LMFDB - Embedded newform 108.3.f.c.19.6

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			19.6
Root			$1.63139 - 1.15696i$ of defining polynomial
Character	$\chi$	$=$	108.19
Dual form			108.3.f.c.91.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63139 - 1.15696i) q^{2} +(1.32286 - 3.77492i) q^{4} +(-3.07403 - 5.32438i) q^{5} +(-0.511543 - 0.295340i) q^{7} +(-2.20934 - 7.68888i) q^{8} +O(q^{10})$	\(q+(1.63139 - 1.15696i) q^{2} +(1.32286 - 3.77492i) q^{4} +(-3.07403 - 5.32438i) q^{5} +(-0.511543 - 0.295340i) q^{7} +(-2.20934 - 7.68888i) q^{8} +(-11.1751 - 5.12959i) q^{10} +(15.1205 + 8.72982i) q^{11} +(-0.892255 - 1.54543i) q^{13} +(-1.17622 + 0.110024i) q^{14} +(-12.5001 - 9.98742i) q^{16} +16.9171 q^{17} +19.5058i q^{19} +(-24.1656 + 4.56079i) q^{20} +(34.7675 - 3.25214i) q^{22} +(-6.86778 + 3.96511i) q^{23} +(-6.39933 + 11.0840i) q^{25} +(-3.24362 - 1.48889i) q^{26} +(-1.79159 + 1.54034i) q^{28} +(-3.17517 + 5.49956i) q^{29} +(-27.6558 + 15.9671i) q^{31} +(-31.9476 - 1.83125i) q^{32} +(27.5984 - 19.5725i) q^{34} +3.63153i q^{35} +58.2834 q^{37} +(22.5675 + 31.8215i) q^{38} +(-34.1469 + 35.3992i) q^{40} +(2.66948 + 4.62368i) q^{41} +(33.9324 + 19.5909i) q^{43} +(52.9567 - 45.5303i) q^{44} +(-6.61653 + 14.4144i) q^{46} +(-9.64117 - 5.56633i) q^{47} +(-24.3255 - 42.1331i) q^{49} +(2.38396 + 25.4861i) q^{50} +(-7.01421 + 1.32380i) q^{52} -35.8770 q^{53} -107.343i q^{55} +(-1.14066 + 4.58570i) q^{56} +(1.18285 + 12.6455i) q^{58} +(-20.8974 + 12.0651i) q^{59} +(-37.9460 + 65.7244i) q^{61} +(-26.6441 + 58.0454i) q^{62} +(-54.2376 + 33.9747i) q^{64} +(-5.48564 + 9.50141i) q^{65} +(31.8200 - 18.3713i) q^{67} +(22.3790 - 63.8607i) q^{68} +(4.20156 + 5.92445i) q^{70} -87.8370i q^{71} -60.0423 q^{73} +(95.0830 - 67.4319i) q^{74} +(73.6328 + 25.8035i) q^{76} +(-5.15652 - 8.93136i) q^{77} +(-32.1841 - 18.5815i) q^{79} +(-14.7512 + 97.2567i) q^{80} +(9.70439 + 4.45452i) q^{82} +(-66.0281 - 38.1214i) q^{83} +(-52.0037 - 90.0730i) q^{85} +(78.0229 - 7.29823i) q^{86} +(33.7161 - 135.547i) q^{88} +27.5873 q^{89} +1.05407i q^{91} +(5.88285 + 31.1706i) q^{92} +(-22.1686 + 2.07364i) q^{94} +(103.856 - 59.9614i) q^{95} +(13.0585 - 22.6180i) q^{97} +(-88.4309 - 40.5917i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	1.63139	−	1.15696i	0.815695	−	0.578482i
$2$	1.63139	−	1.15696i	0.815695	−	0.578482i
$3$		0			0
$3$		0			0
$4$	1.32286	−	3.77492i	0.330716	−	0.943730i
$5$	−3.07403	−	5.32438i	−0.614806	−	1.06488i	−0.990418	−	0.138099i	$-0.955901\pi$
$5$	−3.07403	−	5.32438i	−0.614806	−	1.06488i	0.375612	−	0.926777i	$-0.377432\pi$
$6$		0			0
$7$	−0.511543	−	0.295340i	−0.0730776	−	0.0421914i	0.463016	−	0.886350i	$-0.346767\pi$
$7$	−0.511543	−	0.295340i	−0.0730776	−	0.0421914i	−0.536094	+	0.844159i	$0.680101\pi$
$8$	−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	$-0.0415274\pi$
$11$	15.1205	+	8.72982i	1.37459	+	0.793620i	0.383088	+	0.923712i	$0.374861\pi$
$12$		0			0
$13$	−0.892255	−	1.54543i	−0.0686350	−	0.118879i	0.829666	−	0.558261i	$-0.188531\pi$
$13$	−0.892255	−	1.54543i	−0.0686350	−	0.118879i	−0.898301	+	0.439381i	$0.855198\pi$
$14$	−1.17622	+	0.110024i	−0.0840160	+	0.00785882i
$15$		0			0
$16$	−12.5001	−	9.98742i	−0.781254	−	0.624214i
$17$	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	$0.828419\pi$
$20$	−24.1656	+	4.56079i	−1.20828	+	0.228040i
$21$		0			0
$22$	34.7675	−	3.25214i	1.58034	−	0.147824i
$23$	−6.86778	+	3.96511i	−0.298599	+	0.172396i	−0.641813	−	0.766861i	$-0.721818\pi$
$23$	−6.86778	+	3.96511i	−0.298599	+	0.172396i	0.343214	+	0.939257i	$0.388484\pi$
$24$		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	−0.915563	−	0.402174i	$-0.868255\pi$
$29$	−3.17517	+	5.49956i	−0.109489	+	0.189640i	0.806075	+	0.591814i	$0.201588\pi$
$30$		0			0
$31$	−27.6558	+	15.9671i	−0.892124	+	0.515068i	−0.874637	−	0.484779i	$-0.838900\pi$
$31$	−27.6558	+	15.9671i	−0.892124	+	0.515068i	−0.0174873	+	0.999847i	$0.505567\pi$
$32$	−31.9476	−	1.83125i	−0.998361	−	0.0572266i
$33$		0			0
$34$	27.5984	−	19.5725i	0.811717	−	0.575661i
$35$			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	$0.211316\pi$
$38$	22.5675	+	31.8215i	0.593881	+	0.837408i
$39$		0			0
$40$	−34.1469	+	35.3992i	−0.853672	+	0.884980i
$41$	2.66948	+	4.62368i	0.0651093	+	0.112773i	0.896742	−	0.442553i	$-0.145927\pi$
$41$	2.66948	+	4.62368i	0.0651093	+	0.112773i	−0.831633	+	0.555325i	$0.812594\pi$
$42$		0			0
$43$	33.9324	+	19.5909i	0.789126	+	0.455602i	0.839655	−	0.543121i	$-0.182757\pi$
$43$	33.9324	+	19.5909i	0.789126	+	0.455602i	−0.0505290	+	0.998723i	$0.516091\pi$
$44$	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	$-0.371120\pi$
$47$	−9.64117	−	5.56633i	−0.205131	−	0.118433i	−0.599047	+	0.800714i	$0.704454\pi$
$48$		0			0
$49$	−24.3255	−	42.1331i	−0.496440	−	0.859859i
$50$	2.38396	+	25.4861i	0.0476791	+	0.509721i
$51$		0			0
$52$	−7.01421	+	1.32380i	−0.134889	+	0.0254576i
$53$	−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
$56$	−1.14066	+	4.58570i	−0.0203689	+	0.0818875i
$57$		0			0
$58$	1.18285	+	12.6455i	0.0203940	+	0.218026i
$59$	−20.8974	+	12.0651i	−0.354194	+	0.204494i	−0.666531	−	0.745477i	$-0.732222\pi$
$59$	−20.8974	+	12.0651i	−0.354194	+	0.204494i	0.312337	+	0.949971i	$0.398888\pi$
$60$		0			0
$61$	−37.9460	+	65.7244i	−0.622066	+	1.07745i	0.367034	+	0.930207i	$0.380373\pi$
$61$	−37.9460	+	65.7244i	−0.622066	+	1.07745i	−0.989100	+	0.147243i	$0.952960\pi$
