LMFDB - Embedded newform 462.2.ba.b.61.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(19,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 25, 9]))

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

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

chi := DirichletCharacter("462.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.ba (of order $30$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			61.4
Character	$\chi$	$=$	462.61
Dual form			462.2.ba.b.409.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207912 + 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(1.55595 - 1.40099i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(2.62525 - 0.328695i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(q+(-0.207912 + 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(1.55595 - 1.40099i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(2.62525 - 0.328695i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +(1.04687 + 1.81324i) q^{10} +(-1.10872 - 3.12582i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-1.19925 - 3.69091i) q^{13} +(-0.224308 + 2.63623i) q^{14} +(1.69387 - 1.23067i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.590297 + 0.125472i) q^{17} +(-0.406737 + 0.913545i) q^{18} +(-1.80631 + 0.804222i) q^{19} +(-1.99127 + 0.647002i) q^{20} +(2.64523 - 0.0524810i) q^{21} +(3.28803 - 0.434593i) q^{22} +(1.03779 - 1.79751i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.0644142 + 0.612860i) q^{25} +(3.85959 - 0.405660i) q^{26} +(0.951057 + 0.309017i) q^{27} +(-2.53198 - 0.767509i) q^{28} +(0.865758 + 1.19161i) q^{29} +(0.851602 + 1.91273i) q^{30} +(6.54795 + 5.89580i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.775904 - 3.22459i) q^{33} -0.603485i q^{34} +(3.62428 - 4.18939i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(0.809518 + 7.70205i) q^{37} +(-0.411094 - 1.93405i) q^{38} +(-0.806875 - 3.79605i) q^{39} +(-0.218856 - 2.08227i) q^{40} +(-4.33918 - 3.15260i) q^{41} +(-0.498640 + 2.59834i) q^{42} +8.56947i q^{43} +(-0.258524 + 3.30653i) q^{44} +(1.81324 - 1.04687i) q^{45} +(1.54246 + 1.38884i) q^{46} +(-1.59613 - 3.58496i) q^{47} +(0.587785 + 0.809017i) q^{48} +(6.78392 - 1.72582i) q^{49} +(-0.586075 - 0.190427i) q^{50} +(-0.600179 + 0.0630814i) q^{51} +(-0.405660 + 3.85959i) q^{52} +(-7.18013 + 7.97434i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-6.10435 - 3.31034i) q^{55} +(1.27717 - 2.31708i) q^{56} +(-1.88048 + 0.611005i) q^{57} +(-1.34558 + 0.599089i) q^{58} +(-3.12185 + 7.01178i) q^{59} +(-2.04799 + 0.435314i) q^{60} +(2.09031 + 2.32152i) q^{61} +(-7.12836 + 5.17905i) q^{62} +(2.63623 + 0.224308i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-7.03690 - 4.06276i) q^{65} +(3.31544 - 0.0885192i) q^{66} +(2.26830 + 3.92881i) q^{67} +(0.590297 + 0.125472i) q^{68} +(1.22000 - 1.67918i) q^{69} +(3.34431 + 4.41610i) q^{70} +(2.71182 - 8.34611i) q^{71} +(0.743145 - 0.669131i) q^{72} +(-7.23220 - 3.21998i) q^{73} +(-7.70205 - 0.809518i) q^{74} +(-0.128123 + 0.602770i) q^{75} +1.97725 q^{76} +(-3.93810 - 7.84164i) q^{77} +3.88085 q^{78} +(1.60414 - 7.54689i) q^{79} +(2.08227 + 0.218856i) q^{80} +(0.913545 + 0.406737i) q^{81} +(3.98587 - 3.58889i) q^{82} +(-0.104801 + 0.322544i) q^{83} +(-2.43788 - 1.02797i) q^{84} +(-0.742692 + 1.02223i) q^{85} +(-8.38221 - 1.78169i) q^{86} +(0.736458 + 1.27558i) q^{87} +(-3.18053 - 0.940342i) q^{88} +(-0.117265 - 0.0677028i) q^{89} +(0.647002 + 1.99127i) q^{90} +(-4.36152 - 9.29539i) q^{91} +(-1.67918 + 1.22000i) q^{92} +(5.89580 + 6.54795i) q^{93} +(3.83847 - 0.815893i) q^{94} +(-1.68383 + 3.78195i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(8.97295 - 2.91549i) q^{97} +(0.277648 + 6.99449i) q^{98} +(-0.434593 - 3.28803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.207912	+	0.978148i	−0.147016	+	0.691655i
$2$	−0.207912	+	0.978148i	−0.147016	+	0.691655i
$3$	0.994522	+	0.104528i	0.574187	+	0.0603495i
$3$	0.994522	+	0.104528i	0.574187	+	0.0603495i
$4$	−0.913545	−	0.406737i	−0.456773	−	0.203368i
$5$	1.55595	−	1.40099i	0.695844	−	0.626541i	−0.243345	−	0.969940i	$-0.578245\pi$
$5$	1.55595	−	1.40099i	0.695844	−	0.626541i	0.939190	+	0.343399i	$0.111578\pi$
$6$	−0.309017	+	0.951057i	−0.126156	+	0.388267i
$7$	2.62525	−	0.328695i	0.992253	−	0.124235i
$7$	2.62525	−	0.328695i	0.992253	−	0.124235i
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	0.978148	+	0.207912i	0.326049	+	0.0693039i
$10$	1.04687	+	1.81324i	0.331050	+	0.573395i
$11$	−1.10872	−	3.12582i	−0.334290	−	0.942470i
$11$	−1.10872	−	3.12582i	−0.334290	−	0.942470i
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−1.19925	−	3.69091i	−0.332612	−	1.02367i	−0.967886	−	0.251388i	$-0.919113\pi$
$13$	−1.19925	−	3.69091i	−0.332612	−	1.02367i	0.635274	−	0.772287i	$-0.280887\pi$
$14$	−0.224308	+	2.63623i	−0.0599490	+	0.704561i
$15$	1.69387	−	1.23067i	0.437357	−	0.317758i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−0.590297	+	0.125472i	−0.143168	+	0.0304313i	−0.278938	−	0.960309i	$-0.589982\pi$
$17$	−0.590297	+	0.125472i	−0.143168	+	0.0304313i	0.135770	+	0.990740i	$0.456649\pi$
$18$	−0.406737	+	0.913545i	−0.0958687	+	0.215325i
$19$	−1.80631	+	0.804222i	−0.414396	+	0.184501i	−0.603335	−	0.797488i	$-0.706162\pi$
$19$	−1.80631	+	0.804222i	−0.414396	+	0.184501i	0.188939	+	0.981989i	$0.439495\pi$
$20$	−1.99127	+	0.647002i	−0.445261	+	0.144674i
$21$	2.64523	−	0.0524810i	0.577237	−	0.0114523i
$22$	3.28803	−	0.434593i	0.701010	−	0.0926554i
$23$	1.03779	−	1.79751i	0.216394	−	0.374806i	−0.737309	−	0.675556i	$-0.763904\pi$
$23$	1.03779	−	1.79751i	0.216394	−	0.374806i	0.953703	+	0.300750i	$0.0972370\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	−0.0644142	+	0.612860i	−0.0128828	+	0.122572i
$26$	3.85959	−	0.405660i	0.756929	−	0.0795564i
$27$	0.951057	+	0.309017i	0.183031	+	0.0594703i
$28$	−2.53198	−	0.767509i	−0.478500	−	0.145046i
$29$	0.865758	+	1.19161i	0.160767	+	0.221277i	0.881800	−	0.471624i	$-0.156332\pi$
$29$	0.865758	+	1.19161i	0.160767	+	0.221277i	−0.721032	+	0.692901i	$0.756332\pi$
$30$	0.851602	+	1.91273i	0.155481	+	0.349215i
$31$	6.54795	+	5.89580i	1.17605	+	1.05892i	0.997180	+	0.0750433i	$0.0239095\pi$
$31$	6.54795	+	5.89580i	1.17605	+	1.05892i	0.178866	+	0.983873i	$0.442757\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−0.775904	−	3.22459i	−0.135068	−	0.561329i
$34$		−	0.603485i		−	0.103497i
$35$	3.62428	−	4.18939i	0.612615	−	0.708135i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	0.809518	+	7.70205i	0.133084	+	1.26621i	0.833518	+	0.552492i	$0.186323\pi$
$37$	0.809518	+	7.70205i	0.133084	+	1.26621i	−0.700434	+	0.713717i	$0.747010\pi$
$38$	−0.411094	−	1.93405i	−0.0666883	−	0.313744i
$39$	−0.806875	−	3.79605i	−0.129203	−	0.607854i
$40$	−0.218856	−	2.08227i	−0.0346041	−	0.329236i
$41$	−4.33918	−	3.15260i	−0.677666	−	0.492353i	0.194917	−	0.980820i	$-0.437556\pi$
$41$	−4.33918	−	3.15260i	−0.677666	−	0.492353i	−0.872582	+	0.488467i	$0.837556\pi$
$42$	−0.498640	+	2.59834i	−0.0769419	+	0.400932i
$43$			8.56947i			1.30683i	0.756999	+	0.653416i	$0.226665\pi$
$43$			8.56947i			1.30683i	−0.756999	+	0.653416i	$0.773335\pi$
$44$	−0.258524	+	3.30653i	−0.0389739	+	0.498479i
$45$	1.81324	−	1.04687i	0.270301	−	0.156058i
$46$	1.54246	+	1.38884i	0.227423	+	0.204773i
$47$	−1.59613	−	3.58496i	−0.232819	−	0.522920i	0.758921	−	0.651182i	$-0.225727\pi$
$47$	−1.59613	−	3.58496i	−0.232819	−	0.522920i	−0.991740	+	0.128262i	$0.959060\pi$
$48$	0.587785	+	0.809017i	0.0848395	+	0.116772i
$49$	6.78392	−	1.72582i	0.969131	−	0.246545i
$50$	−0.586075	−	0.190427i	−0.0828836	−	0.0269305i
$51$	−0.600179	+	0.0630814i	−0.0840419	+	0.00883316i
$52$	−0.405660	+	3.85959i	−0.0562549	+	0.535229i
$53$	−7.18013	+	7.97434i	−0.986267	+	1.09536i	0.00917208	+	0.999958i	$0.497080\pi$
$53$	−7.18013	+	7.97434i	−0.986267	+	1.09536i	−0.995439	+	0.0954022i	$0.969586\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−6.10435	−	3.31034i	−0.823110	−	0.446366i
$56$	1.27717	−	2.31708i	0.170668	−	0.309633i
$57$	−1.88048	+	0.611005i	−0.249076	+	0.0809296i
$58$	−1.34558	+	0.599089i	−0.176683	+	0.0786642i
$59$	−3.12185	+	7.01178i	−0.406430	+	0.912856i	0.588138	+	0.808761i	$0.299861\pi$
$59$	−3.12185	+	7.01178i	−0.406430	+	0.912856i	−0.994567	+	0.104095i	$0.966805\pi$
$60$	−2.04799	+	0.435314i	−0.264394	+	0.0561988i
$61$	2.09031	+	2.32152i	0.267637	+	0.297241i	0.861950	−	0.506993i	$-0.169243\pi$
$61$	2.09031	+	2.32152i	0.267637	+	0.297241i	−0.594314	+	0.804233i	$0.702576\pi$
$62$	−7.12836	+	5.17905i	−0.905302	+	0.657741i
$63$	2.63623	+	0.224308i	0.332133	+	0.0282602i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−7.03690	−	4.06276i	−0.872820	−	0.503923i
$66$	3.31544	−	0.0885192i	0.408103	−	0.0108960i
$67$	2.26830	+	3.92881i	0.277117	+	0.479981i	0.970667	−	0.240428i	$-0.0772877\pi$
$67$	2.26830	+	3.92881i	0.277117	+	0.479981i	−0.693550	+	0.720408i	$0.743954\pi$
$68$	0.590297	+	0.125472i	0.0715841	+	0.0152157i
$69$	1.22000	−	1.67918i	0.146870	−	0.202150i
$70$	3.34431	+	4.41610i	0.399721	+	0.527825i
$71$	2.71182	−	8.34611i	0.321833	−	0.990501i	−0.651016	−	0.759064i	$-0.725657\pi$
$71$	2.71182	−	8.34611i	0.321833	−	0.990501i	0.972850	−	0.231438i	$-0.0743429\pi$
$72$	0.743145	−	0.669131i	0.0875805	−	0.0788578i
$73$	−7.23220	−	3.21998i	−0.846465	−	0.376871i	−0.0627791	−	0.998027i	$-0.519996\pi$
