LMFDB - Embedded newform 69.2.e.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.1
Root			$0.142315 - 0.989821i$ of defining polynomial
Character	$\chi$	$=$	69.31
Dual form			69.2.e.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0336545 - 0.234072i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(1.86533 + 0.547710i) q^{4} +(-0.788201 - 0.909632i) q^{5} +(-0.226900 + 0.0666238i) q^{6} +(0.0566239 + 0.0363899i) q^{7} +(0.387454 - 0.848406i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.0336545 - 0.234072i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(1.86533 + 0.547710i) q^{4} +(-0.788201 - 0.909632i) q^{5} +(-0.226900 + 0.0666238i) q^{6} +(0.0566239 + 0.0363899i) q^{7} +(0.387454 - 0.848406i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.239446 + 0.153882i) q^{10} +(0.272084 + 1.89238i) q^{11} +(-0.276671 - 1.92429i) q^{12} +(-3.64444 + 2.34214i) q^{13} +(0.0104235 - 0.0120294i) q^{14} +(-0.500000 + 1.09485i) q^{15} +(3.08538 + 1.98285i) q^{16} +(-6.53922 + 1.92009i) q^{17} +(0.154861 + 0.178719i) q^{18} +(-0.374908 - 0.110083i) q^{19} +(-0.972039 - 2.12847i) q^{20} +(0.00957906 - 0.0666238i) q^{21} +0.452111 q^{22} +(4.60914 - 1.32509i) q^{23} -0.932691 q^{24} +(0.505404 - 3.51516i) q^{25} +(0.425577 + 0.931884i) q^{26} +(0.959493 + 0.281733i) q^{27} +(0.0856910 + 0.0988927i) q^{28} +(1.99138 - 0.584723i) q^{29} +(0.239446 + 0.153882i) q^{30} +(1.55505 - 3.40508i) q^{31} +(1.78953 - 2.06523i) q^{32} +(1.60835 - 1.03362i) q^{33} +(0.229365 + 1.59527i) q^{34} +(-0.0115295 - 0.0801894i) q^{35} +(-1.63546 + 1.05105i) q^{36} +(-2.17398 + 2.50891i) q^{37} +(-0.0383846 + 0.0840506i) q^{38} +(3.64444 + 2.34214i) q^{39} +(-1.07713 + 0.316273i) q^{40} +(2.92796 + 3.37905i) q^{41} +(-0.0152724 - 0.00448438i) q^{42} +(-4.07807 - 8.92974i) q^{43} +(-0.528952 + 3.67894i) q^{44} +1.20362 q^{45} +(-0.155048 - 1.12346i) q^{46} +12.1974 q^{47} +(0.521953 - 3.63026i) q^{48} +(-2.90602 - 6.36330i) q^{49} +(-0.805791 - 0.236602i) q^{50} +(4.46306 + 5.15065i) q^{51} +(-8.08089 + 2.37276i) q^{52} +(-6.34104 - 4.07514i) q^{53} +(0.0982369 - 0.215109i) q^{54} +(1.50692 - 1.73907i) q^{55} +(0.0528126 - 0.0339406i) q^{56} +(0.0556075 + 0.386758i) q^{57} +(-0.0698483 - 0.485806i) q^{58} +(-5.88325 + 3.78094i) q^{59} +(-1.53232 + 1.76840i) q^{60} +(-3.54854 + 7.77021i) q^{61} +(-0.744699 - 0.478589i) q^{62} +(-0.0645824 + 0.0189631i) q^{63} +(4.38034 + 5.05518i) q^{64} +(5.00303 + 1.46902i) q^{65} +(-0.187814 - 0.411254i) q^{66} +(-0.355322 + 2.47132i) q^{67} -13.2494 q^{68} +(-3.12005 - 3.64216i) q^{69} -0.0191581 q^{70} +(-1.74566 + 12.1413i) q^{71} +(0.387454 + 0.848406i) q^{72} +(-4.64395 - 1.36359i) q^{73} +(0.514101 + 0.593304i) q^{74} +(-3.40746 + 1.00052i) q^{75} +(-0.639033 - 0.410682i) q^{76} +(-0.0534573 + 0.117055i) q^{77} +(0.670880 - 0.774237i) q^{78} +(8.33427 - 5.35611i) q^{79} +(-0.628231 - 4.36944i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(0.889479 - 0.571633i) q^{82} +(8.44098 - 9.74141i) q^{83} +(0.0543586 - 0.119029i) q^{84} +(6.90079 + 4.43487i) q^{85} +(-2.22745 + 0.654037i) q^{86} +(-1.35913 - 1.56852i) q^{87} +(1.71093 + 0.502374i) q^{88} +(-5.92471 - 12.9733i) q^{89} +(0.0405070 - 0.281733i) q^{90} -0.291592 q^{91} +(9.32332 + 0.0527453i) q^{92} -3.74336 q^{93} +(0.410498 - 2.85507i) q^{94} +(0.195368 + 0.427796i) q^{95} +(-2.62200 - 0.769888i) q^{96} +(11.9547 + 13.7964i) q^{97} +(-1.58727 + 0.466065i) q^{98} +(-1.60835 - 1.03362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9} - 2 q^{10} + 7 q^{11} + 14 q^{12} - 30 q^{13} + q^{14} - 5 q^{15} + 12 q^{16} - 2 q^{17} - 4 q^{18} + 10 q^{19} + 4 q^{20} - 3 q^{21} + 6 q^{22} - q^{23} - 18 q^{24} + 24 q^{25} + q^{26} + q^{27} + 9 q^{28} - 14 q^{29} + 2 q^{30} - 28 q^{31} + 23 q^{32} - 7 q^{33} - 8 q^{34} - 4 q^{35} - 3 q^{36} + 19 q^{37} - 15 q^{38} + 30 q^{39} - 13 q^{40} + 19 q^{41} + 21 q^{42} - 24 q^{43} + 54 q^{44} - 6 q^{45} + 18 q^{46} + 26 q^{47} + 10 q^{48} - 13 q^{49} - 36 q^{50} + 24 q^{51} - 57 q^{52} - q^{53} + 4 q^{54} - 24 q^{55} - 10 q^{56} + q^{57} + 10 q^{58} + 2 q^{59} + 7 q^{60} + 30 q^{61} - 24 q^{62} - 8 q^{63} + 13 q^{64} - 4 q^{65} - 28 q^{66} + 4 q^{67} - 50 q^{68} + q^{69} + 6 q^{70} - 14 q^{71} - 15 q^{72} - 26 q^{73} - 12 q^{74} - 13 q^{75} + 19 q^{76} - 43 q^{77} + 10 q^{78} + 20 q^{79} - 5 q^{80} - q^{81} + 10 q^{82} + 18 q^{83} - 42 q^{84} + 21 q^{85} + 14 q^{86} - 8 q^{87} - 38 q^{88} - 5 q^{89} + 9 q^{90} + 46 q^{91} + 52 q^{92} - 16 q^{93} - 6 q^{94} + 5 q^{95} - q^{96} + 15 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9 - 2 * q^10 + 7 * q^11 + 14 * q^12 - 30 * q^13 + q^14 - 5 * q^15 + 12 * q^16 - 2 * q^17 - 4 * q^18 + 10 * q^19 + 4 * q^20 - 3 * q^21 + 6 * q^22 - q^23 - 18 * q^24 + 24 * q^25 + q^26 + q^27 + 9 * q^28 - 14 * q^29 + 2 * q^30 - 28 * q^31 + 23 * q^32 - 7 * q^33 - 8 * q^34 - 4 * q^35 - 3 * q^36 + 19 * q^37 - 15 * q^38 + 30 * q^39 - 13 * q^40 + 19 * q^41 + 21 * q^42 - 24 * q^43 + 54 * q^44 - 6 * q^45 + 18 * q^46 + 26 * q^47 + 10 * q^48 - 13 * q^49 - 36 * q^50 + 24 * q^51 - 57 * q^52 - q^53 + 4 * q^54 - 24 * q^55 - 10 * q^56 + q^57 + 10 * q^58 + 2 * q^59 + 7 * q^60 + 30 * q^61 - 24 * q^62 - 8 * q^63 + 13 * q^64 - 4 * q^65 - 28 * q^66 + 4 * q^67 - 50 * q^68 + q^69 + 6 * q^70 - 14 * q^71 - 15 * q^72 - 26 * q^73 - 12 * q^74 - 13 * q^75 + 19 * q^76 - 43 * q^77 + 10 * q^78 + 20 * q^79 - 5 * q^80 - q^81 + 10 * q^82 + 18 * q^83 - 42 * q^84 + 21 * q^85 + 14 * q^86 - 8 * q^87 - 38 * q^88 - 5 * q^89 + 9 * q^90 + 46 * q^91 + 52 * q^92 - 16 * q^93 - 6 * q^94 + 5 * q^95 - q^96 + 15 * q^97 + 58 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	0.0336545	−	0.234072i	0.0237973	−	0.165514i	−0.974457	−	0.224573i	$-0.927901\pi$
$2$	0.0336545	−	0.234072i	0.0237973	−	0.165514i	0.998254	+	0.0590597i	$0.0188102\pi$
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$	1.86533	+	0.547710i	0.932664	+	0.273855i
$5$	−0.788201	−	0.909632i	−0.352494	−	0.406800i	0.551617	−	0.834098i	$-0.314011\pi$
$5$	−0.788201	−	0.909632i	−0.352494	−	0.406800i	−0.904111	+	0.427298i	$0.859466\pi$
$6$	−0.226900	+	0.0666238i	−0.0926315	+	0.0271991i
$7$	0.0566239	+	0.0363899i	0.0214018	+	0.0137541i	0.551298	−	0.834308i	$-0.314133\pi$
$7$	0.0566239	+	0.0363899i	0.0214018	+	0.0137541i	−0.529896	+	0.848063i	$0.677769\pi$
$8$	0.387454	−	0.848406i	0.136986	−	0.299957i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	−0.239446	+	0.153882i	−0.0757194	+	0.0486619i
$11$	0.272084	+	1.89238i	0.0820363	+	0.570575i	0.988835	+	0.149012i	$0.0476093\pi$
