LMFDB - Embedded newform 819.2.bm.f.550.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(478,819)]

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, 5]))

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

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

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (of order $6$, 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 $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			550.4
Root			$0.655911 - 1.25291i$ of defining polynomial
Character	$\chi$	$=$	819.550
Dual form			819.2.bm.f.478.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.180824i q^{2} +1.96730 q^{4} +(2.32670 - 1.34332i) q^{5} +(-2.46263 - 0.967177i) q^{7} +0.717383i q^{8} +O(q^{10})$	\(q+0.180824i q^{2} +1.96730 q^{4} +(2.32670 - 1.34332i) q^{5} +(-2.46263 - 0.967177i) q^{7} +0.717383i q^{8} +(0.242904 + 0.420723i) q^{10} +(-2.33328 + 1.34712i) q^{11} +(1.92153 - 3.05086i) q^{13} +(0.174889 - 0.445303i) q^{14} +3.80489 q^{16} +4.76493 q^{17} +(0.163180 + 0.0942122i) q^{19} +(4.57732 - 2.64272i) q^{20} +(-0.243592 - 0.421913i) q^{22} +4.39929 q^{23} +(1.10902 - 1.92088i) q^{25} +(0.551667 + 0.347458i) q^{26} +(-4.84475 - 1.90273i) q^{28} +(3.54280 - 6.13631i) q^{29} +(-3.20369 - 1.84965i) q^{31} +2.12278i q^{32} +0.861613i q^{34} +(-7.02904 + 1.05778i) q^{35} +7.95413i q^{37} +(-0.0170358 + 0.0295069i) q^{38} +(0.963675 + 1.66913i) q^{40} +(-4.70215 - 2.71479i) q^{41} +(-4.00533 - 6.93743i) q^{43} +(-4.59027 + 2.65020i) q^{44} +0.795496i q^{46} +(1.60118 - 0.924445i) q^{47} +(5.12914 + 4.76361i) q^{49} +(0.347341 + 0.200538i) q^{50} +(3.78023 - 6.00196i) q^{52} +(-3.53622 + 6.12491i) q^{53} +(-3.61923 + 6.26869i) q^{55} +(0.693836 - 1.76665i) q^{56} +(1.10959 + 0.640623i) q^{58} -7.58888i q^{59} +(0.205782 - 0.356425i) q^{61} +(0.334461 - 0.579304i) q^{62} +7.22592 q^{64} +(0.372548 - 9.67966i) q^{65} +(-9.87358 + 5.70051i) q^{67} +9.37407 q^{68} +(-0.191271 - 1.27102i) q^{70} +(-2.89675 + 1.67244i) q^{71} +(12.3112 + 7.10790i) q^{73} -1.43830 q^{74} +(0.321025 + 0.185344i) q^{76} +(7.04893 - 1.06077i) q^{77} +(-4.55529 - 7.89000i) q^{79} +(8.85283 - 5.11118i) q^{80} +(0.490899 - 0.850261i) q^{82} +16.5866i q^{83} +(11.0866 - 6.40083i) q^{85} +(1.25445 - 0.724258i) q^{86} +(-0.966401 - 1.67386i) q^{88} +5.89165i q^{89} +(-7.68275 + 5.65468i) q^{91} +8.65473 q^{92} +(0.167162 + 0.289532i) q^{94} +0.506229 q^{95} +(0.390659 - 0.225547i) q^{97} +(-0.861373 + 0.927470i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7}+O(q^{10}) $ 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7	$ 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7} + 12 q^{10} - 12 q^{11} - 2 q^{13} - 4 q^{14} + 16 q^{16} + 34 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 6 q^{23} - 5 q^{25} + 6 q^{26} - 9 q^{28} + q^{29} + 18 q^{31} + 6 q^{35} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 15 q^{47} - 3 q^{49} - 18 q^{50} - 7 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{56} - 24 q^{58} + 5 q^{61} - 41 q^{62} + 2 q^{64} - 21 q^{65} + 15 q^{67} - 22 q^{68} + 3 q^{70} - 30 q^{71} + 42 q^{73} - 66 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} + 63 q^{80} + 5 q^{82} - 21 q^{85} + 57 q^{86} - 14 q^{88} - 7 q^{91} + 66 q^{92} + q^{94} + 4 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7 + 12 * q^10 - 12 * q^11 - 2 * q^13 - 4 * q^14 + 16 * q^16 + 34 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 6 * q^23 - 5 * q^25 + 6 * q^26 - 9 * q^28 + q^29 + 18 * q^31 + 6 * q^35 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 15 * q^47 - 3 * q^49 - 18 * q^50 - 7 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^56 - 24 * q^58 + 5 * q^61 - 41 * q^62 + 2 * q^64 - 21 * q^65 + 15 * q^67 - 22 * q^68 + 3 * q^70 - 30 * q^71 + 42 * q^73 - 66 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 + 63 * q^80 + 5 * q^82 - 21 * q^85 + 57 * q^86 - 14 * q^88 - 7 * q^91 + 66 * q^92 + q^94 + 4 * q^95 - 3 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$			0.180824i			0.127862i	0.997954	+	0.0639308i	$0.0203637\pi$
$2$			0.180824i			0.127862i	−0.997954	+	0.0639308i	$0.979636\pi$
$3$		0			0
$3$		0			0
$4$	1.96730			0.983651
$5$	2.32670	−	1.34332i	1.04053	−	0.600751i	0.120548	−	0.992708i	$-0.461535\pi$
$5$	2.32670	−	1.34332i	1.04053	−	0.600751i	0.919984	+	0.391956i	$0.128201\pi$
$6$		0			0
$7$	−2.46263	−	0.967177i	−0.930788	−	0.365559i
$7$	−2.46263	−	0.967177i	−0.930788	−	0.365559i
$8$			0.717383i			0.253633i
$9$		0			0
$10$	0.242904	+	0.420723i	0.0768131	+	0.133044i
$11$	−2.33328	+	1.34712i	−0.703511	+	0.406172i	−0.808654	−	0.588285i	$-0.799803\pi$
$11$	−2.33328	+	1.34712i	−0.703511	+	0.406172i	0.105143	+	0.994457i	$0.466470\pi$
$12$		0			0
$13$	1.92153	−	3.05086i	0.532937	−	0.846155i
$13$	1.92153	−	3.05086i	0.532937	−	0.846155i
$14$	0.174889	−	0.445303i	0.0467409	−	0.119012i
$15$		0			0
$16$	3.80489			0.951221
$17$	4.76493			1.15567			0.577833	−	0.816155i	$-0.303898\pi$
$17$	4.76493			1.15567			0.577833	+	0.816155i	$0.303898\pi$
$18$		0			0
$19$	0.163180	+	0.0942122i	0.0374361	+	0.0216138i	0.518601	−	0.855016i	$-0.326453\pi$
$19$	0.163180	+	0.0942122i	0.0374361	+	0.0216138i	−0.481165	+	0.876630i	$0.659786\pi$
$20$	4.57732	−	2.64272i	1.02352	−	0.590930i
$21$		0			0
$22$	−0.243592	−	0.421913i	−0.0519339	−	0.0899521i
$23$	4.39929			0.917315			0.458657	−	0.888613i	$-0.348331\pi$
$23$	4.39929			0.917315			0.458657	+	0.888613i	$0.348331\pi$
$24$		0			0
$25$	1.10902	−	1.92088i	0.221804	−	0.384177i
$26$	0.551667	+	0.347458i	0.108191	+	0.0681422i
$27$		0			0
$28$	−4.84475	−	1.90273i	−0.915571	−	0.359582i
$29$	3.54280	−	6.13631i	0.657882	−	1.13948i	−0.323281	−	0.946303i	$-0.604786\pi$
$29$	3.54280	−	6.13631i	0.657882	−	1.13948i	0.981163	−	0.193182i	$-0.0618807\pi$
$30$		0			0
$31$	−3.20369	−	1.84965i	−0.575400	−	0.332207i	0.183903	−	0.982944i	$-0.441127\pi$
$31$	−3.20369	−	1.84965i	−0.575400	−	0.332207i	−0.759303	+	0.650737i	$0.774460\pi$
$32$			2.12278i			0.375258i
$33$		0			0
$34$			0.861613i			0.147765i
$35$	−7.02904	+	1.05778i	−1.18812	+	0.178797i
$36$		0			0
$37$			7.95413i			1.30765i	0.756645	+	0.653826i	$0.226837\pi$
$37$			7.95413i			1.30765i	−0.756645	+	0.653826i	$0.773163\pi$
$38$	−0.0170358	+	0.0295069i	−0.00276357	+	0.00478665i
$39$		0			0
$40$	0.963675	+	1.66913i	0.152370	+	0.263913i
$41$	−4.70215	−	2.71479i	−0.734353	−	0.423979i	0.0856594	−	0.996324i	$-0.472700\pi$
$41$	−4.70215	−	2.71479i	−0.734353	−	0.423979i	−0.820013	+	0.572345i	$0.806034\pi$
$42$		0			0
$43$	−4.00533	−	6.93743i	−0.610807	−	1.05795i	−0.991105	−	0.133084i	$-0.957512\pi$
$43$	−4.00533	−	6.93743i	−0.610807	−	1.05795i	0.380298	−	0.924864i	$-0.375821\pi$
$44$	−4.59027	+	2.65020i	−0.692010	+	0.399532i
$45$		0			0
$46$			0.795496i			0.117289i
$47$	1.60118	−	0.924445i	0.233557	−	0.134844i	−0.378655	−	0.925538i	$-0.623613\pi$
$47$	1.60118	−	0.924445i	0.233557	−	0.134844i	0.612212	+	0.790694i	$0.290280\pi$
$48$		0			0
$49$	5.12914	+	4.76361i	0.732734	+	0.680515i
$50$	0.347341	+	0.200538i	0.0491215	+	0.0283603i
$51$		0			0
$52$	3.78023	−	6.00196i	0.524224	−	0.832322i
$53$	−3.53622	+	6.12491i	−0.485737	+	0.841321i	−0.999866	−	0.0163917i	$-0.994782\pi$
$53$	−3.53622	+	6.12491i	−0.485737	+	0.841321i	0.514128	+	0.857713i	$0.328115\pi$
$54$		0			0
$55$	−3.61923	+	6.26869i	−0.488017	+	0.845271i
$56$	0.693836	−	1.76665i	0.0927177	−	0.236079i
$57$		0			0
$58$	1.10959	+	0.640623i	0.145696	+	0.0841179i
$59$		−	7.58888i		−	0.987988i	−0.869465	−	0.493994i	$-0.835536\pi$
$59$		−	7.58888i		−	0.987988i	0.869465	−	0.493994i	$-0.164464\pi$
$60$		0			0
$61$	0.205782	−	0.356425i	0.0263477	−	0.0456355i	−0.852551	−	0.522644i	$-0.824946\pi$