$73$	−7.23220	−	3.21998i	−0.846465	−	0.376871i	−0.783686	+	0.621157i	$0.786663\pi$
$74$	−7.70205	−	0.809518i	−0.895345	−	0.0941046i
$75$	−0.128123	+	0.602770i	−0.0147943	+	0.0696019i
$76$	1.97725			0.226807
$77$	−3.93810	−	7.84164i	−0.448788	−	0.893638i
$78$	3.88085			0.439420
$79$	1.60414	−	7.54689i	0.180480	−	0.849091i	−0.790972	−	0.611853i	$-0.790424\pi$
$79$	1.60414	−	7.54689i	0.180480	−	0.849091i	0.971451	−	0.237238i	$-0.0762422\pi$
$80$	2.08227	+	0.218856i	0.232805	+	0.0244688i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	3.98587	−	3.58889i	0.440166	−	0.396327i
$83$	−0.104801	+	0.322544i	−0.0115034	+	0.0354038i	−0.956643	−	0.291262i	$-0.905925\pi$
$83$	−0.104801	+	0.322544i	−0.0115034	+	0.0354038i	0.945140	+	0.326665i	$0.105925\pi$
$84$	−2.43788	−	1.02797i	−0.265995	−	0.112161i
$85$	−0.742692	+	1.02223i	−0.0805563	+	0.110876i
$86$	−8.38221	−	1.78169i	−0.903877	−	0.192125i
$87$	0.736458	+	1.27558i	0.0789566	+	0.136757i
$88$	−3.18053	−	0.940342i	−0.339045	−	0.100241i
$89$	−0.117265	−	0.0677028i	−0.0124300	−	0.00717648i	0.493772	−	0.869591i	$-0.335618\pi$
$89$	−0.117265	−	0.0677028i	−0.0124300	−	0.00717648i	−0.506202	+	0.862415i	$0.668951\pi$
$90$	0.647002	+	1.99127i	0.0682000	+	0.209898i
$91$	−4.36152	−	9.29539i	−0.457212	−	0.974422i
$92$	−1.67918	+	1.22000i	−0.175067	+	0.127193i
$93$	5.89580	+	6.54795i	0.611366	+	0.678991i
$94$	3.83847	−	0.815893i	0.395908	−	0.0841529i
$95$	−1.68383	+	3.78195i	−0.172758	+	0.388020i
$96$	−0.913545	+	0.406737i	−0.0932383	+	0.0415124i
$97$	8.97295	−	2.91549i	0.911065	−	0.296023i	0.184268	−	0.982876i	$-0.441008\pi$
$97$	8.97295	−	2.91549i	0.911065	−	0.296023i	0.726796	+	0.686853i	$0.241008\pi$
$98$	0.277648	+	6.99449i	0.0280467	+	0.706550i
$99$	−0.434593	−	3.28803i	−0.0436782	−	0.330459i
$100$	0.308118	−	0.533676i	0.0308118	−	0.0533676i
$101$	−7.04130	+	7.82016i	−0.700636	+	0.778135i	−0.983477	−	0.181032i	$-0.942056\pi$
$101$	−7.04130	+	7.82016i	−0.700636	+	0.778135i	0.282841	+	0.959167i	$0.408723\pi$
$102$	0.0630814	−	0.600179i	0.00624599	−	0.0594266i
$103$	17.8120	−	1.87212i	1.75507	−	0.184465i	0.828349	−	0.560212i	$-0.189280\pi$
$103$	17.8120	−	1.87212i	1.75507	−	0.184465i	0.926722	+	0.375747i	$0.122614\pi$
$104$	−3.69091	−	1.19925i	−0.361924	−	0.117596i
$105$	4.04233	−	3.78759i	0.394491	−	0.369631i
$106$	−6.30725	−	8.68119i	−0.612614	−	0.843191i
$107$	−2.78491	−	6.25501i	−0.269228	−	0.604695i	0.727448	−	0.686162i	$-0.240706\pi$
$107$	−2.78491	−	6.25501i	−0.269228	−	0.604695i	−0.996676	+	0.0814673i	$0.974039\pi$
$108$	−0.743145	−	0.669131i	−0.0715091	−	0.0643871i
$109$	−17.1867	+	9.92276i	−1.64619	+	0.950428i	−0.667623	+	0.744499i	$0.732688\pi$
$109$	−17.1867	+	9.92276i	−1.64619	+	0.950428i	−0.978567	+	0.205929i	$0.933978\pi$
$110$	4.50716	−	5.28269i	0.429741	−	0.503685i
$111$			7.74448i			0.735073i
$112$	2.00091	+	1.73100i	0.189068	+	0.163564i
$113$	−12.7133	−	9.23674i	−1.19597	−	0.868920i	−0.202084	−	0.979368i	$-0.564771\pi$
$113$	−12.7133	−	9.23674i	−1.19597	−	0.868920i	−0.993882	+	0.110448i	$0.964771\pi$
$114$	−0.206679	−	1.96642i	−0.0193573	−	0.184172i
$115$	−0.903530	−	4.25077i	−0.0842546	−	0.396387i
$116$	−0.306236	−	1.44073i	−0.0284333	−	0.133768i
$117$	−0.405660	−	3.85959i	−0.0375032	−	0.356820i
$118$	−6.20949	−	4.51146i	−0.571630	−	0.415313i
$119$	−1.50844	+	0.523423i	−0.138278	+	0.0479821i
$120$		−	2.09374i		−	0.191132i
$121$	−8.54150	+	6.93129i	−0.776500	+	0.630117i
$122$	−2.70539	+	1.56196i	−0.244935	+	0.141413i
$123$	−3.98587	−	3.58889i	−0.359394	−	0.323600i
$124$	−3.58381	−	8.04937i	−0.321836	−	0.722855i
$125$	6.91174	+	9.51320i	0.618205	+	0.850886i
$126$	−0.767509	+	2.53198i	−0.0683751	+	0.225567i
$127$	−5.37131	−	1.74524i	−0.476627	−	0.154865i	0.0608449	−	0.998147i	$-0.480620\pi$
$127$	−5.37131	−	1.74524i	−0.476627	−	0.154865i	−0.537472	+	0.843282i	$0.680620\pi$
$128$	0.994522	−	0.104528i	0.0879041	−	0.00923910i
$129$	−0.895754	+	8.52253i	−0.0788667	+	0.750367i
$130$	5.43703	−	6.03843i	0.476859	−	0.529606i
$131$	8.24976	−	14.2890i	0.720785	−	1.24844i	−0.239901	−	0.970797i	$-0.577115\pi$
$131$	8.24976	−	14.2890i	0.720785	−	1.24844i	0.960686	−	0.277638i	$-0.0895517\pi$
$132$	−0.602735	+	3.26140i	−0.0524613	+	0.283868i
$133$	−4.47768	+	2.70501i	−0.388264	+	0.234554i
$134$	−4.31456	+	1.40189i	−0.372721	+	0.121105i
$135$	1.91273	−	0.851602i	0.164622	−	0.0732943i
$136$	−0.245459	+	0.551311i	−0.0210480	+	0.0472745i
$137$	0.710598	−	0.151042i	0.0607105	−	0.0129044i	−0.177456	−	0.984129i	$-0.556787\pi$
$137$	0.710598	−	0.151042i	0.0607105	−	0.0129044i	0.238167	+	0.971224i	$0.423454\pi$
$138$	1.38884	+	1.54246i	0.118226	+	0.131303i
$139$	−3.03373	+	2.20414i	−0.257318	+	0.186952i	−0.708964	−	0.705245i	$-0.750837\pi$
$139$	−3.03373	+	2.20414i	−0.257318	+	0.186952i	0.451646	+	0.892197i	$0.350837\pi$
$140$	−5.01492	+	2.35307i	−0.423838	+	0.198870i
$141$	−1.21265	−	3.73216i	−0.102124	−	0.314305i
$142$	7.59991	+	4.38781i	0.637770	+	0.368217i
$143$	−10.2075	+	7.84081i	−0.853594	+	0.655681i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	3.01652	+	0.641181i	0.250508	+	0.0532472i
$146$	4.65328	−	6.40469i	0.385108	−	0.530056i
$147$	6.92715	−	1.00725i	0.571342	−	0.0830767i
$148$	2.39318	−	7.36544i	0.196718	−	0.605435i
$149$	9.40626	−	8.46943i	0.770591	−	0.693843i	−0.186877	−	0.982383i	$-0.559837\pi$
$149$	9.40626	−	8.46943i	0.770591	−	0.693843i	0.957468	+	0.288540i	$0.0931700\pi$
$150$	−0.562960	−	0.250646i	−0.0459655	−	0.0204651i
$151$	−23.1076	−	2.42871i	−1.88047	−	0.197646i	−0.906174	−	0.422904i	$-0.861011\pi$
$151$	−23.1076	−	2.42871i	−1.88047	−	0.197646i	−0.974299	+	0.225258i	$0.927677\pi$
$152$	−0.411094	+	1.93405i	−0.0333441	+	0.156872i
$153$	−0.603485			−0.0487889
$154$	8.48906	−	2.22168i	0.684068	−	0.179028i
$155$	18.4483			1.48180
$156$	−0.806875	+	3.79605i	−0.0646017	+	0.303927i
$157$	−1.98305	−	0.208427i	−0.158265	−	0.0166343i	0.0250647	−	0.999686i	$-0.492021\pi$
$157$	−1.98305	−	0.208427i	−0.158265	−	0.0166343i	−0.183329	+	0.983052i	$0.558688\pi$
$158$	7.04845	+	3.13817i	0.560745	+	0.249660i
$159$	−7.97434	+	7.18013i	−0.632406	+	0.569421i
$160$	−0.647002	+	1.99127i	−0.0511500	+	0.157424i
$161$	2.13363	−	5.06003i	0.168154	−	0.398786i
$162$	−0.587785	+	0.809017i	−0.0461808	+	0.0635624i
$163$	−6.97232	−	1.48201i	−0.546114	−	0.116080i	−0.0734107	−	0.997302i	$-0.523388\pi$
$163$	−6.97232	−	1.48201i	−0.546114	−	0.116080i	−0.472703	+	0.881222i	$0.656722\pi$
$164$	2.68176	+	4.64494i	0.209410	+	0.362709i
$165$	−5.72488	−	3.93028i	−0.445682	−	0.305972i
$166$	−0.293707	−	0.169572i	−0.0227960	−	0.0131613i
$167$	3.53053	+	10.8659i	0.273201	+	0.840825i	0.989690	+	0.143227i	$0.0457480\pi$
$167$	3.53053	+	10.8659i	0.273201	+	0.840825i	−0.716489	+	0.697598i	$0.754252\pi$
$168$	1.51237	−	2.17088i	0.116682	−	0.167487i
$169$	−1.66740	+	1.21144i	−0.128262	+	0.0931876i
$170$	−0.845475	−	0.938996i	−0.0648450	−	0.0720177i
$171$	−1.93405	+	0.411094i	−0.147900	+	0.0314372i
$172$	3.48552	−	7.82860i	0.265768	−	0.596926i
$173$	−10.2319	+	4.55555i	−0.777920	+	0.346352i	−0.756988	−	0.653429i	$-0.773330\pi$
$173$	−10.2319	+	4.55555i	−0.777920	+	0.346352i	−0.0209317	+	0.999781i	$0.506663\pi$
$174$	−1.40083	+	0.455156i	−0.106196	+	0.0345053i
$175$	0.0323407	+	1.63009i	0.00244472	+	0.123223i
$176$	1.58106	−	2.91552i	0.119177	−	0.219765i
$177$	−3.83767	+	6.64705i	−0.288457	+	0.499623i
$178$	0.0906041	−	0.100626i	0.00679106	−	0.00754224i
$179$	−1.41584	+	13.4708i	−0.105824	+	1.00685i	0.804780	+	0.593573i	$0.202283\pi$
$179$	−1.41584	+	13.4708i	−0.105824	+	1.00685i	−0.910604	+	0.413279i	$0.864383\pi$
$180$	−2.08227	+	0.218856i	−0.155204	+	0.0163126i
$181$	−2.14926	−	0.698337i	−0.159753	−	0.0519070i	0.228049	−	0.973650i	$-0.426765\pi$
$181$	−2.14926	−	0.698337i	−0.159753	−	0.0519070i	−0.387802	+	0.921743i	$0.626765\pi$
$182$	9.99908	−	2.33359i	0.741181	−	0.172977i
$183$	1.83619	+	2.52730i	0.135735	+	0.186824i
$184$	−0.844215	−	1.89614i	−0.0622364	−	0.139785i
$185$	12.0501	+	10.8499i	0.885938	+	0.797702i
$186$	−7.63067	+	4.40557i	−0.559508	+	0.323032i
$187$	1.04667	+	1.70605i	0.0765403	+	0.124759i
$188$			3.92423i			0.286204i
$189$	2.59834	+	0.498640i	0.189001	+	0.0362707i
$190$	−3.34922	−	2.43335i	−0.242978	−	0.176534i
$191$	−2.78837	−	26.5296i	−0.201759	−	1.91961i	−0.361354	−	0.932429i	$-0.617686\pi$
$191$	−2.78837	−	26.5296i	−0.201759	−	1.91961i	0.159595	−	0.987183i	$-0.448981\pi$
$192$	−0.207912	−	0.978148i	−0.0150047	−	0.0705917i
$193$	2.94976	+	13.8775i	0.212329	+	0.998928i	0.947181	+	0.320700i	$0.103918\pi$
$193$	2.94976	+	13.8775i	0.212329	+	0.998928i	−0.734852	+	0.678227i	$0.762748\pi$
$194$	0.986196	+	9.38303i	0.0708048	+	0.673662i
$195$	−6.57368	−	4.77606i	−0.470751	−	0.342021i
$196$	−6.89937	−	1.18266i	−0.492812	−	0.0844754i
$197$			9.13948i			0.651161i	0.945514	+	0.325580i	$0.105560\pi$
$197$			9.13948i			0.651161i	−0.945514	+	0.325580i	$0.894440\pi$
$198$	3.30653	+	0.258524i	0.234985	+	0.0183725i
$199$	14.0878	−	8.13361i	0.998660	−	0.576577i	0.0908085	−	0.995868i	$-0.471055\pi$
$199$	14.0878	−	8.13361i	0.998660	−	0.576577i	0.907852	+	0.419292i	$0.137722\pi$
$200$	0.457953	+	0.412343i	0.0323821	+	0.0291570i
$201$	1.84520	+	4.14439i	0.130150	+	0.292323i
$202$	−6.18530	−	8.51334i	−0.435196	−	0.598996i
$203$	2.66451	+	2.84372i	0.187012	+	0.199590i
$204$	0.573948	+	0.186487i	0.0401844	+	0.0130567i
$205$	−11.1683	+	1.17384i	−0.780029	+	0.0819844i
