LMFDB - Embedded newform 354.2.e.b.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	354.121
Dual form			354.2.e.b.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.907575 + 0.419889i) q^{2} +(0.947653 + 0.319302i) q^{3} +(0.647386 - 0.762162i) q^{4} +(-1.91571 - 1.15265i) q^{5} +(-0.994138 + 0.108119i) q^{6} +(0.0631741 - 1.16518i) q^{7} +(-0.267528 + 0.963550i) q^{8} +(0.796093 + 0.605174i) q^{9} +O(q^{10})$	\(q+(-0.907575 + 0.419889i) q^{2} +(0.947653 + 0.319302i) q^{3} +(0.647386 - 0.762162i) q^{4} +(-1.91571 - 1.15265i) q^{5} +(-0.994138 + 0.108119i) q^{6} +(0.0631741 - 1.16518i) q^{7} +(-0.267528 + 0.963550i) q^{8} +(0.796093 + 0.605174i) q^{9} +(2.22264 + 0.241727i) q^{10} +(0.268157 - 1.63568i) q^{11} +(0.856857 - 0.515554i) q^{12} +(2.88253 - 2.19124i) q^{13} +(0.431910 + 1.08401i) q^{14} +(-1.44739 - 1.70400i) q^{15} +(-0.161782 - 0.986827i) q^{16} +(-0.179305 - 3.30709i) q^{17} +(-0.976621 - 0.214970i) q^{18} +(3.45205 - 3.26996i) q^{19} +(-2.11871 + 0.713877i) q^{20} +(0.431910 - 1.08401i) q^{21} +(0.443433 + 1.59710i) q^{22} +(0.109899 - 0.0241907i) q^{23} +(-0.561187 + 0.827689i) q^{24} +(-0.000675007 - 0.00127320i) q^{25} +(-1.69604 + 3.19906i) q^{26} +(0.561187 + 0.827689i) q^{27} +(-0.847156 - 0.802469i) q^{28} +(-1.29927 - 0.601105i) q^{29} +(2.02911 + 0.938765i) q^{30} +(1.66505 + 1.57722i) q^{31} +(0.561187 + 0.827689i) q^{32} +(0.776396 - 1.46444i) q^{33} +(1.55134 + 2.92614i) q^{34} +(-1.46406 + 2.15933i) q^{35} +(0.976621 - 0.214970i) q^{36} +(0.961983 + 3.46475i) q^{37} +(-1.75998 + 4.41722i) q^{38} +(3.43131 - 1.15614i) q^{39} +(1.62314 - 1.53752i) q^{40} +(-0.297680 - 0.0655243i) q^{41} +(0.0631741 + 1.16518i) q^{42} +(-0.582536 - 3.55332i) q^{43} +(-1.07306 - 1.26330i) q^{44} +(-0.827535 - 2.07696i) q^{45} +(-0.0895846 + 0.0681004i) q^{46} +(1.19796 - 0.720786i) q^{47} +(0.161782 - 0.986827i) q^{48} +(5.60532 + 0.609615i) q^{49} +(0.00114722 + 0.000872095i) q^{50} +(0.886039 - 3.19122i) q^{51} +(0.196029 - 3.61554i) q^{52} +(-1.98430 + 0.215806i) q^{53} +(-0.856857 - 0.515554i) q^{54} +(-2.39908 + 2.82441i) q^{55} +(1.10581 + 0.372589i) q^{56} +(4.31545 - 1.99654i) q^{57} +1.43158 q^{58} +(7.48999 + 1.70296i) q^{59} -2.23575 q^{60} +(-9.95262 + 4.60457i) q^{61} +(-2.17341 - 0.732308i) q^{62} +(0.755428 - 0.889358i) q^{63} +(-0.856857 - 0.515554i) q^{64} +(-8.04784 + 0.875256i) q^{65} +(-0.0897363 + 1.65509i) q^{66} +(1.01288 - 3.64807i) q^{67} +(-2.63662 - 2.00430i) q^{68} +(0.111871 + 0.0121667i) q^{69} +(0.422068 - 2.57450i) q^{70} +(-8.76503 + 5.27374i) q^{71} +(-0.796093 + 0.605174i) q^{72} +(2.36115 + 5.92605i) q^{73} +(-2.32788 - 2.74059i) q^{74} +(-0.000233138 - 0.00142208i) q^{75} +(-0.257426 - 4.74795i) q^{76} +(-1.88892 - 0.415783i) q^{77} +(-2.62872 + 2.49006i) q^{78} +(-8.73252 + 2.94233i) q^{79} +(-0.827535 + 2.07696i) q^{80} +(0.267528 + 0.963550i) q^{81} +(0.297680 - 0.0655243i) q^{82} +(-1.97315 + 2.91017i) q^{83} +(-0.546581 - 1.03096i) q^{84} +(-3.46841 + 6.54211i) q^{85} +(2.02069 + 2.98030i) q^{86} +(-1.03932 - 0.984497i) q^{87} +(1.50432 + 0.695974i) q^{88} +(8.16055 + 3.77547i) q^{89} +(1.62314 + 1.53752i) q^{90} +(-2.37109 - 3.49709i) q^{91} +(0.0527101 - 0.0994218i) q^{92} +(1.07428 + 2.02631i) q^{93} +(-0.784585 + 1.15718i) q^{94} +(-10.3823 + 2.28531i) q^{95} +(0.267528 + 0.963550i) q^{96} +(-6.01099 + 15.0865i) q^{97} +(-5.34322 + 1.80034i) q^{98} +(1.20335 - 1.13988i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 30 q^{11} + 2 q^{12} + 5 q^{13} + 28 q^{14} + 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 28 q^{21} - q^{22} - 2 q^{23} - 2 q^{24} + 64 q^{25} - 34 q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - 2 q^{30} + 2 q^{32} - q^{33} + 32 q^{34} - 87 q^{35} - 2 q^{36} + 47 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} + 3 q^{41} + q^{42} - 61 q^{43} + q^{44} - 2 q^{45} - 27 q^{46} + 50 q^{47} + 2 q^{48} - 45 q^{49} - 6 q^{50} + 3 q^{51} - 24 q^{52} - 27 q^{53} - 2 q^{54} - 95 q^{55} - q^{56} + 4 q^{57} + 50 q^{58} - 58 q^{59} + 2 q^{60} - 74 q^{61} - 29 q^{62} + q^{63} - 2 q^{64} - 17 q^{65} + q^{66} + 4 q^{67} - 32 q^{68} + 31 q^{69} - 58 q^{70} - 47 q^{71} + 2 q^{72} + 43 q^{73} - 18 q^{74} - 6 q^{75} - 33 q^{76} - 5 q^{77} + 5 q^{78} + 19 q^{79} - 2 q^{80} - 2 q^{81} - 3 q^{82} + 47 q^{83} - q^{84} - 149 q^{85} - 55 q^{86} + 21 q^{87} + 28 q^{88} + 36 q^{89} + 2 q^{90} + 175 q^{91} - 2 q^{92} - 29 q^{93} - 21 q^{94} + 50 q^{95} - 2 q^{96} + 10 q^{97} - 13 q^{98} + q^{99}+O(q^{100}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 30 * q^11 + 2 * q^12 + 5 * q^13 + 28 * q^14 + 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 28 * q^21 - q^22 - 2 * q^23 - 2 * q^24 + 64 * q^25 - 34 * q^26 + 2 * q^27 + q^28 + 8 * q^29 - 2 * q^30 + 2 * q^32 - q^33 + 32 * q^34 - 87 * q^35 - 2 * q^36 + 47 * q^37 + 4 * q^38 - 5 * q^39 + 2 * q^40 + 3 * q^41 + q^42 - 61 * q^43 + q^44 - 2 * q^45 - 27 * q^46 + 50 * q^47 + 2 * q^48 - 45 * q^49 - 6 * q^50 + 3 * q^51 - 24 * q^52 - 27 * q^53 - 2 * q^54 - 95 * q^55 - q^56 + 4 * q^57 + 50 * q^58 - 58 * q^59 + 2 * q^60 - 74 * q^61 - 29 * q^62 + q^63 - 2 * q^64 - 17 * q^65 + q^66 + 4 * q^67 - 32 * q^68 + 31 * q^69 - 58 * q^70 - 47 * q^71 + 2 * q^72 + 43 * q^73 - 18 * q^74 - 6 * q^75 - 33 * q^76 - 5 * q^77 + 5 * q^78 + 19 * q^79 - 2 * q^80 - 2 * q^81 - 3 * q^82 + 47 * q^83 - q^84 - 149 * q^85 - 55 * q^86 + 21 * q^87 + 28 * q^88 + 36 * q^89 + 2 * q^90 + 175 * q^91 - 2 * q^92 - 29 * q^93 - 21 * q^94 + 50 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{25}{29}\right)$	$1$

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 $

$2$	−0.907575	+	0.419889i	−0.641753	+	0.296906i
$2$	−0.907575	+	0.419889i	−0.641753	+	0.296906i
$3$	0.947653	+	0.319302i	0.547128	+	0.184349i
$3$	0.947653	+	0.319302i	0.547128	+	0.184349i
$4$	0.647386	−	0.762162i	0.323693	−	0.381081i
$5$	−1.91571	−	1.15265i	−0.856734	−	0.515480i	0.0181373	−	0.999836i	$-0.494226\pi$
$5$	−1.91571	−	1.15265i	−0.856734	−	0.515480i	−0.874871	+	0.484356i	$0.839054\pi$
$6$	−0.994138	+	0.108119i	−0.405855	+	0.0441394i
$7$	0.0631741	−	1.16518i	0.0238776	−	0.440396i	−0.962013	−	0.273004i	$-0.911983\pi$
$7$	0.0631741	−	1.16518i	0.0238776	−	0.440396i	0.985890	−	0.167392i	$-0.0535345\pi$
$8$	−0.267528	+	0.963550i	−0.0945856	+	0.340666i
$9$	0.796093	+	0.605174i	0.265364	+	0.201725i
$10$	2.22264	+	0.241727i	0.702860	+	0.0764407i
$11$	0.268157	−	1.63568i	0.0808523	−	0.493177i	−0.915095	−	0.403238i	$-0.867885\pi$
$11$	0.268157	−	1.63568i	0.0808523	−	0.493177i	0.995947	−	0.0899389i	$-0.0286672\pi$
$12$	0.856857	−	0.515554i	0.247353	−	0.148828i
$13$	2.88253	−	2.19124i	0.799471	−	0.607742i	−0.123617	−	0.992330i	$-0.539450\pi$
$13$	2.88253	−	2.19124i	0.799471	−	0.607742i	0.923088	+	0.384588i	$0.125656\pi$
$14$	0.431910	+	1.08401i	0.115433	+	0.289715i
$15$	−1.44739	−	1.70400i	−0.373715	−	0.439971i
$16$	−0.161782	−	0.986827i	−0.0404455	−	0.246707i
$17$	−0.179305	−	3.30709i	−0.0434879	−	0.802086i	−0.936202	−	0.351463i	$-0.885684\pi$
$17$	−0.179305	−	3.30709i	−0.0434879	−	0.802086i	0.892714	−	0.450624i	$-0.148798\pi$
$18$	−0.976621	−	0.214970i	−0.230192	−	0.0506690i
$19$	3.45205	−	3.26996i	0.791956	−	0.750180i	−0.180423	−	0.983589i	$-0.557747\pi$
$19$	3.45205	−	3.26996i	0.791956	−	0.750180i	0.972379	+	0.233409i	$0.0749881\pi$
$20$	−2.11871	+	0.713877i	−0.473758	+	0.159628i
$21$	0.431910	−	1.08401i	0.0942505	−	0.236551i
$22$	0.443433	+	1.59710i	0.0945403	+	0.340503i
$23$	0.109899	−	0.0241907i	0.0229156	−	0.00504411i	−0.203498	−	0.979075i	$-0.565231\pi$
$23$	0.109899	−	0.0241907i	0.0229156	−	0.00504411i	0.226413	+	0.974031i	$0.427300\pi$
$24$	−0.561187	+	0.827689i	−0.114552	+	0.168951i
$25$	−0.000675007	−	0.00127320i	−0.000135001	−	0.000254639i
$26$	−1.69604	+	3.19906i	−0.332620	+	0.627388i
$27$	0.561187	+	0.827689i	0.108001	+	0.159289i
$28$	−0.847156	−	0.802469i	−0.160097	−	0.151652i
$29$	−1.29927	−	0.601105i	−0.241268	−	0.111622i	0.295530	−	0.955334i	$-0.404504\pi$
$29$	−1.29927	−	0.601105i	−0.241268	−	0.111622i	−0.536797	+	0.843711i	$0.680366\pi$
$30$	2.02911	+	0.938765i	0.370463	+	0.171394i
$31$	1.66505	+	1.57722i	0.299051	+	0.283276i	0.822481	−	0.568792i	$-0.192589\pi$
$31$	1.66505	+	1.57722i	0.299051	+	0.283276i	−0.523430	+	0.852069i	$0.675348\pi$
$32$	0.561187	+	0.827689i	0.0992048	+	0.146316i
$33$	0.776396	−	1.46444i	0.135153	−	0.254926i
$34$	1.55134	+	2.92614i	0.266053	+	0.501829i
$35$	−1.46406	+	2.15933i	−0.247472	+	0.364993i
$36$	0.976621	−	0.214970i	0.162770	−	0.0358284i
$37$	0.961983	+	3.46475i	0.158149	+	0.569601i	0.999573	+	0.0292255i	$0.00930409\pi$
$37$	0.961983	+	3.46475i	0.158149	+	0.569601i	−0.841424	+	0.540376i	$0.818282\pi$
$38$	−1.75998	+	4.41722i	−0.285506	+	0.716567i
$39$	3.43131	−	1.15614i	0.549449	−	0.185131i
$40$	1.62314	−	1.53752i	0.256641	−	0.243103i
$41$	−0.297680	−	0.0655243i	−0.0464898	−	0.0102332i	0.191665	−	0.981460i	$-0.438611\pi$
$41$	−0.297680	−	0.0655243i	−0.0464898	−	0.0102332i	−0.238154	+	0.971227i	$0.576542\pi$
$42$	0.0631741	+	1.16518i	0.00974797	+	0.179791i
$43$	−0.582536	−	3.55332i	−0.0888360	−	0.541876i	−0.993322	−	0.115373i	$-0.963194\pi$
$43$	−0.582536	−	3.55332i	−0.0888360	−	0.541876i	0.904486	−	0.426503i	$-0.140255\pi$
$44$	−1.07306	−	1.26330i	−0.161769	−	0.190449i
$45$	−0.827535	−	2.07696i	−0.123362	−	0.309614i
$46$	−0.0895846	+	0.0681004i	−0.0132085	+	0.0100409i
$47$	1.19796	−	0.720786i	0.174740	−	0.105137i	−0.425497	−	0.904960i	$-0.639901\pi$
$47$	1.19796	−	0.720786i	0.174740	−	0.105137i	0.600237	+	0.799822i	$0.295073\pi$
$48$	0.161782	−	0.986827i	0.0233512	−	0.142436i
$49$	5.60532	+	0.609615i	0.800760	+	0.0870879i
$50$	0.00114722		0.000872095i	0.000162242		0.000123333i
$51$	0.886039	−	3.19122i	0.124070	−	0.446861i
$52$	0.196029	−	3.61554i	0.0271843	−	0.501385i
$53$	−1.98430	+	0.215806i	−0.272565	+	0.0296432i	−0.243381	−	0.969931i	$-0.578256\pi$
$53$	−1.98430	+	0.215806i	−0.272565	+	0.0296432i	−0.0291841	+	0.999574i	$0.509291\pi$
$54$	−0.856857	−	0.515554i	−0.116603	−	0.0701580i
