LMFDB - Embedded newform 287.2.z.a.4.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(4,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 9]))

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

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

chi := DirichletCharacter("287.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.z (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$208$
Relative dimension:	$26$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			4.17
Character	$\chi$	$=$	287.4
Dual form			287.2.z.a.72.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.909063 + 0.404741i) q^{2} +(0.864285 + 0.498995i) q^{3} +(-0.675680 - 0.750419i) q^{4} +(2.62197 - 0.557318i) q^{5} +(0.583726 + 0.803430i) q^{6} +(1.31896 + 2.29354i) q^{7} +(-0.925513 - 2.84843i) q^{8} +(-1.00201 - 1.73553i) q^{9} +O(q^{10})$	\(q+(0.909063 + 0.404741i) q^{2} +(0.864285 + 0.498995i) q^{3} +(-0.675680 - 0.750419i) q^{4} +(2.62197 - 0.557318i) q^{5} +(0.583726 + 0.803430i) q^{6} +(1.31896 + 2.29354i) q^{7} +(-0.925513 - 2.84843i) q^{8} +(-1.00201 - 1.73553i) q^{9} +(2.60911 + 0.554583i) q^{10} +(0.0497068 - 0.233852i) q^{11} +(-0.209525 - 0.985737i) q^{12} +(-0.221487 - 0.304851i) q^{13} +(0.270730 + 2.61881i) q^{14} +(2.54423 + 0.826671i) q^{15} +(0.100426 - 0.955487i) q^{16} +(-1.40770 + 6.62270i) q^{17} +(-0.208449 - 1.98326i) q^{18} +(0.773259 + 0.0812728i) q^{19} +(-2.18984 - 1.59101i) q^{20} +(-0.00450663 + 2.64043i) q^{21} +(0.139836 - 0.192468i) q^{22} +(-0.833795 - 0.371229i) q^{23} +(0.621448 - 2.92369i) q^{24} +(1.99642 - 0.888863i) q^{25} +(-0.0779601 - 0.366774i) q^{26} -4.99396i q^{27} +(0.829921 - 2.53948i) q^{28} +(0.0762261 + 0.0247674i) q^{29} +(1.97828 + 1.78125i) q^{30} +(0.936933 + 0.199151i) q^{31} +(-2.51700 + 4.35958i) q^{32} +(0.159652 - 0.177311i) q^{33} +(-3.96017 + 5.45070i) q^{34} +(4.73652 + 5.27853i) q^{35} +(-0.625337 + 1.92459i) q^{36} +(-7.72395 + 1.64178i) q^{37} +(0.670047 + 0.386852i) q^{38} +(-0.0393089 - 0.373999i) q^{39} +(-4.01415 - 6.95272i) q^{40} +(-3.22124 - 5.53386i) q^{41} +(-1.07279 + 2.39849i) q^{42} +(3.58148 - 2.60209i) q^{43} +(-0.209073 + 0.120708i) q^{44} +(-3.59448 - 3.99207i) q^{45} +(-0.607720 - 0.674942i) q^{46} +(-2.03027 + 4.56005i) q^{47} +(0.563580 - 0.775701i) q^{48} +(-3.52067 + 6.05020i) q^{49} +2.17463 q^{50} +(-4.52135 + 5.02146i) q^{51} +(-0.0791114 + 0.372190i) q^{52} +(-8.00606 + 7.20869i) q^{53} +(2.02126 - 4.53982i) q^{54} -0.640857i q^{55} +(5.31229 - 5.87968i) q^{56} +(0.627761 + 0.456095i) q^{57} +(0.0592700 + 0.0533670i) q^{58} +(-1.41836 - 13.4948i) q^{59} +(-1.09874 - 2.46780i) q^{60} +(0.870995 - 8.28696i) q^{61} +(0.771126 + 0.560256i) q^{62} +(2.65890 - 4.58725i) q^{63} +(-5.60714 + 4.07383i) q^{64} +(-0.750632 - 0.675872i) q^{65} +(0.216899 - 0.0965696i) q^{66} +(-5.11228 + 4.60312i) q^{67} +(5.92096 - 3.41847i) q^{68} +(-0.535394 - 0.736907i) q^{69} +(2.16936 + 6.71558i) q^{70} +(13.8585 - 4.50289i) q^{71} +(-4.01617 + 4.46041i) q^{72} +(0.484870 - 0.839820i) q^{73} +(-7.68606 - 1.63372i) q^{74} +(2.16901 + 0.227972i) q^{75} +(-0.461487 - 0.635183i) q^{76} +(0.601911 - 0.194438i) q^{77} +(0.115638 - 0.355899i) q^{78} +(0.124151 - 0.0716786i) q^{79} +(-0.269196 - 2.56123i) q^{80} +(-0.514063 + 0.890383i) q^{81} +(-0.688530 - 6.33440i) q^{82} -1.52620 q^{83} +(1.98447 - 1.78070i) q^{84} +18.1491i q^{85} +(4.30896 - 0.915898i) q^{86} +(0.0535223 + 0.0594425i) q^{87} +(-0.712117 + 0.0748465i) q^{88} +(10.1586 + 1.06771i) q^{89} +(-1.65185 - 5.08388i) q^{90} +(0.407055 - 0.910077i) q^{91} +(0.284801 + 0.876528i) q^{92} +(0.710401 + 0.639648i) q^{93} +(-3.69128 + 3.32364i) q^{94} +(2.07276 - 0.217856i) q^{95} +(-4.35082 + 2.51194i) q^{96} +(-0.883361 - 0.287021i) q^{97} +(-5.64928 + 4.07505i) q^{98} +(-0.455664 + 0.148054i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q - 3 q^{2} + 21 q^{4} + q^{5} - 40 q^{6} - 10 q^{7} - 8 q^{8} + 84 q^{9}+O(q^{10}) $ 208 * q - 3 * q^2 + 21 * q^4 + q^5 - 40 * q^6 - 10 * q^7 - 8 * q^8 + 84 * q^9	\( 208 q - 3 q^{2} + 21 q^{4} + q^{5} - 40 q^{6} - 10 q^{7} - 8 q^{8} + 84 q^{9} - 6 q^{10} - 5 q^{11} - 35 q^{12} - 20 q^{13} - 50 q^{15} + 21 q^{16} - 5 q^{17} + 18 q^{18} - 5 q^{19} - 96 q^{20} + 8 q^{21} + 20 q^{22} + 40 q^{24} + 27 q^{25} - 5 q^{26} + 5 q^{28} + 20 q^{29} - 45 q^{30} - 11 q^{31} - 30 q^{32} - 10 q^{33} + 100 q^{34} - 106 q^{36} - 16 q^{37} - 4 q^{39} + 6 q^{40} - 14 q^{41} - 8 q^{42} - 8 q^{43} + 34 q^{45} - 32 q^{46} + 25 q^{47} - 50 q^{48} + 14 q^{49} - 120 q^{50} + 2 q^{51} - 105 q^{52} + 20 q^{53} - 35 q^{54} + 100 q^{56} - 98 q^{57} - 5 q^{58} - 37 q^{59} - 100 q^{60} + 51 q^{61} - 70 q^{62} - 30 q^{63} - 100 q^{64} + 40 q^{65} - 176 q^{66} + 15 q^{67} - 30 q^{69} + 105 q^{70} - 10 q^{71} - 33 q^{72} - 34 q^{73} - 23 q^{74} - 120 q^{75} + 110 q^{76} + 72 q^{77} - 18 q^{78} + 127 q^{80} - 24 q^{81} - 63 q^{82} - 128 q^{83} + 33 q^{84} - 61 q^{86} + 28 q^{87} + 150 q^{88} + 35 q^{89} - 34 q^{90} + 14 q^{91} + 102 q^{92} - 55 q^{93} - 155 q^{94} + 55 q^{95} + 20 q^{97} + 88 q^{98} + 120 q^{99}+O(q^{100}) \) 208 * q - 3 * q^2 + 21 * q^4 + q^5 - 40 * q^6 - 10 * q^7 - 8 * q^8 + 84 * q^9 - 6 * q^10 - 5 * q^11 - 35 * q^12 - 20 * q^13 - 50 * q^15 + 21 * q^16 - 5 * q^17 + 18 * q^18 - 5 * q^19 - 96 * q^20 + 8 * q^21 + 20 * q^22 + 40 * q^24 + 27 * q^25 - 5 * q^26 + 5 * q^28 + 20 * q^29 - 45 * q^30 - 11 * q^31 - 30 * q^32 - 10 * q^33 + 100 * q^34 - 106 * q^36 - 16 * q^37 - 4 * q^39 + 6 * q^40 - 14 * q^41 - 8 * q^42 - 8 * q^43 + 34 * q^45 - 32 * q^46 + 25 * q^47 - 50 * q^48 + 14 * q^49 - 120 * q^50 + 2 * q^51 - 105 * q^52 + 20 * q^53 - 35 * q^54 + 100 * q^56 - 98 * q^57 - 5 * q^58 - 37 * q^59 - 100 * q^60 + 51 * q^61 - 70 * q^62 - 30 * q^63 - 100 * q^64 + 40 * q^65 - 176 * q^66 + 15 * q^67 - 30 * q^69 + 105 * q^70 - 10 * q^71 - 33 * q^72 - 34 * q^73 - 23 * q^74 - 120 * q^75 + 110 * q^76 + 72 * q^77 - 18 * q^78 + 127 * q^80 - 24 * q^81 - 63 * q^82 - 128 * q^83 + 33 * q^84 - 61 * q^86 + 28 * q^87 + 150 * q^88 + 35 * q^89 - 34 * q^90 + 14 * q^91 + 102 * q^92 - 55 * q^93 - 155 * q^94 + 55 * q^95 + 20 * q^97 + 88 * q^98 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.909063	+	0.404741i	0.642805	+	0.286195i	0.702136	−	0.712043i	$-0.252230\pi$
$2$	0.909063	+	0.404741i	0.642805	+	0.286195i	−0.0593308	+	0.998238i	$0.518897\pi$
$3$	0.864285	+	0.498995i	0.498995	+	0.288095i	0.728298	−	0.685260i	$-0.240311\pi$
$3$	0.864285	+	0.498995i	0.498995	+	0.288095i	−0.229303	+	0.973355i	$0.573645\pi$
$4$	−0.675680	−	0.750419i	−0.337840	−	0.375210i
$5$	2.62197	−	0.557318i	1.17258	−	0.249240i	0.419867	−	0.907586i	$-0.362077\pi$
$5$	2.62197	−	0.557318i	1.17258	−	0.249240i	0.752716	+	0.658346i	$0.228743\pi$
$6$	0.583726	+	0.803430i	0.238305	+	0.327999i
$7$	1.31896	+	2.29354i	0.498521	+	0.866878i
$7$	1.31896	+	2.29354i	0.498521	+	0.866878i
$8$	−0.925513	−	2.84843i	−0.327218	−	1.00707i
$9$	−1.00201	−	1.73553i	−0.334003	−	0.578510i
$10$	2.60911	+	0.554583i	0.825073	+	0.175375i
$11$	0.0497068	−	0.233852i	0.0149872	−	0.0705091i	−0.970018	−	0.243031i	$-0.921858\pi$
$11$	0.0497068	−	0.233852i	0.0149872	−	0.0705091i	0.985006	+	0.172522i	$0.0551916\pi$
$12$	−0.209525	−	0.985737i	−0.0604846	−	0.284558i
$13$	−0.221487	−	0.304851i	−0.0614294	−	0.0845504i	0.777197	−	0.629257i	$-0.216641\pi$
$13$	−0.221487	−	0.304851i	−0.0614294	−	0.0845504i	−0.838626	+	0.544707i	$0.816641\pi$
$14$	0.270730	+	2.61881i	0.0723557	+	0.699907i
$15$	2.54423	+	0.826671i	0.656918	+	0.213446i
$16$	0.100426	−	0.955487i	0.0251064	−	0.238872i
$17$	−1.40770	+	6.62270i	−0.341417	+	1.60624i	0.387655	+	0.921804i	$0.373285\pi$
$17$	−1.40770	+	6.62270i	−0.341417	+	1.60624i	−0.729072	+	0.684437i	$0.760048\pi$
$18$	−0.208449	−	1.98326i	−0.0491319	−	0.467459i
$19$	0.773259	+	0.0812728i	0.177398	+	0.0186453i	0.192811	−	0.981236i	$-0.438240\pi$
$19$	0.773259	+	0.0812728i	0.177398	+	0.0186453i	−0.0154130	+	0.999881i	$0.504906\pi$
$20$	−2.18984	−	1.59101i	−0.489663	−	0.355761i
$21$	−0.00450663	+	2.64043i	−0.000983427	+	0.576189i
$22$	0.139836	−	0.192468i	0.0298132	−	0.0410343i
$23$	−0.833795	−	0.371229i	−0.173858	−	0.0774066i	0.317962	−	0.948103i	$-0.397002\pi$
$23$	−0.833795	−	0.371229i	−0.173858	−	0.0774066i	−0.491820	+	0.870697i	$0.663668\pi$
$24$	0.621448	−	2.92369i	0.126853	−	0.596795i
$25$	1.99642	−	0.888863i	0.399284	−	0.177773i
$26$	−0.0779601	−	0.366774i	−0.0152892	−	0.0719302i
$27$		−	4.99396i		−	0.961088i
$28$	0.829921	−	2.53948i	0.156840	−	0.479916i
$29$	0.0762261	+	0.0247674i	0.0141548	+	0.00459919i	0.316086	−	0.948731i	$-0.397631\pi$
$29$	0.0762261	+	0.0247674i	0.0141548	+	0.00459919i	−0.301931	+	0.953330i	$0.597631\pi$
$30$	1.97828	+	1.78125i	0.361183	+	0.325210i
$31$	0.936933	+	0.199151i	0.168278	+	0.0357686i	0.291280	−	0.956638i	$-0.405919\pi$
$31$	0.936933	+	0.199151i	0.168278	+	0.0357686i	−0.123002	+	0.992406i	$0.539252\pi$
$32$	−2.51700	+	4.35958i	−0.444948	+	0.770672i
$33$	0.159652	−	0.177311i	0.0277918	−	0.0308660i
$34$	−3.96017	+	5.45070i	−0.679163	+	0.934788i
$35$	4.73652	+	5.27853i	0.800618	+	0.892234i
$36$	−0.625337	+	1.92459i	−0.104223	+	0.320765i
$37$	−7.72395	+	1.64178i	−1.26981	+	0.269907i	−0.793066	−	0.609136i	$-0.791517\pi$
$37$	−7.72395	+	1.64178i	−1.26981	+	0.269907i	−0.476744	+	0.879042i	$0.658183\pi$
$38$	0.670047	+	0.386852i	0.108696	+	0.0627556i
$39$	−0.0393089	−	0.373999i	−0.00629445	−	0.0598877i
$40$	−4.01415	−	6.95272i	−0.634693	−	1.09932i
$41$	−3.22124	−	5.53386i	−0.503073	−	0.864244i
$41$	−3.22124	−	5.53386i	−0.503073	−	0.864244i
$42$	−1.07279	+	2.39849i	−0.165535	+	0.370096i
$43$	3.58148	−	2.60209i	0.546170	−	0.396816i	−0.280201	−	0.959941i	$-0.590401\pi$
$43$	3.58148	−	2.60209i	0.546170	−	0.396816i	0.826371	+	0.563126i	$0.190401\pi$
$44$	−0.209073	+	0.120708i	−0.0315190	+	0.0181975i
$45$	−3.59448	−	3.99207i	−0.535833	−	0.595103i
$46$	−0.607720	−	0.674942i	−0.0896035	−	0.0995147i
$47$	−2.03027	+	4.56005i	−0.296145	+	0.665152i	−0.998930	−	0.0462502i	$-0.985273\pi$
$47$	−2.03027	+	4.56005i	−0.296145	+	0.665152i	0.702785	+	0.711402i	$0.251940\pi$
