LMFDB - Embedded newform 378.2.ba.a.47.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(47,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("378.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.ba (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			47.18
Character	$\chi$	$=$	378.47
Dual form			378.2.ba.a.185.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(-0.505130 + 1.65676i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.342190 - 0.124547i) q^{5} +(-0.785149 + 1.54387i) q^{6} +(2.40698 + 1.09838i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.48969 - 1.67375i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(-0.505130 + 1.65676i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.342190 - 0.124547i) q^{5} +(-0.785149 + 1.54387i) q^{6} +(2.40698 + 1.09838i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.48969 - 1.67375i) q^{9} +(-0.315364 - 0.182076i) q^{10} +(1.51312 + 4.15725i) q^{11} +(-1.04131 + 1.38408i) q^{12} +(1.20667 - 3.31531i) q^{13} +(2.17968 + 1.49966i) q^{14} +(0.379195 - 0.504014i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-2.73780 + 4.74201i) q^{17} +(-2.16122 - 2.08066i) q^{18} +(-4.77693 + 2.75796i) q^{19} +(-0.278956 - 0.234072i) q^{20} +(-3.03559 + 3.43296i) q^{21} +(0.768229 + 4.35684i) q^{22} +(4.91243 - 0.866193i) q^{23} +(-1.26583 + 1.18223i) q^{24} +(-3.72864 - 3.12870i) q^{25} +(1.76404 - 3.05541i) q^{26} +(4.03062 - 3.27934i) q^{27} +(1.88615 + 1.85538i) q^{28} +(-0.217053 - 0.596349i) q^{29} +(0.460955 - 0.430510i) q^{30} +(1.70448 - 4.68303i) q^{31} +(0.642788 + 0.766044i) q^{32} +(-7.65187 + 0.406913i) q^{33} +(-3.51965 + 4.19455i) q^{34} +(-0.686846 - 0.675638i) q^{35} +(-1.76708 - 2.42434i) q^{36} +8.60510 q^{37} +(-5.18327 + 1.88656i) q^{38} +(4.88314 + 3.67383i) q^{39} +(-0.234072 - 0.278956i) q^{40} +(-3.52911 - 1.28449i) q^{41} +(-3.58560 + 2.85368i) q^{42} +(1.51425 - 8.58775i) q^{43} +4.42405i q^{44} +(0.643486 + 0.882826i) q^{45} +4.98821 q^{46} +(-5.23789 + 1.90644i) q^{47} +(-1.45189 + 0.944458i) q^{48} +(4.58712 + 5.28756i) q^{49} +(-3.12870 - 3.72864i) q^{50} +(-6.47341 - 6.93120i) q^{51} +(2.26781 - 2.70267i) q^{52} +(7.94780 - 4.58866i) q^{53} +(4.53884 - 2.52961i) q^{54} -1.61103i q^{55} +(1.53532 + 2.15472i) q^{56} +(-2.15630 - 9.30734i) q^{57} +(-0.110201 - 0.624980i) q^{58} +(7.72971 - 6.48600i) q^{59} +(0.528710 - 0.343926i) q^{60} +(-1.89650 - 5.21058i) q^{61} +(2.49179 - 4.31591i) q^{62} +(-4.15421 - 6.76332i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.825825 + 0.984180i) q^{65} +(-7.60628 - 0.928002i) q^{66} +(1.56316 + 8.86511i) q^{67} +(-4.19455 + 3.51965i) q^{68} +(-1.04634 + 8.57624i) q^{69} +(-0.559088 - 0.784643i) q^{70} +(-3.24088 + 1.87112i) q^{71} +(-1.31926 - 2.69436i) q^{72} -4.38604i q^{73} +(8.47437 + 1.49426i) q^{74} +(7.06694 - 4.59705i) q^{75} +(-5.43213 + 0.957830i) q^{76} +(-0.924200 + 11.6684i) q^{77} +(4.17100 + 4.46596i) q^{78} +(2.93558 - 16.6485i) q^{79} +(-0.182076 - 0.315364i) q^{80} +(3.39709 + 8.33425i) q^{81} +(-3.25244 - 1.87780i) q^{82} +(-0.538728 + 0.196081i) q^{83} +(-4.02666 + 2.18769i) q^{84} +(1.52745 - 1.28169i) q^{85} +(2.98250 - 8.19434i) q^{86} +(1.09765 - 0.0583709i) q^{87} +(-0.768229 + 4.35684i) q^{88} +(-0.353311 - 0.611952i) q^{89} +(0.480409 + 0.981154i) q^{90} +(6.54592 - 6.65451i) q^{91} +(4.91243 + 0.866193i) q^{92} +(6.89766 + 5.18946i) q^{93} +(-5.48936 + 0.967922i) q^{94} +(1.97812 - 0.348795i) q^{95} +(-1.59384 + 0.677991i) q^{96} +(-12.0867 - 2.13121i) q^{97} +(3.59926 + 6.00378i) q^{98} +(3.19103 - 12.8828i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{6} + 24 q^{9}+O(q^{10}) $ 144 * q - 18 * q^6 + 24 * q^9	$ 144 q - 18 q^{6} + 24 q^{9} - 24 q^{11} + 6 q^{14} + 12 q^{15} - 30 q^{21} - 42 q^{23} - 6 q^{29} - 18 q^{30} + 6 q^{36} + 48 q^{39} - 48 q^{42} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 12 q^{50} - 36 q^{51} - 90 q^{53} + 6 q^{56} - 6 q^{57} + 18 q^{60} + 54 q^{61} - 24 q^{63} + 72 q^{64} + 78 q^{65} - 72 q^{66} - 54 q^{68} + 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} - 36 q^{74} - 6 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 36 q^{91} - 42 q^{92} + 96 q^{93} - 66 q^{95} - 108 q^{99}+O(q^{100}) $ 144 * q - 18 * q^6 + 24 * q^9 - 24 * q^11 + 6 * q^14 + 12 * q^15 - 30 * q^21 - 42 * q^23 - 6 * q^29 - 18 * q^30 + 6 * q^36 + 48 * q^39 - 48 * q^42 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 12 * q^50 - 36 * q^51 - 90 * q^53 + 6 * q^56 - 6 * q^57 + 18 * q^60 + 54 * q^61 - 24 * q^63 + 72 * q^64 + 78 * q^65 - 72 * q^66 - 54 * q^68 + 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 - 36 * q^74 - 6 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 36 * q^91 - 42 * q^92 + 96 * q^93 - 66 * q^95 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	−0.505130	+	1.65676i	−0.291637	+	0.956529i
$3$	−0.505130	+	1.65676i	−0.291637	+	0.956529i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	−0.342190	−	0.124547i	−0.153032	−	0.0556992i	0.264368	−	0.964422i	$-0.414837\pi$
$5$	−0.342190	−	0.124547i	−0.153032	−	0.0556992i	−0.417401	+	0.908723i	$0.637059\pi$
$6$	−0.785149	+	1.54387i	−0.320536	+	0.630283i
$7$	2.40698	+	1.09838i	0.909754	+	0.415149i
$7$	2.40698	+	1.09838i	0.909754	+	0.415149i
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−2.48969	−	1.67375i	−0.829896	−	0.557918i
$10$	−0.315364	−	0.182076i	−0.0997270	−	0.0575774i
$11$	1.51312	+	4.15725i	0.456221	+	1.25346i	0.928277	+	0.371889i	$0.121290\pi$
$11$	1.51312	+	4.15725i	0.456221	+	1.25346i	−0.472056	+	0.881569i	$0.656488\pi$
$12$	−1.04131	+	1.38408i	−0.300601	+	0.399549i
$13$	1.20667	−	3.31531i	0.334671	−	0.919502i	−0.652208	−	0.758040i	$-0.726157\pi$
$13$	1.20667	−	3.31531i	0.334671	−	0.919502i	0.986879	−	0.161462i	$-0.0516208\pi$
$14$	2.17968	+	1.49966i	0.582545	+	0.400801i
$15$	0.379195	−	0.504014i	0.0979077	−	0.130136i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−2.73780	+	4.74201i	−0.664014	+	1.15011i	0.315537	+	0.948913i	$0.397815\pi$
$17$	−2.73780	+	4.74201i	−0.664014	+	1.15011i	−0.979552	+	0.201193i	$0.935518\pi$
$18$	−2.16122	−	2.08066i	−0.509404	−	0.490415i
$19$	−4.77693	+	2.75796i	−1.09590	+	0.632720i	−0.935142	−	0.354273i	$-0.884728\pi$
$19$	−4.77693	+	2.75796i	−1.09590	+	0.632720i	−0.160761	+	0.986993i	$0.551395\pi$
$20$	−0.278956	−	0.234072i	−0.0623765	−	0.0523401i
$21$	−3.03559	+	3.43296i	−0.662419	+	0.749133i
$22$	0.768229	+	4.35684i	0.163787	+	0.928882i
$23$	4.91243	−	0.866193i	1.02431	−	0.180614i	0.363838	−	0.931462i	$-0.381466\pi$
$23$	4.91243	−	0.866193i	1.02431	−	0.180614i	0.660474	+	0.750849i	$0.270355\pi$
$24$	−1.26583	+	1.18223i	−0.258387	+	0.241321i
$25$	−3.72864	−	3.12870i	−0.745728	−	0.625740i
$26$	1.76404	−	3.05541i	0.345957	−	0.599215i
$27$	4.03062	−	3.27934i	0.775693	−	0.631110i
$28$	1.88615	+	1.85538i	0.356450	+	0.350633i
$29$	−0.217053	−	0.596349i	−0.0403058	−	0.110739i	0.917907	−	0.396796i	$-0.129878\pi$
$29$	−0.217053	−	0.596349i	−0.0403058	−	0.110739i	−0.958213	+	0.286056i	$0.907656\pi$
$30$	0.460955	−	0.430510i	0.0841585	−	0.0786001i
$31$	1.70448	−	4.68303i	0.306135	−	0.841098i	−0.687267	−	0.726405i	$-0.741190\pi$
$31$	1.70448	−	4.68303i	0.306135	−	0.841098i	0.993401	−	0.114692i	$-0.0365882\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	−7.65187	+	0.406913i	−1.33202	+	0.0708345i
$34$	−3.51965	+	4.19455i	−0.603615	+	0.719360i
$35$	−0.686846	−	0.675638i	−0.116098	−	0.114204i
$36$	−1.76708	−	2.42434i	−0.294514	−	0.404056i
$37$	8.60510			1.41467			0.707335	−	0.706878i	$-0.249897\pi$
$37$	8.60510			1.41467			0.707335	+	0.706878i	$0.249897\pi$
$38$	−5.18327	+	1.88656i	−0.840838	+	0.306040i
$39$	4.88314	+	3.67383i	0.781928	+	0.588283i
$40$	−0.234072	−	0.278956i	−0.0370100	−	0.0441069i
$41$	−3.52911	−	1.28449i	−0.551154	−	0.200604i	0.0514050	−	0.998678i	$-0.483630\pi$
$41$	−3.52911	−	1.28449i	−0.551154	−	0.200604i	−0.602559	+	0.798074i	$0.705852\pi$
$42$	−3.58560	+	2.85368i	−0.553270	+	0.440332i
$43$	1.51425	−	8.58775i	0.230921	−	1.30962i	−0.620114	−	0.784512i	$-0.712914\pi$
$43$	1.51425	−	8.58775i	0.230921	−	1.30962i	0.851035	−	0.525109i	$-0.175975\pi$
$44$			4.42405i			0.666951i
$45$	0.643486	+	0.882826i	0.0959252	+	0.131604i
$46$	4.98821			0.735471
$47$	−5.23789	+	1.90644i	−0.764024	+	0.278082i	−0.694495	−	0.719498i	$-0.744372\pi$
$47$	−5.23789	+	1.90644i	−0.764024	+	0.278082i	−0.0695296	+	0.997580i	$0.522150\pi$
$48$	−1.45189	+	0.944458i	−0.209563	+	0.136321i
$49$	4.58712	+	5.28756i	0.655303	+	0.755366i
$50$	−3.12870	−	3.72864i	−0.442465	−	0.527309i
$51$	−6.47341	−	6.93120i	−0.906459	−	0.970562i
$52$	2.26781	−	2.70267i	0.314488	−	0.374792i
$53$	7.94780	−	4.58866i	1.09171	−	0.630301i	0.157681	−	0.987490i	$-0.449598\pi$
$53$	7.94780	−	4.58866i	1.09171	−	0.630301i	0.934032	+	0.357189i	$0.116265\pi$
$54$	4.53884	−	2.52961i	0.617658	−	0.344237i
$55$		−	1.61103i		−	0.217231i
$56$	1.53532	+	2.15472i	0.205165	+	0.287936i
$57$	−2.15630	−	9.30734i	−0.285609	−	1.23279i
$58$	−0.110201	−	0.624980i	−0.0144701	−	0.0820639i
$59$	7.72971	−	6.48600i	1.00632	−	0.844405i	0.0184750	−	0.999829i	$-0.494119\pi$
$59$	7.72971	−	6.48600i	1.00632	−	0.844405i	0.987848	+	0.155424i	$0.0496745\pi$
$60$	0.528710	−	0.343926i	0.0682561	−	0.0444006i
$61$	−1.89650	−	5.21058i	−0.242821	−	0.667146i	−0.999904	−	0.0138277i	$-0.995598\pi$
$61$	−1.89650	−	5.21058i	−0.242821	−	0.667146i	0.757083	−	0.653319i	$-0.226624\pi$
$62$	2.49179	−	4.31591i	0.316458	−	0.548121i
$63$	−4.15421	−	6.76332i	−0.523382	−	0.852098i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−0.825825	+	0.984180i	−0.102431	+	0.122072i
