LMFDB - Embedded newform 729.2.k.a.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(4,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(486))

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

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

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

chi := DirichletCharacter("729.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.k (of order $243$, degree $162$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12960$
Relative dimension:	$80$ over $\Q(\zeta_{243})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{243}]$

Embedding invariants

Embedding label			4.4
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.61310 - 0.0337849i) q^{2} +(1.70554 - 0.301886i) q^{3} +(4.82780 + 0.124859i) q^{4} +(-2.59518 - 0.795260i) q^{5} +(-4.46694 + 0.731236i) q^{6} +(0.853432 - 2.12814i) q^{7} +(-7.38859 - 0.286711i) q^{8} +(2.81773 - 1.02976i) q^{9} +O(q^{10})$	\(q+(-2.61310 - 0.0337849i) q^{2} +(1.70554 - 0.301886i) q^{3} +(4.82780 + 0.124859i) q^{4} +(-2.59518 - 0.795260i) q^{5} +(-4.46694 + 0.731236i) q^{6} +(0.853432 - 2.12814i) q^{7} +(-7.38859 - 0.286711i) q^{8} +(2.81773 - 1.02976i) q^{9} +(6.75458 + 2.16577i) q^{10} +(0.0568816 + 0.0323522i) q^{11} +(8.27170 - 1.24449i) q^{12} +(1.14846 + 2.57054i) q^{13} +(-2.30200 + 5.53221i) q^{14} +(-4.66625 - 0.572899i) q^{15} +(9.65149 + 0.499557i) q^{16} +(4.95951 + 2.25437i) q^{17} +(-7.39779 + 2.59566i) q^{18} +(-0.279974 - 0.408212i) q^{19} +(-12.4297 - 4.16339i) q^{20} +(0.813104 - 3.88727i) q^{21} +(-0.147544 - 0.0864611i) q^{22} +(1.39790 - 4.26474i) q^{23} +(-12.6881 + 1.74152i) q^{24} +(1.96093 + 1.32636i) q^{25} +(-2.91420 - 6.75588i) q^{26} +(4.49488 - 2.60693i) q^{27} +(4.38591 - 10.1677i) q^{28} +(0.714812 - 0.457011i) q^{29} +(12.1740 + 1.65469i) q^{30} +(-2.27510 - 8.38233i) q^{31} +(-10.4460 - 0.676190i) q^{32} +(0.106781 + 0.0380062i) q^{33} +(-12.8835 - 6.05845i) q^{34} +(-3.90723 + 4.84421i) q^{35} +(13.7320 - 4.61965i) q^{36} +(-0.284650 - 0.0559034i) q^{37} +(0.717807 + 1.07616i) q^{38} +(2.73476 + 4.03746i) q^{39} +(18.9467 + 6.61991i) q^{40} +(2.93475 - 1.11134i) q^{41} +(-2.25605 + 10.1303i) q^{42} +(-9.06758 + 3.98109i) q^{43} +(0.270574 + 0.163292i) q^{44} +(-8.13143 + 0.431576i) q^{45} +(-3.79693 + 11.0969i) q^{46} +(3.26040 - 12.0125i) q^{47} +(16.6118 - 2.06164i) q^{48} +(1.25981 + 1.20405i) q^{49} +(-5.07929 - 3.53215i) q^{50} +(9.13920 + 2.34771i) q^{51} +(5.22360 + 12.5535i) q^{52} +(-5.68289 + 6.02352i) q^{53} +(-11.8336 + 6.66029i) q^{54} +(-0.121889 - 0.129195i) q^{55} +(-6.91582 + 15.4793i) q^{56} +(-0.600740 - 0.611701i) q^{57} +(-1.88331 + 1.17006i) q^{58} +(-0.184081 + 0.0312329i) q^{59} +(-22.4562 - 3.34846i) q^{60} +(5.12610 - 9.43383i) q^{61} +(5.66186 + 21.9807i) q^{62} +(0.213267 - 6.87536i) q^{63} +(8.00283 + 0.622029i) q^{64} +(-0.936217 - 7.58434i) q^{65} +(-0.277744 - 0.102921i) q^{66} +(-11.6383 + 6.03462i) q^{67} +(23.6620 + 11.5029i) q^{68} +(1.09671 - 7.69569i) q^{69} +(10.3736 - 12.5264i) q^{70} +(-0.561978 - 0.435566i) q^{71} +(-21.1143 + 6.80058i) q^{72} +(12.0193 - 3.85384i) q^{73} +(0.741929 + 0.155698i) q^{74} +(3.74485 + 1.67017i) q^{75} +(-1.30069 - 2.00572i) q^{76} +(0.117395 - 0.0934419i) q^{77} +(-7.00979 - 10.6427i) q^{78} +(3.14172 - 16.5625i) q^{79} +(-24.6500 - 8.97188i) q^{80} +(6.87920 - 5.80316i) q^{81} +(-7.70633 + 2.80488i) q^{82} +(-1.95457 - 11.9893i) q^{83} +(4.41086 - 18.6654i) q^{84} +(-11.0780 - 9.79459i) q^{85} +(23.8290 - 10.0966i) q^{86} +(1.08117 - 0.995243i) q^{87} +(-0.410999 - 0.255346i) q^{88} +(3.32409 + 1.35804i) q^{89} +(21.2628 - 0.853030i) q^{90} +(6.45062 - 0.250314i) q^{91} +(7.28127 - 20.4148i) q^{92} +(-6.41078 - 13.6096i) q^{93} +(-8.92559 + 31.2798i) q^{94} +(0.401947 + 1.28203i) q^{95} +(-18.0202 + 2.00023i) q^{96} +(-1.10415 + 4.79675i) q^{97} +(-3.25132 - 3.18887i) q^{98} +(0.193592 + 0.0325854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) $ 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{243}\right)$

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 $

$2$	−2.61310	−	0.0337849i	−1.84774	−	0.0238896i	−0.918924	−	0.394435i	$-0.870940\pi$
$2$	−2.61310	−	0.0337849i	−1.84774	−	0.0238896i	−0.928814	+	0.370545i	$0.879171\pi$
$3$	1.70554	−	0.301886i	0.984694	−	0.174294i
$3$	1.70554	−	0.301886i	0.984694	−	0.174294i
$4$	4.82780	+	0.124859i	2.41390	+	0.0624295i
$5$	−2.59518	−	0.795260i	−1.16060	−	0.355651i	−0.347445	−	0.937700i	$-0.612951\pi$
$5$	−2.59518	−	0.795260i	−1.16060	−	0.355651i	−0.813153	+	0.582050i	$0.802251\pi$
$6$	−4.46694	+	0.731236i	−1.82362	+	0.298526i
$7$	0.853432	−	2.12814i	0.322567	−	0.804363i	−0.675204	−	0.737631i	$-0.735944\pi$
$7$	0.853432	−	2.12814i	0.322567	−	0.804363i	0.997771	−	0.0667318i	$-0.0212572\pi$
$8$	−7.38859	−	0.286711i	−2.61226	−	0.101368i
$9$	2.81773	−	1.02976i	0.939243	−	0.343253i
$10$	6.75458	+	2.16577i	2.13598	+	0.684876i
$11$	0.0568816	+	0.0323522i	0.0171505	+	0.00975455i	0.502943	−	0.864320i	$-0.332251\pi$
$11$	0.0568816	+	0.0323522i	0.0171505	+	0.00975455i	−0.485792	+	0.874074i	$0.661469\pi$
$12$	8.27170	−	1.24449i	2.38783	−	0.359255i
$13$	1.14846	+	2.57054i	0.318527	+	0.712941i	0.999818	−	0.0190716i	$-0.00607105\pi$
$13$	1.14846	+	2.57054i	0.318527	+	0.712941i	−0.681291	+	0.732012i	$0.738581\pi$
$14$	−2.30200	+	5.53221i	−0.615235	+	1.47855i
$15$	−4.66625	−	0.572899i	−1.20482	−	0.147922i
$16$	9.65149	+	0.499557i	2.41287	+	0.124889i
$17$	4.95951	+	2.25437i	1.20286	+	0.546766i	0.912075	−	0.410024i	$-0.134480\pi$
$17$	4.95951	+	2.25437i	1.20286	+	0.546766i	0.290782	+	0.956789i	$0.406084\pi$
$18$	−7.39779	+	2.59566i	−1.74368	+	0.611803i
$19$	−0.279974	−	0.408212i	−0.0642304	−	0.0936502i	0.791229	−	0.611519i	$-0.209441\pi$
$19$	−0.279974	−	0.408212i	−0.0642304	−	0.0936502i	−0.855460	+	0.517869i	$0.826725\pi$
$20$	−12.4297	−	4.16339i	−2.77936	−	0.930961i
$21$	0.813104	−	3.88727i	0.177434	−	0.848272i
$22$	−0.147544	−	0.0864611i	−0.0314565	−	0.0184336i
$23$	1.39790	−	4.26474i	0.291482	−	0.889259i	−0.694073	−	0.719905i	$-0.744186\pi$
$23$	1.39790	−	4.26474i	0.291482	−	0.889259i	0.985555	−	0.169355i	$-0.0541684\pi$
$24$	−12.6881	+	1.74152i	−2.58994	+	0.355486i
$25$	1.96093	+	1.32636i	0.392186	+	0.265271i
$26$	−2.91420	−	6.75588i	−0.571522	−	1.32494i
$27$	4.49488	−	2.60693i	0.865040	−	0.501703i
$28$	4.38591	−	10.1677i	0.828860	−	1.92151i
$29$	0.714812	−	0.457011i	0.132737	−	0.0848648i	−0.470619	−	0.882336i	$-0.655969\pi$
$29$	0.714812	−	0.457011i	0.132737	−	0.0848648i	0.603357	+	0.797471i	$0.293830\pi$
$30$	12.1740	+	1.65469i	2.22266	+	0.302103i
$31$	−2.27510	−	8.38233i	−0.408620	−	1.50551i	−0.808253	−	0.588835i	$-0.799587\pi$
$31$	−2.27510	−	8.38233i	−0.408620	−	1.50551i	0.399633	−	0.916675i	$-0.369138\pi$
$32$	−10.4460	−	0.676190i	−1.84661	−	0.119535i
$33$	0.106781	+	0.0380062i	0.0185881	+	0.00661602i
$34$	−12.8835	−	6.05845i	−2.20950	−	1.03902i
$35$	−3.90723	+	4.84421i	−0.660443	+	0.818821i
$36$	13.7320	−	4.61965i	2.28867	−	0.769941i
$37$	−0.284650	−	0.0559034i	−0.0467961	−	0.00919046i	0.169259	−	0.985572i	$-0.445862\pi$
$37$	−0.284650	−	0.0559034i	−0.0467961	−	0.00919046i	−0.216056	+	0.976381i	$0.569319\pi$
$38$	0.717807	+	1.07616i	0.116444	+	0.174575i
$39$	2.73476	+	4.03746i	0.437913	+	0.646511i
$40$	18.9467	+	6.61991i	2.99573	+	1.04670i
$41$	2.93475	−	1.11134i	0.458331	−	0.173561i	−0.114177	−	0.993460i	$-0.536423\pi$
$41$	2.93475	−	1.11134i	0.458331	−	0.173561i	0.572508	+	0.819899i	$0.305970\pi$
$42$	−2.25605	+	10.1303i	−0.348116	+	1.56315i
