LMFDB - Embedded newform 224.2.be.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(3,224)]

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([12, 9, 4]))

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

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

chi := DirichletCharacter("224.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.be (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			3.1
Character	$\chi$	$=$	224.3
Dual form			224.2.be.a.75.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40664 - 0.146150i) q^{2} +(-0.173475 + 0.133112i) q^{3} +(1.95728 + 0.411162i) q^{4} +(1.47800 + 1.13411i) q^{5} +(0.263472 - 0.161888i) q^{6} +(1.10840 - 2.40238i) q^{7} +(-2.69310 - 0.864414i) q^{8} +(-0.764082 + 2.85159i) q^{9} +O(q^{10})$	\(q+(-1.40664 - 0.146150i) q^{2} +(-0.173475 + 0.133112i) q^{3} +(1.95728 + 0.411162i) q^{4} +(1.47800 + 1.13411i) q^{5} +(0.263472 - 0.161888i) q^{6} +(1.10840 - 2.40238i) q^{7} +(-2.69310 - 0.864414i) q^{8} +(-0.764082 + 2.85159i) q^{9} +(-1.91327 - 1.81130i) q^{10} +(1.05222 + 0.138528i) q^{11} +(-0.394270 + 0.189211i) q^{12} +(0.703557 + 0.291423i) q^{13} +(-1.91023 + 3.21730i) q^{14} -0.407361 q^{15} +(3.66189 + 1.60952i) q^{16} +(-1.08632 + 1.88157i) q^{17} +(1.49155 - 3.89950i) q^{18} +(6.52551 - 0.859099i) q^{19} +(2.42657 + 2.82748i) q^{20} +(0.127507 + 0.564295i) q^{21} +(-1.45986 - 0.348642i) q^{22} +(5.38289 + 1.44234i) q^{23} +(0.582250 - 0.208530i) q^{24} +(-0.395810 - 1.47718i) q^{25} +(-0.947061 - 0.512752i) q^{26} +(-0.498066 - 1.20244i) q^{27} +(3.15721 - 4.24641i) q^{28} +(3.35639 + 1.39026i) q^{29} +(0.573011 + 0.0595359i) q^{30} +(-1.61293 + 2.79368i) q^{31} +(-4.91574 - 2.79920i) q^{32} +(-0.200975 + 0.116033i) q^{33} +(1.80306 - 2.48793i) q^{34} +(4.36279 - 2.29369i) q^{35} +(-2.66799 + 5.26721i) q^{36} +(-0.905876 + 1.18056i) q^{37} +(-9.30461 + 0.254741i) q^{38} +(-0.160842 + 0.0430974i) q^{39} +(-3.00007 - 4.33189i) q^{40} +(-5.49509 + 5.49509i) q^{41} +(-0.0968849 - 0.812397i) q^{42} +(-3.23411 - 7.80783i) q^{43} +(2.00254 + 0.703772i) q^{44} +(-4.36335 + 3.34811i) q^{45} +(-7.36099 - 2.81556i) q^{46} +(-3.74457 + 2.16193i) q^{47} +(-0.849494 + 0.208231i) q^{48} +(-4.54291 - 5.32560i) q^{49} +(0.340872 + 2.13571i) q^{50} +(-0.0620094 - 0.471008i) q^{51} +(1.25724 + 0.859672i) q^{52} +(0.309904 - 2.35395i) q^{53} +(0.524864 + 1.76419i) q^{54} +(1.39809 + 1.39809i) q^{55} +(-5.06168 + 5.51175i) q^{56} +(-1.01766 + 1.01766i) q^{57} +(-4.51805 - 2.44614i) q^{58} +(-11.0715 - 1.45759i) q^{59} +(-0.797320 - 0.167491i) q^{60} +(9.02225 - 1.18780i) q^{61} +(2.67711 - 3.69397i) q^{62} +(6.00372 + 4.99632i) q^{63} +(6.50558 + 4.65591i) q^{64} +(0.709354 + 1.22864i) q^{65} +(0.299657 - 0.133844i) q^{66} +(-8.67775 - 11.3091i) q^{67} +(-2.89987 + 3.23610i) q^{68} +(-1.12579 + 0.466317i) q^{69} +(-6.47211 + 2.58877i) q^{70} +(-6.36946 - 6.36946i) q^{71} +(4.52271 - 7.01915i) q^{72} +(-1.49265 - 5.57066i) q^{73} +(1.44678 - 1.52823i) q^{74} +(0.265294 + 0.203567i) q^{75} +(13.1255 + 1.00154i) q^{76} +(1.49908 - 2.37430i) q^{77} +(0.232545 - 0.0371155i) q^{78} +(1.44180 + 2.49727i) q^{79} +(3.58692 + 6.53187i) q^{80} +(-7.42355 - 4.28599i) q^{81} +(8.53273 - 6.92652i) q^{82} +(1.66109 - 4.01022i) q^{83} +(0.0175504 + 1.15691i) q^{84} +(-3.73950 + 1.54895i) q^{85} +(3.40812 + 11.4555i) q^{86} +(-0.767311 + 0.205600i) q^{87} +(-2.71400 - 1.28263i) q^{88} +(-4.81344 + 17.9640i) q^{89} +(6.62699 - 4.07189i) q^{90} +(1.47993 - 1.36720i) q^{91} +(9.94278 + 5.03630i) q^{92} +(-0.0920691 - 0.699334i) q^{93} +(5.58324 - 2.49379i) q^{94} +(10.6190 + 6.13091i) q^{95} +(1.22537 - 0.168753i) q^{96} +13.3638i q^{97} +(5.61190 + 8.15515i) q^{98} +(-1.19901 + 2.89467i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9	$ 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) $ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−1.40664	−	0.146150i	−0.994646	−	0.103344i
$2$	−1.40664	−	0.146150i	−0.994646	−	0.103344i
$3$	−0.173475	+	0.133112i	−0.100156	+	0.0768524i	−0.657625	−	0.753345i	$-0.728439\pi$
$3$	−0.173475	+	0.133112i	−0.100156	+	0.0768524i	0.557469	+	0.830197i	$0.311772\pi$
$4$	1.95728	+	0.411162i	0.978640	+	0.205581i
$5$	1.47800	+	1.13411i	0.660984	+	0.507191i	0.883917	−	0.467643i	$-0.154897\pi$
$5$	1.47800	+	1.13411i	0.660984	+	0.507191i	−0.222934	+	0.974834i	$0.571563\pi$
$6$	0.263472	−	0.161888i	0.107562	−	0.0660904i
$7$	1.10840	−	2.40238i	0.418935	−	0.908016i
$7$	1.10840	−	2.40238i	0.418935	−	0.908016i
$8$	−2.69310	−	0.864414i	−0.952155	−	0.305617i
$9$	−0.764082	+	2.85159i	−0.254694	+	0.950531i
$10$	−1.91327	−	1.81130i	−0.605030	−	0.572784i
$11$	1.05222	+	0.138528i	0.317258	+	0.0417678i	0.287473	−	0.957789i	$-0.407185\pi$
$11$	1.05222	+	0.138528i	0.317258	+	0.0417678i	0.0297841	+	0.999556i	$0.490518\pi$
$12$	−0.394270	+	0.189211i	−0.113816	+	0.0546207i
$13$	0.703557	+	0.291423i	0.195132	+	0.0808261i	0.478109	−	0.878300i	$-0.341322\pi$
$13$	0.703557	+	0.291423i	0.195132	+	0.0808261i	−0.282978	+	0.959126i	$0.591322\pi$
$14$	−1.91023	+	3.21730i	−0.510530	+	0.859860i
$15$	−0.407361			−0.105180
$16$	3.66189	+	1.60952i	0.915473	+	0.402379i
$17$	−1.08632	+	1.88157i	−0.263472	+	0.456347i	−0.967162	−	0.254160i	$-0.918201\pi$
$17$	−1.08632	+	1.88157i	−0.263472	+	0.456347i	0.703690	+	0.710507i	$0.251534\pi$
$18$	1.49155	−	3.89950i	0.351562	−	0.919121i
$19$	6.52551	−	0.859099i	1.49705	−	0.197091i	0.662936	−	0.748676i	$-0.269310\pi$
$19$	6.52551	−	0.859099i	1.49705	−	0.197091i	0.834118	+	0.551585i	$0.185977\pi$
$20$	2.42657	+	2.82748i	0.542597	+	0.632243i
$21$	0.127507	+	0.564295i	0.0278243	+	0.123139i
$22$	−1.45986	−	0.348642i	−0.311242	−	0.0743307i
$23$	5.38289	+	1.44234i	1.12241	+	0.300749i	0.771858	−	0.635795i	$-0.219328\pi$
$23$	5.38289	+	1.44234i	1.12241	+	0.300749i	0.350551	+	0.936544i	$0.385994\pi$
$24$	0.582250	−	0.208530i	0.118851	−	0.0425660i
$25$	−0.395810	−	1.47718i	−0.0791619	−	0.295436i
$26$	−0.947061	−	0.512752i	−0.185734	−	0.100559i
$27$	−0.498066	−	1.20244i	−0.0958529	−	0.231409i
$28$	3.15721	−	4.24641i	0.596658	−	0.802496i
$29$	3.35639	+	1.39026i	0.623266	+	0.258165i	0.671889	−	0.740652i	$-0.265483\pi$
$29$	3.35639	+	1.39026i	0.623266	+	0.258165i	−0.0486228	+	0.998817i	$0.515483\pi$
$30$	0.573011	+	0.0595359i	0.104617	+	0.0108697i
$31$	−1.61293	+	2.79368i	−0.289691	+	0.501759i	−0.973736	−	0.227680i	$-0.926886\pi$
$31$	−1.61293	+	2.79368i	−0.289691	+	0.501759i	0.684045	+	0.729440i	$0.260219\pi$
$32$	−4.91574	−	2.79920i	−0.868988	−	0.494833i
$33$	−0.200975	+	0.116033i	−0.0349852	+	0.0201987i
$34$	1.80306	−	2.48793i	0.309222	−	0.426676i
$35$	4.36279	−	2.29369i	0.737447	−	0.387704i
$36$	−2.66799	+	5.26721i	−0.444665	+	0.877868i
$37$	−0.905876	+	1.18056i	−0.148925	+	0.194083i	−0.861859	−	0.507149i	$-0.830699\pi$
$37$	−0.905876	+	1.18056i	−0.148925	+	0.194083i	0.712934	+	0.701232i	$0.247366\pi$
$38$	−9.30461	+	0.254741i	−1.50941	+	0.0413244i
$39$	−0.160842	+	0.0430974i	−0.0257553	+	0.00690110i
$40$	−3.00007	−	4.33189i	−0.474353	−	0.684932i
$41$	−5.49509	+	5.49509i	−0.858189	+	0.858189i	−0.991125	−	0.132935i	$-0.957560\pi$
$41$	−5.49509	+	5.49509i	−0.858189	+	0.858189i	0.132935	+	0.991125i	$0.457560\pi$
$42$	−0.0968849	−	0.812397i	−0.0149497	−	0.125356i
$43$	−3.23411	−	7.80783i	−0.493197	−	1.19068i	−0.953084	−	0.302706i	$-0.902110\pi$
$43$	−3.23411	−	7.80783i	−0.493197	−	1.19068i	0.459887	−	0.887978i	$-0.347890\pi$
$44$	2.00254	+	0.703772i	0.301894	+	0.106098i
$45$	−4.36335	+	3.34811i	−0.650449	+	0.499107i
$46$	−7.36099	−	2.81556i	−1.08532	−	0.415132i
$47$	−3.74457	+	2.16193i	−0.546202	+	0.315350i	−0.747589	−	0.664162i	$-0.768789\pi$
$47$	−3.74457	+	2.16193i	−0.546202	+	0.315350i	0.201387	+	0.979512i	$0.435455\pi$
$48$	−0.849494	+	0.208231i	−0.122614	+	0.0300556i
$49$	−4.54291	−	5.32560i	−0.648987	−	0.760800i
$50$	0.340872	+	2.13571i	0.0482066	+	0.302035i
$51$	−0.0620094	−	0.471008i	−0.00868306	−	0.0659544i
$52$	1.25724	+	0.859672i	0.174347	+	0.119215i
$53$	0.309904	−	2.35395i	0.0425685	−	0.323340i	−0.956890	−	0.290449i	$-0.906195\pi$
$53$	0.309904	−	2.35395i	0.0425685	−	0.323340i	0.999459	−	0.0328909i	$-0.0104714\pi$
$54$	0.524864	+	1.76419i	0.0714249	+	0.240076i
$55$	1.39809	+	1.39809i	0.188518	+	0.188518i
$56$	−5.06168	+	5.51175i	−0.676396	+	0.736538i
$57$	−1.01766	+	1.01766i	−0.134792	+	0.134792i
$58$	−4.51805	−	2.44614i	−0.593249	−	0.321194i
$59$	−11.0715	−	1.45759i	−1.44139	−	0.189763i	−0.631059	−	0.775735i	$-0.717380\pi$
$59$	−11.0715	−	1.45759i	−1.44139	−	0.189763i	−0.810331	+	0.585972i	$0.800713\pi$
$60$	−0.797320	−	0.167491i	−0.102934	−	0.0216230i
$61$	9.02225	−	1.18780i	1.15518	−	0.152082i	0.471502	−	0.881865i	$-0.343712\pi$
$61$	9.02225	−	1.18780i	1.15518	−	0.152082i	0.683679	+	0.729783i	$0.260379\pi$
$62$	2.67711	−	3.69397i	0.339994	−	0.469135i
$63$	6.00372	+	4.99632i	0.756398	+	0.629477i
$64$	6.50558	+	4.65591i	0.813197	+	0.581988i
$65$	0.709354	+	1.22864i	0.0879845	+	0.152394i
$66$	0.299657	−	0.133844i	0.0368853	−	0.0164751i
$67$	−8.67775	−	11.3091i	−1.06016	−	1.38162i	−0.920193	−	0.391465i	$-0.871968\pi$
$67$	−8.67775	−	11.3091i	−1.06016	−	1.38162i	−0.139963	−	0.990157i	$-0.544698\pi$
$68$	−2.89987	+	3.23610i	−0.351661	+	0.392435i
$69$	−1.12579	+	0.466317i	−0.135529	+	0.0561380i
$70$	−6.47211	+	2.58877i	−0.773565	+	0.309417i
$71$	−6.36946	−	6.36946i	−0.755916	−	0.755916i	0.219660	−	0.975576i	$-0.429505\pi$
$71$	−6.36946	−	6.36946i	−0.755916	−	0.755916i	−0.975576	+	0.219660i	$0.929505\pi$
