LMFDB - Embedded newform 162.4.e.a.73.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,4,Mod(19,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("162.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, degree $6$, not 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:	$9.55830942093$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.3
Character	$\chi$	$=$	162.73
Dual form			162.4.e.a.91.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.347296 + 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(5.66862 - 4.75653i) q^{5} +(-11.1935 + 4.07412i) q^{7} +(4.00000 - 6.92820i) q^{8} +O(q^{10})$	\(q+(-0.347296 + 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(5.66862 - 4.75653i) q^{5} +(-11.1935 + 4.07412i) q^{7} +(4.00000 - 6.92820i) q^{8} +(7.39985 + 12.8169i) q^{10} +(46.3308 + 38.8761i) q^{11} +(2.09014 + 11.8538i) q^{13} +(-4.13696 - 23.4619i) q^{14} +(12.2567 + 10.2846i) q^{16} +(52.1248 + 90.2827i) q^{17} +(22.8348 - 39.5511i) q^{19} +(-27.8143 + 10.1236i) q^{20} +(-92.6616 + 77.7523i) q^{22} +(13.0410 + 4.74653i) q^{23} +(-12.1974 + 69.1750i) q^{25} -24.0732 q^{26} +47.6477 q^{28} +(-29.4992 + 167.298i) q^{29} +(19.5480 + 7.11491i) q^{31} +(-24.5134 + 20.5692i) q^{32} +(-195.925 + 71.3109i) q^{34} +(-44.0732 + 76.3370i) q^{35} +(156.422 + 270.931i) q^{37} +(69.9700 + 58.7118i) q^{38} +(-10.2798 - 58.2995i) q^{40} +(-59.6415 - 338.244i) q^{41} +(-308.776 - 259.094i) q^{43} +(-120.961 - 209.511i) q^{44} +(-13.8779 + 24.0373i) q^{46} +(81.8198 - 29.7800i) q^{47} +(-154.056 + 129.269i) q^{49} +(-132.012 - 48.0485i) q^{50} +(8.36055 - 47.4150i) q^{52} +753.474 q^{53} +447.547 q^{55} +(-16.5479 + 93.8476i) q^{56} +(-319.268 - 116.204i) q^{58} +(-263.901 + 221.440i) q^{59} +(669.676 - 243.742i) q^{61} +(-20.8026 + 36.0311i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(68.2310 + 57.2526i) q^{65} +(-2.10545 - 11.9406i) q^{67} +(-72.4110 - 410.663i) q^{68} +(-135.048 - 113.319i) q^{70} +(-212.776 - 368.538i) q^{71} +(294.170 - 509.518i) q^{73} +(-587.955 + 213.998i) q^{74} +(-139.940 + 117.424i) q^{76} +(-676.991 - 246.405i) q^{77} +(167.873 - 952.056i) q^{79} +118.398 q^{80} +686.924 q^{82} +(-55.6100 + 315.380i) q^{83} +(724.908 + 263.845i) q^{85} +(617.552 - 518.188i) q^{86} +(454.665 - 165.485i) q^{88} +(49.8431 - 86.3309i) q^{89} +(-71.6896 - 124.170i) q^{91} +(-42.5245 - 35.6823i) q^{92} +(30.2394 + 171.496i) q^{94} +(-58.6842 - 332.815i) q^{95} +(-1273.09 - 1068.25i) q^{97} +(-201.106 - 348.326i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) $ 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8	$ 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8} + 30 q^{10} + 12 q^{11} + 60 q^{13} + 66 q^{14} - 102 q^{17} + 171 q^{19} - 96 q^{20} - 24 q^{22} + 708 q^{23} + 864 q^{25} + 468 q^{26} - 336 q^{28} + 381 q^{29} + 909 q^{31} - 48 q^{34} - 624 q^{35} + 555 q^{37} - 66 q^{38} - 96 q^{40} - 618 q^{41} - 1161 q^{43} - 132 q^{44} + 348 q^{46} + 378 q^{47} + 579 q^{49} - 36 q^{50} + 240 q^{52} + 1794 q^{53} - 3906 q^{55} + 264 q^{56} + 444 q^{58} - 1038 q^{59} + 324 q^{61} - 744 q^{62} - 768 q^{64} - 5718 q^{65} - 576 q^{67} - 1056 q^{68} - 1038 q^{70} - 120 q^{71} + 3036 q^{73} + 1110 q^{74} + 132 q^{76} + 3804 q^{77} - 2991 q^{79} + 480 q^{80} - 3408 q^{82} - 513 q^{83} - 2925 q^{85} + 2322 q^{86} + 480 q^{88} - 1065 q^{89} + 2859 q^{91} - 1884 q^{92} - 828 q^{94} - 6357 q^{95} - 2055 q^{97} - 1356 q^{98}+O(q^{100}) $ 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8 + 30 * q^10 + 12 * q^11 + 60 * q^13 + 66 * q^14 - 102 * q^17 + 171 * q^19 - 96 * q^20 - 24 * q^22 + 708 * q^23 + 864 * q^25 + 468 * q^26 - 336 * q^28 + 381 * q^29 + 909 * q^31 - 48 * q^34 - 624 * q^35 + 555 * q^37 - 66 * q^38 - 96 * q^40 - 618 * q^41 - 1161 * q^43 - 132 * q^44 + 348 * q^46 + 378 * q^47 + 579 * q^49 - 36 * q^50 + 240 * q^52 + 1794 * q^53 - 3906 * q^55 + 264 * q^56 + 444 * q^58 - 1038 * q^59 + 324 * q^61 - 744 * q^62 - 768 * q^64 - 5718 * q^65 - 576 * q^67 - 1056 * q^68 - 1038 * q^70 - 120 * q^71 + 3036 * q^73 + 1110 * q^74 + 132 * q^76 + 3804 * q^77 - 2991 * q^79 + 480 * q^80 - 3408 * q^82 - 513 * q^83 - 2925 * q^85 + 2322 * q^86 + 480 * q^88 - 1065 * q^89 + 2859 * q^91 - 1884 * q^92 - 828 * q^94 - 6357 * q^95 - 2055 * q^97 - 1356 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.347296	+	1.96962i	−0.122788	+	0.696364i
$2$	−0.347296	+	1.96962i	−0.122788	+	0.696364i
$3$		0			0
$3$		0			0
$4$	−3.75877	−	1.36808i	−0.469846	−	0.171010i
$5$	5.66862	−	4.75653i	0.507016	−	0.425437i	−0.353061	−	0.935600i	$-0.614859\pi$
$5$	5.66862	−	4.75653i	0.507016	−	0.425437i	0.860078	+	0.510163i	$0.170415\pi$
$6$		0			0
$7$	−11.1935	+	4.07412i	−0.604394	+	0.219982i	−0.626049	−	0.779784i	$-0.715329\pi$
$7$	−11.1935	+	4.07412i	−0.604394	+	0.219982i	0.0216544	+	0.999766i	$0.493107\pi$
$8$	4.00000	−	6.92820i	0.176777	−	0.306186i
$9$		0			0
$10$	7.39985	+	12.8169i	0.234004	+	0.405307i
$11$	46.3308	+	38.8761i	1.26993	+	1.06560i	0.994550	+	0.104265i	$0.0332491\pi$
$11$	46.3308	+	38.8761i	1.26993	+	1.06560i	0.275383	+	0.961335i	$0.411195\pi$
$12$		0			0
$13$	2.09014	+	11.8538i	0.0445923	+	0.252895i	0.998952	−	0.0457631i	$-0.0145719\pi$
$13$	2.09014	+	11.8538i	0.0445923	+	0.252895i	−0.954360	+	0.298659i	$0.903461\pi$
$14$	−4.13696	−	23.4619i	−0.0789750	−	0.447890i
$15$		0			0
$16$	12.2567	+	10.2846i	0.191511	+	0.160697i
$17$	52.1248	+	90.2827i	0.743654	+	1.28805i	0.950821	+	0.309740i	$0.100242\pi$
$17$	52.1248	+	90.2827i	0.743654	+	1.28805i	−0.207167	+	0.978305i	$0.566424\pi$
$18$		0			0
$19$	22.8348	−	39.5511i	0.275720	−	0.477560i	−0.694597	−	0.719399i	$-0.744417\pi$
$19$	22.8348	−	39.5511i	0.275720	−	0.477560i	0.970316	+	0.241839i	$0.0777506\pi$
$20$	−27.8143	+	10.1236i	−0.310974	+	0.113185i
$21$		0			0
$22$	−92.6616	+	77.7523i	−0.897978	+	0.753493i
$23$	13.0410	+	4.74653i	0.118228	+	0.0430313i	0.400457	−	0.916316i	$-0.368852\pi$
$23$	13.0410	+	4.74653i	0.118228	+	0.0430313i	−0.282229	+	0.959347i	$0.591074\pi$
$24$		0			0
$25$	−12.1974	+	69.1750i	−0.0975794	+	0.553400i
$26$	−24.0732			−0.181583
$27$		0			0
$28$	47.6477			0.321592
$29$	−29.4992	+	167.298i	−0.188892	+	1.07126i	0.731960	+	0.681347i	$0.238606\pi$
$29$	−29.4992	+	167.298i	−0.188892	+	1.07126i	−0.920852	+	0.389912i	$0.872505\pi$
$30$		0			0
$31$	19.5480	+	7.11491i	0.113256	+	0.0412218i	0.398026	−	0.917374i	$-0.369695\pi$
$31$	19.5480	+	7.11491i	0.113256	+	0.0412218i	−0.284771	+	0.958596i	$0.591917\pi$
$32$	−24.5134	+	20.5692i	−0.135419	+	0.113630i
$33$		0			0
$34$	−195.925	+	71.3109i	−0.988261	+	0.359698i
$35$	−44.0732	+	76.3370i	−0.212849	+	0.368666i
$36$		0			0
$37$	156.422	+	270.931i	0.695017	+	1.20381i	0.970175	+	0.242406i	$0.0779367\pi$
$37$	156.422	+	270.931i	0.695017	+	1.20381i	−0.275158	+	0.961399i	$0.588730\pi$
$38$	69.9700	+	58.7118i	0.298701	+	0.250640i
$39$		0			0
$40$	−10.2798	−	58.2995i	−0.0406343	−	0.230449i
$41$	−59.6415	−	338.244i	−0.227181	−	1.28841i	−0.858471	−	0.512863i	$-0.828585\pi$
$41$	−59.6415	−	338.244i	−0.227181	−	1.28841i	0.631289	−	0.775548i	$-0.282526\pi$
$42$		0			0
$43$	−308.776	−	259.094i	−1.09507	−	0.918871i	−0.0979842	−	0.995188i	$-0.531239\pi$
$43$	−308.776	−	259.094i	−1.09507	−	0.918871i	−0.997084	+	0.0763170i	$0.975684\pi$
$44$	−120.961	−	209.511i	−0.414445	−	0.717839i
$45$		0			0
$46$	−13.8779	+	24.0373i	−0.0444824	+	0.0770458i
$47$	81.8198	−	29.7800i	0.253929	−	0.0924225i	−0.211920	−	0.977287i	$-0.567971\pi$
$47$	81.8198	−	29.7800i	0.253929	−	0.0924225i	0.465848	+	0.884865i	$0.345749\pi$
$48$		0			0
$49$	−154.056	+	129.269i	−0.449144	+	0.376876i
$50$	−132.012	−	48.0485i	−0.373387	−	0.135902i
$51$		0			0
$52$	8.36055	−	47.4150i	0.0222961	−	0.126448i
$53$	753.474			1.95278			0.976392	−	0.216006i	$-0.0693029\pi$
$53$	753.474			1.95278			0.976392	+	0.216006i	$0.0693029\pi$
$54$		0			0
$55$	447.547			1.09722
$56$	−16.5479	+	93.8476i	−0.0394875	+	0.223945i