$43$	−9.06758	+	3.98109i	−1.38279	+	0.607111i	−0.954957	−	0.296745i	$-0.904099\pi$
$43$	−9.06758	+	3.98109i	−1.38279	+	0.607111i	−0.427837	+	0.903856i	$0.640724\pi$
$44$	0.270574	+	0.163292i	0.0407905	+	0.0246172i
$45$	−8.13143	+	0.431576i	−1.21216	+	0.0643356i
$46$	−3.79693	+	11.0969i	−0.559827	+	1.63616i
$47$	3.26040	−	12.0125i	0.475578	−	1.75221i	−0.166967	−	0.985962i	$-0.553397\pi$
$47$	3.26040	−	12.0125i	0.475578	−	1.75221i	0.642545	−	0.766248i	$-0.277878\pi$
$48$	16.6118	−	2.06164i	2.39771	−	0.297572i
$49$	1.25981	+	1.20405i	0.179972	+	0.172008i
$50$	−5.07929	−	3.53215i	−0.718320	−	0.499521i
$51$	9.13920	+	2.34771i	1.27974	+	0.328746i
$52$	5.22360	+	12.5535i	0.724383	+	1.74085i
$53$	−5.68289	+	6.02352i	−0.780606	+	0.827394i	−0.988573	−	0.150742i	$-0.951834\pi$
$53$	−5.68289	+	6.02352i	−0.780606	+	0.827394i	0.207967	+	0.978136i	$0.433315\pi$
$54$	−11.8336	+	6.66029i	−1.61035	+	0.906351i
$55$	−0.121889	−	0.129195i	−0.0164356	−	0.0174207i
$56$	−6.91582	+	15.4793i	−0.924165	+	2.06851i
$57$	−0.600740	−	0.611701i	−0.0795699	−	0.0810217i
$58$	−1.88331	+	1.17006i	−0.247291	+	0.153637i
$59$	−0.184081	+	0.0312329i	−0.0239653	+	0.00406617i	−0.179249	−	0.983804i	$-0.557367\pi$
$59$	−0.184081	+	0.0312329i	−0.0239653	+	0.00406617i	0.155284	+	0.987870i	$0.450371\pi$
$60$	−22.4562	−	3.34846i	−2.89908	−	0.432285i
$61$	5.12610	−	9.43383i	0.656330	−	1.20788i	−0.310040	−	0.950723i	$-0.600343\pi$
$61$	5.12610	−	9.43383i	0.656330	−	1.20788i	0.966370	−	0.257155i	$-0.0827850\pi$
$62$	5.66186	+	21.9807i	0.719057	+	2.79155i
$63$	0.213267	−	6.87536i	0.0268691	−	0.866214i
$64$	8.00283	+	0.622029i	1.00035	+	0.0777536i
$65$	−0.936217	−	7.58434i	−0.116123	−	0.940722i
$66$	−0.277744	−	0.102921i	−0.0341879	−	0.0126687i
$67$	−11.6383	+	6.03462i	−1.42184	+	0.737246i	−0.986614	−	0.163074i	$-0.947859\pi$
$67$	−11.6383	+	6.03462i	−1.42184	+	0.737246i	−0.435228	+	0.900320i	$0.643332\pi$
$68$	23.6620	+	11.5029i	2.86944	+	1.39493i
$69$	1.09671	−	7.69569i	0.132028	−	0.926452i
$70$	10.3736	−	12.5264i	1.23989	−	1.49719i
$71$	−0.561978	−	0.435566i	−0.0666945	−	0.0516921i	0.578708	−	0.815535i	$-0.303557\pi$
$71$	−0.561978	−	0.435566i	−0.0666945	−	0.0516921i	−0.645402	+	0.763843i	$0.723310\pi$
$72$	−21.1143	+	6.80058i	−2.48834	+	0.801456i
$73$	12.0193	−	3.85384i	1.40675	−	0.451057i	0.497560	−	0.867430i	$-0.334230\pi$
$73$	12.0193	−	3.85384i	1.40675	−	0.451057i	0.909194	+	0.416372i	$0.136699\pi$
$74$	0.741929	+	0.155698i	0.0862475	+	0.0180995i
$75$	3.74485	+	1.67017i	0.432418	+	0.192855i
$76$	−1.30069	−	2.00572i	−0.149199	−	0.230072i
$77$	0.117395	−	0.0934419i	0.0133784	−	0.0106487i
$78$	−7.00979	−	10.6427i	−0.793703	−	1.20504i
$79$	3.14172	−	16.5625i	0.353471	−	1.86343i	−0.134996	−	0.990846i	$-0.543102\pi$
$79$	3.14172	−	16.5625i	0.353471	−	1.86343i	0.488467	−	0.872582i	$-0.337556\pi$
$80$	−24.6500	−	8.97188i	−2.75596	−	1.00309i
$81$	6.87920	−	5.80316i	0.764355	−	0.644795i
$82$	−7.70633	+	2.80488i	−0.851022	+	0.309747i
$83$	−1.95457	−	11.9893i	−0.214542	−	1.31600i	−0.842899	−	0.538072i	$-0.819153\pi$
$83$	−1.95457	−	11.9893i	−0.214542	−	1.31600i	0.628357	−	0.777925i	$-0.283728\pi$
$84$	4.41086	−	18.6654i	0.481265	−	2.03657i
$85$	−11.0780	−	9.79459i	−1.20158	−	1.06237i
$86$	23.8290	−	10.0966i	2.56954	−	1.08875i
$87$	1.08117	−	0.995243i	0.115914	−	0.106701i
$88$	−0.410999	−	0.255346i	−0.0438127	−	0.0272199i
$89$	3.32409	+	1.35804i	0.352353	+	0.143952i	0.547464	−	0.836829i	$-0.315593\pi$
$89$	3.32409	+	1.35804i	0.352353	+	0.143952i	−0.195111	+	0.980781i	$0.562507\pi$
$90$	21.2628	−	0.853030i	2.24129	−	0.0899172i
$91$	6.45062	−	0.250314i	0.676209	−	0.0262400i
$92$	7.28127	−	20.4148i	0.759125	−	2.12839i
$93$	−6.41078	−	13.6096i	−0.664767	−	1.41125i
$94$	−8.92559	+	31.2798i	−0.920604	+	3.22626i
$95$	0.401947	+	1.28203i	0.0412389	+	0.131534i
$96$	−18.0202	+	2.00023i	−1.83918	+	0.204148i
$97$	−1.10415	+	4.79675i	−0.112110	+	0.487036i	0.887544	+	0.460723i	$0.152410\pi$
$97$	−1.10415	+	4.79675i	−0.112110	+	0.487036i	−0.999654	+	0.0263133i	$0.991623\pi$
$98$	−3.25132	−	3.18887i	−0.328433	−	0.322125i
$99$	0.193592	+	0.0325854i	0.0194567	+	0.00327496i
$100$	9.30137	+	6.64822i	0.930137	+	0.664822i
$101$	0.762544	−	5.09105i	0.0758760	−	0.506578i	−0.918044	−	0.396477i	$-0.870232\pi$
$101$	0.762544	−	5.09105i	0.0758760	−	0.506578i	0.993920	−	0.110101i	$-0.0351173\pi$
$102$	−23.8023	−	6.44357i	−2.35678	−	0.638009i
$103$	2.70533	+	7.58502i	0.266564	+	0.747375i	0.997864	+	0.0653194i	$0.0208066\pi$
$103$	2.70533	+	7.58502i	0.266564	+	0.747375i	−0.731301	+	0.682055i	$0.761086\pi$
$104$	−7.74853	−	19.3220i	−0.759806	−	1.89468i
$105$	−5.20154	+	9.44153i	−0.507618	+	0.921399i
$106$	15.0535	−	15.5480i	1.46212	−	1.51016i
$107$	0.0673438	+	1.15625i	0.00651037	+	0.111779i	0.999998	−	0.00216429i	$-0.000688916\pi$
$107$	0.0673438	+	1.15625i	0.00651037	+	0.111779i	−0.993487	+	0.113943i	$0.963652\pi$
$108$	22.0259	−	12.0245i	2.11944	−	1.15706i
$109$	0.419787	−	7.20746i	0.0402083	−	0.690349i	−0.916632	−	0.399733i	$-0.869103\pi$
$109$	0.419787	−	7.20746i	0.0402083	−	0.690349i	0.956840	−	0.290616i	$-0.0938602\pi$
$110$	0.314144	+	0.341718i	0.0299525	+	0.0325815i
$111$	−0.502358	−	0.00941359i	−0.0476817	−	0.000893499i
$112$	9.30002	−	20.1134i	0.878769	−	1.90054i
$113$	2.14795	−	1.57762i	0.202063	−	0.148410i	−0.486260	−	0.873814i	$-0.661639\pi$
$113$	2.14795	−	1.57762i	0.202063	−	0.148410i	0.688323	+	0.725404i	$0.258347\pi$
$114$	1.54912	+	1.61873i	0.145089	+	0.151608i
$115$	−7.01937	+	9.95605i	−0.654560	+	0.928407i
$116$	3.50803	−	2.11711i	0.325713	−	0.196569i
$117$	5.88310	+	6.06046i	0.543893	+	0.560290i
$118$	0.482076	−	0.0753953i	0.0443787	−	0.00694070i
$119$	9.03023	−	8.63059i	0.827800	−	0.791165i
$120$	34.3128	+	5.57078i	3.13231	+	0.508540i
$121$	−5.62051	−	9.45070i	−0.510955	−	0.859154i
$122$	−13.7137	+	24.4783i	−1.24158	+	2.21616i
$123$	4.66984	−	2.78139i	0.421065	−	0.250789i
$124$	−9.93712	−	40.7523i	−0.892380	−	3.65966i
$125$	4.48616	+	5.56197i	0.401255	+	0.497478i
$126$	−0.789571	+	17.9588i	−0.0703405	+	1.59989i
$127$	0.236438	+	12.1907i	0.0209805	+	1.08175i	0.851370	+	0.524566i	$0.175773\pi$
$127$	0.236438	+	12.1907i	0.0209805	+	1.08175i	−0.830389	+	0.557184i	$0.811882\pi$
$128$	−0.0411157	−	0.00373110i	−0.00363415	−	0.000329786i
$129$	−14.2633	+	9.52729i	−1.25581	+	0.838831i
$130$	2.19019	+	19.8502i	0.192092	+	1.74098i
$131$	−16.0429	+	1.45584i	−1.40167	+	0.127197i	−0.765047	−	0.643975i	$-0.777284\pi$
$131$	−16.0429	+	1.45584i	−1.40167	+	0.127197i	−0.636627	+	0.771172i	$0.719671\pi$
$132$	0.510770	+	0.196819i	0.0444568	+	0.0171309i
$133$	−1.10767	+	0.247444i	−0.0960473	+	0.0214561i
$134$	30.6158	−	15.3758i	2.64480	−	1.32827i
$135$	−13.7382	+	3.19084i	−1.18239	+	0.274623i
$136$	−35.9974	−	18.0786i	−3.08675	−	1.55023i
$137$	−13.3356	−	3.34326i	−1.13934	−	0.285634i	−0.372850	−	0.927892i	$-0.621619\pi$
$137$	−13.3356	−	3.34326i	−1.13934	−	0.285634i	−0.766489	+	0.642258i	$0.777998\pi$
$138$	−3.12580	+	20.0725i	−0.266086	+	1.70869i
$139$	17.4087	+	2.49255i	1.47658	+	0.211415i	0.832707	−	0.553713i	$-0.186790\pi$
$139$	17.4087	+	2.49255i	1.47658	+	0.211415i	0.643878	+	0.765129i	$0.277325\pi$
$140$	−19.4682	+	22.8990i	−1.64536	+	1.93532i
$141$	1.93432	−	21.4721i	0.162899	−	1.80828i
$142$	1.45379	+	1.15716i	0.121999	+	0.0971068i
$143$	−0.0178362	+	0.183372i	−0.00149154	+	0.0153343i
$144$	27.7097	−	8.53108i	2.30914	−	0.710923i
$145$	−2.21851	+	0.617563i	−0.184237	+	0.0512858i
$146$	−31.5378	+	9.66437i	−2.61009	+	0.799829i
$147$	2.51214	+	1.67324i	0.207198	+	0.138007i
$148$	−1.36725	−	0.305432i	−0.112387	−	0.0251063i