$61$	0.205782	−	0.356425i	0.0263477	−	0.0456355i	0.878899	+	0.477009i	$0.158279\pi$
$62$	0.334461	−	0.579304i	0.0424766	−	0.0735716i
$63$		0			0
$64$	7.22592			0.903240
$65$	0.372548	−	9.67966i	0.0462089	−	1.20061i
$66$		0			0
$67$	−9.87358	+	5.70051i	−1.20625	+	0.696429i	−0.961938	−	0.273268i	$-0.911895\pi$
$67$	−9.87358	+	5.70051i	−1.20625	+	0.696429i	−0.244312	+	0.969697i	$0.578562\pi$
$68$	9.37407			1.13677
$69$		0			0
$70$	−0.191271	−	1.27102i	−0.0228613	−	0.151916i
$71$	−2.89675	+	1.67244i	−0.343781	+	0.198482i	−0.661943	−	0.749554i	$-0.730268\pi$
$71$	−2.89675	+	1.67244i	−0.343781	+	0.198482i	0.318162	+	0.948037i	$0.396935\pi$
$72$		0			0
$73$	12.3112	+	7.10790i	1.44092	+	0.831917i	0.997911	−	0.0645994i	$-0.0205769\pi$
$73$	12.3112	+	7.10790i	1.44092	+	0.831917i	0.443011	+	0.896516i	$0.353910\pi$
$74$	−1.43830			−0.167199
$75$		0			0
$76$	0.321025	+	0.185344i	0.0368241	+	0.0212604i
$77$	7.04893	−	1.06077i	0.803300	−	0.120886i
$78$		0			0
$79$	−4.55529	−	7.89000i	−0.512511	−	0.887695i	−0.999895	−	0.0145069i	$-0.995382\pi$
$79$	−4.55529	−	7.89000i	−0.512511	−	0.887695i	0.487384	−	0.873188i	$-0.337951\pi$
$80$	8.85283	−	5.11118i	0.989776	−	0.571448i
$81$		0			0
$82$	0.490899	−	0.850261i	0.0542107	−	0.0938956i
$83$			16.5866i			1.82061i	0.413934	+	0.910307i	$0.364155\pi$
$83$			16.5866i			1.82061i	−0.413934	+	0.910307i	$0.635845\pi$
$84$		0			0
$85$	11.0866	−	6.40083i	1.20251	−	0.694268i
$86$	1.25445	−	0.724258i	0.135271	−	0.0780988i
$87$		0			0
$88$	−0.966401	−	1.67386i	−0.103019	−	0.178434i
$89$			5.89165i			0.624513i	0.949998	+	0.312257i	$0.101085\pi$
$89$			5.89165i			0.624513i	−0.949998	+	0.312257i	$0.898915\pi$
$90$		0			0
$91$	−7.68275	+	5.65468i	−0.805371	+	0.592772i
$92$	8.65473			0.902318
$93$		0			0
$94$	0.167162	+	0.289532i	0.0172414	+	0.0298630i
$95$	0.506229			0.0519380
$96$		0			0
$97$	0.390659	−	0.225547i	0.0396654	−	0.0229008i	−0.480036	−	0.877249i	$-0.659376\pi$
$97$	0.390659	−	0.225547i	0.0396654	−	0.0229008i	0.519702	+	0.854348i	$0.326043\pi$
$98$	−0.861373	+	0.927470i	−0.0870118	+	0.0936886i
$99$		0			0
$100$	2.18178	−	3.77896i	0.218178	−	0.377896i
$101$	3.82840	+	6.63098i	0.380940	+	0.659807i	0.991197	−	0.132396i	$-0.0422671\pi$
$101$	3.82840	+	6.63098i	0.380940	+	0.659807i	−0.610257	+	0.792204i	$0.708934\pi$
$102$		0			0
$103$	2.57870	+	4.46644i	0.254087	+	0.440091i	0.964647	−	0.263545i	$-0.0848918\pi$
$103$	2.57870	+	4.46644i	0.254087	+	0.440091i	−0.710560	+	0.703636i	$0.751558\pi$
$104$	2.18863	+	1.37847i	0.214613	+	0.135170i
$105$		0			0
$106$	−1.10753	−	0.639433i	−0.107573	−	0.0621072i
$107$	−8.03289			−0.776569			−0.388284	−	0.921540i	$-0.626932\pi$
$107$	−8.03289			−0.776569			−0.388284	+	0.921540i	$0.626932\pi$
$108$		0			0
$109$	1.15490	+	0.666781i	0.110619	+	0.0638660i	0.554289	−	0.832324i	$-0.312990\pi$
$109$	1.15490	+	0.666781i	0.110619	+	0.0638660i	−0.443670	+	0.896190i	$0.646324\pi$
$110$	−1.13353	−	0.654443i	−0.108078	−	0.0623987i
$111$		0			0
$112$	−9.37004	−	3.68000i	−0.885386	−	0.347727i
$113$	−9.96917	−	17.2671i	−0.937821	−	1.62435i	−0.769525	−	0.638617i	$-0.779507\pi$
$113$	−9.96917	−	17.2671i	−0.937821	−	1.62435i	−0.168296	−	0.985736i	$-0.553827\pi$
$114$		0			0
$115$	10.2358	−	5.90965i	0.954495	−	0.551078i
$116$	6.96976	−	12.0720i	0.647126	−	1.12086i
$117$		0			0
$118$	1.37225			0.126326
$119$	−11.7343	−	4.60853i	−1.07568	−	0.422464i
$120$		0			0
$121$	−1.87053	+	3.23985i	−0.170048	+	0.294532i
$122$	0.0644501	+	0.0372103i	0.00583503	+	0.00336886i
$123$		0			0
$124$	−6.30263	−	3.63883i	−0.565993	−	0.326776i
$125$			7.47412i			0.668505i
$126$		0			0
$127$	−3.98361	+	6.89981i	−0.353488	+	0.612259i	−0.986858	−	0.161590i	$-0.948338\pi$
$127$	−3.98361	+	6.89981i	−0.353488	+	0.612259i	0.633370	+	0.773849i	$0.281671\pi$
$128$			5.55218i			0.490748i
$129$		0			0
$130$	1.75031	+	0.0673655i	0.153513	+	0.00590835i
$131$	5.00897	+	8.67579i	0.437636	+	0.758007i	0.997507	−	0.0705727i	$-0.0224827\pi$
$131$	5.00897	+	8.67579i	0.437636	+	0.758007i	−0.559871	+	0.828580i	$0.689149\pi$
$132$		0			0
$133$	−0.310734	−	0.389835i	−0.0269440	−	0.0338029i
$134$	−1.03079	−	1.78538i	−0.0890465	−	0.154233i
$135$		0			0
$136$			3.41828i			0.293115i
$137$			5.06696i			0.432899i	0.976294	+	0.216450i	$0.0694477\pi$
$137$			5.06696i			0.432899i	−0.976294	+	0.216450i	$0.930552\pi$
$138$		0			0
$139$	−3.86289	−	6.69073i	−0.327646	−	0.567500i	0.654398	−	0.756150i	$-0.272922\pi$
$139$	−3.86289	−	6.69073i	−0.327646	−	0.567500i	−0.982044	+	0.188650i	$0.939589\pi$
$140$	−13.8283	+	2.08097i	−1.16870	+	0.175874i
$141$		0			0
$142$	−0.302417	−	0.523802i	−0.0253783	−	0.0439565i
$143$	−0.373602	+	9.70704i	−0.0312422	+	0.811744i
$144$		0			0
$145$		−	19.0365i		−	1.58089i
$146$	−1.28528	+	2.22617i	−0.106370	+	0.184239i
$147$		0			0
$148$			15.6482i			1.28627i
$149$	−12.4002	−	7.15924i	−1.01586	−	0.586507i	−0.102958	−	0.994686i	$-0.532831\pi$
$149$	−12.4002	−	7.15924i	−1.01586	−	0.586507i	−0.912902	+	0.408178i	$0.866164\pi$
$150$		0			0
$151$	5.60534	+	3.23624i	0.456156	+	0.263362i	0.710427	−	0.703771i	$-0.248502\pi$
$151$	5.60534	+	3.23624i	0.456156	+	0.263362i	−0.254271	+	0.967133i	$0.581835\pi$
$152$	−0.0675862	+	0.117063i	−0.00548197	+	0.00949504i
$153$		0			0
$154$	0.191812	+	1.27461i	0.0154567	+	0.102711i
$155$	−9.93871			−0.798296
$156$		0			0
$157$	−7.95937	+	13.7860i	−0.635227	+	1.10025i	0.351240	+	0.936285i	$0.385760\pi$
$157$	−7.95937	+	13.7860i	−0.635227	+	1.10025i	−0.986467	+	0.163960i	$0.947573\pi$
$158$	1.42670	−	0.823705i	0.113502	−	0.0655305i
$159$		0			0
$160$	2.85157	+	4.93907i	0.225437	+	0.390468i
$161$	−10.8338	−	4.25489i	−0.853826	−	0.335332i
$162$		0			0
$163$	−4.14100	−	2.39081i	−0.324348	−	0.187263i	0.328981	−	0.944337i	$-0.393295\pi$
$163$	−4.14100	−	2.39081i	−0.324348	−	0.187263i	−0.653329	+	0.757074i	$0.726628\pi$
$164$	−9.25056	−	5.34081i	−0.722348	−	0.417048i
$165$		0			0
$166$	−2.99925			−0.232787
$167$	2.34729	+	1.35521i	0.181639	+	0.104869i	0.588062	−	0.808816i	$-0.299891\pi$
$167$	2.34729	+	1.35521i	0.181639	+	0.104869i	−0.406424	+	0.913685i	$0.633224\pi$
$168$		0			0
$169$	−5.61544	−	11.7246i	−0.431957	−	0.901894i
$170$	1.15742	+	2.00472i	0.0887703	+	0.153755i
$171$		0			0
$172$	−7.87969	−	13.6480i	−0.600821	−	1.04065i
$173$	0.449908	−	0.779264i	0.0342059	−	0.0592463i	−0.848416	−	0.529331i	$-0.822443\pi$
$173$	0.449908	−	0.779264i	0.0342059	−	0.0592463i	0.882622	+	0.470084i	$0.155776\pi$
$174$		0			0
$175$	−4.58895	+	3.65781i	−0.346892	+	0.276505i
$176$	−8.87787	+	5.12564i	−0.669195	+	0.386360i
$177$		0			0
$178$	−1.06535			−0.0798513
$179$	5.52791	+	9.57462i	0.413175	+	0.715641i	0.995235	−	0.0975054i	$-0.0310863\pi$
$179$	5.52791	+	9.57462i	0.413175	+	0.715641i	−0.582060	+	0.813146i	$0.697753\pi$
$180$		0			0
$181$	−3.52898			−0.262307			−0.131153	−	0.991362i	$-0.541868\pi$
$181$	−3.52898			−0.262307			−0.131153	+	0.991362i	$0.541868\pi$
$182$	−1.02250	−	1.38922i	−0.0757928	−	0.102976i
$183$		0			0
$184$			3.15597i			0.232661i
$185$	10.6850	+	18.5069i	0.785573	+	1.36065i
$186$		0			0
$187$	−11.1179	+	6.41894i	−0.813024	+	0.469400i
$188$	3.15002	−	1.81866i	0.229738	−	0.132640i
$189$		0			0
$190$			0.0915382i			0.00664088i
$191$	−10.2002	+	17.6672i	−0.738059	+	1.27836i	0.215309	+	0.976546i	$0.430924\pi$
$191$	−10.2002	+	17.6672i	−0.738059	+	1.27836i	−0.953368	+	0.301810i	$0.902409\pi$
$192$		0			0
$193$	−14.9515	+	8.63228i	−1.07624	+	0.621365i	−0.929878	−	0.367867i	$-0.880088\pi$
$193$	−14.9515	+	8.63228i	−1.07624	+	0.621365i	−0.146357	+	0.989232i	$0.546755\pi$
$194$	0.0407842	+	0.0706403i	0.00292814	+	0.00507168i
$195$		0			0
$196$	10.0906	+	9.37146i	0.720755	+	0.669390i
$197$	4.29264	+	2.47836i	0.305838	+	0.176576i	0.645063	−	0.764130i	$-0.276831\pi$