$57$		0			0
$58$	−319.268	−	116.204i	−0.722793	−	0.263075i
$59$	−263.901	+	221.440i	−0.582323	+	0.488627i	−0.885709	−	0.464241i	$-0.846327\pi$
$59$	−263.901	+	221.440i	−0.582323	+	0.488627i	0.303386	+	0.952868i	$0.401883\pi$
$60$		0			0
$61$	669.676	−	243.742i	1.40563	−	0.511606i	0.475783	−	0.879563i	$-0.342165\pi$
$61$	669.676	−	243.742i	1.40563	−	0.511606i	0.929843	+	0.367957i	$0.119943\pi$
$62$	−20.8026	+	36.0311i	−0.0426118	+	0.0738058i
$63$		0			0
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	68.2310	+	57.2526i	0.130200	+	0.109251i
$66$		0			0
$67$	−2.10545	−	11.9406i	−0.00383912	−	0.0217727i	0.982828	−	0.184524i	$-0.0590743\pi$
$67$	−2.10545	−	11.9406i	−0.00383912	−	0.0217727i	−0.986667	+	0.162751i	$0.947963\pi$
$68$	−72.4110	−	410.663i	−0.129134	−	0.732356i
$69$		0			0
$70$	−135.048	−	113.319i	−0.230591	−	0.193488i
$71$	−212.776	−	368.538i	−0.355660	−	0.616020i	0.631571	−	0.775318i	$-0.282410\pi$
$71$	−212.776	−	368.538i	−0.355660	−	0.616020i	−0.987231	+	0.159298i	$0.949077\pi$
$72$		0			0
$73$	294.170	−	509.518i	0.471644	−	0.816912i	−0.527830	−	0.849350i	$-0.676994\pi$
$73$	294.170	−	509.518i	0.471644	−	0.816912i	0.999474	+	0.0324386i	$0.0103273\pi$
$74$	−587.955	+	213.998i	−0.923627	+	0.336173i
$75$		0			0
$76$	−139.940	+	117.424i	−0.211213	+	0.177229i
$77$	−676.991	−	246.405i	−1.00195	−	0.364681i
$78$		0			0
$79$	167.873	−	952.056i	0.239079	−	1.35588i	−0.594773	−	0.803893i	$-0.702758\pi$
$79$	167.873	−	952.056i	0.239079	−	1.35588i	0.833852	−	0.551988i	$-0.186131\pi$
$80$	118.398			0.165466
$81$		0			0
$82$	686.924			0.925098
$83$	−55.6100	+	315.380i	−0.0735420	+	0.417078i	0.925704	+	0.378249i	$0.123474\pi$
$83$	−55.6100	+	315.380i	−0.0735420	+	0.417078i	−0.999246	+	0.0388285i	$0.987637\pi$
$84$		0			0
$85$	724.908	+	263.845i	0.925027	+	0.336682i
$86$	617.552	−	518.188i	0.774330	−	0.649740i
$87$		0			0
$88$	454.665	−	165.485i	0.550766	−	0.200463i
$89$	49.8431	−	86.3309i	0.0593636	−	0.102821i	−0.834816	−	0.550529i	$-0.814426\pi$
$89$	49.8431	−	86.3309i	0.0593636	−	0.102821i	0.894180	+	0.447708i	$0.147760\pi$
$90$		0			0
$91$	−71.6896	−	124.170i	−0.0825837	−	0.143039i
$92$	−42.5245	−	35.6823i	−0.0481900	−	0.0404362i
$93$		0			0
$94$	30.2394	+	171.496i	0.0331804	+	0.188175i
$95$	−58.6842	−	332.815i	−0.0633776	−	0.359432i
$96$		0			0
$97$	−1273.09	−	1068.25i	−1.33260	−	1.11818i	−0.983462	−	0.181113i	$-0.942030\pi$
$97$	−1273.09	−	1068.25i	−1.33260	−	1.11818i	−0.349138	−	0.937071i	$-0.613526\pi$
$98$	−201.106	−	348.326i	−0.207294	−	0.359044i
$99$		0			0
$100$	140.484	−	243.326i	0.140484	−	0.243326i
$101$	−231.684	+	84.3259i	−0.228251	+	0.0830767i	−0.453614	−	0.891198i	$-0.649866\pi$
$101$	−231.684	+	84.3259i	−0.228251	+	0.0830767i	0.225363	+	0.974275i	$0.427643\pi$
$102$		0			0
$103$	−814.444	+	683.400i	−0.779122	+	0.653761i	−0.943027	−	0.332715i	$-0.892035\pi$
$103$	−814.444	+	683.400i	−0.779122	+	0.653761i	0.163906	+	0.986476i	$0.447591\pi$
$104$	90.4858	+	32.9341i	0.0853160	+	0.0310525i
$105$		0			0
$106$	−261.679	+	1484.05i	−0.239778	+	1.35985i
$107$	1532.32			1.38444			0.692219	−	0.721688i	$-0.256633\pi$
$107$	1532.32			1.38444			0.692219	+	0.721688i	$0.256633\pi$
$108$		0			0
$109$	−767.656			−0.674570			−0.337285	−	0.941403i	$-0.609509\pi$
$109$	−767.656			−0.674570			−0.337285	+	0.941403i	$0.609509\pi$
$110$	−155.431	+	881.496i	−0.134726	+	0.764066i
$111$		0			0
$112$	−179.097	−	65.1858i	−0.151099	−	0.0549954i
$113$	−524.906	+	440.448i	−0.436982	+	0.366672i	−0.834579	−	0.550889i	$-0.814289\pi$
$113$	−524.906	+	440.448i	−0.436982	+	0.366672i	0.397596	+	0.917560i	$0.369844\pi$
$114$		0			0
$115$	96.5014	−	35.1236i	0.0782505	−	0.0284808i
$116$	339.758	−	588.479i	0.271946	−	0.471025i
$117$		0			0
$118$	−344.499	−	596.690i	−0.268760	−	0.465506i
$119$	−951.283	−	798.221i	−0.732806	−	0.614898i
$120$		0			0
$121$	404.061	+	2291.55i	0.303577	+	1.72167i
$122$	247.502	+	1403.65i	0.183670	+	1.04165i
$123$		0			0
$124$	−63.7428	−	53.4866i	−0.0461635	−	0.0387358i
$125$	722.382	+	1251.20i	0.516894	+	0.895287i
$126$		0			0
$127$	−1337.64	+	2316.86i	−0.934617	+	1.61880i	−0.159301	+	0.987230i	$0.550924\pi$
$127$	−1337.64	+	2316.86i	−0.934617	+	1.61880i	−0.775316	+	0.631574i	$0.782409\pi$
$128$	120.281	−	43.7786i	0.0830579	−	0.0302306i
$129$		0			0
$130$	−136.462	+	114.505i	−0.0920654	+	0.0772521i
$131$	−890.773	−	324.215i	−0.594101	−	0.216235i	0.0274312	−	0.999624i	$-0.491267\pi$
$131$	−890.773	−	324.215i	−0.594101	−	0.216235i	−0.621532	+	0.783389i	$0.713490\pi$
$132$		0			0
$133$	−94.4669	+	535.749i	−0.0615889	+	0.349288i
$134$	24.2495			0.0156331
$135$		0			0
$136$	833.996			0.525843
$137$	202.017	−	1145.69i	0.125981	−	0.714476i	−0.854739	−	0.519058i	$-0.826283\pi$
$137$	202.017	−	1145.69i	0.125981	−	0.714476i	0.980720	−	0.195417i	$-0.0626062\pi$
$138$		0			0
$139$	−679.027	−	247.146i	−0.414348	−	0.150810i	0.126430	−	0.991975i	$-0.459648\pi$
$139$	−679.027	−	247.146i	−0.414348	−	0.150810i	−0.540778	+	0.841165i	$0.681870\pi$
$140$	270.096	−	226.638i	0.163052	−	0.136817i
$141$		0			0
$142$	799.775	−	291.094i	0.472645	−	0.172029i
$143$	−363.991	+	630.450i	−0.212856	+	0.368678i
$144$		0			0
$145$	628.540	+	1088.66i	0.359982	+	0.623508i
$146$	901.390	+	756.356i	0.510956	+	0.428743i
$147$		0			0
$148$	−217.299	−	1232.37i	−0.120688	−	0.684458i
$149$	209.269	+	1186.83i	0.115061	+	0.652541i	0.986720	+	0.162429i	$0.0519329\pi$
$149$	209.269	+	1186.83i	0.115061	+	0.652541i	−0.871660	+	0.490112i	$0.836956\pi$
$150$		0			0
$151$	−539.880	−	453.013i	−0.290959	−	0.244144i	0.485610	−	0.874175i	$-0.338597\pi$
$151$	−539.880	−	453.013i	−0.290959	−	0.244144i	−0.776569	+	0.630032i	$0.783042\pi$
$152$	−182.679	−	316.409i	−0.0974816	−	0.168843i
$153$		0			0
$154$	720.439	−	1247.84i	0.376978	−	0.652945i
$155$	144.653	−	52.6492i	0.0749599	−	0.0272832i
$156$		0			0
$157$	2277.87	−	1911.36i	1.15792	−	0.971613i	0.158048	−	0.987431i	$-0.449480\pi$
$157$	2277.87	−	1911.36i	1.15792	−	0.971613i	0.999875	+	0.0158184i	$0.00503538\pi$
$158$	1816.88	+	661.291i	0.914832	+	0.332971i
$159$		0			0
$160$	−41.1191	+	233.198i	−0.0203172	+	0.115224i
$161$	−165.313			−0.0809222
$162$		0			0
$163$	−3208.52			−1.54179			−0.770893	−	0.636965i	$-0.780189\pi$
$163$	−3208.52			−1.54179			−0.770893	+	0.636965i	$0.780189\pi$
$164$	−238.566	+	1352.98i	−0.113591	+	0.644205i
$165$		0			0
$166$	−601.864	−	219.061i	−0.281408	−	0.102424i
$167$	−782.322	+	656.446i	−0.362503	+	0.304176i	−0.805787	−	0.592205i	$-0.798258\pi$
$167$	−782.322	+	656.446i	−0.362503	+	0.304176i	0.443285	+	0.896381i	$0.353813\pi$
$168$		0			0
$169$	1928.36	−	701.866i	0.877725	−	0.319466i
$170$	−771.431	+	1336.16i	−0.348036	+	0.602816i
$171$		0			0
$172$	806.157	+	1396.31i	0.357377	+	0.618996i
$173$	1264.45	+	1061.00i	0.555688	+	0.466278i	0.876862	−	0.480743i	$-0.159633\pi$
$173$	1264.45	+	1061.00i	0.555688	+	0.466278i	−0.321174	+	0.947020i	$0.604077\pi$
$174$		0			0
$175$	−145.295	−	824.007i	−0.0627614	−	0.355938i
$176$	168.037	+	952.987i	0.0719676	+	0.408148i
$177$		0			0
$178$	152.728	+	128.154i	0.0643116	+	0.0539639i
$179$	−1562.73	−	2706.74i	−0.652538	−	1.13023i	−0.982505	−	0.186236i	$-0.940371\pi$
$179$	−1562.73	−	2706.74i	−0.652538	−	1.13023i	0.329967	−	0.943992i	$-0.392962\pi$
$180$		0			0
$181$	383.688	−	664.567i	0.157565	−	0.272911i	−0.776425	−	0.630210i	$-0.782969\pi$
$181$	383.688	−	664.567i	0.157565	−	0.272911i	0.933990	+	0.357299i	$0.116302\pi$
$182$	269.465	−	98.0772i	0.109748	−	0.0399448i
$183$		0			0
$184$	85.0489	−	71.3645i	0.0340755	−	0.0285927i
$185$	2175.39	+	791.777i	0.864529	+	0.314663i
$186$		0			0
$187$	−1094.86	+	6209.28i	−0.428152	+	2.42817i
$188$	−348.283			−0.135113
$189$		0			0
$190$	675.898			0.258078
$191$	825.200	−	4679.94i	0.312615	−	1.77293i	−0.272680	−	0.962105i	$-0.587910\pi$
$191$	825.200	−	4679.94i	0.312615	−	1.77293i	0.585294	−	0.810821i	$-0.300979\pi$
$192$		0			0
