LMFDB - Embedded newform 570.2.bi.a.557.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(17,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 9, 20]))

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

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

chi := DirichletCharacter("570.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bi (of order $36$, degree $12$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$40$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			557.31
Character	$\chi$	$=$	570.557
Dual form			570.2.bi.a.263.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0871557 - 0.996195i) q^{2} +(0.363458 + 1.69349i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(-1.95247 - 1.08989i) q^{5} +(1.71872 - 0.214478i) q^{6} +(-1.28322 + 0.343837i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-2.73580 + 1.23102i) q^{9} +O(q^{10})$	\(q+(0.0871557 - 0.996195i) q^{2} +(0.363458 + 1.69349i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(-1.95247 - 1.08989i) q^{5} +(1.71872 - 0.214478i) q^{6} +(-1.28322 + 0.343837i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-2.73580 + 1.23102i) q^{9} +(-1.25591 + 1.85005i) q^{10} +(4.64456 - 2.68154i) q^{11} +(-0.0638656 - 1.73087i) q^{12} +(1.47825 - 3.17012i) q^{13} +(0.230689 + 1.30830i) q^{14} +(1.13607 - 3.70261i) q^{15} +(0.939693 + 0.342020i) q^{16} +(0.458283 - 5.23819i) q^{17} +(0.987899 + 2.83268i) q^{18} +(4.21168 - 1.12327i) q^{19} +(1.73355 + 1.41237i) q^{20} +(-1.04868 - 2.04814i) q^{21} +(-2.26653 - 4.86059i) q^{22} +(6.24450 - 4.37245i) q^{23} +(-1.72985 - 0.0872330i) q^{24} +(2.62429 + 4.25595i) q^{25} +(-3.02921 - 1.74892i) q^{26} +(-3.07907 - 4.18561i) q^{27} +(1.32343 - 0.115785i) q^{28} +(-1.96385 - 1.64787i) q^{29} +(-3.58951 - 1.45445i) q^{30} +(-4.70677 + 8.15237i) q^{31} +(0.422618 - 0.906308i) q^{32} +(6.22925 + 6.89087i) q^{33} +(-5.17832 - 0.913077i) q^{34} +(2.88019 + 0.727229i) q^{35} +(2.90800 - 0.737255i) q^{36} +(-2.77322 - 2.77322i) q^{37} +(-0.751926 - 4.29355i) q^{38} +(5.90583 + 1.35119i) q^{39} +(1.55809 - 1.60386i) q^{40} +(1.57136 - 4.31727i) q^{41} +(-2.13174 + 0.866181i) q^{42} +(0.480575 + 0.336502i) q^{43} +(-5.03964 + 1.83428i) q^{44} +(6.68324 + 0.578169i) q^{45} +(-3.81156 - 6.60182i) q^{46} +(-3.09441 + 0.270725i) q^{47} +(-0.237668 + 1.71567i) q^{48} +(-4.53376 + 2.61757i) q^{49} +(4.46847 - 2.24338i) q^{50} +(9.03738 - 1.12777i) q^{51} +(-2.00628 + 2.86526i) q^{52} +(-1.61214 + 1.12883i) q^{53} +(-4.43804 + 2.70255i) q^{54} +(-11.9909 + 0.173583i) q^{55} -1.32848i q^{56} +(3.43302 + 6.72416i) q^{57} +(-1.81276 + 1.81276i) q^{58} +(11.6185 - 9.74909i) q^{59} +(-1.76176 + 3.44909i) q^{60} +(-1.33887 + 7.59310i) q^{61} +(7.71113 + 5.39939i) q^{62} +(3.08735 - 2.52034i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-6.34131 + 4.57844i) q^{65} +(7.40756 - 5.60496i) q^{66} +(-1.05602 - 12.0703i) q^{67} +(-1.36092 + 5.07903i) q^{68} +(9.67430 + 8.98578i) q^{69} +(0.975486 - 2.80584i) q^{70} +(-5.16453 + 0.910646i) q^{71} +(-0.481001 - 2.96119i) q^{72} +(11.3679 - 5.30093i) q^{73} +(-3.00437 + 2.52096i) q^{74} +(-6.25357 + 5.99107i) q^{75} +(-4.34275 + 0.374857i) q^{76} +(-5.03796 + 5.03796i) q^{77} +(1.86078 - 5.76559i) q^{78} +(0.195979 - 0.538447i) q^{79} +(-1.46196 - 1.69194i) q^{80} +(5.96916 - 6.73566i) q^{81} +(-4.16389 - 1.94165i) q^{82} +(-12.9834 + 3.47889i) q^{83} +(0.677091 + 2.19912i) q^{84} +(-6.60382 + 9.72795i) q^{85} +(0.377106 - 0.449418i) q^{86} +(2.07686 - 3.92469i) q^{87} +(1.38806 + 5.18033i) q^{88} +(-7.24577 + 2.63724i) q^{89} +(1.15845 - 6.60742i) q^{90} +(-0.806911 + 4.57622i) q^{91} +(-6.90890 + 3.22167i) q^{92} +(-15.5167 - 5.00781i) q^{93} +3.10623i q^{94} +(-9.44743 - 2.39710i) q^{95} +(1.68842 + 0.386293i) q^{96} +(3.27952 + 0.286921i) q^{97} +(2.21246 + 4.74464i) q^{98} +(-9.40552 + 13.0537i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q+O(q^{10}) $ 480 * q	$ 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) $ 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$3$	0.363458	+	1.69349i	0.209843	+	0.977735i
$3$	0.363458	+	1.69349i	0.209843	+	0.977735i
$4$	−0.984808	−	0.173648i	−0.492404	−	0.0868241i
$5$	−1.95247	−	1.08989i	−0.873172	−	0.487412i
$5$	−1.95247	−	1.08989i	−0.873172	−	0.487412i
$6$	1.71872	−	0.214478i	0.701665	−	0.0875603i
$7$	−1.28322	+	0.343837i	−0.485010	+	0.129958i	−0.493035	−	0.870010i	$-0.664112\pi$
$7$	−1.28322	+	0.343837i	−0.485010	+	0.129958i	0.00802443	+	0.999968i	$0.497446\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$	−2.73580	+	1.23102i	−0.911932	+	0.410341i
$10$	−1.25591	+	1.85005i	−0.397153	+	0.585038i
$11$	4.64456	−	2.68154i	1.40039	−	0.808513i	0.405954	−	0.913893i	$-0.366939\pi$
$11$	4.64456	−	2.68154i	1.40039	−	0.808513i	0.994432	+	0.105380i	$0.0336059\pi$
$12$	−0.0638656	−	1.73087i	−0.0184364	−	0.499660i
$13$	1.47825	−	3.17012i	0.409993	−	0.879232i	−0.587551	−	0.809187i	$-0.699908\pi$
$13$	1.47825	−	3.17012i	0.409993	−	0.879232i	0.997544	−	0.0700450i	$-0.0223143\pi$
$14$	0.230689	+	1.30830i	0.0616541	+	0.349658i
$15$	1.13607	−	3.70261i	0.293331	−	0.956011i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	0.458283	−	5.23819i	0.111150	−	1.27045i	−0.711819	−	0.702363i	$-0.752129\pi$
$17$	0.458283	−	5.23819i	0.111150	−	1.27045i	0.822969	−	0.568086i	$-0.192316\pi$
$18$	0.987899	+	2.83268i	0.232850	+	0.667668i
$19$	4.21168	−	1.12327i	0.966226	−	0.257696i
$19$	4.21168	−	1.12327i	0.966226	−	0.257696i
$20$	1.73355	+	1.41237i	0.387634	+	0.315816i
$21$	−1.04868	−	2.04814i	−0.228840	−	0.446941i
$22$	−2.26653	−	4.86059i	−0.483226	−	1.03628i
$23$	6.24450	−	4.37245i	1.30207	−	0.911718i	0.302922	−	0.953015i	$-0.402038\pi$
$23$	6.24450	−	4.37245i	1.30207	−	0.911718i	0.999147	+	0.0412973i	$0.0131491\pi$
$24$	−1.72985	−	0.0872330i	−0.353105	−	0.0178064i
$25$	2.62429	+	4.25595i	0.524859	+	0.851189i
$26$	−3.02921	−	1.74892i	−0.594078	−	0.342991i
$27$	−3.07907	−	4.18561i	−0.592567	−	0.805521i
$28$	1.32343	−	0.115785i	0.250104	−	0.0218813i
$29$	−1.96385	−	1.64787i	−0.364678	−	0.306001i	0.441974	−	0.897028i	$-0.354278\pi$
$29$	−1.96385	−	1.64787i	−0.364678	−	0.306001i	−0.806652	+	0.591027i	$0.798723\pi$
$30$	−3.58951	−	1.45445i	−0.655352	−	0.265545i
$31$	−4.70677	+	8.15237i	−0.845362	+	1.46421i	0.0399451	+	0.999202i	$0.487282\pi$
$31$	−4.70677	+	8.15237i	−0.845362	+	1.46421i	−0.885307	+	0.465007i	$0.846052\pi$
$32$	0.422618	−	0.906308i	0.0747091	−	0.160214i
$33$	6.22925	+	6.89087i	1.08437	+	1.19955i
$34$	−5.17832	−	0.913077i	−0.888074	−	0.156591i
$35$	2.88019	+	0.727229i	0.486840	+	0.122924i
$36$	2.90800	−	0.737255i	0.484666	−	0.122876i
$37$	−2.77322	−	2.77322i	−0.455914	−	0.455914i	0.441397	−	0.897312i	$-0.354483\pi$
$37$	−2.77322	−	2.77322i	−0.455914	−	0.455914i	−0.897312	+	0.441397i	$0.854483\pi$
$38$	−0.751926	−	4.29355i	−0.121979	−	0.696506i
$39$	5.90583	+	1.35119i	0.945690	+	0.216364i
$40$	1.55809	−	1.60386i	0.246355	−	0.253592i
$41$	1.57136	−	4.31727i	0.245405	−	0.674245i	−0.754435	−	0.656374i	$-0.772089\pi$
$41$	1.57136	−	4.31727i	0.245405	−	0.674245i	0.999840	−	0.0178703i	$-0.00568858\pi$
$42$	−2.13174	+	0.866181i	−0.328935	+	0.133655i
$43$	0.480575	+	0.336502i	0.0732869	+	0.0513161i	0.609646	−	0.792674i	$-0.291312\pi$
$43$	0.480575	+	0.336502i	0.0732869	+	0.0513161i	−0.536359	+	0.843990i	$0.680201\pi$
$44$	−5.03964	+	1.83428i	−0.759754	+	0.276528i
$45$	6.68324	+	0.578169i	0.996279	+	0.0861883i
$46$	−3.81156	−	6.60182i	−0.561984	−	0.973386i
$47$	−3.09441	+	0.270725i	−0.451365	+	0.0394894i	−0.310573	−	0.950550i	$-0.600521\pi$
$47$	−3.09441	+	0.270725i	−0.451365	+	0.0394894i	−0.140793	+	0.990039i	$0.544965\pi$
$48$	−0.237668	+	1.71567i	−0.0343044	+	0.247635i
$49$	−4.53376	+	2.61757i	−0.647680	+	0.373938i
$50$	4.46847	−	2.24338i	0.631938	−	0.317261i
$51$	9.03738	−	1.12777i	1.26549	−	0.157919i
$52$	−2.00628	+	2.86526i	−0.278220	+	0.397340i
$53$	−1.61214	+	1.12883i	−0.221444	+	0.155057i	−0.679035	−	0.734106i	$-0.737601\pi$
$53$	−1.61214	+	1.12883i	−0.221444	+	0.155057i	0.457591	+	0.889163i	$0.348713\pi$
$54$	−4.43804	+	2.70255i	−0.603941	+	0.367771i
$55$	−11.9909	+	0.173583i	−1.61686	+	0.0234060i
$56$		−	1.32848i		−	0.177526i
$57$	3.43302	+	6.72416i	0.454714	+	0.890637i
$58$	−1.81276	+	1.81276i	−0.238027	+	0.238027i
$59$	11.6185	−	9.74909i	1.51260	−	1.26922i	0.654107	−	0.756402i	$-0.273045\pi$
$59$	11.6185	−	9.74909i	1.51260	−	1.26922i	0.858495	−	0.512822i	$-0.171400\pi$
$60$	−1.76176	+	3.44909i	−0.227442	+	0.445275i
$61$	−1.33887	+	7.59310i	−0.171425	+	0.972197i	0.770766	+	0.637119i	$0.219874\pi$
$61$	−1.33887	+	7.59310i	−0.171425	+	0.972197i	−0.942190	+	0.335078i	$0.891237\pi$
$62$	7.71113	+	5.39939i	0.979314	+	0.685723i
$63$	3.08735	−	2.52034i	0.388969	−	0.317533i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−6.34131	+	4.57844i	−0.786542	+	0.567885i
$66$	7.40756	−	5.60496i	0.911808	−	0.689923i
$67$	−1.05602	−	12.0703i	−0.129013	−	1.47462i	−0.734413	−	0.678703i	$-0.762543\pi$
$67$	−1.05602	−	12.0703i	−0.129013	−	1.47462i	0.605400	−	0.795921i	$-0.293013\pi$
$68$	−1.36092	+	5.07903i	−0.165036	+	0.615923i
$69$	9.67430	+	8.98578i	1.16465	+	1.08176i
$70$	0.975486	−	2.80584i	0.116593	−	0.335363i
$71$	−5.16453	+	0.910646i	−0.612917	+	0.108074i	−0.471485	−	0.881874i	$-0.656282\pi$
$71$	−5.16453	+	0.910646i	−0.612917	+	0.108074i	−0.141432	+	0.989948i	$0.545171\pi$
$72$	−0.481001	−	2.96119i	−0.0566865	−	0.348979i
