LMFDB - Embedded newform 224.2.bd.a.109.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(37,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("224.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, degree $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			109.16
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.131818 + 1.40806i) q^{2} +(-0.751048 - 0.978785i) q^{3} +(-1.96525 + 0.371216i) q^{4} +(-1.09067 - 0.836901i) q^{5} +(1.27918 - 1.18654i) q^{6} +(0.448114 - 2.60753i) q^{7} +(-0.781748 - 2.71825i) q^{8} +(0.382510 - 1.42755i) q^{9} +O(q^{10})$	\(q+(0.131818 + 1.40806i) q^{2} +(-0.751048 - 0.978785i) q^{3} +(-1.96525 + 0.371216i) q^{4} +(-1.09067 - 0.836901i) q^{5} +(1.27918 - 1.18654i) q^{6} +(0.448114 - 2.60753i) q^{7} +(-0.781748 - 2.71825i) q^{8} +(0.382510 - 1.42755i) q^{9} +(1.03463 - 1.64604i) q^{10} +(5.29222 + 0.696734i) q^{11} +(1.83934 + 1.64475i) q^{12} +(-3.19829 - 1.32478i) q^{13} +(3.73061 + 0.287250i) q^{14} +1.69608i q^{15} +(3.72440 - 1.45906i) q^{16} +(-3.67476 - 2.12163i) q^{17} +(2.06049 + 0.350419i) q^{18} +(0.438796 + 3.33299i) q^{19} +(2.45411 + 1.23984i) q^{20} +(-2.88876 + 1.51977i) q^{21} +(-0.283429 + 7.54359i) q^{22} +(1.78678 - 6.66837i) q^{23} +(-2.07345 + 2.80670i) q^{24} +(-0.804936 - 3.00406i) q^{25} +(1.44377 - 4.67801i) q^{26} +(-5.10400 + 2.11415i) q^{27} +(0.0872989 + 5.29078i) q^{28} +(-0.342826 + 0.827656i) q^{29} +(-2.38818 + 0.223575i) q^{30} +(-1.28520 + 2.22602i) q^{31} +(2.54539 + 5.05183i) q^{32} +(-3.29276 - 5.70323i) q^{33} +(2.50297 - 5.45394i) q^{34} +(-2.67099 + 2.46892i) q^{35} +(-0.221800 + 2.94748i) q^{36} +(0.296782 + 0.227728i) q^{37} +(-4.63519 + 1.05720i) q^{38} +(1.10540 + 4.12541i) q^{39} +(-1.42227 + 3.61896i) q^{40} +(5.92559 + 5.92559i) q^{41} +(-2.52072 - 3.86721i) q^{42} +(2.50543 + 6.04865i) q^{43} +(-10.6592 + 0.595300i) q^{44} +(-1.61191 + 1.23686i) q^{45} +(9.62497 + 1.63688i) q^{46} +(5.69194 - 3.28625i) q^{47} +(-4.22531 - 2.54956i) q^{48} +(-6.59839 - 2.33694i) q^{49} +(4.12379 - 1.52939i) q^{50} +(0.683309 + 5.19025i) q^{51} +(6.77722 + 1.41626i) q^{52} +(-6.50416 - 0.856289i) q^{53} +(-3.64964 - 6.90804i) q^{54} +(-5.18897 - 5.18897i) q^{55} +(-7.43821 + 0.820344i) q^{56} +(2.93272 - 2.93272i) q^{57} +(-1.21058 - 0.373618i) q^{58} +(1.38821 - 10.5445i) q^{59} +(-0.629613 - 3.33323i) q^{60} +(5.00297 - 0.658653i) q^{61} +(-3.30378 - 1.51620i) q^{62} +(-3.55096 - 1.63711i) q^{63} +(-6.77774 + 4.24997i) q^{64} +(2.37958 + 4.12155i) q^{65} +(7.59642 - 5.38818i) q^{66} +(9.27915 + 12.0928i) q^{67} +(8.00940 + 2.80539i) q^{68} +(-7.86886 + 3.25939i) q^{69} +(-3.82847 - 3.43545i) q^{70} +(2.99261 - 2.99261i) q^{71} +(-4.17946 + 0.0762257i) q^{72} +(-7.58534 + 2.03249i) q^{73} +(-0.281533 + 0.447904i) q^{74} +(-2.33579 + 3.04406i) q^{75} +(-2.09960 - 6.38726i) q^{76} +(4.18827 - 13.4874i) q^{77} +(-5.66310 + 2.10027i) q^{78} +(-8.00108 + 4.61942i) q^{79} +(-5.28318 - 1.52560i) q^{80} +(2.06294 + 1.19104i) q^{81} +(-7.56247 + 9.12467i) q^{82} +(6.90241 + 2.85907i) q^{83} +(5.11297 - 4.05908i) q^{84} +(2.23237 + 5.38941i) q^{85} +(-8.18658 + 4.32511i) q^{86} +(1.06758 - 0.286056i) q^{87} +(-2.24329 - 14.9302i) q^{88} +(17.5710 + 4.70814i) q^{89} +(-1.95405 - 2.10662i) q^{90} +(-4.88759 + 7.74598i) q^{91} +(-1.03607 + 13.7683i) q^{92} +(3.14404 - 0.413921i) q^{93} +(5.37752 + 7.58139i) q^{94} +(2.31080 - 4.00242i) q^{95} +(3.03295 - 6.28555i) q^{96} +10.7200 q^{97} +(2.42075 - 9.59896i) q^{98} +(3.01895 - 7.28839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	0.131818	+	1.40806i	0.0932097	+	0.995647i
$2$	0.131818	+	1.40806i	0.0932097	+	0.995647i
$3$	−0.751048	−	0.978785i	−0.433618	−	0.565102i	0.524524	−	0.851396i	$-0.324243\pi$
$3$	−0.751048	−	0.978785i	−0.433618	−	0.565102i	−0.958142	+	0.286294i	$0.907577\pi$
$4$	−1.96525	+	0.371216i	−0.982624	+	0.185608i
$5$	−1.09067	−	0.836901i	−0.487763	−	0.374273i	0.335403	−	0.942075i	$-0.391128\pi$
$5$	−1.09067	−	0.836901i	−0.487763	−	0.374273i	−0.823166	+	0.567801i	$0.807794\pi$
$6$	1.27918	−	1.18654i	0.522224	−	0.484403i
$7$	0.448114	−	2.60753i	0.169371	−	0.985552i
$7$	0.448114	−	2.60753i	0.169371	−	0.985552i
$8$	−0.781748	−	2.71825i	−0.276390	−	0.961046i
$9$	0.382510	−	1.42755i	0.127503	−	0.475849i
$10$	1.03463	−	1.64604i	0.327180	−	0.520525i
$11$	5.29222	+	0.696734i	1.59567	+	0.210073i	0.875321	−	0.483543i	$-0.160650\pi$
$11$	5.29222	+	0.696734i	1.59567	+	0.210073i	0.720345	+	0.693616i	$0.243984\pi$
$12$	1.83934	+	1.64475i	0.530971	+	0.474800i
$13$	−3.19829	−	1.32478i	−0.887047	−	0.367427i	−0.107821	−	0.994170i	$-0.534387\pi$
$13$	−3.19829	−	1.32478i	−0.887047	−	0.367427i	−0.779226	+	0.626743i	$0.784387\pi$
$14$	3.73061	+	0.287250i	0.997049	+	0.0767709i
$15$			1.69608i			0.437927i
$16$	3.72440	−	1.45906i	0.931099	−	0.364765i
$17$	−3.67476	−	2.12163i	−0.891261	−	0.514570i	−0.0169063	−	0.999857i	$-0.505382\pi$
$17$	−3.67476	−	2.12163i	−0.891261	−	0.514570i	−0.874355	+	0.485287i	$0.838715\pi$
$18$	2.06049	+	0.350419i	0.485662	+	0.0825946i
$19$	0.438796	+	3.33299i	0.100667	+	0.764639i	0.965098	+	0.261889i	$0.0843453\pi$
$19$	0.438796	+	3.33299i	0.100667	+	0.764639i	−0.864431	+	0.502751i	$0.832321\pi$
$20$	2.45411	+	1.23984i	0.548755	+	0.277238i
$21$	−2.88876	+	1.51977i	−0.630380	+	0.331641i
$22$	−0.283429	+	7.54359i	−0.0604273	+	1.60830i
$23$	1.78678	−	6.66837i	0.372570	−	1.39045i	−0.484292	−	0.874906i	$-0.660923\pi$
$23$	1.78678	−	6.66837i	0.372570	−	1.39045i	0.856863	−	0.515545i	$-0.172410\pi$
$24$	−2.07345	+	2.80670i	−0.423241	+	0.572915i
$25$	−0.804936	−	3.00406i	−0.160987	−	0.600813i
$26$	1.44377	−	4.67801i	0.283146	−	0.917433i
$27$	−5.10400	+	2.11415i	−0.982266	+	0.406868i
$28$	0.0872989	+	5.29078i	0.0164979	+	0.999864i
$29$	−0.342826	+	0.827656i	−0.0636612	+	0.153692i	−0.952509	−	0.304511i	$-0.901507\pi$
$29$	−0.342826	+	0.827656i	−0.0636612	+	0.153692i	0.888847	+	0.458203i	$0.151507\pi$
$30$	−2.38818	+	0.223575i	−0.436021	+	0.0408191i
$31$	−1.28520	+	2.22602i	−0.230828	+	0.399806i	−0.958052	−	0.286594i	$-0.907477\pi$
$31$	−1.28520	+	2.22602i	−0.230828	+	0.399806i	0.727224	+	0.686400i	$0.240810\pi$
$32$	2.54539	+	5.05183i	0.449965	+	0.893046i
$33$	−3.29276	−	5.70323i	−0.573196	−	0.992805i
$34$	2.50297	−	5.45394i	0.429255	−	0.935344i
$35$	−2.67099	+	2.46892i	−0.451479	+	0.417324i
$36$	−0.221800	+	2.94748i	−0.0369666	+	0.491247i
$37$	0.296782	+	0.227728i	0.0487906	+	0.0374383i	0.632869	−	0.774259i	$-0.281877\pi$
$37$	0.296782	+	0.227728i	0.0487906	+	0.0374383i	−0.584078	+	0.811697i	$0.698544\pi$
$38$	−4.63519	+	1.05720i	−0.751927	+	0.171500i
$39$	1.10540	+	4.12541i	0.177006	+	0.660595i
$40$	−1.42227	+	3.61896i	−0.224881	+	0.572208i
$41$	5.92559	+	5.92559i	0.925422	+	0.925422i	0.997406	−	0.0719839i	$-0.0229330\pi$
$41$	5.92559	+	5.92559i	0.925422	+	0.925422i	−0.0719839	+	0.997406i	$0.522933\pi$
$42$	−2.52072	−	3.86721i	−0.388955	−	0.596723i
$43$	2.50543	+	6.04865i	0.382075	+	0.922410i	0.991564	+	0.129616i	$0.0413745\pi$
$43$	2.50543	+	6.04865i	0.382075	+	0.922410i	−0.609489	+	0.792794i	$0.708626\pi$
$44$	−10.6592	+	0.595300i	−1.60693	+	0.0897448i
$45$	−1.61191	+	1.23686i	−0.240289	+	0.184380i
$46$	9.62497	+	1.63688i	1.41913	+	0.241345i
$47$	5.69194	−	3.28625i	0.830255	−	0.479348i	−0.0236847	−	0.999719i	$-0.507540\pi$
$47$	5.69194	−	3.28625i	0.830255	−	0.479348i	0.853940	+	0.520371i	$0.174206\pi$
$48$	−4.22531	−	2.54956i	−0.609871	−	0.367997i
$49$	−6.59839	−	2.33694i	−0.942627	−	0.333848i
$50$	4.12379	−	1.52939i	0.583191	−	0.216288i
$51$	0.683309	+	5.19025i	0.0956824	+	0.726780i
$52$	6.77722	+	1.41626i	0.939831	+	0.196400i
$53$	−6.50416	−	0.856289i	−0.893416	−	0.117620i	−0.330181	−	0.943918i	$-0.607110\pi$
$53$	−6.50416	−	0.856289i	−0.893416	−	0.117620i	−0.563234	+	0.826297i	$0.690443\pi$
$54$	−3.64964	−	6.90804i	−0.496653	−	0.940066i
$55$	−5.18897	−	5.18897i	−0.699681	−	0.699681i
$56$	−7.43821	+	0.820344i	−0.993973	+	0.109623i
$57$	2.93272	−	2.93272i	0.388448	−	0.388448i
$58$	−1.21058	−	0.373618i	−0.158957	−	0.0490585i
$59$	1.38821	−	10.5445i	0.180730	−	1.37278i	−0.625059	−	0.780578i	$-0.714925\pi$
$59$	1.38821	−	10.5445i	0.180730	−	1.37278i	0.805789	−	0.592203i	$-0.201742\pi$
$60$	−0.629613	−	3.33323i	−0.0812827	−	0.430318i
$61$	5.00297	−	0.658653i	0.640565	−	0.0843319i	0.196755	−	0.980453i	$-0.436960\pi$
$61$	5.00297	−	0.658653i	0.640565	−	0.0843319i	0.443810	+	0.896121i	$0.353626\pi$
$62$	−3.30378	−	1.51620i	−0.419580	−	0.192557i
$63$	−3.55096	−	1.63711i	−0.447379	−	0.206257i
$64$	−6.77774	+	4.24997i	−0.847217	+	0.531246i
$65$	2.37958	+	4.12155i	0.295150	+	0.511215i
$66$	7.59642	−	5.38818i	0.935055	−	0.663240i
$67$	9.27915	+	12.0928i	1.13363	+	1.47737i	0.856212	+	0.516625i	$0.172812\pi$
$67$	9.27915	+	12.0928i	1.13363	+	1.47737i	0.277417	+	0.960750i	$0.410522\pi$
$68$	8.00940	+	2.80539i	0.971283	+	0.340204i
$69$	−7.86886	+	3.25939i	−0.947300	+	0.392384i
$70$	−3.82847	−	3.43545i	−0.457590	−	0.410615i
$71$	2.99261	−	2.99261i	0.355157	−	0.355157i	−0.506867	−	0.862024i	$-0.669197\pi$
$71$	2.99261	−	2.99261i	0.355157	−	0.355157i	0.862024	+	0.506867i	$0.169197\pi$
$72$	−4.17946	+	0.0762257i	−0.492554	+	0.00898329i
$73$	−7.58534	+	2.03249i	−0.887797	+	0.237885i	−0.673768	−	0.738943i	$-0.735325\pi$
$73$	−7.58534	+	2.03249i	−0.887797	+	0.237885i	−0.214029	+	0.976827i	$0.568659\pi$