$193$	1130.48	+	411.462i	0.421627	+	0.153460i	0.544115	−	0.839010i	$-0.316865\pi$
$193$	1130.48	+	411.462i	0.421627	+	0.153460i	−0.122489	+	0.992470i	$0.539088\pi$
$194$	2546.17	−	2136.49i	0.942291	−	0.790676i
$195$		0			0
$196$	755.912	−	275.130i	0.275478	−	0.100266i
$197$	−2397.51	+	4152.62i	−0.867085	+	1.50184i	−0.00212390	+	0.999998i	$0.500676\pi$
$197$	−2397.51	+	4152.62i	−0.867085	+	1.50184i	−0.864962	+	0.501838i	$0.832657\pi$
$198$		0			0
$199$	−1731.13	−	2998.40i	−0.616666	−	1.06810i	−0.990090	−	0.140436i	$-0.955150\pi$
$199$	−1731.13	−	2998.40i	−0.616666	−	1.06810i	0.373424	−	0.927661i	$-0.378184\pi$
$200$	430.469	+	361.206i	0.152194	+	0.127706i
$201$		0			0
$202$	−85.6268	−	485.614i	−0.0298252	−	0.169147i
$203$	−351.392	−	1992.84i	−0.121492	−	0.689016i
$204$		0			0
$205$	−1946.95	−	1633.69i	−0.663322	−	0.556594i
$206$	−1063.18	−	1841.48i	−0.359589	−	0.622826i
$207$		0			0
$208$	−96.2930	+	166.784i	−0.0320996	+	0.0555981i
$209$	2595.55	−	944.703i	0.859033	−	0.312663i
$210$		0			0
$211$	534.632	−	448.609i	0.174434	−	0.146368i	−0.551391	−	0.834247i	$-0.685903\pi$
$211$	534.632	−	448.609i	0.174434	−	0.146368i	0.725825	+	0.687879i	$0.241458\pi$
$212$	−2832.13	−	1030.81i	−0.917508	−	0.333946i
$213$		0			0
$214$	−532.169	+	3018.08i	−0.169992	+	0.964073i
$215$	−2982.72			−0.946139
$216$		0			0
$217$	−247.799			−0.0775192
$218$	266.604	−	1511.99i	0.0828290	−	0.469746i
$219$		0			0
$220$	−1682.23	−	612.280i	−0.515526	−	0.187636i
$221$	−961.242	+	806.578i	−0.292580	+	0.245504i
$222$		0			0
$223$	4731.65	−	1722.18i	1.42087	−	0.517155i	0.486571	−	0.873641i	$-0.338247\pi$
$223$	4731.65	−	1722.18i	1.42087	−	0.517155i	0.934301	+	0.356486i	$0.116025\pi$
$224$	190.591	−	330.113i	0.0568499	−	0.0984669i
$225$		0			0
$226$	−685.216	−	1186.83i	−0.201681	−	0.349322i
$227$	−2703.98	−	2268.91i	−0.790616	−	0.663405i	0.155282	−	0.987870i	$-0.450371\pi$
$227$	−2703.98	−	2268.91i	−0.790616	−	0.663405i	−0.945898	+	0.324465i	$0.894816\pi$
$228$		0			0
$229$	−810.900	−	4598.84i	−0.233999	−	1.32708i	−0.844711	−	0.535222i	$-0.820228\pi$
$229$	−810.900	−	4598.84i	−0.233999	−	1.32708i	0.610712	−	0.791853i	$-0.290883\pi$
$230$	35.6655	+	202.269i	0.0102248	+	0.0579879i
$231$		0			0
$232$	1041.08	+	873.570i	0.294613	+	0.247210i
$233$	1467.22	+	2541.30i	0.412535	+	0.714532i	0.995166	−	0.0982048i	$-0.0313100\pi$
$233$	1467.22	+	2541.30i	0.412535	+	0.714532i	−0.582631	+	0.812737i	$0.697977\pi$
$234$		0			0
$235$	322.156	−	557.990i	0.0894260	−	0.154890i
$236$	1294.89	−	471.302i	0.357162	−	0.129996i
$237$		0			0
$238$	1902.57	−	1596.44i	0.518172	−	0.434798i
$239$	2843.49	+	1034.94i	0.769581	+	0.280104i	0.696821	−	0.717245i	$-0.254597\pi$
$239$	2843.49	+	1034.94i	0.769581	+	0.280104i	0.0727596	+	0.997350i	$0.476819\pi$
$240$		0			0
$241$	−381.399	+	2163.02i	−0.101942	+	0.578144i	0.890455	+	0.455071i	$0.150386\pi$
$241$	−381.399	+	2163.02i	−0.101942	+	0.578144i	−0.992398	+	0.123073i	$0.960725\pi$
$242$	−4653.79			−1.23619
$243$		0			0
$244$	−2850.62			−0.747918
$245$	−258.416	+	1465.55i	−0.0673860	+	0.382165i
$246$		0			0
$247$	516.557	+	188.011i	0.133068	+	0.0484327i
$248$	127.486	−	106.973i	0.0326425	−	0.0273903i
$249$		0			0
$250$	−2715.27	+	988.276i	−0.686914	+	0.250016i
$251$	1984.26	−	3436.84i	0.498985	−	0.864268i	−0.501014	−	0.865439i	$-0.667039\pi$
$251$	1984.26	−	3436.84i	0.498985	−	0.864268i	0.999999	+	0.00117126i	$0.000372824\pi$
$252$		0			0
$253$	419.673	+	726.894i	0.104287	+	0.180630i
$254$	−4098.77	−	3439.27i	−1.01252	−	0.849603i
$255$		0			0
$256$	44.4539	+	252.111i	0.0108530	+	0.0615505i
$257$	−613.781	−	3480.92i	−0.148975	−	0.844880i	−0.964089	−	0.265579i	$-0.914437\pi$
$257$	−613.781	−	3480.92i	−0.148975	−	0.844880i	0.815114	−	0.579301i	$-0.196674\pi$
$258$		0			0
$259$	−2854.72	−	2395.40i	−0.684879	−	0.574682i
$260$	−178.138	−	308.545i	−0.0424911	−	0.0735967i
$261$		0			0
$262$	947.941	−	1641.88i	0.223527	−	0.387160i
$263$	−185.627	+	67.5627i	−0.0435219	+	0.0158407i	−0.363689	−	0.931520i	$-0.618483\pi$
$263$	−185.627	+	67.5627i	−0.0435219	+	0.0158407i	0.320167	+	0.947361i	$0.396261\pi$
$264$		0			0
$265$	4271.15	−	3583.92i	0.990094	−	0.830787i
$266$	−1022.41	−	372.127i	−0.235669	−	0.0857766i
$267$		0			0
$268$	−8.42178	+	47.7623i	−0.00191956	+	0.0108864i
$269$	−5218.25			−1.18276			−0.591380	−	0.806393i	$-0.701417\pi$
$269$	−5218.25			−1.18276			−0.591380	+	0.806393i	$0.701417\pi$
$270$		0			0
$271$	4679.73			1.04898			0.524490	−	0.851417i	$-0.324256\pi$
$271$	4679.73			1.04898			0.524490	+	0.851417i	$0.324256\pi$
$272$	−289.644	+	1642.65i	−0.0645671	+	0.366178i
$273$		0			0
$274$	2186.42	+	795.790i	0.482066	+	0.175458i
$275$	−3254.38	+	2730.75i	−0.713623	+	0.598800i
$276$		0			0
$277$	4097.74	−	1491.45i	0.888842	−	0.323512i	0.143069	−	0.989713i	$-0.454303\pi$
$277$	4097.74	−	1491.45i	0.888842	−	0.323512i	0.745773	+	0.666201i	$0.232081\pi$
$278$	722.606	−	1251.59i	0.155896	−	0.270019i
$279$		0			0
$280$	352.586	+	610.696i	0.0752537	+	0.130343i
$281$	2704.01	+	2268.94i	0.574049	+	0.481685i	0.882987	−	0.469398i	$-0.155529\pi$
$281$	2704.01	+	2268.94i	0.574049	+	0.481685i	−0.308938	+	0.951082i	$0.599973\pi$
$282$		0			0
$283$	−128.070	−	726.321i	−0.0269010	−	0.152563i	0.968399	−	0.249408i	$-0.0802360\pi$
$283$	−128.070	−	726.321i	−0.0269010	−	0.152563i	−0.995299	+	0.0968450i	$0.969125\pi$
$284$	295.585	+	1676.35i	0.0617596	+	0.350256i
$285$		0			0
$286$	−1115.33	−	935.875i	−0.230598	−	0.193495i
$287$	2045.64	+	3543.16i	0.420734	+	0.728732i
$288$		0			0
$289$	−2977.48	+	5157.15i	−0.606042	+	1.04969i
$290$	−2362.54	+	859.894i	−0.478390	+	0.174120i
$291$		0			0
$292$	−1802.78	+	1512.71i	−0.361300	+	0.303167i
$293$	4406.96	+	1604.00i	0.878694	+	0.319818i	0.741683	−	0.670751i	$-0.234028\pi$
$293$	4406.96	+	1604.00i	0.878694	+	0.319818i	0.137011	+	0.990569i	$0.456250\pi$
$294$		0			0
$295$	−442.671	+	2510.51i	−0.0873671	+	0.495484i
$296$	2502.75			0.491451
$297$		0			0
$298$	−2410.27			−0.468534
$299$	−29.0068	+	164.506i	−0.00561039	+	0.0318181i
$300$		0			0
$301$	4511.88	+	1642.19i	0.863987	+	0.314466i
$302$	1079.76	−	906.026i	0.205739	−	0.172636i
$303$		0			0
$304$	686.647	−	249.919i	0.129546	−	0.0471508i
$305$	2636.77	−	4567.01i	0.495019	−	0.857398i
$306$		0			0
$307$	−1929.12	−	3341.33i	−0.358634	−	0.621172i	0.629099	−	0.777325i	$-0.283424\pi$
$307$	−1929.12	−	3341.33i	−0.358634	−	0.621172i	−0.987733	+	0.156153i	$0.950091\pi$
$308$	2207.55	+	1852.36i	0.408399	+	0.342688i
$309$		0			0
$310$	53.4614	+	303.195i	0.00979486	+	0.0555494i
$311$	809.595	+	4591.44i	0.147614	+	0.837160i	0.965231	+	0.261398i	$0.0841834\pi$
$311$	809.595	+	4591.44i	0.147614	+	0.837160i	−0.817617	+	0.575762i	$0.804705\pi$
$312$		0			0
$313$	1018.62	+	854.721i	0.183948	+	0.154350i	0.730112	−	0.683328i	$-0.239468\pi$
$313$	1018.62	+	854.721i	0.183948	+	0.154350i	−0.546164	+	0.837678i	$0.683912\pi$
$314$	2973.55	+	5150.34i	0.534418	+	0.925639i
$315$		0			0
$316$	−1933.49	+	3348.90i	−0.344200	+	0.596171i
$317$	3291.09	−	1197.86i	0.583110	−	0.212235i	−0.0335863	−	0.999436i	$-0.510693\pi$
$317$	3291.09	−	1197.86i	0.583110	−	0.212235i	0.616696	+	0.787201i	$0.288471\pi$
$318$		0			0
$319$	−7870.64	+	6604.25i	−1.38141	+	1.15914i
$320$	−445.030	−	161.978i	−0.0777435	−	0.0282963i
$321$		0			0
$322$	57.4125	−	325.603i	0.00993626	−	0.0563513i
$323$	4761.04			0.820159
$324$		0			0
$325$	−845.478			−0.144304
$326$	1114.31	−	6319.56i	0.189312	−	1.07364i
$327$		0			0
$328$	−2581.99	−	939.767i	−0.434654	−	0.158201i
$329$	−794.526	+	666.687i	−0.133142	+	0.111719i
$330$		0			0
$331$	−842.078	+	306.491i	−0.139833	+	0.0508951i	−0.410989	−	0.911640i	$-0.634816\pi$
$331$	−842.078	+	306.491i	−0.139833	+	0.0508951i	0.271155	+	0.962536i	$0.412594\pi$
$332$	640.490	−	1109.36i	0.105878	−	0.183386i
$333$		0			0
$334$	−1021.25	−	1768.86i	−0.167306	−	0.289783i
$335$	−68.7307	−	57.6719i	−0.0112094	−	0.00940583i
