LMFDB - Embedded newform 108.3.f.c.91.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(19,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("108.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.f (of order $6$, degree $2$, 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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 $ x^16 - 3x^15 + 7x^14 - 30x^13 + 76x^12 - 144x^11 + 424x^10 - 912x^9 + 1552x^8 - 3648x^7 + 6784x^6 - 9216x^5 + 19456x^4 - 30720x^3 + 28672x^2 - 49152*x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			91.5
Root			$0.186266 + 1.99131i$ of defining polynomial
Character	$\chi$	$=$	108.91
Dual form			108.3.f.c.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.186266 + 1.99131i) q^{2} +(-3.93061 + 0.741826i) q^{4} +(-3.07403 + 5.32438i) q^{5} +(0.511543 - 0.295340i) q^{7} +(-2.20934 - 7.68888i) q^{8} +O(q^{10})$	\(q+(0.186266 + 1.99131i) q^{2} +(-3.93061 + 0.741826i) q^{4} +(-3.07403 + 5.32438i) q^{5} +(0.511543 - 0.295340i) q^{7} +(-2.20934 - 7.68888i) q^{8} +(-11.1751 - 5.12959i) q^{10} +(-15.1205 + 8.72982i) q^{11} +(-0.892255 + 1.54543i) q^{13} +(0.683395 + 0.963628i) q^{14} +(14.8994 - 5.83166i) q^{16} +16.9171 q^{17} +19.5058i q^{19} +(8.13306 - 23.2084i) q^{20} +(-20.2002 - 28.4835i) q^{22} +(6.86778 + 3.96511i) q^{23} +(-6.39933 - 11.0840i) q^{25} +(-3.24362 - 1.48889i) q^{26} +(-1.79159 + 1.54034i) q^{28} +(-3.17517 - 5.49956i) q^{29} +(27.6558 + 15.9671i) q^{31} +(14.3879 + 28.5830i) q^{32} +(3.15108 + 33.6871i) q^{34} +3.63153i q^{35} +58.2834 q^{37} +(-38.8420 + 3.63326i) q^{38} +(47.7301 + 11.8725i) q^{40} +(2.66948 - 4.62368i) q^{41} +(-33.9324 + 19.5909i) q^{43} +(52.9567 - 45.5303i) q^{44} +(-6.61653 + 14.4144i) q^{46} +(9.64117 - 5.56633i) q^{47} +(-24.3255 + 42.1331i) q^{49} +(20.8796 - 14.8076i) q^{50} +(2.36067 - 6.73638i) q^{52} -35.8770 q^{53} -107.343i q^{55} +(-3.40100 - 3.28069i) q^{56} +(10.3599 - 7.34713i) q^{58} +(20.8974 + 12.0651i) q^{59} +(-37.9460 - 65.7244i) q^{61} +(-26.6441 + 58.0454i) q^{62} +(-54.2376 + 33.9747i) q^{64} +(-5.48564 - 9.50141i) q^{65} +(-31.8200 - 18.3713i) q^{67} +(-66.4945 + 12.5495i) q^{68} +(-7.23150 + 0.676431i) q^{70} -87.8370i q^{71} -60.0423 q^{73} +(10.8562 + 116.060i) q^{74} +(-14.4699 - 76.6696i) q^{76} +(-5.15652 + 8.93136i) q^{77} +(32.1841 - 18.5815i) q^{79} +(-14.7512 + 97.2567i) q^{80} +(9.70439 + 4.45452i) q^{82} +(66.0281 - 38.1214i) q^{83} +(-52.0037 + 90.0730i) q^{85} +(-45.3319 - 63.9207i) q^{86} +(100.529 + 96.9724i) q^{88} +27.5873 q^{89} +1.05407i q^{91} +(-29.9360 - 10.4906i) q^{92} +(12.8801 + 18.1617i) q^{94} +(-103.856 - 59.9614i) q^{95} +(13.0585 + 22.6180i) q^{97} +(-88.4309 - 40.5917i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8	$ 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8} + 20 q^{10} - 46 q^{13} + 12 q^{14} - 17 q^{16} - 12 q^{17} - 36 q^{20} + 33 q^{22} - 30 q^{25} - 72 q^{26} + 12 q^{28} - 42 q^{29} - 87 q^{32} + 11 q^{34} + 56 q^{37} + 99 q^{38} + 68 q^{40} - 84 q^{41} + 222 q^{44} - 264 q^{46} + 58 q^{49} + 219 q^{50} + 110 q^{52} + 72 q^{53} - 270 q^{56} - 16 q^{58} - 34 q^{61} - 516 q^{62} - 254 q^{64} + 30 q^{65} - 375 q^{68} + 150 q^{70} + 116 q^{73} + 372 q^{74} - 15 q^{76} + 330 q^{77} + 720 q^{80} + 254 q^{82} - 140 q^{85} + 273 q^{86} + 75 q^{88} + 384 q^{89} - 258 q^{92} + 36 q^{94} - 148 q^{97} - 1170 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8 + 20 * q^10 - 46 * q^13 + 12 * q^14 - 17 * q^16 - 12 * q^17 - 36 * q^20 + 33 * q^22 - 30 * q^25 - 72 * q^26 + 12 * q^28 - 42 * q^29 - 87 * q^32 + 11 * q^34 + 56 * q^37 + 99 * q^38 + 68 * q^40 - 84 * q^41 + 222 * q^44 - 264 * q^46 + 58 * q^49 + 219 * q^50 + 110 * q^52 + 72 * q^53 - 270 * q^56 - 16 * q^58 - 34 * q^61 - 516 * q^62 - 254 * q^64 + 30 * q^65 - 375 * q^68 + 150 * q^70 + 116 * q^73 + 372 * q^74 - 15 * q^76 + 330 * q^77 + 720 * q^80 + 254 * q^82 - 140 * q^85 + 273 * q^86 + 75 * q^88 + 384 * q^89 - 258 * q^92 + 36 * q^94 - 148 * q^97 - 1170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.186266	+	1.99131i	0.0931330	+	0.995654i
$2$	0.186266	+	1.99131i	0.0931330	+	0.995654i
$3$		0			0
$3$		0			0
$4$	−3.93061	+	0.741826i	−0.982652	+	0.185456i
$5$	−3.07403	+	5.32438i	−0.614806	+	1.06488i	0.375612	+	0.926777i	$0.377432\pi$
$5$	−3.07403	+	5.32438i	−0.614806	+	1.06488i	−0.990418	+	0.138099i	$0.955901\pi$
$6$		0			0
$7$	0.511543	−	0.295340i	0.0730776	−	0.0421914i	−0.463016	−	0.886350i	$-0.653233\pi$
$7$	0.511543	−	0.295340i	0.0730776	−	0.0421914i	0.536094	+	0.844159i	$0.319899\pi$
$8$	−2.20934	−	7.68888i	−0.276168	−	0.961109i
$9$		0			0
$10$	−11.1751	−	5.12959i	−1.11751	−	0.512959i
$11$	−15.1205	+	8.72982i	−1.37459	+	0.793620i	−0.991502	−	0.130092i	$-0.958473\pi$
$11$	−15.1205	+	8.72982i	−1.37459	+	0.793620i	−0.383088	+	0.923712i	$0.625139\pi$
$12$		0			0
$13$	−0.892255	+	1.54543i	−0.0686350	+	0.118879i	−0.898301	−	0.439381i	$-0.855198\pi$
$13$	−0.892255	+	1.54543i	−0.0686350	+	0.118879i	0.829666	+	0.558261i	$0.188531\pi$
$14$	0.683395	+	0.963628i	0.0488140	+	0.0688306i
$15$		0			0
$16$	14.8994	−	5.83166i	0.931212	−	0.364479i
$17$	16.9171			0.995123			0.497562	−	0.867429i	$-0.334229\pi$
$17$	16.9171			0.995123			0.497562	+	0.867429i	$0.334229\pi$
$18$		0			0
$19$			19.5058i			1.02662i	0.858203	+	0.513310i	$0.171581\pi$
$19$			19.5058i			1.02662i	−0.858203	+	0.513310i	$0.828419\pi$
$20$	8.13306	−	23.2084i	0.406653	−	1.16042i
$21$		0			0
$22$	−20.2002	−	28.4835i	−0.918190	−	1.29470i
$23$	6.86778	+	3.96511i	0.298599	+	0.172396i	0.641813	−	0.766861i	$-0.278182\pi$
$23$	6.86778	+	3.96511i	0.298599	+	0.172396i	−0.343214	+	0.939257i	$0.611516\pi$
$24$		0			0
$25$	−6.39933	−	11.0840i	−0.255973	−	0.443359i
$26$	−3.24362	−	1.48889i	−0.124755	−	0.0572651i
$27$		0			0
$28$	−1.79159	+	1.54034i	−0.0639852	+	0.0550122i
$29$	−3.17517	−	5.49956i	−0.109489	−	0.189640i	0.806075	−	0.591814i	$-0.201588\pi$
$29$	−3.17517	−	5.49956i	−0.109489	−	0.189640i	−0.915563	+	0.402174i	$0.868255\pi$
$30$		0			0
$31$	27.6558	+	15.9671i	0.892124	+	0.515068i	0.874637	−	0.484779i	$-0.161100\pi$
$31$	27.6558	+	15.9671i	0.892124	+	0.515068i	0.0174873	+	0.999847i	$0.494433\pi$
$32$	14.3879	+	28.5830i	0.449621	+	0.893219i
$33$		0			0
$34$	3.15108	+	33.6871i	0.0926788	+	0.990798i
$35$			3.63153i			0.103758i
$36$		0			0
$37$	58.2834			1.57523			0.787614	−	0.616169i	$-0.211316\pi$
$37$	58.2834			1.57523			0.787614	+	0.616169i	$0.211316\pi$
$38$	−38.8420	+	3.63326i	−1.02216	+	0.0956122i
$39$		0			0
$40$	47.7301	+	11.8725i	1.19325	+	0.296812i
$41$	2.66948	−	4.62368i	0.0651093	−	0.112773i	−0.831633	−	0.555325i	$-0.812594\pi$
$41$	2.66948	−	4.62368i	0.0651093	−	0.112773i	0.896742	+	0.442553i	$0.145927\pi$
$42$		0			0
$43$	−33.9324	+	19.5909i	−0.789126	+	0.455602i	−0.839655	−	0.543121i	$-0.817243\pi$
$43$	−33.9324	+	19.5909i	−0.789126	+	0.455602i	0.0505290	+	0.998723i	$0.483909\pi$
$44$	52.9567	−	45.5303i	1.20356	−	1.03478i
$45$		0			0
$46$	−6.61653	+	14.4144i	−0.143838	+	0.313357i
$47$	9.64117	−	5.56633i	0.205131	−	0.118433i	−0.393915	−	0.919147i	$-0.628880\pi$
$47$	9.64117	−	5.56633i	0.205131	−	0.118433i	0.599047	+	0.800714i	$0.295546\pi$
$48$		0			0
$49$	−24.3255	+	42.1331i	−0.496440	+	0.859859i
$50$	20.8796	−	14.8076i	0.417592	−	0.296152i
$51$		0			0
$52$	2.36067	−	6.73638i	0.0453974	−	0.129546i
$53$	−35.8770			−0.676925			−0.338462	−	0.940980i	$-0.609907\pi$
$53$	−35.8770			−0.676925			−0.338462	+	0.940980i	$0.609907\pi$
$54$		0			0
$55$		−	107.343i		−	1.95169i
$56$	−3.40100	−	3.28069i	−0.0607322	−	0.0585837i
$57$		0			0
$58$	10.3599	−	7.34713i	0.178619	−	0.126675i
$59$	20.8974	+	12.0651i	0.354194	+	0.204494i	0.666531	−	0.745477i	$-0.267778\pi$
$59$	20.8974	+	12.0651i	0.354194	+	0.204494i	−0.312337	+	0.949971i	$0.601112\pi$