$149$	13.6094	−	3.41190i	1.11493	−	0.279514i	0.358459	−	0.933545i	$-0.383302\pi$
$149$	13.6094	−	3.41190i	1.11493	−	0.279514i	0.756467	+	0.654031i	$0.226924\pi$
$150$	−9.72924	−	4.49085i	−0.794389	−	0.366676i
$151$	5.28502	+	6.21638i	0.430088	+	0.505882i	0.933704	−	0.358046i	$-0.116557\pi$
$151$	5.28502	+	6.21638i	0.430088	+	0.505882i	−0.503616	+	0.863928i	$0.667997\pi$
$152$	1.95157	+	3.09638i	0.158293	+	0.251150i
$153$	16.2960	+	1.24512i	1.31745	+	0.100662i
$154$	−0.309921	+	0.240207i	−0.0249741	+	0.0193564i
$155$	−0.761840	+	23.5629i	−0.0611925	+	1.89262i
$156$	12.6988	+	19.8335i	1.01672	+	1.58795i
$157$	−0.964664	+	7.81479i	−0.0769885	+	0.623688i	0.903708	+	0.428150i	$0.140835\pi$
$157$	−0.964664	+	7.81479i	−0.0769885	+	0.623688i	−0.980696	+	0.195538i	$0.937355\pi$
$158$	−8.76918	+	43.1733i	−0.697638	+	3.43468i
$159$	−7.87398	+	11.9889i	−0.624448	+	0.950784i
$160$	26.5714	+	10.0621i	2.10066	+	0.795479i
$161$	−7.88296	−	6.61459i	−0.621265	−	0.521303i
$162$	−18.1721	+	14.9318i	−1.42773	+	1.17315i
$163$	−16.7326	+	14.0403i	−1.31060	+	1.09972i	−0.322388	+	0.946607i	$0.604486\pi$
$163$	−16.7326	+	14.0403i	−1.31060	+	1.09972i	−0.988209	+	0.153114i	$0.951070\pi$
$164$	14.3072	−	4.99888i	1.11720	−	0.390347i
$165$	−0.246890	−	0.183551i	−0.0192203	−	0.0142894i
$166$	4.70242	+	31.3952i	0.364979	+	2.43674i
$167$	−5.52638	+	10.8288i	−0.427644	+	0.837959i	0.572197	+	0.820116i	$0.306091\pi$
$167$	−5.52638	+	10.8288i	−0.427644	+	0.837959i	−0.999841	+	0.0178424i	$0.994320\pi$
$168$	−7.12221	+	28.4883i	−0.549491	+	2.19792i
$169$	3.38496	−	3.77899i	0.260382	−	0.290691i
$170$	28.6169	+	25.9685i	2.19482	+	1.99169i
$171$	−1.20925	−	0.861925i	−0.0924736	−	0.0659130i
$172$	−44.2736	+	18.0877i	−3.37583	+	1.37918i
$173$	10.7941	+	1.83143i	0.820662	+	0.139241i	0.562433	−	0.826843i	$-0.309865\pi$
$173$	10.7941	+	1.83143i	0.820662	+	0.139241i	0.258228	+	0.966084i	$0.416861\pi$
$174$	−2.85884	+	2.56414i	−0.216728	+	0.194387i
$175$	4.49620	−	3.04119i	0.339881	−	0.229892i
$176$	0.532831	+	0.340663i	0.0401636	+	0.0256784i
$177$	−0.304528	+	0.108840i	−0.0228897	+	0.00818094i
$178$	−8.64030	−	3.66100i	−0.647618	−	0.274403i
$179$	0.373499	+	0.781107i	0.0279166	+	0.0583827i	0.915653	−	0.401969i	$-0.131674\pi$
$179$	0.373499	+	0.781107i	0.0279166	+	0.0583827i	−0.887737	+	0.460352i	$0.847723\pi$
$180$	−39.3108	+	1.06828i	−2.93005	+	0.0796250i
$181$	13.2544	+	3.68961i	0.985191	+	0.274247i	0.723060	−	0.690786i	$-0.242735\pi$
$181$	13.2544	+	3.68961i	0.985191	+	0.274247i	0.262131	+	0.965032i	$0.415575\pi$
$182$	−16.8646	+	0.436159i	−1.25008	+	0.0323303i
$183$	5.89482	−	17.6373i	0.435758	−	1.30378i
$184$	−11.5512	+	31.1096i	−0.851569	+	2.29343i
$185$	0.694259	+	0.371450i	0.0510429	+	0.0273095i
$186$	16.2922	+	35.7797i	1.19460	+	2.62350i
$187$	0.209171	+	0.288683i	0.0152961	+	0.0211106i
$188$	17.2404	−	57.5871i	1.25739	−	4.19997i
$189$	−1.71184	−	11.7906i	−0.124518	−	0.857639i
$190$	−1.00701	−	3.36365i	−0.0730563	−	0.244025i
$191$	−1.49447	+	1.95417i	−0.108136	+	0.141399i	−0.845252	−	0.534368i	$-0.820550\pi$
$191$	−1.49447	+	1.95417i	−0.108136	+	0.141399i	0.737115	+	0.675767i	$0.236187\pi$
$192$	13.8369	−	1.35505i	0.998594	−	0.0977922i
$193$	22.7530	−	10.6996i	1.63780	−	0.770173i	0.637799	−	0.770202i	$-0.279845\pi$
$193$	22.7530	−	10.6996i	1.63780	−	0.770173i	1.00000		2.97435e-5i	$9.46764e-6\pi$
$194$	3.04731	−	12.4971i	0.218784	−	0.897237i
$195$	−3.88636	−	12.6528i	−0.278308	−	0.906083i
$196$	5.93176	+	5.97023i	0.423697	+	0.426445i
$197$	−6.73049	+	1.32182i	−0.479527	+	0.0941761i	−0.426635	−	0.904424i	$-0.640301\pi$
$197$	−6.73049	+	1.32182i	−0.479527	+	0.0941761i	−0.0528927	+	0.998600i	$0.516844\pi$
$198$	−0.504774	−	0.0916893i	−0.0358727	−	0.00651607i
$199$	−14.6121	+	8.06261i	−1.03582	+	0.571543i	−0.907440	−	0.420182i	$-0.861966\pi$
$199$	−14.6121	+	8.06261i	−1.03582	+	0.571543i	−0.128383	+	0.991725i	$0.540979\pi$
$200$	−14.1082	−	10.3621i	−0.997602	−	0.732713i
$201$	−18.0278	+	13.8057i	−1.27158	+	0.973780i
$202$	−2.16460	+	13.2776i	−0.152301	+	0.934211i
$203$	−0.362542	−	1.91125i	−0.0254455	−	0.134143i
$204$	43.8291	+	12.4754i	3.06865	+	0.873453i
$205$	−8.50000	+	0.550222i	−0.593666	+	0.0384292i
$206$	−6.81302	−	19.9118i	−0.474685	−	1.38732i
$207$	−0.452746	−	13.4564i	−0.0314680	−	0.935283i
$208$	9.80026	+	25.3833i	0.679526	+	1.76002i
$209$	−0.00271882	−	0.0322775i	−0.000188065	−	0.00223268i
$210$	13.9111	−	24.4959i	0.959957	−	1.69038i
$211$	10.4361	−	15.6461i	0.718453	−	1.07712i	−0.274838	−	0.961490i	$-0.588624\pi$
$211$	10.4361	−	15.6461i	0.718453	−	1.07712i	0.993292	−	0.115634i	$-0.0368900\pi$
$212$	−28.1880	+	28.3708i	−1.93596	+	1.94851i
$213$	−1.08997	−	0.573221i	−0.0746833	−	0.0392765i
$214$	−0.136912	−	3.02366i	−0.00935911	−	0.206693i
$215$	26.6980	−	3.12055i	1.82079	−	0.212819i
$216$	−33.9582	+	17.9728i	−2.31057	+	1.22289i
$217$	−19.7804	−	2.31200i	−1.34278	−	0.156949i
$218$	−1.34045	+	18.8196i	−0.0907865	+	1.27462i
$219$	19.3360	−	10.2013i	1.30660	−	0.689342i
$220$	−0.572327	−	0.638948i	−0.0385863	−	0.0430779i
$221$	−0.0991471	+	15.3377i	−0.00666935	+	1.03173i
$222$	1.31239	+	0.0415708i	0.0880820	+	0.00279005i
$223$	4.48213	−	3.96287i	0.300146	−	0.265374i	−0.498879	−	0.866672i	$-0.666255\pi$
$223$	4.48213	−	3.96287i	0.300146	−	0.265374i	0.799025	+	0.601298i	$0.205350\pi$
$224$	−10.3540	+	21.6535i	−0.691803	+	1.44678i
$225$	6.89120	+	1.71803i	0.459413	+	0.114535i
$226$	−5.66611	+	4.04989i	−0.376904	+	0.269395i
$227$	−1.31184	−	2.57052i	−0.0870699	−	0.170611i	0.843084	−	0.537783i	$-0.180738\pi$
$227$	−1.31184	−	2.57052i	−0.0870699	−	0.170611i	−0.930153	+	0.367171i	$0.880326\pi$
$228$	−2.82387	−	3.02818i	−0.187016	−	0.200546i
$229$	2.48363	+	3.24759i	0.164123	+	0.214606i	0.869117	−	0.494607i	$-0.164688\pi$
$229$	2.48363	+	3.24759i	0.164123	+	0.214606i	−0.704994	+	0.709214i	$0.749050\pi$
$230$	18.6787	−	25.7790i	1.23163	−	1.69982i
$231$	0.172012	−	0.194809i	0.0113176	−	0.0128175i
$232$	−5.41248	+	3.17172i	−0.355347	+	0.208234i
$233$	3.89450	+	17.9790i	0.255137	+	1.17785i	0.907538	+	0.419971i	$0.137960\pi$
$233$	3.89450	+	17.9790i	0.255137	+	1.17785i	−0.652400	+	0.757875i	$0.726238\pi$
$234$	−15.1684	−	16.0353i	−0.991586	−	1.04826i
$235$	−18.0144	+	28.5818i	−1.17513	+	1.86447i
$236$	−0.892605	+	0.127802i	−0.0581036	+	0.00831919i
$237$	0.358330	−	29.1965i	0.0232760	−	1.89651i
$238$	−23.8884	+	22.2475i	−1.54846	+	1.44209i
$239$	9.44193	+	17.3765i	0.610748	+	1.12399i	0.980807	+	0.194982i	$0.0624650\pi$
$239$	9.44193	+	17.3765i	0.610748	+	1.12399i	−0.370059	+	0.929008i	$0.620663\pi$
$240$	−44.7501	−	7.86039i	−2.88861	−	0.507386i
$241$	−14.1365	+	23.7700i	−0.910611	+	1.53116i	−0.0646573	+	0.997908i	$0.520595\pi$
$241$	−14.1365	+	23.7700i	−0.910611	+	1.53116i	−0.845954	+	0.533256i	$0.820968\pi$
$242$	14.3676	+	24.8855i	0.923587	+	1.59970i
$243$	9.98085	−	11.9742i	0.640272	−	0.768148i
$244$	25.9257	−	44.9046i	1.65972	−	2.87472i
$245$	−2.31189	−	4.12661i	−0.147701	−	0.263639i
$246$	−12.2967	+	7.11026i	−0.784009	+	0.453334i
$247$	0.727786	−	1.18850i	0.0463079	−	0.0756225i
$248$	14.4065	+	62.5859i	0.914812	+	3.97421i
$249$	−6.95300	−	19.8582i	−0.440629	−	1.25846i
$250$	−11.5349	−	14.6855i	−0.729529	−	0.928794i
$251$	12.6813	+	24.0749i	0.800439	+	1.51960i	0.853552	+	0.521008i	$0.174444\pi$
$251$	12.6813	+	24.0749i	0.800439	+	1.51960i	−0.0531129	+	0.998589i	$0.516914\pi$
$252$	1.88806	−	33.1662i	0.118937	−	2.08928i
$253$	0.217488	−	0.197360i	0.0136734	−	0.0124079i
$254$	−0.205974	−	31.8635i	−0.0129240	−	1.99929i
$255$	−21.8508	−	13.3608i	−1.36835	−	0.836684i
$256$	−15.8608	−	1.64631i	−0.991302	−	0.102894i