$62$	−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	$-0.578254\pi$
$67$	31.8200	−	18.3713i	0.474925	−	0.274198i	0.718299	+	0.695734i	$0.244921\pi$
$68$	22.3790	−	63.8607i	0.329103	−	0.939128i
$69$		0			0
$70$	4.20156	+	5.92445i	0.0600222	+	0.0846350i
$71$		−	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	$0.634907\pi$
$74$	95.0830	−	67.4319i	1.28490	−	0.911241i
$75$		0			0
$76$	73.6328	+	25.8035i	0.968852	+	0.339520i
$77$	−5.15652	−	8.93136i	−0.0669678	−	0.115992i
$78$		0			0
$79$	−32.1841	−	18.5815i	−0.407394	−	0.235209i	0.282275	−	0.959333i	$-0.408911\pi$
$79$	−32.1841	−	18.5815i	−0.407394	−	0.235209i	−0.689669	+	0.724124i	$0.742244\pi$
$80$	−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	$-0.485231\pi$
$83$	−66.0281	−	38.1214i	−0.795520	−	0.459294i	−0.841902	+	0.539630i	$0.818564\pi$
$84$		0			0
$85$	−52.0037	−	90.0730i	−0.611808	−	1.05968i
$86$	78.0229	−	7.29823i	0.907243	−	0.0848632i
$87$		0			0
$88$	33.7161	−	135.547i	0.383138	−	1.54030i
$89$	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
$92$	5.88285	+	31.1706i	0.0639440	+	0.338811i
$93$		0			0
$94$	−22.1686	+	2.07364i	−0.235836	+	0.0220600i
$95$	103.856	−	59.9614i	1.09322	−	0.631172i
$96$		0			0
$97$	13.0585	−	22.6180i	0.134624	−	0.233176i	−0.790830	−	0.612036i	$-0.790351\pi$
$97$	13.0585	−	22.6180i	0.134624	−	0.233176i	0.925454	+	0.378861i	$0.123684\pi$
$98$	−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	−0.795173	−	0.606382i	$-0.792620\pi$
$101$	12.8831	−	22.3142i	0.127556	−	0.220933i	0.922729	+	0.385449i	$0.125953\pi$
$102$		0			0
$103$	16.9947	−	9.81187i	0.164997	−	0.0952609i	−0.415228	−	0.909717i	$-0.636298\pi$
$103$	16.9947	−	9.81187i	0.164997	−	0.0952609i	0.580225	+	0.814457i	$0.302965\pi$
$104$	−9.91133	+	10.2748i	−0.0953012	+	0.0987964i
$105$		0			0
$106$	−58.5294	+	41.5085i	−0.552164	+	0.391589i
$107$			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	$0.346926\pi$
$110$	−124.192	−	175.118i	−1.12902	−	1.59198i
$111$		0			0
$112$	3.44464	+	8.80076i	0.0307557	+	0.0785782i
$113$	9.12484	+	15.8047i	0.0807508	+	0.139865i	0.903573	−	0.428435i	$-0.140935\pi$
$113$	9.12484	+	15.8047i	0.0807508	+	0.139865i	−0.822822	+	0.568299i	$0.807602\pi$
$114$		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
$122$	14.1361	+	151.124i	0.115870	+	1.23872i
$123$		0			0
$124$	23.6896	+	125.521i	0.191045	+	1.01227i
$125$	−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	$0.775945\pi$
$128$	−49.1751	+	118.177i	−0.384181	+	0.923258i
$129$		0			0
$130$	2.04358	+	21.8472i	0.0157198	+	0.168055i
$131$	−123.421	+	71.2570i	−0.942143	+	0.543947i	−0.890631	−	0.454726i	$-0.849737\pi$
$131$	−123.421	+	71.2570i	−0.942143	+	0.543947i	−0.0515116	+	0.998672i	$0.516404\pi$
$132$		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	−0.854559	−	0.519354i	$-0.826172\pi$
$137$	3.08176	−	5.33777i	0.0224946	−	0.0389618i	0.877054	+	0.480393i	$0.159506\pi$
$138$		0			0
$139$	−103.168	+	59.5642i	−0.742218	+	0.428519i	−0.822875	−	0.568222i	$-0.807631\pi$
$139$	−103.168	+	59.5642i	−0.742218	+	0.428519i	0.0806575	+	0.996742i	$0.474298\pi$
$140$	13.7088	+	4.80403i	0.0979197	+	0.0343145i
$141$		0			0
$142$	−101.624	−	143.296i	−0.715664	−	1.00913i
$143$		−	31.1569i		−	0.217880i
$144$		0			0
$145$	39.0423			0.269257
$146$	−97.9524	+	69.4669i	−0.670907	+	0.475800i
$147$		0			0
$148$	77.1011	−	220.015i	0.520953	−	1.48659i
$149$	103.365	+	179.034i	0.693726	+	1.20157i	0.970608	+	0.240665i	$0.0773657\pi$
$149$	103.365	+	179.034i	0.693726	+	1.20157i	−0.276882	+	0.960904i	$0.589301\pi$
$150$		0			0
$151$	−127.422	−	73.5670i	−0.843853	−	0.487199i	0.0147190	−	0.999892i	$-0.495315\pi$
$151$	−127.422	−	73.5670i	−0.843853	−	0.487199i	−0.858572	+	0.512693i	$0.828648\pi$
$152$	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	0.948609	−	0.316449i	$-0.102491\pi$
$157$	31.4395	+	54.4548i	0.200251	+	0.346846i	−0.748358	+	0.663295i	$0.769157\pi$
$158$	−74.0030	+	6.92221i	−0.468373	+	0.0438115i
$159$		0			0
$160$	88.4575	+	175.730i	0.552859	+	1.09831i
$161$	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	$0.855104\pi$
$164$	20.9854	−	3.96058i	0.127960	−	0.0241499i
$165$		0			0
$166$	−151.823	+	14.2014i	−0.914595	+	0.0855508i
$167$	150.531	−	86.9089i	0.901381	−	0.520413i	0.0237332	−	0.999718i	$-0.492445\pi$
$167$	150.531	−	86.9089i	0.901381	−	0.520413i	0.877648	+	0.479306i	$0.159111\pi$
$168$		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	−0.230861	−	0.972987i	$-0.574154\pi$
$173$	125.806	−	217.902i	0.727201	−	1.25955i	0.958062	−	0.286562i	$-0.0925125\pi$
$174$		0			0
$175$	6.54707	−	3.77995i	0.0374118	−	0.0215997i
$176$	−101.819	−	260.138i	−0.578515	−	1.47806i
$177$		0			0
$178$	45.0056	−	31.9175i	0.252840	−	0.179312i
$179$			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	$0.862520\pi$
$182$	1.21953	+	1.71960i	0.00670069	+	0.00944838i
$183$		0			0
$184$	45.6605	+	44.0452i	0.248155	+	0.239376i
$185$	−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	$-0.333672\pi$
$191$	−0.351914	−	0.203178i	−0.00184248	−	0.00106376i	−0.500921	+	0.865493i	$0.667005\pi$
$192$		0			0
$193$	−31.2230	−	54.0798i	−0.161777	−	0.280206i	0.773729	−	0.633517i	$-0.218389\pi$
$193$	−31.2230	−	54.0798i	−0.161777	−	0.280206i	−0.935506	+	0.353311i	$0.885056\pi$
$194$	−4.86472	−	52.0071i	−0.0250759	−	0.268078i
$195$		0			0
$196$	−191.228	+	36.0906i	−0.975656	+	0.184136i
$197$	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	$-0.270707\pi$
$200$	99.3616	+	24.7154i	0.496808	+	0.123577i