$60$		0			0
$61$	−37.9460	−	65.7244i	−0.622066	−	1.07745i	−0.989100	−	0.147243i	$-0.952960\pi$
$61$	−37.9460	−	65.7244i	−0.622066	−	1.07745i	0.367034	−	0.930207i	$-0.380373\pi$
$62$	−26.6441	+	58.0454i	−0.429743	+	0.936216i
$63$		0			0
$64$	−54.2376	+	33.9747i	−0.847463	+	0.530855i
$65$	−5.48564	−	9.50141i	−0.0843944	−	0.146175i
$66$		0			0
$67$	−31.8200	−	18.3713i	−0.474925	−	0.274198i	0.243374	−	0.969933i	$-0.421746\pi$
$67$	−31.8200	−	18.3713i	−0.474925	−	0.274198i	−0.718299	+	0.695734i	$0.755079\pi$
$68$	−66.4945	+	12.5495i	−0.977860	+	0.184552i
$69$		0			0
$70$	−7.23150	+	0.676431i	−0.103307	+	0.00966331i
$71$		−	87.8370i		−	1.23714i	−0.785730	−	0.618570i	$-0.787712\pi$
$71$		−	87.8370i		−	1.23714i	0.785730	−	0.618570i	$-0.212288\pi$
$72$		0			0
$73$	−60.0423			−0.822498			−0.411249	−	0.911523i	$-0.634907\pi$
$73$	−60.0423			−0.822498			−0.411249	+	0.911523i	$0.634907\pi$
$74$	10.8562	+	116.060i	0.146706	+	1.56838i
$75$		0			0
$76$	−14.4699	−	76.6696i	−0.190393	−	1.00881i
$77$	−5.15652	+	8.93136i	−0.0669678	+	0.115992i
$78$		0			0
$79$	32.1841	−	18.5815i	0.407394	−	0.235209i	−0.282275	−	0.959333i	$-0.591089\pi$
$79$	32.1841	−	18.5815i	0.407394	−	0.235209i	0.689669	+	0.724124i	$0.257756\pi$
$80$	−14.7512	+	97.2567i	−0.184391	+	1.21571i
$81$		0			0
$82$	9.70439	+	4.45452i	0.118346	+	0.0543234i
$83$	66.0281	−	38.1214i	0.795520	−	0.459294i	−0.0463824	−	0.998924i	$-0.514769\pi$
$83$	66.0281	−	38.1214i	0.795520	−	0.459294i	0.841902	+	0.539630i	$0.181436\pi$
$84$		0			0
$85$	−52.0037	+	90.0730i	−0.611808	+	1.05968i
$86$	−45.3319	−	63.9207i	−0.527115	−	0.743264i
$87$		0			0
$88$	100.529	+	96.9724i	1.14237	+	1.10196i
$89$	27.5873			0.309969			0.154985	−	0.987917i	$-0.450467\pi$
$89$	27.5873			0.309969			0.154985	+	0.987917i	$0.450467\pi$
$90$		0			0
$91$			1.05407i			0.0115832i
$92$	−29.9360	−	10.4906i	−0.325391	−	0.114028i
$93$		0			0
$94$	12.8801	+	18.1617i	0.137022	+	0.193210i
$95$	−103.856	−	59.9614i	−1.09322	−	0.631172i
$96$		0			0
$97$	13.0585	+	22.6180i	0.134624	+	0.233176i	0.925454	−	0.378861i	$-0.123684\pi$
$97$	13.0585	+	22.6180i	0.134624	+	0.233176i	−0.790830	+	0.612036i	$0.790351\pi$
$98$	−88.4309	−	40.5917i	−0.902357	−	0.414201i
$99$		0			0
$100$	33.3757	+	38.8196i	0.333757	+	0.388196i
$101$	12.8831	+	22.3142i	0.127556	+	0.220933i	0.922729	−	0.385449i	$-0.125953\pi$
$101$	12.8831	+	22.3142i	0.127556	+	0.220933i	−0.795173	+	0.606382i	$0.792620\pi$
$102$		0			0
$103$	−16.9947	−	9.81187i	−0.164997	−	0.0952609i	0.415228	−	0.909717i	$-0.363702\pi$
$103$	−16.9947	−	9.81187i	−0.164997	−	0.0952609i	−0.580225	+	0.814457i	$0.697035\pi$
$104$	13.8539	+	3.44605i	0.133211	+	0.0331351i
$105$		0			0
$106$	−6.68267	−	71.4422i	−0.0630441	−	0.673983i
$107$			183.200i			1.71215i	0.516850	+	0.856076i	$0.327105\pi$
$107$			183.200i			1.71215i	−0.516850	+	0.856076i	$0.672895\pi$
$108$		0			0
$109$	100.841			0.925147			0.462573	−	0.886581i	$-0.346926\pi$
$109$	100.841			0.925147			0.462573	+	0.886581i	$0.346926\pi$
$110$	213.753	−	19.9943i	1.94321	−	0.181767i
$111$		0			0
$112$	5.89936	−	7.38353i	0.0526729	−	0.0659243i
$113$	9.12484	−	15.8047i	0.0807508	−	0.139865i	−0.822822	−	0.568299i	$-0.807602\pi$
$113$	9.12484	−	15.8047i	0.0807508	−	0.139865i	0.903573	+	0.428435i	$0.140935\pi$
$114$		0			0
$115$	−42.2235	+	24.3778i	−0.367161	+	0.211981i
$116$	16.5601	+	19.2612i	0.142759	+	0.166045i
$117$		0			0
$118$	−20.1329	+	43.8606i	−0.170618	+	0.371700i
$119$	8.65383	−	4.99629i	0.0727212	−	0.0419856i
$120$		0			0
$121$	91.9194	−	159.209i	0.759664	−	1.31578i
$122$	123.810	−	87.8044i	1.01483	−	0.719708i
$123$		0			0
$124$	−120.549	−	42.2447i	−0.972170	−	0.340683i
$125$	−75.0146			−0.600117
$126$		0			0
$127$			164.386i			1.29438i	0.762331	+	0.647188i	$0.224055\pi$
$127$			164.386i			1.29438i	−0.762331	+	0.647188i	$0.775945\pi$
$128$	−77.7567	−	101.675i	−0.607474	−	0.794339i
$129$		0			0
$130$	17.8984	−	12.6934i	0.137680	−	0.0976414i
$131$	123.421	+	71.2570i	0.942143	+	0.543947i	0.890631	−	0.454726i	$-0.150263\pi$
$131$	123.421	+	71.2570i	0.942143	+	0.543947i	0.0515116	+	0.998672i	$0.483596\pi$
$132$		0			0
$133$	5.76083	+	9.97805i	0.0433145	+	0.0750229i
$134$	30.6559	−	66.7853i	0.228775	−	0.498398i
$135$		0			0
$136$	−37.3757	−	130.073i	−0.274821	−	0.956422i
$137$	3.08176	+	5.33777i	0.0224946	+	0.0389618i	0.877054	−	0.480393i	$-0.159506\pi$
$137$	3.08176	+	5.33777i	0.0224946	+	0.0389618i	−0.854559	+	0.519354i	$0.826172\pi$
$138$		0			0
$139$	103.168	+	59.5642i	0.742218	+	0.428519i	0.822875	−	0.568222i	$-0.192369\pi$
$139$	103.168	+	59.5642i	0.742218	+	0.428519i	−0.0806575	+	0.996742i	$0.525702\pi$
$140$	−2.69397	−	14.2741i	−0.0192426	−	0.101958i
$141$		0			0
$142$	174.910	−	16.3610i	1.23176	−	0.115219i
$143$		−	31.1569i		−	0.217880i
$144$		0			0
$145$	39.0423			0.269257
$146$	−11.1838	−	119.563i	−0.0766017	−	0.818923i
$147$		0			0
$148$	−229.089	+	43.2361i	−1.54790	+	0.292136i
$149$	103.365	−	179.034i	0.693726	−	1.20157i	−0.276882	−	0.960904i	$-0.589301\pi$
$149$	103.365	−	179.034i	0.693726	−	1.20157i	0.970608	−	0.240665i	$-0.0773657\pi$
$150$		0			0
$151$	127.422	−	73.5670i	0.843853	−	0.487199i	−0.0147190	−	0.999892i	$-0.504685\pi$
$151$	127.422	−	73.5670i	0.843853	−	0.487199i	0.858572	+	0.512693i	$0.171352\pi$
$152$	149.977	−	43.0949i	0.986694	−	0.283519i
$153$		0			0
$154$	−18.7456	−	8.60461i	−0.121724	−	0.0558741i
$155$	−170.030	+	98.1668i	−1.09697	+	0.633334i
$156$		0			0
$157$	31.4395	−	54.4548i	0.200251	−	0.346846i	−0.748358	−	0.663295i	$-0.769157\pi$
$157$	31.4395	−	54.4548i	0.200251	−	0.346846i	0.948609	+	0.316449i	$0.102491\pi$
$158$	42.9963	+	60.6274i	0.272129	+	0.383718i
$159$		0			0
$160$	−196.416	−	11.2586i	−1.22760	−	0.0703665i
$161$	4.68422			0.0290946
$162$		0			0
$163$			143.325i			0.879292i	0.898171	+	0.439646i	$0.144896\pi$
$163$			143.325i			0.879292i	−0.898171	+	0.439646i	$0.855104\pi$
$164$	−7.06272	+	20.1542i	−0.0430654	+	0.122891i
$165$		0			0
$166$	88.2102	+	124.382i	0.531386	+	0.749287i
$167$	−150.531	−	86.9089i	−0.901381	−	0.520413i	−0.0237332	−	0.999718i	$-0.507555\pi$
$167$	−150.531	−	86.9089i	−0.901381	−	0.520413i	−0.877648	+	0.479306i	$0.840889\pi$
$168$		0			0
$169$	82.9078	+	143.600i	0.490578	+	0.849707i
$170$	−189.050	−	86.7777i	−1.11206	−	0.510457i
$171$		0			0
$172$	118.842	−	102.176i	0.690942	−	0.594047i
$173$	125.806	+	217.902i	0.727201	+	1.25955i	0.958062	+	0.286562i	$0.0925125\pi$
$173$	125.806	+	217.902i	0.727201	+	1.25955i	−0.230861	+	0.972987i	$0.574154\pi$
$174$		0			0
$175$	−6.54707	−	3.77995i	−0.0374118	−	0.0215997i
$176$	−174.377	+	218.246i	−0.990777	+	1.24004i
$177$		0			0
$178$	5.13857	+	54.9347i	0.0288684	+	0.308622i
$179$			96.0059i			0.536346i	0.963371	+	0.268173i	$0.0864199\pi$
$179$			96.0059i			0.536346i	−0.963371	+	0.268173i	$0.913580\pi$
$180$		0			0
$181$	−328.757			−1.81634			−0.908170	−	0.418603i	$-0.862520\pi$
$181$	−328.757			−1.81634			−0.908170	+	0.418603i	$0.862520\pi$
$182$	−2.09898	+	0.196338i	−0.0115329	+	0.00107878i
$183$		0			0
$184$	15.3140	−	61.5658i	0.0832282	−	0.334597i
$185$	−179.165	+	310.323i	−0.968460	+	1.67742i
$186$		0			0
$187$	−255.795	+	147.683i	−1.36789	+	0.789749i
$188$	−33.7664	+	29.0312i	−0.179609	+	0.154421i
$189$		0			0
$190$	100.057	−	217.978i	0.526614	−	1.14725i
$191$	0.351914	−	0.203178i	0.00184248	−	0.00106376i	−0.499078	−	0.866557i	$-0.666328\pi$
$191$	0.351914	−	0.203178i	0.00184248	−	0.00106376i	0.500921	+	0.865493i	$0.332995\pi$
$192$		0			0
$193$	−31.2230	+	54.0798i	−0.161777	+	0.280206i	−0.935506	−	0.353311i	$-0.885056\pi$
$193$	−31.2230	+	54.0798i	−0.161777	+	0.280206i	0.773729	+	0.633517i	$0.218389\pi$
$194$	−42.6071	+	30.2165i	−0.219624	+	0.155755i
$195$		0			0
$196$	64.3588	−	183.654i	0.328361	−	0.937010i
