LMFDB - Embedded newform 224.2.bd.a.109.15

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			109.15
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0713999 - 1.41241i) q^{2} +(0.118403 + 0.154306i) q^{3} +(-1.98980 - 0.201692i) q^{4} +(2.39583 + 1.83839i) q^{5} +(0.226398 - 0.156217i) q^{6} +(1.47323 + 2.19764i) q^{7} +(-0.426943 + 2.79602i) q^{8} +(0.766666 - 2.86124i) q^{9} +O(q^{10})$	\(q+(0.0713999 - 1.41241i) q^{2} +(0.118403 + 0.154306i) q^{3} +(-1.98980 - 0.201692i) q^{4} +(2.39583 + 1.83839i) q^{5} +(0.226398 - 0.156217i) q^{6} +(1.47323 + 2.19764i) q^{7} +(-0.426943 + 2.79602i) q^{8} +(0.766666 - 2.86124i) q^{9} +(2.76762 - 3.25263i) q^{10} +(5.43183 + 0.715114i) q^{11} +(-0.204477 - 0.330920i) q^{12} +(-5.50652 - 2.28087i) q^{13} +(3.20915 - 1.92389i) q^{14} +0.587363i q^{15} +(3.91864 + 0.802655i) q^{16} +(-3.70249 - 2.13763i) q^{17} +(-3.98650 - 1.28714i) q^{18} +(0.183696 + 1.39531i) q^{19} +(-4.39645 - 4.14125i) q^{20} +(-0.164674 + 0.487536i) q^{21} +(1.39787 - 7.62091i) q^{22} +(-0.326660 + 1.21911i) q^{23} +(-0.481995 + 0.265178i) q^{24} +(1.06625 + 3.97929i) q^{25} +(-3.61470 + 7.61461i) q^{26} +(1.07136 - 0.443773i) q^{27} +(-2.48819 - 4.67000i) q^{28} +(0.497218 - 1.20039i) q^{29} +(0.829598 + 0.0419377i) q^{30} +(-0.251275 + 0.435222i) q^{31} +(1.41347 - 5.47742i) q^{32} +(0.532801 + 0.922838i) q^{33} +(-3.28357 + 5.07681i) q^{34} +(-0.510497 + 7.97352i) q^{35} +(-2.10260 + 5.53867i) q^{36} +(5.39866 + 4.14254i) q^{37} +(1.98386 - 0.159829i) q^{38} +(-0.300037 - 1.11975i) q^{39} +(-6.16304 + 5.91390i) q^{40} +(-3.02206 - 3.02206i) q^{41} +(0.676843 + 0.267397i) q^{42} +(-3.49881 - 8.44689i) q^{43} +(-10.6640 - 2.51849i) q^{44} +(7.09686 - 5.44561i) q^{45} +(1.69856 + 0.548423i) q^{46} +(-7.99998 + 4.61879i) q^{47} +(0.340126 + 0.699708i) q^{48} +(-2.65920 + 6.47523i) q^{49} +(5.69652 - 1.22186i) q^{50} +(-0.108537 - 0.824421i) q^{51} +(10.4969 + 5.64911i) q^{52} +(-7.09730 - 0.934377i) q^{53} +(-0.550295 - 1.54489i) q^{54} +(11.6991 + 11.6991i) q^{55} +(-6.77361 + 3.18091i) q^{56} +(-0.193554 + 0.193554i) q^{57} +(-1.65994 - 0.787983i) q^{58} +(0.00968333 - 0.0735522i) q^{59} +(0.118466 - 1.16874i) q^{60} +(9.08657 - 1.19627i) q^{61} +(0.596771 + 0.385979i) q^{62} +(7.41743 - 2.53040i) q^{63} +(-7.63544 - 2.38748i) q^{64} +(-8.99956 - 15.5877i) q^{65} +(1.34147 - 0.686643i) q^{66} +(0.469449 + 0.611798i) q^{67} +(6.93609 + 5.00024i) q^{68} +(-0.226794 + 0.0939414i) q^{69} +(11.2254 + 1.29034i) q^{70} +(-7.84105 + 7.84105i) q^{71} +(7.67275 + 3.36520i) q^{72} +(-6.92569 + 1.85573i) q^{73} +(6.23643 - 7.32935i) q^{74} +(-0.487783 + 0.635691i) q^{75} +(-0.0840962 - 2.81344i) q^{76} +(6.43076 + 12.9907i) q^{77} +(-1.60297 + 0.343825i) q^{78} +(-0.877666 + 0.506720i) q^{79} +(7.91281 + 9.12700i) q^{80} +(-7.50061 - 4.33048i) q^{81} +(-4.48416 + 4.05261i) q^{82} +(-6.18602 - 2.56233i) q^{83} +(0.426001 - 0.936888i) q^{84} +(-4.94075 - 11.9280i) q^{85} +(-12.1803 + 4.33865i) q^{86} +(0.244100 - 0.0654064i) q^{87} +(-4.31856 + 14.8822i) q^{88} +(-13.9937 - 3.74960i) q^{89} +(-7.18472 - 10.4125i) q^{90} +(-3.09982 - 15.4616i) q^{91} +(0.895875 - 2.35991i) q^{92} +(-0.0969094 + 0.0127584i) q^{93} +(5.95243 + 11.6290i) q^{94} +(-2.12501 + 3.68062i) q^{95} +(1.01256 - 0.430438i) q^{96} +0.451869 q^{97} +(8.95582 + 4.21821i) q^{98} +(6.21051 - 14.9935i) 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 $

$2$	0.0713999	−	1.41241i	0.0504874	−	0.998725i
$2$	0.0713999	−	1.41241i	0.0504874	−	0.998725i
$3$	0.118403	+	0.154306i	0.0683603	+	0.0890888i	0.826282	−	0.563257i	$-0.190452\pi$
$3$	0.118403	+	0.154306i	0.0683603	+	0.0890888i	−0.757922	+	0.652346i	$0.773785\pi$
$4$	−1.98980	−	0.201692i	−0.994902	−	0.100846i
$5$	2.39583	+	1.83839i	1.07145	+	0.822151i	0.984731	−	0.174082i	$-0.0556958\pi$
$5$	2.39583	+	1.83839i	1.07145	+	0.822151i	0.0867170	+	0.996233i	$0.472362\pi$
$6$	0.226398	−	0.156217i	0.0924265	−	0.0637752i
$7$	1.47323	+	2.19764i	0.556828	+	0.830628i
$7$	1.47323	+	2.19764i	0.556828	+	0.830628i
$8$	−0.426943	+	2.79602i	−0.150947	+	0.988542i
$9$	0.766666	−	2.86124i	0.255555	−	0.953746i
$10$	2.76762	−	3.25263i	0.875197	−	1.02857i
$11$	5.43183	+	0.715114i	1.63776	+	0.215615i	0.892464	−	0.451120i	$-0.148975\pi$
$11$	5.43183	+	0.715114i	1.63776	+	0.215615i	0.745295	+	0.666735i	$0.232309\pi$
$12$	−0.204477	−	0.330920i	−0.0590275	−	0.0955285i
$13$	−5.50652	−	2.28087i	−1.52723	−	0.632601i	−0.548209	−	0.836342i	$-0.684690\pi$
$13$	−5.50652	−	2.28087i	−1.52723	−	0.632601i	−0.979025	+	0.203741i	$0.934690\pi$
$14$	3.20915	−	1.92389i	0.857681	−	0.514181i
$15$			0.587363i			0.151657i
$16$	3.91864	+	0.802655i	0.979660	+	0.200664i
$17$	−3.70249	−	2.13763i	−0.897986	−	0.518453i	−0.0214399	−	0.999770i	$-0.506825\pi$
$17$	−3.70249	−	2.13763i	−0.897986	−	0.518453i	−0.876546	+	0.481318i	$0.840158\pi$
$18$	−3.98650	−	1.28714i	−0.939627	−	0.303382i
$19$	0.183696	+	1.39531i	0.0421427	+	0.320105i	0.999512	+	0.0312385i	$0.00994513\pi$
$19$	0.183696	+	1.39531i	0.0421427	+	0.320105i	−0.957369	+	0.288867i	$0.906722\pi$
$20$	−4.39645	−	4.14125i	−0.983075	−	0.926011i
$21$	−0.164674	+	0.487536i	−0.0359348	+	0.106389i
$22$	1.39787	−	7.62091i	0.298026	−	1.62478i
$23$	−0.326660	+	1.21911i	−0.0681133	+	0.254202i	−0.991584	−	0.129467i	$-0.958673\pi$
$23$	−0.326660	+	1.21911i	−0.0681133	+	0.254202i	0.923470	+	0.383670i	$0.125340\pi$
$24$	−0.481995	+	0.265178i	−0.0983868	+	0.0541293i
$25$	1.06625	+	3.97929i	0.213250	+	0.795859i
$26$	−3.61470	+	7.61461i	−0.708900	+	1.49335i
$27$	1.07136	−	0.443773i	0.206184	−	0.0854042i
$28$	−2.48819	−	4.67000i	−0.470224	−	0.882547i
$29$	0.497218	−	1.20039i	0.0923310	−	0.222907i	−0.870967	−	0.491342i	$-0.836507\pi$
$29$	0.497218	−	1.20039i	0.0923310	−	0.222907i	0.963298	+	0.268435i	$0.0865065\pi$
$30$	0.829598	+	0.0419377i	0.151463	+	0.00765674i
$31$	−0.251275	+	0.435222i	−0.0451304	+	0.0781682i	−0.887708	−	0.460406i	$-0.847704\pi$
$31$	−0.251275	+	0.435222i	−0.0451304	+	0.0781682i	0.842578	+	0.538575i	$0.181037\pi$
$32$	1.41347	−	5.47742i	0.249868	−	0.968280i
$33$	0.532801	+	0.922838i	0.0927487	+	0.160646i
$34$	−3.28357	+	5.07681i	−0.563128	+	0.870666i
$35$	−0.510497	+	7.97352i	−0.0862897	+	1.34777i
$36$	−2.10260	+	5.53867i	−0.350434	+	0.923112i
$37$	5.39866	+	4.14254i	0.887535	+	0.681029i	0.948386	−	0.317118i	$-0.102715\pi$
$37$	5.39866	+	4.14254i	0.887535	+	0.681029i	−0.0608517	+	0.998147i	$0.519382\pi$
$38$	1.98386	−	0.159829i	0.321825	−	0.0259276i
$39$	−0.300037	−	1.11975i	−0.0480444	−	0.179304i
$40$	−6.16304	+	5.91390i	−0.974463	+	0.935070i
$41$	−3.02206	−	3.02206i	−0.471966	−	0.471966i	0.430584	−	0.902550i	$-0.358308\pi$
$41$	−3.02206	−	3.02206i	−0.471966	−	0.471966i	−0.902550	+	0.430584i	$0.858308\pi$
$42$	0.676843	+	0.267397i	0.104439	+	0.0412603i
$43$	−3.49881	−	8.44689i	−0.533564	−	1.28814i	−0.929148	−	0.369708i	$-0.879458\pi$
$43$	−3.49881	−	8.44689i	−0.533564	−	1.28814i	0.395584	−	0.918430i	$-0.370542\pi$
$44$	−10.6640	−	2.51849i	−1.60767	−	0.379677i
$45$	7.09686	−	5.44561i	1.05794	−	0.811784i
$46$	1.69856	+	0.548423i	0.250439	+	0.0808605i
$47$	−7.99998	+	4.61879i	−1.16692	+	0.673720i	−0.952952	−	0.303121i	$-0.901971\pi$
$47$	−7.99998	+	4.61879i	−1.16692	+	0.673720i	−0.213965	+	0.976841i	$0.568638\pi$
$48$	0.340126	+	0.699708i	0.0490929	+	0.100994i
$49$	−2.65920	+	6.47523i	−0.379886	+	0.925033i
$50$	5.69652	−	1.22186i	0.805610	−	0.172797i
$51$	−0.108537	−	0.824421i	−0.0151982	−	0.115442i
$52$	10.4969	+	5.64911i	1.45565	+	0.783391i
$53$	−7.09730	−	0.934377i	−0.974889	−	0.128347i	−0.373783	−	0.927516i	$-0.621940\pi$
$53$	−7.09730	−	0.934377i	−0.974889	−	0.128347i	−0.601106	+	0.799169i	$0.705273\pi$
$54$	−0.550295	−	1.54489i	−0.0748856	−	0.210233i
$55$	11.6991	+	11.6991i	1.57751	+	1.57751i
$56$	−6.77361	+	3.18091i	−0.905162	+	0.425066i
$57$	−0.193554	+	0.193554i	−0.0256369	+	0.0256369i
$58$	−1.65994	−	0.787983i	−0.217961	−	0.103467i
$59$	0.00968333	−	0.0735522i	0.00126066	−	0.00957568i	−0.990803	−	0.135313i	$-0.956796\pi$
$59$	0.00968333	−	0.0735522i	0.00126066	−	0.00957568i	0.992064	+	0.125737i	$0.0401295\pi$
$60$	0.118466	−	1.16874i	0.0152939	−	0.150883i
$61$	9.08657	−	1.19627i	1.16342	−	0.153167i	0.476010	−	0.879440i	$-0.342083\pi$
$61$	9.08657	−	1.19627i	1.16342	−	0.153167i	0.687406	+	0.726273i	$0.258749\pi$
$62$	0.596771	+	0.385979i	0.0757900	+	0.0490194i
$63$	7.41743	−	2.53040i	0.934508	−	0.318800i
$64$	−7.63544	−	2.38748i	−0.954430	−	0.298435i
$65$	−8.99956	−	15.5877i	−1.11626	−	1.93342i
$66$	1.34147	−	0.686643i	0.165123	−	0.0845199i
$67$	0.469449	+	0.611798i	0.0573523	+	0.0747430i	0.821149	−	0.570714i	$-0.193334\pi$
$67$	0.469449	+	0.611798i	0.0573523	+	0.0747430i	−0.763796	+	0.645457i	$0.776667\pi$
$68$	6.93609	+	5.00024i	0.841124	+	0.606368i
$69$	−0.226794	+	0.0939414i	−0.0273028	+	0.0113092i
$70$	11.2254	+	1.29034i	1.34170	+	0.154225i
$71$	−7.84105	+	7.84105i	−0.930561	+	0.930561i	−0.997741	−	0.0671798i	$-0.978600\pi$
$71$	−7.84105	+	7.84105i	−0.930561	+	0.930561i	0.0671798	+	0.997741i	$0.478600\pi$
$72$	7.67275	+	3.36520i	0.904242	+	0.396592i
$73$	−6.92569	+	1.85573i	−0.810591	+	0.217197i	−0.640229	−	0.768184i	$-0.721160\pi$
$73$	−6.92569	+	1.85573i	−0.810591	+	0.217197i	−0.170362	+	0.985382i	$0.554494\pi$
$74$	6.23643	−	7.32935i	0.724970	−	0.852019i
$75$	−0.487783	+	0.635691i	−0.0563243	+	0.0734033i
$76$	−0.0840962	−	2.81344i	−0.00964650	−	0.322723i