$66$	−7.60628	−	0.928002i	−0.936269	−	0.114229i
$67$	1.56316	+	8.86511i	0.190970	+	1.08305i	0.918042	+	0.396484i	$0.129770\pi$
$67$	1.56316	+	8.86511i	0.190970	+	1.08305i	−0.727071	+	0.686562i	$0.759119\pi$
$68$	−4.19455	+	3.51965i	−0.508664	+	0.426820i
$69$	−1.04634	+	8.57624i	−0.125965	+	1.03246i
$70$	−0.559088	−	0.784643i	−0.0668238	−	0.0937828i
$71$	−3.24088	+	1.87112i	−0.384622	+	0.222062i	−0.679827	−	0.733372i	$-0.737945\pi$
$71$	−3.24088	+	1.87112i	−0.384622	+	0.222062i	0.295205	+	0.955434i	$0.404612\pi$
$72$	−1.31926	−	2.69436i	−0.155476	−	0.317533i
$73$		−	4.38604i		−	0.513347i	−0.966498	−	0.256674i	$-0.917373\pi$
$73$		−	4.38604i		−	0.513347i	0.966498	−	0.256674i	$-0.0826266\pi$
$74$	8.47437	+	1.49426i	0.985126	+	0.173704i
$75$	7.06694	−	4.59705i	0.816020	−	0.530822i
$76$	−5.43213	+	0.957830i	−0.623108	+	0.109871i
$77$	−0.924200	+	11.6684i	−0.105322	+	1.32974i
$78$	4.17100	+	4.46596i	0.472273	+	0.505671i
$79$	2.93558	−	16.6485i	0.330279	−	1.87311i	−0.139353	−	0.990243i	$-0.544502\pi$
$79$	2.93558	−	16.6485i	0.330279	−	1.87311i	0.469632	−	0.882862i	$-0.344387\pi$
$80$	−0.182076	−	0.315364i	−0.0203567	−	0.0352588i
$81$	3.39709	+	8.33425i	0.377454	+	0.926028i
$82$	−3.25244	−	1.87780i	−0.359172	−	0.207368i
$83$	−0.538728	+	0.196081i	−0.0591331	+	0.0215227i	−0.371417	−	0.928466i	$-0.621128\pi$
$83$	−0.538728	+	0.196081i	−0.0591331	+	0.0215227i	0.312284	+	0.949989i	$0.398906\pi$
$84$	−4.02666	+	2.18769i	−0.439345	+	0.238697i
$85$	1.52745	−	1.28169i	0.165676	−	0.139018i
$86$	2.98250	−	8.19434i	0.321611	−	0.883618i
$87$	1.09765	−	0.0583709i	0.117680	−	0.00625802i
$88$	−0.768229	+	4.35684i	−0.0818934	+	0.464441i
$89$	−0.353311	−	0.611952i	−0.0374509	−	0.0648668i	0.846692	−	0.532083i	$-0.178590\pi$
$89$	−0.353311	−	0.611952i	−0.0374509	−	0.0648668i	−0.884143	+	0.467216i	$0.845257\pi$
$90$	0.480409	+	0.981154i	0.0506395	+	0.103423i
$91$	6.54592	−	6.65451i	0.686198	−	0.697582i
$92$	4.91243	+	0.866193i	0.512156	+	0.0903069i
$93$	6.89766	+	5.18946i	0.715254	+	0.538122i
$94$	−5.48936	+	0.967922i	−0.566184	+	0.0998336i
$95$	1.97812	−	0.348795i	0.202950	−	0.0357856i
$96$	−1.59384	+	0.677991i	−0.162671	+	0.0691972i
$97$	−12.0867	−	2.13121i	−1.22722	−	0.216392i	−0.477788	−	0.878475i	$-0.658561\pi$
$97$	−12.0867	−	2.13121i	−1.22722	−	0.216392i	−0.749430	+	0.662083i	$0.769673\pi$
$98$	3.59926	+	6.00378i	0.363580	+	0.606473i
$99$	3.19103	−	12.8828i	0.320711	−	1.29477i
$100$	−2.43370	−	4.21529i	−0.243370	−	0.421529i
$101$	−2.45335	+	13.9136i	−0.244117	+	1.38446i	0.578417	+	0.815741i	$0.303671\pi$
$101$	−2.45335	+	13.9136i	−0.244117	+	1.38446i	−0.822534	+	0.568716i	$0.807440\pi$
$102$	−5.17148	−	7.95000i	−0.512053	−	0.787167i
$103$	2.29528	−	6.30624i	0.226161	−	0.621372i	−0.773766	−	0.633472i	$-0.781629\pi$
$103$	2.29528	−	6.30624i	0.226161	−	0.621372i	0.999927	+	0.0120994i	$0.00385146\pi$
$104$	2.70267	−	2.26781i	0.265018	−	0.222377i
$105$	1.46631	−	0.796652i	0.143098	−	0.0777453i
$106$	8.62386	−	3.13883i	0.837624	−	0.304870i
$107$	−9.16619	−	5.29210i	−0.886129	−	0.511607i	−0.0134544	−	0.999909i	$-0.504283\pi$
$107$	−9.16619	−	5.29210i	−0.886129	−	0.511607i	−0.872674	+	0.488303i	$0.837616\pi$
$108$	4.90915	−	1.70302i	0.472383	−	0.163873i
$109$	−2.08606	−	3.61316i	−0.199808	−	0.346078i	0.748658	−	0.662957i	$-0.230699\pi$
$109$	−2.08606	−	3.61316i	−0.199808	−	0.346078i	−0.948466	+	0.316878i	$0.897365\pi$
$110$	0.279752	−	1.58655i	0.0266733	−	0.151272i
$111$	−4.34669	+	14.2566i	−0.412570	+	1.35317i
$112$	1.13783	+	2.38859i	0.107515	+	0.225700i
$113$	−9.00372	+	1.58760i	−0.846999	+	0.149349i	−0.580271	−	0.814423i	$-0.697054\pi$
$113$	−9.00372	+	1.58760i	−0.846999	+	0.149349i	−0.266728	+	0.963772i	$0.585942\pi$
$114$	−0.507341	−	9.54038i	−0.0475168	−	0.893539i
$115$	−1.78887	−	0.315426i	−0.166813	−	0.0294136i
$116$		−	0.634622i		−	0.0589231i
$117$	−8.55326	+	6.23441i	−0.790749	+	0.576372i
$118$	8.73856	−	5.04521i	0.804450	−	0.464449i
$119$	−11.7984	+	8.40678i	−1.08155	+	0.770649i
$120$	0.580399	−	0.246891i	0.0529830	−	0.0225380i
$121$	−6.56672	+	5.51013i	−0.596974	+	0.500921i
$122$	−0.962876	−	5.46074i	−0.0871747	−	0.494392i
$123$	3.91075	−	5.19804i	0.352620	−	0.468692i
$124$	3.20338	−	3.81764i	0.287672	−	0.342835i
$125$	1.79661	+	3.11182i	0.160694	+	0.278330i
$126$	−2.91666	−	7.38194i	−0.259837	−	0.657636i
$127$	−3.43029	+	5.94144i	−0.304389	+	0.527217i	−0.977125	−	0.212665i	$-0.931786\pi$
$127$	−3.43029	+	5.94144i	−0.304389	+	0.527217i	0.672736	+	0.739883i	$0.265119\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	13.4629	+	6.84668i	1.18534	+	0.602817i
$130$	−0.984180	+	0.825825i	−0.0863183	+	0.0724296i
$131$	−0.415309	−	2.35533i	−0.0362857	−	0.205786i	0.961275	−	0.275591i	$-0.0888735\pi$
$131$	−0.415309	−	2.35533i	−0.0362857	−	0.205786i	−0.997561	+	0.0698046i	$0.977762\pi$
$132$	−7.32958	−	2.23472i	−0.637958	−	0.194507i
$133$	−14.5273	+	1.39148i	−1.25967	+	0.120656i
$134$			9.00187i			0.777643i
$135$	−1.78767	+	0.620158i	−0.153858	+	0.0533747i
$136$	−4.74201	+	2.73780i	−0.406624	+	0.234764i
$137$	−13.6157	+	16.2266i	−1.16327	+	1.38633i	−0.255527	+	0.966802i	$0.582249\pi$
$137$	−13.6157	+	16.2266i	−1.16327	+	1.38633i	−0.907742	+	0.419528i	$0.862196\pi$
$138$	−2.51969	+	8.26425i	−0.214491	+	0.703500i
$139$	13.4286	+	16.0035i	1.13899	+	1.35740i	0.924729	+	0.380626i	$0.124291\pi$
$139$	13.4286	+	16.0035i	1.13899	+	1.35740i	0.214266	+	0.976775i	$0.431264\pi$
$140$	−0.414342	−	0.869807i	−0.0350183	−	0.0735121i
$141$	−0.512686	−	9.64090i	−0.0431760	−	0.811911i
$142$	−3.51656	+	1.27992i	−0.295103	+	0.107409i
$143$	15.6084			1.30524
$144$	−0.831343	−	2.88251i	−0.0692785	−	0.240209i
$145$			0.231098i			0.0191917i
$146$	0.761628	−	4.31941i	0.0630328	−	0.357477i
$147$	−11.0773	+	4.92884i	−0.913640	+	0.406524i
$148$	8.08615	+	2.94312i	0.664678	+	0.241923i
$149$	−10.8632	−	12.9462i	−0.889945	−	1.06059i	−0.997791	−	0.0664272i	$-0.978840\pi$
$149$	−10.8632	−	12.9462i	−0.889945	−	1.06059i	0.107847	−	0.994168i	$-0.465604\pi$
$150$	7.75785	−	3.30005i	0.633426	−	0.269448i
$151$	−0.295046	+	0.107388i	−0.0240105	+	0.00873912i	−0.353997	−	0.935246i	$-0.615178\pi$
$151$	−0.295046	+	0.107388i	−0.0240105	+	0.00873912i	0.329987	+	0.943985i	$0.392956\pi$
$152$	−5.51592			−0.447401
$153$	14.7532	−	7.22372i	1.19273	−	0.584003i
$154$	−2.93636	+	11.3306i	−0.236618	+	0.913049i
$155$	−1.16652	+	1.39020i	−0.0936969	+	0.111664i
$156$	3.33212	+	5.12240i	0.266783	+	0.410120i
$157$	−6.23447	−	7.42995i	−0.497565	−	0.592975i	0.457560	−	0.889179i	$-0.348724\pi$
$157$	−6.23447	−	7.42995i	−0.497565	−	0.592975i	−0.955125	+	0.296204i	$0.904279\pi$
$158$	5.78197	−	15.8858i	0.459989	−	1.26381i
$159$	3.58763	+	15.4854i	0.284517	+	1.22807i
$160$	−0.124547	−	0.342190i	−0.00984632	−	0.0270525i
$161$	12.7755	+	3.31080i	1.00685	+	0.260928i
$162$	1.89825	+	8.79754i	0.149141	+	0.691200i
$163$	−2.36150	+	4.09023i	−0.184967	+	0.320372i	−0.943565	−	0.331187i	$-0.892551\pi$
$163$	−2.36150	+	4.09023i	−0.184967	+	0.320372i	0.758599	+	0.651558i	$0.225884\pi$
$164$	−2.87696	−	2.41405i	−0.224653	−	0.188506i
$165$	2.66908	+	0.813777i	0.207787	+	0.0633524i
$166$	−0.564593	+	0.0995530i	−0.0438209	+	0.00772681i
$167$	−1.71849	−	9.74603i	−0.132981	−	0.754170i	−0.976245	−	0.216671i	$-0.930480\pi$
$167$	−1.71849	−	9.74603i	−0.132981	−	0.754170i	0.843264	−	0.537499i	$-0.180631\pi$
$168$	−4.34538	+	1.45524i	−0.335253	+	0.112274i
$169$	0.423355	+	0.355237i	0.0325657	+	0.0273259i
$170$	1.72681	−	0.996974i	0.132440	−	0.0764644i
$171$	16.5092	+	1.12895i	1.26249	+	0.0863327i
$172$	4.36012	−	7.55194i	0.332456	−	0.575830i
$173$	7.20304	+	6.04407i	0.547637	+	0.459522i	0.874140	−	0.485674i	$-0.161426\pi$
$173$	7.20304	+	6.04407i	0.547637	+	0.459522i	−0.326503	+	0.945196i	$0.605870\pi$
$174$	1.09111	+	0.133120i	0.0827165	+	0.0100918i
$175$	−5.53827	−	11.6262i	−0.418654	−	0.878857i
$176$	−1.51312	+	4.15725i	−0.114055	+	0.313364i
$177$	6.84122	+	16.0825i	0.514217	+	1.20884i
$178$	−0.241679	−	0.664007i	−0.0181146	−	0.0497694i
$179$	18.0221	+	10.4051i	1.34704	+	0.777711i	0.987829	−	0.155547i	$-0.0497139\pi$
$179$	18.0221	+	10.4051i	1.34704	+	0.777711i	0.359207	+	0.933258i	$0.383047\pi$
$180$	0.302735	+	1.04967i	0.0225645	+	0.0782378i
$181$	18.6917	+	10.7917i	1.38935	+	0.802139i	0.993242	−	0.116066i	$-0.0370284\pi$
$181$	18.6917	+	10.7917i	1.38935	+	0.802139i	0.396105	+	0.918205i	$0.370362\pi$
$182$	7.60201	−	5.41672i	0.563499	−	0.401514i
$183$	9.59064	−	0.510014i	0.708961	−	0.0377013i
$184$	4.68738	+	1.70607i	0.345559	+	0.125773i
$185$	−2.94458	−	1.07174i	−0.216490	−	0.0787960i
$186$	5.89173	+	6.30838i	0.432003	+	0.462553i
$187$	−23.8563	−	4.20651i	−1.74455	−	0.307611i
$188$	−5.57404			−0.406529
$189$	13.3036	−	3.46617i	0.967694	−	0.252127i
$190$	2.00863			0.145721
$191$	−8.87940	−	1.56568i	−0.642491	−	0.113289i	−0.157096	−	0.987583i	$-0.550213\pi$
$191$	−8.87940	−	1.56568i	−0.642491	−	0.113289i	−0.485395	+	0.874295i	$0.661324\pi$
$192$	−1.68736	+	0.390923i	−0.121775	+	0.0282125i
$193$	0.376550	+	0.137053i	0.0271047	+	0.00986529i	0.355537	−	0.934662i	$-0.384298\pi$
$193$	0.376550	+	0.137053i	0.0271047	+	0.00986529i	−0.328432	+	0.944528i	$0.606520\pi$
$194$	−11.5330	−	4.19767i	−0.828021	−	0.301375i
$195$	−1.21340	−	1.86533i	−0.0868932	−	0.133579i
$196$	2.50203	+	6.53757i	0.178717	+	0.466969i
$197$	−16.8084	−	9.70432i	−1.19755	−	0.691405i	−0.237540	−	0.971378i	$-0.576341\pi$
$197$	−16.8084	−	9.70432i	−1.19755	−	0.691405i	−0.960008	+	0.279973i	$0.909674\pi$
$198$	5.37963	−	12.1330i	0.382314	−	0.862255i