$11$	0.272084	+	1.89238i	0.0820363	+	0.570575i	−0.906799	+	0.421563i	$0.861482\pi$
$12$	−0.276671	−	1.92429i	−0.0798681	−	0.555495i
$13$	−3.64444	+	2.34214i	−1.01079	+	0.649592i	−0.937596	−	0.347726i	$-0.886954\pi$
$13$	−3.64444	+	2.34214i	−1.01079	+	0.649592i	−0.0731888	+	0.997318i	$0.523318\pi$
$14$	0.0104235	−	0.0120294i	0.00278580	−	0.00321498i
$15$	−0.500000	+	1.09485i	−0.129099	+	0.282688i
$16$	3.08538	+	1.98285i	0.771344	+	0.495713i
$17$	−6.53922	+	1.92009i	−1.58599	+	0.465690i	−0.951605	−	0.307324i	$-0.900566\pi$
$17$	−6.53922	+	1.92009i	−1.58599	+	0.465690i	−0.634389	+	0.773014i	$0.718748\pi$
$18$	0.154861	+	0.178719i	0.0365010	+	0.0421244i
$19$	−0.374908	−	0.110083i	−0.0860098	−	0.0252548i	0.238445	−	0.971156i	$-0.423362\pi$
$19$	−0.374908	−	0.110083i	−0.0860098	−	0.0252548i	−0.324454	+	0.945901i	$0.605181\pi$
$20$	−0.972039	−	2.12847i	−0.217354	−	0.475940i
$21$	0.00957906	−	0.0666238i	0.00209032	−	0.0145385i
$22$	0.452111			0.0963903
$23$	4.60914	−	1.32509i	0.961071	−	0.276300i
$23$	4.60914	−	1.32509i	0.961071	−	0.276300i
$24$	−0.932691			−0.190385
$25$	0.505404	−	3.51516i	0.101081	−	0.703032i
$26$	0.425577	+	0.931884i	0.0834625	+	0.182757i
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$	0.0856910	+	0.0988927i	0.0161941	+	0.0186890i
$29$	1.99138	−	0.584723i	0.369791	−	0.108580i	−0.0915568	−	0.995800i	$-0.529184\pi$
$29$	1.99138	−	0.584723i	0.369791	−	0.108580i	0.461348	+	0.887219i	$0.347366\pi$
$30$	0.239446	+	0.153882i	0.0437166	+	0.0280950i
$31$	1.55505	−	3.40508i	0.279295	−	0.611570i	−0.717047	−	0.697025i	$-0.754507\pi$
$31$	1.55505	−	3.40508i	0.279295	−	0.611570i	0.996342	+	0.0854542i	$0.0272341\pi$
$32$	1.78953	−	2.06523i	0.316348	−	0.365084i
$33$	1.60835	−	1.03362i	0.279977	−	0.179930i
$34$	0.229365	+	1.59527i	0.0393357	+	0.273586i
$35$	−0.0115295	−	0.0801894i	−0.00194884	−	0.0135545i
$36$	−1.63546	+	1.05105i	−0.272577	+	0.175175i
$37$	−2.17398	+	2.50891i	−0.357400	+	0.412462i	−0.905767	−	0.423776i	$-0.860704\pi$
$37$	−2.17398	+	2.50891i	−0.357400	+	0.412462i	0.548367	+	0.836238i	$0.315250\pi$
$38$	−0.0383846	+	0.0840506i	−0.00622681	+	0.0136348i
$39$	3.64444	+	2.34214i	0.583577	+	0.375042i
$40$	−1.07713	+	0.316273i	−0.170309	+	0.0500072i
$41$	2.92796	+	3.37905i	0.457271	+	0.527718i	0.936827	−	0.349793i	$-0.113748\pi$
$41$	2.92796	+	3.37905i	0.457271	+	0.527718i	−0.479557	+	0.877511i	$0.659202\pi$
$42$	−0.0152724	−	0.00448438i	−0.00235658	−	0.000691954i
$43$	−4.07807	−	8.92974i	−0.621901	−	1.36177i	−0.914129	−	0.405424i	$-0.867124\pi$
$43$	−4.07807	−	8.92974i	−0.621901	−	1.36177i	0.292228	−	0.956349i	$-0.405603\pi$
$44$	−0.528952	+	3.67894i	−0.0797425	+	0.554621i
$45$	1.20362			0.179424
$46$	−0.155048	−	1.12346i	−0.0228606	−	0.165646i
$47$	12.1974			1.77918			0.889589	−	0.456762i	$-0.150991\pi$
$47$	12.1974			1.77918			0.889589	+	0.456762i	$0.150991\pi$
$48$	0.521953	−	3.63026i	0.0753374	−	0.523983i
$49$	−2.90602	−	6.36330i	−0.415146	−	0.909043i
$50$	−0.805791	−	0.236602i	−0.113956	−	0.0334605i
$51$	4.46306	+	5.15065i	0.624954	+	0.721235i
$52$	−8.08089	+	2.37276i	−1.12062	+	0.329043i
$53$	−6.34104	−	4.07514i	−0.871008	−	0.559763i	0.0270527	−	0.999634i	$-0.491388\pi$
$53$	−6.34104	−	4.07514i	−0.871008	−	0.559763i	−0.898061	+	0.439871i	$0.855024\pi$
$54$	0.0982369	−	0.215109i	0.0133683	−	0.0292726i
$55$	1.50692	−	1.73907i	0.203193	−	0.234497i
$56$	0.0528126	−	0.0339406i	0.00705738	−	0.00453550i
$57$	0.0556075	+	0.386758i	0.00736539	+	0.0512274i
$58$	−0.0698483	−	0.485806i	−0.00917153	−	0.0637894i
$59$	−5.88325	+	3.78094i	−0.765934	+	0.492236i	−0.864339	−	0.502910i	$-0.832263\pi$
$59$	−5.88325	+	3.78094i	−0.765934	+	0.492236i	0.0984042	+	0.995147i	$0.468626\pi$
$60$	−1.53232	+	1.76840i	−0.197822	+	0.228299i
$61$	−3.54854	+	7.77021i	−0.454344	+	0.994874i	0.534397	+	0.845234i	$0.320539\pi$
$61$	−3.54854	+	7.77021i	−0.454344	+	0.994874i	−0.988741	+	0.149640i	$0.952188\pi$
$62$	−0.744699	−	0.478589i	−0.0945769	−	0.0607809i
$63$	−0.0645824	+	0.0189631i	−0.00813662	+	0.00238913i
$64$	4.38034	+	5.05518i	0.547542	+	0.631898i
$65$	5.00303	+	1.46902i	0.620550	+	0.182210i
$66$	−0.187814	−	0.411254i	−0.0231183	−	0.0506219i
$67$	−0.355322	+	2.47132i	−0.0434095	+	0.301920i	0.956537	+	0.291610i	$0.0941909\pi$
$67$	−0.355322	+	2.47132i	−0.0434095	+	0.301920i	−0.999947	+	0.0103100i	$0.996718\pi$
$68$	−13.2494			−1.60673
$69$	−3.12005	−	3.64216i	−0.375610	−	0.438464i
$70$	−0.0191581			−0.00228983
$71$	−1.74566	+	12.1413i	−0.207172	+	1.44091i	0.575155	+	0.818044i	$0.304942\pi$
$71$	−1.74566	+	12.1413i	−0.207172	+	1.44091i	−0.782327	+	0.622868i	$0.785968\pi$
$72$	0.387454	+	0.848406i	0.0456619	+	0.0999856i
$73$	−4.64395	−	1.36359i	−0.543533	−	0.159596i	−0.00157129	−	0.999999i	$-0.500500\pi$
$73$	−4.64395	−	1.36359i	−0.543533	−	0.159596i	−0.541962	+	0.840403i	$0.682318\pi$
$74$	0.514101	+	0.593304i	0.0597630	+	0.0689701i
$75$	−3.40746	+	1.00052i	−0.393459	+	0.115530i
$76$	−0.639033	−	0.410682i	−0.0733021	−	0.0471084i
$77$	−0.0534573	+	0.117055i	−0.00609203	+	0.0133397i
$78$	0.670880	−	0.774237i	0.0759622	−	0.0876651i
$79$	8.33427	−	5.35611i	0.937679	−	0.602610i	0.0199432	−	0.999801i	$-0.493651\pi$
$79$	8.33427	−	5.35611i	0.937679	−	0.602610i	0.917736	+	0.397191i	$0.130015\pi$
$80$	−0.628231	−	4.36944i	−0.0702383	−	0.488518i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	0.889479	−	0.571633i	0.0982265	−	0.0631263i
$83$	8.44098	−	9.74141i	0.926518	−	1.06926i	−0.0709025	−	0.997483i	$-0.522588\pi$
$83$	8.44098	−	9.74141i	0.926518	−	1.06926i	0.997421	−	0.0717758i	$-0.0228666\pi$
$84$	0.0543586	−	0.119029i	0.00593101	−	0.0129871i
$85$	6.90079	+	4.43487i	0.748496	+	0.481029i
$86$	−2.22745	+	0.654037i	−0.240192	+	0.0705266i
$87$	−1.35913	−	1.56852i	−0.145714	−	0.168163i
$88$	1.71093	+	0.502374i	0.182386	+	0.0535533i
$89$	−5.92471	−	12.9733i	−0.628018	−	1.37517i	−0.909541	−	0.415613i	$-0.863567\pi$
$89$	−5.92471	−	12.9733i	−0.628018	−	1.37517i	0.281523	−	0.959554i	$-0.409160\pi$
$90$	0.0405070	−	0.281733i	0.00426982	−	0.0296972i
$91$	−0.291592			−0.0305672
$92$	9.32332	+	0.0527453i	0.972023	+	0.00549908i
$93$	−3.74336			−0.388168
$94$	0.410498	−	2.85507i	0.0423396	−	0.294478i
$95$	0.195368	+	0.427796i	0.0200443	+	0.0438909i
$96$	−2.62200	−	0.769888i	−0.267606	−	0.0785764i
$97$	11.9547	+	13.7964i	1.21381	+	1.40081i	0.890786	+	0.454424i	$0.150155\pi$
$97$	11.9547	+	13.7964i	1.21381	+	1.40081i	0.323027	+	0.946390i	$0.395300\pi$
$98$	−1.58727	+	0.466065i	−0.160339	+	0.0470797i
$99$	−1.60835	−	1.03362i	−0.161645	−	0.103883i
$100$	2.86803	−	6.28012i	0.286803	−	0.628012i