$197$	207.861			1.05513			0.527566	−	0.849514i	$-0.323105\pi$
$197$	207.861			1.05513			0.527566	+	0.849514i	$0.323105\pi$
$198$		0			0
$199$		−	299.128i		−	1.50316i	−0.659643	−	0.751579i	$-0.729293\pi$
$199$		−	299.128i		−	1.50316i	0.659643	−	0.751579i	$-0.270707\pi$
$200$	−71.0849	+	73.6919i	−0.355425	+	0.368460i
$201$		0			0
$202$	−42.0348	+	29.8107i	−0.208093	+	0.147578i
$203$	−3.24848	−	1.87551i	−0.0160024	−	0.00923896i
$204$		0			0
$205$	16.4121	+	28.4266i	0.0800592	+	0.138667i
$206$	16.3729	−	35.6692i	0.0794802	−	0.173152i
$207$		0			0
$208$	−4.28163	+	28.2293i	−0.0205848	+	0.135718i
$209$	−170.282	−	294.937i	−0.814746	−	1.41118i
$210$		0			0
$211$	−141.744	−	81.8360i	−0.671773	−	0.387848i	0.124975	−	0.992160i	$-0.460115\pi$
$211$	−141.744	−	81.8360i	−0.671773	−	0.387848i	−0.796748	+	0.604311i	$0.793448\pi$
$212$	141.019	−	26.6145i	0.665182	−	0.125540i
$213$		0			0
$214$	−364.808	+	34.1240i	−1.70471	+	0.159458i
$215$		−	240.892i		−	1.12043i
$216$		0			0
$217$	18.8629			0.0869257
$218$	18.7833	+	200.805i	0.0861617	+	0.921126i
$219$		0			0
$220$	79.6297	+	421.923i	0.361953	+	1.91783i
$221$	−15.0944	+	26.1442i	−0.0683003	+	0.118300i
$222$		0			0
$223$	330.681	−	190.919i	1.48287	−	0.856138i	0.483063	−	0.875586i	$-0.339524\pi$
$223$	330.681	−	190.919i	1.48287	−	0.856138i	0.999811	+	0.0194478i	$0.00619081\pi$
$224$	15.8017	+	10.3721i	0.0705434	+	0.0463042i
$225$		0			0
$226$	33.1717	+	15.2265i	0.146777	+	0.0673739i
$227$	51.5472	−	29.7608i	0.227080	−	0.131105i	−0.382144	−	0.924103i	$-0.624814\pi$
$227$	51.5472	−	29.7608i	0.227080	−	0.131105i	0.609224	+	0.792998i	$0.291481\pi$
$228$		0			0
$229$	64.4366	−	111.608i	0.281383	−	0.487369i	−0.690343	−	0.723482i	$-0.742540\pi$
$229$	64.4366	−	111.608i	0.281383	−	0.487369i	0.971726	+	0.236113i	$0.0758736\pi$
$230$	−56.4084	−	79.5393i	−0.245254	−	0.345823i
$231$		0			0
$232$	−35.2704	+	36.5639i	−0.152028	+	0.157603i
$233$	−14.9939			−0.0643513			−0.0321757	−	0.999482i	$-0.510244\pi$
$233$	−14.9939			−0.0643513			−0.0321757	+	0.999482i	$0.510244\pi$
$234$		0			0
$235$			68.4443i			0.291252i
$236$	−91.0899	−	31.9211i	−0.385974	−	0.135259i
$237$		0			0
$238$	11.5611	+	16.3018i	0.0485759	+	0.0684949i
$239$	315.244	+	182.006i	1.31901	+	0.761532i	0.983570	−	0.180529i	$-0.0577811\pi$
$239$	315.244	+	182.006i	1.31901	+	0.761532i	0.335442	+	0.942061i	$0.391114\pi$
$240$		0			0
$241$	−40.5235	−	70.1888i	−0.168147	−	0.291240i	0.769621	−	0.638501i	$-0.220445\pi$
$241$	−40.5235	−	70.1888i	−0.168147	−	0.291240i	−0.937769	+	0.347261i	$0.887112\pi$
$242$	334.156	+	153.385i	1.38081	+	0.633820i
$243$		0			0
$244$	197.907	+	230.188i	0.811095	+	0.943393i
$245$	−149.555	−	259.037i	−0.610428	−	1.05729i
$246$		0			0
$247$	−30.1448	−	17.4041i	−0.122044	−	0.0704620i
$248$	61.6679	−	247.919i	0.248661	−	0.999674i
$249$		0			0
$250$	−13.9727	−	149.377i	−0.0558907	−	0.597508i
$251$		−	281.883i		−	1.12304i	−0.827463	−	0.561520i	$-0.810217\pi$
$251$		−	281.883i		−	1.12304i	0.827463	−	0.561520i	$-0.189783\pi$
$252$		0			0
$253$	−138.459			−0.547268
$254$	−327.342	+	30.6195i	−1.28875	+	0.120549i
$255$		0			0
$256$	187.984	−	173.776i	0.734311	−	0.678813i
$257$	37.6564	−	65.2227i	0.146523	−	0.253785i	−0.783417	−	0.621496i	$-0.786525\pi$
$257$	37.6564	−	65.2227i	0.146523	−	0.253785i	0.929940	+	0.367711i	$0.119858\pi$
$258$		0			0
$259$	29.8145	−	17.2134i	0.115114	−	0.0664610i
$260$	28.6103	+	33.2769i	0.110040	+	0.127988i
$261$		0			0
$262$	−118.905	+	259.041i	−0.453838	+	0.988708i
$263$	105.914	−	61.1497i	0.402716	−	0.232508i	−0.284939	−	0.958546i	$-0.591973\pi$
$263$	105.914	−	61.1497i	0.402716	−	0.232508i	0.687655	+	0.726037i	$0.258640\pi$
$264$		0			0
$265$	110.287	−	191.023i	0.416178	−	0.720841i
$266$	−18.7963	+	13.3302i	−0.0706628	+	0.0501134i
$267$		0			0
$268$	138.700	+	48.6054i	0.517538	+	0.181364i
$269$	−280.452			−1.04257			−0.521287	−	0.853382i	$-0.674548\pi$
$269$	−280.452			−1.04257			−0.521287	+	0.853382i	$0.674548\pi$
$270$		0			0
$271$		−	81.4468i		−	0.300542i	−0.988645	−	0.150271i	$-0.951985\pi$
$271$		−	81.4468i		−	0.300542i	0.988645	−	0.150271i	$-0.0480146\pi$
$272$	252.054	−	98.6547i	0.926670	−	0.362701i
$273$		0			0
$274$	−10.0551	+	7.13098i	−0.0366975	+	0.0260255i
$275$	193.522	+	111.730i	0.703716	+	0.406291i
$276$		0			0
$277$	224.861	+	389.471i	0.811774	+	1.40603i	0.911622	+	0.411031i	$0.134831\pi$
$277$	224.861	+	389.471i	0.811774	+	1.40603i	−0.0998479	+	0.995003i	$0.531836\pi$
$278$	−99.3939	+	216.534i	−0.357532	+	0.778901i
$279$		0			0
$280$	27.9224	−	8.02330i	0.0997229	−	0.0286546i
$281$	37.8649	+	65.5838i	0.134750	+	0.233394i	0.925502	−	0.378743i	$-0.123643\pi$
$281$	37.8649	+	65.5838i	0.134750	+	0.233394i	−0.790752	+	0.612137i	$0.790310\pi$
$282$		0			0
$283$	−322.061	−	185.942i	−1.13803	−	0.657039i	−0.192084	−	0.981378i	$-0.561525\pi$
$283$	−322.061	−	185.942i	−1.13803	−	0.657039i	−0.945941	+	0.324339i	$0.894858\pi$
$284$	65.1597	+	345.253i	0.229436	+	1.21568i
$285$		0			0
$286$	62.0429	−	5.80347i	0.216933	−	0.0202919i
$287$		−	3.15361i		−	0.0109882i
$288$		0			0
$289$	−2.81196			−0.00972996
$290$	7.27226	+	77.7453i	0.0250768	+	0.268087i
$291$		0			0
$292$	236.003	−	44.5409i	0.808229	−	0.152537i
$293$	66.3946	−	114.999i	0.226603	−	0.392488i	−0.730196	−	0.683237i	$-0.760571\pi$
$293$	66.3946	−	114.999i	0.226603	−	0.392488i	0.956799	+	0.290750i	$0.0939047\pi$
$294$		0			0
$295$	−128.479	+	74.1772i	−0.435521	+	0.251448i
$296$	−128.768	−	448.134i	−0.435027	−	1.51397i
$297$		0			0
$298$	375.765	+	172.484i	1.26096	+	0.578806i
$299$	−12.2556	+	7.07579i	−0.0409887	+	0.0236648i
$300$		0			0
$301$	−11.5719	+	20.0432i	−0.0384450	+	0.0665886i
$302$	170.229	+	240.033i	0.563672	+	0.794811i
$303$		0			0
$304$	113.751	+	290.624i	0.374181	+	0.956000i
$305$	466.589			1.52980
$306$		0			0
$307$			336.514i			1.09614i	0.836434	+	0.548068i	$0.184637\pi$
$307$			336.514i			1.09614i	−0.836434	+	0.548068i	$0.815363\pi$
$308$	13.6428	−	38.9309i	0.0442947	−	0.126399i
$309$		0			0
$310$	−227.151	−	320.296i	−0.732745	−	1.03321i
$311$	−304.206	−	175.634i	−0.978156	−	0.564738i	−0.0764428	−	0.997074i	$-0.524356\pi$
$311$	−304.206	−	175.634i	−0.978156	−	0.564738i	−0.901713	+	0.432336i	$0.857690\pi$
$312$		0			0
$313$	−95.4299	−	165.289i	−0.304888	−	0.528081i	0.672349	−	0.740235i	$-0.265286\pi$
$313$	−95.4299	−	165.289i	−0.304888	−	0.528081i	−0.977236	+	0.212154i	$0.931952\pi$
$314$	114.292	+	52.4626i	0.363988	+	0.167078i
$315$		0			0
$316$	−112.719	+	96.9117i	−0.356706	+	0.306683i
$317$	202.797	+	351.255i	0.639738	+	1.10806i	0.985490	+	0.169733i	$0.0542906\pi$
$317$	202.797	+	351.255i	0.639738	+	1.10806i	−0.345752	+	0.938326i	$0.612376\pi$
$318$		0			0
$319$	96.0203	+	55.4374i	0.301004	+	0.173785i
$320$	−14.1661	−	393.221i	−0.0442692	−	1.22882i
$321$		0			0
$322$	0.872512	+	9.32773i	0.00270966	+	0.0289681i
$323$			329.981i			1.02161i
$324$		0			0
$325$	22.8393			0.0702749
$326$	−285.403	+	26.6965i	−0.875470	+	0.0818911i
$327$		0			0
$328$	−41.4487	−	10.3100i	−0.126368	−	0.0314330i
$329$	3.28792	−	5.69484i	0.00999368	−	0.0173096i
$330$		0			0
$331$	384.104	−	221.763i	1.16044	−	0.669978i	0.209027	−	0.977910i	$-0.432970\pi$
$331$	384.104	−	221.763i	1.16044	−	0.669978i	0.951408	+	0.307932i	$0.0996370\pi$
$332$	−231.251	+	198.822i	−0.696541	+	0.598860i
$333$		0			0
$334$	145.024	−	315.941i	0.434203	−	0.945931i
$335$	195.631	−	112.948i	0.583974	−	0.337158i
$336$		0			0
$337$	−254.239	+	440.356i	−0.754420	+	1.30669i	0.191243	+	0.981543i	$0.438748\pi$
$337$	−254.239	+	440.356i	−0.754420	+	1.30669i	−0.945662	+	0.325150i	$0.894585\pi$
$338$	−270.510	+	191.843i	−0.800325	+	0.567582i
$339$		0			0
$340$	137.588	−	392.619i	0.404670	−	1.15476i
$341$	−557.560			−1.63507
$342$		0			0