$48$	0.563580	−	0.775701i	0.0813457	−	0.111963i
$49$	−3.52067	+	6.05020i	−0.502953	+	0.864314i
$50$	2.17463			0.307539
$51$	−4.52135	+	5.02146i	−0.633115	+	0.703146i
$52$	−0.0791114	+	0.372190i	−0.0109708	+	0.0516134i
$53$	−8.00606	+	7.20869i	−1.09972	+	0.990189i	−0.999988	−	0.00482536i	$-0.998464\pi$
$53$	−8.00606	+	7.20869i	−1.09972	+	0.990189i	−0.0997283	+	0.995015i	$0.531797\pi$
$54$	2.02126	−	4.53982i	0.275059	−	0.617792i
$55$		−	0.640857i		−	0.0864131i
$56$	5.31229	−	5.87968i	0.709884	−	0.785706i
$57$	0.627761	+	0.456095i	0.0831490	+	0.0604113i
$58$	0.0592700	+	0.0533670i	0.00778253	+	0.00700743i
$59$	−1.41836	−	13.4948i	−0.184655	−	1.75687i	−0.558615	−	0.829427i	$-0.688667\pi$
$59$	−1.41836	−	13.4948i	−0.184655	−	1.75687i	0.373960	−	0.927445i	$-0.378000\pi$
$60$	−1.09874	−	2.46780i	−0.141846	−	0.318592i
$61$	0.870995	−	8.28696i	0.111519	−	1.06104i	−0.785444	−	0.618932i	$-0.787566\pi$
$61$	0.870995	−	8.28696i	0.111519	−	1.06104i	0.896964	−	0.442104i	$-0.145768\pi$
$62$	0.771126	+	0.560256i	0.0979331	+	0.0711526i
$63$	2.65890	−	4.58725i	0.334990	−	0.577939i
$64$	−5.60714	+	4.07383i	−0.700893	+	0.509228i
$65$	−0.750632	−	0.675872i	−0.0931044	−	0.0838316i
$66$	0.216899	−	0.0965696i	0.0266984	−	0.0118869i
$67$	−5.11228	+	4.60312i	−0.624564	+	0.562360i	−0.919467	−	0.393167i	$-0.871379\pi$
$67$	−5.11228	+	4.60312i	−0.624564	+	0.562360i	0.294903	+	0.955527i	$0.404713\pi$
$68$	5.92096	−	3.41847i	0.718021	−	0.414550i
$69$	−0.535394	−	0.736907i	−0.0644539	−	0.0887132i
$70$	2.16936	+	6.71558i	0.259288	+	0.802665i
$71$	13.8585	−	4.50289i	1.64470	−	0.534395i	0.667117	−	0.744953i	$-0.267528\pi$
$71$	13.8585	−	4.50289i	1.64470	−	0.534395i	0.977581	+	0.210558i	$0.0675282\pi$
$72$	−4.01617	+	4.46041i	−0.473310	+	0.525664i
$73$	0.484870	−	0.839820i	0.0567498	−	0.0982935i	−0.836255	−	0.548341i	$-0.815260\pi$
$73$	0.484870	−	0.839820i	0.0567498	−	0.0982935i	0.893005	+	0.450047i	$0.148593\pi$
$74$	−7.68606	−	1.63372i	−0.893486	−	0.189916i
$75$	2.16901	+	0.227972i	0.250456	+	0.0263240i
$76$	−0.461487	−	0.635183i	−0.0529362	−	0.0728605i
$77$	0.601911	−	0.194438i	0.0685942	−	0.0221582i
$78$	0.115638	−	0.355899i	0.0130935	−	0.0402976i
$79$	0.124151	−	0.0716786i	0.0139681	−	0.00806448i	−0.493000	−	0.870029i	$-0.664100\pi$
$79$	0.124151	−	0.0716786i	0.0139681	−	0.00806448i	0.506968	+	0.861965i	$0.330766\pi$
$80$	−0.269196	−	2.56123i	−0.0300971	−	0.286354i
$81$	−0.514063	+	0.890383i	−0.0571181	+	0.0989315i
$82$	−0.688530	−	6.33440i	−0.0760354	−	0.699517i
$83$	−1.52620			−0.167522			−0.0837612	−	0.996486i	$-0.526693\pi$
$83$	−1.52620			−0.167522			−0.0837612	+	0.996486i	$0.526693\pi$
$84$	1.98447	−	1.78070i	0.216524	−	0.194291i
$85$			18.1491i			1.96854i
$86$	4.30896	−	0.915898i	0.464647	−	0.0987639i
$87$	0.0535223	+	0.0594425i	0.00573819	+	0.00637291i
$88$	−0.712117	+	0.0748465i	−0.0759119	+	0.00797867i
$89$	10.1586	+	1.06771i	1.07681	+	0.113177i	0.626291	−	0.779590i	$-0.284572\pi$
$89$	10.1586	+	1.06771i	1.07681	+	0.113177i	0.450519	+	0.892767i	$0.351239\pi$
$90$	−1.65185	−	5.08388i	−0.174121	−	0.535888i
$91$	0.407055	−	0.910077i	0.0426709	−	0.0954020i
$92$	0.284801	+	0.876528i	0.0296926	+	0.0913843i
$93$	0.710401	+	0.639648i	0.0736652	+	0.0663284i
$94$	−3.69128	+	3.32364i	−0.380727	+	0.342808i
$95$	2.07276	−	0.217856i	0.212661	−	0.0223515i
$96$	−4.35082	+	2.51194i	−0.444053	+	0.256374i
$97$	−0.883361	−	0.287021i	−0.0896917	−	0.0291426i	0.263827	−	0.964570i	$-0.415015\pi$
$97$	−0.883361	−	0.287021i	−0.0896917	−	0.0291426i	−0.353519	+	0.935427i	$0.615015\pi$
$98$	−5.64928	+	4.07505i	−0.570663	+	0.411642i
$99$	−0.455664	+	0.148054i	−0.0457959	+	0.0148800i
$100$	−2.01596	−	0.897563i	−0.201596	−	0.0897563i
$101$	−0.457865	−	1.02838i	−0.0455593	−	0.102328i	0.889332	−	0.457262i	$-0.151170\pi$
$101$	−0.457865	−	1.02838i	−0.0455593	−	0.102328i	−0.934891	+	0.354934i	$0.884503\pi$
$102$	−6.14258	+	2.73485i	−0.608206	+	0.270791i
$103$	−0.804780	+	7.65697i	−0.0792973	+	0.754464i	0.880552	+	0.473949i	$0.157172\pi$
$103$	−0.804780	+	7.65697i	−0.0792973	+	0.754464i	−0.959850	+	0.280515i	$0.909495\pi$
$104$	−0.663358	+	0.913035i	−0.0650476	+	0.0895304i
$105$	1.45974	+	6.92565i	0.142456	+	0.675874i
$106$	−10.1957	+	3.31277i	−0.990291	+	0.321765i
$107$	1.46511	−	13.9396i	0.141638	−	1.34759i	−0.660667	−	0.750679i	$-0.729726\pi$
$107$	1.46511	−	13.9396i	0.141638	−	1.34759i	0.802304	−	0.596915i	$-0.203607\pi$
$108$	−3.74756	+	3.37432i	−0.360609	+	0.324694i
$109$	9.11054	+	5.25997i	0.872631	+	0.503814i	0.868222	−	0.496176i	$-0.165263\pi$
$109$	9.11054	+	5.25997i	0.872631	+	0.503814i	0.00440941	+	0.999990i	$0.498596\pi$
$110$	0.259381	−	0.582580i	0.0247310	−	0.0555468i
$111$	−7.49494	−	2.43525i	−0.711388	−	0.231144i
$112$	2.32391	−	1.02992i	0.219589	−	0.0973184i
$113$	3.28367	+	10.1061i	0.308901	+	0.950701i	0.978192	+	0.207701i	$0.0665979\pi$
$113$	3.28367	+	10.1061i	0.308901	+	0.950701i	−0.669291	+	0.743000i	$0.733402\pi$
$114$	0.386074	+	0.668700i	0.0361592	+	0.0626295i
$115$	−2.39308	−	0.508665i	−0.223156	−	0.0474333i
$116$	−0.0329186	−	0.0739364i	−0.00305641	−	0.00686482i
$117$	−0.307145	+	0.689860i	−0.0283956	+	0.0637776i
$118$	4.17252	−	12.8417i	0.384111	−	1.18217i
$119$	−17.0461	+	5.50648i	−1.56262	+	0.504778i
$120$		−	8.01217i		−	0.731408i
$121$	9.99678	+	4.45085i	0.908799	+	0.404623i
$122$	4.14586	−	7.18084i	0.375349	−	0.650123i
$123$	−0.0226993	−	6.39021i	−0.00204673	−	0.576186i
$124$	−0.483620	−	0.837655i	−0.0434304	−	0.0752236i
$125$	−6.10388	+	4.43473i	−0.545947	+	0.396654i
$126$	4.27375	−	3.09393i	0.380736	−	0.275629i
$127$	−2.64662	+	8.14544i	−0.234849	+	0.722791i	0.762292	+	0.647233i	$0.224074\pi$
$127$	−2.64662	+	8.14544i	−0.234849	+	0.722791i	−0.997141	+	0.0755583i	$0.975926\pi$
$128$	3.10191	−	0.659331i	0.274173	−	0.0582772i
$129$	4.39385	−	0.461812i	0.386857	−	0.0406603i
$130$	−0.408819	−	0.918222i	−0.0358558	−	0.0805334i
$131$	10.5129	−	11.6758i	0.918520	−	1.02012i	−0.0812056	−	0.996697i	$-0.525877\pi$
$131$	10.5129	−	11.6758i	0.918520	−	1.02012i	0.999726	−	0.0234225i	$-0.00745628\pi$
$132$	−0.240932			−0.0209704
$133$	0.833497	+	1.88070i	0.0722734	+	0.163077i
$134$	−6.51045	+	2.11537i	−0.562418	+	0.182741i
$135$	−2.78322	−	13.0940i	−0.239542	−	1.12695i
$136$	20.1672	−	2.11966i	1.72932	−	0.181759i
$137$	−1.29516	−	0.747762i	−0.110653	−	0.0638856i	0.443652	−	0.896199i	$-0.353683\pi$
$137$	−1.29516	−	0.747762i	−0.110653	−	0.0638856i	−0.554305	+	0.832314i	$0.687016\pi$
$138$	−0.188451	−	0.886591i	−0.0160420	−	0.0754717i
$139$	13.7327	+	9.97737i	1.16479	+	0.846269i	0.990376	−	0.138403i	$-0.0441969\pi$
$139$	13.7327	+	9.97737i	1.16479	+	0.846269i	0.174414	+	0.984672i	$0.444197\pi$
$140$	0.760735	−	7.12097i	0.0642938	−	0.601832i
$141$	−4.03017	+	2.92809i	−0.339402	+	0.246590i
$142$	14.4207	+	1.51568i	1.21016	+	0.127193i
$143$	−0.0822994	+	0.0366421i	−0.00688223	+	0.00306416i
$144$	−1.75890	+	0.783114i	−0.146575	+	0.0652595i
$145$	0.213666	+	0.0224572i	0.0177440	+	0.00186497i
$146$	0.780687	−	0.567203i	0.0646101	−	0.0469420i
$147$	−6.06188	+	3.47229i	−0.499976	+	0.286390i
$148$	6.45095	+	4.68689i	0.530264	+	0.385260i
$149$	−2.64441	−	12.4410i	−0.216638	−	1.01920i	−0.943232	−	0.332135i	$-0.892231\pi$
$149$	−2.64441	−	12.4410i	−0.216638	−	1.01920i	0.726594	−	0.687067i	$-0.241102\pi$
$150$	1.87950	+	1.08513i	0.153461	+	0.0886005i
$151$	1.76675	−	0.185693i	0.143776	−	0.0151115i	−0.0323670	−	0.999476i	$-0.510305\pi$
$151$	1.76675	−	0.185693i	0.143776	−	0.0151115i	0.176143	+	0.984365i	$0.443638\pi$
$152$	−0.484161	−	2.27780i	−0.0392706	−	0.184754i
$153$	12.9044	−	4.19290i	1.04326	−	0.338976i
$154$	0.625873	+	0.0668621i	0.0504343	+	0.00538790i
$155$	2.56760			0.206235
$156$	−0.254096	+	0.282202i	−0.0203439	+	0.0225942i
$157$	8.42344	+	18.9194i	0.672264	+	1.50993i	0.850519	+	0.525945i	$0.176288\pi$
$157$	8.42344	+	18.9194i	0.672264	+	1.50993i	−0.178255	+	0.983984i	$0.557045\pi$
$158$	0.141872	−	0.0149114i	0.0112868	−	0.00118629i
$159$	−10.5166	+	2.23538i	−0.834022	+	0.177277i
$160$	−4.16985	+	12.8335i	−0.329655	+	1.01457i
$161$	−0.248314	−	2.40198i	−0.0195699	−	0.189303i
$162$	−0.827691	+	0.601353i	−0.0650295	+	0.0472467i
$163$	7.79202	+	13.4962i	0.610318	+	1.05710i	0.991187	+	0.132473i	$0.0422917\pi$
$163$	7.79202	+	13.4962i	0.610318	+	1.05710i	−0.380868	+	0.924629i	$0.624375\pi$
$164$	−1.97619	+	6.15640i	−0.154314	+	0.480734i
$165$	0.319784	−	0.553883i	0.0248952	−	0.0431197i
$166$	−1.38741	−	0.617716i	−0.107684	−	0.0479441i
$167$		−	6.40280i		−	0.495464i	−0.968829	−	0.247732i	$-0.920315\pi$
$167$		−	6.40280i		−	0.495464i	0.968829	−	0.247732i	$-0.0796852\pi$
$168$	7.52526	−	2.43091i	0.580587	−	0.187549i
$169$	3.97334	−	12.2287i	0.305642	−	0.940669i
$170$	−7.34568	+	16.4987i	−0.563388	+	1.26539i
$171$	−0.633760	−	1.42345i	−0.0484649	−	0.108854i
$172$	−4.37259	−	0.929424i	−0.333407	−	0.0708679i
$173$	−4.57064	−	7.91658i	−0.347499	−	0.601887i	0.638305	−	0.769783i	$-0.279636\pi$
$173$	−4.57064	−	7.91658i	−0.347499	−	0.601887i	−0.985805	+	0.167897i	$0.946302\pi$
$174$	0.0245963	+	0.0756997i	0.00186464	+	0.00573878i
$175$	4.67185	+	3.40649i	0.353158	+	0.257507i
$176$	−0.218451	−	0.0709790i	−0.0164664	−	0.00535025i
$177$	5.50797	−	12.3711i	0.414004	−	0.929868i
$178$	8.80267	+	5.08222i	0.659788	+	0.380929i
$179$	−13.9809	+	12.5885i	−1.04498	+	0.940905i	−0.998316	−	0.0580053i	$-0.981526\pi$
$179$	−13.9809	+	12.5885i	−1.04498	+	0.940905i	−0.0466649	+	0.998911i	$0.514859\pi$
$180$	−0.567009	+	5.39473i	−0.0422624	+	0.402100i
$181$	8.32320	−	2.70437i	0.618659	−	0.201014i	0.0171141	−	0.999854i	$-0.494552\pi$
$181$	8.32320	−	2.70437i	0.618659	−	0.201014i	0.601545	+	0.798839i	$0.294552\pi$
$182$	0.738384	−	0.662566i	0.0547327	−	0.0491126i
$183$	4.88794	−	6.72767i	0.361327	−	0.497324i
$184$	−0.285735	+	2.71859i	−0.0210647	+	0.200417i
$185$	−19.3370	+	8.60940i	−1.42169	+	0.632975i
$186$	0.386908	+	0.869009i	0.0283695	+	0.0637188i
$187$	1.47876	+	0.658387i	0.108138	+	0.0481460i
$188$	4.79376	−	1.55759i	0.349621	−	0.113599i