$101$	6.25301	−	7.21636i	0.622198	−	0.718054i	−0.353925	−	0.935274i	$-0.615153\pi$
$101$	6.25301	−	7.21636i	0.622198	−	0.718054i	0.976123	+	0.217219i	$0.0696987\pi$
$102$	1.35582	−	0.871335i	0.134247	−	0.0862751i
$103$	0.501188	+	3.48584i	0.0493836	+	0.343470i	0.999501	+	0.0315786i	$0.0100535\pi$
$103$	0.501188	+	3.48584i	0.0493836	+	0.343470i	−0.950118	+	0.311892i	$0.899037\pi$
$104$	0.575031	+	3.99943i	0.0563865	+	0.392177i
$105$	−0.0681534	+	0.0437995i	−0.00665109	+	0.00427439i
$106$	−1.16728	+	1.34711i	−0.113376	+	0.130843i
$107$	−5.20442	+	11.3961i	−0.503131	+	1.10170i	0.472309	+	0.881433i	$0.343421\pi$
$107$	−5.20442	+	11.3961i	−0.503131	+	1.10170i	−0.975439	+	0.220269i	$0.929306\pi$
$108$	1.63546	+	1.05105i	0.157372	+	0.101137i
$109$	−1.42584	+	0.418664i	−0.136571	+	0.0401007i	−0.349303	−	0.937010i	$-0.613582\pi$
$109$	−1.42584	+	0.418664i	−0.136571	+	0.0401007i	0.212733	+	0.977110i	$0.431764\pi$
$110$	−0.356354	−	0.411254i	−0.0339770	−	0.0392116i
$111$	3.18529	+	0.935285i	0.302334	+	0.0887733i
$112$	0.102550	+	0.224553i	0.00969007	+	0.0212183i
$113$	1.00141	−	6.96496i	0.0942048	−	0.655209i	−0.886933	−	0.461898i	$-0.847169\pi$
$113$	1.00141	−	6.96496i	0.0942048	−	0.655209i	0.981138	−	0.193310i	$-0.0619224\pi$
$114$	0.0924007			0.00865412
$115$	−4.83827	−	3.14818i	−0.451171	−	0.293570i
$116$	4.03485			0.374626
$117$	0.616529	−	4.28806i	0.0569982	−	0.396431i
$118$	0.687013	+	1.50435i	0.0632447	+	0.138487i
$119$	−0.440148	−	0.129239i	−0.0403483	−	0.0118473i
$120$	0.735148	+	0.848406i	0.0671095	+	0.0774485i
$121$	7.04733	−	2.06928i	0.640667	−	0.188117i
$122$	1.69936	+	1.09212i	0.153853	+	0.0988755i
$123$	1.85737	−	4.06707i	0.167473	−	0.366716i
$124$	4.76567	−	5.49988i	0.427970	−	0.493904i
$125$	−8.65859	+	5.56454i	−0.774448	+	0.497708i
$126$	0.00226524	+	0.0157551i	0.000201804	+	0.00140358i
$127$	0.630279	+	4.38368i	0.0559282	+	0.388989i	0.998489	+	0.0549542i	$0.0175013\pi$
$127$	0.630279	+	4.38368i	0.0559282	+	0.388989i	−0.942561	+	0.334035i	$0.891590\pi$
$128$	5.92847	−	3.80999i	0.524007	−	0.336759i
$129$	−6.42868	+	7.41909i	−0.566014	+	0.653215i
$130$	0.512231	−	1.12163i	0.0449256	−	0.0983734i
$131$	−10.4167	−	6.69443i	−0.910115	−	0.584895i	−0.000341374	−	1.00000i	$-0.500109\pi$
$131$	−10.4167	−	6.69443i	−0.910115	−	0.584895i	−0.909774	+	0.415104i	$0.863745\pi$
$132$	3.56622	−	1.04714i	0.310399	−	0.0911415i
$133$	−0.0172228	−	0.0198762i	−0.00149341	−	0.00172349i
$134$	0.566509	+	0.166342i	0.0489389	+	0.0143698i
$135$	−0.500000	−	1.09485i	−0.0430331	−	0.0942295i
$136$	−0.904632	+	6.29186i	−0.0775716	+	0.539522i
$137$	−7.43769			−0.635445			−0.317722	−	0.948184i	$-0.602918\pi$
$137$	−7.43769			−0.635445			−0.317722	+	0.948184i	$0.602918\pi$
$138$	−0.957530	+	0.607740i	−0.0815104	+	0.0517343i
$139$	−1.35701			−0.115100			−0.0575500	−	0.998343i	$-0.518329\pi$
$139$	−1.35701			−0.115100			−0.0575500	+	0.998343i	$0.518329\pi$
$140$	0.0224142	−	0.155895i	0.00189435	−	0.0131755i
$141$	−5.06699	−	11.0952i	−0.426718	−	0.934382i
$142$	2.78320	+	0.817220i	0.233561	+	0.0685796i
$143$	−5.42382	−	6.25942i	−0.453562	−	0.523439i
$144$	−3.51903	+	1.03328i	−0.293253	+	0.0861067i
$145$	−2.10149	−	1.35055i	−0.174519	−	0.112157i
$146$	−0.475467	+	1.04113i	−0.0393499	+	0.0861643i
$147$	−4.58106	+	5.28682i	−0.377839	+	0.436050i
$148$	−5.42934	+	3.48923i	−0.446289	+	0.286813i
$149$	3.03955	+	21.1405i	0.249010	+	1.73190i	0.603960	+	0.797015i	$0.293589\pi$
$149$	3.03955	+	21.1405i	0.249010	+	1.73190i	−0.354950	+	0.934885i	$0.615502\pi$
$150$	0.119517	+	0.831262i	0.00975855	+	0.0678722i
$151$	−12.2320	+	7.86103i	−0.995426	+	0.639721i	−0.933582	−	0.358364i	$-0.883335\pi$
$151$	−12.2320	+	7.86103i	−0.995426	+	0.639721i	−0.0618442	+	0.998086i	$0.519698\pi$
$152$	−0.238655	+	0.275422i	−0.0193574	+	0.0223397i
$153$	2.83117	−	6.19940i	0.228887	−	0.501192i
$154$	0.0256003	+	0.0164523i	0.00206293	+	0.00132576i
$155$	−4.32306	+	1.26936i	−0.347236	+	0.101958i
$156$	5.51526	+	6.36495i	0.441574	+	0.509604i
$157$	−0.0361510	−	0.0106149i	−0.00288517	−	0.000847162i	0.280290	−	0.959915i	$-0.409569\pi$
$157$	−0.0361510	−	0.0106149i	−0.00288517	−	0.000847162i	−0.283175	+	0.959068i	$0.591388\pi$
$158$	−0.973230	−	2.13108i	−0.0774260	−	0.169539i
$159$	−1.07271	+	7.46088i	−0.0850717	+	0.591686i
$160$	−3.28911			−0.260027
$161$	0.309207	+	0.0926946i	0.0243689	+	0.00730536i
$162$	−0.236479			−0.0185795
$163$	−0.0931066	+	0.647571i	−0.00729267	+	0.0507217i	−0.993143	−	0.116907i	$-0.962702\pi$
$163$	−0.0931066	+	0.647571i	−0.00729267	+	0.0507217i	0.985850	+	0.167629i	$0.0536111\pi$
$164$	3.61087	+	7.90671i	0.281962	+	0.617410i
$165$	−2.20791	−	0.648302i	−0.171886	−	0.0504702i
$166$	−1.99611	−	2.30364i	−0.154929	−	0.178797i
$167$	7.46242	−	2.19116i	0.577459	−	0.169557i	0.0200555	−	0.999799i	$-0.493616\pi$
$167$	7.46242	−	2.19116i	0.577459	−	0.169557i	0.557404	+	0.830242i	$0.311798\pi$
$168$	−0.0528126	−	0.0339406i	−0.00407458	−	0.00261857i
$169$	2.39592	−	5.24633i	0.184301	−	0.403564i
$170$	1.27032	−	1.46603i	0.0974291	−	0.112439i
$171$	0.328708	−	0.211248i	0.0251369	−	0.0161545i
$172$	−2.71604	−	18.8905i	−0.207096	−	1.44039i
$173$	−0.602858	−	4.19297i	−0.0458344	−	0.318785i	−0.999821	−	0.0189352i	$-0.993972\pi$
$173$	−0.602858	−	4.19297i	−0.0458344	−	0.318785i	0.953986	−	0.299850i	$-0.0969367\pi$
$174$	−0.412888	+	0.265347i	−0.0313010	+	0.0201159i
$175$	0.156534	−	0.180650i	0.0118329	−	0.0136559i
$176$	−2.91283	+	6.37822i	−0.219563	+	0.480776i
$177$	5.88325	+	3.78094i	0.442212	+	0.284193i
$178$	−3.23608	+	0.950199i	−0.242554	+	0.0712204i
$179$	−8.85614	−	10.2205i	−0.661939	−	0.763918i	0.321154	−	0.947027i	$-0.395929\pi$
$179$	−8.85614	−	10.2205i	−0.661939	−	0.763918i	−0.983093	+	0.183109i	$0.941384\pi$
$180$	2.24514	+	0.659232i	0.167343	+	0.0491363i
$181$	8.02218	+	17.5661i	0.596284	+	1.30568i	0.931569	+	0.363564i	$0.118440\pi$
$181$	8.02218	+	17.5661i	0.596284	+	1.30568i	−0.335285	+	0.942117i	$0.608833\pi$
$182$	−0.00981338	+	0.0682536i	−0.000727416	+	0.00505929i
$183$	8.54215			0.631454
$184$	0.661616	−	4.42383i	0.0487750	−	0.326129i
$185$	3.99572			0.293771
$186$	−0.125981	+	0.876215i	−0.00923735	+	0.0642472i
$187$	−5.41276	−	11.8523i	−0.395820	−	0.866725i
$188$	22.7522	+	6.68065i	1.65938	+	0.487237i
$189$	0.0440780	+	0.0508687i	0.00320620	+	0.00370015i
$190$	0.106710	−	0.0313329i	0.00774155	−	0.00227312i
$191$	11.9416	+	7.67438i	0.864061	+	0.555299i	0.895931	−	0.444193i	$-0.146510\pi$
$191$	11.9416	+	7.67438i	0.864061	+	0.555299i	−0.0318694	+	0.999492i	$0.510146\pi$
$192$	2.77870	−	6.08450i	0.200535	−	0.439111i