$201$		0			0
$202$	−4.79938	−	51.3085i	−0.0237593	−	0.254003i
$203$	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	$-0.539885\pi$
$211$	141.744	−	81.8360i	0.671773	−	0.387848i	0.796748	+	0.604311i	$0.206552\pi$
$212$	−47.4605	+	135.433i	−0.223870	+	0.638835i
$213$		0			0
$214$	211.956	+	298.871i	0.990450	+	1.39659i
$215$		−	240.892i		−	1.12043i
$216$		0			0
$217$	18.8629			0.0869257
$218$	164.511	−	116.669i	0.754637	−	0.535181i
$219$		0			0
$220$	−405.211	−	142.000i	−1.84187	−	0.645455i
$221$	−15.0944	−	26.1442i	−0.0683003	−	0.118300i
$222$		0			0
$223$	−330.681	−	190.919i	−1.48287	−	0.856138i	−0.483063	−	0.875586i	$-0.660476\pi$
$223$	−330.681	−	190.919i	−1.48287	−	0.856138i	−0.999811	+	0.0194478i	$0.993809\pi$
$224$	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	$-0.375186\pi$
$227$	−51.5472	−	29.7608i	−0.227080	−	0.131105i	−0.609224	+	0.792998i	$0.708519\pi$
$228$		0			0
$229$	64.4366	+	111.608i	0.281383	+	0.487369i	0.971726	−	0.236113i	$-0.0758736\pi$
$229$	64.4366	+	111.608i	0.281383	+	0.487369i	−0.690343	+	0.723482i	$0.742540\pi$
$230$	97.0873	−	9.08150i	0.422118	−	0.0394848i
$231$		0			0
$232$	49.3005	+	12.2631i	0.212502	+	0.0528582i
$233$	−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
$236$	17.9005	+	94.8467i	0.0758495	+	0.401893i
$237$		0			0
$238$	−19.8983	+	1.86128i	−0.0836063	+	0.00782050i
$239$	−315.244	+	182.006i	−1.31901	+	0.761532i	−0.983570	−	0.180529i	$-0.942219\pi$
$239$	−315.244	+	182.006i	−1.31901	+	0.761532i	−0.335442	+	0.942061i	$0.608886\pi$
$240$		0			0
$241$	−40.5235	+	70.1888i	−0.168147	+	0.291240i	−0.937769	−	0.347261i	$-0.887112\pi$
$241$	−40.5235	+	70.1888i	−0.168147	+	0.291240i	0.769621	+	0.638501i	$0.220445\pi$
$242$	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
$248$	183.870	+	177.366i	0.741413	+	0.715184i
$249$		0			0
$250$	−122.378	+	86.7892i	−0.489512	+	0.347157i
$251$		−	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
$254$	190.188	+	268.177i	0.748773	+	1.05582i
$255$		0			0
$256$	56.5028	+	249.687i	0.220714	+	0.975339i
$257$	37.6564	+	65.2227i	0.146523	+	0.253785i	0.929940	−	0.367711i	$-0.119858\pi$
$257$	37.6564	+	65.2227i	0.146523	+	0.253785i	−0.783417	+	0.621496i	$0.786525\pi$
$258$		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	$-0.408027\pi$
$263$	−105.914	−	61.1497i	−0.402716	−	0.232508i	−0.687655	+	0.726037i	$0.741360\pi$
$264$		0			0
$265$	110.287	+	191.023i	0.416178	+	0.720841i
$266$	−2.14609	−	22.9432i	−0.00806802	−	0.0862525i
$267$		0			0
$268$	−27.2566	−	144.421i	−0.101704	−	0.538883i
$269$	−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	$-0.0480146\pi$
$272$	−211.465	−	168.958i	−0.777443	−	0.621170i
$273$		0			0
$274$	−1.14805	−	12.2735i	−0.00418998	−	0.0447937i
$275$	−193.522	+	111.730i	−0.703716	+	0.406291i
$276$		0			0
$277$	224.861	−	389.471i	0.811774	−	1.40603i	−0.0998479	−	0.995003i	$-0.531836\pi$
$277$	224.861	−	389.471i	0.811774	−	1.40603i	0.911622	−	0.411031i	$-0.134831\pi$
$278$	−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	−0.790752	−	0.612137i	$-0.790310\pi$
$281$	37.8649	−	65.5838i	0.134750	−	0.233394i	0.925502	+	0.378743i	$0.123643\pi$
$282$		0			0
$283$	322.061	−	185.942i	1.13803	−	0.657039i	0.192084	−	0.981378i	$-0.438475\pi$
$283$	322.061	−	185.942i	1.13803	−	0.657039i	0.945941	+	0.324339i	$0.105142\pi$
$284$	−331.578	−	116.196i	−1.16753	−	0.409142i
$285$		0			0
$286$	−36.0474	−	50.8290i	−0.126040	−	0.177724i
$287$		−	3.15361i		−	0.0109882i
$288$		0			0
$289$	−2.81196			−0.00972996
$290$	63.6932	−	45.1706i	0.219632	−	0.155761i
$291$		0			0
$292$	−79.4279	+	226.655i	−0.272013	+	0.776216i
$293$	66.3946	+	114.999i	0.226603	+	0.392488i	0.956799	−	0.290750i	$-0.0939047\pi$
$293$	66.3946	+	114.999i	0.226603	+	0.392488i	−0.730196	+	0.683237i	$0.760571\pi$
$294$		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
$302$	−292.989	+	27.4061i	−0.970163	+	0.0907486i
$303$		0			0
$304$	194.812	−	243.823i	0.640830	−	0.802050i
$305$	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	$0.815363\pi$
$308$	−40.5366	+	7.65048i	−0.131612	+	0.0248392i
$309$		0			0
$310$	390.960	−	36.5703i	1.26116	−	0.117969i
$311$	304.206	−	175.634i	0.978156	−	0.564738i	0.0764428	−	0.997074i	$-0.475644\pi$
$311$	304.206	−	175.634i	0.978156	−	0.564738i	0.901713	+	0.432336i	$0.142310\pi$
$312$		0			0
$313$	−95.4299	+	165.289i	−0.304888	+	0.528081i	−0.977236	−	0.212154i	$-0.931952\pi$
$313$	−95.4299	+	165.289i	−0.304888	+	0.528081i	0.672349	+	0.740235i	$0.265286\pi$
$314$	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	−0.345752	−	0.938326i	$-0.612376\pi$
$317$	202.797	−	351.255i	0.639738	−	1.10806i	0.985490	−	0.169733i	$-0.0542906\pi$
$318$		0			0
$319$	−96.0203	+	55.4374i	−0.301004	+	0.173785i
$320$	347.622	+	184.342i	1.08632	+	0.576069i
$321$		0			0
$322$	7.64179	−	5.41948i	0.0237323	−	0.0168307i
$323$			329.981i			1.02161i
$324$		0			0
$325$	22.8393			0.0702749
$326$	165.821	+	233.818i	0.508655	+	0.717234i
$327$		0			0
$328$	29.6531	−	30.7406i	0.0904057	−	0.0937213i
$329$	3.28792	+	5.69484i	0.00999368	+	0.0173096i
$330$		0			0
$331$	−384.104	−	221.763i	−1.16044	−	0.669978i	−0.209027	−	0.977910i	$-0.567030\pi$
$331$	−384.104	−	221.763i	−1.16044	−	0.669978i	−0.951408	+	0.307932i	$0.900363\pi$
$332$	−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	−0.945662	−	0.325150i	$-0.894585\pi$
$337$	−254.239	−	440.356i	−0.754420	−	1.30669i	0.191243	−	0.981543i	$-0.438748\pi$