$55$	−2.39908	+	2.82441i	−0.323492	+	0.380844i
$56$	1.10581	+	0.372589i	0.147770	+	0.0497894i
$57$	4.31545	−	1.99654i	0.571596	−	0.264448i
$58$	1.43158			0.187976
$59$	7.48999	+	1.70296i	0.975113	+	0.221707i
$59$	7.48999	+	1.70296i	0.975113	+	0.221707i
$60$	−2.23575			−0.288634
$61$	−9.95262	+	4.60457i	−1.27430	+	0.589555i	−0.936171	−	0.351544i	$-0.885657\pi$
$61$	−9.95262	+	4.60457i	−1.27430	+	0.589555i	−0.338131	+	0.941099i	$0.609795\pi$
$62$	−2.17341	−	0.732308i	−0.276024	−	0.0930032i
$63$	0.755428	−	0.889358i	0.0951750	−	0.112049i
$64$	−0.856857	−	0.515554i	−0.107107	−	0.0644442i
$65$	−8.04784	+	0.875256i	−0.998212	+	0.108562i
$66$	−0.0897363	+	1.65509i	−0.0110458	+	0.203727i
$67$	1.01288	−	3.64807i	0.123743	−	0.445682i	−0.875556	−	0.483117i	$-0.839505\pi$
$67$	1.01288	−	3.64807i	0.123743	−	0.445682i	0.999299	+	0.0374344i	$0.0119185\pi$
$68$	−2.63662	−	2.00430i	−0.319737	−	0.243057i
$69$	0.111871	+	0.0121667i	0.0134676	+	0.00146469i
$70$	0.422068	−	2.57450i	0.0504467	−	0.307711i
$71$	−8.76503	+	5.27374i	−1.04022	+	0.625878i	−0.929822	−	0.368010i	$-0.880039\pi$
$71$	−8.76503	+	5.27374i	−1.04022	+	0.625878i	−0.110395	+	0.993888i	$0.535212\pi$
$72$	−0.796093	+	0.605174i	−0.0938205	+	0.0713205i
$73$	2.36115	+	5.92605i	0.276352	+	0.693592i	0.999994	+	0.00341606i	$0.00108737\pi$
$73$	2.36115	+	5.92605i	0.276352	+	0.693592i	−0.723642	+	0.690175i	$0.757533\pi$
$74$	−2.32788	−	2.74059i	−0.270611	−	0.318588i
$75$	−0.000233138	−	0.00142208i	−2.69205e−5	−	0.000164208i
$76$	−0.257426	−	4.74795i	−0.0295288	−	0.544627i
$77$	−1.88892	−	0.415783i	−0.215263	−	0.0473829i
$78$	−2.62872	+	2.49006i	−0.297644	+	0.281943i
$79$	−8.73252	+	2.94233i	−0.982485	+	0.331038i	−0.764294	−	0.644868i	$-0.776912\pi$
$79$	−8.73252	+	2.94233i	−0.982485	+	0.331038i	−0.218191	+	0.975906i	$0.570016\pi$
$80$	−0.827535	+	2.07696i	−0.0925212	+	0.232211i
$81$	0.267528	+	0.963550i	0.0297254	+	0.107061i
$82$	0.297680	−	0.0655243i	0.0328733	−	0.00723595i
$83$	−1.97315	+	2.91017i	−0.216581	+	0.319433i	−0.920423	−	0.390923i	$-0.872156\pi$
$83$	−1.97315	+	2.91017i	−0.216581	+	0.319433i	0.703842	+	0.710356i	$0.251466\pi$
$84$	−0.546581	−	1.03096i	−0.0596368	−	0.112487i
$85$	−3.46841	+	6.54211i	−0.376202	+	0.709592i
$86$	2.02069	+	2.98030i	0.217897	+	0.321374i
$87$	−1.03932	−	0.984497i	−0.111427	−	0.105549i
$88$	1.50432	+	0.695974i	0.160361	+	0.0741911i
$89$	8.16055	+	3.77547i	0.865017	+	0.400199i	0.801652	−	0.597791i	$-0.203955\pi$
$89$	8.16055	+	3.77547i	0.865017	+	0.400199i	0.0633649	+	0.997990i	$0.479817\pi$
$90$	1.62314	+	1.53752i	0.171094	+	0.162069i
$91$	−2.37109	−	3.49709i	−0.248558	−	0.366595i
$92$	0.0527101	−	0.0994218i	0.00549541	−	0.0103654i
$93$	1.07428	+	2.02631i	0.111398	+	0.210118i
$94$	−0.784585	+	1.15718i	−0.0809238	+	0.119354i
$95$	−10.3823	+	2.28531i	−1.06520	+	0.234468i
$96$	0.267528	+	0.963550i	0.0273045	+	0.0983419i
$97$	−6.01099	+	15.0865i	−0.610324	+	1.53180i	0.220573	+	0.975370i	$0.429207\pi$
$97$	−6.01099	+	15.0865i	−0.610324	+	1.53180i	−0.830897	+	0.556427i	$0.812172\pi$
$98$	−5.34322	+	1.80034i	−0.539747	+	0.181862i
$99$	1.20335	−	1.13988i	0.120941	−	0.114562i
$100$	−0.00140737		0.000309786i	−0.000140737		3.09786e-5i
$101$	0.321879	+	5.93670i	0.0320281	+	0.590724i	0.969864	+	0.243646i	$0.0783434\pi$
$101$	0.321879	+	5.93670i	0.0320281	+	0.590724i	−0.937836	+	0.347078i	$0.887174\pi$
$102$	0.535813	+	3.26831i	0.0530534	+	0.323611i
$103$	−10.6429	−	12.5297i	−1.04867	−	1.23459i	−0.971367	−	0.237585i	$-0.923644\pi$
$103$	−10.6429	−	12.5297i	−1.04867	−	1.23459i	−0.0773057	−	0.997007i	$-0.524632\pi$
$104$	1.34021	+	3.36369i	0.131419	+	0.329836i
$105$	−2.07690	+	1.57882i	−0.202685	+	0.154077i
$106$	1.71029	−	1.02905i	0.166118	−	0.0999499i
$107$	0.00900002	−	0.0548977i	0.000870065	−	0.00530716i	−0.986388	−	0.164435i	$-0.947420\pi$
$107$	0.00900002	−	0.0548977i	0.000870065	−	0.00530716i	0.987258	+	0.159128i	$0.0508682\pi$
$108$	0.994138	+	0.108119i	0.0956610	+	0.0104038i
$109$	5.71061	+	4.34109i	0.546977	+	0.415801i	0.841831	−	0.539741i	$-0.181478\pi$
$109$	5.71061	+	4.34109i	0.546977	+	0.415801i	−0.294854	+	0.955542i	$0.595271\pi$
$110$	0.991404	−	3.57072i	0.0945267	−	0.340454i
$111$	−0.194674	+	3.59054i	−0.0184776	+	0.340799i
$112$	−1.16005	+	0.126163i	−0.109614	+	0.0119213i
$113$	−6.20216	−	3.73171i	−0.583450	−	0.351050i	0.193029	−	0.981193i	$-0.438169\pi$
$113$	−6.20216	−	3.73171i	−0.583450	−	0.351050i	−0.776479	+	0.630143i	$0.782996\pi$
$114$	−3.07827	+	3.62402i	−0.288307	+	0.339421i
$115$	−0.238419	−	0.0803328i	−0.0222327	−	0.00749107i
$116$	−1.29927	+	0.601105i	−0.120634	+	0.0558112i
$117$	3.62085			0.334748
$118$	−7.51278	+	1.59940i	−0.691608	+	0.147237i
$119$	−3.86467			−0.354274
$120$	2.02911	−	0.938765i	0.185231	−	0.0856972i
$121$	7.82063	+	2.63508i	0.710966	+	0.239552i
$122$	7.09934	−	8.35799i	0.642744	−	0.756697i
$123$	−0.261175	−	0.157144i	−0.0235494	−	0.0141692i
$124$	2.28002	−	0.247968i	0.204752	−	0.0222681i
$125$	−0.605379	+	11.1656i	−0.0541467	+	0.998677i
$126$	−0.312176	+	1.12436i	−0.0278108	+	0.100166i
$127$	−10.5024	−	7.98372i	−0.931938	−	0.708441i	0.0247081	−	0.999695i	$-0.492134\pi$
$127$	−10.5024	−	7.98372i	−0.931938	−	0.708441i	−0.956646	+	0.291254i	$0.905927\pi$
$128$	0.994138	+	0.108119i	0.0878702	+	0.00955646i
$129$	0.582536	−	3.55332i	0.0512895	−	0.312852i
$130$	6.93652	−	4.17356i	0.608373	−	0.366046i
$131$	15.3221	−	11.6476i	1.33870	−	1.01765i	0.341736	−	0.939796i	$-0.388985\pi$
$131$	15.3221	−	11.6476i	1.33870	−	1.01765i	0.996965	−	0.0778573i	$-0.0248079\pi$
$132$	−0.613511	−	1.53980i	−0.0533993	−	0.134022i
$133$	−3.59200	−	4.22883i	−0.311466	−	0.366686i
$134$	0.612518	+	3.73619i	0.0529135	+	0.322758i
$135$	−0.121041	−	2.23247i	−0.0104175	−	0.192140i
$136$	3.23451	+	0.711970i	0.277357	+	0.0610509i
$137$	8.42994	−	7.98526i	0.720218	−	0.682227i	−0.237027	−	0.971503i	$-0.576173\pi$
$137$	8.42994	−	7.98526i	0.720218	−	0.682227i	0.957246	+	0.289276i	$0.0934145\pi$
$138$	−0.106640	+	0.0359311i	−0.00907777	+	0.00305866i
$139$	−3.56267	+	8.94162i	−0.302182	+	0.758418i	0.696965	+	0.717105i	$0.254533\pi$
$139$	−3.56267	+	8.94162i	−0.302182	+	0.758418i	−0.999146	+	0.0413131i	$0.986846\pi$
$140$	0.697946	+	2.51377i	0.0589872	+	0.212453i
$141$	1.36539	−	0.300546i	0.114987	−	0.0253105i
$142$	5.74054	−	8.46666i	0.481735	−	0.710506i
$143$	−2.81121	−	5.30251i	−0.235086	−	0.443418i
$144$	0.468408	−	0.883512i	0.0390340	−	0.0736260i
$145$	1.79616	+	2.64914i	0.149163	+	0.219999i
$146$	−4.63121	−	4.38691i	−0.383282	−	0.363064i
$147$	5.11725	+	2.36749i	0.422063	+	0.195267i
$148$	3.26347	+	1.50984i	0.268256	+	0.124108i
$149$	14.5447	+	13.7774i	1.19154	+	1.12869i	0.988767	+	0.149466i	$0.0477555\pi$
$149$	14.5447	+	13.7774i	1.19154	+	1.12869i	0.202778	+	0.979225i	$0.435003\pi$
$150$	0.000808707		0.00119275i	6.60306e−5		9.73879e-5i
$151$	3.98349	−	7.51366i	0.324172	−	0.611453i	−0.666844	−	0.745197i	$-0.732355\pi$
$151$	3.98349	−	7.51366i	0.324172	−	0.611453i	0.991016	+	0.133744i	$0.0427001\pi$
$152$	2.22725	+	4.20103i	0.180654	+	0.340749i
$153$	1.85862	−	2.74126i	0.150261	−	0.221618i
$154$	1.88892	−	0.415783i	0.152214	−	0.0335048i
$155$	−1.37178	−	4.94071i	−0.110184	−	0.396847i
$156$	1.34021	−	3.36369i	0.107303	−	0.269310i
$157$	15.9975	−	5.39018i	1.27674	−	0.430183i	0.402383	−	0.915471i	$-0.368182\pi$
$157$	15.9975	−	5.39018i	1.27674	−	0.430183i	0.874354	+	0.485288i	$0.161285\pi$
$158$	6.68997	−	6.33707i	0.532225	−	0.504150i
$159$	−1.94934	−	0.429082i	−0.154593	−	0.0340284i
$160$	−0.121041	−	2.23247i	−0.00956912	−	0.176492i
$161$	−0.0212436	−	0.129580i	−0.00167423	−	0.0102124i
$162$	−0.647386	−	0.762162i	−0.0508635	−	0.0598811i
$163$	−3.38415	−	8.49357i	−0.265067	−	0.665268i	0.734849	−	0.678231i	$-0.237253\pi$
$163$	−3.38415	−	8.49357i	−0.265067	−	0.665268i	−0.999916	+	0.0129631i	$0.995874\pi$
$164$	−0.242654	+	0.184461i	−0.0189481	+	0.0144040i
$165$	−3.17533	+	1.91054i	−0.247199	+	0.148735i
$166$	0.568829	−	3.46971i	0.0441497	−	0.269301i
$167$	1.15140	+	0.125222i	0.0890980	+	0.00968999i	0.152559	−	0.988294i	$-0.451248\pi$
$167$	1.15140	+	0.125222i	0.0890980	+	0.00968999i	−0.0634614	+	0.997984i	$0.520214\pi$
$168$	0.928952	+	0.706171i	0.0716702	+	0.0544823i
$169$	0.0295762	−	0.106524i	0.00227509	−	0.00819414i
$170$	0.400881	−	7.39381i	0.0307461	−	0.567079i
$171$	4.72705	−	0.514098i	0.361487	−	0.0393140i
$172$	−3.08533	−	1.85638i	−0.235254	−	0.141548i
$173$	7.21077	−	8.48917i	0.548225	−	0.645420i	−0.416358	−	0.909201i	$-0.636694\pi$
$173$	7.21077	−	8.48917i	0.548225	−	0.645420i	0.964583	+	0.263781i	$0.0849696\pi$
$174$	1.35664	+	0.457106i	0.102847	+	0.0346531i
$175$	−0.00152614		0.000706069i	−0.000115366		5.33738e-5i
$176$	−1.65752			−0.124940
$177$	6.55415	+	4.00538i	0.492640	+	0.301063i
$178$	−8.99160			−0.673949
$179$	16.3457	−	7.56232i	1.22173	−	0.565234i	0.300328	−	0.953836i	$-0.402904\pi$
$179$	16.3457	−	7.56232i	1.22173	−	0.565234i	0.921406	+	0.388602i	$0.127042\pi$
$180$	−2.11871	−	0.713877i	−0.157919	−	0.0532093i
$181$	−9.18116	+	10.8089i	−0.682430	+	0.803419i	−0.988919	−	0.148455i	$-0.952570\pi$
$181$	−9.18116	+	10.8089i	−0.682430	+	0.803419i	0.306489	+	0.951874i	$0.400846\pi$
$182$	3.62033	+	2.17828i	0.268357	+	0.161465i
$183$	−10.9019	+	1.18565i	−0.805890	+	0.0876458i
$184$	−0.00609227	+	0.112365i	−0.000449128	+	0.00828367i
$185$	2.15075	−	7.74630i	0.158126	−	0.569519i
$186$	−1.82581	−	1.38795i	−0.133875	−	0.101769i
$187$	−5.45743	−	0.593532i	−0.399087	−	0.0434033i
$188$	0.226184	−	1.37966i	0.0164962	−	0.100622i
$189$	0.999857	−	0.601594i	0.0727289	−	0.0437595i
$190$	8.46311	−	6.43349i	0.613979	−	0.466734i
$191$	−2.80831	−	7.04833i	−0.203202	−	0.509999i	0.791692	−	0.610920i	$-0.209200\pi$
$191$	−2.80831	−	7.04833i	−0.203202	−	0.509999i	−0.994894	+	0.100921i	$0.967821\pi$
$192$	−0.647386	−	0.762162i	−0.0467211	−	0.0550043i
$193$	1.96059	+	11.9591i	0.141127	+	0.860834i	0.958577	+	0.284835i	$0.0919388\pi$
$193$	1.96059	+	11.9591i	0.141127	+	0.860834i	−0.817450	+	0.576000i	$0.804613\pi$
