LMFDB - Embedded newform 231.2.bc.a.5.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(5,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 25, 12]))

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

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

chi := DirichletCharacter("231.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.bc (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			5.18
Character	$\chi$	$=$	231.5
Dual form			231.2.bc.a.185.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.170302 - 0.801208i) q^{2} +(1.59941 - 0.664752i) q^{3} +(1.21416 + 0.540578i) q^{4} +(0.800599 + 0.889155i) q^{5} +(-0.260223 - 1.39467i) q^{6} +(-2.04538 + 1.67822i) q^{7} +(1.60281 - 2.20608i) q^{8} +(2.11621 - 2.12642i) q^{9} +O(q^{10})$	\(q+(0.170302 - 0.801208i) q^{2} +(1.59941 - 0.664752i) q^{3} +(1.21416 + 0.540578i) q^{4} +(0.800599 + 0.889155i) q^{5} +(-0.260223 - 1.39467i) q^{6} +(-2.04538 + 1.67822i) q^{7} +(1.60281 - 2.20608i) q^{8} +(2.11621 - 2.12642i) q^{9} +(0.848742 - 0.490022i) q^{10} +(-2.54021 + 2.13245i) q^{11} +(2.30129 + 0.0574900i) q^{12} +(-1.06522 + 0.346110i) q^{13} +(0.996271 + 1.92458i) q^{14} +(1.87155 + 0.889921i) q^{15} +(0.284068 + 0.315489i) q^{16} +(-3.74736 + 0.796526i) q^{17} +(-1.34331 - 2.05766i) q^{18} +(-2.39074 - 5.36970i) q^{19} +(0.491396 + 1.51236i) q^{20} +(-2.15579 + 4.04383i) q^{21} +(1.27593 + 2.39840i) q^{22} +(-2.51812 - 1.45384i) q^{23} +(1.09705 - 4.59389i) q^{24} +(0.373004 - 3.54890i) q^{25} +(0.0958974 + 0.912403i) q^{26} +(1.97114 - 4.80777i) q^{27} +(-3.39063 + 0.931938i) q^{28} +(-0.376877 - 0.518726i) q^{29} +(1.03174 - 1.34795i) q^{30} +(-0.779950 - 0.702270i) q^{31} +(5.02421 - 2.90073i) q^{32} +(-2.64529 + 5.09926i) q^{33} +3.13807i q^{34} +(-3.12973 - 0.475079i) q^{35} +(3.71891 - 1.43784i) q^{36} +(0.0760999 + 0.724042i) q^{37} +(-4.70939 + 1.00101i) q^{38} +(-1.47364 + 1.26168i) q^{39} +(3.24475 - 0.341037i) q^{40} +(8.19908 + 5.95698i) q^{41} +(2.87281 + 2.41591i) q^{42} +2.49683 q^{43} +(-4.23698 + 1.21594i) q^{44} +(3.58495 + 0.179228i) q^{45} +(-1.59367 + 1.76995i) q^{46} +(-10.2325 + 4.55581i) q^{47} +(0.664062 + 0.315761i) q^{48} +(1.36716 - 6.86519i) q^{49} +(-2.77988 - 0.903238i) q^{50} +(-5.46406 + 3.76504i) q^{51} +(-1.48044 - 0.155601i) q^{52} +(5.80813 + 5.22966i) q^{53} +(-3.51633 - 2.39806i) q^{54} +(-3.92977 - 0.551409i) q^{55} +(0.423930 + 7.20213i) q^{56} +(-7.39329 - 6.99908i) q^{57} +(-0.479790 + 0.213616i) q^{58} +(-0.257624 - 0.114702i) q^{59} +(1.79129 + 2.09223i) q^{60} +(-6.16333 + 5.54949i) q^{61} +(-0.695492 + 0.505305i) q^{62} +(-0.759850 + 7.90080i) q^{63} +(-1.20608 - 3.71193i) q^{64} +(-1.16056 - 0.670047i) q^{65} +(3.63507 + 2.98784i) q^{66} +(5.36541 + 9.29317i) q^{67} +(-4.98048 - 1.05863i) q^{68} +(-4.99394 - 0.651352i) q^{69} +(-0.913636 + 2.42666i) q^{70} +(10.0704 + 3.27208i) q^{71} +(-1.29917 - 8.07676i) q^{72} +(0.516493 - 1.16006i) q^{73} +(0.593068 + 0.0623340i) q^{74} +(-1.76255 - 5.92409i) q^{75} -7.81205i q^{76} +(1.61699 - 8.62469i) q^{77} +(0.759901 + 1.39556i) q^{78} +(12.1648 + 2.58570i) q^{79} +(-0.0530945 + 0.505161i) q^{80} +(-0.0433233 - 8.99990i) q^{81} +(6.16910 - 5.55468i) q^{82} +(-2.18111 + 6.71278i) q^{83} +(-4.80348 + 3.74447i) q^{84} +(-3.70837 - 2.69429i) q^{85} +(0.425215 - 2.00048i) q^{86} +(-0.947604 - 0.579125i) q^{87} +(0.632865 + 9.02180i) q^{88} +(-3.33245 + 5.77196i) q^{89} +(0.754124 - 2.84177i) q^{90} +(1.59792 - 2.49559i) q^{91} +(-2.27148 - 3.12643i) q^{92} +(-1.71429 - 0.604743i) q^{93} +(1.90753 + 8.97424i) q^{94} +(2.86047 - 6.42472i) q^{95} +(6.10749 - 7.97931i) q^{96} +(3.44346 - 1.11885i) q^{97} +(-5.26762 - 2.26453i) q^{98} +(-0.841144 + 9.91426i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 9 q^{3} - 30 q^{4} - 16 q^{7} + 3 q^{9}+O(q^{10}) $ 224 * q - 9 * q^3 - 30 * q^4 - 16 * q^7 + 3 * q^9	$ 224 q - 9 q^{3} - 30 q^{4} - 16 q^{7} + 3 q^{9} - 60 q^{10} - 12 q^{12} - 36 q^{15} + 18 q^{16} + 13 q^{18} - 18 q^{19} - 6 q^{21} + 20 q^{22} - 51 q^{24} - 18 q^{25} - 26 q^{28} - 15 q^{30} - 36 q^{31} + 60 q^{33} - 32 q^{36} - 10 q^{37} + 9 q^{39} - 114 q^{42} - 96 q^{43} + 24 q^{45} - 54 q^{46} - 56 q^{49} - 29 q^{51} - 30 q^{52} - 96 q^{54} + 68 q^{57} - 64 q^{58} + 125 q^{60} - 18 q^{61} - 26 q^{63} + 56 q^{64} + 135 q^{66} + 48 q^{67} - 44 q^{70} + 19 q^{72} + 30 q^{73} + 63 q^{75} + 28 q^{78} + 30 q^{79} + 31 q^{81} + 54 q^{82} + 99 q^{84} - 248 q^{85} + 102 q^{87} + 82 q^{88} - 144 q^{91} + 34 q^{93} + 162 q^{94} - 87 q^{96} - 100 q^{99}+O(q^{100}) $ 224 * q - 9 * q^3 - 30 * q^4 - 16 * q^7 + 3 * q^9 - 60 * q^10 - 12 * q^12 - 36 * q^15 + 18 * q^16 + 13 * q^18 - 18 * q^19 - 6 * q^21 + 20 * q^22 - 51 * q^24 - 18 * q^25 - 26 * q^28 - 15 * q^30 - 36 * q^31 + 60 * q^33 - 32 * q^36 - 10 * q^37 + 9 * q^39 - 114 * q^42 - 96 * q^43 + 24 * q^45 - 54 * q^46 - 56 * q^49 - 29 * q^51 - 30 * q^52 - 96 * q^54 + 68 * q^57 - 64 * q^58 + 125 * q^60 - 18 * q^61 - 26 * q^63 + 56 * q^64 + 135 * q^66 + 48 * q^67 - 44 * q^70 + 19 * q^72 + 30 * q^73 + 63 * q^75 + 28 * q^78 + 30 * q^79 + 31 * q^81 + 54 * q^82 + 99 * q^84 - 248 * q^85 + 102 * q^87 + 82 * q^88 - 144 * q^91 + 34 * q^93 + 162 * q^94 - 87 * q^96 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.170302	−	0.801208i	0.120422	−	0.566540i	−0.876021	−	0.482272i	$-0.839812\pi$
$2$	0.170302	−	0.801208i	0.120422	−	0.566540i	0.996443	−	0.0842676i	$-0.0268550\pi$
$3$	1.59941	−	0.664752i	0.923418	−	0.383795i
$3$	1.59941	−	0.664752i	0.923418	−	0.383795i
$4$	1.21416	+	0.540578i	0.607080	+	0.270289i
$5$	0.800599	+	0.889155i	0.358039	+	0.397642i	0.895074	−	0.445917i	$-0.147122\pi$
$5$	0.800599	+	0.889155i	0.358039	+	0.397642i	−0.537035	+	0.843560i	$0.680456\pi$
$6$	−0.260223	−	1.39467i	−0.106235	−	0.569370i
$7$	−2.04538	+	1.67822i	−0.773081	+	0.634307i
$7$	−2.04538	+	1.67822i	−0.773081	+	0.634307i
$8$	1.60281	−	2.20608i	0.566678	−	0.779966i
$9$	2.11621	−	2.12642i	0.705403	−	0.708807i
$10$	0.848742	−	0.490022i	0.268396	−	0.154958i
$11$	−2.54021	+	2.13245i	−0.765903	+	0.642956i
$11$	−2.54021	+	2.13245i	−0.765903	+	0.642956i
$12$	2.30129	+	0.0574900i	0.664324	+	0.0165959i
$13$	−1.06522	+	0.346110i	−0.295438	+	0.0959935i	−0.452986	−	0.891518i	$-0.649641\pi$
$13$	−1.06522	+	0.346110i	−0.295438	+	0.0959935i	0.157548	+	0.987511i	$0.449641\pi$
$14$	0.996271	+	1.92458i	0.266265	+	0.514365i
$15$	1.87155	+	0.889921i	0.483233	+	0.229777i
$16$	0.284068	+	0.315489i	0.0710170	+	0.0788723i
$17$	−3.74736	+	0.796526i	−0.908868	+	0.193186i	−0.638546	−	0.769584i	$-0.720464\pi$
$17$	−3.74736	+	0.796526i	−0.908868	+	0.193186i	−0.270323	+	0.962770i	$0.587130\pi$
$18$	−1.34331	−	2.05766i	−0.316621	−	0.484994i
$19$	−2.39074	−	5.36970i	−0.548474	−	1.23189i	−0.948904	−	0.315566i	$-0.897806\pi$
$19$	−2.39074	−	5.36970i	−0.548474	−	1.23189i	0.400430	−	0.916328i	$-0.368861\pi$
$20$	0.491396	+	1.51236i	0.109880	+	0.338175i
$21$	−2.15579	+	4.04383i	−0.470433	+	0.882436i
$22$	1.27593	+	2.39840i	0.272029	+	0.511340i
$23$	−2.51812	−	1.45384i	−0.525064	−	0.303146i	0.213940	−	0.976847i	$-0.431370\pi$
$23$	−2.51812	−	1.45384i	−0.525064	−	0.303146i	−0.739004	+	0.673701i	$0.764704\pi$
$24$	1.09705	−	4.59389i	0.223934	−	0.937723i
$25$	0.373004	−	3.54890i	0.0746008	−	0.709779i
$26$	0.0958974	+	0.912403i	0.0188070	+	0.178937i
$27$	1.97114	−	4.80777i	0.379345	−	0.925255i
$28$	−3.39063	+	0.931938i	−0.640768	+	0.176120i
$29$	−0.376877	−	0.518726i	−0.0699842	−	0.0963250i	0.772590	−	0.634905i	$-0.218961\pi$
$29$	−0.376877	−	0.518726i	−0.0699842	−	0.0963250i	−0.842574	+	0.538580i	$0.818961\pi$
$30$	1.03174	−	1.34795i	0.188369	−	0.246100i
$31$	−0.779950	−	0.702270i	−0.140083	−	0.126131i	0.596110	−	0.802902i	$-0.296712\pi$
$31$	−0.779950	−	0.702270i	−0.140083	−	0.126131i	−0.736194	+	0.676771i	$0.763379\pi$
$32$	5.02421	−	2.90073i	0.888163	−	0.512781i
$33$	−2.64529	+	5.09926i	−0.460485	+	0.887667i
$34$			3.13807i			0.538174i
$35$	−3.12973	−	0.475079i	−0.529020	−	0.0803030i
$36$	3.71891	−	1.43784i	0.619818	−	0.239639i
$37$	0.0760999	+	0.724042i	0.0125107	+	0.119032i	0.998995	−	0.0448252i	$-0.0142731\pi$
$37$	0.0760999	+	0.724042i	0.0125107	+	0.119032i	−0.986484	+	0.163857i	$0.947606\pi$
$38$	−4.70939	+	1.00101i	−0.763965	+	0.162386i
$39$	−1.47364	+	1.26168i	−0.235971	+	0.202030i
$40$	3.24475	−	0.341037i	0.513040	−	0.0539227i
$41$	8.19908	+	5.95698i	1.28048	+	0.930324i	0.999567	−	0.0294090i	$-0.00936253\pi$
$41$	8.19908	+	5.95698i	1.28048	+	0.930324i	0.280914	+	0.959733i	$0.409363\pi$
$42$	2.87281	+	2.41591i	0.443285	+	0.372783i
$43$	2.49683			0.380762			0.190381	−	0.981710i	$-0.439028\pi$
$43$	2.49683			0.380762			0.190381	+	0.981710i	$0.439028\pi$
$44$	−4.23698	+	1.21594i	−0.638748	+	0.183310i
$45$	3.58495	+	0.179228i	0.534413	+	0.0267178i
$46$	−1.59367	+	1.76995i	−0.234973	+	0.260964i
$47$	−10.2325	+	4.55581i	−1.49257	+	0.664534i	−0.980876	−	0.194636i	$-0.937647\pi$
$47$	−10.2325	+	4.55581i	−1.49257	+	0.664534i	−0.511691	+	0.859169i	$0.670981\pi$
$48$	0.664062	+	0.315761i	0.0958492	+	0.0455762i
$49$	1.36716	−	6.86519i	0.195308	−	0.980742i
$50$	−2.77988	−	0.903238i	−0.393135	−	0.127737i
$51$	−5.46406	+	3.76504i	−0.765122	+	0.527211i
$52$	−1.48044	−	0.155601i	−0.205300	−	0.0215779i
$53$	5.80813	+	5.22966i	0.797808	+	0.718350i	0.963465	−	0.267834i	$-0.0863078\pi$
$53$	5.80813	+	5.22966i	0.797808	+	0.718350i	−0.165657	+	0.986183i	$0.552974\pi$
$54$	−3.51633	−	2.39806i	−0.478512	−	0.326335i
$55$	−3.92977	−	0.551409i	−0.529890	−	0.0743520i
$56$	0.423930	+	7.20213i	0.0566500	+	0.962425i
$57$	−7.39329	−	6.99908i	−0.979265	−	0.927051i
$58$	−0.479790	+	0.213616i	−0.0629996	+	0.0280492i
$59$	−0.257624	−	0.114702i	−0.0335398	−	0.0149329i	0.389898	−	0.920858i	$-0.372510\pi$
$59$	−0.257624	−	0.114702i	−0.0335398	−	0.0149329i	−0.423438	+	0.905925i	$0.639177\pi$