$338$	−30.8858	−	330.190i	−0.0913781	−	0.976893i
$339$		0			0
$340$	−408.812	+	77.1553i	−1.20239	+	0.226927i
$341$	−557.560			−1.63507
$342$		0			0
$343$			57.6805i			0.168165i
$344$	75.6636	−	304.185i	0.219952	−	0.884259i
$345$		0			0
$346$	−46.8667	−	501.036i	−0.135453	−	1.44808i
$347$	492.773	−	284.503i	1.42010	−	0.819893i	0.423790	−	0.905761i	$-0.360700\pi$
$347$	492.773	−	284.503i	1.42010	−	0.819893i	0.996307	+	0.0858678i	$0.0273663\pi$
$348$		0			0
$349$	−206.901	+	358.363i	−0.592840	+	1.02683i	0.401008	+	0.916074i	$0.368660\pi$
$349$	−206.901	+	358.363i	−0.592840	+	1.02683i	−0.993848	+	0.110754i	$0.964673\pi$
$350$	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	−0.940682	−	0.339290i	$-0.889813\pi$
$353$	−62.3070	+	107.919i	−0.176507	+	0.305719i	0.764175	+	0.645009i	$0.223147\pi$
$354$		0			0
$355$	−467.677	+	270.014i	−1.31740	+	0.760602i
$356$	36.4942	−	104.140i	0.102512	−	0.292527i
$357$		0			0
$358$	111.076	+	156.623i	0.310267	+	0.437495i
$359$			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
$362$	−536.331	+	380.361i	−1.48158	+	1.05072i
$363$		0			0
$364$	3.97904	+	1.39440i	0.0109314	+	0.00383076i
$365$	184.572	+	319.688i	0.505677	+	0.875858i
$366$		0			0
$367$	615.571	+	355.400i	1.67730	+	0.968392i	0.963369	+	0.268181i	$0.0864224\pi$
$367$	615.571	+	355.400i	1.67730	+	0.968392i	0.713936	+	0.700211i	$0.246911\pi$
$368$	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	0.998191	−	0.0601254i	$-0.0191501\pi$
$373$	166.740	+	288.803i	0.447025	+	0.774271i	−0.551166	+	0.834396i	$0.685817\pi$
$374$	588.165	−	55.0167i	1.57263	−	0.147103i
$375$		0			0
$376$	−21.4982	+	86.4277i	−0.0571761	+	0.229861i
$377$	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	$-0.338650\pi$
$380$	−88.9618	−	471.369i	−0.234110	−	1.24045i
$381$		0			0
$382$	−0.809179	+	0.0756903i	−0.00211827	+	0.000198142i
$383$	−69.9008	+	40.3572i	−0.182509	+	0.105371i	−0.588471	−	0.808518i	$-0.700270\pi$
$383$	−69.9008	+	40.3572i	−0.182509	+	0.105371i	0.405962	+	0.913890i	$0.366936\pi$
$384$		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	0.0489809	−	0.998800i	$-0.484403\pi$
$389$	346.006	−	599.301i	0.889476	−	1.54062i	0.840495	−	0.541819i	$-0.182264\pi$
$390$		0			0
$391$	−116.183	+	67.0782i	−0.297143	+	0.171556i
$392$	−270.213	+	280.123i	−0.689318	+	0.714598i
$393$		0			0
$394$	339.102	−	240.488i	0.860665	−	0.610375i
$395$			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	$0.189278\pi$
$398$	−346.081	−	487.995i	−0.869550	−	1.22612i
$399$		0			0
$400$	190.692	−	74.6374i	0.476731	−	0.186594i
$401$	−296.433	−	513.437i	−0.739235	−	1.28039i	−0.952840	−	0.303472i	$-0.901854\pi$
$401$	−296.433	−	513.437i	−0.739235	−	1.28039i	0.213606	−	0.976920i	$-0.431479\pi$
$402$		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	0.598018	−	0.801483i	$-0.295955\pi$
$409$	−161.594	−	279.889i	−0.395095	−	0.684325i	−0.993113	+	0.117157i	$0.962622\pi$
$410$	−6.11405	−	65.3632i	−0.0149123	−	0.159422i
$411$		0			0
$412$	−14.5574	−	77.1333i	−0.0353335	−	0.187217i
$413$	14.2533			0.0345115
$414$		0			0
$415$			468.745i			1.12951i
$416$	25.6753	+	51.0067i	0.0617195	+	0.122612i
$417$		0			0
$418$	63.4354	+	678.167i	0.151759	+	1.62241i
$419$	−222.744	+	128.601i	−0.531608	+	0.306924i	−0.741671	−	0.670764i	$-0.765967\pi$
$419$	−222.744	+	128.601i	−0.531608	+	0.306924i	0.210063	+	0.977688i	$0.432633\pi$
$420$		0			0
$421$	41.9905	−	72.7297i	0.0997400	−	0.172755i	−0.811837	−	0.583884i	$-0.801532\pi$
$421$	41.9905	−	72.7297i	0.0997400	−	0.172755i	0.911577	+	0.411129i	$0.134866\pi$
$422$	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
$428$	691.567	+	242.349i	1.61581	+	0.566237i
$429$		0			0
$430$	−278.703	−	392.989i	−0.648148	−	0.913927i
$431$			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	$0.349093\pi$
$434$	30.7727	−	21.8237i	0.0709049	−	0.0502850i
$435$		0			0
$436$	133.399	−	380.667i	0.305961	−	0.873089i
$437$	−77.3426	−	133.961i	−0.176985	−	0.306548i
$438$		0			0
$439$	194.776	+	112.454i	0.443682	+	0.256160i	0.705158	−	0.709050i	$-0.250876\pi$
$439$	194.776	+	112.454i	0.443682	+	0.256160i	−0.261476	+	0.965210i	$0.584209\pi$
$440$	−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	$-0.493113\pi$
$443$	−369.184	−	213.148i	−0.833373	−	0.481148i	−0.855006	+	0.518618i	$0.826447\pi$
$444$		0			0
$445$	−84.8041	−	146.885i	−0.190571	−	0.330079i
$446$	−760.356	+	71.1233i	−1.70483	+	0.159469i
$447$		0			0
$448$	37.7790	−	1.36102i	0.0843281	−	0.00303799i
$449$	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
$452$	71.7324	−	13.5381i	0.158700	−	0.0299515i
$453$		0			0
$454$	−118.526	+	11.0869i	−0.261070	+	0.0244204i
$455$	5.61228	−	3.24025i	0.0123347	−	0.00712144i
$456$		0			0
$457$	−159.600	+	276.435i	−0.349234	+	0.604891i	−0.986114	−	0.166072i	$-0.946892\pi$
$457$	−159.600	+	276.435i	−0.349234	+	0.604891i	0.636879	+	0.770963i	$0.280225\pi$
$458$	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	0.348478	+	0.937317i	$0.386698\pi$
$461$	−293.888	+	509.029i	−0.637501	+	1.10418i	−0.985979	+	0.166867i	$0.946635\pi$
$462$		0			0
$463$	−230.088	+	132.841i	−0.496950	+	0.286914i	−0.727453	−	0.686157i	$-0.759296\pi$
$463$	−230.088	+	132.841i	−0.496950	+	0.286914i	0.230503	+	0.973072i	$0.425963\pi$
$464$	94.6163	−	37.0330i	0.203914	−	0.0798126i
$465$		0			0
$466$	−24.4608	+	17.3474i	−0.0524910	+	0.0372261i
$467$		−	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