$73$	11.3679	−	5.30093i	1.33051	−	0.620427i	0.378246	−	0.925705i	$-0.376527\pi$
$73$	11.3679	−	5.30093i	1.33051	−	0.620427i	0.952263	+	0.305278i	$0.0987494\pi$
$74$	−3.00437	+	2.52096i	−0.349251	+	0.293056i
$75$	−6.25357	+	5.99107i	−0.722100	+	0.691789i
$76$	−4.34275	+	0.374857i	−0.498148	+	0.0429991i
$77$	−5.03796	+	5.03796i	−0.574129	+	0.574129i
$78$	1.86078	−	5.76559i	0.210691	−	0.652825i
$79$	0.195979	−	0.538447i	0.0220493	−	0.0605800i	−0.928180	−	0.372132i	$-0.878627\pi$
$79$	0.195979	−	0.538447i	0.0220493	−	0.0605800i	0.950229	+	0.311552i	$0.100849\pi$
$80$	−1.46196	−	1.69194i	−0.163452	−	0.189165i
$81$	5.96916	−	6.73566i	0.663240	−	0.748407i
$82$	−4.16389	−	1.94165i	−0.459825	−	0.214420i
$83$	−12.9834	+	3.47889i	−1.42511	+	0.381858i	−0.887295	−	0.461203i	$-0.847418\pi$
$83$	−12.9834	+	3.47889i	−1.42511	+	0.381858i	−0.537819	+	0.843061i	$0.680751\pi$
$84$	0.677091	+	2.19912i	0.0738767	+	0.239944i
$85$	−6.60382	+	9.72795i	−0.716285	+	1.05514i
$86$	0.377106	−	0.449418i	0.0406644	−	0.0484620i
$87$	2.07686	−	3.92469i	0.222663	−	0.420771i
$88$	1.38806	+	5.18033i	0.147968	+	0.552225i
$89$	−7.24577	+	2.63724i	−0.768050	+	0.279547i	−0.696180	−	0.717867i	$-0.745119\pi$
$89$	−7.24577	+	2.63724i	−0.768050	+	0.279547i	−0.0718692	+	0.997414i	$0.522896\pi$
$90$	1.15845	−	6.60742i	0.122112	−	0.696483i
$91$	−0.806911	+	4.57622i	−0.0845873	+	0.479718i
$92$	−6.90890	+	3.22167i	−0.720303	+	0.335883i
$93$	−15.5167	−	5.00781i	−1.60900	−	0.519286i
$94$			3.10623i			0.320383i
$95$	−9.44743	−	2.39710i	−0.969286	−	0.245937i
$96$	1.68842	+	0.386293i	0.172324	+	0.0394259i
$97$	3.27952	+	0.286921i	0.332985	+	0.0291324i	0.252422	−	0.967617i	$-0.418773\pi$
$97$	3.27952	+	0.286921i	0.332985	+	0.0291324i	0.0805626	+	0.996750i	$0.474328\pi$
$98$	2.21246	+	4.74464i	0.223492	+	0.479281i
$99$	−9.40552	+	13.0537i	−0.945291	+	1.31195i
$100$	−1.84539	−	4.64699i	−0.184539	−	0.464699i
$101$	2.79744	+	7.68592i	0.278356	+	0.764777i	0.997549	+	0.0699670i	$0.0222894\pi$
$101$	2.79744	+	7.68592i	0.278356	+	0.764777i	−0.719193	+	0.694810i	$0.755488\pi$
$102$	−0.335818	−	9.10128i	−0.0332509	−	0.901161i
$103$	−3.19103	−	0.855033i	−0.314421	−	0.0842489i	0.0981575	−	0.995171i	$-0.468705\pi$
$103$	−3.19103	−	0.855033i	−0.314421	−	0.0842489i	−0.412579	+	0.910922i	$0.635372\pi$
$104$	2.67950	+	2.24837i	0.262746	+	0.220470i
$105$	−0.184725	+	5.14188i	−0.0180273	+	0.501796i
$106$	0.984029	+	1.70439i	0.0955773	+	0.165545i
$107$	−1.55747	−	5.81255i	−0.150566	−	0.561921i	−0.999444	−	0.0333321i	$-0.989388\pi$
$107$	−1.55747	−	5.81255i	−0.150566	−	0.561921i	0.848878	−	0.528589i	$-0.177279\pi$
$108$	2.30547	+	4.65670i	0.221844	+	0.448091i
$109$	2.40479	−	0.424030i	0.230337	−	0.0406147i	−0.0572880	−	0.998358i	$-0.518245\pi$
$109$	2.40479	−	0.424030i	0.230337	−	0.0406147i	0.287625	+	0.957743i	$0.407134\pi$
$110$	−0.872156	+	11.9604i	−0.0831568	+	1.14038i
$111$	3.68846	−	5.70436i	0.350093	−	0.541434i
$112$	−1.32343	−	0.115785i	−0.125052	−	0.0109406i
$113$	2.14681	+	2.14681i	0.201955	+	0.201955i	0.800837	−	0.598882i	$-0.204388\pi$
$113$	2.14681	+	2.14681i	0.201955	+	0.201955i	−0.598882	+	0.800837i	$0.704388\pi$
$114$	6.99778	−	2.83390i	0.655403	−	0.265420i
$115$	−16.9577	+	1.73128i	−1.58131	+	0.161443i
$116$	1.64787	+	1.96385i	0.153001	+	0.182339i
$117$	−0.141702	+	10.4926i	−0.0131003	+	0.970037i
$118$	−8.69937	−	12.4240i	−0.800842	−	1.14372i
$119$	1.21301	+	6.87931i	0.111196	+	0.630625i
$120$	3.28241	+	2.05566i	0.299642	+	0.187656i
$121$	8.88126	−	15.3828i	0.807388	−	1.39844i
$122$	7.44752	+	1.99556i	0.674267	+	0.180669i
$123$	7.88237	+	1.09193i	0.710729	+	0.0984558i
$124$	6.05091	−	7.21120i	0.543388	−	0.647585i
$125$	−0.485361	−	11.1698i	−0.0434120	−	0.999057i
$126$	−2.24167	−	3.29526i	−0.199703	−	0.293565i
$127$	−4.86876	−	2.27034i	−0.432033	−	0.201460i	0.194422	−	0.980918i	$-0.437717\pi$
$127$	−4.86876	−	2.27034i	−0.432033	−	0.201460i	−0.626455	+	0.779458i	$0.715495\pi$
$128$	−0.573576	+	0.819152i	−0.0506975	+	0.0724035i
$129$	−0.395193	+	0.936151i	−0.0347948	+	0.0824235i
$130$	4.00833	+	6.71621i	0.351554	+	0.589051i
$131$	10.5741	+	12.6017i	0.923861	+	1.10101i	0.994627	+	0.103521i	$0.0330110\pi$
$131$	10.5741	+	12.6017i	0.923861	+	1.10101i	−0.0707665	+	0.997493i	$0.522545\pi$
$132$	−4.93802	−	7.86788i	−0.429800	−	0.684811i
$133$	−5.01827	+	2.88953i	−0.435140	+	0.250554i
$134$	−12.1164			−1.04670
$135$	1.44996	+	11.5281i	0.124792	+	0.992183i
$136$	4.94109	+	1.79841i	0.423695	+	0.154212i
$137$	8.44657	+	12.0629i	0.721639	+	1.03061i	0.997587	+	0.0694345i	$0.0221195\pi$
$137$	8.44657	+	12.0629i	0.721639	+	1.03061i	−0.275948	+	0.961173i	$0.588992\pi$
$138$	9.79476	−	8.85432i	0.833785	−	0.753730i
$139$	1.32450	+	3.63904i	0.112343	+	0.308660i	0.983104	−	0.183046i	$-0.0585958\pi$
$139$	1.32450	+	3.63904i	0.112343	+	0.308660i	−0.870761	+	0.491706i	$0.836374\pi$
$140$	−2.71015	−	1.21632i	−0.229049	−	0.102798i
$141$	−1.58316	−	5.14194i	−0.133326	−	0.433029i
$142$	0.457062	+	5.22424i	0.0383558	+	0.438409i
$143$	−1.63497	−	18.6878i	−0.136723	−	1.56275i
$144$	−2.99184	+	0.221086i	−0.249320	+	0.0184239i
$145$	2.03838	+	5.35779i	0.169278	+	0.444940i
$146$	−4.28998	−	11.7866i	−0.355041	−	0.975468i
$147$	−6.08065	−	6.72648i	−0.501523	−	0.554791i
$148$	2.24952	+	3.21265i	0.184910	+	0.264078i
$149$	12.3106	+	4.48069i	1.00852	+	0.367072i	0.792865	−	0.609397i	$-0.208588\pi$
$149$	12.3106	+	4.48069i	1.00852	+	0.367072i	0.215657	+	0.976469i	$0.430811\pi$
$150$	5.42323	+	6.75193i	0.442805	+	0.551293i
$151$	21.4721			1.74737			0.873686	−	0.486490i	$-0.161723\pi$
$151$	21.4721			1.74737			0.873686	+	0.486490i	$0.161723\pi$
$152$	−0.00506498	+	4.35890i	−0.000410824	+	0.353553i
$153$	5.19457	+	14.8948i	0.419956	+	1.20417i
$154$	4.57970	+	5.45787i	0.369043	+	0.439808i
$155$	18.0750	−	10.7874i	1.45182	−	0.866467i
$156$	−5.58148	−	2.35620i	−0.446876	−	0.188647i
$157$	0.0739605	−	0.105627i	0.00590269	−	0.00842992i	−0.816190	−	0.577784i	$-0.803918\pi$
$157$	0.0739605	−	0.105627i	0.00590269	−	0.00842992i	0.822093	+	0.569354i	$0.192807\pi$
$158$	−0.519317	−	0.242162i	−0.0413147	−	0.0192654i
$159$	−2.49761	−	2.31985i	−0.198073	−	0.183976i
$160$	−1.81292	+	1.30893i	−0.143324	+	0.103480i
$161$	−6.50964	+	7.75788i	−0.513031	+	0.611407i
$162$	−6.18978	−	6.53350i	−0.486315	−	0.513320i
$163$	12.9706	+	3.47547i	1.01594	+	0.272220i	0.728109	−	0.685462i	$-0.240400\pi$
$163$	12.9706	+	3.47547i	1.01594	+	0.272220i	0.287830	+	0.957682i	$0.407066\pi$
$164$	−2.29717	+	3.97882i	−0.179379	+	0.310694i
$165$	−4.65217	−	20.2434i	−0.362171	−	1.57595i
$166$	2.33408	+	13.2372i	0.181159	+	1.02741i
$167$	−1.24372	−	1.77622i	−0.0962421	−	0.137448i	0.768143	−	0.640278i	$-0.221181\pi$
$167$	−1.24372	−	1.77622i	−0.0962421	−	0.137448i	−0.864385	+	0.502830i	$0.832292\pi$
$168$	2.24977	−	0.482848i	0.173573	−	0.0372525i
$169$	0.491824	+	0.586133i	0.0378326	+	0.0450872i
$170$	9.11537	+	7.42654i	0.699117	+	0.569589i
$171$	−10.1395	+	8.25772i	−0.775389	+	0.631484i
$172$	−0.414841	−	0.414841i	−0.0316313	−	0.0316313i
$173$	−7.48477	−	0.654833i	−0.569057	−	0.0497860i	−0.201003	−	0.979591i	$-0.564420\pi$
$173$	−7.48477	−	0.654833i	−0.569057	−	0.0497860i	−0.368054	+	0.929805i	$0.619976\pi$
$174$	−3.72874	−	2.41102i	−0.282675	−	0.182779i
$175$	−4.83089	−	4.55897i	−0.365181	−	0.344626i
$176$	5.28159	−	0.931287i	0.398115	−	0.0701984i
$177$	20.7328	+	16.1324i	1.55837	+	1.21259i
$178$	1.99570	+	7.44804i	0.149584	+	0.558255i
$179$	−6.10778	−	10.5790i	−0.456517	−	0.790711i	0.542257	−	0.840213i	$-0.317570\pi$
$179$	−6.10778	−	10.5790i	−0.456517	−	0.790711i	−0.998774	+	0.0495017i	$0.984237\pi$
$180$	−6.48131	−	1.72992i	−0.483088	−	0.128940i
$181$	8.94144	+	7.50276i	0.664612	+	0.557675i	0.911465	−	0.411377i	$-0.134952\pi$
$181$	8.94144	+	7.50276i	0.664612	+	0.557675i	−0.246853	+	0.969053i	$0.579397\pi$
$182$	4.48848	+	1.20268i	0.332708	+	0.0891489i
$183$	−13.3454	+	0.492419i	−0.986524	+	0.0364006i
$184$	2.60726	+	7.16340i	0.192210	+	0.528093i
$185$	2.39214	+	8.43713i	0.175874	+	0.620310i
$186$	−6.34112	+	15.0211i	−0.464954	+	1.10140i
$187$	−11.9179	−	25.5580i	−0.871522	−	1.86898i
$188$	3.09441	+	0.270725i	0.225683	+	0.0197447i
$189$	5.39028	+	4.31234i	0.392085	+	0.313677i
$190$	−3.21137	+	9.20256i	−0.232977	+	0.667624i
$191$			26.1328i			1.89091i	0.325760	+	0.945453i	$0.394380\pi$
$191$			26.1328i			1.89091i	−0.325760	+	0.945453i	$0.605620\pi$
$192$	0.531979	−	1.64833i	0.0383923	−	0.118958i
$193$	−12.8346	+	5.98487i	−0.923855	+	0.430801i	−0.825533	−	0.564354i	$-0.809125\pi$
$193$	−12.8346	+	5.98487i	−0.923855	+	0.430801i	−0.0983220	+	0.995155i	$0.531348\pi$
$194$	0.571659	−	3.24204i	0.0410427	−	0.232765i
$195$	−10.0583	−	9.07485i	−0.720292	−	0.649864i
$196$	4.91942	−	1.79052i	0.351387	−	0.127894i
$197$	−0.464609	−	1.73395i	−0.0331020	−	0.123539i	0.947398	−	0.320059i	$-0.103703\pi$
$197$	−0.464609	−	1.73395i	−0.0331020	−	0.123539i	−0.980500	+	0.196520i	$0.937036\pi$
$198$	12.1843	+	10.5074i	0.865899	+	0.746731i
$199$	−1.70984	+	2.03771i	−0.121207	+	0.144449i	−0.823236	−	0.567700i	$-0.807833\pi$
$199$	−1.70984	+	2.03771i	−0.121207	+	0.144449i	0.702028	+	0.712149i	$0.252278\pi$
$200$	−4.79015	+	1.43335i	−0.338714	+	0.101353i
$201$	20.0571	−	6.17540i	1.41472	−	0.435579i
$202$	7.90048	−	2.11693i	0.555876	−	0.148947i
$203$	3.08664	+	1.43933i	0.216640	+	0.101021i
$204$	−9.09592	−	0.458689i	−0.636841	−	0.0321146i
$205$	−7.77337	+	6.71675i	−0.542916	+	0.469118i
$206$	−1.12990	+	3.10436i	−0.0787235	+	0.216291i