$194$	−0.879208	−	16.2160i	−0.0631235	−	1.16424i
$195$	−7.90604	−	1.74025i	−0.566163	−	0.124622i
$196$	4.09343	−	3.87750i	0.292388	−	0.276965i
$197$	19.1669	−	6.45809i	1.36559	−	0.460120i	0.461376	−	0.887205i	$-0.347356\pi$
$197$	19.1669	−	6.45809i	1.36559	−	0.460120i	0.904212	+	0.427085i	$0.140459\pi$
$198$	−0.613511	+	1.53980i	−0.0436003	+	0.109429i
$199$	0.658025	+	2.36999i	0.0466461	+	0.168004i	0.983204	−	0.182508i	$-0.0584214\pi$
$199$	0.658025	+	2.36999i	0.0466461	+	0.168004i	−0.936558	+	0.350512i	$0.886008\pi$
$200$	0.00140737		0.000309786i	9.95163e−5		2.19052e-5i
$201$	2.12469	−	3.13369i	0.149864	−	0.221033i
$202$	−2.78489	−	5.25285i	−0.195944	−	0.369589i
$203$	−0.782474	+	1.47590i	−0.0549189	+	0.103588i
$204$	−1.85862	−	2.74126i	−0.130129	−	0.191927i
$205$	0.494744	+	0.468646i	0.0345544	+	0.0327317i
$206$	14.9203	+	6.90287i	1.03955	+	0.480946i
$207$	0.102130	+	0.0472502i	0.00709850	+	0.00328412i
$208$	−2.62872	−	2.49006i	−0.182269	−	0.172654i
$209$	−4.42293	−	6.52333i	−0.305940	−	0.451228i
$210$	1.22202	−	2.30497i	0.0843271	−	0.159058i
$211$	7.91708	+	14.9332i	0.545034	+	1.02804i	0.991110	+	0.133048i	$0.0424764\pi$
$211$	7.91708	+	14.9332i	0.545034	+	1.02804i	−0.446076	+	0.894995i	$0.647179\pi$
$212$	−1.12013	+	1.65207i	−0.0769309	+	0.113465i
$213$	−9.99012	+	2.19899i	−0.684512	+	0.150672i
$214$	0.0148828	+	0.0536028i	0.00101736	+	0.00366421i
$215$	−2.97975	+	7.47860i	−0.203217	+	0.510036i
$216$	−0.947653	+	0.319302i	−0.0644796	+	0.0217257i
$217$	1.94293	−	1.84044i	0.131894	−	0.124937i
$218$	−7.00558	−	1.54205i	−0.474478	−	0.104440i
$219$	0.345358	+	6.36976i	0.0233372	+	0.430428i
$220$	0.599530	+	3.65697i	0.0404203	+	0.246553i
$221$	−7.76349	−	9.13989i	−0.522229	−	0.614815i
$222$	−1.33095	−	3.34043i	−0.0893274	−	0.224195i
$223$	−18.9986	+	14.4424i	−1.27224	+	0.967134i	−0.272255	+	0.962225i	$0.587770\pi$
$223$	−18.9986	+	14.4424i	−1.27224	+	0.967134i	−0.999988	+	0.00490918i	$0.998437\pi$
$224$	0.999857	−	0.601594i	0.0668058	−	0.0401957i
$225$	0.000233138	−	0.00142208i	1.55425e−5	−	9.48053e-5i
$226$	7.19583	+	0.782594i	0.478660	+	0.0520574i
$227$	6.12276	+	4.65440i	0.406382	+	0.308924i	0.788321	−	0.615264i	$-0.210951\pi$
$227$	6.12276	+	4.65440i	0.406382	+	0.308924i	−0.381939	+	0.924187i	$0.624744\pi$
$228$	1.27208	−	4.58161i	0.0842454	−	0.303424i
$229$	−1.24351	+	22.9351i	−0.0821732	+	1.51559i	0.609153	+	0.793052i	$0.291509\pi$
$229$	−1.24351	+	22.9351i	−0.0821732	+	1.51559i	−0.691327	+	0.722542i	$0.742973\pi$
$230$	0.250114	−	0.0272016i	0.0164920	−	0.00179362i
$231$	−1.65728	−	0.997154i	−0.109041	−	0.0656079i
$232$	0.926785	−	1.09110i	0.0608464	−	0.0716339i
$233$	12.3480	+	4.16052i	0.808944	+	0.272565i	0.693229	−	0.720718i	$-0.256188\pi$
$233$	12.3480	+	4.16052i	0.808944	+	0.272565i	0.115715	+	0.993282i	$0.463084\pi$
$234$	−3.28619	+	1.52036i	−0.214825	+	0.0993887i
$235$	−3.12575			−0.203902
$236$	6.14685	−	4.60611i	0.400126	−	0.299832i
$237$	−9.21489			−0.598571
$238$	3.50748	−	1.62273i	0.227356	−	0.105186i
$239$	17.0884	+	5.75774i	1.10535	+	0.372437i	0.812053	−	0.583583i	$-0.198350\pi$
$239$	17.0884	+	5.75774i	1.10535	+	0.372437i	0.293300	+	0.956020i	$0.405246\pi$
$240$	−1.44739	+	1.70400i	−0.0934287	+	0.109993i
$241$	−4.81117	−	2.89478i	−0.309915	−	0.186469i	0.352096	−	0.935964i	$-0.385469\pi$
$241$	−4.81117	−	2.89478i	−0.309915	−	0.186469i	−0.662011	+	0.749494i	$0.730297\pi$
$242$	−8.20425	+	0.892266i	−0.527389	+	0.0573570i
$243$	−0.0541389	+	0.998533i	−0.00347301	+	0.0640559i
$244$	−2.93376	+	10.5664i	−0.187815	+	0.676447i
$245$	−10.0355	−	7.62880i	−0.641146	−	0.487386i
$246$	0.303019	+	0.0329553i	0.0193198	+	0.00210116i
$247$	2.78538	−	16.9901i	0.177229	−	1.08105i
$248$	−1.96517	+	1.18241i	−0.124789	+	0.0750829i
$249$	−2.79908	+	2.12781i	−0.177385	+	0.134844i
$250$	−4.13887	−	10.3878i	−0.261765	−	0.656980i
$251$	1.57386	+	1.85289i	0.0993409	+	0.116953i	0.809586	−	0.587001i	$-0.199692\pi$
$251$	1.57386	+	1.85289i	0.0993409	+	0.116953i	−0.710245	+	0.703955i	$0.751416\pi$
$252$	−0.188782	−	1.15152i	−0.0118921	−	0.0725387i
$253$	−0.0100980	−	0.186248i	−0.000634859	−	0.0117093i
$254$	12.8840	+	2.83598i	0.808414	+	0.177945i
$255$	−5.37575	+	5.09218i	−0.336643	+	0.318885i
$256$	−0.947653	+	0.319302i	−0.0592283	+	0.0199563i
$257$	−8.03934	+	20.1772i	−0.501480	+	1.25862i	0.432609	+	0.901581i	$0.357593\pi$
$257$	−8.03934	+	20.1772i	−0.501480	+	1.25862i	−0.934090	+	0.357039i	$0.883786\pi$
$258$	0.963303	+	3.46950i	0.0599726	+	0.216002i
$259$	4.09782	−	0.901998i	0.254626	−	0.0560474i
$260$	−4.54298	+	6.70039i	−0.281743	+	0.415541i
$261$	−0.670564	−	1.26482i	−0.0415069	−	0.0782903i
$262$	−9.01529	+	17.0046i	−0.556967	+	1.05055i
$263$	−15.5817	−	22.9813i	−0.960809	−	1.41709i	−0.908231	−	0.418470i	$-0.862567\pi$
$263$	−15.5817	−	22.9813i	−0.960809	−	1.41709i	−0.0525777	−	0.998617i	$-0.516744\pi$
$264$	1.20335	+	1.13988i	0.0740612	+	0.0701545i
$265$	4.05010	+	1.87378i	0.248796	+	0.115105i
$266$	5.03565	+	2.32974i	0.308756	+	0.142846i
$267$	6.52786	+	6.18352i	0.399498	+	0.378425i
$268$	−2.12469	−	3.13369i	−0.129786	−	0.191420i
$269$	6.48843	−	12.2385i	0.395607	−	0.746193i	−0.603067	−	0.797691i	$-0.706055\pi$
$269$	6.48843	−	12.2385i	0.395607	−	0.746193i	0.998673	+	0.0514977i	$0.0163995\pi$
$270$	1.04724	+	1.97531i	0.0637331	+	0.120213i
$271$	9.02607	−	13.3125i	0.548295	−	0.808674i	−0.448058	−	0.894005i	$-0.647884\pi$
$271$	9.02607	−	13.3125i	0.548295	−	0.808674i	0.996353	+	0.0853302i	$0.0271945\pi$
$272$	−3.23451	+	0.711970i	−0.196121	+	0.0431695i
$273$	−1.13034	−	4.07112i	−0.0684114	−	0.246396i
$274$	−4.29788	+	10.7869i	−0.259645	+	0.651659i
$275$	−0.00226356		0.000762681i	−0.000136498		4.59914e-5i
$276$	0.0816965	−	0.0773870i	0.00491755	−	0.00465815i
$277$	−1.10631	−	0.243516i	−0.0664715	−	0.0146315i	0.181610	−	0.983371i	$-0.441869\pi$
$277$	−1.10631	−	0.243516i	−0.0664715	−	0.0146315i	−0.248082	+	0.968739i	$0.579800\pi$
$278$	−0.521100	−	9.61112i	−0.0312535	−	0.576437i
$279$	0.371042	+	2.26326i	0.0222137	+	0.135498i
$280$	−1.68894	−	1.98838i	−0.100934	−	0.118828i
$281$	2.04719	+	5.13806i	0.122125	+	0.306511i	0.977311	−	0.211811i	$-0.0679362\pi$
$281$	2.04719	+	5.13806i	0.122125	+	0.306511i	−0.855185	+	0.518322i	$0.826557\pi$
$282$	−1.11300	+	0.846083i	−0.0662783	+	0.0503835i
$283$	20.4281	−	12.2912i	1.21433	−	0.730636i	0.243380	−	0.969931i	$-0.421744\pi$
$283$	20.4281	−	12.2912i	1.21433	−	0.730636i	0.970947	+	0.239294i	$0.0769161\pi$
$284$	−1.65491	+	10.0945i	−0.0982010	+	0.598999i
$285$	−10.5685	−	1.14939i	−0.626023	−	0.0680841i
$286$	4.77786	+	3.63203i	0.282521	+	0.214767i
$287$	−0.0951531	+	0.342711i	−0.00561671	+	0.0202296i
$288$	−0.0541389	+	0.998533i	−0.00319017	+	0.0588391i
$289$	5.99567	−	0.652068i	0.352686	−	0.0383570i
$290$	−2.74250	−	1.65011i	−0.161045	−	0.0968976i
$291$	−10.5135	+	12.3774i	−0.616310	+	0.725576i
$292$	6.04519	+	2.03686i	0.353768	+	0.119198i
$293$	−24.4803	+	11.3258i	−1.43016	+	0.661660i	−0.973647	−	0.228059i	$-0.926762\pi$
$293$	−24.4803	+	11.3258i	−1.43016	+	0.661660i	−0.456508	+	0.889719i	$0.650900\pi$
$294$	−5.63837			−0.328836
$295$	−12.3858	−	11.8957i	−0.721127	−	0.692595i
$296$	−3.59582			−0.209003
$297$	1.50432	−	0.695974i	0.0872897	−	0.0403845i
$298$	−18.9854	−	6.39691i	−1.09979	−	0.370563i
$299$	0.263781	−	0.310547i	0.0152548	−	0.0179594i
$300$	−0.00123479		0.000742946i	−7.12904e−5		4.28940e-5i
$301$	−4.17704	+	0.454281i	−0.240761	+	0.0261843i
$302$	−0.460414	+	8.49184i	−0.0264938	+	0.488650i
$303$	−1.59057	+	5.72871i	−0.0913758	+	0.329106i
$304$	−3.78536	−	2.87756i	−0.217105	−	0.165039i
$305$	24.3738	+	2.65081i	1.39564	+	0.151785i
$306$	−0.535813	+	3.26831i	−0.0306304	+	0.186837i
$307$	4.50291	−	2.70931i	0.256995	−	0.154629i	−0.381226	−	0.924482i	$-0.624498\pi$
$307$	4.50291	−	2.70931i	0.256995	−	0.154629i	0.638221	+	0.769853i	$0.279671\pi$
$308$	−1.53976	+	1.17049i	−0.0877358	+	0.0666950i
$309$	−6.08498	−	15.2721i	−0.346162	−	0.868801i
$310$	3.31955	+	3.90807i	0.188537	+	0.221964i
$311$	2.54804	+	15.5423i	0.144486	+	0.881325i	0.955217	+	0.295906i	$0.0956217\pi$
$311$	2.54804	+	15.5423i	0.144486	+	0.881325i	−0.810731	+	0.585419i	$0.800930\pi$
$312$	0.196029	+	3.61554i	0.0110979	+	0.204690i
$313$	−22.2696	−	4.90192i	−1.25875	−	0.277073i	−0.464999	−	0.885311i	$-0.653945\pi$
$313$	−22.2696	−	4.90192i	−1.25875	−	0.277073i	−0.793755	+	0.608238i	$0.791877\pi$
$314$	−12.2556	+	11.6092i	−0.691626	+	0.655143i
$315$	−2.47230	+	0.833015i	−0.139298	+	0.0469351i
$316$	−3.41078	+	8.56041i	−0.191871	+	0.481561i
$317$	−0.454814	−	1.63809i	−0.0255449	−	0.0920043i	0.949679	−	0.313225i	$-0.101410\pi$
$317$	−0.454814	−	1.63809i	−0.0255449	−	0.0920043i	−0.975224	+	0.221221i	$0.928996\pi$
$318$	1.94934	−	0.429082i	0.109313	−	0.0240617i
$319$	−1.33162	+	1.96400i	−0.0745567	+	0.109963i
$320$	1.04724	+	1.97531i	0.0585426	+	0.110423i
$321$	0.0260578	−	0.0491503i	0.00145441	−	0.00274330i
$322$	0.0736896	+	0.108684i	0.00410656	+	0.00605673i
$323$	−11.4330	−	10.8299i	−0.636150	−	0.602593i
$324$	0.907575	+	0.419889i	0.0504209	+	0.0233272i
$325$	−0.00473562	−	0.00219093i	−0.000262685	−	0.000121531i
$326$	6.63772	+	6.28759i	0.367630	+	0.348237i
$327$	4.02556	+	5.93725i	0.222614	+	0.328331i
$328$	0.142774	−	0.269300i	0.00788336	−	0.0148696i
$329$	−0.764164	−	1.44137i	−0.0421297	−	0.0794651i
$330$	2.07964	−	3.06724i	0.114481	−	0.168846i
$331$	−10.0656	+	2.21561i	−0.553256	+	0.121781i	−0.482794	−	0.875734i	$-0.660378\pi$
$331$	−10.0656	+	2.21561i	−0.553256	+	0.121781i	−0.0704613	+	0.997515i	$0.522447\pi$
$332$	0.940636	+	3.38786i	0.0516241	+	0.185933i
$333$	−1.33095	+	3.34043i	−0.0729355	+	0.183054i
$334$	−1.09756	+	0.369812i	−0.0600559	+	0.0202352i
$335$	−6.14532	+	5.82116i	−0.335755	+	0.318044i
$336$	−1.13961	−	0.250847i	−0.0621707	−	0.0136848i
$337$	0.0777869	+	1.43470i	0.00423732	+	0.0781528i	0.999887	−	0.0150210i	$-0.00478152\pi$
$337$	0.0777869	+	1.43470i	0.00423732	+	0.0781528i	−0.995650	+	0.0931739i	$0.970299\pi$
