6.10431 + 10.5730i) q^{10} +(-10.8191 - 12.8937i) q^{11} +(-5.29680 + 2.81850i) q^{12} +(0.524960 - 2.97720i) q^{13} +(-11.6069 - 2.04660i) q^{14} +(-13.7171 + 21.9674i) q^{15} +(3.06418 - 2.57115i) q^{16} +(8.43596 + 4.87051i) q^{17} +(-11.4363 + 5.58678i) q^{18} +(3.84677 + 6.66281i) q^{19} +(5.90519 - 16.2244i) q^{20} +(-24.4570 - 5.19043i) q^{21} +(18.2344 + 15.3005i) q^{22} +(10.1434 + 27.8689i) q^{23} +(6.68484 - 5.22617i) q^{24} +(-8.59998 - 48.7729i) q^{25} +4.27534i q^{26} +(-24.6553 + 11.0052i) q^{27} +16.6678 q^{28} +(-10.5809 + 1.86569i) q^{29} +(13.7096 - 33.9633i) q^{30} +(-10.8017 + 3.93149i) q^{31} +(-3.63616 + 4.33340i) q^{32} +(37.5353 + 33.7755i) q^{33} +(-12.9451 - 4.71163i) q^{34} +(62.3062 - 35.9725i) q^{35} +(14.5556 - 10.5893i) q^{36} +(-11.5925 + 20.0787i) q^{37} +(-6.99373 - 8.33481i) q^{38} +(-0.313655 + 9.06395i) q^{39} +(-4.24001 + 24.0463i) q^{40} +(-16.7264 - 2.94931i) q^{41} +(35.3366 + 1.22281i) q^{42} +(18.0881 - 15.1778i) q^{43} +(-29.1530 - 16.8315i) q^{44} +(31.5567 - 70.9981i) q^{45} +(-20.9710 - 36.3228i) q^{46} +(-5.67901 + 15.6029i) q^{47} +(-8.02675 + 8.92027i) q^{48} +(15.6687 + 13.1476i) q^{49} +(23.9549 + 65.8155i) q^{50} +(-27.0986 - 10.9386i) q^{51} +(-1.04992 - 5.95439i) q^{52} +75.3383i q^{53} +(31.6355 - 21.3821i) q^{54} -145.303 q^{55} +(-23.2137 + 4.09321i) q^{56} +(-14.2156 - 18.1833i) q^{57} +(14.2781 - 5.19681i) q^{58} +(-38.6968 + 46.1170i) q^{59} +(-10.7532 + 50.6683i) q^{60} +(32.1023 + 11.6843i) q^{61} +(14.0783 - 8.12813i) q^{62} +(74.8257 + 5.18485i) q^{63} +(4.00000 - 6.92820i) q^{64} +(-16.7755 - 19.9923i) q^{65} +(-60.5710 - 37.8224i) q^{66} +(6.53483 - 37.0609i) q^{67} +(19.1860 + 3.38302i) q^{68} +(-41.7948 - 78.5447i) q^{69} +(-77.9416 + 65.4008i) q^{70} +(44.0325 + 25.4222i) q^{71} +(-17.6715 + 18.3226i) q^{72} +(49.2453 + 85.2954i) q^{73} +(11.2143 - 30.8110i) q^{74} +(45.9571 + 141.290i) q^{75} +(11.7872 + 9.89063i) q^{76} +(-47.9758 - 131.813i) q^{77} +(-1.78905 - 12.7006i) q^{78} +(-14.0913 - 79.9158i) q^{79} -34.5312i q^{80} +(68.6376 - 43.0102i) q^{81} +24.0196 q^{82} +(-15.8868 + 2.80127i) q^{83} +(-49.5146 + 6.97477i) q^{84} +(79.0209 - 28.7612i) q^{85} +(-21.4646 + 25.5805i) q^{86} +(30.6516 - 9.97000i) q^{87} +(44.7356 + 16.2824i) q^{88} +(14.0161 - 8.09222i) q^{89} +(-26.5145 + 106.631i) q^{90} +(12.5972 - 21.8190i) q^{91} +(38.1269 + 45.4378i) q^{92} +(30.4431 - 16.1992i) q^{93} +(4.07761 - 23.1253i) q^{94} +(65.4078 + 11.5332i) q^{95} +(8.98848 - 14.3947i) q^{96} +(-101.648 + 85.2929i) q^{97} +(-25.0509 - 14.4632i) q^{98} +(-125.639 - 84.6291i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9}+O(q^{10}) $ 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9	$ 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9} - 18 q^{11} - 12 q^{12} - 36 q^{14} - 18 q^{15} - 48 q^{18} - 72 q^{20} - 228 q^{21} + 36 q^{22} - 180 q^{23} + 18 q^{25} + 54 q^{27} + 144 q^{29} + 144 q^{30} - 90 q^{31} + 324 q^{33} - 72 q^{34} + 486 q^{35} + 168 q^{36} + 180 q^{38} + 102 q^{39} - 90 q^{41} + 48 q^{42} + 90 q^{43} - 378 q^{45} - 378 q^{47} - 24 q^{48} + 72 q^{49} - 54 q^{51} - 36 q^{54} - 72 q^{56} + 72 q^{57} + 252 q^{59} + 36 q^{60} - 144 q^{61} + 318 q^{63} + 144 q^{64} + 18 q^{65} - 432 q^{66} - 594 q^{67} - 180 q^{68} - 522 q^{69} - 360 q^{70} - 648 q^{71} - 192 q^{72} + 126 q^{73} - 504 q^{74} - 438 q^{75} - 72 q^{76} - 342 q^{77} - 288 q^{78} - 72 q^{79} + 324 q^{81} + 594 q^{83} + 216 q^{84} + 360 q^{85} + 540 q^{86} + 1062 q^{87} + 144 q^{88} + 648 q^{89} + 720 q^{90} - 198 q^{91} + 396 q^{92} + 462 q^{93} + 504 q^{94} + 252 q^{95} + 96 q^{96} + 702 q^{97} + 648 q^{98} + 126 q^{99}+O(q^{100}) $ 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9 - 18 * q^11 - 12 * q^12 - 36 * q^14 - 18 * q^15 - 48 * q^18 - 72 * q^20 - 228 * q^21 + 36 * q^22 - 180 * q^23 + 18 * q^25 + 54 * q^27 + 144 * q^29 + 144 * q^30 - 90 * q^31 + 324 * q^33 - 72 * q^34 + 486 * q^35 + 168 * q^36 + 180 * q^38 + 102 * q^39 - 90 * q^41 + 48 * q^42 + 90 * q^43 - 378 * q^45 - 378 * q^47 - 24 * q^48 + 72 * q^49 - 54 * q^51 - 36 * q^54 - 72 * q^56 + 72 * q^57 + 252 * q^59 + 36 * q^60 - 144 * q^61 + 318 * q^63 + 144 * q^64 + 18 * q^65 - 432 * q^66 - 594 * q^67 - 180 * q^68 - 522 * q^69 - 360 * q^70 - 648 * q^71 - 192 * q^72 + 126 * q^73 - 504 * q^74 - 438 * q^75 - 72 * q^76 - 342 * q^77 - 288 * q^78 - 72 * q^79 + 324 * q^81 + 594 * q^83 + 216 * q^84 + 360 * q^85 + 540 * q^86 + 1062 * q^87 + 144 * q^88 + 648 * q^89 + 720 * q^90 - 198 * q^91 + 396 * q^92 + 462 * q^93 + 504 * q^94 + 252 * q^95 + 96 * q^96 + 702 * q^97 + 648 * q^98 + 126 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.39273	+	0.245576i	−0.696364	+	0.122788i
$2$	−1.39273	+	0.245576i	−0.696364	+	0.122788i
$3$	−2.97067	+	0.418457i	−0.990224	+	0.139486i
$3$	−2.97067	+	0.418457i	−0.990224	+	0.139486i
$4$	1.87939	−	0.684040i	0.469846	−	0.171010i
$5$	5.54906	−	6.61311i	1.10981	−	1.32262i	0.168264	−	0.985742i	$-0.446184\pi$
$5$	5.54906	−	6.61311i	1.10981	−	1.32262i	0.941547	−	0.336880i	$-0.109372\pi$
$6$	4.03458	−	1.31232i	0.672429	−	0.218720i
$7$	7.83131	+	2.85036i	1.11876	+	0.407195i	0.834199	−	0.551463i	$-0.185930\pi$
$7$	7.83131	+	2.85036i	1.11876	+	0.407195i	0.284560	+	0.958658i	$0.408153\pi$
$8$	−2.44949	+	1.41421i	−0.306186	+	0.176777i
$9$	8.64979	−	2.48620i	0.961087	−	0.276244i
$10$	−6.10431	+	10.5730i	−0.610431	+	1.05730i
$11$	−10.8191	−	12.8937i	−0.983551	−	1.17215i	−0.985070	−	0.172152i	$-0.944928\pi$
$11$	−10.8191	−	12.8937i	−0.983551	−	1.17215i	0.00151930	−	0.999999i	$-0.499516\pi$
$12$	−5.29680	+	2.81850i	−0.441400	+	0.234875i
$13$	0.524960	−	2.97720i	0.0403815	−	0.229015i	−0.957937	−	0.286978i	$-0.907349\pi$
$13$	0.524960	−	2.97720i	0.0403815	−	0.229015i	0.998319	+	0.0579628i	$0.0184605\pi$
$14$	−11.6069	−	2.04660i	−0.829062	−	0.146186i
$15$	−13.7171	+	21.9674i	−0.914475	+	1.46450i
$16$	3.06418	−	2.57115i	0.191511	−	0.160697i
$17$	8.43596	+	4.87051i	0.496233	+	0.286500i	0.727157	−	0.686472i	$-0.240841\pi$
$17$	8.43596	+	4.87051i	0.496233	+	0.286500i	−0.230924	+	0.972972i	$0.574175\pi$
$18$	−11.4363	+	5.58678i	−0.635348	+	0.310376i
$19$	3.84677	+	6.66281i	0.202462	+	0.350674i	0.949321	−	0.314308i	$-0.101772\pi$
$19$	3.84677	+	6.66281i	0.202462	+	0.350674i	−0.746859	+	0.664982i	$0.768439\pi$
$20$	5.90519	−	16.2244i	0.295259	−	0.811218i
$21$	−24.4570	−	5.19043i	−1.16462	−	0.247163i
$22$	18.2344	+	15.3005i	0.828836	+	0.695476i
$23$	10.1434	+	27.8689i	0.441019	+	1.21169i	0.938823	+	0.344400i	$0.111918\pi$
$23$	10.1434	+	27.8689i	0.441019	+	1.21169i	−0.497804	+	0.867290i	$0.665860\pi$
$24$	6.68484	−	5.22617i	0.278535	−	0.217757i
$25$	−8.59998	−	48.7729i	−0.343999	−	1.95092i
$26$			4.27534i			0.164436i
$27$	−24.6553	+	11.0052i	−0.913160	+	0.407602i
$28$	16.6678			0.595279
$29$	−10.5809	+	1.86569i	−0.364858	+	0.0643342i	−0.353072	−	0.935596i	$-0.614863\pi$
$29$	−10.5809	+	1.86569i	−0.364858	+	0.0643342i	−0.0117860	+	0.999931i	$0.503752\pi$
$30$	13.7096	−	33.9633i	0.456986	−	1.13211i
$31$	−10.8017	+	3.93149i	−0.348441	+	0.126822i	−0.510311	−	0.859990i	$-0.670470\pi$
$31$	−10.8017	+	3.93149i	−0.348441	+	0.126822i	0.161870	+	0.986812i	$0.448248\pi$
$32$	−3.63616	+	4.33340i	−0.113630	+	0.135419i
$33$	37.5353	+	33.7755i	1.13743	+	1.02350i
$34$	−12.9451	−	4.71163i	−0.380738	−	0.138577i
$35$	62.3062	−	35.9725i	1.78018	−	1.02779i
$36$	14.5556	−	10.5893i	0.404323	−	0.294148i