$193$	−13.9653	+	16.1169i	−1.00525	+	1.16012i	−0.0181766	+	0.999835i	$0.505786\pi$
$193$	−13.9653	+	16.1169i	−1.00525	+	1.16012i	−0.987071	+	0.160283i	$0.948759\pi$
$194$	3.63168	−	2.33394i	0.260739	−	0.167567i
$195$	−0.742064	−	5.16117i	−0.0531403	−	0.369599i
$196$	−1.93544	−	13.4613i	−0.138246	−	0.961522i
$197$	3.04057	−	1.95406i	0.216632	−	0.139221i	−0.427825	−	0.903862i	$-0.640720\pi$
$197$	3.04057	−	1.95406i	0.216632	−	0.139221i	0.644457	+	0.764641i	$0.277084\pi$
$198$	−0.296070	+	0.341683i	−0.0210407	+	0.0242823i
$199$	9.24508	−	20.2439i	0.655367	−	1.43505i	−0.231411	−	0.972856i	$-0.574334\pi$
$199$	9.24508	−	20.2439i	0.655367	−	1.43505i	0.886778	−	0.462197i	$-0.152939\pi$
$200$	−2.78646	−	1.79075i	−0.197033	−	0.126625i
$201$	2.39560	−	0.703411i	0.168973	−	0.0496148i
$202$	−1.47870	−	1.70652i	−0.104041	−	0.120070i
$203$	0.134038	+	0.0393571i	0.00940762	+	0.00276233i
$204$	5.50402	+	12.0521i	0.385358	+	0.843817i
$205$	0.765869	−	5.32673i	0.0534906	−	0.372035i
$206$	0.832805			0.0580242
$207$	−2.01691	+	4.35110i	−0.140185	+	0.302422i
$208$	−15.8886			−1.10167
$209$	0.106313	−	0.739422i	0.00735381	−	0.0511469i
$210$	0.00795857	+	0.0174268i	0.000549193	+	0.00120257i
$211$	−15.3665	−	4.51202i	−1.05788	−	0.310620i	−0.293881	−	0.955842i	$-0.594947\pi$
$211$	−15.3665	−	4.51202i	−1.05788	−	0.310620i	−0.763995	+	0.645222i	$0.776765\pi$
$212$	−9.59613	−	11.0745i	−0.659065	−	0.760601i
$213$	11.7693	−	3.45578i	0.806421	−	0.236786i
$214$	2.49235	+	1.60174i	0.170374	+	0.109493i
$215$	−4.90843	+	10.7480i	−0.334752	+	0.733006i
$216$	0.610783	−	0.704881i	0.0415585	−	0.0479611i
$217$	0.211963	−	0.136221i	0.0143890	−	0.00924726i
$218$	0.0500116	+	0.347839i	0.00338722	+	0.0235586i
$219$	0.688804	+	4.79074i	0.0465451	+	0.323728i
$220$	3.76340	−	2.41859i	0.253729	−	0.163061i
$221$	19.3347	−	22.3134i	1.30059	−	1.50096i
$222$	0.326123	−	0.714110i	0.0218879	−	0.0479279i
$223$	10.7480	+	6.90732i	0.719739	+	0.462548i	0.848546	−	0.529121i	$-0.177478\pi$
$223$	10.7480	+	6.90732i	0.719739	+	0.462548i	−0.128807	+	0.991670i	$0.541115\pi$
$224$	0.176484	−	0.0518203i	0.0117918	−	0.00346239i
$225$	2.32561	+	2.68390i	0.155041	+	0.178927i
$226$	−1.59660	−	0.468804i	−0.106204	−	0.0311844i
$227$	1.34332	+	2.94145i	0.0891590	+	0.195231i	0.948959	−	0.315401i	$-0.102139\pi$
$227$	1.34332	+	2.94145i	0.0891590	+	0.195231i	−0.859800	+	0.510632i	$0.829412\pi$
$228$	−0.108105	+	0.751888i	−0.00715944	+	0.0497950i
$229$	21.5059			1.42115			0.710575	−	0.703622i	$-0.248435\pi$
$229$	21.5059			1.42115			0.710575	+	0.703622i	$0.248435\pi$
$230$	−0.899730	+	1.02655i	−0.0593265	+	0.0676888i
$231$	0.128684			0.00846679
$232$	0.275487	−	1.91605i	0.0180866	−	0.125795i
$233$	6.78253	+	14.8517i	0.444338	+	0.972965i	0.990782	+	0.135469i	$0.0432541\pi$
$233$	6.78253	+	14.8517i	0.444338	+	0.972965i	−0.546443	+	0.837496i	$0.684019\pi$
$234$	−0.982964	−	0.288624i	−0.0642584	−	0.0188680i
$235$	−9.61402	−	11.0952i	−0.627149	−	0.723769i
$236$	−13.0451	+	3.83038i	−0.849161	+	0.249336i
$237$	−8.33427	−	5.35611i	−0.541369	−	0.347917i
$238$	−0.0450642	+	0.0986767i	−0.00292108	+	0.00639626i
$239$	−0.615635	+	0.710481i	−0.0398221	+	0.0459572i	−0.775311	−	0.631579i	$-0.782407\pi$
$239$	−0.615635	+	0.710481i	−0.0398221	+	0.0459572i	0.735489	+	0.677537i	$0.236952\pi$
$240$	−3.71361	+	2.38659i	−0.239712	+	0.154054i
$241$	1.12257	+	7.80767i	0.0723113	+	0.502936i	0.993501	+	0.113823i	$0.0363096\pi$
$241$	1.12257	+	7.80767i	0.0723113	+	0.502936i	−0.921190	+	0.389114i	$0.872781\pi$
$242$	−0.247187	−	1.71922i	−0.0158898	−	0.110516i
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$	−10.8750	+	12.5504i	−0.696201	+	0.803459i
$245$	−3.49773	+	7.65897i	−0.223462	+	0.489314i
$246$	−0.889479	−	0.571633i	−0.0567111	−	0.0364460i
$247$	1.62416	−	0.476896i	0.103343	−	0.0303442i
$248$	−2.28638	−	2.63862i	−0.145185	−	0.167553i
$249$	−12.3676	−	3.63146i	−0.783766	−	0.230134i
$250$	1.01110	+	2.21400i	0.0639477	+	0.140026i
$251$	2.00798	−	13.9658i	0.126743	−	0.881515i	−0.822901	−	0.568184i	$-0.807646\pi$
$251$	2.00798	−	13.9658i	0.126743	−	0.881515i	0.949644	−	0.313331i	$-0.101445\pi$
$252$	−0.130854			−0.00824301
$253$	3.76165	+	8.36172i	0.236493	+	0.525697i
$254$	1.04731			0.0657140
$255$	1.16741	−	8.11949i	0.0731058	−	0.508462i
$256$	4.86510	+	10.6531i	0.304069	+	0.665818i
$257$	8.15620	+	2.39488i	0.508770	+	0.149388i	0.526035	−	0.850463i	$-0.323678\pi$
$257$	8.15620	+	2.39488i	0.508770	+	0.149388i	−0.0172657	+	0.999851i	$0.505496\pi$
$258$	1.52025	+	1.75446i	0.0946465	+	0.109228i
$259$	−0.214398	+	0.0629530i	−0.0133221	+	0.00391171i
$260$	8.52770	+	5.48042i	0.528866	+	0.339881i
$261$	−0.862175	+	1.88790i	−0.0533673	+	0.116858i
$262$	−1.91755	+	2.21297i	−0.118467	+	0.136718i
$263$	−15.1341	+	9.72607i	−0.933207	+	0.599735i	−0.916461	−	0.400124i	$-0.868967\pi$
$263$	−15.1341	+	9.72607i	−0.933207	+	0.599735i	−0.0167457	+	0.999860i	$0.505331\pi$
$264$	−0.253770	−	1.76501i	−0.0156185	−	0.108629i
$265$	1.29113	+	8.98003i	0.0793137	+	0.551639i
$266$	−0.00523208	+	0.00336246i	−0.000320800	+	0.000206165i
$267$	−9.33972	+	10.7786i	−0.571582	+	0.659640i
$268$	−2.01636	+	4.41521i	−0.123169	+	0.269702i
$269$	−20.2272	−	12.9992i	−1.23327	−	0.792576i	−0.248875	−	0.968536i	$-0.580061\pi$
$269$	−20.2272	−	12.9992i	−1.23327	−	0.792576i	−0.984397	+	0.175960i	$0.943697\pi$
$270$	−0.273100	+	0.0801894i	−0.0166203	+	0.00488017i
$271$	−1.44657	−	1.66943i	−0.0878728	−	0.101411i	0.710110	−	0.704090i	$-0.248645\pi$
$271$	−1.44657	−	1.66943i	−0.0878728	−	0.101411i	−0.797983	+	0.602680i	$0.794100\pi$
$272$	−23.9832	−	7.04210i	−1.45420	−	0.426990i
$273$	0.121132	+	0.265242i	0.00733123	+	0.0160532i
$274$	−0.250311	+	1.74095i	−0.0151219	+	0.105175i
$275$	6.78955			0.409425
$276$	−3.82507	−	8.50270i	−0.230242	−	0.511802i
$277$	−1.98038			−0.118989			−0.0594947	−	0.998229i	$-0.518949\pi$
$277$	−1.98038			−0.118989			−0.0594947	+	0.998229i	$0.518949\pi$
$278$	−0.0456694	+	0.317637i	−0.00273907	+	0.0190506i
$279$	1.55505	+	3.40508i	0.0930983	+	0.203857i
$280$	−0.0725003	−	0.0212880i	−0.00433272	−	0.00127220i
$281$	−8.56440	−	9.88385i	−0.510909	−	0.589621i	0.440422	−	0.897791i	$-0.354829\pi$
$281$	−8.56440	−	9.88385i	−0.510909	−	0.589621i	−0.951331	+	0.308170i	$0.900283\pi$
$282$	−2.76759	+	0.812639i	−0.164808	+	0.0483919i
$283$	−1.02494	−	0.658690i	−0.0609264	−	0.0391550i	0.509823	−	0.860279i	$-0.329711\pi$
$283$	−1.02494	−	0.658690i	−0.0609264	−	0.0391550i	−0.570749	+	0.821124i	$0.693347\pi$
$284$	−9.90616	+	21.6915i	−0.587823	+	1.28715i
$285$	0.307978	−	0.355426i	0.0182430	−	0.0210536i