$257$	0.947785	−	0.123220i	0.0591212	−	0.00768628i	−0.0993059	−	0.995057i	$-0.531662\pi$
$257$	0.947785	−	0.123220i	0.0591212	−	0.00768628i	0.158427	+	0.987371i	$0.449358\pi$
$258$	37.5932	−	24.4138i	2.34045	−	1.51994i
$259$	−0.361900	+	0.558066i	−0.0224873	+	0.0346765i
$260$	−3.57290	−	36.7326i	−0.221582	−	2.27806i
$261$	1.54354	−	2.02382i	0.0955425	−	0.125271i
$262$	41.9708	−	3.26223i	2.59296	−	0.201541i
$263$	−2.19479	−	10.8056i	−0.135336	−	0.666302i	−0.989291	−	0.145955i	$-0.953375\pi$
$263$	−2.19479	−	10.8056i	−0.135336	−	0.666302i	0.853955	−	0.520347i	$-0.174197\pi$
$264$	−0.778061	−	0.311427i	−0.0478863	−	0.0191670i
$265$	19.5384	−	11.1127i	1.20023	−	0.682648i
$266$	2.90281	−	0.609171i	0.177983	−	0.0373507i
$267$	6.07935	+	1.31270i	0.372050	+	0.0803357i
$268$	−56.9408	+	27.6808i	−3.47821	+	1.69087i
$269$	10.3638	−	13.9210i	0.631892	−	0.848778i	−0.364712	−	0.931120i	$-0.618833\pi$
$269$	10.3638	−	13.9210i	0.631892	−	0.848778i	0.996604	+	0.0823423i	$0.0262401\pi$
$270$	36.0070	−	7.87382i	2.19132	−	0.479185i
$271$	−10.7046	−	14.3788i	−0.650261	−	0.873452i	0.347679	−	0.937614i	$-0.386970\pi$
$271$	−10.7046	−	14.3788i	−0.650261	−	0.873452i	−0.997940	+	0.0641619i	$0.979563\pi$
$272$	46.7405	+	24.2356i	2.83406	+	1.46950i
$273$	10.9262	−	2.37427i	0.661285	−	0.143698i
$274$	34.7343	+	9.18680i	2.09838	+	0.554995i
$275$	0.0686304	+	0.138886i	0.00413857	+	0.00837512i
$276$	6.25555	−	37.0163i	0.376540	−	2.22812i
$277$	−1.17146	+	0.814635i	−0.0703862	+	0.0489467i	−0.605594	−	0.795774i	$-0.707065\pi$
$277$	−1.17146	+	0.814635i	−0.0703862	+	0.0489467i	0.535208	+	0.844720i	$0.320233\pi$
$278$	−45.4063	−	7.10142i	−2.72329	−	0.425915i
$279$	−15.0424	−	21.2763i	−0.900564	−	1.27378i
$280$	30.2578	−	34.6716i	1.80825	−	2.07203i
$281$	−9.91285	+	20.0604i	−0.591351	+	1.19670i	0.371943	+	0.928255i	$0.378692\pi$
$281$	−9.91285	+	20.0604i	−0.591351	+	1.19670i	−0.963294	+	0.268447i	$0.913490\pi$
$282$	−5.78000	+	56.0434i	−0.344194	+	3.33734i
$283$	−22.0215	+	18.9687i	−1.30904	+	1.12757i	−0.325763	+	0.945451i	$0.605621\pi$
$283$	−22.0215	+	18.9687i	−1.30904	+	1.12757i	−0.983276	+	0.182121i	$0.941704\pi$
$284$	−2.65873	−	2.17299i	−0.157767	−	0.128943i
$285$	1.07256	+	2.06522i	0.0635332	+	0.122333i
$286$	0.0528029	−	0.478566i	0.00312230	−	0.0282982i
$287$	0.139528	−	7.19402i	0.00823607	−	0.424650i
$288$	−30.1303	+	8.85152i	−1.77544	+	0.521581i
$289$	8.33665	+	9.55274i	0.490391	+	0.561926i
$290$	5.81803	−	1.53880i	0.341647	−	0.0903615i
$291$	−0.435101	+	8.51437i	−0.0255061	+	0.499121i
$292$	58.5080	−	17.1048i	3.42392	−	1.00098i
$293$	−0.266315	+	3.16165i	−0.0155583	+	0.184706i	0.984403	+	0.175927i	$0.0562923\pi$
$293$	−0.266315	+	3.16165i	−0.0155583	+	0.184706i	−0.999961	+	0.00877866i	$0.997206\pi$
$294$	−6.50793	−	4.45722i	−0.379550	−	0.259950i
$295$	0.502560	+	0.0653372i	0.0292602	+	0.00380408i
$296$	2.08713	+	0.494659i	0.121312	+	0.0287515i
$297$	0.340016	−	0.00286707i	0.0197297	−	0.000166364i
$298$	−35.6780	+	8.45584i	−2.06677	+	0.489833i
$299$	12.5681	−	1.30454i	0.726834	−	0.0754434i
$300$	17.8709	+	8.53085i	1.03177	+	0.492529i
$301$	0.733769	+	22.6947i	0.0422938	+	1.30810i
$302$	−13.6002	−	16.4226i	−0.782606	−	0.945012i
$303$	−0.236368	−	8.91318i	−0.0135790	−	0.512049i
$304$	−2.49824	−	4.07971i	−0.143284	−	0.233988i
$305$	−20.8055	+	20.4059i	−1.19132	+	1.16844i
$306$	−42.5410	−	3.80418i	−2.43191	−	0.217471i
$307$	0.764443	−	1.11459i	0.0436291	−	0.0636127i	−0.802247	−	0.596992i	$-0.796362\pi$
$307$	0.764443	−	1.11459i	0.0436291	−	0.0636127i	0.845876	+	0.533380i	$0.179078\pi$
$308$	0.578425	−	0.436461i	0.0329588	−	0.0248697i
$309$	6.90385	+	12.1199i	0.392747	+	0.689474i
$310$	2.78683	−	61.5464i	0.158282	−	3.49560i
$311$	0.567028	+	7.96096i	0.0321532	+	0.451425i	0.987677	+	0.156509i	$0.0500240\pi$
$311$	0.567028	+	7.96096i	0.0321532	+	0.451425i	−0.955523	+	0.294916i	$0.904708\pi$
$312$	−19.0485	−	30.6152i	−1.07841	−	1.73324i
$313$	−3.80318	−	10.2426i	−0.214968	−	0.578949i	0.784166	−	0.620551i	$-0.213091\pi$
$313$	−3.80318	−	10.2426i	−0.214968	−	0.578949i	−0.999134	+	0.0416025i	$0.986754\pi$
$314$	2.78478	−	20.3882i	0.157154	−	1.15057i
$315$	−6.02116	+	17.6732i	−0.339254	+	0.995770i
$316$	17.2356	−	79.5682i	0.969576	−	4.47606i
$317$	5.43585	+	16.5838i	0.305308	+	0.931438i	0.980959	+	0.194217i	$0.0622165\pi$
$317$	5.43585	+	16.5838i	0.305308	+	0.931438i	−0.675651	+	0.737222i	$0.736137\pi$
$318$	20.9805	−	31.0622i	1.17653	−	1.74188i
$319$	0.0554450	−	0.00286981i	0.00310432	−	0.000160679i
$320$	−20.2741	−	7.97860i	−1.13335	−	0.446017i
$321$	0.463913	+	1.95170i	0.0258931	+	0.108933i
$322$	20.3755	+	17.5509i	1.13548	+	0.978073i
$323$	−0.468270	−	2.65569i	−0.0260553	−	0.147767i
$324$	33.9360	−	27.1576i	1.88533	−	1.50875i
$325$	−1.15740	+	6.56393i	−0.0642009	+	0.364101i
$326$	44.1982	−	36.1234i	2.44791	−	2.00069i
$327$	−1.45987	−	12.4193i	−0.0807310	−	0.686791i
$328$	−22.0023	+	7.36978i	−1.21487	+	0.406928i
$329$	−22.7819	−	17.1905i	−1.25601	−	0.947742i
$330$	0.638945	+	0.487977i	0.0351728	+	0.0268623i
$331$	−13.9898	+	7.48496i	−0.768948	+	0.411411i	−0.809016	−	0.587786i	$-0.800000\pi$
$331$	−13.9898	+	7.48496i	−0.768948	+	0.411411i	0.0400683	+	0.999197i	$0.487242\pi$
$332$	−7.93931	−	58.1260i	−0.435726	−	3.19008i
$333$	−0.859633	+	0.135600i	−0.0471076	+	0.00743082i
$334$	14.8068	−	28.1100i	0.810192	−	1.53811i
$335$	35.0025	−	6.40545i	1.91239	−	0.349967i
$336$	9.78958	−	37.1118i	0.534065	−	2.02461i
$337$	18.1762	+	18.7733i	0.990118	+	1.02265i	0.999742	+	0.0226945i	$0.00722451\pi$
$337$	18.1762	+	18.7733i	0.990118	+	1.02265i	−0.00962431	+	0.999954i	$0.503064\pi$
$338$	−8.97290	+	9.76049i	−0.488062	+	0.530901i
$339$	3.18716	−	3.33912i	0.173103	−	0.181356i
$340$	−52.2593	−	48.6695i	−2.83416	−	2.63947i
$341$	0.141775	−	0.550405i	0.00767756	−	0.0298061i
$342$	3.13076	+	2.29315i	0.169292	+	0.123999i
$343$	18.2491	−	8.29523i	0.985358	−	0.447900i
$344$	68.1381	−	26.8149i	3.67376	−	1.44576i
$345$	−8.96621	+	19.0995i	−0.482725	+	1.02828i
$346$	−28.1442	−	5.15038i	−1.51304	−	0.276886i
$347$	−4.18541	+	5.32862i	−0.224685	+	0.286055i	−0.885643	−	0.464367i	$-0.846282\pi$
$347$	−4.18541	+	5.32862i	−0.224685	+	0.286055i	0.660958	+	0.750423i	$0.270150\pi$
$348$	5.34396	−	4.66984i	0.286466	−	0.250330i
$349$	−0.631974	−	2.21476i	−0.0338288	−	0.118553i	0.942874	−	0.333149i	$-0.108111\pi$
$349$	−0.631974	−	2.21476i	−0.0338288	−	0.118553i	−0.976703	+	0.214596i	$0.931157\pi$
$350$	−11.8517	+	7.79501i	−0.633502	+	0.416661i
$351$	11.8634	+	8.56032i	0.633223	+	0.456916i
$352$	−0.572309	−	0.376413i	−0.0305042	−	0.0200629i
$353$	−7.92696	+	25.2835i	−0.421909	+	1.34571i	0.465632	+	0.884978i	$0.345827\pi$
$353$	−7.92696	+	25.2835i	−0.421909	+	1.34571i	−0.887542	+	0.460727i	$0.847589\pi$
$354$	0.799439	−	0.274122i	0.0424897	−	0.0145694i
$355$	1.11204	+	1.57729i	0.0590211	+	0.0837137i
$356$	15.8785	+	6.97140i	0.841559	+	0.369483i
$357$	12.7960	−	17.4459i	0.677234	−	0.923336i
$358$	−0.949600	−	2.05373i	−0.0501879	−	0.108543i
$359$	3.81298	+	2.10391i	0.201241	+	0.111040i	0.580532	−	0.814237i	$-0.302844\pi$
$359$	3.81298	+	2.10391i	0.201241	+	0.111040i	−0.379291	+	0.925277i	$0.623832\pi$
$360$	60.2035	−	0.857369i	3.17300	−	0.0451873i
$361$	6.75513	−	17.4962i	0.355533	−	0.920853i
$362$	−34.5103	−	10.0891i	−1.81382	−	0.530272i
$363$	−12.4390	−	14.4218i	−0.652880	−	0.756947i
$364$	31.1736	−	0.403046i	1.63394	−	0.0211253i
$365$	−34.2570	+	0.442912i	−1.79309	+	0.0231831i
$366$	−15.9996	+	45.8887i	−0.836313	+	2.39864i
$367$	−11.9997	−	3.50813i	−0.626381	−	0.183123i	−0.0479446	−	0.998850i	$-0.515267\pi$