$37$	−11.5925	+	20.0787i	−0.313309	+	0.542668i	−0.979077	−	0.203492i	$-0.934771\pi$
$37$	−11.5925	+	20.0787i	−0.313309	+	0.542668i	0.665767	+	0.746160i	$0.268104\pi$
$38$	−6.99373	−	8.33481i	−0.184046	−	0.219337i
$39$	−0.313655	+	9.06395i	−0.00804244	+	0.232409i
$40$	−4.24001	+	24.0463i	−0.106000	+	0.601158i
$41$	−16.7264	−	2.94931i	−0.407960	−	0.0719344i	−0.0340976	−	0.999419i	$-0.510856\pi$
$41$	−16.7264	−	2.94931i	−0.407960	−	0.0719344i	−0.373863	+	0.927484i	$0.621967\pi$
$42$	35.3366	+	1.22281i	0.841348	+	0.0291146i
$43$	18.0881	−	15.1778i	0.420655	−	0.352971i	−0.407757	−	0.913090i	$-0.633689\pi$
$43$	18.0881	−	15.1778i	0.420655	−	0.352971i	0.828412	+	0.560119i	$0.189245\pi$
$44$	−29.1530	−	16.8315i	−0.662567	−	0.382533i
$45$	31.5567	−	70.9981i	0.701259	−	1.57773i
$46$	−20.9710	−	36.3228i	−0.455891	−	0.789626i
$47$	−5.67901	+	15.6029i	−0.120830	+	0.331977i	−0.985331	−	0.170653i	$-0.945412\pi$
$47$	−5.67901	+	15.6029i	−0.120830	+	0.331977i	0.864501	+	0.502631i	$0.167634\pi$
$48$	−8.02675	+	8.92027i	−0.167224	+	0.185839i
$49$	15.6687	+	13.1476i	0.319769	+	0.268318i
$50$	23.9549	+	65.8155i	0.479097	+	1.31631i
$51$	−27.0986	−	10.9386i	−0.531345	−	0.214482i
$52$	−1.04992	−	5.95439i	−0.0201908	−	0.114508i
$53$			75.3383i			1.42148i	0.703456	+	0.710739i	$0.251639\pi$
$53$			75.3383i			1.42148i	−0.703456	+	0.710739i	$0.748361\pi$
$54$	31.6355	−	21.3821i	0.585843	−	0.395964i
$55$	−145.303			−2.64187
$56$	−23.2137	+	4.09321i	−0.414531	+	0.0730930i
$57$	−14.2156	−	18.1833i	−0.249397	−	0.319005i
$58$	14.2781	−	5.19681i	0.246174	−	0.0896001i
$59$	−38.6968	+	46.1170i	−0.655878	+	0.781645i	−0.986788	−	0.162017i	$-0.948200\pi$
$59$	−38.6968	+	46.1170i	−0.655878	+	0.781645i	0.330910	+	0.943662i	$0.392644\pi$
$60$	−10.7532	+	50.6683i	−0.179219	+	0.844472i
$61$	32.1023	+	11.6843i	0.526267	+	0.191546i	0.591471	−	0.806326i	$-0.298547\pi$
$61$	32.1023	+	11.6843i	0.526267	+	0.191546i	−0.0652037	+	0.997872i	$0.520770\pi$
$62$	14.0783	−	8.12813i	0.227070	−	0.131099i
$63$	74.8257	+	5.18485i	1.18771	+	0.0822992i
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	−16.7755	−	19.9923i	−0.258085	−	0.307573i
$66$	−60.5710	−	37.8224i	−0.917742	−	0.573066i
$67$	6.53483	−	37.0609i	0.0975348	−	0.553147i	−0.896406	−	0.443233i	$-0.853831\pi$
$67$	6.53483	−	37.0609i	0.0975348	−	0.553147i	0.993941	−	0.109914i	$-0.0350575\pi$
$68$	19.1860	+	3.38302i	0.282148	+	0.0497503i
$69$	−41.7948	−	78.5447i	−0.605721	−	1.13833i
$70$	−77.9416	+	65.4008i	−1.11345	+	0.934297i
$71$	44.0325	+	25.4222i	0.620175	+	0.358058i	0.776937	−	0.629578i	$-0.216772\pi$
$71$	44.0325	+	25.4222i	0.620175	+	0.358058i	−0.156762	+	0.987636i	$0.550106\pi$
$72$	−17.6715	+	18.3226i	−0.245438	+	0.254480i
$73$	49.2453	+	85.2954i	0.674593	+	1.16843i	0.976588	+	0.215120i	$0.0690144\pi$
$73$	49.2453	+	85.2954i	0.674593	+	1.16843i	−0.301994	+	0.953310i	$0.597652\pi$
$74$	11.2143	−	30.8110i	0.151545	−	0.416365i
$75$	45.9571	+	141.290i	0.612761	+	1.88386i
$76$	11.7872	+	9.89063i	0.155095	+	0.130140i
$77$	−47.9758	−	131.813i	−0.623063	−	1.71185i
$78$	−1.78905	−	12.7006i	−0.0229365	−	0.162829i
$79$	−14.0913	−	79.9158i	−0.178371	−	1.01159i	−0.934180	−	0.356801i	$-0.883867\pi$
$79$	−14.0913	−	79.9158i	−0.178371	−	1.01159i	0.755809	−	0.654792i	$-0.227244\pi$
$80$		−	34.5312i		−	0.431640i
$81$	68.6376	−	43.0102i	0.847378	−	0.530990i
$82$	24.0196			0.292921
$83$	−15.8868	+	2.80127i	−0.191407	+	0.0337503i	−0.268530	−	0.963271i	$-0.586538\pi$
$83$	−15.8868	+	2.80127i	−0.191407	+	0.0337503i	0.0771226	+	0.997022i	$0.475427\pi$
$84$	−49.5146	+	6.97477i	−0.589460	+	0.0830329i
$85$	79.0209	−	28.7612i	0.929657	−	0.338368i
$86$	−21.4646	+	25.5805i	−0.249588	+	0.297448i
$87$	30.6516	−	9.97000i	0.352317	−	0.114598i
$88$	44.7356	+	16.2824i	0.508359	+	0.185027i
$89$	14.0161	−	8.09222i	0.157485	−	0.0909238i	−0.419187	−	0.907900i	$-0.637685\pi$
$89$	14.0161	−	8.09222i	0.157485	−	0.0909238i	0.576671	+	0.816976i	$0.304351\pi$
$90$	−26.5145	+	106.631i	−0.294605	+	1.18478i
$91$	12.5972	−	21.8190i	0.138431	−	0.239769i
$92$	38.1269	+	45.4378i	0.414422	+	0.493889i
$93$	30.4431	−	16.1992i	0.327345	−	0.174185i
$94$	4.07761	−	23.1253i	0.0433788	−	0.246014i
$95$	65.4078	+	11.5332i	0.688504	+	0.121402i
$96$	8.98848	−	14.3947i	0.0936300	−	0.149945i
$97$	−101.648	+	85.2929i	−1.04792	+	0.879308i	−0.992873	−	0.119176i	$-0.961975\pi$
$97$	−101.648	+	85.2929i	−1.04792	+	0.879308i	−0.0550452	+	0.998484i	$0.517530\pi$
$98$	−25.0509	−	14.4632i	−0.255622	−	0.147583i
$99$	−125.639	−	84.6291i	−1.26908	−	0.854839i
$100$	−49.5253	−	85.7803i	−0.495253	−	0.857803i
$101$	−5.20626	+	14.3041i	−0.0515471	+	0.141625i	−0.962794	−	0.270235i	$-0.912898\pi$
$101$	−5.20626	+	14.3041i	−0.0515471	+	0.141625i	0.911247	+	0.411860i	$0.135121\pi$
$102$	40.4272	+	8.57973i	0.396345	+	0.0841150i
$103$	−28.9968	−	24.3312i	−0.281522	−	0.236225i	0.491082	−	0.871113i	$-0.336602\pi$
$103$	−28.9968	−	24.3312i	−0.281522	−	0.236225i	−0.772604	+	0.634889i	$0.781046\pi$
$104$	2.92451	+	8.03502i	0.0281203	+	0.0772598i
$105$	−170.038	+	132.935i	−1.61941	+	1.26605i
$106$	−18.5013	−	104.926i	−0.174540	−	0.989866i
$107$		−	118.659i		−	1.10897i	−0.832195	−	0.554483i	$-0.812916\pi$
$107$		−	118.659i		−	1.10897i	0.832195	−	0.554483i	$-0.187084\pi$
$108$	−38.8088	+	37.5483i	−0.359341	+	0.347670i
$109$	206.055			1.89042			0.945208	−	0.326468i	$-0.105859\pi$
$109$	206.055			1.89042			0.945208	+	0.326468i	$0.105859\pi$
$110$	202.367	−	35.6828i	1.83970	−	0.324389i
$111$	26.0353	−	64.4982i	0.234552	−	0.581065i
$112$	31.3252	−	11.4015i	0.279690	−	0.101799i
$113$	−45.6567	+	54.4116i	−0.404042	+	0.481519i	−0.929248	−	0.369457i	$-0.879544\pi$
$113$	−45.6567	+	54.4116i	−0.404042	+	0.481519i	0.525206	+	0.850975i	$0.323988\pi$
$114$	24.2638	+	21.8334i	0.212841	+	0.191521i
$115$	240.586	+	87.5663i	2.09206	+	0.761446i
$116$	−18.6093	+	10.7441i	−0.160425	+	0.0926215i
$117$	−2.86111	−	27.0573i	−0.0244539	−	0.231259i
$118$	42.5689	−	73.7315i	0.360753	−	0.624843i
$119$	52.1819	+	62.1880i	0.438504	+	0.522588i
$120$	2.53334	−	73.2079i	0.0211112	−	0.610066i
$121$	−28.1828	+	159.833i	−0.232916	+	1.32093i
$122$	−47.5792	−	8.38949i	−0.389993	−	0.0687663i
$123$	50.9227	+	1.76216i	0.414006	+	0.0143265i
$124$	−17.6112	+	14.7776i	−0.142026	+	0.119174i
$125$	−183.357	−	105.861i	−1.46685	−	0.846888i
$126$	−105.485	+	11.1543i	−0.837184	+	0.0885261i
$127$	−19.1347	−	33.1422i	−0.150667	−	0.260963i	0.780806	−	0.624774i	$-0.214809\pi$
$127$	−19.1347	−	33.1422i	−0.150667	−	0.260963i	−0.931473	+	0.363811i	$0.881475\pi$
$128$	−3.86952	+	10.6314i	−0.0302306	+	0.0830579i
$129$	−47.3827	+	52.6573i	−0.367308	+	0.408196i
$130$	28.2733	+	23.7241i	0.217487	+	0.182493i
$131$	−74.5355	−	204.785i	−0.568973	−	1.56324i	−0.806110	−	0.591765i	$-0.798431\pi$
$131$	−74.5355	−	204.785i	−0.568973	−	1.56324i	0.237137	−	0.971476i	$-0.423791\pi$
$132$	93.6472	+	37.8015i	0.709448	+	0.286375i
$133$	11.1339	+	63.1432i	0.0837132	+	0.474761i
$134$			53.2205i			0.397168i
$135$	−64.0349	+	224.117i	−0.474333	+	1.66013i
$136$	−27.5517			−0.202586
$137$	−181.295	+	31.9672i	−1.32332	+	0.233337i	−0.790277	−	0.612749i	$-0.790064\pi$
$137$	−181.295	+	31.9672i	−1.32332	+	0.233337i	−0.533045	+	0.846087i	$0.678952\pi$
$138$	77.4974	+	99.1277i	0.561575	+	0.718316i
$139$	−228.486	+	83.1623i	−1.64379	+	0.598290i	−0.987695	−	0.156391i	$-0.950014\pi$
$139$	−228.486	+	83.1623i	−1.64379	+	0.598290i	−0.656092	+	0.754681i	$0.727792\pi$