$338$	0.0178856	+	0.109097i	0.000972846	+	0.00593410i
$339$	−4.68595	−	5.51673i	−0.254506	−	0.299628i
$340$	2.74075	+	6.87876i	0.148638	+	0.373053i
$341$	3.02632	−	2.30055i	0.163885	−	0.124582i
$342$	−4.07429	+	2.45142i	−0.220312	+	0.132558i
$343$	2.38589	−	14.5533i	0.128826	−	0.785804i
$344$	3.57964	+	0.389310i	0.193001	+	0.0209902i
$345$	−0.200288	−	0.152255i	−0.0107832	−	0.00819714i
$346$	−2.97980	+	10.7323i	−0.160195	+	0.576971i
$347$	−1.01237	+	18.6720i	−0.0543468	+	1.00237i	0.836472	+	0.548009i	$0.184614\pi$
$347$	−1.01237	+	18.6720i	−0.0543468	+	1.00237i	−0.890819	+	0.454358i	$0.849869\pi$
$348$	−1.42319	+	0.154781i	−0.0762909	+	0.00829713i
$349$	1.23675	+	0.744125i	0.0662015	+	0.0398321i	0.548270	−	0.836302i	$-0.315287\pi$
$349$	1.23675	+	0.744125i	0.0662015	+	0.0398321i	−0.482068	+	0.876134i	$0.660114\pi$
$350$	0.00108862	−	0.00128162i	5.81892e−5	−	6.85056e-5i
$351$	3.43131	+	1.15614i	0.183150	+	0.0617103i
$352$	1.50432	−	0.695974i	0.0801807	−	0.0370956i
$353$	−30.0048			−1.59700			−0.798498	−	0.601997i	$-0.794372\pi$
$353$	−30.0048			−1.59700			−0.798498	+	0.601997i	$0.794372\pi$
$354$	−7.63020	−	0.883167i	−0.405541	−	0.0469398i
$355$	22.8701			1.21382
$356$	8.16055	−	3.77547i	0.432508	−	0.200100i
$357$	−3.66237	−	1.23400i	−0.193833	−	0.0653100i
$358$	−11.6596	+	13.7267i	−0.616229	+	0.725481i
$359$	17.8627	+	10.7476i	0.942756	+	0.567238i	0.901908	−	0.431928i	$-0.142166\pi$
$359$	17.8627	+	10.7476i	0.942756	+	0.567238i	0.0408480	+	0.999165i	$0.486994\pi$
$360$	2.22264	−	0.241727i	0.117143	−	0.0127401i
$361$	0.195404	−	3.60402i	0.0102844	−	0.189685i
$362$	3.79406	−	13.6650i	0.199411	−	0.718214i
$363$	6.56986	+	4.99428i	0.344828	+	0.262132i
$364$	−4.20036	−	0.456817i	−0.220159	−	0.0239437i
$365$	2.30735	−	14.0742i	0.120772	−	0.736677i
$366$	9.39644	−	5.65365i	0.491160	−	0.295521i
$367$	18.6512	−	14.1783i	0.973584	−	0.740099i	0.00793991	−	0.999968i	$-0.497473\pi$
$367$	18.6512	−	14.1783i	0.973584	−	0.740099i	0.965644	+	0.259869i	$0.0836795\pi$
$368$	−0.0416517	−	0.104538i	−0.00217125	−	0.00544942i
$369$	−0.197327	−	0.232312i	−0.0102725	−	0.0120937i
$370$	1.30062	+	7.93343i	0.0676160	+	0.412439i
$371$	0.126096	+	2.32570i	0.00654656	+	0.120744i
$372$	2.23985	+	0.493028i	0.116131	+	0.0255623i
$373$	13.9144	−	13.1804i	0.720460	−	0.682456i	−0.236841	−	0.971548i	$-0.576112\pi$
$373$	13.9144	−	13.1804i	0.720460	−	0.682456i	0.957301	+	0.289092i	$0.0933534\pi$
$374$	5.20225	−	1.75284i	0.269002	−	0.0906373i
$375$	−4.13887	+	10.3878i	−0.213730	+	0.536422i
$376$	0.374026	+	1.34712i	0.0192889	+	0.0694725i
$377$	−5.06235	+	1.11431i	−0.260724	+	0.0573897i
$378$	−0.654843	+	0.965821i	−0.0336815	+	0.0496765i
$379$	−3.23375	−	6.09950i	−0.166106	−	0.313310i	0.786460	−	0.617642i	$-0.211912\pi$
$379$	−3.23375	−	6.09950i	−0.166106	−	0.313310i	−0.952566	+	0.304332i	$0.901567\pi$
$380$	−4.97956	+	9.39244i	−0.255446	+	0.481822i
$381$	−7.40342	−	10.9192i	−0.379289	−	0.559409i
$382$	5.50827	+	5.21771i	0.281828	+	0.266961i
$383$	−33.6927	−	15.5879i	−1.72162	−	0.796505i	−0.993857	−	0.110672i	$-0.964700\pi$
$383$	−33.6927	−	15.5879i	−1.72162	−	0.796505i	−0.727759	−	0.685833i	$-0.759438\pi$
$384$	0.907575	+	0.419889i	0.0463145	+	0.0214274i
$385$	3.13938	+	2.97378i	0.159998	+	0.151558i
$386$	−6.80088	−	10.0305i	−0.346156	−	0.510541i
$387$	1.68662	−	3.18131i	0.0857358	−	0.161715i
$388$	7.60689	+	14.3481i	0.386181	+	0.728415i
$389$	3.01587	−	4.44807i	0.152911	−	0.225526i	−0.743516	−	0.668718i	$-0.766843\pi$
$389$	3.01587	−	4.44807i	0.152911	−	0.225526i	0.896427	+	0.443192i	$0.146154\pi$
$390$	7.90604	−	1.74025i	0.400338	−	0.0881210i
$391$	−0.0997062	−	0.359109i	−0.00504236	−	0.0181609i
$392$	−2.08698	+	5.23791i	−0.105408	+	0.264555i
$393$	18.2391	−	6.14548i	0.920043	−	0.309999i
$394$	−14.6838	+	13.9092i	−0.739757	+	0.700735i
$395$	20.1205	+	4.42885i	1.01237	+	0.222840i
$396$	−0.0897363	−	1.65509i	−0.00450942	−	0.0831713i
$397$	5.31670	+	32.4304i	0.266837	+	1.62764i	0.691565	+	0.722314i	$0.256922\pi$
$397$	5.31670	+	32.4304i	0.266837	+	1.62764i	−0.424727	+	0.905321i	$0.639630\pi$
$398$	−1.59234	−	1.87465i	−0.0798168	−	0.0939676i
$399$	−2.05370	−	5.15440i	−0.102814	−	0.258043i
$400$	−0.00114722		0.000872095i	−5.73611e−5		4.36047e-5i
$401$	8.66069	−	5.21097i	0.432494	−	0.260223i	−0.282618	−	0.959232i	$-0.591203\pi$
$401$	8.66069	−	5.21097i	0.432494	−	0.260223i	0.715113	+	0.699009i	$0.246375\pi$
$402$	−0.612518	+	3.73619i	−0.0305496	+	0.186344i
$403$	8.25562	+	0.897853i	0.411242	+	0.0447252i
$404$	4.73311	+	3.59802i	0.235481	+	0.179008i
$405$	0.598125	−	2.15425i	0.0297211	−	0.107046i
$406$	0.0904387	−	1.66804i	0.00448840	−	0.0827837i
$407$	5.92520	−	0.644404i	0.293701	−	0.0319419i
$408$	2.83786	+	1.70749i	0.140495	+	0.0845331i
$409$	21.5168	−	25.3315i	1.06394	−	1.25256i	0.0976166	−	0.995224i	$-0.468878\pi$
$409$	21.5168	−	25.3315i	1.06394	−	1.25256i	0.966321	−	0.257340i	$-0.0828460\pi$
$410$	−0.645796	−	0.217594i	−0.0318936	−	0.0107462i
$411$	10.5384	−	4.87557i	0.519819	−	0.240494i
$412$	−16.4397			−0.809928
$413$	2.45742	−	8.61958i	0.120922	−	0.424142i
$414$	−0.112530			−0.00553056
$415$	7.13439	−	3.30072i	0.350214	−	0.162026i
$416$	3.43131	+	1.15614i	0.168234	+	0.0566846i
$417$	−6.23125	+	7.33599i	−0.305145	+	0.359245i
$418$	6.75322	+	4.06328i	0.330311	+	0.198741i
$419$	−33.1560	+	3.60593i	−1.61978	+	0.176161i	−0.872590	−	0.488453i	$-0.837561\pi$
$419$	−33.1560	+	3.60593i	−1.61978	+	0.176161i	−0.747187	+	0.664614i	$0.768596\pi$
$420$	−0.141241	+	2.60504i	−0.00689186	+	0.127113i
$421$	−0.0900469	+	0.324319i	−0.00438862	+	0.0158064i	−0.965712	−	0.259616i	$-0.916404\pi$
$421$	−0.0900469	+	0.324319i	−0.00438862	+	0.0158064i	0.961323	+	0.275423i	$0.0888178\pi$
$422$	−13.4556	−	10.2287i	−0.655010	−	0.497925i
$423$	1.38989	+	0.151159i	0.0675785	+	0.00734961i
$424$	0.322917	−	1.96971i	0.0156823	−	0.0956575i
$425$	−0.00408954	+	0.00246060i	−0.000198372	+	0.000119356i
$426$	8.14345	−	6.19049i	0.394552	−	0.299930i
$427$	4.73640	+	11.8875i	0.229210	+	0.575274i
$428$	−0.0360145	−	0.0423995i	−0.00174082	−	0.00204946i
$429$	−0.970956	−	5.92257i	−0.0468782	−	0.285944i
$430$	−0.435838	−	8.03855i	−0.0210180	−	0.387654i
$431$	−0.170526	−	0.0375357i	−0.00821397	−	0.00180803i	0.210862	−	0.977516i	$-0.432373\pi$
$431$	−0.170526	−	0.0375357i	−0.00821397	−	0.00180803i	−0.219076	+	0.975708i	$0.570304\pi$
$432$	0.725995	−	0.687699i	0.0349295	−	0.0330870i
$433$	−28.8866	+	9.73303i	−1.38820	+	0.467740i	−0.911491	−	0.411320i	$-0.865068\pi$
$433$	−28.8866	+	9.73303i	−1.38820	+	0.467740i	−0.476711	+	0.879060i	$0.658171\pi$
$434$	−0.990572	+	2.48615i	−0.0475490	+	0.119339i
$435$	0.856264	+	3.08398i	0.0410547	+	0.147866i
$436$	7.00558	−	1.54205i	0.335507	−	0.0738506i
$437$	0.300276	−	0.442874i	0.0143642	−	0.0211855i
$438$	−2.98803	−	5.63602i	−0.142774	−	0.269300i
$439$	0.421787	−	0.795575i	0.0201308	−	0.0379707i	−0.873243	−	0.487286i	$-0.837987\pi$
$439$	0.421787	−	0.795575i	0.0201308	−	0.0379707i	0.893373	+	0.449315i	$0.148332\pi$
$440$	−2.07964	−	3.06724i	−0.0991431	−	0.146225i
$441$	4.09343	+	3.87750i	0.194925	+	0.184643i
$442$	10.8837	+	5.03533i	0.517684	+	0.239506i
$443$	−6.57663	−	3.04267i	−0.312465	−	0.144562i	0.257389	−	0.966308i	$-0.417138\pi$
$443$	−6.57663	−	3.04267i	−0.312465	−	0.144562i	−0.569853	+	0.821746i	$0.693000\pi$
$444$	2.61055	+	2.47284i	0.123891	+	0.117356i
$445$	−11.2815	−	16.6390i	−0.534794	−	0.788763i
$446$	11.1785	−	21.0849i	0.529317	−	0.998398i
$447$	9.38413	+	17.7004i	0.443854	+	0.837198i
$448$	−0.654843	+	0.965821i	−0.0309384	+	0.0456308i
$449$	−0.345901	+	0.0761385i	−0.0163241	+	0.00359320i	−0.223125	−	0.974790i	$-0.571626\pi$
$449$	−0.345901	+	0.0761385i	−0.0163241	+	0.00359320i	0.206801	+	0.978383i	$0.433695\pi$
$450$	0.000385525		0.00138854i	1.81738e−5		6.54563e-5i
$451$	−0.187002	+	0.469340i	−0.00880558	+	0.0221003i
$452$	−6.85936	+	2.31119i	−0.322637	+	0.108709i
$453$	6.17409	−	5.84841i	0.290084	−	0.274782i
$454$	−7.51120	−	1.65334i	−0.352518	−	0.0775951i
$455$	0.511413	+	9.43246i	0.0239754	+	0.442201i
$456$	0.769261	+	4.69229i	0.0360240	+	0.219736i
$457$	−22.0556	−	25.9659i	−1.03172	−	1.21463i	−0.976357	−	0.216166i	$-0.930645\pi$
$457$	−22.0556	−	25.9659i	−1.03172	−	1.21463i	−0.0553617	−	0.998466i	$-0.517631\pi$
$458$	−8.50163	−	21.3375i	−0.397255	−	0.997035i
$459$	2.63662	−	2.00430i	0.123067	−	0.0935529i
$460$	−0.215576	+	0.129708i	−0.0100513	+	0.00604765i
$461$	−1.64913	+	10.0593i	−0.0768078	+	0.468507i	0.920216	+	0.391411i	$0.128013\pi$
$461$	−1.64913	+	10.0593i	−0.0768078	+	0.468507i	−0.997024	+	0.0770956i	$0.975435\pi$
$462$	1.92280	+	0.209117i	0.0894569	+	0.00972902i
$463$	14.6994	+	11.1742i	0.683141	+	0.519310i	0.888210	−	0.459437i	$-0.151949\pi$
$463$	14.6994	+	11.1742i	0.683141	+	0.519310i	−0.205069	+	0.978747i	$0.565742\pi$
$464$	−0.382988	+	1.37940i	−0.0177798	+	0.0640370i
$465$	0.277603	−	5.12009i	0.0128735	−	0.237439i
$466$	−12.9537	+	1.40880i	−0.600068	+	0.0652614i
$467$	26.1321	+	15.7231i	1.20925	+	0.727580i	0.969935	−	0.243362i	$-0.0782505\pi$
$467$	26.1321	+	15.7231i	1.20925	+	0.727580i	0.239312	+	0.970943i	$0.423078\pi$
$468$	2.34409	−	2.75967i	0.108356	−	0.127566i
$469$	−4.18666	−	1.41065i	−0.193322	−	0.0651377i
$470$	2.83686	−	1.31247i	0.130854	−	0.0605397i
$471$	16.8812			0.777842
$472$	−3.64467	+	6.76139i	−0.167760	+	0.311218i
$473$	−5.96831			−0.274423
$474$	8.36320	−	3.86923i	0.384135	−	0.177720i
$475$	−0.00649346	−	0.00218790i	−0.000297941	−	0.000100388i
$476$	−2.50193	+	2.94551i	−0.114676	+	0.135007i
$477$	−1.71029	−	1.02905i	−0.0783088	−	0.0471168i
$478$	−17.9266	+	1.94963i	−0.819943	+	0.0891742i
$479$	−1.25540	+	23.1545i	−0.0573607	+	1.05796i	0.818227	+	0.574896i	$0.194957\pi$
$479$	−1.25540	+	23.1545i	−0.0573607	+	1.05796i	−0.875587	+	0.483060i	$0.839525\pi$
$480$	0.598125	−	2.15425i	0.0273006	−	0.0983277i
$481$	10.3651	+	7.87931i	0.472606	+	0.359266i
$482$	5.58199	+	0.607078i	0.254252	+	0.0276516i
$483$	0.0212436	−	0.129580i	0.000966619	−	0.00589612i
$484$	7.07132	−	4.25467i	0.321424	−	0.193394i