$189$	11.4539	−	6.58685i	0.833145	−	0.479123i
$190$	1.97245	+	0.640886i	0.143096	+	0.0464948i
$191$	10.6852	−	6.16911i	0.773155	−	0.446381i	−0.0608437	−	0.998147i	$-0.519379\pi$
$191$	10.6852	−	6.16911i	0.773155	−	0.446381i	0.833999	+	0.551766i	$0.186046\pi$
$192$	−6.87899	+	0.723011i	−0.496448	+	0.0521788i
$193$	−11.2881	+	10.1639i	−0.812537	+	0.731612i	−0.966556	−	0.256456i	$-0.917445\pi$
$193$	−11.2881	+	10.1639i	−0.812537	+	0.731612i	0.154019	+	0.988068i	$0.450778\pi$
$194$	−0.686862	−	0.618453i	−0.0493138	−	0.0444023i
$195$	−0.311503	−	0.958708i	−0.0223072	−	0.0686545i
$196$	6.91903	−	1.44602i	0.494217	−	0.103287i
$197$	0.407842	+	1.25521i	0.0290575	+	0.0894299i	0.964534	−	0.263960i	$-0.0850288\pi$
$197$	0.407842	+	1.25521i	0.0290575	+	0.0894299i	−0.935476	+	0.353390i	$0.885029\pi$
$198$	−0.474151	−	0.0498353i	−0.0336964	−	0.00354164i
$199$	14.1489	−	1.48711i	1.00299	−	0.105419i	0.411230	−	0.911531i	$-0.365099\pi$
$199$	14.1489	−	1.48711i	1.00299	−	0.105419i	0.591762	+	0.806113i	$0.298433\pi$
$200$	−4.37958	−	4.86401i	−0.309683	−	0.343938i
$201$	−6.71540	+	1.42740i	−0.473667	+	0.100681i
$202$		−	1.12018i		−	0.0788157i
$203$	0.0437344	+	0.207495i	0.00306956	+	0.0145633i
$204$	6.82319			0.477719
$205$	−11.5301	−	12.7144i	−0.805299	−	0.888011i
$206$	−3.83069	+	6.63495i	−0.266897	+	0.462279i
$207$	0.191190	+	1.81905i	0.0132886	+	0.126433i
$208$	−0.313524	+	0.181013i	−0.0217390	+	0.0125510i
$209$	0.0574421	−	0.176789i	0.00397335	−	0.0122287i
$210$	−1.47610	+	6.88667i	−0.101860	+	0.475226i
$211$	−14.4117	−	19.8360i	−0.992143	−	1.36557i	−0.930024	−	0.367499i	$-0.880214\pi$
$211$	−14.4117	−	19.8360i	−0.992143	−	1.36557i	−0.0621192	−	0.998069i	$-0.519786\pi$
$212$	10.8191	+	1.13713i	0.743057	+	0.0780984i
$213$	14.2246	+	3.02353i	0.974653	+	0.207169i
$214$	6.97382	−	12.0790i	0.476721	−	0.825704i
$215$	7.94034	−	8.81865i	0.541527	−	0.601427i
$216$	−14.2250	+	4.62197i	−0.967886	+	0.314485i
$217$	0.779018	+	2.41157i	0.0528832	+	0.163708i
$218$	6.15313	+	8.46905i	0.416742	+	0.573597i
$219$	0.838132	−	0.483896i	0.0566357	−	0.0326986i
$220$	−0.480911	+	0.433015i	−0.0324230	+	0.0291938i
$221$	2.33072	−	1.03770i	0.156781	−	0.0698035i
$222$	−5.82772	−	5.24731i	−0.391131	−	0.352176i
$223$	2.24873	−	1.63380i	0.150586	−	0.109407i	−0.509941	−	0.860209i	$-0.670333\pi$
$223$	2.24873	−	1.63380i	0.150586	−	0.109407i	0.660527	+	0.750802i	$0.270333\pi$
$224$	−13.3187	−	0.0227321i	−0.889894	−	0.00151885i
$225$	−3.54307	−	2.57419i	−0.236205	−	0.171613i
$226$	−1.10529	+	10.5161i	−0.0735226	+	0.699521i
$227$	−9.66873	−	21.7163i	−0.641736	−	1.44136i	−0.882280	−	0.470724i	$-0.843993\pi$
$227$	−9.66873	−	21.7163i	−0.641736	−	1.44136i	0.240545	−	0.970638i	$-0.422674\pi$
$228$	−0.0819034	−	0.779259i	−0.00542418	−	0.0516077i
$229$	−10.8384	−	9.75895i	−0.716223	−	0.644890i	0.228204	−	0.973613i	$-0.426715\pi$
$229$	−10.8384	−	9.75895i	−0.716223	−	0.644890i	−0.944426	+	0.328724i	$0.893381\pi$
$230$	−1.96958	−	1.43099i	−0.129871	−	0.0943565i
$231$	0.617246	+	0.132301i	0.0406118	+	0.00870478i
$232$		−	0.240048i		−	0.0157599i
$233$	1.68872	−	3.79292i	0.110631	−	0.248482i	−0.849742	−	0.527199i	$-0.823242\pi$
$233$	1.68872	−	3.79292i	0.110631	−	0.248482i	0.960373	+	0.278716i	$0.0899090\pi$
$234$	−0.558429	+	0.502812i	−0.0365057	+	0.0328698i
$235$	−2.78191	+	13.0878i	−0.181472	+	0.853757i
$236$	−9.16839	+	10.1825i	−0.596811	+	0.662826i
$237$	0.143069			0.00929334
$238$	−17.7247	−	1.89354i	−1.14892	−	0.122740i
$239$	7.03636	−	9.68472i	0.455144	−	0.626452i	−0.518349	−	0.855169i	$-0.673453\pi$
$239$	7.03636	−	9.68472i	0.455144	−	0.626452i	0.973493	+	0.228717i	$0.0734530\pi$
$240$	1.04538	−	2.34796i	0.0674790	−	0.151560i
$241$	−6.79290	−	7.54428i	−0.437569	−	0.485970i	0.483513	−	0.875337i	$-0.339360\pi$
$241$	−6.79290	−	7.54428i	−0.437569	−	0.485970i	−0.921083	+	0.389367i	$0.872694\pi$
$242$	7.28627	+	8.09222i	0.468379	+	0.520187i
$243$	−13.8633	+	8.00397i	−0.889330	+	0.513455i
$244$	−6.80721	+	4.94572i	−0.435787	+	0.316618i
$245$	−5.85923	+	17.8256i	−0.374333	+	1.13884i
$246$	2.56575	−	5.81830i	0.163586	−	0.370961i
$247$	−0.146491	−	0.253729i	−0.00932098	−	0.0161444i
$248$	−0.299874	−	2.85311i	−0.0190420	−	0.181173i
$249$	−1.31907	−	0.761567i	−0.0835928	−	0.0482623i
$250$	−7.34373	+	1.56096i	−0.464458	+	0.0987236i
$251$	2.60199	−	8.00809i	0.164236	−	0.505466i	−0.834743	−	0.550639i	$-0.814384\pi$
$251$	2.60199	−	8.00809i	0.164236	−	0.505466i	0.998979	+	0.0451731i	$0.0143840\pi$
$252$	−5.23892	+	1.10422i	−0.330021	+	0.0695596i
$253$	−0.128258	+	0.176532i	−0.00806352	+	0.0110985i
$254$	−5.70274	+	6.33353i	−0.357822	+	0.397401i
$255$	−9.05630	+	15.6860i	−0.567128	+	0.982294i
$256$	16.6454	+	3.53809i	1.04034	+	0.221131i
$257$	−0.923837	−	0.831826i	−0.0576274	−	0.0518879i	0.639814	−	0.768530i	$-0.279011\pi$
$257$	−0.923837	−	0.831826i	−0.0576274	−	0.0518879i	−0.697441	+	0.716642i	$0.745678\pi$
$258$	4.18120	+	1.35855i	0.260310	+	0.0845799i
$259$	−13.9531	−	15.5498i	−0.867003	−	0.966216i
$260$			1.01996i			0.0632554i
$261$	−0.0333947	−	0.157110i	−0.00206708	−	0.00972485i
$262$	14.2826	−	6.35903i	0.882382	−	0.392862i
$263$	5.13858	−	24.1751i	0.316858	−	1.49070i	−0.474995	−	0.879989i	$-0.657550\pi$
$263$	5.13858	−	24.1751i	0.316858	−	1.49070i	0.791853	−	0.610712i	$-0.209117\pi$
$264$	−0.652820	−	0.290654i	−0.0401783	−	0.0178885i
$265$	−16.9741	+	23.3629i	−1.04271	+	1.43517i
$266$	−0.00349382	+	2.04702i	−0.000214220	+	0.125511i
$267$	8.24714	+	5.99190i	0.504717	+	0.366698i
$268$	6.90853	+	0.726116i	0.422006	+	0.0443546i
$269$	0.983036	+	9.35296i	0.0599367	+	0.570260i	0.982740	+	0.184990i	$0.0592251\pi$
$269$	0.983036	+	9.35296i	0.0599367	+	0.570260i	−0.922804	+	0.385270i	$0.874108\pi$
$270$	2.76957	−	13.0298i	0.168550	−	0.792968i
$271$	−2.64607	+	25.1757i	−0.160737	+	1.52931i	0.555534	+	0.831494i	$0.312514\pi$
$271$	−2.64607	+	25.1757i	−0.160737	+	1.52931i	−0.716272	+	0.697821i	$0.754153\pi$
$272$	6.18654	+	2.01013i	0.375114	+	0.121882i
$273$	0.805935	−	0.583447i	0.0487774	−	0.0353118i
$274$	−0.874734	−	1.20397i	−0.0528446	−	0.0727344i
$275$	−0.108627	−	0.511050i	−0.00655045	−	0.0308174i
$276$	−0.191234	+	0.899684i	−0.0115109	+	0.0541546i
$277$	−10.8591	−	2.30818i	−0.652462	−	0.138685i	−0.130224	−	0.991485i	$-0.541569\pi$
$277$	−10.8591	−	2.30818i	−0.652462	−	0.138685i	−0.522238	+	0.852800i	$0.674903\pi$
$278$	8.44562	+	14.6282i	0.506534	+	0.877343i
$279$	−0.593181	−	1.82562i	−0.0355128	−	0.109297i
$280$	10.6518	−	18.3770i	0.636569	−	1.09824i
$281$	11.4269	+	15.7278i	0.681671	+	0.938240i	0.999952	−	0.00975617i	$-0.00310553\pi$
$281$	11.4269	+	15.7278i	0.681671	+	0.938240i	−0.318281	+	0.947996i	$0.603106\pi$
$282$	−4.84880	+	1.03064i	−0.288742	+	0.0613740i
$283$	−2.65416	−	2.94774i	−0.157773	−	0.175225i	0.659076	−	0.752077i	$-0.270948\pi$
$283$	−2.65416	−	2.94774i	−0.157773	−	0.175225i	−0.816849	+	0.576852i	$0.804281\pi$
$284$	−12.7430	−	7.35715i	−0.756155	−	0.436566i
$285$	1.90016	+	0.846007i	0.112556	+	0.0501132i
$286$	−0.0896460			−0.00530088
$287$	8.44345	−	14.6870i	0.498401	−	0.866947i
$288$	10.0882			0.594455
$289$	−26.3483	−	11.7310i	−1.54990	−	0.690059i
$290$	0.185147	+	0.106895i	0.0108722	+	0.00627706i
$291$	−0.620253	−	0.688861i	−0.0363599	−	0.0403817i
$292$	−0.957834	+	0.203594i	−0.0560530	+	0.0119144i
$293$	−0.0945881	−	0.130189i	−0.00552590	−	0.00760574i	0.806245	−	0.591582i	$-0.201496\pi$
$293$	−0.0945881	−	0.130189i	−0.00552590	−	0.00760574i	−0.811771	+	0.583976i	$0.801496\pi$
$294$	−6.91601	+	0.703042i	−0.403350	+	0.0410022i
$295$	−11.2398	−	34.5925i	−0.654406	−	2.01405i
$296$	11.8251	+	20.4817i	0.687321	+	1.19047i
$297$	−1.16785	−	0.248234i	−0.0677654	−	0.0144040i
$298$	2.63143	−	12.3799i	0.152435	−	0.717149i
$299$	0.0715052	+	0.336405i	0.00413525	+	0.0194548i
$300$	−1.29448	−	1.78170i	−0.0747371	−	0.102867i
$301$	10.6918	+	4.78220i	0.616268	+	0.275641i
$302$	1.68125	+	0.546270i	0.0967448	+	0.0314343i
$303$	0.117432	−	1.11729i	0.00674627	−	0.0641865i
$304$	0.155310	−	0.730677i	0.00890765	−	0.0419072i
$305$	−2.33475	−	22.2136i	−0.133687	−	1.27195i
$306$	13.4280	+	1.41134i	0.767626	+	0.0806807i
$307$	10.5214	+	7.64422i	0.600486	+	0.436279i	0.846051	−	0.533101i	$-0.178974\pi$
$307$	10.5214	+	7.64422i	0.600486	+	0.436279i	−0.245565	+	0.969380i	$0.578974\pi$
$308$	−0.552610	−	0.320308i	−0.0314879	−	0.0182512i
$309$	−4.51635	+	6.21622i	−0.256926	+	0.353629i
$310$	2.33411	+	1.03921i	0.132569	+	0.0590234i
$311$	5.31771	−	25.0178i	0.301539	−	1.41863i	−0.522761	−	0.852479i	$-0.675098\pi$
$311$	5.31771	−	25.0178i	0.301539	−	1.41863i	0.824301	−	0.566152i	$-0.191569\pi$
$312$	−1.02893	+	0.458109i	−0.0582517	+	0.0259353i
$313$	1.08843	+	5.12066i	0.0615217	+	0.289437i	0.998144	−	0.0609051i	$-0.0193987\pi$
$313$	1.08843	+	5.12066i	0.0615217	+	0.289437i	−0.936622	+	0.350342i	$0.886065\pi$
$314$			20.6082i			1.16299i
$315$	4.41501	−	13.5095i	0.248757	−	0.761174i
$316$	−0.137675	−	0.0447335i	−0.00774485	−	0.00251645i
$317$	−21.7342	−	19.5695i	−1.22071	−	1.09913i	−0.992078	−	0.125622i	$-0.959907\pi$
$317$	−21.7342	−	19.5695i	−1.22071	−	1.09913i	−0.228635	−	0.973512i	$-0.573426\pi$
$318$	−10.4650	−	2.22441i	−0.586849	−	0.124739i
$319$	0.00958086	−	0.0165945i	0.000536425	−	0.000929116i
$320$	−12.4314	+	13.8064i	−0.694935	+	0.771803i
$321$	8.22208	−	11.3167i	0.458912	−	0.631638i
$322$	0.746447	−	2.28406i	0.0415979	−	0.127285i
$323$	−1.62676	+	5.00666i	−0.0905154	+	0.278578i
$324$	1.01550	−	0.215852i	0.0564168	−	0.0119918i
$325$	−0.713151	−	0.411738i	−0.0395585	−	0.0228391i
$326$	1.62098	+	15.4226i	0.0897780	+	0.854181i
$327$	5.24940	+	9.09223i	0.290292	+	0.502801i
$328$	−12.7815	+	14.2971i	−0.705743	+	0.789428i
$329$	−13.1365	+	1.35804i	−0.724240	+	0.0748711i
$330$	0.514884	−	0.374085i	0.0283434	−	0.0205927i
$331$	−29.9948	+	17.3175i	−1.64866	+	0.951856i	−0.671060	+	0.741403i	$0.734161\pi$
$331$	−29.9948	+	17.3175i	−1.64866	+	0.951856i	−0.977604	+	0.210453i	$0.932506\pi$
$332$	1.03122	+	1.14529i	0.0565958	+	0.0628560i
$333$	10.5888	+	11.7601i	0.580263	+	0.644448i