$286$	−1.64769	+	1.05891i	−0.0974299	+	0.0626144i
$287$	0.0428291	+	0.297883i	0.00252812	+	0.0175835i
$288$	0.388902	+	2.70488i	0.0229163	+	0.159386i
$289$	24.7734	−	15.9209i	1.45726	−	0.936521i
$290$	−0.386850	+	0.446448i	−0.0227166	+	0.0262164i
$291$	7.58352	−	16.6056i	0.444554	−	0.973436i
$292$	−7.91565	−	5.08708i	−0.463228	−	0.297699i
$293$	21.1173	−	6.20059i	1.23368	−	0.362242i	0.401045	−	0.916058i	$-0.368647\pi$
$293$	21.1173	−	6.20059i	1.23368	−	0.362242i	0.832639	+	0.553816i	$0.186829\pi$
$294$	1.08332	+	1.25022i	0.0631807	+	0.0729144i
$295$	8.07645	+	2.37146i	0.470229	+	0.138072i
$296$	1.28625	+	2.81650i	0.0747620	+	0.163706i
$297$	−0.272084	+	1.89238i	−0.0157879	+	0.109807i
$298$	5.05070			0.292579
$299$	−13.6942	+	15.6244i	−0.791954	+	0.903584i
$300$	−6.90402			−0.398604
$301$	0.0940363	−	0.654037i	0.00542016	−	0.0376981i
$302$	1.42838	+	3.12773i	0.0821943	+	0.179980i
$303$	−9.16182	−	2.69015i	−0.526333	−	0.154545i
$304$	−0.938454	−	1.08303i	−0.0538240	−	0.0621163i
$305$	9.86499	−	2.89662i	0.564868	−	0.165860i
$306$	−1.35582	−	0.871335i	−0.0775073	−	0.0498109i
$307$	−9.28955	+	20.3413i	−0.530183	+	1.16094i	0.435256	+	0.900307i	$0.356658\pi$
$307$	−9.28955	+	20.3413i	−0.530183	+	1.16094i	−0.965438	+	0.260631i	$0.916069\pi$
$308$	−0.163828	+	0.189067i	−0.00933496	+	0.0107731i
$309$	2.96263	−	1.90397i	0.168538	−	0.108313i
$310$	0.151632	+	1.05463i	0.00861214	+	0.0598987i
$311$	−1.64336	−	11.4298i	−0.0931863	−	0.648125i	−0.981863	−	0.189591i	$-0.939284\pi$
$311$	−1.64336	−	11.4298i	−0.0931863	−	0.648125i	0.888677	−	0.458534i	$-0.151625\pi$
$312$	3.39913	−	2.18449i	0.192438	−	0.123672i
$313$	−1.34373	+	1.55075i	−0.0759522	+	0.0876535i	−0.792454	−	0.609932i	$-0.791197\pi$
$313$	−1.34373	+	1.55075i	−0.0759522	+	0.0876535i	0.716502	+	0.697585i	$0.245742\pi$
$314$	−0.00370129	+	0.00810470i	−0.000208876	+	0.000457375i
$315$	0.0681534	+	0.0437995i	0.00384001	+	0.00246782i
$316$	18.4798	−	5.42615i	1.03957	−	0.305245i
$317$	−11.3867	−	13.1409i	−0.639539	−	0.738067i	0.339754	−	0.940514i	$-0.389656\pi$
$317$	−11.3867	−	13.1409i	−0.639539	−	0.738067i	−0.979293	+	0.202447i	$0.935111\pi$
$318$	1.71028	+	0.502184i	0.0959078	+	0.0281611i
$319$	1.64834	+	3.60937i	0.0922896	+	0.202086i
$320$	1.14577	−	7.96899i	0.0640504	−	0.445480i
$321$	12.5283			0.699259
$322$	0.0321034	−	0.0692571i	0.00178905	−	0.00385955i
$323$	2.66297			0.148172
$324$	0.276671	−	1.92429i	0.0153706	−	0.106905i
$325$	6.39108	+	13.9945i	0.354513	+	0.776276i
$326$	0.148445	+	0.0435873i	0.00822159	+	0.00241408i
$327$	0.973145	+	1.12307i	0.0538150	+	0.0621059i
$328$	4.00125	−	1.17487i	0.220932	−	0.0648715i
$329$	0.690665	+	0.443864i	0.0380776	+	0.0244710i
$330$	−0.226055	+	0.494992i	−0.0124439	+	0.0272484i
$331$	−5.11606	+	5.90425i	−0.281204	+	0.324527i	−0.878727	−	0.477325i	$-0.841606\pi$
$331$	−5.11606	+	5.90425i	−0.281204	+	0.324527i	0.597522	+	0.801852i	$0.296152\pi$
$332$	21.0807	−	13.5477i	1.15695	−	0.743528i
$333$	−0.472451	−	3.28597i	−0.0258902	−	0.180070i
$334$	−0.261746	−	1.82048i	−0.0143221	−	0.0996125i
$335$	2.52806	−	1.62468i	0.138123	−	0.0887660i
$336$	0.161660	−	0.186566i	0.00881928	−	0.0101780i
$337$	12.5682	−	27.5204i	0.684631	−	1.49913i	−0.173030	−	0.984917i	$-0.555356\pi$
$337$	12.5682	−	27.5204i	0.684631	−	1.49913i	0.857661	−	0.514216i	$-0.171917\pi$
$338$	−1.14739	−	0.737380i	−0.0624095	−	0.0401082i
$339$	−6.75155	+	1.98244i	−0.366694	+	0.107671i
$340$	10.4432	+	12.0521i	0.566363	+	0.653618i
$341$	6.86682	+	2.01628i	0.371859	+	0.109188i
$342$	−0.0383846	−	0.0840506i	−0.00207560	−	0.00454494i
$343$	0.134063	−	0.932431i	0.00723874	−	0.0503466i
$344$	−9.15611			−0.493664
$345$	−0.853799	+	5.70884i	−0.0459670	+	0.307354i
$346$	−1.00174			−0.0538541
$347$	−3.81449	+	26.5303i	−0.204772	+	1.42422i	0.585105	+	0.810958i	$0.301053\pi$
$347$	−3.81449	+	26.5303i	−0.204772	+	1.42422i	−0.789877	+	0.613265i	$0.789856\pi$
$348$	−1.67614	−	3.67022i	−0.0898503	−	0.196745i
$349$	−5.92563	−	1.73992i	−0.317191	−	0.0931358i	0.119262	−	0.992863i	$-0.461947\pi$
$349$	−5.92563	−	1.73992i	−0.317191	−	0.0931358i	−0.436453	+	0.899727i	$0.643765\pi$
$350$	−0.0370171	−	0.0427200i	−0.00197865	−	0.00228348i
$351$	−4.15667	+	1.22051i	−0.221867	+	0.0651459i
$352$	4.39511	+	2.82457i	0.234260	+	0.150550i
$353$	−6.52425	+	14.2861i	−0.347251	+	0.760373i	0.652745	+	0.757577i	$0.273617\pi$
$353$	−6.52425	+	14.2861i	−0.347251	+	0.760373i	−0.999996	+	0.00279565i	$0.999110\pi$
$354$	1.08301	−	1.24986i	0.0575613	−	0.0664292i
$355$	12.4201	−	7.98190i	0.659189	−	0.423635i
$356$	−3.94592	−	27.4445i	−0.209134	−	1.45456i
$357$	0.0652840	+	0.454060i	0.00345520	+	0.0240314i
$358$	−2.69039	+	1.72901i	−0.142191	+	0.0913808i
$359$	14.5784	−	16.8244i	0.769420	−	0.887958i	−0.226878	−	0.973923i	$-0.572852\pi$
$359$	14.5784	−	16.8244i	0.769420	−	0.887958i	0.996298	+	0.0859652i	$0.0273974\pi$
$360$	0.466346	−	1.02115i	0.0245786	−	0.0538196i
$361$	−15.8554	−	10.1896i	−0.834494	−	0.536297i
$362$	4.38172	−	1.28659i	0.230298	−	0.0676216i
$363$	−4.80986	−	5.55087i	−0.252452	−	0.291345i
$364$	−0.543916	−	0.159708i	−0.0285089	−	0.00837098i
$365$	2.42000	+	5.29907i	0.126669	+	0.277366i
$366$	0.287481	−	1.99948i	0.0150269	−	0.104514i
$367$	2.64308			0.137968			0.0689838	−	0.997618i	$-0.478024\pi$
$367$	2.64308			0.137968			0.0689838	+	0.997618i	$0.478024\pi$
$368$	16.8484	+	5.05084i	0.878282	+	0.263293i
$369$	−4.47112			−0.232757
$370$	0.134474	−	0.935285i	0.00699095	−	0.0486231i
$371$	−0.210760	−	0.461500i	−0.0109421	−	0.0239599i
$372$	−6.98260	−	2.05028i	−0.362031	−	0.106302i
$373$	10.4431	+	12.0520i	0.540725	+	0.624030i	0.958697	−	0.284430i	$-0.0918043\pi$
$373$	10.4431	+	12.0520i	0.540725	+	0.624030i	−0.417972	+	0.908460i	$0.637259\pi$
$374$	−2.95645	+	0.868093i	−0.152874	+	0.0448880i
$375$	8.65859	+	5.56454i	0.447128	+	0.287352i
$376$	4.72594	−	10.3484i	0.243722	−	0.533676i
$377$	−5.88797	+	6.79508i	−0.303246	+	0.349965i
$378$	0.0133903	−	0.00860545i	0.000688725	−	0.000442617i
$379$	−3.06432	−	21.3128i	−0.157404	−	1.09477i	−0.903395	−	0.428810i	$-0.858933\pi$
$379$	−3.06432	−	21.3128i	−0.157404	−	1.09477i	0.745991	−	0.665956i	$-0.231976\pi$
$380$	0.130117	+	0.904985i	0.00667487	+	0.0464247i
$381$	3.72571	−	2.39437i	0.190874	−	0.122667i
$382$	2.19824	−	2.53691i	0.112472	−	0.129800i
$383$	−0.481598	+	1.05455i	−0.0246085	+	0.0538851i	−0.921537	−	0.388290i	$-0.873066\pi$
$383$	−0.481598	+	1.05455i	−0.0246085	+	0.0538851i	0.896929	+	0.442175i	$0.145793\pi$
$384$	−5.92847	−	3.80999i	−0.302536	−	0.194428i
$385$	0.148612	−	0.0436365i	0.00757398	−	0.00222392i
$386$	3.30251	+	3.81130i	0.168093	+	0.193990i
