LMFDB - Embedded newform 115.2.g.c.26.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

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("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			26.3
Character	$\chi$	$=$	115.26
Dual form			115.2.g.c.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0393306 - 0.273550i) q^{2} +(0.955665 - 2.09261i) q^{3} +(1.84570 - 0.541947i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-0.610022 - 0.179119i) q^{6} +(-2.63800 + 1.69534i) q^{7} +(-0.450453 - 0.986355i) q^{8} +(-1.50116 - 1.73243i) q^{9} +O(q^{10})$	\(q+(-0.0393306 - 0.273550i) q^{2} +(0.955665 - 2.09261i) q^{3} +(1.84570 - 0.541947i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-0.610022 - 0.179119i) q^{6} +(-2.63800 + 1.69534i) q^{7} +(-0.450453 - 0.986355i) q^{8} +(-1.50116 - 1.73243i) q^{9} +(0.232492 + 0.149413i) q^{10} +(-0.369695 + 2.57128i) q^{11} +(0.629787 - 4.38027i) q^{12} +(-0.0559711 - 0.0359704i) q^{13} +(0.567516 + 0.654948i) q^{14} +(0.955665 + 2.09261i) q^{15} +(2.98441 - 1.91796i) q^{16} +(-1.42241 - 0.417657i) q^{17} +(-0.414865 + 0.478780i) q^{18} +(4.42817 - 1.30023i) q^{19} +(-0.799102 + 1.74979i) q^{20} +(1.02665 + 7.14051i) q^{21} +0.717915 q^{22} +(-2.65025 + 3.99702i) q^{23} -2.49454 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-0.00763835 + 0.0167256i) q^{26} +(1.56205 - 0.458659i) q^{27} +(-3.95019 + 4.55876i) q^{28} +(-9.93501 - 2.91718i) q^{29} +(0.534849 - 0.343726i) q^{30} +(3.45291 + 7.56083i) q^{31} +(-2.06223 - 2.37994i) q^{32} +(5.02740 + 3.23091i) q^{33} +(-0.0583060 + 0.405527i) q^{34} +(0.446271 - 3.10388i) q^{35} +(-3.70958 - 2.38400i) q^{36} +(-3.92880 - 4.53408i) q^{37} +(-0.529840 - 1.16019i) q^{38} +(-0.128762 + 0.0827502i) q^{39} +(1.04042 + 0.305495i) q^{40} +(-2.55857 + 2.95275i) q^{41} +(1.91291 - 0.561681i) q^{42} +(3.26842 - 7.15685i) q^{43} +(0.711153 + 4.94618i) q^{44} +2.29233 q^{45} +(1.19762 + 0.567772i) q^{46} +8.42088 q^{47} +(-1.16146 - 8.07815i) q^{48} +(1.17697 - 2.57722i) q^{49} +(-0.265169 + 0.0778605i) q^{50} +(-2.23334 + 2.57741i) q^{51} +(-0.122800 - 0.0360573i) q^{52} +(-0.190337 + 0.122322i) q^{53} +(-0.186903 - 0.409260i) q^{54} +(-1.70115 - 1.96323i) q^{55} +(2.86051 + 1.83834i) q^{56} +(1.51097 - 10.5090i) q^{57} +(-0.407246 + 2.83246i) q^{58} +(0.709087 + 0.455703i) q^{59} +(2.89796 + 3.34443i) q^{60} +(-3.25234 - 7.12164i) q^{61} +(1.93246 - 1.24192i) q^{62} +(6.89712 + 2.02518i) q^{63} +(4.07641 - 4.70443i) q^{64} +(0.0638379 - 0.0187445i) q^{65} +(0.686087 - 1.50232i) q^{66} +(1.42203 + 9.89044i) q^{67} -2.85169 q^{68} +(5.83147 + 9.36577i) q^{69} -0.866621 q^{70} +(-1.22385 - 8.51208i) q^{71} +(-1.03259 + 2.26105i) q^{72} +(-8.56020 + 2.51350i) q^{73} +(-1.08578 + 1.25305i) q^{74} +(-2.20732 - 0.648128i) q^{75} +(7.46843 - 4.79967i) q^{76} +(-3.38395 - 7.40981i) q^{77} +(0.0277006 + 0.0319682i) q^{78} +(-12.5251 - 8.04939i) q^{79} +(-0.504872 + 3.51146i) q^{80} +(1.51170 - 10.5141i) q^{81} +(0.908355 + 0.583764i) q^{82} +(-5.87671 - 6.78209i) q^{83} +(5.76467 + 12.6229i) q^{84} +(1.24712 - 0.801477i) q^{85} +(-2.08631 - 0.612595i) q^{86} +(-15.5991 + 18.0023i) q^{87} +(2.70273 - 0.793593i) q^{88} +(0.984223 - 2.15515i) q^{89} +(-0.0901588 - 0.627068i) q^{90} +0.208634 q^{91} +(-2.72540 + 8.81361i) q^{92} +19.1217 q^{93} +(-0.331198 - 2.30353i) q^{94} +(-1.91719 + 4.19806i) q^{95} +(-6.95110 + 2.04103i) q^{96} +(5.06792 - 5.84870i) q^{97} +(-0.751289 - 0.220598i) q^{98} +(5.00953 - 3.21943i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.0393306	−	0.273550i	−0.0278109	−	0.193429i	0.971180	−	0.238349i	$-0.0766061\pi$
$2$	−0.0393306	−	0.273550i	−0.0278109	−	0.193429i	−0.998991	+	0.0449192i	$0.985697\pi$
$3$	0.955665	−	2.09261i	0.551754	−	1.20817i	−0.404205	−	0.914669i	$-0.632452\pi$
$3$	0.955665	−	2.09261i	0.551754	−	1.20817i	0.955958	−	0.293503i	$-0.0948211\pi$
$4$	1.84570	−	0.541947i	0.922852	−	0.270974i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$6$	−0.610022	−	0.179119i	−0.249041	−	0.0731249i
$7$	−2.63800	+	1.69534i	−0.997072	+	0.640779i	−0.934016	−	0.357231i	$-0.883721\pi$
$7$	−2.63800	+	1.69534i	−0.997072	+	0.640779i	−0.0630557	+	0.998010i	$0.520085\pi$
$8$	−0.450453	−	0.986355i	−0.159259	−	0.348729i
$9$	−1.50116	−	1.73243i	−0.500386	−	0.577476i
$10$	0.232492	+	0.149413i	0.0735203	+	0.0472486i
$11$	−0.369695	+	2.57128i	−0.111467	+	0.775271i	0.855027	+	0.518583i	$0.173540\pi$
$11$	−0.369695	+	2.57128i	−0.111467	+	0.775271i	−0.966494	+	0.256688i	$0.917369\pi$
$12$	0.629787	−	4.38027i	0.181804	−	1.26447i
$13$	−0.0559711	−	0.0359704i	−0.0155236	−	0.00997640i	0.532856	−	0.846206i	$-0.321119\pi$
$13$	−0.0559711	−	0.0359704i	−0.0155236	−	0.00997640i	−0.548380	+	0.836230i	$0.684755\pi$
$14$	0.567516	+	0.654948i	0.151675	+	0.175042i
$15$	0.955665	+	2.09261i	0.246752	+	0.540311i
$16$	2.98441	−	1.91796i	0.746102	−	0.479491i
$17$	−1.42241	−	0.417657i	−0.344985	−	0.101297i	0.104650	−	0.994509i	$-0.466628\pi$
$17$	−1.42241	−	0.417657i	−0.344985	−	0.101297i	−0.449635	+	0.893212i	$0.648446\pi$
$18$	−0.414865	+	0.478780i	−0.0977846	+	0.112849i
$19$	4.42817	−	1.30023i	1.01589	−	0.298293i	0.268930	−	0.963160i	$-0.413330\pi$
$19$	4.42817	−	1.30023i	1.01589	−	0.298293i	0.746962	+	0.664867i	$0.231512\pi$
$20$	−0.799102	+	1.74979i	−0.178685	+	0.391265i
$21$	1.02665	+	7.14051i	0.224033	+	1.55819i
$22$	0.717915			0.153060
$23$	−2.65025	+	3.99702i	−0.552615	+	0.833436i
$23$	−2.65025	+	3.99702i	−0.552615	+	0.833436i
$24$	−2.49454			−0.509197
$25$	−0.142315	−	0.989821i	−0.0284630	−	0.197964i
$26$	−0.00763835	+	0.0167256i	−0.00149800	+	0.00328017i
$27$	1.56205	−	0.458659i	0.300617	−	0.0882690i
$28$	−3.95019	+	4.55876i	−0.746515	+	0.861524i
$29$	−9.93501	−	2.91718i	−1.84488	−	0.541707i	−0.999977	−	0.00679455i	$-0.997837\pi$
$29$	−9.93501	−	2.91718i	−1.84488	−	0.541707i	−0.844908	−	0.534912i	$-0.820345\pi$
$30$	0.534849	−	0.343726i	0.0976495	−	0.0627556i
$31$	3.45291	+	7.56083i	0.620162	+	1.35796i	0.915402	+	0.402541i	$0.131873\pi$
$31$	3.45291	+	7.56083i	0.620162	+	1.35796i	−0.295240	+	0.955423i	$0.595400\pi$
$32$	−2.06223	−	2.37994i	−0.364554	−	0.420718i
$33$	5.02740	+	3.23091i	0.875158	+	0.562430i
$34$	−0.0583060	+	0.405527i	−0.00999939	+	0.0695473i
$35$	0.446271	−	3.10388i	0.0754336	−	0.524652i
$36$	−3.70958	−	2.38400i	−0.618263	−	0.397333i
$37$	−3.92880	−	4.53408i	−0.645891	−	0.745398i	0.334514	−	0.942391i	$-0.391428\pi$
$37$	−3.92880	−	4.53408i	−0.645891	−	0.745398i	−0.980405	+	0.196993i	$0.936882\pi$
$38$	−0.529840	−	1.16019i	−0.0859515	−	0.188207i
$39$	−0.128762	+	0.0827502i	−0.0206184	+	0.0132506i
$40$	1.04042	+	0.305495i	0.164505	+	0.0483031i
$41$	−2.55857	+	2.95275i	−0.399581	+	0.461141i	−0.919509	−	0.393069i	$-0.871413\pi$
$41$	−2.55857	+	2.95275i	−0.399581	+	0.461141i	0.519928	+	0.854210i	$0.325959\pi$
$42$	1.91291	−	0.561681i	0.295168	−	0.0866692i
$43$	3.26842	−	7.15685i	0.498430	−	1.09141i	−0.478546	−	0.878062i	$-0.658836\pi$
$43$	3.26842	−	7.15685i	0.498430	−	1.09141i	0.976976	−	0.213347i	$-0.0684366\pi$
$44$	0.711153	+	4.94618i	0.107210	+	0.745664i
$45$	2.29233			0.341721
$46$	1.19762	+	0.567772i	0.176580	+	0.0837134i
$47$	8.42088			1.22831			0.614156	−	0.789185i	$-0.289497\pi$
$47$	8.42088			1.22831			0.614156	+	0.789185i	$0.289497\pi$
$48$	−1.16146	−	8.07815i	−0.167643	−	1.16598i
$49$	1.17697	−	2.57722i	0.168139	−	0.368174i
$50$	−0.265169	+	0.0778605i	−0.0375005	+	0.0110111i
$51$	−2.23334	+	2.57741i	−0.312730	+	0.360910i
$52$	−0.122800	−	0.0360573i	−0.0170293	−	0.00500025i
$53$	−0.190337	+	0.122322i	−0.0261448	+	0.0168022i	−0.553648	−	0.832751i	$-0.686765\pi$
$53$	−0.190337	+	0.122322i	−0.0261448	+	0.0168022i	0.527503	+	0.849553i	$0.323128\pi$
$54$	−0.186903	−	0.409260i	−0.0254342	−	0.0556932i
$55$	−1.70115	−	1.96323i	−0.229383	−	0.264722i
$56$	2.86051	+	1.83834i	0.382251	+	0.245658i
$57$	1.51097	−	10.5090i	0.200133	−	1.39196i
$58$	−0.407246	+	2.83246i	−0.0534740	+	0.371920i
$59$	0.709087	+	0.455703i	0.0923153	+	0.0593274i	0.585984	−	0.810323i	$-0.300708\pi$
$59$	0.709087	+	0.455703i	0.0923153	+	0.0593274i	−0.493669	+	0.869650i	$0.664344\pi$
$60$	2.89796	+	3.34443i	0.374125	+	0.431763i
$61$	−3.25234	−	7.12164i	−0.416420	−	0.911832i	−0.995338	−	0.0964468i	$-0.969252\pi$
$61$	−3.25234	−	7.12164i	−0.416420	−	0.911832i	0.578918	−	0.815386i	$-0.303475\pi$
$62$	1.93246	−	1.24192i	0.245423	−	0.157724i
$63$	6.89712	+	2.02518i	0.868956	+	0.255148i
$64$	4.07641	−	4.70443i	0.509551	−	0.588053i
$65$	0.0638379	−	0.0187445i	0.00791812	−	0.00232497i
$66$	0.686087	−	1.50232i	0.0844514	−	0.184923i
$67$	1.42203	+	9.89044i	0.173729	+	1.20831i	0.870920	+	0.491424i	$0.163524\pi$
$67$	1.42203	+	9.89044i	0.173729	+	1.20831i	−0.697192	+	0.716885i	$0.745567\pi$
$68$	−2.85169			−0.345818
$69$	5.83147	+	9.36577i	0.702027	+	1.12751i
$70$	−0.866621			−0.103581
$71$	−1.22385	−	8.51208i	−0.145245	−	1.01020i	−0.923869	−	0.382708i	$-0.874991\pi$
$71$	−1.22385	−	8.51208i	−0.145245	−	1.01020i	0.778625	−	0.627490i	$-0.215918\pi$
$72$	−1.03259	+	2.26105i	−0.121692	+	0.266468i
$73$	−8.56020	+	2.51350i	−1.00190	+	0.294183i	−0.741234	−	0.671247i	$-0.765759\pi$
$73$	−8.56020	+	2.51350i	−1.00190	+	0.294183i	−0.260662	+	0.965430i	$0.583941\pi$
$74$	−1.08578	+	1.25305i	−0.126219	+	0.145664i
$75$	−2.20732	−	0.648128i	−0.254879	−	0.0748393i