$77$	6.43076	+	12.9907i	0.732854	+	1.48043i
$78$	−1.60297	+	0.343825i	−0.181501	+	0.0389305i
$79$	−0.877666	+	0.506720i	−0.0987451	+	0.0570105i	−0.548559	−	0.836112i	$-0.684824\pi$
$79$	−0.877666	+	0.506720i	−0.0987451	+	0.0570105i	0.449814	+	0.893122i	$0.351490\pi$
$80$	7.91281	+	9.12700i	0.884679	+	1.02043i
$81$	−7.50061	−	4.33048i	−0.833402	−	0.481165i
$82$	−4.48416	+	4.05261i	−0.495193	+	0.447536i
$83$	−6.18602	−	2.56233i	−0.679004	−	0.281253i	0.0164063	−	0.999865i	$-0.494777\pi$
$83$	−6.18602	−	2.56233i	−0.679004	−	0.281253i	−0.695411	+	0.718613i	$0.744777\pi$
$84$	0.426001	−	0.936888i	0.0464805	−	0.102223i
$85$	−4.94075	−	11.9280i	−0.535899	−	1.29378i
$86$	−12.1803	+	4.33865i	−1.31343	+	0.467849i
$87$	0.244100	−	0.0654064i	0.0261703	−	0.00701231i
$88$	−4.31856	+	14.8822i	−0.460360	+	1.58645i
$89$	−13.9937	−	3.74960i	−1.48333	−	0.397456i	−0.575849	−	0.817556i	$-0.695328\pi$
$89$	−13.9937	−	3.74960i	−1.48333	−	0.397456i	−0.907478	+	0.420100i	$0.861995\pi$
$90$	−7.18472	−	10.4125i	−0.757336	−	1.09757i
$91$	−3.09982	−	15.4616i	−0.324950	−	1.62081i
$92$	0.895875	−	2.35991i	0.0934014	−	0.246038i
$93$	−0.0969094	+	0.0127584i	−0.0100490	+	0.00132298i
$94$	5.95243	+	11.6290i	0.613946	+	1.19944i
$95$	−2.12501	+	3.68062i	−0.218021	+	0.377624i
$96$	1.01256	−	0.430438i	0.103344	−	0.0439314i
$97$	0.451869			0.0458804			0.0229402	−	0.999737i	$-0.492697\pi$
$97$	0.451869			0.0458804			0.0229402	+	0.999737i	$0.492697\pi$
$98$	8.95582	+	4.21821i	0.904674	+	0.426104i
$99$	6.21051	−	14.9935i	0.624180	−	1.50690i
$100$	−1.31903	−	8.13307i	−0.131903	−	0.813307i
$101$	0.453155	−	3.44206i	0.0450906	−	0.342497i	−0.953998	−	0.299813i	$-0.903076\pi$
$101$	0.453155	−	3.44206i	0.0450906	−	0.342497i	0.999089	−	0.0426844i	$-0.0135910\pi$
$102$	−1.17217	+	0.0944353i	−0.116062	+	0.00935049i
$103$	8.80466	+	2.35920i	0.867549	+	0.232459i	0.665028	−	0.746819i	$-0.268420\pi$
$103$	8.80466	+	2.35920i	0.867549	+	0.232459i	0.202522	+	0.979278i	$0.435086\pi$
$104$	8.72834	−	14.4225i	0.855884	−	1.41424i
$105$	−1.29081	+	0.865320i	−0.125970	+	0.0844466i
$106$	−1.82647	+	9.95758i	−0.177402	+	0.967166i
$107$	7.67351	−	10.0003i	0.741826	−	0.966766i	−0.258174	−	0.966098i	$-0.583121\pi$
$107$	7.67351	−	10.0003i	0.741826	−	0.966766i	1.00000		0.000667722i	$-0.000212542\pi$
$108$	−2.22131	+	0.666937i	−0.213746	+	0.0641760i
$109$	11.0120	−	8.44984i	1.05476	−	0.809348i	0.0725963	−	0.997361i	$-0.476872\pi$
$109$	11.0120	−	8.44984i	1.05476	−	0.809348i	0.982166	+	0.188014i	$0.0602049\pi$
$110$	17.3592	−	15.6886i	1.65514	−	1.49585i
$111$			1.32354i			0.125625i
$112$	4.00911	+	9.79424i	0.378825	+	0.925468i
$113$		−	0.0684958i		−	0.00644354i	−0.999995	−	0.00322177i	$-0.998974\pi$
$113$		−	0.0684958i		−	0.00644354i	0.999995	−	0.00322177i	$-0.00102552\pi$
$114$	0.259559	+	0.287198i	0.0243099	+	0.0268986i
$115$	−3.02382	+	2.32026i	−0.281973	+	0.216365i
$116$	−1.23147	+	2.28826i	−0.114340	+	0.212459i
$117$	−10.7478	+	14.0068i	−0.993633	+	1.29493i
$118$	−0.103194	−	0.0189284i	−0.00949982	−	0.00174250i
$119$	−0.756872	−	11.2859i	−0.0693823	−	1.03458i
$120$	−1.64228	−	0.250771i	−0.149919	−	0.0228921i
$121$	18.3682	+	4.92175i	1.66984	+	0.447432i
$122$	−1.04084	−	12.9194i	−0.0942335	−	1.16967i
$123$	0.108501	−	0.824145i	0.00978318	−	0.0743107i
$124$	0.587770	−	0.815326i	0.0527833	−	0.0732184i
$125$	1.01736	−	2.45613i	0.0909957	−	0.219683i
$126$	−3.04436	−	10.6571i	−0.271213	−	0.949412i
$127$	−6.18288			−0.548642			−0.274321	−	0.961638i	$-0.588453\pi$
$127$	−6.18288			−0.548642			−0.274321	+	0.961638i	$0.588453\pi$
$128$	−3.91728	+	10.6139i	−0.346242	+	0.938145i
$129$	0.889137	−	1.54003i	0.0782841	−	0.135592i
$130$	−22.6588	+	11.5981i	−1.98731	+	1.01722i
$131$	8.65291	−	1.13918i	0.756009	−	0.0995304i	0.257337	−	0.966322i	$-0.417155\pi$
$131$	8.65291	−	1.13918i	0.756009	−	0.0995304i	0.498671	+	0.866791i	$0.333822\pi$
$132$	−0.874040	−	1.94373i	−0.0760755	−	0.169180i
$133$	−2.79575	+	2.45930i	−0.242422	+	0.213248i
$134$	0.897628	−	0.619372i	0.0775432	−	0.0535056i
$135$	3.38263	+	0.906374i	0.291131	+	0.0780082i
$136$	7.55762	−	9.43959i	0.648061	−	0.809438i
$137$	11.1426	−	2.98566i	0.951980	−	0.255082i	0.250778	−	0.968045i	$-0.419314\pi$
$137$	11.1426	−	2.98566i	0.951980	−	0.255082i	0.701202	+	0.712962i	$0.252647\pi$
$138$	0.116491	+	0.327034i	0.00991634	+	0.0278390i
$139$	6.81777	+	16.4595i	0.578275	+	1.39608i	0.894359	+	0.447349i	$0.147632\pi$
$139$	6.81777	+	16.4595i	0.578275	+	1.39608i	−0.316084	+	0.948731i	$0.602368\pi$
$140$	2.62398	−	15.7628i	0.221767	−	1.33220i
$141$	−1.65993	−	0.687567i	−0.139792	−	0.0579036i
$142$	10.5149	+	11.6346i	0.882393	+	0.976356i
$143$	−28.2794	−	16.3271i	−2.36484	−	1.36534i
$144$	5.30087	−	10.5968i	0.441739	−	0.883066i
$145$	3.39803	−	1.96185i	0.282191	−	0.162923i
$146$	2.12656	+	9.91441i	0.175996	+	0.820523i
$147$	−1.31403	+	0.356358i	−0.108379	+	0.0293919i
$148$	−9.90676	−	9.33171i	−0.814331	−	0.767062i
$149$	7.52295	−	9.80409i	0.616304	−	0.803183i	−0.376051	−	0.926599i	$-0.622718\pi$
$149$	7.52295	−	9.80409i	0.616304	−	0.803183i	0.992355	+	0.123416i	$0.0393850\pi$
$150$	0.863029	+	0.734338i	0.0704660	+	0.0599584i
$151$	−6.48936	+	1.73882i	−0.528097	+	0.141503i	−0.513009	−	0.858383i	$-0.671469\pi$
$151$	−6.48936	+	1.73882i	−0.528097	+	0.141503i	−0.0150875	+	0.999886i	$0.504803\pi$
$152$	−3.97973	−	0.0821008i	−0.322799	−	0.00665925i
$153$	−8.95485	+	8.95485i	−0.723957	+	0.723957i
$154$	18.8074	−	8.15534i	1.51554	−	0.657176i
$155$	−1.40212	+	0.580777i	−0.112621	+	0.0466491i
$156$	0.371170	+	2.28861i	0.0297174	+	0.183235i
$157$	0.632229	+	0.823937i	0.0504574	+	0.0657573i	0.817900	−	0.575360i	$-0.195138\pi$
$157$	0.632229	+	0.823937i	0.0504574	+	0.0657573i	−0.767443	+	0.641117i	$0.778471\pi$
$158$	0.653032	+	1.27580i	0.0519524	+	0.101497i
$159$	−0.696164	−	1.20579i	−0.0552094	−	0.0956255i
$160$	13.4560	−	10.5245i	1.06379	−	0.832032i
$161$	−3.16041	+	1.07815i	−0.249075	+	0.0849701i
$162$	−6.65196	+	10.2847i	−0.522627	+	0.808046i
$163$	2.67408	−	0.352050i	0.209450	−	0.0275747i	−0.0250708	−	0.999686i	$-0.507981\pi$
$163$	2.67408	−	0.352050i	0.209450	−	0.0275747i	0.234521	+	0.972111i	$0.424648\pi$
$164$	5.40378	+	6.62283i	0.421964	+	0.517156i
$165$	−0.420032	+	3.19046i	−0.0326994	+	0.248377i
$166$	−4.06075	+	8.55425i	−0.315175	+	0.663939i
$167$	4.37579	−	4.37579i	0.338609	−	0.338609i	−0.517235	−	0.855843i	$-0.673039\pi$
$167$	4.37579	−	4.37579i	0.338609	−	0.338609i	0.855843	+	0.517235i	$0.173039\pi$
$168$	−1.29285	−	0.668582i	−0.0997458	−	0.0515822i
$169$	15.9270	+	15.9270i	1.22515	+	1.22515i
$170$	−17.2000	+	6.12670i	−1.31918	+	0.469897i
$171$	4.13313	+	0.544137i	0.316069	+	0.0416112i
$172$	5.25829	+	17.5133i	0.400941	+	1.33538i
$173$	0.198608	+	1.50858i	0.0150999	+	0.114695i	0.997335	−	0.0729600i	$-0.0232446\pi$
$173$	0.198608	+	1.50858i	0.0150999	+	0.114695i	−0.982235	+	0.187655i	$0.939911\pi$
$174$	−0.0749520	−	0.349439i	−0.00568209	−	0.0264909i
$175$	−7.17421	+	8.20563i	−0.542319	+	0.620287i
$176$	20.7114	+	7.16216i	1.56118	+	0.539868i
$177$	0.0124961	−	0.00721463i	0.000939265	−	0.000542285i
$178$	−6.29511	+	19.4971i	−0.471839	+	1.46137i
$179$	−17.8811	+	13.7206i	−1.33650	+	1.02553i	−0.340127	+	0.940379i	$0.610470\pi$
$179$	−17.8811	+	13.7206i	−1.33650	+	1.02553i	−0.996368	+	0.0851496i	$0.972863\pi$
$180$	−15.2197	+	9.40432i	−1.13441	+	0.700957i
$181$	6.77001	+	16.3442i	0.503211	+	1.21486i	0.947726	+	0.319087i	$0.103376\pi$
$181$	6.77001	+	16.3442i	0.503211	+	1.21486i	−0.444515	+	0.895772i	$0.646624\pi$
$182$	−22.0594	+	3.27427i	−1.63515	+	0.242705i
$183$	1.26047	+	1.26047i	0.0931769	+	0.0931769i
$184$	−3.26919	−	1.43384i	−0.241008	−	0.105704i
$185$	5.31870	+	19.8496i	0.391038	+	1.45937i
$186$	0.0111007	+	0.137787i	0.000813944	+	0.0101030i
$187$	−18.5827	−	14.2590i	−1.35890	−	1.04272i
$188$	16.8500	−	7.57696i	1.22891	−	0.552607i
$189$	2.55361	+	1.70069i	0.185748	+	0.123707i
$190$	5.04682	+	3.26418i	0.366135	+	0.236808i
$191$	10.0442	+	17.3971i	0.726772	+	1.25881i	0.958240	+	0.285964i	$0.0923139\pi$
$191$	10.0442	+	17.3971i	0.726772	+	1.25881i	−0.231468	+	0.972843i	$0.574353\pi$
$192$	−0.535658	−	1.46088i	−0.0386578	−	0.105430i
$193$	8.76441	−	15.1804i	0.630876	−	1.09271i	−0.356497	−	0.934296i	$-0.616029\pi$
$193$	8.76441	−	15.1804i	0.630876	−	1.09271i	0.987373	−	0.158413i	$-0.0506376\pi$
$194$	0.0322634	−	0.638225i	0.00231638	−	0.0458219i
$195$	1.33970	−	3.23433i	0.0959380	−	0.231615i
$196$	6.59729	−	12.3481i	0.471235	−	0.882008i
$197$	−8.32147	+	3.44687i	−0.592880	+	0.245579i	−0.658889	−	0.752240i	$-0.728973\pi$
$197$	−8.32147	+	3.44687i	−0.592880	+	0.245579i	0.0660089	+	0.997819i	$0.478973\pi$
$198$	−20.7335	−	9.84232i	−1.47347	−	0.699463i
$199$	−2.15738	−	8.05144i	−0.152932	−	0.570751i	−0.999274	−	0.0381102i	$-0.987866\pi$
$199$	−2.15738	−	8.05144i	−0.152932	−	0.570751i	0.846341	−	0.532641i	$-0.178800\pi$
$200$	−11.5814	+	1.28232i	−0.818929	+	0.0906735i
$201$	−0.0388199	+	0.144878i	−0.00273815	+	0.0102189i
$202$	−4.82924	−	0.885804i	−0.339784	−	0.0623249i
$203$	3.37053	−	0.675744i	0.236565	−	0.0474279i
$204$	0.0496885	+	1.66233i	0.00347889	+	0.116386i
$205$	−1.68463	−	12.7960i	−0.117660	−	0.893715i
$206$	3.96081	−	12.2673i	0.275963	−	0.854707i
$207$	3.23773	+	1.86930i	0.225038	+	0.129926i
$208$	−19.7473	−	13.3578i	−1.36923	−	0.926194i
$209$			7.71043i			0.533342i
$210$	1.13002	+	1.88494i	0.0779790	+	0.130073i