$470$	79.1877	+	111.659i	0.168484	+	0.237573i
$471$		0			0
$472$	138.937	+	134.022i	0.294358	+	0.283944i
$473$	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	$-0.575990\pi$
$479$	−572.964	−	330.801i	−1.19617	−	0.690607i	−0.959698	+	0.281033i	$0.909323\pi$
$480$		0			0
$481$	−52.0037	−	90.0730i	−0.108116	−	0.187262i
$482$	15.0963	+	161.390i	0.0313202	+	0.334833i
$483$		0			0
$484$	722.599	−	136.376i	1.49297	−	0.281769i
$485$	−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	$0.981311\pi$
$488$	589.183	+	146.554i	1.20734	+	0.300317i
$489$		0			0
$490$	55.7140	+	595.620i	0.113702	+	1.21555i
$491$	48.6600	−	28.0939i	0.0991040	−	0.0572177i	−0.449629	−	0.893215i	$-0.648444\pi$
$491$	48.6600	−	28.0939i	0.0991040	−	0.0572177i	0.548733	+	0.835998i	$0.315110\pi$
$492$		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	$-0.873183\pi$
$499$	−522.225	+	301.507i	−1.04654	+	0.604222i	−0.124863	+	0.992174i	$0.539849\pi$
$500$	−99.2341	+	283.174i	−0.198468	+	0.566348i
$501$		0			0
$502$	−326.129	−	459.861i	−0.649659	−	0.916058i
$503$			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
$506$	−225.880	+	160.192i	−0.446404	+	0.316585i
$507$		0			0
$508$	620.543	+	217.460i	1.22154	+	0.428071i
$509$	119.464	+	206.918i	0.234704	+	0.406519i	0.959187	−	0.282774i	$-0.0912547\pi$
$509$	119.464	+	206.918i	0.234704	+	0.406519i	−0.724483	+	0.689293i	$0.757921\pi$
$510$		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
$518$	−68.5544	+	6.41255i	−0.132344	+	0.0123794i
$519$		0			0
$520$	85.1748	+	21.1865i	0.163798	+	0.0407433i
$521$	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	$-0.356852\pi$
$524$	105.721	+	560.167i	0.201757	+	1.06902i
$525$		0			0
$526$	−243.536	+	22.7802i	−0.462996	+	0.0433084i
$527$	−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
$536$	−211.556	−	204.072i	−0.394694	−	0.380730i
$537$		0			0
$538$	−457.527	+	324.473i	−0.850422	+	0.603110i
$539$		−	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	$0.571874\pi$
$542$	−94.2311	−	132.871i	−0.173858	−	0.245150i
$543$		0			0
$544$	−540.460	−	30.9794i	−0.993492	−	0.0569475i
$545$	−309.988	−	536.915i	−0.568786	−	0.985166i
$546$		0			0
$547$	170.503	+	98.4402i	0.311706	+	0.179964i	0.647690	−	0.761904i	$-0.275735\pi$
$547$	170.503	+	98.4402i	0.311706	+	0.179964i	−0.335983	+	0.941868i	$0.609069\pi$
$548$	−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
$554$	−83.7681	−	895.536i	−0.151206	−	1.61649i
$555$		0			0
$556$	88.3725	+	468.247i	0.158943	+	0.842171i
$557$	−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
$560$	36.2697	−	45.3944i	0.0647672	−	0.0810614i
$561$		0			0
$562$	−14.1059	−	150.801i	−0.0250994	−	0.268329i
$563$	165.774	−	95.7097i	0.294448	−	0.169999i	−0.345498	−	0.938419i	$-0.612290\pi$
$563$	165.774	−	95.7097i	0.294448	−	0.169999i	0.639946	+	0.768420i	$0.278957\pi$
$564$		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	−0.993857	−	0.110675i	$-0.964699\pi$
$569$	−228.215	+	395.280i	−0.401081	+	0.694693i	0.592775	+	0.805368i	$0.298032\pi$
$570$		0			0
$571$	842.764	−	486.570i	1.47594	−	0.852136i	0.476312	−	0.879276i	$-0.341973\pi$
$571$	842.764	−	486.570i	1.47594	−	0.852136i	0.999632	+	0.0271399i	$0.00863995\pi$
$572$	−117.615	−	41.2164i	−0.205620	−	0.0720566i
$573$		0			0
$574$	−3.64862	−	5.14477i	−0.00635648	−	0.00896302i
$575$		−	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	$0.461698\pi$
$578$	−4.58740	+	3.25334i	−0.00793668	+	0.00562861i
$579$		0			0
$580$	51.6477	−	147.382i	0.0890478	−	0.254106i
$581$	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	$-0.124261\pi$
$587$	620.808	+	358.424i	1.05759	+	0.610602i	0.132829	+	0.991139i	$0.457594\pi$
$588$		0			0
$589$	−311.451	−	539.449i	−0.528779	−	0.915872i
$590$	295.419	−	27.6334i	0.500711	−	0.0468363i
$591$		0			0
$592$	−728.546	−	582.101i	−1.23065	−	0.983279i
$593$	−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
$596$	812.577	−	153.358i	1.36338	−	0.257312i
$597$		0			0
$598$	28.1801	−	2.63596i	0.0471240	−	0.00440796i
$599$	−245.527	+	141.755i	−0.409895	+	0.236653i	−0.690744	−	0.723099i	$-0.742717\pi$
$599$	−245.527	+	141.755i	−0.409895	+	0.236653i	0.280850	+	0.959752i	$0.409384\pi$
$600$		0			0
$601$	377.424	−	653.717i	0.627993	−	1.08772i	−0.359961	−	0.932967i	$-0.617210\pi$
$601$	377.424	−	653.717i	0.627993	−	1.08772i	0.987954	−	0.154748i	$-0.0494567\pi$
$602$	−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	$-0.690068\pi$
$607$	−77.2227	+	44.5845i	−0.127220	+	0.0734506i	0.435039	+	0.900411i	$0.356734\pi$
$608$	35.7200	−	623.162i	0.0587499	−	1.02494i
$609$		0			0
$610$	761.189	−	539.827i	1.24785	−	0.884962i
$611$			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	$0.583190\pi$
$614$	389.335	+	548.985i	0.634096	+	0.894113i
$615$		0			0
$616$	−57.2796	+	59.3803i	−0.0929863	+	0.0963966i
$617$	−534.934	−	926.533i	−0.866992	−	1.50167i	−0.865056	−	0.501675i	$-0.832717\pi$
$617$	−534.934	−	926.533i	−0.866992	−	1.50167i	−0.00193565	−	0.999998i	$-0.500616\pi$
$618$		0			0
$619$	−578.542	−	334.021i	−0.934640	−	0.539615i	−0.0463638	−	0.998925i	$-0.514763\pi$
$619$	−578.542	−	334.021i	−0.934640	−	0.539615i	−0.888276	+	0.459310i	$0.848097\pi$
$620$	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
$626$	35.5507	+	380.060i	0.0567902	+	0.607125i
$627$		0			0
$628$	247.153	−	46.6452i	0.393555	−	0.0742759i
$629$	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	$0.961916\pi$
$632$	−71.7652	+	288.513i	−0.113553	+	0.456507i