$334$	2.59148	−	5.82055i	0.141799	−	0.318486i
$335$	−10.8389	+	14.9184i	−0.592190	+	0.815080i
$336$	2.52244	+	0.269473i	0.137611	+	0.0147010i
$337$	−31.5768			−1.72010			−0.860049	−	0.510211i	$-0.829567\pi$
$337$	−31.5768			−1.72010			−0.860049	+	0.510211i	$0.829567\pi$
$338$	8.56148	−	9.50848i	0.465683	−	0.517193i
$339$	−2.20486	+	10.3731i	−0.119752	+	0.563388i
$340$	13.6194	−	12.2630i	0.738617	−	0.665054i
$341$	0.0931439	−	0.209205i	0.00504402	−	0.0113291i
$342$		−	1.55051i		−	0.0838422i
$343$	−18.5200	−	0.0948294i	−0.999987	−	0.00512031i
$344$	−10.7266	−	7.79333i	−0.578339	−	0.420188i
$345$	−1.81448	−	1.63377i	−0.0976884	−	0.0879590i
$346$	−0.950836	−	9.04660i	−0.0511173	−	0.486348i
$347$	10.6843	+	23.9973i	0.573563	+	1.28824i	0.934602	+	0.355694i	$0.115755\pi$
$347$	10.6843	+	23.9973i	0.573563	+	1.28824i	−0.361039	+	0.932551i	$0.617578\pi$
$348$	0.00844284	−	0.0803283i	0.000452584	−	0.00430605i
$349$	13.7950	+	10.0226i	0.738427	+	0.536499i	0.892218	−	0.451605i	$-0.149148\pi$
$349$	13.7950	+	10.0226i	0.738427	+	0.536499i	−0.153791	+	0.988103i	$0.549148\pi$
$350$	2.86826	+	4.98761i	0.153315	+	0.266599i
$351$	−1.52241	+	1.10610i	−0.0812603	+	0.0590391i
$352$	0.894385	+	0.805308i	0.0476709	+	0.0429230i
$353$	−6.16414	+	2.74445i	−0.328084	+	0.146073i	−0.564168	−	0.825660i	$-0.690803\pi$
$353$	−6.16414	+	2.74445i	−0.328084	+	0.146073i	0.236083	+	0.971733i	$0.424136\pi$
$354$	10.0142	−	9.01681i	0.532248	−	0.479238i
$355$	33.8270	−	19.5300i	1.79535	−	1.03655i
$356$	−6.06274	−	8.34464i	−0.321324	−	0.442265i
$357$	−17.4804	−	3.74678i	−0.925163	−	0.198300i
$358$	−17.8046	+	5.78506i	−0.941002	+	0.305750i
$359$	−10.7355	+	11.9229i	−0.566596	+	0.629268i	−0.956551	−	0.291566i	$-0.905824\pi$
$359$	−10.7355	+	11.9229i	−0.566596	+	0.629268i	0.389955	+	0.920834i	$0.372491\pi$
$360$	−8.04443	+	13.9334i	−0.423979	+	0.734352i
$361$	−17.9935	−	3.82463i	−0.947025	−	0.201296i
$362$	8.66089	+	0.910296i	0.455206	+	0.0478441i
$363$	6.41911	+	8.83515i	0.336916	+	0.463725i
$364$	−0.957978	+	0.309459i	−0.0502117	+	0.0162201i
$365$	0.803271	−	2.47221i	0.0420451	−	0.129402i
$366$	7.16641	−	4.13753i	0.374594	−	0.216272i
$367$	−2.17319	−	20.6765i	−0.113439	−	1.07930i	−0.892094	−	0.451851i	$-0.850764\pi$
$367$	−2.17319	−	20.6765i	−0.113439	−	1.07930i	0.778654	−	0.627453i	$-0.215903\pi$
$368$	−0.438439	+	0.759399i	−0.0228552	+	0.0395864i
$369$	−6.37647	+	11.1355i	−0.331946	+	0.579692i
$370$	−21.0632			−1.09502
$371$	−27.0931	−	8.85424i	−1.40660	−	0.459689i
$372$		−	0.965296i		−	0.0500483i
$373$	34.2686	−	7.28401i	1.77436	−	0.377152i	0.799622	−	0.600504i	$-0.205033\pi$
$373$	34.2686	−	7.28401i	1.77436	−	0.377152i	0.974738	+	0.223352i	$0.0716999\pi$
$374$	1.07781	+	1.19703i	0.0557323	+	0.0618970i
$375$	−7.48839	+	0.787062i	−0.386699	+	0.0406437i
$376$	14.8680	+	1.56269i	0.766761	+	0.0805898i
$377$	−0.00933275	−	0.0287232i	−0.000480661	−	0.00147932i
$378$	13.0782	−	1.35201i	0.672672	−	0.0695401i
$379$	1.61082	+	4.95760i	0.0827423	+	0.254655i	0.983866	−	0.178908i	$-0.0572564\pi$
$379$	1.61082	+	4.95760i	0.0827423	+	0.254655i	−0.901124	+	0.433562i	$0.857256\pi$
$380$	−1.56401	−	1.40824i	−0.0802318	−	0.0722411i
$381$	−6.35197	+	5.71934i	−0.325421	+	0.293010i
$382$	12.2104	−	1.28337i	0.624740	−	0.0656628i
$383$	29.5052	−	17.0348i	1.50764	−	0.870439i	0.507684	−	0.861543i	$-0.330502\pi$
$383$	29.5052	−	17.0348i	1.50764	−	0.870439i	0.999960	−	0.00889597i	$-0.00283171\pi$
$384$	3.00994	+	0.977988i	0.153600	+	0.0499077i
$385$	1.46983	−	0.845267i	0.0749096	−	0.0430788i
$386$	−14.3754	+	4.67084i	−0.731687	+	0.237739i
$387$	−8.10468	−	3.60843i	−0.411984	−	0.183427i
$388$	0.381483	+	0.856825i	0.0193669	+	0.0434987i
$389$	11.7179	−	5.21713i	0.594119	−	0.264519i	−0.0875730	−	0.996158i	$-0.527911\pi$
$389$	11.7179	−	5.21713i	0.594119	−	0.264519i	0.681692	+	0.731639i	$0.261244\pi$
$390$	0.104852	−	0.997604i	0.00530941	−	0.0505156i
$391$	3.63227	−	4.99939i	0.183692	−	0.252830i
$392$	20.4920	+	4.42888i	1.03500	+	0.223692i
$393$	14.9123	−	4.84531i	0.752228	−	0.244414i
$394$	−0.137280	+	1.30613i	−0.00691608	+	0.0658021i
$395$	0.285573	−	0.257131i	0.0143687	−	0.0129377i
$396$	0.418986	+	0.241902i	0.0210548	+	0.0121560i
$397$	−10.8782	+	24.4327i	−0.545959	+	1.22624i	0.404255	+	0.914646i	$0.367531\pi$
$397$	−10.8782	+	24.4327i	−0.545959	+	1.22624i	−0.950214	+	0.311598i	$0.899136\pi$
$398$	13.4642	+	4.37478i	0.674899	+	0.219288i
$399$	−0.218080	+	2.04137i	−0.0109176	+	0.102196i
$400$	−0.648805	−	1.99682i	−0.0324403	−	0.0998409i
$401$	17.2245	+	29.8337i	0.860150	+	1.48982i	0.871784	+	0.489891i	$0.162963\pi$
$401$	17.2245	+	29.8337i	0.860150	+	1.48982i	−0.0116337	+	0.999932i	$0.503703\pi$
$402$	−6.68245	−	1.42040i	−0.333290	−	0.0708430i
$403$	−0.146807	−	0.329734i	−0.00731298	−	0.0164252i
$404$	−0.462347	+	1.03845i	−0.0230026	+	0.0516647i
$405$	−0.851634	+	2.62106i	−0.0423180	+	0.130241i
$406$	−0.0442244	+	0.206327i	−0.00219482	+	0.0102399i
$407$			1.88787i			0.0935783i
$408$	18.4879	+	8.23133i	0.915286	+	0.407512i
$409$	−7.73197	+	13.3922i	−0.382322	+	0.662200i	−0.991394	−	0.130915i	$-0.958209\pi$
$409$	−7.73197	+	13.3922i	−0.382322	+	0.662200i	0.609072	+	0.793115i	$0.291542\pi$
$410$	−5.33558	−	16.2249i	−0.263506	−	0.801291i
$411$	−0.746259	−	1.29256i	−0.0368102	−	0.0637572i
$412$	6.28971	−	4.56974i	0.309872	−	0.225135i
$413$	29.0801	−	21.0522i	1.43094	−	1.03591i
$414$	−0.562440	+	1.73101i	−0.0276424	+	0.0850746i
$415$	−4.00166	+	0.850579i	−0.196434	+	0.0417533i
$416$	1.88650	−	0.198280i	0.0924935	−	0.00972146i
$417$	6.89028	+	15.4758i	0.337418	+	0.757854i
$418$	0.123772	−	0.137463i	0.00605389	−	0.00672353i
$419$	1.03545			0.0505851			0.0252925	−	0.999680i	$-0.491948\pi$
$419$	1.03545			0.0505851			0.0252925	+	0.999680i	$0.491948\pi$
$420$	4.21082	−	5.77494i	0.205467	−	0.281788i
$421$	10.7207	−	3.48336i	0.522494	−	0.169769i	−0.0358827	−	0.999356i	$-0.511424\pi$
$421$	10.7207	−	3.48336i	0.522494	−	0.169769i	0.558377	+	0.829587i	$0.311424\pi$
$422$	−5.07271	−	23.8652i	−0.246936	−	1.16174i
$423$	9.94844	−	1.04562i	0.483710	−	0.0508399i
$424$	27.9432	+	16.1330i	1.35704	+	0.783488i
$425$	3.07632	+	14.4729i	0.149223	+	0.702040i
$426$	11.7073	+	8.50585i	0.567221	+	0.412110i
$427$	20.1553	−	8.93253i	0.975383	−	0.432275i
$428$	−11.4505	+	8.31928i	−0.553481	+	0.402128i
$429$	−0.0894144	−	0.00939783i	−0.00431697	−	0.000453731i
$430$	10.7875	−	4.80292i	0.520222	−	0.231618i
$431$	15.2092	−	6.77157i	0.732601	−	0.326175i	−0.00630822	−	0.999980i	$-0.502008\pi$
$431$	15.2092	−	6.77157i	0.732601	−	0.326175i	0.738909	+	0.673805i	$0.235341\pi$
$432$	−4.77166	−	0.501522i	−0.229577	−	0.0241295i
$433$	28.1158	−	20.4273i	1.35116	−	0.981674i	0.352206	−	0.935923i	$-0.385432\pi$
$433$	28.1158	−	20.4273i	1.35116	−	0.981674i	0.998953	−	0.0457514i	$-0.0145682\pi$
$434$	−0.267884	+	2.50757i	−0.0128588	+	0.120367i
$435$	0.173462	+	0.126028i	0.00831689	+	0.00604257i
$436$	−2.20863	−	10.3908i	−0.105774	−	0.497628i
$437$	−0.614568	−	0.354821i	−0.0293988	−	0.0169734i
$438$	0.957767	−	0.100665i	0.0457639	−	0.00480998i
$439$	4.59587	+	21.6219i	0.219349	+	1.03196i	0.940662	+	0.339346i	$0.110206\pi$
$439$	4.59587	+	21.6219i	0.219349	+	1.03196i	−0.721313	+	0.692609i	$0.756461\pi$
$440$	−1.82544	+	0.593121i	−0.0870244	+	0.0282759i
$441$	14.0280	+	0.0478856i	0.668001	+	0.00228027i
$442$	2.53878			0.120757
$443$	5.22190	−	5.79951i	0.248100	−	0.275543i	−0.606212	−	0.795303i	$-0.707312\pi$
$443$	5.22190	−	5.79951i	0.248100	−	0.275543i	0.854313	+	0.519760i	$0.173979\pi$
$444$	3.23672	+	7.26979i	0.153608	+	0.345009i
$445$	27.2307	−	2.86206i	1.29086	−	0.135675i
$446$	2.70550	−	0.575073i	0.128109	−	0.0272305i
$447$	3.92245	−	12.0721i	0.185526	−	0.570989i
$448$	−16.7391	−	7.48699i	−0.790849	−	0.353727i
$449$	−6.09413	+	4.42765i	−0.287600	+	0.208954i	−0.722225	−	0.691658i	$-0.756881\pi$
$449$	−6.09413	+	4.42765i	−0.287600	+	0.208954i	0.434626	+	0.900611i	$0.356881\pi$
$450$	−2.17900	−	3.77413i	−0.102719	−	0.177914i
$451$	−1.45422	+	0.478223i	−0.0684767	+	0.0225187i
$452$	5.36509	−	9.29261i	0.252353	−	0.437088i
$453$	1.61964	+	0.721108i	0.0760971	+	0.0338806i
$454$		−	23.6548i		−	1.11018i
$455$	0.560085	−	2.61306i	0.0262572	−	0.122502i
$456$	0.718157	−	2.21026i	0.0336308	−	0.103505i
$457$	−12.2162	+	27.4381i	−0.571452	+	1.28350i	0.364444	+	0.931225i	$0.381259\pi$
$457$	−12.2162	+	27.4381i	−0.571452	+	1.28350i	−0.935896	+	0.352277i	$0.885408\pi$
$458$	−5.90296	−	13.2583i	−0.275827	−	0.619518i
$459$	33.0735	+	7.02999i	1.54374	+	0.328132i
$460$	1.23525	+	2.13951i	0.0575936	+	0.0997551i
$461$	−12.3958	−	38.1504i	−0.577330	−	1.77684i	−0.628104	−	0.778129i	$-0.716169\pi$
$461$	−12.3958	−	38.1504i	−0.577330	−	1.77684i	0.0507739	−	0.998710i	$-0.483831\pi$
$462$	0.507568	+	0.370095i	0.0236142	+	0.0172184i
$463$	−20.2822	−	6.59008i	−0.942593	−	0.306267i	−0.202891	−	0.979201i	$-0.565034\pi$
$463$	−20.2822	−	6.59008i	−0.942593	−	0.306267i	−0.739702	+	0.672934i	$0.765034\pi$
$464$	0.0313200	−	0.0703458i	0.00145399	−	0.00326572i
$465$	2.21914	+	1.28122i	0.102910	+	0.0594152i
$466$	3.07030	−	2.76451i	0.142229	−	0.128063i
$467$	0.941236	−	8.95526i	0.0435552	−	0.414400i	−0.950921	−	0.309435i	$-0.899860\pi$
$467$	0.941236	−	8.95526i	0.0435552	−	0.414400i	0.994476	−	0.104965i	$-0.0334731\pi$
$468$	0.725216	−	0.235637i	0.0335231	−	0.0108923i
$469$	−17.3003	−	5.65389i	−0.798856	−	0.261072i
$470$	−7.82612	+	10.7717i	−0.360992	+	0.496863i
$471$	−2.16041	+	20.5550i	−0.0995466	+	0.947123i
$472$	−37.1263	+	16.5297i	−1.70888	+	0.760841i
$473$	−0.430482	−	0.966878i	−0.0197936	−	0.0444571i
$474$	0.130059	+	0.0579060i	0.00597380	+	0.00265971i
$475$	1.61599	−	0.525067i	0.0741467	−	0.0240917i
$476$	15.6499	+	9.07113i	0.717313	+	0.415775i
$477$	20.5330	+	6.67158i	0.940142	+	0.305471i
$478$	10.3163	−	5.95612i	0.471857	−	0.272427i
$479$	26.5202	−	2.78739i	1.21174	−	0.127359i	0.522978	−	0.852346i	$-0.324821\pi$
$479$	26.5202	−	2.78739i	1.21174	−	0.127359i	0.688762	+	0.724987i	$0.258154\pi$
$480$	−10.0078	+	9.01104i	−0.456790	+	0.411296i