$197$	4.29264	+	2.47836i	0.305838	+	0.176576i	−0.339224	+	0.940705i	$0.610165\pi$
$198$		0			0
$199$	−7.18195			−0.509115			−0.254557	−	0.967058i	$-0.581930\pi$
$199$	−7.18195			−0.509115			−0.254557	+	0.967058i	$0.581930\pi$
$200$	1.37801	+	0.795593i	0.0974399	+	0.0562569i
$201$		0			0
$202$	−1.19904	+	0.692265i	−0.0843641	+	0.0487076i
$203$	−14.6595	+	11.6850i	−1.02890	+	0.820125i
$204$		0			0
$205$	−14.5873			−1.01882
$206$	−0.807638	+	0.466290i	−0.0562708	+	0.0324880i
$207$		0			0
$208$	7.31121	−	11.6082i	0.506941	−	0.804881i
$209$	−0.507661			−0.0351157
$210$		0			0
$211$	8.79636	−	15.2357i	0.605566	−	1.04887i	−0.386395	−	0.922333i	$-0.626280\pi$
$211$	8.79636	−	15.2357i	0.605566	−	1.04887i	0.991962	−	0.126539i	$-0.0403868\pi$
$212$	−6.95682	+	12.0496i	−0.477796	+	0.827567i
$213$		0			0
$214$		−	1.45254i		−	0.0992934i
$215$	−18.6384	−	10.7609i	−1.27113	−	0.733886i
$216$		0			0
$217$	6.10058	+	7.65356i	0.414135	+	0.519557i
$218$	−0.120570	+	0.208833i	−0.00816602	+	0.0141440i
$219$		0			0
$220$	−7.12013	+	12.3324i	−0.480039	+	0.831452i
$221$	9.15597	−	14.5371i	0.615897	−	0.977873i
$222$		0			0
$223$	12.2157	+	7.05271i	0.818020	+	0.472284i	0.849733	−	0.527213i	$-0.176763\pi$
$223$	12.2157	+	7.05271i	0.818020	+	0.472284i	−0.0317129	+	0.999497i	$0.510096\pi$
$224$	2.05310	−	5.22763i	0.137179	−	0.349286i
$225$		0			0
$226$	3.12230	−	1.80266i	0.207693	−	0.119911i
$227$			2.86877i			0.190407i	0.995458	+	0.0952035i	$0.0303502\pi$
$227$			2.86877i			0.190407i	−0.995458	+	0.0952035i	$0.969650\pi$
$228$		0			0
$229$	7.59860	−	4.38706i	0.502130	−	0.289905i	−0.227463	−	0.973787i	$-0.573043\pi$
$229$	7.59860	−	4.38706i	0.502130	−	0.289905i	0.729593	+	0.683882i	$0.239710\pi$
$230$	1.06861	+	1.85088i	0.0704618	+	0.122043i
$231$		0			0
$232$	4.40208	+	2.54154i	0.289011	+	0.166861i
$233$	−2.55371	−	4.42316i	−0.167299	−	0.289771i	0.770170	−	0.637839i	$-0.220171\pi$
$233$	−2.55371	−	4.42316i	−0.167299	−	0.289771i	−0.937469	+	0.348068i	$0.886838\pi$
$234$		0			0
$235$	2.48365	−	4.30181i	0.162016	−	0.280619i
$236$		−	14.9296i		−	0.971836i
$237$		0			0
$238$	0.833332	−	2.12184i	0.0540169	−	0.137538i
$239$			2.49797i			0.161580i	0.996731	+	0.0807901i	$0.0257443\pi$
$239$			2.49797i			0.161580i	−0.996731	+	0.0807901i	$0.974256\pi$
$240$		0			0
$241$		−	7.98512i		−	0.514367i	−0.966363	−	0.257183i	$-0.917206\pi$
$241$		−	7.98512i		−	0.514367i	0.966363	−	0.257183i	$-0.0827944\pi$
$242$	−0.585842	−	0.338236i	−0.0376593	−	0.0217426i
$243$		0			0
$244$	0.404835	−	0.701195i	0.0259169	−	0.0448894i
$245$	18.3330	+	4.19341i	1.17125	+	0.267907i
$246$		0			0
$247$	0.600984	−	0.316808i	0.0382397	−	0.0201580i
$248$	1.32691	−	2.29827i	0.0842588	−	0.145941i
$249$		0			0
$250$	−1.35150			−0.0854762
$251$	−12.6285	−	21.8732i	−0.797105	−	1.38063i	−0.921494	−	0.388393i	$-0.873030\pi$
$251$	−12.6285	−	21.8732i	−0.797105	−	1.38063i	0.124389	−	0.992234i	$-0.460303\pi$
$252$		0			0
$253$	−10.2648	+	5.92637i	−0.645341	+	0.372588i
$254$	−1.24765	−	0.720331i	−0.0782845	−	0.0451976i
$255$		0			0
$256$	13.4479			0.840493
$257$	−3.37363			−0.210442			−0.105221	−	0.994449i	$-0.533555\pi$
$257$	−3.37363			−0.210442			−0.105221	+	0.994449i	$0.533555\pi$
$258$		0			0
$259$	7.69305	−	19.5881i	0.478023	−	1.21715i
$260$	0.732915	−	19.0428i	0.0454535	−	1.18099i
$261$		0			0
$262$	−1.56879	+	0.905740i	−0.0969201	+	0.0559568i
$263$	−0.0794677	−	0.137642i	−0.00490019	−	0.00848737i	0.863565	−	0.504238i	$-0.168226\pi$
$263$	−0.0794677	−	0.137642i	−0.00490019	−	0.00848737i	−0.868465	+	0.495750i	$0.834893\pi$
$264$		0			0
$265$			19.0011i			1.16723i
$266$	0.0704914	−	0.0561880i	0.00432210	−	0.00344511i
$267$		0			0
$268$	−19.4243	+	11.2146i	−1.18653	+	0.685043i
$269$	23.3266			1.42225			0.711124	−	0.703066i	$-0.248186\pi$
$269$	23.3266			1.42225			0.711124	+	0.703066i	$0.248186\pi$
$270$		0			0
$271$			11.8210i			0.718074i	0.933323	+	0.359037i	$0.116895\pi$
$271$			11.8210i			0.718074i	−0.933323	+	0.359037i	$0.883105\pi$
$272$	18.1300			1.09929
$273$		0			0
$274$	−0.916226			−0.0553513
$275$			5.97595i			0.360363i
$276$		0			0
$277$	27.3653			1.64422			0.822111	−	0.569327i	$-0.192796\pi$
$277$	27.3653			1.64422			0.822111	+	0.569327i	$0.192796\pi$
$278$	1.20984	−	0.698503i	0.0725615	−	0.0418934i
$279$		0			0
$280$	−0.758831	−	5.04251i	−0.0453488	−	0.301348i
$281$		−	28.5383i		−	1.70245i	−0.524801	−	0.851225i	$-0.675860\pi$
$281$		−	28.5383i		−	1.70245i	0.524801	−	0.851225i	$-0.324140\pi$
$282$		0			0
$283$	8.98604	+	15.5643i	0.534165	+	0.925201i	0.999203	+	0.0399101i	$0.0127072\pi$
$283$	8.98604	+	15.5643i	0.534165	+	0.925201i	−0.465038	+	0.885290i	$0.653960\pi$
$284$	−5.69879	+	3.29020i	−0.338161	+	0.195237i
$285$		0			0
$286$	−1.75526	−	0.0675561i	−0.103791	−	0.00399468i
$287$	8.95400	+	11.2334i	0.528538	+	0.663084i
$288$		0			0
$289$	5.70459			0.335564
$290$	3.44225			0.202136
$291$		0			0
$292$	24.2199	+	13.9834i	1.41737	+	0.818316i
$293$	−12.8943	+	7.44453i	−0.753293	+	0.434914i	−0.826882	−	0.562375i	$-0.809888\pi$
$293$	−12.8943	+	7.44453i	−0.753293	+	0.434914i	0.0735896	+	0.997289i	$0.476554\pi$
$294$		0			0
$295$	−10.1943	−	17.6570i	−0.593535	−	1.02803i
$296$	−5.70616			−0.331664
$297$		0			0
$298$	1.29456	−	2.24224i	0.0749918	−	0.129890i
$299$	8.45337	−	13.4216i	0.488871	−	0.776191i
$300$		0			0
$301$	3.15393	+	20.9582i	0.181790	+	1.20801i
$302$	−0.585190	+	1.01358i	−0.0336739	+	0.0583249i
$303$		0			0
$304$	0.620883	+	0.358467i	0.0356101	+	0.0205595i
$305$		−	1.10572i		−	0.0633136i
$306$		0			0
$307$		−	23.5161i		−	1.34214i	−0.741396	−	0.671068i	$-0.765836\pi$
$307$		−	23.5161i		−	1.34214i	0.741396	−	0.671068i	$-0.234164\pi$
$308$	13.8674	−	2.08686i	0.790167	−	0.118910i
$309$		0			0
$310$		−	1.79715i		−	0.102072i
$311$	−0.815450	+	1.41240i	−0.0462399	+	0.0800899i	−0.888219	−	0.459420i	$-0.848057\pi$
$311$	−0.815450	+	1.41240i	−0.0462399	+	0.0800899i	0.841979	+	0.539510i	$0.181391\pi$
$312$		0			0
$313$	0.348367	+	0.603389i	0.0196909	+	0.0341056i	0.875703	−	0.482850i	$-0.160398\pi$
$313$	0.348367	+	0.603389i	0.0196909	+	0.0341056i	−0.856012	+	0.516956i	$0.827065\pi$
$314$	−2.49284	−	1.43924i	−0.140679	−	0.0812212i
$315$		0			0
$316$	−8.96164	−	15.5220i	−0.504132	−	0.873182i
$317$	−18.5579	+	10.7144i	−1.04231	+	0.601780i	−0.920488	−	0.390771i	$-0.872208\pi$
$317$	−18.5579	+	10.7144i	−1.04231	+	0.601780i	−0.121826	+	0.992551i	$0.538875\pi$
$318$		0			0
$319$			19.0903i			1.06885i
$320$	16.8126	−	9.70673i	0.939850	−	0.542623i
$321$		0			0
$322$	0.769385	−	1.95901i	0.0428762	−	0.109172i
$323$	0.777544	+	0.448915i	0.0432637	+	0.0249783i
$324$		0			0
$325$	−3.72932	−	7.07450i	−0.206865	−	0.392423i
$326$	0.432315	−	0.748792i	0.0239437	−	0.0414717i
$327$		0			0
$328$	1.94754	−	3.37324i	0.107535	−	0.186256i
$329$	−4.83723	+	0.727939i	−0.266685	+	0.0401326i
$330$		0			0
$331$	−1.31676	−	0.760232i	−0.0723757	−	0.0417861i	0.463375	−	0.886162i	$-0.346638\pi$
$331$	−1.31676	−	0.760232i	−0.0723757	−	0.0417861i	−0.535751	+	0.844376i	$0.679971\pi$
$332$			32.6308i			1.79085i
$333$		0			0
$334$	−0.245054	+	0.424446i	−0.0134088	+	0.0232247i
$335$	−15.3152	+	26.5268i	−0.836761	+	1.44931i
$336$		0			0
$337$	−32.2304			−1.75570			−0.877850	−	0.478936i	$-0.841023\pi$
$337$	−32.2304			−1.75570			−0.877850	+	0.478936i	$0.841023\pi$
$338$	2.12009	−	1.01540i	0.115318	−	0.0552307i
$339$		0			0
$340$	21.8106	−	12.5924i	1.18285	−	0.682918i
$341$	9.96683			0.539734
$342$		0			0
$343$	−8.02394	−	16.6918i	−0.433252	−	0.901273i
$344$	4.97679	−	2.87335i	0.268331	−	0.154921i
$345$		0			0
$346$	0.140909	+	0.0813541i	0.00757534	+	0.00437362i
$347$	−8.18431			−0.439357			−0.219678	−	0.975572i	$-0.570501\pi$