$206$	−1.87212	+	17.8120i	−0.130437	+	1.24102i
$207$	1.38884	−	1.54246i	0.0965307	−	0.107208i
$208$	1.94043	−	3.36092i	0.134544	−	0.233038i
$209$	4.51654	+	4.75455i	0.312415	+	0.328879i
$210$	2.86438	+	4.74149i	0.197661	+	0.327194i
$211$	17.0054	−	5.52539i	1.17070	−	0.380383i	0.341796	−	0.939774i	$-0.388965\pi$
$211$	17.0054	−	5.52539i	1.17070	−	0.380383i	0.828904	+	0.559391i	$0.188965\pi$
$212$	9.80283	−	4.36450i	0.673261	−	0.299755i
$213$	3.56937	−	8.01693i	0.244569	−	0.549311i
$214$	6.69734	−	1.42356i	0.457821	−	0.0973128i
$215$	12.0057	+	13.3337i	0.818784	+	0.909352i
$216$	0.809017	−	0.587785i	0.0550466	−	0.0399937i
$217$	19.1279	+	13.3257i	1.29849	+	0.904607i
$218$	−6.13260	−	18.8742i	−0.415352	−	1.27832i
$219$	−6.85600	−	3.95832i	−0.463286	−	0.267478i
$220$	4.23016	+	5.50701i	0.285198	+	0.371282i
$221$	1.17102	+	2.02826i	0.0787712	+	0.136436i
$222$	−7.57524	−	1.61017i	−0.508417	−	0.108067i
$223$	12.0084	−	16.5281i	0.804142	−	1.10681i	−0.188059	−	0.982158i	$-0.560220\pi$
$223$	12.0084	−	16.5281i	0.804142	−	1.10681i	0.992201	−	0.124648i	$-0.0397802\pi$
$224$	−2.10919	+	1.59729i	−0.140926	+	0.106723i
$225$	−0.190427	+	0.586075i	−0.0126952	+	0.0390717i
$226$	11.6781	−	10.5150i	0.776818	−	0.699450i
$227$	19.4741	+	8.67042i	1.29254	+	0.575476i	0.933745	−	0.357940i	$-0.116521\pi$
$227$	19.4741	+	8.67042i	1.29254	+	0.575476i	0.358796	+	0.933416i	$0.383187\pi$
$228$	1.96642	+	0.206679i	0.130230	+	0.0136877i
$229$	−5.19942	+	24.4614i	−0.343587	+	1.61645i	0.379154	+	0.925333i	$0.376215\pi$
$229$	−5.19942	+	24.4614i	−0.343587	+	1.61645i	−0.722742	+	0.691118i	$0.757118\pi$
$230$	4.34574			0.286549
$231$	−3.09685	−	8.21033i	−0.203758	−	0.540200i
$232$	1.47292			0.0967017
$233$	0.253220	−	1.19130i	0.0165890	−	0.0780450i	−0.969074	−	0.246769i	$-0.920631\pi$
$233$	0.253220	−	1.19130i	0.0165890	−	0.0780450i	0.985663	+	0.168724i	$0.0539646\pi$
$234$	3.85959	+	0.405660i	0.252310	+	0.0265188i
$235$	−7.50599	−	3.34188i	−0.489637	−	0.218000i
$236$	5.70390	−	5.13581i	0.371292	−	0.334313i
$237$	2.38422	−	7.33787i	0.154872	−	0.476646i
$238$	−0.198363	−	1.58430i	−0.0128579	−	0.102695i
$239$	−12.5422	+	17.2628i	−0.811285	+	1.11664i	0.179838	+	0.983696i	$0.442443\pi$
$239$	−12.5422	+	17.2628i	−0.811285	+	1.11664i	−0.991124	+	0.132942i	$0.957557\pi$
$240$	2.04799	+	0.435314i	0.132197	+	0.0280994i
$241$	−3.50450	−	6.06998i	−0.225745	−	0.391002i	0.730798	−	0.682594i	$-0.239148\pi$
$241$	−3.50450	−	6.06998i	−0.225745	−	0.391002i	−0.956543	+	0.291592i	$0.905815\pi$
$242$	−5.00394	−	9.79594i	−0.321666	−	0.629707i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−0.965344	−	2.97102i	−0.0617998	−	0.190200i
$245$	8.13762	−	12.1895i	0.519894	−	0.778758i
$246$	4.33918	−	3.15260i	0.276656	−	0.201002i
$247$	5.13453	+	5.70247i	0.326702	+	0.362840i
$248$	8.61859	−	1.83194i	0.547281	−	0.116328i
$249$	−0.137942	+	0.309823i	−0.00874171	+	0.0196342i
$250$	−10.7423	+	4.78280i	−0.679406	+	0.302491i
$251$	13.3542	−	4.33905i	0.842912	−	0.273879i	0.144438	−	0.989514i	$-0.453863\pi$
$251$	13.3542	−	4.33905i	0.842912	−	0.273879i	0.698474	+	0.715635i	$0.253863\pi$
$252$	−2.31708	−	1.27717i	−0.145962	−	0.0804539i
$253$	−6.76930	−	1.25102i	−0.425582	−	0.0786513i
$254$	2.82387	−	4.89108i	0.177185	−	0.306894i
$255$	−0.845475	+	0.938996i	−0.0529457	+	0.0588022i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	5.89251	−	0.619328i	0.367565	−	0.0386326i	0.0810542	−	0.996710i	$-0.474171\pi$
$257$	5.89251	−	0.619328i	0.367565	−	0.0386326i	0.286511	+	0.958077i	$0.407505\pi$
$258$	−8.15005	−	2.64811i	−0.507400	−	0.164864i
$259$	4.65682	+	19.9538i	0.289361	+	1.23987i
$260$	4.77606	+	6.57368i	0.296198	+	0.407682i
$261$	0.599089	+	1.34558i	0.0370827	+	0.0832890i
$262$	12.2615	+	11.0403i	0.757520	+	0.682074i
$263$	11.8134	−	6.82049i	0.728447	−	0.420569i	−0.0894065	−	0.995995i	$-0.528497\pi$
$263$	11.8134	−	6.82049i	0.728447	−	0.420569i	0.817854	+	0.575426i	$0.195164\pi$
$264$	−3.06481	−	1.26765i	−0.188626	−	0.0780182i
$265$			22.4670i			1.38014i
$266$	−1.71494	−	4.94224i	−0.105150	−	0.303028i
$267$	−0.109545	−	0.0795894i	−0.00670407	−	0.00487079i
$268$	−0.474204	−	4.51175i	−0.0289666	−	0.275599i
$269$	5.97648	+	28.1171i	0.364392	+	1.71433i	0.653407	+	0.757007i	$0.273339\pi$
$269$	5.97648	+	28.1171i	0.364392	+	1.71433i	−0.289015	+	0.957325i	$0.593328\pi$
$270$	0.435314	+	2.04799i	0.0264924	+	0.124637i
$271$	−0.351286	−	3.34226i	−0.0213391	−	0.203028i	0.978658	−	0.205497i	$-0.0658809\pi$
$271$	−0.351286	−	3.34226i	−0.0213391	−	0.203028i	−0.999997	+	0.00246843i	$0.999214\pi$
$272$	−0.488230	−	0.354720i	−0.0296033	−	0.0215080i
$273$	−3.36599	−	9.70037i	−0.203719	−	0.587093i
$274$			0.726474i			0.0438879i
$275$	1.98711	−	0.478140i	0.119827	−	0.0288329i
$276$	−1.79751	+	1.03779i	−0.108197	+	0.0624677i
$277$	−7.44128	−	6.70016i	−0.447103	−	0.402574i	0.414586	−	0.910010i	$-0.363927\pi$
$277$	−7.44128	−	6.70016i	−0.447103	−	0.402574i	−0.861689	+	0.507437i	$0.830593\pi$
$278$	−1.52522	−	3.42570i	−0.0914767	−	0.205460i
$279$	5.17905	+	7.12836i	0.310062	+	0.426764i
$280$	−1.25899	−	5.39456i	−0.0752388	−	0.322387i
$281$	4.15425	+	1.34980i	0.247822	+	0.0805221i	0.430294	−	0.902689i	$-0.358410\pi$
$281$	4.15425	+	1.34980i	0.247822	+	0.0805221i	−0.182472	+	0.983211i	$0.558410\pi$
$282$	3.90273	−	0.410194i	0.232404	−	0.0244267i
$283$	1.43588	−	13.6615i	0.0853545	−	0.812093i	−0.865177	−	0.501466i	$-0.832794\pi$
$283$	1.43588	−	13.6615i	0.0853545	−	0.812093i	0.950532	−	0.310627i	$-0.100539\pi$
$284$	−5.87204	+	6.52156i	−0.348441	+	0.386983i
$285$	−2.06993	+	3.58523i	−0.122612	+	0.212371i
$286$	−5.54721	−	11.6146i	−0.328013	−	0.686788i
$287$	−12.4277	−	6.85010i	−0.733583	−	0.404349i
$288$	−0.951057	+	0.309017i	−0.0560415	+	0.0182090i
$289$	−15.1976	+	6.76639i	−0.893974	+	0.398023i
$290$	−1.25434	+	2.81729i	−0.0736573	+	0.165437i
$291$	9.22854	−	1.96159i	0.540987	−	0.114990i
$292$	5.29726	+	5.88320i	0.309999	+	0.344288i
$293$	14.8955	−	10.8222i	0.870205	−	0.632241i	−0.0604370	−	0.998172i	$-0.519249\pi$
$293$	14.8955	−	10.8222i	0.870205	−	0.632241i	0.930642	+	0.365931i	$0.119249\pi$
$294$	−0.454996	+	6.98520i	−0.0265359	+	0.407385i
$295$	4.96597	+	15.2837i	0.289130	+	0.889850i
$296$	6.70691	+	3.87224i	0.389831	+	0.225069i
$297$	−0.0885192	−	3.31544i	−0.00513641	−	0.192382i
$298$	6.32868	+	10.9616i	0.366611	+	0.634988i
$299$	−7.87901	−	1.67473i	−0.455655	−	0.0968524i
$300$	0.362215	−	0.498546i	0.0209125	−	0.0287835i
$301$	2.81675	+	22.4970i	0.162355	+	1.29671i
$302$	7.17999	−	22.0977i	0.413162	−	1.27158i
$303$	−7.82016	+	7.04130i	−0.449257	+	0.404512i
$304$	−1.80631	−	0.804222i	−0.103599	−	0.0461253i
$305$	6.50485	+	0.683688i	0.372467	+	0.0391478i
$306$	0.125472	−	0.590297i	0.00717273	−	0.0337451i
$307$	15.7768			0.900431			0.450215	−	0.892920i	$-0.351347\pi$
$307$	15.7768			0.900431			0.450215	+	0.892920i	$0.351347\pi$
$308$	0.408151	+	8.76547i	0.0232566	+	0.499459i
$309$	17.9101			1.01887
$310$	−3.83561	+	18.0451i	−0.217848	+	1.02489i
$311$	−18.6774	−	1.96307i	−1.05910	−	0.111316i	−0.441071	−	0.897472i	$-0.645401\pi$
$311$	−18.6774	−	1.96307i	−1.05910	−	0.111316i	−0.618027	+	0.786157i	$0.712068\pi$
$312$	−3.54534	−	1.57849i	−0.200715	−	0.0893641i
$313$	−7.94114	+	7.15024i	−0.448860	+	0.404155i	−0.862317	−	0.506368i	$-0.830988\pi$
$313$	−7.94114	+	7.15024i	−0.448860	+	0.404155i	0.413458	+	0.910523i	$0.364321\pi$
$314$	0.616172	−	1.89638i	0.0347726	−	0.107019i
$315$	4.41610	−	3.34431i	0.248819	−	0.188430i
$316$	−4.53505	+	6.24196i	−0.255117	+	0.351138i
$317$	−25.4403	−	5.40751i	−1.42887	−	0.303716i	−0.572427	−	0.819956i	$-0.693998\pi$
$317$	−25.4403	−	5.40751i	−1.42887	−	0.303716i	−0.856444	+	0.516240i	$0.827331\pi$
$318$	−5.36527	−	9.29292i	−0.300869	−	0.521121i
$319$	2.76489	−	4.02736i	0.154804	−	0.225489i
$320$	−1.81324	−	1.04687i	−0.101363	−	0.0585219i
$321$	−2.11583	−	6.51185i	−0.118094	−	0.363456i
$322$	4.50585	+	3.13905i	0.251101	+	0.174932i
$323$	0.965354	−	0.701371i	0.0537137	−	0.0390253i
$324$	−0.669131	−	0.743145i	−0.0371739	−	0.0412858i
$325$	2.33926	−	0.497225i	0.129759	−	0.0275811i
$326$	2.89925	−	6.51183i	0.160575	−	0.360657i
$327$	−18.1298	+	8.07190i	−1.00258	+	0.446377i
$328$	−5.10101	+	1.65742i	−0.281656	+	0.0915156i
$329$	−5.36860	−	8.88679i	−0.295980	−	0.489945i
$330$	5.03467	−	4.78263i	0.277149	−	0.263275i
$331$	9.93615	−	17.2099i	0.546140	−	0.945942i	−0.452394	−	0.891818i	$-0.649430\pi$
$331$	9.93615	−	17.2099i	0.546140	−	0.945942i	0.998534	−	0.0541243i	$-0.0172367\pi$
$332$	0.226931	−	0.252032i	0.0124545	−	0.0138321i
$333$	−0.809518	+	7.70205i	−0.0443613	+	0.422070i
$334$	−11.3625	+	1.19424i	−0.621726	+	0.0653460i
$335$	9.03359	+	2.93519i	0.493558	+	0.160367i
$336$	1.80901	+	1.93067i	0.0986894	+	0.105327i
$337$	−17.8449	−	24.5614i	−0.972074	−	1.33794i	−0.940992	−	0.338428i	$-0.890105\pi$
$337$	−17.8449	−	24.5614i	−0.972074	−	1.33794i	−0.0310813	−	0.999517i	$-0.509895\pi$
$338$	−0.838294	−	1.88284i	−0.0455972	−	0.102413i
$339$	−11.6781	−	10.5150i	−0.634270	−	0.571099i
$340$	1.09426	−	0.631772i	0.0593446	−	0.0342626i
$341$	11.1694	−	27.0045i	0.604857	−	1.46237i
$342$		−	1.97725i		−	0.106918i
$343$	17.2422	−	6.76055i	0.930994	−	0.365036i
$344$	6.93285	+	5.03701i	0.373794	+	0.271577i
$345$	−0.454253	−	4.32193i	−0.0244562	−	0.232685i
$346$	−2.32866	−	10.9555i	−0.125190	−	0.588971i