$199$	−5.81573	−	3.35771i	−0.412266	−	0.238022i	0.279497	−	0.960147i	$-0.409832\pi$
$199$	−5.81573	−	3.35771i	−0.412266	−	0.238022i	−0.691763	+	0.722125i	$0.743166\pi$
$200$	−1.66475	−	4.57385i	−0.117715	−	0.323420i
$201$	−15.4769	−	1.88826i	−1.09166	−	0.133188i
$202$	−4.83215	+	13.2762i	−0.339989	+	0.934112i
$203$	0.132575	−	1.67381i	0.00930492	−	0.117478i
$204$	−3.71241	−	8.72724i	−0.259921	−	0.611029i
$205$	1.04765	+	0.879081i	0.0731709	+	0.0613977i
$206$	3.35548	−	5.81186i	0.233787	−	0.404932i
$207$	−13.6802	−	6.06565i	−0.950840	−	0.421592i
$208$	3.05541	−	1.76404i	0.211854	−	0.122314i
$209$	−18.6936	−	15.6858i	−1.29306	−	1.08501i
$210$	1.58237	−	0.529926i	0.109194	−	0.0365684i
$211$	0.986224	+	5.59316i	0.0678945	+	0.385049i	0.999753	+	0.0222268i	$0.00707559\pi$
$211$	0.986224	+	5.59316i	0.0678945	+	0.385049i	−0.931858	+	0.362822i	$0.881813\pi$
$212$	9.03790	−	1.59363i	0.620725	−	0.109451i
$213$	−1.46293	−	6.31451i	−0.100238	−	0.432663i
$214$	−8.10797	−	6.80339i	−0.554249	−	0.465070i
$215$	−1.58774	+	2.75005i	−0.108283	+	0.187552i
$216$	5.13029	−	0.824685i	0.349072	−	0.0561127i
$217$	9.24642	−	9.39980i	0.627688	−	0.638100i
$218$	−1.42695	−	3.92051i	−0.0966452	−	0.265531i
$219$	7.26661	+	2.21552i	0.491032	+	0.149711i
$220$	0.551003	−	1.51387i	0.0371486	−	0.102065i
$221$	12.4176	+	14.7987i	0.835298	+	0.995470i
$222$	−6.75629	+	13.2852i	−0.453452	+	0.891643i
$223$	−16.3914	+	19.5345i	−1.09765	+	1.30813i	−0.150045	+	0.988679i	$0.547942\pi$
$223$	−16.3914	+	19.5345i	−1.09765	+	1.30813i	−0.947604	+	0.319447i	$0.896503\pi$
$224$	0.705770	+	2.54988i	0.0471562	+	0.170371i
$225$	4.04647	+	14.0303i	0.269765	+	0.935354i
$226$	−9.14262			−0.608158
$227$	13.7051	−	4.98825i	0.909641	−	0.331082i	0.155531	−	0.987831i	$-0.450291\pi$
$227$	13.7051	−	4.98825i	0.909641	−	0.331082i	0.754109	+	0.656749i	$0.228069\pi$
$228$	1.15704	−	9.48354i	0.0766266	−	0.628063i
$229$	4.47942	+	5.33836i	0.296008	+	0.352769i	0.893465	−	0.449132i	$-0.148267\pi$
$229$	4.47942	+	5.33836i	0.296008	+	0.352769i	−0.597457	+	0.801901i	$0.703822\pi$
$230$	−1.70692	−	0.621267i	−0.112551	−	0.0409651i
$231$	−18.8649	−	7.42523i	−1.24122	−	0.488544i
$232$	0.110201	−	0.624980i	0.00723504	−	0.0410320i
$233$			10.7075i			0.701471i	0.936475	+	0.350735i	$0.114068\pi$
$233$			10.7075i			0.701471i	−0.936475	+	0.350735i	$0.885932\pi$
$234$	−9.50591	+	4.65444i	−0.621421	+	0.304270i
$235$	2.02980			0.132409
$236$	9.48190	−	3.45113i	0.617219	−	0.224649i
$237$	26.0997	+	13.2732i	1.69536	+	0.862188i
$238$	−13.0789	+	6.23030i	−0.847782	+	0.403850i
$239$	13.6590	+	16.2781i	0.883526	+	1.05295i	0.998226	+	0.0595448i	$0.0189649\pi$
$239$	13.6590	+	16.2781i	0.883526	+	1.05295i	−0.114700	+	0.993400i	$0.536591\pi$
$240$	0.614454	−	0.142355i	0.0396628	−	0.00918899i
$241$	2.84731	−	3.39330i	0.183412	−	0.218581i	−0.666502	−	0.745503i	$-0.732209\pi$
$241$	2.84731	−	3.39330i	0.183412	−	0.218581i	0.849914	+	0.526922i	$0.176654\pi$
$242$	−7.42378	+	4.28612i	−0.477218	+	0.275522i
$243$	−15.5238	+	1.41827i	−0.995853	+	0.0909822i
$244$		−	5.54498i		−	0.354981i
$245$	−0.911119	−	2.38067i	−0.0582092	−	0.152095i
$246$	4.75397	−	4.43998i	0.303102	−	0.283083i
$247$	3.37930	+	19.1650i	0.215020	+	1.21944i
$248$	3.81764	−	3.20338i	0.242421	−	0.203415i
$249$	−0.0527309	−	0.991588i	−0.00334169	−	0.0628393i
$250$	1.22896	+	3.37653i	0.0777260	+	0.213550i
$251$	11.2411	−	19.4702i	0.709533	−	1.22895i	−0.255497	−	0.966810i	$-0.582239\pi$
$251$	11.2411	−	19.4702i	0.709533	−	1.22895i	0.965030	−	0.262138i	$-0.0844275\pi$
$252$	−1.59049	−	7.77627i	−0.100192	−	0.489859i
$253$	11.0341	+	19.1115i	0.693705	+	1.20153i
$254$	−4.40990	+	5.25551i	−0.276701	+	0.329760i
$255$	1.35188	+	3.17804i	0.0846579	+	0.199016i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	5.14264	−	4.31518i	0.320789	−	0.269174i	−0.468145	−	0.883651i	$-0.655078\pi$
$257$	5.14264	−	4.31518i	0.320789	−	0.269174i	0.788934	+	0.614478i	$0.210633\pi$
$258$	12.0695	+	9.08048i	0.751413	+	0.565326i
$259$	20.7123	+	9.45168i	1.28700	+	0.587299i
$260$	−1.11263	+	0.642378i	−0.0690024	+	0.0398386i
$261$	−0.457747	+	1.84802i	−0.0283338	+	0.114389i
$262$		−	2.39167i		−	0.147758i
$263$	−9.54086	−	1.68231i	−0.588315	−	0.103736i	−0.128436	−	0.991718i	$-0.540996\pi$
$263$	−9.54086	−	1.68231i	−0.588315	−	0.103736i	−0.459878	+	0.887982i	$0.652107\pi$
$264$	−6.83017	−	3.47354i	−0.420368	−	0.213782i
$265$	−3.29116	+	0.580321i	−0.202175	+	0.0356488i
$266$	−14.5482	−	1.15230i	−0.892008	−	0.0706518i
$267$	1.19232	−	0.276235i	0.0729690	−	0.0169053i
$268$	−1.56316	+	8.86511i	−0.0954851	+	0.541523i
$269$	−2.20896	−	3.82603i	−0.134683	−	0.233277i	0.790794	−	0.612083i	$-0.209668\pi$
$269$	−2.20896	−	3.82603i	−0.134683	−	0.233277i	−0.925476	+	0.378806i	$0.876335\pi$
$270$	−1.86820	+	0.300310i	−0.113695	+	0.0182763i
$271$	2.02403	+	1.16858i	0.122951	+	0.0709859i	0.560214	−	0.828348i	$-0.310719\pi$
$271$	2.02403	+	1.16858i	0.122951	+	0.0709859i	−0.437263	+	0.899334i	$0.644052\pi$
$272$	−5.14538	+	1.87277i	−0.311985	+	0.113553i
$273$	7.71836	+	14.2064i	0.467136	+	0.859809i
$274$	−16.2266	+	13.6157i	−0.980283	+	0.822555i
$275$	7.36493	−	20.2350i	0.444122	−	1.22021i
$276$	−3.91649	+	7.70116i	−0.235745	+	0.463555i
$277$	−5.15966	+	29.2619i	−0.310014	+	1.75817i	0.288898	+	0.957360i	$0.406711\pi$
$277$	−5.15966	+	29.2619i	−0.310014	+	1.75817i	−0.598912	+	0.800815i	$0.704400\pi$
$278$	10.4456	+	18.0922i	0.626483	+	1.08510i
$279$	−12.0819	+	8.80640i	−0.723324	+	0.527225i
$280$	−0.257007	−	0.928543i	−0.0153591	−	0.0554910i
$281$	−19.7402	−	3.48073i	−1.17760	−	0.207643i	−0.449607	−	0.893226i	$-0.648436\pi$
$281$	−19.7402	−	3.48073i	−1.17760	−	0.207643i	−0.727994	+	0.685583i	$0.759547\pi$
$282$	1.16923	−	9.58346i	0.0696265	−	0.570687i
$283$	−11.6316	+	2.05096i	−0.691425	+	0.121917i	−0.508310	−	0.861174i	$-0.669729\pi$
$283$	−11.6316	+	2.05096i	−0.691425	+	0.121917i	−0.183116	+	0.983091i	$0.558618\pi$
$284$	−3.68539	+	0.649835i	−0.218688	+	0.0385606i
$285$	−0.421337	+	3.45345i	−0.0249578	+	0.204564i
$286$	15.3713	+	2.71037i	0.908923	+	0.160268i
$287$	−7.08364	−	6.96805i	−0.418134	−	0.411311i
$288$	−0.318170	−	2.98308i	−0.0187483	−	0.175780i
$289$	−6.49110	−	11.2429i	−0.381830	−	0.661348i
$290$	−0.0401298	+	0.227587i	−0.00235650	+	0.0133644i
$291$	9.63625	−	18.9482i	0.564887	−	1.11076i
$292$	1.50011	−	4.12153i	0.0877876	−	0.241194i
$293$	−1.27983	+	1.07390i	−0.0747683	+	0.0627380i	−0.679406	−	0.733763i	$-0.737762\pi$
$293$	−1.27983	+	1.07390i	−0.0747683	+	0.0627380i	0.604638	+	0.796501i	$0.293318\pi$
$294$	−11.7649	+	2.93041i	−0.686142	+	0.170905i
$295$	−3.45285	+	1.25673i	−0.201032	+	0.0731698i
$296$	7.45224	+	4.30255i	0.433153	+	0.250081i
$297$	19.7318	+	11.7943i	1.14496	+	0.684373i
$298$	−8.45004	−	14.6359i	−0.489498	−	0.847835i
$299$	3.05600	−	17.3314i	0.176733	−	1.00230i
$300$	8.21304	−	1.90278i	0.474180	−	0.109857i
$301$	13.0774	−	19.0073i	0.753769	−	1.09557i
$302$	−0.309212	+	0.0545224i	−0.0177931	+	0.00313741i
$303$	−21.8122	−	11.0928i	−1.25308	−	0.637264i
$304$	−5.43213	−	0.957830i	−0.311554	−	0.0549353i
$305$			2.01921i			0.115620i
$306$	15.7835	−	4.55210i	0.902281	−	0.260226i
$307$	−24.0725	+	13.8983i	−1.37389	+	0.793216i	−0.991415	−	0.130750i	$-0.958262\pi$
$307$	−24.0725	+	13.8983i	−1.37389	+	0.793216i	−0.382475	+	0.923966i	$0.624928\pi$
$308$	−4.85929	+	10.6486i	−0.276884	+	0.606761i
$309$	9.28849	+	6.98820i	0.528404	+	0.397545i
$310$	−1.39020	+	1.16652i	−0.0789581	+	0.0662537i
$311$	−1.03114	−	5.84786i	−0.0584704	−	0.331602i	0.941515	−	0.336970i	$-0.109402\pi$
$311$	−1.03114	−	5.84786i	−0.0584704	−	0.331602i	−0.999986	+	0.00536850i	$0.998291\pi$
$312$	2.39201	+	5.62320i	0.135421	+	0.318351i
$313$	8.45628	−	10.0778i	0.477977	−	0.569631i	−0.472140	−	0.881523i	$-0.656518\pi$
$313$	8.45628	−	10.0778i	0.477977	−	0.569631i	0.950117	+	0.311892i	$0.100963\pi$
$314$	−4.84956	−	8.39968i	−0.273676	−	0.474021i
$315$	0.579180	+	2.83174i	0.0326331	+	0.159550i
$316$	8.45268	−	14.6405i	0.475500	−	0.823590i
$317$	−7.18226	−	19.7331i	−0.403396	−	1.10832i	−0.960597	−	0.277944i	$-0.910347\pi$
$317$	−7.18226	−	19.7331i	−0.403396	−	1.10832i	0.557201	−	0.830377i	$-0.311875\pi$
$318$	0.844107	+	15.8732i	0.0473352	+	0.890123i
$319$	2.15075	−	1.80469i	0.120419	−	0.101043i
$320$	−0.0632342	−	0.358619i	−0.00353490	−	0.0200474i
$321$	13.3978	−	12.5129i	0.747794	−	0.698404i
$322$	12.0065	+	5.47895i	0.669098	+	0.305330i
$323$		−	30.2030i		−	1.68054i
$324$	0.341737	+	8.99351i	0.0189854	+	0.499639i
$325$	−14.8719	+	8.58628i	−0.824943	+	0.476281i
$326$	−3.03588	+	3.61802i	−0.168142	+	0.200384i
$327$	7.03987	−	1.63098i	0.389306	−	0.0901934i
$328$	−2.41405	−	2.87696i	−0.133294	−	0.158853i
$329$	−14.7015	−	1.16444i	−0.810519	−	0.0641975i
$330$	2.48722	+	1.26489i	0.136917	+	0.0696301i
$331$	0.103591	−	0.0377041i	0.00569388	−	0.00207240i	−0.339172	−	0.940725i	$-0.610147\pi$
$331$	0.103591	−	0.0377041i	0.00569388	−	0.00207240i	0.344866	+	0.938652i	$0.387925\pi$
$332$	−0.573303			−0.0314641
$333$	−21.4240	−	14.4028i	−1.17403	−	0.789270i
$334$		−	9.89638i		−	0.541506i
$335$	0.569227	−	3.22824i	0.0311002	−	0.176378i
$336$	−4.53206	+	0.678561i	−0.247244	+	0.0370186i
$337$	−11.6718	−	4.24817i	−0.635801	−	0.231413i	0.00395335	−	0.999992i	$-0.498742\pi$
$337$	−11.6718	−	4.24817i	−0.635801	−	0.231413i	−0.639754	+	0.768580i	$0.720964\pi$
$338$	0.355237	+	0.423355i	0.0193223	+	0.0230275i
$339$	1.91778	−	15.7189i	0.104160	−	0.853735i
$340$	1.87370	−	0.681970i	0.101616	−	0.0369850i
$341$	22.0476			1.19395
$342$	16.0624	+	3.97859i	0.868553	+	0.215138i