$211$	−0.534006	−	0.221193i	−0.0367625	−	0.0152275i	0.364226	−	0.931310i	$-0.381333\pi$
$211$	−0.534006	−	0.221193i	−0.0367625	−	0.0152275i	−0.400989	+	0.916083i	$0.631333\pi$
$212$	13.9338	+	3.29070i	0.956976	+	0.226006i
$213$	−2.13833	−	0.281517i	−0.146516	−	0.0192892i
$214$	−13.5766	−	11.5522i	−0.928080	−	0.789689i
$215$	7.14607	−	26.6695i	0.487358	−	1.81884i
$216$	0.783387	+	3.18502i	0.0533027	+	0.216713i
$217$	−1.32664	+	0.0889691i	−0.0900585	+	0.00603961i
$218$	−11.1484	−	16.1568i	−0.755064	−	1.09428i
$219$	−1.10638	−	0.848953i	−0.0747620	−	0.0573669i
$220$	−20.9193	−	25.6385i	−1.41038	−	1.72855i
$221$	15.5122	+	20.2158i	1.04346	+	1.35986i
$222$	1.86938	+	0.0945006i	0.125465	+	0.00634246i
$223$	−5.07246			−0.339677			−0.169839	−	0.985472i	$-0.554325\pi$
$223$	−5.07246			−0.339677			−0.169839	+	0.985472i	$0.554325\pi$
$224$	14.1197	−	4.96320i	0.943414	−	0.331617i
$225$	12.2032			0.813544
$226$	−0.0967441	−	0.00489059i	−0.00643532	−	0.000325317i
$227$	6.69399	+	8.72378i	0.444296	+	0.579018i	0.960791	−	0.277272i	$-0.0894304\pi$
$227$	6.69399	+	8.72378i	0.444296	+	0.579018i	−0.516496	+	0.856290i	$0.672764\pi$
$228$	0.424174	−	0.346097i	0.0280916	−	0.0229208i
$229$	12.5005	+	9.59199i	0.826058	+	0.633856i	0.932786	−	0.360432i	$-0.117371\pi$
$229$	12.5005	+	9.59199i	0.826058	+	0.633856i	−0.106728	+	0.994288i	$0.534037\pi$
$230$	3.06126	+	4.43654i	0.201853	+	0.292537i
$231$	−1.24312	+	2.53045i	−0.0817916	+	0.166492i
$232$	3.14403	+	1.90273i	0.206416	+	0.124920i
$233$	−3.50730	+	13.0894i	−0.229771	+	0.857516i	0.750666	+	0.660682i	$0.229733\pi$
$233$	−3.50730	+	13.0894i	−0.229771	+	0.857516i	−0.980437	+	0.196834i	$0.936934\pi$
$234$	19.0159	+	16.1804i	1.24311	+	1.05774i
$235$	−27.6577	−	3.64121i	−1.80419	−	0.237526i
$236$	−0.0341028	+	0.144401i	−0.00221990	+	0.00939973i
$237$	−0.182109	−	0.0754319i	−0.0118292	−	0.00489983i
$238$	−15.9944	+	0.263198i	−1.03676	+	0.0170606i
$239$		−	5.02121i		−	0.324795i	−0.986725	−	0.162397i	$-0.948077\pi$
$239$		−	5.02121i		−	0.324795i	0.986725	−	0.162397i	$-0.0519227\pi$
$240$	−0.471450	+	2.30167i	−0.0304320	+	0.148572i
$241$	−20.7477	−	11.9787i	−1.33648	−	0.771615i	−0.350194	−	0.936677i	$-0.613884\pi$
$241$	−20.7477	−	11.9787i	−1.33648	−	0.771615i	−0.986283	+	0.165062i	$0.947218\pi$
$242$	8.26302	−	25.5920i	0.531167	−	1.64512i
$243$	−0.673966	−	5.11928i	−0.0432349	−	0.328402i
$244$	−18.3218	+	0.547655i	−1.17293	+	0.0350600i
$245$	−18.2750	+	10.6249i	−1.16755	+	0.678802i
$246$	−1.15628	−	0.212091i	−0.0737220	−	0.0135225i
$247$	2.17100	−	8.10227i	0.138137	−	0.515535i
$248$	−1.10961	−	0.888386i	−0.0704602	−	0.0564126i
$249$	−0.337062	−	1.25793i	−0.0213604	−	0.0797182i
$250$	−3.39642	−	1.61230i	−0.214809	−	0.101971i
$251$	15.8433	−	6.56249i	1.00002	−	0.414221i	0.178214	−	0.983992i	$-0.442968\pi$
$251$	15.8433	−	6.56249i	1.00002	−	0.414221i	0.821803	+	0.569771i	$0.192968\pi$
$252$	−15.2696	+	3.53897i	−0.961894	+	0.222934i
$253$	−2.64617	+	6.38841i	−0.166363	+	0.401636i
$254$	−0.441457	+	8.73276i	−0.0276995	+	0.547942i
$255$	1.25557	−	2.17471i	0.0786267	−	0.136185i
$256$	14.7115	+	6.29063i	0.919468	+	0.393164i
$257$	1.21717	+	2.10820i	0.0759249	+	0.131506i	0.901488	−	0.432804i	$-0.142476\pi$
$257$	1.21717	+	2.10820i	0.0759249	+	0.131506i	−0.825563	+	0.564310i	$0.809142\pi$
$258$	−2.11167	−	1.36578i	−0.131467	−	0.0850300i
$259$	−1.15033	+	17.9672i	−0.0714782	+	1.11643i
$260$	14.7634	+	32.8316i	0.915590	+	2.03613i
$261$	−3.05340	−	2.34296i	−0.189001	−	0.145025i
$262$	−0.991169	−	12.3028i	−0.0612346	−	0.760069i
$263$	7.18443	+	26.8126i	0.443011	+	1.65334i	0.721136	+	0.692794i	$0.243620\pi$
$263$	7.18443	+	26.8126i	0.443011	+	1.65334i	−0.278125	+	0.960545i	$0.589713\pi$
$264$	−2.80775	+	1.09572i	−0.172805	+	0.0674370i
$265$	−15.2862	−	15.2862i	−0.939023	−	0.939023i
$266$	3.27392	+	4.12434i	0.200737	+	0.252879i
$267$	−1.07831	−	2.60328i	−0.0659917	−	0.159318i
$268$	−0.810717	−	1.31204i	−0.0495224	−	0.0801457i
$269$	−7.77004	+	5.96216i	−0.473747	+	0.363519i	−0.817868	−	0.575406i	$-0.804844\pi$
$269$	−7.77004	+	5.96216i	−0.473747	+	0.363519i	0.344120	+	0.938926i	$0.388177\pi$
$270$	1.52169	−	4.71295i	0.0926072	−	0.286821i
$271$	23.9839	−	13.8471i	1.45692	−	0.841152i	0.458059	−	0.888922i	$-0.348545\pi$
$271$	23.9839	−	13.8471i	1.45692	−	0.841152i	0.998858	+	0.0477701i	$0.0152115\pi$
$272$	−12.7930	−	11.3484i	−0.775687	−	0.688101i
$273$	2.01879	−	2.30903i	0.122183	−	0.139749i
$274$	−3.42139	−	15.9512i	−0.206694	−	0.963644i
$275$	2.94603	+	22.3773i	0.177652	+	1.34940i
$276$	0.470224	−	0.141182i	0.0283041	−	0.00849817i
$277$	1.11886	+	0.147300i	0.0672256	+	0.00885042i	0.164064	−	0.986450i	$-0.447540\pi$
$277$	1.11886	+	0.147300i	0.0672256	+	0.00885042i	−0.0968384	+	0.995300i	$0.530873\pi$
$278$	23.7344	−	8.45427i	1.42350	−	0.507054i
$279$	1.05263	+	1.05263i	0.0630192	+	0.0630192i
$280$	−22.0762	−	4.83160i	−1.31930	−	0.288743i
$281$	6.68419	−	6.68419i	0.398746	−	0.398746i	−0.479045	−	0.877790i	$-0.659017\pi$
$281$	6.68419	−	6.68419i	0.398746	−	0.398746i	0.877790	+	0.479045i	$0.159017\pi$
$282$	−1.08965	+	2.29542i	−0.0648875	+	0.136690i
$283$	−2.81117	+	21.3530i	−0.167107	+	1.26930i	0.678143	+	0.734930i	$0.262785\pi$
$283$	−2.81117	+	21.3530i	−0.167107	+	1.26930i	−0.845250	+	0.534372i	$0.820548\pi$
$284$	17.1836	−	14.0207i	1.01966	−	0.831974i
$285$	−0.819552	+	0.107896i	−0.0485460	+	0.00639121i
$286$	−25.0797	+	38.7763i	−1.48300	+	2.29289i
$287$	2.18920	−	11.0936i	0.129225	−	0.654832i
$288$	−14.5885	−	8.24362i	−0.859637	−	0.485760i
$289$	0.638965	+	1.10672i	0.0375862	+	0.0651012i
$290$	−2.52832	−	4.93949i	−0.148468	−	0.290057i
$291$	0.0535029	+	0.0697263i	0.00313639	+	0.00408743i
$292$	14.1551	−	2.29569i	0.828362	−	0.134345i
$293$	−11.8675	+	4.91570i	−0.693309	+	0.287178i	−0.701378	−	0.712789i	$-0.747432\pi$
$293$	−11.8675	+	4.91570i	−0.693309	+	0.287178i	0.00806883	+	0.999967i	$0.497432\pi$
$294$	0.409503	+	1.88139i	0.0238827	+	0.109725i
$295$	0.158417	−	0.158417i	0.00922339	−	0.00922339i
$296$	−13.8875	+	13.3261i	−0.807197	+	0.774565i
$297$	6.13682	−	1.64435i	0.356094	−	0.0954151i
$298$	−13.3103	−	11.3255i	−0.771043	−	0.656068i
$299$	4.57940	−	5.96799i	0.264834	−	0.345138i
$300$	1.09881	−	1.16652i	0.0634396	−	0.0673490i
$301$	13.4086	−	20.1333i	0.772860	−	1.16046i
$302$	1.99259	+	9.28979i	0.114660	+	0.534567i
$303$	0.584787	−	0.337627i	0.0335951	−	0.0193961i
$304$	−0.400112	+	5.61515i	−0.0229480	+	0.322051i
$305$	23.9691	+	13.8386i	1.37247	+	0.792394i
$306$	12.0085	+	13.2873i	0.686483	+	0.759584i
$307$	18.8697	+	7.81608i	1.07695	+	0.446087i	0.849438	−	0.527688i	$-0.176941\pi$
$307$	18.8697	+	7.81608i	1.07695	+	0.446087i	0.227512	+	0.973775i	$0.426941\pi$
$308$	−10.1758	−	27.1460i	−0.579822	−	1.54679i
$309$	0.678463	+	1.63795i	0.0385964	+	0.0931799i
$310$	0.720184	+	2.02183i	0.0409037	+	0.114832i
$311$	2.85627	−	0.765335i	0.161964	−	0.0433981i	−0.176926	−	0.984224i	$-0.556615\pi$
$311$	2.85627	−	0.765335i	0.161964	−	0.0433981i	0.338890	+	0.940826i	$0.389949\pi$
$312$	3.25895	−	0.360838i	0.184502	−	0.0204284i
$313$	26.9261	+	7.21483i	1.52195	+	0.407806i	0.920384	−	0.391015i	$-0.127876\pi$
$313$	26.9261	+	7.21483i	1.52195	+	0.407806i	0.601569	+	0.798821i	$0.294542\pi$
$314$	1.20888	−	0.834137i	0.0682209	−	0.0470731i
$315$	22.4228	+	7.57368i	1.26338	+	0.426729i
$316$	1.84858	−	0.831256i	0.103991	−	0.0467618i
$317$	−32.5474	+	4.28495i	−1.82805	+	0.240667i	−0.964590	−	0.263756i	$-0.915039\pi$
$317$	−32.5474	+	4.28495i	−1.82805	+	0.240667i	−0.863457	+	0.504422i	$0.831705\pi$
$318$	−1.75278	+	0.897176i	−0.0982910	+	0.0503111i
$319$	3.55922	−	6.16475i	0.199278	−	0.345160i
$320$	−13.9041	−	19.7569i	−0.777263	−	1.10444i
$321$	2.45168			0.136839
$322$	1.29714	+	4.54077i	0.0722866	+	0.253047i
$323$	2.30252	−	5.55878i	0.128116	−	0.309299i
$324$	14.0513	+	10.1296i	0.780629	+	0.562757i
$325$	3.20495	−	24.3440i	0.177779	−	1.35036i
$326$	−0.306309	−	3.80204i	−0.0169649	−	0.210575i
$327$	2.60773	+	0.698739i	0.144208	+	0.0386403i
$328$	9.73998	−	7.15948i	0.537800	−	0.395316i
$329$	−21.9362	−	10.7765i	−1.20938	−	0.594128i
$330$	4.47624	+	0.821055i	0.246409	+	0.0451976i
$331$	3.65442	−	4.76253i	0.200865	−	0.261772i	−0.682050	−	0.731306i	$-0.738911\pi$
$331$	3.65442	−	4.76253i	0.200865	−	0.261772i	0.882915	+	0.469534i	$0.155578\pi$
$332$	11.7922	+	6.34621i	0.647180	+	0.348294i
$333$	15.9918	−	12.2709i	0.876343	−	0.672441i
$334$	−5.86797	−	6.49284i	−0.321081	−	0.355272i
$335$			2.32879i			0.127236i
$336$	−1.03662	+	1.77830i	−0.0565523	+	0.0970143i
$337$		−	8.26077i		−	0.449993i	−0.974360	−	0.224996i	$-0.927763\pi$
$337$		−	8.26077i		−	0.449993i	0.974360	−	0.224996i	$-0.0722370\pi$
$338$	23.6326	−	21.3582i	1.28544	−	1.16173i
$339$	0.0105693	−	0.00811014i	0.000574048	−	0.000440482i
$340$	7.42533	+	24.7309i	0.402695	+	1.34122i
$341$	−1.67612	+	2.18436i	−0.0907670	+	0.118290i
$342$	1.06365	−	5.79883i	0.0575156	−	0.313565i
$343$	−18.1478	+	3.69554i	−0.979890	+	0.199540i
$344$	25.1114	−	6.17641i	1.35392	−	0.333010i
$345$	−0.716062	−	0.191868i	−0.0385515	−	0.0103298i
$346$	2.14491	−	0.172804i	0.115311	−	0.00929000i
$347$	3.23389	−	24.5639i	0.173605	−	1.31866i	−0.653636	−	0.756809i	$-0.726757\pi$
$347$	3.23389	−	24.5639i	0.173605	−	1.31866i	0.827240	−	0.561848i	$-0.189910\pi$
$348$	−0.498903	+	0.0809130i	−0.0267440	+	0.00433739i
$349$	7.17014	−	17.3102i	0.383809	−	0.926596i	−0.607413	−	0.794386i	$-0.707793\pi$