$367$	−11.9997	−	3.50813i	−0.626381	−	0.183123i	−0.578437	+	0.815727i	$0.696337\pi$
$368$	15.6223	−	40.4628i	0.814368	−	2.10927i
$369$	7.12493	−	6.15353i	0.370909	−	0.320340i
$370$	−1.80162	−	0.994089i	−0.0936615	−	0.0516802i
$371$	7.96895	+	17.2347i	0.413727	+	0.894780i
$372$	−29.2507	−	66.5047i	−1.51658	−	3.44811i
$373$	−4.57552	−	2.00887i	−0.236912	−	0.104015i	0.280173	−	0.959950i	$-0.409608\pi$
$373$	−4.57552	−	2.00887i	−0.236912	−	0.104015i	−0.517084	+	0.855934i	$0.672983\pi$
$374$	−0.536831	−	0.761424i	−0.0277589	−	0.0393723i
$375$	9.33041	+	8.13185i	0.481820	+	0.419927i
$376$	−27.5339	+	87.8210i	−1.41995	+	4.52902i
$377$	1.99570	+	1.31259i	0.102784	+	0.0676021i
$378$	4.07486	+	30.8678i	0.209588	+	1.58767i
$379$	−8.24164	+	5.42061i	−0.423345	+	0.278438i	−0.743253	−	0.669010i	$-0.766718\pi$
$379$	−8.24164	+	5.42061i	−0.423345	+	0.278438i	0.319908	+	0.947448i	$0.396348\pi$
$380$	1.78045	+	6.23958i	0.0913349	+	0.320084i
$381$	4.08346	+	20.7204i	0.209202	+	1.06154i
$382$	3.97122	−	5.05593i	0.203186	−	0.258684i
$383$	−26.7259	−	4.89083i	−1.36563	−	0.249910i	−0.553238	−	0.833023i	$-0.686608\pi$
$383$	−26.7259	−	4.89083i	−1.36563	−	0.249910i	−0.812391	+	0.583113i	$0.801834\pi$
$384$	−0.0712508	+	0.00604872i	−0.00363600	+	0.000308673i
$385$	−0.378971	+	0.149139i	−0.0193141	+	0.00760083i
$386$	−59.8174	+	27.1903i	−3.04462	+	1.38395i
$387$	−21.4504	+	20.5551i	−1.09039	+	1.04487i
$388$	−5.92954	+	23.0199i	−0.301027	+	1.16866i
$389$	10.1786	+	9.47938i	0.516074	+	0.480624i	0.895789	−	0.444480i	$-0.146612\pi$
$389$	10.1786	+	9.47938i	0.516074	+	0.480624i	−0.379715	+	0.925104i	$0.623978\pi$
$390$	9.72797	+	33.1942i	0.492595	+	1.68085i
$391$	16.5472	−	17.9996i	0.836828	−	0.910280i
$392$	−8.96298	−	9.25746i	−0.452699	−	0.467572i
$393$	−26.9223	+	7.32611i	−1.35805	+	0.369553i
$394$	17.6321	−	3.22667i	0.888291	−	0.162557i
$395$	−21.3248	+	40.4842i	−1.07297	+	2.03698i
$396$	0.930555	+	0.181488i	0.0467621	+	0.00912009i
$397$	3.37538	+	24.7122i	0.169406	+	1.24027i	0.857438	+	0.514588i	$0.172055\pi$
$397$	3.37538	+	24.7122i	0.169406	+	1.24027i	−0.688032	+	0.725680i	$0.741525\pi$
$398$	38.4552	−	20.5747i	1.92758	−	1.03132i
$399$	−1.81448	+	0.756415i	−0.0908375	+	0.0378681i
$400$	18.2633	+	13.7809i	0.913166	+	0.689046i
$401$	−1.10524	+	0.370206i	−0.0551931	+	0.0184872i	−0.345073	−	0.938576i	$-0.612146\pi$
$401$	−1.10524	+	0.370206i	−0.0551931	+	0.0184872i	0.289880	+	0.957063i	$0.406385\pi$
$402$	47.5747	−	35.4666i	2.37281	−	1.76891i
$403$	18.9343	−	15.4751i	0.943183	−	0.770867i
$404$	4.31707	−	24.4833i	0.214782	−	1.21809i
$405$	−22.4677	+	9.58947i	−1.11643	+	0.476504i
$406$	0.882786	+	5.00653i	0.0438120	+	0.248470i
$407$	−0.0143828	−	0.0123889i	−0.000712927	−	0.000614096i
$408$	−66.8527	−	19.9666i	−3.30970	−	0.988494i
$409$	5.19197	+	2.04323i	0.256727	+	0.101031i	0.491063	−	0.871124i	$-0.336609\pi$
$409$	5.19197	+	2.04323i	0.256727	+	0.101031i	−0.234336	+	0.972156i	$0.575292\pi$
$410$	22.2299	−	1.15061i	1.09786	−	0.0568246i
$411$	−23.7537	−	1.67622i	−1.17168	−	0.0826820i
$412$	12.1137	+	36.9568i	0.596800	+	1.82073i
$413$	−0.0906323	+	0.418405i	−0.00445972	+	0.0205884i
$414$	0.728445	+	35.1781i	0.0358011	+	1.72891i
$415$	−4.46215	+	32.6687i	−0.219038	+	1.60365i
$416$	−10.2587	−	27.6285i	−0.502973	−	1.35460i
$417$	30.4437	−	1.00430i	1.49083	−	0.0491808i
$418$	0.00601405	+	0.0844361i	0.000294157	+	0.00412990i
$419$	1.13214	−	25.0031i	0.0553089	−	1.22148i	−0.762883	−	0.646536i	$-0.776217\pi$
$419$	1.13214	−	25.0031i	0.0553089	−	1.22148i	0.818192	−	0.574945i	$-0.194976\pi$
$420$	−26.2908	+	44.9323i	−1.28286	+	2.19247i
$421$	−24.9054	+	18.7928i	−1.21382	+	0.915907i	−0.998164	−	0.0605627i	$-0.980710\pi$
$421$	−24.9054	+	18.7928i	−1.21382	+	0.915907i	−0.215653	+	0.976470i	$0.569188\pi$
$422$	−27.7992	+	40.5323i	−1.35325	+	1.97308i
$423$	−3.18308	−	37.2055i	−0.154767	−	1.80899i
$424$	43.7156	−	42.8759i	2.12302	−	2.08224i
$425$	6.73515	+	10.9987i	0.326703	+	0.533517i
$426$	2.82882	+	1.53471i	0.137057	+	0.0743567i
$427$	−15.7018	−	18.9602i	−0.759862	−	0.917549i
$428$	0.180754	+	5.59054i	0.00873709	+	0.270229i
$429$	0.0249372	+	0.318133i	0.00120398	+	0.0153596i
$430$	−69.8698	+	7.25230i	−3.36942	+	0.349737i
$431$	34.6109	−	8.20294i	1.66715	−	0.395122i	0.714607	−	0.699526i	$-0.246605\pi$
$431$	34.6109	−	8.20294i	1.66715	−	0.395122i	0.952543	+	0.304404i	$0.0984573\pi$
$432$	44.6846	−	22.9153i	2.14989	−	1.10251i
$433$	−6.42017	−	1.52161i	−0.308534	−	0.0731238i	0.0734323	−	0.997300i	$-0.476605\pi$
$433$	−6.42017	−	1.52161i	−0.308534	−	0.0731238i	−0.381966	+	0.924176i	$0.624753\pi$
$434$	51.6101	+	6.70977i	2.47736	+	0.322079i
$435$	−3.59732	+	1.72301i	−0.172478	+	0.0826122i
$436$	2.92656	−	34.7437i	0.140157	−	1.66392i
$437$	−2.13229	+	0.623376i	−0.102001	+	0.0298201i
$438$	−50.8714	+	26.0038i	−2.43073	+	1.24251i
$439$	−19.0576	+	5.04050i	−0.909568	+	0.240570i	−0.680420	−	0.732822i	$-0.738203\pi$
$439$	−19.0576	+	5.04050i	−0.909568	+	0.240570i	−0.229147	+	0.973392i	$0.573594\pi$
$440$	0.863550	+	0.989518i	0.0411681	+	0.0471734i
$441$	4.78968	+	2.09540i	0.228080	+	0.0997810i
$442$	0.777264	−	40.0755i	0.0369707	−	1.90620i
$443$	1.78656	−	16.1921i	0.0848821	−	0.769309i	−0.874081	−	0.485779i	$-0.838536\pi$
$443$	1.78656	−	16.1921i	0.0848821	−	0.769309i	0.958964	−	0.283529i	$-0.0915053\pi$
$444$	−2.42411	−	0.108171i	−0.115043	−	0.00513356i
$445$	−7.54661	−	6.16787i	−0.357744	−	0.292385i
$446$	−11.8461	+	10.2039i	−0.560930	+	0.483171i
$447$	22.1814	−	9.92763i	1.04914	−	0.469561i
$448$	8.15363	−	16.5003i	0.385223	−	0.779566i
$449$	−11.9300	+	13.6703i	−0.563012	+	0.645140i	−0.962398	−	0.271643i	$-0.912433\pi$
$449$	−11.9300	+	13.6703i	−0.563012	+	0.645140i	0.399387	+	0.916783i	$0.369223\pi$
$450$	−17.9493	−	4.72220i	−0.846139	−	0.222606i
$451$	0.202888	+	0.0317310i	0.00955361	+	0.00149416i
$452$	10.5669	−	7.34822i	0.497024	−	0.345631i
$453$	10.8904	+	9.00681i	0.511678	+	0.423177i
$454$	3.34112	+	6.76134i	0.156806	+	0.317325i
$455$	−16.9396	−	4.48031i	−0.794139	−	0.210040i
$456$	4.26324	+	4.69184i	0.199644	+	0.219716i
$457$	31.3414	+	16.2510i	1.46609	+	0.760190i	0.992694	−	0.120660i	$-0.0385010\pi$
$457$	31.3414	+	16.2510i	1.46609	+	0.760190i	0.473397	+	0.880849i	$0.343028\pi$
$458$	−6.38025	−	8.57016i	−0.298129	−	0.400457i
$459$	28.1694	−	2.79594i	1.31483	−	0.130503i
$460$	−35.1312	+	47.1894i	−1.63800	+	2.20022i
$461$	−10.4404	+	5.07542i	−0.486258	+	0.236386i	−0.664059	−	0.747681i	$-0.731167\pi$
$461$	−10.4404	+	5.07542i	−0.486258	+	0.236386i	0.177801	+	0.984066i	$0.443102\pi$
$462$	−0.456067	+	0.503243i	−0.0212181	+	0.0234130i
$463$	20.4572	−	4.29305i	0.950726	−	0.199515i	0.295836	−	0.955239i	$-0.404402\pi$
$463$	20.4572	−	4.29305i	0.950726	−	0.199515i	0.654891	+	0.755724i	$0.272715\pi$
$464$	7.12731	−	4.05375i	0.330877	−	0.188191i
$465$	5.81397	+	40.4175i	0.269616	+	1.87432i
$466$	−9.56929	−	47.1125i	−0.443289	−	2.18244i
$467$	21.8618	−	1.69923i	1.01164	−	0.0786310i	0.439043	−	0.898466i	$-0.355318\pi$
$467$	21.8618	−	1.69923i	1.01164	−	0.0786310i	0.572600	+	0.819835i	$0.305935\pi$
$468$	27.6457	+	29.9932i	1.27792	+	1.38644i
$469$	2.91006	+	29.9181i	0.134374	+	1.38149i
$470$	48.0390	−	74.0784i	2.21587	−	3.41698i
$471$	0.713905	+	13.6196i	0.0328950	+	0.627560i
$472$	1.36905	−	0.177989i	0.0630157	−	0.00819260i
$473$	−0.644576	−	0.0669053i	−0.0296376	−	0.00307631i
$474$	−1.92275	+	76.2811i	−0.0883149	+	3.50370i
$475$	−0.00757496	−	1.17182i	−0.000347563	−	0.0537668i
$476$	44.6737	−	40.5393i	2.04762	−	1.85811i
$477$	−9.81010	+	22.8246i	−0.449173	+	1.04507i