$76$	7.46843	−	4.79967i	0.856688	−	0.550560i
$77$	−3.38395	−	7.40981i	−0.385637	−	0.844426i
$78$	0.0277006	+	0.0319682i	0.00313648	+	0.00361969i
$79$	−12.5251	−	8.04939i	−1.40918	−	0.905627i	−0.409206	−	0.912442i	$-0.634194\pi$
$79$	−12.5251	−	8.04939i	−1.40918	−	0.905627i	−0.999977	+	0.00681550i	$0.997831\pi$
$80$	−0.504872	+	3.51146i	−0.0564464	+	0.392594i
$81$	1.51170	−	10.5141i	0.167966	−	1.16823i
$82$	0.908355	+	0.583764i	0.100311	+	0.0644660i
$83$	−5.87671	−	6.78209i	−0.645053	−	0.744431i	0.335207	−	0.942145i	$-0.391194\pi$
$83$	−5.87671	−	6.78209i	−0.645053	−	0.744431i	−0.980260	+	0.197714i	$0.936648\pi$
$84$	5.76467	+	12.6229i	0.628977	+	1.37727i
$85$	1.24712	−	0.801477i	0.135269	−	0.0869324i
$86$	−2.08631	−	0.612595i	−0.224972	−	0.0660579i
$87$	−15.5991	+	18.0023i	−1.67240	+	1.93005i
$88$	2.70273	−	0.793593i	0.288112	−	0.0845973i
$89$	0.984223	−	2.15515i	0.104327	−	0.228445i	−0.850268	−	0.526350i	$-0.823560\pi$
$89$	0.984223	−	2.15515i	0.104327	−	0.228445i	0.954596	+	0.297904i	$0.0962876\pi$
$90$	−0.0901588	−	0.627068i	−0.00950357	−	0.0660988i
$91$	0.208634			0.0218708
$92$	−2.72540	+	8.81361i	−0.284143	+	0.918882i
$93$	19.1217			1.98283
$94$	−0.331198	−	2.30353i	−0.0341605	−	0.237591i
$95$	−1.91719	+	4.19806i	−0.196699	+	0.430711i
$96$	−6.95110	+	2.04103i	−0.709443	+	0.208311i
$97$	5.06792	−	5.84870i	0.514570	−	0.593845i	−0.437693	−	0.899124i	$-0.644204\pi$
$97$	5.06792	−	5.84870i	0.514570	−	0.593845i	0.952263	+	0.305279i	$0.0987498\pi$
$98$	−0.751289	−	0.220598i	−0.0758917	−	0.0222838i
$99$	5.00953	−	3.21943i	0.503477	−	0.323565i
$100$	−0.799102	−	1.74979i	−0.0799102	−	0.174979i
$101$	6.39605	+	7.38144i	0.636431	+	0.734481i	0.978740	−	0.205107i	$-0.0657542\pi$
$101$	6.39605	+	7.38144i	0.636431	+	0.734481i	−0.342308	+	0.939588i	$0.611209\pi$
$102$	0.792891	+	0.509560i	0.0785079	+	0.0504539i
$103$	−1.81971	+	12.6564i	−0.179301	+	1.24707i	0.679083	+	0.734061i	$0.262378\pi$
$103$	−1.81971	+	12.6564i	−0.179301	+	1.24707i	−0.858385	+	0.513007i	$0.828532\pi$
$104$	−0.0102673	+	0.0714104i	−0.00100679	+	0.00700236i
$105$	−6.06875	−	3.90015i	−0.592249	−	0.380615i
$106$	0.0409473	+	0.0472557i	0.00397715	+	0.00458988i
$107$	4.40067	+	9.63613i	0.425429	+	0.931560i	0.994046	+	0.108957i	$0.0347512\pi$
$107$	4.40067	+	9.63613i	0.425429	+	0.931560i	−0.568617	+	0.822602i	$0.692522\pi$
$108$	2.63451	−	1.69310i	0.253506	−	0.162918i
$109$	5.06703	+	1.48781i	0.485333	+	0.142507i	0.515240	−	0.857046i	$-0.327703\pi$
$109$	5.06703	+	1.48781i	0.485333	+	0.142507i	−0.0299066	+	0.999553i	$0.509521\pi$
$110$	−0.470135	+	0.542564i	−0.0448256	+	0.0517315i
$111$	−13.2427	+	3.88841i	−1.25694	+	0.369071i
$112$	−4.62128	+	10.1192i	−0.436670	+	0.956173i
$113$	−1.39643	−	9.71237i	−0.131365	−	0.913663i	−0.943778	−	0.330580i	$-0.892756\pi$
$113$	−1.39643	−	9.71237i	−0.131365	−	0.913663i	0.812413	−	0.583082i	$-0.198154\pi$
$114$	−2.93418			−0.274811
$115$	−1.28520	−	4.62042i	−0.119846	−	0.430856i
$116$	−19.9180			−1.84934
$117$	0.0217052	+	0.150963i	0.00200665	+	0.0139566i
$118$	0.0967688	−	0.211894i	0.00890829	−	0.0195064i
$119$	4.46039	−	1.30969i	0.408883	−	0.120059i
$120$	1.63358	−	1.88525i	0.149125	−	0.172099i
$121$	4.07960	+	1.19788i	0.370873	+	0.108898i
$122$	−1.82021	+	1.16978i	−0.164794	+	0.105907i
$123$	3.73382	+	8.17593i	0.336668	+	0.737199i
$124$	10.4706	+	12.0837i	0.940290	+	1.08515i
$125$	0.841254	+	0.540641i	0.0752440	+	0.0483564i
$126$	0.282720	−	1.96636i	0.0251867	−	0.175177i
$127$	−1.56839	+	10.9084i	−0.139172	+	0.967961i	0.793843	+	0.608123i	$0.208077\pi$
$127$	−1.56839	+	10.9084i	−0.139172	+	0.967961i	−0.933015	+	0.359838i	$0.882832\pi$
$128$	−6.74563	−	4.33515i	−0.596235	−	0.383177i
$129$	−11.8530	−	13.6791i	−1.04360	−	1.20438i
$130$	−0.00763835	−	0.0167256i	−0.000669927	−	0.00146694i
$131$	16.3828	−	10.5286i	1.43138	−	0.919889i	0.431534	−	0.902097i	$-0.357973\pi$
$131$	16.3828	−	10.5286i	1.43138	−	0.919889i	0.999842	−	0.0177925i	$-0.00566382\pi$
$132$	11.0301	+	3.23872i	0.960044	+	0.281894i
$133$	−9.47720	+	10.9373i	−0.821777	+	0.948382i
$134$	2.64960	−	0.777994i	0.228891	−	0.0672084i
$135$	−0.676293	+	1.48088i	−0.0582061	+	0.127454i
$136$	0.228771	+	1.59113i	0.0196169	+	0.136439i
$137$	−1.63434			−0.139631			−0.0698156	−	0.997560i	$-0.522241\pi$
$137$	−1.63434			−0.139631			−0.0698156	+	0.997560i	$0.522241\pi$
$138$	2.33265	−	1.96356i	0.198569	−	0.167150i
$139$	4.91600			0.416970			0.208485	−	0.978026i	$-0.433147\pi$
$139$	4.91600			0.416970			0.208485	+	0.978026i	$0.433147\pi$
$140$	−0.858457	−	5.97070i	−0.0725529	−	0.504616i
$141$	8.04754	−	17.6216i	0.677725	−	1.48401i
$142$	−2.28035	+	0.669570i	−0.191363	+	0.0561891i
$143$	0.113182	−	0.130619i	0.00946478	−	0.0109229i
$144$	−7.80280	−	2.29111i	−0.650234	−	0.190926i
$145$	8.71070	−	5.59803i	0.723385	−	0.464891i
$146$	1.02425	+	2.24279i	0.0847673	+	0.185614i
$147$	−4.26833	−	4.92591i	−0.352046	−	0.406282i
$148$	−9.70863	−	6.23936i	−0.798045	−	0.512872i
$149$	−1.10401	+	7.67859i	−0.0904444	+	0.629055i	0.893297	+	0.449466i	$0.148386\pi$
$149$	−1.10401	+	7.67859i	−0.0904444	+	0.629055i	−0.983742	+	0.179589i	$0.942523\pi$
$150$	−0.0904803	+	0.629304i	−0.00738769	+	0.0513825i
$151$	−7.73630	−	4.97182i	−0.629571	−	0.404601i	0.186580	−	0.982440i	$-0.440260\pi$
$151$	−7.73630	−	4.97182i	−0.629571	−	0.404601i	−0.816151	+	0.577839i	$0.803896\pi$
$152$	−3.27717	−	3.78206i	−0.265814	−	0.306765i
$153$	1.41170	+	3.09119i	0.114129	+	0.249908i
$154$	−1.89386	+	1.21711i	−0.152612	+	0.0980777i
$155$	−7.97527	−	2.34175i	−0.640589	−	0.188094i
$156$	−0.192810	+	0.222514i	−0.0154371	+	0.0178154i
$157$	21.3140	−	6.25834i	1.70104	−	0.499470i	0.720114	−	0.693856i	$-0.244089\pi$
$157$	21.3140	−	6.25834i	1.70104	−	0.499470i	0.980925	+	0.194386i	$0.0622713\pi$
$158$	−1.70929	+	3.74283i	−0.135984	+	0.297764i
$159$	0.0740746	+	0.515201i	0.00587450	+	0.0408581i
$160$	3.14911			0.248959
$161$	0.215052	−	15.0372i	0.0169485	−	1.18510i
$162$	−2.93559			−0.230642
$163$	0.883172	+	6.14260i	0.0691754	+	0.481125i	0.994731	+	0.102515i	$0.0326889\pi$
$163$	0.883172	+	6.14260i	0.0691754	+	0.481125i	−0.925556	+	0.378611i	$0.876402\pi$
$164$	−3.12213	+	6.83650i	−0.243797	+	0.533841i
$165$	−5.73401	+	1.68366i	−0.446392	+	0.131072i
$166$	−1.62411	+	1.87432i	−0.126055	+	0.145475i
$167$	18.9238	+	5.55653i	1.46437	+	0.429977i	0.914264	−	0.405118i	$-0.132770\pi$
$167$	18.9238	+	5.55653i	1.46437	+	0.429977i	0.550104	+	0.835096i	$0.314588\pi$
$168$	6.58062	−	4.22911i	0.507706	−	0.326283i
$169$	−5.39856	−	11.8212i	−0.415274	−	0.909322i
$170$	−0.268295	−	0.309628i	−0.0205772	−	0.0237474i
$171$	−8.89994	−	5.71964i	−0.680595	−	0.437392i
$172$	2.15390	−	14.9807i	0.164234	−	1.14227i
$173$	−0.883039	+	6.14167i	−0.0671362	+	0.466943i	0.928325	+	0.371771i	$0.121249\pi$
$173$	−0.883039	+	6.14167i	−0.0671362	+	0.466943i	−0.995461	+	0.0951721i	$0.969660\pi$
$174$	5.53805	+	3.55909i	0.419839	+	0.269814i
$175$	2.05351	+	2.36988i	0.155231	+	0.179146i
$176$	3.82830	+	8.38282i	0.288569	+	0.631879i
$177$	1.63126	−	1.04835i	0.122613	−	0.0787986i
$178$	−0.628252	−	0.184471i	−0.0470894	−	0.0138267i
$179$	−4.07334	+	4.70088i	−0.304455	+	0.351360i	−0.887275	−	0.461242i	$-0.847404\pi$
$179$	−4.07334	+	4.70088i	−0.304455	+	0.351360i	0.582819	+	0.812602i	$0.301950\pi$
$180$	4.23096	−	1.24232i	0.315357	−	0.0925973i
$181$	−8.12766	+	17.7971i	−0.604124	+	1.32285i	0.322397	+	0.946605i	$0.395511\pi$
$181$	−8.12766	+	17.7971i	−0.604124	+	1.32285i	−0.926521	+	0.376243i	$0.877216\pi$
$182$	−0.00820570	−	0.0570719i	−0.000608247	−	0.00423045i
$183$	−18.0110			−1.33141
$184$	5.13630	+	0.813617i	0.378653	+	0.0599806i
$185$	5.99944			0.441088
$186$	−0.752069	−	5.23075i	−0.0551444	−	0.383538i
$187$	1.59977	−	3.50301i	0.116987	−	0.256165i
$188$	15.5424	−	4.56367i	1.13355	−	0.332840i
$189$	−3.34311	+	3.85815i	−0.243175	+	0.280639i
$190$	1.22378	+	0.359335i	0.0887826	+	0.0260689i
$191$	16.2234	−	10.4261i	1.17388	−	0.754407i	0.199629	−	0.979871i	$-0.436026\pi$
$191$	16.2234	−	10.4261i	1.17388	−	0.754407i	0.974251	+	0.225464i	$0.0723898\pi$
$192$	−5.94887	−	13.0262i	−0.429323	−	0.940086i
$193$	6.97279	+	8.04703i	0.501912	+	0.579238i	0.949009	−	0.315248i	$-0.102088\pi$
$193$	6.97279	+	8.04703i	0.501912	+	0.579238i	−0.447097	+	0.894485i	$0.647542\pi$
$194$	−1.79924	−	1.15630i	−0.129178	−	0.0830175i
$195$	0.0217826	−	0.151502i	0.00155989	−	0.0108493i
$196$	0.775631	−	5.39463i	0.0554022	−	0.385331i
$197$	3.66483	+	2.35524i	0.261108	+	0.167804i	0.664645	−	0.747159i	$-0.268583\pi$
$197$	3.66483	+	2.35524i	0.261108	+	0.167804i	−0.403537	+	0.914963i	$0.632219\pi$
$198$	−1.07770	−	1.24374i	−0.0765891	−	0.0883886i
$199$	−6.56561	−	14.3767i	−0.465424	−	1.01914i	−0.986218	−	0.165453i	$-0.947091\pi$
$199$	−6.56561	−	14.3767i	−0.465424	−	1.01914i	0.520794	−	0.853682i	$-0.325636\pi$
$200$	−0.912210	+	0.586242i	−0.0645030	+	0.0414535i
$201$	22.0559	+	6.47618i	1.55570	+	0.456795i
$202$	1.76763	−	2.03996i	0.124370	−	0.143531i
$203$	31.1542	−	9.14770i	2.18660	−	0.642043i
$204$	−2.72526	+	5.96749i	−0.190806	+	0.417808i
$205$	−0.556030	−	3.86727i	−0.0388348	−	0.270102i
$206$	3.53372			0.246206
$207$	10.9030	−	1.40879i	0.757811	−	0.0979177i
$208$	−0.236030			−0.0163658
$209$	1.70618	+	11.8668i	0.118019	+	0.820841i
$210$	−0.828199	+	1.81350i	−0.0571512	+	0.125144i