$207$	−11.7011	+	19.6493i	−0.813282	+	1.36572i
$208$	2.47334	−	2.47334i	0.171496	−	0.171496i
$209$	16.5493	−	16.5109i	1.14474	−	1.14208i
$210$	5.10621	+	0.632166i	0.352362	+	0.0436236i
$211$	−1.98922	+	1.66915i	−0.136943	+	0.114909i	−0.708686	−	0.705524i	$-0.750712\pi$
$211$	−1.98922	+	1.66915i	−0.136943	+	0.114909i	0.571743	+	0.820433i	$0.306267\pi$
$212$	1.78367	−	0.831737i	0.122503	−	0.0571239i
$213$	−3.41926	−	8.41508i	−0.234284	−	0.576592i
$214$	−5.92618	+	1.04495i	−0.405105	+	0.0714310i
$215$	−0.571559	−	1.18078i	−0.0389800	−	0.0805287i
$216$	4.83991	−	1.89084i	0.329314	−	0.128655i
$217$	3.23672	−	12.0796i	0.219723	−	0.820018i
$218$	−0.212825	−	2.43260i	−0.0144143	−	0.164756i
$219$	13.1088	+	17.3247i	0.885811	+	1.17069i
$220$	11.8389	+	1.91126i	0.798179	+	0.128857i
$221$	−15.9282	−	9.19617i	−1.07145	−	0.618601i
$222$	−5.36118	−	4.17159i	−0.359819	−	0.279979i
$223$	−22.1860	−	15.5348i	−1.48569	−	1.04029i	−0.984586	−	0.174900i	$-0.944040\pi$
$223$	−22.1860	−	15.5348i	−1.48569	−	1.04029i	−0.501101	−	0.865389i	$-0.667071\pi$
$224$	−0.230689	+	1.30830i	−0.0154135	+	0.0874145i
$225$	−12.4187	−	8.41283i	−0.827914	−	0.560856i
$226$	2.32574	−	1.95153i	0.154706	−	0.129814i
$227$	−10.5330	+	10.5330i	−0.699098	+	0.699098i	−0.964216	−	0.265118i	$-0.914589\pi$
$227$	−10.5330	+	10.5330i	−0.699098	+	0.699098i	0.265118	+	0.964216i	$0.414589\pi$
$228$	−2.21322	−	7.21815i	−0.146574	−	0.478033i
$229$			6.15926i			0.407015i	0.979073	+	0.203508i	$0.0652342\pi$
$229$			6.15926i			0.407015i	−0.979073	+	0.203508i	$0.934766\pi$
$230$	0.246733	+	17.0440i	0.0162691	+	1.12385i
$231$	−10.3628	−	6.70063i	−0.681822	−	0.440869i
$232$	2.10000	−	1.47044i	0.137872	−	0.0965388i
$233$	16.0181	−	22.8762i	1.04938	−	1.49867i	0.193773	−	0.981046i	$-0.437927\pi$
$233$	16.0181	−	22.8762i	1.04938	−	1.49867i	0.855608	−	0.517625i	$-0.173184\pi$
$234$	10.4403	+	1.05565i	0.682502	+	0.0690099i
$235$	6.33680	+	2.84397i	0.413367	+	0.185520i
$236$	−13.1349	+	7.58345i	−0.855010	+	0.493640i
$237$	0.983083	+	0.136184i	0.0638581	+	0.00884613i
$238$	6.95885	−	0.608821i	0.451075	−	0.0394640i
$239$	−5.78737	−	10.0240i	−0.374354	−	0.648400i	0.615876	−	0.787843i	$-0.288802\pi$
$239$	−5.78737	−	10.0240i	−0.374354	−	0.648400i	−0.990230	+	0.139443i	$0.955469\pi$
$240$	2.33392	−	3.09076i	0.150654	−	0.199508i
$241$	−0.940669	+	0.342376i	−0.0605938	+	0.0220544i	−0.372139	−	0.928177i	$-0.621376\pi$
$241$	−0.940669	+	0.342376i	−0.0605938	+	0.0220544i	0.311545	+	0.950231i	$0.399153\pi$
$242$	−14.5502	−	10.1882i	−0.935323	−	0.654920i
$243$	13.5763	+	7.66057i	0.870920	+	0.491426i
$244$	2.63706	−	7.24526i	0.168820	−	0.463830i
$245$	11.7049	−	0.169443i	0.747798	−	0.0108253i
$246$	1.77477	−	7.75720i	0.113155	−	0.494581i
$247$	2.66501	−	15.0120i	0.169571	−	0.955190i
$248$	−6.65638	−	6.65638i	−0.422681	−	0.422681i
$249$	−10.6104	−	20.7228i	−0.672406	−	1.31325i
$250$	−11.1696	−	0.489998i	−0.706427	−	0.0309902i
$251$	−20.4656	−	3.60863i	−1.29178	−	0.227775i	−0.514802	−	0.857309i	$-0.672135\pi$
$251$	−20.4656	−	3.60863i	−1.29178	−	0.227775i	−0.776973	+	0.629534i	$0.783246\pi$
$252$	−3.47809	+	1.94593i	−0.219099	+	0.122582i
$253$	17.2781	−	37.0529i	1.08626	−	2.32950i
$254$	−2.68604	+	4.65236i	−0.168537	+	0.291915i
$255$	−18.8744	−	7.64778i	−1.18196	−	0.478923i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−4.47707	+	0.391693i	−0.279272	+	0.0244332i	−0.225931	−	0.974143i	$-0.572543\pi$
$257$	−4.47707	+	0.391693i	−0.279272	+	0.0244332i	−0.0533408	+	0.998576i	$0.516987\pi$
$258$	0.898146	+	0.475280i	0.0559161	+	0.0295896i
$259$	4.51217	+	2.60511i	0.280373	+	0.161873i
$260$	7.04001	−	3.40773i	0.436603	−	0.211338i
$261$	7.40126	+	2.09068i	0.458127	+	0.129410i
$262$	13.4753	−	9.43552i	0.832508	−	0.582929i
$263$	−1.77574	−	3.80808i	−0.109497	−	0.234816i	0.843922	−	0.536465i	$-0.180241\pi$
$263$	−1.77574	−	3.80808i	−0.109497	−	0.234816i	−0.953419	+	0.301649i	$0.902463\pi$
$264$	−8.26832	+	4.23350i	−0.508880	+	0.260554i
$265$	4.37795	−	0.446964i	0.268936	−	0.0274568i
$266$	2.44117	+	5.25102i	0.149677	+	0.321961i
$267$	−7.09967	−	11.3121i	−0.434493	−	0.692288i
$268$	−1.05602	+	12.0703i	−0.0645064	+	0.737312i
$269$	7.87469	+	2.86615i	0.480128	+	0.174752i	0.570735	−	0.821134i	$-0.306658\pi$
$269$	7.87469	+	2.86615i	0.480128	+	0.174752i	−0.0906067	+	0.995887i	$0.528881\pi$
$270$	11.6106	−	0.439698i	0.706600	−	0.0267592i
$271$	−0.0185044	−	0.104944i	−0.00112406	−	0.00637489i	0.984241	−	0.176835i	$-0.0565858\pi$
$271$	−0.0185044	−	0.104944i	−0.00112406	−	0.00637489i	−0.985365	+	0.170460i	$0.945475\pi$
$272$	2.22221	−	4.76555i	0.134741	−	0.288954i
$273$	−8.04305	+	0.296771i	−0.486787	+	0.0179614i
$274$	12.7532	−	7.36307i	0.770450	−	0.444819i
$275$	23.6012	+	12.7298i	1.42320	+	0.767638i
$276$	−7.96696	−	10.5292i	−0.479555	−	0.633783i
$277$	−5.05671	+	18.8719i	−0.303828	+	1.13390i	0.630122	+	0.776496i	$0.283005\pi$
$277$	−5.05671	+	18.8719i	−0.303828	+	1.13390i	−0.933950	+	0.357405i	$0.883662\pi$
$278$	3.74063	−	1.00230i	0.224348	−	0.0601139i
$279$	2.84101	−	28.0974i	0.170087	−	1.68215i
$280$	−1.44790	+	2.59383i	−0.0865283	+	0.155011i
$281$	0.643203	+	0.113414i	0.0383703	+	0.00676571i	0.192800	−	0.981238i	$-0.438243\pi$
$281$	0.643203	+	0.113414i	0.0383703	+	0.00676571i	−0.154430	+	0.988004i	$0.549354\pi$
$282$	−5.26035	+	1.12898i	−0.313249	+	0.0672300i
$283$	−0.567199	+	6.48312i	−0.0337165	+	0.385381i	0.960523	+	0.278200i	$0.0897379\pi$
$283$	−0.567199	+	6.48312i	−0.0337165	+	0.385381i	−0.994240	+	0.107181i	$0.965818\pi$
$284$	5.24420			0.311186
$285$	0.625705	−	16.8703i	0.0370636	−	0.999313i
$286$	−18.7591			−1.10925
$287$	−0.531956	+	6.08028i	−0.0314004	+	0.358908i
$288$	−0.0405112	+	2.99973i	−0.00238715	+	0.176761i
$289$	−10.4869	−	1.84913i	−0.616877	−	0.108772i
$290$	5.51506	−	1.56366i	0.323855	−	0.0918212i
$291$	0.706072	+	5.65811i	0.0413907	+	0.331684i
$292$	−12.1157	+	3.24638i	−0.709016	+	0.189980i
$293$	−6.31955	+	23.5849i	−0.369192	+	1.37784i	0.492456	+	0.870337i	$0.336099\pi$
$293$	−6.31955	+	23.5849i	−0.369192	+	1.37784i	−0.861648	+	0.507506i	$0.830567\pi$
$294$	−7.23085	+	5.47126i	−0.421712	+	0.319090i
$295$	−33.3102	+	6.37196i	−1.93940	+	0.370990i
$296$	3.39649	−	1.96096i	0.197417	−	0.113979i
$297$	−25.5248	−	11.1837i	−1.48110	−	0.648942i
$298$	5.53658	−	11.8732i	0.320725	−	0.687797i
$299$	−4.63023	−	26.2594i	−0.267773	−	1.51862i
$300$	7.19890	−	4.81413i	0.415629	−	0.277944i
$301$	−0.732383	−	0.266566i	−0.0422138	−	0.0153646i
$302$	1.87141	−	21.3904i	0.107688	−	1.23088i
$303$	−11.9992	+	7.53095i	−0.689339	+	0.432642i
$304$	4.34187	+	0.384949i	0.249023	+	0.0220783i
$305$	10.8897	−	13.3661i	0.623544	−	0.765341i
$306$	15.2908	−	3.87664i	0.874119	−	0.221613i
$307$	8.92235	+	19.1341i	0.509226	+	1.09204i	0.977978	+	0.208708i	$0.0669259\pi$
$307$	8.92235	+	19.1341i	0.509226	+	1.09204i	−0.468752	+	0.883330i	$0.655296\pi$
$308$	5.83625	−	4.08659i	0.332551	−	0.232855i
$309$	0.288182	−	5.71473i	0.0163941	−	0.325100i
$310$	−9.17104	−	18.9464i	−0.520880	−	1.07608i
$311$	−24.5864	−	14.1950i	−1.39417	−	0.804923i	−0.400394	−	0.916343i	$-0.631127\pi$
$311$	−24.5864	−	14.1950i	−1.39417	−	0.804923i	−0.993773	+	0.111420i	$0.964460\pi$
$312$	−2.83369	+	5.35488i	−0.160426	+	0.303160i
$313$	−25.3827	+	2.22070i	−1.43472	+	0.125521i	−0.777833	−	0.628471i	$-0.783681\pi$
$313$	−25.3827	+	2.22070i	−1.43472	+	0.125521i	−0.656883	+	0.753992i	$0.728126\pi$
$314$	−0.0987785	−	0.0828850i	−0.00557440	−	0.00467747i
$315$	−8.77484	+	1.55603i	−0.494406	+	0.0876723i
$316$	−0.286502	+	0.496236i	−0.0161170	+	0.0279154i
$317$	4.72325	−	10.1290i	0.265284	−	0.568904i	−0.727870	−	0.685715i	$-0.759489\pi$
$317$	4.72325	−	10.1290i	0.265284	−	0.568904i	0.993154	+	0.116811i	$0.0372673\pi$
$318$	−2.52870	+	2.28591i	−0.141803	+	0.128188i
$319$	−13.5400	−	2.38747i	−0.758096	−	0.133673i
$320$	1.14595	+	1.92011i	0.0640604	+	0.107337i
$321$	9.27741	−	4.75017i	0.517814	−	0.265129i
$322$	7.16101	+	7.16101i	0.399067	+	0.399067i
$323$	−3.95378	−	22.5764i	−0.219994	−	1.25618i
$324$	−7.04811	+	5.59680i	−0.391562	+	0.310933i
$325$	17.3712	−	2.02797i	0.963581	−	0.112491i
$326$	4.59271	−	12.6184i	0.254367	−	0.698867i
$327$	1.59213	+	3.91837i	0.0880450	+	0.216686i
$328$	3.76347	+	2.63521i	0.207803	+	0.145505i
$329$	3.87771	−	1.41137i	0.213785	−	0.0778113i
$330$	−20.5718	+	2.87013i	−1.13244	+	0.157996i
$331$	12.8597	+	22.2737i	0.706835	+	1.22427i	0.966025	+	0.258448i	$0.0832110\pi$
$331$	12.8597	+	22.2737i	0.706835	+	1.22427i	−0.259190	+	0.965826i	$0.583456\pi$
$332$	13.3903	−	1.17150i	0.734886	−	0.0642942i
$333$	11.0009	+	4.17307i	0.602844	+	0.228683i
$334$	−1.87786	+	1.08418i	−0.102752	+	0.0593238i
$335$	−11.0934	+	24.7179i	−0.606099	+	1.35048i
$336$	−0.284930	−	2.28329i	−0.0155442	−	0.124564i
$337$	−2.77873	+	3.96843i	−0.151367	+	0.216174i	−0.887673	−	0.460474i	$-0.847679\pi$
$337$	−2.77873	+	3.96843i	−0.151367	+	0.216174i	0.736306	+	0.676648i	$0.236568\pi$
$338$	0.626768	−	0.438868i	0.0340917	−	0.0238713i
$339$	−2.85531	+	4.41586i	−0.155079	+	0.239837i
$340$	8.19274	−	8.43342i	0.444313	−	0.457366i
$341$			50.4855i			2.73394i
$342$	7.34258	+	10.8207i	0.397041	+	0.585114i
$343$	11.4934	−	11.4934i	0.620587	−	0.620587i
$344$	−0.449418	+	0.377106i	−0.0242310	+	0.0203322i
$345$	−9.09531	−	28.0884i	−0.489675	−	1.51223i
$346$	−1.30468	+	7.39922i	−0.0701401	+	0.397784i
$347$	18.2061	+	12.7480i	0.977354	+	0.684350i	0.949009	−	0.315248i	$-0.102088\pi$
$347$	18.2061	+	12.7480i	0.977354	+	0.684350i	0.0283442	+	0.999598i	$0.490977\pi$