$72$	4.52271	−	7.01915i	0.533006	−	0.827214i
$73$	−1.49265	−	5.57066i	−0.174702	−	0.651996i	−0.996602	−	0.0823649i	$-0.973753\pi$
$73$	−1.49265	−	5.57066i	−0.174702	−	0.651996i	0.821900	−	0.569631i	$-0.192914\pi$
$74$	1.44678	−	1.52823i	0.168185	−	0.177653i
$75$	0.265294	+	0.203567i	0.0306335	+	0.0235059i
$76$	13.1255	+	1.00154i	1.50560	+	0.114885i
$77$	1.49908	−	2.37430i	0.170836	−	0.270577i
$78$	0.232545	−	0.0371155i	0.0263305	−	0.00420251i
$79$	1.44180	+	2.49727i	0.162215	+	0.280965i	0.935663	−	0.352895i	$-0.114803\pi$
$79$	1.44180	+	2.49727i	0.162215	+	0.280965i	−0.773448	+	0.633860i	$0.781469\pi$
$80$	3.58692	+	6.53187i	0.401030	+	0.730286i
$81$	−7.42355	−	4.28599i	−0.824839	−	0.476221i
$82$	8.53273	−	6.92652i	0.942283	−	0.764906i
$83$	1.66109	−	4.01022i	0.182328	−	0.440179i	−0.806118	−	0.591755i	$-0.798435\pi$
$83$	1.66109	−	4.01022i	0.182328	−	0.440179i	0.988445	+	0.151577i	$0.0484351\pi$
$84$	0.0175504	+	1.15691i	0.00191491	+	0.126229i
$85$	−3.73950	+	1.54895i	−0.405606	+	0.168007i
$86$	3.40812	+	11.4555i	0.367507	+	1.23528i
$87$	−0.767311	+	0.205600i	−0.0822644	+	0.0220427i
$88$	−2.71400	−	1.28263i	−0.289313	−	0.136729i
$89$	−4.81344	+	17.9640i	−0.510223	+	1.90418i	−0.0922050	+	0.995740i	$0.529392\pi$
$89$	−4.81344	+	17.9640i	−0.510223	+	1.90418i	−0.418018	+	0.908439i	$0.637275\pi$
$90$	6.62699	−	4.07189i	0.698546	−	0.429215i
$91$	1.47993	−	1.36720i	0.155139	−	0.143322i
$92$	9.94278	+	5.03630i	1.03661	+	0.525071i
$93$	−0.0920691	−	0.699334i	−0.00954712	−	0.0725176i
$94$	5.58324	−	2.49379i	0.575867	−	0.257215i
$95$	10.6190	+	6.13091i	1.08949	+	0.629018i
$96$	1.22537	−	0.168753i	0.125063	−	0.0172233i
$97$			13.3638i			1.35689i	0.734653	+	0.678443i	$0.237345\pi$
$97$			13.3638i			1.35689i	−0.734653	+	0.678443i	$0.762655\pi$
$98$	5.61190	+	8.15515i	0.566888	+	0.823795i
$99$	−1.19901	+	2.89467i	−0.120505	+	0.290925i
$100$	−0.167350	−	3.05400i	−0.0167350	−	0.305400i
$101$	1.11911	−	8.50045i	0.111355	−	0.845826i	−0.841043	−	0.540969i	$-0.818058\pi$
$101$	1.11911	−	8.50045i	0.111355	−	0.845826i	0.952398	−	0.304858i	$-0.0986089\pi$
$102$	0.0183871	+	0.671602i	0.00182059	+	0.0664986i
$103$	−6.88515	−	1.84487i	−0.678414	−	0.181780i	−0.0968718	−	0.995297i	$-0.530884\pi$
$103$	−6.88515	−	1.84487i	−0.678414	−	0.181780i	−0.581542	+	0.813516i	$0.697550\pi$
$104$	−1.64284	−	1.39300i	−0.161094	−	0.136594i
$105$	−0.451519	+	0.978639i	−0.0440637	+	0.0955054i
$106$	−0.779954	+	3.26587i	−0.0757558	+	0.317210i
$107$	4.31090	−	5.61808i	0.416751	−	0.543120i	−0.537054	−	0.843548i	$-0.680463\pi$
$107$	4.31090	−	5.61808i	0.416751	−	0.543120i	0.953805	+	0.300428i	$0.0971294\pi$
$108$	−0.480458	−	2.55829i	−0.0462321	−	0.246172i
$109$	8.17975	+	10.6601i	0.783478	+	1.02105i	0.999007	+	0.0445510i	$0.0141857\pi$
$109$	8.17975	+	10.6601i	0.783478	+	1.02105i	−0.215529	+	0.976497i	$0.569148\pi$
$110$	−1.76228	−	2.17094i	−0.168026	−	0.206991i
$111$		−	0.325381i		−	0.0308838i
$112$	7.92552	−	7.01329i	0.748891	−	0.662693i
$113$		−	16.5069i		−	1.55284i	−0.630217	−	0.776419i	$-0.717034\pi$
$113$		−	16.5069i		−	1.55284i	0.630217	−	0.776419i	$-0.282966\pi$
$114$	1.58021	−	1.28275i	0.148000	−	0.120140i
$115$	6.32015	+	8.23658i	0.589357	+	0.768065i
$116$	5.99777	+	4.10115i	0.556879	+	0.380783i
$117$	−1.36859	+	1.78359i	−0.126527	+	0.164893i
$118$	15.3606	+	3.66842i	1.41406	+	0.337705i
$119$	3.31617	+	4.69529i	0.303993	+	0.430417i
$120$	1.09706	+	0.352129i	0.100148	+	0.0321448i
$121$	−9.53720	−	2.55548i	−0.867018	−	0.232317i
$122$	−12.8647	+	0.352208i	−1.16471	+	0.0318874i
$123$	0.221798	−	1.68473i	0.0199989	−	0.151907i
$124$	−4.30561	+	4.80484i	−0.386655	+	0.431487i
$125$	4.65495	−	11.2380i	0.416351	−	1.00516i
$126$	−7.71487	−	7.90548i	−0.687295	−	0.704276i
$127$			6.44988i			0.572334i	0.958180	+	0.286167i	$0.0923813\pi$
$127$			6.44988i			0.572334i	−0.958180	+	0.286167i	$0.907619\pi$
$128$	−8.47055	−	7.49998i	−0.748698	−	0.662911i
$129$	1.60036	+	0.923966i	0.140903	+	0.0813507i
$130$	−0.818241	−	1.83192i	−0.0717645	−	0.160670i
$131$	−0.492346	−	3.73974i	−0.0430165	−	0.326743i	−0.999400	−	0.0346293i	$-0.988975\pi$
$131$	−0.492346	−	3.73974i	−0.0430165	−	0.326743i	0.956384	−	0.292113i	$-0.0943584\pi$
$132$	−0.441072	+	0.144475i	−0.0383904	+	0.0125750i
$133$	5.16897	−	16.6290i	0.448207	−	1.44192i
$134$	10.5537	+	17.1761i	0.911697	+	1.48378i
$135$	0.627556	−	2.34207i	0.0540114	−	0.201573i
$136$	4.55203	−	4.12822i	0.390334	−	0.353992i
$137$	7.33664	−	1.96585i	0.626812	−	0.167954i	0.0685892	−	0.997645i	$-0.478150\pi$
$137$	7.33664	−	1.96585i	0.626812	−	0.167954i	0.558223	+	0.829691i	$0.311484\pi$
$138$	1.65174	−	0.491407i	0.140605	−	0.0418313i
$139$	−11.9800	+	4.96229i	−1.01613	+	0.420896i	−0.827689	−	0.561187i	$-0.810345\pi$
$139$	−11.9800	+	4.96229i	−1.01613	+	0.420896i	−0.188445	+	0.982084i	$0.560345\pi$
$140$	9.48229	−	2.69557i	0.801399	−	0.227818i
$141$	0.361811	−	0.873490i	0.0304700	−	0.0735611i
$142$	8.02865	+	9.89045i	0.673749	+	0.829988i
$143$	0.699929	+	0.404104i	0.0585310	+	0.0337929i
$144$	−7.38768	+	9.21243i	−0.615640	+	0.767702i
$145$	3.38405	+	5.86134i	0.281030	+	0.486758i
$146$	1.28548	+	8.05407i	0.106387	+	0.666559i
$147$	1.49698	+	0.319143i	0.123469	+	0.0263225i
$148$	−2.25845	+	1.93823i	−0.185644	+	0.159321i
$149$	−8.40071	−	6.44609i	−0.688213	−	0.528084i	0.204412	−	0.978885i	$-0.434472\pi$
$149$	−8.40071	−	6.44609i	−0.688213	−	0.528084i	−0.892625	+	0.450801i	$0.851138\pi$
$150$	−0.343422	−	0.325119i	−0.0280403	−	0.0265458i
$151$	−2.02511	−	7.55780i	−0.164801	−	0.615045i	−0.998066	−	0.0621708i	$-0.980198\pi$
$151$	−2.02511	−	7.55780i	−0.164801	−	0.615045i	0.833265	−	0.552874i	$-0.186469\pi$
$152$	−18.3165	−	3.32710i	−1.48566	−	0.269863i
$153$	−4.53543	−	4.53543i	−0.366668	−	0.366668i
$154$	−2.45567	+	3.12070i	−0.197884	+	0.251473i
$155$	−5.55226	+	2.29982i	−0.445969	+	0.184726i
$156$	−0.332532	+	0.0182217i	−0.0266239	+	0.00145891i
$157$	14.5146	+	18.9158i	1.15839	+	1.50964i	0.823438	+	0.567407i	$0.192053\pi$
$157$	14.5146	+	18.9158i	1.15839	+	1.50964i	0.334952	+	0.942235i	$0.391280\pi$
$158$	−1.66312	−	3.72349i	−0.132311	−	0.296225i
$159$	0.259579	+	0.449604i	0.0205860	+	0.0356559i
$160$	−4.09087	−	9.71223i	−0.323412	−	0.767819i
$161$	9.43144	−	11.3331i	0.743301	−	0.893171i
$162$	9.81587	+	7.11380i	0.771208	+	0.558913i
$163$	7.34767	−	0.967339i	0.575514	−	0.0757679i	0.162850	−	0.986651i	$-0.447931\pi$
$163$	7.34767	−	0.967339i	0.575514	−	0.0757679i	0.412665	+	0.910883i	$0.364598\pi$
$164$	−13.0148	+	8.49606i	−1.01629	+	0.663431i
$165$	−0.428636	−	0.0564309i	−0.0333692	−	0.00439314i
$166$	−2.92265	+	5.39817i	−0.226841	+	0.418979i
$167$	−9.63495	+	9.63495i	−0.745575	+	0.745575i	−0.973645	−	0.228070i	$-0.926758\pi$
$167$	−9.63495	+	9.63495i	−0.745575	+	0.745575i	0.228070	+	0.973645i	$0.426758\pi$
$168$	0.144395	−	1.62992i	0.0111404	−	0.125751i
$169$	−8.78232	−	8.78232i	−0.675563	−	0.675563i
$170$	5.48652	−	1.63229i	0.420797	−	0.125191i
$171$	−2.53622	+	19.2645i	−0.193950	+	1.47319i
$172$	−3.11978	−	16.6119i	−0.237881	−	1.26664i
$173$	0.942514	+	7.15910i	0.0716580	+	0.544296i	0.989191	+	0.146636i	$0.0468445\pi$
$173$	0.942514	+	7.15910i	0.0716580	+	0.544296i	−0.917533	+	0.397661i	$0.869822\pi$
$174$	1.10938	−	0.177063i	0.0841019	−	0.0134231i
$175$	−3.98747	−	0.686418i	−0.301425	−	0.0518884i
$176$	3.63017	+	2.20085i	0.273634	+	0.165895i
$177$	2.11466	−	1.22090i	0.158948	−	0.0917684i
$178$	9.39622	−	24.5654i	0.704276	−	1.84125i
$179$	−1.70356	+	1.30719i	−0.127330	+	0.0977040i	−0.670463	−	0.741943i	$-0.733905\pi$
$179$	−1.70356	+	1.30719i	−0.127330	+	0.0977040i	0.543133	+	0.839647i	$0.317238\pi$
$180$	−9.91691	+	4.75916i	−0.739163	+	0.354726i
$181$	2.43012	+	5.86684i	0.180630	+	0.436079i	0.988097	−	0.153834i	$-0.0491622\pi$
$181$	2.43012	+	5.86684i	0.180630	+	0.436079i	−0.807467	+	0.589913i	$0.799162\pi$
$182$	−2.28155	+	1.70687i	−0.169120	+	0.126522i
$183$	−1.40703	+	1.40703i	−0.104010	+	0.104010i
$184$	−13.2499	−	8.53741i	−0.976793	−	0.629386i
$185$	−2.67778	+	0.717508i	−0.196874	+	0.0527522i
$186$	0.0273004	+	0.997169i	0.00200176	+	0.0731160i
$187$	−1.40371	+	1.82935i	−0.102649	+	0.133775i
$188$	−8.21809	+	2.69188i	−0.599365	+	0.196325i
$189$	−3.44077	−	0.136234i	−0.250279	−	0.00990954i
$190$	−14.0412	−	10.1760i	−1.01865	−	0.738242i
$191$	−6.96557	+	4.02157i	−0.504011	+	0.290991i	−0.730368	−	0.683054i	$-0.760652\pi$
$191$	−6.96557	+	4.02157i	−0.504011	+	0.290991i	0.226358	+	0.974044i	$0.427318\pi$
$192$	−1.74831	+	0.0582872i	−0.126174	+	0.00420652i
$193$	4.92946	−	8.53807i	0.354830	−	0.614584i	−0.632259	−	0.774757i	$-0.717872\pi$
$193$	4.92946	−	8.53807i	0.354830	−	0.614584i	0.987089	+	0.160173i	$0.0512053\pi$
$194$	1.95312	−	18.7980i	0.140226	−	1.34962i
$195$	−0.286602	−	0.118714i	−0.0205240	−	0.00850131i
$196$	−6.70206	−	12.2916i	−0.478718	−	0.877968i
$197$	−8.47003	−	20.4485i	−0.603465	−	1.45689i	−0.869992	−	0.493065i	$-0.835876\pi$
$197$	−8.47003	−	20.4485i	−0.603465	−	1.45689i	0.266527	−	0.963827i	$-0.414124\pi$
$198$	2.10964	−	3.89653i	0.149925	−	0.276914i
$199$	1.84892	+	6.90027i	0.131067	+	0.489147i	0.999983	−	0.00581151i	$-0.00184987\pi$
$199$	1.84892	+	6.90027i	0.131067	+	0.489147i	−0.868917	+	0.494959i	$0.835183\pi$
$200$	−0.210942	+	4.32034i	−0.0149158	+	0.305494i
$201$	3.01075	+	0.806728i	0.212362	+	0.0569022i
$202$	−2.81652	+	11.7935i	−0.198170	+	0.829790i
$203$	7.06016	−	6.52238i	0.495526	−	0.457781i
$204$	0.0722908	−	0.947391i	0.00506137	−	0.0663306i