$211$	−19.7641	+	5.80325i	−1.36061	+	0.399513i	−0.878980	−	0.476859i	$-0.841775\pi$
$211$	−19.7641	+	5.80325i	−1.36061	+	0.399513i	−0.481635	+	0.876372i	$0.659957\pi$
$212$	−0.285013	+	0.328923i	−0.0195748	+	0.0225905i
$213$	−18.9821	−	5.57365i	−1.30063	−	0.381900i
$214$	2.46288	−	1.58280i	0.168359	−	0.108198i
$215$	3.26842	+	7.15685i	0.222905	+	0.488093i
$216$	−1.15603	−	1.33413i	−0.0786580	−	0.0907762i
$217$	−21.9270	−	14.0916i	−1.48850	−	0.956601i
$218$	0.207703	−	1.44460i	0.0140674	−	0.0978409i
$219$	−2.92089	+	20.3153i	−0.197376	+	1.37278i
$220$	−4.20378	−	2.70160i	−0.283419	−	0.182142i
$221$	0.0645904	+	0.0745413i	0.00434482	+	0.00501419i
$222$	1.58452	+	3.46961i	0.106346	+	0.232865i
$223$	−18.1838	+	11.6860i	−1.21768	+	0.782554i	−0.981927	−	0.189260i	$-0.939391\pi$
$223$	−18.1838	+	11.6860i	−1.21768	+	0.782554i	−0.235751	+	0.971814i	$0.575755\pi$
$224$	9.47498	+	2.78210i	0.633074	+	0.185887i
$225$	−1.50116	+	1.73243i	−0.100077	+	0.115495i
$226$	−2.60190	+	0.763987i	−0.173076	+	0.0508196i
$227$	3.73531	−	8.17919i	0.247921	−	0.542872i	−0.744229	−	0.667925i	$-0.767183\pi$
$227$	3.73531	−	8.17919i	0.247921	−	0.542872i	0.992150	+	0.125053i	$0.0399101\pi$
$228$	−2.90654	−	20.2154i	−0.192490	−	1.33880i
$229$	5.95956			0.393819			0.196909	−	0.980422i	$-0.436910\pi$
$229$	5.95956			0.393819			0.196909	+	0.980422i	$0.436910\pi$
$230$	−1.21337	+	0.533291i	−0.0800072	+	0.0351642i
$231$	−18.7398			−1.23299
$232$	1.59788	+	11.1135i	0.104906	+	0.729637i
$233$	−1.20492	+	2.63841i	−0.0789371	+	0.172848i	−0.944986	−	0.327112i	$-0.893925\pi$
$233$	−1.20492	+	2.63841i	−0.0789371	+	0.172848i	0.866049	+	0.499960i	$0.166652\pi$
$234$	0.0404424	−	0.0118749i	0.00264380	−	0.000776290i
$235$	−5.51450	+	6.36407i	−0.359726	+	0.415146i
$236$	1.55573	+	0.456804i	0.101269	+	0.0297354i
$237$	−28.8141	+	18.5177i	−1.87167	+	1.20285i
$238$	−0.533696	−	1.16863i	−0.0345943	−	0.0757510i
$239$	−3.74380	−	4.32058i	−0.242167	−	0.279475i	0.621635	−	0.783307i	$-0.286469\pi$
$239$	−3.74380	−	4.32058i	−0.242167	−	0.279475i	−0.863802	+	0.503832i	$0.831923\pi$
$240$	6.86565	+	4.41229i	0.443176	+	0.284812i
$241$	−3.26674	+	22.7207i	−0.210429	+	1.46357i	0.561297	+	0.827614i	$0.310302\pi$
$241$	−3.26674	+	22.7207i	−0.210429	+	1.46357i	−0.771727	+	0.635954i	$0.780607\pi$
$242$	0.167227	−	1.16309i	0.0107498	−	0.0747663i
$243$	−16.4486	−	10.5709i	−1.05518	−	0.678122i
$244$	−9.86241	−	11.3818i	−0.631376	−	0.728647i
$245$	1.17697	+	2.57722i	0.0751942	+	0.164652i
$246$	2.08968	−	1.34295i	0.133233	−	0.0856236i
$247$	−0.294619	−	0.0865080i	−0.0187462	−	0.00550437i
$248$	5.90229	−	6.81160i	0.374795	−	0.432537i
$249$	−19.8085	+	5.81629i	−1.25531	+	0.368592i
$250$	0.114805	−	0.251389i	0.00726094	−	0.0158992i
$251$	2.89077	+	20.1057i	0.182464	+	1.26906i	0.850914	+	0.525305i	$0.176049\pi$
$251$	2.89077	+	20.1057i	0.182464	+	1.26906i	−0.668450	+	0.743757i	$0.733042\pi$
$252$	13.8276			0.871056
$253$	−9.29769	−	8.29222i	−0.584540	−	0.521327i
$254$	3.04567			0.191103
$255$	−0.485351	−	3.37569i	−0.0303939	−	0.211394i
$256$	4.25122	−	9.30887i	0.265701	−	0.581804i
$257$	−22.6095	+	6.63876i	−1.41034	+	0.414115i	−0.896223	−	0.443603i	$-0.853700\pi$
$257$	−22.6095	+	6.63876i	−1.41034	+	0.414115i	−0.514121	+	0.857717i	$0.671882\pi$
$258$	−3.27574	+	3.78040i	−0.203939	+	0.235358i
$259$	18.0510	+	5.30025i	1.12163	+	0.329342i
$260$	0.107667	−	0.0691935i	0.00667724	−	0.00429120i
$261$	9.86021	+	21.5908i	0.610332	+	1.33644i
$262$	−3.52445	−	4.06744i	−0.217741	−	0.251287i
$263$	23.9371	+	15.3834i	1.47602	+	0.948582i	0.997512	+	0.0705003i	$0.0224596\pi$
$263$	23.9371	+	15.3834i	1.47602	+	0.948582i	0.478511	+	0.878082i	$0.341177\pi$
$264$	0.922220	−	6.41418i	0.0567587	−	0.394765i
$265$	0.0321993	−	0.223951i	0.00197799	−	0.0137572i
$266$	3.36464	+	2.16232i	0.206299	+	0.132580i
$267$	−3.56931	−	4.11920i	−0.218438	−	0.252091i
$268$	7.98474	+	17.4841i	0.487746	+	1.06801i
$269$	10.0570	−	6.46323i	0.613185	−	0.394070i	−0.196865	−	0.980431i	$-0.563076\pi$
$269$	10.0570	−	6.46323i	0.613185	−	0.394070i	0.810050	+	0.586360i	$0.199440\pi$
$270$	0.431693	+	0.126757i	0.0262720	+	0.00771416i
$271$	−2.96267	+	3.41910i	−0.179969	+	0.207696i	−0.838565	−	0.544801i	$-0.816605\pi$
$271$	−2.96267	+	3.41910i	−0.179969	+	0.207696i	0.658596	+	0.752497i	$0.271151\pi$
$272$	−5.04610	+	1.48167i	−0.305965	+	0.0898393i
$273$	0.199384	−	0.436591i	0.0120673	−	0.0264237i
$274$	0.0642796	+	0.447075i	0.00388328	+	0.0270088i
$275$	2.59772			0.156649
$276$	15.8389	+	14.1261i	0.953391	+	0.850290i
$277$	10.9489			0.657855			0.328928	−	0.944355i	$-0.393313\pi$
$277$	10.9489			0.657855			0.328928	+	0.944355i	$0.393313\pi$
$278$	−0.193349	−	1.34477i	−0.0115963	−	0.0806542i
$279$	7.91522	−	17.3319i	0.473872	−	1.03764i
$280$	−3.26256	+	0.957973i	−0.194975	+	0.0572498i
$281$	−1.91116	+	2.20560i	−0.114011	+	0.131575i	−0.809886	−	0.586587i	$-0.800471\pi$
$281$	−1.91116	+	2.20560i	−0.114011	+	0.131575i	0.695875	+	0.718162i	$0.255017\pi$
$282$	−5.13692	−	1.50834i	−0.305899	−	0.0898201i
$283$	12.7349	−	8.18424i	0.757013	−	0.486503i	−0.104320	−	0.994544i	$-0.533267\pi$
$283$	12.7349	−	8.18424i	0.757013	−	0.486503i	0.861333	+	0.508041i	$0.169630\pi$
$284$	−6.87197	−	15.0475i	−0.407776	−	0.892905i
$285$	6.95272	+	8.02387i	0.411844	+	0.475293i
$286$	−0.0401825	−	0.0258237i	−0.00237604	−	0.00152699i
$287$	1.74360	−	12.1270i	0.102921	−	0.715834i
$288$	−1.02734	+	7.14533i	−0.0605368	+	0.421043i
$289$	−12.4525	−	8.00274i	−0.732500	−	0.470749i
$290$	−1.87394	−	2.16264i	−0.110042	−	0.126995i
$291$	−7.39583	−	16.1946i	−0.433551	−	0.949345i
$292$	−14.4374	+	9.27835i	−0.844885	+	0.542975i
$293$	2.26052	+	0.663749i	0.132061	+	0.0387766i	0.347095	−	0.937830i	$-0.387168\pi$
$293$	2.26052	+	0.663749i	0.132061	+	0.0387766i	−0.215034	+	0.976607i	$0.568986\pi$
$294$	−1.17961	+	1.36134i	−0.0687962	+	0.0793950i
$295$	−0.808751	+	0.237471i	−0.0470873	+	0.0138261i
$296$	−2.70247	+	5.91759i	−0.157078	+	0.343953i
$297$	0.601861	+	4.18603i	0.0349235	+	0.242898i
$298$	2.14390			0.124193
$299$	0.292112	−	0.128387i	0.0168933	−	0.00742481i
$300$	−4.42531			−0.255495
$301$	3.51120	+	24.4209i	0.202382	+	1.40760i
$302$	−1.05577	+	2.31181i	−0.0607527	+	0.133030i
$303$	21.5590	−	6.33029i	1.23853	−	0.363666i
$304$	10.7217	−	12.3735i	0.614931	−	0.709668i
$305$	7.51201	+	2.20572i	0.430136	+	0.126299i
$306$	0.790073	−	0.507749i	0.0451655	−	0.0290261i
$307$	1.40309	+	3.07233i	0.0800783	+	0.175347i	0.945436	−	0.325807i	$-0.105636\pi$
$307$	1.40309	+	3.07233i	0.0800783	+	0.175347i	−0.865358	+	0.501154i	$0.832909\pi$
$308$	−10.2615	−	11.8424i	−0.584703	−	0.674783i
$309$	24.7458	+	15.9032i	1.40774	+	0.904701i
$310$	−0.326914	+	2.27374i	−0.0185675	+	0.129140i
$311$	4.80765	−	33.4380i	0.272617	−	1.89609i	−0.148217	−	0.988955i	$-0.547354\pi$
$311$	4.80765	−	33.4380i	0.272617	−	1.89609i	0.420834	−	0.907137i	$-0.361737\pi$
$312$	0.139622	+	0.0897298i	0.00790456	+	0.00507995i
$313$	4.97550	+	5.74203i	0.281232	+	0.324559i	0.878737	−	0.477306i	$-0.158387\pi$
$313$	4.97550	+	5.74203i	0.281232	+	0.324559i	−0.597505	+	0.801865i	$0.703841\pi$
$314$	−2.55026	−	5.58430i	−0.143920	−	0.315140i
$315$	−6.04718	+	3.88629i	−0.340720	+	0.218967i
$316$	−27.4799	−	8.06884i	−1.54587	−	0.453908i
$317$	10.6443	−	12.2842i	0.597846	−	0.689951i	−0.373498	−	0.927631i	$-0.621842\pi$
$317$	10.6443	−	12.2842i	0.597846	−	0.689951i	0.971343	+	0.237680i	$0.0763871\pi$
$318$	0.138020	−	0.0405263i	0.00773977	−	0.00227260i
$319$	11.1738	−	24.4672i	0.625613	−	1.36990i
$320$	0.885888	+	6.16149i	0.0495227	+	0.344438i
$321$	24.3703			1.36022
$322$	−4.12190	+	0.532596i	−0.229704	+	0.0296804i
$323$	−6.84171			−0.380683
$324$	−2.90794	−	20.2252i	−0.161552	−	1.12362i
$325$	−0.0276388	+	0.0605205i	−0.00153312	+	0.00335707i
$326$	1.64557	−	0.483184i	0.0911399	−	0.0267611i
$327$	7.95580	−	9.18149i	0.439957	−	0.507737i
$328$	4.06497	+	1.19358i	0.224451	+	0.0659046i
$329$	−22.2143	+	14.2763i	−1.22471	+	0.787076i
$330$	0.686087	+	1.50232i	0.0377678	+	0.0827000i
$331$	7.49017	+	8.64412i	0.411697	+	0.475124i	0.923290	−	0.384104i	$-0.125490\pi$
$331$	7.49017	+	8.64412i	0.411697	+	0.475124i	−0.511593	+	0.859228i	$0.670944\pi$
$332$	−14.5222	−	9.33285i	−0.797009	−	0.512207i
$333$	−1.95722	+	13.6127i	−0.107255	+	0.745973i
$334$	0.775707	−	5.39516i	0.0424448	−	0.295210i
$335$	−8.40593	−	5.40216i	−0.459265	−	0.295152i
$336$	16.7592	+	19.3411i	0.914288	+	1.05514i
$337$	−9.93247	−	21.7491i	−0.541056	−	1.18475i	−0.960835	−	0.277122i	$-0.910620\pi$
$337$	−9.93247	−	21.7491i	−0.541056	−	1.18475i	0.419779	−	0.907627i	$-0.362108\pi$
$338$	−3.02136	+	1.94171i	−0.164340	+	0.105615i
$339$	−21.6588	−	6.35959i	−1.17634	−	0.345405i
$340$	1.86746	−	2.15516i	0.101277	−	0.116880i
$341$	−20.7175	+	6.08322i	−1.12192	+	0.329425i
$342$	−1.21457	+	2.65954i	−0.0656764	+	0.143811i
$343$	−1.85950	−	12.9331i	−0.100404	−	0.698322i
$344$	−8.53147			−0.459986
$345$	−10.8970	−	1.72614i	−0.586673	−	0.0929322i
$346$	1.71479			0.0921875
$347$	0.129352	+	0.899663i	0.00694398	+	0.0482964i	0.992999	−	0.118124i	$-0.0376881\pi$
$347$	0.129352	+	0.899663i	0.00694398	+	0.0482964i	−0.986055	+	0.166421i	$0.946779\pi$
$348$	−19.0350	+	41.6808i	−1.02038	+	2.23432i
$349$	14.5628	−	4.27601i	0.779527	−	0.228890i	0.132323	−	0.991207i	$-0.457756\pi$