$348$	−2.72683	+	3.50442i	−0.146173	+	0.187857i
$349$	20.1776	+	11.6496i	1.08008	+	0.623587i	0.930919	−	0.365226i	$-0.119008\pi$
$349$	20.1776	+	11.6496i	1.08008	+	0.623587i	0.149165	+	0.988812i	$0.452342\pi$
$350$	−4.96266	+	4.41516i	−0.265265	+	0.236000i
$351$	−17.8205	+	3.57363i	−0.951188	+	0.190746i
$352$	−0.467422	−	5.34266i	−0.0249137	−	0.284765i
$353$	6.17329	−	23.0390i	0.328571	−	1.22624i	−0.582102	−	0.813116i	$-0.697770\pi$
$353$	6.17329	−	23.0390i	0.328571	−	1.22624i	0.910673	−	0.413128i	$-0.135564\pi$
$354$	17.8780	−	19.2479i	0.950206	−	1.02301i
$355$	11.0761	+	3.85074i	0.587858	+	0.204376i
$356$	7.59364	−	1.33896i	0.402462	−	0.0709649i
$357$	−11.2091	+	4.55455i	−0.593251	+	0.241053i
$358$	−11.0711	+	5.16252i	−0.585124	+	0.272848i
$359$	16.9445	−	14.2181i	0.894296	−	0.750404i	−0.0747709	−	0.997201i	$-0.523823\pi$
$359$	16.9445	−	14.2181i	0.894296	−	0.750404i	0.969067	+	0.246797i	$0.0793781\pi$
$360$	−2.28822	+	6.30587i	−0.120600	+	0.332349i
$361$	16.4765	−	9.46173i	0.867185	−	0.497986i
$362$	8.25350	−	8.25350i	0.433794	−	0.433794i
$363$	29.2785	+	9.44930i	1.53672	+	0.495960i
$364$	1.58930	−	4.36658i	0.0833022	−	0.228871i
$365$	−27.9729	−	2.03978i	−1.46417	−	0.106767i
$366$	−0.672587	+	13.3376i	−0.0351567	+	0.697166i
$367$	16.6067	+	7.74385i	0.866865	+	0.404226i	0.804588	−	0.593833i	$-0.202386\pi$
$367$	16.6067	+	7.74385i	0.866865	+	0.404226i	0.0622767	+	0.998059i	$0.480164\pi$
$368$	7.36338	−	1.97301i	0.383843	−	0.102850i
$369$	1.01575	+	13.7456i	0.0528777	+	0.715565i
$370$	8.61351	−	1.64769i	0.447795	−	0.0856594i
$371$	1.68059	−	2.00285i	0.0872518	−	0.103983i
$372$	14.4113	+	7.62617i	0.747192	+	0.395399i
$373$	3.10888	+	11.6025i	0.160972	+	0.600754i	0.998520	+	0.0543907i	$0.0173216\pi$
$373$	3.10888	+	11.6025i	0.160972	+	0.600754i	−0.837548	+	0.546364i	$0.816012\pi$
$374$	−26.4994	+	9.64501i	−1.37025	+	0.498731i
$375$	18.7395	−	4.88171i	0.967704	−	0.252090i
$376$	0.539390	−	3.05904i	0.0278169	−	0.157758i
$377$	−8.12699	+	3.78968i	−0.418562	+	0.195178i
$378$	4.76573	−	4.99392i	0.245123	−	0.256860i
$379$		−	9.26421i		−	0.475871i	−0.971281	−	0.237935i	$-0.923529\pi$
$379$		−	9.26421i		−	0.475871i	0.971281	−	0.237935i	$-0.0764706\pi$
$380$	8.88765	+	4.00121i	0.455927	+	0.205258i
$381$	2.07520	−	9.07036i	0.106316	−	0.464689i
$382$	26.0334	+	2.27763i	1.33198	+	0.116533i
$383$	−3.64878	−	7.82484i	−0.186444	−	0.399831i	0.790762	−	0.612124i	$-0.209685\pi$
$383$	−3.64878	−	7.82484i	−0.186444	−	0.399831i	−0.977206	+	0.212293i	$0.931907\pi$
$384$	−1.59569	−	0.673617i	−0.0814299	−	0.0343754i
$385$	15.3273	−	4.34567i	0.781150	−	0.221476i
$386$	4.84349	+	13.3074i	0.246527	+	0.677328i
$387$	−1.72900	−	0.329002i	−0.0878898	−	0.0167241i
$388$	−3.17988	−	0.852045i	−0.161434	−	0.0432560i
$389$	−3.42337	−	2.87255i	−0.173572	−	0.145644i	0.551863	−	0.833935i	$-0.313917\pi$
$389$	−3.42337	−	2.87255i	−0.173572	−	0.145644i	−0.725435	+	0.688290i	$0.758361\pi$
$390$	−9.91696	+	9.22913i	−0.502165	+	0.467335i
$391$	−20.0420	−	34.7137i	−1.01357	−	1.75555i
$392$	−1.35495	−	5.05675i	−0.0684354	−	0.255404i
$393$	−17.4976	+	22.4872i	−0.882635	+	1.13433i
$394$	−1.76784	+	0.311718i	−0.0890625	+	0.0157041i
$395$	−0.969489	+	0.837708i	−0.0487803	+	0.0421497i
$396$	11.5294	−	11.2221i	0.579373	−	0.563933i
$397$	−0.934852	−	0.0817890i	−0.0469189	−	0.00410487i	0.0636721	−	0.997971i	$-0.479719\pi$
$397$	−0.934852	−	0.0817890i	−0.0469189	−	0.00410487i	−0.110591	+	0.993866i	$0.535274\pi$
$398$	1.88093	+	1.88093i	0.0942825	+	0.0942825i
$399$	−6.71732	−	7.44816i	−0.336287	−	0.372874i
$400$	1.01041	+	4.89684i	0.0505205	+	0.244842i
$401$	4.07946	+	4.86171i	0.203718	+	0.242782i	0.858224	−	0.513275i	$-0.171568\pi$
$401$	4.07946	+	4.86171i	0.203718	+	0.242782i	−0.654506	+	0.756057i	$0.727123\pi$
$402$	−4.40381	−	20.5190i	−0.219642	−	1.02339i
$403$	18.8862	+	26.9723i	0.940788	+	1.34358i
$404$	−1.42030	−	8.05492i	−0.0706626	−	0.400747i
$405$	−18.9957	+	6.64548i	−0.943905	+	0.330216i
$406$	1.70287	−	2.94945i	0.0845119	−	0.146379i
$407$	−20.3169	−	5.44389i	−1.00707	−	0.269843i
$408$	−1.24970	+	9.02133i	−0.0618696	+	0.446622i
$409$	−9.11814	+	10.8666i	−0.450863	+	0.537318i	−0.942820	−	0.333302i	$-0.891837\pi$
$409$	−9.11814	+	10.8666i	−0.450863	+	0.537318i	0.491957	+	0.870619i	$0.336282\pi$
$410$	6.01370	+	8.32919i	0.296995	+	0.411350i
$411$	−17.3585	+	18.6885i	−0.856230	+	0.921837i
$412$	2.99407	+	1.39616i	0.147507	+	0.0687838i
$413$	−11.5570	+	16.5051i	−0.568681	+	0.812161i
$414$	18.5547	+	13.3691i	0.911912	+	0.657056i
$415$	29.1413	+	7.35800i	1.43049	+	0.361190i
$416$	−2.24837	−	2.67950i	−0.110235	−	0.131373i
$417$	−5.68127	+	3.56567i	−0.278213	+	0.174612i
$418$	−15.0057	−	17.9253i	−0.733952	−	0.876757i
$419$	−30.5521			−1.49257			−0.746285	−	0.665627i	$-0.768164\pi$
$419$	−30.5521			−1.49257			−0.746285	+	0.665627i	$0.768164\pi$
$420$	1.07480	−	5.03168i	0.0524447	−	0.245521i
$421$	2.76749	+	1.00728i	0.134879	+	0.0490920i	0.408578	−	0.912723i	$-0.366025\pi$
$421$	2.76749	+	1.00728i	0.134879	+	0.0490920i	−0.273699	+	0.961816i	$0.588247\pi$
$422$	1.48943	+	2.12713i	0.0725043	+	0.103547i
$423$	8.13239	−	4.54994i	0.395411	−	0.221225i
$424$	−0.673115	−	1.84937i	−0.0326894	−	0.0898133i
$425$	23.4961	−	11.7961i	1.13973	−	0.572197i
$426$	−8.68107	+	2.67282i	−0.420599	+	0.129499i
$427$	−0.892730	−	10.2039i	−0.0432022	−	0.493804i
$428$	0.524468	+	5.99470i	0.0253511	+	0.289765i
$429$	31.0532	−	9.56102i	1.49926	−	0.461610i
$430$	−1.22610	+	0.466473i	−0.0591280	+	0.0224953i
$431$	−5.28621	−	14.5237i	−0.254628	−	0.699584i	−0.999477	−	0.0323505i	$-0.989701\pi$
$431$	−5.28621	−	14.5237i	−0.254628	−	0.699584i	0.744849	−	0.667233i	$-0.232521\pi$
$432$	−1.46182	−	4.98629i	−0.0703317	−	0.239903i
$433$	7.60051	+	10.8547i	0.365257	+	0.521642i	0.959148	−	0.282904i	$-0.0912978\pi$
$433$	7.60051	+	10.8547i	0.365257	+	0.521642i	−0.593891	+	0.804546i	$0.702409\pi$
$434$	−11.7516	−	4.27722i	−0.564093	−	0.205313i
$435$	−8.33248	+	5.39930i	−0.399512	+	0.258877i
$436$	−2.44189			−0.116945
$437$	21.3884	−	25.4296i	1.02315	−	1.21646i
$438$	18.4013	−	11.5490i	0.879247	−	0.551831i
$439$	−17.5128	−	20.8709i	−0.835839	−	0.996115i	−0.999953	−	0.00967317i	$-0.996921\pi$
$439$	−17.5128	−	20.8709i	−0.835839	−	0.996115i	0.164114	−	0.986441i	$-0.447524\pi$
$440$	2.93581	−	11.6273i	0.139959	−	0.554309i
$441$	9.18115	−	12.7423i	0.437198	−	0.606776i
$442$	−10.5494	+	15.0661i	−0.501784	+	0.716622i
$443$	19.2043	+	8.95509i	0.912422	+	0.425469i	0.821382	−	0.570378i	$-0.193203\pi$
$443$	19.2043	+	8.95509i	0.912422	+	0.425469i	0.0910394	+	0.995847i	$0.470981\pi$
$444$	−4.62298	+	4.97720i	−0.219397	+	0.236208i
$445$	17.0215	+	2.74792i	0.806894	+	0.130264i
$446$	−17.4094	+	20.7477i	−0.824357	+	0.982430i
$447$	−3.11360	+	22.4764i	−0.147268	+	1.06310i
$448$	1.28322	+	0.343837i	0.0606263	+	0.0162448i
$449$	−10.1864	+	17.6434i	−0.480727	+	0.832643i	−0.999755	−	0.0221135i	$-0.992960\pi$
$449$	−10.1864	+	17.6434i	−0.480727	+	0.832643i	0.519029	+	0.854757i	$0.326294\pi$
$450$	−9.46318	+	11.6382i	−0.446099	+	0.548631i
$451$	−4.27866	−	24.2655i	−0.201474	−	1.14262i
$452$	−1.74140	−	2.48698i	−0.0819087	−	0.116978i
$453$	7.80420	+	36.3627i	0.366673	+	1.70847i
$454$	9.57489	+	11.4109i	0.449372	+	0.535540i
$455$	6.56303	−	8.05550i	0.307680	−	0.377648i
$456$	−7.38357	+	1.57570i	−0.345768	+	0.0737889i
$457$	18.6994	+	18.6994i	0.874723	+	0.874723i	0.992983	−	0.118260i	$-0.0377316\pi$
$457$	18.6994	+	18.6994i	0.874723	+	0.874723i	−0.118260	+	0.992983i	$0.537732\pi$
$458$	6.13582	+	0.536815i	0.286708	+	0.0250837i
$459$	−23.3361	+	14.2106i	−1.08924	+	0.663293i
$460$	17.0007	+	1.23969i	0.792661	+	0.0578009i
$461$	1.99173	−	0.351195i	0.0927639	−	0.0163568i	−0.127074	−	0.991893i	$-0.540558\pi$
$461$	1.99173	−	0.351195i	0.0927639	−	0.0163568i	0.219837	+	0.975537i	$0.429447\pi$
$462$	−7.57831	+	9.73937i	−0.352575	+	0.453117i
$463$	−1.67368	−	6.24627i	−0.0777827	−	0.290289i	0.916067	−	0.401025i	$-0.131346\pi$
$463$	−1.67368	−	6.24627i	−0.0777827	−	0.290289i	−0.993850	+	0.110736i	$0.964679\pi$
$464$	−1.28181	−	2.22017i	−0.0595067	−	0.103069i
$465$	24.8379	+	26.6890i	1.15183	+	1.23767i
$466$	−21.3931	−	17.9509i	−0.991016	−	0.831561i
$467$	17.6589	+	4.73170i	0.817158	+	0.218957i	0.643104	−	0.765779i	$-0.277646\pi$
$467$	17.6589	+	4.73170i	0.817158	+	0.218957i	0.174054	+	0.984736i	$0.444313\pi$
$468$	1.96156	−	10.3085i	0.0906732	−	0.476512i
$469$	5.50531	+	15.1257i	0.254212	+	0.698441i
$470$	3.38543	−	6.06482i	0.156158	−	0.279749i
$471$	0.205759	+	0.0868603i	0.00948086	+	0.00400231i
$472$	6.40981	+	13.7459i	0.295035	+	0.632705i
$473$	3.13440	+	0.274224i	0.144120	+	0.0126088i
$474$	0.221347	−	0.967473i	0.0101668	−	0.0444375i
$475$	15.8333	+	14.9769i	0.726481	+	0.687187i
$476$		−	6.98543i		−	0.320177i
$477$	3.02086	−	5.07283i	0.138316	−	0.232269i
$478$	−10.4903	+	4.89170i	−0.479814	+	0.223741i
$479$	−2.79023	+	15.8242i	−0.127489	+	0.723025i	0.852310	+	0.523037i	$0.175201\pi$
$479$	−2.79023	+	15.8242i	−0.127489	+	0.723025i	−0.979798	+	0.199987i	$0.935910\pi$
$480$	−2.87559	−	2.59442i	−0.131252	−	0.118418i
$481$	−12.8909	+	4.69192i	−0.587776	+	0.213933i
$482$	0.259088	+	0.966930i	0.0118011	+	0.0440424i
$483$	−15.5039	−	8.20432i	−0.705450	−	0.373309i
$484$	−11.4175	+	13.6069i	−0.518979	+	0.618495i
$485$	−6.09047	−	4.13451i	−0.276554	−	0.187739i
$486$	8.81467	−	12.8570i	0.399841	−	0.583204i
$487$	6.43626	−	1.72459i	0.291655	−	0.0781487i	−0.110025	−	0.993929i	$-0.535093\pi$