$336$		0			0
$337$	1035.27	+	5871.30i	0.167343	+	0.949051i	0.946615	+	0.322365i	$0.104478\pi$
$337$	1035.27	+	5871.30i	0.167343	+	0.949051i	−0.779272	+	0.626686i	$0.784411\pi$
$338$	712.694	+	4041.89i	0.114691	+	0.650443i
$339$		0			0
$340$	−2363.80	−	1983.47i	−0.377045	−	0.316378i
$341$	629.076	+	1089.59i	0.0999014	+	0.173034i
$342$		0			0
$343$	3240.67	−	5613.01i	0.510146	−	0.883598i
$344$	−3030.16	+	1102.89i	−0.474928	+	0.172860i
$345$		0			0
$346$	−2528.89	+	2121.99i	−0.392931	+	0.329708i
$347$	7751.93	+	2821.47i	1.19927	+	0.436497i	0.862968	−	0.505259i	$-0.168603\pi$
$347$	7751.93	+	2821.47i	1.19927	+	0.436497i	0.336298	+	0.941756i	$0.390825\pi$
$348$		0			0
$349$	333.247	−	1889.94i	0.0511127	−	0.289874i	−0.948528	−	0.316694i	$-0.897427\pi$
$349$	333.247	−	1889.94i	0.0511127	−	0.289874i	0.999640	+	0.0268201i	$0.00853811\pi$
$350$	1673.44			0.255569
$351$		0			0
$352$	−1935.38			−0.293057
$353$	−549.740	+	3117.73i	−0.0828887	+	0.470085i	0.914904	+	0.403672i	$0.132266\pi$
$353$	−549.740	+	3117.73i	−0.0828887	+	0.470085i	−0.997792	+	0.0664125i	$0.978845\pi$
$354$		0			0
$355$	−2959.11	−	1077.03i	−0.442403	−	0.161022i
$356$	−305.457	+	256.308i	−0.0454752	+	0.0381582i
$357$		0			0
$358$	5873.96	−	2137.95i	0.867174	−	0.315626i
$359$	−244.067	+	422.736i	−0.0358812	+	0.0621480i	−0.883408	−	0.468604i	$-0.844757\pi$
$359$	−244.067	+	422.736i	−0.0358812	+	0.0621480i	0.847527	+	0.530752i	$0.178090\pi$
$360$		0			0
$361$	2386.64	+	4133.78i	0.347957	+	0.602680i
$362$	1175.69	+	986.519i	0.170698	+	0.143233i
$363$		0			0
$364$	99.5901	+	564.804i	0.0143405	+	0.0813290i
$365$	−756.001	−	4287.49i	−0.108413	−	0.614843i
$366$		0			0
$367$	2096.30	+	1759.01i	0.298164	+	0.250189i	0.779580	−	0.626303i	$-0.215433\pi$
$367$	2096.30	+	1759.01i	0.298164	+	0.250189i	−0.481416	+	0.876492i	$0.659877\pi$
$368$	111.023	+	192.298i	0.0157269	+	0.0272398i
$369$		0			0
$370$	−2315.00	+	4009.70i	−0.325273	+	0.563390i
$371$	−8434.04	+	3069.74i	−1.18025	+	0.429576i
$372$		0			0
$373$	−104.296	+	87.5151i	−0.0144779	+	0.0121484i	−0.649998	−	0.759936i	$-0.725230\pi$
$373$	−104.296	+	87.5151i	−0.0144779	+	0.0121484i	0.635520	+	0.772084i	$0.280786\pi$
$374$	−11849.7	−	4312.92i	−1.63832	−	0.596299i
$375$		0			0
$376$	120.958	−	685.984i	0.0165902	−	0.0940876i
$377$	−2044.77			−0.279340
$378$		0			0
$379$	839.393			0.113764			0.0568822	−	0.998381i	$-0.481884\pi$
$379$	839.393			0.113764			0.0568822	+	0.998381i	$0.481884\pi$
$380$	−234.737	+	1331.26i	−0.0316888	+	0.179716i
$381$		0			0
$382$	8931.10	+	3250.65i	1.19622	+	0.435387i
$383$	384.276	−	322.446i	0.0512678	−	0.0430188i	−0.616794	−	0.787125i	$-0.711569\pi$
$383$	384.276	−	322.446i	0.0512678	−	0.0430188i	0.668062	+	0.744106i	$0.267124\pi$
$384$		0			0
$385$	−5009.64	+	1823.36i	−0.663155	+	0.241369i
$386$	−1203.03	+	2083.72i	−0.158634	+	0.274763i
$387$		0			0
$388$	3323.79	+	5756.97i	0.434897	+	0.753263i
$389$	2189.47	+	1837.18i	0.285374	+	0.239457i	0.774226	−	0.632910i	$-0.218140\pi$
$389$	2189.47	+	1837.18i	0.285374	+	0.239457i	−0.488852	+	0.872367i	$0.662584\pi$
$390$		0			0
$391$	251.229	+	1424.79i	0.0324941	+	0.184283i
$392$	279.374	+	1584.41i	0.0359962	+	0.204145i
$393$		0			0
$394$	−7346.41	−	6164.37i	−0.939357	−	0.788214i
$395$	−3576.88	−	6195.33i	−0.455626	−	0.789167i
$396$		0			0
$397$	−1449.95	+	2511.38i	−0.183301	+	0.317487i	−0.943003	−	0.332785i	$-0.892012\pi$
$397$	−1449.95	+	2511.38i	−0.183301	+	0.317487i	0.759701	+	0.650272i	$0.225345\pi$
$398$	6506.92	−	2368.33i	0.819504	−	0.298275i
$399$		0			0
$400$	−860.938	+	722.413i	−0.107617	+	0.0903016i
$401$	−8600.41	−	3130.29i	−1.07103	−	0.389824i	−0.254469	−	0.967081i	$-0.581901\pi$
$401$	−8600.41	−	3130.29i	−1.07103	−	0.389824i	−0.816562	+	0.577257i	$0.804123\pi$
$402$		0			0
$403$	−43.4803	+	246.589i	−0.00537446	+	0.0304801i
$404$	986.210			0.121450
$405$		0			0
$406$	4047.17			0.494724
$407$	−3285.60	+	18633.5i	−0.400150	+	2.26936i
$408$		0			0
$409$	−14107.1	−	5134.57i	−1.70551	−	0.620753i	−0.709073	−	0.705135i	$-0.750886\pi$
$409$	−14107.1	−	5134.57i	−1.70551	−	0.620753i	−0.996433	+	0.0843820i	$0.973108\pi$
$410$	3893.91	−	3267.38i	0.469040	−	0.393571i
$411$		0			0
$412$	3996.25	−	1454.52i	0.477867	−	0.173929i
$413$	2051.82	−	3553.86i	0.244464	−	0.423424i
$414$		0			0
$415$	1184.88	+	2052.28i	0.140153	+	0.242753i
$416$	−295.059	−	247.584i	−0.0347751	−	0.0291798i
$417$		0			0
$418$	959.277	+	5440.33i	0.112248	+	0.636591i
$419$	−1176.74	−	6673.65i	−0.137202	−	0.778112i	−0.973301	−	0.229533i	$-0.926280\pi$
$419$	−1176.74	−	6673.65i	−0.137202	−	0.778112i	0.836099	−	0.548579i	$-0.184831\pi$
$420$		0			0
$421$	−3081.29	−	2585.51i	−0.356705	−	0.299311i	0.446771	−	0.894648i	$-0.352574\pi$
$421$	−3081.29	−	2585.51i	−0.356705	−	0.299311i	−0.803476	+	0.595338i	$0.797018\pi$
$422$	697.912	+	1208.82i	0.0805067	+	0.139442i
$423$		0			0
$424$	3013.89	−	5220.22i	0.345207	−	0.597916i
$425$	−6881.10	+	2504.52i	−0.785370	+	0.285851i
$426$		0			0
$427$	−6503.01	+	5456.67i	−0.737008	+	0.618424i
$428$	−5759.63	−	2096.34i	−0.650473	−	0.236753i
$429$		0			0
$430$	1035.89	−	5874.82i	0.116174	−	0.658858i
$431$	9048.23			1.01122			0.505612	−	0.862761i	$-0.331267\pi$
$431$	9048.23			1.01122			0.505612	+	0.862761i	$0.331267\pi$
$432$		0			0
$433$	7204.53			0.799602			0.399801	−	0.916602i	$-0.369079\pi$
$433$	7204.53			0.799602			0.399801	+	0.916602i	$0.369079\pi$
$434$	86.0596	−	488.068i	0.00951842	−	0.0539816i
$435$		0			0
$436$	2885.44	+	1050.22i	0.316944	+	0.115358i
$437$	485.520	−	407.399i	0.0531477	−	0.0445962i
$438$		0			0
$439$	2182.85	−	794.494i	0.237316	−	0.0863761i	−0.220624	−	0.975359i	$-0.570809\pi$
$439$	2182.85	−	794.494i	0.237316	−	0.0863761i	0.457941	+	0.888983i	$0.348587\pi$
$440$	1790.19	−	3100.70i	0.193963	−	0.335954i
$441$		0			0
$442$	−1254.81	−	2173.40i	−0.135035	−	0.233887i
$443$	−6112.27	−	5128.80i	−0.655536	−	0.550060i	0.253209	−	0.967412i	$-0.418514\pi$
$443$	−6112.27	−	5128.80i	−0.655536	−	0.550060i	−0.908745	+	0.417351i	$0.862958\pi$
$444$		0			0
$445$	−128.094	−	726.457i	−0.0136455	−	0.0773873i
$446$	1748.75	+	9917.63i	0.185663	+	1.05294i
$447$		0			0
$448$	584.004	+	490.037i	0.0615883	+	0.0516788i
$449$	1253.26	+	2170.70i	0.131726	+	0.228155i	0.924342	−	0.381565i	$-0.124615\pi$
$449$	1253.26	+	2170.70i	0.131726	+	0.228155i	−0.792616	+	0.609721i	$0.791282\pi$
$450$		0			0
$451$	10386.4	−	17989.7i	1.08442	−	1.87828i
$452$	2575.57	−	937.431i	0.268019	−	0.0975509i
$453$		0			0
$454$	5407.97	−	4537.83i	0.559050	−	0.469098i
$455$	−997.000	−	362.878i	−0.102725	−	0.0373890i
$456$		0			0
$457$	1951.37	−	11066.8i	0.199740	−	1.13278i	−0.705764	−	0.708447i	$-0.749396\pi$
$457$	1951.37	−	11066.8i	0.199740	−	1.13278i	0.905505	−	0.424337i	$-0.139493\pi$
$458$	9339.58			0.952860
$459$		0			0
$460$	−410.779			−0.0416362
$461$	1632.42	−	9257.91i	0.164923	−	0.935323i	−0.784222	−	0.620481i	$-0.786937\pi$
$461$	1632.42	−	9257.91i	0.164923	−	0.935323i	0.949144	−	0.314842i	$-0.101951\pi$
$462$		0			0
$463$	1847.54	+	672.448i	0.185448	+	0.0674974i	0.433075	−	0.901358i	$-0.357429\pi$
$463$	1847.54	+	672.448i	0.185448	+	0.0674974i	−0.247627	+	0.968855i	$0.579651\pi$
$464$	−2082.16	+	1747.14i	−0.208323	+	0.174804i
$465$		0			0
$466$	−5514.94	+	2007.27i	−0.548229	+	0.199539i
$467$	7125.38	−	12341.5i	0.706046	−	1.22291i	−0.260267	−	0.965537i	$-0.583811\pi$
$467$	7125.38	−	12341.5i	0.706046	−	1.22291i	0.966313	−	0.257370i	$-0.0828561\pi$
$468$		0			0
$469$	72.2146	+	125.079i	0.00710994	+	0.0123148i
$470$	987.142	+	828.310i	0.0968797	+	0.0812917i
$471$		0			0
$472$	478.573	+	2714.12i	0.0466697	+	0.264677i
$473$	−4233.27	−	24008.0i	−0.411513	−	2.33381i
$474$		0			0
$475$	2457.42	+	2062.02i	0.237377	+	0.199183i
$476$	2483.62	+	4301.76i	0.239153	+	0.414225i
$477$		0			0
$478$	−3025.97	+	5241.14i	−0.289550	+	0.501515i
$479$	−2777.79	+	1011.03i	−0.264970	+	0.0964411i	−0.471089	−	0.882086i	$-0.656139\pi$