$140$	92.4907	−	110.226i	0.660648	−	0.787329i
$141$	10.3413	−	48.7276i	0.0733426	−	0.345586i
$142$	−67.5683	−	24.5929i	−0.475833	−	0.173189i
$143$	−44.0665	+	25.4418i	−0.308157	+	0.177915i
$144$	20.1121	−	29.8581i	0.139667	−	0.207348i
$145$	−46.3758	+	80.3253i	−0.319833	+	0.553968i
$146$	−89.5318	−	106.700i	−0.613232	−	0.730821i
$147$	−52.0482	−	32.5005i	−0.354069	−	0.221092i
$148$	−8.05203	+	45.6653i	−0.0544056	+	0.308550i
$149$	141.886	+	25.0183i	0.952255	+	0.167908i	0.628132	−	0.778107i	$-0.283820\pi$
$149$	141.886	+	25.0183i	0.952255	+	0.167908i	0.324123	+	0.946015i	$0.394931\pi$
$150$	−98.7030	−	185.492i	−0.658020	−	1.23661i
$151$	−77.8368	+	65.3129i	−0.515476	+	0.432535i	−0.863051	−	0.505117i	$-0.831449\pi$
$151$	−77.8368	+	65.3129i	−0.515476	+	0.432535i	0.347575	+	0.937652i	$0.387005\pi$
$152$	−18.8453	−	10.8803i	−0.123982	−	0.0715810i
$153$	85.0783	+	21.1554i	0.556068	+	0.138270i
$154$	99.1872	+	171.797i	0.644073	+	1.11557i
$155$	−33.9398	+	93.2488i	−0.218966	+	0.601605i
$156$	5.61063	+	17.2492i	0.0359656	+	0.110572i
$157$	−237.118	−	198.965i	−1.51030	−	1.26730i	−0.863162	−	0.504927i	$-0.831519\pi$
$157$	−237.118	−	198.965i	−1.51030	−	1.26730i	−0.647143	−	0.762369i	$-0.724036\pi$
$158$	39.2508	+	107.841i	0.248423	+	0.682535i
$159$	−31.5259	−	223.805i	−0.198276	−	1.40758i
$160$	8.48002	+	48.0926i	0.0530001	+	0.300579i
$161$			247.162i			1.53517i
$162$	−85.0313	+	76.7572i	−0.524885	+	0.473810i
$163$	160.056			0.981937			0.490969	−	0.871177i	$-0.336643\pi$
$163$	160.056			0.981937			0.490969	+	0.871177i	$0.336643\pi$
$164$	−33.4527	+	5.89862i	−0.203980	+	0.0359672i
$165$	431.647	−	60.8030i	2.61604	−	0.368503i
$166$	21.4381	−	7.80282i	0.129145	−	0.0470050i
$167$	160.019	−	190.703i	0.958197	−	1.14193i	−0.0316076	−	0.999500i	$-0.510063\pi$
$167$	160.019	−	190.703i	0.958197	−	1.14193i	0.989804	−	0.142434i	$-0.0454929\pi$
$168$	67.2476	−	21.8735i	0.400283	−	0.130200i
$169$	150.220	+	54.6756i	0.888875	+	0.323524i
$170$	−102.992	+	59.4622i	−0.605833	+	0.349778i
$171$	49.8388	+	48.0680i	0.291455	+	0.281100i
$172$	23.6124	−	40.8979i	0.137281	−	0.237778i
$173$	43.4383	+	51.7678i	0.251088	+	0.299236i	0.876836	−	0.480790i	$-0.159650\pi$
$173$	43.4383	+	51.7678i	0.251088	+	0.299236i	−0.625747	+	0.780026i	$0.715206\pi$
$174$	−40.2409	+	21.4128i	−0.231270	+	0.123062i
$175$	71.6714	−	406.469i	0.409551	−	2.32268i
$176$	−66.3031	−	11.6910i	−0.376722	−	0.0664262i
$177$	95.6575	−	153.192i	0.540438	−	0.865489i
$178$	−17.5334	+	14.7123i	−0.0985024	+	0.0826533i
$179$	203.717	+	117.616i	1.13808	+	0.657073i	0.945955	−	0.324297i	$-0.105128\pi$
$179$	203.717	+	117.616i	1.13808	+	0.657073i	0.192128	+	0.981370i	$0.438461\pi$
$180$	10.7416	−	155.019i	0.0596756	−	0.861215i
$181$	−108.916	−	188.647i	−0.601744	−	1.04225i	−0.992557	−	0.121781i	$-0.961140\pi$
$181$	−108.916	−	188.647i	−0.601744	−	1.04225i	0.390813	−	0.920470i	$-0.372194\pi$
$182$	−12.1863	+	33.4815i	−0.0669576	+	0.183965i
$183$	−100.255	−	21.2767i	−0.547840	−	0.116266i
$184$	−64.2588	−	53.9195i	−0.349233	−	0.293041i
$185$	68.4556	+	188.080i	0.370030	+	1.01665i
$186$	−38.4208	+	30.0372i	−0.206564	+	0.161490i
$187$	−28.4706	−	161.465i	−0.152249	−	0.863448i
$188$			33.2086i			0.176642i
$189$	−224.452	+	15.9089i	−1.18758	+	0.0841739i
$190$	−93.9276			−0.494356
$191$	253.418	−	44.6844i	1.32679	−	0.233950i	0.535060	−	0.844814i	$-0.320289\pi$
$191$	253.418	−	44.6844i	1.32679	−	0.233950i	0.791735	+	0.610864i	$0.209178\pi$
$192$	−8.98353	+	22.2552i	−0.0467892	+	0.115913i
$193$	72.0472	−	26.2230i	0.373302	−	0.135871i	−0.148554	−	0.988904i	$-0.547462\pi$
$193$	72.0472	−	26.2230i	0.373302	−	0.135871i	0.521856	+	0.853034i	$0.325240\pi$
$194$	120.622	−	143.752i	0.621765	−	0.740990i
$195$	58.2004	+	52.3706i	0.298464	+	0.268567i
$196$	38.4410	+	13.9914i	0.196127	+	0.0713845i
$197$	−211.300	+	121.994i	−1.07259	+	0.619260i	−0.928888	−	0.370361i	$-0.879234\pi$
$197$	−211.300	+	121.994i	−1.07259	+	0.619260i	−0.143702	+	0.989621i	$0.545901\pi$
$198$	195.764	+	87.0115i	0.988705	+	0.439452i
$199$	−41.0539	+	71.1075i	−0.206301	+	0.357324i	−0.950547	−	0.310582i	$-0.899476\pi$
$199$	−41.0539	+	71.1075i	−0.206301	+	0.357324i	0.744245	+	0.667906i	$0.232809\pi$
$200$	90.0408	+	107.307i	0.450204	+	0.536533i
$201$	−3.90445	+	112.830i	−0.0194251	+	0.561344i
$202$	3.73817	−	21.2002i	0.0185058	−	0.104952i
$203$	−88.1800	−	15.5485i	−0.434384	−	0.0765936i
$204$	−58.4111	−	2.02130i	−0.286329	−	0.00990832i
$205$	−112.320	+	94.2474i	−0.547901	+	0.459743i
$206$	46.3597	+	26.7658i	0.225047	+	0.129931i
$207$	157.026	+	215.841i	0.758580	+	1.04271i
$208$	−6.04625	−	10.4724i	−0.0290685	−	0.0503481i
$209$	44.2895	−	121.684i	0.211911	−	0.582221i
$210$	204.172	−	226.900i	0.972246	−	1.08047i
$211$	44.0427	+	36.9562i	0.208733	+	0.175148i	0.741161	−	0.671328i	$-0.234276\pi$
$211$	44.0427	+	36.9562i	0.208733	+	0.175148i	−0.532427	+	0.846476i	$0.678720\pi$
$212$	51.5344	+	141.590i	0.243087	+	0.667876i
$213$	−141.444	−	57.0952i	−0.664057	−	0.268052i
$214$	29.1399	+	165.260i	0.136168	+	0.772245i
$215$		−	203.841i		−	0.948098i
$216$	44.8292	−	61.8251i	0.207542	−	0.286227i
$217$	−95.7975			−0.441463
$218$	−286.979	+	50.6022i	−1.31642	+	0.232120i
$219$	−181.984	−	232.778i	−0.830978	−	1.06291i
$220$	−273.080	+	99.3930i	−1.24127	+	0.451786i
$221$	18.9290	−	22.5587i	0.0856516	−	0.102076i
$222$	−20.4209	+	96.2221i	−0.0919860	+	0.433433i
$223$	−217.997	−	79.3444i	−0.977565	−	0.355805i	−0.196672	−	0.980469i	$-0.563013\pi$
$223$	−217.997	−	79.3444i	−0.977565	−	0.355805i	−0.780893	+	0.624665i	$0.785236\pi$
$224$	−40.8276	+	23.5718i	−0.182266	+	0.105231i
$225$	−195.647	−	400.494i	−0.869542	−	1.77997i
$226$	50.2253	−	86.9928i	0.222236	−	0.384924i
$227$	137.899	+	164.342i	0.607485	+	0.723973i	0.978865	−	0.204508i	$-0.0655595\pi$
$227$	137.899	+	164.342i	0.607485	+	0.723973i	−0.371379	+	0.928481i	$0.621115\pi$
$228$	−39.1547	−	24.4494i	−0.171731	−	0.107234i
$229$	−68.6623	+	389.403i	−0.299835	+	1.70045i	0.347036	+	0.937852i	$0.387188\pi$
$229$	−68.6623	+	389.403i	−0.299835	+	1.70045i	−0.646871	+	0.762599i	$0.723923\pi$
$230$	−356.576	−	62.8739i	−1.55033	−	0.273365i
$231$	197.678	+	371.496i	0.855750	+	1.60821i
$232$	23.2792	−	19.5336i	0.100342	−	0.0841966i
$233$	82.9298	+	47.8796i	0.355922	+	0.205492i	0.667290	−	0.744798i	$-0.267454\pi$
$233$	82.9298	+	47.8796i	0.355922	+	0.205492i	−0.311368	+	0.950289i	$0.600787\pi$
$234$	10.6294	+	36.9808i	0.0454246	+	0.158038i
$235$	71.6708	+	124.138i	0.304982	+	0.528245i
$236$	−41.1803	+	113.142i	−0.174493	+	0.479415i
$237$	75.3020	+	231.507i	0.317730	+	0.976823i
$238$	−87.9471	−	73.7964i	−0.369526	−	0.310069i
$239$	−30.1617	−	82.8687i	−0.126200	−	0.346731i	0.860462	−	0.509514i	$-0.170175\pi$
$239$	−30.1617	−	82.8687i	−0.126200	−	0.346731i	−0.986662	+	0.162784i	$0.947953\pi$
$240$	14.4498	+	102.581i	0.0602076	+	0.427420i
$241$	−66.8780	−	379.284i	−0.277502	−	1.57379i	−0.730901	−	0.682484i	$-0.760900\pi$
$241$	−66.8780	−	379.284i	−0.277502	−	1.57379i	0.453399	−	0.891308i	$-0.350211\pi$
$242$		−	229.525i		−	0.948449i
$243$	−185.902	+	156.491i	−0.765029	+	0.643996i
$244$	68.3251			0.280021
$245$	173.893	−	30.6620i	0.709767	−	0.125151i
$246$	−71.3542	+	10.0512i	−0.290058	+	0.0408584i
$247$	21.8559	−	7.95489i	0.0884854	−	0.0322060i
$248$	20.8986	−	24.9060i	0.0842687	−	0.100428i
$249$	46.0223	−	14.9696i	0.184828	−	0.0601189i