$74$	−0.281533	+	0.447904i	−0.0327276	+	0.0520678i
$75$	−2.33579	+	3.04406i	−0.269713	+	0.351497i
$76$	−2.09960	−	6.38726i	−0.240841	−	0.732668i
$77$	4.18827	−	13.4874i	0.477298	−	1.53703i
$78$	−5.66310	+	2.10027i	−0.641220	+	0.237809i
$79$	−8.00108	+	4.61942i	−0.900192	+	0.519726i	−0.877262	−	0.480011i	$-0.840633\pi$
$79$	−8.00108	+	4.61942i	−0.900192	+	0.519726i	−0.0229292	+	0.999737i	$0.507299\pi$
$80$	−5.28318	−	1.52560i	−0.590678	−	0.170567i
$81$	2.06294	+	1.19104i	0.229215	+	0.132337i
$82$	−7.56247	+	9.12467i	−0.835135	+	1.00765i
$83$	6.90241	+	2.85907i	0.757638	+	0.313824i	0.727854	−	0.685733i	$-0.240518\pi$
$83$	6.90241	+	2.85907i	0.757638	+	0.313824i	0.0297841	+	0.999556i	$0.490518\pi$
$84$	5.11297	−	4.05908i	0.557871	−	0.442882i
$85$	2.23237	+	5.38941i	0.242134	+	0.584563i
$86$	−8.18658	+	4.32511i	−0.882781	+	0.466389i
$87$	1.06758	−	0.286056i	0.114456	−	0.0306684i
$88$	−2.24329	−	14.9302i	−0.239136	−	1.59157i
$89$	17.5710	+	4.70814i	1.86252	+	0.499062i	0.999976	−	0.00691275i	$-0.00220042\pi$
$89$	17.5710	+	4.70814i	1.86252	+	0.499062i	0.862548	+	0.505975i	$0.168867\pi$
$90$	−1.95405	−	2.10662i	−0.205975	−	0.222057i
$91$	−4.88759	+	7.74598i	−0.512359	+	0.812000i
$92$	−1.03607	+	13.7683i	−0.108018	+	1.43544i
$93$	3.14404	−	0.413921i	0.326022	−	0.0429216i
$94$	5.37752	+	7.58139i	0.554649	+	0.781961i
$95$	2.31080	−	4.00242i	0.237083	−	0.410639i
$96$	3.03295	−	6.28555i	0.309549	−	0.641517i
$97$	10.7200			1.08845			0.544226	−	0.838938i	$-0.316823\pi$
$97$	10.7200			1.08845			0.544226	+	0.838938i	$0.316823\pi$
$98$	2.42075	−	9.59896i	0.244533	−	0.969641i
$99$	3.01895	−	7.28839i	0.303416	−	0.732511i
$100$	2.69705	+	5.60492i	0.269705	+	0.560492i
$101$	0.813049	−	6.17572i	0.0809014	−	0.614507i	−0.902183	−	0.431354i	$-0.858036\pi$
$101$	0.813049	−	6.17572i	0.0809014	−	0.614507i	0.983084	−	0.183154i	$-0.0586306\pi$
$102$	−7.21809	+	1.64631i	−0.714697	+	0.163009i
$103$	13.1504	+	3.52365i	1.29575	+	0.347196i	0.839842	−	0.542831i	$-0.182647\pi$
$103$	13.1504	+	3.52365i	1.29575	+	0.347196i	0.455909	+	0.890026i	$0.349314\pi$
$104$	−1.10081	+	9.72940i	−0.107943	+	0.954046i
$105$	4.42259	+	0.760040i	0.431600	+	0.0741723i
$106$	0.348336	−	9.27111i	0.0338334	−	0.900490i
$107$	6.44508	−	8.39939i	0.623069	−	0.812000i	−0.370062	−	0.929007i	$-0.620663\pi$
$107$	6.44508	−	8.39939i	0.623069	−	0.812000i	0.993131	+	0.117007i	$0.0373301\pi$
$108$	9.24583	−	6.04951i	0.889680	−	0.582114i
$109$	−10.2001	+	7.82684i	−0.976995	+	0.749675i	−0.968172	−	0.250286i	$-0.919475\pi$
$109$	−10.2001	+	7.82684i	−0.976995	+	0.749675i	−0.00882350	+	0.999961i	$0.502809\pi$
$110$	6.62237	−	7.99037i	0.631418	−	0.761852i
$111$		−	0.461520i		−	0.0438056i
$112$	−2.13558	−	10.3653i	−0.201794	−	0.979428i
$113$		−	0.637686i		−	0.0599884i	−0.999550	−	0.0299942i	$-0.990451\pi$
$113$		−	0.637686i		−	0.0599884i	0.999550	−	0.0299942i	$-0.00954889\pi$
$114$	4.51602	+	3.74285i	0.422964	+	0.350550i
$115$	−7.52956	+	5.77763i	−0.702135	+	0.538767i
$116$	0.366500	−	1.75381i	0.0340286	−	0.162837i
$117$	−3.11456	+	4.05898i	−0.287941	+	0.375253i
$118$	15.0303	+	0.564720i	1.38365	+	0.0519867i
$119$	−7.17891	+	8.63131i	−0.658089	+	0.791231i
$120$	4.61038	−	1.32591i	0.420868	−	0.121039i
$121$	16.8970	+	4.52754i	1.53609	+	0.411594i
$122$	1.58690	+	6.95764i	0.143672	+	0.629915i
$123$	1.34948	−	10.2503i	0.121678	−	0.924237i
$124$	1.69939	−	4.85177i	0.152610	−	0.435702i
$125$	−4.26667	+	10.3007i	−0.381623	+	0.921319i
$126$	1.83706	−	5.21576i	0.163659	−	0.464656i
$127$	−0.495833			−0.0439981			−0.0219990	−	0.999758i	$-0.507003\pi$
$127$	−0.495833			−0.0439981			−0.0219990	+	0.999758i	$0.507003\pi$
$128$	−6.87763	−	8.98322i	−0.607903	−	0.794012i
$129$	4.03863	−	6.99510i	0.355581	−	0.615885i
$130$	−5.48970	+	3.89388i	−0.481479	+	0.341516i
$131$	−8.48817	+	1.11749i	−0.741615	+	0.0976354i	−0.491861	−	0.870674i	$-0.663683\pi$
$131$	−8.48817	+	1.11749i	−0.741615	+	0.0976354i	−0.249754	+	0.968309i	$0.580350\pi$
$132$	8.58822	+	9.98593i	0.747508	+	0.869164i
$133$	8.88748	+	0.349386i	0.770642	+	0.0302957i
$134$	−15.8042	+	14.6596i	−1.36528	+	1.26640i
$135$	7.33612	+	1.96571i	0.631393	+	0.169181i
$136$	−2.89436	+	11.6475i	−0.248190	+	0.998764i
$137$	1.35035	−	0.361824i	0.115368	−	0.0309127i	−0.200673	−	0.979658i	$-0.564313\pi$
$137$	1.35035	−	0.361824i	0.115368	−	0.0309127i	0.316041	+	0.948746i	$0.397646\pi$
$138$	−5.62667	−	10.6502i	−0.478974	−	0.906602i
$139$	−2.56095	−	6.18268i	−0.217217	−	0.524408i	0.777282	−	0.629152i	$-0.216598\pi$
$139$	−2.56095	−	6.18268i	−0.217217	−	0.524408i	−0.994499	+	0.104744i	$0.966598\pi$
$140$	4.33265	−	5.84356i	0.366175	−	0.493871i
$141$	−7.49145	−	3.10306i	−0.630894	−	0.261325i
$142$	4.60824	+	3.81928i	0.386715	+	0.320507i
$143$	−16.0031	−	9.23937i	−1.33824	−	0.772635i
$144$	−0.658259	−	5.87486i	−0.0548549	−	0.489572i
$145$	1.06658	−	0.615788i	0.0885743	−	0.0511384i
$146$	−3.86174	−	10.4127i	−0.319600	−	0.861759i
$147$	2.66835	+	8.21356i	0.220081	+	0.677443i
$148$	−0.667786	−	0.337373i	−0.0548916	−	0.0277319i
$149$	1.61742	−	2.10786i	0.132504	−	0.172683i	−0.722389	−	0.691487i	$-0.756956\pi$
$149$	1.61742	−	2.10786i	0.132504	−	0.172683i	0.854893	+	0.518804i	$0.173623\pi$
$150$	−4.59410	−	2.88766i	−0.375107	−	0.235776i
$151$	7.87773	−	2.11083i	0.641081	−	0.171777i	0.0763879	−	0.997078i	$-0.475661\pi$
$151$	7.87773	−	2.11083i	0.641081	−	0.171777i	0.564693	+	0.825301i	$0.308995\pi$
$152$	8.71685	−	3.79831i	0.707030	−	0.308084i
$153$	−4.43436	+	4.43436i	−0.358497	+	0.358497i
$154$	19.5431	+	4.11944i	1.57483	+	0.331954i
$155$	3.26469	−	1.35228i	0.262226	−	0.108618i
$156$	−3.70381	−	7.69712i	−0.296542	−	0.616263i
$157$	−5.24248	−	6.83214i	−0.418396	−	0.545264i	0.535840	−	0.844320i	$-0.319995\pi$
$157$	−5.24248	−	6.83214i	−0.418396	−	0.545264i	−0.954236	+	0.299056i	$0.903328\pi$
$158$	−7.55910	−	10.6570i	−0.601370	−	0.847829i
$159$	4.04682	+	7.00929i	0.320933	+	0.555873i
$160$	1.45171	−	7.64012i	0.114767	−	0.604005i
$161$	−16.5873	−	7.64728i	−1.30726	−	0.602690i
$162$	−1.40511	+	3.06173i	−0.110396	+	0.240552i
$163$	−3.42791	+	0.451293i	−0.268495	+	0.0353480i	−0.263571	−	0.964640i	$-0.584900\pi$
$163$	−3.42791	+	0.451293i	−0.268495	+	0.0353480i	−0.00492330	+	0.999988i	$0.501567\pi$
$164$	−13.8449	−	9.44558i	−1.08111	−	0.737576i
$165$	−1.18172	+	8.97606i	−0.0919968	+	0.698785i
$166$	−3.11587	+	10.0959i	−0.241838	+	0.783591i
$167$	5.45656	−	5.45656i	0.422241	−	0.422241i	−0.463734	−	0.885975i	$-0.653491\pi$
$167$	5.45656	−	5.45656i	0.422241	−	0.422241i	0.885975	+	0.463734i	$0.153491\pi$
$168$	6.38940	+	6.66429i	0.492953	+	0.514162i
$169$	−0.718337	−	0.718337i	−0.0552567	−	0.0552567i
$170$	−7.29432	+	3.85372i	−0.559449	+	0.295567i
$171$	4.92584	+	0.648499i	0.376689	+	0.0495920i
$172$	−7.16915	−	10.9570i	−0.546642	−	0.835466i
$173$	−1.90827	−	14.4948i	−0.145083	−	1.10202i	−0.896770	−	0.442497i	$-0.854093\pi$
$173$	−1.90827	−	14.4948i	−0.145083	−	1.10202i	0.751686	−	0.659521i	$-0.229241\pi$
$174$	0.543509	+	1.46550i	0.0412033	+	0.111099i
$175$	−8.19388	+	0.752729i	−0.619399	+	0.0569010i
$176$	20.7269	−	5.12676i	1.56235	−	0.386444i
$177$	−11.3634	+	6.56069i	−0.854128	+	0.493131i
$178$	−4.31315	+	25.3616i	−0.323284	+	1.90093i
$179$	3.28463	−	2.52038i	0.245504	−	0.188382i	−0.478678	−	0.877990i	$-0.658884\pi$
$179$	3.28463	−	2.52038i	0.245504	−	0.188382i	0.724183	+	0.689608i	$0.242217\pi$
$180$	2.70866	−	3.02910i	0.201891	−	0.225776i
$181$	6.41174	+	15.4793i	0.476581	+	1.15057i	0.961202	+	0.275844i	$0.0889573\pi$
$181$	6.41174	+	15.4793i	0.476581	+	1.15057i	−0.484622	+	0.874724i	$0.661043\pi$
$182$	−11.5511	−	5.86094i	−0.856222	−	0.434442i
$183$	−4.40215	−	4.40215i	−0.325416	−	0.325416i
$184$	−19.5231	+	0.356066i	−1.43926	+	0.0262495i
$185$	−0.133105	−	0.496753i	−0.00978605	−	0.0365220i
$186$	0.997267	+	4.37243i	0.0731231	+	0.320602i
$187$	−17.9695	−	13.7884i	−1.31406	−	1.00831i
$188$	−9.96618	+	8.57123i	−0.726858	+	0.625121i
$189$	3.22552	+	14.2562i	0.234622	+	1.03699i
$190$	5.94024	+	2.72614i	0.430950	+	0.197775i
$191$	−2.30357	−	3.98989i	−0.166680	−	0.288698i	0.770571	−	0.637355i	$-0.219971\pi$
$191$	−2.30357	−	3.98989i	−0.166680	−	0.288698i	−0.937251	+	0.348656i	$0.886638\pi$
$192$	9.25022	+	3.44202i	0.667577	+	0.248406i
$193$	2.25385	−	3.90378i	0.162236	−	0.281000i	−0.773435	−	0.633876i	$-0.781463\pi$
$193$	2.25385	−	3.90378i	0.162236	−	0.281000i	0.935670	+	0.352876i	$0.114796\pi$
$194$	1.41310	+	15.0944i	0.101454	+	1.08371i
$195$	2.24693	−	5.42458i	0.160906	−	0.388462i
$196$	13.8350	+	2.14324i	0.988212	+	0.153089i
$197$	−13.6869	+	5.66929i	−0.975150	+	0.403920i	−0.812627	−	0.582785i	$-0.801963\pi$
$197$	−13.6869	+	5.66929i	−0.975150	+	0.403920i	−0.162523	+	0.986705i	$0.551963\pi$
$198$	10.6604	+	3.29011i	0.757603	+	0.233818i
$199$	−4.64150	−	17.3223i	−0.329027	−	1.22795i	−0.910201	−	0.414166i	$-0.864073\pi$
$199$	−4.64150	−	17.3223i	−0.329027	−	1.22795i	0.581174	−	0.813779i	$-0.302593\pi$
$200$	−7.53653	+	4.53644i	−0.532913	+	0.320775i
$201$	4.86719	−	18.1646i	0.343305	−	1.28123i
$202$	8.80294	+	0.330746i	0.619373	+	0.0232712i
$203$	2.00451	+	1.26481i	0.140689	+	0.0887724i
$204$	−3.26957	−	9.94647i	−0.228916	−	0.696392i
$205$	−1.50373	−	11.4220i	−0.105025	−	0.797747i
$206$	−3.22803	+	18.9811i	−0.224907	+	1.32247i
$207$	−8.83596	−	5.10144i	−0.614141	−	0.354575i
$208$	−13.8447	−	0.267489i	−0.959954	−	0.0185470i