$60$	1.79129	+	2.09223i	0.231255	+	0.270105i
$61$	−6.16333	+	5.54949i	−0.789133	+	0.710539i	−0.961593	−	0.274478i	$-0.911495\pi$
$61$	−6.16333	+	5.54949i	−0.789133	+	0.710539i	0.172460	+	0.985016i	$0.444828\pi$
$62$	−0.695492	+	0.505305i	−0.0883276	+	0.0641737i
$63$	−0.759850	+	7.90080i	−0.0957321	+	0.995407i
$64$	−1.20608	−	3.71193i	−0.150760	−	0.463991i
$65$	−1.16056	−	0.670047i	−0.143949	−	0.0831091i
$66$	3.63507	+	2.98784i	0.447446	+	0.367778i
$67$	5.36541	+	9.29317i	0.655490	+	1.13534i	0.981771	+	0.190069i	$0.0608711\pi$
$67$	5.36541	+	9.29317i	0.655490	+	1.13534i	−0.326281	+	0.945273i	$0.605796\pi$
$68$	−4.98048	−	1.05863i	−0.603972	−	0.128378i
$69$	−4.99394	−	0.651352i	−0.601200	−	0.0784135i
$70$	−0.913636	+	2.42666i	−0.109200	+	0.290041i
$71$	10.0704	+	3.27208i	1.19514	+	0.388325i	0.837971	−	0.545715i	$-0.183742\pi$
$71$	10.0704	+	3.27208i	1.19514	+	0.388325i	0.357170	+	0.934039i	$0.383742\pi$
$72$	−1.29917	−	8.07676i	−0.153108	−	0.951856i
$73$	0.516493	−	1.16006i	0.0604509	−	0.135775i	−0.880794	−	0.473500i	$-0.842991\pi$
$73$	0.516493	−	1.16006i	0.0604509	−	0.135775i	0.941245	+	0.337725i	$0.109657\pi$
$74$	0.593068	+	0.0623340i	0.0689428	+	0.00724618i
$75$	−1.76255	−	5.92409i	−0.203522	−	0.684055i
$76$		−	7.81205i		−	0.896104i
$77$	1.61699	−	8.62469i	0.184273	−	0.982875i
$78$	0.759901	+	1.39556i	0.0860418	+	0.158016i
$79$	12.1648	+	2.58570i	1.36864	+	0.290914i	0.832879	−	0.553454i	$-0.186691\pi$
$79$	12.1648	+	2.58570i	1.36864	+	0.290914i	0.535763	+	0.844368i	$0.320024\pi$
$80$	−0.0530945	+	0.505161i	−0.00593615	+	0.0564787i
$81$	−0.0433233	−	8.99990i	−0.00481370	−	0.999988i
$82$	6.16910	−	5.55468i	0.681263	−	0.613412i
$83$	−2.18111	+	6.71278i	−0.239408	+	0.736823i	0.757098	+	0.653302i	$0.226617\pi$
$83$	−2.18111	+	6.71278i	−0.239408	+	0.736823i	−0.996506	+	0.0835213i	$0.973383\pi$
$84$	−4.80348	+	3.74447i	−0.524103	+	0.408556i
$85$	−3.70837	−	2.69429i	−0.402229	−	0.292237i
$86$	0.425215	−	2.00048i	0.0458521	−	0.215717i
$87$	−0.947604	−	0.579125i	−0.101594	−	0.0620887i
$88$	0.632865	+	9.02180i	0.0674636	+	0.961728i
$89$	−3.33245	+	5.77196i	−0.353238	+	0.611827i	−0.986815	−	0.161853i	$-0.948253\pi$
$89$	−3.33245	+	5.77196i	−0.353238	+	0.611827i	0.633576	+	0.773680i	$0.281586\pi$
$90$	0.754124	−	2.84177i	0.0794916	−	0.299549i
$91$	1.59792	−	2.49559i	0.167508	−	0.261609i
$92$	−2.27148	−	3.12643i	−0.236819	−	0.325953i
$93$	−1.71429	−	0.604743i	−0.177764	−	0.0627089i
$94$	1.90753	+	8.97424i	0.196747	+	0.925623i
$95$	2.86047	−	6.42472i	0.293478	−	0.659162i
$96$	6.10749	−	7.97931i	0.623343	−	0.814384i
$97$	3.44346	−	1.11885i	0.349631	−	0.113602i	−0.128936	−	0.991653i	$-0.541156\pi$
$97$	3.44346	−	1.11885i	0.349631	−	0.113602i	0.478567	+	0.878051i	$0.341156\pi$
$98$	−5.26762	−	2.26453i	−0.532110	−	0.228752i
$99$	−0.841144	+	9.91426i	−0.0845381	+	0.996420i
$100$	2.37134	−	4.10729i	0.237134	−	0.410729i
$101$	6.29353	−	6.98967i	0.626229	−	0.695498i	−0.343646	−	0.939099i	$-0.611662\pi$
$101$	6.29353	−	6.98967i	0.626229	−	0.695498i	0.969876	+	0.243601i	$0.0783288\pi$
$102$	2.08604	+	5.01905i	0.206548	+	0.496960i
$103$	−15.7806	+	1.65861i	−1.55491	+	0.163428i	−0.842639	−	0.538479i	$-0.818999\pi$
$103$	−15.7806	+	1.65861i	−1.55491	+	0.163428i	−0.712270	+	0.701906i	$0.752333\pi$
$104$	−0.943793	+	2.90470i	−0.0925465	+	0.284829i
$105$	−5.32152	+	1.32065i	−0.519327	+	0.128882i
$106$	5.17919	−	3.76290i	0.503047	−	0.365485i
$107$	−6.27581	−	14.0957i	−0.606706	−	1.36268i	−0.911908	−	0.410395i	$-0.865391\pi$
$107$	−6.27581	−	14.0957i	−0.606706	−	1.36268i	0.305202	−	0.952288i	$-0.401276\pi$
$108$	4.99225	−	4.77184i	0.480379	−	0.459170i
$109$	4.38809	+	7.60040i	0.420303	+	0.727986i	0.995969	−	0.0896990i	$-0.0285905\pi$
$109$	4.38809	+	7.60040i	0.420303	+	0.727986i	−0.575666	+	0.817685i	$0.695257\pi$
$110$	−1.11104	+	3.05465i	−0.105934	+	0.291250i
$111$	0.603023	+	1.10745i	0.0572364	+	0.105115i
$112$	−1.11049	−	0.168567i	−0.104931	−	0.0159281i
$113$	9.75175	−	13.4221i	0.917368	−	1.26265i	−0.0472193	−	0.998885i	$-0.515036\pi$
$113$	9.75175	−	13.4221i	0.917368	−	1.26265i	0.964587	−	0.263764i	$-0.0849640\pi$
$114$	−6.86681	+	4.73161i	−0.643136	+	0.443156i
$115$	−0.723317	−	3.40294i	−0.0674497	−	0.317326i
$116$	−0.177176	−	0.833547i	−0.0164504	−	0.0773929i
$117$	−1.51824	+	2.99754i	−0.140362	+	0.277122i
$118$	−0.135774	+	0.186877i	−0.0124990	+	0.0172034i
$119$	6.32803	−	7.91809i	0.580090	−	0.725850i
$120$	4.96297	−	2.70241i	0.453056	−	0.246695i
$121$	1.90535	−	10.8337i	0.173214	−	0.984884i
$122$	3.39667	+	5.88320i	0.307520	+	0.532640i
$123$	17.0736	+	4.07728i	1.53947	+	0.367636i
$124$	−0.567352	−	1.27429i	−0.0509497	−	0.114435i
$125$	8.29399	−	6.02594i	0.741837	−	0.538976i
$126$	6.20078	+	1.95432i	0.552409	+	0.174105i
$127$	−3.95468	+	12.1713i	−0.350921	+	1.08002i	0.607415	+	0.794384i	$0.292206\pi$
$127$	−3.95468	+	12.1713i	−0.350921	+	1.08002i	−0.958337	+	0.285641i	$0.907794\pi$
$128$	8.35993	−	0.878664i	0.738920	−	0.0776637i
$129$	3.99344	−	1.65977i	0.351603	−	0.146135i
$130$	−0.734492	+	0.815736i	−0.0644192	+	0.0715448i
$131$	−0.811633	+	1.40579i	−0.0709127	+	0.122824i	−0.899302	−	0.437329i	$-0.855925\pi$
$131$	−0.811633	+	1.40579i	−0.0709127	+	0.122824i	0.828389	+	0.560153i	$0.189258\pi$
$132$	−5.96835	+	4.76133i	−0.519478	+	0.414421i
$133$	13.9015	+	6.97088i	1.20541	+	0.604452i
$134$	8.35951	−	2.71617i	0.722151	−	0.234641i
$135$	5.85294	−	2.09645i	0.503741	−	0.180433i
$136$	−4.24910	+	9.54364i	−0.364358	+	0.818361i
$137$	0.0936429	+	0.440555i	0.00800045	+	0.0376392i	0.981967	−	0.189054i	$-0.0605420\pi$
$137$	0.0936429	+	0.440555i	0.00800045	+	0.0376392i	−0.973966	+	0.226693i	$0.927209\pi$
$138$	−1.37235	+	3.89026i	−0.116822	+	0.331161i
$139$	−7.61385	−	10.4796i	−0.645798	−	0.888865i	0.353110	−	0.935582i	$-0.385124\pi$
$139$	−7.61385	−	10.4796i	−0.645798	−	0.888865i	−0.998908	+	0.0467168i	$0.985124\pi$
$140$	−3.54317	−	2.26868i	−0.299452	−	0.191739i
$141$	−13.3375	+	14.0887i	−1.12322	+	1.18648i
$142$	4.33664	−	7.51127i	0.363922	−	0.630332i
$143$	1.96781	−	3.15071i	0.164557	−	0.263475i
$144$	1.27201	+	0.0635936i	0.106001	+	0.00529947i
$145$	0.159501	−	0.750393i	0.0132458	−	0.0623168i
$146$	−0.841492	−	0.611380i	−0.0696424	−	0.0505981i
$147$	−2.37701	−	11.8891i	−0.196053	−	0.980593i
$148$	−0.299004	+	0.920240i	−0.0245780	+	0.0756433i
$149$	11.1639	−	10.0520i	0.914579	−	0.823491i	−0.0701584	−	0.997536i	$-0.522350\pi$
$149$	11.1639	−	10.0520i	0.914579	−	0.823491i	0.984738	+	0.174045i	$0.0556838\pi$
$150$	−5.04659	+	0.403287i	−0.412053	+	0.0329282i
$151$	1.26315	−	12.0181i	0.102794	−	0.978019i	−0.814596	−	0.580029i	$-0.803041\pi$
$151$	1.26315	−	12.0181i	0.102794	−	0.978019i	0.917390	−	0.397990i	$-0.130292\pi$
$152$	−15.6779	−	3.33243i	−1.27164	−	0.270296i
$153$	−6.23645	+	9.65408i	−0.504187	+	0.780486i
$154$	−6.63480	−	2.76435i	−0.534647	−	0.222757i
$155$		−	1.25573i		−	0.100863i
$156$	−2.47126	+	0.735258i	−0.197859	+	0.0588677i
$157$	−18.2284	−	1.91588i	−1.45478	−	0.152904i	−0.656108	−	0.754667i	$-0.727798\pi$
$157$	−18.2284	−	1.91588i	−1.45478	−	0.152904i	−0.798674	+	0.601764i	$0.794465\pi$
$158$	4.14337	−	9.30616i	0.329629	−	0.740358i
$159$	12.7660	+	4.50340i	1.01241	+	0.357142i
$160$	6.60158	+	2.14498i	0.521901	+	0.169576i
$161$	7.59037	−	1.25231i	0.598205	−	0.0986958i
$162$	−7.21817	−	1.49799i	−0.567113	−	0.117693i
$163$	−16.0958	−	3.42127i	−1.26072	−	0.267974i	−0.471380	−	0.881930i	$-0.656244\pi$
$163$	−16.0958	−	3.42127i	−1.26072	−	0.267974i	−0.789340	+	0.613956i	$0.789577\pi$
$164$	6.73477	+	11.6650i	0.525897	+	0.910881i
$165$	−6.65185	+	1.73039i	−0.517846	+	0.134711i
$166$	5.00688	+	2.89073i	0.388610	+	0.224364i
$167$	1.30251	+	4.00870i	0.100791	+	0.310203i	0.988720	−	0.149779i	$-0.0478561\pi$
$167$	1.30251	+	4.00870i	0.100791	+	0.310203i	−0.887929	+	0.459981i	$0.847856\pi$
$168$	5.46567	+	11.2373i	0.421686	+	0.866979i
$169$	−9.50233	+	6.90385i	−0.730948	+	0.531065i
$170$	−2.79023	+	2.51233i	−0.214001	+	0.192687i
$171$	−16.4775	−	6.27968i	−1.26007	−	0.480219i
$172$	3.03154	+	1.34973i	0.231153	+	0.102916i
$173$	5.31961	−	2.36844i	0.404442	−	0.180069i	−0.194425	−	0.980917i	$-0.562284\pi$
$173$	5.31961	−	2.36844i	0.404442	−	0.180069i	0.598868	+	0.800848i	$0.295618\pi$
$174$	−0.625378	+	0.660602i	−0.0474098	+	0.0500801i
$175$	5.19289	+	7.88482i	0.392546	+	0.596037i
$176$	−1.39436	−	0.195651i	−0.105104	−	0.0147477i
$177$	−0.488295	−	0.0121984i	−0.0367025	−	0.000916891i
$178$	4.05702	+	3.65296i	0.304087	+	0.273801i
$179$	−10.4485	−	1.09818i	−0.780956	−	0.0820818i	−0.294343	−	0.955700i	$-0.595101\pi$
$179$	−10.4485	−	1.09818i	−0.780956	−	0.0820818i	−0.486612	+	0.873618i	$0.661768\pi$
$180$	4.25582	+	2.15556i	0.317210	+	0.160666i
$181$	19.5750	+	6.36029i	1.45499	+	0.472756i	0.926537	−	0.376203i	$-0.122771\pi$
$181$	19.5750	+	6.36029i	1.45499	+	0.472756i	0.528458	+	0.848960i	$0.322771\pi$
$182$	−1.72736	−	1.70527i	−0.128040	−	0.126403i
$183$	−6.16864	+	12.9730i	−0.455999	+	0.958990i
$184$	−7.24334	+	3.22494i	−0.533986	+	0.237746i
$185$	−0.582860	+	0.647332i	−0.0428527	+	0.0475928i
$186$	−0.776473	+	1.27052i	−0.0569337	+	0.0931589i
$187$	7.82054	−	10.0144i	0.571895	−	0.732324i
$188$	−14.8867			−1.08572
$189$	4.03677	+	13.1417i	0.293632	+	0.955919i
$190$	−4.66039	−	3.38597i	−0.338100	−	0.245644i
$191$	−8.09046	+	0.850342i	−0.585405	+	0.0615286i	−0.392601	−	0.919709i	$-0.628425\pi$
$191$	−8.09046	+	0.850342i	−0.585405	+	0.0615286i	−0.192804	+	0.981237i	$0.561758\pi$
$192$	−4.39653	−	5.13514i	−0.317292	−	0.370597i
$193$	0.134618	−	0.0286140i	0.00969004	−	0.00205968i	−0.203064	−	0.979165i	$-0.565090\pi$
$193$	0.134618	−	0.0286140i	0.00969004	−	0.00205968i	0.212754	+	0.977106i	$0.431757\pi$
$194$	−0.310002	−	2.94947i	−0.0222569	−	0.211760i
$195$	−2.30162	−	0.300196i	−0.164822	−	0.0214975i