$347$	0.00870554	+	0.0409564i	0.000467338	+	0.00219865i	0.978381	−	0.206812i	$-0.0663089\pi$
$347$	0.00870554	+	0.0409564i	0.000467338	+	0.00219865i	−0.977913	+	0.209011i	$0.932976\pi$
$348$	−0.153962	−	1.46485i	−0.00825321	−	0.0785240i
$349$	−21.4144	−	15.5584i	−1.14628	−	0.832824i	−0.158302	−	0.987391i	$-0.550602\pi$
$349$	−21.4144	−	15.5584i	−1.14628	−	0.832824i	−0.987982	+	0.154567i	$0.950602\pi$
$350$	−1.60119	−	0.307280i	−0.0855872	−	0.0164248i
$351$		−	3.88085i		−	0.207145i
$352$	2.52309	+	2.15268i	0.134481	+	0.114738i
$353$	22.2545	−	12.8486i	1.18449	−	0.683863i	0.227438	−	0.973793i	$-0.426965\pi$
$353$	22.2545	−	12.8486i	1.18449	−	0.683863i	0.957048	+	0.289929i	$0.0936318\pi$
$354$	−5.70390	−	5.13581i	−0.303159	−	0.272965i
$355$	−7.47334	−	16.7854i	−0.396644	−	0.890876i
$356$	0.0795894	+	0.109545i	0.00421823	+	0.00580590i
$357$	−1.55489	+	0.362881i	−0.0822934	+	0.0192057i
$358$	−12.8820	−	4.18563i	−0.680837	−	0.221217i
$359$	−17.3075	+	1.81909i	−0.913455	+	0.0960080i	−0.549581	−	0.835440i	$-0.685213\pi$
$359$	−17.3075	+	1.81909i	−0.913455	+	0.0960080i	−0.363874	+	0.931448i	$0.618546\pi$
$360$	0.218856	−	2.08227i	0.0115347	−	0.109745i
$361$	−10.0975	+	11.2144i	−0.531447	+	0.590232i
$362$	1.12993	−	1.95710i	0.0593879	−	0.102863i
$363$	−9.21923	+	6.00049i	−0.483884	+	0.314944i
$364$	0.203671	+	10.2658i	0.0106753	+	0.538072i
$365$	−15.7641	+	5.12208i	−0.825133	+	0.268102i
$366$	−2.85384	+	1.27061i	−0.149173	+	0.0664159i
$367$	3.78228	−	8.49515i	0.197434	−	0.443443i	−0.787514	−	0.616297i	$-0.788632\pi$
$367$	3.78228	−	8.49515i	0.197434	−	0.443443i	0.984948	+	0.172854i	$0.0552988\pi$
$368$	2.03023	−	0.431538i	0.105833	−	0.0224955i
$369$	−3.58889	−	3.98587i	−0.186830	−	0.207496i
$370$	−13.1182	+	9.53091i	−0.681981	+	0.495488i
$371$	−16.2285	+	23.2948i	−0.842544	+	1.20940i
$372$	−2.72279	−	8.37989i	−0.141170	−	0.434477i
$373$	6.82204	+	3.93870i	0.353232	+	0.203938i	0.666108	−	0.745856i	$-0.267959\pi$
$373$	6.82204	+	3.93870i	0.353232	+	0.203938i	−0.312876	+	0.949794i	$0.601292\pi$
$374$	−1.88639	+	0.669093i	−0.0975427	+	0.0345980i
$375$	5.87948	+	10.1836i	0.303615	+	0.525877i
$376$	−3.83847	−	0.815893i	−0.197954	−	0.0420765i
$377$	3.35988	−	4.62448i	0.173043	−	0.238173i
$378$	−1.02797	+	2.43788i	−0.0528730	+	0.125391i
$379$	−1.63018	+	5.01717i	−0.0837366	+	0.257715i	−0.984155	−	0.177310i	$-0.943260\pi$
$379$	−1.63018	+	5.01717i	−0.0837366	+	0.257715i	0.900418	+	0.435025i	$0.143260\pi$
$380$	3.07652	−	2.77011i	0.157822	−	0.142104i
$381$	−5.15946	−	2.29714i	−0.264327	−	0.117686i
$382$	26.5296	+	2.78837i	1.35737	+	0.142665i
$383$	−4.53133	+	21.3182i	−0.231540	+	1.08931i	0.696710	+	0.717353i	$0.254646\pi$
$383$	−4.53133	+	21.3182i	−0.231540	+	1.08931i	−0.928250	+	0.371957i	$0.878687\pi$
$384$	1.00000			0.0510310
$385$	−17.1136	−	6.68401i	−0.872188	−	0.340649i
$386$	−14.1876			−0.722129
$387$	−1.78169	+	8.38221i	−0.0905686	+	0.426092i
$388$	−9.38303	−	0.986196i	−0.476351	−	0.0500665i
$389$	−10.8828	−	4.84532i	−0.551778	−	0.245667i	0.111856	−	0.993724i	$-0.464320\pi$
$389$	−10.8828	−	4.84532i	−0.551778	−	0.245667i	−0.663635	+	0.748057i	$0.730987\pi$
$390$	6.03843	−	5.43703i	0.305768	−	0.275315i
$391$	−0.387069	+	1.19128i	−0.0195749	+	0.0602455i
$392$	2.59127	−	6.50272i	0.130879	−	0.328437i
$393$	9.69817	−	13.3484i	0.489208	−	0.673337i
$394$	−8.93976	−	1.90020i	−0.450379	−	0.0957309i
$395$	−8.07713	−	13.9900i	−0.406404	−	0.703913i
$396$	−0.940342	+	3.18053i	−0.0472539	+	0.159828i
$397$	−24.6210	−	14.2149i	−1.23569	−	0.713427i	−0.267481	−	0.963563i	$-0.586191\pi$
$397$	−24.6210	−	14.2149i	−1.23569	−	0.713427i	−0.968211	+	0.250136i	$0.919525\pi$
$398$	5.02685	+	15.4711i	0.251973	+	0.775494i
$399$	−4.73590	+	2.22215i	−0.237092	+	0.111247i
$400$	−0.498546	+	0.362215i	−0.0249273	+	0.0181107i
$401$	10.8397	+	12.0387i	0.541306	+	0.601182i	0.950292	−	0.311359i	$-0.100784\pi$
$401$	10.8397	+	12.0387i	0.541306	+	0.601182i	−0.408986	+	0.912541i	$0.634118\pi$
$402$	−4.43746	+	0.943212i	−0.221321	+	0.0470431i
$403$	13.9082	−	31.2384i	0.692819	−	1.55610i
$404$	9.61330	−	4.28012i	0.478279	−	0.212944i
$405$	1.99127	−	0.647002i	0.0989469	−	0.0321498i
$406$	−3.33556	+	2.01504i	−0.165541	+	0.100005i
$407$	23.1777	−	11.0698i	1.14888	−	0.548709i
$408$	−0.301743	+	0.522633i	−0.0149385	+	0.0258742i
$409$	16.8456	−	18.7090i	0.832964	−	0.925100i	−0.165164	−	0.986266i	$-0.552815\pi$
$409$	16.8456	−	18.7090i	0.832964	−	0.925100i	0.998128	+	0.0611662i	$0.0194820\pi$
$410$	1.17384	−	11.1683i	0.0579717	−	0.551564i
$411$	0.722494	−	0.0759372i	0.0356380	−	0.00374570i
$412$	−17.0336	−	5.53454i	−0.839183	−	0.272667i
$413$	−5.89090	+	19.4338i	−0.289872	+	0.956277i
$414$	1.22000	+	1.67918i	0.0599596	+	0.0825272i
$415$	0.288815	+	0.648689i	0.0141774	+	0.0318429i
$416$	2.88404	+	2.59680i	0.141402	+	0.127318i
$417$	−3.24751	+	1.87495i	−0.159031	+	0.0918167i
$418$	−5.58969	+	3.42931i	−0.273401	+	0.167733i
$419$		−	6.44778i		−	0.314995i	−0.987519	−	0.157497i	$-0.949657\pi$
$419$		−	6.44778i		−	0.314995i	0.987519	−	0.157497i	$-0.0503425\pi$
$420$	−5.23341	+	1.81597i	−0.255364	+	0.0886105i
$421$	−25.4474	−	18.4886i	−1.24023	−	0.901079i	−0.242615	−	0.970123i	$-0.578005\pi$
$421$	−25.4474	−	18.4886i	−1.24023	−	0.901079i	−0.997614	+	0.0690433i	$0.978005\pi$
$422$	1.86902	+	17.7826i	0.0909827	+	0.865642i
$423$	−0.815893	−	3.83847i	−0.0396701	−	0.186633i
$424$	2.23100	+	10.4960i	0.108347	+	0.509733i
$425$	−0.0388730	−	0.369852i	−0.00188562	−	0.0179405i
$426$	7.09963	+	5.15818i	0.343978	+	0.249915i
$427$	6.25067	+	5.40751i	0.302491	+	0.261688i
$428$			6.84697i			0.330961i
$429$	−10.9712	+	6.73088i	−0.529693	+	0.324970i
$430$	−15.5385	+	8.97114i	−0.749332	+	0.432627i
$431$	3.02047	+	2.71965i	0.145491	+	0.131001i	0.738663	−	0.674075i	$-0.235458\pi$
$431$	3.02047	+	2.71965i	0.145491	+	0.131001i	−0.593171	+	0.805076i	$0.702124\pi$
$432$	0.406737	+	0.913545i	0.0195691	+	0.0439530i
$433$	2.20835	+	3.03954i	0.106127	+	0.146071i	0.858777	−	0.512350i	$-0.171225\pi$
$433$	2.20835	+	3.03954i	0.106127	+	0.146071i	−0.752650	+	0.658421i	$0.771225\pi$
$434$	−17.0114	+	15.9394i	−0.816574	+	0.765115i
$435$	2.93297	+	0.952980i	0.140625	+	0.0456919i
$436$	19.7368	−	2.07442i	0.945222	−	0.0993468i
$437$	−0.428980	+	4.08147i	−0.0205209	+	0.195243i
$438$	5.29726	−	5.88320i	0.253113	−	0.281110i
$439$	−9.73650	+	16.8641i	−0.464698	+	0.804880i	−0.999188	−	0.0402948i	$-0.987170\pi$
$439$	−9.73650	+	16.8641i	−0.464698	+	0.804880i	0.534490	+	0.845175i	$0.320504\pi$
$440$	−6.26617	+	2.99275i	−0.298728	+	0.142674i
$441$	6.99449	−	0.277648i	0.333071	−	0.0132214i
$442$	−2.22741	+	0.723729i	−0.105947	+	0.0344243i
$443$	−5.70879	+	2.54172i	−0.271233	+	0.120761i	−0.537846	−	0.843043i	$-0.680762\pi$
$443$	−5.70879	+	2.54172i	−0.271233	+	0.120761i	0.266613	+	0.963804i	$0.414095\pi$
$444$	3.14996	−	7.07493i	0.149491	−	0.335761i
$445$	−0.277309	+	0.0589439i	−0.0131457	+	0.00279421i
$446$	13.6703	+	15.1824i	0.647306	+	0.718906i
$447$	10.2400	−	7.43981i	0.484337	−	0.351891i
$448$	−1.12386	−	2.39519i	−0.0530972	−	0.113162i
$449$	4.05500	+	12.4800i	0.191367	+	0.588968i	1.00000		0.000654043i	$0.000208188\pi$
$449$	4.05500	+	12.4800i	0.191367	+	0.588968i	−0.808632	+	0.588314i	$0.799792\pi$
$450$	−0.533676	−	0.308118i	−0.0251577	−	0.0145248i
$451$	−5.04354	+	17.0588i	−0.237491	+	0.803268i
$452$	7.85724	+	13.6091i	0.369574	+	0.640120i
$453$	−22.7272	−	4.83081i	−1.06782	−	0.226971i
$454$	−12.5298	+	17.2458i	−0.588055	+	0.809388i
$455$	−19.8091	−	8.35277i	−0.928663	−	0.391584i
$456$	−0.611005	+	1.88048i	−0.0286129	+	0.0880616i
$457$	−4.87779	+	4.39198i	−0.228173	+	0.205448i	−0.775285	−	0.631611i	$-0.782394\pi$
$457$	−4.87779	+	4.39198i	−0.228173	+	0.205448i	0.547112	+	0.837060i	$0.315727\pi$
$458$	−22.8458	−	10.1716i	−1.06751	−	0.475288i
$459$	−0.600179	−	0.0630814i	−0.0280140	−	0.00294439i
$460$	−0.903530	+	4.25077i	−0.0421273	+	0.198193i
$461$	2.03405			0.0947350			0.0473675	−	0.998878i	$-0.484917\pi$
$461$	2.03405			0.0947350			0.0473675	+	0.998878i	$0.484917\pi$
$462$	8.67479	−	1.32216i	0.403588	−	0.0615123i
$463$	32.6667			1.51815			0.759076	−	0.651002i	$-0.225651\pi$
$463$	32.6667			1.51815			0.759076	+	0.651002i	$0.225651\pi$
$464$	−0.306236	+	1.44073i	−0.0142167	+	0.0668842i
$465$	18.3472	+	1.92837i	0.850831	+	0.0894259i
$466$	1.11262	+	0.495372i	0.0515413	+	0.0229477i
$467$	28.0459	−	25.2526i	1.29781	−	1.16855i	0.322781	−	0.946474i	$-0.395382\pi$
$467$	28.0459	−	25.2526i	1.29781	−	1.16855i	0.975029	−	0.222079i	$-0.0712844\pi$
$468$	−1.19925	+	3.69091i	−0.0554353	+	0.170612i
$469$	7.24625	+	9.56855i	0.334601	+	0.441834i
$470$	4.82944	−	6.64715i	0.222765	−	0.306610i
$471$	−1.95040	−	0.414571i	−0.0898698	−	0.0191024i
$472$	3.83767	+	6.64705i	0.176643	+	0.305955i
$473$	26.7866	−	9.50111i	1.23165	−	0.436861i
$474$	6.68181	+	3.85774i	0.306906	+	0.177192i
$475$	−0.376523	−	1.15882i	−0.0172761	−	0.0531703i
$476$	1.59092	+	0.135367i	0.0729198	+	0.00620453i
$477$	−8.68119	+	6.30725i	−0.397484	+	0.288789i
$478$	−14.2779	−	15.8572i	−0.653057	−	0.725293i
$479$	−42.1960	+	8.96904i	−1.92799	+	0.409806i	−0.928751	+	0.370705i	$0.879116\pi$
$479$	−42.1960	+	8.96904i	−1.92799	+	0.409806i	−0.999235	+	0.0391012i	$0.987551\pi$
$480$	−0.851602	+	1.91273i	−0.0388702	+	0.0873038i
$481$	27.4568	−	12.2245i	1.25192	−	0.557391i
$482$	6.66596	−	2.16590i	0.303626	−	0.0986542i
$483$	2.65086	−	4.80928i	0.120618	−	0.218830i