$387$	9.41922	+	2.76573i	0.478806	+	0.140590i
$388$	14.7429	+	32.2825i	0.748460	+	1.63890i
$389$	1.99595	−	13.8821i	0.101199	−	0.703853i	−0.874546	−	0.484942i	$-0.838841\pi$
$389$	1.99595	−	13.8821i	0.101199	−	0.703853i	0.975745	−	0.218911i	$-0.0702503\pi$
$390$	−1.23306			−0.0624384
$391$	−27.5959	+	17.5150i	−1.39558	+	0.885771i
$392$	−6.52461			−0.329543
$393$	−1.76220	+	12.2564i	−0.0888912	+	0.618252i
$394$	−0.355061	−	0.777475i	−0.0178877	−	0.0391686i
$395$	−11.4412	−	3.35943i	−0.575668	−	0.169031i
$396$	−2.43397	−	2.80895i	−0.122312	−	0.141155i
$397$	−3.33782	+	0.980073i	−0.167521	+	0.0491885i	−0.364417	−	0.931236i	$-0.618732\pi$
$397$	−3.33782	+	0.980073i	−0.167521	+	0.0491885i	0.196897	+	0.980424i	$0.436914\pi$
$398$	−4.42739	−	2.84531i	−0.221925	−	0.142623i
$399$	−0.0109254	+	0.0239233i	−0.000546954	+	0.00119766i
$400$	8.52940	−	9.84346i	0.426470	−	0.492173i
$401$	−17.1610	+	11.0287i	−0.856977	+	0.550746i	−0.893744	−	0.448578i	$-0.851931\pi$
$401$	−17.1610	+	11.0287i	−0.856977	+	0.550746i	0.0367666	+	0.999324i	$0.488294\pi$
$402$	−0.0840262	−	0.584415i	−0.00419085	−	0.0291480i
$403$	2.30789	+	16.0517i	0.114964	+	0.799594i
$404$	15.6164	−	10.0360i	0.776944	−	0.499312i
$405$	−0.788201	+	0.909632i	−0.0391660	+	0.0452000i
$406$	0.0137234	−	0.0300500i	0.000681079	−	0.00149135i
$407$	−5.33932	−	3.43137i	−0.264660	−	0.170087i
$408$	6.09907	−	1.79085i	0.301949	−	0.0886602i
$409$	−16.6415	−	19.2053i	−0.822870	−	0.949643i	0.176529	−	0.984295i	$-0.443513\pi$
$409$	−16.6415	−	19.2053i	−0.822870	−	0.949643i	−0.999399	+	0.0346523i	$0.988968\pi$
$410$	−1.22106	−	0.358537i	−0.0603040	−	0.0177069i
$411$	3.08973	+	6.76556i	0.152405	+	0.333720i
$412$	−0.974349	+	6.77675i	−0.0480027	+	0.333866i
$413$	−0.470721			−0.0231626
$414$	0.950592	+	0.618535i	0.0467191	+	0.0303994i
$415$	−15.5143			−0.761567
$416$	−1.68478	+	11.7179i	−0.0826033	+	0.574519i
$417$	0.563721	+	1.23438i	0.0276056	+	0.0604477i
$418$	−0.169500	−	0.0497697i	−0.00829051	−	0.00243431i
$419$	−1.13857	−	1.31398i	−0.0556229	−	0.0641923i	0.727256	−	0.686366i	$-0.240795\pi$
$419$	−1.13857	−	1.31398i	−0.0556229	−	0.0641923i	−0.782879	+	0.622174i	$0.786250\pi$
$420$	−0.151118	+	0.0443722i	−0.00737380	+	0.00216514i
$421$	−20.0342	−	12.8752i	−0.976409	−	0.627500i	−0.0479164	−	0.998851i	$-0.515258\pi$
$421$	−20.0342	−	12.8752i	−0.976409	−	0.627500i	−0.928492	+	0.371352i	$0.878894\pi$
$422$	−1.57329	+	3.44502i	−0.0765866	+	0.167701i
$423$	−7.98762	+	9.21820i	−0.388371	+	0.448204i
$424$	−5.91423	+	3.80084i	−0.287220	+	0.184585i
$425$	3.44447	+	23.9568i	0.167082	+	1.16208i
$426$	−0.412812	−	2.87117i	−0.0200008	−	0.139109i
$427$	−0.483690	+	0.310848i	−0.0234074	+	0.0150430i
$428$	−15.9497	+	18.4070i	−0.770959	+	0.889734i
$429$	−3.44063	+	7.53393i	−0.166115	+	0.363742i
$430$	2.35061	+	1.51064i	0.113356	+	0.0728497i
$431$	13.8877	−	4.07781i	0.668949	−	0.196421i	0.0704140	−	0.997518i	$-0.477568\pi$
$431$	13.8877	−	4.07781i	0.668949	−	0.196421i	0.598535	+	0.801097i	$0.295750\pi$
$432$	2.40176	+	2.77178i	0.115555	+	0.133357i
$433$	−28.6769	−	8.42030i	−1.37812	−	0.404654i	−0.493008	−	0.870025i	$-0.664103\pi$
$433$	−28.6769	−	8.42030i	−1.37812	−	0.404654i	−0.885116	+	0.465371i	$0.845921\pi$
$434$	−0.0247519	−	0.0541991i	−0.00118813	−	0.00260164i
$435$	−0.355510	+	2.47262i	−0.0170454	+	0.118553i
$436$	−2.88896			−0.138356
$437$	−1.87387	−	0.0106012i	−0.0896394	−	0.000507122i
$438$	1.14456			0.0546891
$439$	1.20450	−	8.37747i	0.0574875	−	0.399835i	−0.940679	−	0.339299i	$-0.889810\pi$
$439$	1.20450	−	8.37747i	0.0574875	−	0.399835i	0.998166	−	0.0605354i	$-0.0192808\pi$
$440$	−0.891580	−	1.95229i	−0.0425044	−	0.0930717i
$441$	6.71210	+	1.97085i	0.319624	+	0.0938501i
$442$	−4.57224	−	5.27665i	−0.217479	−	0.250984i
$443$	6.51197	−	1.91209i	0.309393	−	0.0908461i	−0.123350	−	0.992363i	$-0.539364\pi$
$443$	6.51197	−	1.91209i	0.309393	−	0.0908461i	0.432743	+	0.901517i	$0.357546\pi$
$444$	5.42934	+	3.48923i	0.257665	+	0.165591i
$445$	−7.13107	+	15.6149i	−0.338045	+	0.740216i
$446$	1.97853	−	2.28334i	0.0936860	−	0.108119i
$447$	17.9674	−	11.5470i	0.849830	−	0.546153i
$448$	0.0640740	+	0.445644i	0.00302721	+	0.0210547i
$449$	3.93728	+	27.3844i	0.185812	+	1.29235i	0.842709	+	0.538369i	$0.180959\pi$
$449$	3.93728	+	27.3844i	0.185812	+	1.29235i	−0.656897	+	0.753980i	$0.728132\pi$
$450$	0.706493	−	0.454035i	0.0333044	−	0.0214034i
$451$	−5.59780	+	6.46021i	−0.263590	+	0.304199i
$452$	5.68274	−	12.4435i	0.267294	−	0.585291i
$453$	12.2320	+	7.86103i	0.574709	+	0.369343i
$454$	0.733719	−	0.215439i	0.0344351	−	0.0101111i
$455$	0.229833	+	0.265242i	0.0107747	+	0.0124347i
$456$	0.349673	+	0.102673i	0.0163750	+	0.00480812i
$457$	−11.3962	−	24.9543i	−0.533093	−	1.16731i	−0.964240	−	0.265030i	$-0.914618\pi$
$457$	−11.3962	−	24.9543i	−0.533093	−	1.16731i	0.431147	−	0.902282i	$-0.358109\pi$
$458$	0.723769	−	5.03392i	0.0338195	−	0.235220i
$459$	−6.81529			−0.318110
$460$	−7.30067	−	8.52236i	−0.340395	−	0.397357i
$461$	−20.3265			−0.946701			−0.473350	−	0.880874i	$-0.656956\pi$
$461$	−20.3265			−0.946701			−0.473350	+	0.880874i	$0.656956\pi$
$462$	0.00433079	−	0.0301213i	0.000201487	−	0.00140137i
$463$	−10.7268	−	23.4884i	−0.498516	−	1.09160i	−0.976949	−	0.213474i	$-0.931522\pi$
$463$	−10.7268	−	23.4884i	−0.498516	−	1.09160i	0.478432	−	0.878124i	$-0.341205\pi$
$464$	7.30359	+	2.14453i	0.339061	+	0.0995572i
$465$	2.95052	+	3.40508i	0.136827	+	0.157907i
$466$	3.70462	−	1.08777i	0.171613	−	0.0503902i
$467$	7.13741	+	4.58693i	0.330280	+	0.212258i	0.695262	−	0.718757i	$-0.255288\pi$
$467$	7.13741	+	4.58693i	0.330280	+	0.212258i	−0.364982	+	0.931015i	$0.618925\pi$
$468$	3.49864	−	7.66096i	0.161725	−	0.354128i
$469$	−0.110051	+	0.127006i	−0.00508168	+	0.00586457i
$470$	−2.92062	+	1.87697i	−0.134718	+	0.0865781i
$471$	0.00536203	+	0.0372937i	0.000247069	+	0.00171840i
$472$	0.928279	+	6.45632i	0.0427275	+	0.297176i
$473$	15.7889	−	10.1469i	0.725975	−	0.466556i
$474$	−1.53420	+	1.77056i	−0.0704682	+	0.0813246i
$475$	−0.576439	+	1.26223i	−0.0264488	+	0.0579149i
$476$	−0.750235	−	0.482147i	−0.0343870	−	0.0220992i
$477$	7.23228	−	2.12359i	0.331143	−	0.0972324i
$478$	0.145585	+	0.168014i	0.00665889	+	0.00768477i
$479$	17.3180	+	5.08504i	0.791282	+	0.232341i	0.652307	−	0.757955i	$-0.273801\pi$
$479$	17.3180	+	5.08504i	0.791282	+	0.232341i	0.138975	+	0.990296i	$0.455619\pi$
$480$	1.36635	+	2.99188i	0.0623648	+	0.136560i
$481$	2.04673	−	14.2353i	0.0933228	−	0.649075i
$482$	1.86534			0.0849637
$483$	−0.0441312	−	0.319771i	−0.00200804	−	0.0145501i
$484$	14.2790			0.649044