$196$	5.37112	−	7.59638i	0.383652	−	0.542599i
$197$			5.31567i			0.378726i	0.981907	+	0.189363i	$0.0606423\pi$
$197$			5.31567i			0.378726i	−0.981907	+	0.189363i	$0.939358\pi$
$198$	7.80013	+	2.36235i	0.554331	+	0.167885i
$199$	19.3488	−	11.1710i	1.37160	−	0.791893i	0.380469	−	0.924794i	$-0.375763\pi$
$199$	19.3488	−	11.1710i	1.37160	−	0.791893i	0.991129	+	0.132901i	$0.0424292\pi$
$200$	−7.23128	−	6.51108i	−0.511329	−	0.460403i
$201$	14.7591	+	11.2969i	1.04103	+	0.796821i
$202$	−4.52838	−	6.23278i	−0.318616	−	0.438537i
$203$	1.64139	+	0.428510i	0.115203	+	0.0300755i
$204$	−8.66954	+	1.61760i	−0.606989	+	0.113255i
$205$	1.26749	+	12.0594i	0.0885257	+	0.842266i
$206$	−1.35858	+	12.9260i	−0.0946567	+	0.900598i
$207$	−8.42033	+	2.27796i	−0.585254	+	0.158329i
$208$	−0.411787	−	0.237746i	−0.0285523	−	0.0164847i
$209$	17.5236	+	8.54204i	1.21213	+	0.590865i
$210$	0.151849	+	4.48855i	0.0104786	+	0.309740i
$211$	−2.30701	−	7.10026i	−0.158821	−	0.488802i	0.839707	−	0.543040i	$-0.182727\pi$
$211$	−2.30701	−	7.10026i	−0.158821	−	0.488802i	−0.998528	+	0.0542384i	$0.982727\pi$
$212$	4.22495	+	9.48939i	0.290171	+	0.651734i
$213$	18.2819	−	1.46095i	1.25265	−	0.100103i
$214$	−12.3624	+	2.62770i	−0.845075	+	0.179626i
$215$	1.99896	+	2.22007i	0.136328	+	0.151407i
$216$	−7.44695	−	12.0544i	−0.506701	−	0.820199i
$217$	2.77386	+	0.127482i	0.188302	+	0.00865401i
$218$	6.83680	−	2.22141i	0.463047	−	0.150453i
$219$	0.0549286	−	2.19875i	0.00371173	−	0.148578i
$220$	−4.47328	−	2.79385i	−0.301589	−	0.188361i
$221$	3.71606	−	2.14547i	0.249969	−	0.144320i
$222$	0.989994	−	0.294546i	0.0664441	−	0.0197686i
$223$	−7.91065	+	10.8881i	−0.529736	+	0.729119i	−0.987090	−	0.160165i	$-0.948797\pi$
$223$	−7.91065	+	10.8881i	−0.529736	+	0.729119i	0.457354	+	0.889285i	$0.348797\pi$
$224$	−5.40836	+	14.3648i	−0.361361	+	0.959790i
$225$	−6.75709	−	8.30337i	−0.450473	−	0.553558i
$226$	−9.09318	−	10.0990i	−0.604870	−	0.671776i
$227$	−23.2803	−	10.3651i	−1.54517	−	0.687954i	−0.555526	−	0.831499i	$-0.687483\pi$
$227$	−23.2803	−	10.3651i	−1.54517	−	0.687954i	−0.989644	+	0.143545i	$0.954150\pi$
$228$	−5.19308	−	12.4947i	−0.343920	−	0.827479i
$229$	−3.56106	+	16.7535i	−0.235321	+	1.10710i	0.688785	+	0.724965i	$0.258144\pi$
$229$	−3.56106	+	16.7535i	−0.235321	+	1.10710i	−0.924107	+	0.382134i	$0.875189\pi$
$230$	−2.84965			−0.187900
$231$	−3.14707	−	14.8693i	−0.207062	−	0.978328i
$232$	−1.74841			−0.114789
$233$	−5.92813	+	27.8897i	−0.388365	+	1.82711i	0.155372	+	0.987856i	$0.450342\pi$
$233$	−5.92813	+	27.8897i	−0.388365	+	1.82711i	−0.543737	+	0.839256i	$0.682991\pi$
$234$	2.14309	+	1.72692i	0.140098	+	0.112892i
$235$	−12.2430	−	5.45092i	−0.798643	−	0.355579i
$236$	−0.250792	−	0.278532i	−0.0163252	−	0.0181309i
$237$	21.1753	−	3.95097i	1.37548	−	0.256643i
$238$	−5.26636	−	6.41854i	−0.341368	−	0.416052i
$239$	2.63657	−	3.62892i	0.170545	−	0.234735i	−0.715186	−	0.698935i	$-0.753658\pi$
$239$	2.63657	−	3.62892i	0.170545	−	0.234735i	0.885731	+	0.464199i	$0.153658\pi$
$240$	0.250887	+	0.843253i	0.0161947	+	0.0544317i
$241$	−10.4114	+	6.01100i	−0.670654	+	0.387202i	−0.796324	−	0.604870i	$-0.793225\pi$
$241$	−10.4114	+	6.01100i	−0.670654	+	0.387202i	0.125670	+	0.992072i	$0.459892\pi$
$242$	−8.35558	−	3.37159i	−0.537117	−	0.216734i
$243$	−6.05199	−	14.3657i	−0.388236	−	0.921560i
$244$	−10.4832	+	3.40620i	−0.671118	+	0.218059i
$245$	7.19877	−	4.28065i	0.459912	−	0.273481i
$246$	6.17442	−	12.9851i	0.393666	−	0.827902i
$247$	4.40516	+	4.89243i	0.280294	+	0.311298i
$248$	−2.79937	+	0.595025i	−0.177760	+	0.0377841i
$249$	0.973845	+	12.1864i	0.0617149	+	0.772280i
$250$	−3.41555	−	7.67145i	−0.216018	−	0.485185i
$251$	2.53854	+	7.81283i	0.160231	+	0.493141i	0.998653	−	0.0518804i	$-0.0165214\pi$
$251$	2.53854	+	7.81283i	0.160231	+	0.493141i	−0.838422	+	0.545022i	$0.816521\pi$
$252$	−5.19358	+	9.18207i	−0.327165	+	0.578416i
$253$	9.49679	−	1.67670i	0.597058	−	0.105413i
$254$	9.07823	+	5.24132i	0.569619	+	0.328869i
$255$	−7.72223	−	1.84412i	−0.483585	−	0.115483i
$256$	1.53566	−	14.6108i	0.0959788	−	0.913177i
$257$	−3.00081	−	28.5508i	−0.187185	−	1.78095i	−0.536456	−	0.843928i	$-0.680237\pi$
$257$	−3.00081	−	28.5508i	−0.187185	−	1.78095i	0.349271	−	0.937022i	$-0.386429\pi$
$258$	−0.649731	−	3.48224i	−0.0404505	−	0.216795i
$259$	−1.37075	−	1.35323i	−0.0851745	−	0.0840855i
$260$	−1.04689	−	1.44092i	−0.0649251	−	0.0893618i
$261$	−1.90058	−	0.296335i	−0.117643	−	0.0183427i
$262$	0.988107	+	0.889696i	0.0610455	+	0.0549656i
$263$	−22.9847	+	13.2702i	−1.41730	+	0.818278i	−0.996061	−	0.0886725i	$-0.971738\pi$
$263$	−22.9847	+	13.2702i	−1.41730	+	0.818278i	−0.421238	+	0.906950i	$0.638404\pi$
$264$	7.00947	+	14.0088i	0.431403	+	0.862185i
$265$			9.35119i			0.574439i
$266$	7.95258	−	9.95085i	0.487604	−	0.610126i
$267$	−1.49301	+	11.4470i	−0.0913708	+	0.700543i
$268$	1.49078	+	14.1838i	0.0910638	+	0.866414i
$269$	18.5708	−	3.94734i	1.13228	−	0.240673i	0.396592	−	0.917995i	$-0.370193\pi$
$269$	18.5708	−	3.94734i	1.13228	−	0.240673i	0.735687	+	0.677322i	$0.236859\pi$
$270$	−0.682922	−	5.04645i	−0.0415613	−	0.307117i
$271$	14.4908	−	1.52304i	0.880251	−	0.0925181i	0.346390	−	0.938090i	$-0.387407\pi$
$271$	14.4908	−	1.52304i	0.880251	−	0.0925181i	0.533861	+	0.845572i	$0.320741\pi$
$272$	−1.31580	−	0.955985i	−0.0797821	−	0.0579651i
$273$	0.896779	−	5.05369i	0.0542755	−	0.305863i
$274$	0.368924			0.0222875
$275$	6.62032	+	9.81036i	0.399220	+	0.591587i
$276$	−5.71133	−	3.49046i	−0.343782	−	0.210101i
$277$	7.01373	−	7.78954i	0.421414	−	0.468028i	−0.494631	−	0.869103i	$-0.664697\pi$
$277$	7.01373	−	7.78954i	0.421414	−	0.468028i	0.916045	+	0.401075i	$0.131363\pi$
$278$	−9.69297	+	4.31559i	−0.581346	+	0.258832i
$279$	−3.14386	+	0.172351i	−0.188218	+	0.0103184i
$280$	−6.06441	+	6.14296i	−0.362418	+	0.367112i
$281$	7.38706	+	2.40020i	0.440675	+	0.143184i	0.520947	−	0.853589i	$-0.325579\pi$
$281$	7.38706	+	2.40020i	0.440675	+	0.143184i	−0.0802719	+	0.996773i	$0.525579\pi$
$282$	9.01658	+	13.0854i	0.536929	+	0.779226i
$283$	10.2263	+	1.07482i	0.607888	+	0.0638916i	0.403471	−	0.914992i	$-0.367804\pi$
$283$	10.2263	+	1.07482i	0.607888	+	0.0638916i	0.204417	+	0.978884i	$0.434470\pi$
$284$	10.4583	+	9.41669i	0.620586	+	0.558778i
$285$	0.304208	−	12.1772i	0.0180197	−	0.721318i
$286$	−2.18925	−	2.11320i	−0.129453	−	0.124956i
$287$	−26.7674	+	1.57557i	−1.58003	+	0.0930031i
$288$	4.46411	−	16.8221i	0.263050	−	0.991254i
$289$	−2.12202	+	0.944782i	−0.124824	+	0.0555754i
$290$	−0.574058	−	0.255587i	−0.0337098	−	0.0150086i
$291$	4.76375	−	4.07855i	0.279256	−	0.239089i
$292$	1.25421	−	1.12930i	0.0733971	−	0.0660870i
$293$	15.9468	−	11.5860i	0.931623	−	0.676864i	−0.0147669	−	0.999891i	$-0.504701\pi$
$293$	15.9468	−	11.5860i	0.931623	−	0.676864i	0.946390	+	0.323027i	$0.104701\pi$
$294$	−9.93042	−	0.120249i	−0.579154	−	0.00701306i
$295$	−0.104266	−	0.320898i	−0.00607061	−	0.0186834i
$296$	1.71927	+	0.992618i	0.0999303	+	0.0576948i
$297$	5.24519	+	16.4161i	0.304357	+	0.952558i
$298$	−6.15251	−	10.6565i	−0.356405	−	0.617312i
$299$	3.18553	+	0.677105i	0.184224	+	0.0391580i
$300$	1.06242	−	8.14558i	0.0613386	−	0.470285i
$301$	−5.10696	+	4.19022i	−0.294360	+	0.241520i
$302$	−9.41388	−	3.05876i	−0.541708	−	0.176012i
$303$	5.41951	−	15.3630i	0.311343	−	0.882579i
$304$	1.01495	−	2.27961i	0.0582113	−	0.130745i
$305$	−9.86871	−	1.03724i	−0.565081	−	0.0593924i
$306$	6.67285	+	6.64080i	0.381461	+	0.379629i
$307$		−	0.539962i		−	0.0308173i	−0.999881	−	0.0154086i	$-0.995095\pi$
$307$		−	0.539962i		−	0.0308173i	0.999881	−	0.0154086i	$-0.00490491\pi$
$308$	6.62560	−	9.59764i	0.377529	−	0.546877i
$309$	−24.1370	+	13.1430i	−1.37311	+	0.747678i
$310$	−1.00610	−	0.213854i	−0.0571429	−	0.0121461i
$311$	−0.179676	+	1.70950i	−0.0101885	+	0.0969370i	−0.998434	−	0.0559357i	$-0.982186\pi$
$311$	−0.179676	+	1.70950i	−0.0101885	+	0.0969370i	0.988246	+	0.152873i	$0.0488525\pi$
$312$	0.421394	+	5.27318i	0.0238567	+	0.298535i
$313$	−1.39379	+	1.25498i	−0.0787818	+	0.0709354i	−0.707581	−	0.706632i	$-0.750213\pi$
$313$	−1.39379	+	1.25498i	−0.0787818	+	0.0709354i	0.628799	+	0.777568i	$0.283547\pi$
$314$	−4.63935	+	14.2784i	−0.261813	+	0.805779i
$315$	−7.63337	+	5.64975i	−0.430092	+	0.318327i
$316$	13.3722	+	9.71546i	0.752244	+	0.546537i
$317$	−1.72641	+	8.12212i	−0.0969649	+	0.456184i	0.902699	+	0.430272i	$0.141582\pi$
$317$	−1.72641	+	8.12212i	−0.0969649	+	0.456184i	−0.999664	+	0.0259120i	$0.991751\pi$
$318$	5.78223	−	9.46129i	0.324252	−	0.530563i
$319$	2.06350	+	0.514006i	0.115534	+	0.0287788i
$320$	2.33490	−	4.04416i	0.130525	−	0.226075i
$321$	−19.4077	−	18.3729i	−1.08323	−	1.02548i
$322$	0.289295	−	6.29474i	0.0161218	−	0.350792i
$323$	13.2361	+	18.2179i	0.736475	+	1.01367i
$324$	4.81255	−	10.9507i	0.267364	−	0.608374i
$325$	0.830977	+	3.90944i	0.0460943	+	0.216857i
$326$	−5.48230	+	12.3134i	−0.303636	+	0.681978i
$327$	12.0707	+	9.23914i	0.667513	+	0.510925i
$328$	26.2831	−	8.53990i	1.45124	−	0.471537i
$329$	13.2837	−	26.4908i	0.732356	−	1.46048i
$330$	0.253582	+	5.62420i	0.0139592	+	0.309602i
$331$	6.75877	−	11.7065i	0.371495	−	0.643449i	−0.618300	−	0.785942i	$-0.712178\pi$
$331$	6.75877	−	11.7065i	0.371495	−	0.643449i	0.989796	+	0.142493i	$0.0455118\pi$
$332$	−6.27700	+	6.97132i	−0.344495	+	0.382601i
$333$	1.70066	+	1.37040i	0.0931956	+	0.0750976i
$334$	3.43363	−	0.360889i	0.187880	−	0.0197469i
$335$	−3.96753	+	12.2108i	−0.216769	+	0.667147i
$336$	−1.88818	+	0.468591i	−0.103008	+	0.0255638i
$337$	29.1983	−	21.2138i	1.59053	−	1.15559i	0.687356	−	0.726320i	$-0.258771\pi$
$337$	29.1983	−	21.2138i	1.59053	−	1.15559i	0.903177	−	0.429269i	$-0.141229\pi$
$338$	3.91315	+	8.78908i	0.212847	+	0.478063i
$339$	6.67463	−	27.9500i	0.362516	−	1.51803i
$340$	−3.04608	−	5.27596i	−0.165197	−	0.286129i
$341$	3.47879	+	0.120714i	0.188387	+	0.00653704i