$484$	10.6223	−	2.85790i	0.482830	−	0.129905i
$485$	9.87694	−	17.1074i	0.448489	−	0.776805i
$486$	−0.669131	+	0.743145i	−0.0303524	+	0.0337097i
$487$	0.0626251	−	0.595838i	0.00283781	−	0.0270000i	−0.993011	−	0.118019i	$-0.962346\pi$
$487$	0.0626251	−	0.595838i	0.00283781	−	0.0270000i	0.995849	+	0.0910188i	$0.0290123\pi$
$488$	3.10680	−	0.326538i	0.140638	−	0.0147817i
$489$	−6.77921	−	2.20270i	−0.306566	−	0.0996095i
$490$	10.2312	+	10.4941i	0.462199	+	0.474077i
$491$	17.7912	+	24.4875i	0.802906	+	1.10510i	0.992379	+	0.123219i	$0.0393218\pi$
$491$	17.7912	+	24.4875i	0.802906	+	1.10510i	−0.189474	+	0.981886i	$0.560678\pi$
$492$	2.18154	+	4.89982i	0.0983514	+	0.220901i
$493$	−0.660569	−	0.594779i	−0.0297505	−	0.0267875i
$494$	−6.64539	+	3.83672i	−0.298990	+	0.172622i
$495$	−5.28269	−	4.50716i	−0.237439	−	0.202582i
$496$			8.81113i			0.395632i
$497$	4.37588	−	22.8020i	0.196285	−	1.02281i
$498$	−0.274373	−	0.199343i	−0.0122949	−	0.00893279i
$499$	0.0983593	+	0.935826i	0.00440317	+	0.0418933i	0.996503	−	0.0835586i	$-0.0266286\pi$
$499$	0.0983593	+	0.935826i	0.00440317	+	0.0418933i	−0.992100	+	0.125452i	$0.959962\pi$
$500$	−2.44483	−	11.5020i	−0.109336	−	0.514385i
$501$	2.37540	+	11.1754i	0.106125	+	0.499279i
$502$	1.46773	+	13.9645i	0.0655081	+	0.623268i
$503$	1.77937	+	1.29279i	0.0793384	+	0.0576427i	0.626747	−	0.779222i	$-0.284386\pi$
$503$	1.77937	+	1.29279i	0.0793384	+	0.0576427i	−0.547409	+	0.836865i	$0.684386\pi$
$504$	1.73100	−	2.00091i	0.0771050	−	0.0891274i
$505$			22.0326i			0.980438i
$506$	2.63110	−	6.36127i	0.116967	−	0.282793i
$507$	−1.78490	+	1.03051i	−0.0792701	+	0.0457666i
$508$	4.19708	+	3.77907i	0.186215	+	0.167669i
$509$	14.4222	+	32.3928i	0.639253	+	1.43579i	0.884600	+	0.466350i	$0.154431\pi$
$509$	14.4222	+	32.3928i	0.639253	+	1.43579i	−0.245347	+	0.969435i	$0.578902\pi$
$510$	−0.742692	−	1.02223i	−0.0328870	−	0.0452650i
$511$	−20.0448	−	6.07609i	−0.886728	−	0.268790i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	−1.96642	+	0.206679i	−0.0868197	+	0.00912512i
$514$	−0.619328	+	5.89251i	−0.0273174	+	0.259908i
$515$	25.0919	−	27.8674i	1.10568	−	1.22798i
$516$	4.28474	−	7.42138i	0.188625	−	0.326708i
$517$	−9.43629	+	8.96391i	−0.415008	+	0.394232i
$518$	−20.4859	+	0.406438i	−0.900100	+	0.0178578i
$519$	−10.6521	+	3.46107i	−0.467574	+	0.151924i
$520$	−7.42303	+	3.30494i	−0.325521	+	0.144931i
$521$	10.9317	−	24.5529i	0.478924	−	1.07568i	−0.498977	−	0.866615i	$-0.666291\pi$
$521$	10.9317	−	24.5529i	0.478924	−	1.07568i	0.977901	−	0.209067i	$-0.0670425\pi$
$522$	−1.44073	+	0.306236i	−0.0630590	+	0.0134036i
$523$	−28.5626	−	31.7220i	−1.24895	−	1.38710i	−0.891403	−	0.453211i	$-0.850278\pi$
$523$	−28.5626	−	31.7220i	−1.24895	−	1.38710i	−0.357552	−	0.933893i	$-0.616388\pi$
$524$	−13.3484	+	9.69817i	−0.583127	+	0.423667i
$525$	−0.138227	+	1.62454i	−0.00603272	+	0.0709006i
$526$	4.21529	+	12.9733i	0.183796	+	0.565665i
$527$	−4.60499	−	2.65869i	−0.200597	−	0.115815i
$528$	1.87716	−	2.73428i	0.0816927	−	0.118994i
$529$	9.34598	+	16.1877i	0.406347	+	0.703814i
$530$	−21.9760	−	4.67115i	−0.954578	−	0.202902i
$531$	−4.51146	+	6.20949i	−0.195781	+	0.269469i
$532$	5.19079	−	0.649914i	0.225049	−	0.0281774i
$533$	−6.43220	+	19.7963i	−0.278609	+	0.857472i
$534$	0.100626	−	0.0906041i	0.00435451	−	0.00392082i
$535$	−13.0964	−	5.83089i	−0.566207	−	0.252091i
$536$	4.51175	+	0.474204i	0.194878	+	0.0204825i
$537$	−2.81616	+	13.2490i	−0.121526	+	0.571736i
$538$	−28.7453			−1.23930
$539$	−12.9160	−	19.2919i	−0.556333	−	0.830960i
$540$	−2.09374			−0.0901004
$541$	1.20268	−	5.65819i	0.0517074	−	0.243264i	−0.944702	−	0.327930i	$-0.893649\pi$
$541$	1.20268	−	5.65819i	0.0517074	−	0.243264i	0.996409	+	0.0846658i	$0.0269823\pi$
$542$	3.34226	+	0.351286i	0.143563	+	0.0150890i
$543$	−2.06449	−	0.919170i	−0.0885957	−	0.0394454i
$544$	0.448477	−	0.403810i	0.0192283	−	0.0173132i
$545$	−12.8401	+	39.5178i	−0.550010	+	1.69276i
$546$	10.1882	−	1.27562i	0.436016	−	0.0545914i
$547$	−5.64256	+	7.76632i	−0.241258	+	0.332064i	−0.912426	−	0.409242i	$-0.865793\pi$
$547$	−5.64256	+	7.76632i	−0.241258	+	0.332064i	0.671167	+	0.741306i	$0.265793\pi$
$548$	−0.710598	−	0.151042i	−0.0303553	−	0.00645221i
$549$	1.56196	+	2.70539i	0.0666628	+	0.115463i
$550$	0.0545488	+	2.04310i	0.00232597	+	0.0871179i
$551$	−2.52215	−	1.45616i	−0.107447	−	0.0620347i
$552$	−0.641390	−	1.97400i	−0.0272994	−	0.0840188i
$553$	1.73065	−	20.3398i	0.0735947	−	0.864935i
$554$	8.10088	−	5.88563i	0.344173	−	0.250057i
$555$	10.8499	+	12.0501i	0.460553	+	0.511496i
$556$	3.66795	−	0.779648i	0.155556	−	0.0330644i
$557$	7.60462	−	17.0803i	0.322218	−	0.723714i	−0.677714	−	0.735325i	$-0.737029\pi$
$557$	7.60462	−	17.0803i	0.322218	−	0.723714i	0.999933	+	0.0116112i	$0.00369606\pi$
$558$	−8.04937	+	3.58381i	−0.340757	+	0.151715i
$559$	31.6292	−	10.2769i	1.33777	−	0.434668i
$560$	5.53844	−	0.109882i	0.234042	−	0.00464335i
$561$	0.862609	+	1.80611i	0.0364194	+	0.0762541i
$562$	−2.18402	+	3.78283i	−0.0921272	+	0.159569i
$563$	−10.2640	+	11.3993i	−0.432575	+	0.480423i	−0.919539	−	0.392999i	$-0.871438\pi$
$563$	−10.2640	+	11.3993i	−0.432575	+	0.480423i	0.486964	+	0.873422i	$0.338104\pi$
$564$	−0.410194	+	3.90273i	−0.0172723	+	0.164335i
$565$	−32.7219	+	3.43921i	−1.37662	+	0.144689i
$566$	13.0645	+	4.24490i	0.549140	+	0.178426i
$567$	2.53198	+	0.767509i	0.106333	+	0.0322323i
$568$	−5.15818	−	7.09963i	−0.216432	−	0.297894i
$569$	−11.9066	−	26.7427i	−0.499152	−	1.12111i	−0.970923	−	0.239392i	$-0.923052\pi$
$569$	−11.9066	−	26.7427i	−0.499152	−	1.12111i	0.471771	−	0.881721i	$-0.343615\pi$
$570$	−3.07652	−	2.77011i	−0.128861	−	0.116027i
$571$	−2.51630	+	1.45279i	−0.105304	+	0.0607973i	−0.551727	−	0.834025i	$-0.686031\pi$
$571$	−2.51630	+	1.45279i	−0.105304	+	0.0607973i	0.446423	+	0.894822i	$0.352698\pi$
$572$	12.5142	−	3.01117i	0.523243	−	0.125903i
$573$		−	26.6757i		−	1.11439i
$574$	9.28427	−	10.7319i	0.387518	−	0.447941i
$575$	1.03477	+	0.751806i	0.0431530	+	0.0313525i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−7.61989	−	35.8488i	−0.317220	−	1.49240i	−0.791030	−	0.611777i	$-0.790455\pi$
$577$	−7.61989	−	35.8488i	−0.317220	−	1.49240i	0.473810	−	0.880627i	$-0.342878\pi$
$578$	−3.45878	−	16.2723i	−0.143866	−	0.676837i
$579$	1.48301	+	14.1099i	0.0616316	+	0.586386i
$580$	−2.49493	−	1.81268i	−0.103597	−	0.0752673i
$581$	−0.169110	+	0.881208i	−0.00701588	+	0.0365587i
$582$			9.43472i			0.391082i
$583$	32.8871	+	13.6025i	1.36204	+	0.563359i
$584$	−6.85600	+	3.95832i	−0.283703	+	0.163796i
$585$	−6.03843	−	5.43703i	−0.249658	−	0.224794i
$586$	7.48878	+	16.8201i	0.309359	+	0.694831i
$587$	−8.16183	−	11.2338i	−0.336875	−	0.463668i	0.606651	−	0.794969i	$-0.292513\pi$
$587$	−8.16183	−	11.2338i	−0.336875	−	0.463668i	−0.943525	+	0.331300i	$0.892513\pi$
$588$	−6.73795	−	1.89736i	−0.277869	−	0.0782457i
$589$	−16.5692	−	5.38365i	−0.682721	−	0.221829i
$590$	−15.9822	+	1.67979i	−0.657976	+	0.0691561i
$591$	−0.955336	+	9.08941i	−0.0392973	+	0.373888i
$592$	−5.18207	+	5.75527i	−0.212982	+	0.236540i
$593$	10.7611	−	18.6387i	0.441904	−	0.765400i	−0.555927	−	0.831231i	$-0.687637\pi$
$593$	10.7611	−	18.6387i	0.441904	−	0.765400i	0.997831	+	0.0658311i	$0.0209699\pi$
$594$	3.26140	+	0.602735i	0.133817	+	0.0247305i
$595$	−1.61375	+	2.92773i	−0.0661575	+	0.120025i
$596$	−12.0379	+	3.91134i	−0.493090	+	0.160215i
$597$	14.8609	−	6.61648i	0.608214	−	0.270794i
$598$	3.27628	−	7.35864i	0.133977	−	0.300917i
$599$	−41.0332	+	8.72187i	−1.67657	+	0.356366i	−0.945421	−	0.325851i	$-0.894349\pi$
$599$	−41.0332	+	8.72187i	−1.67657	+	0.356366i	−0.731150	+	0.682217i	$0.761016\pi$
$600$	0.412343	+	0.457953i	0.0168338	+	0.0186958i
$601$	17.1729	−	12.4769i	0.700499	−	0.508942i	−0.179596	−	0.983740i	$-0.557479\pi$
$601$	17.1729	−	12.4769i	0.700499	−	0.508942i	0.880095	+	0.474798i	$0.157479\pi$
$602$	−22.5911	−	1.92221i	−0.920743	−	0.0783433i
$603$	1.40189	+	4.31456i	0.0570892	+	0.175703i
$604$	20.1220	+	11.6175i	0.818754	+	0.472708i
$605$	−3.57954	+	22.7513i	−0.145529	+	0.924972i
$606$	−5.26153	−	9.11324i	−0.213735	−	0.370200i
$607$	46.2760	+	9.83627i	1.87829	+	0.399242i	0.997270	−	0.0738457i	$-0.0235272\pi$
$607$	46.2760	+	9.83627i	1.87829	+	0.399242i	0.881015	+	0.473088i	$0.156861\pi$
$608$	1.16220	−	1.59963i	0.0471335	−	0.0648737i
$609$	2.35267	+	3.10666i	0.0953349	+	0.125888i
$610$	−2.02118	+	6.22056i	−0.0818353	+	0.251863i
$611$	−11.3176	+	10.1904i	−0.457862	+	0.412261i
$612$	0.551311	+	0.245459i	0.0222854	+	0.00992211i
$613$	40.2716	+	4.23271i	1.62655	+	0.170958i	0.873439	−	0.486933i	$-0.161884\pi$
$613$	40.2716	+	4.23271i	1.62655	+	0.170958i	0.753114	+	0.657890i	$0.228551\pi$
$614$	−3.28019	+	15.4321i	−0.132378	+	0.622787i
$615$	−11.2298			−0.452831
$616$	−8.65878	−	1.42321i	−0.348872	−	0.0573428i
$617$	−14.4832			−0.583071			−0.291535	−	0.956560i	$-0.594166\pi$
$617$	−14.4832			−0.583071			−0.291535	+	0.956560i	$0.594166\pi$
$618$	−3.72373	+	17.5188i	−0.149790	+	0.704708i
$619$	−26.4005	−	2.77480i	−1.06113	−	0.111529i	−0.442152	−	0.896940i	$-0.645785\pi$
$619$	−26.4005	−	2.77480i	−1.06113	−	0.111529i	−0.618974	+	0.785411i	$0.712451\pi$
$620$	−16.8533	−	7.50358i	−0.676846	−	0.301351i
$621$	1.54246	−	1.38884i	0.0618967	−	0.0557320i
$622$	5.80342	−	17.8611i	0.232696	−	0.716165i
$623$	−0.330103	−	0.139193i	−0.0132253	−	0.00557664i
$624$	2.28111	−	3.13968i	0.0913174	−	0.125688i