$481$	2.21125	+	1.99102i	0.100824	+	0.0907827i
$482$	−3.12170	−	9.60760i	−0.142189	−	0.437614i
$483$	0.983962	−	2.19990i	0.0447718	−	0.100099i
$484$	−3.41462	−	10.5091i	−0.155210	−	0.477688i
$485$	−2.47611	−	0.260250i	−0.112434	−	0.0118173i
$486$	−15.8421	+	1.66508i	−0.718614	+	0.0755293i
$487$	10.6573	+	11.8361i	0.482928	+	0.536346i	0.934535	−	0.355871i	$-0.115816\pi$
$487$	10.6573	+	11.8361i	0.482928	+	0.536346i	−0.451607	+	0.892217i	$0.649149\pi$
$488$	−24.4110	+	5.18871i	−1.10503	+	0.234882i
$489$			15.5527i			0.703318i
$490$	−12.5412	+	13.8331i	−0.566552	+	0.624917i
$491$	−6.45196			−0.291173			−0.145586	−	0.989346i	$-0.546507\pi$
$491$	−6.45196			−0.291173			−0.145586	+	0.989346i	$0.546507\pi$
$492$	−4.78000	+	4.33478i	−0.215499	+	0.195427i
$493$	−0.271330	+	0.469958i	−0.0122201	+	0.0211658i
$494$	−0.0304747	−	0.289947i	−0.00137112	−	0.0130453i
$495$	−1.11223	+	0.642144i	−0.0499908	+	0.0288622i
$496$	0.284379	−	0.875227i	0.0127690	−	0.0392989i
$497$	28.6064	+	25.8458i	1.28317	+	1.15934i
$498$	−0.890883	−	1.22620i	−0.0399214	−	0.0549471i
$499$	−7.00805	−	0.736576i	−0.313724	−	0.0329737i	−0.0536417	−	0.998560i	$-0.517083\pi$
$499$	−7.00805	−	0.736576i	−0.313724	−	0.0329737i	−0.260082	+	0.965587i	$0.583750\pi$
$500$	7.45217	+	1.58401i	0.333271	+	0.0708390i
$501$	3.19497	−	5.53384i	0.142741	−	0.247234i
$502$	5.60657	−	6.22673i	0.250234	−	0.277913i
$503$	2.57127	−	0.835456i	0.114647	−	0.0372511i	−0.251132	−	0.967953i	$-0.580803\pi$
$503$	2.57127	−	0.835456i	0.114647	−	0.0372511i	0.365779	+	0.930702i	$0.380803\pi$
$504$	−15.5273	−	3.32814i	−0.691641	−	0.148247i
$505$	−1.77365	−	2.44122i	−0.0789262	−	0.108633i
$506$	−0.188044	+	0.108568i	−0.00835960	+	0.00482642i
$507$	9.53616	−	8.58640i	0.423516	−	0.381335i
$508$	7.90076	−	3.51765i	0.350540	−	0.156070i
$509$	−11.8699	−	10.6877i	−0.526122	−	0.473723i	0.362744	−	0.931889i	$-0.381840\pi$
$509$	−11.8699	−	10.6877i	−0.526122	−	0.473723i	−0.888867	+	0.458166i	$0.848507\pi$
$510$	−14.5815	+	10.5941i	−0.645680	+	0.469114i
$511$	2.56569	+	0.00437906i	0.113499	+	0.000193718i
$512$	8.56859	+	6.22545i	0.378682	+	0.275128i
$513$	0.405873	−	3.86162i	0.0179197	−	0.170495i
$514$	−0.503152	−	1.13010i	−0.0221931	−	0.0498465i
$515$	2.15725	+	20.5249i	0.0950600	+	0.904435i
$516$	−3.31539	−	2.98519i	−0.145952	−	0.131416i
$517$	0.965460	+	0.701448i	0.0424609	+	0.0308496i
$518$	−6.39062	−	19.7831i	−0.280788	−	0.869220i
$519$		−	9.12291i		−	0.400451i
$520$	−1.23046	+	2.76365i	−0.0539592	+	0.121194i
$521$	−27.9844	+	25.1972i	−1.22602	+	1.10391i	−0.234748	+	0.972056i	$0.575427\pi$
$521$	−27.9844	+	25.1972i	−1.22602	+	1.10391i	−0.991269	+	0.131855i	$0.957907\pi$
$522$	0.0332309	−	0.156339i	0.00145448	−	0.00684277i
$523$	14.7270	−	16.3560i	0.643967	−	0.715198i	−0.329466	−	0.944167i	$-0.606869\pi$
$523$	14.7270	−	16.3560i	0.643967	−	0.715198i	0.973434	+	0.228969i	$0.0735355\pi$
$524$	−15.8651			−0.693072
$525$	2.33798	+	5.27541i	0.102038	+	0.230238i
$526$	14.4559	−	19.8969i	0.630309	−	0.867546i
$527$	−2.63784	+	5.92468i	−0.114906	+	0.258083i
$528$	−0.153386	−	0.170352i	−0.00667525	−	0.00741362i
$529$	−14.8326	−	16.4733i	−0.644896	−	0.716229i
$530$	−24.8865	+	14.3682i	−1.08100	+	0.624116i
$531$	−21.9994	+	15.9835i	−0.954692	+	0.693624i
$532$	0.848134	−	1.89622i	0.0367713	−	0.0822117i
$533$	−0.973539	+	2.20768i	−0.0421686	+	0.0956250i
$534$	5.07201	+	8.78497i	0.219487	+	0.380163i
$535$	−3.92731	−	37.3659i	−0.169792	−	1.61547i
$536$	17.8432	+	10.3017i	0.770707	+	0.444968i
$537$	−18.3651	+	3.90361i	−0.792510	+	0.168453i
$538$	−2.89189	+	8.90031i	−0.124678	+	0.383719i
$539$	1.23985	+	1.12405i	0.0534041	+	0.0484164i
$540$	−7.94544	+	10.9360i	−0.341917	+	0.470609i
$541$	−3.33453	+	3.70337i	−0.143363	+	0.159220i	−0.810550	−	0.585670i	$-0.800832\pi$
$541$	−3.33453	+	3.70337i	−0.143363	+	0.159220i	0.667187	+	0.744890i	$0.267498\pi$
$542$	−12.5951	+	21.8153i	−0.541005	+	0.937049i
$543$	8.54309	+	1.81589i	0.366619	+	0.0779273i
$544$	−25.3290	−	22.8063i	−1.08597	−	0.977813i
$545$	26.8191	+	8.71404i	1.14880	+	0.373269i
$546$	0.968791	−	0.204195i	0.0414604	−	0.00873875i
$547$		−	24.0428i		−	1.02799i	−0.857792	−	0.513997i	$-0.828164\pi$
$547$		−	24.0428i		−	1.02799i	0.857792	−	0.513997i	$-0.171836\pi$
$548$	0.313980	+	1.47716i	0.0134126	+	0.0631012i
$549$	−15.2550	+	6.79196i	−0.651067	+	0.289874i
$550$	0.108094	−	0.508542i	0.00460914	−	0.0216843i
$551$	0.0569296	+	0.0253467i	0.00242528	+	0.00107981i
$552$	−1.60352	+	2.20705i	−0.0682502	+	0.0939384i
$553$	0.328149	+	0.190204i	0.0139543	+	0.00808830i
$554$	−8.93742	−	6.49342i	−0.379715	−	0.275879i
$555$	−21.0087	−	2.20811i	−0.891771	−	0.0937289i
$556$	−1.79169	−	17.0468i	−0.0759845	−	0.722944i
$557$	3.93815	−	18.5275i	0.166865	−	0.785037i	−0.812504	−	0.582956i	$-0.801896\pi$
$557$	3.93815	−	18.5275i	0.166865	−	0.785037i	0.979369	−	0.202081i	$-0.0647706\pi$
$558$	0.199666	−	1.89969i	0.00845253	−	0.0804204i
$559$	−1.58650	−	0.515485i	−0.0671018	−	0.0218027i
$560$	5.51923	−	3.99558i	0.233230	−	0.168844i
$561$	0.949539	+	1.30693i	0.0400896	+	0.0551786i
$562$	4.02210	+	18.9225i	0.169662	+	0.798196i
$563$	1.66643	−	7.83996i	0.0702318	−	0.330415i	−0.928979	−	0.370132i	$-0.879312\pi$
$563$	1.66643	−	7.83996i	0.0702318	−	0.330415i	0.999211	+	0.0397173i	$0.0126457\pi$
$564$	4.92040	+	1.04586i	0.207186	+	0.0440388i
$565$	14.2420	+	24.6679i	0.599165	+	1.03778i
$566$	−1.21973	−	3.75393i	−0.0512689	−	0.157789i
$567$	−2.72016	−	0.00464272i	−0.114236	−	0.000194976i
$568$	−25.6524	−	35.3075i	−1.07635	−	1.48147i
$569$	−40.9638	+	8.70712i	−1.71729	+	0.365021i	−0.958230	−	0.285999i	$-0.907675\pi$
$569$	−40.9638	+	8.70712i	−1.71729	+	0.365021i	−0.759061	+	0.651020i	$0.774341\pi$
$570$	1.38496	+	1.53815i	0.0580094	+	0.0644260i
$571$	−17.1367	−	9.89385i	−0.717147	−	0.414045i	0.0965549	−	0.995328i	$-0.469218\pi$
$571$	−17.1367	−	9.89385i	−0.717147	−	0.414045i	−0.813702	+	0.581283i	$0.802551\pi$
$572$	0.0831050	+	0.0370007i	0.00347480	+	0.00154708i
$573$	12.3134			0.514401
$574$	13.6201	−	9.93401i	0.568491	−	0.414638i
$575$	−1.99457			−0.0831795
$576$	12.6886	+	5.64935i	0.528694	+	0.235390i
$577$	1.48896	+	0.859650i	0.0619861	+	0.0357877i	0.530673	−	0.847577i	$-0.321939\pi$
$577$	1.48896	+	0.859650i	0.0619861	+	0.0357877i	−0.468687	+	0.883364i	$0.655273\pi$
$578$	−19.2042	−	21.3285i	−0.798791	−	0.887147i
$579$	−14.8279	+	3.15176i	−0.616226	+	0.130983i
$580$	−0.127518	−	0.175513i	−0.00529489	−	0.00728779i
$581$	−2.01300	−	3.50041i	−0.0835134	−	0.145221i
$582$	−0.285039	−	0.877260i	−0.0118152	−	0.0363636i
$583$	1.28781	+	2.23056i	0.0533357	+	0.0923802i
$584$	−2.84093	−	0.603857i	−0.117558	−	0.0249878i
$585$	−0.420856	+	1.97997i	−0.0174003	+	0.0818618i
$586$	−0.0332936	−	0.156634i	−0.00137535	−	0.00647049i
$587$	21.1633	+	29.1288i	0.873504	+	1.20227i	0.978178	+	0.207768i	$0.0666199\pi$
$587$	21.1633	+	29.1288i	0.873504	+	1.20227i	−0.104675	+	0.994507i	$0.533380\pi$
$588$	6.70157	+	2.20279i	0.276368	+	0.0908416i
$589$	0.708306	+	0.230143i	0.0291852	+	0.00948286i
$590$	3.78333	−	35.9960i	0.155757	−	1.48193i
$591$	−0.273851	+	1.28837i	−0.0112647	+	0.0529964i
$592$	0.793013	+	7.54502i	0.0325926	+	0.310098i
$593$	−34.3983	−	3.61541i	−1.41257	−	0.148467i	−0.632695	−	0.774401i	$-0.718051\pi$
$593$	−34.3983	−	3.61541i	−1.41257	−	0.148467i	−0.779876	+	0.625934i	$0.784718\pi$
$594$	−0.961178	−	0.698336i	−0.0394376	−	0.0286531i
$595$	−41.6257	+	23.9380i	−1.70649	+	0.981361i
$596$	−7.54915	+	10.3905i	−0.309225	+	0.425612i
$597$	12.9708	+	5.77496i	0.530859	+	0.236354i
$598$	−0.0711543	+	0.334755i	−0.00290972	+	0.0136891i
$599$	−16.7243	+	7.44614i	−0.683336	+	0.304241i	−0.718887	−	0.695127i	$-0.755348\pi$
$599$	−16.7243	+	7.44614i	−0.683336	+	0.304241i	0.0355508	+	0.999368i	$0.488681\pi$
$600$	−1.35808	−	6.38928i	−0.0554435	−	0.260841i
$601$			2.51294i			0.102505i	0.998686	+	0.0512524i	$0.0163213\pi$
$601$			2.51294i			0.102505i	−0.998686	+	0.0512524i	$0.983679\pi$
$602$	7.78401	+	8.67475i	0.317253	+	0.353557i
$603$	13.1114	+	4.26015i	0.533937	+	0.173487i
$604$	−1.33311	−	1.20033i	−0.0542433	−	0.0488409i
$605$	28.6919	+	6.09864i	1.16649	+	0.247945i
$606$	0.558965	−	0.968156i	0.0227064	−	0.0393286i
$607$	−24.1326	+	26.8019i	−0.979511	+	1.08786i	0.0166099	+	0.999862i	$0.494713\pi$
$607$	−24.1326	+	26.8019i	−0.979511	+	1.08786i	−0.996121	+	0.0879951i	$0.971954\pi$
$608$	−2.30061	+	3.16652i	−0.0933021	+	0.128419i
$609$	−0.0657400	+	0.201158i	−0.00266392	+	0.00815134i
$610$	6.86833	−	21.1386i	0.278091	−	0.855875i
$611$	1.83981	−	0.391064i	0.0744309	−	0.0158208i
$612$	−11.8657	−	6.85066i	−0.479642	−	0.276921i
$613$	3.99398	+	38.0002i	0.161315	+	1.53481i	0.713241	+	0.700919i	$0.247227\pi$
$613$	3.99398	+	38.0002i	0.161315	+	1.53481i	−0.551926	+	0.833893i	$0.686107\pi$
$614$	6.47066	+	11.2075i	0.261135	+	0.452298i
$615$	−3.62090	−	16.7423i	−0.146009	−	0.675116i
$616$	−1.11092	−	1.53455i	−0.0447602	−	0.0618288i
$617$	−4.92906	+	3.58117i	−0.198436	+	0.144173i	−0.682566	−	0.730824i	$-0.739136\pi$
$617$	−4.92906	+	3.58117i	−0.198436	+	0.144173i	0.484130	+	0.874996i	$0.339136\pi$
$618$	−6.62161	+	3.82299i	−0.266360	+	0.153783i
$619$	27.0987	+	30.0961i	1.08919	+	1.20967i	0.976383	+	0.216049i	$0.0693170\pi$
$619$	27.0987	+	30.0961i	1.08919	+	1.20967i	0.112805	+	0.993617i	$0.464016\pi$
$620$	−1.73488	−	1.92678i	−0.0696744	−	0.0773813i
$621$	−1.85390	+	4.16394i	−0.0743946	+	0.167093i
$622$	14.9599	−	20.5905i	0.599837	−	0.825604i
$623$	10.9500	+	24.7075i	0.438702	+	0.989884i
$624$	−0.361299			−0.0144635
$625$	−20.8441	+	23.1497i	−0.833763	+	0.925988i
$626$	−1.08309	+	5.09554i	−0.0432890	+	0.203659i
$627$	0.137863	−	0.124132i	0.00550571	−	0.00495737i
$628$	8.50589	−	19.1045i	0.339422	−	0.762355i
$629$		−	53.4646i		−	2.13177i
$630$	9.48137	−	10.4940i	0.377747	−	0.418093i
$631$	1.36781	+	0.993770i	0.0544515	+	0.0395613i	0.614678	−	0.788778i	$-0.289286\pi$
$631$	1.36781	+	0.993770i	0.0544515	+	0.0395613i	−0.560227	+	0.828339i	$0.689286\pi$
$632$	−0.319075	−	0.287297i	−0.0126921	−	0.0114280i