$205$	−14.3538	+	1.88972i	−1.00251	+	0.131984i
$206$	9.41530	+	3.60133i	0.655995	+	0.250917i
$207$	−8.22593	+	14.2477i	−0.571742	+	0.990286i
$208$	2.10730	+	2.19955i	0.146115	+	0.152511i
$209$	6.98531			0.483184
$210$	0.778153	−	1.31060i	0.0536977	−	0.0904403i
$211$	14.4197	+	5.97285i	0.992696	+	0.411188i	0.819114	−	0.573631i	$-0.194466\pi$
$211$	14.4197	+	5.97285i	0.992696	+	0.411188i	0.173582	+	0.984819i	$0.444466\pi$
$212$	1.57442	−	4.47992i	0.108132	−	0.307682i
$213$	1.95280	+	0.257091i	0.133803	+	0.0176156i
$214$	−6.88498	+	7.27258i	−0.470647	+	0.497144i
$215$	4.07493	−	15.2079i	0.277908	−	1.03717i
$216$	0.301938	+	3.66882i	0.0205443	+	0.249632i
$217$	4.92372	+	6.97139i	0.334244	+	0.473249i
$218$	−9.94801	−	16.1904i	−0.673764	−	1.09655i
$219$	1.00046	+	0.767680i	0.0676049	+	0.0518750i
$220$	2.16161	+	3.31129i	0.145735	+	0.223247i
$221$	−1.31262	+	1.00721i	−0.0882965	+	0.0677523i
$222$	−0.0475545	+	0.457694i	−0.00319165	+	0.0307184i
$223$	−25.5426			−1.71046			−0.855228	−	0.518252i	$-0.826583\pi$
$223$	−25.5426			−1.71046			−0.855228	+	0.518252i	$0.826583\pi$
$224$	−12.1734	+	8.70687i	−0.813366	+	0.581752i
$225$	4.51475			0.300984
$226$	−2.41249	+	23.2193i	−0.160476	+	1.54452i
$227$	−4.89788	+	3.75828i	−0.325084	+	0.249446i	−0.758390	−	0.651801i	$-0.774014\pi$
$227$	−4.89788	+	3.75828i	−0.325084	+	0.249446i	0.433306	+	0.901247i	$0.357347\pi$
$228$	−2.41026	+	1.57342i	−0.159623	+	0.104202i
$229$	10.1079	+	7.75606i	0.667949	+	0.512535i	0.886168	−	0.463365i	$-0.153358\pi$
$229$	10.1079	+	7.75606i	0.667949	+	0.512535i	−0.218219	+	0.975900i	$0.570025\pi$
$230$	−7.68641	−	12.5096i	−0.506827	−	0.824859i
$231$	0.0559954	+	0.611429i	0.00368423	+	0.0402291i
$232$	−7.83733	−	6.64543i	−0.514546	−	0.436294i
$233$	−1.14934	+	4.28939i	−0.0752956	+	0.281007i	−0.993300	−	0.115563i	$-0.963133\pi$
$233$	−1.14934	+	4.28939i	−0.0752956	+	0.281007i	0.918005	+	0.396570i	$0.129800\pi$
$234$	2.18579	−	2.30885i	0.142890	−	0.150934i
$235$	−7.98637	−	1.05143i	−0.520973	−	0.0685875i
$236$	−21.0708	−	7.40511i	−1.37159	−	0.482032i
$237$	−0.582534	−	0.241294i	−0.0378397	−	0.0156737i
$238$	−3.97845	−	7.08926i	−0.257884	−	0.459528i
$239$	23.1811			1.49946			0.749732	−	0.661742i	$-0.230182\pi$
$239$	23.1811			1.49946			0.749732	+	0.661742i	$0.230182\pi$
$240$	−1.49171	−	0.655655i	−0.0962897	−	0.0423224i
$241$	10.2504	−	17.7543i	0.660289	−	1.14365i	−0.320251	−	0.947333i	$-0.603767\pi$
$241$	10.2504	−	17.7543i	0.660289	−	1.14365i	0.980540	−	0.196321i	$-0.0628995\pi$
$242$	13.0419	+	4.98851i	0.838367	+	0.320674i
$243$	5.72944	−	0.754295i	0.367544	−	0.0483881i
$244$	18.1474	+	1.38474i	1.16177	+	0.0886491i
$245$	−0.674607	−	13.0234i	−0.0430990	−	0.832036i
$246$	−0.558214	+	2.33739i	−0.0355904	+	0.149026i
$247$	4.84143	+	1.29726i	0.308053	+	0.0825425i
$248$	6.75868	−	6.12941i	0.429177	−	0.389218i
$249$	0.245652	+	0.916784i	0.0155675	+	0.0580988i
$250$	−8.19028	+	15.1276i	−0.517999	+	0.956751i
$251$	2.81170	+	6.78803i	0.177473	+	0.428457i	0.987435	−	0.158025i	$-0.0505126\pi$
$251$	2.81170	+	6.78803i	0.177473	+	0.428457i	−0.809963	+	0.586482i	$0.800513\pi$
$252$	9.69666	+	12.2477i	0.610832	+	0.771533i
$253$	5.46420	+	2.26335i	0.343531	+	0.142295i
$254$	0.942651	−	9.07267i	0.0591472	−	0.569270i
$255$	0.442526	−	0.766478i	0.0277121	−	0.0479987i
$256$	10.8189	+	11.7878i	0.676182	+	0.736735i
$257$	9.30315	−	5.37118i	0.580315	−	0.335045i	−0.180944	−	0.983493i	$-0.557915\pi$
$257$	9.30315	−	5.37118i	0.580315	−	0.335045i	0.761258	+	0.648449i	$0.224582\pi$
$258$	−2.11609	−	1.53358i	−0.131742	−	0.0954766i
$259$	1.83209	+	3.48479i	0.113840	+	0.216534i
$260$	0.883236	+	2.69645i	0.0547760	+	0.167227i
$261$	−6.52902	+	8.50879i	−0.404136	+	0.526681i
$262$	0.145991	+	5.33243i	0.00901934	+	0.329439i
$263$	24.6294	−	6.59942i	1.51871	−	0.406938i	0.599395	−	0.800453i	$-0.295408\pi$
$263$	24.6294	−	6.59942i	1.51871	−	0.406938i	0.919318	+	0.393516i	$0.128741\pi$
$264$	0.641545	−	0.138762i	0.0394844	−	0.00854024i
$265$	3.12769	−	3.12769i	0.192132	−	0.192132i
$266$	−9.70123	+	22.6356i	−0.594820	+	1.38788i
$267$	−1.55621	−	3.75703i	−0.0952387	−	0.229927i
$268$	−12.3349	−	25.7030i	−0.753476	−	1.57006i
$269$	21.3128	−	16.3539i	1.29946	−	0.997112i	0.300399	−	0.953814i	$-0.402880\pi$
$269$	21.3128	−	16.3539i	1.29946	−	0.997112i	0.999062	−	0.0432984i	$-0.0137866\pi$
$270$	−1.22504	+	3.20274i	−0.0745536	+	0.194912i
$271$	9.38593	−	5.41897i	0.570155	−	0.329179i	−0.187056	−	0.982349i	$-0.559895\pi$
$271$	9.38593	−	5.41897i	0.570155	−	0.329179i	0.757211	+	0.653170i	$0.226561\pi$
$272$	−7.00642	+	5.14164i	−0.424826	+	0.311758i
$273$	−0.0747401	+	0.434172i	−0.00452347	+	0.0262773i
$274$	−10.6073	+	1.69299i	−0.640813	+	0.102277i
$275$	−0.211850	−	1.60916i	−0.0127750	−	0.0970358i
$276$	−2.39522	+	0.449832i	−0.144175	+	0.0270767i
$277$	−3.70935	+	28.1753i	−0.222873	+	1.69289i	0.404795	+	0.914407i	$0.367343\pi$
$277$	−3.70935	+	28.1753i	−0.222873	+	1.69289i	−0.627668	+	0.778481i	$0.715991\pi$
$278$	17.5769	−	5.22928i	1.05419	−	0.313632i
$279$	−6.73402	−	6.73402i	−0.403155	−	0.403155i
$280$	−13.7321	+	2.40587i	−0.820652	+	0.143778i
$281$	3.29965	−	3.29965i	0.196841	−	0.196841i	−0.601804	−	0.798644i	$-0.705551\pi$
$281$	3.29965	−	3.29965i	0.196841	−	0.196841i	0.798644	+	0.601804i	$0.205551\pi$
$282$	−0.636600	+	1.17581i	−0.0379090	+	0.0700184i
$283$	−15.9930	−	2.10551i	−0.950684	−	0.125160i	−0.360796	−	0.932645i	$-0.617495\pi$
$283$	−15.9930	−	2.10551i	−0.950684	−	0.125160i	−0.589888	+	0.807485i	$0.700828\pi$
$284$	−9.84794	−	15.0857i	−0.584368	−	0.895172i
$285$	−2.65824	+	0.349964i	−0.157461	+	0.0207301i
$286$	−0.925490	−	0.670725i	−0.0547254	−	0.0396608i
$287$	7.11058	+	19.2921i	0.419724	+	1.13878i
$288$	11.7382	−	11.8789i	0.691681	−	0.699969i
$289$	6.13980	+	10.6344i	0.361165	+	0.625556i
$290$	−3.90350	−	8.73938i	−0.229222	−	0.513194i
$291$	−1.77888	−	2.31828i	−0.104280	−	0.135900i
$292$	−0.631099	−	11.5171i	−0.0369323	−	0.673985i
$293$	−7.82593	+	3.24161i	−0.457196	+	0.189377i	−0.599382	−	0.800463i	$-0.704587\pi$
$293$	−7.82593	+	3.24161i	−0.457196	+	0.189377i	0.142186	+	0.989840i	$0.454587\pi$
$294$	−2.05908	−	0.667704i	−0.120088	−	0.0389413i
$295$	−14.7107	−	14.7107i	−0.856490	−	0.856490i
$296$	3.46011	−	2.39631i	0.201115	−	0.139283i
$297$	−0.357506	−	1.33423i	−0.0207446	−	0.0774199i
$298$	10.8747	+	10.2951i	0.629954	+	0.596379i
$299$	3.36684	+	2.58346i	0.194709	+	0.149406i
$300$	0.435556	+	0.507517i	0.0251468	+	0.0293015i
$301$	−22.3421	−	0.884611i	−1.28778	−	0.0509881i
$302$	1.74402	+	10.9271i	0.100357	+	0.628783i
$303$	0.937376	+	1.62358i	0.0538509	+	0.0932724i
$304$	25.2784	+	7.35699i	1.44982	+	0.421952i
$305$	14.6820	+	8.47667i	0.840690	+	0.485373i
$306$	5.71687	+	7.04257i	0.326812	+	0.402597i
$307$	−3.81023	+	9.19871i	−0.217461	+	0.524998i	−0.994534	−	0.104413i	$-0.966704\pi$
$307$	−3.81023	+	9.19871i	−0.217461	+	0.524998i	0.777073	+	0.629411i	$0.216704\pi$
$308$	3.91034	−	4.03081i	0.222813	−	0.229677i
$309$	1.43998	−	0.596458i	0.0819174	−	0.0339313i
$310$	8.14617	−	2.42356i	0.462671	−	0.137649i
$311$	19.7404	−	5.28942i	1.11937	−	0.299935i	0.348744	−	0.937218i	$-0.386608\pi$
$311$	19.7404	−	5.28942i	1.11937	−	0.299935i	0.770630	+	0.637283i	$0.219942\pi$
$312$	0.470416	+	0.0229682i	0.0266321	+	0.00130032i
$313$	−3.94175	+	14.7108i	−0.222801	+	0.831503i	0.760473	+	0.649369i	$0.224967\pi$
$313$	−3.94175	+	14.7108i	−0.222801	+	0.831503i	−0.983274	+	0.182134i	$0.941700\pi$
$314$	−17.6523	−	28.7290i	−0.996175	−	1.62127i
$315$	3.20713	+	14.1935i	0.180701	+	0.799712i
$316$	1.79523	+	5.48068i	0.100989	+	0.308312i
$317$	−0.924503	−	7.02230i	−0.0519253	−	0.394412i	−0.997597	−	0.0692877i	$-0.977927\pi$
$317$	−0.924503	−	7.02230i	−0.0519253	−	0.394412i	0.945671	−	0.325124i	$-0.105406\pi$
$318$	−0.299425	−	0.670369i	−0.0167909	−	0.0375924i
$319$	3.33909	+	1.92782i	0.186953	+	0.107937i
$320$	4.33495	+	14.2595i	0.242331	+	0.797131i
$321$			1.54843i			0.0864250i
$322$	−14.9230	+	14.5632i	−0.831625	+	0.811574i
$323$	−5.47236	+	13.2114i	−0.304490	+	0.735105i
$324$	−12.7677	−	11.4412i	−0.709318	−	0.635620i
$325$	0.152010	−	1.15463i	0.00843199	−	0.0640473i
$326$	−10.4769	+	0.286836i	−0.580263	+	0.0158864i
$327$	−2.83797	−	0.760431i	−0.156940	−	0.0420519i
$328$	19.5489	−	10.0488i	1.07941	−	0.554852i
$329$	1.04331	+	11.3922i	0.0575196	+	0.628072i
$330$	0.594689	+	0.142023i	0.0327366	+	0.00781812i
$331$	9.37391	−	12.2163i	0.515236	−	0.671469i	−0.461195	−	0.887299i	$-0.652579\pi$
$331$	9.37391	−	12.2163i	0.515236	−	0.671469i	0.976431	+	0.215830i	$0.0692456\pi$
$332$	4.90006	−	7.16615i	0.268926	−	0.393293i
$333$	−2.67431	−	3.48523i	−0.146552	−	0.190990i
$334$	14.9611	−	12.1448i	0.818633	−	0.664532i
$335$		−	26.5564i		−	1.45093i
$336$	−0.441326	+	2.27161i	−0.0240763	+	0.123927i
$337$			29.9698i			1.63256i	0.577657	+	0.816280i	$0.303967\pi$
$337$			29.9698i			1.63256i	−0.577657	+	0.816280i	$0.696033\pi$
$338$	11.0700	+	13.6371i	0.602131	+	0.741761i
$339$	2.19727	+	2.86354i	0.119339	+	0.155526i
$340$	−7.95612	+	1.49419i	−0.431481	+	0.0810340i
$341$	−2.08417	+	2.71614i	−0.112864	+	0.147087i
$342$	6.38307	−	26.7276i	0.345157	−	1.44526i
$343$	−17.8295	+	5.01093i	−0.962702	+	0.270565i
$344$	1.96058	+	23.8229i	0.105708	+	1.28444i
$345$	−2.19278	−	0.587553i	−0.118055	−	0.0316328i
$346$	−0.279475	−	10.2080i	−0.0150247	−	0.548787i
$347$	−2.52430	+	19.1739i	−0.135511	+	1.02931i	0.779648	+	0.626219i	$0.215398\pi$