$625$	21.0684	+	4.47822i	0.842736	+	0.179129i
$626$	−5.34293	−	9.25423i	−0.213546	−	0.369873i
$627$	3.99481	+	5.20061i	0.159537	+	0.207692i
$628$	1.72683	+	0.996988i	0.0689082	+	0.0397841i
$629$	−1.44425	−	4.44493i	−0.0575858	−	0.177231i
$630$	2.35307	+	5.01492i	0.0937484	+	0.199799i
$631$	−17.1381	+	12.4515i	−0.682255	+	0.495688i	−0.874105	−	0.485737i	$-0.838551\pi$
$631$	−17.1381	+	12.4515i	−0.682255	+	0.495688i	0.191850	+	0.981424i	$0.438551\pi$
$632$	−5.16267	−	5.73373i	−0.205360	−	0.228075i
$633$	17.4898	−	3.71757i	0.695157	−	0.147760i
$634$	10.5787	−	23.7601i	0.420133	−	0.943634i
$635$	−10.8026	+	4.80962i	−0.428687	+	0.190864i
$636$	10.2053	−	3.31592i	0.404668	−	0.131485i
$637$	−14.5055	−	22.9692i	−0.574727	−	0.910071i
$638$	3.36450	+	3.54181i	0.133202	+	0.140222i
$639$	4.38781	−	7.59991i	0.173579	−	0.300648i
$640$	1.40099	−	1.55595i	0.0553789	−	0.0615045i
$641$	−2.66091	+	25.3168i	−0.105100	+	0.999955i	0.807157	+	0.590337i	$0.201005\pi$
$641$	−2.66091	+	25.3168i	−0.105100	+	0.999955i	−0.912257	+	0.409619i	$0.865662\pi$
$642$	6.80946	−	0.715703i	0.268748	−	0.0282465i
$643$	32.0797	+	10.4233i	1.26510	+	0.411056i	0.863310	−	0.504675i	$-0.168388\pi$
$643$	32.0797	+	10.4233i	1.26510	+	0.411056i	0.401792	+	0.915731i	$0.368388\pi$
$644$	−4.00727	+	3.75474i	−0.157909	+	0.147957i
$645$	10.5462	+	14.5156i	0.415257	+	0.571552i
$646$	0.485336	+	1.09008i	0.0190953	+	0.0428887i
$647$	−24.5335	−	22.0901i	−0.964513	−	0.868451i	0.0268445	−	0.999640i	$-0.491454\pi$
$647$	−24.5335	−	22.0901i	−0.964513	−	0.868451i	−0.991357	+	0.131188i	$0.958121\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	25.3788	+	1.98426i	0.996205	+	0.0778891i
$650$			2.39152i			0.0938032i
$651$	17.6303	+	15.2521i	0.690984	+	0.597777i
$652$	5.76674	+	4.18978i	0.225843	+	0.164084i
$653$	−4.62185	−	43.9739i	−0.180867	−	1.72083i	−0.589189	−	0.807995i	$-0.700553\pi$
$653$	−4.62185	−	43.9739i	−0.180867	−	1.72083i	0.408322	−	0.912838i	$-0.366114\pi$
$654$	−4.12612	−	19.4119i	−0.161344	−	0.759064i
$655$	−7.18247	−	33.7909i	−0.280642	−	1.32032i
$656$	−0.560640	−	5.33414i	−0.0218893	−	0.208263i
$657$	−6.40469	−	4.65328i	−0.249871	−	0.181542i
$658$	9.80879	−	3.40361i	0.382386	−	0.132687i
$659$			50.1361i			1.95303i	0.215459	+	0.976513i	$0.430875\pi$
$659$			50.1361i			1.95303i	−0.215459	+	0.976513i	$0.569125\pi$
$660$	3.63135	+	5.91901i	0.141350	+	0.230397i
$661$	−9.97138	+	5.75698i	−0.387842	+	0.223921i	−0.681225	−	0.732074i	$-0.738552\pi$
$661$	−9.97138	+	5.75698i	−0.387842	+	0.223921i	0.293383	+	0.955995i	$0.405219\pi$
$662$	14.7680	+	13.2972i	0.573974	+	0.516809i
$663$	0.952592	+	2.13956i	0.0369956	+	0.0830935i
$664$	0.199343	+	0.274373i	0.00773602	+	0.0106477i
$665$	−3.17738	+	10.4821i	−0.123214	+	0.406477i
$666$	−7.36544	−	2.39318i	−0.285405	−	0.0927336i
$667$	3.04041	−	0.319560i	0.117725	−	0.0123734i
$668$	1.19424	−	11.3625i	0.0462066	−	0.439627i
$669$	13.6703	−	15.1824i	0.528523	−	0.586985i
$670$	−4.74924	+	8.22592i	−0.183479	+	0.317795i
$671$	4.93911	−	9.10784i	0.190672	−	0.351604i
$672$	−2.26460	+	1.36807i	−0.0873587	+	0.0527743i
$673$	41.0277	−	13.3307i	1.58150	−	0.513861i	0.619058	−	0.785345i	$-0.287515\pi$
$673$	41.0277	−	13.3307i	1.58150	−	0.513861i	0.962443	+	0.271484i	$0.0875145\pi$
$674$	27.7348	−	12.3483i	1.06831	−	0.475640i
$675$	−0.250646	+	0.562960i	−0.00964736	+	0.0216683i
$676$	2.01599	−	0.428511i	0.0775379	−	0.0164812i
$677$	−3.77321	−	4.19058i	−0.145016	−	0.161057i	0.666261	−	0.745719i	$-0.267894\pi$
$677$	−3.77321	−	4.19058i	−0.145016	−	0.161057i	−0.811277	+	0.584662i	$0.801227\pi$
$678$	12.7133	−	9.23674i	0.488251	−	0.354735i
$679$	22.5980	−	10.6033i	0.867230	−	0.406916i
$680$	0.390456	+	1.20170i	0.0149733	+	0.0460831i
$681$	18.4611	+	10.6585i	0.707431	+	0.408435i
$682$	24.0921	+	16.5399i	0.922534	+	0.633344i
$683$	10.6885	+	18.5129i	0.408982	+	0.708378i	0.994776	−	0.102082i	$-0.0325504\pi$
$683$	10.6885	+	18.5129i	0.408982	+	0.708378i	−0.585794	+	0.810460i	$0.699217\pi$
$684$	1.93405	+	0.411094i	0.0739501	+	0.0157186i
$685$	0.894050	−	1.23055i	0.0341599	−	0.0470171i
$686$	3.02795	+	18.2711i	0.115608	+	0.697592i
$687$	−7.72785	+	23.7839i	−0.294836	+	0.907411i
$688$	−6.36836	+	5.73410i	−0.242791	+	0.218610i
$689$	38.0434	+	16.9380i	1.44934	+	0.645286i
$690$	4.32193	+	0.454253i	0.164533	+	0.0172931i
$691$	2.33076	−	10.9654i	0.0886662	−	0.417142i	−0.911319	−	0.411701i	$-0.864935\pi$
$691$	2.33076	−	10.9654i	0.0886662	−	0.417142i	0.999985	−	0.00544075i	$-0.00173185\pi$
$692$	11.2003			0.425770
$693$	−2.22168	−	8.48906i	−0.0843945	−	0.322473i
$694$	−0.0418713			−0.00158941
$695$	−1.63238	+	7.67976i	−0.0619198	+	0.291310i
$696$	1.46485	+	0.153962i	0.0555249	+	0.00583590i
$697$	2.95697	+	1.31653i	0.112003	+	0.0498670i
$698$	19.6707	−	17.7116i	0.744549	−	0.670395i
$699$	0.376358	−	1.15831i	0.0142352	−	0.0438113i
$700$	0.633471	−	1.50231i	0.0239430	−	0.0567821i
$701$	8.44151	−	11.6187i	0.318831	−	0.438834i	−0.619279	−	0.785171i	$-0.712575\pi$
$701$	8.44151	−	11.6187i	0.318831	−	0.438834i	0.938110	+	0.346338i	$0.112575\pi$
$702$	3.79605	+	0.806875i	0.143273	+	0.0304535i
$703$	−7.65640	−	13.2613i	−0.288767	−	0.500158i
$704$	−2.63022	+	2.02038i	−0.0991301	+	0.0761460i
$705$	−7.11555	−	4.10816i	−0.267987	−	0.154722i
$706$	7.94089	+	24.4395i	0.298859	+	0.919794i
$707$	−15.9148	+	22.8444i	−0.598536	+	0.859150i
$708$	6.20949	−	4.51146i	0.233367	−	0.169551i
$709$	19.2229	+	21.3492i	0.721932	+	0.801786i	0.986704	−	0.162525i	$-0.0519637\pi$
$709$	19.2229	+	21.3492i	0.721932	+	0.801786i	−0.264773	+	0.964311i	$0.585297\pi$
$710$	17.9724	−	3.82015i	0.674492	−	0.143368i
$711$	3.13817	−	7.04845i	0.117691	−	0.264338i
$712$	−0.123699	+	0.0550744i	−0.00463582	+	0.00206400i
$713$	17.3931	−	5.65137i	0.651378	−	0.211646i
$714$	−0.0316715	−	1.59636i	−0.00118528	−	0.0597422i
$715$	−4.89753	+	26.5005i	−0.183157	+	0.991063i
$716$	6.77249	−	11.7303i	0.253100	−	0.438382i
$717$	−14.2779	+	15.8572i	−0.533219	+	0.592199i
$718$	1.81909	−	17.3075i	0.0678879	−	0.645910i
$719$	−3.91609	+	0.411597i	−0.146045	+	0.0153500i	−0.177269	−	0.984162i	$-0.556726\pi$
$719$	−3.91609	+	0.411597i	−0.146045	+	0.0153500i	0.0312236	+	0.999512i	$0.490060\pi$
$720$	1.99127	+	0.647002i	0.0742102	+	0.0241124i
$721$	46.1458	−	10.7695i	1.71856	−	0.401078i
$722$	−8.86995	−	12.2084i	−0.330105	−	0.454351i
$723$	−2.85082	−	6.40305i	−0.106023	−	0.238132i
$724$	1.67941	+	1.51214i	0.0624147	+	0.0561984i
$725$	−0.786060	+	0.453832i	−0.0291935	+	0.0168549i
$726$	−3.95258	−	10.2653i	−0.146694	−	0.380982i
$727$			14.0998i			0.522933i	0.965213	+	0.261467i	$0.0842061\pi$
$727$			14.0998i			0.522933i	−0.965213	+	0.261467i	$0.915794\pi$
$728$	−10.0838	−	1.93515i	−0.373729	−	0.0717214i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−1.73260	−	16.4846i	−0.0641264	−	0.610122i
$731$	−1.07523	−	5.05854i	−0.0397687	−	0.187097i
$732$	−0.649499	−	3.05565i	−0.0240062	−	0.112940i
$733$	1.03435	+	9.84116i	0.0382045	+	0.363492i	0.996876	+	0.0789776i	$0.0251655\pi$
$733$	1.03435	+	9.84116i	0.0382045	+	0.363492i	−0.958672	+	0.284514i	$0.908168\pi$
$734$	7.52313	+	5.46587i	0.277684	+	0.201749i
$735$	9.36719	−	11.2721i	0.345514	−	0.415778i
$736$			2.07558i			0.0765070i
$737$	9.76586	−	11.4462i	0.359730	−	0.421627i
$738$	4.64494	−	2.68176i	0.170983	−	0.0987169i
$739$	−11.7339	−	10.5652i	−0.431638	−	0.388649i	0.424473	−	0.905441i	$-0.360459\pi$
$739$	−11.7339	−	10.5652i	−0.431638	−	0.388649i	−0.856111	+	0.516792i	$0.827126\pi$
$740$	−6.59522	−	14.8131i	−0.242445	−	0.544540i
$741$	4.51033	+	6.20794i	0.165691	+	0.228054i
$742$	−19.4116	−	20.7172i	−0.712622	−	0.760551i
$743$	−30.9180	−	10.0459i	−1.13427	−	0.368547i	−0.319073	−	0.947730i	$-0.603371\pi$
$743$	−30.9180	−	10.0459i	−1.13427	−	0.368547i	−0.815197	+	0.579184i	$0.803371\pi$
$744$	8.76286	−	0.921014i	0.321262	−	0.0337660i
$745$	2.77014	−	26.3561i	0.101490	−	0.965613i
$746$	−5.27101	+	5.85405i	−0.192986	+	0.214332i
$747$	−0.169572	+	0.293707i	−0.00620430	+	0.0107462i
$748$	−0.262270	−	1.98428i	−0.00958954	−	0.0725523i
$749$	−9.36710	−	15.5056i	−0.342266	−	0.566563i
$750$	−11.1834	+	3.63372i	−0.408361	+	0.132685i
$751$	−26.9087	+	11.9805i	−0.981912	+	0.437175i	−0.833964	−	0.551820i	$-0.813934\pi$
$751$	−26.9087	+	11.9805i	−0.981912	+	0.437175i	−0.147949	+	0.988995i	$0.547267\pi$
$752$	1.59613	−	3.58496i	0.0582048	−	0.130730i
$753$	13.7346	−	2.91939i	0.500518	−	0.106388i
$754$	3.82486	+	4.24794i	0.139293	+	0.154701i
$755$	−39.3571	+	28.5946i	−1.43235	+	1.04066i
$756$	−2.17088	−	1.51237i	−0.0789543	−	0.0550044i
$757$	7.64245	+	23.5210i	0.277770	+	0.854887i	0.988473	+	0.151395i	$0.0483766\pi$
$757$	7.64245	+	23.5210i	0.277770	+	0.854887i	−0.710704	+	0.703491i	$0.751623\pi$
$758$	−4.56860	−	2.63768i	−0.165939	−	0.0958049i
$759$	−6.60145	−	1.95176i	−0.239617	−	0.0708442i
$760$	2.06993	+	3.58523i	0.0750843	+	0.130050i
$761$	34.5693	+	7.34792i	1.25313	+	0.266362i	0.786224	−	0.617942i	$-0.212033\pi$
$761$	34.5693	+	7.34792i	1.25313	+	0.266362i	0.466911	+	0.884304i	$0.345367\pi$
$762$	3.31965	−	4.56911i	0.120258	−	0.165521i
$763$	−41.8580	+	31.6990i	−1.51536	+	1.14758i
$764$	−8.24324	+	25.3701i	−0.298230	+	0.917857i
$765$	−0.938996	+	0.845475i	−0.0339495	+	0.0305682i
$766$	−19.9102	−	8.86461i	−0.719387	−	0.320292i
$767$	29.6237	+	3.11358i	1.06965	+	0.112425i
$768$	−0.207912	+	0.978148i	−0.00750237	+	0.0352959i