$349$	14.5628	−	4.27601i	0.779527	−	0.228890i	0.647204	+	0.762317i	$0.275938\pi$
$350$	0.567516	−	0.654948i	0.0303350	−	0.0350084i
$351$	−0.103928	−	0.0305159i	−0.00554725	−	0.00162882i
$352$	6.88189	−	4.42272i	0.366806	−	0.235732i
$353$	−11.6955	−	25.6097i	−0.622491	−	1.36306i	−0.913694	−	0.406403i	$-0.866783\pi$
$353$	−11.6955	−	25.6097i	−0.622491	−	1.36306i	0.291203	−	0.956661i	$-0.405944\pi$
$354$	−0.350934	−	0.405000i	−0.0186519	−	0.0215255i
$355$	7.23445	+	4.64930i	0.383965	+	0.246759i
$356$	0.648607	−	4.51116i	0.0343761	−	0.239091i
$357$	1.52197	−	10.5855i	0.0805509	−	0.560244i
$358$	1.44613	+	0.929374i	0.0764306	+	0.0491189i
$359$	2.59360	+	2.99317i	0.136885	+	0.157974i	0.820053	−	0.572288i	$-0.193944\pi$
$359$	2.59360	+	2.99317i	0.136885	+	0.157974i	−0.683168	+	0.730261i	$0.739398\pi$
$360$	−1.03259	−	2.26105i	−0.0544222	−	0.119168i
$361$	1.93428	−	1.24309i	0.101804	−	0.0654257i
$362$	5.18807	+	1.52335i	0.272679	+	0.0800657i
$363$	6.40544	−	7.39227i	0.336198	−	0.387993i
$364$	0.385077	−	0.113069i	0.0201835	−	0.00592641i
$365$	3.70616	−	8.11536i	0.193989	−	0.424777i
$366$	0.708383	+	4.92691i	0.0370278	+	0.257534i
$367$	−9.22073			−0.481318			−0.240659	−	0.970610i	$-0.577364\pi$
$367$	−9.22073			−0.481318			−0.240659	+	0.970610i	$0.577364\pi$
$368$	−0.243291	+	17.0118i	−0.0126824	+	0.886803i
$369$	8.95624			0.466243
$370$	−0.235962	−	1.64115i	−0.0122671	−	0.0853193i
$371$	0.294732	−	0.645372i	0.0153017	−	0.0335060i
$372$	35.2930	−	10.3630i	1.82986	−	0.537295i
$373$	0.867034	−	1.00061i	0.0448933	−	0.0518096i	−0.732859	−	0.680381i	$-0.761814\pi$
$373$	0.867034	−	1.00061i	0.0448933	−	0.0518096i	0.777752	+	0.628571i	$0.216360\pi$
$374$	−1.02117	−	0.299842i	−0.0528034	−	0.0155045i
$375$	1.93531	−	1.24375i	0.0999390	−	0.0642269i
$376$	−3.79321	−	8.30598i	−0.195620	−	0.428348i
$377$	0.451141	+	0.520644i	0.0232349	+	0.0268145i
$378$	1.18689	+	0.762765i	0.0610468	+	0.0392324i
$379$	−0.452623	+	3.14806i	−0.0232497	+	0.161705i	−0.998139	−	0.0609867i	$-0.980575\pi$
$379$	−0.452623	+	3.14806i	−0.0232497	+	0.161705i	0.974889	+	0.222692i	$0.0714844\pi$
$380$	−1.26343	+	8.78738i	−0.0648128	+	0.450783i
$381$	21.3282	+	13.7068i	1.09267	+	0.702219i
$382$	−3.49014	−	4.02784i	−0.178571	−	0.206082i
$383$	0.341123	+	0.746955i	0.0174306	+	0.0381676i	0.918147	−	0.396240i	$-0.129685\pi$
$383$	0.341123	+	0.746955i	0.0174306	+	0.0381676i	−0.900717	+	0.434407i	$0.856958\pi$
$384$	−15.5184	+	9.97304i	−0.791918	+	0.508935i
$385$	7.81598	+	2.29498i	0.398339	+	0.116963i
$386$	1.92702	−	2.22390i	0.0980829	−	0.113194i
$387$	−17.3052	+	5.08125i	−0.879671	+	0.258295i
$388$	6.18420	−	13.5415i	0.313955	−	0.687466i
$389$	0.0969073	+	0.674005i	0.00491340	+	0.0341734i	0.992131	−	0.125207i	$-0.0399595\pi$
$389$	0.0969073	+	0.674005i	0.00491340	+	0.0341734i	−0.987217	+	0.159380i	$0.949050\pi$
$390$	−0.0423000			−0.00214195
$391$	5.43912	−	4.57850i	0.275068	−	0.231545i
$392$	−3.07222			−0.155171
$393$	−6.37582	−	44.3448i	−0.321618	−	2.23690i
$394$	0.500137	−	1.09515i	0.0251966	−	0.0551728i
$395$	14.2855	−	4.19460i	0.718782	−	0.211053i
$396$	7.50135	−	8.65702i	0.376957	−	0.435032i
$397$	−2.18545	−	0.641707i	−0.109685	−	0.0322063i	0.226430	−	0.974028i	$-0.427295\pi$
$397$	−2.18545	−	0.641707i	−0.109685	−	0.0322063i	−0.336114	+	0.941821i	$0.609113\pi$
$398$	−3.67452	+	2.36147i	−0.184187	+	0.118370i
$399$	13.8305	+	30.2845i	0.692389	+	1.51612i
$400$	−2.32317	−	2.68108i	−0.116158	−	0.134054i
$401$	8.27709	+	5.31936i	0.413338	+	0.265636i	0.730741	−	0.682654i	$-0.239175\pi$
$401$	8.27709	+	5.31936i	0.413338	+	0.265636i	−0.317403	+	0.948291i	$0.602811\pi$
$402$	0.904092	−	6.28810i	0.0450920	−	0.313622i
$403$	0.0787028	−	0.547390i	0.00392047	−	0.0272675i
$404$	15.8056	+	10.1576i	0.786356	+	0.505361i
$405$	6.95607	+	8.02773i	0.345650	+	0.398901i
$406$	−3.72767	−	8.16246i	−0.185001	−	0.405096i
$407$	13.1109	−	8.42583i	0.649881	−	0.417653i
$408$	3.54826	+	1.04186i	0.175665	+	0.0515799i
$409$	−8.43840	+	9.73844i	−0.417252	+	0.481535i	−0.924998	−	0.379972i	$-0.875934\pi$
$409$	−8.43840	+	9.73844i	−0.417252	+	0.481535i	0.507746	+	0.861507i	$0.330479\pi$
$410$	−1.03603	+	0.304204i	−0.0511656	+	0.0150236i
$411$	−1.56188	+	3.42005i	−0.0770420	+	0.168698i
$412$	3.50044	+	24.3461i	0.172454	+	1.19944i
$413$	−2.64315			−0.130061
$414$	−0.814197	−	2.92711i	−0.0400156	−	0.143860i
$415$	8.97398			0.440516
$416$	0.0298177	+	0.207387i	0.00146194	+	0.0101680i
$417$	4.69805	−	10.2873i	0.230065	−	0.503771i
$418$	3.17905	−	0.933454i	0.155493	−	0.0456567i
$419$	−14.1784	+	16.3628i	−0.692660	+	0.799373i	−0.987741	−	0.156100i	$-0.950108\pi$
$419$	−14.1784	+	16.3628i	−0.692660	+	0.799373i	0.295081	+	0.955472i	$0.404653\pi$
$420$	−13.3148	−	3.90957i	−0.649695	−	0.190768i
$421$	−26.9215	+	17.3014i	−1.31207	+	0.843219i	−0.994472	−	0.105005i	$-0.966514\pi$
$421$	−26.9215	+	17.3014i	−1.31207	+	0.843219i	−0.317602	+	0.948224i	$0.602878\pi$
$422$	2.36482	+	5.17822i	0.115117	+	0.252072i
$423$	−12.6411	−	14.5886i	−0.614630	−	0.709321i
$424$	0.206391	+	0.132639i	0.0100232	+	0.00644154i
$425$	−0.210976	+	1.46737i	−0.0102338	+	0.0711778i
$426$	−0.778096	+	5.41177i	−0.0376989	+	0.262201i
$427$	20.6533	+	13.2731i	0.999484	+	0.642329i
$428$	13.3446	+	15.4005i	0.645036	+	0.744411i
$429$	−0.165172	−	0.361675i	−0.00797456	−	0.0174618i
$430$	1.82921	−	1.17556i	0.0882123	−	0.0566906i
$431$	−32.6625	−	9.59058i	−1.57330	−	0.461962i	−0.625339	−	0.780353i	$-0.715039\pi$
$431$	−32.6625	−	9.59058i	−1.57330	−	0.461962i	−0.947959	+	0.318391i	$0.896857\pi$
$432$	3.78210	−	4.36478i	0.181967	−	0.210001i
$433$	5.02300	−	1.47489i	0.241390	−	0.0708785i	−0.158800	−	0.987311i	$-0.550762\pi$
$433$	5.02300	−	1.47489i	0.241390	−	0.0708785i	0.400190	+	0.916432i	$0.368944\pi$
$434$	−2.99237	+	6.55237i	−0.143638	+	0.314524i
$435$	−3.39000	−	23.5780i	−0.162538	−	1.13048i
$436$	10.1585			0.486506
$437$	−6.53872	+	21.1454i	−0.312789	+	1.01152i
$438$	5.67213			0.271025
$439$	3.87411	+	26.9450i	0.184901	+	1.28601i	0.844972	+	0.534811i	$0.179617\pi$
$439$	3.87411	+	26.9450i	0.184901	+	1.28601i	−0.660071	+	0.751204i	$0.729474\pi$
$440$	−1.17015	+	2.56228i	−0.0557849	+	0.122152i
$441$	−6.23167	+	1.82978i	−0.296746	+	0.0871325i
$442$	0.0178504	−	0.0206005i	0.000849058	−	0.000979865i
$443$	−13.2521	−	3.89116i	−0.629625	−	0.184874i	−0.0486758	−	0.998815i	$-0.515500\pi$
$443$	−13.2521	−	3.89116i	−0.629625	−	0.184874i	−0.580949	+	0.813940i	$0.697318\pi$
$444$	−22.3348	+	14.3537i	−1.05996	+	0.681196i
$445$	0.984223	+	2.15515i	0.0466566	+	0.102164i
$446$	3.91190	+	4.51457i	0.185234	+	0.213771i
$447$	15.0133	+	9.64844i	0.710103	+	0.456356i
$448$	−2.77797	+	19.3212i	−0.131247	+	0.912841i
$449$	−0.774161	+	5.38441i	−0.0365349	+	0.254106i	−0.999901	−	0.0140846i	$-0.995517\pi$
$449$	−0.774161	+	5.38441i	−0.0365349	+	0.254106i	0.963366	+	0.268191i	$0.0864257\pi$
$450$	0.532948	+	0.342505i	0.0251234	+	0.0161458i
$451$	−6.64645	−	7.67042i	−0.312969	−	0.361186i
$452$	−7.84098	−	17.1694i	−0.368809	−	0.807579i
$453$	−17.7974	+	11.4377i	−0.836195	+	0.537390i
$454$	−2.38433	−	0.700103i	−0.111902	−	0.0328575i
$455$	−0.136626	+	0.157675i	−0.00640514	+	0.00739192i
$456$	−11.0463	+	3.24348i	−0.517289	+	0.151890i
$457$	3.16963	−	6.94051i	0.148269	−	0.324663i	−0.820896	−	0.571078i	$-0.806525\pi$
$457$	3.16963	−	6.94051i	0.148269	−	0.324663i	0.969164	+	0.246415i	$0.0792525\pi$
$458$	−0.234393	−	1.63024i	−0.0109525	−	0.0761761i
$459$	−2.41343			−0.112649
$460$	−4.87612	−	7.83141i	−0.227350	−	0.365141i
$461$	−30.3734			−1.41463			−0.707314	−	0.706899i	$-0.750093\pi$
$461$	−30.3734			−1.41463			−0.707314	+	0.706899i	$0.750093\pi$
$462$	0.737048	+	5.12628i	0.0342906	+	0.238496i
$463$	−9.66261	+	21.1582i	−0.449060	+	0.983304i	0.540786	+	0.841160i	$0.318127\pi$
$463$	−9.66261	+	21.1582i	−0.449060	+	0.983304i	−0.989846	+	0.142144i	$0.954601\pi$
$464$	−35.2452	+	10.3489i	−1.63622	+	0.480436i
$465$	−12.5221	+	14.4512i	−0.580697	+	0.670160i
$466$	0.769129	+	0.225837i	0.0356292	+	0.0104617i
$467$	−7.29941	+	4.69105i	−0.337776	+	0.217076i	−0.698522	−	0.715589i	$-0.746159\pi$
$467$	−7.29941	+	4.69105i	−0.337776	+	0.217076i	0.360746	+	0.932664i	$0.382522\pi$
$468$	0.121876	+	0.266870i	0.00563370	+	0.0123361i
$469$	−20.5190	−	23.6802i	−0.947479	−	1.09345i
$470$	1.95778	+	1.25819i	0.0903058	+	0.0580360i
$471$	7.27271	−	50.5828i	0.335109	−	2.33073i
$472$	0.130074	−	0.904685i	0.00598714	−	0.0416415i
$473$	17.1940	+	11.0499i	0.790579	+	0.508074i
$474$	6.19879	+	7.15378i	0.284720	+	0.328584i
$475$	−1.91719	−	4.19806i	−0.0879666	−	0.192620i
$476$	7.52277	−	4.83459i	0.344806	−	0.221593i
$477$	0.497640	+	0.146120i	0.0227854	+	0.00669039i
$478$	−1.03465	+	1.19405i	−0.0473238	+	0.0546146i
$479$	12.4980	−	3.66974i	0.571048	−	0.167675i	0.0165547	−	0.999863i	$-0.494730\pi$
$479$	12.4980	−	3.66974i	0.571048	−	0.167675i	0.554493	+	0.832188i	$0.312912\pi$
$480$	3.00949	−	6.58987i	0.137364	−	0.300785i
$481$	0.0568065	+	0.395098i	0.00259015	+	0.0180149i
$482$	6.34374			0.288949
$483$	−31.2616	−	14.8206i	−1.42245	−	0.674360i
$484$	8.17893			0.371769
$485$	1.10137	+	7.66016i	0.0500104	+	0.347830i
$486$	−2.24473	+	4.91528i	−0.101823	+	0.222962i
$487$	−5.62751	+	1.65239i	−0.255007	+	0.0748767i	−0.406737	−	0.913545i	$-0.633334\pi$