$347$	−2.52430	+	19.1739i	−0.135511	+	1.02931i	−0.915159	+	0.403093i	$0.867935\pi$
$348$	−1.58638	+	0.0869286i	−0.0850388	+	0.00465986i
$349$	6.67797	−	16.1220i	0.357463	−	0.862993i	−0.638192	−	0.769877i	$-0.720317\pi$
$349$	6.67797	−	16.1220i	0.357463	−	0.862993i	0.995655	−	0.0931157i	$-0.0296826\pi$
$350$	5.50862	+	1.54831i	0.294448	+	0.0827609i
$351$		−	0.991131i		−	0.0529027i
$352$	−4.78469	−	3.62635i	−0.255025	−	0.193285i
$353$	−28.8140	−	16.6357i	−1.53361	−	0.885431i	−0.999191	−	0.0402132i	$-0.987196\pi$
$353$	−28.8140	−	16.6357i	−1.53361	−	0.885431i	−0.534421	−	0.845218i	$-0.679470\pi$
$354$	−3.15300	+	1.40831i	−0.167580	+	0.0748508i
$355$	−2.19041	−	16.6378i	−0.116255	−	0.883042i
$356$	−16.8073	+	33.1815i	−0.890788	+	1.75861i
$357$	−1.20027	−	0.373094i	−0.0635253	−	0.0197462i
$358$	2.58735	−	1.58977i	0.136746	−	0.0840221i
$359$	0.751836	−	2.80589i	0.0396804	−	0.148089i	−0.943243	−	0.332102i	$-0.892242\pi$
$359$	0.751836	−	2.80589i	0.0396804	−	0.148089i	0.982924	+	0.184013i	$0.0589088\pi$
$360$	14.6451	−	5.24507i	0.771864	−	0.276439i
$361$	23.4916	−	6.29456i	1.23640	−	0.331293i
$362$	−2.56087	−	8.60770i	−0.134596	−	0.452411i
$363$	1.99463	−	0.826204i	0.104691	−	0.0433645i
$364$	3.45878	−	2.06751i	0.181289	−	0.108367i
$365$	4.11161	−	9.92629i	0.215211	−	0.519566i
$366$	2.18482	−	1.77354i	0.114202	−	0.0927046i
$367$	−25.6630	−	14.8165i	−1.33960	−	0.773416i	−0.352849	−	0.935680i	$-0.614787\pi$
$367$	−25.6630	−	14.8165i	−1.33960	−	0.773416i	−0.986747	+	0.162264i	$0.948120\pi$
$368$	17.3901	+	13.9455i	0.906520	+	0.726962i
$369$	−11.4711	−	19.8685i	−0.597160	−	1.03431i
$370$	3.87154	−	0.617919i	0.201272	−	0.0321241i
$371$	−5.31160	−	3.35362i	−0.275765	−	0.174111i
$372$	0.107335	−	1.40665i	0.00556504	−	0.0729313i
$373$	1.70909	+	1.31143i	0.0884931	+	0.0679032i	0.652060	−	0.758167i	$-0.273905\pi$
$373$	1.70909	+	1.31143i	0.0884931	+	0.0679032i	−0.563567	+	0.826070i	$0.690571\pi$
$374$	2.24187	−	2.36808i	0.115924	−	0.122451i
$375$	0.688402	+	2.56915i	0.0355489	+	0.132670i
$376$	11.9533	−	2.58543i	0.616445	−	0.133334i
$377$	1.95626	+	1.95626i	0.100752	+	0.100752i
$378$	4.82002	+	0.694502i	0.247915	+	0.0357213i
$379$	−3.75147	+	1.55391i	−0.192700	+	0.0798191i	−0.476947	−	0.878932i	$-0.658257\pi$
$379$	−3.75147	+	1.55391i	−0.192700	+	0.0798191i	0.284247	+	0.958751i	$0.408257\pi$
$380$	18.2637	+	16.3661i	0.936906	+	0.839561i
$381$	−0.858558	−	1.11889i	−0.0439853	−	0.0573227i
$382$	10.3858	−	4.63889i	0.531384	−	0.237346i
$383$	−5.73886	−	9.94000i	−0.293242	−	0.507910i	0.681332	−	0.731974i	$-0.261401\pi$
$383$	−5.73886	−	9.94000i	−0.293242	−	0.507910i	−0.974574	+	0.224064i	$0.928068\pi$
$384$	2.46777	+	0.173527i	0.125933	+	0.00885527i
$385$	4.90838	−	1.80910i	0.250154	−	0.0922005i
$386$	−8.18182	+	11.2896i	−0.416444	+	0.574624i
$387$	24.7359	−	3.25654i	1.25740	−	0.165539i
$388$	−5.49467	+	26.1566i	−0.278950	+	1.32790i
$389$	−28.9880	−	3.81634i	−1.46975	−	0.193496i	−0.647257	−	0.762272i	$-0.724084\pi$
$389$	−28.9880	−	3.81634i	−1.46975	−	0.193496i	−0.822492	+	0.568776i	$0.807417\pi$
$390$	0.385796	+	0.208875i	0.0195355	+	0.0105768i
$391$	−8.56142	+	8.56142i	−0.432969	+	0.432969i
$392$	7.63098	+	18.2693i	0.385423	+	0.922740i
$393$	0.583215	+	0.583215i	0.0294193	+	0.0294193i
$394$	8.92575	+	30.0016i	0.449673	+	1.51146i
$395$	−0.701200	+	5.32615i	−0.0352812	+	0.267987i
$396$	−3.53698	+	5.17269i	−0.177740	+	0.259938i
$397$	0.503980	+	3.82810i	0.0252940	+	0.192127i	0.999427	−	0.0338485i	$-0.0107764\pi$
$397$	0.503980	+	3.82810i	0.0252940	+	0.192127i	−0.974133	+	0.225976i	$0.927443\pi$
$398$	−1.59229	−	9.97642i	−0.0798145	−	0.500073i
$399$	1.31683	+	3.57277i	0.0659242	+	0.178862i
$400$	0.928138	−	6.04634i	0.0464069	−	0.302317i
$401$	−21.4553	+	12.3872i	−1.07143	+	0.618588i	−0.928571	−	0.371156i	$-0.878962\pi$
$401$	−21.4553	+	12.3872i	−1.07143	+	0.618588i	−0.142855	+	0.989744i	$0.545628\pi$
$402$	−4.11714	−	1.57480i	−0.205344	−	0.0785438i
$403$	−1.94893	+	1.49547i	−0.0970831	+	0.0744945i
$404$	5.68546	−	16.1776i	0.282862	−	0.804867i
$405$	−6.11124	−	14.7538i	−0.303670	−	0.733125i
$406$	−10.8844	+	8.14280i	−0.540182	+	0.404121i
$407$	−1.11672	+	1.11672i	−0.0553540	+	0.0553540i
$408$	−0.240149	+	1.32207i	−0.0118891	+	0.0654524i
$409$	−5.48365	+	1.46934i	−0.271149	+	0.0726542i	−0.391832	−	0.920037i	$-0.628158\pi$
$409$	−5.48365	+	1.46934i	−0.271149	+	0.0726542i	0.120682	+	0.992691i	$0.461492\pi$
$410$	20.4669	−	0.560340i	1.01079	−	0.0276732i
$411$	−1.01105	+	1.31762i	−0.0498713	+	0.0649935i
$412$	−12.7176	−	6.44184i	−0.626552	−	0.317366i
$413$	−15.7734	+	24.9825i	−0.776157	+	1.22931i
$414$	13.6533	−	18.8392i	0.671021	−	0.925898i
$415$	7.00313	−	4.04326i	0.343770	−	0.198476i
$416$	−2.64275	−	3.40195i	−0.129571	−	0.166795i
$417$	1.41770	−	2.45552i	0.0694249	−	0.120248i
$418$	−9.82582	−	1.02090i	−0.480597	−	0.0499340i
$419$	29.1631	+	12.0798i	1.42471	+	0.590135i	0.956040	−	0.293237i	$-0.0947325\pi$
$419$	29.1631	+	12.0798i	1.42471	+	0.590135i	0.468672	+	0.883372i	$0.344733\pi$
$420$	−1.28613	+	1.72982i	−0.0627566	+	0.0844067i
$421$	2.18102	+	5.26545i	0.106296	+	0.256622i	0.968074	−	0.250664i	$-0.0806488\pi$
$421$	2.18102	+	5.26545i	0.106296	+	0.256622i	−0.861778	+	0.507286i	$0.830649\pi$
$422$	−19.4105	−	10.5091i	−0.944887	−	0.511575i
$423$	−3.30379	−	12.3299i	−0.160636	−	0.599500i
$424$	−2.86939	+	6.07154i	−0.139350	+	0.294860i
$425$	3.20939	+	0.859955i	0.155679	+	0.0417139i
$426$	−2.70931	−	0.647036i	−0.131267	−	0.0313490i
$427$	7.14669	−	22.9915i	0.345853	−	1.11264i
$428$	10.7476	−	9.22368i	0.519504	−	0.445843i
$429$	−0.175212	+	0.0230670i	−0.00845930	+	0.00111369i
$430$	−7.95460	+	20.7965i	−0.383605	+	1.00289i
$431$	1.17106	−	2.02834i	0.0564082	−	0.0977019i	−0.836442	−	0.548055i	$-0.815369\pi$
$431$	1.17106	−	2.02834i	0.0564082	−	0.0977019i	0.892851	+	0.450353i	$0.148702\pi$
$432$	0.111481	−	5.20484i	0.00536362	−	0.250418i
$433$	13.3220			0.640216			0.320108	−	0.947381i	$-0.396281\pi$
$433$	13.3220			0.640216			0.320108	+	0.947381i	$0.396281\pi$
$434$	−5.90704	−	10.5258i	−0.283547	−	0.505257i
$435$	−1.36726	−	0.566339i	−0.0655553	−	0.0271539i
$436$	11.6271	+	24.2279i	0.556835	+	1.16031i
$437$	36.3652	+	4.78757i	1.73958	+	0.229020i
$438$	−1.29509	−	1.22607i	−0.0618819	−	0.0585838i
$439$	7.68268	−	28.6722i	0.366674	−	1.36845i	−0.498462	−	0.866911i	$-0.666102\pi$
$439$	7.68268	−	28.6722i	0.366674	−	1.36845i	0.865137	−	0.501536i	$-0.167231\pi$
$440$	−2.55666	−	4.97371i	−0.121884	−	0.237112i
$441$	18.6576	−	8.88533i	0.888457	−	0.423111i
$442$	1.99359	−	1.22494i	0.0948256	−	0.0582647i
$443$	6.53350	+	5.01333i	0.310416	+	0.238191i	0.752206	−	0.658928i	$-0.228990\pi$
$443$	6.53350	+	5.01333i	0.310416	+	0.238191i	−0.441790	+	0.897118i	$0.645656\pi$
$444$	0.133784	−	0.636862i	0.00634912	−	0.0302241i
$445$	−27.4875	+	21.0919i	−1.30303	+	0.999851i
$446$	35.9292	+	3.73305i	1.70130	+	0.176765i
$447$	2.31537			0.109513
$448$	18.3961	−	10.4683i	0.869132	−	0.494581i
$449$	−13.5212			−0.638107			−0.319053	−	0.947737i	$-0.603365\pi$
$449$	−13.5212			−0.638107			−0.319053	+	0.947737i	$0.603365\pi$
$450$	−6.35064	−	0.659832i	−0.299372	−	0.0311048i
$451$	−6.54329	+	5.02085i	−0.308112	+	0.236422i
$452$	6.78701	−	32.3086i	0.319234	−	1.51967i
$453$	1.35734	+	1.04152i	0.0637734	+	0.0489351i
$454$	7.43884	−	4.57072i	0.349122	−	0.214515i
$455$	3.73791	−	0.342322i	0.175236	−	0.0160483i
$456$	3.62033	−	1.86098i	0.169537	−	0.0871482i
$457$	−0.215461	+	0.804111i	−0.0100788	+	0.0376147i	−0.970782	−	0.239963i	$-0.922865\pi$
$457$	−0.215461	+	0.804111i	−0.0100788	+	0.0376147i	0.960703	+	0.277577i	$0.0895315\pi$
$458$	−13.0846	−	12.3873i	−0.611405	−	0.578819i
$459$	2.80353	+	0.369092i	0.130858	+	0.0172277i
$460$	8.98374	+	18.7199i	0.418869	+	0.872820i
$461$	3.20718	+	1.32846i	0.149373	+	0.0618724i	0.456117	−	0.889920i	$-0.349240\pi$
$461$	3.20718	+	1.32846i	0.149373	+	0.0618724i	−0.306744	+	0.951792i	$0.599240\pi$
$462$	0.0105950	−	0.868245i	0.000492923	−	0.0403944i
$463$	3.16206			0.146954			0.0734768	−	0.997297i	$-0.476591\pi$
$463$	3.16206			0.146954			0.0734768	+	0.997297i	$0.476591\pi$
$464$	10.0531	+	10.4932i	0.466703	+	0.487133i
$465$	0.657046	−	1.13804i	0.0304698	−	0.0527752i
$466$	2.24360	−	5.86565i	0.103933	−	0.271721i
$467$	−40.3251	+	5.30890i	−1.86602	+	0.245667i	−0.977160	−	0.212506i	$-0.931837\pi$
$467$	−40.3251	+	5.30890i	−1.86602	+	0.245667i	−0.888863	+	0.458173i	$0.848504\pi$
$468$	−3.41207	+	2.92827i	−0.157723	+	0.135359i
$469$	−36.7871	+	8.31235i	−1.69867	+	0.383829i
$470$	11.0803	+	2.64619i	0.511096	+	0.122060i
$471$	−5.03584	−	1.34935i	−0.232039	−	0.0621747i
$472$	28.5568	+	13.4958i	1.31443	+	0.621196i
$473$	−2.32141	−	8.66361i	−0.106738	−	0.398353i
$474$	0.784152	+	0.424551i	0.0360173	+	0.0195003i
$475$	−3.85190	−	9.29932i	−0.176737	−	0.426682i
$476$	4.56015	+	10.5535i	0.209014	+	0.483718i
$477$	6.47572	+	2.68233i	0.296503	+	0.122816i
$478$	−32.6076	−	3.38793i	−1.49144	−	0.154960i
$479$	14.3577	−	24.8683i	0.656022	−	1.13626i	−0.325614	−	0.945503i	$-0.605571\pi$
$479$	14.3577	−	24.8683i	0.656022	−	1.13626i	0.981636	−	0.190761i	$-0.0610956\pi$
$480$	2.00248	+	1.14029i	0.0914004	+	0.0520467i
$481$	−0.981377	+	0.566598i	−0.0447469	+	0.0258347i
$482$	−17.0135	+	23.4758i	−0.774943	+	1.06929i
$483$	−0.127550	+	3.22145i	−0.00580371	+	0.146581i
$484$	−17.6163	−	8.92313i	−0.800739	−	0.405597i
$485$	−15.1560	+	19.7517i	−0.688199	+	0.896879i
$486$	−8.16951	+	0.223664i	−0.370577	+	0.0101456i