$633$		0			0
$634$	−75.5484	−	807.662i	−0.119162	−	1.27392i
$635$	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	0.449990	+	0.893034i	$0.351427\pi$
$641$	−351.521	+	608.852i	−0.548395	+	0.949847i	−0.998385	+	0.0568139i	$0.981906\pi$
$642$		0			0
$643$	−742.057	+	428.427i	−1.15405	+	0.666293i	−0.949872	−	0.312639i	$-0.898787\pi$
$643$	−742.057	+	428.427i	−1.15405	+	0.666293i	−0.204182	+	0.978933i	$0.565454\pi$
$644$	6.19659	−	17.6826i	0.00962204	−	0.0274574i
$645$		0			0
$646$	381.776	+	538.328i	0.590985	+	0.833324i
$647$		−	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
$650$	37.2599	−	26.4243i	0.0573229	−	0.0406528i
$651$		0			0
$652$	541.039	+	189.599i	0.829814	+	0.290796i
$653$	441.773	+	765.173i	0.676528	+	1.17178i	0.976020	+	0.217682i	$0.0698495\pi$
$653$	441.773	+	765.173i	0.676528	+	1.17178i	−0.299492	+	0.954099i	$0.596817\pi$
$654$		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	$-0.441228\pi$
$659$	−379.533	−	219.123i	−0.575922	−	0.332509i	−0.759511	+	0.650494i	$0.774562\pi$
$660$		0			0
$661$	233.924	+	405.168i	0.353894	+	0.612963i	0.986928	−	0.161161i	$-0.0515239\pi$
$661$	233.924	+	405.168i	0.353894	+	0.612963i	−0.633034	+	0.774124i	$0.718191\pi$
$662$	−883.195	+	82.6137i	−1.33413	+	0.124794i
$663$		0			0
$664$	−147.232	+	591.905i	−0.221734	+	0.891424i
$665$	−70.8359			−0.106520
$666$		0			0
$667$		−	50.3597i		−	0.0755018i
$668$	−128.943	−	683.210i	−0.193028	−	1.02277i
$669$		0			0
$670$	−449.827	+	42.0767i	−0.671384	+	0.0628010i
$671$	−1147.52	+	662.524i	−1.71017	+	0.987368i
$672$		0			0
$673$	273.302	−	473.372i	0.406094	−	0.703376i	−0.588354	−	0.808604i	$-0.700224\pi$
$673$	273.302	−	473.372i	0.406094	−	0.703376i	0.994448	+	0.105227i	$0.0335571\pi$
$674$	−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	−0.983714	−	0.179740i	$-0.942475\pi$
$677$	−227.606	+	394.225i	−0.336198	+	0.582312i	0.647516	+	0.762052i	$0.275808\pi$
$678$		0			0
$679$	−13.3600	+	7.71341i	−0.0196760	+	0.0113600i
$680$	−577.666	+	598.852i	−0.849509	+	0.880664i
$681$		0			0
$682$	−909.597	+	645.077i	−1.33372	+	0.945861i
$683$		−	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
$686$	66.7343	+	94.0994i	0.0972803	+	0.137171i
$687$		0			0
$688$	−228.495	−	583.784i	−0.332114	−	0.848524i
$689$	32.0115	+	55.4455i	0.0464607	+	0.0804724i
$690$		0			0
$691$	163.326	+	94.2965i	0.236362	+	0.136464i	0.613504	−	0.789692i	$-0.289760\pi$
$691$	163.326	+	94.2965i	0.236362	+	0.136464i	−0.377141	+	0.926156i	$0.623093\pi$
$692$	−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
$698$	77.0773	+	824.007i	0.110426	+	1.18053i
$699$		0			0
$700$	−5.60814	−	29.7150i	−0.00801162	−	0.0424501i
$701$	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
$704$	−1116.69	+	40.2298i	−1.58621	+	0.0571447i
$705$		0			0
$706$	23.2114	+	248.145i	0.0328773	+	0.351480i
$707$	−13.1806	+	7.60980i	−0.0186429	+	0.0107635i
$708$		0			0
$709$	−651.819	+	1128.98i	−0.919349	+	1.59236i	−0.118944	+	0.992901i	$0.537951\pi$
$709$	−651.819	+	1128.98i	−0.919349	+	1.59236i	−0.800406	+	0.599459i	$0.795382\pi$
$710$	−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
$716$	362.415	+	127.003i	0.506166	+	0.177378i
$717$		0			0
$718$	350.787	+	494.631i	0.488561	+	0.688901i
$719$			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
$722$	−31.7717	+	22.5321i	−0.0440051	+	0.0312080i
$723$		0			0
$724$	−434.902	+	1241.03i	−0.600693	+	1.71413i
$725$	−40.6380	−	70.3870i	−0.0560524	−	0.0970856i
$726$		0			0
$727$	232.676	+	134.335i	0.320049	+	0.184780i	0.651414	−	0.758722i	$-0.274176\pi$
$727$	232.676	+	134.335i	0.320049	+	0.184780i	−0.331365	+	0.943502i	$0.607509\pi$
$728$	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	0.839806	−	0.542887i	$-0.182669\pi$
$733$	−36.8343	−	63.7989i	−0.0502514	−	0.0870380i	−0.890057	+	0.455849i	$0.849336\pi$
$734$	1415.42	−	132.398i	1.92837	−	0.180379i
$735$		0			0
$736$	226.670	−	114.099i	0.307975	−	0.155026i
$737$	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	$0.901918\pi$
$740$	−1408.46	+	265.818i	−1.90332	+	0.359214i
$741$		0			0
$742$	42.1994	−	3.94732i	0.0568725	−	0.00531983i
$743$	656.602	−	379.089i	0.883718	−	0.510215i	0.0118352	−	0.999930i	$-0.496233\pi$
$743$	656.602	−	379.089i	0.883718	−	0.510215i	0.871882	+	0.489715i	$0.162899\pi$
$744$		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	−0.520358	+	0.853948i	$0.674202\pi$
$751$	−1141.58	+	659.091i	−1.52008	+	0.877618i	−0.999720	+	0.0236697i	$0.992465\pi$
$752$	64.9219	+	165.870i	0.0863323	+	0.220572i
$753$		0			0
$754$	18.4873	−	13.1110i	0.0245190	−	0.0173886i
$755$			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	$0.373065\pi$
$758$	−766.705	−	1081.10i	−1.01148	−	1.42625i
$759$		0			0
$760$	−690.489	−	666.062i	−0.908538	−	0.876397i
$761$	188.496	+	326.485i	0.247695	+	0.429021i	0.962886	−	0.269908i	$-0.0869934\pi$
$761$	188.496	+	326.485i	0.247695	+	0.429021i	−0.715191	+	0.698929i	$0.753660\pi$
$762$		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	0.892084	+	0.451869i	$0.149243\pi$
$769$	643.939	+	1115.34i	0.837372	+	1.45037i	−0.0547122	+	0.998502i	$0.517424\pi$
$770$	11.8102	+	126.259i	0.0153380	+	0.163973i
$771$		0			0
$772$	−245.451	+	46.3240i	−0.317941	+	0.0600052i
$773$	−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
$776$	−202.758	−	50.4344i	−0.261286	−	0.0649928i
$777$		0			0
$778$	−128.898	−	1378.01i	−0.165679	−	1.77122i
$779$	−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	$-0.574236\pi$