$485$	3.12699	−	21.7487i	0.141989	−	0.987557i
$486$	0.0982369	+	0.215109i	0.00445612	+	0.00975753i
$487$	32.2853	+	9.47982i	1.46299	+	0.429571i	0.913812	−	0.406137i	$-0.133124\pi$
$487$	32.2853	+	9.47982i	1.46299	+	0.429571i	0.549174	+	0.835708i	$0.314943\pi$
$488$	5.21740	+	6.02120i	0.236181	+	0.272567i
$489$	0.627729	−	0.184318i	0.0283869	−	0.00833514i
$490$	1.67504	+	1.07648i	0.0756704	+	0.0486304i
$491$	13.2009	−	28.9059i	0.595748	−	1.30451i	−0.336158	−	0.941806i	$-0.609128\pi$
$491$	13.2009	−	28.9059i	0.595748	−	1.30451i	0.931906	−	0.362700i	$-0.118145\pi$
$492$	5.69218	−	6.56913i	0.256623	−	0.296159i
$493$	−11.8994	+	7.64727i	−0.535921	+	0.344416i
$494$	−0.0569677	−	0.396219i	−0.00256310	−	0.0178268i
$495$	0.327484	+	2.27770i	0.0147193	+	0.102375i
$496$	11.5497	−	7.42252i	0.518596	−	0.333281i
$497$	−0.540669	+	0.623965i	−0.0242523	+	0.0279886i
$498$	−1.26625	+	2.77270i	−0.0567419	+	0.124247i
$499$	−13.5620	−	8.71580i	−0.607121	−	0.390173i	0.200656	−	0.979662i	$-0.435693\pi$
$499$	−13.5620	−	8.71580i	−0.607121	−	0.390173i	−0.807776	+	0.589489i	$0.799329\pi$
$500$	−19.1989	+	5.63730i	−0.858600	+	0.252108i
$501$	−5.09315	−	5.87781i	−0.227545	−	0.262601i
$502$	−3.20143	−	0.940024i	−0.142887	−	0.0419553i
$503$	9.01387	+	19.7376i	0.401909	+	0.880057i	0.997073	+	0.0764533i	$0.0243596\pi$
$503$	9.01387	+	19.7376i	0.401909	+	0.880057i	−0.595165	+	0.803604i	$0.702913\pi$
$504$	−0.00893430	+	0.0621394i	−0.000397965	+	0.00276791i
$505$	−11.4929			−0.511425
$506$	2.08384	−	0.599087i	0.0926380	−	0.0266326i
$507$	−5.76753			−0.256145
$508$	−1.22531	+	8.52222i	−0.0543644	+	0.378113i
$509$	10.4080	+	22.7904i	0.461328	+	1.01017i	0.987183	+	0.159593i	$0.0510183\pi$
$509$	10.4080	+	22.7904i	0.461328	+	1.01017i	−0.525855	+	0.850574i	$0.676254\pi$
$510$	−1.86126	−	0.546514i	−0.0824178	−	0.0242001i
$511$	−0.213338	−	0.246205i	−0.00943750	−	0.0108915i
$512$	16.1808	−	4.75110i	0.715095	−	0.209971i
$513$	−0.328708	−	0.211248i	−0.0145128	−	0.00932681i
$514$	0.835065	−	1.82854i	0.0368332	−	0.0806534i
$515$	2.77580	−	3.20344i	0.122316	−	0.141160i
$516$	−16.0551	+	10.3180i	−0.706787	+	0.454225i
$517$	3.31872	+	23.0822i	0.145957	+	1.01515i
$518$	0.00752007	+	0.0523032i	0.000330413	+	0.00229807i
$519$	−3.56362	+	2.29020i	−0.156426	+	0.100529i
$520$	3.18477	−	3.67542i	0.139661	−	0.161178i
$521$	4.95908	−	10.8589i	0.217261	−	0.475736i	−0.769349	−	0.638828i	$-0.779420\pi$
$521$	4.95908	−	10.8589i	0.217261	−	0.475736i	0.986611	+	0.163092i	$0.0521468\pi$
$522$	0.412888	+	0.265347i	0.0180716	+	0.0116139i
$523$	22.6223	−	6.64250i	0.989204	−	0.290456i	0.253185	−	0.967418i	$-0.418522\pi$
$523$	22.6223	−	6.64250i	0.989204	−	0.290456i	0.736018	+	0.676961i	$0.236704\pi$
$524$	−15.7640	−	18.1927i	−0.688655	−	0.794751i
$525$	−0.229352	−	0.0673439i	−0.0100097	−	0.00293913i
$526$	1.76727	+	3.86979i	0.0770567	+	0.168731i
$527$	−3.63075	+	25.2524i	−0.158158	+	1.10001i
$528$	7.01187			0.305152
$529$	19.4883	−	12.2150i	0.847317	−	0.531088i
$530$	2.14543			0.0931913
$531$	0.995270	−	6.92225i	0.0431910	−	0.300400i
$532$	−0.0212398	−	0.0465088i	−0.000920864	−	0.00201641i
$533$	−18.5850	−	5.45704i	−0.805004	−	0.236371i
$534$	2.20865	+	2.54891i	0.0955775	+	0.110302i
$535$	14.4684	−	4.24830i	0.625523	−	0.183670i
$536$	1.95901	+	1.25898i	0.0846164	+	0.0543797i
$537$	−5.61795	+	12.3016i	−0.242432	+	0.530853i
$538$	−3.72348	+	4.29713i	−0.160531	+	0.185262i
$539$	11.2511	−	7.23066i	0.484621	−	0.311447i
$540$	−0.333006	−	2.31611i	−0.0143303	−	0.0996693i
$541$	−2.54497	−	17.7006i	−0.109417	−	0.761010i	−0.968471	−	0.249126i	$-0.919857\pi$
$541$	−2.54497	−	17.7006i	−0.109417	−	0.761010i	0.859055	−	0.511884i	$-0.171052\pi$
$542$	−0.439450	+	0.282417i	−0.0188760	+	0.0121309i
$543$	12.6462	−	14.5945i	0.542700	−	0.626309i
$544$	−7.73672	+	16.9411i	−0.331709	+	0.726342i
$545$	1.50468	+	0.966997i	0.0644533	+	0.0414216i
$546$	0.0661623	−	0.0194270i	0.00283148	−	0.000831398i
$547$	−2.16919	−	2.50338i	−0.0927481	−	0.107037i	0.707478	−	0.706735i	$-0.249833\pi$
$547$	−2.16919	−	2.50338i	−0.0927481	−	0.107037i	−0.800226	+	0.599698i	$0.795287\pi$
$548$	−13.8737	−	4.07370i	−0.592657	−	0.174020i
$549$	−3.54854	−	7.77021i	−0.151448	−	0.331625i
$550$	0.228499	−	1.58924i	0.00974321	−	0.0677655i
$551$	−0.810954			−0.0345478
$552$	−4.29890	+	1.23590i	−0.182973	+	0.0526033i
$553$	0.666827			0.0283564
$554$	−0.0666485	+	0.463551i	−0.00283162	+	0.0196944i
$555$	−1.65988	−	3.63463i	−0.0704580	−	0.154281i
$556$	−2.53127	−	0.743247i	−0.107350	−	0.0315207i
$557$	−6.13791	−	7.08352i	−0.260071	−	0.300138i	0.610664	−	0.791889i	$-0.290902\pi$
$557$	−6.13791	−	7.08352i	−0.260071	−	0.300138i	−0.870736	+	0.491751i	$0.836357\pi$
$558$	0.849368	−	0.249397i	0.0359566	−	0.0105578i
$559$	35.7770	+	22.9925i	1.51320	+	0.972477i
$560$	0.123431	−	0.270276i	0.00521591	−	0.0114212i
$561$	−8.53268	+	9.84724i	−0.360250	+	0.415751i
$562$	−2.60176	+	1.67205i	−0.109749	+	0.0705312i
$563$	−2.40845	−	16.7511i	−0.101504	−	0.705976i	−0.975493	−	0.220030i	$-0.929384\pi$
$563$	−2.40845	−	16.7511i	−0.101504	−	0.705976i	0.873989	−	0.485946i	$-0.161525\pi$
$564$	−3.37468	−	23.4714i	−0.142099	−	0.988324i
$565$	−7.12487	+	4.57887i	−0.299745	+	0.192635i
$566$	−0.188675	+	0.217742i	−0.00793058	+	0.00915238i
$567$	0.0279611	−	0.0612263i	0.00117426	−	0.00257126i
$568$	9.62442	+	6.18524i	0.403832	+	0.259527i
$569$	−38.1829	+	11.2115i	−1.60071	+	0.470011i	−0.955744	−	0.294199i	$-0.904947\pi$
$569$	−38.1829	+	11.2115i	−1.60071	+	0.470011i	−0.644967	+	0.764210i	$0.723129\pi$
$570$	−0.0728303	−	0.0840506i	−0.00305053	−	0.00352049i
$571$	31.0950	+	9.13033i	1.30129	+	0.382092i	0.857705	−	0.514142i	$-0.171889\pi$
$571$	31.0950	+	9.13033i	1.30129	+	0.382092i	0.443582	+	0.896234i	$0.353708\pi$
$572$	−6.68886	−	14.6466i	−0.279675	−	0.612403i
$573$	2.02015	−	14.0505i	0.0843932	−	0.586967i
$574$	0.0711674			0.00297047
$575$	−2.32842	−	16.8716i	−0.0971019	−	0.703593i
$576$	−6.68896			−0.278707
$577$	0.431513	−	3.00124i	0.0179641	−	0.124943i	−0.978866	−	0.204503i	$-0.934442\pi$
$577$	0.431513	−	3.00124i	0.0179641	−	0.124943i	0.996830	+	0.0795594i	$0.0253513\pi$
$578$	−2.89289	−	6.33455i	−0.120328	−	0.263483i
$579$	20.4618	+	6.00814i	0.850365	+	0.249690i
$580$	−3.18027	−	3.67022i	−0.132053	−	0.152398i
$581$	0.832451	−	0.244430i	0.0345359	−	0.0101406i
$582$	−3.63168	−	2.33394i	−0.150538	−	0.0967449i
$583$	5.98643	−	13.1085i	0.247933	−	0.542897i
$584$	−2.95619	+	3.41163i	−0.122328	+	0.141174i
$585$	−4.38650	+	2.81903i	−0.181360	+	0.116553i
$586$	−0.740694	−	5.15164i	−0.0305978	−	0.212812i