$343$			57.6805i			0.168165i
$344$	225.600	+	217.619i	0.655814	+	0.632614i
$345$		0			0
$346$	−410.476	+	291.106i	−1.18635	+	0.841346i
$347$	−492.773	−	284.503i	−1.42010	−	0.819893i	−0.423790	−	0.905761i	$-0.639300\pi$
$347$	−492.773	−	284.503i	−1.42010	−	0.819893i	−0.996307	+	0.0858678i	$0.972634\pi$
$348$		0			0
$349$	−206.901	−	358.363i	−0.592840	−	1.02683i	−0.993848	−	0.110754i	$-0.964673\pi$
$349$	−206.901	−	358.363i	−0.592840	−	1.02683i	0.401008	−	0.916074i	$-0.368660\pi$
$350$	6.30755	−	13.7413i	0.0180216	−	0.0392609i
$351$		0			0
$352$	−467.076	−	306.586i	−1.32692	−	0.870982i
$353$	−62.3070	−	107.919i	−0.176507	−	0.305719i	0.764175	−	0.645009i	$-0.223147\pi$
$353$	−62.3070	−	107.919i	−0.176507	−	0.305719i	−0.940682	+	0.339290i	$0.889813\pi$
$354$		0			0
$355$	467.677	+	270.014i	1.31740	+	0.760602i
$356$	−108.435	+	20.4649i	−0.304592	+	0.0574858i
$357$		0			0
$358$	−191.177	+	17.8826i	−0.534015	+	0.0499515i
$359$			303.196i			0.844557i	0.906466	+	0.422278i	$0.138770\pi$
$359$			303.196i			0.844557i	−0.906466	+	0.422278i	$0.861230\pi$
$360$		0			0
$361$	−19.4752			−0.0539480
$362$	−61.2363	−	654.657i	−0.169161	−	1.80844i
$363$		0			0
$364$	−0.781939	−	4.14315i	−0.00214818	−	0.0113823i
$365$	184.572	−	319.688i	0.505677	−	0.875858i
$366$		0			0
$367$	−615.571	+	355.400i	−1.67730	+	0.968392i	−0.713936	+	0.700211i	$0.753089\pi$
$367$	−615.571	+	355.400i	−1.67730	+	0.968392i	−0.963369	+	0.268181i	$0.913578\pi$
$368$	125.449	+	19.0273i	0.340894	+	0.0517045i
$369$		0			0
$370$	−651.321	−	298.970i	−1.76033	−	0.808027i
$371$	−18.3527	+	10.5959i	−0.0494681	+	0.0285604i
$372$		0			0
$373$	166.740	−	288.803i	0.447025	−	0.774271i	−0.551166	−	0.834396i	$-0.685817\pi$
$373$	166.740	−	288.803i	0.447025	−	0.774271i	0.998191	+	0.0601254i	$0.0191501\pi$
$374$	−341.728	−	481.857i	−0.913712	−	1.28839i
$375$		0			0
$376$	−64.0995	−	61.8318i	−0.170477	−	0.164446i
$377$	11.3323			0.0300590
$378$		0			0
$379$		−	662.686i		−	1.74851i	−0.485465	−	0.874256i	$-0.661350\pi$
$379$		−	662.686i		−	1.74851i	0.485465	−	0.874256i	$-0.338650\pi$
$380$	452.699	+	158.642i	1.19131	+	0.417478i
$381$		0			0
$382$	0.470139	+	0.662924i	0.00123073	+	0.00173540i
$383$	69.9008	+	40.3572i	0.182509	+	0.105371i	0.588471	−	0.808518i	$-0.299730\pi$
$383$	69.9008	+	40.3572i	0.182509	+	0.105371i	−0.405962	+	0.913890i	$0.633064\pi$
$384$		0			0
$385$	−31.7026	−	54.9106i	−0.0823445	−	0.142625i
$386$	−113.505	−	52.1013i	−0.294055	−	0.134977i
$387$		0			0
$388$	−68.1066	−	79.2155i	−0.175533	−	0.204164i
$389$	346.006	+	599.301i	0.889476	+	1.54062i	0.840495	+	0.541819i	$0.182264\pi$
$389$	346.006	+	599.301i	0.889476	+	1.54062i	0.0489809	+	0.998800i	$0.484403\pi$
$390$		0			0
$391$	116.183	+	67.0782i	0.297143	+	0.171556i
$392$	377.700	+	93.9497i	0.963519	+	0.239668i
$393$		0			0
$394$	38.7174	+	413.915i	0.0982675	+	1.05055i
$395$			228.481i			0.578432i
$396$		0			0
$397$	657.713			1.65671			0.828354	−	0.560206i	$-0.189278\pi$
$397$	657.713			1.65671			0.828354	+	0.560206i	$0.189278\pi$
$398$	595.657	−	55.7175i	1.49662	−	0.139994i
$399$		0			0
$400$	−159.984	−	127.826i	−0.399960	−	0.319564i
$401$	−296.433	+	513.437i	−0.739235	+	1.28039i	0.213606	+	0.976920i	$0.431479\pi$
$401$	−296.433	+	513.437i	−0.739235	+	1.28039i	−0.952840	+	0.303472i	$0.901854\pi$
$402$		0			0
$403$	−49.3521	+	28.4935i	−0.122462	+	0.0707034i
$404$	−67.1918	−	78.1515i	−0.166316	−	0.193444i
$405$		0			0
$406$	3.12963	−	6.81806i	0.00770846	−	0.0167933i
$407$	−881.274	+	508.804i	−2.16529	+	1.25013i
$408$		0			0
$409$	−161.594	+	279.889i	−0.395095	+	0.684325i	−0.993113	−	0.117157i	$-0.962622\pi$
$409$	−161.594	+	279.889i	−0.395095	+	0.684325i	0.598018	+	0.801483i	$0.295955\pi$
$410$	−53.5492	+	37.9765i	−0.130608	+	0.0926257i
$411$		0			0
$412$	74.0781	+	25.9596i	0.179801	+	0.0630086i
$413$	14.2533			0.0345115
$414$		0			0
$415$			468.745i			1.12951i
$416$	−57.0107	−	3.26788i	−0.137045	−	0.00785549i
$417$		0			0
$418$	555.592	−	394.020i	1.32917	−	0.942632i
$419$	222.744	+	128.601i	0.531608	+	0.306924i	0.741671	−	0.670764i	$-0.234033\pi$
$419$	222.744	+	128.601i	0.531608	+	0.306924i	−0.210063	+	0.977688i	$0.567367\pi$
$420$		0			0
$421$	41.9905	+	72.7297i	0.0997400	+	0.172755i	0.911577	−	0.411129i	$-0.134866\pi$
$421$	41.9905	+	72.7297i	0.0997400	+	0.172755i	−0.811837	+	0.583884i	$0.801532\pi$
$422$	136.559	−	297.499i	0.323598	−	0.704975i
$423$		0			0
$424$	79.2646	+	275.854i	0.186945	+	0.650599i
$425$	−108.258	−	187.509i	−0.254725	−	0.441197i
$426$		0			0
$427$	−38.8221	−	22.4139i	−0.0909182	−	0.0524917i
$428$	−135.903	−	720.089i	−0.317530	−	1.68245i
$429$		0			0
$430$	479.690	−	44.8700i	1.11556	−	0.104349i
$431$			144.348i			0.334914i	0.985879	+	0.167457i	$0.0535555\pi$
$431$			144.348i			0.334914i	−0.985879	+	0.167457i	$0.946445\pi$
$432$		0			0
$433$	395.353			0.913057			0.456528	−	0.889709i	$-0.349093\pi$
$433$	395.353			0.913057			0.456528	+	0.889709i	$0.349093\pi$
$434$	3.51351	+	37.5618i	0.00809566	+	0.0865479i
$435$		0			0
$436$	−396.367	+	74.8065i	−0.909098	+	0.171574i
$437$	−77.3426	+	133.961i	−0.176985	+	0.306548i
$438$		0			0
$439$	−194.776	+	112.454i	−0.443682	+	0.256160i	−0.705158	−	0.709050i	$-0.749124\pi$
$439$	−194.776	+	112.454i	−0.443682	+	0.256160i	0.261476	+	0.965210i	$0.415791\pi$
$440$	−825.346	+	237.157i	−1.87579	+	0.538994i
$441$		0			0
$442$	−54.8727	−	25.1877i	−0.124146	−	0.0569858i
$443$	369.184	−	213.148i	0.833373	−	0.481148i	−0.0216335	−	0.999766i	$-0.506887\pi$
$443$	369.184	−	213.148i	0.833373	−	0.481148i	0.855006	+	0.518618i	$0.173553\pi$
$444$		0			0
$445$	−84.8041	+	146.885i	−0.190571	+	0.330079i
$446$	441.772	+	622.926i	0.990521	+	1.39669i
$447$		0			0
$448$	−17.7108	+	33.3981i	−0.0395331	+	0.0745493i
$449$	406.744			0.905888			0.452944	−	0.891539i	$-0.350374\pi$
$449$	406.744			0.905888			0.452944	+	0.891539i	$0.350374\pi$
$450$		0			0
$451$			93.2163i			0.206688i
$452$	−24.1419	+	68.8911i	−0.0534112	+	0.152414i
$453$		0			0
$454$	68.8644	+	97.1029i	0.151684	+	0.213883i
$455$	−5.61228	−	3.24025i	−0.0123347	−	0.00712144i
$456$		0			0
$457$	−159.600	−	276.435i	−0.349234	−	0.604891i	0.636879	−	0.770963i	$-0.280225\pi$
$457$	−159.600	−	276.435i	−0.349234	−	0.604891i	−0.986114	+	0.166072i	$0.946892\pi$
$458$	234.247	+	107.524i	0.511457	+	0.234770i
$459$		0			0
$460$	147.880	−	127.142i	0.321479	−	0.276396i
$461$	−293.888	−	509.029i	−0.637501	−	1.10418i	−0.985979	−	0.166867i	$-0.946635\pi$
$461$	−293.888	−	509.029i	−0.637501	−	1.10418i	0.348478	−	0.937317i	$-0.386698\pi$
$462$		0			0
$463$	230.088	+	132.841i	0.496950	+	0.286914i	0.727453	−	0.686157i	$-0.240704\pi$
$463$	230.088	+	132.841i	0.496950	+	0.286914i	−0.230503	+	0.973072i	$0.574037\pi$
$464$	−79.3797	−	63.4236i	−0.171077	−	0.136689i
$465$		0			0
$466$	−2.79285	−	29.8574i	−0.00599323	−	0.0640716i
$467$		−	794.598i		−	1.70149i	−0.525575	−	0.850747i	$-0.676150\pi$
$467$		−	794.598i		−	1.70149i	0.525575	−	0.850747i	$-0.323850\pi$
$468$		0			0
$469$	−21.7031			−0.0462752
$470$	−136.294	+	12.7489i	−0.289987	+	0.0271252i
$471$		0			0
$472$	46.5978	−	187.334i	0.0987241	−	0.396894i
$473$	342.050	−	592.447i	0.723149	−	1.25253i
$474$		0			0
$475$	216.201	−	124.824i	0.455161	−	0.262787i
$476$	−30.3084	+	26.0581i	−0.0636732	+	0.0547439i
$477$		0			0
$478$	−303.711	+	661.649i	−0.635378	+	1.38420i
$479$	572.964	−	330.801i	1.19617	−	0.690607i	0.236468	−	0.971639i	$-0.424010\pi$
$479$	572.964	−	330.801i	1.19617	−	0.690607i	0.959698	+	0.281033i	$0.0906769\pi$
$480$		0			0
$481$	−52.0037	+	90.0730i	−0.108116	+	0.187262i
$482$	132.219	−	93.7686i	0.274314	−	0.194541i
$483$		0			0
$484$	−243.194	+	693.977i	−0.502467	+	1.43384i
$485$	−160.569			−0.331071
$486$		0			0
$487$			57.1525i			0.117356i	0.998277	+	0.0586781i	$0.0186886\pi$