$343$	5.23336	+	17.7655i	0.282575	+	0.959245i
$344$	5.60526	−	6.68009i	0.302215	−	0.360166i
$345$	1.42619	−	2.80439i	0.0767837	−	0.150983i
$346$	6.04407	+	7.20304i	0.324931	+	0.387238i
$347$	1.97824	−	5.43517i	0.106197	−	0.291775i	−0.875200	−	0.483761i	$-0.839270\pi$
$347$	1.97824	−	5.43517i	0.106197	−	0.291775i	0.981398	+	0.191986i	$0.0614927\pi$
$348$	1.05141	+	0.320566i	0.0563617	+	0.0171842i
$349$	−10.0647	−	27.6525i	−0.538750	−	1.48020i	−0.848402	−	0.529353i	$-0.822435\pi$
$349$	−10.0647	−	27.6525i	−0.538750	−	1.48020i	0.309652	−	0.950850i	$-0.399788\pi$
$350$	−3.43526	−	12.4113i	−0.183622	−	0.663410i
$351$	−6.00840	−	17.3199i	−0.320705	−	0.924466i
$352$	−2.21203	+	3.83134i	−0.117901	+	0.204211i
$353$	−18.6069	−	15.6130i	−0.990345	−	0.830998i	−0.00472722	−	0.999989i	$-0.501505\pi$
$353$	−18.6069	−	15.6130i	−0.990345	−	0.830998i	−0.985618	+	0.168991i	$0.945949\pi$
$354$	3.94458	+	17.0262i	0.209652	+	0.904930i
$355$	1.34204	−	0.236638i	0.0712282	−	0.0125595i
$356$	−0.122704	−	0.695886i	−0.00650328	−	0.0368819i
$357$	−7.96829	−	23.7935i	−0.421727	−	1.25929i
$358$	15.9415	+	13.3765i	0.842534	+	0.706970i
$359$	6.05821	−	3.49771i	0.319740	−	0.184602i	−0.331537	−	0.943442i	$-0.607567\pi$
$359$	6.05821	−	3.49771i	0.319740	−	0.184602i	0.651277	+	0.758840i	$0.274234\pi$
$360$	0.115862	+	1.08629i	0.00610646	+	0.0572527i
$361$	5.71271	−	9.89471i	0.300669	−	0.520774i
$362$	16.5338	+	13.8735i	0.868998	+	0.729176i
$363$	−5.81190	−	13.6628i	−0.305046	−	0.717110i
$364$	8.42712	−	4.01435i	0.441701	−	0.210409i
$365$	−0.546269	+	1.50086i	−0.0285930	+	0.0785587i
$366$	9.53350	+	1.16313i	0.498324	+	0.0607979i
$367$	5.92523	+	16.2794i	0.309295	+	0.849780i	0.992795	+	0.119829i	$0.0382347\pi$
$367$	5.92523	+	16.2794i	0.309295	+	0.849780i	−0.683500	+	0.729951i	$0.739543\pi$
$368$	4.31992	+	2.49410i	0.225191	+	0.130014i
$369$	6.63646	+	9.10484i	0.345480	+	0.473979i
$370$	−2.71374	−	1.56678i	−0.141081	−	0.0814530i
$371$	24.1703	−	2.31512i	1.25486	−	0.120195i
$372$	4.70678	+	7.23563i	0.244035	+	0.375150i
$373$	−3.09836	−	1.12771i	−0.160427	−	0.0583907i	0.260558	−	0.965458i	$-0.416093\pi$
$373$	−3.09836	−	1.12771i	−0.160427	−	0.0583907i	−0.420985	+	0.907067i	$0.638316\pi$
$374$	−22.7634	−	8.28521i	−1.17707	−	0.428418i
$375$	−6.06306	+	1.40468i	−0.313095	+	0.0725371i
$376$	−5.48936	−	0.967922i	−0.283092	−	0.0499168i
$377$	−2.23900			−0.115314
$378$	13.7034	−	1.10336i	0.704826	−	0.0567509i
$379$	36.0217			1.85031			0.925154	−	0.379591i	$-0.123935\pi$
$379$	36.0217			1.85031			0.925154	+	0.379591i	$0.123935\pi$
$380$	1.97812	+	0.348795i	0.101475	+	0.0178928i
$381$	−8.11078	−	8.68435i	−0.415528	−	0.444913i
$382$	−8.47263	−	3.08378i	−0.433497	−	0.157780i
$383$	11.9209	+	4.33884i	0.609128	+	0.221705i	0.628122	−	0.778115i	$-0.283824\pi$
$383$	11.9209	+	4.33884i	0.609128	+	0.221705i	−0.0189935	+	0.999820i	$0.506046\pi$
$384$	−1.72961	+	0.0919775i	−0.0882636	+	0.00469371i
$385$	1.76952	−	3.87771i	0.0901830	−	0.197626i
$386$	0.347030	+	0.200358i	0.0176634	+	0.0101980i
$387$	−18.1438	+	18.8463i	−0.922302	+	0.958013i
$388$	−10.6289	−	6.13658i	−0.539599	−	0.311538i
$389$	−2.60873	−	7.16741i	−0.132268	−	0.363402i	0.855824	−	0.517267i	$-0.173050\pi$
$389$	−2.60873	−	7.16741i	−0.132268	−	0.363402i	−0.988092	+	0.153864i	$0.950828\pi$
$390$	−0.871053	−	2.04770i	−0.0441075	−	0.103689i
$391$	−9.34175	+	25.6662i	−0.472433	+	1.29800i
$392$	1.32878	+	6.87272i	0.0671137	+	0.347125i
$393$	4.11200	+	0.501683i	0.207423	+	0.0253066i
$394$	−14.8679	−	12.4756i	−0.749033	−	0.628514i
$395$	−3.07805	+	5.33135i	−0.154874	+	0.268249i
$396$	7.40478	−	11.0145i	0.372104	−	0.553500i
$397$	2.08481	−	1.20367i	0.104634	−	0.0604103i	−0.446770	−	0.894649i	$-0.647426\pi$
$397$	2.08481	−	1.20367i	0.104634	−	0.0604103i	0.551404	+	0.834239i	$0.314092\pi$
$398$	−5.14431	−	4.31659i	−0.257861	−	0.216371i
$399$	5.03282	−	24.7710i	0.251956	−	1.24010i
$400$	−0.845214	−	4.79345i	−0.0422607	−	0.239672i
$401$	−13.8549	+	2.44299i	−0.691880	+	0.121997i	−0.508522	−	0.861049i	$-0.669808\pi$
$401$	−13.8549	+	2.44299i	−0.691880	+	0.121997i	−0.183358	+	0.983046i	$0.558697\pi$
$402$	−14.9139	−	4.54711i	−0.743839	−	0.226789i
$403$	−13.4690	−	11.3018i	−0.670936	−	0.562982i
$404$	−7.06413	+	12.2354i	−0.351454	+	0.608736i
$405$	−0.124444	−	3.27500i	−0.00618368	−	0.162736i
$406$	0.421214	−	1.62536i	0.0209045	−	0.0806652i
$407$	13.0205	+	35.7736i	0.645403	+	1.77323i
$408$	−2.14054	−	9.23930i	−0.105973	−	0.457414i
$409$	3.20895	−	8.81651i	0.158672	−	0.435949i	−0.834726	−	0.550666i	$-0.814374\pi$
$409$	3.20895	−	8.81651i	0.158672	−	0.435949i	0.993398	+	0.114717i	$0.0365961\pi$
$410$	0.879081	+	1.04765i	0.0434147	+	0.0517396i
$411$	−20.0058	−	30.7545i	−0.986813	−	1.51701i
$412$	4.31372	−	5.14090i	0.212522	−	0.253274i
$413$	25.7294	−	7.12152i	1.26606	−	0.350427i
$414$	−12.4191	−	8.34904i	−0.610365	−	0.410333i
$415$	0.208769			0.0102481
$416$	3.31531	−	1.20667i	0.162546	−	0.0591621i
$417$	−33.2971	+	14.1640i	−1.63057	+	0.693614i
$418$	−15.6858	−	18.6936i	−0.767217	−	0.914333i
$419$	1.56858	+	0.570915i	0.0766300	+	0.0278910i	0.380051	−	0.924966i	$-0.375907\pi$
$419$	1.56858	+	0.570915i	0.0766300	+	0.0278910i	−0.303421	+	0.952857i	$0.598129\pi$
$420$	1.65036	−	0.247099i	0.0805291	−	0.0120572i
$421$	1.42072	−	8.05732i	0.0692418	−	0.392690i	−0.930415	−	0.366507i	$-0.880554\pi$
$421$	1.42072	−	8.05732i	0.0692418	−	0.392690i	0.999657	−	0.0261830i	$-0.00833526\pi$
$422$			5.67944i			0.276471i
$423$	16.2316	+	4.02051i	0.789208	+	0.195484i
$424$	9.17732			0.445690
$425$	25.0446	−	9.11549i	1.21484	−	0.442166i
$426$	−0.344203	−	6.47262i	−0.0166767	−	0.313599i
$427$	1.15837	−	14.6248i	0.0560573	−	0.707746i
$428$	−6.80339	−	8.10797i	−0.328854	−	0.391913i
$429$	−7.88427	+	25.8593i	−0.380656	+	1.24850i
$430$	−2.04116	+	2.43256i	−0.0984336	+	0.117309i
$431$	−3.36070	+	1.94030i	−0.161879	+	0.0934609i	−0.578751	−	0.815504i	$-0.696460\pi$
$431$	−3.36070	+	1.94030i	−0.161879	+	0.0934609i	0.416872	+	0.908965i	$0.363126\pi$
$432$	5.19556	+	0.0787098i	0.249971	+	0.00378693i
$433$		−	7.95078i		−	0.382090i	−0.981581	−	0.191045i	$-0.938812\pi$
$433$		−	7.95078i		−	0.382090i	0.981581	−	0.191045i	$-0.0611877\pi$
$434$	10.7382	−	7.65138i	0.515450	−	0.367278i
$435$	−0.382874	−	0.116735i	−0.0183574	−	0.00559700i
$436$	−0.724482	−	4.10874i	−0.0346964	−	0.196773i
$437$	−21.0774	+	17.6860i	−1.00827	+	0.846038i
$438$	6.77149	+	3.44369i	0.323554	+	0.164546i
$439$	−5.21903	−	14.3392i	−0.249091	−	0.684372i	−0.999720	−	0.0236483i	$-0.992472\pi$
$439$	−5.21903	−	14.3392i	−0.249091	−	0.684372i	0.750629	−	0.660723i	$-0.229750\pi$
$440$	0.805513	−	1.39519i	0.0384013	−	0.0665130i
$441$	−2.57042	−	20.8421i	−0.122401	−	0.992481i
$442$	9.65918	+	16.7302i	0.459440	+	0.795774i
$443$	12.2786	−	14.6331i	0.583374	−	0.695238i	−0.390944	−	0.920415i	$-0.627851\pi$
$443$	12.2786	−	14.6331i	0.583374	−	0.695238i	0.974318	+	0.225176i	$0.0722958\pi$
$444$	−8.96059	+	11.9101i	−0.425251	+	0.565230i
$445$	0.0446827	+	0.253408i	0.00211816	+	0.0120127i
$446$	−19.5345	+	16.3914i	−0.924985	+	0.776155i
$447$	26.9360	−	11.4581i	1.27403	−	0.541949i
$448$	0.252266	+	2.63370i	0.0119184	+	0.124431i
$449$	−28.8723	+	16.6694i	−1.36257	+	0.786678i	−0.989965	−	0.141313i	$-0.954868\pi$
$449$	−28.8723	+	16.6694i	−1.36257	+	0.786678i	−0.372602	+	0.927991i	$0.621534\pi$
$450$	1.54866	+	14.5198i	0.0730044	+	0.684471i
$451$		−	16.6150i		−	0.782368i
$452$	−9.00372	−	1.58760i	−0.423500	−	0.0746744i
$453$	−0.0288793	−	0.543065i	−0.00135687	−	0.0255154i
$454$	14.3631	−	2.53260i	0.674094	−	0.118861i
$455$	−3.06875	+	1.46183i	−0.143865	+	0.0685318i
$456$	2.78626	−	9.13855i	0.130478	−	0.427952i
$457$	1.62262	−	9.20234i	0.0759030	−	0.430467i	−0.923048	−	0.384684i	$-0.874310\pi$
$457$	1.62262	−	9.20234i	0.0759030	−	0.430467i	0.998951	−	0.0457835i	$-0.0145784\pi$
$458$	3.48437	+	6.03510i	0.162814	+	0.282002i
$459$	4.51565	+	28.0914i	0.210772	+	1.31120i
$460$	−1.57310	−	0.908232i	−0.0733463	−	0.0423465i
$461$	15.3507	−	5.58720i	0.714954	−	0.260222i	0.0411716	−	0.999152i	$-0.486891\pi$
$461$	15.3507	−	5.58720i	0.714954	−	0.260222i	0.673782	+	0.738930i	$0.264669\pi$
$462$	−17.2889	−	10.5883i	−0.804352	−	0.492611i
$463$	−15.6985	+	13.1726i	−0.729569	+	0.612181i	−0.930014	−	0.367524i	$-0.880206\pi$
$463$	−15.6985	+	13.1726i	−0.729569	+	0.612181i	0.200445	+	0.979705i	$0.435761\pi$
$464$	0.217053	−	0.596349i	0.0100764	−	0.0276848i
$465$	−1.71398	−	2.63487i	−0.0794840	−	0.122189i
$466$	−1.85933	+	10.5448i	−0.0861320	+	0.488479i
$467$	−0.926779	−	1.60523i	−0.0428862	−	0.0742811i	0.843786	−	0.536681i	$-0.180322\pi$
$467$	−0.926779	−	1.60523i	−0.0428862	−	0.0742811i	−0.886672	+	0.462399i	$0.846989\pi$
$468$	−10.1697	+	2.93304i	−0.470096	+	0.135580i
$469$	−5.97477	+	23.0551i	−0.275889	+	1.06459i
$470$	1.99896	+	0.352470i	0.0922051	+	0.0162582i
$471$	15.4588	−	6.57591i	0.712306	−	0.303002i
$472$	9.93713	−	1.75218i	0.457393	−	0.0806508i
$473$	37.9927	−	6.69913i	1.74691	−	0.308027i
$474$	23.3983	+	17.6037i	1.07472	+	0.808566i
$475$	26.4403	+	4.66214i	1.21316	+	0.213914i
$476$	−13.9621	+	3.86451i	−0.639953	+	0.177130i
$477$	−27.4678	−	1.87833i	−1.25767	−	0.0860027i
$478$	10.6248	+	18.4027i	0.485967	+	0.841719i
$479$	−5.91275	+	33.5329i	−0.270161	+	1.53216i	0.483766	+	0.875198i	$0.339269\pi$
$479$	−5.91275	+	33.5329i	−0.270161	+	1.53216i	−0.753926	+	0.656959i	$0.771842\pi$
$480$	0.629839	−	0.0334937i	0.0287481	−	0.00152877i
$481$	10.3836	−	28.5286i	0.473450	−	1.30079i
$482$	3.39330	−	2.84731i	0.154560	−	0.129692i
$483$	−11.9385	+	19.4936i	−0.543220	+	0.886988i