$347$	−8.18431			−0.439357			−0.219678	+	0.975572i	$0.570501\pi$
$348$		0			0
$349$	−18.9220	−	10.9246i	−1.01287	−	0.584782i	−0.100841	−	0.994903i	$-0.532153\pi$
$349$	−18.9220	−	10.9246i	−1.01287	−	0.584782i	−0.912031	+	0.410120i	$0.865487\pi$
$350$	−0.661419	−	0.829791i	−0.0353543	−	0.0443542i
$351$		0			0
$352$	−2.85964	−	4.95304i	−0.152419	−	0.263998i
$353$	0.491192	−	0.283590i	0.0261435	−	0.0150940i	−0.486871	−	0.873474i	$-0.661862\pi$
$353$	0.491192	−	0.283590i	0.0261435	−	0.0150940i	0.513015	+	0.858380i	$0.328529\pi$
$354$		0			0
$355$	−4.49325	+	7.78254i	−0.238477	+	0.413054i
$356$			11.5907i			0.614303i
$357$		0			0
$358$	−1.73132	+	0.999577i	−0.0915030	+	0.0528293i
$359$	28.0630	−	16.2022i	1.48111	−	0.855118i	0.481336	−	0.876536i	$-0.340152\pi$
$359$	28.0630	−	16.2022i	1.48111	−	0.855118i	0.999771	+	0.0214184i	$0.00681822\pi$
$360$		0			0
$361$	−9.48225	−	16.4237i	−0.499066	−	0.864407i
$362$		−	0.638123i		−	0.0335390i
$363$		0			0
$364$	−15.1143	+	11.1245i	−0.792204	+	0.583081i
$365$	38.1928			1.99910
$366$		0			0
$367$	3.93444	+	6.81465i	0.205376	+	0.355722i	0.950252	−	0.311481i	$-0.100825\pi$
$367$	3.93444	+	6.81465i	0.205376	+	0.355722i	−0.744876	+	0.667202i	$0.767492\pi$
$368$	16.7388			0.872569
$369$		0			0
$370$	−3.34648	+	1.93209i	−0.173975	+	0.100445i
$371$	14.6323	−	11.6633i	0.759671	−	0.605527i
$372$		0			0
$373$	1.04581	−	1.81140i	0.0541502	−	0.0937909i	−0.837680	−	0.546162i	$-0.816088\pi$
$373$	1.04581	−	1.81140i	0.0541502	−	0.0937909i	0.891830	+	0.452371i	$0.149422\pi$
$374$	−1.16070	−	2.01039i	−0.0600182	−	0.103955i
$375$		0			0
$376$	0.663180	+	1.14866i	0.0342009	+	0.0592377i
$377$	−11.9134	−	22.5997i	−0.613571	−	1.16394i
$378$		0			0
$379$	12.3983	+	7.15817i	0.636859	+	0.367691i	0.783404	−	0.621513i	$-0.213482\pi$
$379$	12.3983	+	7.15817i	0.636859	+	0.367691i	−0.146545	+	0.989204i	$0.546815\pi$
$380$	0.995906			0.0510889
$381$		0			0
$382$	−3.19466	−	1.84444i	−0.163453	−	0.0943695i
$383$	−21.8129	−	12.5937i	−1.11459	−	0.643507i	−0.174573	−	0.984644i	$-0.555854\pi$
$383$	−21.8129	−	12.5937i	−1.11459	−	0.643507i	−0.940013	+	0.341138i	$0.889188\pi$
$384$		0			0
$385$	14.9758	−	11.9371i	0.763237	−	0.608369i
$386$	−1.56092	−	2.70359i	−0.0794488	−	0.137609i
$387$		0			0
$388$	0.768544	−	0.443719i	0.0390169	−	0.0225264i
$389$	−14.0512	+	24.3373i	−0.712422	+	1.23395i	0.251524	+	0.967851i	$0.419068\pi$
$389$	−14.0512	+	24.3373i	−0.712422	+	1.23395i	−0.963946	+	0.266099i	$0.914265\pi$
$390$		0			0
$391$	20.9623			1.06011
$392$	−3.41733	+	3.67955i	−0.172601	+	0.185845i
$393$		0			0
$394$	−0.448146	+	0.776212i	−0.0225773	+	0.0391050i
$395$	−21.1976	−	12.2384i	−1.06657	−	0.615783i
$396$		0			0
$397$	−18.8590	−	10.8882i	−0.946504	−	0.546465i	−0.0545111	−	0.998513i	$-0.517360\pi$
$397$	−18.8590	−	10.8882i	−0.946504	−	0.546465i	−0.891993	+	0.452049i	$0.850693\pi$
$398$		−	1.29867i		−	0.0650963i
$399$		0			0
$400$	4.21970	−	7.30874i	0.210985	−	0.365437i
$401$			20.5290i			1.02517i	0.858637	+	0.512584i	$0.171312\pi$
$401$			20.5290i			1.02517i	−0.858637	+	0.512584i	$0.828688\pi$
$402$		0			0
$403$	−11.7990	+	6.21984i	−0.587751	+	0.309832i
$404$	7.53162	+	13.0451i	0.374712	+	0.649020i
$405$		0			0
$406$	−2.11292	−	2.65079i	−0.104863	−	0.131557i
$407$	−10.7152	−	18.5592i	−0.531132	−	0.919947i
$408$		0			0
$409$		−	6.26862i		−	0.309963i	−0.987917	−	0.154982i	$-0.950468\pi$
$409$		−	6.26862i		−	0.309963i	0.987917	−	0.154982i	$-0.0495319\pi$
$410$		−	2.63774i		−	0.130269i
$411$		0			0
$412$	5.07308	+	8.78683i	0.249933	+	0.432896i
$413$	−7.33979	+	18.6886i	−0.361168	+	0.919608i
$414$		0			0
$415$	22.2811	+	38.5920i	1.09374	+	1.89441i
$416$	6.47629	+	4.07899i	0.317526	+	0.199989i
$417$		0			0
$418$		−	0.0917972i		−	0.00448995i
$419$	17.0817	−	29.5864i	0.834497	−	1.44539i	−0.0599424	−	0.998202i	$-0.519092\pi$
$419$	17.0817	−	29.5864i	0.834497	−	1.44539i	0.894439	−	0.447189i	$-0.147575\pi$
$420$		0			0
$421$		−	11.5233i		−	0.561613i	−0.959764	−	0.280806i	$-0.909398\pi$
$421$		−	11.5233i		−	0.561613i	0.959764	−	0.280806i	$-0.0906019\pi$
$422$	2.75498	+	1.59059i	0.134111	+	0.0774288i
$423$		0			0
$424$	−4.39391	−	2.53682i	−0.213387	−	0.123199i
$425$	5.28442	−	9.15288i	0.256332	−	0.443980i
$426$		0			0
$427$	−0.851492	+	0.678716i	−0.0412066	+	0.0328454i
$428$	−15.8031			−0.763873
$429$		0			0
$430$	1.94582	−	3.37026i	0.0938359	−	0.162529i
$431$	7.59505	−	4.38500i	0.365841	−	0.211218i	−0.305799	−	0.952096i	$-0.598924\pi$
$431$	7.59505	−	4.38500i	0.365841	−	0.211218i	0.671640	+	0.740878i	$0.265590\pi$
$432$		0			0
$433$	11.0535	+	19.1452i	0.531196	+	0.920058i	0.999337	+	0.0364046i	$0.0115905\pi$
$433$	11.0535	+	19.1452i	0.531196	+	0.920058i	−0.468141	+	0.883654i	$0.655076\pi$
$434$	−1.38394	+	1.10313i	−0.0664315	+	0.0529519i
$435$		0			0
$436$	2.27203	+	1.31176i	0.108811	+	0.0628219i
$437$	0.717877	+	0.414467i	0.0343407	+	0.0198266i
$438$		0			0
$439$	10.3709			0.494978			0.247489	−	0.968891i	$-0.420395\pi$
$439$	10.3709			0.494978			0.247489	+	0.968891i	$0.420395\pi$
$440$	−4.49705	−	2.59637i	−0.214389	−	0.123777i
$441$		0			0
$442$	2.62866	+	1.65562i	0.125032	+	0.0787496i
$443$	17.9068	+	31.0156i	0.850780	+	1.47359i	0.880506	+	0.474036i	$0.157203\pi$
$443$	17.9068	+	31.0156i	0.850780	+	1.47359i	−0.0297257	+	0.999558i	$0.509463\pi$
$444$		0			0
$445$	7.91437	+	13.7081i	0.375177	+	0.649826i
$446$	−1.27530	+	2.20888i	−0.0603871	+	0.104593i
$447$		0			0
$448$	−17.7948	−	6.98875i	−0.840726	−	0.330187i
$449$	19.7023	−	11.3751i	0.929809	−	0.536825i	0.0430575	−	0.999073i	$-0.486290\pi$
$449$	19.7023	−	11.3751i	0.929809	−	0.536825i	0.886751	+	0.462247i	$0.152957\pi$
$450$		0			0
$451$	14.6286			0.688834
$452$	−19.6124	−	33.9696i	−0.922489	−	1.59780i
$453$		0			0
$454$	−0.518742			−0.0243458
$455$	−10.2794	+	23.4771i	−0.481905	+	1.10063i
$456$		0			0
$457$		−	31.3172i		−	1.46496i	−0.680791	−	0.732478i	$-0.738364\pi$
$457$		−	31.3172i		−	1.46496i	0.680791	−	0.732478i	$-0.261636\pi$
$458$	0.793284	+	1.37401i	0.0370677	+	0.0642032i
$459$		0			0
$460$	20.1370	−	11.6261i	0.938891	−	0.542069i
$461$	7.28113	−	4.20376i	0.339116	−	0.195789i	−0.320765	−	0.947159i	$-0.603940\pi$
$461$	7.28113	−	4.20376i	0.339116	−	0.195789i	0.659881	+	0.751370i	$0.270607\pi$
$462$		0			0
$463$			10.0392i			0.466563i	0.972409	+	0.233281i	$0.0749463\pi$
$463$			10.0392i			0.466563i	−0.972409	+	0.233281i	$0.925054\pi$
$464$	13.4800	−	23.3480i	0.625791	−	1.08390i
$465$		0			0
$466$	0.799813	−	0.461772i	0.0370506	−	0.0213912i
$467$	13.1756	+	22.8209i	0.609696	+	1.05602i	0.991290	+	0.131695i	$0.0420418\pi$
$467$	13.1756	+	22.8209i	0.609696	+	1.05602i	−0.381594	+	0.924330i	$0.624625\pi$
$468$		0			0
$469$	29.8284	−	4.48878i	1.37735	−	0.207273i
$470$	0.777869	+	0.449103i	0.0358804	+	0.0207156i
$471$		0			0
$472$	5.44413			0.250586
$473$	18.6911	+	10.7913i	0.859418	+	0.496185i
$474$		0			0
$475$	0.361941	−	0.208967i	0.0166070	−	0.00958806i
$476$	−23.0849	−	9.06638i	−1.05809	−	0.415557i
$477$		0			0
$478$	−0.451692			−0.0206599
$479$	7.43409	−	4.29207i	0.339672	−	0.196110i	−0.320455	−	0.947264i	$-0.603836\pi$
$479$	7.43409	−	4.29207i	0.339672	−	0.196110i	0.660127	+	0.751154i	$0.270502\pi$
$480$		0			0
$481$	24.2669	+	15.2841i	1.10648	+	0.696895i
$482$	1.44390			0.0657678
$483$		0			0
$484$	−3.67990	+	6.37377i	−0.167268	+	0.289717i
$485$	0.605963	−	1.04956i	0.0275154	−	0.0476580i
$486$		0			0
$487$		−	21.2562i		−	0.963212i	−0.876388	−	0.481606i	$-0.840054\pi$
$487$		−	21.2562i		−	0.963212i	0.876388	−	0.481606i	$-0.159946\pi$
$488$	0.255693	+	0.147624i	0.0115747	+	0.00668264i
$489$		0			0
$490$	−0.758268	+	3.31504i	−0.0342551	+	0.149758i
$491$	11.2268	−	19.4453i	0.506657	−	0.877556i	−0.493313	−	0.869852i	$-0.664214\pi$
