LMFDB - Embedded newform 819.2.n.d.172.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(100,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("819.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.n (of order $3$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			172.2
Root			$1.16700 + 2.02131i$ of defining polynomial
Character	$\chi$	$=$	819.172
Dual form			819.2.n.d.100.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.952780 + 1.65026i) q^{2} +(-0.815580 - 1.41263i) q^{4} +(-0.736565 - 1.27577i) q^{5} +(-2.62736 - 0.311376i) q^{7} -0.702849 q^{8} +O(q^{10})$	\(q+(-0.952780 + 1.65026i) q^{2} +(-0.815580 - 1.41263i) q^{4} +(-0.736565 - 1.27577i) q^{5} +(-2.62736 - 0.311376i) q^{7} -0.702849 q^{8} +2.80714 q^{10} +4.39361 q^{11} +(2.69752 + 2.39236i) q^{13} +(3.01715 - 4.03917i) q^{14} +(2.30082 - 3.98514i) q^{16} +(-0.601356 - 1.04158i) q^{17} +3.24209 q^{19} +(-1.20145 + 2.08098i) q^{20} +(-4.18615 + 7.25062i) q^{22} +(-2.21855 + 3.84264i) q^{23} +(1.41494 - 2.45075i) q^{25} +(-6.51816 + 2.17223i) q^{26} +(1.70297 + 3.96543i) q^{28} +(0.0837807 + 0.145112i) q^{29} +(-2.62272 + 4.54268i) q^{31} +(3.68150 + 6.37655i) q^{32} +2.29184 q^{34} +(1.53798 + 3.58126i) q^{35} +(-3.52527 + 6.10595i) q^{37} +(-3.08900 + 5.35031i) q^{38} +(0.517694 + 0.896672i) q^{40} +(2.58195 + 4.47206i) q^{41} +(-0.0113752 + 0.0197024i) q^{43} +(-3.58334 - 6.20653i) q^{44} +(-4.22758 - 7.32239i) q^{46} +(5.84178 + 10.1183i) q^{47} +(6.80609 + 1.63620i) q^{49} +(2.69626 + 4.67006i) q^{50} +(1.17946 - 5.76175i) q^{52} +(-0.0708929 + 0.122790i) q^{53} +(-3.23618 - 5.60523i) q^{55} +(1.84664 + 0.218850i) q^{56} -0.319298 q^{58} +(-2.67177 - 4.62764i) q^{59} +11.5457 q^{61} +(-4.99774 - 8.65635i) q^{62} -4.82736 q^{64} +(1.06519 - 5.20354i) q^{65} +4.13546 q^{67} +(-0.980907 + 1.69898i) q^{68} +(-7.37537 - 0.874075i) q^{70} +(-4.98486 + 8.63403i) q^{71} +(-7.62080 + 13.1996i) q^{73} +(-6.71762 - 11.6353i) q^{74} +(-2.64418 - 4.57986i) q^{76} +(-11.5436 - 1.36807i) q^{77} +(-0.387251 - 0.670738i) q^{79} -6.77881 q^{80} -9.84011 q^{82} +16.0186 q^{83} +(-0.885875 + 1.53438i) q^{85} +(-0.0216761 - 0.0375441i) q^{86} -3.08805 q^{88} +(3.27880 - 5.67904i) q^{89} +(-6.34245 - 7.12554i) q^{91} +7.23762 q^{92} -22.2637 q^{94} +(-2.38801 - 4.13616i) q^{95} +(-1.74583 + 3.02387i) q^{97} +(-9.18486 + 9.67291i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8	$ 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8} - 8 q^{10} + 8 q^{11} - 2 q^{13} + 2 q^{14} + 8 q^{16} - 5 q^{17} + 2 q^{19} + q^{20} - 5 q^{22} + q^{23} + 7 q^{25} - 5 q^{26} - 7 q^{28} - 3 q^{29} + 16 q^{31} - 8 q^{32} + 32 q^{34} - 8 q^{35} - 13 q^{37} + 17 q^{38} - 5 q^{40} + 8 q^{41} - 11 q^{43} - 21 q^{44} + 16 q^{46} + q^{47} - 3 q^{49} - 6 q^{50} - 25 q^{52} + 2 q^{53} + 9 q^{55} + 18 q^{56} + 16 q^{58} - 13 q^{59} + 10 q^{61} - 5 q^{62} - 30 q^{64} - 19 q^{65} + 22 q^{67} - 29 q^{68} - 39 q^{70} - 6 q^{71} - 30 q^{73} + 3 q^{74} - 9 q^{76} - 11 q^{77} + 7 q^{79} - 14 q^{80} - 2 q^{82} + 54 q^{83} - q^{85} + 7 q^{86} - 4 q^{89} - 20 q^{91} - 54 q^{92} - 90 q^{94} + 6 q^{95} - 35 q^{97} - 62 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8 - 8 * q^10 + 8 * q^11 - 2 * q^13 + 2 * q^14 + 8 * q^16 - 5 * q^17 + 2 * q^19 + q^20 - 5 * q^22 + q^23 + 7 * q^25 - 5 * q^26 - 7 * q^28 - 3 * q^29 + 16 * q^31 - 8 * q^32 + 32 * q^34 - 8 * q^35 - 13 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 + 16 * q^46 + q^47 - 3 * q^49 - 6 * q^50 - 25 * q^52 + 2 * q^53 + 9 * q^55 + 18 * q^56 + 16 * q^58 - 13 * q^59 + 10 * q^61 - 5 * q^62 - 30 * q^64 - 19 * q^65 + 22 * q^67 - 29 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 + 3 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 - 14 * q^80 - 2 * q^82 + 54 * q^83 - q^85 + 7 * q^86 - 4 * q^89 - 20 * q^91 - 54 * q^92 - 90 * q^94 + 6 * q^95 - 35 * q^97 - 62 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.952780	+	1.65026i	−0.673717	+	1.16691i	0.303125	+	0.952951i	$0.401970\pi$
$2$	−0.952780	+	1.65026i	−0.673717	+	1.16691i	−0.976842	+	0.213962i	$0.931363\pi$
$3$		0			0
$3$		0			0
$4$	−0.815580	−	1.41263i	−0.407790	−	0.706313i
$5$	−0.736565	−	1.27577i	−0.329402	−	0.570541i	0.652991	−	0.757365i	$-0.273514\pi$
$5$	−0.736565	−	1.27577i	−0.329402	−	0.570541i	−0.982393	+	0.186825i	$0.940180\pi$
$6$		0			0
$7$	−2.62736	−	0.311376i	−0.993050	−	0.117689i
$7$	−2.62736	−	0.311376i	−0.993050	−	0.117689i
$8$	−0.702849			−0.248495
$9$		0			0
$10$	2.80714			0.887695
$11$	4.39361			1.32472			0.662362	−	0.749184i	$-0.269554\pi$
$11$	4.39361			1.32472			0.662362	+	0.749184i	$0.269554\pi$
$12$		0			0
$13$	2.69752	+	2.39236i	0.748158	+	0.663520i
$13$	2.69752	+	2.39236i	0.748158	+	0.663520i
$14$	3.01715	−	4.03917i	0.806368	−	1.07951i
$15$		0			0
$16$	2.30082	−	3.98514i	0.575205	−	0.996284i
$17$	−0.601356	−	1.04158i	−0.145850	−	0.252620i	0.783840	−	0.620963i	$-0.213258\pi$
$17$	−0.601356	−	1.04158i	−0.145850	−	0.252620i	−0.929690	+	0.368343i	$0.879925\pi$
$18$		0			0
$19$	3.24209			0.743787			0.371893	−	0.928275i	$-0.378709\pi$
$19$	3.24209			0.743787			0.371893	+	0.928275i	$0.378709\pi$
$20$	−1.20145	+	2.08098i	−0.268653	+	0.465321i
$21$		0			0
$22$	−4.18615	+	7.25062i	−0.892490	+	1.54584i
$23$	−2.21855	+	3.84264i	−0.462600	+	0.801246i	−0.999090	−	0.0426603i	$-0.986417\pi$
$23$	−2.21855	+	3.84264i	−0.462600	+	0.801246i	0.536490	+	0.843907i	$0.319750\pi$
$24$		0			0
$25$	1.41494	−	2.45075i	0.282989	−	0.490151i
$26$	−6.51816	+	2.17223i	−1.27832	+	0.426010i
$27$		0			0
$28$	1.70297	+	3.96543i	0.321831	+	0.749396i
$29$	0.0837807	+	0.145112i	0.0155577	+	0.0269467i	0.873699	−	0.486466i	$-0.161714\pi$
$29$	0.0837807	+	0.145112i	0.0155577	+	0.0269467i	−0.858142	+	0.513413i	$0.828381\pi$
$30$		0			0
$31$	−2.62272	+	4.54268i	−0.471054	+	0.815889i	−0.999452	−	0.0331076i	$-0.989460\pi$
$31$	−2.62272	+	4.54268i	−0.471054	+	0.815889i	0.528398	+	0.848997i	$0.322793\pi$
$32$	3.68150	+	6.37655i	0.650803	+	1.12722i
$33$		0			0
$34$	2.29184			0.393047
$35$	1.53798	+	3.58126i	0.259966	+	0.605343i
$36$		0			0
$37$	−3.52527	+	6.10595i	−0.579552	+	1.00381i	0.415979	+	0.909374i	$0.363439\pi$
$37$	−3.52527	+	6.10595i	−0.579552	+	1.00381i	−0.995531	+	0.0944386i	$0.969894\pi$
$38$	−3.08900	+	5.35031i	−0.501102	+	0.867934i
$39$		0			0
$40$	0.517694	+	0.896672i	0.0818546	+	0.141776i
$41$	2.58195	+	4.47206i	0.403233	+	0.698419i	0.994114	−	0.108339i	$-0.0345533\pi$
$41$	2.58195	+	4.47206i	0.403233	+	0.698419i	−0.590881	+	0.806758i	$0.701220\pi$
$42$		0			0
$43$	−0.0113752	+	0.0197024i	−0.00173470	+	0.00300459i	−0.866891	−	0.498497i	$-0.833886\pi$
$43$	−0.0113752	+	0.0197024i	−0.00173470	+	0.00300459i	0.865157	+	0.501502i	$0.167219\pi$
$44$	−3.58334	−	6.20653i	−0.540209	−	0.935670i
$45$		0			0
$46$	−4.22758	−	7.32239i	−0.623323	−	1.07963i
$47$	5.84178	+	10.1183i	0.852111	+	1.47590i	0.879300	+	0.476269i	$0.158011\pi$
$47$	5.84178	+	10.1183i	0.852111	+	1.47590i	−0.0271891	+	0.999630i	$0.508656\pi$
$48$		0			0
$49$	6.80609	+	1.63620i	0.972299	+	0.233742i
$50$	2.69626	+	4.67006i	0.381309	+	0.660446i
$51$		0			0
$52$	1.17946	−	5.76175i	0.163561	−	0.799010i
$53$	−0.0708929	+	0.122790i	−0.00973788	+	0.0168665i	−0.870853	−	0.491543i	$-0.836433\pi$
$53$	−0.0708929	+	0.122790i	−0.00973788	+	0.0168665i	0.861115	+	0.508410i	$0.169766\pi$
$54$		0			0
$55$	−3.23618	−	5.60523i	−0.436367	−	0.755809i
$56$	1.84664	+	0.218850i	0.246768	+	0.0292451i
$57$		0			0
$58$	−0.319298			−0.0419259
$59$	−2.67177	−	4.62764i	−0.347835	−	0.602468i	0.638030	−	0.770012i	$-0.279750\pi$
$59$	−2.67177	−	4.62764i	−0.347835	−	0.602468i	−0.985865	+	0.167544i	$0.946416\pi$