$487$			57.1525i			0.117356i	−0.998277	+	0.0586781i	$0.981311\pi$
$488$	−421.511	+	436.970i	−0.863753	+	0.895430i
$489$		0			0
$490$	487.965	−	346.060i	0.995847	−	0.706244i
$491$	−48.6600	−	28.0939i	−0.0991040	−	0.0572177i	0.449629	−	0.893215i	$-0.351556\pi$
$491$	−48.6600	−	28.0939i	−0.0991040	−	0.0572177i	−0.548733	+	0.835998i	$0.684890\pi$
$492$		0			0
$493$	−53.7147	−	93.0366i	−0.108955	−	0.188715i
$494$	29.0420	−	63.2694i	0.0587895	−	0.128076i
$495$		0			0
$496$	505.170	+	76.6208i	1.01849	+	0.154477i
$497$	−25.9417	−	44.9324i	−0.0521967	−	0.0904073i
$498$		0			0
$499$	522.225	+	301.507i	1.04654	+	0.604222i	0.921679	−	0.387952i	$-0.126817\pi$
$499$	522.225	+	301.507i	1.04654	+	0.604222i	0.124863	+	0.992174i	$0.460151\pi$
$500$	294.853	−	55.6477i	0.589706	−	0.111295i
$501$		0			0
$502$	561.316	−	52.5052i	1.11816	−	0.104592i
$503$			549.354i			1.09216i	0.837734	+	0.546078i	$0.183880\pi$
$503$			549.354i			1.09216i	−0.837734	+	0.546078i	$0.816120\pi$
$504$		0			0
$505$	−158.413			−0.313688
$506$	−25.7902	−	275.714i	−0.0509687	−	0.544890i
$507$		0			0
$508$	−121.946	−	646.136i	−0.240050	−	1.27192i
$509$	119.464	−	206.918i	0.234704	−	0.406519i	−0.724483	−	0.689293i	$-0.757921\pi$
$509$	119.464	−	206.918i	0.234704	−	0.406519i	0.959187	+	0.282774i	$0.0912547\pi$
$510$		0			0
$511$	−30.7143	+	17.7329i	−0.0601062	+	0.0347023i
$512$	381.057	+	341.964i	0.744252	+	0.667899i
$513$		0			0
$514$	136.893	+	62.8366i	0.266328	+	0.122250i
$515$	104.484	−	60.3240i	0.202882	−	0.117134i
$516$		0			0
$517$	−97.1862	+	168.331i	−0.187981	+	0.325593i
$518$	39.8306	+	56.1636i	0.0768931	+	0.108424i
$519$		0			0
$520$	−60.9355	+	63.1703i	−0.117184	+	0.121481i
$521$	567.711			1.08966			0.544828	−	0.838548i	$-0.316595\pi$
$521$	567.711			1.08966			0.544828	+	0.838548i	$0.316595\pi$
$522$		0			0
$523$		−	941.999i		−	1.80114i	−0.434706	−	0.900572i	$-0.643148\pi$
$523$		−	941.999i		−	1.80114i	0.434706	−	0.900572i	$-0.356852\pi$
$524$	−537.979	−	188.527i	−1.02668	−	0.359784i
$525$		0			0
$526$	141.496	+	199.518i	0.269004	+	0.379312i
$527$	467.856	+	270.117i	0.887773	+	0.512556i
$528$		0			0
$529$	−233.056	−	403.664i	−0.440559	−	0.763071i
$530$	400.928	+	184.034i	0.756468	+	0.347235i
$531$		0			0
$532$	−30.0456	−	34.9463i	−0.0564766	−	0.0656885i
$533$	4.76372	+	8.25100i	0.00893755	+	0.0154803i
$534$		0			0
$535$	−975.428	−	563.163i	−1.82323	−	1.05264i
$536$	−70.9532	+	285.248i	−0.132375	+	0.532180i
$537$		0			0
$538$	−52.2387	−	558.467i	−0.0970980	−	1.03804i
$539$		−	849.430i		−	1.57594i
$540$		0			0
$541$	−242.245			−0.447772			−0.223886	−	0.974615i	$-0.571874\pi$
$541$	−242.245			−0.447772			−0.223886	+	0.974615i	$0.571874\pi$
$542$	162.186	−	15.1708i	0.299235	−	0.0279904i
$543$		0			0
$544$	243.401	+	483.542i	0.447428	+	0.888863i
$545$	−309.988	+	536.915i	−0.568786	+	0.985166i
$546$		0			0
$547$	−170.503	+	98.4402i	−0.311706	+	0.179964i	−0.647690	−	0.761904i	$-0.724265\pi$
$547$	−170.503	+	98.4402i	−0.311706	+	0.179964i	0.335983	+	0.941868i	$0.390931\pi$
$548$	−16.0729	−	18.6945i	−0.0293301	−	0.0341141i
$549$		0			0
$550$	−186.442	+	406.173i	−0.338986	+	0.738497i
$551$	107.273	−	61.9342i	0.194688	−	0.112403i
$552$		0			0
$553$	10.9757	−	19.0105i	0.0198476	−	0.0343770i
$554$	−733.673	+	520.313i	−1.32432	+	0.939194i
$555$		0			0
$556$	−449.700	−	157.591i	−0.808814	−	0.283437i
$557$	−958.121			−1.72015			−0.860073	−	0.510171i	$-0.829582\pi$
$557$	−958.121			−1.72015			−0.860073	+	0.510171i	$0.829582\pi$
$558$		0			0
$559$		−	69.9202i		−	0.125081i
$560$	21.1779	+	54.1076i	0.0378176	+	0.0966208i
$561$		0			0
$562$	−123.545	+	87.6166i	−0.219830	+	0.155901i
$563$	−165.774	−	95.7097i	−0.294448	−	0.169999i	0.345498	−	0.938419i	$-0.387710\pi$
$563$	−165.774	−	95.7097i	−0.294448	−	0.169999i	−0.639946	+	0.768420i	$0.721043\pi$
$564$		0			0
$565$	56.1001	+	97.1682i	0.0992922	+	0.171979i
$566$	310.279	−	675.957i	0.548196	−	1.19427i
$567$		0			0
$568$	−675.368	+	194.062i	−1.18903	+	0.341658i
$569$	−228.215	−	395.280i	−0.401081	−	0.694693i	0.592775	−	0.805368i	$-0.298032\pi$
$569$	−228.215	−	395.280i	−0.401081	−	0.694693i	−0.993857	+	0.110675i	$0.964699\pi$
$570$		0			0
$571$	−842.764	−	486.570i	−1.47594	−	0.852136i	−0.476312	−	0.879276i	$-0.658027\pi$
$571$	−842.764	−	486.570i	−1.47594	−	0.852136i	−0.999632	+	0.0271399i	$0.991360\pi$
$572$	23.1130	+	122.466i	0.0404073	+	0.214101i
$573$		0			0
$574$	6.27982	−	0.587411i	0.0109404	−	0.00102336i
$575$		−	101.496i		−	0.176515i
$576$		0			0
$577$	138.527			0.240081			0.120040	−	0.992769i	$-0.461698\pi$
$577$	138.527			0.240081			0.120040	+	0.992769i	$0.461698\pi$
$578$	−0.523773	−	5.59948i	−0.000906181	−	0.00968768i
$579$		0			0
$580$	−153.460	+	28.9626i	−0.264586	+	0.0499355i
$581$	22.5175	−	39.0015i	0.0387565	−	0.0671282i
$582$		0			0
$583$	542.478	−	313.200i	0.930494	−	0.537221i
$584$	132.654	+	461.658i	0.227147	+	0.790510i
$585$		0			0
$586$	241.365	+	110.792i	0.411886	+	0.189064i
$587$	−620.808	+	358.424i	−1.05759	+	0.610602i	−0.924766	−	0.380537i	$-0.875739\pi$
$587$	−620.808	+	358.424i	−1.05759	+	0.610602i	−0.132829	+	0.991139i	$0.542406\pi$
$588$		0			0
$589$	−311.451	+	539.449i	−0.528779	+	0.915872i
$590$	−171.641	−	242.024i	−0.290917	−	0.410210i
$591$		0			0
$592$	868.387	−	339.889i	1.46687	−	0.574137i
$593$	−542.129			−0.914214			−0.457107	−	0.889412i	$-0.651114\pi$
$593$	−542.129			−0.914214			−0.457107	+	0.889412i	$0.651114\pi$
$594$		0			0
$595$			61.4350i			0.103252i
$596$	−273.477	+	780.391i	−0.458853	+	1.30938i
$597$		0			0
$598$	−16.3729	−	23.0867i	−0.0273794	−	0.0386066i
$599$	245.527	+	141.755i	0.409895	+	0.236653i	0.690744	−	0.723099i	$-0.257283\pi$
$599$	245.527	+	141.755i	0.409895	+	0.236653i	−0.280850	+	0.959752i	$0.590616\pi$
$600$		0			0
$601$	377.424	+	653.717i	0.627993	+	1.08772i	0.987954	+	0.154748i	$0.0494567\pi$
$601$	377.424	+	653.717i	0.627993	+	1.08772i	−0.359961	+	0.932967i	$0.617210\pi$
$602$	−42.0676	−	19.3099i	−0.0698797	−	0.0320763i
$603$		0			0
$604$	−446.272	+	383.688i	−0.738860	+	0.635245i
$605$	565.126	+	978.827i	0.934093	+	1.61790i
$606$		0			0
$607$	77.2227	+	44.5845i	0.127220	+	0.0734506i	0.562260	−	0.826961i	$-0.309932\pi$
$607$	77.2227	+	44.5845i	0.127220	+	0.0734506i	−0.435039	+	0.900411i	$0.643266\pi$
$608$	−557.534	+	280.647i	−0.916997	+	0.461590i
$609$		0			0
$610$	86.9097	+	929.122i	0.142475	+	1.52315i
$611$			19.8664i			0.0325145i
$612$		0			0
$613$	−316.779			−0.516769			−0.258385	−	0.966042i	$-0.583190\pi$
$613$	−316.779			−0.516769			−0.258385	+	0.966042i	$0.583190\pi$
$614$	−670.103	+	62.6811i	−1.09137	+	0.102087i
$615$		0			0
$616$	80.0646	+	19.9154i	0.129975	+	0.0323302i
$617$	−534.934	+	926.533i	−0.866992	+	1.50167i	−0.00193565	+	0.999998i	$0.500616\pi$
$617$	−534.934	+	926.533i	−0.866992	+	1.50167i	−0.865056	+	0.501675i	$0.832717\pi$
$618$		0			0
$619$	578.542	−	334.021i	0.934640	−	0.539615i	0.0463638	−	0.998925i	$-0.485237\pi$
$619$	578.542	−	334.021i	0.934640	−	0.539615i	0.888276	+	0.459310i	$0.151903\pi$
$620$	595.498	−	511.988i	0.960481	−	0.825787i
$621$		0			0
$622$	293.077	−	638.483i	0.471185	−	1.02650i
$623$	14.1121	−	8.14762i	0.0226518	−	0.0130780i
$624$		0			0
$625$	390.580	−	676.505i	0.624929	−	1.08241i
$626$	311.367	−	220.818i	0.497391	−	0.352744i
$627$		0			0
$628$	−83.1804	+	237.363i	−0.132453	+	0.377967i
$629$	985.986			1.56755
$630$		0			0
$631$			150.631i			0.238718i	0.992851	+	0.119359i	$0.0380839\pi$
$631$			150.631i			0.238718i	−0.992851	+	0.119359i	$0.961916\pi$
$632$	−213.977	−	206.407i	−0.338571	−	0.326593i
$633$		0			0
$634$	−661.682	+	469.258i	−1.04366	+	0.740155i
$635$	−875.252	−	505.327i	−1.37835	−	0.795790i
$636$		0			0
$637$	−43.4092	−	75.1869i	−0.0681463	−	0.118033i
$638$	−92.5075	+	201.532i	−0.144996	+	0.315881i