$787$	390.283	−	225.330i	0.495913	−	0.286315i	0.727024	+	0.686612i	$0.240903\pi$
$788$	274.972	−	784.658i	0.348949	−	0.995759i
$789$		0			0
$790$	264.344	+	372.741i	0.334613	+	0.471824i
$791$		−	10.7797i		−	0.0136280i
$792$		0			0
$793$	135.430			0.170782
$794$	1072.99	−	760.950i	1.35137	−	0.958376i
$795$		0			0
$796$	−1129.19	−	395.707i	−1.41858	−	0.497119i
$797$	182.891	+	316.776i	0.229474	+	0.397461i	0.957652	−	0.287927i	$-0.0929661\pi$
$797$	182.891	+	316.776i	0.229474	+	0.397461i	−0.728178	+	0.685388i	$0.759633\pi$
$798$		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
$806$	113.478	−	10.6147i	0.140792	−	0.0131696i
$807$		0			0
$808$	−200.035	−	49.7570i	−0.247568	−	0.0615804i
$809$	−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	$0.833533\pi$
$812$	−2.78260	−	14.7438i	−0.00342685	−	0.0181574i
$813$		0			0
$814$	2026.37	−	189.546i	2.48940	−	0.232857i
$815$	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	−0.643071	−	0.765806i	$-0.722340\pi$
$821$	280.513	−	485.862i	0.341672	−	0.591793i	0.984743	+	0.174013i	$0.0556734\pi$
$822$		0			0
$823$	1016.04	−	586.612i	1.23456	−	0.712773i	0.266583	−	0.963812i	$-0.414105\pi$
$823$	1016.04	−	586.612i	1.23456	−	0.712773i	0.967977	+	0.251039i	$0.0807722\pi$
$824$	−112.989	−	108.992i	−0.137123	−	0.132272i
$825$		0			0
$826$	23.2526	−	16.4905i	0.0281509	−	0.0199643i
$827$		−	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	$0.584000\pi$
$830$	542.321	+	764.706i	0.653399	+	0.921332i
$831$		0			0
$832$	100.899	+	53.5064i	0.121273	+	0.0643105i
$833$	−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	$-0.435649\pi$
$839$	−459.103	−	265.063i	−0.547202	−	0.315927i	−0.747993	+	0.663707i	$0.768982\pi$
$840$		0			0
$841$	400.337	+	693.403i	0.476024	+	0.824499i
$842$	−15.6428	−	167.232i	−0.0185782	−	0.198613i
$843$		0			0
$844$	−121.416	−	643.331i	−0.143858	−	0.762240i
$845$	−1019.44			−1.20644
$846$		0			0
$847$		−	108.590i		−	0.128205i
$848$	448.465	+	358.319i	0.528850	+	0.422546i
$849$		0			0
$850$	40.3296	+	431.150i	0.0474466	+	0.507236i
$851$	−400.278	+	231.100i	−0.470361	+	0.271563i
$852$		0			0
$853$	88.3868	−	153.090i	0.103619	−	0.179473i	−0.809554	−	0.587045i	$-0.800291\pi$
$853$	88.3868	−	153.090i	0.103619	−	0.179473i	0.913173	+	0.407572i	$0.133624\pi$
$854$	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	−0.729656	−	0.683815i	$-0.760320\pi$
$857$	194.859	−	337.505i	0.227373	−	0.393821i	0.957029	+	0.289993i	$0.0936531\pi$
$858$		0			0
$859$	503.279	−	290.568i	0.585889	−	0.338263i	−0.177581	−	0.984106i	$-0.556827\pi$
$859$	503.279	−	290.568i	0.585889	−	0.338263i	0.763470	+	0.645843i	$0.223494\pi$
$860$	−909.348	−	318.667i	−1.05738	−	0.370544i
$861$		0			0
$862$	167.005	+	235.488i	0.193742	+	0.273187i
$863$			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
$866$	644.976	−	457.410i	0.744776	−	0.528187i
$867$		0			0
$868$	24.9530	−	71.2059i	0.0287478	−	0.0820344i
$869$	−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	0.661233	−	0.750181i	$-0.270033\pi$
$877$	−279.815	−	484.653i	−0.319059	−	0.552626i	−0.980292	+	0.197554i	$0.936700\pi$
$878$	447.862	−	41.8928i	0.510093	−	0.0477139i
$879$		0			0
$880$	−1072.08	+	1341.79i	−1.21827	+	1.52476i
$881$	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	$-0.115196\pi$
$884$	−118.660	+	22.3948i	−0.134231	+	0.0253335i
$885$		0			0
$886$	−848.888	+	79.4047i	−0.958113	+	0.0896215i
$887$	921.187	−	531.847i	1.03854	−	0.599602i	0.119122	−	0.992880i	$-0.461992\pi$
$887$	921.187	−	531.847i	1.03854	−	0.599602i	0.919420	+	0.393277i	$0.128659\pi$
$888$		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
$896$	60.0576	−	45.9293i	0.0670285	−	0.0512604i
$897$		0			0
$898$	663.557	−	470.588i	0.738928	−	0.524040i
$899$		−	202.793i		−	0.225577i
$900$		0			0
$901$	−606.935			−0.673624
$902$	107.848	+	152.072i	0.119565	+	0.168594i
$903$		0			0
$904$	101.360	−	105.078i	0.112124	−	0.116236i
$905$	1010.61	+	1750.43i	1.11670	+	1.93418i
$906$		0			0
$907$	−207.207	−	119.631i	−0.228453	−	0.131898i	0.381405	−	0.924408i	$-0.375440\pi$
$907$	−207.207	−	119.631i	−0.228453	−	0.131898i	−0.609858	+	0.792510i	$0.708774\pi$
$908$	−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	$-0.297794\pi$
$911$	175.804	+	101.501i	0.192980	+	0.111417i	−0.400397	+	0.916342i	$0.631128\pi$
$912$		0			0
$913$	−665.585	−	1152.83i	−0.729009	−	1.26268i
$914$	59.4561	+	635.625i	0.0650505	+	0.695433i
$915$		0			0
$916$	506.551	−	95.6015i	0.553003	−	0.104368i
$917$	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	$-0.158666\pi$
$920$	94.1514	−	378.510i	0.102338	−	0.411424i
$921$		0			0
$922$	109.483	+	1170.44i	0.118745	+	1.26946i
$923$	−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	−0.981148	−	0.193259i	$-0.938094\pi$
$929$	−300.259	+	520.064i	−0.323207	+	0.559810i	0.657941	+	0.753069i	$0.271428\pi$
$930$		0			0
$931$	821.838	−	474.489i	0.882748	−	0.509655i
$932$	−19.8348	+	56.6006i	−0.0212820	+	0.0607303i
$933$		0			0
$934$	−919.322	−	1296.30i	−0.984284	−	1.38790i
$935$		−	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	$0.531359\pi$
$938$	−35.4062	+	25.1097i	−0.0377465	+	0.0267694i
$939$		0			0
$940$	258.372	+	90.5426i	0.274864	+	0.0963219i
$941$	377.587	+	653.999i	0.401261	+	0.695005i	0.993878	−	0.110479i	$-0.0352386\pi$
$941$	377.587	+	653.999i	0.401261	+	0.695005i	−0.592617	+	0.805484i	$0.701905\pi$
$942$		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	$-0.488870\pi$