$769$	18.5193			0.667824			0.333912	−	0.942604i	$-0.391631\pi$
$769$	18.5193			0.667824			0.333912	+	0.942604i	$0.391631\pi$
$770$	10.0961	−	15.3499i	0.363837	−	0.553172i
$771$	5.92497			0.213383
$772$	2.94976	−	13.8775i	0.106164	−	0.499464i
$773$	23.8970	+	2.51167i	0.859515	+	0.0903387i	0.524023	−	0.851704i	$-0.324431\pi$
$773$	23.8970	+	2.51167i	0.859515	+	0.0903387i	0.335492	+	0.942043i	$0.391097\pi$
$774$	−7.82860	−	3.48552i	−0.281393	−	0.125284i
$775$	−4.03508	+	3.63320i	−0.144944	+	0.130509i
$776$	2.91549	−	8.97295i	0.104660	−	0.322110i
$777$	2.54557	+	20.3312i	0.0913219	+	0.729378i
$778$	7.00209	−	9.63755i	0.251037	−	0.345523i
$779$	10.3733	+	2.20491i	0.371662	+	0.0789992i
$780$	4.06276	+	7.03690i	0.145470	+	0.251961i
$781$	−29.0951	+	0.776811i	−1.04110	+	0.0277965i
$782$	−1.08477	−	0.626291i	−0.0387912	−	0.0223961i
$783$	0.455156	+	1.40083i	0.0162659	+	0.0500614i
$784$	5.82186	+	3.88664i	0.207924	+	0.138808i
$785$	−3.37754	+	2.45393i	−0.120550	+	0.0875845i
$786$	11.0403	+	12.2615i	0.393796	+	0.437354i
$787$	21.9687	−	4.66958i	0.783098	−	0.166453i	0.201022	−	0.979587i	$-0.435574\pi$
$787$	21.9687	−	4.66958i	0.783098	−	0.166453i	0.582076	+	0.813134i	$0.302240\pi$
$788$	3.71736	−	8.34933i	0.132425	−	0.297433i
$789$	12.4617	−	5.54829i	0.443647	−	0.197524i
$790$	15.3636	−	4.99194i	0.546613	−	0.177605i
$791$	−36.4117	−	20.0700i	−1.29465	−	0.713607i
$792$	−2.91552	−	1.58106i	−0.103598	−	0.0561806i
$793$	6.06173	−	10.4992i	0.215258	−	0.372839i
$794$	19.0233	−	21.1275i	0.675112	−	0.749787i
$795$	−2.34844	+	22.3439i	−0.0832906	+	0.792457i
$796$	−16.1781	+	1.70039i	−0.573418	+	0.0602687i
$797$	−39.9209	−	12.9711i	−1.41407	−	0.459459i	−0.500357	−	0.865819i	$-0.666798\pi$
$797$	−39.9209	−	12.9711i	−1.41407	−	0.459459i	−0.913713	+	0.406359i	$0.866798\pi$
$798$	−1.18894	−	5.09442i	−0.0420880	−	0.180341i
$799$	1.39200	+	1.91592i	0.0492454	+	0.0677805i
$800$	−0.250646	−	0.562960i	−0.00886167	−	0.0199036i
$801$	−0.100626	−	0.0906041i	−0.00355544	−	0.00320134i
$802$	−14.0293	+	8.09980i	−0.495391	+	0.286014i
$803$	−2.04664	+	26.1766i	−0.0722243	+	0.923753i
$804$		−	4.53660i		−	0.159994i
$805$	−3.76920	−	10.8624i	−0.132847	−	0.382848i
$806$	27.6641	+	20.0991i	0.974427	+	0.707962i
$807$	3.00470	+	28.5878i	0.105770	+	1.00634i
$808$	2.18787	+	10.2931i	0.0769689	+	0.362110i
$809$	−3.54686	−	16.6867i	−0.124701	−	0.586672i	−0.995478	−	0.0949934i	$-0.969717\pi$
$809$	−3.54686	−	16.6867i	−0.124701	−	0.586672i	0.870777	−	0.491678i	$-0.163616\pi$
$810$	0.218856	+	2.08227i	0.00768981	+	0.0731637i
$811$	−17.8035	−	12.9350i	−0.625166	−	0.454210i	0.229556	−	0.973295i	$-0.426273\pi$
$811$	−17.8035	−	12.9350i	−0.625166	−	0.454210i	−0.854722	+	0.519086i	$0.826273\pi$
$812$	−1.27751	−	3.68162i	−0.0448318	−	0.129200i
$813$		−	3.36068i		−	0.117864i
$814$	6.00897	+	24.9728i	0.210614	+	0.875295i
$815$	−12.9249	+	7.46219i	−0.452739	+	0.261389i
$816$	−0.448477	−	0.403810i	−0.0156998	−	0.0141362i
$817$	−6.89176	−	15.4791i	−0.241112	−	0.541547i
$818$	14.7977	+	20.3673i	0.517391	+	0.712128i
$819$	−2.33359	−	9.99908i	−0.0815422	−	0.349396i
$820$	10.6802	+	3.47021i	0.372969	+	0.121185i
$821$	−44.8793	+	4.71700i	−1.56630	+	0.164625i	−0.847577	−	0.530673i	$-0.821939\pi$
$821$	−44.8793	+	4.71700i	−1.56630	+	0.164625i	−0.718722	+	0.695298i	$0.755273\pi$
$822$	−0.0759372	+	0.722494i	−0.00264861	+	0.0251999i
$823$	20.9527	−	23.2703i	0.730364	−	0.811152i	−0.257532	−	0.966270i	$-0.582909\pi$
$823$	20.9527	−	23.2703i	0.730364	−	0.811152i	0.987896	+	0.155118i	$0.0495758\pi$
$824$	8.95507	−	15.5106i	0.311965	−	0.540339i
$825$	2.02620	−	0.267812i	0.0705433	−	0.00932400i
$826$	−17.7844	−	9.80269i	−0.618798	−	0.341079i
$827$	−18.7705	+	6.09889i	−0.652713	+	0.212079i	−0.616610	−	0.787269i	$-0.711494\pi$
$827$	−18.7705	+	6.09889i	−0.652713	+	0.212079i	−0.0361027	+	0.999348i	$0.511494\pi$
$828$	−1.89614	+	0.844215i	−0.0658954	+	0.0293385i
$829$	9.64518	−	21.6634i	0.334991	−	0.752402i	−0.664994	−	0.746849i	$-0.731566\pi$
$829$	9.64518	−	21.6634i	0.334991	−	0.752402i	0.999985	−	0.00555296i	$-0.00176757\pi$
$830$	−0.694562	+	0.147634i	−0.0241086	+	0.00512444i
$831$	−6.70016	−	7.44128i	−0.232426	−	0.258135i
$832$	−3.13968	+	2.28111i	−0.108849	+	0.0790832i
$833$	−3.78799	+	1.86993i	−0.131246	+	0.0647894i
$834$	−1.15878	−	3.56637i	−0.0401254	−	0.123493i
$835$	20.7163	+	11.9606i	0.716917	+	0.413912i
$836$	−2.19221	−	6.18054i	−0.0758192	−	0.213758i
$837$	4.40557	+	7.63067i	0.152279	+	0.263754i
$838$	6.30688	+	1.34057i	0.217867	+	0.0463092i
$839$	−1.51766	+	2.08888i	−0.0523955	+	0.0721163i	−0.834411	−	0.551143i	$-0.814192\pi$
$839$	−1.51766	+	2.08888i	−0.0523955	+	0.0721163i	0.782015	+	0.623259i	$0.214192\pi$
$840$	−0.688204	−	5.49661i	−0.0237453	−	0.189651i
$841$	8.29109	−	25.5173i	0.285900	−	0.879908i
$842$	23.3754	−	21.0473i	0.805569	−	0.725338i
$843$	3.99040	+	1.77664i	0.137437	+	0.0611907i
$844$	−17.7826	−	1.86902i	−0.612102	−	0.0643345i
$845$	−0.897192	+	4.22096i	−0.0308643	+	0.145205i
$846$	3.92423			0.134918
$847$	−20.1453	+	21.0039i	−0.692202	+	0.721704i
$848$	−10.7305			−0.368488
$849$	2.85604	−	13.4366i	0.0980189	−	0.461143i
$850$	0.369852	+	0.0388730i	0.0126858	+	0.00133333i
$851$	14.6846	+	6.53801i	0.503382	+	0.224120i
$852$	−6.52156	+	5.87204i	−0.223425	+	0.201173i
$853$	−4.25255	+	13.0880i	−0.145604	+	0.448124i	−0.997088	−	0.0762566i	$-0.975703\pi$
$853$	−4.25255	+	13.0880i	−0.145604	+	0.448124i	0.851484	+	0.524381i	$0.175703\pi$
$854$	−6.58893	+	4.98979i	−0.225469	+	0.170747i
$855$	−2.43335	+	3.34922i	−0.0832189	+	0.114541i
$856$	−6.69734	−	1.42356i	−0.228910	−	0.0486564i
$857$	−16.4153	−	28.4322i	−0.560737	−	0.971224i	−0.997432	−	0.0716151i	$-0.977185\pi$
$857$	−16.4153	−	28.4322i	−0.560737	−	0.971224i	0.436696	−	0.899609i	$-0.356149\pi$
$858$	−4.30276	−	12.1308i	−0.146894	−	0.414140i
$859$	−35.7309	−	20.6293i	−1.21912	−	0.703861i	−0.254393	−	0.967101i	$-0.581876\pi$
$859$	−35.7309	−	20.6293i	−1.21912	−	0.703861i	−0.964730	+	0.263240i	$0.915209\pi$
$860$	−5.54447	−	17.0641i	−0.189065	−	0.581882i
$861$	−11.6436	−	8.11162i	−0.396812	−	0.276443i
$862$	−3.28821	+	2.38902i	−0.111997	+	0.0813704i
$863$	26.2017	+	29.1000i	0.891917	+	0.990574i	0.999994	−	0.00356825i	$-0.00113581\pi$
$863$	26.2017	+	29.1000i	0.891917	+	0.990574i	−0.108077	+	0.994143i	$0.534469\pi$
$864$	−0.978148	+	0.207912i	−0.0332773	+	0.00707330i
$865$	−9.53816	+	21.4231i	−0.324307	+	0.728406i
$866$	−3.43226	+	1.52814i	−0.116633	+	0.0519283i
$867$	−15.8216	+	5.14075i	−0.537329	+	0.174589i
$868$	−12.0542	−	19.9537i	−0.409146	−	0.677271i
$869$	−25.3687	+	3.35309i	−0.860576	+	0.113746i
$870$	−1.54195	+	2.67074i	−0.0522771	+	0.0905467i
$871$	11.7806	−	13.0837i	0.399172	−	0.443325i
$872$	−2.07442	+	19.7368i	−0.0702488	+	0.668373i
$873$	9.38303	−	0.986196i	0.317567	−	0.0333777i
$874$	−3.90309	−	1.26819i	−0.132024	−	0.0428972i
$875$	21.2720	+	22.7027i	0.719126	+	0.767492i
$876$	4.65328	+	6.40469i	0.157220	+	0.216394i
$877$	9.79135	+	21.9917i	0.330630	+	0.742608i	1.00000		0.000321655i	$-0.000102386\pi$
$877$	9.79135	+	21.9917i	0.330630	+	0.742608i	−0.669370	+	0.742930i	$0.733436\pi$
$878$	−14.4713	−	13.0300i	−0.488381	−	0.439740i
$879$	15.9451	−	9.20593i	0.537816	−	0.310508i
$880$	−1.62454	−	6.75146i	−0.0547634	−	0.227592i
$881$		−	14.3401i		−	0.483130i	−0.970385	−	0.241565i	$-0.922339\pi$
$881$		−	14.3401i		−	0.483130i	0.970385	−	0.241565i	$-0.0776607\pi$
$882$	−1.18266	+	6.89937i	−0.0398221	+	0.232314i
$883$	18.1669	+	13.1990i	0.611363	+	0.444181i	0.849894	−	0.526953i	$-0.176666\pi$
$883$	18.1669	+	13.1990i	0.611363	+	0.444181i	−0.238531	+	0.971135i	$0.576666\pi$
$884$	−0.244810	−	2.32921i	−0.00823384	−	0.0783397i
$885$	3.34119	+	15.7190i	0.112313	+	0.528390i
$886$	−1.29925	−	6.11250i	−0.0436492	−	0.205353i
$887$	5.06078	+	48.1502i	0.169925	+	1.61672i	0.664294	+	0.747472i	$0.268732\pi$
$887$	5.06078	+	48.1502i	0.169925	+	1.61672i	−0.494369	+	0.869252i	$0.664601\pi$
$888$	6.26541	+	4.55209i	0.210254	+	0.152758i
$889$	−14.6747	−	2.81619i	−0.492174	−	0.0944518i
$890$		−	0.283505i		−	0.00950310i
$891$	0.258524	−	3.30653i	0.00866088	−	0.110773i
$892$	−17.6928	+	10.2150i	−0.592399	+	0.342022i
$893$	5.76621	+	5.19192i	0.192959	+	0.173741i
$894$	5.14821	+	11.5631i	0.172182	+	0.386727i
$895$	16.6694	+	22.9435i	0.557197	+	0.766916i
$896$	2.57651	−	0.601309i	0.0860753	−	0.0200883i
$897$	−7.66079	−	2.48914i	−0.255786	−	0.0831100i
$898$	−13.0504	+	1.37165i	−0.435497	+	0.0457726i
$899$	−1.35658	+	12.9070i	−0.0452444	+	0.430471i
$900$	0.412343	−	0.457953i	0.0137448	−	0.0152651i
$901$	3.23786	−	5.60814i	0.107869	−	0.186834i
$902$	−15.6374	−	8.48005i	−0.520670	−	0.282355i
$903$	0.449734	+	22.6682i	0.0149662	+	0.754352i
$904$	−14.9454	+	4.85604i	−0.497075	+	0.161510i
$905$	−4.32251	+	1.92451i	−0.143685	+	0.0639728i
$906$	9.45050	−	21.2262i	0.313972	−	0.705192i
$907$	12.6764	−	2.69445i	0.420913	−	0.0894679i	0.00741446	−	0.999973i	$-0.497640\pi$
$907$	12.6764	−	2.69445i	0.420913	−	0.0894679i	0.413499	+	0.910505i	$0.364307\pi$
$908$	−14.2639	−	15.8416i	−0.473364	−	0.525724i
$909$	−8.51334	+	6.18530i	−0.282370	+	0.205154i
$910$	12.2888	−	17.6395i	0.407369	−	0.584745i
$911$	−9.09444	−	27.9898i	−0.301312	−	0.927344i	−0.981028	−	0.193868i	$-0.937897\pi$
$911$	−9.09444	−	27.9898i	−0.301312	−	0.927344i	0.679715	−	0.733476i	$-0.262103\pi$
$912$	−1.71235	−	0.988627i	−0.0567017	−	0.0327367i