$484$	−8.05527	+	2.93188i	−0.366149	+	0.133267i
$485$	3.87052	+	2.23464i	0.175751	+	0.101470i
$486$	−15.5342	−	1.29896i	−0.704648	−	0.0589218i
$487$	1.09498	+	1.89656i	0.0496182	+	0.0859412i	0.889768	−	0.456414i	$-0.150866\pi$
$487$	1.09498	+	1.89656i	0.0496182	+	0.0859412i	−0.840150	+	0.542355i	$0.817533\pi$
$488$	0.962876	−	5.46074i	0.0435874	−	0.247196i
$489$	−5.58366	−	5.97852i	−0.252502	−	0.270358i
$490$	−0.483878	−	2.50271i	−0.0218594	−	0.113061i
$491$	−33.3404	+	5.87881i	−1.50463	+	0.265307i	−0.864372	−	0.502853i	$-0.832284\pi$
$491$	−33.3404	+	5.87881i	−1.50463	+	0.265307i	−0.640258	+	0.768160i	$0.721173\pi$
$492$	5.45274	−	3.54701i	0.245828	−	0.159911i
$493$	3.42214	+	0.603416i	0.154126	+	0.0271765i
$494$			19.4606i			0.875575i
$495$	−2.69646	+	4.01095i	−0.121197	+	0.180279i
$496$	4.31591	−	2.49179i	0.193790	−	0.111885i
$497$	−9.85595	+	0.944041i	−0.442100	+	0.0423460i
$498$	0.120258	−	0.985680i	0.00538887	−	0.0441694i
$499$	6.56118	−	5.50548i	0.293719	−	0.246459i	−0.484005	−	0.875065i	$-0.660819\pi$
$499$	6.56118	−	5.50548i	0.293719	−	0.246459i	0.777724	+	0.628606i	$0.216374\pi$
$500$	0.623957	+	3.53864i	0.0279042	+	0.158253i
$501$	17.0149	+	2.07589i	0.760168	+	0.0927441i
$502$	14.4513	−	17.2224i	0.644993	−	0.768673i
$503$	−15.3427	−	26.5744i	−0.684098	−	1.18489i	−0.973719	−	0.227752i	$-0.926863\pi$
$503$	−15.3427	−	26.5744i	−0.684098	−	1.18489i	0.289621	−	0.957141i	$-0.406471\pi$
$504$	−0.215994	−	7.93431i	−0.00962114	−	0.353422i
$505$	2.57241	−	4.45555i	0.114471	−	0.198269i
$506$	7.54773	+	20.7372i	0.335538	+	0.921882i
$507$	−0.802390	+	0.521955i	−0.0356354	+	0.0231808i
$508$	−5.25551	+	4.40990i	−0.233176	+	0.195658i
$509$	4.45622	+	25.2725i	0.197519	+	1.12018i	0.908786	+	0.417262i	$0.137010\pi$
$509$	4.45622	+	25.2725i	0.197519	+	1.12018i	−0.711268	+	0.702921i	$0.751879\pi$
$510$	0.779481	+	3.36451i	0.0345160	+	0.148983i
$511$	4.81754	−	10.5571i	0.213115	−	0.467020i
$512$			1.00000i			0.0441942i
$513$	−10.2097	+	26.7815i	−0.450769	+	1.18243i
$514$	5.81383	−	3.35662i	0.256437	−	0.148054i
$515$	−1.57085	+	1.87206i	−0.0692199	+	0.0824930i
$516$	10.3093	+	11.0384i	0.453842	+	0.485937i
$517$	−15.8511	−	18.8905i	−0.697129	−	0.830805i
$518$	18.7564	+	12.9047i	0.824109	+	0.567002i
$519$	−13.6520	+	8.88065i	−0.599258	+	0.389817i
$520$	−1.20728	+	0.439412i	−0.0529425	+	0.0192695i
$521$	24.8024			1.08661			0.543307	−	0.839534i	$-0.317172\pi$
$521$	24.8024			1.08661			0.543307	+	0.839534i	$0.317172\pi$
$522$	−0.771698	+	1.74045i	−0.0337763	+	0.0761776i
$523$			20.3770i			0.891026i	0.895275	+	0.445513i	$0.146979\pi$
$523$			20.3770i			0.891026i	−0.895275	+	0.445513i	$0.853021\pi$
$524$	0.415309	−	2.35533i	0.0181429	−	0.102893i
$525$	22.0593	−	3.30283i	0.962747	−	0.144147i
$526$	−9.10378	−	3.31351i	−0.396944	−	0.144476i
$527$	17.5405	+	20.9039i	0.764074	+	0.910588i
$528$	−6.12323	−	4.60681i	−0.266479	−	0.200486i
$529$	1.76872	−	0.643762i	0.0769010	−	0.0279897i
$530$	−3.34194			−0.145164
$531$	−30.1005	+	3.21047i	−1.30625	+	0.139322i
$532$	−14.1271	−	3.66106i	−0.612487	−	0.158727i
$533$	−8.51697	+	10.1501i	−0.368911	+	0.439651i
$534$	1.22218	−	0.0649933i	0.0528888	−	0.00281253i
$535$	2.47747	+	2.95253i	0.107110	+	0.127649i
$536$	−3.07882	+	8.45899i	−0.132985	+	0.365373i
$537$	−26.3422	+	24.6023i	−1.13675	+	1.06167i
$538$	−1.51102	−	4.15149i	−0.0651446	−	0.178983i
$539$	−15.0409	+	27.0705i	−0.647856	+	1.16601i
$540$	−1.89197	−	0.0286623i	−0.0814174	−	0.00123343i
$541$	−3.60386	+	6.24207i	−0.154942	+	0.268368i	−0.933038	−	0.359778i	$-0.882852\pi$
$541$	−3.60386	+	6.24207i	−0.154942	+	0.268368i	0.778096	+	0.628146i	$0.216186\pi$
$542$	1.79036	+	1.50229i	0.0769026	+	0.0645290i
$543$	−27.3210	+	25.5165i	−1.17245	+	1.09502i
$544$	−5.39241	+	0.950828i	−0.231198	+	0.0407664i
$545$	0.263821	+	1.49620i	0.0113009	+	0.0640903i
$546$	5.13419	+	15.3308i	0.219723	+	0.656099i
$547$	12.4492	+	10.4461i	0.532290	+	0.446644i	0.868891	−	0.495003i	$-0.164833\pi$
$547$	12.4492	+	10.4461i	0.532290	+	0.446644i	−0.336602	+	0.941647i	$0.609278\pi$
$548$	−18.3444	+	10.5911i	−0.783634	+	0.452431i
$549$	−3.99955	+	16.1470i	−0.170697	+	0.689137i
$550$	10.7668	−	18.6486i	0.459098	−	0.795181i
$551$	2.68156	+	2.25009i	0.114238	+	0.0958572i
$552$	−5.19428	+	6.90407i	−0.221083	+	0.293857i
$553$	25.3523	−	36.8483i	1.07809	−	1.56695i
$554$	−10.1625	+	27.9213i	−0.431765	+	1.18626i
$555$	3.26301	−	4.33709i	0.138507	−	0.184099i
$556$	7.14518	+	19.6312i	0.303023	+	0.832550i
$557$	−13.6654	−	7.88970i	−0.579020	−	0.334297i	0.181724	−	0.983350i	$-0.441832\pi$
$557$	−13.6654	−	7.88970i	−0.579020	−	0.334297i	−0.760744	+	0.649052i	$0.775166\pi$
$558$	−13.4276	+	6.57462i	−0.568434	+	0.278326i
$559$	−26.6439	−	15.3828i	−1.12692	−	0.650625i
$560$	−0.0918629	−	0.959065i	−0.00388192	−	0.0405279i
$561$	19.0197	−	37.3993i	0.803013	−	1.57900i
$562$	−18.8359	−	6.85570i	−0.794544	−	0.289190i
$563$	16.2686	+	5.92128i	0.685639	+	0.249552i	0.661267	−	0.750151i	$-0.270019\pi$
$563$	16.2686	+	5.92128i	0.685639	+	0.249552i	0.0243721	+	0.999703i	$0.492241\pi$
$564$	2.81562	−	9.23484i	0.118559	−	0.388857i
$565$	3.27872	+	0.578127i	0.137937	+	0.0243220i
$566$	−11.8110			−0.496454
$567$	−0.977447	+	23.7917i	−0.0410489	+	0.999157i
$568$	−3.74225			−0.157021
$569$	25.6181	+	4.51716i	1.07397	+	0.189369i	0.682545	−	0.730843i	$-0.260873\pi$
$569$	25.6181	+	4.51716i	1.07397	+	0.189369i	0.391420	+	0.920212i	$0.371984\pi$
$570$	−1.01462	+	3.32782i	−0.0424978	+	0.139387i
$571$	11.3590	+	4.13434i	0.475360	+	0.173017i	0.568579	−	0.822629i	$-0.307493\pi$
$571$	11.3590	+	4.13434i	0.475360	+	0.173017i	−0.0932191	+	0.995646i	$0.529716\pi$
$572$	14.6671	+	5.33839i	0.613263	+	0.223209i
$573$	7.07920	−	13.9201i	0.295738	−	0.581522i
$574$	−5.76604	−	8.09225i	−0.240670	−	0.337764i
$575$	−21.0267	−	12.1398i	−0.876875	−	0.506264i
$576$	0.204670	−	2.99301i	0.00852793	−	0.124709i
$577$	−21.1130	−	12.1896i	−0.878944	−	0.507458i	−0.00863380	−	0.999963i	$-0.502748\pi$
$577$	−21.1130	−	12.1896i	−0.878944	−	0.507458i	−0.870310	+	0.492504i	$0.836082\pi$
$578$	−4.44018	−	12.1993i	−0.184687	−	0.507423i
$579$	−0.417270	+	0.554622i	−0.0173412	+	0.0230493i
$580$	−0.0790403	+	0.217161i	−0.00328197	+	0.00901714i
$581$	−1.51208	−	0.119765i	−0.0627317	−	0.00496869i
$582$	12.7802	−	16.9870i	0.529755	−	0.704134i
$583$	31.1021	+	26.0978i	1.28812	+	1.08086i
$584$	2.19302	−	3.79842i	0.0907478	−	0.157180i
$585$	3.70332	−	1.06807i	0.153114	−	0.0441593i
$586$	−1.44686	+	0.835347i	−0.0597694	+	0.0345079i
$587$	35.5459	+	29.8265i	1.46714	+	1.23107i	0.918746	+	0.394850i	$0.129203\pi$
$587$	35.5459	+	29.8265i	1.46714	+	1.23107i	0.548389	+	0.836223i	$0.315241\pi$
$588$	−12.0950	+	0.842937i	−0.498790	+	0.0347621i
$589$	4.77342	+	27.0714i	0.196686	+	1.11546i
$590$	−3.61862	+	0.638060i	−0.148976	+	0.0262685i
$591$	24.5681	−	22.9455i	1.01060	−	0.943850i
$592$	6.59189	+	5.53125i	0.270925	+	0.227333i
$593$	22.2867	−	38.6017i	0.915204	−	1.58518i	0.108602	−	0.994085i	$-0.465362\pi$
$593$	22.2867	−	38.6017i	0.915204	−	1.58518i	0.806602	−	0.591095i	$-0.201304\pi$
$594$	17.3840	+	15.0415i	0.713275	+	0.617160i
$595$	5.08433	−	1.40727i	0.208437	−	0.0576924i
$596$	−5.78017	−	15.8809i	−0.236765	−	0.650506i
$597$	8.50061	−	7.93917i	0.347907	−	0.324928i
$598$	6.01915	−	16.5375i	0.246141	−	0.676267i
$599$	1.36187	+	1.62301i	0.0556446	+	0.0663146i	0.793149	−	0.609028i	$-0.208440\pi$
$599$	1.36187	+	1.62301i	0.0556446	+	0.0663146i	−0.737504	+	0.675342i	$0.763996\pi$
$600$	8.41868	−	0.447691i	0.343691	−	0.0182769i
$601$	−26.4199	+	31.4861i	−1.07769	+	1.28434i	−0.121186	+	0.992630i	$0.538670\pi$
$601$	−26.4199	+	31.4861i	−1.07769	+	1.28434i	−0.956506	+	0.291713i	$0.905775\pi$
$602$	16.1793	−	16.4477i	0.659420	−	0.670359i
$603$	10.9463	−	24.6877i	0.445766	−	1.00536i
$604$	−0.313982			−0.0127757
$605$	2.93334	−	1.06765i	0.119257	−	0.0434061i
$606$	−19.5546	−	14.7119i	−0.794352	−	0.597631i
$607$	22.1781	+	26.4309i	0.900182	+	1.07280i	0.996993	+	0.0774924i	$0.0246913\pi$
$607$	22.1781	+	26.4309i	0.900182	+	1.07280i	−0.0968109	+	0.995303i	$0.530864\pi$
$608$	−5.18327	−	1.88656i	−0.210210	−	0.0765100i
$609$	2.70613	+	1.06513i	0.109658	+	0.0431614i
$610$	−0.350633	+	1.98854i	−0.0141967	+	0.0805135i
$611$			19.6657i			0.795588i
$612$	16.3342	−	1.74217i	0.660269	−	0.0704231i
$613$	−23.6422			−0.954898			−0.477449	−	0.878659i	$-0.658438\pi$
$613$	−23.6422			−0.954898			−0.477449	+	0.878659i	$0.658438\pi$
$614$	−26.1202	+	9.50697i	−1.05413	+	0.383670i
$615$	−1.98562	+	1.29165i	−0.0800680	+	0.0520843i
$616$	−6.63458	+	9.64303i	−0.267315	+	0.388529i
$617$	16.2616	+	19.3798i	0.654665	+	0.780200i	0.986610	−	0.163099i	$-0.0521491\pi$
$617$	16.2616	+	19.3798i	0.654665	+	0.780200i	−0.331944	+	0.943299i	$0.607705\pi$
$618$	7.93389	+	8.49496i	0.319148	+	0.341718i
$619$	−26.6761	+	31.7914i	−1.07220	+	1.27780i	−0.113458	+	0.993543i	$0.536193\pi$
$619$	−26.6761	+	31.7914i	−1.07220	+	1.27780i	−0.958747	+	0.284261i	$0.908252\pi$
$620$	−1.57164	+	0.907389i	−0.0631187	+	0.0364416i
$621$	16.9596	−	19.6008i	0.680565	−	0.786554i
$622$		−	5.93808i		−	0.238095i
$623$	−0.178256	−	1.86103i	−0.00714169	−	0.0745605i
$624$	1.37921	+	5.95314i	0.0552125	+	0.238316i
$625$	3.99886	+	22.6786i	0.159954	+	0.907145i
$626$	10.0778	−	8.45628i	0.402790	−	0.337981i
$627$	35.4302	−	23.0474i	1.41495	−	0.920423i
$628$	−3.31729	−	9.11418i	−0.132374	−	0.363696i
$629$	−23.5591	+	40.8055i	−0.939361	+	1.62702i
$630$	0.0786545	+	2.88929i	0.00313367	+	0.115112i
$631$	−0.927696	−	1.60682i	−0.0369310	−	0.0639664i	0.846969	−	0.531642i	$-0.178425\pi$