$478$	−24.0856	−	45.7254i	−1.10165	−	2.09143i
$479$	−11.5040	−	14.6463i	−0.525633	−	0.669206i	0.448866	−	0.893599i	$-0.351828\pi$
$479$	−11.5040	−	14.6463i	−0.525633	−	0.669206i	−0.974499	+	0.224394i	$0.927960\pi$
$480$	48.3562	+	9.13977i	2.20715	+	0.417171i
$481$	−0.183208	−	0.795908i	−0.00835357	−	0.0362903i
$482$	37.7431	−	61.6358i	1.71915	−	2.80743i
$483$	−15.4416	−	8.90169i	−0.702615	−	0.405041i
$484$	−25.9547	−	46.3279i	−1.17976	−	2.10581i
$485$	6.68013	−	11.5703i	0.303329	−	0.525381i
$486$	−26.4855	+	30.9527i	−1.20141	+	1.40404i
$487$	17.7269	+	30.7038i	0.803281	+	1.39132i	0.917446	+	0.397861i	$0.130247\pi$
$487$	17.7269	+	30.7038i	0.803281	+	1.39132i	−0.114165	+	0.993462i	$0.536419\pi$
$488$	−40.5794	+	68.2330i	−1.83694	+	3.08876i
$489$	−24.2995	+	28.9976i	−1.09886	+	1.31132i
$490$	5.90177	+	10.8613i	0.266615	+	0.490665i
$491$	12.9701	−	12.0792i	0.585333	−	0.545125i	−0.331983	−	0.943285i	$-0.607718\pi$
$491$	12.9701	−	12.0792i	0.585333	−	0.545125i	0.917316	+	0.398161i	$0.130351\pi$
$492$	22.8923	−	12.8449i	1.03207	−	0.579093i
$493$	4.57539	−	0.655098i	0.206065	−	0.0295041i
$494$	−1.94193	+	3.08108i	−0.0873715	+	0.138624i
$495$	−0.476491	−	0.238521i	−0.0214167	−	0.0107207i
$496$	−17.7707	−	82.0385i	−0.797926	−	3.68364i
$497$	−1.40656	+	0.824244i	−0.0630926	+	0.0369724i
$498$	17.4980	+	52.1262i	0.784102	+	2.33583i
$499$	15.8759	−	21.9109i	0.710705	−	0.980865i	−0.289018	−	0.957324i	$-0.593329\pi$
$499$	15.8759	−	21.9109i	0.710705	−	0.980865i	0.999723	−	0.0235416i	$-0.00749423\pi$
$500$	20.9638	+	27.4122i	0.937531	+	1.22591i
$501$	−6.15638	+	20.1373i	−0.275047	+	0.899668i
$502$	−32.3242	−	63.3386i	−1.44270	−	2.82694i
$503$	7.10285	−	5.07681i	0.316700	−	0.226364i	−0.412021	−	0.911174i	$-0.635177\pi$
$503$	7.10285	−	5.07681i	0.316700	−	0.226364i	0.728721	+	0.684811i	$0.240115\pi$
$504$	−3.54698	+	50.7381i	−0.157995	+	2.26005i
$505$	−6.02764	+	12.6057i	−0.268227	+	0.560948i
$506$	−0.574986	+	0.508373i	−0.0255612	+	0.0226000i
$507$	4.63236	−	7.46708i	0.205730	−	0.331625i
$508$	−0.380641	+	58.8838i	−0.0168882	+	2.61255i
$509$	−27.9553	−	31.2094i	−1.23910	−	1.38333i	−0.896012	−	0.444029i	$-0.853549\pi$
$509$	−27.9553	−	31.2094i	−1.23910	−	1.38333i	−0.343085	−	0.939304i	$-0.611472\pi$
$510$	56.6468	+	35.6512i	2.50836	+	1.57866i
$511$	2.05614	−	28.8678i	0.0909583	−	1.27704i
$512$	41.4723	+	4.84741i	1.83283	+	0.214227i
$513$	−2.32263	−	1.10499i	−0.102546	−	0.0487865i
$514$	−2.48082	+	0.289966i	−0.109424	+	0.0127898i
$515$	−0.988734	−	21.8359i	−0.0435688	−	0.962205i
$516$	−70.0499	+	44.2149i	−3.08377	+	1.94645i
$517$	0.574089	−	0.577812i	0.0252484	−	0.0254122i
$518$	0.964533	−	1.44605i	0.0423791	−	0.0635359i
$519$	18.9627	−	0.135019i	0.832369	−	0.00592666i
$520$	4.74281	+	56.3060i	0.207986	+	2.46918i
$521$	−4.19192	−	10.8574i	−0.183652	−	0.475669i	0.810231	−	0.586110i	$-0.199342\pi$
$521$	−4.19192	−	10.8574i	−0.183652	−	0.475669i	−0.993883	+	0.110441i	$0.964774\pi$
$522$	−4.10178	+	5.23628i	−0.179530	+	0.229186i
$523$	−1.17951	−	3.44725i	−0.0515764	−	0.150738i	0.917353	−	0.398074i	$-0.130321\pi$
$523$	−1.17951	−	3.44725i	−0.0515764	−	0.150738i	−0.968930	+	0.247336i	$0.920445\pi$
$524$	−77.6336	+	5.02538i	−3.39144	+	0.219535i
$525$	6.75035	−	6.54421i	0.294609	−	0.285613i
$526$	5.37012	+	28.3102i	0.234149	+	1.23438i
$527$	7.61351	−	46.7011i	0.331650	−	2.03433i
$528$	1.01161	+	0.420159i	0.0440245	+	0.0182851i
$529$	2.30336	+	1.69176i	0.100146	+	0.0735546i
$530$	−51.4311	+	28.3785i	−2.23402	+	1.23268i
$531$	−0.486527	+	0.277564i	−0.0211135	+	0.0120453i
$532$	−5.37851	+	1.05631i	−0.233188	+	0.0457966i
$533$	6.22719	+	6.26758i	0.269730	+	0.271479i
$534$	−15.8416	−	3.63559i	−0.685532	−	0.157327i
$535$	0.744748	−	3.05422i	0.0321983	−	0.132046i
$536$	87.7207	−	41.2505i	3.78896	−	1.78175i
$537$	0.872823	+	1.21946i	0.0376651	+	0.0526234i
$538$	−27.5519	+	36.0268i	−1.18785	+	1.55322i
$539$	0.0327061	+	0.109246i	0.00140875	+	0.00470556i
$540$	−66.7236	+	13.6894i	−2.87133	+	0.589097i
$541$	0.301515	−	1.00713i	0.0129632	−	0.0432999i	−0.951263	−	0.308380i	$-0.900213\pi$
$541$	0.301515	−	1.00713i	0.0129632	−	0.0432999i	0.964226	+	0.265080i	$0.0853984\pi$
$542$	27.4865	+	37.9349i	1.18065	+	1.62944i
$543$	23.7197	+	2.29146i	1.01791	+	0.0983359i
$544$	−50.2826	−	26.9027i	−2.15585	−	1.15344i
$545$	−6.82122	+	18.3708i	−0.292189	+	0.786918i
$546$	−28.6315	+	5.83506i	−1.22531	+	0.249718i
$547$	−35.9208	+	0.929002i	−1.53586	+	0.0397213i	−0.784484	−	0.620149i	$-0.787072\pi$
$547$	−35.9208	+	0.929002i	−1.53586	+	0.0397213i	−0.751380	+	0.659870i	$0.770611\pi$
$548$	−63.9642	−	17.8057i	−2.73242	−	0.760620i
$549$	4.72940	−	31.8606i	0.201846	−	1.35978i
$550$	−0.174646	−	0.365240i	−0.00744692	−	0.0155739i
$551$	−0.386686	−	0.163843i	−0.0164734	−	0.00697997i
$552$	−10.3095	+	56.5458i	−0.438804	+	2.40675i
$553$	−32.5662	−	20.8210i	−1.38485	−	0.885399i
$554$	3.08866	−	2.08914i	0.131225	−	0.0887591i
$555$	1.29622	+	0.423935i	0.0550215	+	0.0179950i
$556$	83.7344	+	14.2072i	3.55113	+	0.602518i
$557$	5.56383	−	2.27308i	0.235747	−	0.0963133i	−0.257248	−	0.966345i	$-0.582816\pi$
$557$	5.56383	−	2.27308i	0.235747	−	0.0963133i	0.492995	+	0.870032i	$0.335902\pi$
$558$	38.5884	+	56.1053i	1.63358	+	2.37513i
$559$	−20.6474	−	18.7365i	−0.873291	−	0.792469i
$560$	−40.1306	+	44.8019i	−1.69583	+	1.89323i
$561$	0.443899	+	0.429215i	0.0187414	+	0.0181215i
$562$	26.5810	−	52.0848i	1.12125	−	2.19707i
$563$	3.22939	+	21.5606i	0.136102	+	0.908673i	0.946479	+	0.322764i	$0.104612\pi$
$563$	3.22939	+	21.5606i	0.136102	+	0.908673i	−0.810377	+	0.585909i	$0.800738\pi$
$564$	12.0195	−	103.422i	0.506112	−	4.35484i
$565$	−6.82894	+	2.38601i	−0.287295	+	0.100380i
$566$	58.1850	−	48.8230i	2.44570	−	2.05219i
$567$	−6.47903	−	19.5925i	−0.272094	−	0.822808i
$568$	4.02734	+	3.37934i	0.168983	+	0.141794i
$569$	25.6201	+	9.70184i	1.07405	+	0.406722i	0.826954	−	0.562269i	$-0.190072\pi$
$569$	25.6201	+	9.70184i	1.07405	+	0.406722i	0.247095	+	0.968991i	$0.420524\pi$
$570$	−2.73294	−	5.43284i	−0.114470	−	0.227557i
$571$	2.75263	−	13.5520i	0.115194	−	0.567135i	−0.880469	−	0.474103i	$-0.842772\pi$
$571$	2.75263	−	13.5520i	0.115194	−	0.567135i	0.995663	−	0.0930315i	$-0.0296557\pi$
$572$	−0.109005	+	0.883057i	−0.00455774	+	0.0369225i
$573$	−1.95895	+	3.78407i	−0.0818362	+	0.158082i
$574$	−0.607649	+	18.7940i	−0.0253628	+	0.784445i
$575$	8.39775	−	6.50874i	0.350210	−	0.271433i
$576$	23.1903	−	6.48826i	0.966264	−	0.270344i
$577$	−5.26514	−	8.35372i	−0.219191	−	0.347770i	0.718328	−	0.695705i	$-0.244908\pi$
$577$	−5.26514	−	8.35372i	−0.219191	−	0.347770i	−0.937519	+	0.347935i	$0.886883\pi$
$578$	−21.4617	−	25.2439i	−0.892691	−	1.05001i
$579$	35.5761	−	25.1174i	1.47849	−	1.04384i
$580$	−10.7876	+	2.70447i	−0.447931	+	0.112297i
$581$	−27.1831	−	6.07244i	−1.12774	−	0.251927i
$582$	1.42462	−	22.2342i	0.0590523	−	0.921636i
$583$	−0.518126	+	0.158773i	−0.0214586	+	0.00657572i
$584$	−89.9107	+	25.0283i	−3.72053	+	1.03568i
$585$	−10.4480	−	20.4065i	−0.431973	−	0.843707i
$586$	0.802722	−	8.25271i	0.0331602	−	0.340916i
$587$	−23.3902	−	18.6177i	−0.965415	−	0.768436i	0.00741084	−	0.999973i	$-0.497641\pi$
$587$	−23.3902	−	18.6177i	−0.965415	−	0.768436i	−0.972826	+	0.231537i	$0.925625\pi$
$588$	11.9192	+	8.39175i	0.491539	+	0.346070i
$589$	−2.78480	+	3.27555i	−0.114745	+	0.134967i
$590$	−1.31103	−	0.187711i	−0.0539743	−	0.00772796i
$591$	−11.0801	+	4.28626i	−0.455773	+	0.176313i
$592$	−2.71937	−	0.681750i	−0.111765	−	0.0280198i
$593$	−1.32156	−	0.663710i	−0.0542698	−	0.0272553i	0.421457	−	0.906848i	$-0.361519\pi$