$487$	6.43626	−	1.72459i	0.291655	−	0.0781487i	0.401680	+	0.915780i	$0.368426\pi$
$488$	−6.98785	−	3.25849i	−0.316325	−	0.147505i
$489$	−1.17138	+	23.2288i	−0.0529717	+	1.05044i
$490$	0.851350	−	11.6751i	0.0384601	−	0.527428i
$491$	13.9132	−	38.2263i	0.627895	−	1.72513i	−0.0588875	−	0.998265i	$-0.518755\pi$
$491$	13.9132	−	38.2263i	0.627895	−	1.72513i	0.686783	−	0.726863i	$-0.259022\pi$
$492$	−7.57301	−	2.44410i	−0.341417	−	0.110188i
$493$	−9.53185	+	9.53185i	−0.429293	+	0.429293i
$494$	−14.7226	−	3.96325i	−0.662401	−	0.178315i
$495$	32.5911	−	15.2360i	1.46486	−	0.684808i
$496$	−7.21120	+	6.05091i	−0.323792	+	0.271694i
$497$	6.31409	−	2.94431i	0.283226	−	0.132070i
$498$	−21.5687	+	8.76390i	−0.966516	+	0.392720i
$499$	28.7195	−	5.06402i	1.28566	−	0.226697i	0.511279	−	0.859415i	$-0.329172\pi$
$499$	28.7195	−	5.06402i	1.28566	−	0.226697i	0.774382	+	0.632718i	$0.218061\pi$
$500$	−1.46163	+	11.0844i	−0.0653660	+	0.495709i
$501$	2.55596	−	2.75181i	0.114192	−	0.122942i
$502$	−5.37859	+	20.0732i	−0.240058	+	0.895910i
$503$	−0.433445	−	4.95430i	−0.0193264	−	0.220901i	−0.999716	−	0.0238323i	$-0.992413\pi$
$503$	−0.433445	−	4.95430i	−0.0193264	−	0.220901i	0.980390	−	0.197069i	$-0.0631423\pi$
$504$	1.63539	+	3.63446i	0.0728462	+	0.161892i
$505$	2.91485	−	18.0554i	0.129709	−	0.803456i
$506$	−35.4060	−	20.4417i	−1.57399	−	0.908744i
$507$	−0.813852	+	1.04593i	−0.0361444	+	0.0464515i
$508$	4.40056	+	3.08130i	0.195243	+	0.136711i
$509$	−2.14239	+	12.1501i	−0.0949598	+	0.538544i	0.899800	+	0.436303i	$0.143712\pi$
$509$	−2.14239	+	12.1501i	−0.0949598	+	0.538544i	−0.994760	+	0.102241i	$0.967399\pi$
$510$	−9.26369	+	18.1360i	−0.410203	+	0.803076i
$511$	−12.7648	+	10.7109i	−0.564681	+	0.473824i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−17.6696	−	14.1698i	−0.780134	−	0.625613i
$514$			4.49418i			0.198230i
$515$	5.29850	+	5.14728i	0.233480	+	0.226816i
$516$	0.551750	−	0.853304i	0.0242894	−	0.0375646i
$517$	−13.6462	+	9.55516i	−0.600158	+	0.420235i
$518$	2.98845	−	4.26795i	0.131305	−	0.187523i
$519$	−1.61145	−	12.9134i	−0.0707349	−	0.566834i
$520$	−2.78118	−	7.31022i	−0.121963	−	0.320574i
$521$	−1.73288	+	1.00048i	−0.0759189	+	0.0438318i	−0.537479	−	0.843277i	$-0.680623\pi$
$521$	−1.73288	+	1.00048i	−0.0759189	+	0.0438318i	0.461560	+	0.887109i	$0.347290\pi$
$522$	2.72779	−	7.19088i	0.119392	−	0.314736i
$523$	−2.98972	+	0.261567i	−0.130731	+	0.0114375i	−0.152334	−	0.988329i	$-0.548679\pi$
$523$	−2.98972	+	0.261567i	−0.130731	+	0.0114375i	0.0216022	+	0.999767i	$0.493123\pi$
$524$	−8.22517	−	14.2464i	−0.359318	−	0.622357i
$525$	5.96473	−	9.83804i	0.260322	−	0.429367i
$526$	−3.94835	+	1.43708i	−0.172156	+	0.0626598i
$527$	40.5467	+	28.3911i	1.76624	+	1.23674i
$528$	3.49676	+	8.60583i	0.152177	+	0.374521i
$529$	12.0090	−	32.9946i	0.522132	−	1.43455i
$530$	−0.0636990	−	4.40025i	−0.00276691	−	0.191135i
$531$	−19.7845	+	40.9742i	−0.858576	+	1.77813i
$532$	5.44380	−	1.97422i	0.236019	−	0.0855933i
$533$	−11.3634	−	11.3634i	−0.492203	−	0.492203i
$534$	−11.8878	+	6.08674i	−0.514436	+	0.263399i
$535$	−3.29411	+	13.0463i	−0.142417	+	0.564041i
$536$	11.9323	+	2.10399i	0.515399	+	0.0908787i
$537$	15.6955	−	14.1885i	0.677309	−	0.612278i
$538$	3.54157	−	7.59492i	0.152688	−	0.327440i
$539$	−14.0382	+	24.3149i	−0.604668	+	1.04732i
$540$	0.573908	−	11.6048i	0.0246971	−	0.499390i
$541$	−14.4373	−	12.1144i	−0.620710	−	0.520837i	0.277317	−	0.960779i	$-0.410555\pi$
$541$	−14.4373	−	12.1144i	−0.620710	−	0.520837i	−0.898027	+	0.439941i	$0.854999\pi$
$542$	−0.106157	+	0.00928756i	−0.00455985	+	0.000398935i
$543$	−9.45598	+	17.8691i	−0.405795	+	0.766838i
$544$	−4.55374	−	2.62910i	−0.195240	−	0.112722i
$545$	−5.15744	−	1.79305i	−0.220920	−	0.0768056i
$546$	−0.405356	+	8.03831i	−0.0173476	+	0.344008i
$547$	14.8732	−	10.4144i	0.635934	−	0.445286i	−0.210635	−	0.977565i	$-0.567553\pi$
$547$	14.8732	−	10.4144i	0.635934	−	0.445286i	0.846569	+	0.532279i	$0.178664\pi$
$548$	−6.22354	−	13.3464i	−0.265856	−	0.570131i
$549$	−5.68442	−	22.4214i	−0.242605	−	0.956920i
$550$	14.7384	−	22.4019i	0.628447	−	0.955219i
$551$	−10.1221	−	4.73435i	−0.431217	−	0.201690i
$552$	−11.1835	+	7.01896i	−0.476001	+	0.298747i
$553$	−0.0663452	+	0.758329i	−0.00282128	+	0.0322474i
$554$	18.3593	+	6.68226i	0.780014	+	0.283902i
$555$	−13.4187	+	7.11760i	−0.569593	+	0.302125i
$556$	−0.672468	−	3.81376i	−0.0285190	−	0.161739i
$557$	−10.6482	+	22.8352i	−0.451179	+	0.967557i	0.540799	+	0.841152i	$0.318122\pi$
$557$	−10.6482	+	22.8352i	−0.451179	+	0.967557i	−0.991979	+	0.126405i	$0.959656\pi$
$558$	−27.7429	−	5.27905i	−1.17445	−	0.223480i
$559$	1.77716	−	1.02604i	0.0751658	−	0.0433970i
$560$	2.45776	+	1.66845i	0.103859	+	0.0705050i
$561$	38.9505	−	29.4720i	1.64449	−	1.24431i
$562$	0.169041	−	0.630870i	0.00713057	−	0.0266117i
$563$	−14.4554	+	3.87331i	−0.609222	+	0.163241i	−0.550224	−	0.835017i	$-0.685458\pi$
$563$	−14.4554	+	3.87331i	−0.609222	+	0.163241i	−0.0589989	+	0.998258i	$0.518791\pi$
$564$	0.666217	+	5.33873i	0.0280528	+	0.224801i
$565$	−1.85180	−	6.53136i	−0.0779060	−	0.274776i
$566$	6.40901	+	1.13008i	0.269391	+	0.0475009i
$567$	−5.34376	+	10.6957i	−0.224417	+	0.449178i
$568$	0.457062	−	5.22424i	0.0191779	−	0.219204i
$569$	−19.4507			−0.815414			−0.407707	−	0.913113i	$-0.633672\pi$
$569$	−19.4507			−0.815414			−0.407707	+	0.913113i	$0.633672\pi$
$570$	−16.7516	−	2.09367i	−0.701648	−	0.0876943i
$571$	21.2385			0.888803			0.444401	−	0.895828i	$-0.353416\pi$
$571$	21.2385			0.888803			0.444401	+	0.895828i	$0.353416\pi$
$572$	−1.63497	+	18.6878i	−0.0683614	+	0.781374i
$573$	−44.2556	+	9.49819i	−1.84880	+	0.396793i
$574$	6.01078	+	1.05986i	0.250885	+	0.0442378i
$575$	34.9963	+	15.1017i	1.45945	+	0.629783i
$576$	2.98478	+	0.301800i	0.124366	+	0.0125750i
$577$	−19.3178	+	5.17619i	−0.804210	+	0.215487i	−0.637432	−	0.770507i	$-0.720003\pi$
$577$	−19.3178	+	5.17619i	−0.804210	+	0.215487i	−0.166779	+	0.985994i	$0.553337\pi$
$578$	−2.75608	+	10.2858i	−0.114638	+	0.427835i
$579$	−14.8001	−	19.5600i	−0.615073	−	0.812885i
$580$	−1.07704	−	5.63036i	−0.0447216	−	0.233788i
$581$	15.4643	−	8.92834i	0.641569	−	0.370410i
$582$	5.69812	−	0.210249i	0.236195	−	0.00871509i
$583$	−4.46066	+	9.56593i	−0.184742	+	0.396180i
$584$	2.17808	+	12.3525i	0.0901296	+	0.511150i
$585$	11.7124	−	20.3320i	0.484247	−	0.840624i
$586$	22.9444	+	8.35106i	0.947822	+	0.344979i
$587$	−0.743185	+	8.49465i	−0.0306745	+	0.350612i	0.965311	+	0.261101i	$0.0840857\pi$
$587$	−0.743185	+	8.49465i	−0.0306745	+	0.350612i	−0.995986	+	0.0895102i	$0.971470\pi$
$588$	4.82023	+	7.68019i	0.198783	+	0.316726i
$589$	−10.6661	+	39.6222i	−0.439489	+	1.63260i
$590$	3.44454	+	33.7388i	0.141809	+	1.38901i
$591$	2.76755	−	1.41703i	0.113842	−	0.0582887i
$592$	−1.65748	−	3.55447i	−0.0681219	−	0.146088i
$593$	−3.29616	+	2.30799i	−0.135357	+	0.0947779i	−0.639294	−	0.768963i	$-0.720773\pi$
$593$	−3.29616	+	2.30799i	−0.135357	+	0.0947779i	0.503937	+	0.863740i	$0.331884\pi$
$594$	−13.3657	+	24.4529i	−0.548403	+	1.00332i
$595$	5.12930	−	14.7537i	0.210281	−	0.604843i
$596$	−11.3455	−	6.55033i	−0.464730	−	0.268312i
$597$	−4.07228	−	2.15497i	−0.166668	−	0.0881970i
$598$	−26.5630	+	2.32396i	−1.08624	+	0.0950338i
$599$	−3.86227	−	3.24083i	−0.157808	−	0.132417i	0.560465	−	0.828178i	$-0.310623\pi$
$599$	−3.86227	−	3.24083i	−0.157808	−	0.132417i	−0.718273	+	0.695762i	$0.755067\pi$
$600$	−4.16838	−	7.59109i	−0.170174	−	0.309905i
$601$	1.91160	−	3.31099i	0.0779759	−	0.135058i	−0.824401	−	0.566007i	$-0.808488\pi$
$601$	1.91160	−	3.31099i	0.0779759	−	0.135058i	0.902377	+	0.430948i	$0.141821\pi$
$602$	−0.329383	+	0.706363i	−0.0134246	+	0.0287892i
$603$	17.7479	+	31.7219i	0.722750	+	1.29182i
$604$	−21.1459	−	3.72859i	−0.860413	−	0.151714i
$605$	−34.1059	+	20.3549i	−1.38660	+	0.827545i
$606$	6.45648	+	12.6099i	0.262277	+	0.512244i
$607$	2.84202	+	2.84202i	0.115354	+	0.115354i	0.762428	−	0.647074i	$-0.224007\pi$
$607$	2.84202	+	2.84202i	0.115354	+	0.115354i	−0.647074	+	0.762428i	$0.724007\pi$
$608$	0.761902	−	4.29180i	0.0308992	−	0.174055i
$609$	−1.31561	+	5.75033i	−0.0533113	+	0.233015i
$610$	−12.3661	−	12.0132i	−0.500690	−	0.486401i
$611$	−3.71607	+	10.2098i	−0.150336	+	0.413045i
$612$	−2.52920	−	15.5705i	−0.102237	−	0.629401i
$613$	5.51236	+	3.85979i	0.222642	+	0.155896i	0.679576	−	0.733605i	$-0.262164\pi$
$613$	5.51236	+	3.85979i	0.222642	+	0.155896i	−0.456934	+	0.889500i	$0.651053\pi$
$614$	19.8389	−	7.22076i	0.800632	−	0.291406i
$615$	−14.2000	−	10.7228i	−0.572600	−	0.432387i
$616$	−3.56237	−	6.17021i	−0.143532	−	0.248605i
$617$	−6.14646	+	0.537745i	−0.247447	+	0.0216488i	−0.210204	−	0.977657i	$-0.567413\pi$
$617$	−6.14646	+	0.537745i	−0.247447	+	0.0216488i	−0.0372425	+	0.999306i	$0.511857\pi$
$618$	−5.66787	−	0.785157i	−0.227995	−	0.0315836i
$619$	−13.5446	+	7.81999i	−0.544404	+	0.314312i	−0.746862	−	0.664979i	$-0.768440\pi$
$619$	−13.5446	+	7.81999i	−0.544404	+	0.314312i	0.202458	+	0.979291i	$0.435107\pi$
$620$	−19.6736	+	7.48485i	−0.790112	+	0.300599i
$621$	−37.5286	−	12.6740i	−1.50597	−	0.508589i
$622$	−16.2838	+	23.2557i	−0.652921	+	0.932468i
$623$	8.39110	−	5.87551i	0.336182	−	0.235397i
$624$	5.08753	+	3.28962i	0.203664	+	0.131690i
$625$	−11.2262	+	22.3377i	−0.449047	+	0.893508i
$626$			25.4797i			1.01837i
$627$	33.9759	+	22.0250i	1.35687	+	0.879594i
$628$	−0.0911788	+	0.0911788i	−0.00363843	+	0.00363843i
$629$	−15.7976	+	13.2557i	−0.629891	+	0.528541i