$485$	28.9047	−	21.9728i	1.31249	−	0.997733i
$486$	−0.370138	−	0.928977i	−0.0167898	−	0.0421392i
$487$	−14.5496	−	17.1292i	−0.659307	−	0.776196i	0.326297	−	0.945267i	$-0.394199\pi$
$487$	−14.5496	−	17.1292i	−0.659307	−	0.776196i	−0.985604	+	0.169071i	$0.945923\pi$
$488$	−1.77413	−	10.8217i	−0.0803110	−	0.489875i
$489$	−0.494988	−	9.12952i	−0.0223841	−	0.412851i
$490$	12.3112	+	2.70991i	0.556165	+	0.122421i
$491$	−13.7695	+	13.0432i	−0.621411	+	0.588631i	−0.932243	−	0.361833i	$-0.882151\pi$
$491$	−13.7695	+	13.0432i	−0.621411	+	0.588631i	0.310832	+	0.950465i	$0.399392\pi$
$492$	−0.288851	+	0.0973251i	−0.0130224	+	0.00438775i
$493$	−1.75494	+	4.40457i	−0.0790385	+	0.198372i
$494$	4.60600	+	16.5893i	0.207234	+	0.746389i
$495$	−3.61915	+	0.796636i	−0.162669	+	0.0358061i
$496$	1.28706	−	1.89828i	0.0577909	−	0.0852352i
$497$	5.59112	+	10.5460i	0.250796	+	0.473052i
$498$	1.64694	−	3.10645i	0.0738009	−	0.139203i
$499$	−6.04363	−	8.91369i	−0.270550	−	0.399032i	0.668007	−	0.744155i	$-0.267147\pi$
$499$	−6.04363	−	8.91369i	−0.270550	−	0.399032i	−0.938557	+	0.345123i	$0.887837\pi$
$500$	8.11805	+	7.68982i	0.363050	+	0.343899i
$501$	1.05114	+	0.486311i	0.0469617	+	0.0217268i
$502$	−2.20640	−	1.02079i	−0.0984764	−	0.0455600i
$503$	−4.53071	−	4.29172i	−0.202014	−	0.191358i	0.580004	−	0.814614i	$-0.303051\pi$
$503$	−4.53071	−	4.29172i	−0.202014	−	0.191358i	−0.782018	+	0.623256i	$0.785810\pi$
$504$	0.654843	+	0.965821i	0.0291690	+	0.0430211i
$505$	6.22630	−	11.7440i	0.277067	−	0.522603i
$506$	0.0873681	+	0.164794i	0.00388398	+	0.00732597i
$507$	0.0620412	−	0.0915039i	0.00275535	−	0.00406383i
$508$	−12.8840	+	2.83598i	−0.571635	+	0.125826i
$509$	−3.34361	−	12.0426i	−0.148203	−	0.533779i	−0.999952	−	0.00982844i	$-0.996871\pi$
$509$	−3.34361	−	12.0426i	−0.148203	−	0.533779i	0.851749	−	0.523951i	$-0.175542\pi$
$510$	2.74075	−	6.87876i	0.121362	−	0.304597i
$511$	7.05406	−	2.37679i	0.312053	−	0.105143i
$512$	0.725995	−	0.687699i	0.0320848	−	0.0303923i
$513$	4.64376	+	1.02217i	0.205027	+	0.0451298i
$514$	−1.17589	−	21.6880i	−0.0518662	−	0.956616i
$515$	5.94631	+	36.2709i	0.262026	+	1.59829i
$516$	−2.33108	−	2.74435i	−0.102620	−	0.120813i
$517$	−0.857738	−	2.15276i	−0.0377233	−	0.0946783i
$518$	−3.34034	+	2.53926i	−0.146766	+	0.111569i
$519$	9.54391	−	5.74238i	0.418931	−	0.252063i
$520$	1.30967	−	7.98866i	0.0574330	−	0.350326i
$521$	−16.7665	−	1.82346i	−0.734552	−	0.0798873i	−0.266806	−	0.963750i	$-0.585968\pi$
$521$	−16.7665	−	1.82346i	−0.734552	−	0.0798873i	−0.467746	+	0.883863i	$0.654934\pi$
$522$	1.13967	+	0.866355i	0.0498820	+	0.0379193i
$523$	−1.01066	+	3.64006i	−0.0441930	+	0.159169i	−0.982354	−	0.187030i	$-0.940114\pi$
$523$	−1.01066	+	3.64006i	−0.0441930	+	0.159169i	0.938161	+	0.346199i	$0.112528\pi$
$524$	1.04199	−	19.2184i	0.0455197	−	0.839561i
$525$	−0.00167170		0.000181809i	−7.29592e−5		7.93479e-6i
$526$	23.7912	+	14.3147i	1.03734	+	0.624149i
$527$	4.91744	−	5.78926i	0.214207	−	0.252184i
$528$	−1.57075	−	0.529249i	−0.0683583	−	0.0230326i
$529$	−20.8627	+	9.65213i	−0.907076	+	0.419658i
$530$	−4.46255			−0.193841
$531$	4.93214	+	5.88846i	0.214037	+	0.255538i
$532$	−5.54847			−0.240557
$533$	−1.00165	+	0.463414i	−0.0433864	+	0.0200727i
$534$	−8.52092	−	2.87103i	−0.368736	−	0.124242i
$535$	−0.0805192	+	0.0947945i	−0.00348115	+	0.00409832i
$536$	3.24412	+	1.95192i	0.140125	+	0.0843102i
$537$	17.9047	−	1.94725i	0.772645	−	0.0840302i
$538$	−0.749936	+	13.8318i	−0.0323321	+	0.596330i
$539$	2.50024	−	9.00506i	0.107693	−	0.387875i
$540$	−1.77986	−	1.35302i	−0.0765931	−	0.0582245i
$541$	17.3027	+	1.88178i	0.743899	+	0.0809039i	0.472216	−	0.881483i	$-0.343454\pi$
$541$	17.3027	+	1.88178i	0.743899	+	0.0809039i	0.271683	+	0.962387i	$0.412420\pi$
$542$	−2.60208	+	15.8720i	−0.111769	+	0.681761i
$543$	−12.1519	+	7.31153i	−0.521486	+	0.313768i
$544$	2.63662	−	2.00430i	0.113044	−	0.0859338i
$545$	−5.93615	−	14.8986i	−0.254277	−	0.638186i
$546$	2.73529	+	3.22023i	0.117060	+	0.137813i
$547$	−3.90107	−	23.7955i	−0.166798	−	1.01742i	−0.928999	−	0.370081i	$-0.879330\pi$
$547$	−3.90107	−	23.7955i	−0.166798	−	1.01742i	0.762202	−	0.647339i	$-0.224118\pi$
$548$	−0.628637	−	11.5945i	−0.0268541	−	0.495294i
$549$	−10.7098	−	2.35740i	−0.457082	−	0.100611i
$550$	0.00173411	−	0.00164263i	7.39426e−5	−	7.00421e-5i
$551$	−6.45073	+	2.17350i	−0.274810	+	0.0925943i
$552$	−0.0416517	+	0.104538i	−0.00177282	+	0.00444943i
$553$	2.87666	+	10.3608i	0.122328	+	0.440586i
$554$	1.10631	−	0.243516i	0.0470025	−	0.0103460i
$555$	4.51157	−	6.65407i	0.191505	−	0.282449i
$556$	4.50854	+	8.50401i	0.191205	+	0.360651i
$557$	−11.7714	+	22.2032i	−0.498770	+	0.940780i	0.498497	+	0.866892i	$0.333886\pi$
$557$	−11.7714	+	22.2032i	−0.498770	+	0.940780i	−0.997267	+	0.0738883i	$0.976459\pi$
$558$	−1.28706	−	1.89828i	−0.0544858	−	0.0803605i
$559$	−9.46537	−	8.96607i	−0.400342	−	0.379224i
$560$	2.36774	+	1.09543i	0.100055	+	0.0462906i
$561$	−4.98224	−	2.30503i	−0.210350	−	0.0973184i
$562$	−4.01540	−	3.80358i	−0.169379	−	0.160445i
$563$	−13.9620	−	20.5923i	−0.588426	−	0.867864i	0.410607	−	0.911812i	$-0.365317\pi$
$563$	−13.9620	−	20.5923i	−0.588426	−	0.867864i	−0.999034	+	0.0439483i	$0.986006\pi$
$564$	0.654873	−	1.23522i	0.0275751	−	0.0520122i
$565$	7.58021	+	14.2978i	0.318902	+	0.601513i
$566$	−13.3791	+	19.7328i	−0.562367	+	0.829430i
$567$	1.13961	−	0.250847i	0.0478590	−	0.0105346i
$568$	−2.73662	−	9.85642i	−0.114826	−	0.413566i
$569$	−4.74537	+	11.9100i	−0.198936	+	0.499292i	−0.994272	−	0.106876i	$-0.965915\pi$
$569$	−4.74537	+	11.9100i	−0.198936	+	0.499292i	0.795336	+	0.606169i	$0.207294\pi$
$570$	10.0743	−	3.39443i	0.421967	−	0.142177i
$571$	1.98561	−	1.88087i	0.0830952	−	0.0787120i	−0.645025	−	0.764162i	$-0.723153\pi$
$571$	1.98561	−	1.88087i	0.0830952	−	0.0787120i	0.728120	+	0.685450i	$0.240394\pi$
$572$	−5.86131	−	1.29017i	−0.245074	−	0.0539448i
$573$	−0.410763	−	7.57607i	−0.0171599	−	0.316495i
$574$	−0.0575418	−	0.350989i	−0.00240175	−	0.0146500i
$575$	−0.000104982	0	0.000123595i	−4.37806e−6	0	5.15426e-6i
$576$	−0.370138	−	0.928977i	−0.0154224	−	0.0387074i
$577$	22.8931	−	17.4029i	0.953052	−	0.724491i	−0.00825624	−	0.999966i	$-0.502628\pi$
$577$	22.8931	−	17.4029i	0.953052	−	0.724491i	0.961308	+	0.275475i	$0.0888350\pi$
$578$	−5.16773	+	3.10932i	−0.214949	+	0.129331i
$579$	−1.96059	+	11.9591i	−0.0814795	+	0.497003i
$580$	3.18189	+	0.346051i	0.132121	+	0.0143690i
$581$	3.26622	+	2.48291i	0.135506	+	0.103009i
$582$	4.34462	−	15.6479i	0.180090	−	0.648627i
$583$	−0.179114	+	3.30356i	−0.00741814	+	0.136820i
$584$	−6.34172	+	0.689704i	−0.262422	+	0.0285401i
$585$	−6.93652	−	4.17356i	−0.286790	−	0.172556i
$586$	17.4622	−	20.5580i	0.721355	−	0.849245i
$587$	−1.25161	−	0.421716i	−0.0516594	−	0.0174061i	0.293353	−	0.956004i	$-0.405229\pi$
$587$	−1.25161	−	0.421716i	−0.0516594	−	0.0174061i	−0.345013	+	0.938598i	$0.612125\pi$
$588$	5.11725	−	2.36749i	0.211032	−	0.0976337i
$589$	10.9053			0.449344
$590$	16.2359	+	5.59560i	0.668421	+	0.230367i
$591$	20.2257			0.831973
$592$	3.26347	−	1.50984i	0.134128	−	0.0620542i
$593$	−10.0430	−	3.38387i	−0.412415	−	0.138959i	0.105443	−	0.994425i	$-0.466374\pi$
$593$	−10.0430	−	3.38387i	−0.412415	−	0.138959i	−0.517858	+	0.855466i	$0.673271\pi$
$594$	−1.07306	+	1.26330i	−0.0440280	+	0.0518338i
$595$	7.40361	+	4.45460i	0.303518	+	0.182621i
$596$	19.9166	−	2.16607i	0.815818	−	0.0887255i
$597$	−0.133162	+	2.45604i	−0.00544998	+	0.100519i
$598$	−0.109006	+	0.392603i	−0.00445758	+	0.0160547i
$599$	−17.4800	−	13.2879i	−0.714212	−	0.542930i	0.183766	−	0.982970i	$-0.441171\pi$
$599$	−17.4800	−	13.2879i	−0.714212	−	0.542930i	−0.897978	+	0.440040i	$0.854964\pi$
$600$	0.00143262		0.000155806i	5.84863e−5		6.36077e-6i
$601$	3.96017	−	24.1559i	0.161539	−	0.985342i	−0.774276	−	0.632848i	$-0.781886\pi$
$601$	3.96017	−	24.1559i	0.161539	−	0.985342i	0.935814	−	0.352493i	$-0.114666\pi$
$602$	3.60024	−	2.16619i	0.146735	−	0.0882873i
$603$	3.01406	−	2.29123i	0.122742	−	0.0933061i
$604$	−3.14777	−	7.90030i	−0.128081	−	0.321459i
$605$	−11.9448	−	14.0625i	−0.485624	−	0.571721i
$606$	−0.961862	−	5.86710i	−0.0390730	−	0.238335i
$607$	1.34790	+	24.8606i	0.0547096	+	1.00906i	0.889050	+	0.457810i	$0.151366\pi$
$607$	1.34790	+	24.8606i	0.0547096	+	1.00906i	−0.834340	+	0.551249i	$0.814151\pi$
$608$	4.64376	+	1.02217i	0.188329	+	0.0414544i
$609$	−1.21277	+	1.14880i	−0.0491440	+	0.0465516i
$610$	−23.2341	+	7.82849i	−0.940723	+	0.316966i
$611$	1.87373	−	4.70270i	0.0758029	−	0.190251i
$612$	−0.886039	−	3.19122i	−0.0358160	−	0.128998i
$613$	8.92446	−	1.96442i	0.360455	−	0.0793422i	−0.0310506	−	0.999518i	$-0.509885\pi$
$613$	8.92446	−	1.96442i	0.360455	−	0.0793422i	0.391506	+	0.920176i	$0.371954\pi$
$614$	−2.94912	+	4.34963i	−0.119017	+	0.175537i
$615$	0.319206	+	0.602086i	0.0128716	+	0.0242785i
$616$	0.905968	−	1.70884i	0.0365025	−	0.0688510i
$617$	−18.3070	−	27.0008i	−0.737011	−	1.08701i	−0.992742	−	0.120262i	$-0.961626\pi$
$617$	−18.3070	−	27.0008i	−0.737011	−	1.08701i	0.255731	−	0.966748i	$-0.417684\pi$
$618$	11.9352	+	11.3056i	0.480103	+	0.454778i
$619$	7.90029	+	3.65506i	0.317540	+	0.146909i	0.572184	−	0.820125i	$-0.306096\pi$
$619$	7.90029	+	3.65506i	0.317540	+	0.146909i	−0.254644	+	0.967035i	$0.581958\pi$
$620$	−4.65369	−	2.15303i	−0.186897	−	0.0864677i
$621$	0.0816965	+	0.0773870i	0.00327837	+	0.00310543i
$622$	−8.83860	−	13.0360i	−0.354395	−	0.522694i
$623$	4.91463	−	9.26998i	0.196901	−	0.371394i
$624$	−1.69604	−	3.19906i	−0.0678958	−	0.128065i
$625$	14.0256	−	20.6863i	0.561025	−	0.827450i
$626$	22.2696	−	4.90192i	0.890073	−	0.195920i
$627$	−2.10849	−	7.59411i	−0.0842051	−	0.303279i
$628$	6.24836	−	15.6822i	0.249337	−	0.625788i
$629$	11.2857	−	3.80261i	0.449992	−	0.151620i
$630$	1.89403	−	1.79412i	0.0754598	−	0.0714793i
$631$	−34.1107	−	7.50834i	−1.35793	−	0.298902i	−0.524442	−	0.851446i	$-0.675726\pi$
$631$	−34.1107	−	7.50834i	−1.35793	−	0.298902i	−0.833484	+	0.552544i	$0.813657\pi$
$632$	−0.498884	−	9.20137i	−0.0198445	−	0.366011i