$349$	7.17014	−	17.3102i	0.383809	−	0.926596i	0.991222	−	0.132210i	$-0.0422073\pi$
$350$	11.0775	+	10.7188i	0.592116	+	0.572944i
$351$	−6.91168			−0.368918
$352$	11.5947	−	28.7416i	0.618000	−	1.53193i
$353$	−1.24335	+	2.15355i	−0.0661769	+	0.114622i	−0.897215	−	0.441593i	$-0.854413\pi$
$353$	−1.24335	+	2.15355i	−0.0661769	+	0.114622i	0.831039	+	0.556215i	$0.187747\pi$
$354$	−0.00929780	−	0.0181648i	−0.000494172	−	0.000965446i
$355$	−33.2007	+	4.37095i	−1.76211	+	0.231986i
$356$	27.0884	+	10.2834i	1.43568	+	0.545018i
$357$	1.65188	−	1.45309i	0.0874266	−	0.0769054i
$358$	18.1025	+	26.2351i	0.956745	+	1.38657i
$359$	−16.1733	−	4.33362i	−0.853594	−	0.228720i	−0.194614	−	0.980880i	$-0.562345\pi$
$359$	−16.1733	−	4.33362i	−0.853594	−	0.228720i	−0.658980	+	0.752160i	$0.729012\pi$
$360$	12.1961	+	22.1679i	0.642789	+	1.16835i
$361$	16.4395	−	4.40494i	0.865234	−	0.231839i
$362$	23.5682	−	8.39505i	1.23871	−	0.441234i
$363$	1.41540	+	3.41709i	0.0742894	+	0.179350i
$364$	3.04957	+	31.3907i	0.159841	+	1.64532i
$365$	−20.0043	−	8.28607i	−1.04707	−	0.433712i
$366$	1.87030	−	1.69031i	0.0977623	−	0.0883538i
$367$	−6.07154	−	3.50540i	−0.316932	−	0.182981i	0.333092	−	0.942894i	$-0.391908\pi$
$367$	−6.07154	−	3.50540i	−0.316932	−	0.182981i	−0.650024	+	0.759914i	$0.725241\pi$
$368$	−2.25859	+	4.51507i	−0.117737	+	0.235364i
$369$	−10.9637	+	6.32991i	−0.570749	+	0.329522i
$370$	28.4156	−	6.09492i	1.47726	−	0.316860i
$371$	−8.40252	−	16.9738i	−0.436237	−	0.881237i
$372$	0.195404	−	0.00584081i	0.0101312	−	0.000302832i
$373$	10.9932	−	14.3266i	0.569207	−	0.741805i	−0.416710	−	0.909039i	$-0.636817\pi$
$373$	10.9932	−	14.3266i	0.569207	−	0.741805i	0.985917	+	0.167234i	$0.0534836\pi$
$374$	−21.4663	+	25.2282i	−1.11000	+	1.30452i
$375$	0.499456	−	0.133829i	0.0257918	−	0.00691089i
$376$	−9.49869	−	24.3401i	−0.489857	−	1.25524i
$377$	−5.47588	+	5.47588i	−0.282022	+	0.282022i
$378$	2.58440	−	3.48532i	0.132927	−	0.179266i
$379$	−3.29244	+	1.36377i	−0.169121	+	0.0700523i	−0.465638	−	0.884975i	$-0.654175\pi$
$379$	−3.29244	+	1.36377i	−0.169121	+	0.0700523i	0.296516	+	0.955028i	$0.404175\pi$
$380$	4.97070	−	6.89512i	0.254992	−	0.353712i
$381$	−0.732074	−	0.954058i	−0.0375053	−	0.0488779i
$382$	25.2889	−	12.9444i	1.29389	−	0.662292i
$383$	−10.0023	−	17.3246i	−0.511096	−	0.885244i	−0.999917	−	0.0128604i	$-0.995906\pi$
$383$	−10.0023	−	17.3246i	−0.511096	−	0.885244i	0.488821	−	0.872384i	$-0.337427\pi$
$384$	−2.10161	+	0.652262i	−0.107247	+	0.0332856i
$385$	−8.47491	+	42.9458i	−0.431922	+	2.18872i
$386$	−20.8152	−	13.4628i	−1.05946	−	0.685239i
$387$	−26.8510	+	3.53500i	−1.36491	+	0.179694i
$388$	−0.899131	−	0.0911384i	−0.0456465	−	0.00462685i
$389$	−0.604023	+	4.58801i	−0.0306252	+	0.232621i	−0.999911	−	0.0133142i	$-0.995762\pi$
$389$	−0.604023	+	4.58801i	−0.0306252	+	0.232621i	0.969286	+	0.245936i	$0.0790952\pi$
$390$	−4.47254	−	2.12314i	−0.226476	−	0.107509i
$391$	3.81547	−	3.81547i	0.192957	−	0.192957i
$392$	−16.9695	−	10.1997i	−0.857091	−	0.515164i
$393$	1.20032	+	1.20032i	0.0605480	+	0.0605480i
$394$	4.27424	+	11.9994i	0.215333	+	0.604523i
$395$	−3.03429	−	0.399471i	−0.152671	−	0.0200996i
$396$	−15.3818	+	28.5815i	−0.772963	+	1.43628i
$397$	3.56041	+	27.0440i	0.178692	+	1.35730i	0.812117	+	0.583495i	$0.198315\pi$
$397$	3.56041	+	27.0440i	0.178692	+	1.35730i	−0.633425	+	0.773804i	$0.718352\pi$
$398$	−11.5260	+	2.47223i	−0.577745	+	0.123922i
$399$	−0.710512	−	0.140212i	−0.0355701	−	0.00701940i
$400$	0.984246	+	16.4493i	0.0492123	+	0.822463i
$401$	1.09372	−	0.631459i	0.0546177	−	0.0315336i	−0.472442	−	0.881362i	$-0.656628\pi$
$401$	1.09372	−	0.631459i	0.0546177	−	0.0315336i	0.527060	+	0.849828i	$0.323294\pi$
$402$	0.201855	+	0.0651739i	0.0100676	+	0.00325058i
$403$	2.37634	−	1.82343i	0.118374	−	0.0908315i
$404$	−1.59593	+	6.75762i	−0.0794003	+	0.336204i
$405$	−10.0091	−	24.1641i	−0.497357	−	1.20072i
$406$	−0.713772	−	4.80882i	−0.0354239	−	0.238658i
$407$	26.3622	+	26.3622i	1.30673	+	1.30673i
$408$	2.35144	+	0.0485095i	0.116413	+	0.00240158i
$409$	−2.26792	−	8.46400i	−0.112142	−	0.418518i	0.886916	−	0.461931i	$-0.152843\pi$
$409$	−2.26792	−	8.46400i	−0.112142	−	0.418518i	−0.999057	+	0.0434134i	$0.986177\pi$
$410$	−18.1936	+	1.46575i	−0.898515	+	0.0723884i
$411$	1.78003	+	1.36587i	0.0878026	+	0.0673733i
$412$	−17.0437	−	6.47018i	−0.839684	−	0.318763i
$413$	0.175907	−	0.0870787i	0.00865580	−	0.00428486i
$414$	2.87140	−	4.43953i	0.141121	−	0.218191i
$415$	−10.1101	−	17.5112i	−0.496286	−	0.859592i
$416$	−20.2766	+	26.9376i	−0.994142	+	1.32072i
$417$	−1.73257	+	3.00089i	−0.0848441	+	0.146954i
$418$	10.8903	+	0.550524i	0.532662	+	0.0269270i
$419$	0.789499	−	1.90602i	0.0385696	−	0.0931152i	−0.903421	−	0.428755i	$-0.858952\pi$
$419$	0.789499	−	1.90602i	0.0385696	−	0.0931152i	0.941990	+	0.335640i	$0.108952\pi$
$420$	2.74299	−	1.46147i	0.133844	−	0.0713125i
$421$	8.35055	−	3.45891i	0.406981	−	0.168577i	−0.169795	−	0.985479i	$-0.554311\pi$
$421$	8.35055	−	3.45891i	0.406981	−	0.168577i	0.576776	+	0.816902i	$0.304311\pi$
$422$	−0.350543	+	0.738442i	−0.0170641	+	0.0359468i
$423$	7.08214	+	26.4309i	0.344346	+	1.28512i
$424$	5.64268	−	19.4453i	0.274033	−	0.944345i
$425$	4.55850	−	17.0126i	0.221120	−	0.825230i
$426$	−0.550293	+	3.00010i	−0.0266618	+	0.145355i
$427$	16.0156	+	18.2066i	0.775047	+	0.881079i
$428$	−17.2858	+	18.3510i	−0.835538	+	0.887028i
$429$	−0.829000	−	6.29688i	−0.0400245	−	0.304016i
$430$	−37.1580	−	11.9974i	−1.79192	−	0.578565i
$431$	2.36261	+	1.36406i	0.113803	+	0.0657043i	0.555821	−	0.831302i	$-0.312404\pi$
$431$	2.36261	+	1.36406i	0.113803	+	0.0657043i	−0.442018	+	0.897006i	$0.645737\pi$
$432$	4.55449	−	0.879053i	0.219128	−	0.0422935i
$433$		−	23.1713i		−	1.11354i	−0.830666	−	0.556771i	$-0.812040\pi$
$433$		−	23.1713i		−	1.11354i	0.830666	−	0.556771i	$-0.187960\pi$
$434$	0.0309385	+	1.88012i	0.00148509	+	0.0902486i
$435$	0.705065	+	0.292047i	0.0338053	+	0.0140026i
$436$	−23.6161	+	14.5925i	−1.13101	+	0.698853i
$437$	−1.76104	−	0.231845i	−0.0842420	−	0.0110907i
$438$	−1.27806	+	1.50204i	−0.0610683	+	0.0717704i
$439$	−4.54888	+	16.9766i	−0.217106	+	0.810251i	0.768308	+	0.640080i	$0.221099\pi$
$439$	−4.54888	+	16.9766i	−0.217106	+	0.810251i	−0.985415	+	0.170171i	$0.945568\pi$
$440$	−37.7057	+	27.7160i	−1.79755	+	1.32131i
$441$	16.4885	+	12.5729i	0.785165	+	0.598712i
$442$	29.6606	−	20.4661i	1.41081	−	0.973474i
$443$	5.38327	+	4.13073i	0.255767	+	0.196257i	0.728684	−	0.684850i	$-0.240132\pi$
$443$	5.38327	+	4.13073i	0.255767	+	0.196257i	−0.472917	+	0.881107i	$0.656799\pi$
$444$	0.266947	−	2.63358i	0.0126687	−	0.124984i
$445$	−26.6333	−	34.7092i	−1.26254	−	1.64537i
$446$	−0.362173	+	7.16440i	−0.0171494	+	0.339244i
$447$	2.40358			0.113685
$448$	−6.00192	−	20.2972i	−0.283564	−	0.958953i
$449$	18.3637			0.866635			0.433318	−	0.901241i	$-0.357343\pi$
$449$	18.3637			0.866635			0.433318	+	0.901241i	$0.357343\pi$
$450$	0.871304	−	17.2359i	0.0410737	−	0.812506i
$451$	−14.2542	−	18.5764i	−0.671204	−	0.874730i
$452$	−0.0138150	+	0.136293i	−0.000649805	+	0.00641069i
$453$	−1.03667	−	0.795468i	−0.0487072	−	0.0373743i
$454$	12.7995	−	8.83178i	0.600710	−	0.414496i
$455$	20.9977	−	42.7420i	0.984386	−	2.00377i
$456$	−0.458545	−	0.623819i	−0.0214733	−	0.0292130i
$457$	−6.02250	+	22.4763i	−0.281720	+	1.05140i	0.669482	+	0.742828i	$0.266516\pi$
$457$	−6.02250	+	22.4763i	−0.281720	+	1.05140i	−0.951203	+	0.308567i	$0.900151\pi$
$458$	14.4404	−	16.9710i	0.674753	−	0.793002i
$459$	−4.91534	−	0.647117i	−0.229428	−	0.0302048i
$460$	6.48479	−	4.00698i	0.302355	−	0.186826i
$461$	−25.1245	−	10.4069i	−1.17016	−	0.484698i	−0.288917	−	0.957354i	$-0.593295\pi$
$461$	−25.1245	−	10.4069i	−1.17016	−	0.484698i	−0.881247	+	0.472657i	$0.843295\pi$
$462$	3.48528	+	1.93648i	0.162150	+	0.0900930i
$463$			11.5497i			0.536761i	0.963313	+	0.268381i	$0.0864885\pi$
$463$			11.5497i			0.536761i	−0.963313	+	0.268381i	$0.913512\pi$
$464$	2.91192	−	4.30480i	0.135182	−	0.199845i
$465$	−0.255633	−	0.147590i	−0.0118547	−	0.00684432i
$466$	18.2372	+	5.88833i	0.844822	+	0.272772i
$467$	1.34169	+	10.1912i	0.0620861	+	0.471590i	0.994040	+	0.109014i	$0.0347694\pi$
$467$	1.34169	+	10.1912i	0.0620861	+	0.471590i	−0.931954	+	0.362576i	$0.881897\pi$
$468$	24.2110	−	25.7030i	1.11916	−	1.18812i
$469$	−0.652903	+	1.93299i	−0.0301483	+	0.0892574i
$470$	−7.11764	+	38.8041i	−0.328312	+	1.78990i
$471$	−0.0522806	+	0.195114i	−0.00240896	+	0.00899037i
$472$	0.201519	+	0.0584774i	0.00927566	+	0.00269164i
$473$	−12.9645	−	48.3841i	−0.596108	−	2.22470i
$474$	−0.119543	+	0.251826i	−0.00549081	+	0.0115668i
$475$	−5.35647	+	2.21872i	−0.245772	+	0.101802i
$476$	−0.770258	+	22.6095i	−0.0353047	+	1.03630i
$477$	−8.11473	+	19.5907i	−0.371548	+	0.896997i
$478$	−7.09200	−	0.358514i	−0.324381	−	0.0163980i
$479$	−8.77291	+	15.1951i	−0.400844	+	0.694283i	−0.993828	−	0.110932i	$-0.964617\pi$
$479$	−8.77291	+	15.1951i	−0.400844	+	0.694283i	0.592984	+	0.805215i	$0.297950\pi$
$480$	3.21723	+	0.830219i	0.146846	+	0.0378941i
$481$	−20.2792	−	35.1246i	−0.924653	−	1.60155i
$482$	−18.4002	+	28.4490i	−0.838106	+	1.29582i
$483$	−0.540569	−	0.360015i	−0.0245967	−	0.0163812i
$484$	−35.5565	−	13.4980i	−1.61620	−	0.613547i
$485$	1.08260	+	0.830710i	0.0491584	+	0.0377206i
$486$	−7.27865	+	0.586400i	−0.330166	+	0.0265997i
$487$	−3.33054	−	12.4297i	−0.150921	−	0.563245i	−0.999420	−	0.0340483i	$-0.989160\pi$
$487$	−3.33054	−	12.4297i	−0.150921	−	0.563245i	0.848499	−	0.529197i	$-0.177507\pi$