$60$		0			0
$61$	11.5457			1.47828			0.739141	−	0.673551i	$-0.235232\pi$
$61$	11.5457			1.47828			0.739141	+	0.673551i	$0.235232\pi$
$62$	−4.99774	−	8.65635i	−0.634714	−	1.09936i
$63$		0			0
$64$	−4.82736			−0.603420
$65$	1.06519	−	5.20354i	0.132121	−	0.645420i
$66$		0			0
$67$	4.13546			0.505226			0.252613	−	0.967567i	$-0.418710\pi$
$67$	4.13546			0.505226			0.252613	+	0.967567i	$0.418710\pi$
$68$	−0.980907	+	1.69898i	−0.118952	+	0.206032i
$69$		0			0
$70$	−7.37537	−	0.874075i	−0.881526	−	0.104472i
$71$	−4.98486	+	8.63403i	−0.591594	+	1.02467i	0.402424	+	0.915453i	$0.368168\pi$
$71$	−4.98486	+	8.63403i	−0.591594	+	1.02467i	−0.994018	+	0.109217i	$0.965166\pi$
$72$		0			0
$73$	−7.62080	+	13.1996i	−0.891947	+	1.54490i	−0.0544080	+	0.998519i	$0.517327\pi$
$73$	−7.62080	+	13.1996i	−0.891947	+	1.54490i	−0.837539	+	0.546378i	$0.816006\pi$
$74$	−6.71762	−	11.6353i	−0.780908	−	1.35257i
$75$		0			0
$76$	−2.64418	−	4.57986i	−0.303309	−	0.525346i
$77$	−11.5436	−	1.36807i	−1.31552	−	0.155906i
$78$		0			0
$79$	−0.387251	−	0.670738i	−0.0435691	−	0.0754639i	0.843418	−	0.537257i	$-0.180540\pi$
$79$	−0.387251	−	0.670738i	−0.0435691	−	0.0754639i	−0.886988	+	0.461793i	$0.847206\pi$
$80$	−6.77881			−0.757894
$81$		0			0
$82$	−9.84011			−1.08666
$83$	16.0186			1.75827			0.879136	−	0.476571i	$-0.158121\pi$
$83$	16.0186			1.75827			0.879136	+	0.476571i	$0.158121\pi$
$84$		0			0
$85$	−0.885875	+	1.53438i	−0.0960866	+	0.166427i
$86$	−0.0216761	−	0.0375441i	−0.00233740	−	0.00404849i
$87$		0			0
$88$	−3.08805			−0.329187
$89$	3.27880	−	5.67904i	0.347552	−	0.601977i	−0.638262	−	0.769819i	$-0.720346\pi$
$89$	3.27880	−	5.67904i	0.347552	−	0.601977i	0.985814	+	0.167842i	$0.0536797\pi$
$90$		0			0
$91$	−6.34245	−	7.12554i	−0.664870	−	0.746959i
$92$	7.23762			0.754574
$93$		0			0
$94$	−22.2637			−2.29633
$95$	−2.38801	−	4.13616i	−0.245005	−	0.424361i
$96$		0			0
$97$	−1.74583	+	3.02387i	−0.177262	+	0.307027i	−0.940942	−	0.338568i	$-0.890057\pi$
$97$	−1.74583	+	3.02387i	−0.177262	+	0.307027i	0.763680	+	0.645595i	$0.223391\pi$
$98$	−9.18486	+	9.67291i	−0.927811	+	0.977111i
$99$		0			0
$100$	−4.61600			−0.461600
$101$	−2.57780			−0.256500			−0.128250	−	0.991742i	$-0.540936\pi$
$101$	−2.57780			−0.256500			−0.128250	+	0.991742i	$0.540936\pi$
$102$		0			0
$103$	8.43173	+	14.6042i	0.830803	+	1.43899i	0.897402	+	0.441213i	$0.145452\pi$
$103$	8.43173	+	14.6042i	0.830803	+	1.43899i	−0.0665997	+	0.997780i	$0.521215\pi$
$104$	−1.89595	−	1.68146i	−0.185913	−	0.164881i
$105$		0			0
$106$	−0.135091	−	0.233984i	−0.0131212	−	0.0227265i
$107$	4.34132	−	7.51939i	0.419692	−	0.726927i	−0.576217	−	0.817297i	$-0.695472\pi$
$107$	4.34132	−	7.51939i	0.419692	−	0.726927i	0.995908	+	0.0903697i	$0.0288049\pi$
$108$		0			0
$109$	6.02026	−	10.4274i	0.576637	−	0.998764i	−0.419225	−	0.907882i	$-0.637698\pi$
$109$	6.02026	−	10.4274i	0.576637	−	0.998764i	0.995862	−	0.0908816i	$-0.0289685\pi$
$110$	12.3335			1.17595
$111$		0			0
$112$	−7.28597	+	9.75398i	−0.688459	+	0.921665i
$113$	4.68616	−	8.11667i	0.440837	−	0.763552i	−0.556915	−	0.830570i	$-0.688015\pi$
$113$	4.68616	−	8.11667i	0.440837	−	0.763552i	0.997752	+	0.0670176i	$0.0213484\pi$
$114$		0			0
$115$	6.53643			0.609525
$116$	0.136660	−	0.236701i	0.0126885	−	0.0219772i
$117$		0			0
$118$	10.1824			0.937369
$119$	1.25566	+	2.92385i	0.115106	+	0.268029i
$120$		0			0
$121$	8.30385			0.754895
$122$	−11.0006	+	19.0535i	−0.995944	+	1.72503i
$123$		0			0
$124$	8.55614			0.768364
$125$	−11.5344			−1.03167
$126$		0			0
$127$	−7.94269	−	13.7571i	−0.704800	−	1.22075i	−0.966764	−	0.255672i	$-0.917703\pi$
$127$	−7.94269	−	13.7571i	−0.704800	−	1.22075i	0.261964	−	0.965078i	$-0.415630\pi$
$128$	−2.76359	+	4.78667i	−0.244269	+	0.423086i
$129$		0			0
$130$	7.57232	+	6.71567i	0.664136	+	0.589004i
$131$	0.928725	+	1.60860i	0.0811430	+	0.140544i	0.903741	−	0.428079i	$-0.140810\pi$
$131$	0.928725	+	1.60860i	0.0811430	+	0.140544i	−0.822598	+	0.568623i	$0.807476\pi$
$132$		0			0
$133$	−8.51816	−	1.00951i	−0.738618	−	0.0875356i
$134$	−3.94018	+	6.82459i	−0.340380	+	0.589555i
$135$		0			0
$136$	0.422662	+	0.732072i	0.0362430	+	0.0627747i
$137$	−6.40011	−	11.0853i	−0.546798	−	0.947082i	−0.998491	−	0.0549088i	$-0.982513\pi$
$137$	−6.40011	−	11.0853i	−0.546798	−	0.947082i	0.451693	−	0.892173i	$-0.350820\pi$
$138$		0			0
$139$	0.169365	−	0.293348i	0.0143653	−	0.0248815i	−0.858753	−	0.512389i	$-0.828761\pi$
$139$	0.169365	−	0.293348i	0.0143653	−	0.0248815i	0.873119	+	0.487508i	$0.162094\pi$
$140$	3.80463	−	5.09339i	0.321550	−	0.430470i
$141$		0			0
$142$	−9.49894	−	16.4527i	−0.797134	−	1.38068i
$143$	11.8519	+	10.5111i	0.991104	+	0.878982i
$144$		0			0
$145$	0.123420	−	0.213769i	0.0102495	−	0.0177526i
$146$	−14.5219	−	25.1526i	−1.20184	−	2.08165i
$147$		0			0
$148$	11.5006			0.945341
$149$	−3.92316			−0.321398			−0.160699	−	0.987003i	$-0.551375\pi$
$149$	−3.92316			−0.321398			−0.160699	+	0.987003i	$0.551375\pi$
$150$		0			0
$151$	1.05939	−	1.83492i	0.0862122	−	0.149324i	−0.819695	−	0.572800i	$-0.805857\pi$
$151$	1.05939	−	1.83492i	0.0862122	−	0.149324i	0.905907	+	0.423476i	$0.139190\pi$
$152$	−2.27870			−0.184827
$153$		0			0
$154$	13.2562	−	17.7466i	1.06822	−	1.43006i
$155$	7.72721			0.620664
$156$		0			0
$157$	11.0564	−	19.1502i	0.882397	−	1.52836i	0.0337285	−	0.999431i	$-0.489262\pi$
$157$	11.0564	−	19.1502i	0.882397	−	1.52836i	0.848668	−	0.528925i	$-0.177405\pi$
$158$	1.47586			0.117413
$159$		0			0
$160$	5.42333	−	9.39348i	0.428752	−	0.742620i
$161$	7.02545	−	9.40522i	0.553683	−	0.741235i
$162$		0			0
$163$	3.85214			0.301723			0.150861	−	0.988555i	$-0.451795\pi$
$163$	3.85214			0.301723			0.150861	+	0.988555i	$0.451795\pi$
$164$	4.21157	−	7.29465i	0.328868	−	0.569616i
$165$		0			0
$166$	−15.2622	+	26.4349i	−1.18458	+	2.05175i
$167$	1.06947	+	1.85238i	0.0827582	+	0.143341i	0.904434	−	0.426614i	$-0.140294\pi$
$167$	1.06947	+	1.85238i	0.0827582	+	0.143341i	−0.821676	+	0.569956i	$0.806960\pi$
$168$		0			0
$169$	1.55326	+	12.9069i	0.119482	+	0.992836i
$170$	−1.68809	−	2.92385i	−0.129470	−	0.224249i
$171$		0			0
$172$	0.0371095			0.00282957
$173$	16.6133			1.26308			0.631542	−	0.775342i	$-0.282422\pi$
$173$	16.6133			1.26308			0.631542	+	0.775342i	$0.282422\pi$
$174$		0			0
$175$	−4.48068	+	5.99845i	−0.338708	+	0.453440i
$176$	10.1089	−	17.5091i	0.761988	−	1.31980i
$177$		0			0
$178$	6.24795	+	10.8218i	0.468303	+	0.811125i
$179$	0.539496			0.0403238			0.0201619	−	0.999797i	$-0.493582\pi$
$179$	0.539496			0.0403238			0.0201619	+	0.999797i	$0.493582\pi$
$180$		0			0
$181$	2.77164			0.206014			0.103007	−	0.994681i	$-0.467154\pi$
$181$	2.77164			0.206014			0.103007	+	0.994681i	$0.467154\pi$
$182$	17.8020	−	3.67765i	1.31957	−	0.272606i
$183$		0			0
$184$	1.55931	−	2.70080i	0.114954	−	0.199105i
$185$	10.3864			0.763621
$186$		0			0
$187$	−2.64213	−	4.57629i	−0.193211	−	0.334652i
$188$	9.52887	−	16.5045i	0.694964	−	1.20371i
$189$		0			0
$190$	9.10100			0.660256
$191$	20.2407			1.46457			0.732284	−	0.680999i	$-0.238454\pi$
$191$	20.2407			1.46457			0.732284	+	0.680999i	$0.238454\pi$
$192$		0			0
$193$	−16.3771			−1.17885			−0.589425	−	0.807823i	$-0.700646\pi$
$193$	−16.3771			−1.17885			−0.589425	+	0.807823i	$0.700646\pi$
$194$	−3.32678	−	5.76216i	−0.238849	−	0.413699i
$195$		0			0
$196$	−3.23958	−	10.9489i	−0.231398	−	0.782064i
$197$	9.86676	+	17.0897i	0.702977	+	1.21759i	0.967417	+	0.253190i	$0.0814798\pi$
$197$	9.86676	+	17.0897i	0.702977	+	1.21759i	−0.264439	+	0.964402i	$0.585187\pi$
$198$		0			0
$199$	7.05873	+	12.2261i	0.500380	+	0.866683i	1.00000		0.000438630i	$0.000139620\pi$