$593$	−1.32156	−	0.663710i	−0.0542698	−	0.0272553i	−0.475727	+	0.879593i	$0.657815\pi$
$594$	−0.888591	−	0.00399550i	−0.0364593	−	0.000163937i
$595$	−30.2986	+	15.2165i	−1.24212	+	0.623817i
$596$	66.1295	−	14.7727i	2.70877	−	0.605114i
$597$	−22.4875	+	18.1623i	−0.920352	+	0.743333i
$598$	−32.8858	+	2.98427i	−1.34480	+	0.122036i
$599$	0.314757	+	2.85273i	0.0128606	+	0.116559i	0.998688	−	0.0512017i	$-0.0163051\pi$
$599$	0.314757	+	2.85273i	0.0128606	+	0.116559i	−0.985828	+	0.167761i	$0.946346\pi$
$600$	−27.1903	−	13.4139i	−1.11004	−	0.547621i
$601$	41.8133	+	3.79441i	1.70560	+	0.154777i	0.899477	−	0.436968i	$-0.143948\pi$
$601$	41.8133	+	3.79441i	1.70560	+	0.154777i	0.806125	+	0.591745i	$0.201561\pi$
$602$	−1.15067	−	59.3283i	−0.0468978	−	2.41804i
$603$	−26.5793	+	28.9885i	−1.08239	+	1.18050i
$604$	24.7388	+	30.6713i	1.00661	+	1.24800i
$605$	7.07045	+	28.9960i	0.287455	+	1.17885i
$606$	0.316520	+	23.2990i	0.0128577	+	0.946457i
$607$	−0.200994	+	0.358764i	−0.00815808	+	0.0145618i	−0.876466	−	0.481464i	$-0.840105\pi$
$607$	−0.200994	+	0.358764i	−0.00815808	+	0.0145618i	0.868308	+	0.496026i	$0.165208\pi$
$608$	2.64857	+	4.45349i	0.107414	+	0.180613i
$609$	−1.19531	−	3.15027i	−0.0484364	−	0.127655i
$610$	55.0561	−	52.6196i	2.22916	−	2.13050i
$611$	34.6232	−	5.41498i	1.40071	−	0.219066i
$612$	78.5184	+	8.04590i	3.17392	+	0.325236i
$613$	18.1217	−	10.9365i	0.731927	−	0.441720i	−0.101154	−	0.994871i	$-0.532254\pi$
$613$	18.1217	−	10.9365i	0.731927	−	0.441720i	0.833081	+	0.553150i	$0.186575\pi$
$614$	−2.03522	+	2.88669i	−0.0821348	+	0.116497i
$615$	−14.3310	+	3.50446i	−0.577881	+	0.141313i
$616$	−0.894172	+	0.656746i	−0.0360272	+	0.0264610i
$617$	−5.33215	+	11.5320i	−0.214664	+	0.464261i	−0.984816	−	0.173600i	$-0.944460\pi$
$617$	−5.33215	+	11.5320i	−0.214664	+	0.464261i	0.770152	+	0.637860i	$0.220180\pi$
$618$	−17.6310	−	31.9036i	−0.709222	−	1.28335i
$619$	27.1396	+	29.5218i	1.09083	+	1.18658i	0.981277	+	0.192601i	$0.0616923\pi$
$619$	27.1396	+	29.5218i	1.09083	+	1.18658i	0.109557	+	0.993980i	$0.465057\pi$
$620$	−6.62005	+	113.662i	−0.265868	+	4.56477i
$621$	−4.83447	−	22.8137i	−0.194001	−	0.915482i
$622$	−1.21274	−	20.8219i	−0.0486264	−	0.834883i
$623$	5.72699	−	5.91515i	0.229447	−	0.236986i
$624$	24.3776	+	40.3337i	0.975885	+	1.61464i
$625$	−11.6250	−	28.9883i	−0.464998	−	1.15953i
$626$	9.59203	+	26.8935i	0.383374	+	1.07488i
$627$	−0.0143812	−	0.0542298i	−0.000574330	−	0.00216573i
$628$	−5.63295	+	37.6078i	−0.224779	+	1.50071i
$629$	−1.28570	−	0.918960i	−0.0512640	−	0.0366413i
$630$	16.3310	−	45.9783i	0.650641	−	1.83182i
$631$	−33.8377	−	33.1877i	−1.34706	−	1.32118i	−0.905741	−	0.423831i	$-0.860685\pi$
$631$	−33.8377	−	33.1877i	−1.34706	−	1.32118i	−0.441315	−	0.897352i	$-0.645488\pi$
$632$	−27.9615	+	121.473i	−1.11225	+	4.83193i
$633$	13.0759	−	29.8356i	0.519720	−	1.18586i
$634$	−13.6441	−	43.5187i	−0.541877	−	1.72835i
$635$	9.08118	−	31.8251i	0.360376	−	1.26294i
$636$	−39.5109	+	56.8970i	−1.56671	+	2.25611i
$637$	−1.64823	+	4.62120i	−0.0653052	+	0.183099i
$638$	−0.144980	+	0.00562589i	−0.00573982	+	0.000222731i
$639$	−2.03203	−	0.648605i	−0.0803858	−	0.0256584i
$640$	0.103735	+	0.0423805i	0.00410050	+	0.00167524i
$641$	16.0685	+	9.98304i	0.634668	+	0.394306i	0.806848	−	0.590759i	$-0.201172\pi$
$641$	16.0685	+	9.98304i	0.634668	+	0.394306i	−0.172180	+	0.985065i	$0.555081\pi$
$642$	−1.14631	−	5.11564i	−0.0452413	−	0.201898i
$643$	31.0734	−	13.1662i	1.22541	−	0.519223i	0.321489	−	0.946913i	$-0.395817\pi$
$643$	31.0734	−	13.1662i	1.22541	−	0.519223i	0.903925	+	0.427691i	$0.140673\pi$
$644$	−37.2315	−	32.9182i	−1.46713	−	1.29716i
$645$	44.5924	−	13.3820i	1.75582	−	0.526914i
$646$	1.13391	+	6.95540i	0.0446132	+	0.273657i
$647$	−32.8670	+	11.9626i	−1.29214	+	0.470299i	−0.894428	−	0.447213i	$-0.852417\pi$
$647$	−32.8670	+	11.9626i	−1.29214	+	0.470299i	−0.397709	+	0.917512i	$0.630194\pi$
$648$	−52.4914	+	40.9048i	−2.06206	+	1.60689i
$649$	−0.0114813	−	0.00417884i	−0.000450679	−	0.000164034i
$650$	3.24616	−	17.1131i	0.127325	−	0.671230i
$651$	−34.4343	+	2.02823i	−1.34959	+	0.0794927i
$652$	−82.5346	+	65.6946i	−3.23230	+	2.57280i
$653$	1.38697	+	2.13877i	0.0542763	+	0.0836965i	0.865116	−	0.501571i	$-0.167245\pi$
$653$	1.38697	+	2.13877i	0.0542763	+	0.0836965i	−0.810840	+	0.585268i	$0.800989\pi$
$654$	3.39519	+	32.5022i	0.132763	+	1.27094i
$655$	42.7919	+	8.98012i	1.67202	+	0.350882i
$656$	28.8799	−	9.25997i	1.12757	−	0.361541i
$657$	29.8986	−	23.2360i	1.16646	−	0.906524i
$658$	58.9505	+	45.6901i	2.29813	+	1.78119i
$659$	−5.04251	+	6.08893i	−0.196428	+	0.237191i	−0.859212	−	0.511620i	$-0.829046\pi$
$659$	−5.04251	+	6.08893i	−0.196428	+	0.237191i	0.662784	+	0.748811i	$0.269375\pi$
$660$	−1.16902	−	0.916973i	−0.0455039	−	0.0356931i
$661$	16.9992	+	8.26387i	0.661192	+	0.321427i	0.737195	−	0.675680i	$-0.236150\pi$
$661$	16.9992	+	8.26387i	0.661192	+	0.321427i	−0.0760032	+	0.997108i	$0.524216\pi$
$662$	36.8095	−	19.0863i	1.43064	−	0.741810i
$663$	4.46114	+	26.1890i	0.173256	+	1.01710i
$664$	11.0041	+	89.1444i	0.427040	+	3.45947i
$665$	3.07138	+	0.238727i	0.119103	+	0.00925743i
$666$	2.25089	−	0.325292i	0.0872200	−	0.0126048i
$667$	−0.949798	−	3.68734i	−0.0367763	−	0.142774i
$668$	−28.0323	+	51.5893i	−1.08460	+	1.99605i
$669$	6.44812	−	8.11193i	0.249299	−	0.313625i
$670$	−91.6812	+	15.5555i	−3.54196	+	0.600961i
$671$	0.596786	−	0.370771i	0.0230387	−	0.0143135i
$672$	−11.1222	+	40.0566i	−0.429048	+	1.54522i
$673$	4.27541	−	9.56942i	0.164805	−	0.368874i	−0.811793	−	0.583945i	$-0.801508\pi$
$673$	4.27541	−	9.56942i	0.164805	−	0.368874i	0.976598	+	0.215071i	$0.0689982\pi$
$674$	−46.8618	−	49.6706i	−1.80505	−	1.91324i
$675$	12.2719	+	0.849809i	0.472344	+	0.0327092i
$676$	16.8138	−	17.8215i	0.646683	−	0.685444i
$677$	13.2940	+	31.9484i	0.510929	+	1.22788i	0.945022	+	0.327008i	$0.106040\pi$
$677$	13.2940	+	31.9484i	0.510929	+	1.22788i	−0.434093	+	0.900868i	$0.642931\pi$
$678$	−8.44117	+	8.61778i	−0.324181	+	0.330964i
$679$	9.26585	+	6.44349i	0.355591	+	0.247278i
$680$	79.0424	+	75.5444i	3.03114	+	2.89699i
$681$	−3.01340	−	3.98810i	−0.115474	−	0.152824i
$682$	−0.389068	+	1.43347i	−0.0148982	+	0.0548905i
$683$	3.98466	−	11.6456i	0.152469	−	0.445607i	−0.843306	−	0.537433i	$-0.819394\pi$
$683$	3.98466	−	11.6456i	0.152469	−	0.445607i	0.995775	+	0.0918264i	$0.0292705\pi$
$684$	−5.73039	−	4.31219i	−0.219107	−	0.164881i
$685$	31.9495	+	19.2816i	1.22073	+	0.736713i
$686$	−47.9669	+	21.0597i	−1.83138	+	0.804063i
$687$	5.21633	+	4.78911i	0.199016	+	0.182716i
$688$	−89.5045	+	33.8937i	−3.41233	+	1.29218i
$689$	−22.0103	−	7.69034i	−0.838526	−	0.292979i
$690$	24.0749	−	49.6059i	0.916514	−	1.88846i
$691$	24.7345	+	37.0826i	0.940944	+	1.41069i	0.911582	+	0.411119i	$0.134862\pi$
$691$	24.7345	+	37.0826i	0.940944	+	1.41069i	0.0293618	+	0.999569i	$0.490653\pi$
$692$	51.8832	+	10.1895i	1.97230	+	0.387347i
$693$	0.234564	−	0.384182i	0.00891035	−	0.0145939i
$694$	11.1169	−	13.7828i	0.421992	−	0.523188i
$695$	−43.1964	−	20.3130i	−1.63853	−	0.770517i
$696$	−8.27370	+	7.04345i	−0.313614	+	0.266981i
$697$	17.0603	+	1.10435i	0.646204	+	0.0418301i
$698$	1.57658	+	5.80873i	0.0596746	+	0.219864i
$699$	12.0699	+	29.4882i	0.456524	+	1.11535i
$700$	22.0865	−	14.1209i	0.834790	−	0.533718i
$701$	2.71510	−	6.29430i	0.102548	−	0.237732i	−0.859216	−	0.511613i	$-0.829048\pi$
$701$	2.71510	−	6.29430i	0.102548	−	0.237732i	0.961764	+	0.273881i	$0.0883074\pi$
$702$	−30.7111	−	22.7698i	−1.15911	−	0.859389i
$703$	0.0568740	+	0.131849i	0.00214505	+	0.00497277i
$704$	0.435090	+	0.294291i	0.0163981	+	0.0110915i