$487$	−5.62751	+	1.65239i	−0.255007	+	0.0748767i	0.151731	+	0.988422i	$0.451515\pi$
$488$	−5.55944	+	6.41593i	−0.251664	+	0.290436i
$489$	13.6981	+	4.02213i	0.619450	+	0.181887i
$490$	0.658707	−	0.423325i	0.0297574	−	0.0191239i
$491$	3.89188	+	8.52202i	0.175638	+	0.384593i	0.976893	−	0.213730i	$-0.0685612\pi$
$491$	3.89188	+	8.52202i	0.175638	+	0.384593i	−0.801255	+	0.598323i	$0.795834\pi$
$492$	11.3225	+	13.0668i	0.510456	+	0.589097i
$493$	12.9133	+	8.29884i	0.581584	+	0.373761i
$494$	−0.0120767	+	0.0839956i	−0.000543358	+	0.00377914i
$495$	−0.847463	+	5.89423i	−0.0380906	+	0.264926i
$496$	24.8063	+	15.9420i	1.11384	+	0.715818i
$497$	17.6594	+	20.3801i	0.792133	+	0.914170i
$498$	2.37013	+	5.18985i	0.106208	+	0.232563i
$499$	23.9106	−	15.3664i	1.07039	−	0.687896i	0.118069	−	0.993005i	$-0.462329\pi$
$499$	23.9106	−	15.3664i	1.07039	−	0.687896i	0.952317	+	0.305110i	$0.0986931\pi$
$500$	1.84570	+	0.541947i	0.0825423	+	0.0242366i
$501$	29.7125	−	34.2901i	1.32746	−	1.53197i
$502$	5.38623	−	1.58154i	0.240399	−	0.0705876i
$503$	6.89847	−	15.1055i	0.307588	−	0.673523i	−0.691204	−	0.722659i	$-0.742920\pi$
$503$	6.89847	−	15.1055i	0.307588	−	0.673523i	0.998792	+	0.0491363i	$0.0156469\pi$
$504$	−1.10929	−	7.71526i	−0.0494116	−	0.343665i
$505$	−9.76704			−0.434628
$506$	−1.90266	+	2.86952i	−0.0845834	+	0.127566i
$507$	−29.8964			−1.32775
$508$	3.01698	+	20.9836i	0.133857	+	0.930996i
$509$	4.01449	−	8.79052i	0.177939	−	0.389633i	−0.799555	−	0.600592i	$-0.794932\pi$
$509$	4.01449	−	8.79052i	0.177939	−	0.389633i	0.977495	+	0.210959i	$0.0676588\pi$
$510$	−0.904333	+	0.265536i	−0.0400445	+	0.0117581i
$511$	18.3206	−	21.1431i	0.810455	−	0.935315i
$512$	−18.1011	−	5.31497i	−0.799964	−	0.234891i
$513$	6.32066	−	4.06204i	0.279064	−	0.179344i
$514$	2.70528	+	5.92374i	0.119325	+	0.261285i
$515$	−8.37338	−	9.66340i	−0.368975	−	0.425820i
$516$	−29.2905	−	18.8239i	−1.28944	−	0.828674i
$517$	−3.11315	+	21.6524i	−0.136916	+	0.952274i
$518$	0.739929	−	5.14632i	0.0325106	−	0.226116i
$519$	12.0083	+	7.71724i	0.527104	+	0.338749i
$520$	−0.0472447	−	0.0545233i	−0.00207182	−	0.00239101i
$521$	0.754424	+	1.65196i	0.0330519	+	0.0723736i	0.925438	−	0.378899i	$-0.123697\pi$
$521$	0.754424	+	1.65196i	0.0330519	+	0.0723736i	−0.892386	+	0.451273i	$0.850970\pi$
$522$	5.51838	−	3.54644i	0.241533	−	0.155224i
$523$	−26.6379	−	7.82159i	−1.16479	−	0.342014i	−0.358500	−	0.933530i	$-0.616712\pi$
$523$	−26.6379	−	7.82159i	−1.16479	−	0.342014i	−0.806293	+	0.591516i	$0.798530\pi$
$524$	24.5319	−	28.3113i	1.07168	−	1.23679i
$525$	6.92172	−	2.03240i	0.302089	−	0.0887012i
$526$	3.26668	−	7.15303i	0.142434	−	0.311887i
$527$	−1.75362	−	12.1967i	−0.0763890	−	0.531297i
$528$	21.2006			0.922637
$529$	−8.95235	−	21.1862i	−0.389233	−	0.921139i
$530$	−0.0625283			−0.00271605
$531$	−0.274980	−	1.91253i	−0.0119331	−	0.0829965i
$532$	−11.5647	+	25.3231i	−0.501392	+	1.09790i
$533$	0.249417	−	0.0732355i	0.0108035	−	0.00317218i
$534$	−0.986425	+	1.13840i	−0.0426868	+	0.0492632i
$535$	−10.1643	−	2.98452i	−0.439442	−	0.129032i
$536$	9.11493	−	5.85781i	0.393705	−	0.253019i
$537$	5.94439	+	13.0164i	0.256519	+	0.561699i
$538$	−2.16357	−	2.49689i	−0.0932780	−	0.107649i
$539$	6.19163	+	3.97912i	0.266692	+	0.171393i
$540$	−0.445680	+	3.09977i	−0.0191790	+	0.133393i
$541$	3.19556	−	22.2256i	0.137388	−	0.955553i	−0.798183	−	0.602415i	$-0.794205\pi$
$541$	3.19556	−	22.2256i	0.137388	−	0.955553i	0.935571	−	0.353139i	$-0.114886\pi$
$542$	1.05182	+	0.675964i	0.0451796	+	0.0290351i
$543$	29.4751	+	34.0161i	1.26490	+	1.45977i
$544$	1.93933	+	4.24655i	0.0831482	+	0.182069i
$545$	−4.44261	+	2.85509i	−0.190301	+	0.122299i
$546$	−0.127271	−	0.0373703i	−0.00544672	−	0.00159930i
$547$	12.6958	−	14.6517i	0.542832	−	0.626461i	−0.416366	−	0.909197i	$-0.636696\pi$
$547$	12.6958	−	14.6517i	0.542832	−	0.626461i	0.959198	+	0.282736i	$0.0912419\pi$
$548$	−3.01651	+	0.885727i	−0.128859	+	0.0378364i
$549$	−7.45545	+	16.3252i	−0.318191	+	0.696741i
$550$	−0.102170	−	0.710608i	−0.00435654	−	0.0303004i
$551$	−47.7869			−2.03579
$552$	6.61117	−	9.97075i	0.281390	−	0.424383i
$553$	46.6877			1.98536
$554$	−0.430627	−	2.99507i	−0.0182956	−	0.127249i
$555$	5.73346	−	12.5545i	0.243372	−	0.532910i
$556$	9.07348	−	2.66421i	0.384801	−	0.112988i
$557$	−10.3699	+	11.9675i	−0.439385	+	0.507078i	−0.931645	−	0.363371i	$-0.881626\pi$
$557$	−10.3699	+	11.9675i	−0.439385	+	0.507078i	0.492259	+	0.870449i	$0.336171\pi$
$558$	−5.05246	−	1.48354i	−0.213888	−	0.0628031i
$559$	−0.440372	+	0.283010i	−0.0186258	+	0.0119700i
$560$	−4.62128	−	10.1192i	−0.195285	−	0.427614i
$561$	−5.80160	−	6.69540i	−0.244944	−	0.282680i
$562$	0.678510	+	0.436052i	0.0286212	+	0.0183937i
$563$	1.09881	−	7.64237i	0.0463092	−	0.322088i	−0.953478	−	0.301462i	$-0.902525\pi$
$563$	1.09881	−	7.64237i	0.0463092	−	0.322088i	0.999787	−	0.0206252i	$-0.00656567\pi$
$564$	5.30336	−	36.8857i	0.223312	−	1.55317i
$565$	8.25458	+	5.30490i	0.347273	+	0.223179i
$566$	−2.73967	−	3.16175i	−0.115157	−	0.132898i
$567$	13.8371	+	30.2991i	0.581104	+	1.27244i
$568$	−7.84465	+	5.04145i	−0.329154	+	0.211535i
$569$	20.9662	+	6.15623i	0.878948	+	0.258082i	0.689917	−	0.723889i	$-0.257647\pi$
$569$	20.9662	+	6.15623i	0.878948	+	0.258082i	0.189031	+	0.981971i	$0.439465\pi$
$570$	1.92148	−	2.21750i	0.0804819	−	0.0928810i
$571$	−16.4478	+	4.82951i	−0.688318	+	0.202108i	−0.607144	−	0.794591i	$-0.707685\pi$
$571$	−16.4478	+	4.82951i	−0.688318	+	0.202108i	−0.0811739	+	0.996700i	$0.525867\pi$
$572$	0.138112	−	0.302423i	0.00577476	−	0.0126450i
$573$	−6.31375	−	43.9131i	−0.263761	−	1.83450i
$574$	−3.38592			−0.141326
$575$	4.33351	+	2.05444i	0.180720	+	0.0856760i
$576$	−14.2694			−0.594559
$577$	1.10116	+	7.65874i	0.0458419	+	0.318838i	0.999820	+	0.0189619i	$0.00603612\pi$
$577$	1.10116	+	7.65874i	0.0458419	+	0.318838i	−0.953978	+	0.299876i	$0.903055\pi$
$578$	−1.69939	+	3.72114i	−0.0706852	+	0.154779i
$579$	23.5030	−	6.90110i	0.976750	−	0.286800i
$580$	13.0435	−	15.0530i	0.541603	−	0.625044i
$581$	27.0007	+	7.92813i	1.12018	+	0.328914i
$582$	−4.13916	+	2.66008i	−0.171574	+	0.110264i
$583$	−0.244158	−	0.534631i	−0.0101120	−	0.0221422i
$584$	6.33518	+	7.31118i	0.262151	+	0.302539i
$585$	−0.128304	−	0.0824562i	−0.00530473	−	0.00340914i
$586$	0.0926611	−	0.644472i	0.00382779	−	0.0266229i
$587$	−2.19687	+	15.2795i	−0.0906744	+	0.630654i	0.892914	+	0.450227i	$0.148657\pi$
$587$	−2.19687	+	15.2795i	−0.0906744	+	0.630654i	−0.983588	+	0.180427i	$0.942252\pi$
$588$	−10.5476	−	6.77856i	−0.434978	−	0.279543i
$589$	25.1209	+	28.9911i	1.03509	+	1.19456i
$590$	0.0967688	+	0.211894i	0.00398391	+	0.00872354i
$591$	8.43096	−	5.41825i	0.346803	−	0.222877i
$592$	−20.4213	−	5.99625i	−0.839312	−	0.246444i
$593$	−1.03824	+	1.19820i	−0.0426356	+	0.0492041i	−0.776667	−	0.629912i	$-0.783091\pi$
$593$	−1.03824	+	1.19820i	−0.0426356	+	0.0492041i	0.734031	+	0.679116i	$0.237637\pi$
$594$	1.12142	−	0.329278i	0.0460124	−	0.0135105i
$595$	−1.93114	+	4.22860i	−0.0791689	+	0.173356i
$596$	2.12371	+	14.7707i	0.0869905	+	0.605032i
$597$	−36.3594			−1.48809
$598$	−0.0466092	−	0.0748578i	−0.00190599	−	0.00306116i
$599$	−38.5966			−1.57701			−0.788506	−	0.615026i	$-0.789145\pi$
$599$	−38.5966			−1.57701			−0.788506	+	0.615026i	$0.789145\pi$
$600$	0.355011	+	2.46915i	0.0144933	+	0.100803i
$601$	3.43545	−	7.52260i	0.140135	−	0.306853i	−0.826532	−	0.562890i	$-0.809690\pi$
$601$	3.43545	−	7.52260i	0.140135	−	0.306853i	0.966667	+	0.256037i	$0.0824168\pi$
$602$	6.54225	−	1.92098i	0.266642	−	0.0782932i
$603$	14.9998	−	17.3107i	0.610839	−	0.704945i
$604$	−16.9734	−	4.98383i	−0.690637	−	0.202789i
$605$	−3.57687	+	2.29871i	−0.145420	+	0.0934560i
$606$	−2.57958	−	5.64850i	−0.104788	−	0.229454i
$607$	7.80808	+	9.01100i	0.316920	+	0.365745i	0.891751	−	0.452527i	$-0.149477\pi$
$607$	7.80808	+	9.01100i	0.316920	+	0.365745i	−0.574830	+	0.818273i	$0.694932\pi$
$608$	−12.2264	−	7.85741i	−0.495845	−	0.318660i
$609$	10.6304	−	73.9359i	0.430765	−	2.99603i
$610$	0.307925	−	2.14166i	0.0124675	−	0.0867135i
$611$	−0.471325	−	0.302902i	−0.0190678	−	0.0122541i
$612$	4.28084	+	4.94035i	0.173043	+	0.199702i
$613$	−9.53205	−	20.8723i	−0.384996	−	0.843023i	−0.998574	−	0.0533891i	$-0.982998\pi$
$613$	−9.53205	−	20.8723i	−0.384996	−	0.843023i	0.613578	−	0.789634i	$-0.289730\pi$
$614$	0.785252	−	0.504651i	0.0316902	−	0.0203661i
$615$	−8.62409	−	2.53226i	−0.347757	−	0.102111i
$616$	−5.78440	+	6.67555i	−0.233060	+	0.268966i
$617$	−45.8528	+	13.4636i	−1.84597	+	0.542025i	−0.846005	+	0.533175i	$0.820999\pi$
$617$	−45.8528	+	13.4636i	−1.84597	+	0.542025i	−0.999961	+	0.00884982i	$0.997183\pi$
$618$	3.37705	−	7.39472i	0.135845	−	0.297459i
$619$	2.47034	+	17.1816i	0.0992914	+	0.690587i	0.977287	+	0.211919i	$0.0679712\pi$
$619$	2.47034	+	17.1816i	0.0992914	+	0.690587i	−0.877996	+	0.478668i	$0.841120\pi$
$620$	−15.9891			−0.642137
$621$	−2.30655	+	7.45911i	−0.0925587	+	0.299324i
$622$	−9.33605			−0.374342
$623$	1.05733	+	7.35388i	0.0423610	+	0.294627i
$624$	−0.225566	+	0.493921i	−0.00902987	+	0.0197727i
$625$	−0.959493	+	0.281733i	−0.0383797	+	0.0112693i
$626$	1.37504	−	1.58689i	0.0549578	−	0.0634247i
$627$	26.4631	+	7.77027i	1.05683	+	0.310315i
$628$	35.9475	−	23.1021i	1.43446	−	0.921874i
$629$	3.69467	+	8.09020i	0.147316	+	0.322577i
$630$	1.30093	+	1.50136i	0.0518305	+	0.0598156i