$199$	7.05873	+	12.2261i	0.500380	+	0.866683i	−0.499620	+	0.866245i	$0.666527\pi$
$200$	−0.994491	+	1.72251i	−0.0703212	+	0.121800i
$201$		0			0
$202$	2.45607	−	4.25404i	0.172809	−	0.299313i
$203$	−0.174938	−	0.407351i	−0.0122782	−	0.0285904i
$204$		0			0
$205$	3.80354	−	6.58793i	0.265651	−	0.460121i
$206$	−32.1343			−2.23890
$207$		0			0
$208$	15.7404	−	5.24562i	1.09140	−	0.363718i
$209$	14.2445			0.985313
$210$		0			0
$211$	2.31317	+	4.00652i	0.159245	+	0.275820i	0.934597	−	0.355709i	$-0.115761\pi$
$211$	2.31317	+	4.00652i	0.159245	+	0.275820i	−0.775352	+	0.631530i	$0.782427\pi$
$212$	0.231275			0.0158840
$213$		0			0
$214$	8.27265	+	14.3287i	0.565507	+	0.979487i
$215$	0.0335143			0.00228565
$216$		0			0
$217$	8.30532	−	11.1186i	0.563802	−	0.754781i
$218$	11.4720	+	19.8700i	0.776980	+	1.34577i
$219$		0			0
$220$	−5.27873	+	9.14303i	−0.355892	+	0.616423i
$221$	0.869656	−	4.24834i	0.0584994	−	0.285774i
$222$		0			0
$223$	10.6761	+	18.4916i	0.714926	+	1.23829i	0.962988	+	0.269545i	$0.0868732\pi$
$223$	10.6761	+	18.4916i	0.714926	+	1.23829i	−0.248061	+	0.968744i	$0.579793\pi$
$224$	−7.68714	−	17.8998i	−0.513619	−	1.19598i
$225$		0			0
$226$	8.92976	+	15.4668i	0.593999	+	1.02884i
$227$	−5.22451	−	9.04911i	−0.346763	−	0.600611i	0.638910	−	0.769282i	$-0.279386\pi$
$227$	−5.22451	−	9.04911i	−0.346763	−	0.600611i	−0.985672	+	0.168671i	$0.946052\pi$
$228$		0			0
$229$	−7.22901	−	12.5210i	−0.477706	−	0.827412i	0.521967	−	0.852966i	$-0.325198\pi$
$229$	−7.22901	−	12.5210i	−0.477706	−	0.827412i	−0.999673	+	0.0255538i	$0.991865\pi$
$230$	−6.22778	+	10.7868i	−0.410648	+	0.711262i
$231$		0			0
$232$	−0.0588852	−	0.101992i	−0.00386600	−	0.00669611i
$233$	−4.64413	−	8.04388i	−0.304247	−	0.526972i	0.672846	−	0.739783i	$-0.265072\pi$
$233$	−4.64413	−	8.04388i	−0.304247	−	0.526972i	−0.977093	+	0.212811i	$0.931738\pi$
$234$		0			0
$235$	8.60570	−	14.9055i	0.561374	−	0.972328i
$236$	−4.35808	+	7.54842i	−0.283687	+	0.491360i
$237$		0			0
$238$	−6.02150	−	0.713623i	−0.390316	−	0.0462573i
$239$	−19.6332			−1.26997			−0.634983	−	0.772526i	$-0.718993\pi$
$239$	−19.6332			−1.26997			−0.634983	+	0.772526i	$0.718993\pi$
$240$		0			0
$241$	−3.65552	−	6.33155i	−0.235473	−	0.407851i	0.723937	−	0.689866i	$-0.242331\pi$
$241$	−3.65552	−	6.33155i	−0.235473	−	0.407851i	−0.959410	+	0.282015i	$0.908997\pi$
$242$	−7.91174	+	13.7035i	−0.508586	+	0.880897i
$243$		0			0
$244$	−9.41648	−	16.3098i	−0.602828	−	1.04413i
$245$	−2.92572	−	9.88816i	−0.186917	−	0.631731i
$246$		0			0
$247$	8.74562	+	7.75624i	0.556470	+	0.493518i
$248$	1.84337	−	3.19282i	0.117054	−	0.202744i
$249$		0			0
$250$	10.9898	−	19.0349i	0.695055	−	1.20387i
$251$	−5.93191	+	10.2744i	−0.374419	+	0.648512i	−0.990240	−	0.139374i	$-0.955491\pi$
$251$	−5.93191	+	10.2744i	−0.374419	+	0.648512i	0.615821	+	0.787886i	$0.288824\pi$
$252$		0			0
$253$	−9.74746	+	16.8831i	−0.612817	+	1.06143i
$254$	30.2706			1.89934
$255$		0			0
$256$	−10.0935	−	17.4825i	−0.630846	−	1.09266i
$257$	−7.58608	+	13.1395i	−0.473206	+	0.819618i	−0.999530	−	0.0306670i	$-0.990237\pi$
$257$	−7.58608	+	13.1395i	−0.473206	+	0.819618i	0.526323	+	0.850285i	$0.323570\pi$
$258$		0			0
$259$	11.1634	−	14.9449i	0.693662	−	0.928630i
$260$	−8.21940	+	2.73919i	−0.509745	+	0.169877i
$261$		0			0
$262$	−3.53948			−0.218670
$263$	−17.1964			−1.06037			−0.530187	−	0.847880i	$-0.677878\pi$
$263$	−17.1964			−1.06037			−0.530187	+	0.847880i	$0.677878\pi$
$264$		0			0
$265$	0.208869			0.0128307
$266$	9.78189	−	13.0954i	0.599766	−	0.802928i
$267$		0			0
$268$	−3.37279	−	5.84185i	−0.206026	−	0.356848i
$269$	9.46102	+	16.3870i	0.576849	+	0.999131i	0.995838	+	0.0911401i	$0.0290511\pi$
$269$	9.46102	+	16.3870i	0.576849	+	0.999131i	−0.418989	+	0.907991i	$0.637616\pi$
$270$		0			0
$271$	−16.0667	+	27.8283i	−0.975982	+	1.69045i	−0.299324	+	0.954151i	$0.596761\pi$
$271$	−16.0667	+	27.8283i	−0.975982	+	1.69045i	−0.676657	+	0.736298i	$0.736572\pi$
$272$	−5.53444			−0.335575
$273$		0			0
$274$	24.3916			1.47355
$275$	6.21672	−	10.7677i	0.374882	−	0.649315i
$276$		0			0
$277$	−9.20269	−	15.9395i	−0.552936	−	0.957714i	−0.998061	−	0.0622450i	$-0.980174\pi$
$277$	−9.20269	−	15.9395i	−0.552936	−	0.957714i	0.445125	−	0.895469i	$-0.353159\pi$
$278$	0.322734	+	0.558992i	0.0193563	+	0.0335261i
$279$		0			0
$280$	−1.08097	−	2.51708i	−0.0646002	−	0.150424i
$281$	14.2252			0.848603			0.424302	−	0.905521i	$-0.360520\pi$
$281$	14.2252			0.848603			0.424302	+	0.905521i	$0.360520\pi$
$282$		0			0
$283$	−11.4289			−0.679378			−0.339689	−	0.940538i	$-0.610322\pi$
$283$	−11.4289			−0.679378			−0.339689	+	0.940538i	$0.610322\pi$
$284$	16.2622			0.964983
$285$		0			0
$286$	−28.6383	+	9.54396i	−1.69342	+	0.564346i
$287$	−5.39123	−	12.5537i	−0.318234	−	0.741022i
$288$		0			0
$289$	7.77674	−	13.4697i	0.457455	−	0.792336i
$290$	0.235184	+	0.407351i	0.0138105	+	0.0239205i
$291$		0			0
$292$	24.8615			1.45491
$293$	−6.60231	+	11.4355i	−0.385711	+	0.668071i	−0.991868	−	0.127274i	$-0.959377\pi$
$293$	−6.60231	+	11.4355i	−0.385711	+	0.668071i	0.606156	+	0.795345i	$0.292711\pi$
$294$		0			0
$295$	−3.93586	+	6.81712i	−0.229155	+	0.396908i
$296$	2.47773	−	4.29156i	0.144015	−	0.249442i
$297$		0			0
$298$	3.73791	−	6.47425i	0.216531	−	0.375043i
$299$	−15.1776	+	5.05805i	−0.877741	+	0.292515i
$300$		0			0
$301$	0.0360216	−	0.0482235i	0.00207625	−	0.00277955i
$302$	2.01874	+	3.49656i	0.116165	+	0.201204i
$303$		0			0
$304$	7.45947	−	12.9202i	0.427830	−	0.741023i
$305$	−8.50420	−	14.7297i	−0.486949	−	0.843420i
$306$		0			0
$307$	−6.65903			−0.380051			−0.190026	−	0.981779i	$-0.560857\pi$
$307$	−6.65903			−0.380051			−0.190026	+	0.981779i	$0.560857\pi$
$308$	7.48218	+	17.4226i	0.426337	+	0.992744i
$309$		0			0
$310$	−7.36233	+	12.7519i	−0.418152	+	0.724261i
$311$	−1.02298	+	1.77186i	−0.0580081	+	0.100473i	−0.893571	−	0.448922i	$-0.851808\pi$
$311$	−1.02298	+	1.77186i	−0.0580081	+	0.100473i	0.835563	+	0.549395i	$0.185142\pi$
$312$		0			0
$313$	−4.70883	−	8.15594i	−0.266159	−	0.461001i	0.701708	−	0.712465i	$-0.252421\pi$
$313$	−4.70883	−	8.15594i	−0.266159	−	0.461001i	−0.967867	+	0.251464i	$0.919088\pi$
$314$	21.0686	+	36.4919i	1.18897	+	2.05936i
$315$		0			0
$316$	−0.631667	+	1.09408i	−0.0355341	+	0.0615468i
$317$	−16.6856	−	28.9004i	−0.937159	−	1.62321i	−0.770738	−	0.637153i	$-0.780112\pi$
$317$	−16.6856	−	28.9004i	−0.937159	−	1.62321i	−0.166421	−	0.986055i	$-0.553221\pi$
$318$		0			0
$319$	0.368100	+	0.637568i	0.0206097	+	0.0356970i
$320$	3.55567	+	6.15860i	0.198768	+	0.344276i
$321$		0			0
$322$	8.82739	+	20.5549i	0.491931	+	1.14548i
$323$	−1.94965	−	3.37689i	−0.108481	−	0.187895i
$324$		0			0
$325$	9.67992	−	3.22592i	0.536946	−	0.178942i
$326$	−3.67024	+	6.35704i	−0.203276	+	0.352084i
$327$		0			0
$328$	−1.81472	−	3.14318i	−0.100201	−	0.173553i
$329$	−12.1979	−	28.4033i	−0.672492	−	1.56593i
$330$		0			0
$331$	19.0660			1.04796			0.523980	−	0.851731i	$-0.324447\pi$
$331$	19.0660			1.04796			0.523980	+	0.851731i	$0.324447\pi$
$332$	−13.0645	−	22.6283i	−0.717005	−	1.24189i
$333$		0			0
$334$	−4.07589			−0.223023
$335$	−3.04603	−	5.27588i	−0.166423	−	0.288252i
$336$		0			0
$337$	−31.2849			−1.70420			−0.852098	−	0.523382i	$-0.824670\pi$
$337$	−31.2849			−1.70420			−0.852098	+	0.523382i	$0.824670\pi$
$338$	−22.7797	−	9.73412i	−1.23905	−	0.529466i
$339$		0			0
$340$	2.89001			0.156733
$341$	−11.5232	+	19.9588i	−0.624017	+	1.08083i
$342$		0			0
$343$	−17.3726	−	6.41814i	−0.938033	−	0.346547i
$344$	0.00799504	−	0.0138478i	0.000431064	−	0.000746624i
$345$		0			0
$346$	−15.8288	+	27.4163i	−0.850961	+	1.47391i