$479$	−2777.79	+	1011.03i	−0.264970	+	0.0964411i	0.206119	+	0.978527i	$0.433917\pi$
$480$		0			0
$481$	−2884.61	+	2420.47i	−0.273444	+	0.229447i
$482$	−4127.87	−	1502.42i	−0.390081	−	0.141978i
$483$		0			0
$484$	1616.24	−	9166.18i	0.151789	−	0.860836i
$485$	−12297.8			−1.15137
$486$		0			0
$487$	4304.17			0.400494			0.200247	−	0.979745i	$-0.435826\pi$
$487$	4304.17			0.400494			0.200247	+	0.979745i	$0.435826\pi$
$488$	990.008	−	5614.62i	0.0918352	−	0.520823i
$489$		0			0
$490$	−2796.82	−	1017.96i	−0.257852	−	0.0938504i
$491$	2624.29	−	2202.04i	0.241207	−	0.202396i	−0.514168	−	0.857689i	$-0.671899\pi$
$491$	2624.29	−	2202.04i	0.241207	−	0.202396i	0.755375	+	0.655293i	$0.227455\pi$
$492$		0			0
$493$	−16641.8	+	6057.12i	−1.52030	+	0.553345i
$494$	−549.709	+	952.123i	−0.0500659	+	0.0867167i
$495$		0			0
$496$	166.421	+	288.249i	0.0150655	+	0.0260943i
$497$	3883.18	+	3258.38i	0.350472	+	0.294081i
$498$		0			0
$499$	−2427.85	−	13769.0i	−0.217806	−	1.23524i	−0.875970	−	0.482366i	$-0.839777\pi$
$499$	−2427.85	−	13769.0i	−0.217806	−	1.23524i	0.658163	−	0.752875i	$-0.271334\pi$
$500$	−1003.52	−	5691.26i	−0.0897577	−	0.509041i
$501$		0			0
$502$	6080.12	+	5101.83i	0.540576	+	0.453597i
$503$	80.5977	+	139.599i	0.00714448	+	0.0123746i	0.869576	−	0.493800i	$-0.164392\pi$
$503$	80.5977	+	139.599i	0.00714448	+	0.0123746i	−0.862431	+	0.506175i	$0.831059\pi$
$504$		0			0
$505$	−912.226	+	1580.02i	−0.0803832	+	0.139228i
$506$	−1577.45	+	574.146i	−0.138590	+	0.0504425i
$507$		0			0
$508$	8197.53	−	6878.55i	0.715958	−	0.600760i
$509$	2690.05	+	979.096i	0.234252	+	0.0852607i	0.456479	−	0.889734i	$-0.349110\pi$
$509$	2690.05	+	979.096i	0.234252	+	0.0852607i	−0.222227	+	0.974995i	$0.571333\pi$
$510$		0			0
$511$	−1216.97	+	6901.79i	−0.105354	+	0.597490i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	7069.25			0.606636
$515$	−1366.16	+	7747.86i	−0.116893	+	0.662935i
$516$		0			0
$517$	4948.51	+	1801.11i	0.420958	+	0.153216i
$518$	5709.44	−	4790.79i	0.484283	−	0.406362i
$519$		0			0
$520$	669.581	−	243.708i	0.0564675	−	0.0205525i
$521$	−6324.76	+	10954.8i	−0.531848	+	0.921187i	0.467461	+	0.884014i	$0.345169\pi$
$521$	−6324.76	+	10954.8i	−0.531848	+	0.921187i	−0.999309	+	0.0371736i	$0.988165\pi$
$522$		0			0
$523$	7489.19	+	12971.7i	0.626155	+	1.08453i	0.988316	+	0.152417i	$0.0487058\pi$
$523$	7489.19	+	12971.7i	0.626155	+	1.08453i	−0.362161	+	0.932116i	$0.617961\pi$
$524$	2904.66	+	2437.30i	0.242158	+	0.203195i
$525$		0			0
$526$	−68.6050	−	389.078i	−0.00568692	−	0.0322521i
$527$	376.584	+	2135.71i	0.0311276	+	0.176533i
$528$		0			0
$529$	−9172.92	−	7697.00i	−0.753918	−	0.632613i
$530$	5575.59	+	9657.21i	0.456959	+	0.791476i
$531$		0			0
$532$	1088.03	−	1884.52i	0.0886691	−	0.153579i
$533$	3884.80	−	1413.95i	0.315703	−	0.114906i
$534$		0			0
$535$	8686.13	−	7288.52i	0.701933	−	0.588991i
$536$	−91.1485	−	33.1753i	−0.00734518	−	0.00267343i
$537$		0			0
$538$	1812.28	−	10278.0i	0.145229	−	0.823632i
$539$	−12163.0			−0.971982
$540$		0			0
$541$	6564.59			0.521689			0.260844	−	0.965381i	$-0.415999\pi$
$541$	6564.59			0.521689			0.260844	+	0.965381i	$0.415999\pi$
$542$	−1625.25	+	9217.28i	−0.128802	+	0.730472i
$543$		0			0
$544$	−3134.80	−	1140.97i	−0.247065	−	0.0899244i
$545$	−4351.55	+	3651.38i	−0.342018	+	0.286987i
$546$		0			0
$547$	−5715.92	+	2080.43i	−0.446792	+	0.162619i	−0.555611	−	0.831443i	$-0.687515\pi$
$547$	−5715.92	+	2080.43i	−0.446792	+	0.162619i	0.108819	+	0.994062i	$0.465293\pi$
$548$	−2326.74	+	4030.02i	−0.181374	+	0.314150i
$549$		0			0
$550$	−4248.29	−	7358.25i	−0.329359	−	0.570467i
$551$	5943.22	+	4986.96i	0.459510	+	0.385574i
$552$		0			0
$553$	1999.69	+	11340.8i	0.153771	+	0.872080i
$554$	1514.46	+	8588.95i	0.116143	+	0.658681i
$555$		0			0
$556$	2214.19	+	1857.93i	0.168890	+	0.141715i
$557$	−10541.0	−	18257.6i	−0.801863	−	1.38887i	−0.918389	−	0.395680i	$-0.870509\pi$
$557$	−10541.0	−	18257.6i	−0.801863	−	1.38887i	0.116525	−	0.993188i	$-0.462824\pi$
$558$		0			0
$559$	2425.85	−	4201.70i	0.183547	−	0.317912i
$560$	−1325.29	+	482.366i	−0.100007	+	0.0363994i
$561$		0			0
$562$	−5408.02	+	4537.87i	−0.405914	+	0.340602i
$563$	11759.2	+	4280.00i	0.880269	+	0.320392i	0.742318	−	0.670047i	$-0.233726\pi$
$563$	11759.2	+	4280.00i	0.880269	+	0.320392i	0.137951	+	0.990439i	$0.455948\pi$
$564$		0			0
$565$	−880.482	+	4993.46i	−0.0655614	+	0.371817i
$566$	1475.05			0.109542
$567$		0			0
$568$	−3404.41			−0.251489
$569$	1170.85	−	6640.20i	0.0862644	−	0.489230i	−0.910812	−	0.412821i	$-0.864543\pi$
$569$	1170.85	−	6640.20i	0.0862644	−	0.489230i	0.997077	−	0.0764088i	$-0.0243454\pi$
$570$		0			0
$571$	−20826.8	−	7580.35i	−1.52640	−	0.555565i	−0.563665	−	0.826003i	$-0.690609\pi$
$571$	−20826.8	−	7580.35i	−1.52640	−	0.555565i	−0.962737	+	0.270438i	$0.912832\pi$
$572$	2230.66	−	1871.75i	0.163057	−	0.136821i
$573$		0			0
$574$	−7689.11	+	2798.61i	−0.559124	+	0.203504i
$575$	−487.408	+	844.216i	−0.0353501	+	0.0612282i
$576$		0			0
$577$	−4751.88	−	8230.49i	−0.342848	−	0.593830i	0.642113	−	0.766610i	$-0.278058\pi$
$577$	−4751.88	−	8230.49i	−0.342848	−	0.593830i	−0.984960	+	0.172781i	$0.944725\pi$
$578$	−9123.54	−	7655.56i	−0.656555	−	0.550915i
$579$		0			0
$580$	−873.159	−	4951.93i	−0.0625103	−	0.354513i
$581$	−662.422	−	3756.78i	−0.0473010	−	0.268257i
$582$		0			0
$583$	34909.0	+	29292.1i	2.47990	+	2.08089i
$584$	−2353.36	−	4076.14i	−0.166751	−	0.288822i
$585$		0			0
$586$	−4689.79	+	8122.95i	−0.330603	+	0.572621i
$587$	7375.59	−	2684.50i	0.518609	−	0.188758i	−0.0694363	−	0.997586i	$-0.522120\pi$
$587$	7375.59	−	2684.50i	0.518609	−	0.188758i	0.588045	+	0.808828i	$0.299898\pi$
$588$		0			0
$589$	727.779	−	610.679i	0.0509127	−	0.0427209i
$590$	−4791.01	−	1743.78i	−0.334309	−	0.121679i
$591$		0			0
$592$	−869.197	+	4929.46i	−0.0603442	+	0.342229i
$593$	11931.9			0.826277			0.413139	−	0.910668i	$-0.364432\pi$
$593$	11931.9			0.826277			0.413139	+	0.910668i	$0.364432\pi$
$594$		0			0
$595$	−9189.22			−0.633145
$596$	837.078	−	4747.30i	0.0575303	−	0.326270i
$597$		0			0
$598$	−313.939	−	114.264i	−0.0214681	−	0.00781375i
$599$	−15419.1	+	12938.1i	−1.05176	+	0.882533i	−0.993278	−	0.115755i	$-0.963071\pi$
$599$	−15419.1	+	12938.1i	−1.05176	+	0.882533i	−0.0584842	+	0.998288i	$0.518627\pi$
$600$		0			0
$601$	1748.24	−	636.306i	0.118656	−	0.0431871i	−0.282010	−	0.959411i	$-0.591001\pi$
$601$	1748.24	−	636.306i	0.118656	−	0.0431871i	0.400666	+	0.916224i	$0.368779\pi$
$602$	−4801.44	+	8316.34i	−0.325070	+	0.563037i
$603$		0			0
$604$	1409.53	+	2441.37i	0.0949550	+	0.164467i
$605$	13190.3	+	11068.0i	0.886382	+	0.743763i
$606$		0			0
$607$	2233.48	+	12666.7i	0.149348	+	0.846993i	0.963773	+	0.266724i	$0.0859413\pi$
$607$	2233.48	+	12666.7i	0.149348	+	0.846993i	−0.814425	+	0.580269i	$0.802948\pi$
$608$	253.775	+	1439.23i	0.0169275	+	0.0960006i
$609$		0			0
$610$	8079.52	+	6779.52i	0.536279	+	0.449992i
$611$	524.019	+	907.628i	0.0346965	+	0.0600961i
$612$		0			0
$613$	−13134.7	+	22749.9i	−0.865422	+	1.49896i	0.00120540	+	0.999999i	$0.499616\pi$
$613$	−13134.7	+	22749.9i	−0.865422	+	1.49896i	−0.866627	+	0.498956i	$0.833717\pi$
$614$	7251.11	−	2639.19i	0.476598	−	0.173467i
$615$		0			0
$616$	−4415.11	+	3704.71i	−0.288782	+	0.242317i
$617$	6412.47	+	2333.95i	0.418406	+	0.152287i	0.542639	−	0.839966i	$-0.317425\pi$
$617$	6412.47	+	2333.95i	0.418406	+	0.152287i	−0.124234	+	0.992253i	$0.539647\pi$
$618$		0			0
$619$	3289.67	−	18656.6i	0.213607	−	1.21143i	−0.669700	−	0.742632i	$-0.733577\pi$
$619$	3289.67	−	18656.6i	0.213607	−	1.21143i	0.883307	−	0.468795i	$-0.155312\pi$
$620$	−615.744			−0.0398853
$621$		0			0
$622$	−9324.54			−0.601093
$623$	−206.199	+	1169.41i	−0.0132604	+	0.0752032i
$624$		0			0
$625$	1795.53	+	653.519i	0.114914	+	0.0418252i
$626$	−2037.23	+	1709.44i	−0.130071	+	0.109142i
$627$		0			0
$628$	−11176.9	+	4068.06i	−0.710202	+	0.258492i
$629$	−16306.9	+	28244.4i	−1.03370	+	1.79043i