$631$	−0.927696	−	1.60682i	−0.0369310	−	0.0639664i	−0.883900	+	0.467676i	$0.845092\pi$
$632$	10.8666	−	12.9503i	0.432248	−	0.515133i
$633$	−9.76467	−	1.19134i	−0.388111	−	0.0473514i
$634$	−3.64653	−	20.6805i	−0.144822	−	0.821327i
$635$	1.91380	−	1.60587i	0.0759469	−	0.0637270i
$636$	−1.92506	+	15.7786i	−0.0763337	+	0.625662i
$637$	23.0651	−	8.82737i	0.913872	−	0.349753i
$638$	2.43145	−	1.40380i	0.0962621	−	0.0555770i
$639$	11.2006	+	0.765927i	0.443088	+	0.0302996i
$640$		−	0.364151i		−	0.0143944i
$641$	−40.2243	−	7.09262i	−1.58876	−	0.280142i	−0.691747	−	0.722140i	$-0.743159\pi$
$641$	−40.2243	−	7.09262i	−1.58876	−	0.280142i	−0.897016	+	0.441998i	$0.854270\pi$
$642$	15.3671	−	9.99634i	0.606493	−	0.394524i
$643$	−11.4195	+	2.01357i	−0.450342	+	0.0794074i	−0.394219	−	0.919016i	$-0.628985\pi$
$643$	−11.4195	+	2.01357i	−0.450342	+	0.0794074i	−0.0561227	+	0.998424i	$0.517874\pi$
$644$	10.8727	+	7.48062i	0.428445	+	0.294778i
$645$	−3.75415	−	4.01964i	−0.147820	−	0.158273i
$646$	5.24470	−	29.7442i	0.206350	−	1.17027i
$647$	5.83779	+	10.1113i	0.229507	+	0.397518i	0.957662	−	0.287895i	$-0.0929553\pi$
$647$	5.83779	+	10.1113i	0.229507	+	0.397518i	−0.728155	+	0.685412i	$0.759622\pi$
$648$	−1.22516	+	8.91622i	−0.0481289	+	0.350262i
$649$	38.6599	+	22.3203i	1.51753	+	0.876148i
$650$	−16.1369	+	5.87336i	−0.632942	+	0.230372i
$651$	10.9026	+	20.0672i	0.427305	+	0.786495i
$652$	−3.61802	+	3.03588i	−0.141693	+	0.118894i
$653$	−13.8274	+	37.9904i	−0.541108	+	1.48668i	0.304309	+	0.952573i	$0.401574\pi$
$653$	−13.8274	+	37.9904i	−0.541108	+	1.48668i	−0.845417	+	0.534108i	$0.820648\pi$
$654$	7.21613	−	0.383741i	0.282173	−	0.0150055i
$655$	−0.151235	+	0.857698i	−0.00590925	+	0.0335130i
$656$	−1.87780	−	3.25244i	−0.0733158	−	0.126987i
$657$	−7.34116	+	10.9199i	−0.286406	+	0.426025i
$658$	−14.2759	−	3.69963i	−0.556534	−	0.144227i
$659$	−10.2802	−	1.81267i	−0.400459	−	0.0706117i	−0.0302084	−	0.999544i	$-0.509617\pi$
$659$	−10.2802	−	1.81267i	−0.400459	−	0.0706117i	−0.370251	+	0.928932i	$0.620728\pi$
$660$	2.22978	+	1.67758i	0.0867942	+	0.0652996i
$661$	38.3519	−	6.76247i	1.49172	−	0.263030i	0.632467	−	0.774587i	$-0.282042\pi$
$661$	38.3519	−	6.76247i	1.49172	−	0.263030i	0.859249	+	0.511558i	$0.170931\pi$
$662$	0.108565	−	0.0191429i	0.00421948	−	0.000744008i
$663$	−30.7904	+	13.0977i	−1.19580	+	0.508671i
$664$	−0.564593	−	0.0995530i	−0.0219105	−	0.00386340i
$665$	5.14440	+	1.33318i	0.199491	+	0.0516985i
$666$	−18.5975	−	17.9043i	−0.720639	−	0.693776i
$667$	−1.58281	−	2.74151i	−0.0612867	−	0.106152i
$668$	1.71849	−	9.74603i	0.0664903	−	0.377085i
$669$	−24.0841	−	37.0240i	−0.931146	−	1.43143i
$670$	1.12116	−	3.08036i	0.0433141	−	0.119004i
$671$	18.7921	−	15.7684i	0.725460	−	0.608733i
$672$	−4.58104	−	0.118731i	−0.176717	−	0.00458016i
$673$	20.4081	−	7.42794i	0.786675	−	0.286326i	0.0827217	−	0.996573i	$-0.473639\pi$
$673$	20.4081	−	7.42794i	0.786675	−	0.286326i	0.703953	+	0.710246i	$0.251417\pi$
$674$	−10.7567	−	6.21041i	−0.414334	−	0.239216i
$675$	−25.2888	−	0.383111i	−0.973367	−	0.0147460i
$676$	0.276325	+	0.478609i	0.0106279	+	0.0184080i
$677$	4.43343	−	25.1433i	0.170391	−	0.966334i	−0.772940	−	0.634479i	$-0.781215\pi$
$677$	4.43343	−	25.1433i	0.170391	−	0.966334i	0.943331	−	0.331855i	$-0.107674\pi$
$678$	4.61821	−	15.1471i	0.177361	−	0.581721i
$679$	−26.7516	−	18.4056i	−1.02663	−	0.706341i
$680$	1.96366	−	0.346245i	0.0753028	−	0.0132779i
$681$	1.34146	+	25.2258i	0.0514049	+	0.966653i
$682$	21.7127	+	3.82853i	0.831421	+	0.146602i
$683$		−	0.469818i		−	0.0179771i	−0.999960	−	0.00898855i	$-0.997139\pi$
$683$		−	0.469818i		−	0.0179771i	0.999960	−	0.00898855i	$-0.00286118\pi$
$684$	15.1275	+	6.70735i	0.578413	+	0.256462i
$685$	6.68014	−	3.85678i	0.255235	−	0.147360i
$686$	2.06892	+	18.4043i	0.0789916	+	0.702681i
$687$	−11.1071	+	4.72474i	−0.423760	+	0.180260i
$688$	6.68009	−	5.60526i	0.254676	−	0.213698i
$689$	−5.62244	−	31.8864i	−0.214198	−	1.21478i
$690$	1.89150	−	2.51413i	0.0720083	−	0.0957112i
$691$	15.5069	−	18.4804i	0.589910	−	0.703028i	−0.385678	−	0.922633i	$-0.626033\pi$
$691$	15.5069	−	18.4804i	0.589910	−	0.703028i	0.975589	+	0.219605i	$0.0704770\pi$
$692$	4.70145	+	8.14316i	0.178722	+	0.309556i
$693$	21.8310	−	27.5038i	0.829291	−	1.04478i
$694$	2.89199	−	5.00908i	0.109779	−	0.190142i
$695$	−2.60193	−	7.14874i	−0.0986968	−	0.271167i
$696$	0.979775	+	0.498272i	0.0371383	+	0.0188870i
$697$	15.7531	−	13.2184i	0.596690	−	0.500682i
$698$	−5.10997	−	28.9801i	−0.193415	−	1.09691i
$699$	−17.7397	−	5.40867i	−0.670977	−	0.204575i
$700$	−1.22788	−	12.8192i	−0.0464094	−	0.484522i
$701$			11.9842i			0.452636i	0.974053	+	0.226318i	$0.0726688\pi$
$701$			11.9842i			0.452636i	−0.974053	+	0.226318i	$0.927331\pi$
$702$	−2.90955	−	18.1001i	−0.109814	−	0.683144i
$703$	−41.1060	+	23.7326i	−1.55034	+	0.895090i
$704$	−2.84373	+	3.38902i	−0.107177	+	0.127729i
$705$	−1.02531	+	3.36288i	−0.0386154	+	0.126653i
$706$	−15.6130	−	18.6069i	−0.587604	−	0.700280i
$707$	−21.1876	+	30.7951i	−0.796842	+	1.15817i
$708$	0.928092	+	17.4525i	0.0348798	+	0.655904i
$709$	−5.45696	+	1.98617i	−0.204940	+	0.0745922i	−0.442451	−	0.896793i	$-0.645891\pi$
$709$	−5.45696	+	1.98617i	−0.204940	+	0.0745922i	0.237510	+	0.971385i	$0.423669\pi$
$710$	1.36275			0.0511429
$711$	−35.1742	+	36.5362i	−1.31914	+	1.37021i
$712$		−	0.706622i		−	0.0264818i
$713$	4.31674	−	24.4815i	0.161663	−	0.916839i
$714$	−3.71553	−	24.8157i	−0.139050	−	0.928706i
$715$	−5.34105	−	1.94398i	−0.199744	−	0.0727008i
$716$	13.3765	+	15.9415i	0.499903	+	0.595761i
$717$	−33.8685	+	14.4070i	−1.26484	+	0.538041i
$718$	6.57354	−	2.39257i	0.245322	−	0.0892900i
$719$	24.3978			0.909885			0.454943	−	0.890521i	$-0.349660\pi$
$719$	24.3978			0.909885			0.454943	+	0.890521i	$0.349660\pi$
$720$	−0.0745310	+	1.08991i	−0.00277761	+	0.0406185i
$721$	12.4514	−	12.6579i	0.463713	−	0.471405i
$722$	7.34412	−	8.75238i	0.273320	−	0.325730i
$723$	4.18360	+	6.43136i	0.155590	+	0.239185i
$724$	13.8735	+	16.5338i	0.515605	+	0.614474i
$725$	−1.05648	+	2.90267i	−0.0392368	+	0.107802i
$726$	−3.35109	−	14.4644i	−0.124371	−	0.536826i
$727$	9.60418	+	26.3873i	0.356199	+	0.978650i	0.980336	+	0.197335i	$0.0632286\pi$
$727$	9.60418	+	26.3873i	0.356199	+	0.978650i	−0.624137	+	0.781315i	$0.714549\pi$
$728$	8.99618	−	2.49001i	0.333421	−	0.0922860i
$729$	5.49181	−	26.4356i	0.203400	−	0.979096i
$730$	−0.798592	+	1.38320i	−0.0295572	+	0.0511946i
$731$	36.5775	+	30.6922i	1.35287	+	1.13519i
$732$	9.18669	+	2.80094i	0.339550	+	0.103526i
$733$	−19.7152	+	3.47633i	−0.728199	+	0.128401i	−0.525444	−	0.850828i	$-0.676101\pi$
$733$	−19.7152	+	3.47633i	−0.728199	+	0.128401i	−0.202755	+	0.979229i	$0.564990\pi$
$734$	3.00832	+	17.0610i	0.111039	+	0.629734i
$735$	4.40442	−	0.306957i	0.162459	−	0.0113223i
$736$	3.82119	+	3.20636i	0.140851	+	0.118188i
$737$	−34.4893	+	19.9124i	−1.27043	+	0.733482i
$738$	4.95460	+	10.1189i	0.182381	+	0.372483i
$739$	21.4861	−	37.2150i	0.790378	−	1.36898i	−0.135355	−	0.990797i	$-0.543217\pi$
$739$	21.4861	−	37.2150i	0.790378	−	1.36898i	0.925733	−	0.378178i	$-0.123449\pi$
$740$	−2.40045	−	2.01421i	−0.0882422	−	0.0740440i
$741$	−33.4587	−	4.08212i	−1.22914	−	0.149960i
$742$	24.2051	+	1.91718i	0.888598	+	0.0703817i
$743$	7.69035	−	21.1291i	0.282132	−	0.775150i	−0.714976	−	0.699149i	$-0.753562\pi$
$743$	7.69035	−	21.1291i	0.282132	−	0.775150i	0.997108	−	0.0760014i	$-0.0242154\pi$
$744$	3.37882	+	7.94303i	0.123874	+	0.291206i
$745$	2.10486	+	5.78304i	0.0771160	+	0.211874i
$746$	−2.85547	−	1.64861i	−0.104546	−	0.0603597i
$747$	1.66946	+	0.413518i	0.0610822	+	0.0151298i
$748$	−20.9789	−	12.1122i	−0.767065	−	0.442865i
$749$	−16.2501	−	22.8059i	−0.593766	−	0.833311i
$750$	−6.21487	+	0.330496i	−0.226935	+	0.0120680i
$751$	−10.2591	−	3.73399i	−0.374358	−	0.136255i	0.147987	−	0.988989i	$-0.452721\pi$
$751$	−10.2591	−	3.73399i	−0.374358	−	0.136255i	−0.522345	+	0.852734i	$0.674943\pi$
$752$	−5.23789	−	1.90644i	−0.191006	−	0.0695205i
$753$	26.5791	+	28.4588i	0.968598	+	1.03710i
$754$	−2.20498	−	0.388798i	−0.0803006	−	0.0141592i
$755$	0.114337			0.00416115
$756$	13.6868	+	1.29297i	0.497784	+	0.0470247i
$757$	−41.5719			−1.51096			−0.755478	−	0.655174i	$-0.772595\pi$
$757$	−41.5719			−1.51096			−0.755478	+	0.655174i	$0.772595\pi$
$758$	35.4744	+	6.25510i	1.28849	+	0.227195i
$759$	−37.2368	+	8.62693i	−1.35161	+	0.313138i
$760$	1.88750	+	0.686993i	0.0684667	+	0.0249198i
$761$	−5.08751	−	1.85170i	−0.184422	−	0.0671242i	0.248158	−	0.968719i	$-0.420175\pi$
$761$	−5.08751	−	1.85170i	−0.184422	−	0.0671242i	−0.432581	+	0.901595i	$0.642397\pi$
$762$	−6.47953	−	9.96084i	−0.234729	−	0.360843i
$763$	−1.05248	−	10.9881i	−0.0381025	−	0.397796i
$764$	−7.80842	−	4.50819i	−0.282499	−	0.163101i
$765$	−5.94811	+	0.634414i	−0.215054	+	0.0229373i
$766$	10.9863	+	6.34297i	0.396953	+	0.229181i
$767$	−12.1759	−	33.4529i	−0.439645	−	1.20791i
$768$	−1.71930	−	0.209763i	−0.0620400	−	0.00756917i
$769$	8.02830	−	22.0576i	0.289508	−	0.795416i	−0.706628	−	0.707586i	$-0.749784\pi$
$769$	8.02830	−	22.0576i	0.289508	−	0.795416i	0.996135	−	0.0878306i	$-0.0279934\pi$
$770$	2.41599	−	3.51152i	0.0870663	−	0.126547i
$771$	4.55151	+	10.6998i	0.163919	+	0.385345i
$772$	0.306966	+	0.257575i	0.0110480	+	0.00927034i
$773$	25.9845	−	45.0065i	0.934598	−	1.61877i	0.159249	−	0.987238i	$-0.449093\pi$
$773$	25.9845	−	45.0065i	0.934598	−	1.61877i	0.775349	−	0.631533i	$-0.217574\pi$
$774$	−21.1408	+	15.4094i	−0.759890	+	0.553879i
$775$	−21.0072	+	12.1285i	−0.754602	+	0.435669i
$776$	−9.40178	−	7.88903i	−0.337504	−	0.283200i