$347$	5.83759	+	10.1110i	0.313378	+	0.542787i	0.979091	−	0.203420i	$-0.0652058\pi$
$347$	5.83759	+	10.1110i	0.313378	+	0.542787i	−0.665713	+	0.746208i	$0.731872\pi$
$348$		0			0
$349$	−11.9952	−	20.7763i	−0.642089	−	1.11213i	−0.984966	−	0.172750i	$-0.944735\pi$
$349$	−11.9952	−	20.7763i	−0.642089	−	1.11213i	0.342877	−	0.939380i	$-0.388599\pi$
$350$	−5.62992	−	13.1095i	−0.300932	−	0.700732i
$351$		0			0
$352$	16.1751	+	28.0161i	0.862135	+	1.49326i
$353$	−12.7934			−0.680922			−0.340461	−	0.940259i	$-0.610583\pi$
$353$	−12.7934			−0.680922			−0.340461	+	0.940259i	$0.610583\pi$
$354$		0			0
$355$	14.6867			0.779488
$356$	−10.6965			−0.566912
$357$		0			0
$358$	−0.514021	+	0.890310i	−0.0271668	+	0.0470544i
$359$	6.16986	+	10.6865i	0.325633	+	0.564012i	0.981640	−	0.190742i	$-0.0610894\pi$
$359$	6.16986	+	10.6865i	0.325633	+	0.564012i	−0.656008	+	0.754754i	$0.727756\pi$
$360$		0			0
$361$	−8.48884			−0.446781
$362$	−2.64076	+	4.57393i	−0.138795	+	0.240401i
$363$		0			0
$364$	−4.89294	+	14.7710i	−0.256460	+	0.774208i
$365$	22.4528			1.17524
$366$		0			0
$367$	2.03077			0.106005			0.0530026	−	0.998594i	$-0.483121\pi$
$367$	2.03077			0.106005			0.0530026	+	0.998594i	$0.483121\pi$
$368$	10.2090	+	17.6825i	0.532179	+	0.921762i
$369$		0			0
$370$	−9.89593	+	17.1403i	−0.514465	+	0.891079i
$371$	0.224495	−	0.300540i	0.0116552	−	0.0156033i
$372$		0			0
$373$	−3.87400			−0.200588			−0.100294	−	0.994958i	$-0.531978\pi$
$373$	−3.87400			−0.200588			−0.100294	+	0.994958i	$0.531978\pi$
$374$	10.0695			0.520679
$375$		0			0
$376$	−4.10588	−	7.11160i	−0.211745	−	0.366753i
$377$	−0.121160	+	0.591877i	−0.00624007	+	0.0304832i
$378$		0			0
$379$	7.28396	+	12.6162i	0.374152	+	0.648050i	0.990200	−	0.139659i	$-0.0446006\pi$
$379$	7.28396	+	12.6162i	0.374152	+	0.648050i	−0.616048	+	0.787709i	$0.711267\pi$
$380$	−3.89523	+	6.74673i	−0.199821	+	0.346100i
$381$		0			0
$382$	−19.2850	+	33.4025i	−0.986705	+	1.70902i
$383$	26.7818			1.36849			0.684243	−	0.729254i	$-0.260133\pi$
$383$	26.7818			1.36849			0.684243	+	0.729254i	$0.260133\pi$
$384$		0			0
$385$	6.75730	+	15.7347i	0.344384	+	0.801912i
$386$	15.6038	−	27.0266i	0.794212	−	1.37562i
$387$		0			0
$388$	5.69545			0.289143
$389$	6.00738	−	10.4051i	0.304586	−	0.527559i	−0.672583	−	0.740022i	$-0.734815\pi$
$389$	6.00738	−	10.4051i	0.304586	−	0.527559i	0.977169	+	0.212463i	$0.0681485\pi$
$390$		0			0
$391$	5.33655			0.269881
$392$	−4.78365	−	1.15000i	−0.241611	−	0.0580837i
$393$		0			0
$394$	−37.6034			−1.89443
$395$	−0.570470	+	0.988084i	−0.0287035	+	0.0497159i
$396$		0			0
$397$	−1.65765			−0.0831951			−0.0415975	−	0.999134i	$-0.513245\pi$
$397$	−1.65765			−0.0831951			−0.0415975	+	0.999134i	$0.513245\pi$
$398$	−26.9017			−1.34846
$399$		0			0
$400$	−6.51106	−	11.2775i	−0.325553	−	0.563874i
$401$	−10.2414	+	17.7386i	−0.511430	+	0.885823i	0.488482	+	0.872574i	$0.337551\pi$
$401$	−10.2414	+	17.7386i	−0.511430	+	0.885823i	−0.999912	+	0.0132488i	$0.995783\pi$
$402$		0			0
$403$	−17.9425	+	5.97951i	−0.893782	+	0.297861i
$404$	2.10240	+	3.64146i	0.104598	+	0.181169i
$405$		0			0
$406$	0.838913	+	0.0994218i	0.0416346	+	0.00493422i
$407$	−15.4887	+	26.8272i	−0.767746	+	1.32978i
$408$		0			0
$409$	−7.43293	−	12.8742i	−0.367535	−	0.636589i	0.621645	−	0.783299i	$-0.286465\pi$
$409$	−7.43293	−	12.8742i	−0.367535	−	0.636589i	−0.989180	+	0.146710i	$0.953131\pi$
$410$	7.24788	+	12.5537i	0.357947	+	0.619983i
$411$		0			0
$412$	13.7535	−	23.8217i	0.677586	−	1.17361i
$413$	5.57878	+	12.9904i	0.274514	+	0.639217i
$414$		0			0
$415$	−11.7988	−	20.4360i	−0.579178	−	1.00317i
$416$	−5.32404	+	26.0083i	−0.261032	+	1.27516i
$417$		0			0
$418$	−13.5719	+	23.5072i	−0.663822	+	1.14977i
$419$	−11.8087	−	20.4533i	−0.576895	−	0.999211i	−0.995833	−	0.0911962i	$-0.970931\pi$
$419$	−11.8087	−	20.4533i	−0.576895	−	0.999211i	0.418938	−	0.908015i	$-0.362402\pi$
$420$		0			0
$421$	26.0822			1.27117			0.635585	−	0.772031i	$-0.280759\pi$
$421$	26.0822			1.27117			0.635585	+	0.772031i	$0.280759\pi$
$422$	−8.81576			−0.429144
$423$		0			0
$424$	0.0498269	−	0.0863028i	0.00241981	−	0.00419123i
$425$	−3.40354			−0.165096
$426$		0			0
$427$	−30.3349	−	3.59507i	−1.46801	−	0.173978i
$428$	−14.1628			−0.684584
$429$		0			0
$430$	−0.0319317	+	0.0553074i	−0.00153988	+	0.00266716i
$431$	13.3172			0.641466			0.320733	−	0.947170i	$-0.396071\pi$
$431$	13.3172			0.641466			0.320733	+	0.947170i	$0.396071\pi$
$432$		0			0
$433$	−10.2110	+	17.6860i	−0.490711	+	0.849937i	−0.999943	−	0.0106929i	$-0.996596\pi$
$433$	−10.2110	+	17.6860i	−0.490711	+	0.849937i	0.509232	+	0.860629i	$0.329930\pi$
$434$	10.4355	+	24.2996i	0.500921	+	1.16642i
$435$		0			0
$436$	−19.6400			−0.940586
$437$	−7.19275	+	12.4582i	−0.344076	+	0.595957i
$438$		0			0
$439$	4.88537	−	8.46171i	0.233166	−	0.403855i	−0.725572	−	0.688146i	$-0.758425\pi$
$439$	4.88537	−	8.46171i	0.233166	−	0.403855i	0.958738	+	0.284291i	$0.0917581\pi$
$440$	2.27455	+	3.93963i	0.108435	+	0.187814i
$441$		0			0
$442$	6.18229	+	5.48290i	0.294061	+	0.260795i
$443$	10.5819	+	18.3285i	0.502763	+	0.870811i	0.999995	+	0.00319331i	$0.00101646\pi$
$443$	10.5819	+	18.3285i	0.502763	+	0.870811i	−0.497232	+	0.867618i	$0.665650\pi$
$444$		0			0
$445$	−9.66019			−0.457937
$446$	−40.6880			−1.92663
$447$		0			0
$448$	12.6832	+	1.50312i	0.599227	+	0.0710160i
$449$	−9.07320	+	15.7152i	−0.428191	+	0.741648i	−0.996712	−	0.0810200i	$-0.974182\pi$
$449$	−9.07320	+	15.7152i	−0.428191	+	0.741648i	0.568522	+	0.822668i	$0.307516\pi$
$450$		0			0
$451$	11.3441	+	19.6485i	0.534172	+	0.925213i
$452$	−15.2877			−0.719075
$453$		0			0
$454$	19.9112			0.934480
$455$	−4.41890	+	13.3399i	−0.207161	+	0.625385i
$456$		0			0
$457$	9.00991	−	15.6056i	0.421466	−	0.730000i	−0.574617	−	0.818422i	$-0.694849\pi$
$457$	9.00991	−	15.6056i	0.421466	−	0.730000i	0.996083	+	0.0884220i	$0.0281824\pi$
$458$	27.5506			1.28736
$459$		0			0
$460$	−5.33098	−	9.23352i	−0.248558	−	0.430515i
$461$	−14.8873	+	25.7855i	−0.693370	+	1.20095i	0.277357	+	0.960767i	$0.410542\pi$
$461$	−14.8873	+	25.7855i	−0.693370	+	1.20095i	−0.970727	+	0.240185i	$0.922792\pi$
$462$		0			0
$463$	17.7067			0.822900			0.411450	−	0.911432i	$-0.365023\pi$
$463$	17.7067			0.822900			0.411450	+	0.911432i	$0.365023\pi$
$464$	0.771057			0.0357954
$465$		0			0
$466$	17.6994			0.819907
$467$	−2.91461	−	5.04825i	−0.134872	−	0.233605i	0.790677	−	0.612234i	$-0.209729\pi$
$467$	−2.91461	−	5.04825i	−0.134872	−	0.233605i	−0.925549	+	0.378629i	$0.876396\pi$
$468$		0			0
$469$	−10.8654	−	1.28768i	−0.501715	−	0.0594596i
$470$	16.3987	+	28.4033i	0.756414	+	1.31015i
$471$		0			0
$472$	1.87785	+	3.25253i	0.0864350	+	0.149710i
$473$	−0.0499782	+	0.0865648i	−0.00229800	+	0.00398025i
$474$		0			0
$475$	4.58738	−	7.94557i	0.210483	−	0.364568i
$476$	3.10622	−	4.15841i	0.142373	−	0.190600i
$477$		0			0
$478$	18.7061	−	32.4000i	0.855598	−	1.48194i
$479$	−14.4913			−0.662125			−0.331062	−	0.943609i	$-0.607407\pi$
$479$	−14.4913			−0.662125			−0.331062	+	0.943609i	$0.607407\pi$
$480$		0			0
$481$	−24.1171	+	8.03724i	−1.09965	+	0.366467i
$482$	13.9316			0.634569
$483$		0			0
$484$	−6.77245	−	11.7302i	−0.307839	−	0.533192i
$485$	5.14367			0.233562
$486$		0			0
$487$	8.98006	+	15.5539i	0.406926	+	0.704816i	0.994543	−	0.104323i	$-0.0332675\pi$
$487$	8.98006	+	15.5539i	0.406926	+	0.704816i	−0.587618	+	0.809139i	$0.699934\pi$
$488$	−8.11491			−0.367345
$489$		0			0
$490$	19.1056	+	4.59303i	0.863104	+	0.207492i
$491$	−18.1505	−	31.4375i	−0.819119	−	1.41876i	−0.906332	−	0.422566i	$-0.861130\pi$
$491$	−18.1505	−	31.4375i	−0.819119	−	1.41876i	0.0872134	−	0.996190i	$-0.472204\pi$
$492$		0			0