$250$	281.363	+	102.408i	1.12545	+	0.409631i
$251$	−126.850	+	73.2368i	−0.505378	+	0.291780i	−0.730932	−	0.682451i	$-0.760914\pi$
$251$	−126.850	+	73.2368i	−0.505378	+	0.291780i	0.225554	+	0.974231i	$0.427581\pi$
$252$	144.173	−	41.4395i	0.572115	−	0.164442i
$253$	249.589	−	432.301i	0.986518	−	1.70870i
$254$	34.7883	+	41.4591i	0.136962	+	0.163225i
$255$	−222.710	+	118.507i	−0.873371	+	0.464734i
$256$	2.77837	−	15.7569i	0.0108530	−	0.0615505i
$257$	204.456	+	36.0511i	0.795548	+	0.140277i	0.556627	−	0.830762i	$-0.312095\pi$
$257$	204.456	+	36.0511i	0.795548	+	0.140277i	0.238921	+	0.971039i	$0.423206\pi$
$258$	53.0599	−	84.9733i	0.205659	−	0.329354i
$259$	−148.016	+	124.200i	−0.571489	+	0.479536i
$260$	−45.2031	−	26.0980i	−0.173858	−	0.100377i
$261$	−86.8838	+	42.4440i	−0.332888	+	0.162621i
$262$	154.098	+	266.905i	0.588160	+	1.01872i
$263$	−11.3833	+	31.2753i	−0.0432825	+	0.118918i	−0.959451	−	0.281876i	$-0.909043\pi$
$263$	−11.3833	+	31.2753i	−0.0432825	+	0.118918i	0.916168	+	0.400794i	$0.131266\pi$
$264$	−139.708	−	29.6498i	−0.529198	−	0.112310i
$265$	498.221	+	418.057i	1.88008	+	1.57757i
$266$	−31.0129	−	85.2071i	−0.116590	−	0.320328i
$267$	−38.2511	+	29.9045i	−0.143263	+	0.112002i
$268$	−13.0697	−	74.1217i	−0.0487674	−	0.276574i
$269$		−	399.099i		−	1.48364i	−0.670599	−	0.741820i	$-0.733963\pi$
$269$		−	399.099i		−	1.48364i	0.670599	−	0.741820i	$-0.266037\pi$
$270$	34.1455	−	327.860i	0.126465	−	1.21430i
$271$	−83.9974			−0.309954			−0.154977	−	0.987918i	$-0.549530\pi$
$271$	−83.9974			−0.309954			−0.154977	+	0.987918i	$0.549530\pi$
$272$	38.3721	−	6.76604i	0.141074	−	0.0248751i
$273$	−28.2919	+	70.0886i	−0.103633	+	0.256735i
$274$	244.645	−	89.0434i	0.892864	−	0.324976i
$275$	−535.817	+	638.562i	−1.94843	+	2.32204i
$276$	−132.276	−	119.026i	−0.479262	−	0.431255i
$277$	−168.403	−	61.2936i	−0.607953	−	0.221277i	0.0196546	−	0.999807i	$-0.493743\pi$
$277$	−168.403	−	61.2936i	−0.607953	−	0.221277i	−0.627607	+	0.778530i	$0.715966\pi$
$278$	297.797	−	171.933i	1.07121	−	0.618465i
$279$	−83.6578	+	60.8617i	−0.299849	+	0.218142i
$280$	−101.746	+	176.228i	−0.363377	+	0.629387i
$281$	−298.873	−	356.183i	−1.06361	−	1.26756i	−0.962093	−	0.272722i	$-0.912076\pi$
$281$	−298.873	−	356.183i	−1.06361	−	1.26756i	−0.101513	−	0.994834i	$-0.532368\pi$
$282$	−2.43631	+	70.4039i	−0.00863938	+	0.249659i
$283$	45.4847	−	257.956i	0.160723	−	0.911507i	−0.792642	−	0.609687i	$-0.791295\pi$
$283$	45.4847	−	257.956i	0.160723	−	0.911507i	0.953365	−	0.301819i	$-0.0975939\pi$
$284$	100.144	+	17.6580i	0.352619	+	0.0621762i
$285$	−199.131	−	6.89088i	−0.698707	−	0.0241785i
$286$	55.1248	−	46.2552i	0.192744	−	0.161731i
$287$	−122.583	−	70.7732i	−0.427118	−	0.246596i
$288$	−20.6783	+	46.5232i	−0.0717996	+	0.161539i
$289$	−97.0563	−	168.107i	−0.335835	−	0.581683i
$290$	44.8630	−	123.260i	0.154700	−	0.425035i
$291$	266.272	−	295.913i	0.915023	−	1.01688i
$292$	150.896	+	126.617i	0.516769	+	0.433620i
$293$	−33.5970	−	92.3071i	−0.114666	−	0.315041i	0.869063	−	0.494701i	$-0.164722\pi$
$293$	−33.5970	−	92.3071i	−0.114666	−	0.315041i	−0.983729	+	0.179660i	$0.942500\pi$
$294$	80.4703	+	32.4826i	0.273709	+	0.110485i
$295$	90.2463	+	511.812i	0.305920	+	1.73496i
$296$		−	65.5768i		−	0.221543i
$297$	408.645	+	198.831i	1.37591	+	0.669464i
$298$	−203.753			−0.683733
$299$	88.2960	−	15.5690i	0.295304	−	0.0520701i
$300$	183.019	+	234.101i	0.610063	+	0.780337i
$301$	184.916	−	67.3039i	0.614339	−	0.223601i
$302$	92.3663	−	110.078i	0.305849	−	0.364496i
$303$	9.48045	−	44.6713i	0.0312886	−	0.147430i
$304$	28.9183	+	10.5254i	0.0951259	+	0.0346230i
$305$	255.407	−	147.459i	0.837400	−	0.483473i
$306$	−123.686	−	8.57051i	−0.404203	−	0.0280082i
$307$	−246.426	+	426.822i	−0.802690	+	1.39030i	0.115150	+	0.993348i	$0.463265\pi$
$307$	−246.426	+	426.822i	−0.802690	+	1.39030i	−0.917840	+	0.396952i	$0.870068\pi$
$308$	−180.330	−	214.909i	−0.585487	−	0.697757i
$309$	96.3214	+	60.1460i	0.311720	+	0.194647i
$310$	24.3693	−	138.205i	0.0786106	−	0.445823i
$311$	−16.6486	−	2.93559i	−0.0535324	−	0.00943921i	0.146818	−	0.989164i	$-0.453097\pi$
$311$	−16.6486	−	2.93559i	−0.0535324	−	0.00943921i	−0.200350	+	0.979724i	$0.564208\pi$
$312$	−12.0501	−	22.6456i	−0.0386220	−	0.0725821i
$313$	319.525	−	268.113i	1.02085	−	0.856591i	0.0311120	−	0.999516i	$-0.490095\pi$
$313$	319.525	−	268.113i	1.02085	−	0.856591i	0.989734	+	0.142925i	$0.0456507\pi$
$314$	379.102	+	218.875i	1.20733	+	0.697053i
$315$	449.500	−	466.060i	1.42699	−	1.47956i
$316$	−81.1487	−	140.554i	−0.256800	−	0.444790i
$317$	155.193	−	426.388i	0.489567	−	1.34507i	−0.411507	−	0.911407i	$-0.634997\pi$
$317$	155.193	−	426.388i	0.489567	−	1.34507i	0.901074	−	0.433666i	$-0.142780\pi$
$318$	98.8681	+	303.958i	0.310906	+	0.955844i
$319$	138.531	+	116.241i	0.434265	+	0.364392i
$320$	−23.6207	−	64.8975i	−0.0738148	−	0.202805i
$321$	49.6539	+	352.498i	0.154685	+	1.09813i
$322$	−60.6970	−	344.230i	−0.188500	−	1.06904i
$323$			74.9429i			0.232021i
$324$	99.5759	−	127.784i	0.307333	−	0.394394i
$325$	−149.721			−0.460680
$326$	−222.914	+	39.3058i	−0.683786	+	0.120570i
$327$	−612.123	+	86.2254i	−1.87194	+	0.263686i
$328$	45.1420	−	16.4303i	0.137628	−	0.0500925i
$329$	−88.9481	+	106.004i	−0.270359	+	0.322201i
$330$	−586.235	+	190.684i	−1.77647	+	0.577830i
$331$	220.616	+	80.2978i	0.666515	+	0.242591i	0.653046	−	0.757318i	$-0.273491\pi$
$331$	220.616	+	80.2978i	0.666515	+	0.242591i	0.0134681	+	0.999909i	$0.495713\pi$
$332$	−27.9412	+	16.1319i	−0.0841604	+	0.0485900i
$333$	−50.3526	+	202.498i	−0.151209	+	0.608101i
$334$	−176.031	+	304.894i	−0.527038	+	0.912857i
$335$	−208.825	−	248.868i	−0.623360	−	0.742891i
$336$	−88.2860	+	46.9783i	−0.262756	+	0.139816i
$337$	−55.0894	+	312.428i	−0.163470	+	0.927085i	0.787158	+	0.616752i	$0.211552\pi$
$337$	−55.0894	+	312.428i	−0.163470	+	0.927085i	−0.950628	+	0.310333i	$0.899559\pi$
$338$	−222.643	−	39.2579i	−0.658706	−	0.116148i
$339$	112.862	−	180.744i	0.332927	−	0.533169i
$340$	128.837	−	108.107i	0.378932	−	0.317961i
$341$	167.555	+	96.7381i	0.491365	+	0.283689i
$342$	−81.2163	−	54.7065i	−0.237475	−	0.159961i
$343$	−118.950	−	206.027i	−0.346793	−	0.600662i
$344$	−22.8421	+	62.7583i	−0.0664016	+	0.182437i
$345$	−751.346	−	159.456i	−2.17782	−	0.462190i
$346$	−73.2107	−	61.4310i	−0.211592	−	0.177546i
$347$	−15.0965	−	41.4774i	−0.0435059	−	0.119531i	0.916037	−	0.401093i	$-0.131370\pi$
$347$	−15.0965	−	41.4774i	−0.0435059	−	0.119531i	−0.959543	+	0.281562i	$0.909147\pi$
$348$	50.7862	−	39.7044i	0.145937	−	0.114093i
$349$	57.3986	+	325.523i	0.164466	+	0.932732i	0.949614	+	0.313423i	$0.101476\pi$
$349$	57.3986	+	325.523i	0.164466	+	0.932732i	−0.785148	+	0.619309i	$0.787413\pi$
$350$			583.701i			1.66772i
$351$	19.8217	+	79.1810i	0.0564721	+	0.225587i
$352$	95.2132			0.270492
$353$	−466.298	+	82.2209i	−1.32096	+	0.232920i	−0.789283	−	0.614029i	$-0.789548\pi$
$353$	−466.298	+	82.2209i	−1.32096	+	0.232920i	−0.531673	+	0.846949i	$0.678437\pi$
$354$	−95.6048	+	236.845i	−0.270070	+	0.669055i
$355$	412.458	−	150.123i	1.16185	−	0.422880i
$356$	20.8063	−	24.7960i	0.0584447	−	0.0696517i
$357$	−181.038	−	162.904i	−0.507111	−	0.456315i
$358$	−312.606	−	113.779i	−0.873201	−	0.317819i
$359$	378.055	−	218.270i	1.05308	−	0.607994i	0.129568	−	0.991571i	$-0.458641\pi$
$359$	378.055	−	218.270i	1.05308	−	0.607994i	0.923509	+	0.383576i	$0.125308\pi$
$360$	23.1087	+	218.537i	0.0641908	+	0.607047i