$633$	−2.55775	−	24.3353i	−0.101661	−	0.967243i
$634$	−11.8371	−	26.5867i	−0.470113	−	1.05589i
$635$	−2.39976	+	22.8321i	−0.0952314	+	0.906066i
$636$	8.78334	+	6.38147i	0.348282	+	0.253042i
$637$	2.62419	−	0.266760i	0.103974	−	0.0105694i
$638$	0.0154261	−	0.0112077i	0.000610725	−	0.000443718i
$639$	−21.7012	−	19.5398i	−0.858486	−	0.772984i
$640$	7.76567	−	3.45750i	0.306965	−	0.136670i
$641$	−20.4144	+	18.3812i	−0.806321	+	0.726015i	−0.965265	−	0.261273i	$-0.915858\pi$
$641$	−20.4144	+	18.3812i	−0.806321	+	0.726015i	0.158944	+	0.987288i	$0.449191\pi$
$642$	12.0547	−	6.95980i	0.475762	−	0.274682i
$643$	−1.58969	−	2.18802i	−0.0626912	−	0.0862870i	0.776520	−	0.630092i	$-0.216983\pi$
$643$	−1.58969	−	2.18802i	−0.0626912	−	0.0862870i	−0.839211	+	0.543805i	$0.816983\pi$
$644$	−1.63471	+	1.80931i	−0.0644166	+	0.0712968i
$645$	11.2632	−	3.65963i	0.443487	−	0.144098i
$646$	−3.50523	+	3.89295i	−0.137911	+	0.153166i
$647$	−14.7208	+	25.4971i	−0.578733	+	1.00240i	0.416892	+	0.908956i	$0.363119\pi$
$647$	−14.7208	+	25.4971i	−0.578733	+	1.00240i	−0.995625	+	0.0934392i	$0.970214\pi$
$648$	3.01197	+	0.640214i	0.118321	+	0.0251500i
$649$	−3.22629	−	0.339097i	−0.126643	−	0.0133107i
$650$	−0.481652	−	0.662938i	−0.0188920	−	0.0260026i
$651$	−0.530067	+	2.47301i	−0.0207750	+	0.0969248i
$652$	4.86287	−	14.9664i	0.190445	−	0.586129i
$653$	31.4591	−	18.1629i	1.23109	−	0.710771i	0.263834	−	0.964568i	$-0.415013\pi$
$653$	31.4591	−	18.1629i	1.23109	−	0.710771i	0.967257	+	0.253798i	$0.0816797\pi$
$654$	1.09204	+	10.3901i	0.0427021	+	0.406283i
$655$	21.0575	−	36.4727i	0.822786	−	1.42511i
$656$	−5.61103	+	2.52211i	−0.219074	+	0.0984719i
$657$	−1.94338			−0.0758183
$658$	−12.4916	−	4.08234i	−0.486973	−	0.159146i
$659$			37.8879i			1.47590i	0.674855	+	0.737951i	$0.264206\pi$
$659$			37.8879i			1.47590i	−0.674855	+	0.737951i	$0.735794\pi$
$660$	−0.631716	+	0.134275i	−0.0245895	+	0.00522667i
$661$	−28.4986	−	31.6510i	−1.10847	−	1.23108i	−0.970618	−	0.240627i	$-0.922647\pi$
$661$	−28.4986	−	31.6510i	−1.10847	−	1.23108i	−0.137851	−	0.990453i	$-0.544020\pi$
$662$	−34.2763	+	3.60258i	−1.33219	+	0.140018i
$663$	2.53222	+	0.266147i	0.0983432	+	0.0103363i
$664$	1.41252	+	4.34729i	0.0548164	+	0.168707i
$665$	3.23356	+	4.46662i	0.125392	+	0.173208i
$666$	4.86612	+	14.9764i	0.188558	+	0.580323i
$667$	−0.0543626	−	0.0489483i	−0.00210493	−	0.00189528i
$668$	−4.80478	+	4.32625i	−0.185903	+	0.167388i
$669$	2.75880	−	0.289962i	0.106661	−	0.0112106i
$670$	−15.8913	+	9.17485i	−0.613935	+	0.354455i
$671$	−1.89463	−	0.615602i	−0.0731414	−	0.0237651i
$672$	−11.4998	−	6.66562i	−0.443615	−	0.257132i
$673$	5.09073	−	1.65408i	0.196233	−	0.0637601i	−0.209251	−	0.977862i	$-0.567103\pi$
$673$	5.09073	−	1.65408i	0.196233	−	0.0637601i	0.405485	+	0.914102i	$0.367103\pi$
$674$	−28.7053	−	12.7804i	−1.10569	−	0.492284i
$675$	−4.43894	−	9.97003i	−0.170855	−	0.383747i
$676$	−11.8614	+	5.28102i	−0.456206	+	0.203116i
$677$	1.69348	−	16.1124i	0.0650859	−	0.619251i	−0.912553	−	0.408959i	$-0.865892\pi$
$677$	1.69348	−	16.1124i	0.0650859	−	0.619251i	0.977639	−	0.210292i	$-0.0674414\pi$
$678$	−6.20277	+	8.53738i	−0.238216	+	0.327876i
$679$	−0.506825	−	2.40460i	−0.0194501	−	0.0922799i
$680$	51.6965	−	16.7972i	1.98247	−	0.644144i
$681$	2.47980	−	23.5937i	0.0950262	−	0.904114i
$682$	0.169347	−	0.152481i	0.00648465	−	0.00583880i
$683$	1.87093	+	1.08018i	0.0715892	+	0.0413320i	0.535367	−	0.844619i	$-0.320173\pi$
$683$	1.87093	+	1.08018i	0.0715892	+	0.0413320i	−0.463778	+	0.885951i	$0.653507\pi$
$684$	−0.639964	+	1.43738i	−0.0244696	+	0.0549597i
$685$	−3.81262	−	1.23880i	−0.145673	−	0.0473320i
$686$	−16.7975	−	7.58202i	−0.641331	−	0.289483i
$687$	−4.49781	−	13.8428i	−0.171602	−	0.528137i
$688$	−2.12660	−	3.68337i	−0.0810757	−	0.140427i
$689$	3.97081	+	0.844022i	0.151276	+	0.0321547i
$690$	−0.988226	−	2.21959i	−0.0376211	−	0.0844985i
$691$	9.90137	−	22.2388i	0.376666	−	0.846005i	−0.621379	−	0.783510i	$-0.713427\pi$
$691$	9.90137	−	22.2388i	0.376666	−	0.846005i	0.998045	−	0.0624954i	$-0.0199059\pi$
$692$	−2.85246	+	8.77898i	−0.108434	+	0.333727i
$693$	−0.940572	−	0.849806i	−0.0357294	−	0.0322815i
$694$			26.1395i			0.992241i
$695$	41.5673	+	18.5069i	1.57674	+	0.702008i
$696$	0.119783	−	0.207470i	0.00454035	−	0.00786411i
$697$	41.1836	−	13.5433i	1.55994	−	0.512989i
$698$	8.48392	+	14.6946i	0.321121	+	0.556198i
$699$	3.35218	−	2.43550i	0.126791	−	0.0921191i
$700$	−0.600378	−	5.80754i	−0.0226921	−	0.219505i
$701$	−1.96183	+	6.03790i	−0.0740974	+	0.228048i	−0.981245	−	0.192764i	$-0.938255\pi$
$701$	−1.96183	+	6.03790i	−0.0740974	+	0.228048i	0.907148	+	0.420812i	$0.138255\pi$
$702$	−1.83165	+	0.389330i	−0.0691312	+	0.0146943i
$703$	−6.10605	+	0.641772i	−0.230294	+	0.0242049i
$704$	0.673960	+	1.51374i	0.0254008	+	0.0570512i
$705$	−8.93513	+	9.92346i	−0.336516	+	0.373739i
$706$	−6.71439			−0.252699
$707$	1.75473	−	2.40653i	0.0659934	−	0.0905069i
$708$	−13.0051	+	4.22562i	−0.488763	+	0.158809i
$709$	6.04757	+	28.4516i	0.227121	+	1.06852i	0.932913	+	0.360102i	$0.117258\pi$
$709$	6.04757	+	28.4516i	0.227121	+	1.06852i	−0.705792	+	0.708420i	$0.749408\pi$
$710$	38.6555	−	4.06286i	1.45072	−	0.152476i
$711$	−0.248801	−	0.143645i	−0.00933075	−	0.00538711i
$712$	−6.36061	−	29.9243i	−0.238374	−	1.12146i
$713$	−0.707278	−	0.513868i	−0.0264878	−	0.0192445i
$714$	−14.3743	−	10.4811i	−0.537946	−	0.392246i
$715$	−0.195366	+	0.141942i	−0.00730626	+	0.00530831i
$716$	18.8932	+	1.98576i	0.706073	+	0.0742113i
$717$	10.9140	−	4.85925i	0.407592	−	0.181472i
$718$	−14.5849	+	6.49362i	−0.544304	+	0.242340i
$719$	7.95220	+	0.835810i	0.296567	+	0.0311705i	0.251644	−	0.967820i	$-0.419029\pi$
$719$	7.95220	+	0.835810i	0.296567	+	0.0311705i	0.0449235	+	0.998990i	$0.485696\pi$
$720$	−4.17535	+	3.03357i	−0.155606	+	0.113055i
$721$	−18.6231	+	8.25347i	−0.693559	+	0.307375i
$722$	−14.8092	−	10.7595i	−0.551142	−	0.400428i
$723$	−2.10644	−	9.91003i	−0.0783394	−	0.368558i
$724$	−7.65324	−	4.41860i	−0.284430	−	0.164216i
$725$	0.174194	−	0.0183085i	0.00646941	−	0.000679962i
$726$	2.25943	+	10.6298i	0.0838554	+	0.394509i
$727$	10.7763	−	3.50143i	0.399670	−	0.129861i	−0.102283	−	0.994755i	$-0.532615\pi$
$727$	10.7763	−	3.50143i	0.399670	−	0.129861i	0.501954	+	0.864895i	$0.332615\pi$
$728$	−2.96903	−	0.317182i	−0.110040	−	0.0117555i
$729$	−12.8914			−0.477459
$730$	1.73083	−	1.92228i	0.0640609	−	0.0711468i
$731$	12.1913	+	27.3820i	0.450910	+	1.01276i
$732$	−8.35126	+	0.877752i	−0.308671	+	0.0324427i
$733$	0.343451	−	0.0730027i	0.0126856	−	0.00269642i	−0.201564	−	0.979475i	$-0.564603\pi$
$733$	0.343451	−	0.0730027i	0.0126856	−	0.00269642i	0.214250	+	0.976779i	$0.431269\pi$
$734$	6.39306	−	19.6758i	0.235972	−	0.726248i
$735$	−13.9589	+	12.4827i	−0.514883	+	0.460430i
$736$	3.71707	−	2.70061i	0.137013	−	0.0995457i
$737$	0.822334	+	1.42432i	0.0302911	+	0.0524656i
$738$	−10.3036	+	7.54208i	−0.379281	+	0.277628i
$739$	−9.00178	+	15.5915i	−0.331136	+	0.573544i	−0.982735	−	0.185020i	$-0.940765\pi$
$739$	−9.00178	+	15.5915i	−0.331136	+	0.573544i	0.651599	+	0.758564i	$0.274098\pi$
$740$	19.5263	+	8.69367i	0.717801	+	0.319586i
$741$		−	0.292393i		−	0.0107413i
$742$	−21.0457	−	19.0148i	−0.772612	−	0.698054i
$743$	0.857962	−	2.64053i	0.0314756	−	0.0968718i	−0.934085	−	0.357052i	$-0.883782\pi$
$743$	0.857962	−	2.64053i	0.0314756	−	0.0968718i	0.965560	+	0.260180i	$0.0837819\pi$
$744$	1.16451	−	2.61553i	0.0426930	−	0.0958901i
$745$	−13.8671	−	31.1461i	−0.508052	−	1.14110i
$746$	34.1005	+	7.24827i	1.24851	+	0.265378i
$747$	1.52927	+	2.64877i	0.0559529	+	0.0969133i
$748$	−0.505104	−	1.55455i	−0.0184684	−	0.0568400i
$749$	33.9036	−	15.0256i	1.23881	−	0.549022i
$750$	−7.12598	−	2.31537i	−0.260204	−	0.0845454i
$751$	−6.13558	+	13.7807i	−0.223891	+	0.502867i	−0.990209	−	0.139595i	$-0.955420\pi$
$751$	−6.13558	+	13.7807i	−0.223891	+	0.502867i	0.766318	+	0.642461i	$0.222087\pi$
$752$	4.15318	+	2.39784i	0.151451	+	0.0874402i
$753$	6.24486	−	5.62289i	0.227575	−	0.204910i
$754$	0.00314142	−	0.0298886i	0.000114404	−	0.00108848i
$755$	4.52888	−	1.47152i	0.164823	−	0.0535542i
$756$	−12.6820	−	4.14459i	−0.461241	−	0.150737i
$757$	16.3460	−	22.4984i	0.594107	−	0.817718i	−0.401046	−	0.916058i	$-0.631353\pi$
$757$	16.3460	−	22.4984i	0.594107	−	0.817718i	0.995153	+	0.0983398i	$0.0313532\pi$
$758$	−0.542205	+	5.15874i	−0.0196938	+	0.187374i
$759$	−0.198940	+	0.0885739i	−0.00722107	+	0.00321503i
$760$	−2.53891	−	5.70249i	−0.0920961	−	0.206851i
$761$	23.1212	+	10.2942i	0.838143	+	0.373165i	0.780488	−	0.625171i	$-0.214971\pi$
$761$	23.1212	+	10.2942i	0.838143	+	0.373165i	0.0576556	+	0.998337i	$0.481637\pi$
$762$	−8.08919	+	2.62834i	−0.293040	+	0.0952146i
$763$	−0.0475050	+	27.8331i	−0.00171979	+	1.00763i
$764$	−11.8492	−	3.85004i	−0.428690	−	0.139290i
$765$	31.4983	−	18.1855i	1.13882	−	0.657499i
$766$	33.7168	−	3.54378i	1.21824	−	0.128042i
$767$	−3.79975	+	3.42131i	−0.137201	+	0.123536i
$768$	12.6209	+	11.3639i	0.455417	+	0.410059i
$769$	0.258192	+	0.794633i	0.00931064	+	0.0286552i	0.955604	−	0.294654i	$-0.0952045\pi$
$769$	0.258192	+	0.794633i	0.00931064	+	0.0286552i	−0.946293	+	0.323310i	$0.895205\pi$
$770$	1.67829	−	0.173499i	0.0604812	−	0.00625248i
$771$	−0.383381	−	1.17992i	−0.0138071	−	0.0424940i
$772$	15.2543	+	1.60329i	0.549015	+	0.0577038i
$773$	10.2052	−	1.07260i	0.367054	−	0.0385789i	0.0807937	−	0.996731i	$-0.474255\pi$
$773$	10.2052	−	1.07260i	0.367054	−	0.0385789i	0.286260	+	0.958152i	$0.407588\pi$
$774$	−5.90718	−	6.56059i	−0.212329	−	0.235816i
$775$	2.04753	−	0.435215i	0.0735494	−	0.0156334i
$776$			2.78184i			0.0998621i
$777$	−4.30019	−	20.4020i	−0.154268	−	0.731916i
$778$	12.7639			0.457607
$779$	−2.04110	−	4.54091i	−0.0731300	−	0.162695i
$780$	−0.508956	+	0.881538i	−0.0182235	+	0.0315641i
$781$	−0.364150	−	3.46466i	−0.0130303	−	0.123975i
$782$	5.32542	−	3.07464i	0.190437	−	0.109949i
$783$	0.123687	−	0.380670i	0.00442022	−	0.0136040i
$784$	5.42732	+	3.97155i	0.193833	+	0.141841i
$785$	32.6301	+	44.9115i	1.16462	+	1.60296i
$786$	15.5174	+	1.63094i	0.553486	+	0.0581737i