$633$	2.73445	+	16.6794i	0.108685	+	0.662947i
$634$	1.10059	+	1.29572i	0.0437102	+	0.0514596i
$635$	10.9172	+	27.4001i	0.433236	+	1.08734i
$636$	−1.58900	+	1.20793i	−0.0630081	+	0.0478975i
$637$	17.4933	−	10.5254i	0.693111	−	0.417031i
$638$	0.383888	−	2.34161i	0.0151983	−	0.0927053i
$639$	−10.1693	−	1.10598i	−0.402292	−	0.0437519i
$640$	−1.77986	−	1.35302i	−0.0703552	−	0.0534826i
$641$	−12.7493	+	45.9189i	−0.503567	+	1.81369i	0.0738918	+	0.997266i	$0.476458\pi$
$641$	−12.7493	+	45.9189i	−0.503567	+	1.81369i	−0.577459	+	0.816420i	$0.695956\pi$
$642$	−0.00301178	+	0.0555490i	−0.000118865	+	0.00219234i
$643$	44.1375	−	4.80025i	1.74061	−	0.189303i	0.818050	−	0.575147i	$-0.195055\pi$
$643$	44.1375	−	4.80025i	1.74061	−	0.189303i	0.922564	+	0.385844i	$0.126090\pi$
$644$	−0.112514	−	0.0676975i	−0.00443368	−	0.00266766i
$645$	−5.21169	+	6.13568i	−0.205210	+	0.241592i
$646$	14.9237	+	5.02838i	0.587165	+	0.197839i
$647$	−12.9130	+	5.97419i	−0.507663	+	0.234870i	−0.656964	−	0.753922i	$-0.728160\pi$
$647$	−12.9130	+	5.97419i	−0.507663	+	0.234870i	0.149301	+	0.988792i	$0.452298\pi$
$648$	−1.00000			−0.0392837
$649$	4.79400	−	11.7946i	0.188181	−	0.462978i
$650$	0.00521788			0.000204662
$651$	2.42887	−	1.12372i	0.0951951	−	0.0440419i
$652$	−8.66432	−	2.91935i	−0.339321	−	0.114331i
$653$	−10.3956	+	12.2387i	−0.406811	+	0.478935i	−0.926971	−	0.375134i	$-0.877597\pi$
$653$	−10.3956	+	12.2387i	−0.406811	+	0.478935i	0.520159	+	0.854069i	$0.325873\pi$
$654$	−6.14648	−	3.69822i	−0.240347	−	0.144612i
$655$	−42.7784	+	4.65243i	−1.67149	+	0.181785i
$656$	−0.0165019	+	0.304359i	−0.000644290	+	0.0118832i
$657$	−1.70659	+	6.14660i	−0.0665806	+	0.239802i
$658$	1.29875	+	0.987284i	0.0506306	+	0.0384883i
$659$	43.4521	+	4.72571i	1.69266	+	0.184087i	0.903052	−	0.429531i	$-0.141321\pi$
$659$	43.4521	+	4.72571i	1.69266	+	0.184087i	0.789603	+	0.613618i	$0.210286\pi$
$660$	−0.599530	+	3.65697i	−0.0233367	+	0.142348i
$661$	25.9903	−	15.6379i	1.01091	−	0.608243i	0.0891530	−	0.996018i	$-0.471584\pi$
$661$	25.9903	−	15.6379i	1.01091	−	0.608243i	0.921754	+	0.387775i	$0.126756\pi$
$662$	8.20499	−	6.23727i	0.318896	−	0.242418i
$663$	−4.43872	−	11.1403i	−0.172385	−	0.432655i
$664$	−2.27623	−	2.67978i	−0.0883347	−	0.103996i
$665$	2.00690	+	12.2416i	0.0778243	+	0.474707i
$666$	−0.194674	−	3.59054i	−0.00754345	−	0.139131i
$667$	−0.157330	−	0.0346309i	−0.00609183	−	0.00134091i
$668$	0.840840	−	0.796486i	0.0325331	−	0.0308170i
$669$	−22.6156	+	7.62008i	−0.874370	+	0.294609i
$670$	3.13310	−	7.86350i	0.121042	−	0.303793i
$671$	4.86276	+	17.5141i	0.187725	+	0.676124i
$672$	1.13961	−	0.250847i	0.0439613	−	0.00967662i
$673$	−17.5377	+	25.8662i	−0.676031	+	0.997070i	0.322690	+	0.946505i	$0.395413\pi$
$673$	−17.5377	+	25.8662i	−0.676031	+	0.997070i	−0.998721	+	0.0505658i	$0.983898\pi$
$674$	−0.673010	−	1.26943i	−0.0259234	−	0.0488967i
$675$	0.000675007	−	0.00127320i	2.59810e−5	−	4.90054e-5i
$676$	−0.0620412	−	0.0915039i	−0.00238620	−	0.00351938i
$677$	−27.6414	−	26.1833i	−1.06234	−	1.00631i	−0.999966	−	0.00825374i	$-0.997373\pi$
$677$	−27.6414	−	26.1833i	−1.06234	−	1.00631i	−0.0623787	−	0.998053i	$-0.519869\pi$
$678$	6.56927	+	3.03927i	0.252291	+	0.116722i
$679$	17.1987	+	7.95694i	0.660024	+	0.305360i
$680$	−5.37575	−	5.09218i	−0.206151	−	0.195276i
$681$	4.31610	+	6.36577i	0.165393	+	0.243937i
$682$	−1.78064	+	3.35864i	−0.0681842	+	0.128609i
$683$	5.06244	+	9.54877i	0.193709	+	0.365374i	0.961273	−	0.275599i	$-0.0888761\pi$
$683$	5.06244	+	9.54877i	0.193709	+	0.365374i	−0.767564	+	0.640972i	$0.778531\pi$
$684$	2.66840	−	3.93560i	0.102029	−	0.150481i
$685$	−25.3536	+	5.58074i	−0.968710	+	0.213229i
$686$	3.94539	+	14.2100i	0.150636	+	0.542541i
$687$	−8.50163	+	21.3375i	−0.324357	+	0.814076i
$688$	−3.41226	+	1.14972i	−0.130091	+	0.0438329i
$689$	−5.24693	+	4.97016i	−0.199892	+	0.189348i
$690$	0.245707	+	0.0540842i	0.00935391	+	0.00205895i
$691$	1.56676	+	28.8972i	0.0596023	+	1.09930i	0.863440	+	0.504452i	$0.168305\pi$
$691$	1.56676	+	28.8972i	0.0596023	+	1.09930i	−0.803838	+	0.594849i	$0.797212\pi$
$692$	−1.80197	−	10.9915i	−0.0685007	−	0.417836i
$693$	−1.25214	−	1.47413i	−0.0475647	−	0.0559975i
$694$	−6.92138	−	17.3714i	−0.262732	−	0.659408i
$695$	17.1316	−	13.0231i	0.649838	−	0.493994i
$696$	1.22666	−	0.738056i	0.0464964	−	0.0279760i
$697$	−0.163319	+	0.996203i	−0.00618615	+	0.0377339i
$698$	−1.43489	−	0.156054i	−0.0543114	−	0.00590672i
$699$	10.3732	+	7.88547i	0.392349	+	0.298256i
$700$	−0.000449865		0.00162027i	−1.70033e−5		6.12404e-5i
$701$	0.126633	−	2.33561i	0.00478287	−	0.0882148i	−0.995167	−	0.0981935i	$-0.968694\pi$
$701$	0.126633	−	2.33561i	0.00478287	−	0.0882148i	0.999950	+	0.00997866i	$0.00317636\pi$
$702$	−3.59962	+	0.391483i	−0.135859	+	0.0147756i
$703$	14.6504	+	8.81486i	0.552551	+	0.332459i
$704$	−1.07306	+	1.26330i	−0.0404423	+	0.0476124i
$705$	−2.96213	−	0.998058i	−0.111560	−	0.0375890i
$706$	27.2317	−	12.5987i	1.02488	−	0.474159i
$707$	6.93765			0.260917
$708$	7.29582	−	2.40230i	0.274194	−	0.0902839i
$709$	31.0214			1.16503			0.582516	−	0.812819i	$-0.302068\pi$
$709$	31.0214			1.16503			0.582516	+	0.812819i	$0.302068\pi$
$710$	−20.7563	+	9.60289i	−0.778970	+	0.360390i
$711$	−8.73252	−	2.94233i	−0.327495	−	0.110346i
$712$	−5.82104	+	6.85305i	−0.218153	+	0.256829i
$713$	0.221142	+	0.133056i	0.00828182	+	0.00498300i
$714$	3.84202	−	0.417844i	0.143784	−	0.0156374i
$715$	−0.726442	+	13.3984i	−0.0271674	+	0.501073i
$716$	4.81826	−	17.3538i	0.180067	−	0.648542i
$717$	14.3554	+	10.9127i	0.536111	+	0.407541i
$718$	−20.7245	−	2.25393i	−0.773433	−	0.0841159i
$719$	−2.35494	+	14.3645i	−0.0878246	+	0.535706i	0.905867	+	0.423562i	$0.139220\pi$
$719$	−2.35494	+	14.3645i	−0.0878246	+	0.535706i	−0.993692	+	0.112145i	$0.964228\pi$
$720$	−1.91571	+	1.15265i	−0.0713945	+	0.0429566i
$721$	−15.2717	+	11.6093i	−0.568749	+	0.432352i
$722$	1.33595	+	3.35297i	0.0497188	+	0.124785i
$723$	−3.63501	−	4.27946i	−0.135187	−	0.159155i
$724$	2.29437	+	13.9951i	0.0852697	+	0.520122i
$725$	0.000111688		0.00205997i	4.14801e−6		7.65055e-5i
$726$	−8.05969	−	1.77407i	−0.299123	−	0.0658420i
$727$	−6.24575	+	5.91629i	−0.231642	+	0.219423i	−0.794713	−	0.606986i	$-0.792378\pi$
$727$	−6.24575	+	5.91629i	−0.231642	+	0.219423i	0.563071	+	0.826409i	$0.309620\pi$
$728$	4.00396	−	1.34909i	0.148397	−	0.0500006i
$729$	−0.370138	+	0.928977i	−0.0137088	+	0.0344065i
$730$	3.81551	+	13.7422i	0.141218	+	0.508623i
$731$	−11.6467	+	2.56363i	−0.430768	+	0.0948191i
$732$	−6.15407	+	9.07657i	−0.227461	+	0.335480i
$733$	17.4137	+	32.8458i	0.643191	+	1.21319i	0.963964	+	0.266031i	$0.0857125\pi$
$733$	17.4137	+	32.8458i	0.643191	+	1.21319i	−0.320773	+	0.947156i	$0.603943\pi$
$734$	−10.9741	+	20.6993i	−0.405060	+	0.764024i
$735$	−7.07430	−	10.4338i	−0.260940	−	0.384857i
$736$	0.0816965	+	0.0773870i	0.00301137	+	0.00285252i
$737$	−5.69547	−	2.63501i	−0.209795	−	0.0970617i
$738$	0.276635	+	0.127985i	0.0101831	+	0.00471119i
$739$	0.688101	+	0.651804i	0.0253122	+	0.0239770i	0.700251	−	0.713897i	$-0.253071\pi$
$739$	0.688101	+	0.651804i	0.0253122	+	0.0239770i	−0.674939	+	0.737874i	$0.735830\pi$
$740$	−4.51157	−	6.65407i	−0.165849	−	0.244608i
$741$	8.06453	−	15.2113i	0.296258	−	0.558802i
$742$	−1.09098	−	2.05780i	−0.0400510	−	0.0755442i
$743$	−23.2051	+	34.2250i	−0.851314	+	1.25559i	0.113732	+	0.993511i	$0.463719\pi$
$743$	−23.2051	+	34.2250i	−0.851314	+	1.25559i	−0.965046	+	0.262082i	$0.915591\pi$
$744$	−2.23985	+	0.493028i	−0.0821168	+	0.0180753i
$745$	−11.9829	−	43.1585i	−0.439019	−	1.58120i
$746$	−7.09405	+	17.8047i	−0.259732	+	0.651878i
$747$	−3.33197	+	1.12267i	−0.121910	+	0.0410764i
$748$	−3.98543	+	3.77520i	−0.145722	+	0.138035i
$749$	−0.0633970	−	0.0139547i	−0.00231648	−	0.000509895i
$750$	−0.605379	−	11.1656i	−0.0221053	−	0.407708i
$751$	7.83304	+	47.7794i	0.285832	+	1.74350i	0.605390	+	0.795929i	$0.293017\pi$
$751$	7.83304	+	47.7794i	0.285832	+	1.74350i	−0.319558	+	0.947567i	$0.603534\pi$
$752$	−0.905098	−	1.06556i	−0.0330055	−	0.0388571i
$753$	0.899840	+	2.25843i	0.0327920	+	0.0823017i
$754$	4.12658	−	3.13694i	0.150281	−	0.114241i
$755$	−16.2918	+	9.80247i	−0.592920	+	0.356748i
$756$	0.188782	−	1.15152i	0.00686592	−	0.0418803i
$757$	−0.345209	−	0.0375438i	−0.0125468	−	0.00136455i	0.101843	−	0.994800i	$-0.467526\pi$
$757$	−0.345209	−	0.0375438i	−0.0125468	−	0.00136455i	−0.114390	+	0.993436i	$0.536491\pi$
$758$	5.49598	+	4.17794i	0.199623	+	0.151750i
$759$	0.0498997	−	0.179722i	0.00181124	−	0.00652351i
$760$	0.575540	−	10.6152i	0.0208770	−	0.385054i
$761$	24.0470	−	2.61527i	0.871703	−	0.0948034i	0.338677	−	0.940903i	$-0.390020\pi$
$761$	24.0470	−	2.61527i	0.871703	−	0.0948034i	0.533026	+	0.846099i	$0.321055\pi$
$762$	11.3040	+	6.80141i	0.409502	+	0.246389i
$763$	5.41890	−	6.37963i	0.196177	−	0.230958i
$764$	−7.19003	−	2.42260i	−0.260126	−	0.0876467i
$765$	−6.72029	+	3.10914i	−0.242973	+	0.112411i
$766$	37.1239			1.34134
$767$	25.3217	−	11.5036i	0.914315	−	0.415369i
$768$	−1.00000			−0.0360844
$769$	−27.1319	+	12.5525i	−0.978400	+	0.452656i	−0.842870	−	0.538117i	$-0.819136\pi$
$769$	−27.1319	+	12.5525i	−0.978400	+	0.452656i	−0.135530	+	0.990773i	$0.543274\pi$
$770$	−4.09789	−	1.38074i	−0.147678	−	0.0497584i
$771$	−14.0611	+	16.5540i	−0.506399	+	0.596179i
$772$	10.3840	+	6.24786i	0.373729	+	0.224866i
$773$	−30.8754	+	3.35790i	−1.11051	+	0.120775i	−0.644939	−	0.764234i	$-0.723117\pi$
$773$	−30.8754	+	3.35790i	−1.11051	+	0.120775i	−0.465573	+	0.885010i	$0.654152\pi$
$774$	−0.194941	+	3.59547i	−0.00700700	+	0.129236i
$775$	0.000884190	−	0.00318457i	3.17611e−5	−	0.000114393i
$776$	−12.9284	−	9.82794i	−0.464104	−	0.352803i
$777$	4.17132	+	0.453659i	0.149645	+	0.0162749i
$778$	−0.869430	+	5.30329i	−0.0311706	+	0.190132i
$779$	−1.24187	+	0.747208i	−0.0444946	+	0.0267715i
$780$	−6.44461	+	4.89907i	−0.230754	+	0.175415i
$781$	6.27577	+	15.7510i	0.224565	+	0.563615i
$782$	0.241277	+	0.284053i	0.00862805	+	0.0101577i
$783$	−0.231604	−	1.41272i	−0.00827684	−	0.0504865i