$209$			17.9446i			1.24126i
$210$	−0.487201	+	6.32744i	−0.0336201	+	0.436635i
$211$	2.81698	+	1.16683i	0.193929	+	0.0803279i	0.477534	−	0.878613i	$-0.341531\pi$
$211$	2.81698	+	1.16683i	0.193929	+	0.0803279i	−0.283606	+	0.958941i	$0.591531\pi$
$212$	13.1002	−	0.731626i	0.899723	−	0.0502483i
$213$	−5.17671	−	0.681527i	−0.354702	−	0.0466974i
$214$	12.6764	+	7.96784i	0.866541	+	0.544671i
$215$	2.32952	−	8.69388i	0.158872	−	0.592918i
$216$	9.73682	+	12.2212i	0.662507	+	0.831548i
$217$	5.22850	+	4.34869i	0.354934	+	0.295209i
$218$	−12.3652	−	13.3306i	−0.837477	−	0.902865i
$219$	7.68633	+	5.89793i	0.519394	+	0.398545i
$220$	12.1238	+	8.27139i	0.817390	+	0.557657i
$221$	8.94229	+	11.6538i	0.601524	+	0.783921i
$222$	0.649847	−	0.0608369i	0.0436149	−	0.00408310i
$223$	−20.6847			−1.38515			−0.692576	−	0.721345i	$-0.743524\pi$
$223$	−20.6847			−1.38515			−0.692576	+	0.721345i	$0.743524\pi$
$224$	14.3134	−	4.37336i	0.956355	−	0.292207i
$225$	−4.59634			−0.306423
$226$	0.897898	−	0.0840587i	0.0597273	−	0.00559150i
$227$	1.56612	+	2.04101i	0.103947	+	0.135467i	0.842430	−	0.538805i	$-0.181124\pi$
$227$	1.56612	+	2.04101i	0.103947	+	0.135467i	−0.738483	+	0.674272i	$0.764458\pi$
$228$	−4.67485	+	6.85219i	−0.309599	+	0.453798i
$229$	5.61092	+	4.30541i	0.370780	+	0.284509i	0.777297	−	0.629134i	$-0.216590\pi$
$229$	5.61092	+	4.30541i	0.370780	+	0.284509i	−0.406517	+	0.913643i	$0.633257\pi$
$230$	−9.12777	−	9.84045i	−0.601867	−	0.648860i
$231$	−16.3469	+	6.03026i	−1.07554	+	0.396762i
$232$	2.51778	+	0.284868i	0.165300	+	0.0187025i
$233$	−3.90521	+	14.5744i	−0.255839	+	0.954803i	0.711783	+	0.702399i	$0.247888\pi$
$233$	−3.90521	+	14.5744i	−0.255839	+	0.954803i	−0.967622	+	0.252404i	$0.918779\pi$
$234$	−6.12583	−	3.85043i	−0.400458	−	0.251711i
$235$	−8.95830	−	1.17938i	−0.584375	−	0.0769344i
$236$	1.18611	+	21.2379i	0.0772092	+	1.38247i
$237$	10.5306	+	4.36192i	0.684037	+	0.283337i
$238$	−13.0997	−	8.97055i	−0.849127	−	0.581474i
$239$			21.6519i			1.40054i	0.713877	+	0.700271i	$0.246938\pi$
$239$			21.6519i			1.40054i	−0.713877	+	0.700271i	$0.753062\pi$
$240$	2.47469	+	6.31689i	0.159741	+	0.407754i
$241$	16.6150	+	9.59269i	1.07027	+	0.617920i	0.928255	−	0.371945i	$-0.121309\pi$
$241$	16.6150	+	9.59269i	1.07027	+	0.617920i	0.142014	+	0.989865i	$0.454642\pi$
$242$	−4.14769	+	24.3887i	−0.266624	+	1.56777i
$243$	1.77969	+	13.5181i	0.114167	+	0.867188i
$244$	−9.58757	+	3.15160i	−0.613781	+	0.201760i
$245$	5.24088	+	8.07103i	0.334828	+	0.515639i
$246$	14.6109	+	0.548962i	0.931555	+	0.0350005i
$247$	3.01206	−	11.2412i	0.191653	−	0.715259i
$248$	7.05558	+	1.75329i	0.448030	+	0.111334i
$249$	−2.38562	−	8.90327i	−0.151183	−	0.564222i
$250$	−15.0663	−	4.64990i	−0.952879	−	0.294086i
$251$	−14.2059	+	5.88428i	−0.896670	+	0.371413i	−0.782939	−	0.622099i	$-0.786280\pi$
$251$	−14.2059	+	5.88428i	−0.896670	+	0.371413i	−0.113731	+	0.993512i	$0.536280\pi$
$252$	7.58624	+	1.89916i	0.477888	+	0.119636i
$253$	14.1021	−	34.0456i	0.886594	−	2.14043i
$254$	−0.0653599	−	0.698161i	−0.00410105	−	0.0438065i
$255$	3.59846	−	6.23271i	0.225344	−	0.390307i
$256$	11.7423	−	10.8682i	0.733893	−	0.679266i
$257$	−5.88985	−	10.2015i	−0.367399	−	0.636353i	0.621759	−	0.783208i	$-0.286418\pi$
$257$	−5.88985	−	10.2015i	−0.367399	−	0.636353i	−0.989158	+	0.146855i	$0.953085\pi$
$258$	10.3819	+	4.76453i	0.646347	+	0.296627i
$259$	0.726800	−	0.671817i	0.0451612	−	0.0417447i
$260$	−6.20644	−	7.21653i	−0.384907	−	0.447550i
$261$	1.05038	+	0.805988i	0.0650171	+	0.0498894i
$262$	−2.69238	−	11.8045i	−0.166336	−	0.729286i
$263$	4.53377	+	16.9203i	0.279564	+	1.04335i	0.952720	+	0.303848i	$0.0982716\pi$
$263$	4.53377	+	16.9203i	0.279564	+	1.04335i	−0.673156	+	0.739500i	$0.735062\pi$
$264$	−12.9287	+	13.4090i	−0.795705	+	0.825269i
$265$	6.37727	+	6.37727i	0.391753	+	0.391753i
$266$	0.679577	+	12.5601i	0.0416676	+	0.770111i
$267$	−8.58842	−	20.7343i	−0.525603	−	1.26892i
$268$	−22.7249	−	20.3208i	−1.38814	−	1.24129i
$269$	15.8619	−	12.1712i	0.967116	−	0.742094i	0.000945779	−	1.00000i	$-0.499699\pi$
$269$	15.8619	−	12.1712i	0.967116	−	0.742094i	0.966170	+	0.257905i	$0.0830323\pi$
$270$	−1.80079	+	10.5888i	−0.109593	+	0.644413i
$271$	−8.90638	+	5.14210i	−0.541024	+	0.312360i	−0.745494	−	0.666513i	$-0.767786\pi$
$271$	−8.90638	+	5.14210i	−0.541024	+	0.312360i	0.204470	+	0.978873i	$0.434453\pi$
$272$	−16.7819	−	2.54007i	−1.01755	−	0.154015i
$273$	11.2525	−	1.03371i	0.681030	−	0.0625628i
$274$	0.687470	+	1.85367i	0.0415316	+	0.111984i
$275$	−2.16687	−	16.4590i	−0.130667	−	0.992515i
$276$	14.2543	−	9.32655i	0.858010	−	0.561392i
$277$	−17.4642	−	2.29921i	−1.04932	−	0.138146i	−0.413910	−	0.910318i	$-0.635837\pi$
$277$	−17.4642	−	2.29921i	−1.04932	−	0.138146i	−0.635414	+	0.772172i	$0.719170\pi$
$278$	8.36798	−	4.42095i	0.501878	−	0.265151i
$279$	2.68616	+	2.68616i	0.160816	+	0.160816i
$280$	8.79919	+	5.33032i	0.525852	+	0.318548i
$281$	−4.64771	+	4.64771i	−0.277259	+	0.277259i	−0.832014	−	0.554755i	$-0.812812\pi$
$281$	−4.64771	+	4.64771i	−0.277259	+	0.277259i	0.554755	+	0.832014i	$0.312812\pi$
$282$	3.38178	−	10.9574i	0.201382	−	0.652506i
$283$	−0.128183	+	0.973645i	−0.00761968	+	0.0578772i	−0.994832	−	0.101532i	$-0.967626\pi$
$283$	−0.128183	+	0.973645i	−0.00761968	+	0.0578772i	0.987213	+	0.159409i	$0.0509589\pi$
$284$	−4.77031	+	6.99212i	−0.283066	+	0.414906i
$285$	−5.65303	+	0.744235i	−0.334856	+	0.0440847i
$286$	10.9001	−	23.7511i	0.644534	−	1.40443i
$287$	18.1065	−	12.7958i	1.06879	−	0.755312i
$288$	8.18537	−	1.70128i	0.482328	−	0.100249i
$289$	0.502591	+	0.870512i	0.0295642	+	0.0512066i
$290$	1.00766	+	1.42063i	0.0591718	+	0.0834221i
$291$	−8.05125	−	10.4926i	−0.471973	−	0.615087i
$292$	14.1526	−	6.81014i	0.828218	−	0.398533i
$293$	24.2730	−	10.0542i	1.41804	−	0.587372i	0.463673	−	0.886006i	$-0.346531\pi$
$293$	24.2730	−	10.0542i	1.41804	−	0.587372i	0.954368	+	0.298634i	$0.0965311\pi$
$294$	−11.2134	+	4.83988i	−0.653980	+	0.282268i
$295$	−10.3388	+	10.3388i	−0.601949	+	0.601949i
$296$	0.387014	−	0.984752i	0.0224947	−	0.0572375i
$297$	−28.4845	+	7.63241i	−1.65284	+	0.442877i
$298$	3.18120	+	1.99957i	0.184282	+	0.115832i
$299$	−14.5488	+	18.9603i	−0.841377	+	1.09650i
$300$	3.46040	−	6.84940i	0.199786	−	0.395450i
$301$	16.8947	−	3.82249i	0.973796	−	0.220325i
$302$	4.01060	+	10.8140i	0.230784	+	0.622279i
$303$	−6.65534	+	3.84246i	−0.382339	+	0.220744i
$304$	6.49728	+	11.7731i	0.372645	+	0.675236i
$305$	−6.00782	−	3.46862i	−0.344007	−	0.198612i
$306$	−6.82836	−	5.65930i	−0.390351	−	0.323521i
$307$	−4.58938	−	1.90098i	−0.261930	−	0.108495i	0.247854	−	0.968797i	$-0.420275\pi$
$307$	−4.58938	−	1.90098i	−0.261930	−	0.108495i	−0.509784	+	0.860303i	$0.670275\pi$
$308$	−3.22426	+	28.0608i	−0.183720	+	1.59891i
$309$	−6.42772	−	15.5179i	−0.365660	−	0.882782i
$310$	2.33443	+	4.41861i	0.132587	+	0.250960i
$311$	13.8659	−	3.71535i	0.786261	−	0.210678i	0.156718	−	0.987643i	$-0.449909\pi$
$311$	13.8659	−	3.71535i	0.786261	−	0.210678i	0.629543	+	0.776965i	$0.283242\pi$
$312$	10.3497	−	6.22979i	0.585939	−	0.352692i
$313$	−32.3648	−	8.67212i	−1.82937	−	0.490177i	−0.831503	−	0.555520i	$-0.812519\pi$
$313$	−32.3648	−	8.67212i	−1.82937	−	0.490177i	−0.997863	+	0.0653425i	$0.979186\pi$
$314$	8.92898	−	8.28232i	0.503892	−	0.467398i
$315$	2.50283	+	4.75735i	0.141018	+	0.268046i
$316$	14.0093	−	12.0484i	0.788085	−	0.677778i
$317$	17.0255	−	2.24145i	0.956246	−	0.125892i	0.363778	−	0.931486i	$-0.381487\pi$
$317$	17.0255	−	2.24145i	0.956246	−	0.125892i	0.592468	+	0.805594i	$0.298153\pi$
$318$	−9.33604	+	6.62210i	−0.523539	+	0.371349i
$319$	−2.39097	+	4.14128i	−0.133869	+	0.231867i
$320$	10.9491	+	1.03698i	0.612072	+	0.0579688i
$321$	−13.0618			−0.729036
$322$	8.58130	−	24.3639i	0.478217	−	1.35775i
$323$	5.45888	−	13.1789i	0.303740	−	0.733293i
$324$	−4.49631	−	1.57489i	−0.249795	−	0.0874938i
$325$	−1.40529	+	10.6742i	−0.0779515	+	0.592100i
$326$	−1.08731	−	4.76721i	−0.0602204	−	0.264031i
$327$	15.3216	+	4.10541i	0.847285	+	0.227029i
$328$	11.4749	−	20.7395i	0.633595	−	1.14515i
$329$	−6.01833	−	16.3145i	−0.331801	−	0.899448i
$330$	−12.7946	−	0.480720i	−0.704318	−	0.0264628i
$331$	2.67205	−	3.48229i	0.146869	−	0.191404i	−0.714125	−	0.700018i	$-0.753175\pi$
$331$	2.67205	−	3.48229i	0.146869	−	0.191404i	0.860995	+	0.508614i	$0.169842\pi$
$332$	−14.6263	−	3.05650i	−0.802721	−	0.167747i
$333$	0.438615	−	0.336561i	0.0240360	−	0.0184434i
$334$	8.40241	+	6.96387i	0.459760	+	0.381046i
$335$		−	20.9550i		−	1.14490i
$336$	−8.54147	+	9.87511i	−0.465975	+	0.538732i
$337$		−	12.5218i		−	0.682103i	−0.940045	−	0.341052i	$-0.889217\pi$
$337$		−	12.5218i		−	0.682103i	0.940045	−	0.341052i	$-0.110783\pi$
$338$	0.916769	−	1.10615i	0.0498657	−	0.0601666i
$339$	−0.624157	+	0.478933i	−0.0338996	+	0.0260121i
$340$	−6.38778	−	9.76283i	−0.346426	−	0.529464i
$341$	−8.35249	+	10.8852i	−0.452312	+	0.589465i
$342$	−0.263807	+	7.02135i	−0.0142651	+	0.379671i
$343$	−9.05046	+	16.1583i	−0.488679	+	0.872464i
$344$	14.4831	−	11.5389i	0.780877	−	0.622136i
$345$	11.3101	+	3.03054i	0.608916	+	0.163159i
$346$	20.1579	−	4.59764i	1.08370	−	0.247171i
$347$	0.488622	−	3.71145i	0.0262306	−	0.199241i	−0.973312	−	0.229486i	$-0.926295\pi$
$347$	0.488622	−	3.71145i	0.0262306	−	0.199241i	0.999543	+	0.0302450i	$0.00962875\pi$
$348$	−1.99186	+	0.958472i	−0.106775	+	0.0513795i