$630$	0.785329	+	8.87707i	0.0312883	+	0.353671i
$631$	−1.33425	+	7.56690i	−0.0531156	+	0.301234i	−0.999780	−	0.0209884i	$-0.993319\pi$
$631$	−1.33425	+	7.56690i	−0.0531156	+	0.301234i	0.946664	+	0.322222i	$0.104430\pi$
$632$	0.469377	+	0.328661i	0.0186708	+	0.0130734i
$633$	−3.54969	−	2.76205i	−0.141087	−	0.109782i
$634$	−9.67885	−	5.58808i	−0.384396	−	0.221931i
$635$	7.03171	+	9.73918i	0.279045	+	0.386488i
$636$	2.05682	+	2.71831i	0.0815584	+	0.107788i
$637$	1.59596	+	18.2420i	0.0632344	+	0.722773i
$638$	−3.55848	+	13.2804i	−0.140882	+	0.525777i
$639$	13.0081	−	8.84900i	0.514591	−	0.350061i
$640$	2.01267	−	0.974238i	0.0795580	−	0.0385101i
$641$	−26.2425	+	4.62726i	−1.03652	+	0.182766i	−0.665916	−	0.746027i	$-0.731959\pi$
$641$	−26.2425	+	4.62726i	−1.03652	+	0.182766i	−0.370600	+	0.928792i	$0.620848\pi$
$642$	−3.92352	−	9.65611i	−0.154849	−	0.381096i
$643$	−1.71344	+	0.798990i	−0.0675715	+	0.0315091i	−0.456110	−	0.889923i	$-0.650758\pi$
$643$	−1.71344	+	0.798990i	−0.0675715	+	0.0315091i	0.388539	+	0.921432i	$0.372980\pi$
$644$	7.75788	−	6.50964i	0.305703	−	0.256516i
$645$	1.79190	−	1.39709i	0.0705561	−	0.0550105i
$646$	−22.8351	+	1.97107i	−0.898433	+	0.0775509i
$647$	25.1858	−	25.1858i	0.990157	−	0.990157i	−0.00979501	−	0.999952i	$-0.503118\pi$
$647$	25.1858	−	25.1858i	0.990157	−	0.990157i	0.999952	+	0.00979501i	$0.00311790\pi$
$648$	4.96121	+	7.50908i	0.194895	+	0.294985i
$649$	27.8203	−	76.4357i	1.09204	−	3.00036i
$650$	−0.506249	−	17.4819i	−0.0198567	−	0.685695i
$651$	21.6331	+	1.09091i	0.847868	+	0.0427563i
$652$	−12.1701	−	5.67500i	−0.476617	−	0.222250i
$653$	−10.4769	+	2.80727i	−0.409992	+	0.109857i	−0.457919	−	0.888994i	$-0.651405\pi$
$653$	−10.4769	+	2.80727i	−0.409992	+	0.109857i	0.0479273	+	0.998851i	$0.484738\pi$
$654$	4.04222	−	1.24456i	0.158063	−	0.0486663i
$655$	−6.91117	−	36.1290i	−0.270042	−	1.41168i
$656$	2.95319	−	3.51947i	0.115303	−	0.137412i
$657$	−24.5746	+	28.4964i	−0.958748	+	1.11175i
$658$	−1.06803	−	3.98596i	−0.0416363	−	0.155389i
$659$	4.15751	−	1.51321i	0.161954	−	0.0589463i	−0.259771	−	0.965670i	$-0.583647\pi$
$659$	4.15751	−	1.51321i	0.161954	−	0.0589463i	0.421725	+	0.906724i	$0.361425\pi$
$660$	1.06626	+	20.7437i	0.0415041	+	0.807447i
$661$	1.45703	−	8.26320i	0.0566717	−	0.321401i	−0.943272	−	0.332021i	$-0.892269\pi$
$661$	1.45703	−	8.26320i	0.0566717	−	0.321401i	0.999944	+	0.0106200i	$0.00338051\pi$
$662$	23.3098	−	10.8695i	0.905959	−	0.422456i
$663$	9.78434	−	30.3167i	0.379992	−	1.17740i
$664$		−	13.4414i		−	0.521628i
$665$	12.9473	−	0.172381i	0.502075	−	0.00668463i
$666$	5.11597	−	10.5953i	0.198240	−	0.410559i
$667$	−19.4685	−	1.70327i	−0.753823	−	0.0659510i
$668$	0.916390	+	1.96520i	0.0354562	+	0.0760360i
$669$	18.2443	−	43.2180i	0.705367	−	1.67091i
$670$	23.6570	+	13.2055i	0.913949	+	0.510174i
$671$	14.1427	+	38.8568i	0.545974	+	1.50005i
$672$	−2.29944	+	0.0848443i	−0.0887026	+	0.00327294i
$673$	3.41229	+	0.914320i	0.131534	+	0.0352445i	0.323985	−	0.946062i	$-0.394977\pi$
$673$	3.41229	+	0.914320i	0.131534	+	0.0352445i	−0.192451	+	0.981307i	$0.561644\pi$
$674$	3.71115	+	3.11403i	0.142948	+	0.119948i
$675$	9.73335	−	24.0886i	0.374637	−	0.927172i
$676$	−0.382571	−	0.662633i	−0.0147143	−	0.0254859i
$677$	7.01459	+	26.1788i	0.269593	+	1.00613i	0.959379	+	0.282120i	$0.0910377\pi$
$677$	7.01459	+	26.1788i	0.269593	+	1.00613i	−0.689786	+	0.724013i	$0.742296\pi$
$678$	4.15020	+	3.22932i	0.159388	+	0.124021i
$679$	−4.30699	+	0.759439i	−0.165287	+	0.0291446i
$680$	−7.68728	−	8.89658i	−0.294794	−	0.341168i
$681$	−21.6658	−	14.0092i	−0.830234	−	0.536832i
$682$	50.2934	+	4.40010i	1.92583	+	0.168489i
$683$	−7.49846	−	7.49846i	−0.286921	−	0.286921i	0.548941	−	0.835861i	$-0.315031\pi$
$683$	−7.49846	−	7.49846i	−0.286921	−	0.286921i	−0.835861	+	0.548941i	$0.815031\pi$
$684$	11.4194	−	6.37156i	0.436633	−	0.243623i
$685$	−3.34444	−	32.7584i	−0.127784	−	1.25163i
$686$	−10.4480	−	12.4514i	−0.398906	−	0.475397i
$687$	−10.4306	+	2.23863i	−0.397953	+	0.0854092i
$688$	0.336502	+	0.480575i	0.0128290	+	0.0183217i
$689$	1.19538	+	6.77936i	0.0455405	+	0.258273i
$690$	−28.7742	+	6.61264i	−1.09541	+	0.251739i
$691$	−13.9113	+	24.0952i	−0.529212	+	0.916623i	0.470207	+	0.882556i	$0.344179\pi$
$691$	−13.9113	+	24.0952i	−0.529212	+	0.916623i	−0.999420	+	0.0340667i	$0.989154\pi$
$692$	7.25735	+	1.94460i	0.275883	+	0.0739227i
$693$	7.58098	−	19.9847i	0.287978	−	0.759155i
$694$	14.2863	−	17.0257i	0.542300	−	0.646288i
$695$	1.38009	−	8.54869i	0.0523498	−	0.324270i
$696$	3.25343	+	3.02188i	0.123321	+	0.114544i
$697$	−21.8946	−	10.2096i	−0.829316	−	0.386717i
$698$	13.3638	−	19.0855i	0.505828	−	0.722398i
$699$	44.5625	+	18.8119i	1.68551	+	0.711531i
$700$	3.96584	+	5.32858i	0.149895	+	0.201402i
$701$	1.82151	+	2.17079i	0.0687974	+	0.0819895i	0.799345	−	0.600872i	$-0.205180\pi$
$701$	1.82151	+	2.17079i	0.0687974	+	0.0819895i	−0.730548	+	0.682861i	$0.760735\pi$
$702$	2.00688	+	18.0642i	0.0757447	+	0.681787i
$703$	−14.7950	−	8.56483i	−0.558004	−	0.323029i
$704$	−5.36307			−0.202128
$705$	−2.51306	+	11.7650i	−0.0946473	+	0.443094i
$706$	−22.4133	−	8.15778i	−0.843536	−	0.307022i
$707$	−6.23243	−	8.90083i	−0.234395	−	0.334750i
$708$	−17.6165	−	19.4875i	−0.662067	−	0.732387i
$709$	13.7840	+	37.8711i	0.517668	+	1.42228i	0.873083	+	0.487572i	$0.162117\pi$
$709$	13.7840	+	37.8711i	0.517668	+	1.42228i	−0.355416	+	0.934708i	$0.615661\pi$
$710$	4.80143	−	10.6983i	0.180195	−	0.401501i
$711$	0.126683	+	1.71434i	0.00475099	+	0.0642926i
$712$	−0.672039	−	7.68144i	−0.0251857	−	0.287874i
$713$	6.25436	+	71.4876i	0.234227	+	2.67723i
$714$	3.56028	+	11.5634i	0.133240	+	0.432751i
$715$	−17.1753	+	38.2693i	−0.642320	+	1.43119i
$716$	4.17797	+	11.4789i	0.156138	+	0.428986i
$717$	14.8721	−	13.4441i	0.555408	−	0.502081i
$718$	−12.6872	−	18.1192i	−0.473482	−	0.676203i
$719$	−8.02032	−	2.91916i	−0.299107	−	0.108866i	0.188107	−	0.982149i	$-0.439765\pi$
$719$	−8.02032	−	2.91916i	−0.299107	−	0.108866i	−0.487214	+	0.873282i	$0.661987\pi$
$720$	6.08245	+	2.82910i	0.226679	+	0.105434i
$721$	4.38877			0.163446
$722$	−7.98971	−	17.2385i	−0.297346	−	0.641549i
$723$	−0.921703	−	1.46857i	−0.0342785	−	0.0546168i
$724$	−7.50276	−	8.94144i	−0.278838	−	0.332306i
$725$	1.85951	−	12.6825i	0.0690605	−	0.471018i
$726$	11.9651	−	28.3436i	0.444068	−	1.05193i
$727$	16.8770	−	24.1028i	0.625933	−	0.893925i	−0.373499	−	0.927631i	$-0.621842\pi$
$727$	16.8770	−	24.1028i	0.625933	−	0.893925i	0.999432	+	0.0337057i	$0.0107309\pi$
$728$	−4.21145	−	1.96383i	−0.156087	−	0.0727844i
$729$	−8.03866	+	25.7756i	−0.297728	+	0.954651i
$730$	−4.47002	+	27.6887i	−0.165443	+	1.02480i
$731$	1.98290	−	2.36313i	0.0733403	−	0.0874035i
$732$	13.2282	+	1.83247i	0.488929	+	0.0677302i
$733$	20.4915	+	5.49067i	0.756869	+	0.202802i	0.616563	−	0.787306i	$-0.288525\pi$
$733$	20.4915	+	5.49067i	0.756869	+	0.202802i	0.140306	+	0.990108i	$0.455191\pi$
$734$	9.16176	−	15.8686i	0.338167	−	0.585722i
$735$	4.54119	+	19.7605i	0.167504	+	0.728877i
$736$	−1.32374	−	7.50732i	−0.0487938	−	0.276723i
$737$	−37.2717	−	53.2295i	−1.37292	−	1.96073i
$738$	13.7818	+	0.186123i	0.507314	+	0.00685127i
$739$	20.8102	+	24.8006i	0.765515	+	0.912306i	0.998183	−	0.0602505i	$-0.0191900\pi$
$739$	20.8102	+	24.8006i	0.765515	+	0.912306i	−0.232668	+	0.972556i	$0.574746\pi$
$740$	−0.890704	−	8.72434i	−0.0327429	−	0.320713i
$741$	26.3912	−	0.943074i	0.969506	−	0.0346447i
$742$	−1.84875	−	1.84875i	−0.0678698	−	0.0678698i
$743$	35.2898	+	3.08746i	1.29466	+	0.113268i	0.713576	−	0.700578i	$-0.247074\pi$
$743$	35.2898	+	3.08746i	1.29466	+	0.113268i	0.581081	+	0.813846i	$0.302630\pi$
$744$	8.85318	−	13.6918i	0.324573	−	0.501966i
$745$	−19.1526	−	22.1656i	−0.701698	−	0.812083i
$746$	11.8293	−	2.08582i	0.433101	−	0.0763674i
$747$	31.2373	−	25.5004i	1.14291	−	0.933011i
$748$	7.29873	+	27.2392i	0.266868	+	0.995964i
$749$	3.99714	+	6.92325i	0.146052	+	0.252970i
$750$	−3.22988	−	19.0937i	−0.117938	−	0.697202i
$751$	26.9627	+	22.6244i	0.983884	+	0.825576i	0.984671	−	0.174423i	$-0.0558061\pi$
$751$	26.9627	+	22.6244i	0.983884	+	0.825576i	−0.000787037		1.00000i	$0.500251\pi$
$752$	−3.00038	−	0.803950i	−0.109413	−	0.0293171i
$753$	−1.32721	−	35.9698i	−0.0483661	−	1.31081i
$754$	3.06694	+	8.42636i	0.111692	+	0.306870i
$755$	−41.9236	−	23.4021i	−1.52576	−	0.851691i
$756$	−4.55956	−	5.18284i	−0.165829	−	0.188498i
$757$	−4.60745	−	9.88071i	−0.167461	−	0.359120i	0.804612	−	0.593801i	$-0.202373\pi$
$757$	−4.60745	−	9.88071i	−0.167461	−	0.359120i	−0.972073	+	0.234681i	$0.924596\pi$
$758$	−9.22896	−	0.807429i	−0.335211	−	0.0293272i
$759$	69.0285	+	15.7930i	2.50558	+	0.573249i
$760$	4.76059	−	8.50510i	0.172685	−	0.308512i
$761$			44.9557i			1.62964i	0.579713	+	0.814821i	$0.303165\pi$
$761$			44.9557i			1.62964i	−0.579713	+	0.814821i	$0.696835\pi$
$762$	−8.85498	−	2.85784i	−0.320782	−	0.103529i
$763$	−2.94007	+	1.37098i	−0.106438	+	0.0496327i
$764$	4.53792	−	25.7358i	0.164176	−	0.931089i
$765$	6.09137	−	34.7431i	0.220234	−	1.25614i
$766$	−8.11308	+	2.95292i	−0.293138	+	0.106693i
$767$	−13.7307	−	51.2436i	−0.495787	−	1.85030i
$768$	−0.810127	+	1.53091i	−0.0292330	+	0.0552421i
$769$	3.37191	−	4.01849i	0.121594	−	0.144910i	−0.701813	−	0.712361i	$-0.747626\pi$
$769$	3.37191	−	4.01849i	0.121594	−	0.144910i	0.823407	+	0.567451i	$0.192070\pi$
$770$	−2.99327	−	15.6477i	−0.107870	−	0.563904i
$771$	−2.29056	−	7.43950i	−0.0824924	−	0.267927i
$772$	13.6789	−	3.66524i	0.492314	−	0.131915i