$487$	−4.00155	+	1.07221i	−0.181327	+	0.0485865i	−0.348340	−	0.937368i	$-0.613255\pi$
$487$	−4.00155	+	1.07221i	−0.181327	+	0.0485865i	0.167013	+	0.985955i	$0.446588\pi$
$488$	−25.3246	−	4.60009i	−1.14639	−	0.208236i
$489$	−1.14587	+	1.14587i	−0.0518182	+	0.0518182i
$490$	−0.954446	+	18.4179i	−0.0431175	+	0.832035i
$491$	−2.88914	−	6.97499i	−0.130385	−	0.314777i	0.845182	−	0.534478i	$-0.179492\pi$
$491$	−2.88914	−	6.97499i	−0.130385	−	0.314777i	−0.975567	+	0.219701i	$0.929492\pi$
$492$	1.12682	−	3.20629i	0.0508008	−	0.144551i
$493$	−6.26200	+	4.80500i	−0.282026	+	0.216406i
$494$	−6.62056	−	2.53235i	−0.297873	−	0.113936i
$495$	−5.05503	+	2.91852i	−0.227207	+	0.131178i
$496$	−10.4029	+	7.63411i	−0.467102	+	0.342782i
$497$	−22.3618	+	8.24200i	−1.00306	+	0.369704i
$498$	−0.211556	−	1.32549i	−0.00948003	−	0.0593966i
$499$	0.757266	+	5.75200i	0.0338999	+	0.257495i	1.00000		0.000673425i	$-0.000214358\pi$
$499$	0.757266	+	5.75200i	0.0338999	+	0.257495i	−0.966100	+	0.258169i	$0.916881\pi$
$500$	13.7317	−	20.0821i	0.614100	−	0.898097i
$501$	0.388895	−	2.95395i	0.0173746	−	0.131973i
$502$	−2.96297	−	9.95926i	−0.132244	−	0.444503i
$503$	−12.6887	−	12.6887i	−0.565762	−	0.565762i	0.365176	−	0.930938i	$-0.381009\pi$
$503$	−12.6887	−	12.6887i	−0.565762	−	0.565762i	−0.930938	+	0.365176i	$0.881009\pi$
$504$	−11.8497	−	18.6453i	−0.527829	−	0.830527i
$505$	11.2945	−	11.2945i	0.502599	−	0.502599i
$506$	−7.35538	−	3.98231i	−0.326987	−	0.177035i
$507$	2.69255	+	0.354481i	0.119580	+	0.0157430i
$508$	−2.65194	+	12.6242i	−0.117661	+	0.560109i
$509$	−27.7131	+	3.64849i	−1.22836	+	0.161717i	−0.716645	−	0.697438i	$-0.754323\pi$
$509$	−27.7131	+	3.64849i	−1.22836	+	0.161717i	−0.511715	+	0.859155i	$0.670990\pi$
$510$	−0.734497	+	1.01348i	−0.0325241	+	0.0448778i
$511$	−15.0373	−	2.58858i	−0.665212	−	0.114512i
$512$	−13.4955	−	18.1623i	−0.596424	−	0.802669i
$513$	−4.28315	−	7.41863i	−0.189106	−	0.327540i
$514$	−13.8712	+	6.19566i	−0.611832	+	0.273279i
$515$	−8.08399	−	10.5353i	−0.356223	−	0.464239i
$516$	2.75245	+	2.46647i	0.121170	+	0.108580i
$517$	−4.23962	+	1.75611i	−0.186458	+	0.0772336i
$518$	−2.06779	−	5.16961i	−0.0908534	−	0.227140i
$519$	−1.11647	−	1.11647i	−0.0490074	−	0.0490074i
$520$	−0.848310	−	3.92202i	−0.0372009	−	0.171992i
$521$	−2.80412	−	10.4651i	−0.122851	−	0.458485i	0.876903	−	0.480667i	$-0.159605\pi$
$521$	−2.80412	−	10.4651i	−0.122851	−	0.458485i	−0.999754	+	0.0221820i	$0.992939\pi$
$522$	10.4276	−	11.0146i	0.456402	−	0.482096i
$523$	12.8278	+	9.84309i	0.560919	+	0.430408i	0.849913	−	0.526922i	$-0.176654\pi$
$523$	12.8278	+	9.84309i	0.560919	+	0.430408i	−0.288994	+	0.957331i	$0.593321\pi$
$524$	0.573979	−	7.52215i	0.0250744	−	0.328607i
$525$	0.783098	−	0.411705i	0.0341772	−	0.0179683i
$526$	−35.6092	+	5.68343i	−1.55264	+	0.247809i
$527$	−3.50433	−	6.06968i	−0.152651	−	0.264399i
$528$	−0.922704	+	0.101427i	−0.0401555	+	0.00441405i
$529$	6.97652	+	4.02790i	0.303327	+	0.175126i
$530$	−4.85664	+	3.94242i	−0.210959	+	0.171248i
$531$	12.6160	−	30.4578i	0.547489	−	1.32176i
$532$	16.9543	−	30.4223i	0.735064	−	1.31898i
$533$	−5.46751	+	2.26471i	−0.236824	+	0.0980957i
$534$	1.63994	+	5.51224i	0.0709673	+	0.238538i
$535$	12.7431	−	3.41450i	0.550931	−	0.147622i
$536$	13.5943	+	37.9576i	0.587186	+	1.63952i
$537$	0.121523	−	0.453530i	0.00524411	−	0.0195713i
$538$	−32.3695	+	19.8891i	−1.39555	+	0.857482i
$539$	−4.04241	−	6.23304i	−0.174119	−	0.268476i
$540$	2.19127	−	4.32606i	0.0942974	−	0.186164i
$541$	−0.00430409	−	0.0326928i	−0.000185047	−	0.00140557i	0.991352	−	0.131229i	$-0.0418923\pi$
$541$	−0.00430409	−	0.0326928i	−0.000185047	−	0.00140557i	−0.991537	+	0.129823i	$0.958559\pi$
$542$	−13.9946	+	6.25079i	−0.601121	+	0.268495i
$543$	−1.20251	−	0.694271i	−0.0516048	−	0.0297940i
$544$	10.6070	−	6.20846i	0.454770	−	0.266185i
$545$			25.0324i			1.07227i
$546$	0.168587	−	0.599802i	0.00721485	−	0.0256691i
$547$	−15.9370	+	38.4753i	−0.681417	+	1.64509i	0.0799768	+	0.996797i	$0.474515\pi$
$547$	−15.9370	+	38.4753i	−0.681417	+	1.64509i	−0.761394	+	0.648290i	$0.775485\pi$
$548$	15.1681	−	0.831168i	0.647951	−	0.0355057i
$549$	−3.50661	+	26.6354i	−0.149659	+	1.13677i
$550$	0.0628178	+	2.29447i	0.00267856	+	0.0978365i
$551$	23.0965	+	6.18870i	0.983945	+	0.263647i
$552$	3.43496	−	0.282691i	0.146201	−	0.0120321i
$553$	7.59750	−	0.695788i	0.323079	−	0.0295879i
$554$	9.33554	−	39.0904i	0.396629	−	1.66079i
$555$	0.369019	−	0.480914i	0.0156640	−	0.0204137i
$556$	−25.4886	+	4.78687i	−1.08096	+	0.203008i
$557$	−7.04310	−	9.17875i	−0.298426	−	0.388916i	0.619940	−	0.784650i	$-0.287157\pi$
$557$	−7.04310	−	9.17875i	−0.298426	−	0.388916i	−0.918365	+	0.395733i	$0.870490\pi$
$558$	8.48818	+	10.4565i	0.359333	+	0.442660i
$559$		−	6.43575i		−	0.272203i
$560$	19.6678	−	1.37724i	0.831117	−	0.0581991i
$561$		−	0.504196i		−	0.0212872i
$562$	−5.12367	+	4.15918i	−0.216129	+	0.175444i
$563$	−12.8498	−	16.7462i	−0.541554	−	0.705767i	0.439774	−	0.898109i	$-0.355059\pi$
$563$	−12.8498	−	16.7462i	−0.541554	−	0.705767i	−0.981328	+	0.192341i	$0.938392\pi$
$564$	1.06731	−	1.56090i	0.0449419	−	0.0657258i
$565$	18.7207	−	24.3973i	0.787585	−	1.02640i
$566$	22.1887	+	5.29908i	0.932659	+	0.222737i
$567$	−18.5248	+	13.0836i	−0.777970	+	0.549461i
$568$	11.6477	+	22.6594i	0.488729	+	0.950769i
$569$	−9.32467	−	2.49854i	−0.390910	−	0.104744i	0.0580097	−	0.998316i	$-0.481525\pi$
$569$	−9.32467	−	2.49854i	−0.390910	−	0.104744i	−0.448920	+	0.893572i	$0.648191\pi$
$570$	3.79034	−	0.103772i	0.158760	−	0.00434651i
$571$	4.20221	−	31.9189i	0.175857	−	1.33577i	−0.644803	−	0.764349i	$-0.723061\pi$
$571$	4.20221	−	31.9189i	0.175857	−	1.33577i	0.820660	−	0.571417i	$-0.193606\pi$
$572$	1.20381	+	1.07873i	0.0503337	+	0.0451040i
$573$	0.673033	−	1.62484i	0.0281163	−	0.0678789i
$574$	−7.18249	−	28.1762i	−0.299791	−	1.17605i
$575$		−	8.52239i		−	0.355408i
$576$	−18.2476	+	14.9938i	−0.760315	+	0.624740i
$577$	31.6801	+	18.2905i	1.31886	+	0.761445i	0.983545	−	0.180661i	$-0.0578237\pi$
$577$	31.6801	+	18.2905i	1.31886	+	0.761445i	0.335316	+	0.942106i	$0.391157\pi$
$578$	−7.08227	−	15.8562i	−0.294584	−	0.659530i
$579$	0.281383	+	2.13731i	0.0116939	+	0.0888238i
$580$	4.21357	+	12.8637i	0.174959	+	0.534135i
$581$	−7.79294	−	8.43549i	−0.323306	−	0.349963i
$582$	2.16343	+	3.52098i	0.0896770	+	0.145949i
$583$	0.652176	−	2.43395i	0.0270104	−	0.100804i
$584$	−0.795490	+	16.2926i	−0.0329176	+	0.674193i
$585$	−4.04558	+	1.08401i	−0.167264	+	0.0448183i
$586$	11.4820	−	3.41602i	0.474319	−	0.141114i
$587$	6.49231	−	2.68920i	0.267966	−	0.110995i	−0.244655	−	0.969610i	$-0.578675\pi$
$587$	6.49231	−	2.68920i	0.267966	−	0.110995i	0.512621	+	0.858615i	$0.328675\pi$
$588$	2.79880	+	1.24015i	0.115420	+	0.0511431i
$589$	−8.12515	+	19.6158i	−0.334791	+	0.808256i
$590$	18.5427	+	22.8426i	0.763391	+	0.940417i
$591$	4.19128	+	2.41984i	0.172406	+	0.0995388i
$592$	−5.21735	+	2.86506i	−0.214432	+	0.117753i
$593$	12.6112	+	21.8432i	0.517879	+	0.896992i	0.999784	+	0.0207689i	$0.00661142\pi$
$593$	12.6112	+	21.8432i	0.517879	+	0.896992i	−0.481906	+	0.876223i	$0.660055\pi$
$594$	0.307885	+	1.92903i	0.0126327	+	0.0791492i
$595$	−0.423678	+	10.7006i	−0.0173691	+	0.438681i
$596$	−13.7922	−	16.0709i	−0.564949	−	0.658288i
$597$	−1.23925	−	0.950911i	−0.0507192	−	0.0389182i
$598$	−4.35836	−	4.12607i	−0.178226	−	0.168728i
$599$	9.25025	+	34.5224i	0.377955	+	1.41055i	0.848979	+	0.528427i	$0.177218\pi$
$599$	9.25025	+	34.5224i	0.377955	+	1.41055i	−0.471024	+	0.882120i	$0.656116\pi$
$600$	−0.538497	−	0.777551i	−0.0219840	−	0.0317434i
$601$	−3.48404	−	3.48404i	−0.142117	−	0.142117i	0.632469	−	0.774586i	$-0.282042\pi$
$601$	−3.48404	−	3.48404i	−0.142117	−	0.142117i	−0.774586	+	0.632469i	$0.782042\pi$
$602$	31.2980	+	4.50963i	1.27561	+	0.183799i
$603$	38.8794	−	16.1044i	1.58329	−	0.655820i
$604$	−0.856222	−	15.6254i	−0.0348392	−	0.635788i
$605$	−11.1978	−	14.5933i	−0.455256	−	0.593301i
$606$	−1.08127	−	2.42080i	−0.0439234	−	0.0983382i
$607$	−18.3899	−	31.8522i	−0.746421	−	1.29284i	−0.949528	−	0.313683i	$-0.898437\pi$
$607$	−18.3899	−	31.8522i	−0.746421	−	1.29284i	0.203106	−	0.979157i	$-0.434896\pi$
$608$	−34.4825	−	14.0431i	−1.39845	−	0.569523i
$609$	−0.356555	+	2.07126i	−0.0144483	+	0.0839319i
$610$	−19.4135	−	14.0694i	−0.786029	−	0.569654i
$611$	−3.26456	+	0.429787i	−0.132070	+	0.0173873i
$612$	−7.01231	−	10.7419i	−0.283456	−	0.434215i
$613$	28.0890	+	3.69799i	1.13450	+	0.149360i	0.674304	−	0.738454i	$-0.264444\pi$
$613$	28.0890	+	3.69799i	1.13450	+	0.149360i	0.460201	+	0.887815i	$0.347777\pi$
$614$	6.70402	−	12.3824i	0.270552	−	0.499714i
$615$	2.23849	−	2.23849i	0.0902645	−	0.0902645i
$616$	−6.08956	+	5.09841i	−0.245355	+	0.205421i
$617$	19.6083	+	19.6083i	0.789402	+	0.789402i	0.981396	−	0.191994i	$-0.0614955\pi$
$617$	19.6083	+	19.6083i	0.789402	+	0.789402i	−0.191994	+	0.981396i	$0.561496\pi$
$618$	−2.11270	+	0.628549i	−0.0849854	+	0.0252840i
$619$	−5.25228	+	39.8950i	−0.211107	+	1.60352i	0.477668	+	0.878540i	$0.341482\pi$
$619$	−5.25228	+	39.8950i	−0.211107	+	1.60352i	−0.688775	+	0.724975i	$0.741851\pi$
$620$	−11.8129	+	2.21852i	−0.474419	+	0.0890979i
$621$	−0.946709	−	7.19097i	−0.0379901	−	0.288563i
$622$	−28.5407	+	4.55526i	−1.14438	+	0.182649i
$623$	37.8212	+	31.4750i	1.51527	+	1.26102i
$624$	−0.658350	−	0.101059i	−0.0263551	−	0.00404562i
$625$	13.0032	−	7.50741i	0.520129	−	0.300296i
$626$	7.69461	−	20.1167i	0.307538	−	0.804026i
$627$	−1.21178	+	0.929830i	−0.0483937	+	0.0371338i