$493$	0.100764	−	0.174528i	0.00453818	−	0.00786036i
$494$	−21.1325	+	7.04258i	−0.950796	+	0.316861i
$495$		0			0
$496$	12.0688	+	20.9038i	0.541905	+	0.938607i
$497$	15.7855	−	21.1326i	0.708075	−	0.947925i
$498$		0			0
$499$	−11.8538	−	20.5314i	−0.530649	−	0.919112i	−0.999360	−	0.0357602i	$-0.988615\pi$
$499$	−11.8538	−	20.5314i	−0.530649	−	0.919112i	0.468711	−	0.883352i	$-0.344719\pi$
$500$	9.40726	+	16.2938i	0.420705	+	0.728683i
$501$		0			0
$502$	−11.3036	−	19.5784i	−0.504505	−	0.873828i
$503$	13.8876	−	24.0540i	0.619217	−	1.07252i	−0.370411	−	0.928868i	$-0.620783\pi$
$503$	13.8876	−	24.0540i	0.619217	−	1.07252i	0.989629	−	0.143648i	$-0.0458834\pi$
$504$		0			0
$505$	1.89871	+	3.28867i	0.0844916	+	0.146344i
$506$	−18.5744	−	32.1717i	−0.825731	−	1.43021i
$507$		0			0
$508$	−12.9558	+	22.4401i	−0.574820	+	0.995618i
$509$	4.35208	−	7.53802i	0.192902	−	0.334117i	−0.753308	−	0.657667i	$-0.771543\pi$
$509$	4.35208	−	7.53802i	0.192902	−	0.334117i	0.946211	+	0.323551i	$0.104877\pi$
$510$		0			0
$511$	24.1326	−	32.3072i	1.06757	−	1.42919i
$512$	27.4134			1.21151
$513$		0			0
$514$	−14.4557	−	25.0380i	−0.637615	−	1.10438i
$515$	12.4210	−	21.5139i	0.547336	−	0.948014i
$516$		0			0
$517$	25.6665	+	44.4557i	1.12881	+	1.95516i
$518$	14.0267	+	32.6618i	0.616298	+	1.43508i
$519$		0			0
$520$	−0.748668	+	3.65730i	−0.0328313	+	0.160383i
$521$	−4.28573	+	7.42310i	−0.187761	+	0.325212i	−0.944504	−	0.328501i	$-0.893456\pi$
$521$	−4.28573	+	7.42310i	−0.187761	+	0.325212i	0.756742	+	0.653713i	$0.226790\pi$
$522$		0			0
$523$	−14.9746	+	25.9369i	−0.654796	+	1.13414i	0.327149	+	0.944973i	$0.393912\pi$
$523$	−14.9746	+	25.9369i	−0.654796	+	1.13414i	−0.981945	+	0.189167i	$0.939421\pi$
$524$	1.51490	−	2.62388i	0.0661786	−	0.114625i
$525$		0			0
$526$	16.3844	−	28.3786i	0.714393	−	1.23736i
$527$	6.30874			0.274813
$528$		0			0
$529$	1.65606	+	2.86838i	0.0720027	+	0.124712i
$530$	−0.199006	+	0.344689i	−0.00864427	+	0.0149723i
$531$		0			0
$532$	5.52118	+	12.8563i	0.239373	+	0.557391i
$533$	−3.73391	+	18.2404i	−0.161734	+	0.790081i
$534$		0			0
$535$	−12.7907			−0.552989
$536$	−2.90660			−0.125546
$537$		0			0
$538$	−36.0571			−1.55453
$539$	29.9033	+	7.18882i	1.28803	+	0.309644i
$540$		0			0
$541$	−5.24095	−	9.07760i	−0.225326	−	0.390276i	0.731091	−	0.682280i	$-0.239011\pi$
$541$	−5.24095	−	9.07760i	−0.225326	−	0.390276i	−0.956417	+	0.292003i	$0.905678\pi$
$542$	−30.6160	−	53.0285i	−1.31507	−	2.27777i
$543$		0			0
$544$	4.42778	−	7.66914i	0.189840	−	0.328812i
$545$	−17.7373			−0.759781
$546$		0			0
$547$	15.2216			0.650829			0.325415	−	0.945571i	$-0.394496\pi$
$547$	15.2216			0.650829			0.325415	+	0.945571i	$0.394496\pi$
$548$	−10.4396	+	18.0819i	−0.445957	+	0.772421i
$549$		0			0
$550$	11.8463	+	20.5184i	0.505129	+	0.874909i
$551$	0.271625	+	0.470468i	0.0115716	+	0.0200426i
$552$		0			0
$553$	0.808597	+	1.88285i	0.0343850	+	0.0800671i
$554$	35.0726			1.49009
$555$		0			0
$556$	−0.552521			−0.0234321
$557$	−11.8597			−0.502513			−0.251256	−	0.967921i	$-0.580844\pi$
$557$	−11.8597			−0.502513			−0.251256	+	0.967921i	$0.580844\pi$
$558$		0			0
$559$	−0.0778200	+	0.0259342i	−0.00329144	+	0.00109690i
$560$	17.8104	+	2.11076i	0.752627	+	0.0891958i
$561$		0			0
$562$	−13.5535	+	23.4753i	−0.571719	+	0.990246i
$563$	3.84675	+	6.66276i	0.162121	+	0.280802i	0.935629	−	0.352985i	$-0.114833\pi$
$563$	3.84675	+	6.66276i	0.162121	+	0.280802i	−0.773508	+	0.633786i	$0.781500\pi$
$564$		0			0
$565$	−13.8066			−0.580850
$566$	10.8892	−	18.8607i	0.457709	−	0.792775i
$567$		0			0
$568$	3.50360	−	6.06841i	0.147008	−	0.254625i
$569$	18.7098	−	32.4063i	0.784355	−	1.35854i	−0.145029	−	0.989427i	$-0.546327\pi$
$569$	18.7098	−	32.4063i	0.784355	−	1.35854i	0.929384	−	0.369115i	$-0.120339\pi$
$570$		0			0
$571$	−7.08285	+	12.2679i	−0.296408	+	0.513394i	−0.975311	−	0.220834i	$-0.929122\pi$
$571$	−7.08285	+	12.2679i	−0.296408	+	0.513394i	0.678903	+	0.734228i	$0.262456\pi$
$572$	5.18208	−	25.3149i	0.216674	−	1.05847i
$573$		0			0
$574$	25.8536	+	3.06397i	1.07911	+	0.127888i
$575$	6.27825	+	10.8742i	0.261821	+	0.453488i
$576$		0			0
$577$	7.48776	−	12.9692i	0.311720	−	0.539914i	−0.667015	−	0.745044i	$-0.732428\pi$
$577$	7.48776	−	12.9692i	0.311720	−	0.539914i	0.978735	+	0.205130i	$0.0657617\pi$
$578$	14.8190	+	25.6673i	0.616391	+	1.06762i
$579$		0			0
$580$	−0.402635			−0.0167185
$581$	−42.0867	−	4.98781i	−1.74605	−	0.206929i
$582$		0			0
$583$	−0.311476	+	0.539492i	−0.0129000	+	0.0223435i
$584$	5.35627	−	9.27732i	0.221644	−	0.383898i
$585$		0			0
$586$	−12.5811	−	21.7911i	−0.519720	−	0.900182i
$587$	−6.58821	−	11.4111i	−0.271925	−	0.470987i	0.697430	−	0.716653i	$-0.254327\pi$
$587$	−6.58821	−	11.4111i	−0.271925	−	0.470987i	−0.969355	+	0.245666i	$0.920993\pi$
$588$		0			0
$589$	−8.50309	+	14.7278i	−0.350364	+	0.606848i
$590$	−7.50003	−	12.9904i	−0.308771	−	0.534807i
$591$		0			0
$592$	16.2220	+	28.0974i	0.666722	+	1.15480i
$593$	−22.0663	−	38.2200i	−0.906156	−	1.56951i	−0.819357	−	0.573283i	$-0.805670\pi$
$593$	−22.0663	−	38.2200i	−0.906156	−	1.56951i	−0.0867989	−	0.996226i	$-0.527664\pi$
$594$		0			0
$595$	2.80529	−	3.75554i	0.115006	−	0.153962i
$596$	3.19965	+	5.54195i	0.131063	+	0.227007i
$597$		0			0
$598$	6.11376	−	29.8662i	0.250010	−	1.22132i
$599$	−3.01349	+	5.21952i	−0.123128	+	0.213264i	−0.921000	−	0.389564i	$-0.872626\pi$
$599$	−3.01349	+	5.21952i	−0.123128	+	0.213264i	0.797872	+	0.602827i	$0.205959\pi$
$600$		0			0
$601$	−1.86260	−	3.22612i	−0.0759770	−	0.131596i	0.825534	−	0.564353i	$-0.190874\pi$
$601$	−1.86260	−	3.22612i	−0.0759770	−	0.131596i	−0.901511	+	0.432757i	$0.857541\pi$
$602$	0.0452607	+	0.105392i	0.00184469	+	0.00429544i
$603$		0			0
$604$	−3.45608			−0.140626
$605$	−6.11632	−	10.5938i	−0.248664	−	0.430698i
$606$		0			0
$607$	−6.01651			−0.244203			−0.122101	−	0.992518i	$-0.538963\pi$
$607$	−6.01651			−0.244203			−0.122101	+	0.992518i	$0.538963\pi$
$608$	11.9358	+	20.6733i	0.484059	+	0.838415i
$609$		0			0
$610$	32.4105			1.31226
$611$	−8.44814	+	41.2698i	−0.341775	+	1.66960i
$612$		0			0
$613$	9.80825			0.396152			0.198076	−	0.980187i	$-0.436531\pi$
$613$	9.80825			0.396152			0.198076	+	0.980187i	$0.436531\pi$
$614$	6.34459	−	10.9892i	0.256047	−	0.443486i
$615$		0			0
$616$	8.11342	+	0.961543i	0.326899	+	0.0387417i
$617$	16.8838	−	29.2436i	0.679716	−	1.17730i	−0.295350	−	0.955389i	$-0.595436\pi$
$617$	16.8838	−	29.2436i	0.679716	−	1.17730i	0.975066	−	0.221914i	$-0.0712304\pi$
$618$		0			0
$619$	−2.04671	+	3.54501i	−0.0822644	+	0.142486i	−0.904222	−	0.427062i	$-0.859549\pi$
$619$	−2.04671	+	3.54501i	−0.0822644	+	0.142486i	0.821958	+	0.569548i	$0.192882\pi$
$620$	−6.30215	−	10.9156i	−0.253100	−	0.438383i
$621$		0			0
$622$	−1.94936	−	3.37639i	−0.0781621	−	0.135381i
$623$	−10.3829	+	13.9000i	−0.415983	+	0.556891i
$624$		0			0
$625$	1.42115	+	2.46150i	0.0568459	+	0.0984599i
$626$	17.9459			0.717264
$627$		0			0
$628$	−36.0695			−1.43933
$629$	8.47978			0.338111
$630$		0			0
$631$	13.3868	−	23.1866i	0.532921	−	0.923046i	−0.466340	−	0.884605i	$-0.654428\pi$
$631$	13.3868	−	23.1866i	0.532921	−	0.923046i	0.999261	−	0.0384402i	$-0.0122389\pi$
$632$	0.272179	+	0.471427i	0.0108267	+	0.0187524i
$633$		0			0
$634$	63.5910			2.52552
$635$	−11.7006	+	20.2661i	−0.464325	+	0.804234i
$636$		0			0
$637$	14.4452	+	20.6963i	0.572340	+	0.820016i
$638$	−1.40287			−0.0555403
$639$		0			0
$640$	8.14224			0.321850
$641$	−9.28610	−	16.0840i	−0.366779	−	0.635279i	0.622281	−	0.782794i	$-0.286206\pi$
$641$	−9.28610	−	16.0840i	−0.366779	−	0.635279i	−0.989060	+	0.147514i	$0.952873\pi$
$642$		0			0