$488$	−0.534660	+	25.9170i	−0.0242029	+	1.17321i
$489$	0.370944	+	0.370944i	0.0167747	+	0.0167747i
$490$	13.7019	+	26.5704i	0.618990	+	1.20033i
$491$	15.2024	+	36.7019i	0.686076	+	1.65633i	0.752542	+	0.658544i	$0.228828\pi$
$491$	15.2024	+	36.7019i	0.686076	+	1.65633i	−0.0664663	+	0.997789i	$0.521172\pi$
$492$	−0.382119	+	1.61800i	−0.0172272	+	0.0729452i
$493$	−4.40694	+	3.38156i	−0.198479	+	0.152298i
$494$	−11.2887	−	3.64484i	−0.507903	−	0.163989i
$495$	42.4432	−	24.5046i	1.90768	−	1.10140i
$496$	−1.33399	+	1.50379i	−0.0598980	+	0.0675222i
$497$	−28.7834	−	5.68011i	−1.29111	−	0.254788i
$498$	−1.80078	+	0.386253i	−0.0806950	+	0.0173084i
$499$	3.23014	+	24.5353i	0.144601	+	1.09835i	0.897751	+	0.440504i	$0.145200\pi$
$499$	3.23014	+	24.5353i	0.144601	+	1.09835i	−0.753150	+	0.657849i	$0.771467\pi$
$500$	−2.51973	+	4.68203i	−0.112686	+	0.209387i
$501$	1.19332	+	0.157104i	0.0533136	+	0.00701887i
$502$	−8.13772	−	22.8457i	−0.363204	−	1.01965i
$503$	−13.6066	−	13.6066i	−0.606689	−	0.606689i	0.335390	−	0.942079i	$-0.391132\pi$
$503$	−13.6066	−	13.6066i	−0.606689	−	0.606689i	−0.942079	+	0.335390i	$0.891132\pi$
$504$	3.90822	+	21.8196i	0.174086	+	0.971922i
$505$	7.41351	−	7.41351i	0.329897	−	0.329897i
$506$	8.83412	+	4.19361i	0.392725	+	0.186428i
$507$	−0.571825	+	4.34344i	−0.0253956	+	0.192899i
$508$	12.3027	+	1.24704i	0.545845	+	0.0553283i
$509$	−24.1716	+	3.18225i	−1.07139	+	0.141051i	−0.645527	−	0.763738i	$-0.723362\pi$
$509$	−24.1716	+	3.18225i	−1.07139	+	0.141051i	−0.425861	+	0.904789i	$0.640029\pi$
$510$	−2.98193	−	1.92865i	−0.132042	−	0.0854021i
$511$	−14.2813	−	12.4862i	−0.631769	−	0.552358i
$512$	9.93535	−	20.3295i	0.439085	−	0.898446i
$513$	0.816005	+	1.41336i	0.0360275	+	0.0624014i
$514$	3.06455	−	1.56862i	0.135171	−	0.0691887i
$515$	16.7574	+	21.8386i	0.738418	+	0.962324i
$516$	−2.07982	+	2.88503i	−0.0915589	+	0.127006i
$517$	−46.7575	+	19.3676i	−2.05639	+	0.851786i
$518$	25.2949	+	2.90760i	1.11139	+	0.127752i
$519$	−0.209268	+	0.209268i	−0.00918583	+	0.00918583i
$520$	47.4258	−	18.5079i	2.07976	−	0.811624i
$521$	19.7383	−	5.28886i	0.864750	−	0.231709i	0.200934	−	0.979605i	$-0.435602\pi$
$521$	19.7383	−	5.28886i	0.864750	−	0.231709i	0.663816	+	0.747896i	$0.268936\pi$
$522$	−3.52723	+	4.14537i	−0.154383	+	0.181438i
$523$	−21.5776	+	28.1205i	−0.943525	+	1.22963i	0.0296506	+	0.999560i	$0.490561\pi$
$523$	−21.5776	+	28.1205i	−0.943525	+	1.22963i	−0.973175	+	0.230065i	$0.926106\pi$
$524$	−17.4474	+	0.521518i	−0.762192	+	0.0227826i
$525$	−2.11563	−	0.135451i	−0.0923338	−	0.00591158i
$526$	38.3834	−	8.23294i	1.67360	−	0.358973i
$527$	1.86069	−	1.07427i	0.0810530	−	0.0467960i
$528$	1.34713	+	4.04393i	0.0586265	+	0.175989i
$529$	18.5391	+	10.7035i	0.806046	+	0.465371i
$530$	−22.6818	+	20.4989i	−0.985234	+	0.890417i
$531$	−0.203026	−	0.0840963i	−0.00881059	−	0.00364947i
$532$	6.05901	−	4.32964i	0.262692	−	0.187714i
$533$	9.74808	+	23.5340i	0.422236	+	1.01937i
$534$	−3.75389	+	1.33715i	−0.162447	+	0.0578640i
$535$	36.7688	−	9.85218i	1.58966	−	0.425947i
$536$	−1.91103	+	1.05138i	−0.0825438	+	0.0454129i
$537$	−4.23437	−	1.13459i	−0.182726	−	0.0489614i
$538$	7.86623	+	11.4002i	0.339137	+	0.491496i
$539$	−19.0749	+	33.2707i	−0.821613	+	1.43307i
$540$	−6.54797	−	2.48576i	−0.281780	−	0.106970i
$541$	9.81306	−	1.29191i	0.421896	−	0.0555437i	0.0834107	−	0.996515i	$-0.473419\pi$
$541$	9.81306	−	1.29191i	0.421896	−	0.0555437i	0.338486	+	0.940972i	$0.390085\pi$
$542$	−17.8453	−	34.8638i	−0.766523	−	1.49753i
$543$	−1.72043	+	2.97987i	−0.0738307	+	0.127878i
$544$	−16.9421	+	17.2586i	−0.726385	+	0.739957i
$545$	41.9171			1.79553
$546$	−3.11715	−	3.01622i	−0.133402	−	0.129082i
$547$	−2.30920	+	5.57491i	−0.0987344	+	0.238366i	−0.965527	−	0.260303i	$-0.916178\pi$
$547$	−2.30920	+	5.57491i	−0.0987344	+	0.238366i	0.866793	+	0.498669i	$0.166178\pi$
$548$	−22.7739	+	3.69350i	−0.972851	+	0.157779i
$549$	3.54356	−	26.9160i	0.151235	−	1.14875i
$550$	31.8163	−	2.56327i	1.35665	−	0.109298i
$551$	1.76625	+	0.473265i	0.0752447	+	0.0201618i
$552$	−0.165833	−	0.674229i	−0.00705834	−	0.0286971i
$553$	−2.40659	−	1.18227i	−0.102339	−	0.0502754i
$554$	0.287935	−	1.56977i	0.0122332	−	0.0666930i
$555$	−2.43317	+	3.17098i	−0.103283	+	0.134600i
$556$	−10.2463	−	34.1264i	−0.434538	−	1.44728i
$557$	−26.1993	+	20.1034i	−1.11010	+	0.851810i	−0.990016	−	0.140953i	$-0.954983\pi$
$557$	−26.1993	+	20.1034i	−1.11010	+	0.851810i	−0.120085	+	0.992764i	$0.538317\pi$
$558$	1.56190	−	1.41159i	0.0661205	−	0.0597572i
$559$			54.4933i			2.30482i
$560$	−8.40044	+	30.8356i	−0.354983	+	1.30304i
$561$		−	4.55574i		−	0.192343i
$562$	−8.96357	−	9.91807i	−0.378105	−	0.418369i
$563$	33.6425	−	25.8148i	1.41786	−	1.08797i	0.435668	−	0.900108i	$-0.356512\pi$
$563$	33.6425	−	25.8148i	1.41786	−	1.08797i	0.982196	−	0.187858i	$-0.0601543\pi$
$564$	3.16427	+	1.70292i	0.133240	+	0.0717059i
$565$	0.125922	−	0.164104i	0.00529757	−	0.00690392i
$566$	29.9584	+	5.49512i	1.25925	+	0.230977i
$567$	−1.53329	−	22.8634i	−0.0643922	−	0.960172i
$568$	−18.5760	−	25.2714i	−0.779433	−	1.06036i
$569$	−0.667826	−	0.178943i	−0.0279967	−	0.00750170i	0.244794	−	0.969575i	$-0.421280\pi$
$569$	−0.667826	−	0.178943i	−0.0279967	−	0.00750170i	−0.272790	+	0.962074i	$0.587946\pi$
$570$	0.0938775	+	1.16525i	0.00393210	+	0.0488068i
$571$	−0.400155	+	3.03948i	−0.0167460	+	0.127198i	−0.997776	−	0.0666583i	$-0.978766\pi$
$571$	−0.400155	+	3.03948i	−0.0167460	+	0.127198i	0.981030	+	0.193856i	$0.0620996\pi$
$572$	52.9774	+	38.1915i	2.21510	+	1.59687i
$573$	−1.49521	+	3.60975i	−0.0624633	+	0.150800i
$574$	−15.5123	−	3.88413i	−0.647473	−	0.162120i
$575$	−5.19951			−0.216834
$576$	−12.6850	+	20.0164i	−0.528541	+	0.834016i
$577$	−23.0936	+	39.9993i	−0.961399	+	1.66519i	−0.242406	+	0.970175i	$0.577936\pi$
$577$	−23.0936	+	39.9993i	−0.961399	+	1.66519i	−0.718993	+	0.695017i	$0.755397\pi$
$578$	1.60876	−	0.823461i	0.0669158	−	0.0342515i
$579$	3.38017	−	0.445008i	0.140475	−	0.0184939i
$580$	−7.15710	+	3.21835i	−0.297183	+	0.133635i
$581$	−3.48234	−	17.3695i	−0.144472	−	0.720609i
$582$	0.102302	−	0.0705895i	0.00424056	−	0.00292603i
$583$	−37.8832	−	10.1508i	−1.56896	−	0.420402i
$584$	−2.23179	−	20.1566i	−0.0923519	−	0.834088i
$585$	−51.4997	+	13.7993i	−2.12925	+	0.570531i
$586$	6.09564	+	17.1128i	0.251809	+	0.706924i
$587$	−0.997077	−	2.40716i	−0.0411538	−	0.0993540i	0.901966	−	0.431807i	$-0.142124\pi$
$587$	−0.997077	−	2.40716i	−0.0411538	−	0.0993540i	−0.943120	+	0.332453i	$0.892124\pi$
$588$	2.68653	−	0.444054i	0.110791	−	0.0183125i
$589$	−0.653426	−	0.270658i	−0.0269239	−	0.0111523i
$590$	−0.212439	−	0.235061i	−0.00874596	−	0.00967729i
$591$	−1.51716	−	0.875935i	−0.0624078	−	0.0360312i
$592$	17.8304	+	20.5664i	0.732824	+	0.845273i
$593$	19.2249	−	11.0995i	0.789473	−	0.455802i	−0.0503042	−	0.998734i	$-0.516019\pi$
$593$	19.2249	−	11.0995i	0.789473	−	0.455802i	0.839777	+	0.542932i	$0.182686\pi$
$594$	−1.88434	−	8.78511i	−0.0773152	−	0.360457i
$595$	18.9346	−	28.4306i	0.776243	−	1.16554i
$596$	−16.9466	+	17.9909i	−0.694160	+	0.736936i
$597$	0.986948	−	1.28622i	0.0403931	−	0.0526413i
$598$	−8.10228	−	6.89411i	−0.331327	−	0.281921i
$599$	−19.3702	+	5.19023i	−0.791446	+	0.212067i	−0.631825	−	0.775111i	$-0.717694\pi$
$599$	−19.3702	+	5.19023i	−0.791446	+	0.212067i	−0.159621	+	0.987178i	$0.551027\pi$
$600$	−1.56915	−	1.63525i	−0.0640602	−	0.0667590i
$601$	17.5555	−	17.5555i	0.716102	−	0.716102i	−0.251703	−	0.967805i	$-0.580991\pi$
$601$	17.5555	−	17.5555i	0.716102	−	0.716102i	0.967805	+	0.251703i	$0.0809905\pi$
$602$	−27.4791	−	20.3760i	−1.11996	−	0.830463i
$603$	2.11041	−	0.874160i	0.0859425	−	0.0355985i
$604$	13.2633	−	2.15106i	0.539675	−	0.0875253i
$605$	34.9591	+	45.5596i	1.42129	+	1.85226i
$606$	−0.435114	−	0.850065i	−0.0176753	−	0.0345315i
$607$	15.1703	+	26.2757i	0.615742	+	1.06650i	0.990254	+	0.139274i	$0.0444768\pi$
$607$	15.1703	+	26.2757i	0.615742	+	1.06650i	−0.374512	+	0.927222i	$0.622190\pi$
$608$	7.90232	+	0.966044i	0.320482	+	0.0391782i
$609$	0.503355	+	0.440084i	0.0203970	+	0.0178331i
$610$	21.2571	−	32.8661i	0.860676	−	1.33071i
$611$	54.5869	−	7.18651i	2.20835	−	0.290735i
$612$	19.6245	−	16.0123i	0.793274	−	0.647258i
$613$	−0.908361	+	6.89968i	−0.0366883	+	0.278676i	0.963261	+	0.268569i	$0.0865506\pi$
$613$	−0.908361	+	6.89968i	−0.0366883	+	0.278676i	−0.999949	+	0.0101071i	$0.996783\pi$
$614$	12.3868	−	26.0937i	0.499891	−	1.05305i
$615$	1.77505	−	1.77505i	0.0715768	−	0.0715768i
$616$	−39.0678	+	12.4342i	−1.57409	+	0.500990i
$617$	3.00134	+	3.00134i	0.120829	+	0.120829i	0.764936	−	0.644106i	$-0.222771\pi$
$617$	3.00134	+	3.00134i	0.120829	+	0.120829i	−0.644106	+	0.764936i	$0.722771\pi$
$618$	2.36190	−	0.841318i	0.0950097	−	0.0338428i
$619$	0.367838	+	0.0484268i	0.0147847	+	0.00194644i	0.137915	−	0.990444i	$-0.455960\pi$
$619$	0.367838	+	0.0484268i	0.0147847	+	0.00194644i	−0.123130	+	0.992391i	$0.539293\pi$
$620$	2.90708	−	0.872836i	0.116751	−	0.0350539i
$621$	0.191038	+	1.45108i	0.00766608	+	0.0582297i
$622$	−0.877029	−	4.08887i	−0.0351657	−	0.163949i
$623$	−12.3756	−	36.2770i	−0.495819	−	1.45341i
$624$	−0.276962	−	4.62874i	−0.0110874	−	0.185298i
$625$	24.7914	−	14.3133i	0.991657	−	0.572534i
$626$	12.1128	−	37.5156i	0.484126	−	1.49942i
$627$	−1.18977	+	0.912942i	−0.0475148	+	0.0364594i
$628$	−1.09183	−	1.76699i	−0.0435688	−	0.0705105i
$629$	−11.1333	−	26.8781i	−0.443912	−	1.07170i