$628$	20.6317	+	42.9913i	0.823293	+	1.71554i
$629$	−1.23723	−	2.98694i	−0.0493316	−	0.119097i
$630$	−2.43690	−	20.4339i	−0.0970886	−	0.814105i
$631$	−18.3409	+	18.3409i	−0.730138	+	0.730138i	−0.970647	−	0.240509i	$-0.922686\pi$
$631$	−18.3409	+	18.3409i	−0.730138	+	0.730138i	0.240509	+	0.970647i	$0.422686\pi$
$632$	−1.72424	−	7.97172i	−0.0685865	−	0.317098i
$633$	−3.29653	+	0.883302i	−0.131025	+	0.0351081i
$634$	0.274134	+	10.0130i	0.0108873	+	0.397666i
$635$	−7.31489	+	9.53295i	−0.290283	+	0.378304i
$636$	0.323209	+	0.986730i	0.0128161	+	0.0391264i
$637$	−1.64419	−	5.07077i	−0.0651453	−	0.200911i
$638$	−4.41515	−	3.19976i	−0.174797	−	0.126680i
$639$	23.0299	−	13.2963i	0.911049	−	0.525995i
$640$	−4.01369	−	20.6916i	−0.158655	−	0.817906i
$641$	15.1691	−	26.2736i	0.599142	−	1.03774i	−0.393806	−	0.919194i	$-0.628842\pi$
$641$	15.1691	−	26.2736i	0.599142	−	1.03774i	0.992948	−	0.118551i	$-0.0378249\pi$
$642$	0.226303	−	2.17809i	0.00893149	−	0.0859622i
$643$	34.2926	+	14.2045i	1.35237	+	0.560169i	0.936951	−	0.349462i	$-0.113636\pi$
$643$	34.2926	+	14.2045i	1.35237	+	0.560169i	0.415417	+	0.909631i	$0.363636\pi$
$644$	23.1197	−	18.3042i	0.911043	−	0.721285i
$645$	1.31745	+	3.18061i	0.0518746	+	0.125236i
$646$	9.62851	−	17.7840i	0.378828	−	0.699701i
$647$	3.15269	+	11.7660i	0.123945	+	0.462570i	0.999800	−	0.0200053i	$-0.00636831\pi$
$647$	3.15269	+	11.7660i	0.123945	+	0.462570i	−0.875855	+	0.482575i	$0.839702\pi$
$648$	16.2875	+	17.9596i	0.639833	+	0.705520i
$649$	−11.4478	−	3.06743i	−0.449366	−	0.120407i
$650$	−0.382573	+	1.60193i	−0.0150057	+	0.0628330i
$651$	−1.78212	−	0.553956i	−0.0698468	−	0.0217112i
$652$	14.7792	+	1.12773i	0.578798	+	0.0441652i
$653$	20.2526	−	2.66631i	0.792546	−	0.104341i	0.276626	−	0.960978i	$-0.410784\pi$
$653$	20.2526	−	2.66631i	0.792546	−	0.104341i	0.515920	+	0.856637i	$0.327450\pi$
$654$	3.88087	+	1.48442i	0.151754	+	0.0580455i
$655$	3.51360	−	6.08573i	0.137288	−	0.237789i
$656$	−28.9669	+	11.2780i	−1.13097	+	0.440331i
$657$	17.0258			0.664238
$658$	0.197407	−	16.1772i	0.00769571	−	0.630653i
$659$	−4.04381	−	1.67500i	−0.157524	−	0.0652488i	0.302528	−	0.953140i	$-0.402169\pi$
$659$	−4.04381	−	1.67500i	−0.157524	−	0.0652488i	−0.460052	+	0.887892i	$0.652169\pi$
$660$	−0.815758	−	0.286690i	−0.0317533	−	0.0111594i
$661$	21.8350	+	2.87463i	0.849282	+	0.111810i	0.542589	−	0.839998i	$-0.317444\pi$
$661$	21.8350	+	2.87463i	0.849282	+	0.111810i	0.306693	+	0.951808i	$0.400777\pi$
$662$	−14.9711	+	15.8140i	−0.581870	+	0.614628i
$663$	0.0936354	−	0.349452i	0.00363650	−	0.0135716i
$664$	−7.93996	+	9.36405i	−0.308130	+	0.363396i
$665$	26.4989	−	18.7155i	1.02758	−	0.725758i
$666$	3.25243	+	5.29333i	0.126029	+	0.205112i
$667$	16.0618	+	12.3247i	0.621917	+	0.477213i
$668$	−22.8198	+	14.8968i	−0.882925	+	0.576373i
$669$	4.43100	−	3.40003i	0.171312	−	0.131453i
$670$	−3.88122	+	37.3553i	−0.149945	+	1.44316i
$671$	9.65797			0.372842
$672$	0.952785	−	3.13085i	0.0367545	−	0.120775i
$673$	−40.4075			−1.55759			−0.778796	−	0.627277i	$-0.784169\pi$
$673$	−40.4075			−1.55759			−0.778796	+	0.627277i	$0.784169\pi$
$674$	4.38009	−	42.1568i	0.168715	−	1.62382i
$675$	−1.57908	+	1.21167i	−0.0607788	+	0.0466372i
$676$	−13.5785	−	20.8004i	−0.522250	−	0.800016i
$677$	29.7576	+	22.8338i	1.14368	+	0.877576i	0.993806	−	0.111129i	$-0.0354467\pi$
$677$	29.7576	+	22.8338i	1.14368	+	0.877576i	0.149873	+	0.988705i	$0.452113\pi$
$678$	−2.67226	−	4.34910i	−0.102628	−	0.167026i
$679$	32.1049	+	14.8124i	1.23207	+	0.568447i
$680$	11.4098	−	0.939006i	0.437545	−	0.0360092i
$681$	0.349388	−	1.30394i	0.0133886	−	0.0499669i
$682$	3.32864	−	3.51603i	0.127460	−	0.134636i
$683$	−11.5639	−	1.52242i	−0.442480	−	0.0582536i	−0.0940052	−	0.995572i	$-0.529967\pi$
$683$	−11.5639	−	1.52242i	−0.442480	−	0.0582536i	−0.348475	+	0.937318i	$0.613300\pi$
$684$	−12.8849	+	36.6633i	−0.492668	+	1.40186i
$685$	13.0731	+	5.41505i	0.499497	+	0.206898i
$686$	25.8120	−	4.44279i	0.985508	−	0.169627i
$687$	−2.78590			−0.106289
$688$	0.723882	−	33.7968i	0.0275978	−	1.28849i
$689$	0.904030	−	1.56583i	0.0344408	−	0.0596532i
$690$	2.99858	+	1.14695i	0.114154	+	0.0436637i
$691$	−9.57268	+	1.26027i	−0.364162	+	0.0479428i	−0.310387	−	0.950610i	$-0.600459\pi$
$691$	−9.57268	+	1.26027i	−0.364162	+	0.0479428i	−0.0537748	+	0.998553i	$0.517125\pi$
$692$	−1.09879	+	14.3999i	−0.0417696	+	0.547402i
$693$	5.62513	+	6.08893i	0.213681	+	0.231300i
$694$	6.35306	−	26.6019i	0.241159	−	1.00980i
$695$	−23.3344	−	6.25242i	−0.885123	−	0.237168i
$696$	2.24417	+	0.109572i	0.0850651	+	0.00415332i
$697$	−4.36994	−	16.3088i	−0.165523	−	0.617741i
$698$	−11.7497	+	21.7019i	−0.444734	+	0.821431i
$699$	−0.371588	−	0.897093i	−0.0140547	−	0.0339312i
$700$	−7.52237	−	2.98301i	−0.284319	−	0.112747i
$701$	35.0609	+	14.5227i	1.32423	+	0.548514i	0.929004	−	0.370069i	$-0.120666\pi$
$701$	35.0609	+	14.5227i	1.32423	+	0.548514i	0.395227	+	0.918584i	$0.370666\pi$
$702$	−0.144854	+	1.39417i	−0.00546716	+	0.0526194i
$703$	−4.89708	+	8.48199i	−0.184697	+	0.319904i
$704$	6.20035	+	5.80026i	0.233685	+	0.218606i
$705$	1.52539	−	0.880687i	0.0574497	−	0.0331686i
$706$	38.0996	+	27.6117i	1.43390	+	1.03918i
$707$	−19.1809	−	12.1104i	−0.721373	−	0.455459i
$708$	4.64097	−	1.52017i	0.174418	−	0.0571317i
$709$	31.2494	−	40.7251i	1.17360	−	1.52946i	0.375622	−	0.926773i	$-0.377429\pi$
$709$	31.2494	−	40.7251i	1.17360	−	1.52946i	0.797976	−	0.602689i	$-0.205904\pi$
$710$	0.649500	+	23.7235i	0.0243753	+	0.890328i
$711$	−8.22286	+	2.20331i	−0.308381	+	0.0826306i
$712$	28.4914	−	44.2180i	1.06776	−	1.65714i
$713$	−12.7117	+	12.7117i	−0.476055	+	0.476055i
$714$	1.63383	+	0.700230i	0.0611445	+	0.0262055i
$715$	0.576199	+	1.39107i	0.0215486	+	0.0520230i
$716$	−3.87182	+	1.85810i	−0.144697	+	0.0694404i
$717$	−4.02135	+	3.08569i	−0.150180	+	0.115237i
$718$	−1.46765	+	3.83700i	−0.0547721	+	0.143196i
$719$	−29.7761	+	17.1912i	−1.11046	+	0.641125i	−0.938949	−	0.344057i	$-0.888199\pi$
$719$	−29.7761	+	17.1912i	−1.11046	+	0.641125i	−0.171512	+	0.985182i	$0.554865\pi$
$720$	−21.3670	+	5.23755i	−0.796299	+	0.195192i
$721$	−12.0636	+	14.4959i	−0.449271	+	0.539856i
$722$	−33.9642	+	5.42088i	−1.26402	+	0.201744i
$723$	0.585114	+	4.44439i	0.0217606	+	0.165288i
$724$	2.34421	+	12.4822i	0.0871220	+	0.463898i
$725$	0.725178	−	5.50828i	0.0269325	−	0.204572i
$726$	−2.92648	+	0.870657i	−0.108612	+	0.0323131i
$727$	35.8012	+	35.8012i	1.32779	+	1.32779i	0.907293	+	0.420500i	$0.138145\pi$
$727$	35.8012	+	35.8012i	1.32779	+	1.32779i	0.420500	+	0.907293i	$0.361855\pi$
$728$	−5.16743	+	2.40274i	−0.191518	+	0.0890514i
$729$	17.2904	−	17.2904i	0.640385	−	0.640385i
$730$	−7.23428	+	13.3618i	−0.267753	+	0.494543i
$731$	18.2043	+	2.39664i	0.673309	+	0.0886428i
$732$	−3.33246	+	2.17543i	−0.123171	+	0.0804061i
$733$	−13.5864	+	1.78868i	−0.501824	+	0.0660664i	−0.377189	−	0.926136i	$-0.623109\pi$
$733$	−13.5864	+	1.78868i	−0.501824	+	0.0660664i	−0.124635	+	0.992203i	$0.539776\pi$
$734$	33.9332	+	24.5922i	1.25250	+	0.907714i
$735$	1.85060	+	2.16944i	0.0682606	+	0.0800211i
$736$	−22.4235	−	22.1579i	−0.826539	−	0.816752i
$737$	−7.56432	−	13.1018i	−0.278635	−	0.482610i
$738$	13.2319	+	29.6243i	0.487073	+	1.09049i
$739$	−27.0116	−	35.2022i	−0.993638	−	1.29493i	−0.955290	−	0.295670i	$-0.904457\pi$
$739$	−27.0116	−	35.2022i	−0.993638	−	1.29493i	−0.0383483	−	0.999264i	$-0.512210\pi$
$740$	−5.53617	+	0.303365i	−0.203514	+	0.0111519i
$741$	−1.01255	+	0.419411i	−0.0371969	+	0.0154075i
$742$	6.98139	+	5.49364i	0.256295	+	0.201678i
$743$	34.5854	+	34.5854i	1.26881	+	1.26881i	0.946701	+	0.322113i	$0.104393\pi$
$743$	34.5854	+	34.5854i	1.26881	+	1.26881i	0.322113	+	0.946701i	$0.395607\pi$
$744$	−0.356563	+	1.96296i	−0.0130722	+	0.0719657i
$745$	−5.10569	−	19.0547i	−0.187058	−	0.698110i
$746$	−2.21241	−	2.09449i	−0.0810019	−	0.0766848i
$747$	10.1663	+	7.80088i	0.371966	+	0.285419i
$748$	−3.49960	+	3.00339i	−0.127958	+	0.109815i
$749$	−8.71859	−	16.5835i	−0.318570	−	0.605949i
$750$	−0.592853	−	3.71448i	−0.0216479	−	0.135634i
$751$	−9.22817	−	15.9837i	−0.336741	−	0.583252i	0.647077	−	0.762425i	$-0.275991\pi$
$751$	−9.22817	−	15.9837i	−0.336741	−	0.583252i	−0.983818	+	0.179173i	$0.942658\pi$
$752$	−17.1919	+	1.88980i	−0.626924	+	0.0689139i
$753$	−1.39133	−	0.803284i	−0.0507029	−	0.0292733i
$754$	−2.46585	−	3.03766i	−0.0898008	−	0.110625i
$755$	5.57828	−	13.4672i	0.203014	−	0.490120i
$756$	−6.67854	−	1.68136i	−0.242896	−	0.0611506i
$757$	17.2335	−	7.13835i	0.626362	−	0.259448i	−0.0468445	−	0.998902i	$-0.514917\pi$
$757$	17.2335	−	7.13835i	0.626362	−	0.259448i	0.673206	+	0.739455i	$0.264917\pi$
$758$	5.50408	−	1.63752i	0.199917	−	0.0594773i
$759$	−1.24918	+	0.334717i	−0.0453424	+	0.0121495i
$760$	−23.2985	−	25.6904i	−0.845126	−	0.931889i
$761$	−7.25755	+	27.0855i	−0.263086	+	0.981850i	0.700326	+	0.713824i	$0.253038\pi$
$761$	−7.25755	+	27.0855i	−0.263086	+	0.981850i	−0.963411	+	0.268027i	$0.913628\pi$
$762$	1.04416	+	1.69936i	0.0378258	+	0.0615614i
$763$	34.6760	−	7.83532i	1.25535	−	0.283658i
$764$	−15.2871	+	5.00737i	−0.553067	+	0.181160i
$765$	−1.55970	−	11.8471i	−0.0563909	−	0.428332i
$766$	6.61979	+	14.8207i	0.239183	+	0.535495i
$767$	−7.36468	−	4.25200i	−0.265923	−	0.153531i
$768$	−3.44591	−	0.604755i	−0.124343	−	0.0218222i
$769$			33.0106i			1.19039i	0.803581	+	0.595196i	$0.202925\pi$
$769$			33.0106i			1.19039i	−0.803581	+	0.595196i	$0.797075\pi$
$770$	−7.16873	+	1.82740i	−0.258343	+	0.0658550i