$630$		0			0
$631$	−2944.48	−	5099.98i	−0.185765	−	0.321755i	0.758069	−	0.652174i	$-0.226143\pi$
$631$	−2944.48	−	5099.98i	−0.185765	−	0.321755i	−0.943834	+	0.330420i	$0.892810\pi$
$632$	−5924.54	−	4971.28i	−0.372889	−	0.312891i
$633$		0			0
$634$	1216.34	+	6898.19i	0.0761938	+	0.432117i
$635$	3437.66	+	19495.9i	0.214833	+	1.21838i
$636$		0			0
$637$	−1854.32	−	1555.96i	−0.115339	−	0.0967806i
$638$	−10274.4	−	17795.8i	−0.637566	−	1.10430i
$639$		0			0
$640$	473.591	−	820.283i	0.0292505	−	0.0506633i
$641$	6633.97	−	2414.57i	0.408777	−	0.148783i	−0.129443	−	0.991587i	$-0.541319\pi$
$641$	6633.97	−	2414.57i	0.408777	−	0.148783i	0.538220	+	0.842804i	$0.319097\pi$
$642$		0			0
$643$	−9885.05	+	8294.54i	−0.606265	+	0.508717i	−0.893452	−	0.449158i	$-0.851724\pi$
$643$	−9885.05	+	8294.54i	−0.606265	+	0.508717i	0.287188	+	0.957874i	$0.407280\pi$
$644$	621.373	+	226.161i	0.0380210	+	0.0138385i
$645$		0			0
$646$	−1653.49	+	9377.42i	−0.100706	+	0.571130i
$647$	23050.1			1.40061			0.700305	−	0.713844i	$-0.253047\pi$
$647$	23050.1			1.40061			0.700305	+	0.713844i	$0.253047\pi$
$648$		0			0
$649$	−20835.5			−1.26019
$650$	293.632	−	1665.27i	0.0177187	−	0.100488i
$651$		0			0
$652$	12060.1	+	4389.52i	0.724402	+	0.263661i
$653$	4397.76	−	3690.16i	0.263549	−	0.221144i	−0.501431	−	0.865197i	$-0.667193\pi$
$653$	4397.76	−	3690.16i	0.263549	−	0.221144i	0.764981	+	0.644053i	$0.222749\pi$
$654$		0			0
$655$	−6591.59	+	2399.14i	−0.393213	+	0.143118i
$656$	2747.69	−	4759.15i	0.163536	−	0.283252i
$657$		0			0
$658$	−1037.18	−	1796.45i	−0.0614491	−	0.106433i
$659$	−20829.1	−	17477.7i	−1.23124	−	1.03313i	−0.998157	−	0.0606773i	$-0.980674\pi$
$659$	−20829.1	−	17477.7i	−1.23124	−	1.03313i	−0.233084	−	0.972457i	$-0.574882\pi$
$660$		0			0
$661$	−4738.68	−	26874.4i	−0.278840	−	1.58138i	−0.726493	−	0.687174i	$-0.758851\pi$
$661$	−4738.68	−	26874.4i	−0.278840	−	1.58138i	0.447653	−	0.894207i	$-0.352260\pi$
$662$	−311.220	−	1765.01i	−0.0182717	−	0.103624i
$663$		0			0
$664$	1962.58	+	1646.80i	0.114703	+	0.0962472i
$665$	2012.81	+	3486.29i	0.117374	+	0.203297i
$666$		0			0
$667$	−1178.79	+	2041.72i	−0.0684300	+	0.118524i
$668$	3838.64	−	1397.15i	0.222338	−	0.0809243i
$669$		0			0
$670$	137.461	−	115.344i	0.00792626	−	0.00665092i
$671$	40502.3	+	14741.6i	2.33022	+	0.848130i
$672$		0			0
$673$	888.691	−	5040.02i	0.0509012	−	0.288675i	−0.948722	−	0.316111i	$-0.897623\pi$
$673$	888.691	−	5040.02i	0.0509012	−	0.288675i	0.999624	+	0.0274354i	$0.00873406\pi$
$674$	−11923.8			−0.681433
$675$		0			0
$676$	−8208.48			−0.467028
$677$	433.103	−	2456.25i	0.0245871	−	0.139441i	−0.970043	−	0.242933i	$-0.921891\pi$
$677$	433.103	−	2456.25i	0.0245871	−	0.139441i	0.994630	+	0.103492i	$0.0330017\pi$
$678$		0			0
$679$	18602.5	+	6770.75i	1.05140	+	0.382677i
$680$	4727.60	−	3966.93i	0.266611	−	0.223713i
$681$		0			0
$682$	−2364.55	+	860.627i	−0.132762	+	0.0483213i
$683$	−1280.87	+	2218.53i	−0.0717586	+	0.124289i	−0.899672	−	0.436566i	$-0.856194\pi$
$683$	−1280.87	+	2218.53i	−0.0717586	+	0.124289i	0.827914	+	0.560856i	$0.189528\pi$
$684$		0			0
$685$	−4304.37	−	7455.39i	−0.240090	−	0.415848i
$686$	9930.00	+	8332.26i	0.552666	+	0.463742i
$687$		0			0
$688$	−1119.90	−	6351.28i	−0.0620579	−	0.351948i
$689$	1574.86	+	8931.49i	0.0870791	+	0.493850i
$690$		0			0
$691$	16748.0	+	14053.2i	0.922032	+	0.773677i	0.974370	−	0.224952i	$-0.0722227\pi$
$691$	16748.0	+	14053.2i	0.922032	+	0.773677i	−0.0523374	+	0.998629i	$0.516667\pi$
$692$	−3301.23	−	5717.90i	−0.181350	−	0.314107i
$693$		0			0
$694$	−8249.43	+	14288.4i	−0.451216	+	0.781529i
$695$	−5024.70	+	1828.84i	−0.274241	+	0.0998157i
$696$		0			0
$697$	27428.8	−	23015.5i	1.49059	−	1.25075i
$698$	3606.72	+	1312.74i	0.195582	+	0.0711861i
$699$		0			0
$700$	−581.179	+	3296.03i	−0.0313807	+	0.177969i
$701$	6799.85			0.366372			0.183186	−	0.983078i	$-0.441359\pi$
$701$	6799.85			0.366372			0.183186	+	0.983078i	$0.441359\pi$
$702$		0			0
$703$	14287.5			0.766519
$704$	672.149	−	3811.95i	0.0359838	−	0.204074i
$705$		0			0
$706$	−5949.81	−	2165.55i	−0.317173	−	0.115441i
$707$	2249.81	−	1887.81i	0.119678	−	0.100422i
$708$		0			0
$709$	−11713.5	+	4263.38i	−0.620468	+	0.225832i	−0.633077	−	0.774089i	$-0.718208\pi$
$709$	−11713.5	+	4263.38i	−0.620468	+	0.225832i	0.0126095	+	0.999920i	$0.495986\pi$
$710$	3149.02	−	5454.26i	0.166451	−	0.288302i
$711$		0			0
$712$	−398.745	−	690.647i	−0.0209882	−	0.0363527i
$713$	221.155	+	185.571i	0.0116161	+	0.00974710i
$714$		0			0
$715$	935.435	+	5305.11i	0.0489277	+	0.277483i
$716$	2170.93	+	12311.9i	0.113312	+	0.642624i
$717$		0			0
$718$	−747.863	−	627.532i	−0.0388719	−	0.0326174i
$719$	−784.462	−	1358.73i	−0.0406892	−	0.0704757i	0.844964	−	0.534824i	$-0.179622\pi$
$719$	−784.462	−	1358.73i	−0.0406892	−	0.0704757i	−0.885653	+	0.464348i	$0.846289\pi$
$720$		0			0
$721$	6332.26	−	10967.8i	0.327081	−	0.566522i
$722$	−8970.83	+	3265.12i	−0.462410	+	0.168303i
$723$		0			0
$724$	−2351.38	+	1973.04i	−0.120702	+	0.101281i
$725$	−11213.1	−	4081.22i	−0.574403	−	0.209066i
$726$		0			0
$727$	2390.05	−	13554.7i	0.121929	−	0.691492i	−0.861156	−	0.508341i	$-0.830259\pi$
$727$	2390.05	−	13554.7i	0.121929	−	0.691492i	0.983085	−	0.183151i	$-0.0586298\pi$
$728$	−1147.03			−0.0583955
$729$		0			0
$730$	8707.27			0.441466
$731$	7296.83	−	41382.4i	0.369197	−	2.09382i
$732$		0			0
$733$	34358.7	+	12505.6i	1.73133	+	0.630154i	0.998724	−	0.0504942i	$-0.0160797\pi$
$733$	34358.7	+	12505.6i	1.73133	+	0.630154i	0.732610	+	0.680648i	$0.238302\pi$
$734$	−4192.60	+	3518.01i	−0.210834	+	0.176910i
$735$		0			0
$736$	−417.312	+	151.889i	−0.0208999	+	0.00760694i
$737$	366.656	−	635.068i	0.0183256	−	0.0317409i
$738$		0			0
$739$	−8065.87	−	13970.5i	−0.401499	−	0.695417i	0.592408	−	0.805638i	$-0.298177\pi$
$739$	−8065.87	−	13970.5i	−0.401499	−	0.695417i	−0.993907	+	0.110221i	$0.964844\pi$
$740$	−7093.58	−	5952.22i	−0.352385	−	0.295686i
$741$		0			0
$742$	−3117.09	−	17677.9i	−0.154221	−	0.874632i
$743$	3481.71	+	19745.7i	0.171913	+	0.974967i	0.941647	+	0.336602i	$0.109278\pi$
$743$	3481.71	+	19745.7i	0.171913	+	0.974967i	−0.769734	+	0.638365i	$0.779611\pi$
$744$		0			0
$745$	6831.45	+	5732.26i	0.335953	+	0.281898i
$746$	−136.149	−	235.818i	−0.00668201	−	0.0115736i
$747$		0			0
$748$	12610.1	−	21841.4i	0.616407	−	1.06765i
$749$	−17152.1	+	6242.84i	−0.836746	+	0.304551i
$750$		0			0
$751$	13793.4	−	11574.0i	0.670210	−	0.562373i	−0.242918	−	0.970047i	$-0.578105\pi$
$751$	13793.4	−	11574.0i	0.670210	−	0.562373i	0.913127	+	0.407674i	$0.133660\pi$
$752$	1309.12	+	476.480i	0.0634822	+	0.0231056i
$753$		0			0
$754$	710.142	−	4027.41i	0.0342995	−	0.194522i
$755$	−5215.14			−0.251389
$756$		0			0
$757$	−33197.8			−1.59392			−0.796959	−	0.604034i	$-0.793559\pi$
$757$	−33197.8			−1.59392			−0.796959	+	0.604034i	$0.793559\pi$
$758$	−291.518	+	1653.28i	−0.0139689	+	0.0792215i
$759$		0			0
$760$	−2540.54	−	924.683i	−0.121257	−	0.0441339i
$761$	−12058.7	+	10118.4i	−0.574412	+	0.481989i	−0.883107	−	0.469172i	$-0.844552\pi$
$761$	−12058.7	+	10118.4i	−0.574412	+	0.481989i	0.308695	+	0.951161i	$0.400108\pi$
$762$		0			0
$763$	8592.79	−	3127.52i	0.407706	−	0.148393i
$764$	−9504.28	+	16461.9i	−0.450069	+	0.779542i
$765$		0			0
$766$	501.636	+	868.860i	0.0236617	+	0.0409833i
$767$	−3176.48	−	2665.38i	−0.149539	−	0.125478i
$768$		0			0
$769$	1156.79	+	6560.48i	0.0542456	+	0.307642i	0.999843	−	0.0176957i	$-0.00563302\pi$
$769$	1156.79	+	6560.48i	0.0542456	+	0.307642i	−0.945598	+	0.325338i	$0.894522\pi$
$770$	−1851.49	−	10500.3i	−0.0866532	−	0.491435i
$771$		0			0
$772$	−3686.31	−	3093.18i	−0.171857	−	0.144205i
$773$	5109.26	+	8849.49i	0.237732	+	0.411765i	0.960063	−	0.279783i	$-0.0902625\pi$
$773$	5109.26	+	8849.49i	0.237732	+	0.411765i	−0.722331	+	0.691548i	$0.756929\pi$
$774$		0			0
$775$	−730.610	+	1265.45i	−0.0338636	+	0.0586534i
$776$	−12493.4	+	4547.21i	−0.577945	+	0.210355i