$913$	1.12441	−	0.0300207i	0.0372125	−	0.000993540i
$914$	−3.28186	−	5.68435i	−0.108554	−	0.188021i
$915$	6.39775	+	1.35988i	0.211503	+	0.0449564i
$916$	14.6992	−	20.2318i	0.485676	−	0.668476i
$917$	16.9610	−	40.2239i	0.560101	−	1.32831i
$918$	0.186487	−	0.573948i	0.00615499	−	0.0189431i
$919$	3.77867	−	3.40233i	0.124647	−	0.112233i	−0.604450	−	0.796643i	$-0.706607\pi$
$919$	3.77867	−	3.40233i	0.124647	−	0.112233i	0.729097	+	0.684411i	$0.239940\pi$
$920$	−3.97003	−	1.76757i	−0.130888	−	0.0582751i
$921$	15.6904	+	1.64913i	0.517016	+	0.0543406i
$922$	−0.422902	+	1.98960i	−0.0139275	+	0.0655239i
$923$	−34.0569			−1.12100
$924$	−0.510325	+	8.76011i	−0.0167885	+	0.288187i
$925$	−4.77243			−0.156916
$926$	−6.79180	+	31.9529i	−0.223192	+	1.05004i
$927$	17.8120	+	1.87212i	0.585024	+	0.0614885i
$928$	−1.34558	−	0.599089i	−0.0441707	−	0.0196661i
$929$	−6.65749	+	5.99443i	−0.218425	+	0.196671i	−0.771078	−	0.636741i	$-0.780282\pi$
$929$	−6.65749	+	5.99443i	−0.218425	+	0.196671i	0.552653	+	0.833411i	$0.313616\pi$
$930$	−5.70082	+	17.5453i	−0.186937	+	0.575334i
$931$	−10.8659	+	8.57314i	−0.356117	+	0.280973i
$932$	−0.715875	+	0.985317i	−0.0234493	+	0.0322751i
$933$	−18.3699	−	3.90464i	−0.601403	−	0.127832i
$934$	18.8697	+	32.6834i	0.617437	+	1.06943i
$935$	4.01873	+	1.18816i	0.131427	+	0.0388571i
$936$	−3.36092	−	1.94043i	−0.109855	−	0.0634248i
$937$	3.44911	+	10.6153i	0.112678	+	0.346786i	0.991456	−	0.130445i	$-0.0416405\pi$
$937$	3.44911	+	10.6153i	0.112678	+	0.346786i	−0.878778	+	0.477231i	$0.841641\pi$
$938$	−10.8660	+	5.09849i	−0.354788	+	0.166471i
$939$	−8.64504	+	6.28099i	−0.282120	+	0.204972i
$940$	5.49780	+	6.10592i	0.179318	+	0.199153i
$941$	−25.9049	+	5.50626i	−0.844476	+	0.179499i	−0.609781	−	0.792570i	$-0.708743\pi$
$941$	−25.9049	+	5.50626i	−0.844476	+	0.179499i	−0.234695	+	0.972069i	$0.575409\pi$
$942$	0.811023	−	1.82159i	0.0264246	−	0.0593505i
$943$	−10.1700	+	4.52796i	−0.331180	+	0.147451i
$944$	−7.29969	+	2.37181i	−0.237585	+	0.0771959i
$945$	4.74149	−	2.86438i	0.154241	−	0.0931782i
$946$	3.72423	+	28.1767i	0.121085	+	0.916103i
$947$	−13.4970	+	23.3775i	−0.438594	+	0.759667i	−0.997581	−	0.0695089i	$-0.977857\pi$
$947$	−13.4970	+	23.3775i	−0.438594	+	0.759667i	0.558987	+	0.829176i	$0.311190\pi$
$948$	−5.16267	+	5.73373i	−0.167676	+	0.186223i
$949$	−3.21146	+	30.5550i	−0.104248	+	0.991857i
$950$	1.21178	−	0.127363i	0.0393154	−	0.00413221i
$951$	−24.7357	−	8.03712i	−0.802111	−	0.260622i
$952$	−0.463180	+	1.52801i	−0.0150118	+	0.0495232i
$953$	−8.77507	−	12.0778i	−0.284252	−	0.391240i	0.642884	−	0.765963i	$-0.277738\pi$
$953$	−8.77507	−	12.0778i	−0.284252	−	0.391240i	−0.927137	+	0.374724i	$0.877738\pi$
$954$	−4.36450	−	9.80283i	−0.141306	−	0.317378i
$955$	−41.5062	−	37.3723i	−1.34311	−	1.20934i
$956$	18.4793	−	10.6690i	0.597662	−	0.345060i
$957$	3.17072	−	3.71629i	0.102495	−	0.120131i
$958$		−	43.1387i		−	1.39375i
$959$	1.81585	−	0.630095i	0.0586370	−	0.0203468i
$960$	−1.69387	−	1.23067i	−0.0546696	−	0.0397198i
$961$	4.87480	+	46.3806i	0.157251	+	1.49615i
$962$	6.24882	+	29.3984i	0.201470	+	0.947843i
$963$	−1.42356	−	6.69734i	−0.0458737	−	0.215819i
$964$	0.732641	+	6.97061i	0.0235968	+	0.224508i
$965$	24.0320	+	17.4603i	0.773617	+	0.562065i
$966$	4.15304	+	3.59284i	0.133622	+	0.115598i
$967$			0.721483i			0.0232013i	0.999933	+	0.0116007i	$0.00369269\pi$
$967$			0.721483i			0.0232013i	−0.999933	+	0.0116007i	$0.996307\pi$
$968$	0.586961	+	10.9843i	0.0188656	+	0.353050i
$969$	1.03338	−	0.596622i	0.0331969	−	0.0191663i
$970$	14.6800	+	13.2179i	0.471346	+	0.424402i
$971$	5.28041	+	11.8600i	0.169456	+	0.380605i	0.978233	−	0.207511i	$-0.0665363\pi$
$971$	5.28041	+	11.8600i	0.169456	+	0.380605i	−0.808776	+	0.588116i	$0.799870\pi$
$972$	−0.587785	−	0.809017i	−0.0188532	−	0.0259492i
$973$	−7.23983	+	6.78359i	−0.232098	+	0.217472i
$974$	0.569797	+	0.185138i	0.0182575	+	0.00593221i
$975$	2.37842	−	0.249982i	0.0761704	−	0.00800584i
$976$	−0.326538	+	3.10680i	−0.0104522	+	0.0994464i
$977$	−1.50893	+	1.67583i	−0.0482749	+	0.0536147i	−0.766799	−	0.641888i	$-0.778151\pi$
$977$	−1.50893	+	1.67583i	−0.0482749	+	0.0536147i	0.718524	+	0.695502i	$0.244818\pi$
$978$	3.56404	−	6.17310i	0.113965	−	0.197394i
$979$	−0.0816137	+	0.441612i	−0.00260838	+	0.0141140i
$980$	−12.3920	+	7.82578i	−0.395848	+	0.249985i
$981$	−18.8742	+	6.13260i	−0.602607	+	0.195799i
$982$	−27.6514	+	12.3112i	−0.882391	+	0.392866i
$983$	−6.93924	+	15.5858i	−0.221327	+	0.497109i	−0.989746	−	0.142838i	$-0.954377\pi$
$983$	−6.93924	+	15.5858i	−0.221327	+	0.497109i	0.768419	+	0.639947i	$0.221044\pi$
$984$	−5.24631	+	1.11514i	−0.167246	+	0.0355493i
$985$	12.8043	+	14.2206i	0.407979	+	0.453107i
$986$	0.719121	−	0.522472i	0.0229015	−	0.0166389i
$987$	−4.41027	−	9.39928i	−0.140380	−	0.299182i
$988$	−2.37122	−	7.29787i	−0.0754386	−	0.232176i
$989$	15.4037	+	8.89332i	0.489809	+	0.282791i
$990$	5.50701	−	4.23016i	0.175024	−	0.134443i
$991$	−5.36602	−	9.29422i	−0.170457	−	0.295241i	0.768123	−	0.640303i	$-0.221191\pi$
$991$	−5.36602	−	9.29422i	−0.170457	−	0.295241i	−0.938580	+	0.345062i	$0.887858\pi$
$992$	−8.61859	−	1.83194i	−0.273640	−	0.0581641i
$993$	11.6806	−	16.0770i	0.370674	−	0.510189i
$994$	21.3940	+	9.02106i	0.678575	+	0.286131i
$995$	10.5249	−	32.3924i	0.333663	−	1.02691i
$996$	0.252032	−	0.226931i	0.00798595	−	0.00719058i
$997$	17.6314	+	7.85001i	0.558392	+	0.248612i	0.666472	−	0.745530i	$-0.267804\pi$
$997$	17.6314	+	7.85001i	0.558392	+	0.248612i	−0.108080	+	0.994142i	$0.534470\pi$
$998$	−0.935826	−	0.0983593i	−0.0296231	−	0.00311351i
$999$	−1.61017	+	7.57524i	−0.0509434	+	0.239670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.ba.b.61.4	yes	64
7.3	odd	6		462.2.ba.a.325.1	yes	64
11.2	odd	10		462.2.ba.a.145.1	✓	64
77.24	even	30	inner	462.2.ba.b.409.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.145.1	✓	64	11.2	odd	10
462.2.ba.a.325.1	yes	64	7.3	odd	6
462.2.ba.b.61.4	yes	64	1.1	even	1	trivial
462.2.ba.b.409.4	yes	64	77.24	even	30	inner

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207912 + 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(1.55595 - 1.40099i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(2.62525 - 0.328695i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(q+(-0.207912 + 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(1.55595 - 1.40099i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(2.62525 - 0.328695i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +(1.04687 + 1.81324i) q^{10} +(-1.10872 - 3.12582i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-1.19925 - 3.69091i) q^{13} +(-0.224308 + 2.63623i) q^{14} +(1.69387 - 1.23067i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.590297 + 0.125472i) q^{17} +(-0.406737 + 0.913545i) q^{18} +(-1.80631 + 0.804222i) q^{19} +(-1.99127 + 0.647002i) q^{20} +(2.64523 - 0.0524810i) q^{21} +(3.28803 - 0.434593i) q^{22} +(1.03779 - 1.79751i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.0644142 + 0.612860i) q^{25} +(3.85959 - 0.405660i) q^{26} +(0.951057 + 0.309017i) q^{27} +(-2.53198 - 0.767509i) q^{28} +(0.865758 + 1.19161i) q^{29} +(0.851602 + 1.91273i) q^{30} +(6.54795 + 5.89580i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.775904 - 3.22459i) q^{33} -0.603485i q^{34} +(3.62428 - 4.18939i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(0.809518 + 7.70205i) q^{37} +(-0.411094 - 1.93405i) q^{38} +(-0.806875 - 3.79605i) q^{39} +(-0.218856 - 2.08227i) q^{40} +(-4.33918 - 3.15260i) q^{41} +(-0.498640 + 2.59834i) q^{42} +8.56947i q^{43} +(-0.258524 + 3.30653i) q^{44} +(1.81324 - 1.04687i) q^{45} +(1.54246 + 1.38884i) q^{46} +(-1.59613 - 3.58496i) q^{47} +(0.587785 + 0.809017i) q^{48} +(6.78392 - 1.72582i) q^{49} +(-0.586075 - 0.190427i) q^{50} +(-0.600179 + 0.0630814i) q^{51} +(-0.405660 + 3.85959i) q^{52} +(-7.18013 + 7.97434i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-6.10435 - 3.31034i) q^{55} +(1.27717 - 2.31708i) q^{56} +(-1.88048 + 0.611005i) q^{57} +(-1.34558 + 0.599089i) q^{58} +(-3.12185 + 7.01178i) q^{59} +(-2.04799 + 0.435314i) q^{60} +(2.09031 + 2.32152i) q^{61} +(-7.12836 + 5.17905i) q^{62} +(2.63623 + 0.224308i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-7.03690 - 4.06276i) q^{65} +(3.31544 - 0.0885192i) q^{66} +(2.26830 + 3.92881i) q^{67} +(0.590297 + 0.125472i) q^{68} +(1.22000 - 1.67918i) q^{69} +(3.34431 + 4.41610i) q^{70} +(2.71182 - 8.34611i) q^{71} +(0.743145 - 0.669131i) q^{72} +(-7.23220 - 3.21998i) q^{73} +(-7.70205 - 0.809518i) q^{74} +(-0.128123 + 0.602770i) q^{75} +1.97725 q^{76} +(-3.93810 - 7.84164i) q^{77} +3.88085 q^{78} +(1.60414 - 7.54689i) q^{79} +(2.08227 + 0.218856i) q^{80} +(0.913545 + 0.406737i) q^{81} +(3.98587 - 3.58889i) q^{82} +(-0.104801 + 0.322544i) q^{83} +(-2.43788 - 1.02797i) q^{84} +(-0.742692 + 1.02223i) q^{85} +(-8.38221 - 1.78169i) q^{86} +(0.736458 + 1.27558i) q^{87} +(-3.18053 - 0.940342i) q^{88} +(-0.117265 - 0.0677028i) q^{89} +(0.647002 + 1.99127i) q^{90} +(-4.36152 - 9.29539i) q^{91} +(-1.67918 + 1.22000i) q^{92} +(5.89580 + 6.54795i) q^{93} +(3.83847 - 0.815893i) q^{94} +(-1.68383 + 3.78195i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(8.97295 - 2.91549i) q^{97} +(0.277648 + 6.99449i) q^{98} +(-0.434593 - 3.28803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

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