$361$	150.905	−	261.375i	0.418018	−	0.724029i
$362$	198.017	+	235.988i	0.547009	+	0.651899i
$363$	16.8388	−	486.604i	0.0463878	−	1.34051i
$364$	8.74994	−	49.6234i	0.0240383	−	0.136328i
$365$	837.333	+	147.644i	2.29406	+	0.404505i
$366$	144.853	+	5.01258i	0.395772	+	0.0136956i
$367$	365.154	−	306.401i	0.994970	−	0.834879i	0.00869048	−	0.999962i	$-0.497234\pi$
$367$	365.154	−	306.401i	0.994970	−	0.834879i	0.986280	+	0.165083i	$0.0527893\pi$
$368$	102.736	+	59.3149i	0.279175	+	0.161182i
$369$	−152.012	+	16.0742i	−0.411957	+	0.0435614i
$370$	−141.528	−	245.134i	−0.382508	−	0.662523i
$371$	−214.742	+	589.998i	−0.578818	+	1.59029i
$372$	46.1334	−	51.2688i	0.124014	−	0.137819i
$373$	−282.763	−	237.266i	−0.758077	−	0.636102i	0.179549	−	0.983749i	$-0.442536\pi$
$373$	−282.763	−	237.266i	−0.758077	−	0.636102i	−0.937625	+	0.347647i	$0.886981\pi$
$374$	79.3036	+	217.885i	0.212042	+	0.582580i
$375$	588.991	+	237.752i	1.57064	+	0.634004i
$376$	−8.15522	−	46.2506i	−0.0216894	−	0.123007i
$377$			32.4807i			0.0861558i
$378$	308.694	−	77.2768i	0.816652	−	0.204436i
$379$	−216.903			−0.572304			−0.286152	−	0.958184i	$-0.592376\pi$
$379$	−216.903			−0.572304			−0.286152	+	0.958184i	$0.592376\pi$
$380$	130.816	−	23.0663i	0.344252	−	0.0607009i
$381$	70.7115	+	90.4477i	0.185594	+	0.237396i
$382$	−341.969	+	124.466i	−0.895206	+	0.325828i
$383$	−346.686	+	413.164i	−0.905185	+	1.07876i	0.0913699	+	0.995817i	$0.470875\pi$
$383$	−346.686	+	413.164i	−0.905185	+	1.07876i	−0.996555	+	0.0829400i	$0.973569\pi$
$384$	7.04628	−	33.2017i	0.0183497	−	0.0864626i
$385$	−1137.91	−	414.166i	−2.95561	−	1.07576i
$386$	−93.9025	+	54.2146i	−0.243271	+	0.140452i
$387$	118.724	−	176.255i	0.306780	−	0.455439i
$388$	−132.692	+	229.830i	−0.341990	+	0.592344i
$389$	94.9161	+	113.117i	0.244000	+	0.290788i	0.874120	−	0.485710i	$-0.161439\pi$
$389$	94.9161	+	113.117i	0.244000	+	0.290788i	−0.630120	+	0.776498i	$0.716994\pi$
$390$	−93.9183	−	58.6454i	−0.240816	−	0.150373i
$391$	−50.1658	+	284.504i	−0.128301	+	0.727633i
$392$	−56.9738	−	10.0460i	−0.145341	−	0.0256276i
$393$	307.114	+	577.158i	0.781461	+	1.46860i
$394$	264.325	−	221.795i	0.670875	−	0.562931i
$395$	−606.686	−	350.270i	−1.53591	−	0.886760i
$396$	−294.013	−	73.1086i	−0.742458	−	0.184618i
$397$	251.308	+	435.278i	0.633017	+	1.09642i	0.986932	+	0.161139i	$0.0515169\pi$
$397$	251.308	+	435.278i	0.633017	+	1.09642i	−0.353915	+	0.935278i	$0.615150\pi$
$398$	39.7147	−	109.115i	0.0997857	−	0.274159i
$399$	−59.4978	−	182.919i	−0.149117	−	0.458443i
$400$	−151.754	−	127.337i	−0.379386	−	0.318342i
$401$	79.1589	+	217.487i	0.197404	+	0.542362i	0.998415	−	0.0562876i	$-0.0179264\pi$
$401$	79.1589	+	217.487i	0.197404	+	0.542362i	−0.801011	+	0.598650i	$0.795704\pi$
$402$	−22.2705	−	158.101i	−0.0553993	−	0.393285i
$403$	6.03437	+	34.2226i	0.0149736	+	0.0849196i
$404$			30.4442i			0.0753569i
$405$	96.4433	−	692.574i	0.238132	−	1.71006i
$406$	126.629			0.311894
$407$	384.307	−	67.7638i	0.944244	−	0.166496i
$408$	81.8472	−	11.5292i	0.200606	−	0.0282579i
$409$	−423.279	+	154.061i	−1.03491	+	0.376677i	−0.802949	−	0.596048i	$-0.796737\pi$
$409$	−423.279	+	154.061i	−1.03491	+	0.376677i	−0.231963	+	0.972725i	$0.574515\pi$
$410$	133.286	−	158.844i	0.325088	−	0.387424i
$411$	525.192	−	170.828i	1.27784	−	0.415641i
$412$	−71.1396	−	25.8927i	−0.172669	−	0.0628463i
$413$	−434.497	+	250.857i	−1.05205	+	0.607402i
$414$	−271.700	−	262.046i	−0.656280	−	0.632962i
$415$	−69.6317	+	120.606i	−0.167787	+	0.290616i
$416$	10.9926	+	13.1004i	0.0264244	+	0.0314914i
$417$	643.959	−	342.660i	1.54427	−	0.821726i
$418$	−31.8005	+	180.350i	−0.0760777	+	0.431458i
$419$	−324.142	−	57.1549i	−0.773608	−	0.136408i	−0.227111	−	0.973869i	$-0.572928\pi$
$419$	−324.142	−	57.1549i	−0.773608	−	0.136408i	−0.546497	+	0.837461i	$0.684039\pi$
$420$	−228.635	+	366.149i	−0.544368	+	0.871783i
$421$	−156.740	+	131.520i	−0.372303	+	0.312399i	−0.809672	−	0.586883i	$-0.800355\pi$
$421$	−156.740	+	131.520i	−0.372303	+	0.312399i	0.437369	+	0.899282i	$0.355910\pi$
$422$	−70.4151	−	40.6542i	−0.166860	−	0.0963369i
$423$	−10.3302	+	149.081i	−0.0244213	+	0.352438i
$424$	−106.544	−	184.540i	−0.251284	−	0.435237i
$425$	165.000	−	453.333i	0.388234	−	1.06666i
$426$	211.014	+	44.7829i	0.495339	+	0.105124i
$427$	218.099	+	183.006i	0.510770	+	0.428587i
$428$	−81.1678	−	223.007i	−0.189645	−	0.521044i
$429$	120.261	−	94.0192i	0.280328	−	0.219159i
$430$	50.0584	+	283.895i	0.116415	+	0.660222i
$431$			5.85402i			0.0135824i	0.999977	+	0.00679120i	$0.00216172\pi$
$431$			5.85402i			0.0135824i	−0.999977	+	0.00679120i	$0.997838\pi$
$432$	−47.2521	+	97.1146i	−0.109380	+	0.224802i
$433$	233.310			0.538821			0.269411	−	0.963025i	$-0.413171\pi$
$433$	233.310			0.538821			0.269411	+	0.963025i	$0.413171\pi$
$434$	133.420	−	23.5255i	0.307419	−	0.0542063i
$435$	104.155	−	258.026i	0.239436	−	0.593164i
$436$	387.257	−	140.950i	0.888205	−	0.323280i
$437$	−146.665	+	174.789i	−0.335619	+	0.399975i
$438$	310.619	+	279.505i	0.709176	+	0.638140i
$439$	126.662	+	46.1012i	0.288524	+	0.105014i	0.482227	−	0.876046i	$-0.339828\pi$
$439$	126.662	+	46.1012i	0.288524	+	0.105014i	−0.193704	+	0.981060i	$0.562050\pi$
$440$	355.918	−	205.489i	0.808904	−	0.467021i
$441$	168.218	+	74.7683i	0.381447	+	0.169543i
$442$	−20.8231	+	36.0666i	−0.0471110	+	0.0815987i
$443$	18.4121	+	21.9426i	0.0415622	+	0.0495319i	0.786425	−	0.617686i	$-0.211930\pi$
$443$	18.4121	+	21.9426i	0.0415622	+	0.0495319i	−0.744863	+	0.667218i	$0.767485\pi$
$444$	4.81096	−	139.026i	0.0108355	−	0.313122i
$445$	24.2616	−	137.594i	0.0545205	−	0.309201i
$446$	323.096	+	56.9705i	0.724430	+	0.127737i
$447$	−431.966	−	14.9480i	−0.966367	−	0.0334408i
$448$	51.0731	−	42.8555i	0.114003	−	0.0956595i
$449$	430.226	+	248.391i	0.958188	+	0.553210i	0.895615	−	0.444831i	$-0.146736\pi$
$449$	430.226	+	248.391i	0.958188	+	0.553210i	0.0625728	+	0.998040i	$0.480069\pi$
$450$	370.835	+	509.733i	0.824077	+	1.13274i
$451$	142.936	+	247.573i	0.316932	+	0.548942i
$452$	−48.5869	+	133.491i	−0.107493	+	0.295335i
$453$	203.897	−	226.594i	0.450104	−	0.500209i
$454$	−232.414	−	195.019i	−0.511926	−	0.429557i
$455$	−74.3889	−	204.382i	−0.163492	−	0.449191i
$456$	60.5360	+	24.4359i	0.132754	+	0.0535875i
$457$	−80.5387	−	456.758i	−0.176234	−	0.999470i	−0.936710	−	0.350105i	$-0.886146\pi$
$457$	−80.5387	−	456.758i	−0.176234	−	0.999470i	0.760477	−	0.649365i	$-0.224965\pi$
$458$		−	559.195i		−	1.22095i
$459$	−261.592	−	27.2440i	−0.569918	−	0.0593551i
$460$	512.054			1.11316
$461$	−262.335	+	46.2568i	−0.569057	+	0.100340i	−0.450771	−	0.892640i	$-0.648851\pi$
$461$	−262.335	+	46.2568i	−0.569057	+	0.100340i	−0.118286	+	0.992980i	$0.537740\pi$
$462$	−366.543	−	468.848i	−0.793382	−	1.01482i
$463$	−224.935	+	81.8697i	−0.485821	+	0.176824i	−0.573306	−	0.819341i	$-0.694339\pi$
$463$	−224.935	+	81.8697i	−0.485821	+	0.176824i	0.0874848	+	0.996166i	$0.472117\pi$
$464$	−27.6247	+	32.9218i	−0.0595360	+	0.0709522i
$465$	61.8033	−	291.214i	0.132910	−	0.626266i
$466$	−127.257	−	46.3177i	−0.273083	−	0.0993942i
$467$	−184.565	+	106.559i	−0.395215	+	0.228177i	−0.684417	−	0.729091i	$-0.739943\pi$
$467$	−184.565	+	106.559i	−0.395215	+	0.228177i	0.289202	+	0.957268i	$0.406610\pi$
$468$	−23.8854	−	48.8939i	−0.0510371	−	0.104474i
$469$	156.813	−	271.609i	0.334357	−	0.579123i
$470$	−130.303	−	155.289i	−0.277241	−	0.330403i
$471$	787.658	+	491.838i	1.67231	+	1.04424i