$491$	11.2268	−	19.4453i	0.506657	−	0.877556i	0.999970	−	0.00770409i	$-0.00245231\pi$
$492$		0			0
$493$	16.8812	−	29.2391i	0.760292	−	1.31686i
$494$	0.0572864	+	0.108672i	0.00257744	+	0.00488939i
$495$		0			0
$496$	−12.1897	−	7.03772i	−0.547333	−	0.316003i
$497$	8.75119	−	1.31694i	0.392545	−	0.0590727i
$498$		0			0
$499$	−33.6694	+	19.4390i	−1.50725	+	0.870210i	−0.507284	+	0.861779i	$0.669350\pi$
$499$	−33.6694	+	19.4390i	−1.50725	+	0.870210i	−0.999964	+	0.00843082i	$0.997316\pi$
$500$			14.7039i			0.657576i
$501$		0			0
$502$	3.95520	−	2.28354i	0.176529	−	0.101919i
$503$	2.72850	+	4.72591i	0.121658	+	0.210718i	0.920422	−	0.390927i	$-0.127846\pi$
$503$	2.72850	+	4.72591i	0.121658	+	0.210718i	−0.798764	+	0.601645i	$0.794512\pi$
$504$		0			0
$505$	17.8151	+	10.2855i	0.792760	+	0.457700i
$506$	−1.07163	−	1.85612i	−0.0476397	−	0.0825144i
$507$		0			0
$508$	−7.83697	+	13.5740i	−0.347709	+	0.602250i
$509$		−	10.8925i		−	0.482800i	−0.970426	−	0.241400i	$-0.922393\pi$
$509$		−	10.8925i		−	0.482800i	0.970426	−	0.241400i	$-0.0776066\pi$
$510$		0			0
$511$	−23.4435	−	29.4113i	−1.03708	−	1.30108i
$512$			13.5360i			0.598214i
$513$		0			0
$514$		−	0.610033i		−	0.0269074i
$515$	11.9997	+	6.92804i	0.528771	+	0.305286i
$516$		0			0
$517$	−2.49068	+	4.31398i	−0.109540	+	0.189729i
$518$	3.54200	+	1.39109i	0.155626	+	0.0611209i
$519$		0			0
$520$	6.94402	+	0.267260i	0.304515	+	0.0117201i
$521$	13.9480	−	24.1587i	0.611074	−	1.05841i	−0.379985	−	0.924993i	$-0.624071\pi$
$521$	13.9480	−	24.1587i	0.611074	−	1.05841i	0.991060	−	0.133419i	$-0.0425957\pi$
$522$		0			0
$523$	16.7236			0.731272			0.365636	−	0.930758i	$-0.380852\pi$
$523$	16.7236			0.731272			0.365636	+	0.930758i	$0.380852\pi$
$524$	9.85416	+	17.0679i	0.430481	+	0.745615i
$525$		0			0
$526$	0.0248890	−	0.0143696i	0.00108521	−	0.000626546i
$527$	−15.2654	−	8.81347i	−0.664970	−	0.383921i
$528$		0			0
$529$	−3.64627			−0.158534
$530$	−3.43585			−0.149244
$531$		0			0
$532$	−0.611307	−	0.766923i	−0.0265035	−	0.0332503i
$533$	−17.3178	+	9.12904i	−0.750116	+	0.395423i
$534$		0			0
$535$	−18.6901	+	10.7907i	−0.808045	+	0.466525i
$536$	−4.08945	−	7.08313i	−0.176637	−	0.305945i
$537$		0			0
$538$			4.21800i			0.181851i
$539$	−18.3849	−	4.20527i	−0.791893	−	0.181134i
$540$		0			0
$541$	9.66528	−	5.58025i	0.415543	−	0.239914i	−0.277626	−	0.960689i	$-0.589547\pi$
$541$	9.66528	−	5.58025i	0.415543	−	0.239914i	0.693169	+	0.720776i	$0.256214\pi$
$542$	−2.13751			−0.0918141
$543$		0			0
$544$			10.1149i			0.433673i
$545$	3.58280			0.153470
$546$		0			0
$547$	36.6556			1.56728			0.783640	−	0.621215i	$-0.213361\pi$
$547$	36.6556			1.56728			0.783640	+	0.621215i	$0.213361\pi$
$548$			9.96824i			0.425822i
$549$		0			0
$550$	−1.08059			−0.0460767
$551$	1.15623	−	0.667551i	0.0492571	−	0.0284386i
$552$		0			0
$553$	3.58700	+	23.8360i	0.152535	+	1.01361i
$554$			4.94830i			0.210233i
$555$		0			0
$556$	−7.59948	−	13.1627i	−0.322290	−	0.558222i
$557$	28.6461	−	16.5388i	1.21377	−	0.700772i	0.250193	−	0.968196i	$-0.419506\pi$
$557$	28.6461	−	16.5388i	1.21377	−	0.700772i	0.963579	+	0.267424i	$0.0861725\pi$
$558$		0			0
$559$	−28.8615	−	1.11081i	−1.22071	−	0.0469823i
$560$	−26.7447	+	4.02472i	−1.13017	+	0.170076i
$561$		0			0
$562$	5.16039			0.217678
$563$	17.7967			0.750043			0.375021	−	0.927016i	$-0.377635\pi$
$563$	17.7967			0.750043			0.375021	+	0.927016i	$0.377635\pi$
$564$		0			0
$565$	−46.3906	−	26.7836i	−1.95167	−	1.12679i
$566$	−2.81439	+	1.62489i	−0.118298	+	0.0682992i
$567$		0			0
$568$	−1.19978	−	2.07808i	−0.0503417	−	0.0871943i
$569$	−8.22094			−0.344640			−0.172320	−	0.985041i	$-0.555126\pi$
$569$	−8.22094			−0.344640			−0.172320	+	0.985041i	$0.555126\pi$
$570$		0			0
$571$	−12.8776	+	22.3047i	−0.538912	+	0.933424i	0.460051	+	0.887893i	$0.347831\pi$
$571$	−12.8776	+	22.3047i	−0.538912	+	0.933424i	−0.998963	+	0.0455309i	$0.985502\pi$
$572$	−0.734988	+	19.0967i	−0.0307314	+	0.798473i
$573$		0			0
$574$	−2.03126	+	1.61910i	−0.0847830	+	0.0675798i
$575$	4.87891	−	8.45051i	0.203464	−	0.352411i
$576$		0			0
$577$	−0.666314	−	0.384697i	−0.0277390	−	0.0160151i	0.486066	−	0.873922i	$-0.338431\pi$
$577$	−0.666314	−	0.384697i	−0.0277390	−	0.0160151i	−0.513805	+	0.857907i	$0.671765\pi$
$578$			1.03152i			0.0429058i
$579$		0			0
$580$		−	37.4505i		−	1.55505i
$581$	16.0422	−	40.8467i	0.665541	−	1.69461i
$582$		0			0
$583$		−	19.0549i		−	0.789172i
$584$	−5.09908	+	8.83187i	−0.211002	+	0.365465i
$585$		0			0
$586$	−1.34615	−	2.33159i	−0.0556088	−	0.0963173i
$587$	10.4727	+	6.04644i	0.432256	+	0.249563i	0.700307	−	0.713841i	$-0.253046\pi$
$587$	10.4727	+	6.04644i	0.432256	+	0.249563i	−0.268051	+	0.963405i	$0.586380\pi$
$588$		0			0
$589$	−0.348520	−	0.603654i	−0.0143605	−	0.0248731i
$590$	3.19281	−	1.84337i	0.131446	−	0.0758904i
$591$		0			0
$592$			30.2646i			1.24387i
$593$	13.8115	−	7.97406i	0.567170	−	0.327456i	−0.188848	−	0.982006i	$-0.560475\pi$
$593$	13.8115	−	7.97406i	0.567170	−	0.327456i	0.756018	+	0.654551i	$0.227142\pi$
$594$		0			0
$595$	−33.4929	+	5.04024i	−1.37308	+	0.206630i
$596$	−24.3949	−	14.0844i	−0.999253	−	0.576919i
$597$		0			0
$598$	2.42694	+	1.52857i	0.0992450	+	0.0625078i
$599$	−3.55511	+	6.15763i	−0.145258	+	0.251594i	−0.929469	−	0.368900i	$-0.879734\pi$
$599$	−3.55511	+	6.15763i	−0.145258	+	0.251594i	0.784211	+	0.620494i	$0.213068\pi$
$600$		0			0
$601$	−10.3953	+	18.0051i	−0.424032	+	0.734445i	−0.996329	−	0.0856011i	$-0.972719\pi$
$601$	−10.3953	+	18.0051i	−0.424032	+	0.734445i	0.572297	+	0.820046i	$0.306052\pi$
$602$	−3.78974	+	0.570306i	−0.154458	+	0.0232439i
$603$		0			0
$604$	11.0274	+	6.36667i	0.448698	+	0.259056i
$605$			10.0509i			0.408626i
$606$		0			0
$607$	3.85702	−	6.68056i	0.156552	−	0.271156i	−0.777071	−	0.629413i	$-0.783296\pi$
$607$	3.85702	−	6.68056i	0.156552	−	0.271156i	0.933623	+	0.358257i	$0.116629\pi$
$608$	−0.199992	+	0.346396i	−0.00811074	+	0.0140482i
$609$		0			0
$610$	0.199941			0.00809539
$611$	0.256380	−	6.66133i	0.0103720	−	0.269489i
$612$		0			0
$613$	−17.6997	+	10.2189i	−0.714883	+	0.412738i	−0.812867	−	0.582450i	$-0.802094\pi$
$613$	−17.6997	+	10.2189i	−0.714883	+	0.412738i	0.0979832	+	0.995188i	$0.468761\pi$
$614$	4.25227			0.171608
$615$		0			0
$616$	0.760978	+	5.05678i	0.0306607	+	0.203743i
$617$	3.98209	−	2.29906i	0.160313	−	0.0925567i	−0.417697	−	0.908586i	$-0.637163\pi$
$617$	3.98209	−	2.29906i	0.160313	−	0.0925567i	0.578010	+	0.816030i	$0.303829\pi$
$618$		0			0
$619$	−8.70599	−	5.02641i	−0.349923	−	0.202028i	0.314728	−	0.949182i	$-0.398087\pi$
$619$	−8.70599	−	5.02641i	−0.349923	−	0.202028i	−0.664651	+	0.747154i	$0.731420\pi$
$620$	−19.5525			−0.785245
$621$		0			0
$622$	−0.255396	−	0.147453i	−0.0102404	−	0.00591232i
$623$	5.69827	−	14.5090i	0.228296	−	0.581290i
$624$		0			0
$625$	15.5853	+	26.9944i	0.623410	+	1.07978i
$626$	−0.109107	+	0.0629930i	−0.00436080	+	0.00251771i
$627$		0			0
$628$	−15.6585	+	27.1213i	−0.624842	+	1.08226i
$629$			37.9009i			1.51121i
$630$		0			0
$631$	−6.29923	+	3.63686i	−0.250768	+	0.144781i	−0.620116	−	0.784510i	$-0.712914\pi$
$631$	−6.29923	+	3.63686i	−0.250768	+	0.144781i	0.369348	+	0.929291i	$0.379581\pi$
$632$	5.66015	−	3.26789i	0.225149	−	0.129990i
$633$		0			0
$634$	−1.93742	−	3.35570i	−0.0769447	−	0.133272i
$635$			21.4051i			0.849434i
$636$		0			0
$637$	24.3889	−	6.49484i	0.966322	−	0.257335i
$638$	−3.45199			−0.136665
$639$		0			0
$640$	7.45835	+	12.9182i	0.294817	+	0.510639i
$641$	3.85033			0.152079			0.0760394	−	0.997105i	$-0.475773\pi$
$641$	3.85033			0.152079			0.0760394	+	0.997105i	$0.475773\pi$
$642$		0			0
$643$	2.49163	−	1.43855i	0.0982605	−	0.0567307i	−0.450065	−	0.892996i	$-0.648599\pi$