$643$	1.96695	−	3.40686i	0.0775690	−	0.134353i	−0.824632	−	0.565670i	$-0.808618\pi$
$643$	1.96695	−	3.40686i	0.0775690	−	0.134353i	0.902201	+	0.431317i	$0.141951\pi$
$644$	−19.0159	−	2.25362i	−0.749330	−	0.0888051i
$645$		0			0
$646$	7.43035			0.292343
$647$	0.197076			0.00774784			0.00387392	−	0.999992i	$-0.498767\pi$
$647$	0.197076			0.00774784			0.00387392	+	0.999992i	$0.498767\pi$
$648$		0			0
$649$	−11.7387	−	20.3321i	−0.460785	−	0.798104i
$650$	−3.89922	+	19.0480i	−0.152940	+	0.747125i
$651$		0			0
$652$	−3.14172	−	5.44163i	−0.123039	−	0.213110i
$653$	−7.23363	+	12.5290i	−0.283074	+	0.490298i	−0.972140	−	0.234400i	$-0.924687\pi$
$653$	−7.23363	+	12.5290i	−0.283074	+	0.490298i	0.689066	+	0.724698i	$0.258021\pi$
$654$		0			0
$655$	1.36813	−	2.36967i	0.0534573	−	0.0925908i
$656$	23.7624			0.927765
$657$		0			0
$658$	58.4949	+	6.93238i	2.28037	+	0.270252i
$659$	−11.7066	+	20.2764i	−0.456024	+	0.789857i	−0.998746	−	0.0500552i	$-0.984060\pi$
$659$	−11.7066	+	20.2764i	−0.456024	+	0.789857i	0.542722	+	0.839912i	$0.317394\pi$
$660$		0			0
$661$	−4.04817			−0.157456			−0.0787278	−	0.996896i	$-0.525086\pi$
$661$	−4.04817			−0.157456			−0.0787278	+	0.996896i	$0.525086\pi$
$662$	−18.1657	+	31.4638i	−0.706028	+	1.22288i
$663$		0			0
$664$	−11.2587			−0.436921
$665$	4.98628	+	11.6108i	0.193360	+	0.450246i
$666$		0			0
$667$	−0.743487			−0.0287879
$668$	1.74448	−	3.02153i	0.0674959	−	0.116906i
$669$		0			0
$670$	11.6088			0.448487
$671$	50.7276			1.95832
$672$		0			0
$673$	−3.64704	−	6.31685i	−0.140583	−	0.243497i	0.787133	−	0.616783i	$-0.211564\pi$
$673$	−3.64704	−	6.31685i	−0.140583	−	0.243497i	−0.927716	+	0.373286i	$0.878231\pi$
$674$	29.8076	−	51.6283i	1.14815	−	1.98865i
$675$		0			0
$676$	16.9658	−	12.7208i	0.652529	−	0.489260i
$677$	−7.87553	−	13.6408i	−0.302681	−	0.524259i	0.674061	−	0.738676i	$-0.264548\pi$
$677$	−7.87553	−	13.6408i	−0.302681	−	0.524259i	−0.976742	+	0.214416i	$0.931215\pi$
$678$		0			0
$679$	5.52849	−	7.40119i	0.212164	−	0.284032i
$680$	0.622636	−	1.07844i	0.0238770	−	0.0413562i
$681$		0			0
$682$	−21.9582	−	38.0327i	−0.840822	−	1.45635i
$683$	20.7427	+	35.9274i	0.793697	+	1.37472i	0.923664	+	0.383204i	$0.125180\pi$
$683$	20.7427	+	35.9274i	0.793697	+	1.37472i	−0.129967	+	0.991518i	$0.541487\pi$
$684$		0			0
$685$	−9.42819	+	16.3301i	−0.360233	+	0.623941i
$686$	27.1439	−	22.5543i	1.03636	−	0.861127i
$687$		0			0
$688$	0.0523445	+	0.0906634i	0.00199562	+	0.00345651i
$689$	−0.484993	+	0.161628i	−0.0184767	+	0.00615754i
$690$		0			0
$691$	23.4108	−	40.5487i	0.890589	−	1.54255i	0.0514184	−	0.998677i	$-0.483626\pi$
$691$	23.4108	−	40.5487i	0.890589	−	1.54255i	0.839171	−	0.543868i	$-0.183041\pi$
$692$	−13.5494	−	23.4683i	−0.515073	−	0.892132i
$693$		0			0
$694$	−22.2478			−0.844514
$695$	−0.498992			−0.0189278
$696$		0			0
$697$	3.10534	−	5.37860i	0.117623	−	0.203729i
$698$	45.7152			1.73034
$699$		0			0
$700$	12.1279	+	1.43731i	0.458392	+	0.0543252i
$701$	−29.8626			−1.12790			−0.563948	−	0.825810i	$-0.690718\pi$
$701$	−29.8626			−1.12790			−0.563948	+	0.825810i	$0.690718\pi$
$702$		0			0
$703$	−11.4293	+	19.7961i	−0.431063	+	0.746623i
$704$	−21.2096			−0.799366
$705$		0			0
$706$	12.1893	−	21.1124i	0.458749	−	0.794576i
$707$	6.77281	+	0.802663i	0.254718	+	0.0301873i
$708$		0			0
$709$	26.9332			1.01150			0.505750	−	0.862680i	$-0.331216\pi$
$709$	26.9332			1.01150			0.505750	+	0.862680i	$0.331216\pi$
$710$	−13.9932	+	24.2369i	−0.525155	+	0.909595i
$711$		0			0
$712$	−2.30450	+	3.99151i	−0.0863647	+	0.149588i
$713$	−11.6373	−	20.1563i	−0.435819	−	0.754861i
$714$		0			0
$715$	4.68004	−	22.8623i	0.175023	−	0.855003i
$716$	−0.440002	−	0.762105i	−0.0164436	−	0.0284812i
$717$		0			0
$718$	−23.5141			−0.877537
$719$	14.4988			0.540713			0.270356	−	0.962760i	$-0.412859\pi$
$719$	14.4988			0.540713			0.270356	+	0.962760i	$0.412859\pi$
$720$		0			0
$721$	−17.6058	−	40.9959i	−0.655675	−	1.52677i
$722$	8.08799	−	14.0088i	0.301004	−	0.521354i
$723$		0			0
$724$	−2.26049	−	3.91528i	−0.0840105	−	0.145510i
$725$	0.474180			0.0176106
$726$		0			0
$727$	−6.26424			−0.232328			−0.116164	−	0.993230i	$-0.537060\pi$
$727$	−6.26424			−0.232328			−0.116164	+	0.993230i	$0.537060\pi$
$728$	4.45779	+	5.00817i	0.165217	+	0.185615i
$729$		0			0
$730$	−21.3926	+	37.0531i	−0.791776	+	1.37140i
$731$	0.0273621			0.00101203
$732$		0			0
$733$	5.99189	+	10.3783i	0.221316	+	0.383330i	0.955208	−	0.295936i	$-0.0956316\pi$
$733$	5.99189	+	10.3783i	0.221316	+	0.383330i	−0.733892	+	0.679266i	$0.762298\pi$
$734$	−1.93487	+	3.35130i	−0.0714175	+	0.123699i
$735$		0			0
$736$	−32.6704			−1.20425
$737$	18.1696			0.669286
$738$		0			0
$739$	13.5254			0.497539			0.248770	−	0.968563i	$-0.419974\pi$
$739$	13.5254			0.497539			0.248770	+	0.968563i	$0.419974\pi$
$740$	−8.47091	−	14.6721i	−0.311397	−	0.539355i
$741$		0			0
$742$	0.282075	+	0.656825i	0.0103553	+	0.0241128i
$743$	−19.2299	−	33.3072i	−0.705477	−	1.22192i	−0.966519	−	0.256594i	$-0.917400\pi$
$743$	−19.2299	−	33.3072i	−0.705477	−	1.22192i	0.261043	−	0.965327i	$-0.415934\pi$
$744$		0			0
$745$	2.88966	+	5.00504i	0.105869	+	0.183371i
$746$	3.69107	−	6.39312i	0.135140	−	0.234069i
$747$		0			0
$748$	−4.30973	+	7.46466i	−0.157579	+	0.272935i
$749$	−13.7476	+	18.4044i	−0.502326	+	0.672482i
$750$		0			0
$751$	−5.85573	+	10.1424i	−0.213679	+	0.370102i	−0.952863	−	0.303401i	$-0.901878\pi$
$751$	−5.85573	+	10.1424i	−0.213679	+	0.370102i	0.739184	+	0.673503i	$0.235211\pi$
$752$	53.7635			1.96055
$753$		0			0
$754$	−0.861315	−	0.763875i	−0.0313672	−	0.0278187i
$755$	−3.12125			−0.113594
$756$		0			0
$757$	−4.65791	−	8.06773i	−0.169295	−	0.293227i	0.768877	−	0.639396i	$-0.220816\pi$
$757$	−4.65791	−	8.06773i	−0.169295	−	0.293227i	−0.938172	+	0.346169i	$0.887482\pi$
$758$	−27.7600			−1.00829
$759$		0			0
$760$	1.67841	+	2.90709i	0.0608824	+	0.105451i
$761$	43.9381			1.59276			0.796378	−	0.604799i	$-0.206747\pi$
$761$	43.9381			1.59276			0.796378	+	0.604799i	$0.206747\pi$
$762$		0			0
$763$	−19.0643	+	25.5220i	−0.690173	+	0.923959i
$764$	−16.5079	−	28.5926i	−0.597236	−	1.03444i
$765$		0			0
$766$	−25.5172	+	44.1971i	−0.921973	+	1.59690i
$767$	3.86381	−	18.8750i	0.139514	−	0.681537i
$768$		0			0
$769$	−12.6771	−	21.9573i	−0.457147	−	0.791802i	0.541662	−	0.840597i	$-0.317795\pi$
$769$	−12.6771	−	21.9573i	−0.457147	−	0.791802i	−0.998809	+	0.0487946i	$0.984462\pi$
$770$	−32.4045	−	3.84035i	−1.16778	−	0.138397i
$771$		0			0
$772$	13.3568	+	23.1347i	0.480723	+	0.832637i
$773$	−11.5542	−	20.0125i	−0.415576	−	0.719798i	0.579913	−	0.814678i	$-0.303087\pi$
$773$	−11.5542	−	20.0125i	−0.415576	−	0.719798i	−0.995489	+	0.0948801i	$0.969753\pi$
$774$		0			0
$775$	7.42200	+	12.8553i	0.266606	+	0.461775i
$776$	1.22705	−	2.12532i	0.0440487	−	0.0762946i
$777$		0			0
$778$	11.4474	+	19.8275i	0.410410	+	0.710851i
$779$	8.37091	+	14.4988i	0.299919	+	0.519475i
$780$		0			0
$781$	−21.9015	+	37.9346i	−0.783699	+	1.35741i
$782$	−5.08456	+	8.80672i	−0.181824	+	0.314928i
$783$		0			0
$784$	22.1800	−	23.3586i	0.792145	−	0.834236i
$785$	−32.5750			−1.16265
$786$		0			0
$787$	12.3346	+	21.3642i	0.439682	+	0.761551i	0.997665	−	0.0683012i	$-0.0217579\pi$
$787$	12.3346	+	21.3642i	0.439682	+	0.761551i	−0.557983	+	0.829852i	$0.688425\pi$
$788$	16.0943	−	27.8761i	0.573334	−	0.993044i
$789$		0			0
$790$	−1.08707	−	1.88285i	−0.0386761	−	0.0669889i
$791$	−14.8396	+	19.8663i	−0.527635	+	0.706364i
$792$		0			0
$793$	31.1449	+	27.6215i	1.10599	+	0.980870i
$794$	1.57938	−	2.73556i	0.0560500	−	0.0970814i
$795$		0			0
$796$	11.5139	−	19.9427i	0.408100	−	0.706849i
$797$	5.65686	−	9.79797i	0.200376	−	0.347062i	−0.748273	−	0.663390i	$-0.769117\pi$