$342$	−7.83749	+	12.1325i	−0.423803	+	0.656051i
$343$	8.72495	+	16.3363i	0.471103	+	0.882078i
$344$	4.00193	−	5.50819i	0.215770	−	0.296982i
$345$	−3.41899	−	4.96186i	−0.184072	−	0.267138i
$346$	−0.991675	−	4.66546i	−0.0533128	−	0.250817i
$347$	−3.81076	−	17.9282i	−0.204573	−	0.962438i	−0.953874	−	0.300209i	$-0.902944\pi$
$347$	−3.81076	−	17.9282i	−0.204573	−	0.962438i	0.749301	−	0.662229i	$-0.230390\pi$
$348$	−0.837479	−	1.21540i	−0.0448936	−	0.0651525i
$349$	−4.18762	+	5.76376i	−0.224158	+	0.308527i	−0.906252	−	0.422737i	$-0.861069\pi$
$349$	−4.18762	+	5.76376i	−0.224158	+	0.308527i	0.682094	+	0.731264i	$0.261069\pi$
$350$	7.20174	−	2.81779i	0.384949	−	0.150617i
$351$	−0.435672	+	5.80354i	−0.0232545	+	0.309770i
$352$	−6.57691	+	18.0823i	−0.350551	+	0.963791i
$353$	−7.13902	−	12.3652i	−0.379972	−	0.658131i	0.611086	−	0.791564i	$-0.290733\pi$
$353$	−7.13902	−	12.3652i	−0.379972	−	0.658131i	−0.991058	+	0.133434i	$0.957400\pi$
$354$	−0.0929311	+	0.389148i	−0.00493923	+	0.0206830i
$355$	5.15299	+	11.5738i	0.273492	+	0.614274i
$356$	−7.16632	+	5.20663i	−0.379814	+	0.275951i
$357$	4.85753	−	16.8708i	0.257088	−	0.892899i
$358$	−2.65927	+	8.18438i	−0.140547	+	0.432558i
$359$	−15.8125	+	1.66196i	−0.834552	+	0.0877150i	−0.512159	−	0.858891i	$-0.671154\pi$
$359$	−15.8125	+	1.66196i	−0.834552	+	0.0877150i	−0.322393	+	0.946606i	$0.604487\pi$
$360$	6.14138	−	7.62141i	0.323679	−	0.401684i
$361$	−10.4045	+	11.5554i	−0.547606	+	0.608178i
$362$	8.42957	−	14.6004i	0.443048	−	0.767382i
$363$	−4.15431	−	18.5941i	−0.218045	−	0.975939i
$364$	3.28920	−	2.16624i	0.172401	−	0.113542i
$365$	1.44498	−	0.469502i	0.0756337	−	0.0245749i
$366$	9.34352	+	7.15169i	0.488394	+	0.373825i
$367$	7.16330	−	16.0890i	0.373921	−	0.839841i	−0.624354	−	0.781141i	$-0.714638\pi$
$367$	7.16330	−	16.0890i	0.373921	−	0.839841i	0.998276	−	0.0586999i	$-0.0186955\pi$
$368$	−0.256647	−	1.20743i	−0.0133786	−	0.0629415i
$369$	30.0180	−	4.82847i	1.56267	−	0.251360i
$370$	0.419385	+	0.577234i	0.0218028	+	0.0300090i
$371$	−20.6564	−	0.949329i	−1.07242	−	0.0492867i
$372$	−1.75452	−	1.66096i	−0.0909674	−	0.0861170i
$373$	−1.81869	+	3.15006i	−0.0941680	+	0.163104i	−0.909261	−	0.416226i	$-0.863352\pi$
$373$	−1.81869	+	3.15006i	−0.0941680	+	0.163104i	0.815093	+	0.579330i	$0.196686\pi$
$374$	−6.69175	−	7.97135i	−0.346022	−	0.412189i
$375$	9.25972	−	15.1514i	0.478170	−	0.782414i
$376$	−6.35030	+	29.8758i	−0.327492	+	1.54073i
$377$	0.580991	+	0.422115i	0.0299226	+	0.0217400i
$378$	11.2167	−	0.996230i	0.576926	−	0.0512405i
$379$	−4.18682	+	12.8857i	−0.215062	+	0.661894i	0.784087	+	0.620651i	$0.213132\pi$
$379$	−4.18682	+	12.8857i	−0.215062	+	0.661894i	−0.999149	+	0.0412425i	$0.986868\pi$
$380$	6.94613	−	6.25432i	0.356329	−	0.320840i
$381$	1.76573	+	22.0957i	0.0904609	+	1.13200i
$382$	−0.696521	+	6.62696i	−0.0356371	+	0.339065i
$383$	10.7908	+	2.29366i	0.551386	+	0.117201i	0.475176	−	0.879891i	$-0.342385\pi$
$383$	10.7908	+	2.29366i	0.551386	+	0.117201i	0.0762107	+	0.997092i	$0.475718\pi$
$384$	12.7868	−	6.96263i	0.652526	−	0.355310i
$385$	8.96325	−	5.46717i	0.456810	−	0.278633i
$386$		−	0.112730i		−	0.00573782i
$387$	5.28380	−	5.30930i	0.268591	−	0.269887i
$388$	4.78574	+	0.503002i	0.242959	+	0.0255360i
$389$	−12.7766	+	28.6968i	−0.647801	+	1.45498i	0.228658	+	0.973507i	$0.426566\pi$
$389$	−12.7766	+	28.6968i	−0.647801	+	1.45498i	−0.876459	+	0.481477i	$0.840100\pi$
$390$	−0.632490	+	1.79295i	−0.0320274	+	0.0907896i
$391$	10.5943	+	3.44230i	0.535778	+	0.174085i
$392$	−12.9539	−	14.0196i	−0.654268	−	0.708099i
$393$	−0.363630	+	2.78796i	−0.0183427	+	0.140634i
$394$	4.25896	+	0.905270i	0.214563	+	0.0456068i
$395$	7.44001	+	12.8865i	0.374347	+	0.648389i
$396$	−6.38072	+	11.5828i	−0.320643	+	0.582057i
$397$	−2.08725	−	1.20507i	−0.104756	−	0.0604809i	0.446707	−	0.894680i	$-0.352597\pi$
$397$	−2.08725	−	1.20507i	−0.104756	−	0.0604809i	−0.551463	+	0.834200i	$0.685930\pi$
$398$	−5.65518	−	17.4048i	−0.283468	−	0.872426i
$399$	26.8681	+	1.90821i	1.34509	+	0.0955300i
$400$	1.22560	−	0.890448i	0.0612799	−	0.0445224i
$401$	−5.26911	+	4.74432i	−0.263127	+	0.236920i	−0.790125	−	0.612946i	$-0.789984\pi$
$401$	−5.26911	+	4.74432i	−0.263127	+	0.236920i	0.526998	+	0.849867i	$0.323318\pi$
$402$	11.5647	−	9.90126i	0.576794	−	0.493830i
$403$	1.07388	+	0.478121i	0.0534937	+	0.0238169i
$404$	11.4198	−	5.08443i	0.568157	−	0.252960i
$405$	7.96762	−	7.24383i	0.395914	−	0.359949i
$406$	0.622858	−	1.24212i	0.0309119	−	0.0616454i
$407$	−1.73729	−	1.67694i	−0.0861142	−	0.0831229i
$408$	−0.451888	+	18.0888i	−0.0223718	+	0.895528i
$409$	15.1128	+	13.6076i	0.747280	+	0.672854i	0.952045	−	0.305957i	$-0.0989765\pi$
$409$	15.1128	+	13.6076i	0.747280	+	0.672854i	−0.204765	+	0.978811i	$0.565643\pi$
$410$	9.87795	+	1.03821i	0.487837	+	0.0512738i
$411$	0.442633	+	0.642378i	0.0218335	+	0.0316862i
$412$	−20.0568	−	6.51684i	−0.988126	−	0.321062i
$413$	0.719435	−	0.197742i	0.0354011	−	0.00973023i
$414$	0.391118	+	7.13438i	0.0192224	+	0.350636i
$415$	−7.71490	+	3.43489i	−0.378709	+	0.168612i
$416$	−4.34790	+	4.82883i	−0.213173	+	0.236753i
$417$	−19.1440	−	11.6998i	−0.937484	−	0.572940i
$418$	9.82825	−	12.5853i	0.480716	−	0.615568i
$419$	21.6403			1.05720			0.528599	−	0.848871i	$-0.322717\pi$
$419$	21.6403			1.05720			0.528599	+	0.848871i	$0.322717\pi$
$420$	−7.17508	−	1.27322i	−0.350108	−	0.0621268i
$421$	−27.9888	−	20.3351i	−1.36409	−	0.991071i	−0.998173	−	0.0604251i	$-0.980754\pi$
$421$	−27.9888	−	20.3351i	−1.36409	−	0.991071i	−0.365920	−	0.930646i	$-0.619246\pi$
$422$	−6.08167	+	0.639210i	−0.296051	+	0.0311162i
$423$	−11.9666	+	31.3997i	−0.581835	+	1.52671i
$424$	20.8464	−	4.43103i	1.01239	−	0.215190i
$425$	1.42901	+	13.5961i	0.0693171	+	0.659508i
$426$	1.94291	−	14.8964i	0.0941343	−	0.721732i
$427$	3.29309	−	21.6942i	0.159364	−	1.04986i
$428$		−	20.5070i		−	0.991243i
$429$	1.05290	−	6.34737i	0.0508343	−	0.306454i
$430$	2.11916	−	1.22350i	0.102195	−	0.0590023i
$431$	−7.28352	−	6.55811i	−0.350835	−	0.315893i	0.474805	−	0.880091i	$-0.342519\pi$
$431$	−7.28352	−	6.55811i	−0.350835	−	0.315893i	−0.825639	+	0.564198i	$0.809185\pi$
$432$	2.07674	−	0.743859i	0.0999170	−	0.0357889i
$433$	−7.36319	−	10.1346i	−0.353852	−	0.487036i	0.594571	−	0.804043i	$-0.297322\pi$
$433$	−7.36319	−	10.1346i	−0.353852	−	0.487036i	−0.948423	+	0.317007i	$0.897322\pi$
$434$	0.574533	−	2.20073i	0.0275785	−	0.105638i
$435$	−0.243719	−	1.30621i	−0.0116854	−	0.0626281i
$436$	1.21923	+	11.6002i	0.0583905	+	0.555549i
$437$	−1.78649	+	16.9973i	−0.0854593	+	0.813091i
$438$	−1.75230	−	0.418461i	−0.0837283	−	0.0199949i
$439$	−0.0945822	−	0.0546070i	−0.00451416	−	0.00260625i	0.497741	−	0.867326i	$-0.334163\pi$
$439$	−0.0945822	−	0.0546070i	−0.00451416	−	0.00260625i	−0.502255	+	0.864719i	$0.667496\pi$
$440$	−7.51511	+	7.78556i	−0.358269	+	0.371162i
$441$	−11.7051	−	17.4353i	−0.557386	−	0.830254i
$442$	−1.08611	−	3.34272i	−0.0516612	−	0.158997i
$443$	7.89343	+	17.7289i	0.375028	+	0.842328i	0.998185	+	0.0602301i	$0.0191834\pi$
$443$	7.89343	+	17.7289i	0.375028	+	0.842328i	−0.623156	+	0.782097i	$0.714150\pi$
$444$	0.133502	+	1.67060i	0.00633574	+	0.0792833i
$445$	−7.80012	+	1.65797i	−0.369761	+	0.0785952i
$446$	7.37641	+	8.19234i	0.349283	+	0.387918i
$447$	11.1735	−	23.4984i	0.528488	−	1.11144i
$448$	8.69633	+	5.56824i	0.410863	+	0.263075i
$449$	−31.0262	+	10.0810i	−1.46422	+	0.475753i	−0.929355	−	0.369186i	$-0.879636\pi$
$449$	−31.0262	+	10.0810i	−1.46422	+	0.475753i	−0.534862	+	0.844939i	$0.679636\pi$
$450$	−7.80347	+	3.99975i	−0.367859	+	0.188550i
$451$	−33.5303	+	2.35210i	−1.57888	+	0.110756i
$452$	19.0959	−	11.0250i	0.898196	−	0.518573i
$453$	−5.96876	−	20.0615i	−0.280437	−	0.942572i
$454$	−12.2693	+	16.8872i	−0.575825	+	0.792556i
$455$	3.49826	−	0.577167i	0.164001	−	0.0270580i
$456$	−27.2905	+	5.09198i	−1.27800	+	0.238454i
$457$	−12.6039	−	13.9981i	−0.589587	−	0.654803i	0.372344	−	0.928095i	$-0.378554\pi$
$457$	−12.6039	−	13.9981i	−0.589587	−	0.654803i	−0.961931	+	0.273292i	$0.911887\pi$
$458$	12.8166	+	5.70630i	0.598878	+	0.266638i
$459$	−3.55705	+	19.5865i	−0.166029	+	0.914219i
$460$	0.961334	−	4.52272i	0.0448224	−	0.210873i
$461$	−10.3853			−0.483691			−0.241846	−	0.970315i	$-0.577753\pi$
$461$	−10.3853			−0.483691			−0.241846	+	0.970315i	$0.577753\pi$
$462$	−12.4494	−	0.0108156i	−0.579196	−	0.000503189i
$463$	−42.0271			−1.95316			−0.976581	−	0.215148i	$-0.930977\pi$
$463$	−42.0271			−1.95316			−0.976581	+	0.215148i	$0.930977\pi$
$464$	0.0565940	−	0.266254i	0.00262731	−	0.0123605i
$465$	−0.834752	−	2.00843i	−0.0387107	−	0.0931387i
$466$	21.3358	+	9.49933i	0.988364	+	0.440048i
$467$	−22.3464	−	24.8181i	−1.03407	−	1.14845i	−0.988766	−	0.149473i	$-0.952242\pi$
$467$	−22.3464	−	24.8181i	−1.03407	−	1.14845i	−0.0453002	−	0.998973i	$-0.514424\pi$
$468$	−3.46379	+	2.81876i	−0.160114	+	0.130297i
$469$	−26.5703	−	10.0037i	−1.22690	−	0.461929i
$470$	−6.45233	+	8.88087i	−0.297624	+	0.409644i
$471$	−30.4282	+	9.05308i	−1.40206	+	0.417144i
$472$	−0.665964	+	0.384494i	−0.0306535	+	0.0176978i
$473$	−6.34247	+	5.32434i	−0.291627	+	0.244814i
$474$	0.440644	−	17.6386i	0.0202394	−	0.810170i
$475$	−19.9483	+	6.48158i	−0.915289	+	0.297395i
$476$	11.9636	−	6.19303i	0.548350	−	0.283857i
$477$	23.4117	−	1.28346i	1.07195	−	0.0587658i
$478$	−2.45851	−	2.73045i	−0.112450	−	0.124888i
$479$	−27.0086	+	5.74086i	−1.23405	+	0.262306i	−0.778353	−	0.627826i	$-0.783945\pi$
$479$	−27.0086	+	5.74086i	−1.23405	+	0.262306i	−0.455701	+	0.890133i	$0.650611\pi$
$480$	11.9845	−	0.957713i	0.547015	−	0.0437134i
$481$	−0.331661	−	0.744922i	−0.0151224	−	0.0339655i
$482$	3.04298	+	9.36534i	0.138604	+	0.426580i
$483$	11.3076	−	7.04867i	0.514514	−	0.320726i
$484$	8.16988	−	12.1239i	0.371358	−	0.551085i
$485$	3.75167	+	2.16603i	0.170354	+	0.0983541i