$349$	1.85153	−	4.46998i	0.0991100	−	0.239273i	−0.866546	−	0.499098i	$-0.833665\pi$
$349$	1.85153	−	4.46998i	0.0991100	−	0.239273i	0.965656	+	0.259825i	$0.0836649\pi$
$350$	−2.13999	−	11.4382i	−0.114387	−	0.611399i
$351$	19.1249			1.02081
$352$	9.95096	+	28.5089i	0.530388	+	1.51953i
$353$	−2.43897	+	4.22441i	−0.129813	+	0.224843i	−0.923604	−	0.383348i	$-0.874771\pi$
$353$	−2.43897	+	4.22441i	−0.129813	+	0.224843i	0.793791	+	0.608191i	$0.208104\pi$
$354$	−10.7357	−	15.1356i	−0.570598	−	0.804445i
$355$	−5.76846	+	0.759432i	−0.306158	+	0.0403065i
$356$	−36.2791	−	2.73003i	−1.92279	−	0.144691i
$357$	13.8399	+	0.544077i	0.732485	+	0.0287956i
$358$	3.98182	+	4.29271i	0.210445	+	0.226877i
$359$	23.7592	+	6.36625i	1.25396	+	0.335998i	0.823865	−	0.566786i	$-0.191813\pi$
$359$	23.7592	+	6.36625i	1.25396	+	0.335998i	0.430095	+	0.902784i	$0.358480\pi$
$360$	4.62220	+	3.41465i	0.243611	+	0.179968i
$361$	7.43634	−	1.99256i	0.391386	−	0.104872i
$362$	−20.9506	+	11.0685i	−1.10114	+	0.581750i
$363$	−8.25897	−	19.9389i	−0.433484	−	1.04652i
$364$	6.72990	−	17.0371i	0.352743	−	0.892988i
$365$	9.97410	+	4.13141i	0.522068	+	0.216248i
$366$	5.61819	−	6.77876i	0.293668	−	0.354332i
$367$	29.0429	+	16.7679i	1.51603	+	0.875278i	0.999823	+	0.0188114i	$0.00598822\pi$
$367$	29.0429	+	16.7679i	1.51603	+	0.875278i	0.516203	+	0.856466i	$0.327345\pi$
$368$	−3.07486	−	27.4427i	−0.160288	−	1.43055i
$369$	10.7257	−	6.19247i	0.558356	−	0.322367i
$370$	0.681911	−	0.252900i	0.0354509	−	0.0131477i
$371$	−5.14741	+	16.5761i	−0.267240	+	0.860586i
$372$	−6.02517	+	1.98057i	−0.312390	+	0.102688i
$373$	−5.06276	+	6.59792i	−0.262140	+	0.341627i	−0.905816	−	0.423670i	$-0.860742\pi$
$373$	−5.06276	+	6.59792i	−0.262140	+	0.341627i	0.643677	+	0.765298i	$0.277408\pi$
$374$	17.0462	−	27.1196i	0.881439	−	1.40232i
$375$	13.2866	−	3.56014i	0.686117	−	0.183845i
$376$	−13.3825	−	12.9031i	−0.690150	−	0.665426i
$377$	2.19292	−	2.19292i	0.112941	−	0.112941i
$378$	−19.6484	+	6.42094i	−1.01060	+	0.330258i
$379$	4.00023	−	1.65695i	0.205478	−	0.0851117i	−0.277571	−	0.960705i	$-0.589529\pi$
$379$	4.00023	−	1.65695i	0.205478	−	0.0851117i	0.483049	+	0.875593i	$0.339529\pi$
$380$	−3.05553	+	8.72355i	−0.156745	+	0.447509i
$381$	0.372395	+	0.485314i	0.0190784	+	0.0248634i
$382$	5.31434	−	3.76949i	0.271905	−	0.192864i
$383$	6.27184	+	10.8631i	0.320476	+	0.555080i	0.980586	−	0.196088i	$-0.0628239\pi$
$383$	6.27184	+	10.8631i	0.320476	+	0.555080i	−0.660110	+	0.751169i	$0.729491\pi$
$384$	−3.62720	+	13.4786i	−0.185100	+	0.687824i
$385$	−15.8556	+	11.2051i	−0.808078	+	0.571066i
$386$	5.79384	+	2.65896i	0.294899	+	0.135337i
$387$	9.59309	−	1.26295i	0.487644	−	0.0641996i
$388$	−21.0675	+	3.97944i	−1.06954	+	0.202025i
$389$	0.531504	−	4.03718i	0.0269483	−	0.204693i	−0.972674	−	0.232175i	$-0.925416\pi$
$389$	0.531504	−	4.03718i	0.0269483	−	0.204693i	0.999622	+	0.0274824i	$0.00874901\pi$
$390$	7.93430	+	2.44875i	0.401769	+	0.123997i
$391$	−20.7138	+	20.7138i	−1.04754	+	1.04754i
$392$	−1.19410	+	19.7629i	−0.0603112	+	0.998180i
$393$	7.46880	+	7.46880i	0.376751	+	0.376751i
$394$	−9.78686	−	18.5246i	−0.493055	−	0.933255i
$395$	12.5925	+	1.65784i	0.633599	+	0.0834149i
$396$	−3.22742	+	15.4442i	−0.162184	+	0.776099i
$397$	4.33930	+	32.9602i	0.217783	+	1.65423i	0.655560	+	0.755143i	$0.272432\pi$
$397$	4.33930	+	32.9602i	0.217783	+	1.65423i	−0.437777	+	0.899083i	$0.644234\pi$
$398$	23.7790	−	8.81889i	1.19193	−	0.442051i
$399$	−6.33295	−	8.96134i	−0.317044	−	0.448628i
$400$	−7.38101	−	10.0139i	−0.369051	−	0.500694i
$401$	−30.0264	+	17.3358i	−1.49945	+	0.865706i	−1.00000		0.000638279i	$-0.999797\pi$
$401$	−30.0264	+	17.3358i	−1.49945	+	0.865706i	−0.499447	+	0.866344i	$0.666463\pi$
$402$	26.2184	+	4.45885i	1.30765	+	0.222387i
$403$	7.05942	−	5.41688i	0.351655	−	0.269834i
$404$	0.694681	+	12.4386i	0.0345617	+	0.618845i
$405$	−1.25320	−	3.02550i	−0.0622722	−	0.150338i
$406$	−1.51670	+	2.98919i	−0.0752724	+	0.148351i
$407$	1.41197	+	1.41197i	0.0699886	+	0.0699886i
$408$	13.5742	−	5.91487i	0.672023	−	0.292830i
$409$	−0.487584	−	1.81969i	−0.0241095	−	0.0899777i	0.952823	−	0.303527i	$-0.0981643\pi$
$409$	−0.487584	−	1.81969i	−0.0241095	−	0.0899777i	−0.976932	+	0.213549i	$0.931498\pi$
$410$	15.8846	−	3.62297i	0.784485	−	0.178926i
$411$	−1.36832	−	1.04995i	−0.0674944	−	0.0517903i
$412$	−27.1519	−	2.04320i	−1.33768	−	0.100661i
$413$	−26.8731	−	8.34496i	−1.32234	−	0.410628i
$414$	6.01838	−	13.1140i	0.295787	−	0.644517i
$415$	−5.13549	−	8.89494i	−0.252091	−	0.436635i
$416$	−1.44834	−	19.5293i	−0.0710107	−	0.957503i
$417$	−4.12812	+	7.15011i	−0.202155	+	0.350142i
$418$	−25.2671	+	2.36543i	−1.23585	+	0.115697i
$419$	7.16473	−	17.2972i	0.350020	−	0.845023i	−0.646597	−	0.762832i	$-0.723808\pi$
$419$	7.16473	−	17.2972i	0.350020	−	0.845023i	0.996617	−	0.0821907i	$-0.0261917\pi$
$420$	−8.97362	+	0.148066i	−0.437868	+	0.00722490i
$421$	−14.1217	+	5.84942i	−0.688252	+	0.285083i	−0.699272	−	0.714856i	$-0.746492\pi$
$421$	−14.1217	+	5.84942i	−0.688252	+	0.285083i	0.0110199	+	0.999939i	$0.496492\pi$
$422$	−1.27163	+	4.12028i	−0.0619022	+	0.200572i
$423$	−2.51405	−	9.38255i	−0.122237	−	0.456195i
$424$	2.75701	+	18.3493i	0.133892	+	0.891122i
$425$	−3.41555	+	12.7470i	−0.165678	+	0.618320i
$426$	0.277243	−	7.37894i	0.0134325	−	0.357511i
$427$	0.524446	−	13.3405i	0.0253797	−	0.645593i
$428$	−9.54819	+	18.8994i	−0.461529	+	0.913537i
$429$	2.97571	+	22.6028i	0.143669	+	1.09127i
$430$	12.5486	+	2.13408i	0.605145	+	0.102914i
$431$	24.3945	+	14.0842i	1.17504	+	0.678410i	0.954862	−	0.297049i	$-0.0960025\pi$
$431$	24.3945	+	14.0842i	1.17504	+	0.678410i	0.220179	+	0.975459i	$0.429336\pi$
$432$	−15.9247	+	15.3210i	−0.766176	+	0.737131i
$433$		−	21.6031i		−	1.03818i	−0.854719	−	0.519090i	$-0.826271\pi$
$433$		−	21.6031i		−	1.03818i	0.854719	−	0.519090i	$-0.173729\pi$
$434$	−5.43399	+	7.93526i	−0.260840	+	0.380905i
$435$	−1.40377	−	0.581462i	−0.0673058	−	0.0278790i
$436$	17.1403	−	19.1681i	0.820874	−	0.917986i
$437$	23.0096	+	3.02927i	1.10070	+	0.144910i
$438$	−7.29141	+	11.6002i	−0.348397	+	0.554281i
$439$	−2.83675	+	10.5869i	−0.135391	+	0.505285i	0.864605	+	0.502452i	$0.167569\pi$
$439$	−2.83675	+	10.5869i	−0.135391	+	0.505285i	−0.999996	+	0.00283328i	$0.999098\pi$
$440$	−10.0484	+	18.1614i	−0.479041	+	0.865810i
$441$	−5.86004	+	8.52561i	−0.279050	+	0.405982i
$442$	−15.2305	+	14.1274i	−0.724440	+	0.671974i
$443$	25.6982	+	19.7189i	1.22096	+	0.936873i	0.999268	−	0.0382443i	$-0.0121765\pi$
$443$	25.6982	+	19.7189i	1.22096	+	0.936873i	0.221689	+	0.975118i	$0.428843\pi$
$444$	0.171324	+	0.907002i	0.00813066	+	0.0430444i
$445$	−15.2239	−	19.8402i	−0.721684	−	0.940517i
$446$	−2.72663	−	29.1253i	−0.129110	−	1.37912i
$447$	−3.27791			−0.155040
$448$	8.04471	+	19.5776i	0.380077	+	0.924955i
$449$	23.4677			1.10751			0.553756	−	0.832679i	$-0.313194\pi$
$449$	23.4677			1.10751			0.553756	+	0.832679i	$0.313194\pi$
$450$	−0.605882	−	6.47191i	−0.0285616	−	0.305089i
$451$	27.2310	+	35.4881i	1.28226	+	1.67107i
$452$	0.236719	+	1.25321i	0.0111343	+	0.0589461i
$453$	−7.98261	−	6.12527i	−0.375056	−	0.287790i
$454$	−2.66742	+	2.47423i	−0.125188	+	0.116122i
$455$	11.8134	−	4.35789i	0.553819	−	0.204301i
$456$	−10.2645	−	5.67921i	−0.480680	−	0.265953i
$457$	9.95643	−	37.1579i	0.465742	−	1.73817i	−0.188675	−	0.982040i	$-0.560419\pi$
$457$	9.95643	−	37.1579i	0.465742	−	1.73817i	0.654417	−	0.756134i	$-0.272914\pi$
$458$	−5.32264	+	8.46802i	−0.248710	+	0.395685i
$459$	23.2414	+	3.05979i	1.08482	+	0.142819i
$460$	12.6527	−	14.1496i	0.589935	−	0.659727i
$461$	−31.3546	−	12.9875i	−1.46033	−	0.604888i	−0.495699	−	0.868494i	$-0.665088\pi$
$461$	−31.3546	−	12.9875i	−1.46033	−	0.604888i	−0.964630	+	0.263606i	$0.915088\pi$
$462$	−10.6458	−	22.2224i	−0.495286	−	1.03388i
$463$			42.8472i			1.99128i	0.0932871	+	0.995639i	$0.470263\pi$
$463$			42.8472i			1.99128i	−0.0932871	+	0.995639i	$0.529737\pi$
$464$	−0.0692209	+	3.58272i	−0.00321350	+	0.166324i
$465$	−3.77552	−	2.17980i	−0.175086	−	0.101086i
$466$	−21.0364	−	3.57758i	−0.974493	−	0.165728i
$467$	−1.61010	−	12.2299i	−0.0745065	−	0.565933i	−0.987460	−	0.157869i	$-0.949538\pi$
$467$	−1.61010	−	12.2299i	−0.0745065	−	0.565933i	0.912954	−	0.408064i	$-0.133796\pi$
$468$	4.61413	−	9.13307i	0.213288	−	0.422176i
$469$	35.6905	−	18.7767i	1.64803	−	0.867026i
$470$	0.479769	−	12.7693i	0.0221301	−	0.589002i
$471$	−2.74984	+	10.2625i	−0.126706	+	0.472872i
$472$	−29.7479	+	4.46966i	−1.36926	+	0.205733i
$473$	9.04500	+	33.7564i	0.415890	+	1.55212i
$474$	−4.75371	+	15.4027i	−0.218345	+	0.707469i
$475$	9.65930	−	4.00101i	0.443199	−	0.183579i
$476$	10.9043	−	19.6276i	0.499796	−	0.899629i
$477$	−3.71030	+	8.95747i	−0.169883	+	0.410134i
$478$	−30.4871	+	2.85411i	−1.39445	+	0.130544i
$479$	−10.2610	+	17.7726i	−0.468838	+	0.812051i	−0.999366	−	0.0356166i	$-0.988660\pi$
$479$	−10.2610	+	17.7726i	−0.468838	+	0.812051i	0.530528	+	0.847668i	$0.321994\pi$
$480$	−8.56834	+	4.31719i	−0.391089	+	0.197052i
$481$	−0.647505	−	1.12151i	−0.0295237	−	0.0511365i
$482$	−11.3169	+	24.6594i	−0.515470	+	1.12321i
$483$	4.97279	+	21.9788i	0.226270	+	1.00007i
$484$	−34.8875	−	2.62530i	−1.58579	−	0.119332i
$485$	−11.6920	−	8.97159i	−0.530907	−	0.407379i
$486$	−18.7997	+	4.28785i	−0.852771	+	0.194501i
$487$	−6.91880	−	25.8213i	−0.313521	−	1.17007i	−0.925359	−	0.379092i	$-0.876236\pi$