$705$	−22.0958	+	54.1857i	−0.832177	+	2.04075i
$706$	21.5681	−	65.8004i	0.811727	−	2.47643i
$707$	−10.1837	−	5.96766i	−0.382997	−	0.224437i
$708$	−1.48379	+	0.487436i	−0.0557643	+	0.0183190i
$709$	−0.432334	−	0.144812i	−0.0162367	−	0.00543855i	0.309481	−	0.950906i	$-0.399845\pi$
$709$	−0.432334	−	0.144812i	−0.0162367	−	0.00543855i	−0.325718	+	0.945467i	$0.605606\pi$
$710$	−2.85259	−	4.15917i	−0.107056	−	0.156091i
$711$	−8.20286	−	49.9039i	−0.307631	−	1.87154i
$712$	−24.1710	−	10.9871i	−0.905846	−	0.411758i
$713$	−38.9288	−	2.01494i	−1.45790	−	0.0754601i
$714$	−34.0265	+	45.1555i	−1.27341	+	1.68990i
$715$	0.192117	−	0.461699i	0.00718475	−	0.0172665i
$716$	1.70565	+	3.81766i	0.0637432	+	0.142673i
$717$	21.3493	+	26.7859i	0.797304	+	1.00034i
$718$	−9.89261	−	5.62655i	−0.369189	−	0.209981i
$719$	13.6891	+	4.38922i	0.510516	+	0.163690i	0.549410	−	0.835553i	$-0.314853\pi$
$719$	13.6891	+	4.38922i	0.510516	+	0.163690i	−0.0388938	+	0.999243i	$0.512383\pi$
$720$	−78.6960	+	0.103237i	−2.93283	+	0.00384742i
$721$	18.4508	+	0.715976i	0.687145	+	0.0266643i
$722$	−18.2429	+	45.4911i	−0.678931	+	1.69300i
$723$	−16.9345	+	44.8084i	−0.629801	+	1.66644i
$724$	63.5288	+	19.4676i	2.36103	+	0.723509i
$725$	2.00786	+	0.0519282i	0.0745699	+	0.00192856i
$726$	32.0172	+	38.1058i	1.18827	+	1.41424i
$727$	−27.8921	−	0.360619i	−1.03446	−	0.0133746i	−0.506166	−	0.862436i	$-0.668938\pi$
$727$	−27.8921	−	0.360619i	−1.03446	−	0.0133746i	−0.528294	+	0.849062i	$0.677168\pi$
$728$	−47.7328			−1.76909
$729$	13.4079	−	23.4356i	0.496588	−	0.867986i
$730$	89.5319			3.31372
$731$	−53.9456	−	0.697467i	−1.99525	−	0.0257968i
$732$	30.6612	−	84.4132i	1.13327	−	3.12000i
$733$	15.0034	+	0.388025i	0.554163	+	0.0143320i	0.301922	−	0.953333i	$-0.402372\pi$
$733$	15.0034	+	0.388025i	0.554163	+	0.0143320i	0.252241	+	0.967665i	$0.418833\pi$
$734$	31.2380	+	9.57249i	1.15301	+	0.353327i
$735$	−5.18878	−	6.34016i	−0.191391	−	0.233860i
$736$	−17.4862	+	43.6042i	−0.644550	+	1.60727i
$737$	−0.857238	−	0.0332647i	−0.0315768	−	0.00122532i
$738$	−18.8260	+	15.8390i	−0.692995	+	0.583043i
$739$	28.1729	+	9.03327i	1.03636	+	0.332294i	0.774340	−	0.632769i	$-0.218082\pi$
$739$	28.1729	+	9.03327i	1.03636	+	0.332294i	0.262016	+	0.965064i	$0.415613\pi$
$740$	3.30536	+	1.87997i	0.121508	+	0.0691090i
$741$	0.882476	−	2.24674i	0.0324186	−	0.0825362i
$742$	−20.2414	−	45.3051i	−0.743083	−	1.66320i
$743$	−13.3571	+	32.1001i	−0.490025	+	1.17764i	0.466114	+	0.884725i	$0.345654\pi$
$743$	−13.3571	+	32.1001i	−0.490025	+	1.17764i	−0.956139	+	0.292914i	$0.905375\pi$
$744$	43.4646	+	102.394i	1.59349	+	3.75393i
$745$	−38.0322	−	1.96853i	−1.39339	−	0.0721214i
$746$	11.8884	+	5.40395i	0.435266	+	0.197853i
$747$	−17.8535	−	31.7699i	−0.653226	−	1.16240i
$748$	0.973791	+	1.41982i	0.0356053	+	0.0519138i
$749$	2.51813	+	0.843461i	0.0920106	+	0.0308194i
$750$	−24.1065	−	21.5645i	−0.880246	−	0.787425i
$751$	−1.08994	−	0.638704i	−0.0397723	−	0.0233066i	0.485567	−	0.874199i	$-0.338613\pi$
$751$	−1.08994	−	0.638704i	−0.0397723	−	0.0233066i	−0.525340	+	0.850893i	$0.676062\pi$
$752$	37.4687	−	114.310i	1.36634	−	4.16847i
$753$	28.8964	+	37.2324i	1.05304	+	1.35682i
$754$	−5.17062	−	3.49736i	−0.188303	−	0.127366i
$755$	−8.77191	−	20.3356i	−0.319242	−	0.740087i
$756$	−6.79227	−	57.1363i	−0.247032	−	2.07803i
$757$	4.66975	−	10.8257i	0.169725	−	0.393467i	−0.812030	−	0.583615i	$-0.801638\pi$
$757$	4.66975	−	10.8257i	0.169725	−	0.393467i	0.981755	+	0.190148i	$0.0608969\pi$
$758$	21.7193	−	13.8861i	0.788882	−	0.504367i
$759$	0.311355	−	0.402262i	0.0113015	−	0.0146012i
$760$	−2.60225	−	9.58765i	−0.0943934	−	0.347781i
$761$	−52.1029	−	3.37273i	−1.88873	−	0.122261i	−0.923488	−	0.383626i	$-0.874675\pi$
$761$	−52.1029	−	3.37273i	−1.88873	−	0.122261i	−0.965240	+	0.261365i	$0.915827\pi$
$762$	−9.97044	−	54.2822i	−0.361191	−	1.96644i
$763$	−14.9802	−	7.04444i	−0.542321	−	0.255026i
$764$	−7.45901	+	9.24773i	−0.269858	+	0.334571i
$765$	−41.3008	−	16.1909i	−1.49323	−	0.585382i
$766$	69.6721	+	13.6832i	2.51736	+	0.494392i
$767$	−0.291696	−	0.437318i	−0.0105325	−	0.0157906i

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.k (of order \(243\), degree \(162\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.61310 - 0.0337849i) q^{2} +(1.70554 - 0.301886i) q^{3} +(4.82780 + 0.124859i) q^{4} +(-2.59518 - 0.795260i) q^{5} +(-4.46694 + 0.731236i) q^{6} +(0.853432 - 2.12814i) q^{7} +(-7.38859 - 0.286711i) q^{8} +(2.81773 - 1.02976i) q^{9} +O(q^{10})\)	\(q+(-2.61310 - 0.0337849i) q^{2} +(1.70554 - 0.301886i) q^{3} +(4.82780 + 0.124859i) q^{4} +(-2.59518 - 0.795260i) q^{5} +(-4.46694 + 0.731236i) q^{6} +(0.853432 - 2.12814i) q^{7} +(-7.38859 - 0.286711i) q^{8} +(2.81773 - 1.02976i) q^{9} +(6.75458 + 2.16577i) q^{10} +(0.0568816 + 0.0323522i) q^{11} +(8.27170 - 1.24449i) q^{12} +(1.14846 + 2.57054i) q^{13} +(-2.30200 + 5.53221i) q^{14} +(-4.66625 - 0.572899i) q^{15} +(9.65149 + 0.499557i) q^{16} +(4.95951 + 2.25437i) q^{17} +(-7.39779 + 2.59566i) q^{18} +(-0.279974 - 0.408212i) q^{19} +(-12.4297 - 4.16339i) q^{20} +(0.813104 - 3.88727i) q^{21} +(-0.147544 - 0.0864611i) q^{22} +(1.39790 - 4.26474i) q^{23} +(-12.6881 + 1.74152i) q^{24} +(1.96093 + 1.32636i) q^{25} +(-2.91420 - 6.75588i) q^{26} +(4.49488 - 2.60693i) q^{27} +(4.38591 - 10.1677i) q^{28} +(0.714812 - 0.457011i) q^{29} +(12.1740 + 1.65469i) q^{30} +(-2.27510 - 8.38233i) q^{31} +(-10.4460 - 0.676190i) q^{32} +(0.106781 + 0.0380062i) q^{33} +(-12.8835 - 6.05845i) q^{34} +(-3.90723 + 4.84421i) q^{35} +(13.7320 - 4.61965i) q^{36} +(-0.284650 - 0.0559034i) q^{37} +(0.717807 + 1.07616i) q^{38} +(2.73476 + 4.03746i) q^{39} +(18.9467 + 6.61991i) q^{40} +(2.93475 - 1.11134i) q^{41} +(-2.25605 + 10.1303i) q^{42} +(-9.06758 + 3.98109i) q^{43} +(0.270574 + 0.163292i) q^{44} +(-8.13143 + 0.431576i) q^{45} +(-3.79693 + 11.0969i) q^{46} +(3.26040 - 12.0125i) q^{47} +(16.6118 - 2.06164i) q^{48} +(1.25981 + 1.20405i) q^{49} +(-5.07929 - 3.53215i) q^{50} +(9.13920 + 2.34771i) q^{51} +(5.22360 + 12.5535i) q^{52} +(-5.68289 + 6.02352i) q^{53} +(-11.8336 + 6.66029i) q^{54} +(-0.121889 - 0.129195i) q^{55} +(-6.91582 + 15.4793i) q^{56} +(-0.600740 - 0.611701i) q^{57} +(-1.88331 + 1.17006i) q^{58} +(-0.184081 + 0.0312329i) q^{59} +(-22.4562 - 3.34846i) q^{60} +(5.12610 - 9.43383i) q^{61} +(5.66186 + 21.9807i) q^{62} +(0.213267 - 6.87536i) q^{63} +(8.00283 + 0.622029i) q^{64} +(-0.936217 - 7.58434i) q^{65} +(-0.277744 - 0.102921i) q^{66} +(-11.6383 + 6.03462i) q^{67} +(23.6620 + 11.5029i) q^{68} +(1.09671 - 7.69569i) q^{69} +(10.3736 - 12.5264i) q^{70} +(-0.561978 - 0.435566i) q^{71} +(-21.1143 + 6.80058i) q^{72} +(12.0193 - 3.85384i) q^{73} +(0.741929 + 0.155698i) q^{74} +(3.74485 + 1.67017i) q^{75} +(-1.30069 - 2.00572i) q^{76} +(0.117395 - 0.0934419i) q^{77} +(-7.00979 - 10.6427i) q^{78} +(3.14172 - 16.5625i) q^{79} +(-24.6500 - 8.97188i) q^{80} +(6.87920 - 5.80316i) q^{81} +(-7.70633 + 2.80488i) q^{82} +(-1.95457 - 11.9893i) q^{83} +(4.41086 - 18.6654i) q^{84} +(-11.0780 - 9.79459i) q^{85} +(23.8290 - 10.0966i) q^{86} +(1.08117 - 0.995243i) q^{87} +(-0.410999 - 0.255346i) q^{88} +(3.32409 + 1.35804i) q^{89} +(21.2628 - 0.853030i) q^{90} +(6.45062 - 0.250314i) q^{91} +(7.28127 - 20.4148i) q^{92} +(-6.41078 - 13.6096i) q^{93} +(-8.92559 + 31.2798i) q^{94} +(0.401947 + 1.28203i) q^{95} +(-18.0202 + 2.00023i) q^{96} +(-1.10415 + 4.79675i) q^{97} +(-3.25132 - 3.18887i) q^{98} +(0.193592 + 0.0325854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Introduction

L-functions

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