$771$	−0.898897	+	2.17013i	−0.0323730	+	0.0781553i
$772$	13.1589	−	14.6846i	0.473598	−	0.528510i
$773$	−2.35530	+	17.8903i	−0.0847143	+	0.643469i	0.895433	+	0.445197i	$0.146866\pi$
$773$	−2.35530	+	17.8903i	−0.0847143	+	0.643469i	−0.980147	+	0.198272i	$0.936467\pi$
$774$	−35.2705	+	0.965632i	−1.26777	+	0.0347089i
$775$	4.76518	+	1.27683i	0.171170	+	0.0458650i
$776$	11.5518	−	35.9900i	0.414686	−	1.29196i
$777$	−0.781690	−	0.360652i	−0.0280430	−	0.0129383i
$778$	40.2179	+	9.60482i	1.44188	+	0.344349i
$779$	−31.1374	+	40.5791i	−1.11561	+	1.45390i
$780$	−0.512149	−	0.350197i	−0.0183379	−	0.0125391i
$781$	−5.81975	−	7.58445i	−0.208247	−	0.271393i
$782$	13.2941	−	10.7916i	0.475396	−	0.385907i
$783$		−	4.72829i		−	0.168975i
$784$	−8.06399	−	26.8137i	−0.288000	−	0.957631i
$785$			44.4187i			1.58537i
$786$	−0.735137	−	0.905611i	−0.0262215	−	0.0323021i
$787$	−11.1202	−	14.4921i	−0.396392	−	0.516589i	0.551933	−	0.833889i	$-0.313890\pi$
$787$	−11.1202	−	14.4921i	−0.396392	−	0.516589i	−0.948325	+	0.317300i	$0.897224\pi$
$788$	−8.17060	−	43.5059i	−0.291066	−	1.54983i
$789$	−3.39412	+	4.42331i	−0.120834	+	0.157474i
$790$	1.76475	−	7.38950i	0.0627872	−	0.262906i
$791$	−39.6559	−	18.2962i	−1.41000	−	0.650539i
$792$	5.73125	−	6.75919i	0.203651	−	0.240177i
$793$	6.69382	+	1.79360i	0.237704	+	0.0636927i
$794$	−0.149440	−	5.45843i	−0.00530344	−	0.193712i
$795$	−0.126243	+	0.958909i	−0.00447737	+	0.0340090i
$796$	0.781731	+	14.2660i	0.0277077	+	0.505644i
$797$	17.5837	−	42.4508i	0.622847	−	1.50369i	−0.225499	−	0.974243i	$-0.572401\pi$
$797$	17.5837	−	42.4508i	0.622847	−	1.50369i	0.848346	−	0.529442i	$-0.177599\pi$
$798$	−1.33015	−	5.21807i	−0.0470869	−	0.184718i
$799$		−	9.39423i		−	0.332344i
$800$	−2.18923	+	8.36939i	−0.0774010	+	0.295902i
$801$	−47.5481	−	27.4519i	−1.68003	−	0.969966i
$802$	31.9903	−	14.2887i	1.12962	−	0.504551i
$803$	−0.798914	−	6.06835i	−0.0281931	−	0.214148i
$804$	5.56118	+	2.81690i	0.196128	+	0.0993443i
$805$	26.7927	−	6.05402i	0.944318	−	0.213376i
$806$	2.96001	−	1.81875i	0.104262	−	0.0640627i
$807$	−1.52034	+	5.67397i	−0.0535184	+	0.199733i
$808$	−10.3618	+	21.9252i	−0.364526	+	0.771325i
$809$	−16.7036	+	4.47572i	−0.587268	+	0.157358i	−0.540204	−	0.841534i	$-0.681653\pi$
$809$	−16.7036	+	4.47572i	−0.587268	+	0.157358i	−0.0470635	+	0.998892i	$0.514986\pi$
$810$	6.44005	+	21.6465i	0.226280	+	0.760582i
$811$	20.4761	−	8.48146i	0.719011	−	0.297824i	0.00698369	−	0.999976i	$-0.497777\pi$
$811$	20.4761	−	8.48146i	0.719011	−	0.297824i	0.712028	+	0.702151i	$0.247777\pi$
$812$	16.5005	−	9.86325i	0.579053	−	0.346132i
$813$	−0.906895	+	2.18944i	−0.0318062	+	0.0767870i
$814$	1.73404	−	1.40762i	0.0607781	−	0.0493371i
$815$	11.9570	+	6.90336i	0.418834	+	0.241814i
$816$	0.531024	−	1.82459i	0.0185896	−	0.0638733i
$817$	−27.8119	−	48.1717i	−0.973016	−	1.68531i
$818$	7.92828	−	1.26540i	0.277206	−	0.0442436i
$819$	2.76792	+	5.26482i	0.0967188	+	0.183968i
$820$	−28.8714	−	2.20304i	−1.00823	−	0.0769334i
$821$	2.64776	+	2.03170i	0.0924076	+	0.0709068i	0.653932	−	0.756553i	$-0.273118\pi$
$821$	2.64776	+	2.03170i	0.0924076	+	0.0709068i	−0.561524	+	0.827460i	$0.689785\pi$
$822$	1.61475	−	1.70566i	0.0563209	−	0.0594916i
$823$	0.731973	+	2.73176i	0.0255150	+	0.0952231i	0.977509	−	0.210893i	$-0.0676371\pi$
$823$	0.731973	+	2.73176i	0.0255150	+	0.0952231i	−0.951994	+	0.306116i	$0.900970\pi$
$824$	16.9477	+	10.9200i	0.590400	+	0.380417i
$825$	0.250949	+	0.250949i	0.00873692	+	0.00873692i
$826$	25.8387	−	32.8361i	0.899042	−	1.14251i
$827$	−7.10339	+	2.94232i	−0.247009	+	0.102315i	−0.502753	−	0.864430i	$-0.667680\pi$
$827$	−7.10339	+	2.94232i	−0.247009	+	0.102315i	0.255744	+	0.966745i	$0.417680\pi$
$828$	−21.9586	+	24.5046i	−0.763114	+	0.851595i
$829$	−22.7559	−	29.6560i	−0.790344	−	1.03000i	−0.998651	−	0.0519330i	$-0.983462\pi$
$829$	−22.7559	−	29.6560i	−0.790344	−	1.03000i	0.208306	−	0.978064i	$-0.433205\pi$
$830$	−10.4418	+	4.66391i	−0.362441	+	0.161887i
$831$	−3.10699	−	5.38147i	−0.107780	−	0.186681i
$832$	3.22021	+	5.17157i	0.111641	+	0.179292i
$833$	14.9555	−	2.76246i	0.518179	−	0.0957137i
$834$	−2.35307	+	3.24685i	−0.0814801	+	0.112429i
$835$	−25.1676	+	3.31338i	−0.870961	+	0.114664i
$836$	13.6722	+	2.87209i	0.472863	+	0.0993334i
$837$	4.16257	+	0.548013i	0.143879	+	0.0189421i
$838$	−39.2566	−	21.2541i	−1.35610	−	0.734210i
$839$	−25.1688	+	25.1688i	−0.868922	+	0.868922i	−0.992353	−	0.123431i	$-0.960610\pi$
$839$	−25.1688	+	25.1688i	−0.868922	+	0.868922i	0.123431	+	0.992353i	$0.460610\pi$
$840$	2.06193	−	2.24527i	0.0711435	−	0.0774693i
$841$	−11.1736	−	11.1736i	−0.385295	−	0.385295i
$842$	−2.29837	−	7.72535i	−0.0792069	−	0.266233i
$843$	−0.133184	+	1.01163i	−0.00458709	+	0.0348424i
$844$	25.7677	+	17.6194i	0.886960	+	0.606485i
$845$	−3.02017	−	22.9405i	−0.103897	−	0.789176i
$846$	2.84523	+	17.8266i	0.0978209	+	0.612891i
$847$	−16.7103	+	20.0795i	−0.574172	+	0.689941i
$848$	4.92356	−	8.12112i	0.169076	−	0.278880i
$849$	3.05465	−	1.76360i	0.104835	−	0.0605268i
$850$	−4.38878	−	1.67870i	−0.150534	−	0.0575790i
$851$	−6.57899	+	5.04824i	−0.225525	+	0.173051i
$852$	3.71646	+	1.30611i	0.127324	+	0.0447467i
$853$	0.944574	+	2.28040i	0.0323416	+	0.0780796i	0.939225	−	0.343302i	$-0.111545\pi$
$853$	0.944574	+	2.28040i	0.0323416	+	0.0780796i	−0.906884	+	0.421381i	$0.861545\pi$
$854$	−13.4130	+	31.2963i	−0.458985	+	1.07094i
$855$	−25.5967	+	25.5967i	−0.875388	+	0.875388i
$856$	−16.4660	+	11.4036i	−0.562798	+	0.389769i
$857$	−24.2911	+	6.50879i	−0.829770	+	0.222336i	−0.648613	−	0.761118i	$-0.724651\pi$
$857$	−24.2911	+	6.50879i	−0.829770	+	0.222336i	−0.181157	+	0.983454i	$0.557984\pi$
$858$	0.249831	−	0.00683986i	0.00852910	−	0.000233509i
$859$	16.2107	−	21.1262i	0.553101	−	0.720816i	−0.430213	−	0.902727i	$-0.641562\pi$
$859$	16.2107	−	21.1262i	0.553101	−	0.720816i	0.983315	+	0.181911i	$0.0582284\pi$
$860$	14.2287	−	28.0906i	0.485194	−	0.957881i
$861$	−3.80152	−	2.40019i	−0.129555	−	0.0817983i
$862$	−1.94371	+	2.68200i	−0.0662031	+	0.0913493i
$863$	−27.0567	+	15.6212i	−0.921021	+	0.531752i	−0.883961	−	0.467561i	$-0.845133\pi$
$863$	−27.0567	+	15.6212i	−0.921021	+	0.531752i	−0.0370603	+	0.999313i	$0.511799\pi$
$864$	−0.917502	+	7.30506i	−0.0312141	+	0.248523i
$865$	−6.72619	+	11.6501i	−0.228697	+	0.396115i
$866$	−18.7393	−	1.94702i	−0.636789	−	0.0661624i
$867$	−2.48068	−	1.02753i	−0.0842482	−	0.0348968i
$868$	6.77073	+	15.6694i	0.229814	+	0.531854i
$869$	1.17116	+	2.82742i	0.0397288	+	0.0959137i
$870$	1.84048	+	0.996462i	0.0623981	+	0.0337832i
$871$	−2.80957	−	10.4855i	−0.0951987	−	0.355286i
$872$	−12.8142	−	35.7793i	−0.433943	−	1.21164i
$873$	−38.1080	−	10.2110i	−1.28976	−	0.345591i
$874$	−50.4531	−	12.0492i	−1.70660	−	0.407569i
$875$	−21.8386	−	23.6392i	−0.738278	−	0.799151i
$876$	1.64254	+	1.91392i	0.0554963	+	0.0646653i
$877$	7.78049	−	1.02432i	0.262728	−	0.0345888i	0.00198878	−	0.999998i	$-0.499367\pi$
$877$	7.78049	−	1.02432i	0.262728	−	0.0345888i	0.260740	+	0.965409i	$0.416034\pi$
$878$	−14.9972	+	39.2086i	−0.506132	+	1.32323i
$879$	0.926107	−	1.60407i	0.0312368	−	0.0541038i
$880$	2.86940	+	7.36988i	0.0967273	+	0.248439i
$881$	6.32816			0.213201			0.106601	−	0.994302i	$-0.466003\pi$
$881$	6.32816			0.213201			0.106601	+	0.994302i	$0.466003\pi$
$882$	−27.5431	+	9.77166i	−0.927426	+	0.329029i
$883$	7.75416	+	3.21188i	0.260948	+	0.108088i	0.509322	−	0.860576i	$-0.329896\pi$
$883$	7.75416	+	3.21188i	0.260948	+	0.108088i	−0.248374	+	0.968664i	$0.579896\pi$
$884$	−2.98330	+	1.43169i	−0.100339	+	0.0481531i
$885$	4.51011	+	0.593768i	0.151606	+	0.0199593i
$886$	−8.45759	−	8.00683i	−0.284138	−	0.268995i
$887$	−7.33214	+	27.3639i	−0.246189	+	0.918791i	0.726593	+	0.687068i	$0.241103\pi$
$887$	−7.33214	+	27.3639i	−0.246189	+	0.918791i	−0.972782	+	0.231722i	$0.925564\pi$
$888$	−0.281264	+	0.876283i	−0.00943860	+	0.0294061i
$889$	15.4951	+	7.14904i	0.519689	+	0.239771i
$890$	41.7476	−	25.6514i	1.39938	−	0.859837i
$891$	−7.21751	−	5.53819i	−0.241796	−	0.185536i
$892$	−49.9939	−	10.5021i	−1.67392	−	0.351637i
$893$	−22.5779	+	17.3247i	−0.755542	+	0.579748i
$894$	−3.25689	−	0.338391i	−0.108927	−	0.0113175i
$895$	−4.00038			−0.133718
$896$	−27.4066	+	12.0366i	−0.915590	+	0.402113i
$897$	−0.927953			−0.0309834
$898$	19.0195	+	1.97613i	0.634690	+	0.0659444i
$899$	−9.29757	+	7.13428i	−0.310091	+	0.237941i
$900$	8.83664	+	1.85629i	0.294555	+	0.0618765i
$901$	4.09246	+	3.14026i	0.136340	+	0.104617i
$902$	9.93787	−	6.10623i	0.330895	−	0.203315i
$903$	3.99355	−	2.82055i	0.132897	−	0.0938620i
$904$	−14.2688	+	44.4547i	−0.474573	+	1.47854i
$905$	−3.06192	+	11.4272i	−0.101782	+	0.379854i
$906$	−1.75707	−	1.66343i	−0.0583748	−	0.0552637i
$907$	−28.6023	−	3.76557i	−0.949725	−	0.125034i	−0.360282	−	0.932843i	$-0.617320\pi$
$907$	−28.6023	−	3.76557i	−0.949725	−	0.125034i	−0.589443	+	0.807810i	$0.700653\pi$
$908$	−11.1318	+	5.34218i	−0.369421	+	0.177286i
$909$	23.3847	+	9.68628i	0.775623	+	0.321274i
$910$	−5.30792	−	0.0647713i	−0.175956	−	0.00214715i
$911$	46.1277			1.52828			0.764139	−	0.645051i	$-0.223164\pi$
$911$	46.1277			1.52828			0.764139	+	0.645051i	$0.223164\pi$
$912$	−5.36449	+	2.08861i	−0.177636	+	0.0691609i
$913$	2.30336	−	3.98954i	0.0762302	−	0.132035i
$914$	0.420597	−	1.09961i	0.0139121	−	0.0363718i
$915$	−3.67532	+	0.483864i	−0.121502	+	0.0159961i
$916$	16.5950	+	19.3368i	0.548314	+	0.638905i
$917$	−9.53001	−	2.96232i	−0.314709	−	0.0978243i
$918$	−3.88962	−	0.928916i	−0.128377	−	0.0306588i