$487$	−6.91880	−	25.8213i	−0.313521	−	1.17007i	0.611838	−	0.790983i	$-0.290430\pi$
$488$	−5.70145	−	13.0844i	−0.258092	−	0.592303i
$489$	3.01625	+	3.01625i	0.136399	+	0.136399i
$490$	−10.6736	+	8.44337i	−0.482185	+	0.381432i
$491$	4.27842	+	10.3290i	0.193082	+	0.466142i	0.990539	−	0.137235i	$-0.0438215\pi$
$491$	4.27842	+	10.3290i	0.193082	+	0.466142i	−0.797456	+	0.603377i	$0.793821\pi$
$492$	1.15301	+	20.6453i	0.0519818	+	0.930762i
$493$	3.01578	−	2.31409i	0.135824	−	0.104221i
$494$	16.2253	+	2.75936i	0.730009	+	0.124150i
$495$	−9.39235	+	5.42267i	−0.422155	+	0.243731i
$496$	−1.53867	+	10.1658i	−0.0690885	+	0.456457i
$497$	−6.46227	−	9.14433i	−0.289872	−	0.410179i
$498$	12.2218	−	4.53271i	0.547674	−	0.203116i
$499$	−3.38493	−	25.7111i	−0.151530	−	1.15099i	−0.883088	−	0.469208i	$-0.844540\pi$
$499$	−3.38493	−	25.7111i	−0.151530	−	1.15099i	0.731558	−	0.681780i	$-0.238794\pi$
$500$	4.56130	−	21.8272i	0.203988	−	0.976142i
$501$	−9.43893	−	1.24266i	−0.421700	−	0.0555179i
$502$	−10.1580	−	19.2271i	−0.453374	−	0.858147i
$503$	21.6046	+	21.6046i	0.963300	+	0.963300i	0.999350	−	0.0360503i	$-0.0114776\pi$
$503$	21.6046	+	21.6046i	0.963300	+	0.963300i	−0.0360503	+	0.999350i	$0.511478\pi$
$504$	−1.67411	+	10.9322i	−0.0745709	+	0.486959i
$505$	−6.05524	+	6.05524i	−0.269454	+	0.269454i
$506$	49.7970	+	15.3688i	2.21375	+	0.683226i
$507$	−0.163592	+	1.24260i	−0.00726537	+	0.0551859i
$508$	0.974435	−	0.184061i	0.0432336	−	0.00816639i
$509$	36.5049	−	4.80596i	1.61805	−	0.213021i	0.733576	−	0.679607i	$-0.237850\pi$
$509$	36.5049	−	4.80596i	1.61805	−	0.213021i	0.884475	+	0.466587i	$0.154517\pi$
$510$	9.25035	+	4.24525i	0.409613	+	0.187983i
$511$	1.90066	+	20.6898i	0.0840803	+	0.915262i
$512$	16.8510	+	15.1012i	0.744714	+	0.667383i
$513$	−9.28604	−	16.0839i	−0.409989	−	0.710121i
$514$	13.5879	−	9.63799i	0.599338	−	0.425114i
$515$	−11.3939	−	14.8488i	−0.502073	−	0.654315i
$516$	−5.34021	+	15.2463i	−0.235090	+	0.671182i
$517$	32.4127	−	13.4258i	1.42551	−	0.590465i
$518$	1.04176	+	0.934818i	0.0457724	+	0.0410735i
$519$	−12.7541	+	12.7541i	−0.559842	+	0.559842i
$520$	9.34316	−	9.69030i	0.409725	−	0.424948i
$521$	−36.3412	+	9.73760i	−1.59214	+	0.426612i	−0.942656	−	0.333766i	$-0.891681\pi$
$521$	−36.3412	+	9.73760i	−1.59214	+	0.426612i	−0.649481	+	0.760378i	$0.725014\pi$
$522$	−0.996417	+	1.58524i	−0.0436120	+	0.0693842i
$523$	−7.76009	+	10.1131i	−0.339325	+	0.442217i	−0.931581	−	0.363533i	$-0.881571\pi$
$523$	−7.76009	+	10.1131i	−0.339325	+	0.442217i	0.592257	+	0.805749i	$0.298237\pi$
$524$	16.2665	−	5.34708i	0.710607	−	0.233588i
$525$	6.89076	+	7.45471i	0.300737	+	0.325350i
$526$	−23.2271	+	8.61421i	−1.01275	+	0.375598i
$527$	9.44558	−	5.45341i	0.411456	−	0.237554i
$528$	−20.5849	−	16.4368i	−0.895843	−	0.715318i
$529$	−21.3560	−	12.3299i	−0.928521	−	0.536082i
$530$	−8.13892	+	9.82020i	−0.353532	+	0.426562i
$531$	−14.5218	−	6.01513i	−0.630193	−	0.261035i
$532$	−17.5958	+	2.61254i	−0.762875	+	0.113268i
$533$	−11.1017	−	26.8019i	−0.480868	−	1.16092i
$534$	28.0629	−	14.8262i	1.21440	−	0.641590i
$535$	−14.0589	+	3.76707i	−0.607820	+	0.162865i
$536$	25.6173	−	34.6766i	1.10650	−	1.49780i
$537$	−4.93382	−	1.32201i	−0.212910	−	0.0570491i
$538$	19.2287	+	20.7300i	0.829008	+	0.893735i
$539$	−33.2919	−	16.9649i	−1.43398	−	0.730731i
$540$	−15.1470	−	1.13982i	−0.651823	−	0.0490500i
$541$	−35.4268	+	4.66403i	−1.52312	+	0.200522i	−0.845134	−	0.534554i	$-0.820480\pi$
$541$	−35.4268	+	4.66403i	−1.52312	+	0.200522i	−0.677984	+	0.735077i	$0.737146\pi$
$542$	−8.41439	−	11.8629i	−0.361429	−	0.509554i
$543$	10.3354	−	17.9014i	0.443534	−	0.768223i
$544$	1.36441	−	23.9646i	0.0584986	−	1.02748i
$545$	17.6753			0.757125
$546$	2.93880	+	15.7079i	0.125769	+	0.672234i
$547$	14.0554	−	33.9327i	0.600964	−	1.45086i	−0.271626	−	0.962403i	$-0.587561\pi$
$547$	14.0554	−	33.9327i	0.600964	−	1.45086i	0.872590	−	0.488453i	$-0.162439\pi$
$548$	−2.51945	+	1.21234i	−0.107626	+	0.0517888i
$549$	0.973428	−	7.39392i	0.0415449	−	0.315565i
$550$	22.8896	−	5.22067i	0.976014	−	0.222610i
$551$	−2.90900	−	0.779463i	−0.123927	−	0.0332062i
$552$	15.0113	+	18.8415i	0.638923	+	0.801947i
$553$	8.45987	+	22.9330i	0.359750	+	0.975212i
$554$	0.935310	−	24.8937i	0.0397375	−	1.05763i
$555$	−0.386247	+	0.503367i	−0.0163953	+	0.0213667i
$556$	7.32801	+	11.1998i	0.310777	+	0.474979i
$557$	−24.7502	+	18.9915i	−1.04870	+	0.804694i	−0.981194	−	0.193025i	$-0.938170\pi$
$557$	−24.7502	+	18.9915i	−1.04870	+	0.804694i	−0.0675042	+	0.997719i	$0.521504\pi$
$558$	−3.42817	+	4.13634i	−0.145126	+	0.175105i
$559$		−	22.6645i		−	0.958606i
$560$	−6.34550	+	13.0924i	−0.268146	+	0.553255i
$561$			27.9440i			1.17980i
$562$	−7.15690	−	5.93159i	−0.301895	−	0.250209i
$563$	−27.2704	+	20.9253i	−1.14931	+	0.881897i	−0.994363	−	0.106026i	$-0.966187\pi$
$563$	−27.2704	+	20.9253i	−1.14931	+	0.881897i	−0.154947	+	0.987923i	$0.549521\pi$
$564$	15.8745	+	3.31734i	0.668436	+	0.139685i
$565$	−0.533680	+	0.695505i	−0.0224521	+	0.0292601i
$566$	−1.38784	−	0.0521443i	−0.0583355	−	0.00219179i
$567$	4.03009	−	4.84544i	0.169248	−	0.203489i
$568$	−10.4741	−	5.79518i	−0.439484	−	0.243160i
$569$	−29.5829	−	7.92671i	−1.24018	−	0.332305i	−0.421644	−	0.906761i	$-0.638547\pi$
$569$	−29.5829	−	7.92671i	−1.24018	−	0.332305i	−0.818535	+	0.574456i	$0.805213\pi$
$570$	−1.79310	−	7.86168i	−0.0751046	−	0.329289i
$571$	−3.92618	+	29.8223i	−0.164305	+	1.24802i	0.688284	+	0.725442i	$0.258365\pi$
$571$	−3.92618	+	29.8223i	−0.164305	+	1.24802i	−0.852589	+	0.522582i	$0.824969\pi$
$572$	34.8798	+	12.2171i	1.45840	+	0.510821i
$573$	−2.17516	+	5.25130i	−0.0908685	+	0.219376i
$574$	20.4040	+	23.8082i	0.851645	+	0.993736i
$575$	−21.4704			−0.895380
$576$	3.47448	+	11.3012i	0.144770	+	0.470884i
$577$	−10.6131	+	18.3824i	−0.441829	+	0.765270i	−0.997825	−	0.0659145i	$-0.979004\pi$
$577$	−10.6131	+	18.3824i	−0.441829	+	0.765270i	0.555996	+	0.831185i	$0.312337\pi$
$578$	−1.15948	+	0.822426i	−0.0482280	+	0.0342084i
$579$	−5.51371	+	0.725894i	−0.229142	+	0.0301671i
$580$	−1.86750	+	1.60611i	−0.0775436	+	0.0666899i
$581$	10.5482	−	16.7170i	0.437612	−	0.693539i
$582$	13.7129	−	12.7197i	0.568416	−	0.527250i
$583$	−33.8249	−	9.06335i	−1.40088	−	0.375366i
$584$	11.4546	+	19.0299i	0.473996	+	0.787465i
$585$	6.79392	−	1.82043i	0.280894	−	0.0752654i
$586$	17.3565	+	32.8524i	0.716990	+	1.35712i
$587$	3.24110	+	7.82470i	0.133774	+	0.322960i	0.976545	−	0.215313i	$-0.0690770\pi$
$587$	3.24110	+	7.82470i	0.133774	+	0.322960i	−0.842771	+	0.538273i	$0.819077\pi$
$588$	−8.29296	−	15.1511i	−0.341996	−	0.624823i
$589$	−7.98324	−	3.30677i	−0.328944	−	0.136253i
$590$	−15.9205	−	13.1948i	−0.655436	−	0.543221i
$591$	15.8285	+	9.13860i	0.651098	+	0.375912i
$592$	1.43760	+	0.415129i	0.0590851	+	0.0170617i
$593$	32.5092	−	18.7692i	1.33499	−	0.770759i	0.348934	−	0.937147i	$-0.386544\pi$
$593$	32.5092	−	18.7692i	1.33499	−	0.770759i	0.986060	+	0.166388i	$0.0532105\pi$
$594$	−14.5016	−	39.1017i	−0.595010	−	1.60436i
$595$	15.0534	−	3.40588i	0.617128	−	0.139628i
$596$	−2.39616	+	4.74289i	−0.0981506	+	0.194276i
$597$	−13.4688	+	17.5529i	−0.551242	+	0.718393i
$598$	−28.6150	−	17.9862i	−1.17015	−	0.735509i
$599$	−20.3749	+	5.45944i	−0.832496	+	0.223067i	−0.649802	−	0.760103i	$-0.725148\pi$
$599$	−20.3749	+	5.45944i	−0.832496	+	0.223067i	−0.182694	+	0.983170i	$0.558482\pi$
$600$	10.1005	+	3.96956i	0.412351	+	0.162057i
$601$	15.6077	−	15.6077i	0.636650	−	0.636650i	−0.313078	−	0.949728i	$-0.601360\pi$
$601$	15.6077	−	15.6077i	0.636650	−	0.636650i	0.949728	+	0.313078i	$0.101360\pi$
$602$	7.60933	+	23.2849i	0.310133	+	0.949020i
$603$	20.8125	−	8.62081i	0.847549	−	0.351066i
$604$	−14.6981	+	7.07265i	−0.598058	+	0.287782i
$605$	−14.6400	−	19.0792i	−0.595199	−	0.775678i
$606$	−6.28770	−	8.86459i	−0.255421	−	0.360099i
$607$	−2.47414	−	4.28534i	−0.100422	−	0.173937i	0.811436	−	0.584441i	$-0.198686\pi$
$607$	−2.47414	−	4.28534i	−0.100422	−	0.173937i	−0.911859	+	0.410504i	$0.865353\pi$
$608$	−15.7208	+	10.7005i	−0.637562	+	0.433961i
$609$	−0.267503	−	2.91192i	−0.0108398	−	0.117997i
$610$	4.09207	−	8.91658i	0.165683	−	0.361022i
$611$	−22.5581	+	2.96982i	−0.912601	+	0.120146i
$612$	7.06851	−	10.3607i	0.285728	−	0.418807i
$613$	2.04084	−	15.5018i	0.0824289	−	0.626110i	−0.899508	−	0.436903i	$-0.856075\pi$
$613$	2.04084	−	15.5018i	0.0824289	−	0.626110i	0.981937	−	0.189206i	$-0.0605915\pi$
$614$	2.07173	−	6.71269i	0.0836081	−	0.270902i
$615$	−10.0503	+	10.0503i	−0.405267	+	0.405267i
$616$	−39.9362	−	0.841014i	−1.60908	−	0.0338854i
$617$	5.36374	+	5.36374i	0.215936	+	0.215936i	0.806783	−	0.590847i	$-0.201206\pi$
$617$	5.36374	+	5.36374i	0.215936	+	0.215936i	−0.590847	+	0.806783i	$0.701206\pi$
$618$	21.0028	−	11.0961i	0.844856	−	0.446352i
$619$	8.08716	+	1.06469i	0.325050	+	0.0427937i	0.291286	−	0.956636i	$-0.405917\pi$
$619$	8.08716	+	1.06469i	0.325050	+	0.0427937i	0.0337646	+	0.999430i	$0.489250\pi$
$620$	−5.91393	+	3.86946i	−0.237509	+	0.155401i
$621$	4.97816	+	37.8129i	0.199767	+	1.51738i
$622$	7.05920	+	19.0342i	0.283048	+	0.763201i
$623$	20.1504	−	43.7071i	0.807310	−	1.75109i
$624$	10.1362	+	13.7518i	0.405772	+	0.550514i
$625$	−0.192681	+	0.111245i	−0.00770725	+	0.00444978i
$626$	7.94456	−	46.7146i	0.317529	−	1.86709i
$627$	17.5639	−	13.4773i	0.701436	−	0.538231i
$628$	12.8390	+	11.4808i	0.512331	+	0.458132i
$629$	−0.607447	−	1.46651i	−0.0242205	−	0.0584735i