$643$	2.49163	−	1.43855i	0.0982605	−	0.0567307i	0.548325	+	0.836265i	$0.315266\pi$
$644$	−21.3134	−	8.37066i	−0.839867	−	0.329850i
$645$		0			0
$646$	−0.0811745	+	0.140598i	−0.00319377	+	0.00553177i
$647$	−18.5501	−	32.1296i	−0.729278	−	1.26315i	−0.957189	−	0.289464i	$-0.906523\pi$
$647$	−18.5501	−	32.1296i	−0.729278	−	1.26315i	0.227911	−	0.973682i	$-0.426810\pi$
$648$		0			0
$649$	10.2231	+	17.7070i	0.401293	+	0.695061i
$650$	1.27924	−	0.674349i	0.0501758	−	0.0264501i
$651$		0			0
$652$	−8.14661	−	4.70345i	−0.319046	−	0.184201i
$653$	−20.0950			−0.786377			−0.393189	−	0.919458i	$-0.628628\pi$
$653$	−20.0950			−0.786377			−0.393189	+	0.919458i	$0.628628\pi$
$654$		0			0
$655$	23.3087	+	13.4573i	0.910748	+	0.525820i
$656$	−17.8912	−	10.3295i	−0.698532	−	0.403298i
$657$		0			0
$658$	−0.131629	−	0.874687i	−0.00513142	−	0.0340988i
$659$	4.95529	+	8.58281i	0.193031	+	0.334339i	0.946253	−	0.323427i	$-0.104835\pi$
$659$	4.95529	+	8.58281i	0.193031	+	0.334339i	−0.753223	+	0.657766i	$0.771502\pi$
$660$		0			0
$661$	40.8994	−	23.6133i	1.59080	−	0.918450i	0.597633	−	0.801770i	$-0.296108\pi$
$661$	40.8994	−	23.6133i	1.59080	−	0.918450i	0.993170	−	0.116680i	$-0.0372252\pi$
$662$	0.137468	−	0.238102i	0.00534284	−	0.00925408i
$663$		0			0
$664$	−11.8989			−0.461768
$665$	−1.24666	−	0.489613i	−0.0483433	−	0.0189864i
$666$		0			0
$667$	15.5858	−	26.9954i	0.603485	−	1.04527i
$668$	4.61783	+	2.66611i	0.178669	+	0.103155i
$669$		0			0
$670$	−4.79667	−	2.76936i	−0.185312	−	0.106990i
$671$			1.10885i			0.0428068i
$672$		0			0
$673$	3.45845	−	5.99020i	0.133313	−	0.230905i	−0.791639	−	0.610990i	$-0.790772\pi$
$673$	3.45845	−	5.99020i	0.133313	−	0.230905i	0.924952	+	0.380084i	$0.124105\pi$
$674$		−	5.82801i		−	0.224487i
$675$		0			0
$676$	−11.0473	−	23.0659i	−0.424895	−	0.887150i
$677$	−6.16453	−	10.6773i	−0.236922	−	0.410361i	0.722908	−	0.690945i	$-0.242805\pi$
$677$	−6.16453	−	10.6773i	−0.236922	−	0.410361i	−0.959830	+	0.280584i	$0.909472\pi$
$678$		0			0
$679$	−1.18019	+	0.177603i	−0.0452916	+	0.00681579i
$680$	4.59185	+	7.95331i	0.176089	+	0.304996i
$681$		0			0
$682$			1.80224i			0.0690113i
$683$			24.5364i			0.938859i	0.882970	+	0.469430i	$0.155540\pi$
$683$			24.5364i			0.938859i	−0.882970	+	0.469430i	$0.844460\pi$
$684$		0			0
$685$	6.80655	+	11.7893i	0.260065	+	0.450446i
$686$	3.01828	−	1.45092i	0.115238	−	0.0553963i
$687$		0			0
$688$	−15.2398	−	26.3961i	−0.581012	−	1.00634i
$689$	11.8913	+	22.5577i	0.453021	+	0.859380i
$690$		0			0
$691$		−	9.10716i		−	0.346453i	−0.984882	−	0.173226i	$-0.944581\pi$
$691$		−	9.10716i		−	0.346453i	0.984882	−	0.173226i	$-0.0554192\pi$
$692$	0.885106	−	1.53305i	0.0336467	−	0.0582777i
$693$		0			0
$694$		−	1.47992i		−	0.0561769i
$695$	−17.9756	−	10.3782i	−0.681853	−	0.393668i
$696$		0			0
$697$	−22.4055	−	12.9358i	−0.848667	−	0.489978i
$698$	1.97543	−	3.42155i	0.0747712	−	0.129508i
$699$		0			0
$700$	−9.02785	+	7.19602i	−0.341221	+	0.271984i
$701$	−0.286950			−0.0108380			−0.00541898	−	0.999985i	$-0.501725\pi$
$701$	−0.286950			−0.0108380			−0.00541898	+	0.999985i	$0.501725\pi$
$702$		0			0
$703$	−0.749377	+	1.29796i	−0.0282633	+	0.0489534i
$704$	−16.8601	+	9.73419i	−0.635440	+	0.366871i
$705$		0			0
$706$	0.0512797	+	0.0888191i	0.00192994	+	0.00334275i
$707$	−3.01461	−	20.0324i	−0.113376	−	0.753397i
$708$		0			0
$709$	16.0949	+	9.29241i	0.604457	+	0.348984i	0.770793	−	0.637086i	$-0.219860\pi$
$709$	16.0949	+	9.29241i	0.604457	+	0.348984i	−0.166336	+	0.986069i	$0.553194\pi$
$710$	−1.40727	−	0.812486i	−0.0528138	−	0.0304921i
$711$		0			0
$712$	−4.22656			−0.158397
$713$	−14.0940	−	8.13715i	−0.527823	−	0.304739i
$714$		0			0
$715$	12.1704	+	23.0872i	0.455148	+	0.863414i
$716$	10.8751	+	18.8362i	0.406421	+	0.703941i
$717$		0			0
$718$	2.92974	+	5.07445i	0.109337	+	0.189377i
$719$	−20.8475	+	36.1088i	−0.777479	+	1.34663i	0.155912	+	0.987771i	$0.450168\pi$
$719$	−20.8475	+	36.1088i	−0.777479	+	1.34663i	−0.933391	+	0.358862i	$0.883165\pi$
$720$		0			0
$721$	−2.03056	−	13.4933i	−0.0756218	−	0.502515i
$722$	2.96980	−	1.71462i	0.110525	−	0.0638114i
$723$		0			0
$724$	−6.94257			−0.258019
$725$	−7.85809	−	13.6106i	−0.291842	−	0.505486i
$726$		0			0
$727$	32.7039			1.21292			0.606461	−	0.795113i	$-0.292589\pi$
$727$	32.7039			1.21292			0.606461	+	0.795113i	$0.292589\pi$
$728$	−4.05657	−	5.51147i	−0.150346	−	0.204269i
$729$		0			0
$730$			6.90616i			0.255608i
$731$	−19.0851	−	33.0564i	−0.705888	−	1.22263i
$732$		0			0
$733$	8.60423	−	4.96765i	0.317804	−	0.183484i	−0.332609	−	0.943065i	$-0.607929\pi$
$733$	8.60423	−	4.96765i	0.317804	−	0.183484i	0.650413	+	0.759580i	$0.274596\pi$
$734$	−1.23225	+	0.711440i	−0.0454832	+	0.0262597i
$735$		0			0
$736$			9.33871i			0.344230i
$737$	15.3586	−	26.6018i	0.565740	−	0.979891i
$738$		0			0
$739$	−9.00853	+	5.20108i	−0.331384	+	0.191325i	−0.656455	−	0.754365i	$-0.727945\pi$
$739$	−9.00853	+	5.20108i	−0.331384	+	0.191325i	0.325071	+	0.945690i	$0.394612\pi$
$740$	21.0205	+	36.4086i	0.772730	+	1.33841i
$741$		0			0
$742$	2.10900	+	2.64587i	0.0774237	+	0.0971328i
$743$	1.47972	+	0.854317i	0.0542857	+	0.0313419i	0.526897	−	0.849929i	$-0.323355\pi$
$743$	1.47972	+	0.854317i	0.0542857	+	0.0313419i	−0.472612	+	0.881271i	$0.656689\pi$
$744$		0			0
$745$	−38.4686			−1.40938
$746$	0.327545	+	0.189108i	0.0119923	+	0.00692374i
$747$		0			0
$748$	−21.8723	+	12.6280i	−0.799732	+	0.461726i
$749$	19.7821	+	7.76923i	0.722821	+	0.283881i
$750$		0			0
$751$	−29.9812			−1.09403			−0.547015	−	0.837123i	$-0.684236\pi$
$751$	−29.9812			−1.09403			−0.547015	+	0.837123i	$0.684236\pi$
$752$	6.09233	−	3.51741i	0.222164	−	0.128267i
$753$		0			0
$754$	4.08656	−	2.15423i	0.148824	−	0.0784523i
$755$	17.3893			0.632860
$756$		0			0
$757$	−4.20229	+	7.27858i	−0.152735	+	0.264545i	−0.932232	−	0.361861i	$-0.882141\pi$
$757$	−4.20229	+	7.27858i	−0.152735	+	0.264545i	0.779497	+	0.626406i	$0.215475\pi$
$758$	−1.29437	+	2.24191i	−0.0470136	+	0.0814299i
$759$		0			0
$760$			0.363160i			0.0131732i
$761$	−44.2184	−	25.5295i	−1.60292	−	0.925444i	−0.990900	−	0.134598i	$-0.957026\pi$
$761$	−44.2184	−	25.5295i	−1.60292	−	0.925444i	−0.612015	−	0.790846i	$-0.709641\pi$
$762$		0			0
$763$	−2.19920	−	2.75903i	−0.0796163	−	0.0998835i
$764$	−20.0668	+	34.7568i	−0.725993	+	1.25746i
$765$		0			0
$766$	2.27723	−	3.94429i	0.0822798	−	0.142513i
$767$	−23.1526	−	14.5823i	−0.835991	−	0.526535i
$768$		0			0
$769$	−0.610062	−	0.352220i	−0.0219994	−	0.0127014i	0.488960	−	0.872306i	$-0.337376\pi$
$769$	−0.610062	−	0.352220i	−0.0219994	−	0.0127014i	−0.510959	+	0.859605i	$0.670710\pi$
$770$	2.15850	+	2.70798i	0.0777871	+	0.0975887i
$771$		0			0
$772$	−29.4142	+	16.9823i	−1.05864	+	0.611206i
$773$		−	1.26521i		−	0.0455066i	−0.999741	−	0.0227533i	$-0.992757\pi$
$773$		−	1.26521i		−	0.0455066i	0.999741	−	0.0227533i	$-0.00724323\pi$
$774$		0			0
$775$	−7.10593	+	4.10261i	−0.255253	+	0.147370i
$776$	0.161803	+	0.280252i	0.00580840	+	0.0100604i
$777$		0			0
$778$	−4.40076	−	2.54078i	−0.157775	−	0.0910914i
$779$	−0.511533	−	0.886001i	−0.0183276	−	0.0317443i
$780$		0			0
$781$	4.50596	−	7.80456i	0.161236	−	0.279269i
$782$			3.79048i			0.135547i
$783$		0			0
$784$	19.5158	+	18.1250i	0.696992	+	0.647321i
$785$			42.7679i			1.52645i
$786$		0			0
$787$		−	43.7969i		−	1.56119i	−0.625037	−	0.780595i	$-0.714916\pi$
$787$		−	43.7969i		−	1.56119i	0.625037	−	0.780595i	$-0.285084\pi$
$788$	8.44493	+	4.87568i	0.300838	+	0.173689i
$789$		0			0
$790$	2.21300	−	3.83303i	0.0787351	−	0.136373i
$791$	7.85007	+	52.1646i	0.279116	+	1.85476i
$792$		0			0
$793$	−0.691984	−	1.31269i	−0.0245731	−	0.0466151i
$794$	1.96885	−	3.41015i	0.0698719	−	0.121022i
$795$		0			0
$796$	−14.1291			−0.500792