$630$	12.2981	−	31.1294i	0.489969	−	1.24022i
$631$	−34.5848	−	34.5848i	−1.37680	−	1.37680i	−0.849971	−	0.526830i	$-0.823381\pi$
$631$	−34.5848	−	34.5848i	−1.37680	−	1.37680i	−0.526830	−	0.849971i	$-0.676619\pi$
$632$	−1.04209	−	2.67031i	−0.0414520	−	0.106219i
$633$	−0.0290967	−	0.108591i	−0.00115649	−	0.00431609i
$634$	3.72822	+	46.2763i	0.148067	+	1.83787i
$635$	−14.8131	−	11.3665i	−0.587841	−	0.451067i
$636$	1.14203	+	2.53970i	0.0452845	+	0.100706i
$637$	29.4121	−	29.5907i	1.16535	−	1.17243i
$638$	−8.45302	−	5.46724i	−0.334658	−	0.216450i
$639$	16.4236	+	28.4466i	0.649709	+	1.12533i
$640$	−28.8976	+	18.2277i	−1.14228	+	0.720511i
$641$	3.23073	−	5.59579i	0.127606	−	0.221021i	−0.795142	−	0.606423i	$-0.792604\pi$
$641$	3.23073	−	5.59579i	0.127606	−	0.221021i	0.922749	+	0.385402i	$0.125937\pi$
$642$	0.175050	−	3.46278i	0.00690866	−	0.136665i
$643$	2.82466	−	6.81934i	0.111394	−	0.268929i	−0.858345	−	0.513073i	$-0.828507\pi$
$643$	2.82466	−	6.81934i	0.111394	−	0.268929i	0.969739	+	0.244144i	$0.0785070\pi$
$644$	6.50605	−	1.50788i	0.256374	−	0.0594187i
$645$	4.96139	−	2.05508i	0.195355	−	0.0809185i
$646$	−7.68688	−	3.64900i	−0.302436	−	0.143568i
$647$	−0.271500	−	1.01325i	−0.0106738	−	0.0398351i	0.960384	−	0.278682i	$-0.0898974\pi$
$647$	−0.271500	−	1.01325i	−0.0106738	−	0.0398351i	−0.971057	+	0.238846i	$0.923231\pi$
$648$	15.3104	−	19.1230i	0.601451	−	0.751222i
$649$	0.105196	−	0.392598i	0.00412932	−	0.0154108i
$650$	−34.1549	−	6.26487i	−1.33967	−	0.245728i
$651$	−0.170808	−	0.194176i	−0.00669449	−	0.00761034i
$652$	−5.39191	+	0.161169i	−0.211163	+	0.00631187i
$653$	1.71660	+	13.0389i	0.0671757	+	0.510250i	0.991645	+	0.128994i	$0.0411749\pi$
$653$	1.71660	+	13.0389i	0.0671757	+	0.510250i	−0.924470	+	0.381256i	$0.875492\pi$
$654$	1.17310	−	3.63329i	0.0458717	−	0.142073i
$655$	22.8252	+	13.1781i	0.891853	+	0.514912i
$656$	−9.41669	−	14.2680i	−0.367660	−	0.557073i
$657$			21.2388i			0.828603i
$658$	−16.7871	+	30.2135i	−0.654429	+	1.17784i
$659$	−9.08982	−	3.76512i	−0.354089	−	0.146668i	0.198547	−	0.980091i	$-0.436378\pi$
$659$	−9.08982	−	3.76512i	−0.354089	−	0.146668i	−0.552636	+	0.833423i	$0.686378\pi$
$660$	1.47927	−	6.26367i	0.0575805	−	0.243813i
$661$	26.6893	+	3.51371i	1.03809	+	0.136668i	0.630256	−	0.776387i	$-0.282950\pi$
$661$	26.6893	+	3.51371i	1.03809	+	0.136668i	0.407837	+	0.913055i	$0.366283\pi$
$662$	−6.46572	−	5.50158i	−0.251297	−	0.213825i
$663$	−1.28274	+	4.78725i	−0.0498175	+	0.185921i
$664$	9.80542	−	16.2023i	0.380524	−	0.628770i
$665$	−11.2193	+	0.752401i	−0.435065	+	0.0291769i
$666$	−16.1897	−	23.4631i	−0.627340	−	0.909175i
$667$	1.30099	+	0.998284i	0.0503745	+	0.0386537i
$668$	−9.58952	+	7.82440i	−0.371030	+	0.302735i
$669$	−0.600597	−	0.782713i	−0.0232204	−	0.0302614i
$670$	3.28921	+	0.166276i	0.127073	+	0.00642379i
$671$	50.2122			1.93842
$672$	2.43768	+	1.59110i	0.0940354	+	0.0613782i
$673$	−28.1530			−1.08522			−0.542609	−	0.839985i	$-0.682563\pi$
$673$	−28.1530			−1.08522			−0.542609	+	0.839985i	$0.682563\pi$
$674$	−11.6676	−	0.589818i	−0.449419	−	0.0227189i
$675$	2.90824	+	3.79010i	0.111938	+	0.145881i
$676$	−28.4792	−	34.9039i	−1.09535	−	1.34246i
$677$	20.6879	+	15.8744i	0.795102	+	0.610103i	0.924366	−	0.381507i	$-0.124595\pi$
$677$	20.6879	+	15.8744i	0.795102	+	0.610103i	−0.129264	+	0.991610i	$0.541261\pi$
$678$	−0.0107002	−	0.0155073i	−0.000410938	−	0.000595554i
$679$	0.665706	+	0.993044i	0.0255475	+	0.0381095i
$680$	35.4604	−	8.72183i	1.35984	−	0.334467i
$681$	−0.553543	+	2.06585i	−0.0212118	+	0.0791636i
$682$	2.96554	+	2.52333i	0.113556	+	0.0966233i
$683$	3.51722	+	0.463050i	0.134583	+	0.0177181i	0.197516	−	0.980300i	$-0.436712\pi$
$683$	3.51722	+	0.463050i	0.134583	+	0.0177181i	−0.0629339	+	0.998018i	$0.520046\pi$
$684$	−8.11438	−	1.91635i	−0.310261	−	0.0732734i
$685$	32.1847	+	13.3313i	1.22971	+	0.509364i
$686$	3.92386	+	25.8960i	0.149814	+	0.988714i
$687$			3.06463i			0.116923i
$688$	−6.93067	−	35.9087i	−0.264229	−	1.36900i
$689$	36.9502	+	21.3332i	1.40769	+	0.812731i
$690$	−0.322123	+	0.997673i	−0.0122630	+	0.0379808i
$691$	−0.159432	−	1.21101i	−0.00606507	−	0.0460688i	0.988145	−	0.153525i	$-0.0490627\pi$
$691$	−0.159432	−	1.21101i	−0.00606507	−	0.0460688i	−0.994210	+	0.107457i	$0.965729\pi$
$692$	−0.0909233	−	3.04184i	−0.00345639	−	0.115633i
$693$	42.0997	−	8.44040i	1.59924	−	0.320624i
$694$	−34.4634	−	6.32144i	−1.30821	−	0.239959i
$695$	−13.9248	+	51.9680i	−0.528197	+	1.97126i
$696$	0.0786606	+	0.710433i	0.00298162	+	0.0269289i
$697$	4.72909	+	17.6492i	0.179127	+	0.668511i
$698$	−23.9372	−	11.3631i	−0.906037	−	0.430101i
$699$	−2.43506	+	1.00863i	−0.0921023	+	0.0381500i
$700$	15.9303	−	14.8806i	0.602108	−	0.562434i
$701$	9.67092	−	23.3477i	0.365266	−	0.881830i	−0.629246	−	0.777206i	$-0.716636\pi$
$701$	9.67092	−	23.3477i	0.365266	−	0.881830i	0.994512	−	0.104623i	$-0.0333637\pi$
$702$	−0.493493	+	9.76212i	−0.0186257	+	0.368447i
$703$	−4.78840	+	8.29375i	−0.180598	+	0.312805i
$704$	−39.7671	−	18.4286i	−1.49878	−	0.694555i
$705$	−2.71291	−	4.69890i	−0.102174	−	0.176971i
$706$	2.95292	+	1.90988i	0.111134	+	0.0718794i
$707$	8.23199	−	4.07506i	0.309596	−	0.153259i
$708$	−0.0263199	+	0.0118353i	−0.000989164	+	0.000444799i
$709$	−1.27025	−	0.974694i	−0.0477051	−	0.0366054i	0.584634	−	0.811297i	$-0.301238\pi$
$709$	−1.27025	−	0.974694i	−0.0477051	−	0.0366054i	−0.632339	+	0.774692i	$0.717905\pi$
$710$	3.80305	+	47.2051i	0.142726	+	1.77157i
$711$	0.776971	+	2.89969i	0.0291387	+	0.108747i
$712$	16.4584	−	37.5257i	0.616806	−	1.40634i
$713$	−0.448503	−	0.448503i	−0.0167966	−	0.0167966i
$714$	−1.93441	−	2.43688i	−0.0723934	−	0.0911979i
$715$	−37.7371	−	91.1054i	−1.41129	−	3.40715i
$716$	38.3472	−	23.6949i	1.43310	−	0.885521i
$717$	0.774804	−	0.594528i	0.0289356	−	0.0222031i
$718$	−7.27563	+	22.5339i	−0.271524	+	0.840958i
$719$	−6.32208	+	3.65005i	−0.235774	+	0.136124i	−0.613233	−	0.789902i	$-0.710131\pi$
$719$	−6.32208	+	3.65005i	−0.235774	+	0.136124i	0.377459	+	0.926026i	$0.376798\pi$
$720$	32.1810	−	15.6431i	1.19931	−	0.582983i
$721$	7.78661	+	22.8251i	0.289988	+	0.850050i
$722$	−5.04780	−	23.5338i	−0.187860	−	0.875836i
$723$	−0.608211	−	4.61982i	−0.0226196	−	0.171813i
$724$	−10.1745	−	33.8873i	−0.378132	−	1.25941i
$725$	5.30686	+	0.698662i	0.197092	+	0.0259476i
$726$	4.92739	−	1.75515i	0.182872	−	0.0651397i
$727$	−15.9338	−	15.9338i	−0.590952	−	0.590952i	0.346937	−	0.937888i	$-0.387222\pi$
$727$	−15.9338	−	15.9338i	−0.590952	−	0.590952i	−0.937888	+	0.346937i	$0.887222\pi$
$728$	44.5543	−	2.06595i	1.65129	−	0.0765692i
$729$	−17.6625	+	17.6625i	−0.654168	+	0.654168i
$730$	−13.1316	+	27.6627i	−0.486023	+	1.02384i
$731$	−5.10202	+	38.7537i	−0.188705	+	1.43336i
$732$	−2.25387	−	2.76232i	−0.0833054	−	0.102098i
$733$	8.04946	−	1.05973i	0.297314	−	0.0391421i	0.0196063	−	0.999808i	$-0.493759\pi$
$733$	8.04946	−	1.05973i	0.297314	−	0.0391421i	0.277707	+	0.960666i	$0.410425\pi$
$734$	−5.38457	+	8.32521i	−0.198748	+	0.307289i
$735$	−3.80331	−	1.56192i	−0.140287	−	0.0576122i
$736$	6.21586	+	3.51243i	0.229120	+	0.129470i
$737$	2.11246	+	3.65889i	0.0778135	+	0.134777i
$738$	8.15763	+	15.9372i	0.300286	+	0.586658i
$739$	−24.1438	−	31.4648i	−0.888143	−	1.15745i	−0.986738	−	0.162323i	$-0.948101\pi$
$739$	−24.1438	−	31.4648i	−0.888143	−	1.15745i	0.0985941	−	0.995128i	$-0.468565\pi$
$740$	−6.57965	−	40.5696i	−0.241873	−	1.49137i
$741$	1.50728	−	0.624338i	0.0553715	−	0.0229356i
$742$	−24.5739	+	10.6559i	−0.902138	+	0.391189i
$743$	−33.9729	+	33.9729i	−1.24634	+	1.24634i	−0.289020	+	0.957323i	$0.593329\pi$
$743$	−33.9729	+	33.9729i	−1.24634	+	1.24634i	−0.957323	+	0.289020i	$0.906671\pi$
$744$	0.00570221	−	0.276408i	0.000209053	−	0.0101336i
$745$	36.0474	−	9.65887i	1.32067	−	0.353874i
$746$	−19.4502	−	16.5498i	−0.712121	−	0.605933i
$747$	−12.0741	+	15.7352i	−0.441767	+	0.575722i
$748$	34.0999	+	32.1205i	1.24682	+	1.17444i
$749$	33.2818	+	2.13084i	1.21609	+	0.0778591i
$750$	−0.153360	−	0.714992i	−0.00559992	−	0.0261078i
$751$	9.05161	−	5.22595i	0.330298	−	0.190698i	−0.325675	−	0.945482i	$-0.605592\pi$
$751$	9.05161	−	5.22595i	0.330298	−	0.190698i	0.655973	+	0.754784i	$0.272258\pi$
$752$	−35.0564	+	11.6782i	−1.27837	+	0.425859i
$753$	2.88853	+	1.66769i	0.105264	+	0.0607741i
$754$	7.34321	+	8.12516i	0.267424	+	0.295901i
$755$	−18.7440	−	7.76403i	−0.682165	−	0.282562i
$756$	−4.73818	−	3.89908i	−0.172326	−	0.141808i
$757$	2.64470	+	6.38487i	0.0961232	+	0.232062i	0.964626	−	0.263622i	$-0.0849173\pi$
$757$	2.64470	+	6.38487i	0.0961232	+	0.232062i	−0.868503	+	0.495684i	$0.834917\pi$
$758$	1.69113	+	4.74765i	0.0614245	+	0.172442i
$759$	−1.29909	+	0.348090i	−0.0471539	+	0.0126349i
$760$	−9.38383	−	7.51298i	−0.340387	−	0.272524i
$761$	−43.3060	−	11.6038i	−1.56984	−	0.420637i	−0.634078	−	0.773269i	$-0.718620\pi$
$761$	−43.3060	−	11.6038i	−1.56984	−	0.420637i	−0.935762	+	0.352632i	$0.885287\pi$
$762$	−1.39979	+	0.965870i	−0.0507091	+	0.0349898i
$763$	34.7929	+	11.7519i	1.25959	+	0.425448i
$764$	−16.4771	−	36.6426i	−0.596122	−	1.32568i
$765$	−37.9168	+	4.99184i	−1.37088	+	0.180480i
$766$	−25.1836	+	12.8904i	−0.909919	+	0.465751i
$767$	−0.221085	+	0.382930i	−0.00798291	+	0.0138268i
$768$	0.771207	+	3.01491i	0.0278285	+	0.108791i
$769$	−24.3333			−0.877480			−0.438740	−	0.898614i	$-0.644575\pi$
$769$	−24.3333			−0.877480			−0.438740	+	0.898614i	$0.644575\pi$
$770$	60.0519	+	15.0364i	2.16412	+	0.541873i
$771$	−0.181191	+	0.437435i	−0.00652545	+	0.0157538i