$639$		0			0
$640$	780.385	−	101.453i	1.21935	−	0.158520i
$641$	−351.521	−	608.852i	−0.548395	−	0.949847i	−0.998385	−	0.0568139i	$-0.981906\pi$
$641$	−351.521	−	608.852i	−0.548395	−	0.949847i	0.449990	−	0.893034i	$-0.351427\pi$
$642$		0			0
$643$	742.057	+	428.427i	1.15405	+	0.666293i	0.949872	−	0.312639i	$-0.101213\pi$
$643$	742.057	+	428.427i	1.15405	+	0.666293i	0.204182	+	0.978933i	$0.434546\pi$
$644$	−18.4119	+	3.47488i	−0.0285898	+	0.00539577i
$645$		0			0
$646$	−657.094	+	61.4643i	−1.01717	+	0.0951459i
$647$		−	156.257i		−	0.241510i	−0.992682	−	0.120755i	$-0.961468\pi$
$647$		−	156.257i		−	0.241510i	0.992682	−	0.120755i	$-0.0385316\pi$
$648$		0			0
$649$	−421.306			−0.649162
$650$	4.25419	+	45.4802i	0.00654491	+	0.0699695i
$651$		0			0
$652$	−106.322	−	563.353i	−0.163070	−	0.864038i
$653$	441.773	−	765.173i	0.676528	−	1.17178i	−0.299492	−	0.954099i	$-0.596817\pi$
$653$	441.773	−	765.173i	0.676528	−	1.17178i	0.976020	−	0.217682i	$-0.0698495\pi$
$654$		0			0
$655$	−758.798	+	438.092i	−1.15847	+	0.668843i
$656$	12.8099	−	84.4574i	0.0195273	−	0.128746i
$657$		0			0
$658$	11.9526	+	5.48650i	0.0181651	+	0.00833815i
$659$	379.533	−	219.123i	0.575922	−	0.332509i	−0.183589	−	0.983003i	$-0.558772\pi$
$659$	379.533	−	219.123i	0.575922	−	0.332509i	0.759511	+	0.650494i	$0.225438\pi$
$660$		0			0
$661$	233.924	−	405.168i	0.353894	−	0.612963i	−0.633034	−	0.774124i	$-0.718191\pi$
$661$	233.924	−	405.168i	0.353894	−	0.612963i	0.986928	+	0.161161i	$0.0515239\pi$
$662$	513.143	+	723.562i	0.775140	+	1.09299i
$663$		0			0
$664$	−438.989	−	423.459i	−0.661128	−	0.637739i
$665$	−70.8359			−0.106520
$666$		0			0
$667$		−	50.3597i		−	0.0755018i
$668$	656.149	+	229.938i	0.982259	+	0.344218i
$669$		0			0
$670$	261.353	+	368.524i	0.390079	+	0.550035i
$671$	1147.52	+	662.524i	1.71017	+	0.987368i
$672$		0			0
$673$	273.302	+	473.372i	0.406094	+	0.703376i	0.994448	−	0.105227i	$-0.0335571\pi$
$673$	273.302	+	473.372i	0.406094	+	0.703376i	−0.588354	+	0.808604i	$0.700224\pi$
$674$	−924.240	−	424.246i	−1.37128	−	0.629444i
$675$		0			0
$676$	−432.405	−	502.934i	−0.639652	−	0.743986i
$677$	−227.606	−	394.225i	−0.336198	−	0.582312i	0.647516	−	0.762052i	$-0.275808\pi$
$677$	−227.606	−	394.225i	−0.336198	−	0.582312i	−0.983714	+	0.179740i	$0.942475\pi$
$678$		0			0
$679$	13.3600	+	7.71341i	0.0196760	+	0.0113600i
$680$	807.454	+	200.848i	1.18743	+	0.295364i
$681$		0			0
$682$	−103.854	−	1110.27i	−0.152279	−	1.62797i
$683$		−	123.214i		−	0.180400i	−0.995924	−	0.0902002i	$-0.971249\pi$
$683$		−	123.214i		−	0.180400i	0.995924	−	0.0902002i	$-0.0287507\pi$
$684$		0			0
$685$	−37.8937			−0.0553193
$686$	−114.860	+	10.7439i	−0.167434	+	0.0156617i
$687$		0			0
$688$	−391.325	+	489.774i	−0.568786	+	0.711881i
$689$	32.0115	−	55.4455i	0.0464607	−	0.0804724i
$690$		0			0
$691$	−163.326	+	94.2965i	−0.236362	+	0.136464i	−0.613504	−	0.789692i	$-0.710240\pi$
$691$	−163.326	+	94.2965i	−0.236362	+	0.136464i	0.377141	+	0.926156i	$0.376907\pi$
$692$	−656.139	−	763.162i	−0.948177	−	1.10283i
$693$		0			0
$694$	474.746	−	1034.26i	0.684071	−	1.49028i
$695$	−634.285	+	366.204i	−0.912640	+	0.526913i
$696$		0			0
$697$	45.1599	−	78.2192i	0.0647918	−	0.112223i
$698$	675.073	−	478.754i	0.967153	−	0.685895i
$699$		0			0
$700$	28.5381	+	10.0007i	0.0407686	+	0.0142868i
$701$	810.064			1.15558			0.577792	−	0.816184i	$-0.303915\pi$
$701$	810.064			1.15558			0.577792	+	0.816184i	$0.303915\pi$
$702$		0			0
$703$			1136.86i			1.61716i
$704$	523.506	−	987.199i	0.743616	−	1.40227i
$705$		0			0
$706$	203.294	−	144.174i	0.287952	−	0.204212i
$707$	13.1806	+	7.60980i	0.0186429	+	0.0107635i
$708$		0			0
$709$	−651.819	−	1128.98i	−0.919349	−	1.59236i	−0.800406	−	0.599459i	$-0.795382\pi$
$709$	−651.819	−	1128.98i	−0.919349	−	1.59236i	−0.118944	−	0.992901i	$-0.537951\pi$
$710$	−450.568	+	981.583i	−0.634602	+	1.38251i
$711$		0			0
$712$	−60.9497	−	212.115i	−0.0856035	−	0.297914i
$713$	126.623	+	219.317i	0.177592	+	0.307598i
$714$		0			0
$715$	165.891	+	95.7772i	0.232015	+	0.133954i
$716$	−71.2197	−	377.362i	−0.0994688	−	0.527042i
$717$		0			0
$718$	−603.756	+	56.4751i	−0.840886	+	0.0786561i
$719$			788.981i			1.09733i	0.836042	+	0.548666i	$0.184864\pi$
$719$			788.981i			1.09733i	−0.836042	+	0.548666i	$0.815136\pi$
$720$		0			0
$721$	−11.5913			−0.0160768
$722$	−3.62757	−	38.7812i	−0.00502434	−	0.0537135i
$723$		0			0
$724$	1292.22	−	243.881i	1.78483	−	0.336852i
$725$	−40.6380	+	70.3870i	−0.0560524	+	0.0970856i
$726$		0			0
$727$	−232.676	+	134.335i	−0.320049	+	0.184780i	−0.651414	−	0.758722i	$-0.725824\pi$
$727$	−232.676	+	134.335i	−0.320049	+	0.184780i	0.331365	+	0.943502i	$0.392491\pi$
$728$	8.10464	−	2.32881i	0.0111327	−	0.00319891i
$729$		0			0
$730$	670.977	+	307.992i	0.919146	+	0.421907i
$731$	−574.038	+	331.421i	−0.785277	+	0.453380i
$732$		0			0
$733$	−36.8343	+	63.7989i	−0.0502514	+	0.0870380i	−0.890057	−	0.455849i	$-0.849336\pi$
$733$	−36.8343	+	63.7989i	−0.0502514	+	0.0870380i	0.839806	+	0.542887i	$0.182669\pi$
$734$	−822.370	−	1159.59i	−1.12040	−	1.57982i
$735$		0			0
$736$	−14.5222	+	253.351i	−0.0197313	+	0.344227i
$737$	641.512			0.870437
$738$		0			0
$739$			448.249i			0.606562i	0.952901	+	0.303281i	$0.0980820\pi$
$739$			448.249i			0.606562i	−0.952901	+	0.303281i	$0.901918\pi$
$740$	474.022	−	1352.67i	0.640571	−	1.82793i
$741$		0			0
$742$	−24.5182	−	34.5721i	−0.0330434	−	0.0465932i
$743$	−656.602	−	379.089i	−0.883718	−	0.510215i	−0.0118352	−	0.999930i	$-0.503767\pi$
$743$	−656.602	−	379.089i	−0.883718	−	0.510215i	−0.871882	+	0.489715i	$0.837101\pi$
$744$		0			0
$745$	635.496	+	1100.71i	0.853015	+	1.47746i
$746$	606.153	+	278.237i	0.812538	+	0.372972i
$747$		0			0
$748$	895.874	−	770.240i	1.19769	−	1.02973i
$749$	54.1063	+	93.7149i	0.0722381	+	0.125120i
$750$		0			0
$751$	1141.58	+	659.091i	1.52008	+	0.877618i	0.999720	+	0.0236697i	$0.00753501\pi$
$751$	1141.58	+	659.091i	1.52008	+	0.877618i	0.520358	+	0.853948i	$0.325798\pi$
$752$	111.187	−	139.159i	0.147855	−	0.185052i
$753$		0			0
$754$	2.11081	+	22.5660i	0.00279949	+	0.0299284i
$755$			904.589i			1.19813i
$756$		0			0
$757$	587.874			0.776583			0.388292	−	0.921537i	$-0.373065\pi$
$757$	587.874			0.776583			0.388292	+	0.921537i	$0.373065\pi$
$758$	1319.61	−	123.436i	1.74091	−	0.162844i
$759$		0			0
$760$	−231.582	+	931.012i	−0.304713	+	1.22502i
$761$	188.496	−	326.485i	0.247695	−	0.429021i	−0.715191	−	0.698929i	$-0.753660\pi$
$761$	188.496	−	326.485i	0.247695	−	0.429021i	0.962886	+	0.269908i	$0.0869934\pi$
$762$		0			0
$763$	51.5845	−	29.7823i	0.0676075	−	0.0390332i
$764$	−1.23252	+	1.05967i	−0.00161324	+	0.00138701i
$765$		0			0
$766$	−67.3435	+	146.711i	−0.0879158	+	0.191529i
$767$	−37.2917	+	21.5304i	−0.0486202	+	0.0280709i
$768$		0			0
$769$	643.939	−	1115.34i	0.837372	−	1.45037i	−0.0547122	−	0.998502i	$-0.517424\pi$
$769$	643.939	−	1115.34i	0.837372	−	1.45037i	0.892084	−	0.451869i	$-0.149243\pi$
$770$	103.439	−	73.3576i	0.134336	−	0.0952697i
$771$		0			0
$772$	82.6075	−	235.728i	0.107005	−	0.305348i
$773$	−778.578			−1.00722			−0.503608	−	0.863932i	$-0.667994\pi$
$773$	−778.578			−1.00722			−0.503608	+	0.863932i	$0.667994\pi$
$774$		0			0
$775$		−	408.715i		−	0.527375i
$776$	145.057	−	150.376i	0.186929	−	0.193784i
$777$		0			0
$778$	−1128.94	+	800.634i	−1.45108	+	1.02909i
$779$	90.1884	+	52.0703i	0.115775	+	0.0668425i
$780$		0			0
$781$	766.801	+	1328.14i	0.981819	+	1.70056i
$782$	−111.932	+	243.850i	−0.143136	+	0.311829i
$783$		0			0
$784$	−116.730	+	769.615i	−0.148890	+	0.981652i
$785$	193.292	+	334.791i	0.246232	+	0.426486i
$786$		0			0
$787$	−390.283	−	225.330i	−0.495913	−	0.286315i	0.231111	−	0.972927i	$-0.425764\pi$
$787$	−390.283	−	225.330i	−0.495913	−	0.286315i	−0.727024	+	0.686612i	$0.759097\pi$