$472$	29.5681	−	167.689i	0.0626442	−	0.355273i
$473$	−391.394	−	69.0132i	−0.827470	−	0.145905i
$474$	−161.728	−	303.934i	−0.341198	−	0.641212i
$475$	291.882	−	244.918i	0.614489	−	0.515617i
$476$	140.609	+	81.1807i	0.295397	+	0.170548i
$477$	187.306	+	651.660i	0.392675	+	1.36616i
$478$	62.3576	+	108.007i	0.130455	+	0.225955i
$479$	136.882	−	376.079i	0.285765	−	0.785134i	−0.710882	−	0.703312i	$-0.751704\pi$
$479$	136.882	−	376.079i	0.285765	−	0.785134i	0.996647	−	0.0818220i	$-0.0260739\pi$
$480$	−45.3161	−	139.319i	−0.0944085	−	0.290248i
$481$	53.6927	+	45.0535i	0.111627	+	0.0936664i
$482$	186.286	+	511.816i	0.386485	+	1.06186i
$483$	−103.427	−	734.238i	−0.214134	−	1.52016i
$484$	56.3657	+	319.666i	0.116458	+	0.660466i
$485$			1145.51i			2.36187i
$486$	220.481	−	263.603i	0.453664	−	0.542392i
$487$	−323.676			−0.664632			−0.332316	−	0.943168i	$-0.607830\pi$
$487$	−323.676			−0.664632			−0.332316	+	0.943168i	$0.607830\pi$
$488$	−95.1583	+	16.7790i	−0.194997	+	0.0343832i
$489$	−475.473	+	66.9765i	−0.972338	+	0.136966i
$490$	−234.656	+	85.4077i	−0.478889	+	0.174301i
$491$	589.862	−	702.970i	1.20135	−	1.43171i	0.327956	−	0.944693i	$-0.393640\pi$
$491$	589.862	−	702.970i	1.20135	−	1.43171i	0.873392	−	0.487018i	$-0.161915\pi$
$492$	96.9088	−	31.5214i	0.196969	−	0.0640679i
$493$	−98.3467	−	35.7953i	−0.199486	−	0.0726070i
$494$	−28.4858	+	16.4463i	−0.0576635	+	0.0332921i
$495$	−1256.84	+	361.252i	−2.53907	+	0.729801i
$496$	−22.9898	+	39.8195i	−0.0463504	+	0.0802813i
$497$	272.369	+	324.597i	0.548027	+	0.653113i
$498$	−60.4204	+	32.1505i	−0.121326	+	0.0645593i
$499$	−37.5201	+	212.787i	−0.0751906	+	0.426427i	0.923855	+	0.382743i	$0.125021\pi$
$499$	−37.5201	+	212.787i	−0.0751906	+	0.426427i	−0.999045	+	0.0436840i	$0.986091\pi$
$500$	−417.011	−	73.5303i	−0.834022	−	0.147061i
$501$	−395.562	+	633.477i	−0.789546	+	1.26443i
$502$	158.682	−	133.150i	0.316100	−	0.265240i
$503$	31.3557	+	18.1032i	0.0623373	+	0.0359905i	0.530845	−	0.847469i	$-0.321875\pi$
$503$	31.3557	+	18.1032i	0.0623373	+	0.0359905i	−0.468507	+	0.883460i	$0.655208\pi$
$504$	−190.617	+	93.1193i	−0.378209	+	0.184761i
$505$	65.7046	+	113.804i	0.130108	+	0.225354i
$506$	−241.447	+	663.371i	−0.477169	+	1.31101i
$507$	−469.134	−	99.5626i	−0.925313	−	0.196376i
$508$	−58.6321	−	49.1982i	−0.115417	−	0.0968468i
$509$	−79.8138	−	219.287i	−0.156805	−	0.430818i	0.836267	−	0.548322i	$-0.184733\pi$
$509$	−79.8138	−	219.287i	−0.156805	−	0.430818i	−0.993072	+	0.117503i	$0.962511\pi$
$510$	281.072	−	219.740i	0.551121	−	0.430863i
$511$	142.532	+	808.342i	0.278929	+	1.58188i
$512$			22.6274i			0.0441942i
$513$	−168.169	−	121.939i	−0.327815	−	0.237698i
$514$	−293.605			−0.571216
$515$	−321.809	+	56.7437i	−0.624873	+	0.110182i
$516$	−53.0307	+	131.375i	−0.102773	+	0.254603i
$517$	262.620	−	95.5860i	0.507970	−	0.184886i
$518$	175.645	−	209.326i	0.339083	−	0.404104i
$519$	−150.704	−	135.608i	−0.290373	−	0.261287i
$520$	69.3647	+	25.2467i	0.133394	+	0.0485513i
$521$	−119.806	+	69.1700i	−0.229954	+	0.132764i	−0.610551	−	0.791977i	$-0.709052\pi$
$521$	−119.806	+	69.1700i	−0.229954	+	0.132764i	0.380597	+	0.924741i	$0.375719\pi$
$522$	110.582	−	80.4495i	0.211844	−	0.154118i
$523$	98.4346	−	170.494i	0.188212	−	0.325992i	−0.756442	−	0.654060i	$-0.773064\pi$
$523$	98.4346	−	170.494i	0.188212	−	0.325992i	0.944654	+	0.328068i	$0.106398\pi$
$524$	−280.162	−	333.884i	−0.534660	−	0.637183i
$525$	−42.8225	+	1237.48i	−0.0815667	+	2.35710i
$526$	8.17338	−	46.3535i	0.0155387	−	0.0881246i
$527$	−110.271	−	19.4437i	−0.209243	−	0.0368951i
$528$	201.857	+	6.98519i	0.382305	+	0.0132295i
$529$	−268.547	+	225.338i	−0.507651	+	0.425969i
$530$	−796.551	−	459.889i	−1.50293	−	0.867715i
$531$	−220.063	+	495.111i	−0.414431	+	0.932412i
$532$	64.1173	+	111.054i	0.120521	+	0.208749i
$533$	−17.5613	+	48.2494i	−0.0329481	+	0.0905242i
$534$	45.9296	−	51.0424i	0.0860105	−	0.0955850i
$535$	−784.708	−	658.448i	−1.46674	−	1.23074i
$536$	36.4050	+	100.022i	0.0679197	+	0.186608i
$537$	−654.394	−	264.152i	−1.21861	−	0.491903i
$538$	98.0090	+	555.837i	0.182173	+	1.03315i
$539$		−	344.271i		−	0.638722i
$540$	32.9589	+	465.005i	0.0610350	+	0.861120i
$541$	−136.735			−0.252745			−0.126373	−	0.991983i	$-0.540334\pi$
$541$	−136.735			−0.252745			−0.126373	+	0.991983i	$0.540334\pi$
$542$	116.986	−	20.6277i	0.215841	−	0.0380585i
$543$	402.493	+	514.833i	0.741240	+	0.948127i
$544$	−51.7803	+	18.8465i	−0.0951844	+	0.0346443i
$545$	1143.41	−	1362.67i	2.09801	−	2.50031i
$546$	22.1909	−	104.562i	0.0406426	−	0.191506i
$547$	625.697	+	227.735i	1.14387	+	0.416335i	0.843310	−	0.537428i	$-0.180604\pi$
$547$	625.697	+	227.735i	1.14387	+	0.416335i	0.300561	+	0.953763i	$0.402826\pi$
$548$	−318.857	+	184.092i	−0.581855	+	0.335934i
$549$	306.727	+	21.2539i	0.558702	+	0.0387138i
$550$	589.433	−	1020.93i	1.07170	−	1.85623i
$551$	−53.1330	−	63.3214i	−0.0964300	−	0.114921i
$552$	213.455	+	133.288i	0.386694	+	0.241463i
$553$	117.436	−	666.011i	0.212361	−	1.20436i
$554$	249.592	+	44.0098i	0.450527	+	0.0794400i
$555$	−282.063	−	530.079i	−0.508221	−	0.955097i
$556$	−372.528	+	312.588i	−0.670014	+	0.562208i
$557$	−943.861	−	544.939i	−1.69454	−	0.978346i	−0.950761	−	0.309926i	$-0.899696\pi$
$557$	−943.861	−	544.939i	−1.69454	−	0.978346i	−0.743784	−	0.668420i	$-0.766971\pi$
$558$	101.566	−	105.308i	0.182019	−	0.188724i
$559$	−35.6916	−	61.8197i	−0.0638490	−	0.110590i
$560$	98.4265	−	270.425i	0.175762	−	0.482901i
$561$	152.143	+	467.745i	0.271199	+	0.833770i
$562$	503.719	+	422.671i	0.896298	+	0.752083i
$563$	209.400	+	575.323i	0.371937	+	1.02189i	0.974612	+	0.223901i	$0.0718793\pi$
$563$	209.400	+	575.323i	0.371937	+	1.02189i	−0.602675	+	0.797987i	$0.705898\pi$
$564$	−13.8964	−	98.6519i	−0.0246390	−	0.174915i
$565$	106.478	+	603.866i	0.188457	+	1.06879i
$566$			370.433i			0.654475i
$567$	660.117	−	141.184i	1.16423	−	0.249001i
$568$	−143.809			−0.253186
$569$	491.784	−	86.7148i	0.864295	−	0.152399i	0.276111	−	0.961126i	$-0.410954\pi$
$569$	491.784	−	86.7148i	0.864295	−	0.152399i	0.588184	+	0.808727i	$0.299843\pi$
$570$	279.028	−	39.3047i	0.489523	−	0.0689556i
$571$	284.552	−	103.569i	0.498341	−	0.181381i	−0.0806069	−	0.996746i	$-0.525686\pi$
$571$	284.552	−	103.569i	0.498341	−	0.181381i	0.578947	+	0.815365i	$0.303464\pi$
$572$	−65.4147	+	77.9582i	−0.114361	+	0.136291i
$573$	−734.123	+	238.787i	−1.28119	+	0.416732i
$574$	188.105	+	68.4645i	0.327708	+	0.119276i
$575$	1272.01	−	734.397i	2.21220	−	1.27721i
$576$	17.3743	−	69.8723i	0.0301637	−	0.121306i
$577$	−18.5614	+	32.1493i	−0.0321688	+	0.0557181i	−0.881662	−	0.471882i	$-0.843575\pi$
$577$	−18.5614	+	32.1493i	−0.0321688	+	0.0557181i	0.849493	+	0.527600i	$0.176908\pi$
$578$	176.456	+	210.292i	0.305287	+	0.363827i
$579$	−203.055	+	108.049i	−0.350700	+	0.186613i
$580$	−32.2123	+	182.685i	−0.0555385	+	0.314974i
$581$	−132.399	−	23.3455i	−0.227881	−	0.0401817i
$582$	−298.175	+	477.516i	−0.512329	+	0.820474i
$583$	971.386	−	815.090i	1.66619	−	1.39810i
$584$	−241.252	−	139.287i	−0.413102	−	0.238505i
$585$	−194.809	−	131.222i	−0.333007	−	0.224310i
$586$	69.4599	+	120.308i	0.118532	+	0.205304i
$587$	−299.988	+	824.210i	−0.511053	+	1.40411i	0.369088	+	0.929394i	$0.379670\pi$
$587$	−299.988	+	824.210i	−0.511053	+	1.40411i	−0.880141	+	0.474712i	$0.842552\pi$
$588$	−120.050	−	25.4779i	−0.204167	−	0.0433297i
$589$	−67.7464	−	56.8459i	−0.115019	−	0.0965126i
$590$	−251.377	−	690.653i	−0.426063	−	1.17060i