$772$	−20.5012	+	28.4383i	−0.737855	+	1.02352i
$773$	1.78908	−	13.5894i	0.0643486	−	0.488776i	−0.928678	−	0.370887i	$-0.879054\pi$
$773$	1.78908	−	13.5894i	0.0643486	−	0.488776i	0.993027	−	0.117890i	$-0.0376129\pi$
$774$	3.07571	+	38.1770i	0.110554	+	1.37224i
$775$	−1.99980	−	0.535844i	−0.0718349	−	0.0192481i
$776$	−0.192923	+	1.26343i	−0.00692552	+	0.0453547i
$777$	−2.90866	+	1.94987i	−0.104347	+	0.0699513i
$778$	6.43703	+	1.18071i	0.230779	+	0.0423306i
$779$	3.66156	−	4.77184i	0.131189	−	0.170969i
$780$	−3.31808	+	6.16547i	−0.118806	+	0.220759i
$781$	−48.1985	+	36.9840i	−1.72468	+	1.32339i
$782$	−5.11659	−	5.66144i	−0.182969	−	0.202453i
$783$		−	1.50671i		−	0.0538453i
$784$	−15.6178	+	23.2397i	−0.557780	+	0.829989i
$785$			3.13629i			0.111939i
$786$	1.78104	−	1.60964i	0.0635277	−	0.0574139i
$787$	43.4167	−	33.3148i	1.54764	−	1.18754i	0.639561	−	0.768740i	$-0.279116\pi$
$787$	43.4167	−	33.3148i	1.54764	−	1.18754i	0.908076	−	0.418804i	$-0.137551\pi$
$788$	17.2533	−	5.18022i	0.614624	−	0.184538i
$789$	−3.28670	+	4.28331i	−0.117010	+	0.152490i
$790$	−0.780865	+	4.25713i	−0.0277819	+	0.151462i
$791$	0.150529	−	0.100910i	0.00535219	−	0.00358794i
$792$	39.2706	+	23.7661i	1.39542	+	0.844491i
$793$	−52.7639	−	14.1381i	−1.87370	−	0.502057i
$794$	38.4514	−	3.09782i	1.36459	−	0.109937i
$795$	0.548819	−	4.16869i	0.0194646	−	0.147848i
$796$	2.66885	+	16.4559i	0.0945948	+	0.583264i
$797$	13.4980	−	32.5870i	0.478122	−	1.15429i	−0.482366	−	0.875970i	$-0.660223\pi$
$797$	13.4980	−	32.5870i	0.478122	−	1.15429i	0.960489	−	0.278320i	$-0.0897774\pi$
$798$	−0.248768	+	0.993523i	−0.00880628	+	0.0351703i
$799$	39.4932			1.39717
$800$	23.3034	−	0.215684i	0.823898	−	0.00762558i
$801$	−21.4570	+	37.1645i	−0.758144	+	1.31314i
$802$	−0.813787	−	1.58987i	−0.0287358	−	0.0561401i
$803$	−38.9462	+	5.12737i	−1.37438	+	0.180941i
$804$	0.106465	−	0.280449i	0.00375472	−	0.00989068i
$805$	−9.55386	−	3.22699i	−0.336729	−	0.113736i
$806$	−2.40576	−	3.48656i	−0.0847393	−	0.122809i
$807$	−1.84000	−	0.493026i	−0.0647710	−	0.0173553i
$808$	9.43058	+	2.73659i	0.331767	+	0.0962731i
$809$	23.5700	−	6.31557i	0.828678	−	0.222043i	0.180541	−	0.983567i	$-0.442215\pi$
$809$	23.5700	−	6.31557i	0.828678	−	0.222043i	0.648137	+	0.761524i	$0.275549\pi$
$810$	−34.8443	+	12.4116i	−1.22430	+	0.436101i
$811$	−16.1023	−	38.8745i	−0.565429	−	1.36507i	−0.905371	−	0.424621i	$-0.860407\pi$
$811$	−16.1023	−	38.8745i	−0.565429	−	1.36507i	0.339942	−	0.940446i	$-0.389593\pi$
$812$	−6.84299	+	0.664789i	−0.240142	+	0.0233295i
$813$	4.97647	+	2.06132i	0.174532	+	0.0722937i
$814$	39.1165	−	35.3520i	1.37103	−	1.23909i
$815$	7.05385	+	4.07254i	0.247086	+	0.142655i
$816$	0.236408	−	3.31773i	0.00827593	−	0.116144i
$817$	11.1433	−	6.43357i	0.389854	−	0.225082i
$818$	−12.1166	+	2.59891i	−0.423646	+	0.0908687i
$819$	−46.6157	−	2.98453i	−1.62889	−	0.104288i
$820$	0.771228	+	25.8014i	0.0269324	+	0.901024i
$821$	0.799478	−	1.04190i	0.0279020	−	0.0363625i	−0.779194	−	0.626783i	$-0.784371\pi$
$821$	0.799478	−	1.04190i	0.0279020	−	0.0363625i	0.807096	+	0.590420i	$0.201038\pi$
$822$	2.05626	−	2.41661i	0.0717203	−	0.0842891i
$823$	8.10536	−	2.17183i	0.282535	−	0.0757051i	−0.114768	−	0.993392i	$-0.536613\pi$
$823$	8.10536	−	2.17183i	0.282535	−	0.0757051i	0.397304	+	0.917687i	$0.369946\pi$
$824$	−10.3555	+	23.6108i	−0.360750	+	0.822520i
$825$	−3.10415	+	3.10415i	−0.108072	+	0.108072i
$826$	−0.110431	−	0.254670i	−0.00384239	−	0.00886109i
$827$	−9.70756	+	4.02100i	−0.337565	+	0.139824i	−0.545026	−	0.838419i	$-0.683480\pi$
$827$	−9.70756	+	4.02100i	−0.337565	+	0.139824i	0.207461	+	0.978243i	$0.433480\pi$
$828$	−6.06542	−	4.37257i	−0.210788	−	0.151957i
$829$	−9.33231	−	12.1621i	−0.324125	−	0.422407i	0.602661	−	0.797997i	$-0.294107\pi$
$829$	−9.33231	−	12.1621i	−0.324125	−	0.422407i	−0.926786	+	0.375589i	$0.877440\pi$
$830$	−25.4549	+	13.0293i	−0.883552	+	0.452254i
$831$	0.109747	+	0.190088i	0.00380709	+	0.00659407i
$832$	36.5991	+	30.5622i	1.26885	+	1.05955i
$833$	23.6874	−	18.2901i	0.820718	−	0.633714i
$834$	4.11479	+	2.66136i	0.142483	+	0.0921553i
$835$	18.5280	−	2.43926i	0.641189	−	0.0844141i
$836$	1.55513	−	15.3422i	0.0537854	−	0.530623i
$837$	−0.0760675	+	0.577790i	−0.00262928	+	0.0199714i
$838$	−2.63571	−	1.25119i	−0.0910491	−	0.0432215i
$839$	13.7601	−	13.7601i	0.475050	−	0.475050i	−0.428494	−	0.903545i	$-0.640956\pi$
$839$	13.7601	−	13.7601i	0.475050	−	0.475050i	0.903545	+	0.428494i	$0.140956\pi$
$840$	−1.86835	−	3.97857i	−0.0644641	−	0.137274i
$841$	19.3124	+	19.3124i	0.665944	+	0.665944i
$842$	−4.28917	−	12.0414i	−0.147815	−	0.414973i
$843$	1.82285	+	0.239982i	0.0627821	+	0.00826542i
$844$	1.01795	+	0.547835i	0.0350395	+	0.0188572i
$845$	8.87841	+	67.4382i	0.305427	+	2.31995i
$846$	37.8370	−	8.11572i	1.30086	−	0.279024i
$847$	16.2444	+	47.6175i	0.558163	+	1.63616i
$848$	−27.0618	−	9.35817i	−0.929306	−	0.321361i
$849$	−3.62775	+	2.09448i	−0.124504	+	0.0718825i
$850$	−23.7032	−	7.65316i	−0.813014	−	0.262501i
$851$	−6.81375	+	5.22837i	−0.233572	+	0.179226i
$852$	4.19808	+	0.991447i	0.143824	+	0.0339664i
$853$	18.5187	+	44.7080i	0.634067	+	1.53077i	0.834467	+	0.551058i	$0.185776\pi$
$853$	18.5187	+	44.7080i	0.634067	+	1.53077i	−0.200400	+	0.979714i	$0.564224\pi$
$854$	26.8587	−	21.3206i	0.919085	−	0.729575i
$855$	8.90196	+	8.90196i	0.304441	+	0.304441i
$856$	24.6849	+	25.7248i	0.843712	+	0.879257i
$857$	−6.34114	−	23.6655i	−0.216609	−	0.808397i	−0.985594	−	0.169129i	$-0.945904\pi$
$857$	−6.34114	−	23.6655i	−0.216609	−	0.808397i	0.768985	−	0.639267i	$-0.220762\pi$
$858$	−8.95296	+	0.721291i	−0.305649	+	0.0246245i
$859$	4.83863	+	3.71281i	0.165092	+	0.126680i	0.688003	−	0.725708i	$-0.258487\pi$
$859$	4.83863	+	3.71281i	0.165092	+	0.126680i	−0.522911	+	0.852387i	$0.675154\pi$
$860$	−19.5983	+	51.6257i	−0.668296	+	1.76042i
$861$	1.97102	−	0.975708i	0.0671721	−	0.0332520i
$862$	2.09530	−	3.23959i	0.0713661	−	0.110341i
$863$	−24.9061	−	43.1386i	−0.847814	−	1.46846i	−0.883155	−	0.469081i	$-0.844585\pi$
$863$	−24.9061	−	43.1386i	−0.847814	−	1.46846i	0.0353411	−	0.999375i	$-0.488748\pi$
$864$	−0.916394	−	6.49557i	−0.0311764	−	0.220984i
$865$	−2.29752	+	3.97942i	−0.0781181	+	0.135304i
$866$	−32.7274	−	1.65443i	−1.11212	−	0.0562198i
$867$	−0.0951183	+	0.229636i	−0.00323039	+	0.00779884i
$868$	2.65771	+	0.0905425i	0.0902085	+	0.00307321i
$869$	−5.12969	+	2.12479i	−0.174013	+	0.0720785i
$870$	0.462832	−	0.974989i	0.0156915	−	0.0330552i
$871$	−1.18960	−	4.43963i	−0.0403079	−	0.150431i
$872$	18.9244	+	34.3975i	0.640861	+	1.16485i
$873$	0.346433	−	1.29290i	0.0117250	−	0.0437582i
$874$	−0.453199	+	2.47076i	−0.0153297	+	0.0835746i
$875$	6.89649	−	1.38265i	0.233144	−	0.0467420i
$876$	2.03025	+	1.91240i	0.0685957	+	0.0646139i
$877$	−4.30096	−	32.6691i	−0.145233	−	1.10316i	−0.896464	−	0.443116i	$-0.853873\pi$
$877$	−4.30096	−	32.6691i	−0.145233	−	1.10316i	0.751231	−	0.660039i	$-0.229460\pi$
$878$	23.6532	+	7.63701i	0.798256	+	0.257737i
$879$	−2.16368	−	1.24920i	−0.0729792	−	0.0421345i
$880$	36.4542	+	55.2349i	1.22887	+	1.86197i
$881$			6.14703i			0.207099i	0.994624	+	0.103549i	$0.0330200\pi$
$881$			6.14703i			0.207099i	−0.994624	+	0.103549i	$0.966980\pi$
$882$	18.9354	−	22.3908i	0.637589	−	0.753936i
$883$	36.8658	+	15.2703i	1.24063	+	0.513887i	0.903913	−	0.427717i	$-0.140682\pi$
$883$	36.8658	+	15.2703i	1.24063	+	0.513887i	0.336721	+	0.941604i	$0.390682\pi$
$884$	−26.7888	−	43.3543i	−0.901005	−	1.45816i
$885$	0.0432018	+	0.00568763i	0.00145221	+	0.000191188i
$886$	6.21865	−	7.30846i	0.208920	−	0.245532i
$887$	−7.05302	+	26.3222i	−0.236817	+	0.883814i	0.740504	+	0.672052i	$0.234587\pi$
$887$	−7.05302	+	26.3222i	−0.236817	+	0.883814i	−0.977321	+	0.211762i	$0.932080\pi$
$888$	−3.70064	−	0.565076i	−0.124185	−	0.0189627i
$889$	−9.10879	−	13.5877i	−0.305499	−	0.455717i
$890$	−50.9252	+	35.1389i	−1.70702	+	1.17786i
$891$	−37.6453	−	28.8862i	−1.26116	−	0.967725i
$892$	10.0932	+	1.02307i	0.337946	+	0.0342551i
$893$	−7.91419	−	10.3140i	−0.264838	−	0.345144i
$894$	0.171615	−	3.39484i	0.00573967	−	0.113540i
$895$	−68.0639			−2.27513
$896$	−29.0965	+	7.02795i	−0.972047	+	0.234787i
$897$	1.46312			0.0488520
$898$	1.31116	−	25.9370i	0.0437541	−	0.865530i
$899$	0.397497	+	0.518029i	0.0132573	+	0.0172772i
$900$	−24.2819	−	2.46128i	−0.809396	−	0.0820426i
$901$	24.2803	+	18.6310i	0.808895	+	0.620687i
$902$	−27.2553	+	18.8064i	−0.907502	+	0.626185i
$903$	4.69432	−	0.314816i	0.156217	−	0.0104764i
$904$	0.191516	+	0.0292438i	0.00636971	+	0.000972635i
$905$	−13.8272	+	51.6039i	−0.459633	+	1.71537i
$906$	−1.19755	+	1.40741i	−0.0397858	+	0.0467581i
$907$	19.5273	+	2.57082i	0.648394	+	0.0853627i	0.447548	−	0.894260i	$-0.352297\pi$
$907$	19.5273	+	2.57082i	0.648394	+	0.0853627i	0.200847	+	0.979623i	$0.435631\pi$
$908$	−11.5602	−	18.7087i	−0.383639	−	0.620871i
$909$	−9.50112	−	3.93549i	−0.315132	−	0.130532i
$910$	−58.8700	−	32.7091i	−1.95152	−	1.08430i
$911$		−	15.2338i		−	0.504719i	−0.967634	−	0.252360i	$-0.918793\pi$
$911$		−	15.2338i		−	0.504719i	0.967634	−	0.252360i	$-0.0812066\pi$
$912$	−0.913828	+	0.603113i	−0.0302599	+	0.0199711i
$913$	−31.7691	−	18.3419i	−1.05140	−	0.607028i
$914$	31.3157	+	10.1110i	1.03583	+	0.334443i
$915$	0.702645	+	5.33712i	0.0232287	+	0.176440i
$916$	−22.9390	−	21.6074i	−0.757925	−	0.713930i
$917$	15.2512	+	17.3377i	0.503639	+	0.572541i
$918$	−1.26495	+	6.89627i	−0.0417496	+	0.227611i