$788$	−817.020	+	154.197i	−1.03683	+	0.195681i
$789$		0			0
$790$	−454.975	+	42.5582i	−0.575918	+	0.0538711i
$791$		−	10.7797i		−	0.0136280i
$792$		0			0
$793$	135.430			0.170782
$794$	122.510	+	1309.71i	0.154294	+	1.64951i
$795$		0			0
$796$	221.901	+	1175.76i	0.278770	+	1.47708i
$797$	182.891	−	316.776i	0.229474	−	0.397461i	−0.728178	−	0.685388i	$-0.759633\pi$
$797$	182.891	−	316.776i	0.229474	−	0.397461i	0.957652	+	0.287927i	$0.0929661\pi$
$798$		0			0
$799$	163.101	−	94.1662i	0.204131	−	0.117855i
$800$	224.741	−	342.387i	0.280926	−	0.427984i
$801$		0			0
$802$	−1077.63	−	494.653i	−1.34367	−	0.616775i
$803$	907.869	−	524.158i	1.13060	−	0.652750i
$804$		0			0
$805$	−14.3994	+	24.9406i	−0.0178875	+	0.0309821i
$806$	−65.9319	−	92.9679i	−0.0818013	−	0.115345i
$807$		0			0
$808$	143.108	−	148.357i	0.177114	−	0.183610i
$809$	−1167.70			−1.44339			−0.721695	−	0.692212i	$-0.756636\pi$
$809$	−1167.70			−1.44339			−0.721695	+	0.692212i	$0.756636\pi$
$810$		0			0
$811$			810.121i			0.998916i	0.866338	+	0.499458i	$0.166467\pi$
$811$			810.121i			0.998916i	−0.866338	+	0.499458i	$0.833533\pi$
$812$	14.1598	+	4.96209i	0.0174382	+	0.00611095i
$813$		0			0
$814$	−1177.34	−	1660.11i	−1.44636	−	2.03945i
$815$	−763.114	−	440.584i	−0.936336	−	0.540594i
$816$		0			0
$817$	−382.135	−	661.878i	−0.467730	−	0.810132i
$818$	−587.445	−	269.650i	−0.718148	−	0.329645i
$819$		0			0
$820$	−85.5973	−	99.5591i	−0.104387	−	0.121414i
$821$	280.513	+	485.862i	0.341672	+	0.591793i	0.984743	−	0.174013i	$-0.0556734\pi$
$821$	280.513	+	485.862i	0.341672	+	0.591793i	−0.643071	+	0.765806i	$0.722340\pi$
$822$		0			0
$823$	−1016.04	−	586.612i	−1.23456	−	0.712773i	−0.266583	−	0.963812i	$-0.585895\pi$
$823$	−1016.04	−	586.612i	−1.23456	−	0.712773i	−0.967977	+	0.251039i	$0.919228\pi$
$824$	−37.8952	+	152.348i	−0.0459894	+	0.184888i
$825$		0			0
$826$	2.65490	+	28.3826i	0.00321416	+	0.0343615i
$827$		−	267.739i		−	0.323747i	−0.986811	−	0.161874i	$-0.948246\pi$
$827$		−	267.739i		−	0.323747i	0.986811	−	0.161874i	$-0.0517537\pi$
$828$		0			0
$829$	−432.474			−0.521682			−0.260841	−	0.965382i	$-0.584000\pi$
$829$	−432.474			−0.521682			−0.260841	+	0.965382i	$0.584000\pi$
$830$	−933.415	+	87.3113i	−1.12460	+	0.105194i
$831$		0			0
$832$	−4.11180	−	114.135i	−0.00494207	−	0.137181i
$833$	−411.518	+	712.769i	−0.494019	+	0.855665i
$834$		0			0
$835$	925.472	−	534.321i	1.10835	−	0.639906i
$836$	888.103	+	1032.96i	1.06232	+	1.23560i
$837$		0			0
$838$	−214.595	+	467.506i	−0.256080	+	0.557883i
$839$	459.103	−	265.063i	0.547202	−	0.315927i	−0.200790	−	0.979634i	$-0.564351\pi$
$839$	459.103	−	265.063i	0.547202	−	0.315927i	0.747993	+	0.663707i	$0.231018\pi$
$840$		0			0
$841$	400.337	−	693.403i	0.476024	−	0.824499i
$842$	−137.006	+	97.1632i	−0.162715	+	0.115396i
$843$		0			0
$844$	617.849	+	216.516i	0.732049	+	0.256536i
$845$	−1019.44			−1.20644
$846$		0			0
$847$		−	108.590i		−	0.128205i
$848$	−534.546	+	209.222i	−0.630361	+	0.246725i
$849$		0			0
$850$	353.222	−	250.502i	0.415556	−	0.294708i
$851$	400.278	+	231.100i	0.470361	+	0.271563i
$852$		0			0
$853$	88.3868	+	153.090i	0.103619	+	0.179473i	0.913173	−	0.407572i	$-0.133624\pi$
$853$	88.3868	+	153.090i	0.103619	+	0.179473i	−0.809554	+	0.587045i	$0.800291\pi$
$854$	37.4018	−	81.4816i	0.0437960	−	0.0954118i
$855$		0			0
$856$	1408.60	−	404.752i	1.64557	−	0.472841i
$857$	194.859	+	337.505i	0.227373	+	0.393821i	0.957029	−	0.289993i	$-0.0936531\pi$
$857$	194.859	+	337.505i	0.227373	+	0.393821i	−0.729656	+	0.683815i	$0.760320\pi$
$858$		0			0
$859$	−503.279	−	290.568i	−0.585889	−	0.338263i	0.177581	−	0.984106i	$-0.443173\pi$
$859$	−503.279	−	290.568i	−0.585889	−	0.338263i	−0.763470	+	0.645843i	$0.776506\pi$
$860$	178.700	+	946.852i	0.207791	+	1.10099i
$861$		0			0
$862$	−287.441	+	26.8871i	−0.333458	+	0.0311915i
$863$			827.326i			0.958663i	0.877634	+	0.479331i	$0.159121\pi$
$863$			827.326i			0.958663i	−0.877634	+	0.479331i	$0.840879\pi$
$864$		0			0
$865$	−1546.92			−1.78835
$866$	73.6409	+	787.270i	0.0850357	+	0.909088i
$867$		0			0
$868$	−74.1426	+	13.9930i	−0.0854178	+	0.0161209i
$869$	−324.426	+	561.923i	−0.373333	+	0.646632i
$870$		0			0
$871$	56.7831	−	32.7837i	0.0651930	−	0.0376392i
$872$	−222.792	−	775.354i	−0.255496	−	0.889167i
$873$		0			0
$874$	−281.165	−	129.060i	−0.321699	−	0.147666i
$875$	−38.3732	+	22.1548i	−0.0438551	+	0.0253198i
$876$		0			0
$877$	−279.815	+	484.653i	−0.319059	+	0.552626i	−0.980292	−	0.197554i	$-0.936700\pi$
$877$	−279.815	+	484.653i	−0.319059	+	0.552626i	0.661233	+	0.750181i	$0.270033\pi$
$878$	−260.211	−	366.913i	−0.296368	−	0.417897i
$879$		0			0
$880$	−625.987	−	1599.34i	−0.711349	−	1.81744i
$881$	957.127			1.08641			0.543205	−	0.839600i	$-0.317211\pi$
$881$	957.127			1.08641			0.543205	+	0.839600i	$0.317211\pi$
$882$		0			0
$883$		−	625.252i		−	0.708100i	−0.935227	−	0.354050i	$-0.884804\pi$
$883$		−	625.252i		−	0.708100i	0.935227	−	0.354050i	$-0.115196\pi$
$884$	39.9356	−	113.960i	0.0451760	−	0.128914i
$885$		0			0
$886$	493.211	+	695.457i	0.556671	+	0.784940i
$887$	−921.187	−	531.847i	−1.03854	−	0.599602i	−0.119122	−	0.992880i	$-0.538008\pi$
$887$	−921.187	−	531.847i	−1.03854	−	0.599602i	−0.919420	+	0.393277i	$0.871341\pi$
$888$		0			0
$889$	48.5496	+	84.0904i	0.0546115	+	0.0945899i
$890$	−308.289	−	141.511i	−0.346393	−	0.159002i
$891$		0			0
$892$	−1158.15	+	995.735i	−1.29837	+	1.11629i
$893$	108.576	+	188.059i	0.121585	+	0.210592i
$894$		0			0
$895$	−511.172	−	295.125i	−0.571142	−	0.329749i
$896$	−69.8047	−	29.0467i	−0.0779071	−	0.0324182i
$897$		0			0
$898$	75.7625	+	809.951i	0.0843681	+	0.901950i
$899$		−	202.793i		−	0.225577i
$900$		0			0
$901$	−606.935			−0.673624
$902$	−185.622	+	17.3630i	−0.205790	+	0.0192495i
$903$		0			0
$904$	−141.680	−	35.2418i	−0.156726	−	0.0389843i
$905$	1010.61	−	1750.43i	1.11670	−	1.93418i
$906$		0			0
$907$	207.207	−	119.631i	0.228453	−	0.131898i	−0.381405	−	0.924408i	$-0.624560\pi$
$907$	207.207	−	119.631i	0.228453	−	0.131898i	0.609858	+	0.792510i	$0.291226\pi$
$908$	−180.535	+	155.217i	−0.198827	+	0.170944i
$909$		0			0
$910$	5.40696	−	11.7793i	0.00594172	−	0.0129443i
$911$	−175.804	+	101.501i	−0.192980	+	0.111417i	−0.593377	−	0.804925i	$-0.702206\pi$
$911$	−175.804	+	101.501i	−0.192980	+	0.111417i	0.400397	+	0.916342i	$0.368872\pi$
$912$		0			0
$913$	−665.585	+	1152.83i	−0.729009	+	1.26268i
$914$	520.740	−	369.303i	0.569737	−	0.404052i
$915$		0			0
$916$	−170.482	+	486.486i	−0.186116	+	0.531099i
$917$	84.1801			0.0917994
$918$		0			0
$919$		−	878.708i		−	0.956156i	−0.878317	−	0.478078i	$-0.841334\pi$
$919$		−	878.708i		−	0.956156i	0.878317	−	0.478078i	$-0.158666\pi$
$920$	280.724	+	270.793i	0.305135	+	0.294340i
$921$		0			0
$922$	958.892	−	680.036i	1.04001	−	0.737566i
$923$	135.746	+	78.3730i	0.147070	+	0.0849111i
$924$		0			0
$925$	−372.975	−	646.011i	−0.403216	−	0.698391i
$926$	−221.670	+	482.920i	−0.239385	+	0.521512i
$927$		0			0
$928$	111.510	−	169.883i	0.120162	−	0.183064i
$929$	−300.259	−	520.064i	−0.323207	−	0.559810i	0.657941	−	0.753069i	$-0.271428\pi$
$929$	−300.259	−	520.064i	−0.323207	−	0.559810i	−0.981148	+	0.193259i	$0.938094\pi$
$930$		0			0
$931$	−821.838	−	474.489i	−0.882748	−	0.509655i
$932$	58.9350	−	11.1228i	0.0632350	−	0.0119344i
$933$		0			0
$934$	1582.29	−	148.007i	1.69410	−	0.158465i
$935$		−	1815.93i		−	1.94217i
$936$		0			0
$937$	−184.325			−0.196718			−0.0983589	−	0.995151i	$-0.531359\pi$
$937$	−184.325			−0.196718			−0.0983589	+	0.995151i	$0.531359\pi$
$938$	−4.04255	−	43.2175i	−0.00430975	−	0.0460741i
$939$		0			0
$940$	−50.7738	−	269.028i	−0.0540147	−	0.286200i
$941$	377.587	−	653.999i	0.401261	−	0.695005i	−0.592617	−	0.805484i	$-0.701905\pi$