$777$		0			0
$778$	−4378.94	+	3674.37i	−0.201790	+	0.169322i
$779$	−14739.8	−	5364.86i	−0.677932	−	0.246747i
$780$		0			0
$781$	4469.28	−	25346.6i	0.204768	−	1.16130i
$782$	−2893.54			−0.132318
$783$		0			0
$784$	−3217.70			−0.146579
$785$	3820.93	−	21669.5i	0.173726	−	0.985247i
$786$		0			0
$787$	8402.50	+	3058.26i	0.380580	+	0.138520i	0.525224	−	0.850964i	$-0.323981\pi$
$787$	8402.50	+	3058.26i	0.380580	+	0.138520i	−0.144644	+	0.989484i	$0.546204\pi$
$788$	14692.8	−	12328.7i	0.664226	−	0.557352i
$789$		0			0
$790$	13444.7	−	4893.46i	0.605493	−	0.220381i
$791$	4081.12	−	7068.70i	0.183449	−	0.317742i
$792$		0			0
$793$	4288.97	+	7428.72i	0.192063	+	0.332663i
$794$	−4442.89	−	3728.03i	−0.198580	−	0.166628i
$795$		0			0
$796$	2404.86	+	13638.6i	0.107083	+	0.607298i
$797$	−5814.54	−	32975.9i	−0.258421	−	1.46558i	−0.787137	−	0.616779i	$-0.788437\pi$
$797$	−5814.54	−	32975.9i	−0.258421	−	1.46558i	0.528716	−	0.848799i	$-0.322674\pi$
$798$		0			0
$799$	6953.46	+	5834.64i	0.307879	+	0.258341i
$800$	−1123.87	−	1946.61i	−0.0496687	−	0.0860288i
$801$		0			0
$802$	9152.36	−	15852.4i	0.402969	−	0.697963i
$803$	33437.2	−	12170.2i	1.46946	−	0.534839i
$804$		0			0
$805$	−937.095	+	786.316i	−0.0410289	+	0.0344273i
$806$	−470.585	−	171.279i	−0.0205653	−	0.00748516i
$807$		0			0
$808$	−342.507	+	1942.46i	−0.0149126	+	0.0845734i
$809$	−18877.7			−0.820399			−0.410200	−	0.911996i	$-0.634541\pi$
$809$	−18877.7			−0.820399			−0.410200	+	0.911996i	$0.634541\pi$
$810$		0			0
$811$	−11057.8			−0.478784			−0.239392	−	0.970923i	$-0.576948\pi$
$811$	−11057.8			−0.478784			−0.239392	+	0.970923i	$0.576948\pi$
$812$	−1405.57	+	7971.38i	−0.0607460	+	0.344508i
$813$		0			0
$814$	−35559.8	−	12942.7i	−1.53117	−	0.557300i
$815$	−18187.9	+	15261.5i	−0.781710	+	0.655933i
$816$		0			0
$817$	−17298.3	+	6296.07i	−0.740748	+	0.269610i
$818$	15012.5	−	26002.4i	0.641686	−	1.11143i
$819$		0			0
$820$	5083.13	+	8804.25i	0.216477	+	0.374948i
$821$	−11528.4	−	9673.49i	−0.490067	−	0.411215i	0.363984	−	0.931405i	$-0.381416\pi$
$821$	−11528.4	−	9673.49i	−0.490067	−	0.411215i	−0.854050	+	0.520191i	$0.825861\pi$
$822$		0			0
$823$	−2003.08	−	11360.0i	−0.0848395	−	0.481148i	−0.997391	−	0.0721870i	$-0.977002\pi$
$823$	−2003.08	−	11360.0i	−0.0848395	−	0.481148i	0.912552	−	0.408961i	$-0.134109\pi$
$824$	1476.96	+	8376.23i	0.0624420	+	0.354126i
$825$		0			0
$826$	6287.14	+	5275.54i	0.264840	+	0.222227i
$827$	−3374.22	−	5844.32i	−0.141878	−	0.245740i	0.786326	−	0.617812i	$-0.211981\pi$
$827$	−3374.22	−	5844.32i	−0.141878	−	0.245740i	−0.928204	+	0.372072i	$0.878647\pi$
$828$		0			0
$829$	−7810.47	+	13528.1i	−0.327224	+	0.566769i	−0.981960	−	0.189089i	$-0.939447\pi$
$829$	−7810.47	+	13528.1i	−0.327224	+	0.566769i	0.654736	+	0.755858i	$0.272780\pi$
$830$	−4453.71	+	1621.02i	−0.186253	+	0.0677907i
$831$		0			0
$832$	590.117	−	495.167i	0.0245897	−	0.0206332i
$833$	−19700.9	−	7170.53i	−0.819442	−	0.298252i
$834$		0			0
$835$	−1312.28	+	7442.29i	−0.0543870	+	0.308444i
$836$	−11048.5			−0.457082
$837$		0			0
$838$	13553.2			0.558696
$839$	−6175.43	+	35022.6i	−0.254111	+	1.44114i	0.544232	+	0.838935i	$0.316821\pi$
$839$	−6175.43	+	35022.6i	−0.254111	+	1.44114i	−0.798344	+	0.602202i	$0.794290\pi$
$840$		0			0
$841$	−4200.37	−	1528.81i	−0.172224	−	0.0626844i
$842$	6162.57	−	5171.01i	0.252228	−	0.211645i
$843$		0			0
$844$	−2623.29	+	954.800i	−0.106988	+	0.0389403i
$845$	7592.69	−	13150.9i	0.309108	−	0.535391i
$846$		0			0
$847$	−13858.9	−	24004.3i	−0.562216	−	0.973787i
$848$	9235.11	+	7749.18i	0.373980	+	0.313806i
$849$		0			0
$850$	−2543.15	−	14422.9i	−0.102623	−	0.582003i
$851$	753.917	+	4275.67i	0.0303689	+	0.172231i
$852$		0			0
$853$	13397.6	+	11241.9i	0.537779	+	0.451250i	0.870778	−	0.491677i	$-0.163616\pi$
$853$	13397.6	+	11241.9i	0.537779	+	0.451250i	−0.332998	+	0.942927i	$0.608060\pi$
$854$	−8489.07	−	14703.5i	−0.340152	−	0.589161i
$855$		0			0
$856$	6129.27	−	10616.2i	0.244736	−	0.423896i
$857$	12430.2	−	4524.21i	0.495456	−	0.180331i	−0.0821930	−	0.996616i	$-0.526192\pi$
$857$	12430.2	−	4524.21i	0.495456	−	0.180331i	0.577649	+	0.816285i	$0.303970\pi$
$858$		0			0
$859$	−26244.1	+	22021.4i	−1.04242	+	0.874693i	−0.992276	−	0.124050i	$-0.960412\pi$
$859$	−26244.1	+	22021.4i	−1.04242	+	0.874693i	−0.0501419	+	0.998742i	$0.515967\pi$
$860$	11211.4	+	4080.60i	0.444540	+	0.161799i
$861$		0			0
$862$	−3142.42	+	17821.5i	−0.124166	+	0.704181i
$863$	−26527.5			−1.04636			−0.523179	−	0.852223i	$-0.675254\pi$
$863$	−26527.5			−1.04636			−0.523179	+	0.852223i	$0.675254\pi$
$864$		0			0
$865$	12214.3			0.480115
$866$	−2502.11	+	14190.2i	−0.0981814	+	0.556814i
$867$		0			0
$868$	931.419	+	339.009i	0.0364221	+	0.0132566i
$869$	44790.0	−	37583.2i	1.74844	−	1.46712i
$870$		0			0
$871$	137.140	−	49.9149i	0.00533503	−	0.00194179i
$872$	−3070.63	+	5318.48i	−0.119248	+	0.206544i
$873$		0			0
$874$	633.801	+	1097.78i	0.0245293	+	0.0424860i
$875$	−13183.5	−	11062.3i	−0.509355	−	0.427399i
$876$		0			0
$877$	−1772.16	−	10050.4i	−0.0682345	−	0.386977i	−0.999730	−	0.0232250i	$-0.992607\pi$
$877$	−1772.16	−	10050.4i	−0.0682345	−	0.386977i	0.931496	−	0.363752i	$-0.118505\pi$
$878$	806.750	+	4575.31i	0.0310097	+	0.175865i
$879$		0			0
$880$	5485.46	+	4602.84i	0.210130	+	0.176320i
$881$	3285.54	+	5690.72i	0.125644	+	0.217622i	0.921985	−	0.387227i	$-0.126567\pi$
$881$	3285.54	+	5690.72i	0.125644	+	0.217622i	−0.796340	+	0.604849i	$0.793234\pi$
$882$		0			0
$883$	−8202.95	+	14207.9i	−0.312629	+	0.541489i	−0.978931	−	0.204193i	$-0.934543\pi$
$883$	−8202.95	+	14207.9i	−0.312629	+	0.541489i	0.666302	+	0.745682i	$0.267876\pi$
$884$	4716.55	−	1716.68i	0.179451	−	0.0653149i
$885$		0			0
$886$	12224.5	−	10257.6i	0.463534	−	0.388951i
$887$	−27634.7	−	10058.2i	−1.04609	−	0.380747i	−0.238906	−	0.971043i	$-0.576789\pi$
$887$	−27634.7	−	10058.2i	−1.04609	−	0.380747i	−0.807187	+	0.590296i	$0.799011\pi$
$888$		0			0
$889$	5533.77	−	31383.6i	0.208770	−	1.18399i
$890$	1475.33			0.0555653
$891$		0			0
$892$	−20141.2			−0.756030
$893$	690.511	−	3916.08i	0.0258758	−	0.146749i
$894$		0			0
$895$	−21733.2	−	7910.24i	−0.811689	−	0.295431i
$896$	−1168.01	+	980.074i	−0.0435495	+	0.0365424i
$897$		0			0
$898$	−4710.70	+	1714.55i	−0.175054	+	0.0637143i
$899$	−1766.96	+	3060.47i	−0.0655523	+	0.113540i
$900$		0			0
$901$	39274.6	+	68025.7i	1.45220	+	2.51528i
$902$	31825.7	+	26704.9i	1.17481	+	0.985784i
$903$		0			0
$904$	951.892	+	5398.45i	0.0350215	+	0.198617i
$905$	−986.055	−	5592.20i	−0.0362183	−	0.205404i
$906$		0			0
$907$	−37157.2	−	31178.6i	−1.36029	−	1.14142i	−0.975892	−	0.218256i	$-0.929963\pi$
$907$	−37157.2	−	31178.6i	−1.36029	−	1.14142i	−0.384402	−	0.923166i	$-0.625592\pi$
$908$	7059.60	+	12227.6i	0.258019	+	0.446902i
$909$		0			0
$910$	1060.98	−	1837.68i	0.0386498	−	0.0669434i
$911$	76.7148	−	27.9219i	0.00278998	−	0.00101547i	−0.340625	−	0.940199i	$-0.610639\pi$
$911$	76.7148	−	27.9219i	0.00278998	−	0.00101547i	0.343415	+	0.939184i	$0.388416\pi$
$912$		0			0
$913$	−14837.2	+	12449.9i	−0.537831	+	0.451294i
$914$	21119.6	+	7686.90i	0.764304	+	0.278184i
$915$		0			0
$916$	−3243.60	+	18395.4i	−0.117000	+	0.663538i
$917$	11291.8			0.406639
$918$		0			0
$919$	28051.4			1.00689			0.503444	−	0.864028i	$-0.332066\pi$
$919$	28051.4			1.00689			0.503444	+	0.864028i	$0.332066\pi$
$920$	142.662	−	809.076i	0.00511242	−	0.0289940i
$921$		0			0
$922$	17667.6	+	6430.47i	0.631075	+	0.229692i
$923$	3923.83	−	3292.49i	0.139929	−	0.117414i
$924$		0			0
$925$	−20649.6	+	7515.85i	−0.734006	+	0.267156i
$926$	−1966.11	+	3405.40i	−0.0697735	+	0.120851i
$927$		0			0
$928$	−2718.07	−	4707.83i	−0.0961475	−	0.166532i
$929$	24607.0	+	20647.7i	0.869030	+	0.729203i	0.963894	−	0.266287i	$-0.0857970\pi$
$929$	24607.0	+	20647.7i	0.869030	+	0.729203i	−0.0948634	+	0.995490i	$0.530241\pi$
$930$		0			0
$931$	1594.86	+	9044.93i	0.0561435	+	0.318405i
$932$	−2038.24	−	11559.4i	−0.0716360	−	0.406268i