$591$	576.654	−	450.825i	0.975726	−	0.762817i
$592$	16.1041	+	91.3307i	0.0272028	+	0.154275i
$593$		−	284.591i		−	0.479917i	−0.970783	−	0.239958i	$-0.922866\pi$
$593$		−	284.591i		−	0.479917i	0.970783	−	0.239958i	$-0.0771338\pi$
$594$	−617.960	−	176.564i	−1.04034	−	0.297246i
$595$	700.817			1.17784
$596$	283.772	−	50.0367i	0.476127	−	0.0839541i
$597$	92.2024	−	228.416i	0.154443	−	0.382607i
$598$	−119.149	+	43.3667i	−0.199246	+	0.0725195i
$599$	−211.516	+	252.075i	−0.353115	+	0.420827i	−0.913138	−	0.407651i	$-0.866348\pi$
$599$	−211.516	+	252.075i	−0.353115	+	0.420827i	0.560022	+	0.828477i	$0.310793\pi$
$600$	−312.385	−	281.094i	−0.520642	−	0.468490i
$601$	−6.64685	−	2.41926i	−0.0110597	−	0.00402538i	0.336484	−	0.941689i	$-0.390762\pi$
$601$	−6.64685	−	2.41926i	−0.0110597	−	0.00402538i	−0.347544	+	0.937664i	$0.612984\pi$
$602$	−241.010	+	139.147i	−0.400348	+	0.231141i
$603$	−35.6158	−	336.815i	−0.0590643	−	0.558566i
$604$	−101.609	+	175.992i	−0.168226	+	0.291377i
$605$	900.604	+	1073.30i	1.48860	+	1.77405i
$606$	−2.23350	+	64.5432i	−0.00368564	+	0.106507i
$607$	83.8924	−	475.778i	0.138208	−	0.783818i	−0.834363	−	0.551215i	$-0.814165\pi$
$607$	83.8924	−	475.778i	0.138208	−	0.783818i	0.972572	−	0.232603i	$-0.0747244\pi$
$608$	−42.8601	−	7.55739i	−0.0704936	−	0.0124299i
$609$	268.460	+	9.28998i	0.440821	+	0.0152545i
$610$	−319.500	+	268.092i	−0.523771	+	0.439496i
$611$	43.4718	+	25.0984i	0.0711485	+	0.0410776i
$612$	174.366	−	18.4379i	0.284912	−	0.0301273i
$613$	−287.932	−	498.713i	−0.469710	−	0.813562i	0.529690	−	0.848191i	$-0.322308\pi$
$613$	−287.932	−	498.713i	−0.469710	−	0.813562i	−0.999400	+	0.0346296i	$0.988975\pi$
$614$	238.387	−	654.963i	0.388253	−	1.06672i
$615$	294.226	−	326.979i	0.478417	−	0.531673i
$616$	303.927	+	255.025i	0.493389	+	0.414002i
$617$	−239.991	−	659.369i	−0.388964	−	1.06867i	−0.967469	−	0.252991i	$-0.918586\pi$
$617$	−239.991	−	659.369i	−0.388964	−	1.06867i	0.578505	−	0.815679i	$-0.303636\pi$
$618$	−148.920	−	60.1129i	−0.240971	−	0.0972700i
$619$	78.3389	+	444.282i	0.126557	+	0.717741i	0.980371	+	0.197162i	$0.0631726\pi$
$619$	78.3389	+	444.282i	0.126557	+	0.717741i	−0.853814	+	0.520579i	$0.825716\pi$
$620$			198.467i			0.320107i
$621$	−556.793	−	575.485i	−0.896608	−	0.926707i
$622$	23.9079			0.0384371
$623$	132.830	−	23.4216i	0.213211	−	0.0375949i
$624$	22.3437	+	28.5800i	0.0358072	+	0.0458013i
$625$	−554.064	+	201.663i	−0.886502	+	0.322660i
$626$	−379.169	+	451.876i	−0.605701	+	0.721847i
$627$	−80.6498	+	380.017i	−0.128628	+	0.606088i
$628$	−581.736	−	211.735i	−0.926331	−	0.337157i
$629$	−195.587	+	112.922i	−0.310949	+	0.179527i
$630$	−511.579	+	759.481i	−0.812030	+	1.20553i
$631$	283.716	−	491.411i	0.449630	−	0.778782i	−0.548732	−	0.835998i	$-0.684889\pi$
$631$	283.716	−	491.411i	0.449630	−	0.778782i	0.998362	+	0.0572166i	$0.0182226\pi$
$632$	147.535	+	175.825i	0.233441	+	0.278204i
$633$	−146.301	−	91.3548i	−0.231123	−	0.144320i
$634$	−111.431	+	631.954i	−0.175758	+	0.996773i
$635$	−325.353	−	57.3685i	−0.512367	−	0.0903441i
$636$	−212.341	−	399.052i	−0.333870	−	0.627440i
$637$	47.3684	−	39.7468i	0.0743616	−	0.0623968i
$638$	−221.482	−	127.872i	−0.347150	−	0.200427i
$639$	444.076	+	110.423i	0.694954	+	0.172806i
$640$	48.8345	+	84.5839i	0.0763039	+	0.132162i
$641$	50.9735	−	140.049i	0.0795219	−	0.218485i	−0.893560	−	0.448943i	$-0.851800\pi$
$641$	50.9735	−	140.049i	0.0795219	−	0.218485i	0.973082	+	0.230459i	$0.0740227\pi$
$642$	−155.719	−	478.741i	−0.242554	−	0.745702i
$643$	−20.8996	−	17.5368i	−0.0325032	−	0.0272734i	0.626391	−	0.779509i	$-0.284531\pi$
$643$	−20.8996	−	17.5368i	−0.0325032	−	0.0272734i	−0.658895	+	0.752235i	$0.728976\pi$
$644$	169.069	+	464.513i	0.262529	+	0.721294i
$645$	85.2988	+	605.545i	0.132246	+	0.938830i
$646$	−18.4042	−	104.375i	−0.0284894	−	0.161571i
$647$			263.970i			0.407991i	0.978972	+	0.203996i	$0.0653929\pi$
$647$			263.970i			0.407991i	−0.978972	+	0.203996i	$0.934607\pi$
$648$	−107.302	+	202.421i	−0.165589	+	0.312378i
$649$	1013.28			1.56129
$650$	208.521	−	36.7679i	0.320801	−	0.0565659i
$651$	284.583	−	40.0871i	0.437147	−	0.0615778i
$652$	300.806	−	109.485i	0.461360	−	0.167921i
$653$	−538.345	+	641.575i	−0.824418	+	0.982503i	−0.999998	−	0.00196193i	$-0.999375\pi$
$653$	−538.345	+	641.575i	−0.824418	+	0.982503i	0.175580	+	0.984465i	$0.443820\pi$
$654$	831.346	−	270.411i	1.27117	−	0.413472i
$655$	−1767.87	−	643.450i	−2.69903	−	0.982367i
$656$	−58.8357	+	33.9688i	−0.0896885	+	0.0517817i
$657$	638.023	+	615.353i	0.971115	+	0.936611i
$658$	97.8485	−	169.479i	0.148706	−	0.257566i
$659$	−477.726	−	569.332i	−0.724926	−	0.863933i	0.270173	−	0.962812i	$-0.412919\pi$
$659$	−477.726	−	569.332i	−0.724926	−	0.863933i	−0.995100	+	0.0988784i	$0.968475\pi$
$660$	769.639	−	409.536i	1.16612	−	0.620509i
$661$	46.6386	−	264.501i	0.0705577	−	0.400152i	−0.928991	−	0.370103i	$-0.879322\pi$
$661$	46.6386	−	264.501i	0.0705577	−	0.400152i	0.999548	−	0.0300495i	$-0.00956649\pi$
$662$	−326.978	−	57.6550i	−0.493924	−	0.0870922i
$663$	−46.7920	+	74.9355i	−0.0705762	+	0.113025i
$664$	34.9530	−	29.3290i	0.0526400	−	0.0441702i
$665$	479.355	+	276.756i	0.720835	+	0.416174i
$666$	20.3990	−	294.390i	0.0306291	−	0.442027i
$667$	−159.321	−	275.952i	−0.238862	−	0.413722i
$668$	170.289	−	467.864i	0.254923	−	0.700395i
$669$	680.800	+	144.484i	1.01764	+	0.215970i
$670$	351.953	+	295.324i	0.525303	+	0.440782i
$671$	−196.664	−	540.329i	−0.293090	−	0.805259i
$672$	111.422	−	87.1089i	0.165806	−	0.129626i
$673$	114.573	+	649.776i	0.170242	+	0.965492i	0.943493	+	0.331392i	$0.107518\pi$
$673$	114.573	+	649.776i	0.170242	+	0.965492i	−0.773251	+	0.634100i	$0.781371\pi$
$674$		−	448.656i		−	0.665661i
$675$	748.793	+	1107.87i	1.10932	+	1.64128i
$676$	319.721			0.472961
$677$	251.116	−	44.2786i	0.370925	−	0.0654041i	0.0149216	−	0.999889i	$-0.495250\pi$
$677$	251.116	−	44.2786i	0.370925	−	0.0654041i	0.356004	+	0.934485i	$0.384139\pi$
$678$	−112.800	+	279.444i	−0.166372	+	0.412159i
$679$	−1039.15	+	378.221i	−1.53042	+	0.557026i
$680$	−152.886	+	182.203i	−0.224833	+	0.267945i
$681$	−478.423	−	430.501i	−0.702531	−	0.632160i
$682$	−257.116	−	93.5824i	−0.377002	−	0.137218i
$683$	−376.413	+	217.322i	−0.551117	+	0.318187i	−0.749572	−	0.661923i	$-0.769741\pi$
$683$	−376.413	+	217.322i	−0.551117	+	0.318187i	0.198456	+	0.980110i	$0.436407\pi$
$684$	126.547	+	56.2466i	0.185010	+	0.0822318i
$685$	−794.615	+	1376.31i	−1.16002	+	2.00922i
$686$	216.260	+	257.729i	0.315248	+	0.375698i
$687$	41.0246	−	1185.52i	0.0597156	−	1.72565i
$688$	16.4010	−	93.0147i	0.0238387	−	0.135196i
$689$	224.297	+	39.5496i	0.325540	+	0.0574015i
$690$	1085.58	+	37.5662i	1.57330	+	0.0544437i
$691$	−1022.63	+	858.086i	−1.47992	+	1.24180i	−0.573657	+	0.819096i	$0.694476\pi$
$691$	−1022.63	+	858.086i	−1.47992	+	1.24180i	−0.906266	+	0.422707i	$0.861080\pi$
$692$	117.049	+	67.5780i	0.169145	+	0.0976561i
$693$	−742.693	−	1020.87i	−1.07171	−	1.47312i
$694$	31.2112	+	54.0594i	0.0449729	+	0.0778954i
$695$	−717.924	+	1972.48i	−1.03298	+	2.83810i
$696$	−60.9810	+	67.7693i	−0.0876164	+	0.0973697i
$697$	−126.738	−	106.346i	−0.181834	−	0.152577i
$698$	−159.881	−	439.270i	−0.229056	−	0.629327i
$699$	−266.393	−	107.532i	−0.381106	−	0.153837i
$700$	−143.343	−	812.938i	−0.204775	−	1.16134i
$701$		−	1001.61i		−	1.42883i	−0.699722	−	0.714415i	$-0.746693\pi$
$701$		−	1001.61i		−	1.42883i	0.699722	−	0.714415i	$-0.253307\pi$