$947$	−769.965	−	444.539i	−0.813057	−	0.469419i	−0.848016	+	0.529970i	$0.822203\pi$
$948$		0			0
$949$	53.5731	+	92.7913i	0.0564521	+	0.0977779i
$950$	−497.126	+	46.5009i	−0.523290	+	0.0489483i
$951$		0			0
$952$	−19.2966	+	77.5767i	−0.0202695	+	0.0814881i
$953$	−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
$956$	270.034	+	1430.79i	0.282462	+	1.49664i
$957$		0			0
$958$	−1317.45	+	123.234i	−1.37521	+	0.128637i
$959$	−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	$-0.835637\pi$
$967$	−847.921	+	489.548i	−0.876858	+	0.506254i	−0.00723669	+	0.999974i	$0.502304\pi$
$968$	1021.06	−	1058.50i	1.05481	−	1.09350i
$969$		0			0
$970$	−261.951	+	185.773i	−0.270053	+	0.191519i
$971$			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
$974$	66.1234	+	93.2379i	0.0678885	+	0.0957268i
$975$		0			0
$976$	1130.75	−	442.576i	1.15855	−	0.453459i
$977$	−353.710	−	612.644i	−0.362037	−	0.627067i	0.626259	−	0.779615i	$-0.284585\pi$
$977$	−353.710	−	612.644i	−0.362037	−	0.627067i	−0.988296	+	0.152549i	$0.951252\pi$
$978$		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	$-0.397105\pi$
$983$	−338.829	−	195.623i	−0.344689	−	0.199006i	−0.662343	+	0.749200i	$0.730438\pi$
$984$		0			0
$985$	−638.971	−	1106.73i	−0.648701	−	1.12358i
$986$	20.0104	+	213.925i	0.0202946	+	0.216962i
$987$		0			0
$988$	−25.8217	−	136.818i	−0.0261353	−	0.138479i
$989$	−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	$-0.0168690\pi$
$992$	912.776	−	459.465i	0.920137	−	0.463171i
$993$		0			0
$994$	9.66413	+	103.316i	0.00972247	+	0.103940i
$995$	−1592.67	+	919.530i	−1.60068	+	0.924151i
$996$		0			0
$997$	−39.0028	+	67.5547i	−0.0391201	+	0.0677580i	−0.884923	−	0.465738i	$-0.845789\pi$
$997$	−39.0028	+	67.5547i	−0.0391201	+	0.0677580i	0.845802	+	0.533496i	$0.179122\pi$
$998$	−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.19.6		16
3.2	odd	2		36.3.f.c.7.3	✓	16
4.3	odd	2	inner	108.3.f.c.19.5		16
8.3	odd	2		1728.3.o.g.127.8		16
8.5	even	2		1728.3.o.g.127.7		16
9.2	odd	6		324.3.d.i.163.8		8
9.4	even	3	inner	108.3.f.c.91.5		16
9.5	odd	6		36.3.f.c.31.4	yes	16
9.7	even	3		324.3.d.g.163.1		8
12.11	even	2		36.3.f.c.7.4	yes	16
24.5	odd	2		576.3.o.g.511.2		16
24.11	even	2		576.3.o.g.511.7		16
36.7	odd	6		324.3.d.g.163.2		8
36.11	even	6		324.3.d.i.163.7		8
36.23	even	6		36.3.f.c.31.3	yes	16
36.31	odd	6	inner	108.3.f.c.91.6		16
72.5	odd	6		576.3.o.g.319.7		16
72.13	even	6		1728.3.o.g.1279.8		16
72.59	even	6		576.3.o.g.319.2		16
72.67	odd	6		1728.3.o.g.1279.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.3	✓	16	3.2	odd	2
36.3.f.c.7.4	yes	16	12.11	even	2
36.3.f.c.31.3	yes	16	36.23	even	6
36.3.f.c.31.4	yes	16	9.5	odd	6
108.3.f.c.19.5		16	4.3	odd	2	inner
108.3.f.c.19.6		16	1.1	even	1	trivial
108.3.f.c.91.5		16	9.4	even	3	inner
108.3.f.c.91.6		16	36.31	odd	6	inner
324.3.d.g.163.1		8	9.7	even	3
324.3.d.g.163.2		8	36.7	odd	6
324.3.d.i.163.7		8	36.11	even	6
324.3.d.i.163.8		8	9.2	odd	6
576.3.o.g.319.2		16	72.59	even	6
576.3.o.g.319.7		16	72.5	odd	6
576.3.o.g.511.2		16	24.5	odd	2
576.3.o.g.511.7		16	24.11	even	2
1728.3.o.g.127.7		16	8.5	even	2
1728.3.o.g.127.8		16	8.3	odd	2
1728.3.o.g.1279.7		16	72.67	odd	6
1728.3.o.g.1279.8		16	72.13	even	6

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)

\(f(q)\)	\(=\)	\(q+(1.63139 - 1.15696i) q^{2} +(1.32286 - 3.77492i) q^{4} +(-3.07403 - 5.32438i) q^{5} +(-0.511543 - 0.295340i) q^{7} +(-2.20934 - 7.68888i) q^{8} +O(q^{10})\)	\(q+(1.63139 - 1.15696i) q^{2} +(1.32286 - 3.77492i) q^{4} +(-3.07403 - 5.32438i) q^{5} +(-0.511543 - 0.295340i) q^{7} +(-2.20934 - 7.68888i) q^{8} +(-11.1751 - 5.12959i) q^{10} +(15.1205 + 8.72982i) q^{11} +(-0.892255 - 1.54543i) q^{13} +(-1.17622 + 0.110024i) q^{14} +(-12.5001 - 9.98742i) q^{16} +16.9171 q^{17} +19.5058i q^{19} +(-24.1656 + 4.56079i) q^{20} +(34.7675 - 3.25214i) q^{22} +(-6.86778 + 3.96511i) q^{23} +(-6.39933 + 11.0840i) q^{25} +(-3.24362 - 1.48889i) q^{26} +(-1.79159 + 1.54034i) q^{28} +(-3.17517 + 5.49956i) q^{29} +(-27.6558 + 15.9671i) q^{31} +(-31.9476 - 1.83125i) q^{32} +(27.5984 - 19.5725i) q^{34} +3.63153i q^{35} +58.2834 q^{37} +(22.5675 + 31.8215i) q^{38} +(-34.1469 + 35.3992i) q^{40} +(2.66948 + 4.62368i) q^{41} +(33.9324 + 19.5909i) q^{43} +(52.9567 - 45.5303i) q^{44} +(-6.61653 + 14.4144i) q^{46} +(-9.64117 - 5.56633i) q^{47} +(-24.3255 - 42.1331i) q^{49} +(2.38396 + 25.4861i) q^{50} +(-7.01421 + 1.32380i) q^{52} -35.8770 q^{53} -107.343i q^{55} +(-1.14066 + 4.58570i) q^{56} +(1.18285 + 12.6455i) q^{58} +(-20.8974 + 12.0651i) q^{59} +(-37.9460 + 65.7244i) q^{61} +(-26.6441 + 58.0454i) q^{62} +(-54.2376 + 33.9747i) q^{64} +(-5.48564 + 9.50141i) q^{65} +(31.8200 - 18.3713i) q^{67} +(22.3790 - 63.8607i) q^{68} +(4.20156 + 5.92445i) q^{70} -87.8370i q^{71} -60.0423 q^{73} +(95.0830 - 67.4319i) q^{74} +(73.6328 + 25.8035i) q^{76} +(-5.15652 - 8.93136i) q^{77} +(-32.1841 - 18.5815i) q^{79} +(-14.7512 + 97.2567i) q^{80} +(9.70439 + 4.45452i) q^{82} +(-66.0281 - 38.1214i) q^{83} +(-52.0037 - 90.0730i) q^{85} +(78.0229 - 7.29823i) q^{86} +(33.7161 - 135.547i) q^{88} +27.5873 q^{89} +1.05407i q^{91} +(5.88285 + 31.1706i) q^{92} +(-22.1686 + 2.07364i) q^{94} +(103.856 - 59.9614i) q^{95} +(13.0585 - 22.6180i) q^{97} +(-88.4309 - 40.5917i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8}+O(q^{10}) \) 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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