$631$	−13.0026	−	8.35628i	−0.517627	−	0.332658i	0.255606	−	0.966781i	$-0.417725\pi$
$631$	−13.0026	−	8.35628i	−0.517627	−	0.332658i	−0.773232	+	0.634123i	$0.781361\pi$
$632$	−2.29759	+	15.9801i	−0.0913931	+	0.635653i
$633$	−6.74386	+	46.9046i	−0.268044	+	1.86429i
$634$	−3.77900	−	2.42862i	−0.150083	−	0.0964527i
$635$	−7.21692	−	8.32877i	−0.286395	−	0.330517i
$636$	0.415931	+	0.910763i	0.0164928	+	0.0361141i
$637$	−0.158580	+	0.101913i	−0.00628317	+	0.00403795i
$638$	−7.13250	−	2.09429i	−0.282378	−	0.0829137i
$639$	−12.9094	+	14.8982i	−0.510687	+	0.589364i
$640$	7.69373	−	2.25908i	0.304122	−	0.0892981i
$641$	4.43285	−	9.70659i	0.175087	−	0.383387i	−0.801661	−	0.597780i	$-0.796050\pi$
$641$	4.43285	−	9.70659i	0.175087	−	0.383387i	0.976748	+	0.214392i	$0.0687771\pi$
$642$	−0.958497	−	6.66650i	−0.0378289	−	0.263106i
$643$	−1.93216			−0.0761969			−0.0380984	−	0.999274i	$-0.512130\pi$
$643$	−1.93216			−0.0761969			−0.0380984	+	0.999274i	$0.512130\pi$
$644$	−7.75247	−	27.8708i	−0.305490	−	1.09826i
$645$	18.1000			0.712689
$646$	0.269089	+	1.87155i	0.0105872	+	0.0736353i
$647$	18.3937	−	40.2765i	0.723130	−	1.58343i	−0.0863359	−	0.996266i	$-0.527516\pi$
$647$	18.3937	−	40.2765i	0.723130	−	1.58343i	0.809466	−	0.587167i	$-0.199757\pi$
$648$	−11.0516	+	3.24504i	−0.434147	+	0.127477i
$649$	−1.43389	+	1.65479i	−0.0562850	+	0.0649563i
$650$	0.0176425	+	0.00518029i	0.000691994	+	0.000203188i
$651$	−50.4432	+	32.4179i	−1.97702	+	1.27056i
$652$	4.95904	+	10.8588i	0.194211	+	0.425263i
$653$	16.2168	+	18.7152i	0.634613	+	0.732383i	0.978413	−	0.206660i	$-0.0662595\pi$
$653$	16.2168	+	18.7152i	0.634613	+	0.732383i	−0.343799	+	0.939043i	$0.611714\pi$
$654$	−2.82451	−	1.81520i	−0.110447	−	0.0709799i
$655$	−2.77148	+	19.2761i	−0.108291	+	0.753180i
$656$	−1.97256	+	13.7194i	−0.0770154	+	0.535654i
$657$	17.2047	+	11.0568i	0.671218	+	0.431366i
$658$	4.77898	+	5.51524i	0.186304	+	0.215006i
$659$	2.18226	+	4.77849i	0.0850089	+	0.186144i	0.947362	−	0.320163i	$-0.103738\pi$
$659$	2.18226	+	4.77849i	0.0850089	+	0.186144i	−0.862354	+	0.506307i	$0.831010\pi$
$660$	−9.67082	+	6.21506i	−0.376436	+	0.241921i
$661$	39.7139	+	11.6610i	1.54469	+	0.453562i	0.939509	−	0.342525i	$-0.111282\pi$
$661$	39.7139	+	11.6610i	1.54469	+	0.453562i	0.605182	+	0.796087i	$0.293100\pi$
$662$	2.07001	−	2.38892i	0.0804532	−	0.0928479i
$663$	0.217713	−	0.0639263i	0.00845527	−	0.00248269i
$664$	−4.04236	+	8.85154i	−0.156874	+	0.343506i
$665$	−2.05959	−	14.3248i	−0.0798676	−	0.555491i
$666$	3.80075			0.147276
$667$	37.9903	−	31.9792i	1.47099	−	1.23824i
$668$	37.9391			1.46791
$669$	7.07671	+	49.2196i	0.273602	+	1.90294i
$670$	−1.14715	+	2.51191i	−0.0443184	+	0.0970437i
$671$	19.5141	−	5.72986i	0.753334	−	0.221199i
$672$	14.8768	−	17.1687i	0.573884	−	0.662298i
$673$	−16.5847	−	4.86971i	−0.639294	−	0.187714i	−0.0540080	−	0.998541i	$-0.517200\pi$
$673$	−16.5847	−	4.86971i	−0.639294	−	0.187714i	−0.585286	+	0.810827i	$0.699018\pi$
$674$	−5.55882	+	3.57244i	−0.214118	+	0.137605i
$675$	−0.676293	−	1.48088i	−0.0260305	−	0.0569989i
$676$	−16.3706	−	18.8927i	−0.629638	−	0.726641i
$677$	15.3509	+	9.86543i	0.589984	+	0.379159i	0.801304	−	0.598257i	$-0.204140\pi$
$677$	15.3509	+	9.86543i	0.589984	+	0.379159i	−0.211320	+	0.977417i	$0.567776\pi$
$678$	−0.887815	+	6.17489i	−0.0340963	+	0.237145i
$679$	−3.45366	+	24.0207i	−0.132539	+	0.921832i
$680$	−1.35231	−	0.869078i	−0.0518588	−	0.0333276i
$681$	−13.5462	−	15.6331i	−0.519091	−	0.599063i
$682$	2.47890	+	5.42803i	0.0949220	+	0.207850i
$683$	−28.7531	+	18.4785i	−1.10021	+	0.707059i	−0.959137	−	0.282941i	$-0.908690\pi$
$683$	−28.7531	+	18.4785i	−1.10021	+	0.707059i	−0.141068	+	0.990000i	$0.545054\pi$
$684$	−19.5264	−	5.73346i	−0.746610	−	0.219225i
$685$	1.07027	−	1.23515i	0.0408928	−	0.0471928i
$686$	−3.46472	+	1.01733i	−0.132284	+	0.0388420i
$687$	5.69534	−	12.4711i	0.217291	−	0.475801i
$688$	−3.97226	−	27.6277i	−0.151441	−	1.05330i
$689$	0.0150533			0.000573486
$690$	−0.0436012	+	3.04876i	−0.00165987	+	0.116064i
$691$	14.3111			0.544418			0.272209	−	0.962238i	$-0.412246\pi$
$691$	14.3111			0.544418			0.272209	+	0.962238i	$0.412246\pi$
$692$	1.69863	+	11.8143i	0.0645724	+	0.449111i
$693$	−7.75713	+	16.9857i	−0.294669	+	0.645235i
$694$	0.241016	−	0.0707686i	0.00914883	−	0.00268634i
$695$	−3.21930	+	3.71527i	−0.122115	+	0.140928i
$696$	24.7833	+	7.27704i	0.939409	+	0.275835i
$697$	4.87256	−	3.13141i	0.184561	−	0.118610i
$698$	−1.74247	−	3.81547i	−0.0659533	−	0.144418i
$699$	4.36968	+	5.04288i	0.165276	+	0.190739i
$700$	5.07453	+	3.26120i	0.191799	+	0.123262i
$701$	5.96362	−	41.4779i	0.225243	−	1.56660i	−0.492514	−	0.870305i	$-0.663922\pi$
$701$	5.96362	−	41.4779i	0.225243	−	1.56660i	0.717757	−	0.696294i	$-0.245169\pi$
$702$	−0.00426011	+	0.0296297i	−0.000160787	+	0.00111830i
$703$	−23.2927	−	14.9693i	−0.878502	−	0.564579i
$704$	10.5894	+	12.2208i	0.399102	+	0.460589i
$705$	8.04754	+	17.6216i	0.303088	+	0.663670i
$706$	−6.54554	+	4.20656i	−0.246345	+	0.158316i
$707$	−29.3869	−	8.62877i	−1.10521	−	0.324518i
$708$	2.44267	−	2.81900i	0.0918013	−	0.105944i
$709$	−25.0816	+	7.36464i	−0.941961	+	0.276585i	−0.716436	−	0.697653i	$-0.754228\pi$
$709$	−25.0816	+	7.36464i	−0.941961	+	0.276585i	−0.225525	+	0.974237i	$0.572410\pi$
$710$	0.987282	−	2.16185i	0.0370521	−	0.0811327i
$711$	4.85715	+	33.7822i	0.182157	+	1.26693i
$712$	−2.56909			−0.0962807
$713$	−39.3719	−	6.23671i	−1.47449	−	0.233567i
$714$	−2.95553			−0.110608
$715$	0.0245969	+	0.171075i	0.000919871	+	0.00639784i
$716$	−4.97054	+	10.8840i	−0.185758	+	0.406753i
$717$	−12.6191	+	3.70531i	−0.471270	+	0.138377i
$718$	0.716775	−	0.827203i	0.0267498	−	0.0308709i
$719$	41.0422	+	12.0511i	1.53062	+	0.449430i	0.935239	−	0.354017i	$-0.115184\pi$
$719$	41.0422	+	12.0511i	1.53062	+	0.449430i	0.595377	+	0.803446i	$0.297003\pi$
$720$	6.84126	−	4.39661i	0.254959	−	0.163852i
$721$	−16.6565	−	36.4726i	−0.620319	−	1.35831i
$722$	−0.416124	−	0.480233i	−0.0154865	−	0.0178724i
$723$	44.4237	+	28.5494i	1.65214	+	1.06176i
$724$	−5.35616	+	37.2529i	−0.199060	+	1.38449i
$725$	−1.47359	+	10.2490i	−0.0547277	+	0.380640i
$726$	−2.27409	−	1.46147i	−0.0843993	−	0.0542401i
$727$	−16.1111	−	18.5932i	−0.597528	−	0.689584i	0.373750	−	0.927529i	$-0.378072\pi$
$727$	−16.1111	−	18.5932i	−0.597528	−	0.689584i	−0.971279	+	0.237945i	$0.923526\pi$
$728$	−0.0939799	−	0.205787i	−0.00348313	−	0.00762699i
$729$	−11.0322	+	7.08996i	−0.408600	+	0.262591i
$730$	−2.36572	−	0.694640i	−0.0875594	−	0.0257098i
$731$	−7.63814	+	8.81488i	−0.282507	+	0.326030i
$732$	−33.2430	+	9.76101i	−1.22869	+	0.360777i
$733$	−14.2036	+	31.1015i	−0.524620	+	1.14876i	0.443040	+	0.896502i	$0.353900\pi$
$733$	−14.2036	+	31.1015i	−0.524620	+	1.14876i	−0.967660	+	0.252257i	$0.918827\pi$
$734$	0.362657	+	2.52233i	0.0133859	+	0.0931010i
$735$	6.51791			0.240417
$736$	14.9781	−	1.93534i	0.552100	−	0.0713375i
$737$	−25.9568			−0.956132
$738$	−0.352254	−	2.44998i	−0.0129667	−	0.0901851i
$739$	−13.6906	+	29.9782i	−0.503617	+	1.10277i	0.471660	+	0.881780i	$0.343655\pi$
$739$	−13.6906	+	29.9782i	−0.503617	+	1.10277i	−0.975277	+	0.220986i	$0.929072\pi$
$740$	11.0732	−	3.25138i	0.407059	−	0.119523i
$741$	−0.462585	+	0.533852i	−0.0169935	+	0.0196115i
$742$	−0.188134	−	0.0552410i	−0.00690661	−	0.00202796i
$743$	−19.5079	+	12.5370i	−0.715676	+	0.459937i	−0.847130	−	0.531385i	$-0.821672\pi$
$743$	−19.5079	+	12.5370i	−0.715676	+	0.459937i	0.131455	+	0.991322i	$0.458035\pi$
$744$	−8.61345	−	18.8608i	−0.315784	−	0.691471i
$745$	−5.08012	−	5.86277i	−0.186121	−	0.214795i
$746$	−0.307818	−	0.197823i	−0.0112700	−	0.00724281i
$747$	−2.92761	+	20.3620i	−0.107116	+	0.745005i
$748$	1.05425	−	7.33250i	0.0385474	−	0.268103i
$749$	−27.9455	−	17.9595i	−1.02111	−	0.656226i
$750$	−0.416345	−	0.480487i	−0.0152028	−	0.0175449i
$751$	0.0493668	+	0.108098i	0.00180142	+	0.00394456i	0.910531	−	0.413442i	$-0.135673\pi$
$751$	0.0493668	+	0.108098i	0.00180142	+	0.00394456i	−0.908729	+	0.417386i	$0.862946\pi$
$752$	25.1313	−	16.1509i	0.916445	−	0.588964i
$753$	44.8361	+	13.1651i	1.63392	+	0.479762i
$754$	0.124679	−	0.143887i	0.00454053	−	0.00524005i
$755$	8.82364	−	2.59086i	0.321125	−	0.0942909i
$756$	−4.07947	+	8.93279i	−0.148369	+	0.324883i
$757$	−3.62855	−	25.2371i	−0.131882	−	0.917258i	−0.943099	−	0.332513i	$-0.892103\pi$
$757$	−3.62855	−	25.2371i	−0.131882	−	0.917258i	0.811217	−	0.584745i	$-0.198806\pi$
$758$	0.878956			0.0319251
$759$	−26.2379	+	11.5319i	−0.952375	+	0.418581i
$760$	5.00438			0.181528
$761$	2.54953	+	17.7324i	0.0924205	+	0.642799i	0.982399	+	0.186796i	$0.0598103\pi$
$761$	2.54953	+	17.7324i	0.0924205	+	0.642799i	−0.889978	+	0.456003i	$0.849281\pi$
$762$	2.91064	−	6.37342i	0.105441	−	0.230885i
$763$	−15.8892	+	4.66549i	−0.575228	+	0.168902i
$764$	24.2931	−	28.0357i	0.878893	−	1.01430i
$765$	−3.26063	−	0.957408i	−0.117888	−	0.0346152i
$766$	0.190913	−	0.122692i	0.00689797	−	0.00443306i
$767$	−0.0232966	−	0.0510123i	−0.000841190	−	0.00184195i
$768$	−15.4171	−	17.7923i	−0.556318	−	0.642025i
$769$	−33.4532	−	21.4991i	−1.20635	−	0.775276i	−0.226309	−	0.974056i	$-0.572666\pi$
$769$	−33.4532	−	21.4991i	−1.20635	−	0.775276i	−0.980044	+	0.198779i	$0.936302\pi$
$770$	0.320385	−	2.22833i	0.0115459	−	0.0803033i
$771$	−7.71478	+	53.6575i	−0.277841	+	1.93243i