$702$	−47.0512	−	105.410i	−0.0670245	−	0.150157i
$703$	−178.374			−0.253733
$704$	−132.606	+	23.3820i	−0.188361	+	0.0332131i
$705$	−264.857	−	338.781i	−0.375683	−	0.480540i
$706$	629.235	−	229.023i	0.891267	−	0.324395i
$707$	−81.5437	+	97.1800i	−0.115338	+	0.137454i
$708$	74.9881	−	353.340i	0.105915	−	0.499067i
$709$	720.055	+	262.078i	1.01559	+	0.369645i	0.795578	−	0.605852i	$-0.207167\pi$
$709$	720.055	+	262.078i	1.01559	+	0.369645i	0.220014	+	0.975497i	$0.429390\pi$
$710$	−537.576	+	310.370i	−0.757149	+	0.437140i
$711$	−320.574	−	656.221i	−0.450877	−	0.922955i
$712$	−22.8883	+	39.6436i	−0.0321464	+	0.0556792i
$713$	−219.132	−	261.152i	−0.307339	−	0.366272i
$714$	292.143	+	182.423i	0.409163	+	0.255494i
$715$	−76.2782	+	432.595i	−0.106683	+	0.605028i
$716$	463.317	+	81.6953i	0.647090	+	0.114100i
$717$	124.278	+	233.554i	0.173330	+	0.325738i
$718$	−472.926	+	396.832i	−0.658671	+	0.552691i
$719$	544.595	+	314.422i	0.757434	+	0.437305i	0.828374	−	0.560176i	$-0.189267\pi$
$719$	544.595	+	314.422i	0.757434	+	0.437305i	−0.0709399	+	0.997481i	$0.522600\pi$
$720$	−85.8514	−	298.688i	−0.119238	−	0.414844i
$721$	−157.730	−	273.196i	−0.218765	−	0.378913i
$722$	−145.982	+	401.082i	−0.202191	+	0.555516i
$723$	357.387	+	1098.74i	0.494311	+	1.51970i
$724$	−333.737	−	280.038i	−0.460962	−	0.386793i
$725$	181.990	+	500.015i	0.251021	+	0.689675i
$726$	96.0463	+	681.843i	0.132295	+	0.939177i
$727$	−116.145	−	658.690i	−0.159759	−	0.906039i	−0.954305	−	0.298835i	$-0.903402\pi$
$727$	−116.145	−	658.690i	−0.159759	−	0.906039i	0.794546	−	0.607204i	$-0.207709\pi$
$728$			71.2606i			0.0978855i
$729$	486.769	−	542.676i	0.667722	−	0.744411i
$730$	−1202.44			−1.64717
$731$	226.514	−	39.9406i	0.309869	−	0.0546383i
$732$	−202.971	+	28.5911i	−0.277283	+	0.0390589i
$733$	−104.288	+	37.9578i	−0.142276	+	0.0517842i	−0.412177	−	0.911104i	$-0.635231\pi$
$733$	−104.288	+	37.9578i	−0.142276	+	0.0517842i	0.269901	+	0.962888i	$0.413009\pi$
$734$	−433.316	+	516.406i	−0.590349	+	0.703550i
$735$	−503.748	+	163.853i	−0.685371	+	0.222930i
$736$	−157.650	−	57.3800i	−0.214199	−	0.0779619i
$737$	−548.551	+	316.706i	−0.744302	+	0.429723i
$738$	207.764	−	59.7174i	0.281523	−	0.0809179i
$739$	−231.298	+	400.619i	−0.312987	+	0.542110i	−0.979008	−	0.203824i	$-0.934663\pi$
$739$	−231.298	+	400.619i	−0.312987	+	0.542110i	0.666020	+	0.745934i	$0.267996\pi$
$740$	257.309	+	306.649i	0.347715	+	0.414390i
$741$	−61.5979	+	32.7771i	−0.0831280	+	0.0442336i
$742$	154.188	−	874.442i	0.207800	−	1.17849i
$743$	952.218	+	167.902i	1.28159	+	0.225978i	0.772653	−	0.634829i	$-0.218929\pi$
$743$	952.218	+	167.902i	1.28159	+	0.225978i	0.508932	+	0.860807i	$0.330040\pi$
$744$	−51.6609	+	82.7328i	−0.0694367	+	0.111200i
$745$	952.783	−	799.480i	1.27890	−	1.07313i
$746$	452.078	+	261.007i	0.606003	+	0.349876i
$747$	−130.453	+	63.7282i	−0.174636	+	0.0853121i
$748$	−163.956	−	283.979i	−0.219192	−	0.379652i
$749$	338.223	−	929.259i	0.451566	−	1.24067i
$750$	−878.690	−	186.481i	−1.17159	−	0.248642i
$751$	−805.112	−	675.569i	−1.07205	−	0.899560i	−0.0768166	−	0.997045i	$-0.524476\pi$
$751$	−805.112	−	675.569i	−1.07205	−	0.899560i	−0.995237	+	0.0974855i	$0.968920\pi$
$752$	22.7160	+	62.4118i	0.0302075	+	0.0829944i
$753$	346.183	−	270.644i	0.459739	−	0.359421i
$754$	−7.97648	−	45.2368i	−0.0105789	−	0.0599958i
$755$			877.168i			1.16181i
$756$	−410.950	+	183.433i	−0.543585	+	0.242637i
$757$	−266.724			−0.352343			−0.176172	−	0.984359i	$-0.556371\pi$
$757$	−266.724			−0.352343			−0.176172	+	0.984359i	$0.556371\pi$
$758$	302.087	−	53.2662i	0.398532	−	0.0702720i
$759$	−560.548	+	1388.67i	−0.738535	+	1.82960i
$760$	−176.526	+	64.2503i	−0.232271	+	0.0845399i
$761$	−0.229396	+	0.273383i	−0.000301440	+	0.000359242i	−0.766195	−	0.642608i	$-0.777852\pi$
$761$	−0.229396	+	0.273383i	−0.000301440	+	0.000359242i	0.765894	+	0.642967i	$0.222297\pi$
$762$	−120.694	−	108.604i	−0.158391	−	0.142525i
$763$	1613.68	+	587.333i	2.11492	+	0.769768i
$764$	445.704	−	257.327i	0.583382	−	0.336816i
$765$	612.007	−	445.240i	0.800010	−	0.582013i
$766$	381.376	−	660.563i	0.497880	−

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.39273 + 0.245576i) q^{2} +(-2.97067 + 0.418457i) q^{3} +(1.87939 - 0.684040i) q^{4} +(5.54906 - 6.61311i) q^{5} +(4.03458 - 1.31232i) q^{6} +(7.83131 + 2.85036i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(8.64979 - 2.48620i) q^{9} +O(q^{10})\)	\(q+(-1.39273 + 0.245576i) q^{2} +(-2.97067 + 0.418457i) q^{3} +(1.87939 - 0.684040i) q^{4} +(5.54906 - 6.61311i) q^{5} +(4.03458 - 1.31232i) q^{6} +(7.83131 + 2.85036i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(8.64979 - 2.48620i) q^{9} +(-6.10431 + 10.5730i) q^{10} +(-10.8191 - 12.8937i) q^{11} +(-5.29680 + 2.81850i) q^{12} +(0.524960 - 2.97720i) q^{13} +(-11.6069 - 2.04660i) q^{14} +(-13.7171 + 21.9674i) q^{15} +(3.06418 - 2.57115i) q^{16} +(8.43596 + 4.87051i) q^{17} +(-11.4363 + 5.58678i) q^{18} +(3.84677 + 6.66281i) q^{19} +(5.90519 - 16.2244i) q^{20} +(-24.4570 - 5.19043i) q^{21} +(18.2344 + 15.3005i) q^{22} +(10.1434 + 27.8689i) q^{23} +(6.68484 - 5.22617i) q^{24} +(-8.59998 - 48.7729i) q^{25} +4.27534i q^{26} +(-24.6553 + 11.0052i) q^{27} +16.6678 q^{28} +(-10.5809 + 1.86569i) q^{29} +(13.7096 - 33.9633i) q^{30} +(-10.8017 + 3.93149i) q^{31} +(-3.63616 + 4.33340i) q^{32} +(37.5353 + 33.7755i) q^{33} +(-12.9451 - 4.71163i) q^{34} +(62.3062 - 35.9725i) q^{35} +(14.5556 - 10.5893i) q^{36} +(-11.5925 + 20.0787i) q^{37} +(-6.99373 - 8.33481i) q^{38} +(-0.313655 + 9.06395i) q^{39} +(-4.24001 + 24.0463i) q^{40} +(-16.7264 - 2.94931i) q^{41} +(35.3366 + 1.22281i) q^{42} +(18.0881 - 15.1778i) q^{43} +(-29.1530 - 16.8315i) q^{44} +(31.5567 - 70.9981i) q^{45} +(-20.9710 - 36.3228i) q^{46} +(-5.67901 + 15.6029i) q^{47} +(-8.02675 + 8.92027i) q^{48} +(15.6687 + 13.1476i) q^{49} +(23.9549 + 65.8155i) q^{50} +(-27.0986 - 10.9386i) q^{51} +(-1.04992 - 5.95439i) q^{52} +75.3383i q^{53} +(31.6355 - 21.3821i) q^{54} -145.303 q^{55} +(-23.2137 + 4.09321i) q^{56} +(-14.2156 - 18.1833i) q^{57} +(14.2781 - 5.19681i) q^{58} +(-38.6968 + 46.1170i) q^{59} +(-10.7532 + 50.6683i) q^{60} +(32.1023 + 11.6843i) q^{61} +(14.0783 - 8.12813i) q^{62} +(74.8257 + 5.18485i) q^{63} +(4.00000 - 6.92820i) q^{64} +(-16.7755 - 19.9923i) q^{65} +(-60.5710 - 37.8224i) q^{66} +(6.53483 - 37.0609i) q^{67} +(19.1860 + 3.38302i) q^{68} +(-41.7948 - 78.5447i) q^{69} +(-77.9416 + 65.4008i) q^{70} +(44.0325 + 25.4222i) q^{71} +(-17.6715 + 18.3226i) q^{72} +(49.2453 + 85.2954i) q^{73} +(11.2143 - 30.8110i) q^{74} +(45.9571 + 141.290i) q^{75} +(11.7872 + 9.89063i) q^{76} +(-47.9758 - 131.813i) q^{77} +(-1.78905 - 12.7006i) q^{78} +(-14.0913 - 79.9158i) q^{79} -34.5312i q^{80} +(68.6376 - 43.0102i) q^{81} +24.0196 q^{82} +(-15.8868 + 2.80127i) q^{83} +(-49.5146 + 6.97477i) q^{84} +(79.0209 - 28.7612i) q^{85} +(-21.4646 + 25.5805i) q^{86} +(30.6516 - 9.97000i) q^{87} +(44.7356 + 16.2824i) q^{88} +(14.0161 - 8.09222i) q^{89} +(-26.5145 + 106.631i) q^{90} +(12.5972 - 21.8190i) q^{91} +(38.1269 + 45.4378i) q^{92} +(30.4431 - 16.1992i) q^{93} +(4.07761 - 23.1253i) q^{94} +(65.4078 + 11.5332i) q^{95} +(8.98848 - 14.3947i) q^{96} +(-101.648 + 85.2929i) q^{97} +(-25.0509 - 14.4632i) q^{98} +(-125.639 - 84.6291i) 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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