$787$	32.7296	+	6.95689i	1.16668	+	0.247986i	0.750234	−	0.661173i	$-0.229941\pi$
$787$	32.7296	+	6.95689i	1.16668	+	0.247986i	0.416450	+	0.909159i	$0.363274\pi$
$788$	0.666362	−	1.15417i	0.0237382	−	0.0411157i
$789$	16.5044	−	18.3300i	0.587574	−	0.652567i
$790$	0.363676	−	0.118165i	0.0129390	−	0.00420413i
$791$	−18.8477	+	20.8608i	−0.670147	+	0.741724i
$792$	0.843445	+	1.16090i	0.0299705	+	0.0412509i
$793$	−2.71920	+	1.56993i	−0.0965616	+	0.0557499i
$794$	−19.7779	+	17.8081i	−0.701890	+	0.631985i
$795$	−26.3285	+	11.7222i	−0.933775	+	0.415743i
$796$	−10.6761	−	9.61283i	−0.378405	−	0.340718i
$797$	13.7446	−	9.98602i	0.486858	−	0.353723i	−0.317117	−	0.948386i	$-0.602715\pi$
$797$	13.7446	−	9.98602i	0.486858	−	0.353723i	0.803975	+	0.594664i	$0.202715\pi$
$798$	−1.02447	+	1.76747i	−0.0362660	+	0.0625677i
$799$	−27.3419	−	19.8650i	−0.967285	−	0.702774i
$800$	−1.14993	+	10.9408i	−0.0406560	+	0.386816i
$801$	−8.32596	−	18.7004i	−0.294183	−	0.660746i
$802$	3.58323	+	34.0922i	0.126528	+	1.20384i
$803$	−0.172292	−	0.155133i	−0.00608007	−	0.00547452i
$804$	5.60861	+	4.07489i	0.197800	+	0.143710i
$805$	−1.98974	−	6.15954i	−0.0701291	−	0.217095i
$806$		−	0.359168i		−	0.0126511i
$807$	−3.81746	+	8.57415i	−0.134381	+	0.301824i
$808$	−2.50552	+	2.25598i	−0.0881439	+	0.0793651i
$809$	−3.94073	+	18.5397i	−0.138549	+	0.651820i	0.852981	+	0.521942i	$0.174792\pi$
$809$	−3.94073	+	18.5397i	−0.138549	+	0.651820i	−0.991530	+	0.129879i	$0.958541\pi$
$810$	−1.83504	+	2.03802i	−0.0644767	+	0.0716086i
$811$	0.202089			0.00709630			0.00354815	−	0.999994i	$-0.498871\pi$
$811$	0.202089			0.00709630			0.00354815	+	0.999994i	$0.498871\pi$
$812$	0.126158	−	0.173020i	0.00442727	−	0.00607180i
$813$	−14.8495	+	20.4386i	−0.520795	+	0.716813i
$814$	−0.764099	+	1.71619i	−0.0267817	+	0.0601526i
$815$	27.9521	+	31.0440i	0.979121	+	1.08742i
$816$	4.34389	+	4.82437i	0.152066	+	0.168887i
$817$	2.98089	−	1.72102i	0.104288	−	0.0602107i
$818$	−12.4492	+	9.04489i	−0.435277	+	0.316247i
$819$	−1.98734	+	0.205449i	−0.0694432	+	0.00717896i
$820$	−1.75044	+	17.2433i	−0.0611279	+	0.602162i
$821$	10.5433	+	18.2615i	0.367963	+	0.637330i	0.989247	−	0.146255i	$-0.0467221\pi$
$821$	10.5433	+	18.2615i	0.367963	+	0.637330i	−0.621284	+	0.783585i	$0.713389\pi$
$822$	−0.155245	−	1.47706i	−0.00541480	−	0.0515184i
$823$	−7.48080	−	4.31904i	−0.260764	−	0.150552i	0.363919	−	0.931431i	$-0.381439\pi$
$823$	−7.48080	−	4.31904i	−0.260764	−	0.150552i	−0.624683	+	0.780878i	$0.714772\pi$
$824$	22.5552	−	4.79426i	0.785748	−	0.167016i
$825$	0.161127	−	0.495897i	0.00560971	−	0.0172649i
$826$	34.9563	−	7.36787i	1.21629	−	0.256361i
$827$	−9.06603	+	12.4783i	−0.315257	+	0.433914i	−0.937012	−	0.349298i	$-0.886420\pi$
$827$	−9.06603	+	12.4783i	−0.315257	+	0.433914i	0.621755	+	0.783212i	$0.286420\pi$
$828$	1.23587	−	1.37257i	0.0429493	−	0.0477000i
$829$	−6.05875	+	10.4941i	−0.210429	+	0.364474i	−0.951849	−	0.306567i	$-0.900819\pi$
$829$	−6.05875	+	10.4941i	−0.210429	+	0.364474i	0.741420	+	0.671042i	$0.234153\pi$
$830$	−3.98203	−	0.846406i	−0.138218	−	0.0293792i
$831$	−8.23361	−	7.41358i	−0.285621	−	0.257174i
$832$	2.48382	+	0.807042i	0.0861109	+	0.0279791i
$833$	−35.1126	−	31.8332i	−1.21658	−	1.10296i
$834$			16.8573i			0.583720i
$835$	−3.56840	−	16.7880i	−0.123489	−	0.580972i
$836$	−0.171478	+	0.0763469i	−0.00593069	+	0.00264051i
$837$	0.994553	−	4.67900i	0.0343768	−	0.161730i
$838$	0.941290	+	0.419089i	0.0325163	+	0.0144772i
$839$	−9.72267	+	13.3821i	−0.335664	+	0.462002i	−0.943169	−	0.332314i	$-0.892171\pi$
$839$	−9.72267	+	13.3821i	−0.335664	+	0.462002i	0.607505	+	0.794316i	$0.292171\pi$
$840$	18.3763	−	10.5678i	0.634041	−	0.364622i
$841$	−23.4563	−	17.0420i	−0.808838	−	0.587655i
$842$	11.1556	+	1.17251i	0.384449	+	0.0404072i
$843$	2.02801	+	19.2952i	0.0698484	+	0.664563i
$844$	−5.14762	+	24.2176i	−0.177188	+	0.833605i
$845$	3.60274	−	34.2777i	0.123938	−	1.17919i
$846$	9.46697	+	3.07601i	0.325481	+	0.105755i
$847$	2.97716	+	28.7986i	0.102297	+	0.989530i
$848$	6.08379	+	8.37362i	0.208918	+	0.287551i
$849$	−0.823040	−	3.87210i	−0.0282467	−	0.132890i
$850$	−3.06122	+	14.4019i	−0.104999	+	0.493982i
$851$	7.04967	+	1.49845i	0.241659	+	0.0513663i
$852$	−7.34236	−	12.7173i	−0.251545	−	0.435689i
$853$	10.0558	+	30.9487i	0.344305	+	1.05966i	0.961955	+	0.273209i	$0.0880852\pi$
$853$	10.0558	+	30.9487i	0.344305	+	1.05966i	−0.617649	+	0.786454i	$0.711915\pi$
$854$	21.9378	+	0.0374430i	0.750696	+	0.00128127i
$855$	−2.45502	−	3.37904i	−0.0839598	−	0.115561i
$856$	−41.0621	+	8.72802i	−1.40347	+	0.298318i
$857$	−35.7453	−	39.6992i	−1.22104	−	1.35610i	−0.914679	−	0.404182i	$-0.867556\pi$
$857$	−35.7453	−	39.6992i	−1.22104	−	1.35610i	−0.306358	−	0.951916i	$-0.599110\pi$
$858$	−0.0774796	−	0.0447329i	−0.00264511	−	0.00152716i
$859$	44.7740	+	19.9347i	1.52767	+	0.680162i	0.986948	−	0.161039i	$-0.0514846\pi$
$859$	44.7740	+	19.9347i	1.52767	+	0.680162i	0.540722	+	0.841202i	$0.318151\pi$
$860$	−11.9828			−0.408611
$861$	14.6263	−	8.48052i	0.498463	−	0.289015i
$862$	16.5668			0.564269
$863$	−30.8838	−	13.7504i	−1.05130	−	0.468068i	−0.192989	−	0.981201i	$-0.561818\pi$
$863$	−30.8838	−	13.7504i	−1.05130	−	0.468068i	−0.858309	+	0.513133i	$0.828485\pi$
$864$	21.7715	+	12.5698i	0.740683	+	0.427634i
$865$	−16.3962	−	18.2098i	−0.557486	−	0.619151i
$866$	33.8268	−	7.19011i	1.14948	−	0.244330i
$867$	−16.9187	−	23.2866i	−0.574589	−	0.790854i
$868$	1.28332	−	2.21404i	0.0435587	−	0.0751494i
$869$	−0.0105911	−	0.0325959i	−0.000359277	−	0.00110574i
$870$	0.106680	+	0.184775i	0.00361678	+	0.00626445i
$871$	2.53557	+	0.538951i	0.0859144	+	0.0182617i
$872$	6.55077	−	30.8189i	0.221837	−	1.04366i
$873$	0.387001	+	1.82070i	0.0130980	+	0.0616212i
$874$	−0.415071	−	0.571296i	−0.0140400	−	0.0193244i
$875$	−18.2220	−	8.15026i	−0.616017	−	0.275529i
$876$	−0.929434	−	0.301991i	−0.0314027	−	0.0102033i
$877$	6.05431	−	57.6029i	0.204440	−	1.94511i	−0.105646	−	0.994404i	$-0.533691\pi$
$877$	6.05431	−	57.6029i	0.204440	−	1.94511i	0.310086	−	0.950709i	$-0.399642\pi$
$878$	−4.57332	+	21.5158i	−0.154342	+	0.726123i
$879$	−0.0167872	−	0.159720i	−0.000566219	−	0.00538721i
$880$	−0.612331	−	0.0643586i	−0.0206417	−	0.00216953i
$881$	−10.2056	−	7.41479i	−0.343835	−	0.249811i	0.402443	−	0.915445i	$-0.368161\pi$
$881$	−10.2056	−	7.41479i	−0.343835	−	0.249811i	−0.746278	+	0.665634i	$0.768161\pi$
$882$	12.7330	+	5.72125i	0.428742	+	0.192645i
$883$	−11.6074	+	15.9761i	−0.390619	+	0.537640i	−0.958359	−	0.285568i	$-0.907818\pi$
$883$	−11.6074	+	15.9761i	−0.390619	+	0.537640i	0.567740	+	0.823208i	$0.307818\pi$
$884$	−2.35354	−	1.04786i	−0.0791580	−	0.0352434i
$885$	7.54711	−	35.5064i	0.253693	−	1.19353i
$886$	7.09434	−	3.15860i	0.238339	−	0.106115i
$887$	−1.46921	−	6.91207i	−0.0493311	−	0.232085i	0.946574	−	0.322486i	$-0.104518\pi$
$887$	−1.46921	−	6.91207i	−0.0493311	−	0.232085i	−0.995905	+	0.0904011i	$0.971185\pi$
$888$			23.6027i			0.792054i
$889$	−22.1727	+	4.67342i	−0.743649	+	0.156741i
$890$	25.9128	+	8.41957i	0.868598	+	0.282225i
$891$	0.182666	+	0.164473i	0.00611953	+	0.00551005i
$892$	−2.74546	−	0.583565i	−0.0919247	−	0.0195392i
$893$	−1.94053	+	3.36110i	−0.0649373	+	0.112475i
$894$	8.45182	−	9.38670i	0.282671	−	0.313938i
$895$	−29.6418	+	40.7984i	−0.990815	+	1.36374i
$896$	5.60351	+	6.24473i	0.187200	+	0.208622i
$897$	−0.106064	+	0.326431i	−0.00354137	+	0.0108992i
$898$	−7.33200	+	1.55847i	−0.244672	+	0.0520067i
$899$	0.0664863	+	0.0383859i	0.00221744	+	0.00128024i
$900$	0.462261	+	4.39812i	0.0154087	+	0.146604i
$901$	−36.4709	−	63.1694i	−1.21502	−	2.10448i
$902$	−1.51554	−	0.153849i	−0.0504619	−	0.00512260i
$903$	6.85451	+	9.46836i	0.228104	+	0.315087i
$904$	25.7475	−	18.7066i	0.856348	−	0.622173i
$905$	20.3160	−	11.7295i	0.675328	−	0.389901i
$906$	1.18049	+	1.31107i	0.0392191	+	0.0435572i
$907$	−15.9472	−	17.7111i	−0.529518	−	0.588089i	0.417738	−	0.908568i	$-0.362823\pi$
$907$	−15.9472	−	17.7111i	−0.529518	−	0.588089i	−0.947256	+	0.320478i	$0.896156\pi$
$908$	−9.76337	+	21.9289i	−0.324009	+	0.727736i
$909$	−1.32600	+	1.82509i	−0.0439807	+	0.0605343i
$910$	1.56676	−	2.14874i	0.0519377	−	0.0712302i
$911$	−21.0708			−0.698106			−0.349053	−	0.937103i	$-0.613497\pi$
$911$	−21.0708			−0.698106			−0.349053	+	0.937103i	$0.613497\pi$
$912$	0.498837	−	0.554014i	0.0165181	−	0.0183452i
$913$	−0.0758626	+	0.356906i	−0.00251069	+	0.0118119i
$914$	−22.2107	+	19.9986i	−0.734664	+	0.661495i
$915$	9.06660	−	20.3639i	0.299733	−	0.673210i
$916$			14.7273i			0.486603i
$917$	40.6451	+	8.71192i	1.34222	+	0.287693i
$918$	27.2206	+	19.7769i	0.898413	+	0.652735i
$919$	27.8470	+	25.0736i	0.918588	+	0.827100i	0.985328	−	0.170670i	$-0.0545932\pi$
$919$	27.8470	+	25.0736i	0.918588	+	0.827100i	−0.0667402	+	0.997770i	$0.521260\pi$
$920$	0.765927	+	7.28731i	0.0252519	+	0.240255i
$921$	5.27903	+	11.8569i	0.173950	+	0.390698i
$922$	4.17245	−	39.6982i	0.137412	−	1.30739i
$923$	−4.44218	−	3.22743i	−0.146216	−	0.106232i
$924$	−0.317780	−	0.552587i	−0.0104542	−	0.0181788i
$925$	−13.9609	+	10.1432i	−0.459033	+	0.333507i
$926$	−15.7705	−	14.1998i	−0.518251	−	0.466636i
$927$	14.0953	−	6.27563i	0.462950	−	0.206119i
$928$	−0.299837	+	0.269974i	−0.00984262	+	0.00886234i
$929$	20.9195	−	12.0779i	0.686348	−	0.396263i	−0.115894	−	0.993262i	$-0.536973\pi$
$929$	20.9195	−	12.0779i	0.686348	−	0.396263i	0.802242	+	0.596998i	$0.203640\pi$
$930$	1.49878	+	2.06289i	0.0491468	+	0.0676448i
$931$	−3.21411	+	4.39223i	−0.105338	+	0.143950i
$932$	−3.98731	+	1.29556i	−0.130609	+	0.0424373i
$933$	17.0798	−	18.9690i	0.559167	−	0.621018i
$934$	4.48020	−	7.75994i	0.146597	−	0.253913i
$935$	4.24420	+	0.902134i	0.138800	+	0.0295029i
$936$	2.24929	+	0.236410i	0.0735203	+	0.00772729i
$937$	−9.24910	−	12.7303i	−0.302155	−	0.415880i	0.630760	−	0.775978i	$-0.282743\pi$
$937$	−9.24910	−	12.7303i	−0.302155	−	0.415880i	−0.932915	+	0.360098i	$0.882743\pi$
$938$	−13.4388	−	12.1419i	−0.438791	−	0.396447i
$939$	−1.61447	+	4.96883i	−0.0526863	+	0.162152i
$940$	11.7010	−	6.75560i	0.381646	−	0.220343i