$933$		0			0
$934$	21833.4	+	18320.4i	0.764895	+	0.641823i
$935$	23328.3	+	40405.8i	0.815954	+	1.41327i
$936$		0			0
$937$	−4147.52	+	7183.72i	−0.144604	+	0.250461i	−0.929225	−	0.369514i	$-0.879524\pi$
$937$	−4147.52	+	7183.72i	−0.144604	+	0.250461i	0.784621	+	0.619975i	$0.212857\pi$
$938$	−271.438	+	98.7955i	−0.00944859	+	0.00343900i
$939$		0			0
$940$	−1974.28	+	1656.62i	−0.0685043	+	0.0574819i
$941$	−26036.6	−	9476.55i	−0.901986	−	0.328296i	−0.150938	−	0.988543i	$-0.548229\pi$
$941$	−26036.6	−	9476.55i	−0.901986	−	0.328296i	−0.751048	+	0.660247i	$0.770452\pi$
$942$		0			0
$943$	827.701	−	4694.13i	0.0285829	−	0.162102i
$944$	−5511.98			−0.190042
$945$		0			0
$946$	48756.8			1.67571
$947$	−6408.08	+	36342.0i	−0.219889	+	1.24705i	0.652330	+	0.757935i	$0.273792\pi$
$947$	−6408.08	+	36342.0i	−0.219889	+	1.24705i	−0.872219	+	0.489116i	$0.837319\pi$
$948$		0			0
$949$	6654.56	+	2422.06i	0.227625	+	0.0828487i
$950$	−4914.85	+	4124.05i	−0.167851	+	0.140844i
$951$		0			0
$952$	−9335.37	+	3397.80i	−0.317816	+	0.115676i
$953$	−18315.5	+	31723.4i	−0.622559	+	1.07830i	0.366449	+	0.930438i	$0.380574\pi$
$953$	−18315.5	+	31723.4i	−0.622559	+	1.07830i	−0.989008	+	0.147865i	$0.952760\pi$
$954$		0			0
$955$	−17582.6	−	30453.9i	−0.595768	−	1.03190i
$956$	−9272.12	−	7780.23i	−0.313684	−	0.263212i
$957$		0			0
$958$	−1026.63	−	5822.31i	−0.0346231	−	0.196357i
$959$	2406.41	+	13647.4i	0.0810291	+	0.459539i
$960$		0			0
$961$	−22489.7	−	18871.1i	−0.754917	−	0.633450i
$962$	−3765.59	−	6522.19i	−0.126203	−	0.218590i
$963$		0			0
$964$	4392.78	−	7608.52i	0.146766	−	0.254205i
$965$	8365.40	−	3044.76i	0.279059	−	0.101569i
$966$		0			0
$967$	7350.22	−	6167.57i	0.244434	−	0.205104i	−0.512337	−	0.858784i	$-0.671220\pi$
$967$	7350.22	−	6167.57i	0.244434	−	0.205104i	0.756771	+	0.653680i	$0.226776\pi$
$968$	17492.5	+	6366.76i	0.580818	+	0.211400i
$969$		0			0
$970$	4270.97	−	24221.9i	0.141374	−	0.801771i
$971$	43330.1			1.43206			0.716030	−	0.698070i	$-0.245958\pi$
$971$	43330.1			1.43206			0.716030	+	0.698070i	$0.245958\pi$
$972$		0			0
$973$	8607.62			0.283605
$974$	−1494.82	+	8477.56i	−0.0491758	+	0.278890i
$975$		0			0
$976$	10714.8	+	3899.87i	0.351406	+	0.127901i
$977$	−40390.4	+	33891.6i	−1.32262	+	1.10981i	−0.336884	+	0.941546i	$0.609373\pi$
$977$	−40390.4	+	33891.6i	−1.32262	+	1.10981i	−0.985741	+	0.168268i	$0.946183\pi$
$978$		0			0
$979$	5665.48	−	2062.07i	0.184954	−	0.0673176i
$980$	2976.31	−	5155.13i	0.0970151	−	0.168035i
$981$		0			0
$982$	3425.76	+	5933.60i	0.111324	+	0.192819i
$983$	−15775.7	−	13237.4i	−0.511868	−	0.429509i	0.349918	−	0.936780i	$-0.386210\pi$
$983$	−15775.7	−	13237.4i	−0.511868	−	0.429509i	−0.861786	+	0.507272i	$0.830654\pi$
$984$		0			0
$985$	6161.47	+	34943.4i	0.199310	+	1.13035i
$986$	−6150.56	−	34881.5i	−0.198655	−	1.12663i
$987$		0			0
$988$	−1684.40	−	1413.38i	−0.0542389	−	0.0455119i
$989$	−2796.95	−	4844.46i	−0.0899270	−	0.155758i
$990$		0			0
$991$	−1290.22	+	2234.73i	−0.0413574	+	0.0716332i	−0.885963	−	0.463756i	$-0.846502\pi$
$991$	−1290.22	+	2234.73i	−0.0413574	+	0.0716332i	0.844606	+	0.535389i	$0.179835\pi$
$992$	−625.537	+	227.677i	−0.0200210	+	0.00728705i
$993$		0			0
$994$	−7766.36	+	6516.75i	−0.247821	+	0.207946i
$995$	−24075.1	−	8762.63i	−0.767068	−	0.279190i
$996$		0			0
$997$	−4604.11	+	26111.2i	−0.146252	+	0.829438i	0.820101	+	0.572219i	$0.193917\pi$
$997$	−4604.11	+	26111.2i	−0.146252	+	0.829438i	−0.966353	+	0.257219i	$0.917194\pi$
$998$	27962.8			0.886922
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.a.73.3		24
3.2	odd	2		54.4.e.a.25.1	yes	24
27.11	odd	18		1458.4.a.h.1.4		12
27.13	even	9	inner	162.4.e.a.91.3		24
27.14	odd	18		54.4.e.a.13.1	✓	24
27.16	even	9		1458.4.a.e.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.a.13.1	✓	24	27.14	odd	18
54.4.e.a.25.1	yes	24	3.2	odd	2
162.4.e.a.73.3		24	1.1	even	1	trivial
162.4.e.a.91.3		24	27.13	even	9	inner
1458.4.a.e.1.9		12	27.16	even	9
1458.4.a.h.1.4		12	27.11	odd	18

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.347296 + 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(5.66862 - 4.75653i) q^{5} +(-11.1935 + 4.07412i) q^{7} +(4.00000 - 6.92820i) q^{8} +O(q^{10})\)	\(q+(-0.347296 + 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(5.66862 - 4.75653i) q^{5} +(-11.1935 + 4.07412i) q^{7} +(4.00000 - 6.92820i) q^{8} +(7.39985 + 12.8169i) q^{10} +(46.3308 + 38.8761i) q^{11} +(2.09014 + 11.8538i) q^{13} +(-4.13696 - 23.4619i) q^{14} +(12.2567 + 10.2846i) q^{16} +(52.1248 + 90.2827i) q^{17} +(22.8348 - 39.5511i) q^{19} +(-27.8143 + 10.1236i) q^{20} +(-92.6616 + 77.7523i) q^{22} +(13.0410 + 4.74653i) q^{23} +(-12.1974 + 69.1750i) q^{25} -24.0732 q^{26} +47.6477 q^{28} +(-29.4992 + 167.298i) q^{29} +(19.5480 + 7.11491i) q^{31} +(-24.5134 + 20.5692i) q^{32} +(-195.925 + 71.3109i) q^{34} +(-44.0732 + 76.3370i) q^{35} +(156.422 + 270.931i) q^{37} +(69.9700 + 58.7118i) q^{38} +(-10.2798 - 58.2995i) q^{40} +(-59.6415 - 338.244i) q^{41} +(-308.776 - 259.094i) q^{43} +(-120.961 - 209.511i) q^{44} +(-13.8779 + 24.0373i) q^{46} +(81.8198 - 29.7800i) q^{47} +(-154.056 + 129.269i) q^{49} +(-132.012 - 48.0485i) q^{50} +(8.36055 - 47.4150i) q^{52} +753.474 q^{53} +447.547 q^{55} +(-16.5479 + 93.8476i) q^{56} +(-319.268 - 116.204i) q^{58} +(-263.901 + 221.440i) q^{59} +(669.676 - 243.742i) q^{61} +(-20.8026 + 36.0311i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(68.2310 + 57.2526i) q^{65} +(-2.10545 - 11.9406i) q^{67} +(-72.4110 - 410.663i) q^{68} +(-135.048 - 113.319i) q^{70} +(-212.776 - 368.538i) q^{71} +(294.170 - 509.518i) q^{73} +(-587.955 + 213.998i) q^{74} +(-139.940 + 117.424i) q^{76} +(-676.991 - 246.405i) q^{77} +(167.873 - 952.056i) q^{79} +118.398 q^{80} +686.924 q^{82} +(-55.6100 + 315.380i) q^{83} +(724.908 + 263.845i) q^{85} +(617.552 - 518.188i) q^{86} +(454.665 - 165.485i) q^{88} +(49.8431 - 86.3309i) q^{89} +(-71.6896 - 124.170i) q^{91} +(-42.5245 - 35.6823i) q^{92} +(30.2394 + 171.496i) q^{94} +(-58.6842 - 332.815i) q^{95} +(-1273.09 - 1068.25i) q^{97} +(-201.106 - 348.326i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) \) 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8} + 30 q^{10} + 12 q^{11} + 60 q^{13} + 66 q^{14} - 102 q^{17} + 171 q^{19} - 96 q^{20} - 24 q^{22} + 708 q^{23} + 864 q^{25} + 468 q^{26} - 336 q^{28} + 381 q^{29} + 909 q^{31} - 48 q^{34} - 624 q^{35} + 555 q^{37} - 66 q^{38} - 96 q^{40} - 618 q^{41} - 1161 q^{43} - 132 q^{44} + 348 q^{46} + 378 q^{47} + 579 q^{49} - 36 q^{50} + 240 q^{52} + 1794 q^{53} - 3906 q^{55} + 264 q^{56} + 444 q^{58} - 1038 q^{59} + 324 q^{61} - 744 q^{62} - 768 q^{64} - 5718 q^{65} - 576 q^{67} - 1056 q^{68} - 1038 q^{70} - 120 q^{71} + 3036 q^{73} + 1110 q^{74} + 132 q^{76} + 3804 q^{77} - 2991 q^{79} + 480 q^{80} - 3408 q^{82} - 513 q^{83} - 2925 q^{85} + 2322 q^{86} + 480 q^{88} - 1065 q^{89} + 2859 q^{91} - 1884 q^{92} - 828 q^{94} - 6357 q^{95} - 2055 q^{97} - 1356 q^{98}+O(q^{100}) \) 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8 + 30 * q^10 + 12 * q^11 + 60 * q^13 + 66 * q^14 - 102 * q^17 + 171 * q^19 - 96 * q^20 - 24 * q^22 + 708 * q^23 + 864 * q^25 + 468 * q^26 - 336 * q^28 + 381 * q^29 + 909 * q^31 - 48 * q^34 - 624 * q^35 + 555 * q^37 - 66 * q^38 - 96 * q^40 - 618 * q^41 - 1161 * q^43 - 132 * q^44 + 348 * q^46 + 378 * q^47 + 579 * q^49 - 36 * q^50 + 240 * q^52 + 1794 * q^53 - 3906 * q^55 + 264 * q^56 + 444 * q^58 - 1038 * q^59 + 324 * q^61 - 744 * q^62 - 768 * q^64 - 5718 * q^65 - 576 * q^67 - 1056 * q^68 - 1038 * q^70 - 120 * q^71 + 3036 * q^73 + 1110 * q^74 + 132 * q^76 + 3804 * q^77 - 2991 * q^79 + 480 * q^80 - 3408 * q^82 - 513 * q^83 - 2925 * q^85 + 2322 * q^86 + 480 * q^88 - 1065 * q^89 + 2859 * q^91 - 1884 * q^92 - 828 * q^94 - 6357 * q^95 - 2055 * q^97 - 1356 * q^98

Introduction

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