$784$	−0.305255	−	5.63010i	−0.0109020	−	0.201075i
$785$	−36.8596	−	8.11341i	−1.31557	−	0.289580i
$786$	−13.9730	+	13.2359i	−0.498400	+	0.472109i
$787$	−37.9222	+	12.7775i	−1.35178	+	0.455468i	−0.899700	−	0.436509i	$-0.856215\pi$
$787$	−37.9222	+	12.7775i	−1.35178	+	0.455468i	−0.452080	+	0.891977i	$0.649318\pi$
$788$	7.48630	−	18.7892i	0.266688	−	0.669337i
$789$	−7.42808	−	26.7535i	−0.264447	−	0.952451i
$790$	−20.1205	+	4.42885i	−0.715854	+	0.157571i
$791$	−4.73992	+	6.99087i	−0.168532	+	0.248567i
$792$	0.776396	+	1.46444i	0.0275880	+	0.0520366i
$793$	−18.5990	+	35.0815i	−0.660470	+	1.24578i
$794$	−18.4425	−	27.2006i	−0.654499	−	0.965314i
$795$	3.23979	+	3.06890i	0.114904	+	0.108843i
$796$	2.23231	+	1.03278i	0.0791222	+	0.0366058i
$797$	−31.5838	−	14.6122i	−1.11876	−	0.517591i	−0.228724	−	0.973491i	$-0.573455\pi$
$797$	−31.5838	−	14.6122i	−1.11876	−	0.517591i	−0.890031	+	0.455900i	$0.849317\pi$
$798$	4.02816	+	3.81568i	0.142595	+	0.135074i
$799$	−2.59850	−	3.83250i	−0.0919284	−	0.135584i
$800$	0.000675007	−	0.00127320i	2.38651e−5	−	4.50143e-5i
$801$	4.21174	+	7.94418i	0.148815	+	0.280694i
$802$	−5.67220	+	8.36587i	−0.200292	+	0.295409i
$803$	10.3263	−	2.27299i	0.364407	−	0.0802121i
$804$	−1.01288	−	3.64807i	−0.0357215	−	0.128657i
$805$	−0.108664	+	0.272726i	−0.00382990	+	0.00961232i
$806$	−7.86960	+	2.65158i	−0.277195	+	0.0933978i
$807$	10.0565	−	9.52607i	0.354007	−	0.335333i
$808$	−5.80642	−	1.27809i	−0.204269	−	0.0449631i
$809$	−1.77949	−	32.8207i	−0.0625634	−	1.15391i	−0.846260	−	0.532770i	$-0.821151\pi$
$809$	−1.77949	−	32.8207i	−0.0625634	−	1.15391i	0.783697	−	0.621144i	$-0.213332\pi$
$810$	0.361703	+	2.20629i	0.0127090	+	0.0775212i
$811$	−15.8062	−	18.6085i	−0.555032	−	0.653434i	0.411067	−	0.911605i	$-0.365156\pi$
$811$	−15.8062	−	18.6085i	−0.555032	−	0.653434i	−0.966099	+	0.258171i	$0.916880\pi$
$812$	0.618314	+	1.55185i	0.0216986	+	0.0544593i
$813$	12.8043	−	9.73356i	0.449065	−	0.341371i
$814$	−5.10699	+	3.07277i	−0.179000	+	0.107701i
$815$	−3.30703	+	20.1720i	−0.115840	+	0.706594i
$816$	−3.29253	−	0.358084i	−0.115262	−	0.0125355i
$817$	−13.6301	−	10.3614i	−0.476858	−	0.362498i
$818$	−8.89169	+	32.0250i	−0.310890	+	1.11973i
$819$	0.228744	−	4.21893i	0.00799296	−	0.147421i
$820$	0.677474	−	0.0736798i	0.0236584	−	0.00257301i
$821$	0.0811343	+	0.0488169i	0.00283161	+	0.00170372i	0.516969	−	0.856004i	$-0.327060\pi$
$821$	0.0811343	+	0.0488169i	0.00283161	+	0.00170372i	−0.514137	+	0.857708i	$0.671888\pi$
$822$	−7.51716	+	8.84989i	−0.262191	+	0.308675i
$823$	0.907839	+	0.305887i	0.0316453	+	0.0106625i	0.335080	−	0.942190i	$-0.391237\pi$
$823$	0.907839	+	0.305887i	0.0316453	+	0.0106625i	−0.303434	+	0.952852i	$0.598133\pi$
$824$	14.9203	−	6.90287i	0.519773	−	0.240473i
$825$	−0.00238859			−8.31601e−5
$826$	1.38897	+	8.85477i	0.0483285	+	0.308097i
$827$	24.2728			0.844049			0.422024	−	0.906584i	$-0.361320\pi$
$827$	24.2728			0.844049			0.422024	+	0.906584i	$0.361320\pi$
$828$	0.102130	−	0.0472502i	0.00354925	−	0.00164206i
$829$	−12.1335	−	4.08824i	−0.421412	−	0.141990i	0.100603	−	0.994927i	$-0.467923\pi$
$829$	−12.1335	−	4.08824i	−0.421412	−	0.141990i	−0.522015	+	0.852936i	$0.674819\pi$
$830$	−5.08906	+	5.99131i	−0.176644	+	0.207961i
$831$	−0.970640	−	0.584015i	−0.0336711	−	0.0202592i
$832$	−3.59962	+	0.391483i	−0.124795	+	0.0135722i
$833$	1.01099	−	18.6466i	0.0350287	−	0.646066i
$834$	2.57502	−	9.27440i	0.0891658	−	0.321146i
$835$	−2.06142	−	1.56705i	−0.0713383	−	0.0542300i
$836$	−7.83518	−	0.852127i	−0.270985	−	0.0294714i
$837$	−0.371042	+	2.26326i	−0.0128251	+	0.0782295i
$838$	28.5775	−	17.1945i	0.987193	−	0.593974i
$839$	−11.1575	+	8.48174i	−0.385201	+	0.292822i	−0.779797	−	0.626033i	$-0.784678\pi$
$839$	−11.1575	+	8.48174i	−0.385201	+	0.292822i	0.394596	+	0.918855i	$0.370885\pi$
$840$	−0.965641	−	2.42358i	−0.0333178	−	0.0836213i
$841$	−17.4474	−	20.5407i	−0.601636	−	0.708300i
$842$	−0.0544539	−	0.332154i	−0.00187661	−	0.0114468i
$843$	0.299436	+	5.52277i	0.0103131	+	0.190214i
$844$	16.5069	+	3.63345i	0.568192	+	0.125068i
$845$	−0.179444	+	0.169978i	−0.00617306	+	0.00584743i
$846$	−1.32490	+	0.446409i	−0.0455509	+	0.0153479i
$847$	3.56439	−	8.94595i	0.122474	−	0.307387i
$848$	0.533987	+	1.92325i	0.0183372	+	0.0660446i
$849$	23.2834	−	5.12506i	0.799084	−	0.175892i
$850$	0.00267839	−	0.00395033i	9.18681e−5	−	0.000135495i
$851$	0.189536	+	0.357503i	0.00649721	+	0.0122550i
$852$	−4.79148	+	9.03769i	−0.164153	+	0.309626i
$853$	15.3186	+	22.5932i	0.524497	+	0.773576i	0.994003	−	0.109354i	$-0.0348781\pi$
$853$	15.3186	+	22.5932i	0.524497	+	0.773576i	−0.469505	+	0.882930i	$0.655568\pi$
$854$	−9.29005	−	8.80000i	−0.317899	−	0.301130i
$855$	−9.64826	−	4.46376i	−0.329963	−	0.152657i
$856$	0.0504889	+	0.0233587i	0.00172568	+	0.000798383i
$857$	21.1900	+	20.0722i	0.723835	+	0.685653i	0.958072	−	0.286526i	$-0.0925006\pi$
$857$	21.1900	+	20.0722i	0.723835	+	0.685653i	−0.234237	+	0.972179i	$0.575259\pi$
$858$	3.36804	+	4.96748i	0.114983	+	0.169587i
$859$	4.92920	−	9.29746i	0.168182	−	0.317225i	−0.785067	−	0.619411i	$-0.787371\pi$
$859$	4.92920	−	9.29746i	0.168182	−	0.317225i	0.953249	+	0.302186i	$0.0977163\pi$
$860$	3.77086	+	7.11259i	0.128585	+	0.242537i
$861$	−0.199600	+	0.294388i	−0.00680236	+	0.0100327i
$862$	0.170526	−	0.0375357i	0.00580815	−	0.00127847i
$863$	−9.07759	−	32.6945i	−0.309005	−	1.11293i	−0.941123	−	0.338063i	$-0.890228\pi$
$863$	−9.07759	−	32.6945i	−0.309005	−	1.11293i	0.632119	−	0.774872i	$-0.282186\pi$
$864$	−0.370138	+	0.928977i	−0.0125924	+	0.0316044i
$865$	−23.5988	+	7.95136i	−0.802383	+	0.270354i
$866$	22.1300	−	20.9626i	0.752007	−	0.712339i
$867$	5.89002	+	1.29649i	0.200036	+	0.0440312i
$868$	−0.144888	−	2.67230i	−0.00491781	−	0.0907037i
$869$	2.47103	+	15.0726i	0.0838241	+	0.511304i
$870$	−2.07206	−	2.43941i	−0.0702493	−	0.0827038i
$871$	−5.07414	−	12.7351i	−0.171931	−	0.431514i
$872$	−5.71061	+	4.34109i	−0.193386	+	0.147008i
$873$	−13.9152	+	8.37252i	−0.470960	+	0.283367i
$874$	−0.0865652	+	0.528024i	−0.00292811	+	0.0178607i
$875$	12.9716	+	1.41075i	0.438520	+	0.0476920i
$876$	5.07837	+	3.86048i	0.171582	+	0.130433i
$877$	−2.64527	+	9.52739i	−0.0893243	+	0.321717i	−0.994690	−	0.102915i	$-0.967183\pi$
$877$	−2.64527	+	9.52739i	−0.0893243	+	0.321717i	0.905366	+	0.424632i	$0.139597\pi$
$878$	−0.0487504	+	0.899148i	−0.00164525	+	0.0303448i
$879$	−26.8152	+	2.91633i	−0.904454	+	0.0983653i
$880$	3.17533	+	1.91054i	0.107041	+	0.0644041i
$881$	14.1436	−	16.6511i	0.476509	−	0.560990i	−0.470416	−	0.882445i	$-0.655896\pi$
$881$	14.1436	−	16.6511i	0.476509	−	0.560990i	0.946925	+	0.321455i	$0.104172\pi$
$882$	−5.34322	−	1.80034i	−0.179916	−	0.0606206i
$883$	27.0436	−	12.5117i	0.910090	−	0.421053i	0.0917471	−	0.995782i	$-0.470755\pi$
$883$	27.0436	−	12.5117i	0.910090	−	0.421053i	0.818343	+	0.574730i	$0.194893\pi$
$884$	−11.9921			−0.403336
$885$	−7.93910	−	15.2278i	−0.266870	−	0.511877i
$886$	7.24637			0.243447
$887$	21.9618	−	10.1606i	0.737404	−	0.341159i	−0.0149769	−	0.999888i	$-0.504767\pi$
$887$	21.9618	−	10.1606i	0.737404	−	0.341159i	0.752381	+	0.658729i	$0.228905\pi$
$888$	−3.40759	−	1.14815i	−0.114351	−	0.0385294i
$889$	−9.96593	+	11.7328i	−0.334247	+	0.393505i
$890$	17.2253	+	10.3641i	0.577395	+	0.347407i
$891$	1.64780	−	0.179209i	0.0552035	−	0.00600374i
$892$	−1.29202	+	23.8299i	−0.0432599	+	0.797882i
$893$	1.77847	−	6.40546i	0.0595141	−	0.214351i
$894$	−15.9490	−	12.1241i	−0.533414	−	0.405491i
$895$	−40.0303	−	4.35356i	−1.33807	−	0.145524i
$896$	0.188782	−	1.15152i	0.00630675	−	0.0384695i
$897$	0.349131	−	0.210065i	0.0116571	−	0.00701387i
$898$	0.281961	−	0.214341i	0.00940917	−	0.00715267i
$899$	−1.21527	−	3.05009i	−0.0405315	−	0.101726i
$900$	−0.000932925	−	0.00109832i	−3.10975e−5	−	3.66108e-5i
$901$	1.06948	+	6.52356i	0.0356297	+	0.217331i
$902$	−0.0273522	−	0.504481i	−0.000910728	−	0.0167974i
$903$	−4.10344	−	0.903236i	−0.136554	−	0.0300578i
$904$	5.25495	−	4.97775i	0.174777	−	0.165557i
$905$	30.0473	−	10.1241i	0.998807	−	0.336537i
$906$	−3.14777	+	7.90030i	−0.104578	+	0.262470i
$907$	5.28410	+	19.0316i	0.175456	+	0.631935i	0.997999	+	0.0632318i	$0.0201408\pi$
$907$	5.28410	+	19.0316i	0.175456	+	0.631935i	−0.822543	+	0.568703i	$0.807445\pi$
$908$	7.51120	−	1.65334i	0.249268	−	0.0548680i
$909$	−3.33649	+	4.92096i	−0.110665	+	0.163218i
$910$	−4.42473	−	8.34593i	−0.146678	−	0.276665i
$911$	18.8884	−	35.6273i	0.625800	−	1.18038i	−0.344570	−	0.938761i	$-0.611975\pi$
$911$	18.8884	−	35.6273i	0.625800	−	1.18038i	0.970370	−	0.241624i	$-0.0776799\pi$
$912$	−2.66840	−	3.93560i	−0.0883596	−	0.130321i
$913$	4.23101	+	4.00783i	0.140026	+	0.132640i
$914$	30.9199	+	14.3051i	1.02274	+	0.473170i
$915$	22.2515	+	10.2947i	0.735613	+	0.340331i
$916$	16.6752	+	15.7956i	0.550966	+	0.521902i
$917$	−12.6035	−	18.5888i	−0.416205	−	0.613857i
$918$	−1.55134	+	2.92614i	−0.0512019	+	0.0965771i
$919$	−7.89167	−	14.8853i	−0.260322	−	0.491020i	0.718555	−	0.695471i	$-0.244804\pi$
$919$	−7.89167	−	14.8853i	−0.260322	−	0.491020i	−0.978877	+	0.204451i	$0.934459\pi$
$920$	0.141189	−	0.208237i	0.00465485	−	0.00686539i
$921$	5.13229	−	1.12970i	0.169115	−	0.0372250i
$922$	−2.72706	−	9.82200i	−0.0898111	−	0.323470i
$923$	−13.7094	+	34.4081i	−0.451251	+	1.13256i
$924$	−1.83289	+	0.617574i	−0.0602978	+	0.0203167i
$925$	0.00376196	−	0.00356352i	0.000123693	−	0.000117168i
$926$	−18.0328	−	3.96932i	−0.592594	−	0.130440i
$927$	−0.890030	−	16.4156i	−0.0292324	−	0.539160i
$928$	−0.231604	−	1.41272i	−0.00760277	−	0.0463748i
$929$	33.4130	+	39.3368i	1.09625	+	1.29060i	0.953683	+	0.300814i	$0.0972582\pi$
$929$	33.4130	+	39.3368i	1.09625	+	1.29060i	0.142562	+	0.989786i	$0.454466\pi$
$930$	1.89792	+	4.76343i	0.0622354	+	0.156199i
$931$	21.3433	−	16.2247i	0.699498	−	0.531744i
$932$	11.1649	−	6.71771i	0.365719	−	0.220046i
$933$	−2.54804	+	15.5423i	−0.0834190	+	0.508833i
$934$	−30.3188	−	3.29737i	−0.992061	−	0.107893i
$935$	9.77075	+	7.42753i	0.319538	+	0.242906i
$936$	−0.968680	+	3.48887i	−0.0316623	+	0.114037i