$486$	−12.5406	+	2.40240i	−0.568852	+	0.108975i
$487$	3.63343	−	34.5698i	0.164646	−	1.56651i	−0.530529	−	0.847667i	$-0.678007\pi$
$487$	3.63343	−	34.5698i	0.164646	−	1.56651i	0.695176	−	0.718840i	$-0.255327\pi$
$488$	2.36396	+	22.4915i	0.107011	+	1.01814i
$489$	−28.0180	+	5.22772i	−1.26702	+	0.236406i
$490$	−2.20373	−	6.49672i	−0.0995543	−	0.293492i
$491$	24.7267	+	34.0334i	1.11590	+	1.53590i	0.812425	+	0.583065i	$0.198147\pi$
$491$	24.7267	+	34.0334i	1.11590	+	1.53590i	0.303475	+	0.952839i	$0.401853\pi$
$492$	18.5260	+	14.1801i	0.835215	+	0.639287i
$493$	1.82547	+	1.64366i	0.0822151	+	0.0740268i
$494$	4.67006	−	2.69626i	0.210116	−	0.121311i
$495$	−9.48873	+	7.18944i	−0.426487	+	0.323141i
$496$		−	0.445558i		−	0.0200062i
$497$	−26.0891	+	10.2078i	−1.17026	+	0.457880i
$498$	9.92966	+	1.29511i	0.444959	+	0.0580353i
$499$	2.14038	+	20.3643i	0.0958163	+	0.911632i	0.931823	+	0.362913i	$0.118218\pi$
$499$	2.14038	+	20.3643i	0.0958163	+	0.911632i	−0.836007	+	0.548719i	$0.815116\pi$
$500$	13.3277	−	2.83289i	0.596034	−	0.126691i
$501$	4.74803	+	5.54571i	0.212127	+	0.247764i
$502$	6.69202	−	0.703360i	0.298679	−	0.0313925i
$503$	−5.18250	−	3.76531i	−0.231076	−	0.167887i	0.466222	−	0.884668i	$-0.345615\pi$
$503$	−5.18250	−	3.76531i	−0.231076	−	0.167887i	−0.697298	+	0.716781i	$0.745615\pi$
$504$	16.2119	+	14.3398i	0.722134	+	0.638743i
$505$	11.2535			0.500774
$506$	0.273938	−	7.89445i	0.0121780	−	0.350951i
$507$	−10.6087	+	17.3588i	−0.471151	+	0.770929i
$508$	−11.3811	+	12.6400i	−0.504956	+	0.560811i
$509$	−3.33433	+	1.48454i	−0.147791	+	0.0658010i	−0.479300	−	0.877651i	$-0.659109\pi$
$509$	−3.33433	+	1.48454i	−0.147791	+	0.0658010i	0.331508	+	0.943452i	$0.392443\pi$
$510$	−2.79263	+	5.87305i	−0.123660	+	0.260063i
$511$	0.890415	+	3.23956i	0.0393897	+	0.143310i
$512$	4.54433	+	1.47654i	0.200833	+	0.0652546i
$513$	−30.5287	+	0.909727i	−1.34788	+	0.0401654i
$514$	−23.3862	−	2.45799i	−1.03152	−	0.108417i
$515$	−14.1087	−	12.7035i	−0.621703	−	0.559784i
$516$	5.74591	+	0.143543i	0.252950	+	0.00631911i
$517$	16.2778	−	33.3930i	0.715895	−	1.46862i
$518$	−1.31766	+	0.867802i	−0.0578947	+	0.0381290i
$519$	6.93379	−	7.32432i	0.304360	−	0.321502i
$520$	−3.33832	+	1.48632i	−0.146395	+	0.0651793i
$521$	7.65921	+	3.41010i	0.335556	+	0.149399i	0.567596	−	0.823307i	$-0.307873\pi$
$521$	7.65921	+	3.41010i	0.335556	+	0.149399i	−0.232040	+	0.972706i	$0.574540\pi$
$522$	−0.561098	+	1.47229i	−0.0245586	+	0.0644405i
$523$	−1.60057	+	1.44116i	−0.0699881	+	0.0630175i	−0.703382	−	0.710812i	$-0.748328\pi$
$523$	−1.60057	+	1.44116i	−0.0699881	+	0.0630175i	0.633394	+	0.773829i	$0.281661\pi$
$524$	−1.74539	+	1.26810i	−0.0762477	+	0.0553972i
$525$	13.5470	+	9.15906i	0.591240	+	0.399734i
$526$	6.71788	+	20.6755i	0.292913	+	0.901494i
$527$	3.48213	+	2.01041i	0.151684	+	0.0875748i
$528$	−2.36020	+	0.613977i	−0.102715	+	0.0267199i
$529$	−7.27272	−	12.5967i	−0.316205	−	0.547683i
$530$	7.49225	+	1.59253i	0.325443	+	0.0691750i
$531$	−0.789091	+	0.305085i	−0.0342436	+	0.0132396i
$532$	13.1103	+	15.9786i	0.568405	+	0.692761i
$533$	−10.7956	−	3.50769i	−0.467607	−	0.151935i
$534$	8.91715	+	3.14566i	0.385883	+	0.136126i
$535$	7.50886	−	16.8652i	0.324636	−	0.729145i
$536$	29.1012	+	3.05866i	1.25698	+	0.132114i
$537$	−17.4414	+	5.18921i	−0.752652	+	0.223931i
$538$		−	15.5513i		−	0.670463i
$539$	11.1668	+	20.3544i	0.480987	+	0.876727i
$540$	8.23970	+	0.618555i	0.354580	+	0.0266184i
$541$	31.5207	+	6.69993i	1.35518	+	0.288053i	0.827536	−	0.561413i	$-0.189742\pi$
$541$	31.5207	+	6.69993i	1.35518	+	0.288053i	0.527645	+	0.849465i	$0.323075\pi$
$542$	1.24753	−	11.8695i	0.0535862	−	0.509839i
$543$	35.5363	−	2.83981i	1.52501	−	0.121868i
$544$	−16.5170	+	14.8720i	−0.708162	+	0.637632i
$545$	−3.24483	+	9.98656i	−0.138993	+	0.427777i
$546$	−3.89634	−	1.57916i	−0.166748	−	0.0675818i
$547$	4.49510	+	3.26588i	0.192197	+	0.139639i	0.679722	−	0.733470i	$-0.262100\pi$
$547$	4.49510	+	3.26588i	0.192197	+	0.139639i	−0.487525	+	0.873109i	$0.662100\pi$
$548$	−0.124457	+	0.585525i	−0.00531655	+	0.0250124i
$549$	−1.24235	+	24.8497i	−0.0530222	+	1.06056i
$550$	8.98759	−	3.63353i	0.383232	−	0.154934i
$551$	−1.88439	+	3.26385i	−0.0802776	+	0.139045i
$552$	−9.44126	+	9.97302i	−0.401847	+	0.424480i
$553$	−29.2209	+	15.1264i	−1.24260	+	0.643240i
$554$	−5.04659	−	6.94603i	−0.214409	−	0.295109i
$555$	−0.501916	+	1.42280i	−0.0213051	+	0.0603947i
$556$	−3.57940	−	16.8397i	−0.151800	−	0.714164i
$557$	−3.10030	+	6.96340i	−0.131364	+	0.295049i	−0.967237	−	0.253874i	$-0.918295\pi$
$557$	−3.10030	+	6.96340i	−0.131364	+	0.295049i	0.835873	+	0.548923i	$0.184962\pi$
$558$	−0.397316	+	2.54824i	−0.0168197	+	0.107876i
$559$	−2.65966	+	0.864175i	−0.112492	+	0.0365507i
$560$	−0.739172	−	1.12235i	−0.0312357	−	0.0474279i
$561$	5.85114	−	21.2158i	0.247036	−	0.895732i
$562$	3.18109	−	5.50982i	0.134186	−	0.232418i
$563$	−8.00593	+	8.89148i	−0.337410	+	0.374731i	−0.887842	−	0.460148i	$-0.847796\pi$
$563$	−8.00593	+	8.89148i	−0.337410	+	0.374731i	0.550432	+	0.834880i	$0.314463\pi$
$564$	−23.8099	+	9.89596i	−1.00258	+	0.416695i
$565$	19.7416	−	2.07493i	0.830536	−	0.0872928i
$566$	2.60271	−	8.01032i	0.109400	−	0.336699i
$567$	15.1924	+	18.3355i	0.638022	+	0.770019i
$568$	23.3595	−	16.9716i	0.980141	−	0.712114i
$569$	−5.79487	−	13.0155i	−0.242933	−	0.545637i	0.750391	−	0.660995i	$-0.229865\pi$
$569$	−5.79487	−	13.0155i	−0.242933	−	0.545637i	−0.993324	+	0.115357i	$0.963199\pi$
$570$	−9.70470	−	2.31754i	−0.406485	−	0.0970712i
$571$	12.5985	+	21.8213i	0.527233	+	0.913194i	0.999496	+	0.0317366i	$0.0101038\pi$
$571$	12.5985	+	21.8213i	0.527233	+	0.913194i	−0.472263	+	0.881457i	$0.656563\pi$
$572$	4.09244	−	2.76170i	0.171114	−	0.115473i
$573$	−12.3747	+	6.73820i	−0.516959	+	0.281492i
$574$	−3.29617	+	21.7145i	−0.137580	+	0.906348i
$575$	−6.09878	+	8.39426i	−0.254337	+	0.350065i
$576$	−10.4454	−	5.29059i	−0.435227	−	0.220441i
$577$	2.12999	+	10.0208i	0.0886728	+	0.417173i	0.999985	+	0.00545700i	$0.00173703\pi$
$577$	2.12999	+	10.0208i	0.0886728	+	0.417173i	−0.911312	+	0.411716i	$0.864930\pi$
$578$	0.395584	+	1.86107i	0.0164541	+	0.0774105i
$579$	0.196288	−	0.135253i	0.00815747	−	0.00562094i
$580$	0.599306	−	0.824874i	0.0248848	−	0.0342510i
$581$	−6.80431	−	17.3906i	−0.282290	−	0.721482i
$582$	−2.45649	−	4.51134i	−0.101825	−	0.187001i
$583$	−25.9059	−	0.898934i	−1.07291	−	0.0372301i
$584$	−1.73135	−	2.99878i	−0.0716437	−	0.124090i
$585$	−3.88078	+	1.04987i	−0.160451	+	0.0434068i
$586$	−6.56705	−	14.7498i	−0.271282	−	0.609310i
$587$	10.5130	−	7.63813i	0.433917	−	0.315259i	−0.349296	−	0.937012i	$-0.613579\pi$
$587$	10.5130	−	7.63813i	0.433917	−	0.315259i	0.783213	+	0.621753i	$0.213579\pi$
$588$	3.54090	−	15.7202i	0.146024	−	0.648289i
$589$	−1.90632	+	5.86705i	−0.0785485	+	0.241747i
$590$	−0.274863	+	0.0288893i	−0.0113159	+	0.00118935i
$591$	3.53361	+	8.50192i	0.145353	+	0.349722i
$592$	−0.206810	+	0.229686i	−0.00849984	+	0.00944002i
$593$	0.0270141	−	0.0467898i	0.00110934	−	0.00192143i	−0.865470	−	0.500960i	$-0.832980\pi$
$593$	0.0270141	−	0.0467898i	0.00110934	−	0.00192143i	0.866580	+	0.499039i	$0.166314\pi$
$594$	14.0460	−	1.40680i	0.576313	−	0.0577217i
$595$	12.1066	−	0.712617i	0.496323	−	0.0292144i
$596$	18.9886	−	6.16977i	0.777803	−	0.252724i
$597$	23.5206	−	30.7292i	0.962635	−	1.25766i
$598$	1.08500	−	2.43696i	0.0443691	−	0.0996546i
$599$	−3.41493	−	16.0660i	−0.139530	−	0.656439i	−0.991201	−	0.132362i	$-0.957744\pi$
$599$	−3.41493	−	16.0660i	−0.139530	−	0.656439i	0.851671	−	0.524077i	$-0.175590\pi$
$600$	−15.8940	−	5.60685i	−0.648871	−	0.228899i
$601$	3.26940	+	4.49994i	0.133362	+	0.183556i	0.870475	−	0.492213i	$-0.163812\pi$
$601$	3.26940	+	4.49994i	0.133362	+	0.183556i	−0.737114	+	0.675769i	$0.763812\pi$
$602$	2.48752	+	4.80534i	0.101384	+	0.195851i
$603$	31.1155	+	8.25716i	1.26712	+	0.336258i
$604$	8.03039	−	13.9090i	0.326752	−	0.565951i
$605$	11.1583	−	6.97932i	0.453649	−	0.283750i
$606$	−11.3860	−	6.95850i	−0.462524	−	0.282670i
$607$	1.19815	−	5.63686i	0.0486315	−	0.228793i	−0.947119	−	0.320881i	$-0.896021\pi$
$607$	1.19815	−	5.63686i	0.0486315	−	0.228793i	0.995751	+	0.0920884i	$0.0293542\pi$
$608$	−27.5876	−	20.0436i	−1.11883	−	0.812875i
$609$	2.91011	−	0.405757i	0.117924	−	0.0164421i
$610$	−2.51171	+	7.73025i	−0.101696	+	0.312988i
$611$	9.32303	−	8.39450i	0.377170	−	0.339605i
$612$	−12.7908	+	8.35030i	−0.517038	+	0.337541i
$613$	−1.70724	+	16.2433i	−0.0689550	+	0.656063i	0.904388	+	0.426710i	$0.140328\pi$
$613$	−1.70724	+	16.2433i	−0.0689550	+	0.656063i	−0.973343	+	0.229352i	$0.926339\pi$
$614$	−0.432622	−	0.0919567i	−0.0174592	−	0.00371107i
$615$	10.0438	+	18.4453i	0.405004	+	0.743788i
$616$	−16.4350	−	17.3909i	−0.662186	−	0.700700i
$617$		−	24.2116i		−	0.974722i	−0.873201	−	0.487361i	$-0.837960\pi$
$617$		−	24.2116i		−	0.974722i	0.873201	−	0.487361i	$-0.162040\pi$
$618$	6.41968	+	21.5771i	0.258237	+	0.867957i
$619$	16.3480	+	1.71824i	0.657081	+	0.0690620i	0.427201	−	0.904157i	$-0.359500\pi$
$619$	16.3480	+	1.71824i	0.657081	+	0.0690620i	0.229881	+	0.973219i	$0.426166\pi$
$620$	0.678823	−	1.52466i	0.0272622	−	0.0612319i
$621$	−11.9533	+	9.24082i	−0.479668	+	0.370821i
$622$	1.33907	+	0.435090i	0.0536918	+	0.0174455i
$623$	−2.87051	−	17.3984i	−0.115005	−	0.697054i
$624$	−0.816658	−	0.106515i	−0.0326925	−	0.00426403i
$625$	−5.45416	−	1.15932i	−0.218167	−	0.0463727i
$626$	0.768131	+	1.33044i	0.0307007	+	0.0531752i
$627$	33.7057	+	2.01336i	1.34608	+	0.0804058i
$628$	−21.0965	−	12.1800i	−0.841840	−	0.486037i
$629$	−0.861892	−	2.65263i	−0.0343659	−	0.105767i
$630$	3.22664	+	7.07808i	0.128553	+	0.281998i
$631$	−11.1122	+	8.07347i	−0.442369	+	0.321400i	−0.786575	−	0.617494i	$-0.788148\pi$
$631$	−11.1122	+	8.07347i	−0.442369	+	0.321400i	0.344207	+	0.938894i	$0.388148\pi$
$632$	25.2020	−	22.6920i	1.00248	−	0.902640i