$630$	−6.36870	+	4.15123i	−0.253735	+	0.165389i
$631$	−3.80696	−	3.80696i	−0.151553	−	0.151553i	0.627258	−	0.778811i	$-0.284177\pi$
$631$	−3.80696	−	3.80696i	−0.151553	−	0.151553i	−0.778811	+	0.627258i	$0.784177\pi$
$632$	18.8116	+	18.1377i	0.748284	+	0.721478i
$633$	−0.973610	−	3.63356i	−0.0386975	−	0.144421i
$634$	5.40036	+	23.6774i	0.214476	+	0.940349i
$635$	0.540791	+	0.414963i	0.0214606	+	0.0164673i
$636$	−10.5550	−	12.2728i	−0.418531	−	0.486646i
$637$	18.0077	+	16.2156i	0.713489	+	0.642486i
$638$	−6.14633	−	2.82072i	−0.243335	−	0.111673i
$639$	−3.12739	−	5.41679i	−0.123717	−	0.214285i
$640$	−0.0168317	+	15.5536i	−0.000665331	+	0.614811i
$641$	1.92354	−	3.33166i	0.0759751	−	0.131593i	−0.825535	−	0.564351i	$-0.809126\pi$
$641$	1.92354	−	3.33166i	0.0759751	−	0.131593i	0.901510	+	0.432758i	$0.142460\pi$
$642$	−1.72178	−	18.3917i	−0.0679533	−	0.725863i
$643$	−9.01366	+	21.7609i	−0.355464	+	0.858167i	0.640462	+	0.767990i	$0.278743\pi$
$643$	−9.01366	+	21.7609i	−0.355464	+	0.858167i	−0.995926	+	0.0901764i	$0.971257\pi$
$644$	35.4369	+	8.87135i	1.39641	+	0.349580i
$645$	−10.2590	+	4.24943i	−0.403949	+	0.167321i
$646$	19.2762	+	5.94919i	0.758412	+	0.234068i
$647$	−4.98925	−	18.6201i	−0.196148	−	0.732033i	−0.991967	−	0.126499i	$-0.959626\pi$
$647$	−4.98925	−	18.6201i	−0.196148	−	0.732033i	0.795819	−	0.605535i	$-0.207041\pi$
$648$	1.62483	−	6.53866i	0.0638295	−	0.256863i
$649$	14.6935	−	54.8368i	0.576769	−	2.15253i
$650$	−15.2152	−	0.571667i	−0.596788	−	0.0224226i
$651$	0.329580	−	8.38366i	0.0129173	−	0.328581i
$652$	6.56917	−	2.15940i	0.257268	−	0.0845685i
$653$	−2.26992	−	17.2417i	−0.0888287	−	0.674721i	−0.976697	−	0.214623i	$-0.931148\pi$
$653$	−2.26992	−	17.2417i	−0.0888287	−	0.674721i	0.887868	−	0.460098i	$-0.152186\pi$
$654$	−3.76098	+	22.1148i	−0.147066	+	0.864758i
$655$	10.1930	+	5.88494i	0.398274	+	0.229944i
$656$	30.7151	+	13.4235i	1.19922	+	0.524098i
$657$			11.6059i			0.452789i
$658$	22.1784	−	10.6247i	0.864605	−	0.414194i
$659$	0.195635	+	0.0810345i	0.00762084	+	0.00315666i	0.386491	−	0.922293i	$-0.373687\pi$
$659$	0.195635	+	0.0810345i	0.00762084	+	0.00315666i	−0.378870	+	0.925450i	$0.623687\pi$
$660$	−1.00968	−	18.0789i	−0.0393017	−	0.703718i
$661$	36.2681	+	4.77479i	1.41067	+	0.185718i	0.797063	−	0.603897i	$-0.206386\pi$
$661$	36.2681	+	4.77479i	1.41067	+	0.185718i	0.613603	+	0.789614i	$0.289719\pi$
$662$	5.25549	+	3.30337i	0.204260	+	0.128389i
$663$	4.69050	−	17.5052i	0.182164	−	0.679844i
$664$	2.37572	−	20.9975i	0.0921956	−	0.814862i
$665$	−9.40091	−	7.81900i	−0.364552	−	0.303208i
$666$	0.531715	+	0.573230i	0.0206035	+	0.0222122i
$667$	4.90656	+	3.76493i	0.189983	+	0.145779i
$668$	−8.69793	+	12.7490i	−0.336533	+	0.493275i
$669$	15.5352	+	20.2459i	0.600627	+	0.782752i
$670$	29.5059	−	2.76226i	1.13991	−	0.106715i
$671$	26.9357			1.03984
$672$	−15.0306	−	10.7251i	−0.579820	−	0.413732i
$673$	3.80762			0.146773			0.0733865	−	0.997304i	$-0.476619\pi$
$673$	3.80762			0.146773			0.0733865	+	0.997304i	$0.476619\pi$
$674$	17.6313	−	1.65060i	0.679134	−	0.0635786i
$675$	10.4594	+	13.6310i	0.402584	+	0.524657i
$676$	1.67837	+	1.14505i	0.0645526	+	0.0440405i
$677$	−9.83068	−	7.54335i	−0.377824	−	0.289914i	0.402339	−	0.915491i	$-0.368197\pi$
$677$	−9.83068	−	7.54335i	−0.377824	−	0.289914i	−0.780163	+	0.625576i	$0.784864\pi$
$678$	−0.756640	−	0.815717i	−0.0290586	−	0.0313274i
$679$	4.80379	−	27.9527i	0.184353	−	1.07273i
$680$	12.9046	−	10.2813i	0.494869	−	0.394269i
$681$	0.821478	−	3.06580i	0.0314791	−	0.117482i
$682$	−16.4280	−	10.3259i	−0.629059	−	0.395399i
$683$	−35.8318	−	4.71734i	−1.37106	−	0.180504i	−0.591236	−	0.806498i	$-0.701360\pi$
$683$	−35.8318	−	4.71734i	−1.37106	−	0.180504i	−0.779828	+	0.625994i	$0.784693\pi$
$684$	−9.92123	+	0.554087i	−0.379348	+	0.0211861i
$685$	−1.77559	−	0.735475i	−0.0678420	−	0.0281011i
$686$	−23.9448	−	10.6136i	−0.914215	−	0.405229i
$687$		−	8.72545i		−	0.332897i
$688$	18.1566	+	18.8720i	0.692213	+	0.719488i
$689$	19.6678	+	11.3552i	0.749285	+	0.432600i
$690$	−2.77629	+	16.3248i	−0.105691	+	0.621473i
$691$	−3.52150	−	26.7485i	−0.133964	−	1.01756i	−0.917926	−	0.396751i	$-0.870138\pi$
$691$	−3.52150	−	26.7485i	−0.133964	−	1.01756i	0.783962	−	0.620809i	$-0.213196\pi$
$692$	9.13092	+	27.7775i	0.347106	+	1.05594i
$693$	−17.6518	−	11.1380i	−0.670538	−	0.423099i
$694$	5.29034	+	0.198770i	0.200819	+	0.00754520i
$695$	−2.38114	+	8.88653i	−0.0903217	+	0.337085i
$696$	−1.61215	−	2.67831i	−0.0611083	−	0.101521i
$697$	−9.20326	−	34.3470i	−0.348598	−	1.30099i
$698$	6.53805	+	2.01783i	0.247469	+	0.0763760i
$699$	17.1982	−	7.12374i	0.650497	−	0.269445i
$700$	15.8236	−	4.52099i	0.598075	−	0.170878i
$701$	−6.78327	+	16.3763i	−0.256201	+	0.618523i	−0.998681	−	0.0513449i	$-0.983649\pi$
$701$	−6.78327	+	16.3763i	−0.256201	+	0.618523i	0.742480	+	0.669868i	$0.233649\pi$
$702$	2.52101	+	26.9289i	0.0951494	+	1.01637i
$703$	−0.628789	+	1.08909i	−0.0237152	+	0.0410760i
$704$	−38.8304	+	17.7695i	−1.46348	+	0.669714i
$705$	5.57375	+	9.65402i	0.209920	+	0.363591i
$706$	−6.26971	−	2.87735i	−0.235964	−	0.108290i
$707$	−15.7390	−	4.88748i	−0.591927	−	0.183812i
$708$	19.8965	−	17.1117i	0.747758	−	0.643096i
$709$	−18.2380	−	13.9945i	−0.684944	−	0.525576i	0.206648	−	0.978415i	$-0.433744\pi$
$709$	−18.2380	−	13.9945i	−0.684944	−	0.525576i	−0.891592	+	0.452839i	$0.850411\pi$
$710$	−1.82971	−	8.02222i	−0.0686679	−	0.301068i
$711$	3.53396	+	13.1889i	0.132534	+	0.494622i
$712$	−0.938227	−	51.4430i	−0.0351615	−	1.92791i
$713$	12.5476	+	12.5476i	0.469911	+	0.469911i
$714$	1.05826	+	19.5591i	0.0396045	+	0.731981i
$715$	9.72163	+	23.4701i	0.363568	+	0.877732i
$716$	−5.51950	+	6.17248i	−0.206273	+	0.230676i
$717$	21.1925	−	16.2616i	0.791449	−	0.607300i
$718$	−5.83214	+	34.2934i	−0.217654	+	1.27982i
$719$	20.0090	−	11.5522i	0.746209	−	0.430824i	−0.0781138	−	0.996944i	$-0.524890\pi$
$719$	20.0090	−	11.5522i	0.746209	−	0.430824i	0.824322	+	0.566121i	$0.191556\pi$
$720$	−4.19873	+	6.95844i	−0.156478	+	0.259326i
$721$	15.0809	−	32.7111i	0.561643	−	1.21823i
$722$	3.78589	+	10.2081i	0.140896	+	0.379907i
$723$	−3.08950	−	23.4671i	−0.114900	−	0.872752i
$724$	−18.3468	−	28.0405i	−0.681854	−	1.04212i
$725$	2.76228	+	0.363661i	0.102589	+	0.0135060i
$726$	26.9865	−	14.2574i	1.00156	−	0.529142i
$727$	9.34423	+	9.34423i	0.346558	+	0.346558i	0.858826	−	0.512268i	$-0.171194\pi$
$727$	9.34423	+	9.34423i	0.346558	+	0.346558i	−0.512268	+	0.858826i	$0.671194\pi$
$728$	24.8764	+	7.23027i	0.921980	+	0.267972i
$729$	16.9478	−	16.9478i	0.627698	−	0.627698i
$730$	−4.50249	+	14.5887i	−0.166645	+	0.539952i
$731$	3.62610	−	27.5429i	0.134116	−	1.01871i
$732$	10.2855	+	7.01717i	0.380162	+	0.259362i
$733$	−33.4129	+	4.39889i	−1.23413	+	0.162477i	−0.719230	−	0.694772i	$-0.755505\pi$
$733$	−33.4129	+	4.39889i	−1.23413	+	0.162477i	−0.514902	+	0.857249i	$0.672172\pi$
$734$	−19.7818	+	43.1043i	−0.730159	+	1.59101i
$735$	3.96365	−	11.1914i	0.146201	−	0.412802i
$736$	38.2355	−	7.94704i	1.40938	−	0.292932i
$737$	40.6819	+	70.4630i	1.49854	+	2.59554i
$738$	10.1332	+	14.2861i	0.373008	+	0.525877i
$739$	−6.90710	−	9.00151i	−0.254082	−	0.331126i	0.648845	−	0.760921i	$-0.275252\pi$
$739$	−6.90710	−	9.00151i	−0.254082	−	0.331126i	−0.902926	+	0.429795i	$0.858586\pi$
$740$	0.445986	+	0.926833i	0.0163948	+	0.0340711i
$741$	−13.2649	+	5.49450i	−0.487298	+	0.201846i
$742$	−24.0186	−	5.06281i	−0.881749	−	0.185862i
$743$	−2.91737	+	2.91737i	−0.107028	+	0.107028i	−0.758593	−	0.651565i	$-0.774113\pi$
$743$	−2.91737	+	2.91737i	−0.107028	+	0.107028i	0.651565	+	0.758593i	$0.274113\pi$
$744$	−3.58299	−	8.22270i	−0.131359	−	0.301459i
$745$	−3.52815	+	0.945364i	−0.129261	+	0.0346355i
$746$	−9.95761	−	6.25893i	−0.364574	−	0.229156i
$747$	6.72170	−	8.75989i	0.245934	−	0.320508i
$748$	40.4329	+	20.4272i	1.47837	+	0.746892i
$749$	−19.0135	−	20.5696i	−0.694738	−	0.751597i
$750$	6.76429	+	18.2390i	0.246997	+	0.665994i
$751$	−35.0511	+	20.2367i	−1.27903	+	0.738449i	−0.976670	−	0.214744i	$-0.931108\pi$
$751$	−35.0511	+	20.2367i	−1.27903	+	0.738449i	−0.302361	+	0.953193i	$0.597775\pi$
$752$	16.4042	−	20.5442i	0.598201	−	0.749169i
$753$	16.4288	+	9.48516i	0.598698	+	0.345658i
$754$	3.37682	+	2.79869i	0.122977	+	0.101922i
$755$	−10.3586	−	4.29066i	−0.376987	−	0.156153i
$756$	−11.6311	−	26.8196i	−0.423018	−	0.975420i
$757$	0.293739	+	0.709148i	0.0106761	+	0.0257744i	0.929128	−	0.369759i	$-0.120560\pi$
$757$	0.293739	+	0.709148i	0.0106761	+	0.0257744i	−0.918452	+	0.395533i	$0.870560\pi$
$758$	2.86038	+	5.41413i	0.103894	+	0.196650i
$759$	−43.9147	+	11.7669i	−1.59400	+	0.427112i
$760$	−12.6860	−	3.15243i	−0.460170	−	0.114351i
$761$	−19.1882	−	5.14147i	−0.695573	−	0.186378i	−0.106326	−	0.994331i	$-0.533909\pi$
$761$	−19.1882	−	5.14147i	−0.695573	−	0.186378i	−0.589247	+	0.807953i	$0.700575\pi$
$762$	−0.634261	+	0.588326i	−0.0229769	+	0.0213128i
$763$	15.8379	+	30.1044i	0.573369	+	1.08985i
$764$	6.00819	+	6.98601i	0.217369	+	0.252745i
$765$	8.54754	−	1.12531i	0.309037	−	0.0406855i
$766$	−14.4692	+	10.2631i	−0.522792	+	0.370820i
$767$	−18.4091	+	31.8854i	−0.664713	+	1.15132i
$768$	−19.4567	−	3.33059i	−0.702083	−	0.120182i
$769$	−23.5369			−0.848762			−0.424381	−	0.905484i	$-0.639508\pi$
$769$	−23.5369			−0.848762			−0.424381	+	0.905484i	$0.639508\pi$
$770$	−17.8675	−	20.8486i	−0.643901	−	0.751331i
$771$	−5.56153	+	13.4267i	−0.200294	+	0.483552i