$777$	−26.1215	+	29.5410i	−0.937105	+	1.05978i
$778$	−1.32448	−	7.51153i	−0.0474851	−	0.269301i
$779$	20.4009	−	3.59723i	0.730938	−	0.128884i
$780$	−0.502241	−	2.16784i	−0.0179831	−	0.0776212i
$781$	−12.6826	−	10.6419i	−0.453818	−	0.380798i
$782$	−13.6567	+	23.6541i	−0.488363	+	0.845870i
$783$	−2.83049	−	1.69186i	−0.101154	−	0.0604623i
$784$	0.115160	+	6.99905i	0.00411285	+	0.249966i
$785$	1.20800	+	3.31894i	0.0431153	+	0.118458i
$786$	3.96241	+	1.20810i	0.141335	+	0.0430916i
$787$	14.6954	−	40.3752i	0.523834	−	1.43922i	−0.342387	−	0.939559i	$-0.611235\pi$
$787$	14.6954	−	40.3752i	0.523834	−	1.43922i	0.866220	−	0.499662i	$-0.166542\pi$
$788$	−12.4756	−	14.8679i	−0.444426	−	0.529647i
$789$	7.60655	−	14.9571i	0.270800	−	0.532487i
$790$	−3.95707	+	4.71585i	−0.140786	+	0.167783i
$791$	−23.4156	−	6.06819i	−0.832562	−	0.215760i
$792$	9.20493	−	9.56135i	0.327083	−	0.339748i
$793$	−19.5631			−0.694708
$794$	2.26215	−	0.823357i	0.0802808	−	0.0292198i
$795$	0.701014	−	5.74580i	0.0248624	−	0.203782i
$796$	−4.31659	−	5.14431i	−0.152998	−	0.182335i
$797$	13.6311	+	4.96131i	0.482838	+	0.175739i	0.571959	−	0.820282i	$-0.306184\pi$
$797$	13.6311	+	4.96131i	0.482838	+	0.175739i	−0.0891211	+	0.996021i	$0.528406\pi$
$798$	9.25781	−	23.5208i	0.327723	−	0.832627i
$799$	5.29996	−	30.0576i	0.187499	−	1.06336i
$800$		−	4.86739i		−	0.172088i
$801$	−0.144625	+	2.11493i	−0.00511006	+	0.0747272i
$802$	−14.0686			−0.496780
$803$	18.2339	−	6.63659i	0.643459	−	0.234200i
$804$	−13.8977	−	7.06781i	−0.490136	−	0.249262i
$805$	−3.95931	−	2.72408i	−0.139548	−	0.0960112i
$806$	−11.3018	−	13.4690i	−0.398089	−	0.474424i
$807$	7.45461	−	1.72707i	0.262415	−	0.0607956i
$808$	−9.08147	+	10.8229i	−0.319485	+	0.380747i
$809$	−13.5722	+	7.83592i	−0.477173	+	0.275496i	−0.719238	−	0.694764i	$-0.755509\pi$
$809$	−13.5722	+	7.83592i	−0.477173	+	0.275496i	0.242064	+	0.970260i	$0.422175\pi$
$810$	0.446144	−	3.24685i	0.0156759	−	0.114083i
$811$			24.2880i			0.852865i	0.904519	+	0.426433i	$0.140230\pi$
$811$			24.2880i			0.852865i	−0.904519	+	0.426433i	$0.859770\pi$
$812$	0.697056	−	1.52752i	0.0244619	−	0.0536055i
$813$	−2.95844	+	2.76305i	−0.103757	+	0.0969043i
$814$	6.61069	+	37.4911i	0.231704	+	1.31406i
$815$	1.31751	−	1.10552i	0.0461503	−	0.0387247i
$816$	−0.503632	−	9.47064i	−0.0176306	−	0.331539i
$817$	16.4512	+	45.1994i	0.575555	+	1.58133i
$818$	4.69117	−	8.12534i	0.164023	−	0.284096i
$819$	−27.4353	+	5.61138i	−0.958667	+	0.196078i
$820$	0.683804	+	1.18438i	0.0238795	+	0.0413604i
$821$	−4.27265	+	5.09195i	−0.149117	+	0.177710i	−0.835432	−	0.549594i	$-0.814783\pi$
$821$	−4.27265	+	5.09195i	−0.149117	+	0.177710i	0.686315	+	0.727304i	$0.259227\pi$
$822$	−14.3614	−	33.7612i	−0.500911	−	1.17756i
$823$	4.94271	+	28.0315i	0.172292	+	0.977117i	0.941223	+	0.337785i	$0.109678\pi$
$823$	4.94271	+	28.0315i	0.172292	+	0.977117i	−0.768931	+	0.639332i	$0.779211\pi$
$824$	5.14090	−	4.31372i	0.179092	−	0.150276i
$825$	29.8042	+	22.4232i	1.03765	+	0.780675i
$826$	26.5751	−	2.54547i	0.924667	−	0.0885681i
$827$	−2.40667	+	1.38949i	−0.0836880	+	0.0483173i	−0.541260	−	0.840855i	$-0.682053\pi$
$827$	−2.40667	+	1.38949i	−0.0836880	+	0.0483173i	0.457572	+	0.889173i	$0.348719\pi$
$828$	−10.7806	−	10.3788i	−0.374652	−	0.360687i
$829$		−	10.6985i		−	0.371574i	−0.982590	−	0.185787i	$-0.940517\pi$
$829$		−	10.6985i		−	0.371574i	0.982590	−	0.185787i	$-0.0594834\pi$
$830$	0.205597	+	0.0362524i	0.00713639	+	0.00125834i
$831$	−45.8735	−	23.3293i	−1.59133	−	0.809286i
$832$	3.47448	−	0.612645i	0.120456	−	0.0212396i
$833$	−37.6323	+	7.27589i	−1.30388	+	0.252094i
$834$	−35.2508	+	8.16682i	−1.22064	+	0.282794i
$835$	−0.625790	+	3.54903i	−0.0216564	+	0.122819i
$836$	−12.2014	−	21.1334i	−0.421993	−	0.730914i
$837$	−8.48715	−	24.4651i	−0.293359	−	0.845638i
$838$	1.44561	+	0.834622i	0.0499377	+	0.0288315i
$839$	−12.9560	+	4.71560i	−0.447291	+	0.162801i	−0.555838	−	0.831291i	$-0.687602\pi$
$839$	−12.9560	+	4.71560i	−0.447291	+	0.162801i	0.108547	+	0.994091i	$0.465380\pi$
$840$	1.66819	+	0.0432361i	0.0575581	+	0.00149179i
$841$	21.9068	−	18.3820i	0.755406	−	0.633861i
$842$	2.79828	−	7.68821i	0.0964351	−	0.264953i
$843$	15.7381	−	30.9465i	0.542049	−	1.06585i
$844$	−0.986224	+	5.59316i	−0.0339472	+	0.192524i
$845$	−0.100624	−	0.174286i	−0.00346158	−	0.00599563i
$846$	15.2869	+	6.77802i	0.525573	+	0.233033i
$847$	−21.8582	+	6.05003i	−0.751056	+	0.207881i
$848$	9.03790	+	1.59363i	0.310363	+	0.0547253i
$849$	2.47751	−	20.3067i	0.0850280	−	0.696924i
$850$	26.2470	−	4.62805i	0.900265	−	0.158741i
$851$	42.2719	−	7.45369i	1.44906	−	0.255509i
$852$	0.784985	−	6.43405i	0.0268931	−	0.220427i
$853$	−27.4528	−	4.84068i	−0.939967	−	0.165742i	−0.317386	−	0.948297i	$-0.602805\pi$
$853$	−27.4528	−	4.84068i	−0.939967	−	0.165742i	−0.622582	+	0.782555i	$0.713916\pi$
$854$	3.68035	−	14.2015i	0.125939	−	0.485966i
$855$	−5.50869	−	2.44249i	−0.188393	−	0.0835314i
$856$	−5.29210	−	9.16619i	−0.180880	−	0.313294i
$857$	−4.39297	+	24.9138i	−0.150061	+	0.851038i	0.813102	+	0.582121i	$0.197777\pi$
$857$	−4.39297	+	24.9138i	−0.150061	+	0.851038i	−0.963163	+	0.268917i	$0.913334\pi$
$858$	−12.2549	+	24.0974i	−0.418376	+	0.822671i
$859$	10.3939	−	28.5571i	0.354636	−	0.974354i	−0.626225	−	0.779643i	$-0.715401\pi$
$859$	10.3939	−	28.5571i	0.354636	−	0.974354i	0.980861	−	0.194712i	$-0.0623771\pi$
$860$	−2.43256	+	2.04116i	−0.0829497	+	0.0696031i
$861$	15.1225	−	8.21610i	0.515374	−	0.280004i
$862$	−3.64657	+	1.32724i	−0.124203	+	0.0452061i
$863$	−35.3881	−	20.4314i	−1.20463	−	0.695492i	−0.243046	−	0.970015i	$-0.578147\pi$
$863$	−35.3881	−	20.4314i	−1.20463	−	0.695492i	−0.961580	+	0.274523i	$0.911480\pi$
$864$	5.10296	+	0.979713i	0.173606	+	0.0333305i
$865$	−1.71204	−	2.96534i	−0.0582111	−	0.100825i
$866$	1.38064	−	7.82999i	0.0469160	−	0.266074i
$867$	21.9056	−	5.07505i	0.743954	−	0.172358i
$868$	11.9037	−	5.67047i	0.404038	−	0.192468i
$869$	73.6539	−	12.9872i	2.49854	−	0.440560i
$870$	−0.356786	−	0.181447i	−0.0120962	−	0.00615161i
$871$	31.2768	+	5.51495i	1.05978	+	0.186867i
$872$		−	4.17212i		−	0.141286i
$873$	26.5250	+	25.5362i	0.897735	+	0.864270i
$874$	−23.8283	+	13.7573i	−0.806005	+	0.465347i
$875$	0.906448	+	9.46347i	0.0306435	+	0.319924i
$876$	6.07062	+	4.56723i	0.205107	+	0.154313i
$877$	39.7872	−	33.3854i	1.34352	−	1.12735i	0.362812	−	0.931862i	$-0.381817\pi$
$877$	39.7872	−	33.3854i	1.34352	−	1.12735i	0.980707	−	0.195484i	$-0.0626276\pi$
$878$	−2.64977	−	15.0276i	−0.0894255	−	0.507157i
$879$	−1.13272	−	2.66282i	−0.0382056	−	0.0898147i
$880$	1.03555	−	1.23412i	0.0349083	−	0.0416021i
$881$	−5.54571	−	9.60546i	−0.186840	−	0.323616i	0.757355	−	0.653003i	$-0.226491\pi$
$881$	−5.54571	−	9.60546i	−0.186840	−	0.323616i	−0.944195	+	0.329387i	$0.893158\pi$
$882$	1.08782	−	20.9718i	0.0366289	−	0.706157i
$883$	−10.9736	+	19.0069i	−0.369292	+	0.639633i	−0.989455	−	0.144840i	$-0.953733\pi$
$883$	−10.9736	+	19.0069i	−0.369292	+	0.639633i	0.620163	+	0.784473i	$0.287067\pi$
$884$	6.60727	+	18.1533i	0.222226	+	0.610562i
$885$	−0.337966	−	6.35534i	−0.0113606	−	0.213632i
$886$	14.6331	−	12.2786i	0.491608	−	0.412508i
$887$	3.62134	+	20.5376i	0.121593	+	0.689586i	0.983273	+	0.182135i	$0.0583009\pi$
$887$	3.62134	+	20.5376i	0.121593	+	0.689586i	−0.861681	+	0.507451i	$0.830588\pi$
$888$	−10.8926	+	10.1732i	−0.365533	+	0.341390i
$889$	−14.7826	+	10.5332i	−0.495793	+	0.353271i
$890$			0.257317i			0.00862530i
$891$	−29.5074	+	26.7332i	−0.988535	+	0.895597i
$892$	−22.0841	+	12.7502i	−0.739429	+	0.426910i
$893$	19.7632	−	23.5528i	0.661349	−	0.788165i
$894$	28.5165	−	6.60663i	0.953734	−	0.220959i
$895$	−4.87107	−	5.80512i	−0.162822	−	0.194044i
$896$	−0.208904	+	2.63749i	−0.00697898	+	0.0881124i
$897$	27.1703	+	13.8177i	0.907190	+	0.461359i
$898$	−31.3282	+	11.4025i	−1.04544	+	0.380508i
$899$	−3.16269			−0.105482
$900$	−0.996211	+	14.5682i	−0.0332070	+	0.485605i
$901$			50.2514i			1.67412i
$902$	2.88516	−	16.3626i	0.0960653	−	0.544813i
$903$	24.8848	+	31.2672i	0.828113	+	1.04051i
$904$	−8.59125	−	3.12696i	−0.285741	−	0.104001i
$905$	−5.05206	−	6.02081i	−0.167936	−	0.200139i
$906$	0.0658618	−	0.539830i	0.00218811	−	0.0179346i
$907$	−1.45854	+	0.530865i	−0.0484300	+	0.0176271i	−0.366122	−	0.930567i	$-0.619315\pi$
$907$	−1.45854	+	0.530865i	−0.0484300	+	0.0176271i	0.317692	+	0.948194i	$0.397092\pi$
$908$	14.5847			0.484010
$909$	29.3961	−	30.5343i	0.975006	−	1.01276i
$910$	−3.27597	+	0.906742i	−0.108597	+	0.0300582i
$911$	33.7086	−	40.1724i	1.11682	−	1.33097i	0.178995	−	0.983850i	$-0.442715\pi$
$911$	33.7086	−	40.1724i	1.11682	−	1.33097i	0.937821	−	0.347120i	$-0.112840\pi$
$912$	4.33082	−	8.51588i	0.143408	−	0.281989i
$913$	−1.63032	−	1.94293i	−0.0539556	−	0.0643017i
$914$	3.19594	−	8.78077i	0.105712	−	0.290442i
$915$	−3.34535	−	1.01997i	−0.110594	−	0.0337190i
$916$	2.38345	+	6.54847i	0.0787513	+	0.216367i
$917$	1.58741	−	6.12541i	0.0524209	−	0.202279i
$918$	−0.430983	+	28.4488i	−0.0142246	+	0.938950i
$919$	26.4651	−	45.8389i	0.873002	−	1.51208i	0.0141269	−	0.999900i	$-0.495503\pi$
$919$	26.4651	−	45.8389i	0.873002	−	1.51208i	0.858876	−	0.512184i	$-0.171164\pi$
$920$	−1.39149	−	1.16760i	−0.0458761	−	0.0384946i
$921$	−10.8663	−	46.9027i	−0.358057	−	1.54550i
$922$	16.0877	−	2.83670i	0.529820	−	0.0934216i
$923$	2.29267	+	13.0024i	0.0754641	+	0.427978i
$924$	−15.1876	−	13.4296i	−0.499635	−	0.441801i
$925$	−32.0853	−	26.9228i	−1.05496	−	0.885216i
$926$	−17.7474	+	10.2464i	−0.583214	+	0.336719i
$927$	−16.2696	+	11.8588i	−0.534365	+	0.389495i
$928$	0.317311	−	0.549598i	0.0104162	−	0.0180415i