$772$	17.2308	+	11.0735i	0.620149	+	0.398545i
$773$	−22.1965	−	25.6161i	−0.798353	−	0.921348i	0.199937	−	0.979809i	$-0.435926\pi$
$773$	−22.1965	−	25.6161i	−0.798353	−	0.921348i	−0.998290	+	0.0584605i	$0.981381\pi$
$774$	2.07060	+	4.53398i	0.0744262	+	0.162971i
$775$	6.99247	−	4.49379i	0.251177	−	0.161422i
$776$	−8.05176	−	2.36421i	−0.289041	−	0.0848702i
$777$	28.3421	−	32.7085i	1.01677	−	1.17341i
$778$	0.180563	−	0.0530181i	0.00647350	−	0.00190079i
$779$	−7.49054	+	16.4020i	−0.268376	+	0.587662i
$780$	−0.0419016	−	0.291432i	−0.00150032	−	0.0104349i
$781$	22.3394			0.799367
$782$	−1.46637	−	1.30780i	−0.0524374	−	0.0467668i
$783$	−16.8570			−0.602419
$784$	−1.43043	−	9.94886i	−0.0510868	−	0.355316i
$785$	−9.22794	+	20.2064i	−0.329359	+	0.721196i
$786$	−11.8798	+	3.48822i	−0.423737	+	0.124421i
$787$	−8.41029	+	9.70599i	−0.299794	+	0.345981i	−0.885582	−	0.464484i	$-0.846240\pi$
$787$	−8.41029	+	9.70599i	−0.299794	+	0.345981i	0.585787	+	0.810465i	$0.300785\pi$
$788$	8.04060	+	2.36093i	0.286435	+	0.0841048i
$789$	55.0674	−	35.3897i	1.96045	−	1.25991i
$790$	−1.70929	−	3.74283i	−0.0608139	−	0.133164i
$791$	20.1496	+	23.2538i	0.716436	+	0.826811i
$792$	−5.43207	−	3.49098i	−0.193020	−	0.124046i
$793$	−0.0741312	+	0.515594i	−0.00263248	+	0.0183093i
$794$	−0.0895839	+	0.623070i	−0.00317921	+	0.0221119i
$795$	−0.437871	−	0.281403i	−0.0155297	−	0.00998033i
$796$	−19.9096	−	22.9769i	−0.705676	−	0.814393i
$797$	−15.1640	−	33.2045i	−0.537136	−	1.17616i	−0.962535	−	0.271158i	$-0.912593\pi$
$797$	−15.1640	−	33.2045i	−0.537136	−	1.17616i	0.425399	−	0.905006i	$-0.360134\pi$
$798$	7.74037	−	4.97444i	0.274006	−	0.176093i
$799$	−11.9779	−	3.51704i	−0.423748	−	0.124424i
$800$	−2.06223	+	2.37994i	−0.0729108	+	0.0841435i
$801$	−5.21112	+	1.53012i	−0.184126	+	0.0540642i
$802$	1.12957	−	2.47341i	0.0398865	−	0.0873393i
$803$	−3.29826	−	22.9399i	−0.116393	−	0.809532i
$804$	44.2183			1.55946
$805$	11.2236	+	10.0098i	0.395578	+	0.352800i
$806$	−0.152834			−0.00538336
$807$	−3.91394	−	27.2221i	−0.137777	−	0.958262i
$808$	4.39960	−	9.63378i	0.154777	−	0.338915i
$809$	−21.2273	+	6.23290i	−0.746312	+	0.219137i	−0.632710	−	0.774389i	$-0.718057\pi$
$809$	−21.2273	+	6.23290i	−0.746312	+	0.219137i	−0.113603	+	0.993526i	$0.536239\pi$
$810$	1.92240	−	2.21857i	0.0675463	−	0.0779526i
$811$	11.4030	+	3.34824i	0.400415	+	0.117572i	0.475739	−	0.879587i	$-0.342181\pi$
$811$	11.4030	+	3.34824i	0.400415	+	0.117572i	−0.0753237	+	0.997159i	$0.523999\pi$
$812$	52.5438	−	33.7679i	1.84393	−	1.18502i
$813$	4.32355	+	9.46725i	0.151633	+	0.332031i
$814$	−2.82055	−	3.25508i	−0.0988601	−	0.114091i
$815$	−5.22062	−	3.35509i	−0.182870	−	0.117524i
$816$	−1.72182	+	11.9755i	−0.0602757	+	0.419227i
$817$	5.16760	−	35.9415i	0.180791	−	1.25743i
$818$	2.99584	+	1.92531i	0.104747	+	0.0673169i
$819$	−0.313193	−	0.361444i	−0.0109438	−	0.0126299i
$820$	−3.12213	−	6.83650i	−0.109029	−	0.238741i
$821$	−25.6419	+	16.4790i	−0.894907	+	0.575122i	−0.905276	−	0.424824i	$-0.860336\pi$
$821$	−25.6419	+	16.4790i	−0.894907	+	0.575122i	0.0103686	+	0.999946i	$0.496700\pi$
$822$	0.996985	+	0.292741i	0.0347738	+	0.0102105i
$823$	13.3437	−	15.3994i	0.465132	−	0.536791i	−0.473919	−	0.880568i	$-0.657161\pi$
$823$	13.3437	−	15.3994i	0.465132	−	0.536791i	0.939051	+	0.343777i	$0.111707\pi$
$824$	13.3034	−	3.90622i	0.463445	−	0.136080i
$825$	2.48255	−	5.43603i	0.0864314	−	0.189258i
$826$	0.103957	+	0.723034i	0.00361711	+	0.0251576i
$827$	31.1290			1.08246			0.541231	−	0.840874i	$-0.317958\pi$
$827$	31.1290			1.08246			0.541231	+	0.840874i	$0.317958\pi$
$828$	19.3602	−	8.50906i	0.672814	−	0.295710i
$829$	15.4020			0.534935			0.267468	−	0.963567i	$-0.413813\pi$
$829$	15.4020			0.534935			0.267468	+	0.963567i	$0.413813\pi$
$830$	−0.352952	−	2.45484i	−0.0122512	−	0.0852086i
$831$	10.4635	−	22.9118i	0.362974	−	0.794802i
$832$	−0.397381	+	0.116682i	−0.0137767	+	0.00404521i
$833$	−2.75053	+	3.17428i	−0.0953002	+	0.109982i
$834$	−2.99887	−	0.880548i	−0.103842	−	0.0304909i
$835$	−16.5918	+	10.6629i	−0.574183	+	0.369005i
$836$	9.58027	+	20.9779i	0.331340	+	0.725534i
$837$	8.86146	+	10.2267i	0.306297	+	0.353486i
$838$	5.03368	+	3.23495i	0.173886	+	0.111750i
$839$	−0.575038	+	3.99948i	−0.0198525	+	0.138077i	−0.997337	−	0.0729296i	$-0.976765\pi$
$839$	−0.575038	+	3.99948i	−0.0198525	+	0.138077i	0.977485	+	0.211007i	$0.0676742\pi$
$840$	−1.11324	+	7.74278i	−0.0384105	+	0.267151i
$841$	65.7981	+	42.2858i	2.26890	+	1.45813i
$842$	5.79164	+	6.68391i	0.199593	+	0.230343i
$843$	2.78904	+	6.10715i	0.0960597	+	0.210341i
$844$	−33.3335	+	21.4222i	−1.14739	+	0.737381i
$845$	12.4692	+	3.66128i	0.428952	+	0.125952i
$846$	−3.49353	+	4.03175i	−0.120110	+	0.138614i
$847$	−12.7928	+	3.75631i	−0.439567	+	0.129068i
$848$	−0.333434	+	0.730118i	−0.0114502	+	0.0250724i
$849$	−4.95614	−	34.4707i	−0.170094	−	1.18303i
$850$	0.409697			0.0140525
$851$	28.5351	−	3.68706i	0.978171	−	0.126391i
$852$	−38.0559			−1.30377
$853$	−2.76241	−	19.2130i	−0.0945831	−	0.657840i	−0.980864	−	0.194692i	$-0.937629\pi$
$853$	−2.76241	−	19.2130i	−0.0945831	−	0.657840i	0.886281	−	0.463147i	$-0.153280\pi$
$854$	2.81855	−	6.17176i	0.0964487	−	0.211193i
$855$	10.1508	−	2.98055i	0.347151	−	0.101933i
$856$	7.52235	−	8.68125i	0.257109	−	0.296719i
$857$	20.2364	+	5.94195i	0.691263	+	0.202973i	0.608450	−	0.793592i	$-0.291792\pi$
$857$	20.2364	+	5.94195i	0.691263	+	0.202973i	0.0828125	+	0.996565i	$0.473610\pi$
$858$	−0.0924401	+	0.0594077i	−0.00315585	+	0.00202814i
$859$	−0.827870	−	1.81278i	−0.0282466	−	0.0618514i	0.894983	−	0.446101i	$-0.147188\pi$
$859$	−0.827870	−	1.81278i	−0.0282466	−	0.0618514i	−0.923229	+	0.384249i	$0.874460\pi$
$860$	9.91118	+	11.4381i	0.337968	+	0.390036i
$861$	−23.7109	−	15.2380i	−0.808064	−	0.519311i
$862$	−1.33887	+	9.31205i	−0.0456021	+	0.317170i
$863$	−5.76603	+	40.1037i	−0.196278	+	1.36514i	0.618689	+	0.785636i	$0.287664\pi$
$863$	−5.76603	+	40.1037i	−0.196278	+	1.36514i	−0.814967	+	0.579508i	$0.803245\pi$
$864$	−4.31288	−	2.77172i	−0.146727	−	0.0942959i
$865$	−4.06330	−	4.68930i	−0.138156	−	0.159441i
$866$	−0.601014	−	1.31604i	−0.0204233	−	0.0447207i
$867$	−28.6471	+	18.4104i	−0.972905	+	0.625248i
$868$	−48.1076	−	14.1257i	−1.63288	−	0.479457i
$869$	25.3277	−	29.2297i	0.859183	−	0.991550i
$870$	−6.31644	+	1.85467i	−0.214147	+	0.0628793i
$871$	0.276171	−	0.604729i	0.00935769	−	0.0204905i
$872$	−0.814947	−	5.66808i	−0.0275976	−	0.191945i
$873$	−17.7402			−0.600415
$874$	6.04151	+	0.957007i	0.204357	+	0.0323712i
$875$	−3.13580			−0.106009
$876$	5.61870	+	39.0789i	0.189838	+	1.32035i
$877$	8.26627	−	18.1006i	0.279132	−	0.611214i	−0.717192	−	0.696875i	$-0.754573\pi$
$877$	8.26627	−	18.1006i	0.279132	−	0.611214i	0.996324	+	0.0856614i	$0.0273003\pi$
$878$	7.21844	−	2.11953i	0.243611	−	0.0715305i
$879$	3.54927	−	4.09608i	0.119714	−	0.138157i
$880$	−8.84232	−	2.59634i	−0.298074	−	0.0875226i
$881$	−23.8216	+	15.3092i	−0.802570	+	0.515781i	−0.876454	−	0.481486i	$-0.840097\pi$
$881$	−23.8216	+	15.3092i	−0.802570	+	0.515781i	0.0738833	+	0.997267i	$0.476461\pi$
$882$	0.745633	+	1.63271i	0.0251068	+	0.0549762i
$883$	−1.99349	−	2.30061i	−0.0670862	−	0.0774215i	0.721214	−	0.692712i	$-0.243584\pi$
$883$	−1.99349	−	2.30061i	−0.0670862	−	0.0774215i	−0.788301	+	0.615290i	$0.789039\pi$
$884$	0.159612	+	0.102577i	0.00536834	+	0.00345002i
$885$	−0.275960	+	1.91935i	−0.00927630	+	0.0645181i
$886$	−0.543216	+	3.77815i	−0.0182497	+	0.126929i
$887$	−25.7965	−	16.5784i	−0.866160	−	0.556648i	0.0304156	−	0.999537i	$-0.490317\pi$
$887$	−25.7965	−	16.5784i	−0.866160	−	0.556648i	−0.896576	+	0.442890i	$0.853953\pi$
$888$	9.80057	+	11.3105i	0.328886	+	0.379554i
$889$	−14.3560	−	31.4353i	−0.481485	−	1.05430i
$890$	0.550831	−	0.353998i	0.0184639	−	0.0118660i
$891$	26.4758	+	7.77400i	0.886974	+	0.260439i
$892$	−27.2287	+	31.4236i	−0.911684	+	1.05214i
$893$	37.2891	−	10.9491i	1.24783	−	0.366396i
$894$	2.04885	−	4.48636i	0.0685239	−	0.150046i
$895$	−0.885220	−	6.15684i	−0.0295897	−	0.205801i
$896$	25.1446			0.840020
$897$	0.0104967	−	0.733972i	0.000350476	−	0.0245066i
$898$	1.50336			0.0501676
$899$	−12.2484	−	85.1896i	−0.408508	−	2.84123i
$900$	−1.83181	+	4.01110i	−0.0610602	+	0.133703i
$901$	0.321825	−	0.0944964i	0.0107216	−	0.00314813i
$902$	−1.83684	+	2.11982i	−0.0611600	+	0.0705823i
$903$	54.4591	+	15.9906i	1.81228	+	0.532135i
$904$	−8.95082	+	5.75234i	−0.297700	+	0.191320i
$905$	−8.12766	−	17.7971i	−0.270173	−	0.591595i
$906$	3.82877	+	4.41863i	0.127202	+	0.146799i
$907$	14.4361	+	9.27755i	0.479344	+	0.308056i	0.757908	−	0.652362i	$-0.226222\pi$
$907$	14.4361	+	9.27755i	0.479344	+	0.308056i	−0.278563	+	0.960418i	$0.589858\pi$
$908$	2.46158	−	17.1207i	0.0816905	−	0.568170i
$909$	3.18633	−	22.1614i	0.105684	−	0.735048i
$910$	0.0485057	+	0.0311727i	0.00160795	+	0.00103337i
$911$	−3.14149	−	3.62547i	−0.104082	−	0.120117i	0.701318	−	0.712848i	$-0.252595\pi$
$911$	−3.14149	−	3.62547i	−0.104082	−	0.120117i	−0.805401	+	0.592731i	$0.798050\pi$
$912$	−15.6466	−	34.2612i	−0.518110	−	1.13450i
$913$	19.6112	−	12.6034i	0.649037	−	0.417111i
$914$	−2.02324	−	0.594078i	−0.0669229	−	0.0196503i
$915$	11.7947	−	13.6118i	0.389921	−	0.449992i
$916$	10.9996	−	3.22977i	0.363436	−	0.106715i
$917$	−25.3684	+	55.5490i	−0.837738	+	1.83439i
$918$	0.0949218	+	0.660196i	0.00313289	+	0.0217897i