$797$	−6.84183	−	11.8504i	−0.242350	−	0.419763i	0.719033	−	0.694976i	$-0.244585\pi$
$797$	−6.84183	−	11.8504i	−0.242350	−	0.419763i	−0.961383	+	0.275213i	$0.911252\pi$
$798$		0			0
$799$	7.62954	−	4.40492i	0.269914	−	0.155835i
$800$	4.07761	+	2.35421i	0.144165	+	0.0832338i
$801$		0			0
$802$	−3.71212			−0.131080
$803$	−38.3008			−1.35161
$804$		0			0
$805$	−30.9228	+	4.65347i	−1.08988	+	0.164013i
$806$	−1.12469	−	2.13354i	−0.0396157	−	0.0751508i
$807$		0			0
$808$	−4.75695	+	2.74643i	−0.167349	+	0.0966189i
$809$	4.55688	+	7.89274i	0.160211	+	0.277494i	0.934944	−	0.354794i	$-0.115449\pi$
$809$	4.55688	+	7.89274i	0.160211	+	0.277494i	−0.774733	+	0.632288i	$0.782116\pi$
$810$		0			0
$811$			2.31899i			0.0814309i	0.999171	+	0.0407154i	$0.0129637\pi$
$811$			2.31899i			0.0814309i	−0.999171	+	0.0407154i	$0.987036\pi$
$812$	−28.8397	+	22.9879i	−1.01208	+	0.806717i
$813$		0			0
$814$	3.35595	−	1.93756i	0.117626	−	0.0679114i
$815$	−12.8465			−0.449993
$816$		0			0
$817$		−	1.50940i		−	0.0528073i
$818$	1.13352			0.0396325
$819$		0			0
$820$	−28.6977			−1.00217
$821$		−	10.1447i		−	0.354053i	−0.984206	−	0.177026i	$-0.943352\pi$
$821$		−	10.1447i		−	0.354053i	0.984206	−	0.177026i	$-0.0566478\pi$
$822$		0			0
$823$	26.8178			0.934811			0.467405	−	0.884043i	$-0.345189\pi$
$823$	26.8178			0.934811			0.467405	+	0.884043i	$0.345189\pi$
$824$	−3.20414	+	1.84991i	−0.111622	+	0.0644448i
$825$		0			0
$826$	−3.37935	−	1.32721i	−0.117583	−	0.0461795i
$827$			33.6015i			1.16844i	0.811596	+	0.584219i	$0.198599\pi$
$827$			33.6015i			1.16844i	−0.811596	+	0.584219i	$0.801401\pi$
$828$		0			0
$829$	5.93328	+	10.2767i	0.206071	+	0.356926i	0.950473	−	0.310806i	$-0.100599\pi$
$829$	5.93328	+	10.2767i	0.206071	+	0.356926i	−0.744402	+	0.667731i	$0.767265\pi$
$830$	−6.97835	+	4.02895i	−0.242222	+	0.139847i
$831$		0			0
$832$	13.8848	−	22.0452i	0.481370	−	0.764281i
$833$	24.4400	+	22.6983i	0.846796	+	0.786448i
$834$		0			0
$835$	7.28193			0.252001
$836$	−0.998723			−0.0345416
$837$		0			0
$838$	5.34993	+	3.08878i	0.184810	+	0.106700i
$839$	29.9798	−	17.3088i	1.03502	−	0.597568i	0.116600	−	0.993179i	$-0.462801\pi$
$839$	29.9798	−	17.3088i	1.03502	−	0.597568i	0.918418	+	0.395611i	$0.129467\pi$
$840$		0			0
$841$	−10.6029	−	18.3648i	−0.365617	−	0.633267i
$842$	2.08369			0.0718088
$843$		0			0
$844$	17.3051	−	29.9733i	0.595666	−	1.03172i
$845$	−28.8154	−	19.7364i	−0.991279	−	0.678951i
$846$		0			0
$847$	7.73994	−	6.16943i	0.265947	−	0.211984i
$848$	−13.4549	+	23.3046i	−0.462044	+	0.800283i
$849$		0			0
$850$	1.65506	+	0.955548i	0.0567680	+	0.0327750i
$851$			34.9925i			1.19953i
$852$		0			0
$853$			29.1897i			0.999436i	0.866188	+	0.499718i	$0.166563\pi$
$853$			29.1897i			0.999436i	−0.866188	+	0.499718i	$0.833437\pi$
$854$	−0.122728	−	0.153970i	−0.00419967	−	0.00526874i
$855$		0			0
$856$		−	5.76265i		−	0.196963i
$857$	12.6599	−	21.9276i	0.432455	−	0.749033i	−0.564629	−	0.825345i	$-0.690981\pi$
$857$	12.6599	−	21.9276i	0.432455	−	0.749033i	0.997084	+	0.0763112i	$0.0243142\pi$
$858$		0			0
$859$	−13.0424	−	22.5902i	−0.445002	−	0.770766i	0.553050	−	0.833148i	$-0.313464\pi$
$859$	−13.0424	−	22.5902i	−0.445002	−	0.770766i	−0.998052	+	0.0623818i	$0.980130\pi$
$860$	−36.6674	−	21.1699i	−1.25035	−	0.721888i
$861$		0			0
$862$	0.792913	+	1.37337i	0.0270067	+	0.0467770i
$863$	−31.2061	+	18.0169i	−1.06227	+	0.613302i	−0.926059	−	0.377378i	$-0.876826\pi$
$863$	−31.2061	+	18.0169i	−1.06227	+	0.613302i	−0.136210	+	0.990680i	$0.543492\pi$
$864$		0			0
$865$		−	2.41748i		−	0.0821969i
$866$	−3.46190	+	1.99873i	−0.117640	+	0.0679196i
$867$		0			0
$868$	12.0017	+	15.0569i	0.407364	+	0.511063i
$869$	21.2576	+	12.2731i	0.721114	+	0.416335i
$870$		0			0
$871$	−1.58094	+	41.0766i	−0.0535683	+	1.39183i
$872$	−0.478337	+	0.828504i	−0.0161985	+	0.0280567i
$873$		0			0
$874$	−0.0749454	+	0.129809i	−0.00253507	+	0.00439086i
$875$	7.22880	−	18.4060i	0.244378	−	0.622237i
$876$		0			0
$877$	7.89961	+	4.56084i	0.266751	+	0.154009i	0.627410	−	0.778689i	$-0.284115\pi$
$877$	7.89961	+	4.56084i	0.266751	+	0.154009i	−0.360659	+	0.932698i	$0.617448\pi$
$878$			1.87531i			0.0632887i
$879$		0			0
$880$	−13.7708	+	23.8517i	−0.464212	+	0.804039i
$881$	−6.51653	+	11.2870i	−0.219548	+	0.380268i	−0.954670	−	0.297667i	$-0.903791\pi$
$881$	−6.51653	+	11.2870i	−0.219548	+	0.380268i	0.735122	+	0.677935i	$0.237125\pi$
$882$		0			0
$883$	−2.13222			−0.0717548			−0.0358774	−	0.999356i	$-0.511423\pi$
$883$	−2.13222			−0.0717548			−0.0358774	+	0.999356i	$0.511423\pi$
$884$	18.0126	−	28.5989i	0.605828	−	0.961886i
$885$		0			0
$886$	−5.60835	+	3.23798i	−0.188416	+	0.108782i
$887$	47.1715			1.58386			0.791932	−	0.610610i	$-0.209076\pi$
$887$	47.1715			1.58386			0.791932	+	0.610610i	$0.209076\pi$
$888$		0			0
$889$	16.4835	−	13.1389i	0.552839	−	0.440663i
$890$	−2.47875	+	1.43111i	−0.0830878	+	0.0479708i
$891$		0			0
$892$	24.0319	+	13.8748i	0.804647	+	0.464563i
$893$	0.348376			0.0116580
$894$		0			0
$895$	25.7236	+	14.8515i	0.859844	+	0.496431i
$896$	5.36994	−	13.6730i	0.179397	−	0.456782i
$897$		0			0
$898$	2.05689	+	3.56264i	0.0686394	+	0.118887i
$899$	−22.7001	+	13.1059i	−0.757091	+	0.437107i
$900$		0			0
$901$	−16.8499	+	29.1848i	−0.561350	+	0.972287i
$902$			2.64520i			0.0880755i
$903$		0			0
$904$	12.3871	−	7.15171i	0.411990	−	0.237862i
$905$	−8.21087	+	4.74055i	−0.272939	+	0.157581i
$906$		0			0
$907$	8.02154	+	13.8937i	0.266351	+	0.461333i	0.967917	−	0.251271i	$-0.0808487\pi$
$907$	8.02154	+	13.8937i	0.266351	+	0.461333i	−0.701566	+	0.712605i	$0.747515\pi$
$908$			5.64374i			0.187294i
$909$		0			0
$910$	−4.24522	−	1.85876i	−0.140728	−	0.0616172i
$911$	24.4319			0.809466			0.404733	−	0.914435i	$-0.367364\pi$
$911$	24.4319			0.809466			0.404733	+	0.914435i	$0.367364\pi$
$912$		0			0
$913$	−22.3441	−	38.7012i	−0.739483	−	1.28082i
$914$	5.66289			0.187312
$915$		0			0
$916$	14.9488	−	8.63067i	0.493921	−	0.285165i
$917$	−3.94423	−	26.2099i	−0.130250	−	0.865526i
$918$		0			0
$919$	−7.95800	+	13.7837i	−0.262510	+	0.454681i	−0.966908	−	0.255124i	$-0.917884\pi$
$919$	−7.95800	+	13.7837i	−0.262510	+	0.454681i	0.704398	+	0.709805i	$0.251217\pi$
$920$	4.23948	+	7.34300i	0.139772	+	0.242092i
$921$		0			0
$922$	0.760140	+	1.31660i	0.0250339	+	0.0433600i
$923$	−0.463824	+	12.0512i	−0.0152670	+	0.396671i
$924$		0			0
$925$	15.2790	+	8.82131i	0.502369	+	0.290043i
$926$	−1.81533			−0.0596555
$927$		0			0
$928$	13.0260	+	7.52059i	0.427601	+	0.246875i
$929$	40.9834	+	23.6618i	1.34462	+	0.776317i	0.987482	−	0.157734i	$-0.0504189\pi$
$929$	40.9834	+	23.6618i	1.34462	+	0.776317i	0.357139	+	0.934051i	$0.383752\pi$
$930$		0			0
$931$	0.388184	+	1.26055i	0.0127222	+	0.0413130i
$932$	−5.02393	−	8.70170i	−0.164564	−	0.285034i
$933$		0			0
$934$	−4.12656	+	2.38247i	−0.135025	+	0.0779568i
$935$	−17.2454	+	29.8699i	−0.563985	+	0.976850i
$936$		0			0
$937$	−29.7044			−0.970401			−0.485200	−	0.874403i	$-0.661253\pi$
$937$	−29.7044			−0.970401			−0.485200	+	0.874403i	$0.661253\pi$
$938$	0.811678	+	5.39369i	0.0265022	+	0.176110i
$939$		0			0
$940$	4.88609	−	8.46296i	0.159367	−	0.276031i
$941$	−35.0068	−	20.2112i	−1.14119	−	0.658866i	−0.194465	−	0.980909i	$-0.562297\pi$
$941$	−35.0068	−	20.2112i	−1.14119	−	0.658866i	−0.946725	+	0.322043i	$0.895630\pi$
$942$		0			0
$943$	−20.6861	−	11.9431i	−0.673633	−	0.388922i
$944$		−	28.8748i		−	0.939795i
$945$		0			0
$946$	−1.95133	+	3.37980i	−0.0634431	+	0.109887i
$947$		−	45.9228i		−	1.49229i	−0.665783	−	0.746146i	$-0.731902\pi$
$947$		−	45.9228i		−	1.49229i	0.665783	−	0.746146i	$-0.268098\pi$
$948$		0			0
$949$	45.3416	−	23.9018i	1.47185	−	0.775885i
$950$	0.0377862	+	0.0654476i	0.00122595	+	0.00212340i
$951$		0			0