$929$	27.9564	+	23.4582i	0.917219	+	0.769638i	0.973479	−	0.228778i	$-0.0734731\pi$
$929$	27.9564	+	23.4582i	0.917219	+	0.769638i	−0.0562599	+	0.998416i	$0.517918\pi$
$930$	−1.23040	−	2.89247i	−0.0403465	−	0.0948477i
$931$	−36.4953	−	12.6072i	−1.19608	−	0.413185i
$932$	−3.66217	+	10.0617i	−0.119959	+	0.329583i
$933$	10.2093	+	1.24559i	0.334239	+	0.0407787i
$934$	−0.633954	−	1.74177i	−0.0207436	−	0.0569926i
$935$	7.63950	+	4.41067i	0.249838	+	0.144244i
$936$	−10.5245	+	1.12253i	−0.344006	+	0.0366910i
$937$	43.3970	+	25.0553i	1.41772	+	0.818519i	0.996098	−	0.0882536i	$-0.0281286\pi$
$937$	43.3970	+	25.0553i	1.41772	+	0.818519i	0.421619	+	0.906773i	$0.361462\pi$
$938$	−9.88748	+	21.6673i	−0.322838	+	0.707464i
$939$	12.4250	+	19.1006i	0.405473	+	0.623325i
$940$	1.90738	+	0.694231i	0.0622120	+	0.0226433i
$941$	−16.7305	−	6.08940i	−0.545398	−	0.198509i	0.0546024	−	0.998508i	$-0.482611\pi$
$941$	−16.7305	−	6.08940i	−0.545398	−	0.198509i	−0.600001	+	0.799999i	$0.704833\pi$
$942$	16.3659	−	3.79161i	0.533229	−	0.123537i
$943$	−18.4491	−	3.25308i	−0.600786	−	0.105935i
$944$	10.0904			0.328415
$945$	−4.98406	−	0.470836i	−0.162132	−	0.0153163i
$946$	38.5788			1.25430
$947$	−28.9430	−	5.10343i	−0.940521	−	0.165839i	−0.317689	−	0.948195i	$-0.602907\pi$
$947$	−28.9430	−	5.10343i	−0.940521	−	0.165839i	−0.622832	+	0.782356i	$0.714018\pi$
$948$	19.9860	+	21.3994i	0.649115	+	0.695019i
$949$	−14.5411	−	5.29252i	−0.472024	−	0.171803i
$950$	25.2290	+	9.18262i	0.818538	+	0.297923i
$951$	36.3209	−	1.93148i	1.17779	−	0.0626326i
$952$	−14.4211	+	1.38131i	−0.467390	+	0.0447684i
$953$	−31.2086	−	18.0183i	−1.01095	−	0.583670i	−0.0994780	−	0.995040i	$-0.531717\pi$
$953$	−31.2086	−	18.0183i	−1.01095	−	0.583670i	−0.911469	+	0.411369i	$0.865051\pi$
$954$	−26.7244	−	6.61953i	−0.865233	−	0.214315i
$955$	2.84345	+	1.64166i	0.0920118	+	0.0531230i
$956$	7.26779	+	19.9681i	0.235057	+	0.645814i
$957$	1.90353	+	4.47487i	0.0615323	+	0.144652i
$958$	−11.6459	+	31.9967i	−0.376260	+	1.03377i
$959$	−50.5957	+	24.1018i	−1.63382	+	0.778289i
$960$	0.626086	+	0.0763855i	0.0202069	+	0.00246533i
$961$	4.72184	+	3.96210i	0.152317	+	0.127810i
$962$	15.1797	−	26.2921i	0.489415	−	0.847691i
$963$	13.9633	+	28.5176i	0.449960	+	0.918968i
$964$	3.83617	−	2.21482i	0.123555	−	0.0713344i
$965$	−0.111782	−	0.0937965i	−0.00359840	−	0.00301942i
$966$	−15.1421	+	17.1243i	−0.487191	+	0.550966i
$967$	9.90852	+	56.1940i	0.318636	+	1.80708i	0.551064	+	0.834463i	$0.314222\pi$
$967$	9.90852	+	56.1940i	0.318636	+	1.80708i	−0.232427	+	0.972614i	$0.574667\pi$
$968$	−8.44201	+	1.48855i	−0.271336	+	0.0478439i
$969$	50.0390	+	15.2564i	1.60749	+	0.490107i
$970$	3.42367	+	2.87280i	0.109928	+	0.0922402i
$971$	−23.0207	+	39.8730i	−0.738770	+	1.27959i	0.214280	+	0.976772i	$0.431259\pi$
$971$	−23.0207	+	39.8730i	−0.738770	+	1.27959i	−0.953050	+	0.302814i	$0.902074\pi$
$972$	−15.0727	−	3.97671i	−0.483456	−	0.127553i
$973$	14.7443	+	53.2698i	0.472681	+	1.70775i
$974$	0.749008	+	2.05788i	0.0239998	+	0.0659389i
$975$	−6.71315	−	28.9763i	−0.214993	−	0.927983i
$976$	1.89650	−	5.21058i	0.0607054	−	0.166787i
$977$	−19.5029	−	23.2426i	−0.623952	−	0.743597i	0.357792	−	0.933801i	$-0.383530\pi$
$977$	−19.5029	−	23.2426i	−0.623952	−	0.743597i	−0.981745	+	0.190204i	$0.939085\pi$
$978$	−4.46067	−	6.85729i	−0.142636	−	0.219272i
$979$	2.00944	−	2.39476i	0.0642219	−	0.0765367i
$980$	−0.0419356	−	2.54872i	−0.00133958	−	0.0814157i
$981$	−0.853910	+	12.4872i	−0.0272632	+	0.398686i
$982$	−33.8547			−1.08035
$983$	−43.8950	+	15.9765i	−1.40003	+	0.509570i	−0.928188	−	0.372111i	$-0.878634\pi$
$983$	−43.8950	+	15.9765i	−1.40003	+	0.509570i	−0.471845	+	0.881682i	$0.656412\pi$
$984$	5.98583	−	2.54626i	0.190821	−	0.0811719i
$985$	4.54302	+	5.41416i	0.144753	+	0.172510i
$986$	3.26537	+	1.18850i	0.103991	+	0.0378495i
$987$	9.35535	−	23.7686i	0.297784	−	0.756563i
$988$	−3.37930	+	19.1650i	−0.107510	+	0.609719i
$989$		−	43.4984i		−	1.38317i
$990$	−3.35199	+	3.48178i	−0.106533	+	0.110658i
$991$	8.27384			0.262827			0.131414	−	0.991328i	$-0.458048\pi$
$991$	8.27384			0.262827			0.131414	+	0.991328i	$0.458048\pi$
$992$	4.68303	−	1.70448i	0.148686	−	0.0541174i
$993$	0.0101395	+	0.190671i	0.000321768	+	0.00605075i
$994$	−9.87015	−	0.781769i	−0.313062	−	0.0247962i
$995$	1.57189	+	1.87331i	0.0498324	+	0.0593879i
$996$	0.289592	−	0.949823i	0.00917608	−	0.0300963i
$997$	3.13553	−	3.73678i	0.0993032	−	0.118345i	−0.714104	−	0.700040i	$-0.753166\pi$
$997$	3.13553	−	3.73678i	0.0993032	−	0.118345i	0.813407	+	0.581695i	$0.197610\pi$
$998$	7.41752	−	4.28251i	0.234797	−	0.135560i
$999$	34.6839	−	28.2191i	1.09735	−	0.892813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.ba.a.47.18	✓	144
7.3	odd	6		378.2.bf.a.101.2	yes	144
27.23	odd	18		378.2.bf.a.131.2	yes	144
189.185	even	18	inner	378.2.ba.a.185.18	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.47.18	✓	144	1.1	even	1	trivial
378.2.ba.a.185.18	yes	144	189.185	even	18	inner
378.2.bf.a.101.2	yes	144	7.3	odd	6
378.2.bf.a.131.2	yes	144	27.23	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.505130 + 1.65676i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.342190 - 0.124547i) q^{5} +(-0.785149 + 1.54387i) q^{6} +(2.40698 + 1.09838i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.48969 - 1.67375i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.505130 + 1.65676i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.342190 - 0.124547i) q^{5} +(-0.785149 + 1.54387i) q^{6} +(2.40698 + 1.09838i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.48969 - 1.67375i) q^{9} +(-0.315364 - 0.182076i) q^{10} +(1.51312 + 4.15725i) q^{11} +(-1.04131 + 1.38408i) q^{12} +(1.20667 - 3.31531i) q^{13} +(2.17968 + 1.49966i) q^{14} +(0.379195 - 0.504014i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-2.73780 + 4.74201i) q^{17} +(-2.16122 - 2.08066i) q^{18} +(-4.77693 + 2.75796i) q^{19} +(-0.278956 - 0.234072i) q^{20} +(-3.03559 + 3.43296i) q^{21} +(0.768229 + 4.35684i) q^{22} +(4.91243 - 0.866193i) q^{23} +(-1.26583 + 1.18223i) q^{24} +(-3.72864 - 3.12870i) q^{25} +(1.76404 - 3.05541i) q^{26} +(4.03062 - 3.27934i) q^{27} +(1.88615 + 1.85538i) q^{28} +(-0.217053 - 0.596349i) q^{29} +(0.460955 - 0.430510i) q^{30} +(1.70448 - 4.68303i) q^{31} +(0.642788 + 0.766044i) q^{32} +(-7.65187 + 0.406913i) q^{33} +(-3.51965 + 4.19455i) q^{34} +(-0.686846 - 0.675638i) q^{35} +(-1.76708 - 2.42434i) q^{36} +8.60510 q^{37} +(-5.18327 + 1.88656i) q^{38} +(4.88314 + 3.67383i) q^{39} +(-0.234072 - 0.278956i) q^{40} +(-3.52911 - 1.28449i) q^{41} +(-3.58560 + 2.85368i) q^{42} +(1.51425 - 8.58775i) q^{43} +4.42405i q^{44} +(0.643486 + 0.882826i) q^{45} +4.98821 q^{46} +(-5.23789 + 1.90644i) q^{47} +(-1.45189 + 0.944458i) q^{48} +(4.58712 + 5.28756i) q^{49} +(-3.12870 - 3.72864i) q^{50} +(-6.47341 - 6.93120i) q^{51} +(2.26781 - 2.70267i) q^{52} +(7.94780 - 4.58866i) q^{53} +(4.53884 - 2.52961i) q^{54} -1.61103i q^{55} +(1.53532 + 2.15472i) q^{56} +(-2.15630 - 9.30734i) q^{57} +(-0.110201 - 0.624980i) q^{58} +(7.72971 - 6.48600i) q^{59} +(0.528710 - 0.343926i) q^{60} +(-1.89650 - 5.21058i) q^{61} +(2.49179 - 4.31591i) q^{62} +(-4.15421 - 6.76332i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.825825 + 0.984180i) q^{65} +(-7.60628 - 0.928002i) q^{66} +(1.56316 + 8.86511i) q^{67} +(-4.19455 + 3.51965i) q^{68} +(-1.04634 + 8.57624i) q^{69} +(-0.559088 - 0.784643i) q^{70} +(-3.24088 + 1.87112i) q^{71} +(-1.31926 - 2.69436i) q^{72} -4.38604i q^{73} +(8.47437 + 1.49426i) q^{74} +(7.06694 - 4.59705i) q^{75} +(-5.43213 + 0.957830i) q^{76} +(-0.924200 + 11.6684i) q^{77} +(4.17100 + 4.46596i) q^{78} +(2.93558 - 16.6485i) q^{79} +(-0.182076 - 0.315364i) q^{80} +(3.39709 + 8.33425i) q^{81} +(-3.25244 - 1.87780i) q^{82} +(-0.538728 + 0.196081i) q^{83} +(-4.02666 + 2.18769i) q^{84} +(1.52745 - 1.28169i) q^{85} +(2.98250 - 8.19434i) q^{86} +(1.09765 - 0.0583709i) q^{87} +(-0.768229 + 4.35684i) q^{88} +(-0.353311 - 0.611952i) q^{89} +(0.480409 + 0.981154i) q^{90} +(6.54592 - 6.65451i) q^{91} +(4.91243 + 0.866193i) q^{92} +(6.89766 + 5.18946i) q^{93} +(-5.48936 + 0.967922i) q^{94} +(1.97812 - 0.348795i) q^{95} +(-1.59384 + 0.677991i) q^{96} +(-12.0867 - 2.13121i) q^{97} +(3.59926 + 6.00378i) q^{98} +(3.19103 - 12.8828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{6} + 24 q^{9}+O(q^{10}) \) 144 * q - 18 * q^6 + 24 * q^9	\( 144 q - 18 q^{6} + 24 q^{9} - 24 q^{11} + 6 q^{14} + 12 q^{15} - 30 q^{21} - 42 q^{23} - 6 q^{29} - 18 q^{30} + 6 q^{36} + 48 q^{39} - 48 q^{42} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 12 q^{50} - 36 q^{51} - 90 q^{53} + 6 q^{56} - 6 q^{57} + 18 q^{60} + 54 q^{61} - 24 q^{63} + 72 q^{64} + 78 q^{65} - 72 q^{66} - 54 q^{68} + 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} - 36 q^{74} - 6 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 36 q^{91} - 42 q^{92} + 96 q^{93} - 66 q^{95} - 108 q^{99}+O(q^{100}) \) 144 * q - 18 * q^6 + 24 * q^9 - 24 * q^11 + 6 * q^14 + 12 * q^15 - 30 * q^21 - 42 * q^23 - 6 * q^29 - 18 * q^30 + 6 * q^36 + 48 * q^39 - 48 * q^42 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 12 * q^50 - 36 * q^51 - 90 * q^53 + 6 * q^56 - 6 * q^57 + 18 * q^60 + 54 * q^61 - 24 * q^63 + 72 * q^64 + 78 * q^65 - 72 * q^66 - 54 * q^68 + 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 - 36 * q^74 - 6 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 36 * q^91 - 42 * q^92 + 96 * q^93 - 66 * q^95 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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