$773$	−19.3703	−	9.03251i	−0.696700	−	0.324877i	0.0418036	−	0.999126i	$-0.486690\pi$
$773$	−19.3703	−	9.03251i	−0.696700	−	0.324877i	−0.738504	+	0.674249i	$0.764467\pi$
$774$	−0.478442	+	1.69374i	−0.0171972	+	0.0608803i
$775$	−47.0480	+	1.36244i	−1.69001	+	0.0489403i
$776$	−1.12595	+	3.09352i	−0.0404192	+	0.111051i
$777$	−2.77172	+	8.58816i	−0.0994351	+	0.308098i
$778$	−3.15999	+	3.15999i	−0.113291	+	0.113291i
$779$	1.76859	−	19.9480i	0.0633662	−	0.714713i
$780$	8.32969	+	10.6836i	0.298251	+	0.382534i
$781$	−21.5450	+	18.0784i	−0.770941	+	0.646896i
$782$	−36.3284	+	16.9402i	−1.29910	+	0.605781i
$783$	−0.850492	+	13.2938i	−0.0303941	+	0.475082i
$784$	−5.15560	+	0.909071i	−0.184129	+	0.0324668i
$785$	−0.259527	+	0.125624i	−0.00926291	+	0.00448372i
$786$	20.8767	+	19.3909i	0.744645	+	0.691649i
$787$	−10.1149	+	37.7492i	−0.360556	+	1.34561i	0.512790	+	0.858514i	$0.328612\pi$
$787$	−10.1149	+	37.7492i	−0.360556	+	1.34561i	−0.873346	+	0.487100i	$0.838055\pi$
$788$	0.156454	+	1.78828i	0.00557346	+	0.0637049i
$789$	5.80353	−	4.39126i	0.206611	−	0.156333i
$790$	0.750024	+	1.03881i	0.0266847	+	0.0369592i
$791$	−3.49297	−	2.01667i	−0.124196	−	0.0717044i
$792$	−10.1746	−	12.4636i	−0.361538	−	0.442874i
$793$	22.0918	+	15.4689i	0.784504	+	0.549316i
$794$	−0.162955	+	0.924166i	−0.00578307	+	0.0327974i
$795$	2.34813	+	7.25155i	0.0832796	+	0.257186i
$796$	2.03771	−	1.70984i	0.0722246	−	0.0606036i
$797$	−13.5281	+	13.5281i	−0.479189	+	0.479189i	−0.904872	−	0.425683i	$-0.860034\pi$
$797$	−13.5281	+	13.5281i	−0.479189	+	0.479189i	0.425683	+	0.904872i	$0.360034\pi$
$798$	−8.00527	+	6.04261i	−0.283383	+	0.213906i
$799$			16.3332i			0.577826i
$800$	4.96627	−	0.579777i	0.175584	−	0.0204982i
$801$	16.5764	−	16.1347i	0.585699	−	0.570090i
$802$	5.19875	−	3.64021i	0.183574	−	0.128540i
$803$	38.5841	−	55.1038i	1.36160	−	1.94457i
$804$	−20.8247	+	2.59871i	−0.734432	+	0.0916493i
$805$	21.1651	−	8.05228i	0.745972	−	0.283806i
$806$	28.5157	−	16.4635i	1.00442	−	0.579903i
$807$	−1.99167	+	14.3774i	−0.0701102	+	0.506109i
$808$	−8.14806	+	0.712863i	−0.286648	+	0.0250784i
$809$	11.9583	+	20.7123i	0.420430	+	0.728206i	0.995981	−	0.0895595i	$-0.0285459\pi$
$809$	11.9583	+	20.7123i	0.420430	+	0.728206i	−0.575552	+	0.817766i	$0.695213\pi$
$810$	4.96460	+	19.5026i	0.174438	+	0.685253i
$811$	24.5664	−	8.94144i	0.862644	−	0.313977i	0.127459	−	0.991844i	$-0.459318\pi$
$811$	24.5664	−	8.94144i	0.862644	−	0.313977i	0.735184	+	0.677867i	$0.237096\pi$
$812$	−2.78981	−	1.95345i	−0.0979033	−	0.0685526i
$813$	0.170995	−	0.0694797i	0.00599707	−	0.00243676i
$814$	−7.19390	+	19.7651i	−0.252146	+	0.692766i
$815$	−21.5369	−	20.9223i	−0.754406	−	0.732876i
$816$	8.87808	+	2.03121i	0.310795	+	0.0711066i
$817$	2.40201	+	0.877423i	0.0840357	+	0.0306971i
$818$	10.0305	+	10.0305i	0.350709	+	0.350709i
$819$	−3.42589	−	13.5129i	−0.119710	−	0.472180i
$820$	8.82163	−	5.26488i	0.308065	−	0.183857i
$821$	38.0768	+	6.71397i	1.32889	+	0.234319i	0.792614	−	0.609724i	$-0.208720\pi$
$821$	38.0768	+	6.71397i	1.32889	+	0.234319i	0.536275	+	0.844043i	$0.319831\pi$
$822$	17.1045	+	18.9212i	0.596589	+	0.659954i
$823$	14.4056	−	30.8929i	0.502148	−	1.07686i	−0.477957	−	0.878383i	$-0.658623\pi$
$823$	14.4056	−	30.8929i	0.502148	−	1.07686i	0.980105	−	0.198477i	$-0.0635996\pi$
$824$	1.65180	−	2.86099i	0.0575430	−	0.0996675i
$825$	−12.9798	+	44.5950i	−0.451898	+	1.55260i
$826$	15.4350	+	12.9515i	0.537052	+	0.450641i
$827$	6.46161	−	0.565317i	0.224692	−	0.0196580i	0.0257463	−	0.999669i	$-0.491804\pi$
$827$	6.46161	−	0.565317i	0.224692	−	0.0196580i	0.198946	+	0.980011i	$0.436248\pi$
$828$	14.9354	−	17.3189i	0.519041	−	0.601872i
$829$	−43.8683	−	25.3274i	−1.52361	−	0.879655i	−0.999610	−	0.0279360i	$-0.991107\pi$
$829$	−43.8683	−	25.3274i	−1.52361	−	0.879655i	−0.523998	−	0.851719i	$-0.675560\pi$
$830$	9.86983	−	28.3891i	0.342587	−	0.985401i
$831$	−33.7972	−	1.70432i	−1.17241	−	0.0591223i
$832$	−2.86526	+	2.00628i	−0.0993350	+	0.0695551i
$833$	11.6336	+	24.9483i	0.403080	+	0.864407i
$834$	3.05695	+	5.97042i	0.105853	+	0.206739i
$835$	0.492455	+	4.82353i	0.0170421	+	0.166925i
$836$	−19.1650	+	13.3863i	−0.662834	+	0.462974i
$837$	48.6151	−	5.40101i	1.68039	−	0.186686i
$838$	−2.66279	+	30.4359i	−0.0919847	+	1.05139i
$839$	34.4572	+	12.5414i	1.18960	+	0.432977i	0.859581	−	0.510999i	$-0.170724\pi$
$839$	34.4572	+	12.5414i	1.18960	+	0.432977i	0.330014	+	0.943976i	$0.392947\pi$
$840$	−4.91886	−	1.50925i	−0.169717	−	0.0520739i
$841$	−3.89455	−	22.0871i	−0.134295	−	0.761624i
$842$	1.24465	−	2.66917i	0.0428936	−	0.0919856i
$843$	0.0417122	+	1.13048i	0.00143664	+	0.0389357i
$844$	2.24884	−	1.29837i	0.0774084	−	0.0446918i
$845$	−0.321454	−	1.68044i	−0.0110584	−	0.0578089i
$846$	−3.82384	−	8.49800i	−0.131466	−	0.292167i
$847$	−6.10741	+	22.7932i	−0.209853	+	0.783182i
$848$	−1.90100	+	0.509371i	−0.0652805	+	0.0174919i
$849$	−11.1852	+	1.39580i	−0.383876	+	0.0479036i
$850$	−9.70342	−	24.4348i	−0.332825	−	0.838108i
$851$	−29.4431	−	5.19162i	−1.00930	−	0.177966i
$852$	1.90605	+	8.88098i	0.0653001	+	0.304257i
$853$	−0.582006	+	6.65236i	−0.0199275	+	0.227772i	0.979700	+	0.200471i	$0.0642471\pi$
$853$	−0.582006	+	6.65236i	−0.0199275	+	0.227772i	−0.999627	+	0.0273019i	$0.991308\pi$
$854$	−10.2429			−0.350506
$855$	28.7971	−	5.07204i	0.984841	−	0.173460i
$856$	6.01760			0.205677
$857$	−4.27292	+	48.8397i	−0.145960	+	1.66833i	0.471602	+	0.881811i	$0.343676\pi$
$857$	−4.27292	+	48.8397i	−0.145960	+	1.66833i	−0.617562	+	0.786522i	$0.711880\pi$
$858$	−6.81816	−	31.7684i	−0.232768	−	1.08455i
$859$	15.0770	+	2.65848i	0.514419	+	0.0907060i	0.424831	−	0.905273i	$-0.360334\pi$
$859$	15.0770	+	2.65848i	0.514419	+	0.0907060i	0.0895887	+	0.995979i	$0.471445\pi$
$860$	0.357835	+	1.26209i	0.0122021	+	0.0430371i
$861$	−10.4902	+	1.30907i	−0.357506	+	0.0446129i
$862$	−14.9292	+	4.00026i	−0.508490	+	0.136250i
$863$	−9.33986	+	34.8568i	−0.317933	+	1.18654i	0.603295	+	0.797518i	$0.293854\pi$
$863$	−9.33986	+	34.8568i	−0.317933	+	1.18654i	−0.921228	+	0.389023i	$0.872813\pi$
$864$	−5.09472	+	1.02167i	−0.173326	+	0.0347579i
$865$	13.9001	+	9.43610i	0.472618	+	0.320837i
$866$	11.4758	−	6.62555i	0.389963	−	0.225145i
$867$	−0.680085	−	18.4315i	−0.0230969	−	0.625968i
$868$	−5.28515	+	11.3341i	−0.179390	+	0.384703i
$869$	−0.533631	−	3.02637i	−0.0181022	−	0.102663i
$870$	4.65253	+	8.77136i	0.157735	+	0.297377i
$871$	−39.8254	−	14.4952i	−1.34943	−	0.491153i
$872$	−0.212825	+	2.43260i	−0.00720716	+	0.0823782i
$873$	−9.32531	+	3.25221i	−0.315614	+	0.110071i
$874$	−23.4687	−	23.5233i	−0.793842	−	0.795689i
$875$	4.46341	+	14.1664i	0.150891	+	0.478911i
$876$	−9.90125	−	19.3378i	−0.334532	−	0.653364i
$877$	2.94840	+	6.32286i	0.0995604	+	0.213508i	0.949779	−	0.312922i	$-0.101308\pi$
$877$	2.94840	+	6.32286i	0.0995604	+	0.213508i	−0.850218	+	0.526430i	$0.823530\pi$
$878$	−22.3178	+	15.6271i	−0.753191	+	0.527390i
$879$	−42.2376	−	2.12996i	−1.42464	−	0.0718417i
$880$	−11.3272	−	3.93803i	−0.381839	−	0.132751i
$881$	25.1146	+	14.4999i	0.846133	+	0.488515i	0.859344	−	0.511397i	$-0.170872\pi$
$881$	25.1146	+	14.4999i	0.846133	+	0.488515i	−0.0132110	+	0.999913i	$0.504205\pi$
$882$	−11.8936	−	10.2568i	−0.400479	−	0.345364i
$883$	5.03079	−	0.440137i	0.169300	−	0.0148118i	−0.00219075	−	0.999998i	$-0.500697\pi$
$883$	5.03079	−	0.440137i	0.169300	−	0.0148118i	0.171490	+	0.985186i	$0.445142\pi$
$884$	14.0893	+	11.8224i	0.473876	+	0.397629i
$885$	−22.8977	−	54.0945i	−0.769698	−	1.81837i
$886$	10.5948	−	18.3507i	0.355938	−	0.616503i
$887$	−1.39388	+	2.98920i	−0.0468021	+	0.100367i	−0.928318	−	0.371786i	$-0.878745\pi$
$887$	−1.39388	+	2.98920i	−0.0468021	+	0.100367i	0.881516	+	0.472154i	$0.156523\pi$
$888$	4.55535	+	5.03918i	0.152867	+	0.169104i
$889$	7.02830	+	1.23928i	0.235722	+	0.0415641i
$890$	4.22098	−	16.7172i	0.141488	−	0.560361i
$891$	9.66220	−	47.2907i	0.323696	−	1.58430i
$892$	19.1514	+	19.1514i	0.641236	+	0.641236i
$893$	−12.7286	+	4.61607i	−0.425945	+	0.154471i
$894$	22.1195	+	5.06070i	0.739786	+	0.169255i
$895$	0.395374	+	27.3120i	0.0132159	+	0.912939i
$896$	0.454368	−	1.24837i	0.0151794	−	0.0417050i
$897$	42.7870	−	17.3854i	1.42862	−	0.580482i
$898$	16.6885	+	11.6854i	0.556901	+	0.389946i
$899$	22.6774	−	8.25391i	0.756335	−	0.275283i
$900$	10.7692	+	10.4415i	0.358972	+	0.348050i
$901$	5.17422	+	8.96202i	0.172378	+	0.298568i
$902$	−24.5460	+	2.14750i	−0.817294	+	0.0715039i
$903$	0.185235	−	1.33717i	0.00616423	−	0.0444981i
$904$	−2.62929	+	1.51802i	−0.0874489	+	0.0504886i
$905$	−9.28075	−	24.3941i	−0.308503	−	0.810886i
$906$	36.9045	−	4.60529i	1.22607	−	0.153000i
$907$	−16.7917	+	23.9810i	−0.557558	+	0.796275i	−0.994668	−	0.103133i	$-0.967113\pi$
$907$	−16.7917	+	23.9810i	−0.557558	+	0.796275i	0.437110	+	0.899408i	$0.356002\pi$
$908$	12.2020	−	8.54393i	0.404937	−	0.283540i
$909$	−17.1148	−	17.5834i	−0.567661	−	0.583204i
$910$	−7.45284	−	7.24014i	−0.247059	−	0.240008i
$911$		−	46.8456i		−	1.55206i	−0.630694	−	0.776031i	$-0.717230\pi$
$911$		−	46.8456i		−	1.55206i	0.630694	−	0.776031i	$-0.282770\pi$
$912$	0.926182	+	7.49281i	0.0306690	+	0.248112i
$913$	−50.9734	+	50.9734i	−1.68697	+	1.68697i
$914$	20.2580	−	16.9985i	0.670076	−	0.562261i
$915$	26.5933	+	13.5836i	0.879147	+	0.449060i
$916$	1.06954	−	6.06569i	0.0353387	−	0.200416i
$917$	−17.9017	−	12.5349i	−0.591167	−	0.413940i
$918$	12.1226	+	24.4858i	0.400106	+	0.808153i
$919$	−27.5839	−	15.9256i	−0.909908	−	0.525336i	−0.0295065	−	0.999565i	$-0.509394\pi$