$952$	3.30608	−	8.41797i	0.107151	−	0.272828i
$953$	−6.19465	−	10.7294i	−0.200664	−	0.347561i	0.748078	−	0.663610i	$-0.230977\pi$
$953$	−6.19465	−	10.7294i	−0.200664	−	0.347561i	−0.948743	+	0.316050i	$0.897643\pi$
$954$		0			0
$955$			54.8085i			1.77356i
$956$			4.91426i			0.158939i
$957$		0			0
$958$	0.776108	+	1.34426i	0.0250749	+	0.0434310i
$959$	4.90065	−	12.4781i	0.158250	−	0.402938i
$960$		0			0
$961$	−8.65757	−	14.9953i	−0.279276	−	0.483721i
$962$	−2.76373	+	4.38803i	−0.0891062	+	0.141476i
$963$		0			0
$964$		−	15.7091i		−	0.505958i
$965$	−23.1918	+	40.1694i	−0.746572	+	1.29310i
$966$		0			0
$967$		−	9.44932i		−	0.303870i	−0.988391	−	0.151935i	$-0.951450\pi$
$967$		−	9.44932i		−	0.303870i	0.988391	−	0.151935i	$-0.0485504\pi$
$968$	−2.32421	−	1.34188i	−0.0747030	−	0.0431298i
$969$		0			0
$970$	0.189785	+	0.109573i	0.00609364	+	0.00351816i
$971$	−10.4882	+	18.1660i	−0.336581	+	0.582976i	−0.983787	−	0.179339i	$-0.942604\pi$
$971$	−10.4882	+	18.1660i	−0.336581	+	0.582976i	0.647206	+	0.762315i	$0.275937\pi$
$972$		0			0
$973$	3.04177	+	20.2129i	0.0975148	+	0.647996i
$974$	3.84363			0.123158
$975$		0			0
$976$	0.782977	−	1.35616i	0.0250625	−	0.0434095i
$977$	11.4179	−	6.59214i	0.365292	−	0.210901i	−0.306108	−	0.951997i	$-0.599027\pi$
$977$	11.4179	−	6.59214i	0.365292	−	0.210901i	0.671400	+	0.741096i	$0.265693\pi$
$978$		0			0
$979$	−7.93676	−	13.7469i	−0.253660	−	0.439352i
$980$	36.0666	+	8.24971i	1.15211	+	0.263527i
$981$		0			0
$982$	3.51618	+	2.03007i	0.112206	+	0.0647820i
$983$	20.2294	+	11.6794i	0.645216	+	0.372516i	0.786621	−	0.617436i	$-0.211829\pi$
$983$	20.2294	+	11.6794i	0.645216	+	0.372516i	−0.141405	+	0.989952i	$0.545162\pi$
$984$		0			0
$985$	13.3169			0.424313
$986$	5.28713	+	3.05252i	0.168376	+	0.0972122i
$987$		0			0
$988$	1.18232	−	0.623257i	0.0376145	−	0.0198285i
$989$	−17.6206	−	30.5197i	−0.560302	−	0.970471i
$990$		0			0
$991$	−19.7465	−	34.2019i	−0.627267	−	1.08646i	−0.988098	−	0.153827i	$-0.950840\pi$
$991$	−19.7465	−	34.2019i	−0.627267	−	1.08646i	0.360831	−	0.932631i	$-0.382493\pi$
$992$	3.92640	−	6.80073i	0.124663	−	0.215923i
$993$		0			0
$994$	0.238134	+	1.58242i	0.00755314	+	0.0501914i
$995$	−16.7102	+	9.64766i	−0.529750	+	0.305851i
$996$		0			0
$997$	−51.4791			−1.63036			−0.815180	−	0.579208i	$-0.803362\pi$
$997$	−51.4791			−1.63036			−0.815180	+	0.579208i	$0.803362\pi$
$998$	−3.51504	−	6.08822i	−0.111267	−	0.192719i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bm.f.550.4		12
3.2	odd	2		91.2.k.b.4.3	✓	12
7.2	even	3		819.2.do.e.667.4		12
13.10	even	6		819.2.do.e.361.4		12
21.2	odd	6		91.2.u.b.30.3	yes	12
21.5	even	6		637.2.u.g.30.3		12
21.11	odd	6		637.2.q.g.589.4		12
21.17	even	6		637.2.q.i.589.4		12
21.20	even	2		637.2.k.i.459.3		12
39.20	even	12		1183.2.e.j.508.6		24
39.23	odd	6		91.2.u.b.88.3	yes	12
39.32	even	12		1183.2.e.j.508.7		24
91.23	even	6	inner	819.2.bm.f.478.3		12
273.23	odd	6		91.2.k.b.23.4	yes	12
273.32	even	12		8281.2.a.cp.1.6		12
273.59	odd	12		8281.2.a.co.1.7		12
273.62	even	6		637.2.u.g.361.3		12
273.101	even	6		637.2.q.i.491.4		12
273.137	even	12		8281.2.a.cp.1.7		12
273.149	even	12		1183.2.e.j.170.7		24
273.179	odd	6		637.2.q.g.491.4		12
273.227	odd	12		8281.2.a.co.1.6		12
273.254	even	12		1183.2.e.j.170.6		24
273.257	even	6		637.2.k.i.569.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.3	✓	12	3.2	odd	2
91.2.k.b.23.4	yes	12	273.23	odd	6
91.2.u.b.30.3	yes	12	21.2	odd	6
91.2.u.b.88.3	yes	12	39.23	odd	6
637.2.k.i.459.3		12	21.20	even	2
637.2.k.i.569.4		12	273.257	even	6
637.2.q.g.491.4		12	273.179	odd	6
637.2.q.g.589.4		12	21.11	odd	6
637.2.q.i.491.4		12	273.101	even	6
637.2.q.i.589.4		12	21.17	even	6
637.2.u.g.30.3		12	21.5	even	6
637.2.u.g.361.3		12	273.62	even	6
819.2.bm.f.478.3		12	91.23	even	6	inner
819.2.bm.f.550.4		12	1.1	even	1	trivial
819.2.do.e.361.4		12	13.10	even	6
819.2.do.e.667.4		12	7.2	even	3
1183.2.e.j.170.6		24	273.254	even	12
1183.2.e.j.170.7		24	273.149	even	12
1183.2.e.j.508.6		24	39.20	even	12
1183.2.e.j.508.7		24	39.32	even	12
8281.2.a.co.1.6		12	273.227	odd	12
8281.2.a.co.1.7		12	273.59	odd	12
8281.2.a.cp.1.6		12	273.32	even	12
8281.2.a.cp.1.7		12	273.137	even	12

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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.180824i q^{2} +1.96730 q^{4} +(2.32670 - 1.34332i) q^{5} +(-2.46263 - 0.967177i) q^{7} +0.717383i q^{8} +O(q^{10})\)	\(q+0.180824i q^{2} +1.96730 q^{4} +(2.32670 - 1.34332i) q^{5} +(-2.46263 - 0.967177i) q^{7} +0.717383i q^{8} +(0.242904 + 0.420723i) q^{10} +(-2.33328 + 1.34712i) q^{11} +(1.92153 - 3.05086i) q^{13} +(0.174889 - 0.445303i) q^{14} +3.80489 q^{16} +4.76493 q^{17} +(0.163180 + 0.0942122i) q^{19} +(4.57732 - 2.64272i) q^{20} +(-0.243592 - 0.421913i) q^{22} +4.39929 q^{23} +(1.10902 - 1.92088i) q^{25} +(0.551667 + 0.347458i) q^{26} +(-4.84475 - 1.90273i) q^{28} +(3.54280 - 6.13631i) q^{29} +(-3.20369 - 1.84965i) q^{31} +2.12278i q^{32} +0.861613i q^{34} +(-7.02904 + 1.05778i) q^{35} +7.95413i q^{37} +(-0.0170358 + 0.0295069i) q^{38} +(0.963675 + 1.66913i) q^{40} +(-4.70215 - 2.71479i) q^{41} +(-4.00533 - 6.93743i) q^{43} +(-4.59027 + 2.65020i) q^{44} +0.795496i q^{46} +(1.60118 - 0.924445i) q^{47} +(5.12914 + 4.76361i) q^{49} +(0.347341 + 0.200538i) q^{50} +(3.78023 - 6.00196i) q^{52} +(-3.53622 + 6.12491i) q^{53} +(-3.61923 + 6.26869i) q^{55} +(0.693836 - 1.76665i) q^{56} +(1.10959 + 0.640623i) q^{58} -7.58888i q^{59} +(0.205782 - 0.356425i) q^{61} +(0.334461 - 0.579304i) q^{62} +7.22592 q^{64} +(0.372548 - 9.67966i) q^{65} +(-9.87358 + 5.70051i) q^{67} +9.37407 q^{68} +(-0.191271 - 1.27102i) q^{70} +(-2.89675 + 1.67244i) q^{71} +(12.3112 + 7.10790i) q^{73} -1.43830 q^{74} +(0.321025 + 0.185344i) q^{76} +(7.04893 - 1.06077i) q^{77} +(-4.55529 - 7.89000i) q^{79} +(8.85283 - 5.11118i) q^{80} +(0.490899 - 0.850261i) q^{82} +16.5866i q^{83} +(11.0866 - 6.40083i) q^{85} +(1.25445 - 0.724258i) q^{86} +(-0.966401 - 1.67386i) q^{88} +5.89165i q^{89} +(-7.68275 + 5.65468i) q^{91} +8.65473 q^{92} +(0.167162 + 0.289532i) q^{94} +0.506229 q^{95} +(0.390659 - 0.225547i) q^{97} +(-0.861373 + 0.927470i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7}+O(q^{10}) \) 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7	\( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7} + 12 q^{10} - 12 q^{11} - 2 q^{13} - 4 q^{14} + 16 q^{16} + 34 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 6 q^{23} - 5 q^{25} + 6 q^{26} - 9 q^{28} + q^{29} + 18 q^{31} + 6 q^{35} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 15 q^{47} - 3 q^{49} - 18 q^{50} - 7 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{56} - 24 q^{58} + 5 q^{61} - 41 q^{62} + 2 q^{64} - 21 q^{65} + 15 q^{67} - 22 q^{68} + 3 q^{70} - 30 q^{71} + 42 q^{73} - 66 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} + 63 q^{80} + 5 q^{82} - 21 q^{85} + 57 q^{86} - 14 q^{88} - 7 q^{91} + 66 q^{92} + q^{94} + 4 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7 + 12 * q^10 - 12 * q^11 - 2 * q^13 - 4 * q^14 + 16 * q^16 + 34 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 6 * q^23 - 5 * q^25 + 6 * q^26 - 9 * q^28 + q^29 + 18 * q^31 + 6 * q^35 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 15 * q^47 - 3 * q^49 - 18 * q^50 - 7 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^56 - 24 * q^58 + 5 * q^61 - 41 * q^62 + 2 * q^64 - 21 * q^65 + 15 * q^67 - 22 * q^68 + 3 * q^70 - 30 * q^71 + 42 * q^73 - 66 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 + 63 * q^80 + 5 * q^82 - 21 * q^85 + 57 * q^86 - 14 * q^88 - 7 * q^91 + 66 * q^92 + q^94 + 4 * q^95 - 3 * q^97 + 18 * q^98

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