$919$	34.2738			1.13059			0.565295	−	0.824889i	$-0.308762\pi$
$919$	34.2738			1.13059			0.565295	+	0.824889i	$0.308762\pi$
$920$	−3.97845	+	3.34895i	−0.131166	+	0.110412i
$921$	7.77008			0.256033
$922$	1.19460	+	8.30865i	0.0393422	+	0.273631i
$923$	−0.237683	+	0.520453i	−0.00782342	+	0.0171309i
$924$	−34.5881	+	10.1560i	−1.13787	+	0.334107i
$925$	−3.92880	+	4.53408i	−0.129178	+	0.149080i
$926$	6.16786	+	1.81105i	0.202688	+	0.0595147i
$927$	24.6579	−	15.8467i	0.809872	−	0.520473i
$928$	13.5455	+	29.6606i	0.444654	+	0.973657i
$929$	−4.58533	−	5.29175i	−0.150440	−	0.173617i	0.675528	−	0.737335i	$-0.263916\pi$
$929$	−4.58533	−	5.29175i	−0.150440	−	0.173617i	−0.825967	+	0.563718i	$0.809370\pi$
$930$	4.44564	+	2.85704i	0.145778	+	0.0936860i
$931$	1.86088	−	12.9427i	0.0609878	−	0.424179i
$932$	−0.794049	+	5.52273i	−0.0260099	+	0.180903i
$933$	−65.3782	−	42.0160i	−2.14039	−	1.37554i
$934$	1.57033	+	1.81225i	0.0513827	+	0.0592988i
$935$	1.59977	+	3.50301i	0.0523181	+	0.114561i
$936$	0.139126	−	0.0894110i	0.00454748	−	0.00292249i
$937$	−6.05697	−	1.77849i	−0.197873	−	0.0581007i	0.181294	−	0.983429i	$-0.441971\pi$
$937$	−6.05697	−	1.77849i	−0.197873	−	0.0581007i	−0.379167	+	0.925328i	$0.623789\pi$
$938$	−5.67070	+	6.54433i	−0.185155	+	0.213680i
$939$	16.7708	−	4.92434i	0.547293	−	0.160700i
$940$	−6.72914	+	14.7348i	−0.219480	+	0.480595i
$941$	2.86661	+	19.9377i	0.0934488	+	0.649951i	0.981678	+	0.190549i	$0.0610270\pi$
$941$	2.86661	+	19.9377i	0.0934488	+	0.649951i	−0.888229	+	0.459401i	$0.848064\pi$
$942$	−14.1230			−0.460152
$943$	−5.02134	−	18.0522i	−0.163517	−	0.587859i
$944$	2.99023			0.0973236
$945$	−0.726527	−	5.05311i	−0.0236339	−	0.164378i
$946$	2.34645	−	5.13801i	0.0762897	−	0.167051i
$947$	5.72212	−	1.68017i	0.185944	−	0.0545981i	−0.187435	−	0.982277i	$-0.560017\pi$
$947$	5.72212	−	1.68017i	0.185944	−	0.0545981i	0.373379	+	0.927679i	$0.378199\pi$
$948$	−43.1466	+	49.7938i	−1.40134	+	1.61723i
$949$	0.569535	+	0.167231i	0.0184879	+	0.00542854i
$950$	−1.07298	+	0.689560i	−0.0348119	+	0.0223723i
$951$	−15.5337	−	34.0141i	−0.503715	−	1.10298i
$952$	−3.30102	−	3.80958i	−0.106987	−	0.123469i
$953$	9.06785	+	5.82756i	0.293737	+	0.188773i	0.679206	−	0.733947i	$-0.262324\pi$
$953$	9.06785	+	5.82756i	0.293737	+	0.188773i	−0.385470	+	0.922721i	$0.625961\pi$
$954$	0.0203988	−	0.141877i	0.000660435	−	0.00459342i
$955$	−2.74450	+	19.0884i	−0.0888101	+	0.617688i
$956$	−9.25148	−	5.94556i	−0.299214	−	0.192293i
$957$	−40.5221	−	46.7650i	−1.30989	−	1.51170i
$958$	−1.49541	−	3.27450i	−0.0483146	−	0.105794i
$959$	4.31140	−	2.77077i	0.139222	−	0.0894728i
$960$	13.7402	+	4.03450i	0.443464	+	0.130213i
$961$	−24.9428	+	28.7855i	−0.804606	+	0.928565i
$962$	0.105845	−	0.0310789i	0.00341258	−	0.00100202i
$963$	10.0878	−	22.0892i	0.325075	−	0.711815i
$964$	6.28398	+	43.7060i	0.202393	+	1.40768i
$965$	−10.6477			−0.342763
$966$	−2.82464	+	9.13453i	−0.0908812	+	0.293899i
$967$	1.85620			0.0596915			0.0298457	−	0.999555i	$-0.490498\pi$
$967$	1.85620			0.0596915			0.0298457	+	0.999555i	$0.490498\pi$
$968$	−0.656136	−	4.56353i	−0.0210890	−	0.146677i
$969$	−6.53839	+	14.3171i	−0.210043	+	0.459931i
$970$	2.05212	−	0.602558i	0.0658897	−	0.0193470i
$971$	13.3345	−	15.3889i	0.427926	−	0.493853i	−0.500309	−	0.865847i	$-0.666780\pi$
$971$	13.3345	−	15.3889i	0.427926	−	0.493853i	0.928235	+	0.371994i	$0.121326\pi$
$972$	−36.0881	−	10.5964i	−1.15753	−	0.339880i
$973$	−12.9684	+	8.33431i	−0.415749	+	0.267186i
$974$	0.673344	+	1.47442i	0.0215753	+	0.0472434i
$975$	0.100233	+	0.115675i	0.00321001	+	0.00370455i
$976$	−23.3654	−	15.0160i	−0.747907	−	0.480651i
$977$	−2.39784	+	16.6774i	−0.0767138	+	0.533556i	0.914836	+	0.403826i	$0.132320\pi$
$977$	−2.39784	+	16.6774i	−0.0767138	+	0.533556i	−0.991549	+	0.129730i	$0.958589\pi$
$978$	0.561499	−	3.90531i	0.0179548	−	0.124878i
$979$	5.17763	+	3.32746i	0.165478	+	0.106346i
$980$	3.56906	+	4.11892i	0.114009	+	0.131574i
$981$	−5.02888	−	11.0117i	−0.160560	−	0.351577i
$982$	2.17813	−	1.39980i	0.0695070	−	0.0446694i
$983$	33.9545	+	9.96994i	1.08298	+	0.317992i	0.774070	−	0.633100i	$-0.218218\pi$
$983$	33.9545	+	9.96994i	1.08298	+	0.317992i	0.308910	+	0.951091i	$0.400036\pi$
$984$	6.38246	−	7.36576i	0.203466	−	0.234812i
$985$	−4.17993	+	1.22734i	−0.133183	+	0.0391062i
$986$	1.76227	−	3.85882i	0.0561220	−	0.122890i
$987$	8.64529	+	60.1293i	0.275183	+	1.91394i
$988$	−0.590662			−0.0187915
$989$	19.9439	+	32.0314i	0.634180	+	1.01854i
$990$	1.64570			0.0523038
$991$	8.16589	+	56.7950i	0.259398	+	1.80415i	0.537136	+	0.843496i	$0.319506\pi$
$991$	8.16589	+	56.7950i	0.259398	+	1.80415i	−0.277738	+	0.960657i	$0.589585\pi$
$992$	10.8736	−	23.8099i	0.345237	−	0.755964i
$993$	25.2469	−	7.41316i	0.801186	−	0.235250i
$994$	4.88041	−	5.63230i	0.154797	−	0.178646i
$995$	15.1647	+	4.45276i	0.480754	+	0.141162i
$996$	−33.4084	+	21.4703i	−1.05859	+	0.680312i
$997$	14.2590	+	31.2228i	0.451587	+	0.988837i	0.989325	+	0.145725i	$0.0465515\pi$
$997$	14.2590	+	31.2228i	0.451587	+	0.988837i	−0.537739	+	0.843112i	$0.680721\pi$
$998$	−5.14391	−	5.93639i	−0.162828	−	0.187913i
$999$	−8.21658	−	5.28047i	−0.259961	−	0.167067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.c.26.3	✓	50
5.2	odd	4		575.2.p.d.49.6		100
5.3	odd	4		575.2.p.d.49.5		100
5.4	even	2		575.2.k.d.26.3		50
23.8	even	11	inner	115.2.g.c.31.3	yes	50
23.10	odd	22		2645.2.a.x.1.14		25
23.13	even	11		2645.2.a.y.1.14		25
115.8	odd	44		575.2.p.d.399.6		100
115.54	even	22		575.2.k.d.376.3		50
115.77	odd	44		575.2.p.d.399.5		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.c.26.3	✓	50	1.1	even	1	trivial
115.2.g.c.31.3	yes	50	23.8	even	11	inner
575.2.k.d.26.3		50	5.4	even	2
575.2.k.d.376.3		50	115.54	even	22
575.2.p.d.49.5		100	5.3	odd	4
575.2.p.d.49.6		100	5.2	odd	4
575.2.p.d.399.5		100	115.77	odd	44
575.2.p.d.399.6		100	115.8	odd	44
2645.2.a.x.1.14		25	23.10	odd	22
2645.2.a.y.1.14		25	23.13	even	11

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0393306 - 0.273550i) q^{2} +(0.955665 - 2.09261i) q^{3} +(1.84570 - 0.541947i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-0.610022 - 0.179119i) q^{6} +(-2.63800 + 1.69534i) q^{7} +(-0.450453 - 0.986355i) q^{8} +(-1.50116 - 1.73243i) q^{9} +O(q^{10})\)	\(q+(-0.0393306 - 0.273550i) q^{2} +(0.955665 - 2.09261i) q^{3} +(1.84570 - 0.541947i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-0.610022 - 0.179119i) q^{6} +(-2.63800 + 1.69534i) q^{7} +(-0.450453 - 0.986355i) q^{8} +(-1.50116 - 1.73243i) q^{9} +(0.232492 + 0.149413i) q^{10} +(-0.369695 + 2.57128i) q^{11} +(0.629787 - 4.38027i) q^{12} +(-0.0559711 - 0.0359704i) q^{13} +(0.567516 + 0.654948i) q^{14} +(0.955665 + 2.09261i) q^{15} +(2.98441 - 1.91796i) q^{16} +(-1.42241 - 0.417657i) q^{17} +(-0.414865 + 0.478780i) q^{18} +(4.42817 - 1.30023i) q^{19} +(-0.799102 + 1.74979i) q^{20} +(1.02665 + 7.14051i) q^{21} +0.717915 q^{22} +(-2.65025 + 3.99702i) q^{23} -2.49454 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-0.00763835 + 0.0167256i) q^{26} +(1.56205 - 0.458659i) q^{27} +(-3.95019 + 4.55876i) q^{28} +(-9.93501 - 2.91718i) q^{29} +(0.534849 - 0.343726i) q^{30} +(3.45291 + 7.56083i) q^{31} +(-2.06223 - 2.37994i) q^{32} +(5.02740 + 3.23091i) q^{33} +(-0.0583060 + 0.405527i) q^{34} +(0.446271 - 3.10388i) q^{35} +(-3.70958 - 2.38400i) q^{36} +(-3.92880 - 4.53408i) q^{37} +(-0.529840 - 1.16019i) q^{38} +(-0.128762 + 0.0827502i) q^{39} +(1.04042 + 0.305495i) q^{40} +(-2.55857 + 2.95275i) q^{41} +(1.91291 - 0.561681i) q^{42} +(3.26842 - 7.15685i) q^{43} +(0.711153 + 4.94618i) q^{44} +2.29233 q^{45} +(1.19762 + 0.567772i) q^{46} +8.42088 q^{47} +(-1.16146 - 8.07815i) q^{48} +(1.17697 - 2.57722i) q^{49} +(-0.265169 + 0.0778605i) q^{50} +(-2.23334 + 2.57741i) q^{51} +(-0.122800 - 0.0360573i) q^{52} +(-0.190337 + 0.122322i) q^{53} +(-0.186903 - 0.409260i) q^{54} +(-1.70115 - 1.96323i) q^{55} +(2.86051 + 1.83834i) q^{56} +(1.51097 - 10.5090i) q^{57} +(-0.407246 + 2.83246i) q^{58} +(0.709087 + 0.455703i) q^{59} +(2.89796 + 3.34443i) q^{60} +(-3.25234 - 7.12164i) q^{61} +(1.93246 - 1.24192i) q^{62} +(6.89712 + 2.02518i) q^{63} +(4.07641 - 4.70443i) q^{64} +(0.0638379 - 0.0187445i) q^{65} +(0.686087 - 1.50232i) q^{66} +(1.42203 + 9.89044i) q^{67} -2.85169 q^{68} +(5.83147 + 9.36577i) q^{69} -0.866621 q^{70} +(-1.22385 - 8.51208i) q^{71} +(-1.03259 + 2.26105i) q^{72} +(-8.56020 + 2.51350i) q^{73} +(-1.08578 + 1.25305i) q^{74} +(-2.20732 - 0.648128i) q^{75} +(7.46843 - 4.79967i) q^{76} +(-3.38395 - 7.40981i) q^{77} +(0.0277006 + 0.0319682i) q^{78} +(-12.5251 - 8.04939i) q^{79} +(-0.504872 + 3.51146i) q^{80} +(1.51170 - 10.5141i) q^{81} +(0.908355 + 0.583764i) q^{82} +(-5.87671 - 6.78209i) q^{83} +(5.76467 + 12.6229i) q^{84} +(1.24712 - 0.801477i) q^{85} +(-2.08631 - 0.612595i) q^{86} +(-15.5991 + 18.0023i) q^{87} +(2.70273 - 0.793593i) q^{88} +(0.984223 - 2.15515i) q^{89} +(-0.0901588 - 0.627068i) q^{90} +0.208634 q^{91} +(-2.72540 + 8.81361i) q^{92} +19.1217 q^{93} +(-0.331198 - 2.30353i) q^{94} +(-1.91719 + 4.19806i) q^{95} +(-6.95110 + 2.04103i) q^{96} +(5.06792 - 5.84870i) q^{97} +(-0.751289 - 0.220598i) q^{98} +(5.00953 - 3.21943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Introduction

L-functions

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