$941$	−2.70278	−	25.7152i	−0.0881080	−	0.838292i	−0.945936	−	0.324354i	$-0.894853\pi$
$941$	−2.70278	−	25.7152i	−0.0881080	−	0.838292i	0.857828	−	0.513937i	$-0.171814\pi$
$942$	−10.2834	+	17.8114i	−0.335051	+	0.580326i
$943$	0.631521	+	5.80992i	0.0205652	+	0.189197i
$944$	−13.0365			−0.424303
$945$	26.3607	−	23.6540i	0.857515	−	0.769464i
$946$		−	1.05319i		−	0.0342421i
$947$	−56.0961	+	11.9236i	−1.82288	+	0.387465i	−0.986905	−	0.161303i	$-0.948430\pi$
$947$	−56.0961	+	11.9236i	−1.82288	+	0.387465i	−0.835975	+	0.548768i	$0.815097\pi$
$948$	−0.0966690	−	0.107362i	−0.00313966	−	0.00348695i
$949$	−0.363412	+	0.0381962i	−0.0117969	+	0.00123990i
$950$	1.68155	+	0.176738i	0.0545568	+	0.00573415i
$951$	−9.01941	−	27.7589i	−0.292475	−	0.900144i
$952$	31.4613	+	43.4585i	1.01967	+	1.40850i
$953$	13.6121	+	41.8937i	0.440939	+	1.35707i	0.886876	+	0.462007i	$0.152871\pi$
$953$	13.6121	+	41.8937i	0.440939	+	1.35707i	−0.445937	+	0.895064i	$0.647129\pi$
$954$	15.9655	+	14.3754i	0.516904	+	0.465422i
$955$	24.5782	−	22.1303i	0.795332	−	0.716120i
$956$	−12.0219	+	1.26356i	−0.388817	+	0.0408663i
$957$	0.0165612	−	0.00956161i	0.000535347	−	0.000309083i
$958$	25.2367	+	8.19991i	0.815362	+	0.264927i
$959$	0.00675335	−	3.95678i	0.000218077	−	0.127771i
$960$	−17.6336	+	5.72950i	−0.569121	+	0.184919i
$961$	−27.4817	−	12.2357i	−0.886507	−	0.394699i
$962$	1.20432	+	2.70495i	0.0388289	+	0.0872111i
$963$	−25.6607	+	11.4249i	−0.826904	+	0.368161i
$964$	−1.07154	+	10.1950i	−0.0345121	+	0.328360i
$965$	−23.9327	+	32.9405i	−0.770420	+	1.06039i
$966$	1.78488	−	1.60160i	0.0574274	−	0.0515307i
$967$	6.25320	−	2.03179i	0.201089	−	0.0653379i	−0.206741	−	0.978396i	$-0.566286\pi$
$967$	6.25320	−	2.03179i	0.201089	−	0.0653379i	0.407830	+	0.913058i	$0.366286\pi$
$968$	3.42582	−	32.5945i	0.110110	−	1.04763i
$969$	−3.90428	+	3.51543i	−0.125424	+	0.112932i
$970$	−2.14561	−	1.23877i	−0.0688913	−	0.0397744i
$971$	−3.95325	+	8.87914i	−0.126866	+	0.284945i	−0.965800	−	0.259287i	$-0.916512\pi$
$971$	−3.95325	+	8.87914i	−0.126866	+	0.284945i	0.838934	+	0.544232i	$0.183179\pi$
$972$	15.3735	+	4.99514i	0.493104	+	0.160219i
$973$	−4.77063	+	44.6562i	−0.152940	+	1.43161i
$974$	4.89759	+	15.0732i	0.156929	+	0.482977i
$975$	−0.410911	−	0.711718i	−0.0131597	−	0.0227932i
$976$	−7.83061	−	1.66445i	−0.250652	−	0.0532777i
$977$	−15.4803	−	34.7693i	−0.495259	−	1.11237i	−0.972353	−	0.233517i	$-0.924976\pi$
$977$	−15.4803	−	34.7693i	−0.495259	−	1.11237i	0.477094	−	0.878852i	$-0.341690\pi$
$978$	−6.29482	+	14.1384i	−0.201286	+	0.452096i
$979$	0.754639	−	2.32254i	0.0241184	−	0.0742287i
$980$	17.3356	−	7.64752i	0.553766	−	0.244291i
$981$		−	21.0821i		−	0.673101i
$982$	−5.86524	−	2.61137i	−0.187167	−	0.0833322i
$983$	−16.5930	+	28.7400i	−0.529236	+	0.916664i	0.470183	+	0.882569i	$0.344188\pi$
$983$	−16.5930	+	28.7400i	−0.529236	+	0.916664i	−0.999419	+	0.0340944i	$0.989145\pi$
$984$	−18.1811	+	5.97888i	−0.579592	+	0.190600i
$985$	1.76890	+	3.06383i	0.0563619	+	0.0976217i
$986$	−0.436868	+	0.317403i	−0.0139127	+	0.0101082i
$987$	−12.0313	−	5.38132i	−0.382962	−	0.171289i
$988$	−0.0914225	+	0.281369i	−0.00290854	+	0.00895155i
$989$	−3.95219	+	0.840064i	−0.125672	+	0.0267125i
$990$	−1.27099	+	0.133586i	−0.0403946	+	0.00424564i
$991$	7.21416	+	16.2033i	0.229165	+	0.514714i	0.991129	−	0.132906i	$-0.0424310\pi$
$991$	7.21416	+	16.2033i	0.229165	+	0.514714i	−0.761963	+	0.647620i	$0.775764\pi$
$992$	−3.22648	+	3.58337i	−0.102441	+	0.113772i
$993$	−34.5654			−1.09690
$994$	15.5441	+	35.0737i	0.493030	+	1.11247i
$995$	36.2694	−	11.7846i	1.14982	−	0.373598i
$996$	0.319777	+	1.50443i	0.0101325	+	0.0476698i
$997$	27.8392	−	2.92602i	0.881678	−	0.0926681i	0.347141	−	0.937813i	$-0.387153\pi$
$997$	27.8392	−	2.92602i	0.881678	−	0.0926681i	0.534537	+	0.845145i	$0.320486\pi$
$998$	−6.07264	−	3.50604i	−0.192226	−	0.110982i
$999$	8.19897	+	38.5731i	0.259404	+	1.22040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.z.a.4.17	✓	208
7.2	even	3	inner	287.2.z.a.86.10	yes	208
41.31	even	10	inner	287.2.z.a.277.10	yes	208
287.72	even	30	inner	287.2.z.a.72.17	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.z.a.4.17	✓	208	1.1	even	1	trivial
287.2.z.a.72.17	yes	208	287.72	even	30	inner
287.2.z.a.86.10	yes	208	7.2	even	3	inner
287.2.z.a.277.10	yes	208	41.31	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.z (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.909063 + 0.404741i) q^{2} +(0.864285 + 0.498995i) q^{3} +(-0.675680 - 0.750419i) q^{4} +(2.62197 - 0.557318i) q^{5} +(0.583726 + 0.803430i) q^{6} +(1.31896 + 2.29354i) q^{7} +(-0.925513 - 2.84843i) q^{8} +(-1.00201 - 1.73553i) q^{9} +O(q^{10})\)	\(q+(0.909063 + 0.404741i) q^{2} +(0.864285 + 0.498995i) q^{3} +(-0.675680 - 0.750419i) q^{4} +(2.62197 - 0.557318i) q^{5} +(0.583726 + 0.803430i) q^{6} +(1.31896 + 2.29354i) q^{7} +(-0.925513 - 2.84843i) q^{8} +(-1.00201 - 1.73553i) q^{9} +(2.60911 + 0.554583i) q^{10} +(0.0497068 - 0.233852i) q^{11} +(-0.209525 - 0.985737i) q^{12} +(-0.221487 - 0.304851i) q^{13} +(0.270730 + 2.61881i) q^{14} +(2.54423 + 0.826671i) q^{15} +(0.100426 - 0.955487i) q^{16} +(-1.40770 + 6.62270i) q^{17} +(-0.208449 - 1.98326i) q^{18} +(0.773259 + 0.0812728i) q^{19} +(-2.18984 - 1.59101i) q^{20} +(-0.00450663 + 2.64043i) q^{21} +(0.139836 - 0.192468i) q^{22} +(-0.833795 - 0.371229i) q^{23} +(0.621448 - 2.92369i) q^{24} +(1.99642 - 0.888863i) q^{25} +(-0.0779601 - 0.366774i) q^{26} -4.99396i q^{27} +(0.829921 - 2.53948i) q^{28} +(0.0762261 + 0.0247674i) q^{29} +(1.97828 + 1.78125i) q^{30} +(0.936933 + 0.199151i) q^{31} +(-2.51700 + 4.35958i) q^{32} +(0.159652 - 0.177311i) q^{33} +(-3.96017 + 5.45070i) q^{34} +(4.73652 + 5.27853i) q^{35} +(-0.625337 + 1.92459i) q^{36} +(-7.72395 + 1.64178i) q^{37} +(0.670047 + 0.386852i) q^{38} +(-0.0393089 - 0.373999i) q^{39} +(-4.01415 - 6.95272i) q^{40} +(-3.22124 - 5.53386i) q^{41} +(-1.07279 + 2.39849i) q^{42} +(3.58148 - 2.60209i) q^{43} +(-0.209073 + 0.120708i) q^{44} +(-3.59448 - 3.99207i) q^{45} +(-0.607720 - 0.674942i) q^{46} +(-2.03027 + 4.56005i) q^{47} +(0.563580 - 0.775701i) q^{48} +(-3.52067 + 6.05020i) q^{49} +2.17463 q^{50} +(-4.52135 + 5.02146i) q^{51} +(-0.0791114 + 0.372190i) q^{52} +(-8.00606 + 7.20869i) q^{53} +(2.02126 - 4.53982i) q^{54} -0.640857i q^{55} +(5.31229 - 5.87968i) q^{56} +(0.627761 + 0.456095i) q^{57} +(0.0592700 + 0.0533670i) q^{58} +(-1.41836 - 13.4948i) q^{59} +(-1.09874 - 2.46780i) q^{60} +(0.870995 - 8.28696i) q^{61} +(0.771126 + 0.560256i) q^{62} +(2.65890 - 4.58725i) q^{63} +(-5.60714 + 4.07383i) q^{64} +(-0.750632 - 0.675872i) q^{65} +(0.216899 - 0.0965696i) q^{66} +(-5.11228 + 4.60312i) q^{67} +(5.92096 - 3.41847i) q^{68} +(-0.535394 - 0.736907i) q^{69} +(2.16936 + 6.71558i) q^{70} +(13.8585 - 4.50289i) q^{71} +(-4.01617 + 4.46041i) q^{72} +(0.484870 - 0.839820i) q^{73} +(-7.68606 - 1.63372i) q^{74} +(2.16901 + 0.227972i) q^{75} +(-0.461487 - 0.635183i) q^{76} +(0.601911 - 0.194438i) q^{77} +(0.115638 - 0.355899i) q^{78} +(0.124151 - 0.0716786i) q^{79} +(-0.269196 - 2.56123i) q^{80} +(-0.514063 + 0.890383i) q^{81} +(-0.688530 - 6.33440i) q^{82} -1.52620 q^{83} +(1.98447 - 1.78070i) q^{84} +18.1491i q^{85} +(4.30896 - 0.915898i) q^{86} +(0.0535223 + 0.0594425i) q^{87} +(-0.712117 + 0.0748465i) q^{88} +(10.1586 + 1.06771i) q^{89} +(-1.65185 - 5.08388i) q^{90} +(0.407055 - 0.910077i) q^{91} +(0.284801 + 0.876528i) q^{92} +(0.710401 + 0.639648i) q^{93} +(-3.69128 + 3.32364i) q^{94} +(2.07276 - 0.217856i) q^{95} +(-4.35082 + 2.51194i) q^{96} +(-0.883361 - 0.287021i) q^{97} +(-5.64928 + 4.07505i) q^{98} +(-0.455664 + 0.148054i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q - 3 q^{2} + 21 q^{4} + q^{5} - 40 q^{6} - 10 q^{7} - 8 q^{8} + 84 q^{9}+O(q^{10}) \) 208 * q - 3 * q^2 + 21 * q^4 + q^5 - 40 * q^6 - 10 * q^7 - 8 * q^8 + 84 * q^9	\( 208 q - 3 q^{2} + 21 q^{4} + q^{5} - 40 q^{6} - 10 q^{7} - 8 q^{8} + 84 q^{9} - 6 q^{10} - 5 q^{11} - 35 q^{12} - 20 q^{13} - 50 q^{15} + 21 q^{16} - 5 q^{17} + 18 q^{18} - 5 q^{19} - 96 q^{20} + 8 q^{21} + 20 q^{22} + 40 q^{24} + 27 q^{25} - 5 q^{26} + 5 q^{28} + 20 q^{29} - 45 q^{30} - 11 q^{31} - 30 q^{32} - 10 q^{33} + 100 q^{34} - 106 q^{36} - 16 q^{37} - 4 q^{39} + 6 q^{40} - 14 q^{41} - 8 q^{42} - 8 q^{43} + 34 q^{45} - 32 q^{46} + 25 q^{47} - 50 q^{48} + 14 q^{49} - 120 q^{50} + 2 q^{51} - 105 q^{52} + 20 q^{53} - 35 q^{54} + 100 q^{56} - 98 q^{57} - 5 q^{58} - 37 q^{59} - 100 q^{60} + 51 q^{61} - 70 q^{62} - 30 q^{63} - 100 q^{64} + 40 q^{65} - 176 q^{66} + 15 q^{67} - 30 q^{69} + 105 q^{70} - 10 q^{71} - 33 q^{72} - 34 q^{73} - 23 q^{74} - 120 q^{75} + 110 q^{76} + 72 q^{77} - 18 q^{78} + 127 q^{80} - 24 q^{81} - 63 q^{82} - 128 q^{83} + 33 q^{84} - 61 q^{86} + 28 q^{87} + 150 q^{88} + 35 q^{89} - 34 q^{90} + 14 q^{91} + 102 q^{92} - 55 q^{93} - 155 q^{94} + 55 q^{95} + 20 q^{97} + 88 q^{98} + 120 q^{99}+O(q^{100}) \) 208 * q - 3 * q^2 + 21 * q^4 + q^5 - 40 * q^6 - 10 * q^7 - 8 * q^8 + 84 * q^9 - 6 * q^10 - 5 * q^11 - 35 * q^12 - 20 * q^13 - 50 * q^15 + 21 * q^16 - 5 * q^17 + 18 * q^18 - 5 * q^19 - 96 * q^20 + 8 * q^21 + 20 * q^22 + 40 * q^24 + 27 * q^25 - 5 * q^26 + 5 * q^28 + 20 * q^29 - 45 * q^30 - 11 * q^31 - 30 * q^32 - 10 * q^33 + 100 * q^34 - 106 * q^36 - 16 * q^37 - 4 * q^39 + 6 * q^40 - 14 * q^41 - 8 * q^42 - 8 * q^43 + 34 * q^45 - 32 * q^46 + 25 * q^47 - 50 * q^48 + 14 * q^49 - 120 * q^50 + 2 * q^51 - 105 * q^52 + 20 * q^53 - 35 * q^54 + 100 * q^56 - 98 * q^57 - 5 * q^58 - 37 * q^59 - 100 * q^60 + 51 * q^61 - 70 * q^62 - 30 * q^63 - 100 * q^64 + 40 * q^65 - 176 * q^66 + 15 * q^67 - 30 * q^69 + 105 * q^70 - 10 * q^71 - 33 * q^72 - 34 * q^73 - 23 * q^74 - 120 * q^75 + 110 * q^76 + 72 * q^77 - 18 * q^78 + 127 * q^80 - 24 * q^81 - 63 * q^82 - 128 * q^83 + 33 * q^84 - 61 * q^86 + 28 * q^87 + 150 * q^88 + 35 * q^89 - 34 * q^90 + 14 * q^91 + 102 * q^92 - 55 * q^93 - 155 * q^94 + 55 * q^95 + 20 * q^97 + 88 * q^98 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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