$633$	−8.40977	−	9.82261i	−0.334258	−	0.390414i
$634$	6.21350	+	2.76643i	0.246770	+	0.109869i
$635$	−13.9883	+	6.22797i	−0.555107	+	0.247150i
$636$	13.0655	+	12.3689i	0.518081	+	0.490457i
$637$	0.919793	+	7.78610i	0.0364435	+	0.308496i
$638$	0.763244	−	1.56576i	0.0302171	−	0.0619890i
$639$	28.2690	−	14.4896i	1.11830	−	0.573198i
$640$	7.47422	+	6.72982i	0.295445	+	0.266019i
$641$	−10.0452	−	1.05579i	−0.396760	−	0.0417012i	−0.0959522	−	0.995386i	$-0.530590\pi$
$641$	−10.0452	−	1.05579i	−0.396760	−	0.0417012i	−0.300808	+	0.953685i	$0.597256\pi$
$642$	−18.0257	+	12.4207i	−0.711418	+	0.490206i
$643$	40.9320	+	13.2996i	1.61420	+	0.524486i	0.970564	−	0.240845i	$-0.0774246\pi$
$643$	40.9320	+	13.2996i	1.61420	+	0.524486i	0.643637	+	0.765331i	$0.277425\pi$
$644$	9.89289	+	2.58269i	0.389834	+	0.101772i
$645$	4.67294	+	2.22198i	0.183997	+	0.0874903i
$646$	16.8505	−	7.50231i	0.662973	−	0.295174i
$647$	24.2808	−	26.9666i	0.954578	−	1.06017i	−0.0435528	−	0.999051i	$-0.513868\pi$
$647$	24.2808	−	26.9666i	0.954578	−	1.06017i	0.998131	−	0.0611150i	$-0.0194657\pi$
$648$	−19.9239	−	14.3295i	−0.782685	−	0.562917i
$649$	0.899016	−	0.258003i	0.0352895	−	0.0101275i
$650$	3.27379			0.128409
$651$	4.52127	−	1.64003i	0.177203	−	0.0642780i
$652$	−17.6934	−	12.8550i	−0.692927	−	0.503441i
$653$	18.2840	−	1.92173i	0.715510	−	0.0752031i	0.260224	−	0.965548i	$-0.416204\pi$
$653$	18.2840	−	1.92173i	0.715510	−	0.0752031i	0.455286	+	0.890345i	$0.349537\pi$
$654$	9.45814	−	8.09772i	0.369843	−	0.316646i
$655$	−1.89976	+	0.403806i	−0.0742297	+	0.0157780i
$656$	0.449731	+	4.27891i	0.0175591	+	0.167063i
$657$	−1.37377	−	3.55322i	−0.0535960	−	0.138624i
$658$	−18.9624	−	15.1545i	−0.739231	−	0.590783i
$659$			1.02522i			0.0399370i	0.999801	+	0.0199685i	$0.00635659\pi$
$659$			1.02522i			0.0399370i	−0.999801	+	0.0199685i	$0.993643\pi$
$660$	−9.01182	−	1.49487i	−0.350784	−	0.0581878i
$661$	9.46396	−	5.46402i	0.368105	−	0.212526i	−0.304525	−	0.952504i	$-0.598498\pi$
$661$	9.46396	−	5.46402i	0.368105	−	0.212526i	0.672630	+	0.739979i	$0.265164\pi$
$662$	−8.22833	−	7.40882i	−0.319803	−	0.287952i
$663$	4.51729	−	5.90174i	0.175437	−	0.229205i
$664$	11.3130	+	15.5710i	0.439029	+	0.604272i
$665$	4.93134	+	17.9415i	0.191229	+	0.695741i
$666$	1.38760	−	1.12920i	0.0537686	−	0.0437556i
$667$	0.194877	+	1.85413i	0.00754567	+	0.0717923i
$668$	−0.585568	+	5.57131i	−0.0226563	+	0.215561i
$669$	−5.41448	+	22.6731i	−0.209336	+	0.876592i
$670$	9.10771	+	5.25834i	0.351861	+	0.203147i
$671$	3.82218	−	27.2398i	0.147554	−	1.05158i
$672$	0.898884	+	26.5704i	0.0346752	+	1.02498i
$673$	5.59229	+	17.2113i	0.215567	+	0.663447i	0.999113	+	0.0421130i	$0.0134090\pi$
$673$	5.59229	+	17.2113i	0.215567	+	0.663447i	−0.783546	+	0.621334i	$0.786591\pi$
$674$	−12.0241	−	27.0067i	−0.463153	−	1.04026i
$675$	−16.3270	−	8.78868i	−0.628427	−	0.338276i
$676$	−15.2694	+	3.24561i	−0.587285	+	0.124831i
$677$	18.5359	+	20.5862i	0.712393	+	0.791193i	0.985297	−	0.170849i	$-0.0546509\pi$
$677$	18.5359	+	20.5862i	0.712393	+	0.791193i	−0.272904	+	0.962041i	$0.587984\pi$
$678$	−21.2570	−	10.1077i	−0.816372	−	0.388184i
$679$	−5.16552	+	8.06736i	−0.198234	+	0.309597i
$680$	−11.8876	+	3.86252i	−0.455869	+	0.148121i
$681$	−44.1249	−	1.10232i	−1.69087	−	0.0422409i
$682$	0.689163	−	2.76668i	0.0263894	−	0.105942i
$683$	21.4967	−	12.4111i	0.822547	−	0.474898i	−0.0287471	−	0.999587i	$-0.509152\pi$
$683$	21.4967	−	12.4111i	0.822547	−	0.474898i	0.851294	+	0.524689i	$0.175818\pi$
$684$	−16.6117	−	16.5319i	−0.635164	−	0.632114i
$685$	−0.316751	+	0.435971i	−0.0121025	+	0.0166576i
$686$	14.5747	−	4.20839i	0.556463	−	0.160677i
$687$	5.44132	+	29.1628i	0.207599	+	1.11263i
$688$	0.709268	+	0.787722i	0.0270406	+	0.0300316i
$689$	−7.99695	−	3.56047i	−0.304660	−	0.135643i
$690$	−4.55774	+	1.89431i	−0.173510	+	0.0721151i
$691$	0.335623	−	1.57898i	0.0127677	−	0.0600673i	−0.971303	−	0.237847i	$-0.923558\pi$
$691$	0.335623	−	1.57898i	0.0127677	−	0.0600673i	0.984070	+	0.177780i	$0.0568916\pi$
$692$	7.73918			0.294199
$693$	−14.9178	−	21.6900i	−0.566682	−	0.823937i
$694$	−15.0132			−0.569894
$695$	3.22232	−	15.1598i	0.122230	−	0.575045i
$696$	−2.79642	+	1.16226i	−0.105998	+	0.0440554i
$697$	−35.4698	−	15.7922i	−1.34351	−	0.598171i
$698$	3.90481	+	4.33673i	0.147799	+	0.164148i
$699$	9.05822	+	48.5477i	0.342613	+	1.83624i
$700$	2.04263	+	12.3806i	0.0772043	+	0.467942i
$701$	15.3646	−	21.1475i	0.580313	−	0.798732i	−0.413417	−	0.910542i	$-0.635665\pi$
$701$	15.3646	−	21.1475i	0.580313	−	0.798732i	0.993730	+	0.111810i	$0.0356648\pi$
$702$	4.57565	+	1.33742i	0.172697	+	0.0504776i
$703$	3.70595	−	2.13963i	0.139773	−	0.0806977i
$704$	10.9792	+	6.85719i	0.413794	+	0.258440i
$705$	−23.2050	−	0.579701i	−0.873951	−	0.0218328i
$706$	−11.1229	+	3.61403i	−0.418614	+	0.136016i
$707$	−1.14245	+	24.8584i	−0.0429662	+	0.934898i
$708$	−0.586273	−	0.278772i	−0.0220335	−	0.0104769i
$709$	−11.1119	−	12.3410i	−0.417317	−	0.463477i	0.497431	−	0.867504i	$-0.334277\pi$
$709$	−11.1119	−	12.3410i	−0.417317	−	0.463477i	−0.914747	+	0.404027i	$0.867610\pi$
$710$	10.1506	−	2.15758i	0.380945	−	0.0809724i
$711$	31.2415	−	20.3955i	1.17165	−	0.764891i
$712$	7.39212	+	16.6030i	0.277032	+	0.622223i
$713$	0.943021	+	2.90232i	0.0353164	+	0.108693i
$714$	−12.6898	−	6.76503i	−0.474904	−	0.253175i
$715$	4.37690	−	0.772760i	0.163687	−	0.0288996i
$716$	−12.0925	−	6.98159i	−0.451917	−	0.260914i
$717$	1.80461	−	7.55679i	0.0673944	−	0.282213i
$718$	−1.36133	+	12.9521i	−0.0508042	+	0.483370i
$719$	−3.02512	−	28.7821i	−0.112818	−	1.07339i	−0.893686	−	0.448694i	$-0.851889\pi$
$719$	−3.02512	−	28.7821i	−0.112818	−	1.07339i	0.780868	−	0.624696i	$-0.214777\pi$
$720$	0.961825	+	1.18193i	0.0358451	+	0.0440478i
$721$	29.4938	−	29.8758i	1.09841	−	1.11263i
$722$	7.48636	+	10.3041i	0.278613	+	0.383479i
$723$	−12.6562	+	16.5350i	−0.470688	+	0.614943i
$724$	20.3289	+	18.3042i	0.755517	+	0.680270i
$725$	−1.98148	+	1.14401i	−0.0735904	+	0.0424874i
$726$	−15.6053	+	0.161848i	−0.579165	+	0.00600674i
$727$			31.5855i			1.17144i	0.810514	+	0.585720i	$0.199188\pi$
$727$			31.5855i			1.17144i	−0.810514	+	0.585720i	$0.800812\pi$
$728$	−2.94430	−	7.52510i	−0.109123	−	0.278899i
$729$	−19.2292	−	18.9535i	−0.712194	−	0.701983i
$730$	−0.130086	−	1.23769i	−0.00481470	−	0.0458088i
$731$	−9.35651	+	1.98879i	−0.346063	+	0.0735579i
$732$	−14.5026	+	12.4166i	−0.536032	+	0.458932i
$733$	−11.6294	+	1.22230i	−0.429542	+	0.0451467i	−0.316833	−	0.948481i	$-0.602619\pi$
$733$	−11.6294	+	1.22230i	−0.429542	+	0.0451467i	−0.112709	+	0.993628i	$0.535953\pi$
$734$	−11.6707	−	8.47929i	−0.430775	−	0.312976i
$735$	8.66819	−	11.6319i	0.319731	−	0.429049i
$736$	−16.8688			−0.621790
$737$	−33.4465	−	12.1652i	−1.23202	−	0.448110i
$738$	1.24351	−	24.8730i	0.0457744	−	0.915587i
$739$	23.8972	−	26.5405i	0.879073	−	0.976310i	−0.120793	−	0.992678i	$-0.538544\pi$
$739$	23.8972	−	26.5405i	0.879073	−	0.976310i	0.999866	+	0.0163681i	$0.00521037\pi$
$740$	−1.05762	+	0.470882i	−0.0388788	+	0.0173100i
$741$	10.2979	+	4.89664i	0.378303	+	0.179883i
$742$	−4.27843	+	16.3884i	−0.157066	+	0.601636i
$743$	−1.70870	−	0.555190i	−0.0626861	−	0.0203680i	0.277506	−	0.960724i	$-0.410492\pi$
$743$	−1.70870	−	0.555190i	−0.0626861	−	0.0203680i	−0.340192	+	0.940356i	$0.610492\pi$
$744$	−4.08179	+	2.81258i	−0.149646	+	0.103114i
$745$	17.8756	+	1.87880i	0.654910	+	0.0688338i
$746$	2.21413	+	1.99361i	0.0810649	+	0.0729912i
$747$	9.65849	+	18.8436i	0.353386	+	0.689451i
$748$	14.9089	−	7.93144i	0.545125	−	0.290002i
$749$	36.4921	+	18.2989i	1.33339	+	0.668626i
$750$	−10.5625	−	9.99928i	−0.385687	−	0.365122i
$751$	25.6093	−	11.4020i	0.934497	−	0.416065i	0.117739	−	0.993045i	$-0.462435\pi$
$751$	25.6093	−	11.4020i	0.934497	−	0.416065i	0.816759	+	0.576980i	$0.195769\pi$
$752$	−4.34404	−	1.93409i	−0.158411	−	0.0705291i
$753$	9.25376	+	10.8084i	0.337226	+	0.393880i
$754$	0.437146	−	0.393608i	0.0159199	−	0.0143343i
$755$	11.6972	−	8.49854i	0.425706	−	0.309293i
$756$	−2.20285	+	18.1383i	−0.0801168	+	0.659684i
$757$	7.47943	+	23.0193i	0.271845	+	0.836651i	0.990037	+	0.140807i	$0.0449697\pi$
$757$	7.47943	+	23.0193i	0.271845	+	0.836651i	−0.718193	+	0.695844i	$0.755030\pi$
$758$	9.61110	+	5.54897i	0.349091	+	0.201548i
$759$	14.0746	−	8.99473i	0.510877	−	0.326488i
$760$	−9.58863	−	16.6080i	−0.347816	−	0.602436i
$761$	25.2515	+	5.36737i	0.915366	+	0.194567i	0.641431	−	0.767181i	$-0.278341\pi$
$761$	25.2515	+	5.36737i	0.915366	+	0.194567i	0.273935	+	0.961748i	$0.411675\pi$
$762$	18.0040	+	2.34823i	0.652215	+	0.0850673i
$763$	−21.7304	−	8.18151i	−0.786695	−	0.296191i
$764$	−10.2828	−	3.34108i	−0.372018	−	0.120876i
$765$	−13.5769	+	2.18387i	−0.490873	+	0.0789582i
$766$	3.67541	−	8.25510i	0.132798	−	0.298269i
$767$	0.314125	+	0.0330159i	0.0113424	+	0.00119213i
$768$	−7.25644	−	24.3895i	−0.261844	−	0.880080i
$769$		−	3.57843i		−	0.129042i	−0.997916	−	0.0645208i	$-0.979448\pi$
$769$		−	3.57843i		−	0.129042i	0.997916	−	0.0645208i	$-0.0205519\pi$
$770$	−2.85388	−	8.11250i	−0.102847	−	0.292354i
$771$	−23.7787	−	43.6696i	−0.856370	−	1.57272i
$772$	0.178916	+	0.0380298i	0.00643934	+	0.00136872i
$773$	0.218513	−	2.07901i	0.00785935	−	0.0747767i	−0.989889	−	0.141843i	$-0.954697\pi$
$773$	0.218513	−	2.07901i	0.00785935	−	0.0747767i	0.997749	+	0.0670662i	$0.0213639\pi$
$774$	−3.35401	−	5.13761i	−0.120557	−	0.184668i
$775$	−2.78321	+	2.50601i	−0.0999758	+	0.0900186i
$776$	3.05095	−	9.38985i	0.109523	−	0.337076i
$777$	−3.09196	−	1.25315i	−0.110923	−	0.0449565i
$778$	20.8162	+	15.1239i	0.746297	+	0.542217i
$779$	12.3853	−	58.2682i	0.443749	−	2.08767i
$780$	−2.63225	−	1.60869i	−0.0942497	−	0.0576004i
$781$	−32.5586	+	13.1629i	−1.16504	+	0.471005i
$782$	4.56224	−	7.90203i	0.163145	−	0.282576i
$783$	−3.23679	+	0.789454i	−0.115673	+	0.0282128i