$919$	46.3398	+	12.4167i	1.52861	+	0.409590i	0.922566	−	0.385840i	$-0.126088\pi$
$919$	46.3398	+	12.4167i	1.52861	+	0.409590i	0.606045	+	0.795430i	$0.292755\pi$
$920$	−9.90099	−	27.6452i	−0.326426	−	0.911434i
$921$	−0.563480	−	2.10293i	−0.0185673	−	0.0692941i
$922$	−4.31719	−	2.33739i	−0.142179	−	0.0769779i
$923$	−2.62507	−	6.33748i	−0.0864053	−	0.208601i
$924$	−0.141797	+	1.21976i	−0.00466479	+	0.0401272i
$925$	2.10246	+	0.870866i	0.0691283	+	0.0286339i
$926$	−4.44789	−	0.462136i	−0.146167	−	0.0151867i
$927$	10.5216	−	18.2240i	0.345576	−	0.598555i
$928$	−12.6075	−	16.2294i	−0.413862	−	0.532755i
$929$	−34.5852	+	19.9678i	−1.13470	+	0.655122i	−0.945114	−	0.326742i	$-0.894049\pi$
$929$	−34.5852	+	19.9678i	−1.13470	+	0.655122i	−0.189590	+	0.981863i	$0.560716\pi$
$930$	−1.09055	+	1.50478i	−0.0357606	+	0.0493437i
$931$	−34.2200	−	30.8494i	−1.12151	−	1.01105i
$932$	−4.01321	+	7.92297i	−0.131457	+	0.259525i
$933$	−2.72038	+	3.54527i	−0.0890612	+	0.116067i
$934$	57.4988	−	1.57420i	1.88142	−	0.0515093i
$935$	−4.14937	+	1.11182i	−0.135699	+	0.0363604i
$936$	5.22752	−	3.62035i	0.170867	−	0.118335i
$937$	15.3251	−	15.3251i	0.500651	−	0.500651i	−0.410989	−	0.911640i	$-0.634817\pi$
$937$	15.3251	−	15.3251i	0.500651	−	0.500651i	0.911640	+	0.410989i	$0.134817\pi$
$938$	52.9612	−	6.31605i	1.72924	−	0.206226i
$939$	−1.27439	−	3.07665i	−0.0415882	−	0.100403i
$940$	−15.1993	−	5.34163i	−0.495745	−	0.174225i
$941$	25.5136	−	19.5773i	0.831720	−	0.638202i	−0.102565	−	0.994726i	$-0.532705\pi$
$941$	25.5136	−	19.5773i	0.831720	−	0.638202i	0.934286	+	0.356525i	$0.116038\pi$
$942$	6.88641	+	2.63404i	0.224371	+	0.0858216i
$943$	−37.5052	+	21.6537i	−1.22134	+	0.705140i
$944$	−38.1967	−	23.1574i	−1.24320	−	0.753708i
$945$	−4.93098	−	4.10358i	−0.160405	−	0.133489i
$946$	1.99920	+	12.5259i	0.0649996	+	0.407251i
$947$	−4.72047	−	35.8555i	−0.153395	−	1.16515i	−0.878926	−	0.476958i	$-0.841739\pi$
$947$	−4.72047	−	35.8555i	−0.153395	−	1.16515i	0.725532	−	0.688189i	$-0.241594\pi$
$948$	−1.04097	−	0.711795i	−0.0338092	−	0.0231180i
$949$	0.573250	−	4.35427i	0.0186085	−	0.141345i
$950$	4.05915	+	13.6438i	0.131696	+	0.442662i
$951$	1.09513	+	1.09513i	0.0355121	+	0.0355121i
$952$	−4.87210	−	15.5114i	−0.157906	−	0.502729i
$953$	32.1960	−	32.1960i	1.04293	−	1.04293i	0.0438930	−	0.999036i	$-0.486024\pi$
$953$	32.1960	−	32.1960i	1.04293	−	1.04293i	0.999036	−	0.0438930i	$-0.0139761\pi$
$954$	−8.71700	−	4.71951i	−0.282223	−	0.152800i
$955$	−14.8561	−	1.95584i	−0.480731	−	0.0632894i
$956$	45.3720	+	9.53120i	1.46744	+	0.308261i
$957$	−0.835865	+	0.110044i	−0.0270197	+	0.00355721i
$958$	−23.8307	+	32.8825i	−0.769935	+	1.06238i
$959$	3.40920	−	19.8044i	0.110089	−	0.639517i
$960$	−2.65012	−	1.89664i	−0.0855323	−	0.0612137i
$961$	10.2969	+	17.8348i	0.332158	+	0.575315i
$962$	1.46325	−	0.653572i	0.0471772	−	0.0210720i
$963$	12.7266	+	16.5856i	0.410109	+	0.534464i
$964$	27.3629	−	30.5355i	0.881299	−	0.983483i
$965$	16.9689	−	7.02875i	0.546248	−	0.226263i
$966$	0.650232	−	4.51278i	0.0209209	−	0.145196i
$967$	−33.2878	−	33.2878i	−1.07047	−	1.07047i	−0.997321	−	0.0731436i	$-0.976697\pi$
$967$	−33.2878	−	33.2878i	−1.07047	−	1.07047i	−0.0731436	−	0.997321i	$-0.523303\pi$
$968$	23.4756	+	15.1263i	0.754535	+	0.486177i
$969$	−0.809286	−	3.02030i	−0.0259980	−	0.0970259i
$970$	24.2058	−	25.5685i	0.777202	−	0.820956i
$971$	21.1332	+	16.2161i	0.678197	+	0.520398i	0.889450	−	0.457033i	$-0.151088\pi$
$971$	21.1332	+	16.2161i	0.678197	+	0.520398i	−0.211253	+	0.977431i	$0.567754\pi$
$972$	11.5243	+	0.879360i	0.369641	+	0.0282055i
$973$	−1.35731	+	34.2809i	−0.0435135	+	1.09899i
$974$	5.78545	−	0.923390i	0.185378	−	0.0295873i
$975$	0.127325	+	0.220534i	0.00407767	+	0.00706274i
$976$	34.9503	+	10.1719i	1.11873	+	0.325594i
$977$	−13.2324	−	7.63975i	−0.423343	−	0.244417i	0.273163	−	0.961968i	$-0.411930\pi$
$977$	−13.2324	−	7.63975i	−0.423343	−	0.244417i	−0.696507	+	0.717550i	$0.745263\pi$
$978$	1.77930	−	1.44436i	0.0568959	−	0.0461857i
$979$	−7.55333	+	18.2353i	−0.241405	+	0.582804i
$980$	4.03434	−	25.7679i	0.128872	−	0.823124i
$981$	−36.6482	+	15.1802i	−1.17009	+	0.484665i
$982$	3.04458	+	10.2336i	0.0971565	+	0.326566i
$983$	0.648070	−	0.173650i	0.0206702	−	0.00553857i	−0.248469	−	0.968640i	$-0.579927\pi$
$983$	0.648070	−	0.173650i	0.0206702	−	0.00553857i	0.269139	+	0.963101i	$0.413261\pi$
$984$	−2.05363	+	4.34541i	−0.0654672	+	0.138527i
$985$	10.6721	−	39.8289i	0.340042	−	1.26905i
$986$	9.51064	−	5.84372i	0.302881	−	0.186102i
$987$	−1.69743	−	1.83738i	−0.0540297	−	0.0584846i
$988$	8.94265	+	4.52970i	0.284504	+	0.144109i
$989$	−6.14730	−	46.6934i	−0.195473	−	1.48476i
$990$	7.53715	−	3.36652i	0.239546	−	0.106995i
$991$	28.6826	+	16.5599i	0.911132	+	0.526042i	0.880795	−	0.473498i	$-0.157009\pi$
$991$	28.6826	+	16.5599i	0.911132	+	0.526042i	0.0303367	+	0.999540i	$0.490342\pi$
$992$	15.7488	−	9.21807i	0.500025	−	0.292674i
$993$			3.36701i			0.106849i
$994$	32.6596	−	8.32535i	1.03590	−	0.264064i
$995$	−5.09297	+	12.2955i	−0.161458	+	0.389794i
$996$	0.103862	+	1.89541i	0.00329101	+	0.0600582i
$997$	−6.86748	+	52.1637i	−0.217495	+	1.65204i	0.439572	+	0.898208i	$0.355130\pi$
$997$	−6.86748	+	52.1637i	−0.217495	+	1.65204i	−0.657067	+	0.753832i	$0.728203\pi$
$998$	−0.224545	−	8.20168i	−0.00710785	−	0.259620i
$999$	1.87074	+	0.501262i	0.0591875	+	0.0158592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.be.a.3.1	✓	240
4.3	odd	2		896.2.bi.a.815.16		240
7.5	odd	6	inner	224.2.be.a.131.19	yes	240
28.19	even	6		896.2.bi.a.47.15		240
32.11	odd	8	inner	224.2.be.a.171.19	yes	240
32.21	even	8		896.2.bi.a.591.15		240
224.75	even	24	inner	224.2.be.a.75.1	yes	240
224.117	odd	24		896.2.bi.a.719.16		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.be.a.3.1	✓	240	1.1	even	1	trivial
224.2.be.a.75.1	yes	240	224.75	even	24	inner
224.2.be.a.131.19	yes	240	7.5	odd	6	inner
224.2.be.a.171.19	yes	240	32.11	odd	8	inner
896.2.bi.a.47.15		240	28.19	even	6
896.2.bi.a.591.15		240	32.21	even	8
896.2.bi.a.719.16		240	224.117	odd	24
896.2.bi.a.815.16		240	4.3	odd	2

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.be (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40664 - 0.146150i) q^{2} +(-0.173475 + 0.133112i) q^{3} +(1.95728 + 0.411162i) q^{4} +(1.47800 + 1.13411i) q^{5} +(0.263472 - 0.161888i) q^{6} +(1.10840 - 2.40238i) q^{7} +(-2.69310 - 0.864414i) q^{8} +(-0.764082 + 2.85159i) q^{9} +O(q^{10})\)	\(q+(-1.40664 - 0.146150i) q^{2} +(-0.173475 + 0.133112i) q^{3} +(1.95728 + 0.411162i) q^{4} +(1.47800 + 1.13411i) q^{5} +(0.263472 - 0.161888i) q^{6} +(1.10840 - 2.40238i) q^{7} +(-2.69310 - 0.864414i) q^{8} +(-0.764082 + 2.85159i) q^{9} +(-1.91327 - 1.81130i) q^{10} +(1.05222 + 0.138528i) q^{11} +(-0.394270 + 0.189211i) q^{12} +(0.703557 + 0.291423i) q^{13} +(-1.91023 + 3.21730i) q^{14} -0.407361 q^{15} +(3.66189 + 1.60952i) q^{16} +(-1.08632 + 1.88157i) q^{17} +(1.49155 - 3.89950i) q^{18} +(6.52551 - 0.859099i) q^{19} +(2.42657 + 2.82748i) q^{20} +(0.127507 + 0.564295i) q^{21} +(-1.45986 - 0.348642i) q^{22} +(5.38289 + 1.44234i) q^{23} +(0.582250 - 0.208530i) q^{24} +(-0.395810 - 1.47718i) q^{25} +(-0.947061 - 0.512752i) q^{26} +(-0.498066 - 1.20244i) q^{27} +(3.15721 - 4.24641i) q^{28} +(3.35639 + 1.39026i) q^{29} +(0.573011 + 0.0595359i) q^{30} +(-1.61293 + 2.79368i) q^{31} +(-4.91574 - 2.79920i) q^{32} +(-0.200975 + 0.116033i) q^{33} +(1.80306 - 2.48793i) q^{34} +(4.36279 - 2.29369i) q^{35} +(-2.66799 + 5.26721i) q^{36} +(-0.905876 + 1.18056i) q^{37} +(-9.30461 + 0.254741i) q^{38} +(-0.160842 + 0.0430974i) q^{39} +(-3.00007 - 4.33189i) q^{40} +(-5.49509 + 5.49509i) q^{41} +(-0.0968849 - 0.812397i) q^{42} +(-3.23411 - 7.80783i) q^{43} +(2.00254 + 0.703772i) q^{44} +(-4.36335 + 3.34811i) q^{45} +(-7.36099 - 2.81556i) q^{46} +(-3.74457 + 2.16193i) q^{47} +(-0.849494 + 0.208231i) q^{48} +(-4.54291 - 5.32560i) q^{49} +(0.340872 + 2.13571i) q^{50} +(-0.0620094 - 0.471008i) q^{51} +(1.25724 + 0.859672i) q^{52} +(0.309904 - 2.35395i) q^{53} +(0.524864 + 1.76419i) q^{54} +(1.39809 + 1.39809i) q^{55} +(-5.06168 + 5.51175i) q^{56} +(-1.01766 + 1.01766i) q^{57} +(-4.51805 - 2.44614i) q^{58} +(-11.0715 - 1.45759i) q^{59} +(-0.797320 - 0.167491i) q^{60} +(9.02225 - 1.18780i) q^{61} +(2.67711 - 3.69397i) q^{62} +(6.00372 + 4.99632i) q^{63} +(6.50558 + 4.65591i) q^{64} +(0.709354 + 1.22864i) q^{65} +(0.299657 - 0.133844i) q^{66} +(-8.67775 - 11.3091i) q^{67} +(-2.89987 + 3.23610i) q^{68} +(-1.12579 + 0.466317i) q^{69} +(-6.47211 + 2.58877i) q^{70} +(-6.36946 - 6.36946i) q^{71} +(4.52271 - 7.01915i) q^{72} +(-1.49265 - 5.57066i) q^{73} +(1.44678 - 1.52823i) q^{74} +(0.265294 + 0.203567i) q^{75} +(13.1255 + 1.00154i) q^{76} +(1.49908 - 2.37430i) q^{77} +(0.232545 - 0.0371155i) q^{78} +(1.44180 + 2.49727i) q^{79} +(3.58692 + 6.53187i) q^{80} +(-7.42355 - 4.28599i) q^{81} +(8.53273 - 6.92652i) q^{82} +(1.66109 - 4.01022i) q^{83} +(0.0175504 + 1.15691i) q^{84} +(-3.73950 + 1.54895i) q^{85} +(3.40812 + 11.4555i) q^{86} +(-0.767311 + 0.205600i) q^{87} +(-2.71400 - 1.28263i) q^{88} +(-4.81344 + 17.9640i) q^{89} +(6.62699 - 4.07189i) q^{90} +(1.47993 - 1.36720i) q^{91} +(9.94278 + 5.03630i) q^{92} +(-0.0920691 - 0.699334i) q^{93} +(5.58324 - 2.49379i) q^{94} +(10.6190 + 6.13091i) q^{95} +(1.22537 - 0.168753i) q^{96} +13.3638i q^{97} +(5.61190 + 8.15515i) q^{98} +(-1.19901 + 2.89467i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

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