$919$	−27.5839	−	15.9256i	−0.909908	−	0.525336i	−0.880402	+	0.474229i	$0.842727\pi$
$920$	2.71668	−	16.8280i	0.0895664	−	0.554801i
$921$	−29.1604	+	22.0643i	−0.960867	+	0.727044i
$922$	−0.176268	−	2.01476i	−0.00580509	−	0.0663525i
$923$	−4.74761	+	17.7183i	−0.156269	+	0.583205i
$924$	9.04182	+	8.39831i	0.297454	+	0.276284i
$925$	4.52493	−	19.0804i	0.148779	−	0.627360i
$926$	−6.36837	+	1.12292i	−0.209278	+	0.0369013i
$927$	9.78256	−	1.58903i	0.321301	−	0.0521907i
$928$	−2.32343	+	1.08344i	−0.0762705	+	0.0355655i
$929$	11.4861	−	9.63802i	0.376848	−	0.316213i	−0.434615	−	0.900616i	$-0.643116\pi$
$929$	11.4861	−	9.63802i	0.376848	−	0.316213i	0.811464	+	0.584403i	$0.198671\pi$
$930$	28.7522	−	22.4173i	0.942822	−	0.735091i
$931$	−16.1545	+	16.1170i	−0.529442	+	0.528213i
$932$	−19.7472	+	19.7472i	−0.646840	+	0.646840i
$933$	15.1029	−	46.7960i	0.494446	−	1.53203i
$934$	6.25277	−	17.1793i	0.204597	−	0.562125i
$935$	−4.58597	+	62.8904i	−0.149977	+	2.05674i
$936$	−10.0984	−	2.85255i	−0.330075	−	0.0932384i
$937$	−35.6861	−	16.6407i	−1.16581	−	0.543628i	−0.259297	−	0.965798i	$-0.583491\pi$
$937$	−35.6861	−	16.6407i	−1.16581	−	0.543628i	−0.906517	+	0.422170i	$0.861269\pi$
$938$	15.5480	−	4.16607i	0.507660	−	0.136027i
$939$	−12.9863	−	42.1782i	−0.423791	−	1.37643i
$940$	−5.74668	−	3.90114i	−0.187436	−	0.127241i
$941$	14.5461	−	17.3354i	0.474190	−	0.565118i	−0.474933	−	0.880022i	$-0.657528\pi$
$941$	14.5461	−	17.3354i	0.474190	−	0.565118i	0.949124	+	0.314904i	$0.101972\pi$
$942$	0.104463	−	0.197405i	0.00340358	−	0.00643182i
$943$	−9.06469	−	33.8299i	−0.295187	−	1.10165i
$944$	14.2522	−	5.18738i	0.463870	−	0.168835i
$945$	−5.82440	−	14.2945i	−0.189468	−	0.465001i
$946$	0.546361	−	3.09857i	0.0177637	−	0.100743i
$947$	16.2380	−	7.57192i	0.527665	−	0.246054i	−0.140482	−	0.990083i	$-0.544865\pi$
$947$	16.2380	−	7.57192i	0.527665	−	0.246054i	0.668147	+	0.744029i	$0.267088\pi$
$948$	−0.944500	−	0.304826i	−0.0306759	−	0.00990029i
$949$		−	43.8736i		−	1.42420i
$950$	16.2999	−	14.4677i	0.528837	−	0.469394i
$951$	18.8701	+	4.31728i	0.611905	+	0.139997i
$952$	−6.95885	−	0.608821i	−0.225538	−	0.0197320i
$953$	−15.3526	−	32.9237i	−0.497318	−	1.06650i	−0.981487	−	0.191527i	$-0.938656\pi$
$953$	−15.3526	−	32.9237i	−0.497318	−	1.06650i	0.484169	−	0.874974i	$-0.339122\pi$
$954$	−4.79024	−	3.45149i	−0.155090	−	0.111746i
$955$	28.4818	−	51.0236i	0.921650	−	1.65109i
$956$	3.95879	+	10.8767i	0.128037	+	0.351777i
$957$	−0.878082	−	23.7976i	−0.0283844	−	0.769268i
$958$	15.5208	+	4.15878i	0.501453	+	0.134364i
$959$	−14.9865	−	12.5751i	−0.483938	−	0.406072i
$960$	−2.83517	+	2.63852i	−0.0915047	+	0.0851580i
$961$	−28.8075	−	49.8960i	−0.929273	−	1.60955i
$962$	3.55054	+	13.2508i	0.114474	+	0.427223i
$963$	11.4163	+	13.9847i	0.367885	+	0.450650i
$964$	0.985831	−	0.173829i	0.0317515	−	0.00559864i
$965$	31.5820	+	2.30296i	1.01666	+	0.0741351i
$966$	−9.52435	+	14.7298i	−0.306441	+	0.473924i
$967$	−26.2538	−	2.29691i	−0.844265	−	0.0738636i	−0.343189	−	0.939267i	$-0.611507\pi$
$967$	−26.2538	−	2.29691i	−0.844265	−	0.0738636i	−0.501077	+	0.865403i	$0.667063\pi$
$968$	12.5600	+	12.5600i	0.403694	+	0.403694i
$969$	36.7958	−	14.9012i	1.18205	−	0.478697i
$970$	−4.64960	+	5.70694i	−0.149290	+	0.183239i
$971$	−13.4540	−	16.0338i	−0.431758	−	0.514549i	0.505671	−	0.862727i	$-0.331245\pi$
$971$	−13.4540	−	16.0338i	−0.431758	−	0.514549i	−0.937429	+	0.348177i	$0.886801\pi$
$972$	−12.0398	−	9.90168i	−0.386177	−	0.317597i
$973$	−2.95086	−	4.21427i	−0.0946002	−	0.135103i
$974$	−1.15707	−	6.56208i	−0.0370749	−	0.210262i
$975$	9.74804	+	28.6808i	0.312187	+	0.918522i
$976$	−3.85512	+	6.67726i	−0.123399	+	0.213734i
$977$	23.4908	+	6.29434i	0.751538	+	0.201374i	0.614200	−	0.789150i	$-0.289479\pi$
$977$	23.4908	+	6.29434i	0.751538	+	0.201374i	0.137338	+	0.990524i	$0.456145\pi$
$978$	23.0383	+	3.19145i	0.736684	+	0.102051i
$979$	−26.5815	+	31.6786i	−0.849548	+	1.01245i
$980$	−11.5565	−	1.86566i	−0.369158	−	0.0595964i
$981$	−6.05703	+	4.12042i	−0.193386	+	0.131555i
$982$	−36.8682	−	17.1919i	−1.17651	−	0.548616i
$983$	16.7592	−	23.9347i	0.534536	−	0.763397i	−0.457519	−	0.889200i	$-0.651262\pi$
$983$	16.7592	−	23.9347i	0.534536	−	0.763397i	0.992055	+	0.125803i	$0.0401507\pi$
$984$	−3.09483	+	7.33117i	−0.0986595	+	0.233709i
$985$	−0.982668	+	3.89185i	−0.0313104	+	0.124005i
$986$	8.66482	+	10.3263i	0.275944	+	0.328857i
$987$	3.79952	+	6.05387i	0.120940	+	0.192697i
$988$	−5.23133	+	14.3212i	−0.166431	+	0.455617i
$989$	4.47229			0.142210
$990$	−12.3375	−	33.7950i	−0.392113	−	1.07407i
$991$	47.4218	+	17.2601i	1.50640	+	0.548286i	0.957709	−	0.287738i	$-0.0929031\pi$
$991$	47.4218	+	17.2601i	1.50640	+	0.548286i	0.548694	+	0.836023i	$0.315125\pi$
$992$	5.39939	+	7.71113i	0.171431	+	0.244829i
$993$	−33.0463	+	29.8734i	−1.04869	+	0.948002i
$994$	−2.38280	−	6.54668i	−0.0755777	−	0.207648i
$995$	5.55928	−	2.11503i	0.176241	−	0.0670511i
$996$	6.85071	+	22.2504i	0.217073	+	0.705032i
$997$	−0.398737	−	4.55759i	−0.0126281	−	0.144340i	0.987263	−	0.159097i	$-0.0508582\pi$
$997$	−0.398737	−	4.55759i	−0.0126281	−	0.144340i	−0.999891	+	0.0147566i	$0.995303\pi$
$998$	−2.54168	−	29.0516i	−0.0804556	−	0.919611i
$999$	−3.06868	+	20.1466i	−0.0970887	+	0.637409i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.557.31	yes	480
3.2	odd	2	inner	570.2.bi.a.557.7	yes	480
5.3	odd	4	inner	570.2.bi.a.443.2	yes	480
15.8	even	4	inner	570.2.bi.a.443.37	yes	480
19.16	even	9	inner	570.2.bi.a.377.37	yes	480
57.35	odd	18	inner	570.2.bi.a.377.2	yes	480
95.73	odd	36	inner	570.2.bi.a.263.7	✓	480
285.263	even	36	inner	570.2.bi.a.263.31	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.263.7	✓	480	95.73	odd	36	inner
570.2.bi.a.263.31	yes	480	285.263	even	36	inner
570.2.bi.a.377.2	yes	480	57.35	odd	18	inner
570.2.bi.a.377.37	yes	480	19.16	even	9	inner
570.2.bi.a.443.2	yes	480	5.3	odd	4	inner
570.2.bi.a.443.37	yes	480	15.8	even	4	inner
570.2.bi.a.557.7	yes	480	3.2	odd	2	inner
570.2.bi.a.557.31	yes	480	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0871557 - 0.996195i) q^{2} +(0.363458 + 1.69349i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(-1.95247 - 1.08989i) q^{5} +(1.71872 - 0.214478i) q^{6} +(-1.28322 + 0.343837i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-2.73580 + 1.23102i) q^{9} +O(q^{10})\)	\(q+(0.0871557 - 0.996195i) q^{2} +(0.363458 + 1.69349i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(-1.95247 - 1.08989i) q^{5} +(1.71872 - 0.214478i) q^{6} +(-1.28322 + 0.343837i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-2.73580 + 1.23102i) q^{9} +(-1.25591 + 1.85005i) q^{10} +(4.64456 - 2.68154i) q^{11} +(-0.0638656 - 1.73087i) q^{12} +(1.47825 - 3.17012i) q^{13} +(0.230689 + 1.30830i) q^{14} +(1.13607 - 3.70261i) q^{15} +(0.939693 + 0.342020i) q^{16} +(0.458283 - 5.23819i) q^{17} +(0.987899 + 2.83268i) q^{18} +(4.21168 - 1.12327i) q^{19} +(1.73355 + 1.41237i) q^{20} +(-1.04868 - 2.04814i) q^{21} +(-2.26653 - 4.86059i) q^{22} +(6.24450 - 4.37245i) q^{23} +(-1.72985 - 0.0872330i) q^{24} +(2.62429 + 4.25595i) q^{25} +(-3.02921 - 1.74892i) q^{26} +(-3.07907 - 4.18561i) q^{27} +(1.32343 - 0.115785i) q^{28} +(-1.96385 - 1.64787i) q^{29} +(-3.58951 - 1.45445i) q^{30} +(-4.70677 + 8.15237i) q^{31} +(0.422618 - 0.906308i) q^{32} +(6.22925 + 6.89087i) q^{33} +(-5.17832 - 0.913077i) q^{34} +(2.88019 + 0.727229i) q^{35} +(2.90800 - 0.737255i) q^{36} +(-2.77322 - 2.77322i) q^{37} +(-0.751926 - 4.29355i) q^{38} +(5.90583 + 1.35119i) q^{39} +(1.55809 - 1.60386i) q^{40} +(1.57136 - 4.31727i) q^{41} +(-2.13174 + 0.866181i) q^{42} +(0.480575 + 0.336502i) q^{43} +(-5.03964 + 1.83428i) q^{44} +(6.68324 + 0.578169i) q^{45} +(-3.81156 - 6.60182i) q^{46} +(-3.09441 + 0.270725i) q^{47} +(-0.237668 + 1.71567i) q^{48} +(-4.53376 + 2.61757i) q^{49} +(4.46847 - 2.24338i) q^{50} +(9.03738 - 1.12777i) q^{51} +(-2.00628 + 2.86526i) q^{52} +(-1.61214 + 1.12883i) q^{53} +(-4.43804 + 2.70255i) q^{54} +(-11.9909 + 0.173583i) q^{55} -1.32848i q^{56} +(3.43302 + 6.72416i) q^{57} +(-1.81276 + 1.81276i) q^{58} +(11.6185 - 9.74909i) q^{59} +(-1.76176 + 3.44909i) q^{60} +(-1.33887 + 7.59310i) q^{61} +(7.71113 + 5.39939i) q^{62} +(3.08735 - 2.52034i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-6.34131 + 4.57844i) q^{65} +(7.40756 - 5.60496i) q^{66} +(-1.05602 - 12.0703i) q^{67} +(-1.36092 + 5.07903i) q^{68} +(9.67430 + 8.98578i) q^{69} +(0.975486 - 2.80584i) q^{70} +(-5.16453 + 0.910646i) q^{71} +(-0.481001 - 2.96119i) q^{72} +(11.3679 - 5.30093i) q^{73} +(-3.00437 + 2.52096i) q^{74} +(-6.25357 + 5.99107i) q^{75} +(-4.34275 + 0.374857i) q^{76} +(-5.03796 + 5.03796i) q^{77} +(1.86078 - 5.76559i) q^{78} +(0.195979 - 0.538447i) q^{79} +(-1.46196 - 1.69194i) q^{80} +(5.96916 - 6.73566i) q^{81} +(-4.16389 - 1.94165i) q^{82} +(-12.9834 + 3.47889i) q^{83} +(0.677091 + 2.19912i) q^{84} +(-6.60382 + 9.72795i) q^{85} +(0.377106 - 0.449418i) q^{86} +(2.07686 - 3.92469i) q^{87} +(1.38806 + 5.18033i) q^{88} +(-7.24577 + 2.63724i) q^{89} +(1.15845 - 6.60742i) q^{90} +(-0.806911 + 4.57622i) q^{91} +(-6.90890 + 3.22167i) q^{92} +(-15.5167 - 5.00781i) q^{93} +3.10623i q^{94} +(-9.44743 - 2.39710i) q^{95} +(1.68842 + 0.386293i) q^{96} +(3.27952 + 0.286921i) q^{97} +(2.21246 + 4.74464i) q^{98} +(-9.40552 + 13.0537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q+O(q^{10}) \) 480 * q	\( 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) \) 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more