$937$	−1.08737	+	20.0553i	−0.0355228	+	0.655179i	0.925506	+	0.378732i	$0.123640\pi$
$937$	−1.08737	+	20.0553i	−0.0355228	+	0.655179i	−0.961029	+	0.276447i	$0.910843\pi$
$938$	4.39202	−	0.477661i	0.143405	−	0.0155962i
$939$	−19.5387	−	11.7560i	−0.637621	−	0.383644i
$940$	−2.02357	+	2.38233i	−0.0660016	+	0.0777031i
$941$	−19.9347	−	6.71678i	−0.649852	−	0.218961i	−0.0249801	−	0.999688i	$-0.507952\pi$
$941$	−19.9347	−	6.71678i	−0.649852	−	0.218961i	−0.624872	+	0.780727i	$0.714849\pi$
$942$	−15.3209	+	7.08821i	−0.499182	+	0.230946i
$943$	−0.0342999			−0.00111696
$944$	0.468781	−	7.66683i	0.0152575	−	0.249534i
$945$	−2.60887			−0.0848664
$946$	5.41669	−	2.50603i	0.176112	−	0.0814781i
$947$	45.6151	+	15.3695i	1.48229	+	0.499443i	0.940126	−	0.340828i	$-0.110707\pi$
$947$	45.6151	+	15.3695i	1.48229	+	0.499443i	0.542167	+	0.840271i	$0.317604\pi$
$948$	−5.96559	+	7.02324i	−0.193753	+	0.228104i
$949$	19.7915	+	11.9082i	0.642460	+	0.386555i
$950$	0.00681198		0.000740848i	0.000221010		2.40363e-5i
$951$	0.0920393	−	1.69756i	0.00298458	−	0.0550473i
$952$	1.03391	−	3.72380i	0.0335092	−	0.120689i
$953$	7.10897	+	5.40410i	0.230282	+	0.175056i	0.713952	−	0.700195i	$-0.246903\pi$
$953$	7.10897	+	5.40410i	0.230282	+	0.175056i	−0.483670	+	0.875250i	$0.660697\pi$
$954$	1.98430	+	0.215806i	0.0642442	+	0.00698697i
$955$	−2.74432	+	16.7396i	−0.0888039	+	0.541680i
$956$	15.4511	−	9.29662i	0.499724	−	0.300674i
$957$	−1.88903	+	1.43600i	−0.0610635	+	0.0464193i
$958$	−8.58294	−	21.5416i	−0.277302	−	0.695976i
$959$	−8.77170	−	10.3268i	−0.283253	−	0.333471i
$960$	0.361703	+	2.20629i	0.0116739	+	0.0712078i
$961$	−1.39354	−	25.7023i	−0.0449528	−	0.829105i
$962$	−12.7155	−	2.79890i	−0.409965	−	0.0902400i
$963$	0.0403875	−	0.0382571i	0.00130147	−	0.00123282i
$964$	−5.32098	+	1.79285i	−0.171377	+	0.0577437i
$965$	10.0287	−	25.1701i	0.322835	−	0.810254i
$966$	0.0351292	+	0.126524i	0.00113026	+	0.00407084i
$967$	27.1373	−	5.97338i	0.872677	−	0.192091i	0.244017	−	0.969771i	$-0.421535\pi$
$967$	27.1373	−	5.97338i	0.872677	−	0.192091i	0.628660	+	0.777680i	$0.283604\pi$
$968$	−4.63127	+	6.83061i	−0.148855	+	0.219544i
$969$	−7.37652	−	13.9136i	−0.236968	−	0.446969i
$970$	−17.0071	+	32.0787i	−0.546064	+	1.02999i
$971$	−24.0870	−	35.5257i	−0.772989	−	1.14007i	−0.986601	−	0.163154i	$-0.947833\pi$
$971$	−24.0870	−	35.5257i	−0.772989	−	1.14007i	0.213612	−	0.976919i	$-0.431477\pi$
$972$	0.725995	+	0.687699i	0.0232863	+	0.0220580i
$973$	10.1935	+	4.71602i	0.326789	+	0.151189i
$974$	20.3972	+	9.43677i	0.653570	+	0.302374i
$975$	−0.00378815	−	0.00358833i	−0.000121318	−	0.000114919i
$976$	6.15407	+	9.07657i	0.196987	+	0.290534i
$977$	16.8783	−	31.8359i	0.539985	−	1.01852i	−0.451982	−	0.892027i	$-0.649283\pi$
$977$	16.8783	−	31.8359i	0.539985	−	1.01852i	0.991968	−	0.126493i	$-0.0403721\pi$
$978$	4.28262	+	8.07789i	0.136943	+	0.258302i
$979$	8.36379	−	12.3357i	0.267308	−	0.394250i
$980$	−12.3112	+	2.70991i	−0.393268	+	0.0865649i
$981$	1.91906	+	6.91182i	0.0612708	+	0.220678i
$982$	7.02020	−	17.6194i	0.224024	−	0.562257i
$983$	14.6355	−	4.93126i	0.466799	−	0.157283i	−0.0760663	−	0.997103i	$-0.524236\pi$
$983$	14.6355	−	4.93126i	0.466799	−	0.157283i	0.542865	+	0.839820i	$0.317340\pi$
$984$	0.221288	−	0.209615i	0.00705440	−	0.00668228i
$985$	−44.1623	−	9.72085i	−1.40713	−	0.309732i
$986$	−0.256689	−	4.73436i	−0.00817466	−	0.150773i
$987$	−0.263932	−	1.60991i	−0.00840105	−	0.0512441i
$988$	−11.1460	−	13.1220i	−0.354600	−	0.417468i
$989$	−0.149978	−	0.376415i	−0.00476901	−	0.0119693i
$990$	2.95016	−	2.24265i	0.0937621	−	0.0712761i
$991$	−12.6297	+	7.59906i	−0.401197	+	0.241392i	−0.701825	−	0.712349i	$-0.747631\pi$
$991$	−12.6297	+	7.59906i	−0.401197	+	0.241392i	0.300628	+	0.953741i	$0.402804\pi$
$992$	−0.371042	+	2.26326i	−0.0117806	+	0.0718584i
$993$	−10.2462	−	1.11434i	−0.325152	−	0.0353624i
$994$	−9.50251	−	7.22362i	−0.301401	−	0.229119i
$995$	1.47118	−	5.29870i	0.0466394	−	0.167980i
$996$	−0.190354	+	3.51087i	−0.00603159	+	0.111246i
$997$	51.5823	−	5.60991i	1.63363	−	0.177668i	0.755184	−	0.655513i	$-0.227548\pi$
$997$	51.5823	−	5.60991i	1.63363	−	0.177668i	0.878444	+	0.477846i	$0.158582\pi$
$998$	9.22781	+	5.55219i	0.292101	+	0.175752i
$999$	−2.32788	+	2.74059i	−0.0736509	+	0.0867086i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.b.121.1	yes	56
59.20	even	29	inner	354.2.e.b.79.1	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.b.79.1	✓	56	59.20	even	29	inner
354.2.e.b.121.1	yes	56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.907575 + 0.419889i) q^{2} +(0.947653 + 0.319302i) q^{3} +(0.647386 - 0.762162i) q^{4} +(-1.91571 - 1.15265i) q^{5} +(-0.994138 + 0.108119i) q^{6} +(0.0631741 - 1.16518i) q^{7} +(-0.267528 + 0.963550i) q^{8} +(0.796093 + 0.605174i) q^{9} +O(q^{10})\)	\(q+(-0.907575 + 0.419889i) q^{2} +(0.947653 + 0.319302i) q^{3} +(0.647386 - 0.762162i) q^{4} +(-1.91571 - 1.15265i) q^{5} +(-0.994138 + 0.108119i) q^{6} +(0.0631741 - 1.16518i) q^{7} +(-0.267528 + 0.963550i) q^{8} +(0.796093 + 0.605174i) q^{9} +(2.22264 + 0.241727i) q^{10} +(0.268157 - 1.63568i) q^{11} +(0.856857 - 0.515554i) q^{12} +(2.88253 - 2.19124i) q^{13} +(0.431910 + 1.08401i) q^{14} +(-1.44739 - 1.70400i) q^{15} +(-0.161782 - 0.986827i) q^{16} +(-0.179305 - 3.30709i) q^{17} +(-0.976621 - 0.214970i) q^{18} +(3.45205 - 3.26996i) q^{19} +(-2.11871 + 0.713877i) q^{20} +(0.431910 - 1.08401i) q^{21} +(0.443433 + 1.59710i) q^{22} +(0.109899 - 0.0241907i) q^{23} +(-0.561187 + 0.827689i) q^{24} +(-0.000675007 - 0.00127320i) q^{25} +(-1.69604 + 3.19906i) q^{26} +(0.561187 + 0.827689i) q^{27} +(-0.847156 - 0.802469i) q^{28} +(-1.29927 - 0.601105i) q^{29} +(2.02911 + 0.938765i) q^{30} +(1.66505 + 1.57722i) q^{31} +(0.561187 + 0.827689i) q^{32} +(0.776396 - 1.46444i) q^{33} +(1.55134 + 2.92614i) q^{34} +(-1.46406 + 2.15933i) q^{35} +(0.976621 - 0.214970i) q^{36} +(0.961983 + 3.46475i) q^{37} +(-1.75998 + 4.41722i) q^{38} +(3.43131 - 1.15614i) q^{39} +(1.62314 - 1.53752i) q^{40} +(-0.297680 - 0.0655243i) q^{41} +(0.0631741 + 1.16518i) q^{42} +(-0.582536 - 3.55332i) q^{43} +(-1.07306 - 1.26330i) q^{44} +(-0.827535 - 2.07696i) q^{45} +(-0.0895846 + 0.0681004i) q^{46} +(1.19796 - 0.720786i) q^{47} +(0.161782 - 0.986827i) q^{48} +(5.60532 + 0.609615i) q^{49} +(0.00114722 + 0.000872095i) q^{50} +(0.886039 - 3.19122i) q^{51} +(0.196029 - 3.61554i) q^{52} +(-1.98430 + 0.215806i) q^{53} +(-0.856857 - 0.515554i) q^{54} +(-2.39908 + 2.82441i) q^{55} +(1.10581 + 0.372589i) q^{56} +(4.31545 - 1.99654i) q^{57} +1.43158 q^{58} +(7.48999 + 1.70296i) q^{59} -2.23575 q^{60} +(-9.95262 + 4.60457i) q^{61} +(-2.17341 - 0.732308i) q^{62} +(0.755428 - 0.889358i) q^{63} +(-0.856857 - 0.515554i) q^{64} +(-8.04784 + 0.875256i) q^{65} +(-0.0897363 + 1.65509i) q^{66} +(1.01288 - 3.64807i) q^{67} +(-2.63662 - 2.00430i) q^{68} +(0.111871 + 0.0121667i) q^{69} +(0.422068 - 2.57450i) q^{70} +(-8.76503 + 5.27374i) q^{71} +(-0.796093 + 0.605174i) q^{72} +(2.36115 + 5.92605i) q^{73} +(-2.32788 - 2.74059i) q^{74} +(-0.000233138 - 0.00142208i) q^{75} +(-0.257426 - 4.74795i) q^{76} +(-1.88892 - 0.415783i) q^{77} +(-2.62872 + 2.49006i) q^{78} +(-8.73252 + 2.94233i) q^{79} +(-0.827535 + 2.07696i) q^{80} +(0.267528 + 0.963550i) q^{81} +(0.297680 - 0.0655243i) q^{82} +(-1.97315 + 2.91017i) q^{83} +(-0.546581 - 1.03096i) q^{84} +(-3.46841 + 6.54211i) q^{85} +(2.02069 + 2.98030i) q^{86} +(-1.03932 - 0.984497i) q^{87} +(1.50432 + 0.695974i) q^{88} +(8.16055 + 3.77547i) q^{89} +(1.62314 + 1.53752i) q^{90} +(-2.37109 - 3.49709i) q^{91} +(0.0527101 - 0.0994218i) q^{92} +(1.07428 + 2.02631i) q^{93} +(-0.784585 + 1.15718i) q^{94} +(-10.3823 + 2.28531i) q^{95} +(0.267528 + 0.963550i) q^{96} +(-6.01099 + 15.0865i) q^{97} +(-5.34322 + 1.80034i) q^{98} +(1.20335 - 1.13988i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 30 q^{11} + 2 q^{12} + 5 q^{13} + 28 q^{14} + 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 28 q^{21} - q^{22} - 2 q^{23} - 2 q^{24} + 64 q^{25} - 34 q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - 2 q^{30} + 2 q^{32} - q^{33} + 32 q^{34} - 87 q^{35} - 2 q^{36} + 47 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} + 3 q^{41} + q^{42} - 61 q^{43} + q^{44} - 2 q^{45} - 27 q^{46} + 50 q^{47} + 2 q^{48} - 45 q^{49} - 6 q^{50} + 3 q^{51} - 24 q^{52} - 27 q^{53} - 2 q^{54} - 95 q^{55} - q^{56} + 4 q^{57} + 50 q^{58} - 58 q^{59} + 2 q^{60} - 74 q^{61} - 29 q^{62} + q^{63} - 2 q^{64} - 17 q^{65} + q^{66} + 4 q^{67} - 32 q^{68} + 31 q^{69} - 58 q^{70} - 47 q^{71} + 2 q^{72} + 43 q^{73} - 18 q^{74} - 6 q^{75} - 33 q^{76} - 5 q^{77} + 5 q^{78} + 19 q^{79} - 2 q^{80} - 2 q^{81} - 3 q^{82} + 47 q^{83} - q^{84} - 149 q^{85} - 55 q^{86} + 21 q^{87} + 28 q^{88} + 36 q^{89} + 2 q^{90} + 175 q^{91} - 2 q^{92} - 29 q^{93} - 21 q^{94} + 50 q^{95} - 2 q^{96} + 10 q^{97} - 13 q^{98} + q^{99}+O(q^{100}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 30 * q^11 + 2 * q^12 + 5 * q^13 + 28 * q^14 + 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 28 * q^21 - q^22 - 2 * q^23 - 2 * q^24 + 64 * q^25 - 34 * q^26 + 2 * q^27 + q^28 + 8 * q^29 - 2 * q^30 + 2 * q^32 - q^33 + 32 * q^34 - 87 * q^35 - 2 * q^36 + 47 * q^37 + 4 * q^38 - 5 * q^39 + 2 * q^40 + 3 * q^41 + q^42 - 61 * q^43 + q^44 - 2 * q^45 - 27 * q^46 + 50 * q^47 + 2 * q^48 - 45 * q^49 - 6 * q^50 + 3 * q^51 - 24 * q^52 - 27 * q^53 - 2 * q^54 - 95 * q^55 - q^56 + 4 * q^57 + 50 * q^58 - 58 * q^59 + 2 * q^60 - 74 * q^61 - 29 * q^62 + q^63 - 2 * q^64 - 17 * q^65 + q^66 + 4 * q^67 - 32 * q^68 + 31 * q^69 - 58 * q^70 - 47 * q^71 + 2 * q^72 + 43 * q^73 - 18 * q^74 - 6 * q^75 - 33 * q^76 - 5 * q^77 + 5 * q^78 + 19 * q^79 - 2 * q^80 - 2 * q^81 - 3 * q^82 + 47 * q^83 - q^84 - 149 * q^85 - 55 * q^86 + 21 * q^87 + 28 * q^88 + 36 * q^89 + 2 * q^90 + 175 * q^91 - 2 * q^92 - 29 * q^93 - 21 * q^94 + 50 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + q^99

Introduction

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