$784$	2.55426	−	1.51886i	0.0912236	−	0.0542449i
$785$	−12.8901	−	17.7417i	−0.460067	−	0.633228i
$786$	2.17181	+	0.766139i	0.0774660	+	0.0273273i
$787$	4.25247	+	20.0063i	0.151584	+	0.713148i	0.986631	+	0.162969i	$0.0521071\pi$
$787$	4.25247	+	20.0063i	0.151584	+	0.713148i	−0.835047	+	0.550179i	$0.814560\pi$
$788$	−2.87354	+	6.45407i	−0.102366	+	0.229917i
$789$	−27.9405	+	36.5037i	−0.994709	+	1.29956i
$790$	11.5918	−	3.76640i	0.412418	−	0.134003i
$791$	2.57926	+	43.8190i	0.0917079	+	1.55802i
$792$	20.5234	+	17.7463i	0.729268	+	0.630587i
$793$	4.64454	−	8.04459i	0.164933	−	0.285672i
$794$	−1.32098	+	1.46709i	−0.0468798	+	0.0520652i
$795$	6.21623	+	14.9564i	0.220467	+	0.530448i
$796$	29.5313	−	3.10387i	1.04671	−	0.110014i
$797$	−7.71130	+	23.7329i	−0.273148	+	0.840664i	0.716555	+	0.697530i	$0.245718\pi$
$797$	−7.71130	+	23.7329i	−0.273148	+	0.840664i	−0.989703	+	0.143133i	$0.954282\pi$
$798$	6.10456	−	21.2020i	0.216099	−	0.750541i
$799$	34.7161	−	25.2227i	1.22817	−	0.892316i
$800$	−8.42034	−	18.9124i	−0.297704	−	0.668654i
$801$	5.22147	+	19.3009i	0.184492	+	0.681962i
$802$	2.90385	+	5.02962i	0.102539	+	0.177602i
$803$	1.16177	+	4.04820i	0.0409979	+	0.142858i
$804$	11.8131	+	21.6947i	0.416615	+	0.765113i
$805$	7.19034	+	5.74642i	0.253426	+	0.202535i
$806$	0.565958	−	0.778975i	0.0199350	−	0.0274382i
$807$	27.0782	−	18.6584i	0.953198	−	0.656805i
$808$	−5.33243	−	25.0871i	−0.187594	−	0.882561i
$809$	−0.689570	−	3.24417i	−0.0242440	−	0.114059i	0.964362	−	0.264588i	$-0.0852358\pi$
$809$	−0.689570	−	3.24417i	−0.0242440	−	0.114059i	−0.988606	+	0.150529i	$0.951902\pi$
$810$	−4.44691	−	7.61736i	−0.156249	−	0.267647i
$811$	−26.7395	+	36.8038i	−0.938952	+	1.29236i	0.0173111	+	0.999850i	$0.494489\pi$
$811$	−26.7395	+	36.8038i	−0.938952	+	1.29236i	−0.956263	+	0.292507i	$0.905511\pi$
$812$	1.76127	+	1.40758i	0.0618084	+	0.0493964i
$813$	22.1642	−	12.0687i	0.777332	−	0.423269i
$814$	−1.63944	+	1.10634i	−0.0574624	+	0.0387773i
$815$	−9.84424	−	17.0507i	−0.344829	−	0.597261i
$816$	−2.73999	−	0.654328i	−0.0959190	−	0.0229061i
$817$	−5.96927	−	13.4072i	−0.208838	−	0.469058i
$818$	13.4763	−	9.79109i	0.471187	−	0.342338i
$819$	−1.92514	−	8.67905i	−0.0672698	−	0.303270i
$820$	−4.98012	+	15.3272i	−0.173913	+	0.535250i
$821$	13.4248	−	1.41101i	0.468530	−	0.0492445i	0.132678	−	0.991159i	$-0.457642\pi$
$821$	13.4248	−	1.41101i	0.468530	−	0.0492445i	0.335852	+	0.941915i	$0.390976\pi$
$822$	0.590060	−	0.245243i	0.0205807	−	0.00855383i
$823$	−7.97300	+	8.85491i	−0.277921	+	0.308663i	−0.865904	−	0.500211i	$-0.833256\pi$
$823$	−7.97300	+	8.85491i	−0.277921	+	0.308663i	0.587982	+	0.808874i	$0.299922\pi$
$824$	−21.6343	+	37.4716i	−0.753665	+	1.30539i
$825$	17.1100	+	11.2899i	0.595695	+	0.393063i
$826$	−0.0359111	−	0.610093i	−0.00124951	−	0.0212278i
$827$	4.72127	−	1.53403i	0.164175	−	0.0533436i	−0.225777	−	0.974179i	$-0.572492\pi$
$827$	4.72127	−	1.53403i	0.164175	−	0.0533436i	0.389951	+	0.920836i	$0.372492\pi$
$828$	−11.4550	−	1.78605i	−0.398090	−	0.0620695i
$829$	5.77995	−	12.9820i	0.200746	−	0.450883i	−0.784919	−	0.619599i	$-0.787295\pi$
$829$	5.77995	−	12.9820i	0.200746	−	0.450883i	0.985665	+	0.168716i	$0.0539620\pi$
$830$	1.43820	+	6.76621i	0.0499207	+	0.234859i
$831$	6.03970	−	17.1210i	0.209515	−	0.593922i
$832$	2.56947	+	3.53657i	0.0890803	+	0.122609i
$833$	0.345078	+	26.8153i	0.0119562	+	0.929096i
$834$	−12.6342	+	13.3458i	−0.437487	+	0.462127i
$835$	−2.52157	+	4.36749i	−0.0872627	+	0.151143i
$836$	16.6588	+	19.8443i	0.576156	+	0.686328i
$837$	−4.91374	+	2.36555i	−0.169844	+	0.0817653i
$838$	3.68539	−	17.3384i	0.127310	−	0.598945i
$839$	13.6558	+	9.92152i	0.471451	+	0.342529i	0.798006	−	0.602649i	$-0.205888\pi$
$839$	13.6558	+	9.92152i	0.471451	+	0.342529i	−0.326556	+	0.945178i	$0.605888\pi$
$840$	−5.61592	+	13.8564i	−0.193768	+	0.478092i
$841$	8.83445	−	27.1896i	0.304636	−	0.937574i
$842$	−21.0592	+	18.9618i	−0.725748	+	0.653466i
$843$	13.4105	−	1.07167i	0.461881	−	0.0369102i
$844$	1.03716	−	9.86796i	0.0357007	−	0.339669i
$845$	−13.7461	−	2.92183i	−0.472882	−	0.100514i
$846$	23.1198	+	14.9352i	0.794873	+	0.513481i
$847$	14.2842	+	25.3567i	0.490811	+	0.871266i
$848$			3.31798i			0.113940i
$849$	17.0704	−	5.07885i	0.585856	−	0.174306i
$850$	11.1367	+	1.17051i	0.381985	+	0.0401482i
$851$	0.861010	−	1.93386i	0.0295151	−	0.0662919i
$852$	22.9868	+	8.10895i	0.787516	+	0.277808i
$853$	−9.34386	−	3.03600i	−0.319928	−	0.103951i	0.144651	−	0.989483i	$-0.453794\pi$
$853$	−9.34386	−	3.03600i	−0.319928	−	0.103951i	−0.464578	+	0.885532i	$0.653794\pi$
$854$	−16.8208	−	6.33302i	−0.575595	−	0.216712i
$855$	−7.60830	−	19.6786i	−0.260198	−	0.672994i
$856$	−41.1551	−	8.74779i	−1.40665	−	0.298993i
$857$	−22.7739	−	39.4455i	−0.777941	−	1.34743i	−0.933127	−	0.359548i	$-0.882931\pi$
$857$	−22.7739	−	39.4455i	−0.777941	−	1.34743i	0.155186	−	0.987885i	$-0.450402\pi$
$858$	−4.90626	−	1.92456i	−0.167497	−	0.0657034i
$859$	−2.78240	−	1.60642i	−0.0949344	−	0.0548104i	0.451781	−	0.892129i	$-0.350789\pi$
$859$	−2.78240	−	1.60642i	−0.0949344	−	0.0548104i	−0.546716	+	0.837318i	$0.684122\pi$
$860$	1.22693	+	3.77611i	0.0418380	+	0.128764i
$861$	−41.7645	+	20.3136i	−1.42333	+	0.692287i
$862$	−6.49481	+	4.71876i	−0.221214	+	0.160721i
$863$	−31.8974	+	28.7206i	−1.08580	+	0.977659i	−0.999826	−	0.0186380i	$-0.994067\pi$
$863$	−31.8974	+	28.7206i	−1.08580	+	0.977659i	−0.0859744	+	0.996297i	$0.527400\pi$
$864$	−4.04262	−	29.8730i	−0.137533	−	1.01630i
$865$	6.36478	+	2.83378i	0.216409	+	0.0963515i
$866$	−9.37386	+	4.17351i	−0.318537	+	0.141822i
$867$	−2.76592	+	2.92171i	−0.0939356	+	0.0992263i
$868$	3.29899	+	1.65427i	0.111975	+	0.0561496i
$869$	−36.4149	+	19.3725i	−1.23529	+	0.657166i
$870$	−1.08805	−	0.0271815i	−0.0368885	−	0.000921538i
$871$	−8.93178	−	8.04221i	−0.302642	−	0.272500i
$872$	23.8003	+	2.50151i	0.805981	+	0.0847120i
$873$	4.90795	−	9.68997i	0.166109	−	0.327956i
$874$	13.3141	+	4.32602i	0.450357	+	0.146330i
$875$	−6.85152	+	26.2445i	−0.231624	+	0.887225i
$876$	1.25529	−	2.63994i	0.0424123	−	0.0891954i
$877$	12.3292	−	5.48932i	0.416328	−	0.185361i	−0.187872	−	0.982193i	$-0.560159\pi$
$877$	12.3292	−	5.48932i	0.416328	−	0.185361i	0.604201	+	0.796832i	$0.293492\pi$
$878$	−0.0598591	+	0.0664803i	−0.00202015	+	0.00224360i
$879$	17.8036	−	29.1315i	0.600501	−	0.982580i
$880$	−0.942357	−	1.39644i	−0.0317668	−	0.0470739i
$881$	−15.5530			−0.523993			−0.261996	−	0.965069i	$-0.584381\pi$
$881$	−15.5530			−0.523993			−0.261996	+	0.965069i	$0.584381\pi$
$882$	−15.9627	+	6.40895i	−0.537493	+	0.215800i
$883$	38.5693	+	28.0222i	1.29796	+	0.943023i	0.999933	−	0.0115344i	$-0.00367161\pi$
$883$	38.5693	+	28.0222i	1.29796	+	0.943023i	0.298027	+	0.954558i	$0.403672\pi$
$884$	5.67169	−	0.596118i	0.190759	−	0.0200496i
$885$	−0.380082	−	0.443936i	−0.0127763	−	0.0149227i
$886$	15.5488	−	3.30501i	0.522374	−	0.111034i
$887$	5.46206	+	51.9681i	0.183398	+	1.74492i	0.569078	+	0.822284i	$0.307300\pi$
$887$	5.46206	+	51.9681i	0.183398	+	1.74492i	−0.385680	+	0.922633i	$0.626033\pi$
$888$	3.40965	+	0.444715i	0.114420	+	0.0149237i
$889$	−12.3372	−	31.5317i	−0.413777	−	1.05754i
$890$			6.53188i			0.218949i
$891$	19.3018	+	22.7693i	0.646636	+	0.762799i
$892$	−15.4906	+	8.94353i	−0.518665	+	0.299451i
$893$	48.9267	+	44.0538i	1.63727	+	1.47420i
$894$	−16.9243	−	12.9541i	−0.566032	−	0.433250i
$895$	−7.38859	−	10.1695i	−0.246973	−	0.339930i
$896$	−15.6246	+	15.8270i	−0.521983	+	0.528743i
$897$	5.54506	−	1.03462i	0.185144	−	0.0345450i
$898$	2.79317	+	26.5753i	0.0932094	+	0.886828i
$899$	−0.0703410	+	0.669250i	−0.00234600	+	0.0223207i
$900$	−3.71556	−	13.7343i	−0.123852	−	0.457811i
$901$	−25.9307	−	14.9711i	−0.863878	−	0.498760i
$902$	−3.82577	+	27.2653i	−0.127384	+	0.907837i
$903$	−5.38264	+	10.0967i	−0.179123	+	0.335998i
$904$	−13.9801	−	43.0262i	−0.464970	−	1.43103i
$905$	10.0164	+	22.4972i	0.332957	+	0.747833i
$906$	−17.0899	+	1.36570i	−0.567775	+	0.0453725i
$907$	−17.0069	+	3.61493i	−0.564705	+	0.120032i	−0.481414	−	0.876494i	$-0.659876\pi$
$907$	−17.0069	+	3.61493i	−0.564705	+	0.120032i	−0.0832911	+	0.996525i	$0.526543\pi$
$908$	−22.6629	−	25.1697i	−0.752095	−	0.835286i
$909$	−1.54456	−	28.1743i	−0.0512297	−	0.934482i
$910$	0.133331	−	2.90113i	0.00441987	−	0.0961715i
$911$	−50.3401	+	16.3565i	−1.66784	+	0.541915i	−0.982493	−	0.186299i	$-0.940351\pi$
$911$	−50.3401	+	16.3565i	−1.66784	+	0.541915i	−0.685350	+	0.728214i	$0.740351\pi$
$912$	0.107939	−	4.32072i	0.00357421	−	0.143073i
$913$	−8.77414	−	21.7030i	−0.290382	−	0.718264i
$914$	−13.3619	+	7.71447i	−0.441971	+	0.255172i
$915$	−16.4736	+	4.90127i	−0.544600	+	0.162031i
$916$	−13.3802	+	18.4163i	−0.442096	+	0.608493i
$917$	−0.699126	−	4.23747i	−0.0230872	−	0.139934i
$918$	15.0871	+	6.18556i	0.497948	+	0.204154i
$919$	9.51965	+	10.5726i	0.314024	+	0.348759i	0.879408	−	0.476069i	$-0.157939\pi$
$919$	9.51965	+	10.5726i	0.314024	+	0.348759i	−0.565384	+	0.824828i	$0.691272\pi$
$920$	−8.66648	−	3.85857i	−0.285726	−	0.127213i
$921$	−0.358941	−	0.863620i	−0.0118275	−	0.0284572i
$922$	−1.76864	+	8.32078i	−0.0582469	+	0.274030i
$923$	−11.8597			−0.390366
$924$	4.21698	−	19.7549i	0.138728	−	0.649889i
$925$	2.59793			0.0854196
$926$	−7.15729	+	33.6724i	−0.235203	+	1.10654i
$927$	−29.8681	+	37.0661i	−0.980999	+	1.21741i
$928$	−3.39819	−	1.51297i	−0.111551	−	0.0496658i
$929$	−16.8629	−	18.7281i	−0.553253	−	0.614450i	0.400039	−	0.916498i	$-0.368996\pi$
$929$	−16.8629	−	18.7281i	−0.553253	−	0.614450i	−0.953293	+	0.302048i	$0.902330\pi$
$930$	−1.75133	+	0.326770i	−0.0574284	+	0.0107152i
$931$	−40.1325	+	9.07170i	−1.31529	+	0.297313i
$932$	−22.2742	+	30.6579i	−0.729617	+	1.00423i
$933$	0.849021	+	2.85363i	0.0277957	+	0.0934237i
$934$	−23.6901	+	13.6775i	−0.775165	+	0.447542i
$935$	15.1655	−	1.06383i	0.495964	−	0.0347910i