$772$	−2.98023	+	8.50856i	−0.107261	+	0.306230i
$773$	−4.65840	+	35.3841i	−0.167551	+	1.27268i	0.676512	+	0.736432i	$0.263491\pi$
$773$	−4.65840	+	35.3841i	−0.167551	+	1.27268i	−0.844063	+	0.536244i	$0.819843\pi$
$774$	3.04286	+	13.3411i	0.109373	+	0.479537i
$775$	7.72161	+	2.06900i	0.277369	+	0.0743207i
$776$	−8.38036	−	29.1397i	−0.300837	−	1.04605i
$777$	−1.20343	−	0.206814i	−0.0431727	−	0.00741940i
$778$	5.75464	+	0.216214i	0.206314	+	0.00775165i
$779$	−17.1498	+	22.3500i	−0.614455	+	0.800773i
$780$	−2.40209	+	11.4947i	−0.0860088	+	0.411578i
$781$	17.9226	−	13.7525i	0.641321	−	0.492103i
$782$	−31.8967	−	26.4357i	−1.14062	−	0.945340i
$783$		−	4.94914i		−	0.176868i
$784$	−27.9848	+	0.923759i	−0.999456	+	0.0329914i
$785$			11.8391i			0.422554i
$786$	−9.53198	+	11.5010i	−0.339994	+	0.410228i
$787$	−3.48066	+	2.67080i	−0.124072	+	0.0952039i	−0.668934	−	0.743322i	$-0.733249\pi$
$787$	−3.48066	+	2.67080i	−0.124072	+	0.0952039i	0.544861	+	0.838526i	$0.316582\pi$
$788$	24.7936	−	16.2223i	0.883235	−	0.577897i
$789$	13.1562	−	17.1455i	0.468374	−	0.610397i
$790$	−0.674403	+	17.9495i	−0.0239942	+	0.638616i
$791$	−1.66278	−	0.285756i	−0.0591217	−	0.0101603i
$792$	−22.1717	−	2.50857i	−0.787838	−	0.0891380i
$793$	−16.8735	−	4.52125i	−0.599197	−	0.160554i
$794$	−45.8379	+	10.4547i	−1.62672	+	0.371025i
$795$	1.45234	−	11.0316i	0.0515092	−	0.391251i
$796$	15.5520	+	32.3196i	0.551226	+	1.14554i
$797$	−9.46002	+	22.8385i	−0.335091	+	0.808981i	0.663081	+	0.748548i	$0.269248\pi$
$797$	−9.46002	+	22.8385i	−0.335091	+	0.808981i	−0.998172	+	0.0604338i	$0.980752\pi$
$798$	11.7833	−	10.0984i	0.417123	−	0.357480i
$799$	−27.8887			−0.986632
$800$	13.1271	−	11.7129i	0.464115	−	0.414114i
$801$	13.4422	−	23.2826i	0.474957	−	0.822649i
$802$	−28.3678	−	39.9937i	−1.00170	−	1.41223i
$803$	−41.5594	+	5.47140i	−1.46660	+	0.193082i
$804$	−2.82225	+	37.5047i	−0.0995331	+	1.32269i
$805$	11.6912	+	22.2226i	0.412062	+	0.783242i
$806$	8.55784	+	9.22601i	0.301437	+	0.324972i
$807$	−23.8261	−	6.38418i	−0.838718	−	0.224734i
$808$	−17.4227	+	2.61779i	−0.612930	+	0.0920936i
$809$	−5.34013	+	1.43088i	−0.187749	+	0.0503072i	−0.351468	−	0.936200i	$-0.614318\pi$
$809$	−5.34013	+	1.43088i	−0.187749	+	0.0503072i	0.163719	+	0.986507i	$0.447651\pi$
$810$	4.09488	−	2.16340i	0.143879	−	0.0760141i
$811$	−7.60273	−	18.3546i	−0.266968	−	0.644518i	0.732370	−	0.680907i	$-0.238414\pi$
$811$	−7.60273	−	18.3546i	−0.266968	−	0.644518i	−0.999338	+	0.0363896i	$0.988414\pi$
$812$	−4.40887	−	1.74157i	−0.154721	−	0.0611170i
$813$	11.7221	+	4.85547i	0.411113	+	0.170289i
$814$	−1.80201	+	2.17425i	−0.0631603	+	0.0762076i
$815$	4.11641	+	2.37661i	0.144192	+	0.0832490i
$816$	10.1178	+	18.3336i	0.354194	+	0.641803i
$817$	−19.0607	+	11.0047i	−0.666849	+	0.385005i
$818$	2.49795	−	0.926414i	0.0873388	−	0.0323913i
$819$	9.18821	+	9.94019i	0.321062	+	0.347338i
$820$	7.19524	+	21.8889i	0.251269	+	0.764392i
$821$	23.9492	−	31.2112i	0.835832	−	1.08928i	−0.158953	−	0.987286i	$-0.550812\pi$
$821$	23.9492	−	31.2112i	0.835832	−	1.08928i	0.994785	−	0.101992i	$-0.0325216\pi$
$822$	1.29802	−	2.06508i	0.0452737	−	0.0720280i
$823$	32.4621	−	8.69819i	1.13156	−	0.303200i	0.356006	−	0.934484i	$-0.384138\pi$
$823$	32.4621	−	8.69819i	1.13156	−	0.303200i	0.775552	+	0.631284i	$0.217472\pi$
$824$	−0.702184	−	38.5008i	−0.0244618	−	1.34124i
$825$	−14.4824	+	14.4824i	−0.504212	+	0.504212i
$826$	8.20781	−	38.9388i	0.285586	−	1.35485i
$827$	−1.10459	+	0.457534i	−0.0384102	+	0.0159100i	−0.401806	−	0.915725i	$-0.631617\pi$
$827$	−1.10459	+	0.457534i	−0.0384102	+	0.0159100i	0.363396	+	0.931635i	$0.381617\pi$
$828$	19.2586	+	6.74555i	0.669282	+	0.234424i
$829$	5.94715	+	7.75047i	0.206553	+	0.269185i	0.885130	−	0.465345i	$-0.154070\pi$
$829$	5.94715	+	7.75047i	0.206553	+	0.269185i	−0.678577	+	0.734530i	$0.737403\pi$
$830$	11.8476	−	8.40358i	0.411237	−	0.291693i
$831$	10.8660	+	18.8205i	0.376939	+	0.652877i
$832$	27.3075	−	4.61367i	0.946716	−	0.159950i
$833$	19.2894	+	22.5870i	0.668338	+	0.782593i
$834$	−10.6119	−	4.87011i	−0.367461	−	0.168638i
$835$	−10.5179	+	1.38471i	−0.363987	+	0.0479198i
$836$	−6.66132	−	35.2656i	−0.230387	−	1.21969i
$837$	1.85350	−	14.0787i	0.0640663	−	0.486632i
$838$	25.2999	+	7.80826i	0.873969	+	0.269732i
$839$	9.37610	−	9.37610i	0.323699	−	0.323699i	−0.526485	−	0.850184i	$-0.676491\pi$
$839$	9.37610	−	9.37610i	0.323699	−	0.323699i	0.850184	+	0.526485i	$0.176491\pi$
$840$	−1.39137	−	12.6158i	−0.0480070	−	0.435288i
$841$	19.9386	+	19.9386i	0.687538	+	0.687538i
$842$	−10.0978	−	19.1132i	−0.347994	−	0.658683i
$843$	8.03977	+	1.05846i	0.276904	+	0.0364551i
$844$	−5.96921	−	1.24741i	−0.205469	−	0.0429375i
$845$	0.182292	+	1.38465i	0.00627104	+	0.0476333i
$846$	12.8798	−	4.77671i	0.442815	−	0.164227i
$847$	19.3775	−	42.0305i	0.665817	−	1.44419i
$848$	−25.4735	+	6.30081i	−0.874763	+	0.216371i
$849$	1.04926	−	0.605791i	0.0360105	−	0.0207907i
$850$	−18.3987	−	3.12900i	−0.631071	−	0.107324i
$851$	2.04886	−	1.57215i	0.0702341	−	0.0538925i
$852$	10.4265	−	0.582306i	0.357206	−	0.0199495i
$853$	−10.4041	−	25.1178i	−0.356230	−	0.860016i	−0.995823	−	0.0913022i	$-0.970897\pi$
$853$	−10.4041	−	25.1178i	−0.356230	−	0.860016i	0.639593	−	0.768714i	$-0.279103\pi$
$854$	18.8534	−	1.02008i	0.645148	−	0.0349063i
$855$	−4.82974	−	4.82974i	−0.165174	−	0.165174i
$856$	−27.8701	−	10.9531i	−0.952579	−	0.374370i
$857$	5.83161	+	21.7639i	0.199204	+	0.743440i	0.991138	+	0.132833i	$0.0424075\pi$
$857$	5.83161	+	21.7639i	0.199204	+	0.743440i	−0.791934	+	0.610606i	$0.790926\pi$
$858$	−31.4337	+	7.16943i	−1.07313	+	0.244760i
$859$	25.4887	+	19.5581i	0.869662	+	0.667315i	0.944010	−	0.329917i	$-0.107021\pi$
$859$	25.4887	+	19.5581i	0.869662	+	0.667315i	−0.0743478	+	0.997232i	$0.523687\pi$
$860$	−1.35078	+	17.9504i	−0.0460611	+	0.612103i
$861$	−26.1232	−	8.11209i	−0.890275	−	0.276459i
$862$	−16.6157	+	36.2054i	−0.565932	+	1.23316i
$863$	−7.15842	−	12.3987i	−0.243675	−	0.422058i	0.718083	−	0.695957i	$-0.245020\pi$
$863$	−7.15842	−	12.3987i	−0.243675	−	0.422058i	−0.961758	+	0.273899i	$0.911686\pi$
$864$	−23.6720	−	20.4033i	−0.805337	−	0.694133i
$865$	−10.0494	+	17.4061i	−0.341690	+	0.591824i
$866$	30.4185	−	2.84769i	1.03366	−	0.0967685i
$867$	0.474575	−	1.14572i	0.0161174	−	0.0389109i
$868$	−11.8896	−	6.60536i	−0.403559	−	0.224200i
$869$	−45.5620	+	18.8724i	−1.54558	+	0.640202i
$870$	0.633689	−	2.05324i	0.0214841	−	0.0696114i
$871$	−13.6572	−	50.9692i	−0.462755	−	1.72703i
$872$	29.2492	+	21.6079i	0.990503	+	0.731735i
$873$	4.10052	−	15.3033i	0.138781	−	0.517940i
$874$	−1.23230	+	32.7982i	−0.0416831	+	1.10941i
$875$	24.9473	+	15.7413i	0.843372	+	0.532154i
$876$	−17.2949	−	8.73760i	−0.584342	−	0.295216i
$877$	6.39322	+	48.5613i	0.215884	+	1.63980i	0.665371	+	0.746513i	$0.268273\pi$
$877$	6.39322	+	48.5613i	0.215884	+	1.63980i	−0.449488	+	0.893287i	$0.648393\pi$
$878$	−15.2809	−	2.59876i	−0.515705	−	0.0877038i
$879$	−28.0710	−	16.2068i	−0.946813	−	0.546643i
$880$	−26.8968	−	11.7548i	−0.906692	−	0.396253i
$881$		−	40.8520i		−	1.37634i	−0.725550	−	0.688169i	$-0.758415\pi$
$881$		−	40.8520i		−	1.37634i	0.725550	−	0.688169i	$-0.241585\pi$
$882$	−12.7770	−	7.12744i	−0.430224	−	0.239993i
$883$	−20.3685	−	8.43690i	−0.685454	−	0.283924i	0.0126506	−	0.999920i	$-0.495973\pi$
$883$	−20.3685	−	8.43690i	−0.685454	−	0.283924i	−0.698105	+	0.715996i	$0.745973\pi$
$884$	−21.8999	−	19.5831i	−0.736573	−	0.658652i
$885$	17.8844	+	2.35453i	0.601178	+	0.0791466i
$886$	−24.3778	+	38.7838i	−0.818990	+	1.30297i
$887$	−0.800955	+	2.98921i	−0.0268934	+	0.100368i	−0.978068	−	0.208286i	$-0.933212\pi$
$887$	−0.800955	+	2.98921i	−0.0268934	+	0.100368i	0.951175	+	0.308653i	$0.0998783\pi$
$888$	−1.25453	+	0.360793i	−0.0420992	+	0.0121074i
$889$	−0.222190	+	1.29290i	−0.00745201	+	0.0433624i
$890$	25.9294	−	24.0515i	0.869155	−	0.806208i
$891$	10.0877	+	7.74055i	0.337950	+	0.259318i
$892$	40.6506	−	7.67850i	1.36108	−	0.257095i
$893$	13.4506	+	17.5292i	0.450108	+	0.586592i
$894$	−0.432088	−	4.61548i	−0.0144512	−	0.154365i
$895$	−5.69176			−0.190254
$896$	−26.5059	+	13.9081i	−0.885501	+	0.464637i
$897$	29.4849			0.984472
$898$	3.09348	+	33.0439i	0.103231	+	1.10269i
$899$	−1.40178	−	1.82684i	−0.0467521	−	0.0609285i
$900$	9.03295	−	1.70623i	0.301098	−	0.0568744i
$901$	22.0845	+	16.9461i	0.735743	+	0.564555i
$902$	−46.3797	+	43.0208i	−1.54428	+	1.43243i
$903$	−16.4302	−	13.6654i	−0.546761	−	0.454757i
$904$	−1.73339	+	0.498510i	−0.0576516	+	0.0165802i
$905$	5.96155	−	22.2488i	0.198169	−	0.739576i
$906$	7.57247	−	12.0474i	0.251579	−	0.400248i
$907$	−43.7868	−	5.76464i	−1.45392	−	0.191412i	−0.638203	−	0.769868i	$-0.720322\pi$
$907$	−43.7868	−	5.76464i	−1.45392	−	0.191412i	−0.815713	+	0.578456i	$0.803655\pi$
$908$	−3.83548	−	3.42972i	−0.127285	−	0.113819i
$909$	−8.50514	−	3.52294i	−0.282098	−	0.116849i
$910$	7.69337	+	16.0595i	0.255033	+	0.532366i
$911$		−	18.2674i		−	0.605225i	−0.953114	−	0.302612i	$-0.902141\pi$
$911$		−	18.2674i		−	0.605225i	0.953114	−	0.302612i	$-0.0978588\pi$
$912$	6.64360	−	15.2016i	0.219991	−	0.503376i
$913$	34.5371	+	19.9400i	1.14301	+	0.659917i
$914$	53.6329	+	9.12112i	1.77402	+	0.301700i
$915$	1.11713	+	8.48546i	0.0369312	+	0.280521i
$916$	−12.6251	−	6.37833i	−0.417144	−	0.210746i
$917$	−0.889788	+	22.6339i	−0.0293834	+	0.747437i
$918$	−1.24471	+	33.1286i	−0.0410817	+	1.09341i