$919$	−13.9437	+	52.0387i	−0.459961	+	1.71660i	0.213118	+	0.977026i	$0.431638\pi$
$919$	−13.9437	+	52.0387i	−0.459961	+	1.71660i	−0.673079	+	0.739571i	$0.735029\pi$
$920$	−5.19649	−	9.44528i	−0.171323	−	0.311402i
$921$	1.02816	+	3.83716i	0.0338792	+	0.126439i
$922$	−16.4927	+	34.7430i	−0.543158	+	1.14420i
$923$	61.0613	−	25.2924i	2.00986	−	0.832510i
$924$	2.98395	−	4.78438i	0.0981646	−	0.157394i
$925$	−10.7281	+	25.8998i	−0.352737	+	0.851581i
$926$	16.3129	+	0.824649i	0.536077	+	0.0270997i
$927$	13.5005	−	23.3835i	0.443414	−	0.768015i
$928$	−5.87224	−	4.42018i	−0.192766	−	0.145100i
$929$	−11.2640	−	19.5098i	−0.369559	−	0.640095i	0.619938	−	0.784651i	$-0.287158\pi$
$929$	−11.2640	−	19.5098i	−0.369559	−	0.640095i	−0.989497	+	0.144556i	$0.953824\pi$
$930$	−0.226710	+	0.350521i	−0.00743411	+	0.0114940i
$931$	−9.52342	−	2.52093i	−0.312117	−	0.0826201i
$932$	9.61887	−	25.3380i	0.315077	−	0.829973i
$933$	0.456288	+	0.350122i	0.0149382	+	0.0114625i
$934$	14.4899	−	1.16737i	0.474124	−	0.0381975i
$935$	−18.3074	−	68.3242i	−0.598716	−	2.23444i
$936$	−34.5745	−	36.0311i	−1.13010	−	1.17771i
$937$	−10.5179	−	10.5179i	−0.343606	−	0.343606i	0.514115	−	0.857721i	$-0.328120\pi$
$937$	−10.5179	−	10.5179i	−0.343606	−	0.343606i	−0.857721	+	0.514115i	$0.828120\pi$
$938$	2.68356	+	1.06018i	0.0876215	+	0.0346162i
$939$	2.07485	+	5.00913i	0.0677102	+	0.163467i
$940$	54.2991	+	12.8236i	1.77104	+	0.418261i
$941$	23.6476	−	18.1455i	0.770890	−	0.591525i	−0.146640	−	0.989190i	$-0.546846\pi$
$941$	23.6476	−	18.1455i	0.770890	−	0.591525i	0.917531	+	0.397665i	$0.130179\pi$
$942$	0.271848	+	0.0877728i	0.00885729	+	0.00285979i
$943$	4.67141	−	2.69704i	0.152122	−	0.0878278i
$944$	0.0969825	−	0.280452i	0.00315651	−	0.00912794i
$945$	2.99151	+	8.76909i	0.0973138	+	0.285258i
$946$	−69.2639	+	14.8565i	−2.25196	+	0.483028i
$947$	−6.68210	−	50.7556i	−0.217139	−	1.64934i	−0.658920	−	0.752213i	$-0.728987\pi$
$947$	−6.68210	−	50.7556i	−0.217139	−	1.64934i	0.441781	−	0.897123i	$-0.354347\pi$
$948$	0.347147	+	0.186825i	0.0112748	+	0.00606778i
$949$	42.3691	+	5.57800i	1.37536	+	0.181070i
$950$	2.75129	+	7.72395i	0.0892637	+	0.250598i
$951$	−4.51493	−	4.51493i	−0.146406	−	0.146406i
$952$	31.8789	+	2.70223i	1.03320	+	0.0875799i
$953$	−6.86940	+	6.86940i	−0.222522	+	0.222522i	−0.809560	−	0.587038i	$-0.800294\pi$
$953$	−6.86940	+	6.86940i	−0.222522	+	0.222522i	0.587038	+	0.809560i	$0.300294\pi$
$954$	27.0907	+	12.8601i	0.877094	+	0.416361i
$955$	−7.91831	+	60.1455i	−0.256230	+	1.94626i
$956$	−1.01274	+	9.99122i	−0.0327543	+	0.323139i
$957$	1.37268	−	0.180717i	0.0443726	−	0.00584176i
$958$	20.8354	+	13.4759i	0.673160	+	0.435386i
$959$	22.9770	+	20.0889i	0.741967	+	0.648704i
$960$	1.40232	−	4.48478i	0.0452597	−	0.144746i
$961$	15.3737	+	26.6281i	0.495926	+	0.858970i
$962$	−51.0583	+	26.1347i	−1.64619	+	0.842616i
$963$	−22.7302	−	29.6226i	−0.732471	−	0.954575i
$964$	38.8678	+	28.0199i	1.25185	+	0.902460i
$965$	48.9055	−	20.2573i	1.57432	−	0.652106i
$966$	−0.547085	+	0.737800i	−0.0176022	+	0.0237383i
$967$	10.0451	−	10.0451i	0.323029	−	0.323029i	−0.526899	−	0.849928i	$-0.676645\pi$
$967$	10.0451	−	10.0451i	0.323029	−	0.323029i	0.849928	+	0.526899i	$0.176645\pi$
$968$	−21.6035	+	49.2566i	−0.694363	+	1.58317i
$969$	1.13038	−	0.302885i	0.0363131	−	0.00973007i
$970$	1.25060	−	1.46977i	0.0401544	−	0.0471913i
$971$	3.80805	−	4.96274i	0.122206	−	0.159262i	−0.728244	−	0.685318i	$-0.759663\pi$
$971$	3.80805	−	4.96274i	0.122206	−	0.159262i	0.850450	+	0.526056i	$0.176330\pi$
$972$	0.308543	+	10.3223i	0.00989652	+	0.331088i
$973$	−26.1280	+	39.2316i	−0.837624	+	1.25771i
$974$	−17.7937	+	3.81660i	−0.570146	+	0.122292i
$975$	4.13592	−	2.38787i	0.132455	−	0.0764731i
$976$	36.5672	+	2.60563i	1.17049	+	0.0834041i
$977$	−42.1874	−	24.3569i	−1.34969	−	0.779246i	−0.361488	−	0.932377i	$-0.617731\pi$
$977$	−42.1874	−	24.3569i	−1.34969	−	0.779246i	−0.988206	+	0.153131i	$0.951064\pi$
$978$	0.550411	−	0.497440i	0.0176002	−	0.0159064i
$979$	−73.3299	−	30.3743i	−2.34363	−	0.970765i
$980$	38.5066	−	17.4556i	1.23005	−	0.557599i
$981$	−15.7344	−	37.9863i	−0.502362	−	1.21281i
$982$	52.9236	−	18.8515i	1.68886	−	0.601577i
$983$	−49.5761	+	13.2839i	−1.58123	+	0.423690i	−0.939307	−	0.343078i	$-0.888530\pi$
$983$	−49.5761	+	13.2839i	−1.58123	+	0.423690i	−0.641925	+	0.766768i	$0.721864\pi$
$984$	2.25800	+	0.655233i	0.0719824	+	0.0208881i
$985$	−26.2735	−	7.03997i	−0.837144	−	0.224312i
$986$	4.46150	+	6.46585i	0.142083	+	0.205915i
$987$	−0.934439	−	4.66087i	−0.0297435	−	0.148357i
$988$	−5.95402	+	15.6841i	−0.189423	+	0.498976i
$989$	11.4406	−	1.50619i	0.363791	−	0.0478940i
$990$	−31.5801	−	61.6968i	−1.00368	−	1.96085i
$991$	−26.5712	+	46.0226i	−0.844062	+	1.46196i	0.0423722	+	0.999102i	$0.486508\pi$
$991$	−26.5712	+	46.0226i	−0.844062	+	1.46196i	−0.886434	+	0.462856i	$0.846825\pi$
$992$	2.02872	+	1.99151i	0.0644120	+	0.0632306i
$993$	1.16758			0.0370522
$994$	−10.0778	+	40.2484i	−0.319648	+	1.27660i
$995$	9.63294	−	23.2560i	0.305385	−	0.737264i
$996$	0.416972	+	2.57102i	0.0132123	+	0.0814659i
$997$	4.40157	−	33.4332i	0.139399	−	1.05884i	−0.768559	−	0.639779i	$-0.779026\pi$
$997$	4.40157	−	33.4332i	0.139399	−	1.05884i	0.907958	−	0.419062i	$-0.137641\pi$
$998$	34.8846	−	2.81046i	1.10425	−	0.0889635i
$999$	7.62228	+	2.04238i	0.241158	+	0.0646182i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.15	yes	240
4.3	odd	2		896.2.bh.a.529.15		240
7.2	even	3	inner	224.2.bd.a.205.5	yes	240
28.23	odd	6		896.2.bh.a.401.16		240
32.5	even	8	inner	224.2.bd.a.165.5	yes	240
32.27	odd	8		896.2.bh.a.753.16		240
224.37	even	24	inner	224.2.bd.a.37.15	✓	240
224.219	odd	24		896.2.bh.a.625.15		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.15	✓	240	224.37	even	24	inner
224.2.bd.a.109.15	yes	240	1.1	even	1	trivial
224.2.bd.a.165.5	yes	240	32.5	even	8	inner
224.2.bd.a.205.5	yes	240	7.2	even	3	inner
896.2.bh.a.401.16		240	28.23	odd	6
896.2.bh.a.529.15		240	4.3	odd	2
896.2.bh.a.625.15		240	224.219	odd	24
896.2.bh.a.753.16		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)

\(f(q)\)	\(=\)	\(q+(0.0713999 - 1.41241i) q^{2} +(0.118403 + 0.154306i) q^{3} +(-1.98980 - 0.201692i) q^{4} +(2.39583 + 1.83839i) q^{5} +(0.226398 - 0.156217i) q^{6} +(1.47323 + 2.19764i) q^{7} +(-0.426943 + 2.79602i) q^{8} +(0.766666 - 2.86124i) q^{9} +O(q^{10})\)	\(q+(0.0713999 - 1.41241i) q^{2} +(0.118403 + 0.154306i) q^{3} +(-1.98980 - 0.201692i) q^{4} +(2.39583 + 1.83839i) q^{5} +(0.226398 - 0.156217i) q^{6} +(1.47323 + 2.19764i) q^{7} +(-0.426943 + 2.79602i) q^{8} +(0.766666 - 2.86124i) q^{9} +(2.76762 - 3.25263i) q^{10} +(5.43183 + 0.715114i) q^{11} +(-0.204477 - 0.330920i) q^{12} +(-5.50652 - 2.28087i) q^{13} +(3.20915 - 1.92389i) q^{14} +0.587363i q^{15} +(3.91864 + 0.802655i) q^{16} +(-3.70249 - 2.13763i) q^{17} +(-3.98650 - 1.28714i) q^{18} +(0.183696 + 1.39531i) q^{19} +(-4.39645 - 4.14125i) q^{20} +(-0.164674 + 0.487536i) q^{21} +(1.39787 - 7.62091i) q^{22} +(-0.326660 + 1.21911i) q^{23} +(-0.481995 + 0.265178i) q^{24} +(1.06625 + 3.97929i) q^{25} +(-3.61470 + 7.61461i) q^{26} +(1.07136 - 0.443773i) q^{27} +(-2.48819 - 4.67000i) q^{28} +(0.497218 - 1.20039i) q^{29} +(0.829598 + 0.0419377i) q^{30} +(-0.251275 + 0.435222i) q^{31} +(1.41347 - 5.47742i) q^{32} +(0.532801 + 0.922838i) q^{33} +(-3.28357 + 5.07681i) q^{34} +(-0.510497 + 7.97352i) q^{35} +(-2.10260 + 5.53867i) q^{36} +(5.39866 + 4.14254i) q^{37} +(1.98386 - 0.159829i) q^{38} +(-0.300037 - 1.11975i) q^{39} +(-6.16304 + 5.91390i) q^{40} +(-3.02206 - 3.02206i) q^{41} +(0.676843 + 0.267397i) q^{42} +(-3.49881 - 8.44689i) q^{43} +(-10.6640 - 2.51849i) q^{44} +(7.09686 - 5.44561i) q^{45} +(1.69856 + 0.548423i) q^{46} +(-7.99998 + 4.61879i) q^{47} +(0.340126 + 0.699708i) q^{48} +(-2.65920 + 6.47523i) q^{49} +(5.69652 - 1.22186i) q^{50} +(-0.108537 - 0.824421i) q^{51} +(10.4969 + 5.64911i) q^{52} +(-7.09730 - 0.934377i) q^{53} +(-0.550295 - 1.54489i) q^{54} +(11.6991 + 11.6991i) q^{55} +(-6.77361 + 3.18091i) q^{56} +(-0.193554 + 0.193554i) q^{57} +(-1.65994 - 0.787983i) q^{58} +(0.00968333 - 0.0735522i) q^{59} +(0.118466 - 1.16874i) q^{60} +(9.08657 - 1.19627i) q^{61} +(0.596771 + 0.385979i) q^{62} +(7.41743 - 2.53040i) q^{63} +(-7.63544 - 2.38748i) q^{64} +(-8.99956 - 15.5877i) q^{65} +(1.34147 - 0.686643i) q^{66} +(0.469449 + 0.611798i) q^{67} +(6.93609 + 5.00024i) q^{68} +(-0.226794 + 0.0939414i) q^{69} +(11.2254 + 1.29034i) q^{70} +(-7.84105 + 7.84105i) q^{71} +(7.67275 + 3.36520i) q^{72} +(-6.92569 + 1.85573i) q^{73} +(6.23643 - 7.32935i) q^{74} +(-0.487783 + 0.635691i) q^{75} +(-0.0840962 - 2.81344i) q^{76} +(6.43076 + 12.9907i) q^{77} +(-1.60297 + 0.343825i) q^{78} +(-0.877666 + 0.506720i) q^{79} +(7.91281 + 9.12700i) q^{80} +(-7.50061 - 4.33048i) q^{81} +(-4.48416 + 4.05261i) q^{82} +(-6.18602 - 2.56233i) q^{83} +(0.426001 - 0.936888i) q^{84} +(-4.94075 - 11.9280i) q^{85} +(-12.1803 + 4.33865i) q^{86} +(0.244100 - 0.0654064i) q^{87} +(-4.31856 + 14.8822i) q^{88} +(-13.9937 - 3.74960i) q^{89} +(-7.18472 - 10.4125i) q^{90} +(-3.09982 - 15.4616i) q^{91} +(0.895875 - 2.35991i) q^{92} +(-0.0969094 + 0.0127584i) q^{93} +(5.95243 + 11.6290i) q^{94} +(-2.12501 + 3.68062i) q^{95} +(1.01256 - 0.430438i) q^{96} +0.451869 q^{97} +(8.95582 + 4.21821i) q^{98} +(6.21051 - 14.9935i) 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

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