$797$	5.65686	−	9.79797i	0.200376	−	0.347062i	0.948650	+	0.316329i	$0.102450\pi$
$798$		0			0
$799$	7.02597	−	12.1693i	0.248561	−	0.430520i
$800$	20.8365			0.736680
$801$		0			0
$802$	−19.5156	−	33.8019i	−0.689118	−	1.19359i
$803$	−33.4828	+	57.9940i	−1.18158	+	2.04656i
$804$		0			0
$805$	−17.1736	−	2.03529i	−0.605289	−	0.0717344i
$806$	7.22754	−	35.3071i	0.254579	−	1.24364i
$807$		0			0
$808$	1.81180			0.0637389
$809$	−16.3708			−0.575566			−0.287783	−	0.957696i	$-0.592918\pi$
$809$	−16.3708			−0.575566			−0.287783	+	0.957696i	$0.592918\pi$
$810$		0			0
$811$	−29.0412			−1.01978			−0.509888	−	0.860241i	$-0.670313\pi$
$811$	−29.0412			−1.01978			−0.509888	+	0.860241i	$0.670313\pi$
$812$	−0.432758	+	0.579349i	−0.0151868	+	0.0203311i
$813$		0			0
$814$	−29.5146	−	51.1209i	−1.03449	−	1.79179i
$815$	−2.83735	−	4.91443i	−0.0993880	−	0.172145i
$816$		0			0
$817$	−0.0368794	+	0.0638770i	−0.00129025	+	0.00223477i
$818$	28.3278			0.990458
$819$		0			0
$820$	−12.4084			−0.433319
$821$	−6.87589	+	11.9094i	−0.239970	+	0.415640i	−0.960705	−	0.277570i	$-0.910471\pi$
$821$	−6.87589	+	11.9094i	−0.239970	+	0.415640i	0.720735	+	0.693210i	$0.243804\pi$
$822$		0			0
$823$	14.5577	+	25.2146i	0.507448	+	0.878926i	0.999963	+	0.00862197i	$0.00274449\pi$
$823$	14.5577	+	25.2146i	0.507448	+	0.878926i	−0.492515	+	0.870304i	$0.663922\pi$
$824$	−5.92623	−	10.2645i	−0.206450	−	0.357582i
$825$		0			0
$826$	−26.7530	−	3.17057i	−0.930855	−	0.110318i
$827$	22.9118			0.796722			0.398361	−	0.917229i	$-0.369579\pi$
$827$	22.9118			0.796722			0.398361	+	0.917229i	$0.369579\pi$
$828$		0			0
$829$	−23.3829			−0.812121			−0.406061	−	0.913846i	$-0.633098\pi$
$829$	−23.3829			−0.812121			−0.406061	+	0.913846i	$0.633098\pi$
$830$	44.9665			1.56081
$831$		0			0
$832$	−13.0219	−	11.5488i	−0.451454	−	0.400382i
$833$	−2.38865	−	8.07301i	−0.0827620	−	0.279713i
$834$		0			0
$835$	1.57547	−	2.72880i	0.0545214	−	0.0944339i
$836$	−11.6175	−	20.1221i	−0.401801	−	0.695939i
$837$		0			0
$838$	45.0045			1.55466
$839$	0.367168	−	0.635954i	0.0126761	−	0.0219556i	−0.859618	−	0.510938i	$-0.829298\pi$
$839$	0.367168	−	0.635954i	0.0126761	−	0.0219556i	0.872294	+	0.488982i	$0.162632\pi$
$840$		0			0
$841$	14.4860	−	25.0904i	0.499516	−	0.865187i
$842$	−24.8506	+	43.0426i	−0.856409	+	1.48334i
$843$		0			0
$844$	3.77314	−	6.53528i	0.129877	−	0.224954i
$845$	15.3221	−	11.4884i	0.527096	−	0.395211i
$846$		0			0
$847$	−21.8172	−	2.58562i	−0.749649	−	0.0888429i
$848$	0.326223	+	0.565035i	0.0112026	+	0.0194034i
$849$		0			0
$850$	3.24282	−	5.61674i	0.111228	−	0.192652i
$851$	−15.6420	−	27.0927i	−0.536201	−	0.928727i
$852$		0			0
$853$	54.3567			1.86114			0.930569	−	0.366118i	$-0.119313\pi$
$853$	54.3567			1.86114			0.930569	+	0.366118i	$0.119313\pi$
$854$	34.8353	−	46.6353i	1.19204	−	1.59583i
$855$		0			0
$856$	−3.05129	+	5.28500i	−0.104291	+	0.180637i
$857$	−10.5106	+	18.2048i	−0.359034	+	0.621864i	−0.987800	−	0.155730i	$-0.950227\pi$
$857$	−10.5106	+	18.2048i	−0.359034	+	0.621864i	0.628766	+	0.777595i	$0.283560\pi$
$858$		0			0
$859$	25.6814	+	44.4816i	0.876240	+	1.51769i	0.855436	+	0.517908i	$0.173289\pi$
$859$	25.6814	+	44.4816i	0.876240	+	1.51769i	0.0208035	+	0.999784i	$0.493378\pi$
$860$	−0.0273336	−	0.0473431i	−0.000932066	−	0.00161439i
$861$		0			0
$862$	−12.6884	+	21.9769i	−0.432167	+	0.748535i
$863$	3.55660	+	6.16021i	0.121068	+	0.209696i	0.920189	−	0.391474i	$-0.128035\pi$
$863$	3.55660	+	6.16021i	0.121068	+	0.209696i	−0.799121	+	0.601170i	$0.794701\pi$
$864$		0			0
$865$	−12.2368	−	21.1947i	−0.416062	−	0.720641i
$866$	−19.4577	−	33.7018i	−0.661201	−	1.14523i
$867$		0			0
$868$	−22.4801	−	2.66418i	−0.763024	−	0.0904280i
$869$	−1.70143	−	2.94696i	−0.0577171	−	0.0999689i
$870$		0			0
$871$	11.1555	+	9.89349i	0.377989	+	0.335228i
$872$	−4.23133	+	7.32888i	−0.143291	+	0.248187i
$873$		0			0
$874$	−13.7062	−	23.7399i	−0.463620	−	0.803013i
$875$	30.3052	+	3.59155i	1.02450	+	0.121416i
$876$		0			0
$877$	0.512476			0.0173051			0.00865255	−	0.999963i	$-0.497246\pi$
$877$	0.512476			0.0173051			0.00865255	+	0.999963i	$0.497246\pi$
$878$	9.30937	+	16.1243i	0.314176	+	0.544169i
$879$		0			0
$880$	−29.7835			−1.00400
$881$	−18.5464	−	32.1232i	−0.624843	−	1.08226i	−0.988571	−	0.150754i	$-0.951830\pi$
$881$	−18.5464	−	32.1232i	−0.624843	−	1.08226i	0.363729	−	0.931505i	$-0.381503\pi$
$882$		0			0
$883$	−15.5667			−0.523860			−0.261930	−	0.965087i	$-0.584359\pi$
$883$	−15.5667			−0.523860			−0.261930	+	0.965087i	$0.584359\pi$
$884$	−6.71059	+	2.23636i	−0.225701	+	0.0752169i
$885$		0			0
$886$	−40.3290			−1.35488
$887$	13.7900	−	23.8849i	0.463022	−	0.801977i	−0.536088	−	0.844162i	$-0.680099\pi$
$887$	13.7900	−	23.8849i	0.463022	−	0.801977i	0.999110	+	0.0421849i	$0.0134319\pi$
$888$		0			0
$889$	16.5847	+	38.6182i	0.556233	+	1.29521i
$890$	9.20404	−	15.9419i	0.308520	−	0.534372i
$891$		0			0
$892$	17.4145	−	30.1627i	0.583079	−	1.00992i
$893$	18.9396	+	32.8043i	0.633789	+	1.09775i
$894$		0			0
$895$	−0.397374	−	0.688272i	−0.0132827	−	0.0230064i
$896$	8.75140	−	11.7158i	0.292364	−	0.391398i
$897$		0			0
$898$	−17.2895	−	29.9463i	−0.576959	−	0.999323i
$899$	−0.878932			−0.0293140
$900$		0			0
$901$	0.170527			0.00568109
$902$	−43.2337			−1.43952
$903$		0			0
$904$	−3.29366	+	5.70479i	−0.109546	+	0.189738i
$905$	−2.04149	−	3.53597i	−0.0678615	−	0.117539i
$906$		0			0
$907$	−45.0471			−1.49576			−0.747882	−	0.663831i	$-0.768929\pi$
$907$	−45.0471			−1.49576			−0.747882	+	0.663831i	$0.768929\pi$
$908$	−8.52200	+	14.7605i	−0.282813	+	0.489846i
$909$		0			0
$910$	−17.8041	−	20.0024i	−0.590202	−	0.663072i
$911$	−35.4678			−1.17510			−0.587550	−	0.809188i	$-0.699907\pi$
$911$	−35.4678			−1.17510			−0.587550	+	0.809188i	$0.699907\pi$
$912$		0			0
$913$	70.3796			2.32923
$914$	17.1689	+	29.7375i	0.567898	+	0.983627i
$915$		0			0
$916$	−11.7917	+	20.4238i	−0.389608	+	0.674820i
$917$	−1.93922	−	4.51556i	−0.0640387	−	0.149117i
$918$		0			0
$919$	17.3724			0.573064			0.286532	−	0.958071i	$-0.407497\pi$
$919$	17.3724			0.573064			0.286532	+	0.958071i	$0.407497\pi$
$920$	−4.59412			−0.151464
$921$		0			0
$922$	−28.3686	−	49.1359i	−0.934271	−	1.61820i
$923$	−34.1024	+	11.3649i	−1.12250	+	0.374081i
$924$		0			0
$925$	9.97613	+	17.2792i	0.328013	+	0.568136i
$926$	−16.8706	+	29.2207i	−0.554402	+	0.960252i
$927$		0			0
$928$	−0.616877	+	1.06846i	−0.0202500	+	0.0350740i
$929$	−10.7600			−0.353025			−0.176512	−	0.984298i	$-0.556482\pi$
$929$	−10.7600			−0.353025			−0.176512	+	0.984298i	$0.556482\pi$
$930$		0			0
$931$	22.0660	+	5.30470i	0.723183	+	0.173854i
$932$	−7.57532	+	13.1208i	−0.248138	+	0.429788i
$933$		0			0
$934$	11.1079			0.363463
$935$	−3.89219	+	6.74148i	−0.127288	+	0.220470i
$936$		0			0
$937$	−10.9816			−0.358755			−0.179377	−	0.983780i	$-0.557408\pi$
$937$	−10.9816			−0.358755			−0.179377	+	0.983780i	$0.557408\pi$
$938$	12.4773	−	16.7038i	0.407398	−	0.545399i
$939$		0			0
$940$	−28.0745			−0.915690
$941$	4.08897	−	7.08231i	0.133297	−	0.230877i	−0.791649	−	0.610976i	$-0.790777\pi$
$941$	4.08897	−	7.08231i	0.133297	−	0.230877i	0.924946	+	0.380100i	$0.124110\pi$
$942$		0			0
$943$	−22.9127			−0.746141
$944$	−24.5890			−0.800305
$945$		0			0
$946$	−0.0952365	−	0.164954i	−0.00309640	−	0.00536313i
$947$	−2.29689	+	3.97833i	−0.0746389	+	0.129278i	−0.900929	−	0.433966i	$-0.857114\pi$
$947$	−2.29689	+	3.97833i	−0.0746389	+	0.129278i	0.826290	+	0.563244i	$0.190447\pi$
$948$		0			0
$949$	−52.1354	+	17.3746i	−1.69239	+	0.564003i
$950$	8.74153	+	15.1408i	0.283613	+	0.491231i
$951$		0			0
$952$	−0.882538	−	2.05503i	−0.0286032	−	0.0666038i