$919$	−2.83264	+	10.5716i	−0.0934402	+	0.348724i	−0.996778	−	0.0802055i	$-0.974442\pi$
$919$	−2.83264	+	10.5716i	−0.0934402	+	0.348724i	0.903338	+	0.428929i	$0.141109\pi$
$920$	21.5913	+	15.9505i	0.711843	+	0.525874i
$921$	1.58619	+	5.91974i	0.0522668	+	0.195062i
$922$	14.1540	−	45.8611i	0.466138	−	1.51035i
$923$	−13.5358	+	5.60670i	−0.445535	+	0.184547i
$924$	29.8871	−	17.9192i	0.983213	−	0.589497i
$925$	0.445220	−	1.07486i	0.0146388	−	0.0353411i
$926$	−60.3313	+	5.64805i	−1.98261	+	0.185606i
$927$	10.0604	−	17.4251i	0.330426	−	0.572314i
$928$	−5.05380	+	0.374802i	−0.165899	+	0.0123035i
$929$	−19.3624	−	33.5367i	−0.635261	−	1.10030i	−0.986460	−	0.164003i	$-0.947559\pi$
$929$	−19.3624	−	33.5367i	−0.635261	−	1.10030i	0.351199	−	0.936301i	$-0.385774\pi$
$930$	2.57160	−	5.60349i	0.0843260	−	0.183746i
$931$	4.89364	−	23.0178i	0.160383	−	0.754377i
$932$	2.26444	−	30.0920i	0.0741743	−	0.985698i
$933$	−14.0505	−	10.7813i	−0.459991	−	0.352964i
$934$	17.0082	−	3.87924i	0.556524	−	0.126933i
$935$	8.05919	+	30.0773i	0.263564	+	0.983633i
$936$	13.4681	+	5.29305i	0.440219	+	0.173009i
$937$	16.6700	+	16.6700i	0.544584	+	0.544584i	0.924869	−	0.380286i	$-0.124174\pi$
$937$	16.6700	+	16.6700i	0.544584	+	0.544584i	−0.380286	+	0.924869i	$0.624174\pi$
$938$	31.1433	+	47.7791i	1.01686	+	1.56004i
$939$	15.8194	+	38.1914i	0.516246	+	1.24633i
$940$	18.0431	−	1.00768i	0.588500	−	0.0328669i
$941$	−28.1354	+	21.5891i	−0.917189	+	0.703784i	−0.955346	−	0.295488i	$-0.904518\pi$
$941$	−28.1354	+	21.5891i	−0.917189	+	0.703784i	0.0381577	+	0.999272i	$0.487851\pi$
$942$	−14.8127	−	2.51914i	−0.482624	−	0.0820779i
$943$	50.1018	−	28.9263i	1.63154	−	0.941969i
$944$	−10.2149	−	41.2975i	−0.332465	−	1.34412i
$945$	8.41305	−	18.2483i	0.273677	−	0.593616i
$946$	−46.3386	+	17.1856i	−1.50660	+	0.558752i
$947$	2.45907	+	18.6785i	0.0799091	+	0.606970i	0.983808	+	0.179224i	$0.0573587\pi$
$947$	2.45907	+	18.6785i	0.0799091	+	0.606970i	−0.903899	+	0.427746i	$0.859308\pi$
$948$	−22.3145	−	4.66313i	−0.724741	−	0.151452i
$949$	26.9528	+	3.54840i	0.874923	+	0.115186i
$950$	6.90692	+	13.0734i	0.224090	+	0.424158i
$951$	−14.9808	−	14.9808i	−0.485787	−	0.485787i
$952$	29.0741	+	12.7665i	0.942298	+	0.413766i
$953$	−27.5698	+	27.5698i	−0.893072	+	0.893072i	−0.994811	−	0.101739i	$-0.967559\pi$
$953$	−27.5698	+	27.5698i	−0.893072	+	0.893072i	0.101739	+	0.994811i	$0.467559\pi$
$954$	−13.1017	−	4.04356i	−0.424184	−	0.130915i
$955$	−0.826714	+	6.27951i	−0.0267518	+	0.203200i
$956$	−8.03751	−	42.5513i	−0.259952	−	1.37621i
$957$	5.84915	−	0.770056i	0.189076	−	0.0248924i
$958$	−26.3774	−	12.1053i	−0.852216	−	0.391106i
$959$	−0.338357	−	3.68320i	−0.0109261	−	0.118937i
$960$	−7.20831	−	11.4956i	−0.232647	−	0.371020i
$961$	12.1965	+	21.1250i	0.393437	+	0.681453i
$962$	1.49380	−	1.05956i	0.0481620	−	0.0341616i
$963$	−9.52522	−	12.4135i	−0.306946	−	0.400020i
$964$	−36.2136	−	12.6843i	−1.16636	−	0.408533i
$965$	−5.72528	+	2.37149i	−0.184303	+	0.0763410i
$966$	−30.2920	+	9.89919i	−0.974628	+	0.318501i
$967$	8.61008	−	8.61008i	0.276881	−	0.276881i	−0.554981	−	0.831863i	$-0.687275\pi$
$967$	8.61008	−	8.61008i	0.276881	−	0.276881i	0.831863	+	0.554981i	$0.187275\pi$
$968$	−0.902236	−	49.4696i	−0.0289990	−	1.59001i
$969$	−16.9992	+	4.55492i	−0.546092	+	0.146325i
$970$	11.0913	−	17.6456i	0.356120	−	0.566567i
$971$	−17.9976	+	23.4549i	−0.577571	+	0.752705i	−0.987190	−	0.159552i	$-0.948995\pi$
$971$	−17.9976	+	23.4549i	−0.577571	+	0.752705i	0.409619	+	0.912257i	$0.365662\pi$
$972$	−8.51568	−	25.9058i	−0.273140	−	0.830929i
$973$	−17.2691	+	3.90720i	−0.553622	+	0.125259i
$974$	35.4458	−	13.1458i	1.13576	−	0.421218i
$975$	11.5032	−	6.64139i	0.368398	−	0.212695i
$976$	17.6720	−	9.75273i	0.565668	−	0.312177i
$977$	−2.56717	−	1.48215i	−0.0821309	−	0.0474183i	0.458372	−	0.888760i	$-0.348433\pi$
$977$	−2.56717	−	1.48215i	−0.0821309	−	0.0474183i	−0.540503	+	0.841342i	$0.681766\pi$
$978$	−3.84945	+	4.64464i	−0.123092	+	0.148519i
$979$	89.7094	+	37.1589i	2.86713	+	1.18760i
$980$	−13.2957	−	13.9161i	−0.424716	−	0.444533i
$981$	7.27153	+	17.5550i	0.232162	+	0.560489i
$982$	−13.9799	+	7.38582i	−0.446116	+	0.235691i
$983$	−20.0674	+	5.37705i	−0.640052	+	0.171501i	−0.564227	−	0.825620i	$-0.690826\pi$
$983$	−20.0674	+	5.37705i	−0.640052	+	0.171501i	−0.0758249	+	0.997121i	$0.524159\pi$
$984$	−28.9178	+	4.34494i	−0.921865	+	0.138511i
$985$	19.6725	+	5.27123i	0.626818	+	0.167955i
$986$	3.65590	+	3.94135i	0.116428	+	0.125518i
$987$	−11.4483	+	18.1436i	−0.364405	+	0.577518i
$988$	−1.74655	+	23.2098i	−0.0555652	+	0.738403i
$989$	44.8113	−	5.89952i	1.42492	−	0.187594i
$990$	−8.87352	−	12.5101i	−0.282019	−	0.397599i
$991$	−5.87252	+	10.1715i	−0.186547	+	0.323109i	−0.944097	−	0.329669i	$-0.893063\pi$
$991$	−5.87252	+	10.1715i	−0.186547	+	0.323109i	0.757550	+	0.652777i	$0.226396\pi$
$992$	−14.5168	−	0.826504i	−0.460909	−	0.0262415i
$993$	−5.41525			−0.171848
$994$	12.0239	−	10.3046i	0.381375	−	0.326843i
$995$	−9.43471	+	22.7774i	−0.299100	+	0.722092i
$996$	7.99338	+	16.6116i	0.253280	+	0.526357i
$997$	−4.42159	+	33.5853i	−0.140033	+	1.06366i	0.766715	+	0.641987i	$0.221890\pi$
$997$	−4.42159	+	33.5853i	−0.140033	+	1.06366i	−0.906749	+	0.421671i	$0.861444\pi$
$998$	35.7565	−	8.15537i	1.13185	−	0.258154i
$999$	−1.99623	−	0.534887i	−0.0631578	−	0.0169231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.16	yes	240
4.3	odd	2		896.2.bh.a.529.20		240
7.2	even	3	inner	224.2.bd.a.205.26	yes	240
28.23	odd	6		896.2.bh.a.401.11		240
32.5	even	8	inner	224.2.bd.a.165.26	yes	240
32.27	odd	8		896.2.bh.a.753.11		240
224.37	even	24	inner	224.2.bd.a.37.16	✓	240
224.219	odd	24		896.2.bh.a.625.20		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.16	✓	240	224.37	even	24	inner
224.2.bd.a.109.16	yes	240	1.1	even	1	trivial
224.2.bd.a.165.26	yes	240	32.5	even	8	inner
224.2.bd.a.205.26	yes	240	7.2	even	3	inner
896.2.bh.a.401.11		240	28.23	odd	6
896.2.bh.a.529.20		240	4.3	odd	2
896.2.bh.a.625.20		240	224.219	odd	24
896.2.bh.a.753.11		240	32.27	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.131818 + 1.40806i) q^{2} +(-0.751048 - 0.978785i) q^{3} +(-1.96525 + 0.371216i) q^{4} +(-1.09067 - 0.836901i) q^{5} +(1.27918 - 1.18654i) q^{6} +(0.448114 - 2.60753i) q^{7} +(-0.781748 - 2.71825i) q^{8} +(0.382510 - 1.42755i) q^{9} +O(q^{10})\)	\(q+(0.131818 + 1.40806i) q^{2} +(-0.751048 - 0.978785i) q^{3} +(-1.96525 + 0.371216i) q^{4} +(-1.09067 - 0.836901i) q^{5} +(1.27918 - 1.18654i) q^{6} +(0.448114 - 2.60753i) q^{7} +(-0.781748 - 2.71825i) q^{8} +(0.382510 - 1.42755i) q^{9} +(1.03463 - 1.64604i) q^{10} +(5.29222 + 0.696734i) q^{11} +(1.83934 + 1.64475i) q^{12} +(-3.19829 - 1.32478i) q^{13} +(3.73061 + 0.287250i) q^{14} +1.69608i q^{15} +(3.72440 - 1.45906i) q^{16} +(-3.67476 - 2.12163i) q^{17} +(2.06049 + 0.350419i) q^{18} +(0.438796 + 3.33299i) q^{19} +(2.45411 + 1.23984i) q^{20} +(-2.88876 + 1.51977i) q^{21} +(-0.283429 + 7.54359i) q^{22} +(1.78678 - 6.66837i) q^{23} +(-2.07345 + 2.80670i) q^{24} +(-0.804936 - 3.00406i) q^{25} +(1.44377 - 4.67801i) q^{26} +(-5.10400 + 2.11415i) q^{27} +(0.0872989 + 5.29078i) q^{28} +(-0.342826 + 0.827656i) q^{29} +(-2.38818 + 0.223575i) q^{30} +(-1.28520 + 2.22602i) q^{31} +(2.54539 + 5.05183i) q^{32} +(-3.29276 - 5.70323i) q^{33} +(2.50297 - 5.45394i) q^{34} +(-2.67099 + 2.46892i) q^{35} +(-0.221800 + 2.94748i) q^{36} +(0.296782 + 0.227728i) q^{37} +(-4.63519 + 1.05720i) q^{38} +(1.10540 + 4.12541i) q^{39} +(-1.42227 + 3.61896i) q^{40} +(5.92559 + 5.92559i) q^{41} +(-2.52072 - 3.86721i) q^{42} +(2.50543 + 6.04865i) q^{43} +(-10.6592 + 0.595300i) q^{44} +(-1.61191 + 1.23686i) q^{45} +(9.62497 + 1.63688i) q^{46} +(5.69194 - 3.28625i) q^{47} +(-4.22531 - 2.54956i) q^{48} +(-6.59839 - 2.33694i) q^{49} +(4.12379 - 1.52939i) q^{50} +(0.683309 + 5.19025i) q^{51} +(6.77722 + 1.41626i) q^{52} +(-6.50416 - 0.856289i) q^{53} +(-3.64964 - 6.90804i) q^{54} +(-5.18897 - 5.18897i) q^{55} +(-7.43821 + 0.820344i) q^{56} +(2.93272 - 2.93272i) q^{57} +(-1.21058 - 0.373618i) q^{58} +(1.38821 - 10.5445i) q^{59} +(-0.629613 - 3.33323i) q^{60} +(5.00297 - 0.658653i) q^{61} +(-3.30378 - 1.51620i) q^{62} +(-3.55096 - 1.63711i) q^{63} +(-6.77774 + 4.24997i) q^{64} +(2.37958 + 4.12155i) q^{65} +(7.59642 - 5.38818i) q^{66} +(9.27915 + 12.0928i) q^{67} +(8.00940 + 2.80539i) q^{68} +(-7.86886 + 3.25939i) q^{69} +(-3.82847 - 3.43545i) q^{70} +(2.99261 - 2.99261i) q^{71} +(-4.17946 + 0.0762257i) q^{72} +(-7.58534 + 2.03249i) q^{73} +(-0.281533 + 0.447904i) q^{74} +(-2.33579 + 3.04406i) q^{75} +(-2.09960 - 6.38726i) q^{76} +(4.18827 - 13.4874i) q^{77} +(-5.66310 + 2.10027i) q^{78} +(-8.00108 + 4.61942i) q^{79} +(-5.28318 - 1.52560i) q^{80} +(2.06294 + 1.19104i) q^{81} +(-7.56247 + 9.12467i) q^{82} +(6.90241 + 2.85907i) q^{83} +(5.11297 - 4.05908i) q^{84} +(2.23237 + 5.38941i) q^{85} +(-8.18658 + 4.32511i) q^{86} +(1.06758 - 0.286056i) q^{87} +(-2.24329 - 14.9302i) q^{88} +(17.5710 + 4.70814i) q^{89} +(-1.95405 - 2.10662i) q^{90} +(-4.88759 + 7.74598i) q^{91} +(-1.03607 + 13.7683i) q^{92} +(3.14404 - 0.413921i) q^{93} +(5.37752 + 7.58139i) q^{94} +(2.31080 - 4.00242i) q^{95} +(3.03295 - 6.28555i) q^{96} +10.7200 q^{97} +(2.42075 - 9.59896i) q^{98} +(3.01895 - 7.28839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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