$941$	377.587	−	653.999i	0.401261	−	0.695005i	0.993878	+	0.110479i	$0.0352386\pi$
$942$		0			0
$943$	36.6668	−	21.1696i	0.0388831	−	0.0224492i
$944$	381.719	+	57.8966i	0.404363	+	0.0613311i
$945$		0			0
$946$	1243.46	+	570.773i	1.31444	+	0.603354i
$947$	769.965	−	444.539i	0.813057	−	0.469419i	−0.0349595	−	0.999389i	$-0.511130\pi$
$947$	769.965	−	444.539i	0.813057	−	0.469419i	0.848016	+	0.529970i	$0.177797\pi$
$948$		0			0
$949$	53.5731	−	92.7913i	0.0564521	−	0.0977779i
$950$	288.834	+	407.273i	0.304036	+	0.428708i
$951$		0			0
$952$	−57.5351	−	55.4997i	−0.0604360	−	0.0582980i
$953$	−15.5920			−0.0163610			−0.00818050	−	0.999967i	$-0.502604\pi$
$953$	−15.5920			−0.0163610			−0.00818050	+	0.999967i	$0.502604\pi$
$954$		0			0
$955$			2.49830i			0.00261602i
$956$	−1374.12	−	481.539i	−1.43736	−	0.503702i
$957$		0			0
$958$	765.449	+	1079.33i	0.799008	+	1.12665i
$959$	3.15291	+	1.82033i	0.00328770	+	0.00189816i
$960$		0			0
$961$	29.3970	+	50.9172i	0.0305900	+	0.0529835i
$962$	−189.050	−	86.7777i	−0.196517	−	0.0902056i
$963$		0			0
$964$	211.350	+	245.824i	0.219243	+	0.255004i
$965$	−191.961	−	332.486i	−0.198923	−	0.344545i
$966$		0			0
$967$	847.921	+	489.548i	0.876858	+	0.506254i	0.869621	−	0.493720i	$-0.164363\pi$
$967$	847.921	+	489.548i	0.876858	+	0.506254i	0.00723669	+	0.999974i	$0.497696\pi$
$968$	−1427.22	−	355.009i	−1.47440	−	0.366745i
$969$		0			0
$970$	−29.9086	−	319.743i	−0.0308336	−	0.329632i
$971$			67.3838i			0.0693963i	0.999398	+	0.0346982i	$0.0110470\pi$
$971$			67.3838i			0.0693963i	−0.999398	+	0.0346982i	$0.988953\pi$
$972$		0			0
$973$	70.3667			0.0723193
$974$	−113.808	+	10.6456i	−0.116846	+	0.0109297i
$975$		0			0
$976$	−948.655	−	757.966i	−0.971983	−	0.776604i
$977$	−353.710	+	612.644i	−0.362037	+	0.627067i	−0.988296	−	0.152549i	$-0.951252\pi$
$977$	−353.710	+	612.644i	−0.362037	+	0.627067i	0.626259	+	0.779615i	$0.284585\pi$
$978$		0			0
$979$	−417.133	+	240.832i	−0.426081	+	0.245998i
$980$	780.002	+	907.229i	0.795921	+	0.925744i
$981$		0			0
$982$	46.8799	−	102.130i	0.0477392	−	0.104002i
$983$	338.829	−	195.623i	0.344689	−	0.199006i	−0.317655	−	0.948206i	$-0.602895\pi$
$983$	338.829	−	195.623i	0.344689	−	0.199006i	0.662343	+	0.749200i	$0.269562\pi$
$984$		0			0
$985$	−638.971	+	1106.73i	−0.648701	+	1.12358i
$986$	175.259	−	124.292i	0.177748	−	0.126057i
$987$		0			0
$988$	131.398	+	46.0466i	0.132994	+	0.0466059i
$989$	−310.720			−0.314176
$990$		0			0
$991$		−	104.988i		−	0.105941i	−0.998596	−	0.0529706i	$-0.983131\pi$
$991$		−	104.988i		−	0.105941i	0.998596	−	0.0529706i	$-0.0168690\pi$
$992$	−58.4795	+	1020.22i	−0.0589512	+	1.02845i
$993$		0			0
$994$	84.6422	−	60.0274i	0.0851531	−	0.0603897i
$995$	1592.67	+	919.530i	1.60068	+	0.924151i
$996$		0			0
$997$	−39.0028	−	67.5547i	−0.0391201	−	0.0677580i	0.845802	−	0.533496i	$-0.179122\pi$
$997$	−39.0028	−	67.5547i	−0.0391201	−	0.0677580i	−0.884923	+	0.465738i	$0.845789\pi$
$998$	−503.120	+	1096.07i	−0.504128	+	1.09827i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.f.c.91.5		16
3.2	odd	2		36.3.f.c.31.4	yes	16
4.3	odd	2	inner	108.3.f.c.91.6		16
8.3	odd	2		1728.3.o.g.1279.7		16
8.5	even	2		1728.3.o.g.1279.8		16
9.2	odd	6		36.3.f.c.7.3	✓	16
9.4	even	3		324.3.d.g.163.1		8
9.5	odd	6		324.3.d.i.163.8		8
9.7	even	3	inner	108.3.f.c.19.6		16
12.11	even	2		36.3.f.c.31.3	yes	16
24.5	odd	2		576.3.o.g.319.7		16
24.11	even	2		576.3.o.g.319.2		16
36.7	odd	6	inner	108.3.f.c.19.5		16
36.11	even	6		36.3.f.c.7.4	yes	16
36.23	even	6		324.3.d.i.163.7		8
36.31	odd	6		324.3.d.g.163.2		8
72.11	even	6		576.3.o.g.511.7		16
72.29	odd	6		576.3.o.g.511.2		16
72.43	odd	6		1728.3.o.g.127.8		16
72.61	even	6		1728.3.o.g.127.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.3	✓	16	9.2	odd	6
36.3.f.c.7.4	yes	16	36.11	even	6
36.3.f.c.31.3	yes	16	12.11	even	2
36.3.f.c.31.4	yes	16	3.2	odd	2
108.3.f.c.19.5		16	36.7	odd	6	inner
108.3.f.c.19.6		16	9.7	even	3	inner
108.3.f.c.91.5		16	1.1	even	1	trivial
108.3.f.c.91.6		16	4.3	odd	2	inner
324.3.d.g.163.1		8	9.4	even	3
324.3.d.g.163.2		8	36.31	odd	6
324.3.d.i.163.7		8	36.23	even	6
324.3.d.i.163.8		8	9.5	odd	6
576.3.o.g.319.2		16	24.11	even	2
576.3.o.g.319.7		16	24.5	odd	2
576.3.o.g.511.2		16	72.29	odd	6
576.3.o.g.511.7		16	72.11	even	6
1728.3.o.g.127.7		16	72.61	even	6
1728.3.o.g.127.8		16	72.43	odd	6
1728.3.o.g.1279.7		16	8.3	odd	2
1728.3.o.g.1279.8		16	8.5	even	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.186266 + 1.99131i) q^{2} +(-3.93061 + 0.741826i) q^{4} +(-3.07403 + 5.32438i) q^{5} +(0.511543 - 0.295340i) q^{7} +(-2.20934 - 7.68888i) q^{8} +O(q^{10})\)	\(q+(0.186266 + 1.99131i) q^{2} +(-3.93061 + 0.741826i) q^{4} +(-3.07403 + 5.32438i) q^{5} +(0.511543 - 0.295340i) q^{7} +(-2.20934 - 7.68888i) q^{8} +(-11.1751 - 5.12959i) q^{10} +(-15.1205 + 8.72982i) q^{11} +(-0.892255 + 1.54543i) q^{13} +(0.683395 + 0.963628i) q^{14} +(14.8994 - 5.83166i) q^{16} +16.9171 q^{17} +19.5058i q^{19} +(8.13306 - 23.2084i) q^{20} +(-20.2002 - 28.4835i) q^{22} +(6.86778 + 3.96511i) q^{23} +(-6.39933 - 11.0840i) q^{25} +(-3.24362 - 1.48889i) q^{26} +(-1.79159 + 1.54034i) q^{28} +(-3.17517 - 5.49956i) q^{29} +(27.6558 + 15.9671i) q^{31} +(14.3879 + 28.5830i) q^{32} +(3.15108 + 33.6871i) q^{34} +3.63153i q^{35} +58.2834 q^{37} +(-38.8420 + 3.63326i) q^{38} +(47.7301 + 11.8725i) q^{40} +(2.66948 - 4.62368i) q^{41} +(-33.9324 + 19.5909i) q^{43} +(52.9567 - 45.5303i) q^{44} +(-6.61653 + 14.4144i) q^{46} +(9.64117 - 5.56633i) q^{47} +(-24.3255 + 42.1331i) q^{49} +(20.8796 - 14.8076i) q^{50} +(2.36067 - 6.73638i) q^{52} -35.8770 q^{53} -107.343i q^{55} +(-3.40100 - 3.28069i) q^{56} +(10.3599 - 7.34713i) q^{58} +(20.8974 + 12.0651i) q^{59} +(-37.9460 - 65.7244i) q^{61} +(-26.6441 + 58.0454i) q^{62} +(-54.2376 + 33.9747i) q^{64} +(-5.48564 - 9.50141i) q^{65} +(-31.8200 - 18.3713i) q^{67} +(-66.4945 + 12.5495i) q^{68} +(-7.23150 + 0.676431i) q^{70} -87.8370i q^{71} -60.0423 q^{73} +(10.8562 + 116.060i) q^{74} +(-14.4699 - 76.6696i) q^{76} +(-5.15652 + 8.93136i) q^{77} +(32.1841 - 18.5815i) q^{79} +(-14.7512 + 97.2567i) q^{80} +(9.70439 + 4.45452i) q^{82} +(66.0281 - 38.1214i) q^{83} +(-52.0037 + 90.0730i) q^{85} +(-45.3319 - 63.9207i) q^{86} +(100.529 + 96.9724i) q^{88} +27.5873 q^{89} +1.05407i q^{91} +(-29.9360 - 10.4906i) q^{92} +(12.8801 + 18.1617i) q^{94} +(-103.856 - 59.9614i) q^{95} +(13.0585 + 22.6180i) q^{97} +(-88.4309 - 40.5917i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8	\( 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8} + 20 q^{10} - 46 q^{13} + 12 q^{14} - 17 q^{16} - 12 q^{17} - 36 q^{20} + 33 q^{22} - 30 q^{25} - 72 q^{26} + 12 q^{28} - 42 q^{29} - 87 q^{32} + 11 q^{34} + 56 q^{37} + 99 q^{38} + 68 q^{40} - 84 q^{41} + 222 q^{44} - 264 q^{46} + 58 q^{49} + 219 q^{50} + 110 q^{52} + 72 q^{53} - 270 q^{56} - 16 q^{58} - 34 q^{61} - 516 q^{62} - 254 q^{64} + 30 q^{65} - 375 q^{68} + 150 q^{70} + 116 q^{73} + 372 q^{74} - 15 q^{76} + 330 q^{77} + 720 q^{80} + 254 q^{82} - 140 q^{85} + 273 q^{86} + 75 q^{88} + 384 q^{89} - 258 q^{92} + 36 q^{94} - 148 q^{97} - 1170 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8 + 20 * q^10 - 46 * q^13 + 12 * q^14 - 17 * q^16 - 12 * q^17 - 36 * q^20 + 33 * q^22 - 30 * q^25 - 72 * q^26 + 12 * q^28 - 42 * q^29 - 87 * q^32 + 11 * q^34 + 56 * q^37 + 99 * q^38 + 68 * q^40 - 84 * q^41 + 222 * q^44 - 264 * q^46 + 58 * q^49 + 219 * q^50 + 110 * q^52 + 72 * q^53 - 270 * q^56 - 16 * q^58 - 34 * q^61 - 516 * q^62 - 254 * q^64 + 30 * q^65 - 375 * q^68 + 150 * q^70 + 116 * q^73 + 372 * q^74 - 15 * q^76 + 330 * q^77 + 720 * q^80 + 254 * q^82 - 140 * q^85 + 273 * q^86 + 75 * q^88 + 384 * q^89 - 258 * q^92 + 36 * q^94 - 148 * q^97 - 1170 * q^98

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