$936$	4.17934	+	8.15384i	0.136606	+	0.266517i
$937$	−36.2489	+	11.7780i	−1.18420	+	0.384770i	−0.833925	−	0.551877i	$-0.813912\pi$
$937$	−36.2489	+	11.7780i	−1.18420	+	0.384770i	−0.350274	+	0.936647i	$0.613912\pi$
$938$	−12.5400	+	19.5847i	−0.409447	+	0.639463i
$939$	−1.39499	+	2.93374i	−0.0455239	+	0.0957391i
$940$	−11.9183	−	13.2366i	−0.388731	−	0.431729i
$941$	30.5491	−	6.49341i	0.995872	−	0.211679i	0.318980	−	0.947762i	$-0.396660\pi$
$941$	30.5491	−	6.49341i	0.995872	−	0.211679i	0.676892	+	0.736082i	$0.263326\pi$
$942$	2.07142	+	25.9211i	0.0674906	+	0.844554i
$943$	−11.9858	−	26.9205i	−0.390311	−	0.876653i
$944$	−0.0369956	−	0.113861i	−0.00120411	−	0.00370586i
$945$	−8.45319	+	14.1106i	−0.274982	+	0.459016i
$946$	3.18577	+	5.98838i	0.103578	+	0.194699i
$947$	22.1154	+	12.7683i	0.718653	+	0.414915i	0.814257	−	0.580505i	$-0.197145\pi$
$947$	22.1154	+	12.7683i	0.718653	+	0.414915i	−0.0956035	+	0.995419i	$0.530478\pi$
$948$	27.8459	+	6.64979i	0.904394	+	0.215975i
$949$	−0.148668	+	1.41448i	−0.00482596	+	0.0459160i
$950$	1.79587	+	17.0865i	0.0582656	+	0.554360i
$951$	2.63797	+	14.1382i	0.0855420	+	0.458463i
$952$	−7.32530	−	26.6513i	−0.237414	−	0.863774i
$953$	−17.8013	−	24.5014i	−0.576641	−	0.793678i	0.416681	−	0.909053i	$-0.363193\pi$
$953$	−17.8013	−	24.5014i	−0.576641	−	0.793678i	−0.993322	+	0.115375i	$0.963193\pi$
$954$	2.95873	−	18.9762i	0.0957926	−	0.614377i
$955$	−7.23330	−	6.51289i	−0.234064	−	0.210752i
$956$	5.16293	−	2.98082i	0.166981	−	0.0964065i
$957$	3.64207	−	0.549613i	0.117731	−	0.0177665i
$958$			22.6172i			0.730728i
$959$	−0.930883	−	0.743949i	−0.0300598	−	0.0240234i
$960$	1.04609	−	8.02039i	0.0337623	−	0.258857i
$961$	−3.12524	−	29.7347i	−0.100814	−	0.959184i
$962$	−0.653320	+	0.138867i	−0.0210639	+	0.00447727i
$963$	−43.2543	−	16.4844i	−1.39385	−	0.531204i
$964$	−15.8905	+	1.67015i	−0.511797	+	0.0537920i
$965$	0.133218	+	0.0967883i	0.00428843	+	0.00311572i
$966$	−3.72174	−	10.2602i	−0.119745	−	0.330115i
$967$	2.47539			0.0796031			0.0398015	−	0.999208i	$-0.487327\pi$
$967$	2.47539			0.0796031			0.0398015	+	0.999208i	$0.487327\pi$
$968$	−20.8461	−	21.5677i	−0.670020	−	0.693214i
$969$	33.2803	+	20.3391i	1.06912	+	0.653387i
$970$	2.37435	−	2.63699i	0.0762359	−	0.0846685i
$971$	38.4672	−	17.1267i	1.23447	−	0.549622i	0.317379	−	0.948299i	$-0.397197\pi$
$971$	38.4672	−	17.1267i	1.23447	−	0.549622i	0.917091	+	0.398677i	$0.130531\pi$
$972$	0.417705	−	20.7138i	0.0133979	−	0.664396i
$973$	33.1602	+	8.65698i	1.06307	+	0.277530i
$974$	−27.0788	−	8.79844i	−0.867661	−	0.281920i
$975$	3.92788	+	5.70039i	0.125793	+	0.182559i
$976$	−3.50161	−	0.368034i	−0.112084	−	0.0117805i
$977$	6.22804	+	5.60775i	0.199253	+	0.179408i	0.762717	−	0.646733i	$-0.223865\pi$
$977$	6.22804	+	5.60775i	0.199253	+	0.179408i	−0.563464	+	0.826141i	$0.690532\pi$
$978$	−0.583037	+	23.3386i	−0.0186435	+	0.746285i
$979$	−3.84328	−	21.7683i	−0.122832	−	0.695717i
$980$	11.0545	−	1.30590i	0.353122	−	0.0417153i
$981$	25.4477	+	6.75310i	0.812484	+	0.215610i
$982$	31.4788	−	14.0153i	1.00453	−	0.447245i
$983$	−23.4041	−	10.4202i	−0.746475	−	0.332352i	−0.00199625	−	0.999998i	$-0.500635\pi$
$983$	−23.4041	−	10.4202i	−0.746475	−	0.332352i	−0.744479	+	0.667646i	$0.767302\pi$
$984$	36.3605	−	31.1305i	1.15913	−	0.992405i
$985$	−4.72646	+	4.25572i	−0.150597	+	0.135599i
$986$	1.62780	−	1.18266i	0.0518396	−	0.0376637i
$987$	3.63630	−	51.2000i	0.115745	−	1.62971i
$988$	2.70383	+	8.32152i	0.0860202	+	0.264743i
$989$	−6.28731	−	3.62998i	−0.199925	−	0.115427i
$990$	4.14428	+	8.82683i	0.131714	+	0.280535i
$991$	24.6840	+	42.7540i	0.784114	+	1.35812i	0.929527	+	0.368754i	$0.120215\pi$
$991$	24.6840	+	42.7540i	0.784114	+	1.35812i	−0.145414	+	0.989371i	$0.546451\pi$
$992$	−5.95573	−	1.26593i	−0.189095	−	0.0401933i
$993$	3.02808	−	23.2164i	0.0960932	−	0.736751i
$994$	3.73550	+	22.6412i	0.118483	+	0.718136i
$995$	25.4234	+	8.26056i	0.805975	+	0.261877i
$996$	−5.40528	+	15.3226i	−0.171273	+	0.485516i
$997$	−23.3450	+	52.4337i	−0.739343	+	1.66059i	0.0113444	+	0.999936i	$0.496389\pi$
$997$	−23.3450	+	52.4337i	−0.739343	+	1.66059i	−0.750688	+	0.660657i	$0.770278\pi$
$998$	16.6806	+	1.75320i	0.528014	+	0.0554965i
$999$	3.63103	+	1.06132i	0.114881	+	0.0335785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.bc.a.5.18	yes	224
3.2	odd	2	inner	231.2.bc.a.5.11	✓	224
7.3	odd	6	inner	231.2.bc.a.38.18	yes	224
11.9	even	5	inner	231.2.bc.a.152.11	yes	224
21.17	even	6	inner	231.2.bc.a.38.11	yes	224
33.20	odd	10	inner	231.2.bc.a.152.18	yes	224
77.31	odd	30	inner	231.2.bc.a.185.11	yes	224
231.185	even	30	inner	231.2.bc.a.185.18	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.bc.a.5.11	✓	224	3.2	odd	2	inner
231.2.bc.a.5.18	yes	224	1.1	even	1	trivial
231.2.bc.a.38.11	yes	224	21.17	even	6	inner
231.2.bc.a.38.18	yes	224	7.3	odd	6	inner
231.2.bc.a.152.11	yes	224	11.9	even	5	inner
231.2.bc.a.152.18	yes	224	33.20	odd	10	inner
231.2.bc.a.185.11	yes	224	77.31	odd	30	inner
231.2.bc.a.185.18	yes	224	231.185	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.170302 - 0.801208i) q^{2} +(1.59941 - 0.664752i) q^{3} +(1.21416 + 0.540578i) q^{4} +(0.800599 + 0.889155i) q^{5} +(-0.260223 - 1.39467i) q^{6} +(-2.04538 + 1.67822i) q^{7} +(1.60281 - 2.20608i) q^{8} +(2.11621 - 2.12642i) q^{9} +O(q^{10})\)	\(q+(0.170302 - 0.801208i) q^{2} +(1.59941 - 0.664752i) q^{3} +(1.21416 + 0.540578i) q^{4} +(0.800599 + 0.889155i) q^{5} +(-0.260223 - 1.39467i) q^{6} +(-2.04538 + 1.67822i) q^{7} +(1.60281 - 2.20608i) q^{8} +(2.11621 - 2.12642i) q^{9} +(0.848742 - 0.490022i) q^{10} +(-2.54021 + 2.13245i) q^{11} +(2.30129 + 0.0574900i) q^{12} +(-1.06522 + 0.346110i) q^{13} +(0.996271 + 1.92458i) q^{14} +(1.87155 + 0.889921i) q^{15} +(0.284068 + 0.315489i) q^{16} +(-3.74736 + 0.796526i) q^{17} +(-1.34331 - 2.05766i) q^{18} +(-2.39074 - 5.36970i) q^{19} +(0.491396 + 1.51236i) q^{20} +(-2.15579 + 4.04383i) q^{21} +(1.27593 + 2.39840i) q^{22} +(-2.51812 - 1.45384i) q^{23} +(1.09705 - 4.59389i) q^{24} +(0.373004 - 3.54890i) q^{25} +(0.0958974 + 0.912403i) q^{26} +(1.97114 - 4.80777i) q^{27} +(-3.39063 + 0.931938i) q^{28} +(-0.376877 - 0.518726i) q^{29} +(1.03174 - 1.34795i) q^{30} +(-0.779950 - 0.702270i) q^{31} +(5.02421 - 2.90073i) q^{32} +(-2.64529 + 5.09926i) q^{33} +3.13807i q^{34} +(-3.12973 - 0.475079i) q^{35} +(3.71891 - 1.43784i) q^{36} +(0.0760999 + 0.724042i) q^{37} +(-4.70939 + 1.00101i) q^{38} +(-1.47364 + 1.26168i) q^{39} +(3.24475 - 0.341037i) q^{40} +(8.19908 + 5.95698i) q^{41} +(2.87281 + 2.41591i) q^{42} +2.49683 q^{43} +(-4.23698 + 1.21594i) q^{44} +(3.58495 + 0.179228i) q^{45} +(-1.59367 + 1.76995i) q^{46} +(-10.2325 + 4.55581i) q^{47} +(0.664062 + 0.315761i) q^{48} +(1.36716 - 6.86519i) q^{49} +(-2.77988 - 0.903238i) q^{50} +(-5.46406 + 3.76504i) q^{51} +(-1.48044 - 0.155601i) q^{52} +(5.80813 + 5.22966i) q^{53} +(-3.51633 - 2.39806i) q^{54} +(-3.92977 - 0.551409i) q^{55} +(0.423930 + 7.20213i) q^{56} +(-7.39329 - 6.99908i) q^{57} +(-0.479790 + 0.213616i) q^{58} +(-0.257624 - 0.114702i) q^{59} +(1.79129 + 2.09223i) q^{60} +(-6.16333 + 5.54949i) q^{61} +(-0.695492 + 0.505305i) q^{62} +(-0.759850 + 7.90080i) q^{63} +(-1.20608 - 3.71193i) q^{64} +(-1.16056 - 0.670047i) q^{65} +(3.63507 + 2.98784i) q^{66} +(5.36541 + 9.29317i) q^{67} +(-4.98048 - 1.05863i) q^{68} +(-4.99394 - 0.651352i) q^{69} +(-0.913636 + 2.42666i) q^{70} +(10.0704 + 3.27208i) q^{71} +(-1.29917 - 8.07676i) q^{72} +(0.516493 - 1.16006i) q^{73} +(0.593068 + 0.0623340i) q^{74} +(-1.76255 - 5.92409i) q^{75} -7.81205i q^{76} +(1.61699 - 8.62469i) q^{77} +(0.759901 + 1.39556i) q^{78} +(12.1648 + 2.58570i) q^{79} +(-0.0530945 + 0.505161i) q^{80} +(-0.0433233 - 8.99990i) q^{81} +(6.16910 - 5.55468i) q^{82} +(-2.18111 + 6.71278i) q^{83} +(-4.80348 + 3.74447i) q^{84} +(-3.70837 - 2.69429i) q^{85} +(0.425215 - 2.00048i) q^{86} +(-0.947604 - 0.579125i) q^{87} +(0.632865 + 9.02180i) q^{88} +(-3.33245 + 5.77196i) q^{89} +(0.754124 - 2.84177i) q^{90} +(1.59792 - 2.49559i) q^{91} +(-2.27148 - 3.12643i) q^{92} +(-1.71429 - 0.604743i) q^{93} +(1.90753 + 8.97424i) q^{94} +(2.86047 - 6.42472i) q^{95} +(6.10749 - 7.97931i) q^{96} +(3.44346 - 1.11885i) q^{97} +(-5.26762 - 2.26453i) q^{98} +(-0.841144 + 9.91426i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 9 q^{3} - 30 q^{4} - 16 q^{7} + 3 q^{9}+O(q^{10}) \) 224 * q - 9 * q^3 - 30 * q^4 - 16 * q^7 + 3 * q^9	\( 224 q - 9 q^{3} - 30 q^{4} - 16 q^{7} + 3 q^{9} - 60 q^{10} - 12 q^{12} - 36 q^{15} + 18 q^{16} + 13 q^{18} - 18 q^{19} - 6 q^{21} + 20 q^{22} - 51 q^{24} - 18 q^{25} - 26 q^{28} - 15 q^{30} - 36 q^{31} + 60 q^{33} - 32 q^{36} - 10 q^{37} + 9 q^{39} - 114 q^{42} - 96 q^{43} + 24 q^{45} - 54 q^{46} - 56 q^{49} - 29 q^{51} - 30 q^{52} - 96 q^{54} + 68 q^{57} - 64 q^{58} + 125 q^{60} - 18 q^{61} - 26 q^{63} + 56 q^{64} + 135 q^{66} + 48 q^{67} - 44 q^{70} + 19 q^{72} + 30 q^{73} + 63 q^{75} + 28 q^{78} + 30 q^{79} + 31 q^{81} + 54 q^{82} + 99 q^{84} - 248 q^{85} + 102 q^{87} + 82 q^{88} - 144 q^{91} + 34 q^{93} + 162 q^{94} - 87 q^{96} - 100 q^{99}+O(q^{100}) \) 224 * q - 9 * q^3 - 30 * q^4 - 16 * q^7 + 3 * q^9 - 60 * q^10 - 12 * q^12 - 36 * q^15 + 18 * q^16 + 13 * q^18 - 18 * q^19 - 6 * q^21 + 20 * q^22 - 51 * q^24 - 18 * q^25 - 26 * q^28 - 15 * q^30 - 36 * q^31 + 60 * q^33 - 32 * q^36 - 10 * q^37 + 9 * q^39 - 114 * q^42 - 96 * q^43 + 24 * q^45 - 54 * q^46 - 56 * q^49 - 29 * q^51 - 30 * q^52 - 96 * q^54 + 68 * q^57 - 64 * q^58 + 125 * q^60 - 18 * q^61 - 26 * q^63 + 56 * q^64 + 135 * q^66 + 48 * q^67 - 44 * q^70 + 19 * q^72 + 30 * q^73 + 63 * q^75 + 28 * q^78 + 30 * q^79 + 31 * q^81 + 54 * q^82 + 99 * q^84 - 248 * q^85 + 102 * q^87 + 82 * q^88 - 144 * q^91 + 34 * q^93 + 162 * q^94 - 87 * q^96 - 100 * q^99

Introduction

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