$953$	10.5714	−	18.3102i	0.342442	−	0.593126i	−0.642444	−	0.766333i	$-0.722079\pi$
$953$	10.5714	−	18.3102i	0.342442	−	0.593126i	0.984886	+	0.173206i	$0.0554128\pi$
$954$		0			0
$955$	−14.9086	−	25.8225i	−0.482432	−	0.835596i
$956$	16.0124	+	27.7344i	0.517879	+	0.896993i
$957$		0			0
$958$	13.8070	−	23.9145i	0.446085	−	0.772641i
$959$	13.3637	+	31.1180i	0.431537	+	1.00485i
$960$		0			0
$961$	1.74271	+	3.01846i	0.0562164	+	0.0973697i
$962$	9.71476	−	47.4573i	0.313216	−	1.53009i
$963$		0			0
$964$	−5.96274	+	10.3278i	−0.192047	+	0.332635i
$965$	12.0628	+	20.8934i	0.388316	+	0.672582i
$966$		0			0
$967$	−32.0750			−1.03146			−0.515731	−	0.856750i	$-0.672480\pi$
$967$	−32.0750			−1.03146			−0.515731	+	0.856750i	$0.672480\pi$
$968$	−5.83635			−0.187587
$969$		0			0
$970$	−4.90079	+	8.48841i	−0.157355	+	0.272546i
$971$	52.0835			1.67144			0.835719	−	0.549157i	$-0.185051\pi$
$971$	52.0835			1.67144			0.835719	+	0.549157i	$0.185051\pi$
$972$		0			0
$973$	−0.536324	+	0.717996i	−0.0171938	+	0.0230179i
$974$	−34.2241			−1.09661
$975$		0			0
$976$	26.5647	−	46.0114i	0.850315	−	1.47279i
$977$	−19.2580			−0.616117			−0.308058	−	0.951367i	$-0.599679\pi$
$977$	−19.2580			−0.616117			−0.308058	+	0.951367i	$0.599679\pi$
$978$		0			0
$979$	14.4058	−	24.9515i	0.460410	−	0.797454i
$980$	−11.5821	+	12.1975i	−0.369977	+	0.389636i
$981$		0			0
$982$	69.1736			2.20742
$983$	−8.03657	+	13.9197i	−0.256327	+	0.443971i	−0.965255	−	0.261310i	$-0.915846\pi$
$983$	−8.03657	+	13.9197i	−0.256327	+	0.443971i	0.708928	+	0.705280i	$0.249179\pi$
$984$		0			0
$985$	14.5350	−	25.1754i	0.463124	−	0.802155i
$986$	0.192012	+	0.332574i	0.00611490	+	0.0105913i
$987$		0			0
$988$	3.82391	−	18.6801i	0.121655	−	0.594294i
$989$	−0.0504729	−	0.0874216i	−0.00160494	−	0.00277985i
$990$		0			0
$991$	21.4265			0.680635			0.340317	−	0.940311i	$-0.389466\pi$
$991$	21.4265			0.680635			0.340317	+	0.940311i	$0.389466\pi$
$992$	−38.6221			−1.22625
$993$		0			0
$994$	19.8342	+	46.1849i	0.629104	+	1.46489i
$995$	10.3984	−	18.0106i	0.329652	−	0.570974i
$996$		0			0
$997$	8.47687	+	14.6824i	0.268465	+	0.464996i	0.968466	−	0.249147i	$-0.0801502\pi$
$997$	8.47687	+	14.6824i	0.268465	+	0.464996i	−0.700000	+	0.714142i	$0.746817\pi$
$998$	45.1763			1.43003
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.n.d.172.2		12
3.2	odd	2		91.2.g.b.81.5	yes	12
7.2	even	3		819.2.s.d.289.5		12
13.9	even	3		819.2.s.d.802.5		12
21.2	odd	6		91.2.h.b.16.2	yes	12
21.5	even	6		637.2.h.l.471.2		12
21.11	odd	6		637.2.f.k.393.5		12
21.17	even	6		637.2.f.j.393.5		12
21.20	even	2		637.2.g.l.263.5		12
39.23	odd	6		1183.2.e.g.508.2		12
39.29	odd	6		1183.2.e.h.508.5		12
39.35	odd	6		91.2.h.b.74.2	yes	12
91.9	even	3	inner	819.2.n.d.100.2		12
273.23	odd	6		1183.2.e.g.170.2		12
273.74	odd	6		637.2.f.k.295.5		12
273.101	even	6		8281.2.a.cf.1.5		6
273.107	odd	6		1183.2.e.h.170.5		12
273.152	even	6		637.2.g.l.373.5		12
273.179	odd	6		8281.2.a.ce.1.5		6
273.185	even	6		8281.2.a.ca.1.2		6
273.191	odd	6		91.2.g.b.9.5	✓	12
273.230	even	6		637.2.h.l.165.2		12
273.263	odd	6		8281.2.a.bz.1.2		6
273.269	even	6		637.2.f.j.295.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.5	✓	12	273.191	odd	6
91.2.g.b.81.5	yes	12	3.2	odd	2
91.2.h.b.16.2	yes	12	21.2	odd	6
91.2.h.b.74.2	yes	12	39.35	odd	6
637.2.f.j.295.5		12	273.269	even	6
637.2.f.j.393.5		12	21.17	even	6
637.2.f.k.295.5		12	273.74	odd	6
637.2.f.k.393.5		12	21.11	odd	6
637.2.g.l.263.5		12	21.20	even	2
637.2.g.l.373.5		12	273.152	even	6
637.2.h.l.165.2		12	273.230	even	6
637.2.h.l.471.2		12	21.5	even	6
819.2.n.d.100.2		12	91.9	even	3	inner
819.2.n.d.172.2		12	1.1	even	1	trivial
819.2.s.d.289.5		12	7.2	even	3
819.2.s.d.802.5		12	13.9	even	3
1183.2.e.g.170.2		12	273.23	odd	6
1183.2.e.g.508.2		12	39.23	odd	6
1183.2.e.h.170.5		12	273.107	odd	6
1183.2.e.h.508.5		12	39.29	odd	6
8281.2.a.bz.1.2		6	273.263	odd	6
8281.2.a.ca.1.2		6	273.185	even	6
8281.2.a.ce.1.5		6	273.179	odd	6
8281.2.a.cf.1.5		6	273.101	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.n (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.952780 + 1.65026i) q^{2} +(-0.815580 - 1.41263i) q^{4} +(-0.736565 - 1.27577i) q^{5} +(-2.62736 - 0.311376i) q^{7} -0.702849 q^{8} +O(q^{10})\)	\(q+(-0.952780 + 1.65026i) q^{2} +(-0.815580 - 1.41263i) q^{4} +(-0.736565 - 1.27577i) q^{5} +(-2.62736 - 0.311376i) q^{7} -0.702849 q^{8} +2.80714 q^{10} +4.39361 q^{11} +(2.69752 + 2.39236i) q^{13} +(3.01715 - 4.03917i) q^{14} +(2.30082 - 3.98514i) q^{16} +(-0.601356 - 1.04158i) q^{17} +3.24209 q^{19} +(-1.20145 + 2.08098i) q^{20} +(-4.18615 + 7.25062i) q^{22} +(-2.21855 + 3.84264i) q^{23} +(1.41494 - 2.45075i) q^{25} +(-6.51816 + 2.17223i) q^{26} +(1.70297 + 3.96543i) q^{28} +(0.0837807 + 0.145112i) q^{29} +(-2.62272 + 4.54268i) q^{31} +(3.68150 + 6.37655i) q^{32} +2.29184 q^{34} +(1.53798 + 3.58126i) q^{35} +(-3.52527 + 6.10595i) q^{37} +(-3.08900 + 5.35031i) q^{38} +(0.517694 + 0.896672i) q^{40} +(2.58195 + 4.47206i) q^{41} +(-0.0113752 + 0.0197024i) q^{43} +(-3.58334 - 6.20653i) q^{44} +(-4.22758 - 7.32239i) q^{46} +(5.84178 + 10.1183i) q^{47} +(6.80609 + 1.63620i) q^{49} +(2.69626 + 4.67006i) q^{50} +(1.17946 - 5.76175i) q^{52} +(-0.0708929 + 0.122790i) q^{53} +(-3.23618 - 5.60523i) q^{55} +(1.84664 + 0.218850i) q^{56} -0.319298 q^{58} +(-2.67177 - 4.62764i) q^{59} +11.5457 q^{61} +(-4.99774 - 8.65635i) q^{62} -4.82736 q^{64} +(1.06519 - 5.20354i) q^{65} +4.13546 q^{67} +(-0.980907 + 1.69898i) q^{68} +(-7.37537 - 0.874075i) q^{70} +(-4.98486 + 8.63403i) q^{71} +(-7.62080 + 13.1996i) q^{73} +(-6.71762 - 11.6353i) q^{74} +(-2.64418 - 4.57986i) q^{76} +(-11.5436 - 1.36807i) q^{77} +(-0.387251 - 0.670738i) q^{79} -6.77881 q^{80} -9.84011 q^{82} +16.0186 q^{83} +(-0.885875 + 1.53438i) q^{85} +(-0.0216761 - 0.0375441i) q^{86} -3.08805 q^{88} +(3.27880 - 5.67904i) q^{89} +(-6.34245 - 7.12554i) q^{91} +7.23762 q^{92} -22.2637 q^{94} +(-2.38801 - 4.13616i) q^{95} +(-1.74583 + 3.02387i) q^{97} +(-9.18486 + 9.67291i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8	\( 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8} - 8 q^{10} + 8 q^{11} - 2 q^{13} + 2 q^{14} + 8 q^{16} - 5 q^{17} + 2 q^{19} + q^{20} - 5 q^{22} + q^{23} + 7 q^{25} - 5 q^{26} - 7 q^{28} - 3 q^{29} + 16 q^{31} - 8 q^{32} + 32 q^{34} - 8 q^{35} - 13 q^{37} + 17 q^{38} - 5 q^{40} + 8 q^{41} - 11 q^{43} - 21 q^{44} + 16 q^{46} + q^{47} - 3 q^{49} - 6 q^{50} - 25 q^{52} + 2 q^{53} + 9 q^{55} + 18 q^{56} + 16 q^{58} - 13 q^{59} + 10 q^{61} - 5 q^{62} - 30 q^{64} - 19 q^{65} + 22 q^{67} - 29 q^{68} - 39 q^{70} - 6 q^{71} - 30 q^{73} + 3 q^{74} - 9 q^{76} - 11 q^{77} + 7 q^{79} - 14 q^{80} - 2 q^{82} + 54 q^{83} - q^{85} + 7 q^{86} - 4 q^{89} - 20 q^{91} - 54 q^{92} - 90 q^{94} + 6 q^{95} - 35 q^{97} - 62 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8 - 8 * q^10 + 8 * q^11 - 2 * q^13 + 2 * q^14 + 8 * q^16 - 5 * q^17 + 2 * q^19 + q^20 - 5 * q^22 + q^23 + 7 * q^25 - 5 * q^26 - 7 * q^28 - 3 * q^29 + 16 * q^31 - 8 * q^32 + 32 * q^34 - 8 * q^35 - 13 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 + 16 * q^46 + q^47 - 3 * q^49 - 6 * q^50 - 25 * q^52 + 2 * q^53 + 9 * q^55 + 18 * q^56 + 16 * q^58 - 13 * q^59 + 10 * q^61 - 5 * q^62 - 30 * q^64 - 19 * q^65 + 22 * q^67 - 29 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 + 3 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 - 14 * q^80 - 2 * q^82 + 54 * q^83 - q^85 + 7 * q^86 - 4 * q^89 - 20 * q^91 - 54 * q^92 - 90 * q^94 + 6 * q^95 - 35 * q^97 - 62 * q^98

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