$587$	−1.42349	−	9.90061i	−0.0587538	−	0.408642i	−0.997881	−	0.0650711i	$-0.979273\pi$
$587$	−1.42349	−	9.90061i	−0.0587538	−	0.408642i	0.939127	−	0.343571i	$-0.111637\pi$
$588$	−11.4408	+	7.35257i	−0.471812	+	0.303215i
$589$	−0.957841	+	1.10541i	−0.0394671	+	0.0455475i
$590$	0.826900	−	1.81066i	0.0340429	−	0.0745436i
$591$	−3.04057	−	1.95406i	−0.125072	−	0.0803791i
$592$	−11.6823	+	3.43024i	−0.480141	+	0.140982i
$593$	19.3815	+	22.3675i	0.795904	+	0.918523i	0.998149	−	0.0608124i	$-0.0193691\pi$
$593$	19.3815	+	22.3675i	0.795904	+	0.918523i	−0.202245	+	0.979335i	$0.564824\pi$
$594$	0.433797	+	0.127374i	0.0177989	+	0.00522623i
$595$	0.229365	+	0.502239i	0.00940304	+	0.0205898i
$596$	−5.90912	+	41.0988i	−0.242047	+	1.68347i
$597$	−22.2551			−0.910839
$598$	3.19637	+	3.73125i	0.130709	+	0.152582i
$599$	11.0198			0.450255			0.225128	−	0.974329i	$-0.427720\pi$
$599$	11.0198			0.450255			0.225128	+	0.974329i	$0.427720\pi$
$600$	−0.471386	+	3.27856i	−0.0192442	+	0.133847i
$601$	−4.16364	−	9.11710i	−0.169839	−	0.371894i	0.805504	−	0.592590i	$-0.201895\pi$
$601$	−4.16364	−	9.11710i	−0.169839	−	0.371894i	−0.975343	+	0.220696i	$0.929167\pi$
$602$	−0.149927	−	0.0440225i	−0.00611057	−	0.00179422i
$603$	−1.63501	−	1.88691i	−0.0665829	−	0.0768408i
$604$	−27.1223	+	7.96382i	−1.10359	+	0.324043i
$605$	−7.43700	−	4.77947i	−0.302357	−	0.194313i
$606$	−0.938025	+	2.05399i	−0.0381047	+	0.0834376i
$607$	−7.94444	+	9.16837i	−0.322455	+	0.372133i	−0.893714	−	0.448637i	$-0.851910\pi$
$607$	−7.94444	+	9.16837i	−0.322455	+	0.372133i	0.571259	+	0.820770i	$0.306455\pi$
$608$	−0.898256	+	0.577274i	−0.0364291	+	0.0234116i
$609$	−0.0198809	−	0.138275i	−0.000805615	−	0.00560317i
$610$	−0.346017	−	2.40660i	−0.0140098	−	0.0974405i
$611$	−44.4528	+	28.5681i	−1.79837	+	1.15574i
$612$	8.67654	−	10.0133i	0.350728	−	0.404762i
$613$	−15.3303	+	33.5687i	−0.619185	+	1.35583i	0.296926	+	0.954900i	$0.404039\pi$
$613$	−15.3303	+	33.5687i	−0.619185	+	1.35583i	−0.916111	+	0.400925i	$0.868689\pi$
$614$	4.44869	+	2.85900i	0.179534	+	0.115380i
$615$	−5.16352	+	1.51615i	−0.208213	+	0.0611369i
$616$	0.0785981	+	0.0907070i	0.00316681	+	0.00365469i
$617$	6.79897	+	1.99636i	0.273716	+	0.0803704i	0.415710	−	0.909497i	$-0.363533\pi$
$617$	6.79897	+	1.99636i	0.273716	+	0.0803704i	−0.141994	+	0.989868i	$0.545351\pi$
$618$	−0.345960	−	0.757546i	−0.0139165	−	0.0304730i
$619$	−4.91711	+	34.1992i	−0.197635	+	1.37458i	0.613486	+	0.789705i	$0.289767\pi$
$619$	−4.91711	+	34.1992i	−0.197635	+	1.37458i	−0.811121	+	0.584878i	$0.801142\pi$
$620$	−8.75917			−0.351777
$621$	4.79575	+	0.0271313i	0.192447	+	0.00108874i
$622$	−2.73070			−0.109491
$623$	0.136618	−	0.950199i	0.00547348	−	0.0380689i
$624$	6.60035	+	14.4528i	0.264225	+	0.578573i
$625$	−5.15089	−	1.51244i	−0.206036	−	0.0604975i
$626$	0.317764	+	0.366720i	0.0127004	+	0.0146571i
$627$	−0.716766	+	0.210461i	−0.0286249	+	0.00840502i
$628$	−0.0616197	−	0.0396006i	−0.00245889	−	0.00158024i
$629$	9.39881	−	20.5805i	0.374755	−	0.820600i
$630$	0.0125459	−	0.0144787i	0.000499840	−	0.000576847i
$631$	−1.00628	+	0.646698i	−0.0400594	+	0.0257446i	−0.560517	−	0.828143i	$-0.689398\pi$
$631$	−1.00628	+	0.646698i	−0.0400594	+	0.0257446i	0.520458	+	0.853887i	$0.325761\pi$
$632$	−1.31501	−	9.14609i	−0.0523083	−	0.363812i
$633$	2.27921	+	15.8523i	0.0905905	+	0.630071i
$634$	−3.45913	+	2.22305i	−0.137380	+	0.0882885i
$635$	3.49075	−	4.02854i	0.138526	−	0.159868i
$636$	−6.08736	+	13.3295i	−0.241380	+	0.528548i
$637$	25.4945	+	16.3844i	1.01013	+	0.649172i
$638$	0.900326	−	0.264360i	0.0356443	−	0.0104661i
$639$	−8.03265	−	9.27017i	−0.317767	−	0.366722i
$640$	−8.13851	−	2.38968i	−0.321703	−	0.0944605i
$641$	2.55638	+	5.59770i	0.100971	+	0.221096i	0.953375	−	0.301788i	$-0.0975834\pi$
$641$	2.55638	+	5.59770i	0.100971	+	0.221096i	−0.852404	+	0.522884i	$0.824856\pi$
$642$	0.421631	−	2.93251i	0.0166405	−	0.115737i
$643$	13.4574			0.530708			0.265354	−	0.964151i	$-0.414511\pi$
$643$	13.4574			0.530708			0.265354	+	0.964151i	$0.414511\pi$
$644$	0.526003	+	0.342262i	0.0207274	+	0.0134870i
$645$	11.8157			0.465244
$646$	0.0896210	−	0.623327i	0.00352609	−	0.0245245i
$647$	−11.7055	−	25.6316i	−0.460193	−	1.00768i	−0.987444	−	0.157972i	$-0.949505\pi$
$647$	−11.7055	−	25.6316i	−0.460193	−	1.00768i	0.527251	−	0.849710i	$-0.323223\pi$
$648$	−0.894911	−	0.262769i	−0.0351554	−	0.0103226i
$649$	−8.75572	−	10.1046i	−0.343692	−	0.396642i
$650$	3.49081	−	1.02499i	0.136921	−	0.0402036i
$651$	−0.211963	−	0.136221i	−0.00830750	−	0.00533891i
$652$	−0.528355	+	1.15694i	−0.0206920	+	0.0453091i
$653$	0.870856	−	1.00502i	0.0340792	−	0.0393295i	−0.738454	−	0.674304i	$-0.764444\pi$
$653$	0.870856	−	1.00502i	0.0340792	−	0.0393295i	0.772533	+	0.634974i	$0.218989\pi$
$654$	0.295630	−	0.189990i	0.0115600	−	0.00742918i
$655$	2.12101	+	14.7520i	0.0828748	+	0.576407i
$656$	2.33371	+	16.2313i	0.0911162	+	0.633727i
$657$	4.07167	−	2.61670i	0.158851	−	0.102087i
$658$	0.127140	−	0.146727i	0.00495643	−	0.00572003i
$659$	11.1888	−	24.5001i	0.435855	−	0.954390i	−0.556485	−	0.830858i	$-0.687850\pi$
$659$	11.1888	−	24.5001i	0.435855	−	0.954390i	0.992341	−	0.123533i	$-0.0394224\pi$
$660$	−3.76340	−	2.41859i	−0.146490	−	0.0941436i
$661$	6.90258	−	2.02678i	0.268479	−	0.0788326i	−0.144722	−	0.989472i	$-0.546229\pi$
$661$	6.90258	−	2.02678i	0.268479	−	0.0788326i	0.413201	+	0.910640i	$0.364411\pi$
$662$	1.20984	+	1.39623i	0.0470218	+	0.0542661i
$663$	−28.3289	−	8.31811i	−1.10020	−	0.323049i
$664$	−4.99418	−	10.9357i	−0.193812	−	0.424388i
$665$	−0.00450499	+	0.0313329i	−0.000174696	+	0.00121504i
$666$	−0.785053			−0.0304202
$667$	8.40375	−	5.33383i	0.325395	−	0.206527i
$668$	15.1200			0.585010
$669$	1.81824	−	12.6461i	0.0702972	−	0.488928i
$670$	−0.295213	−	0.646425i	−0.0114051	−	0.0249736i
$671$	−15.6697	−	4.60105i	−0.604923	−	0.177621i
$672$	−0.120451	−	0.139008i	−0.00464651	−	0.00536236i
$673$	13.9543	−	4.09735i	0.537898	−	0.157941i	−0.00148929	−	0.999999i	$-0.500474\pi$
$673$	13.9543	−	4.09735i	0.537898	−	0.157941i	0.539387	+	0.842058i	$0.318656\pi$
$674$	−6.01878	−	3.86803i	−0.231835	−	0.148991i
$675$	1.47527	−	3.23038i	0.0567831	−	0.124338i
$676$	7.34264	−	8.47386i	0.282409	−	0.325918i
$677$	−5.66168	+	3.63854i	−0.217596	+	0.139841i	−0.644898	−	0.764268i	$-0.723100\pi$
$677$	−5.66168	+	3.63854i	−0.217596	+	0.139841i	0.427302	+	0.904109i	$0.359464\pi$
$678$	0.236812	+	1.64707i	0.00909473	+	0.0632552i
$679$	0.174868	+	1.21624i	0.00671083	+	0.0466748i
$680$	6.43631	−	4.13636i	0.246821	−	0.158622i
$681$	2.11760	−	2.44384i	0.0811467	−	0.0936483i
$682$	0.703054	−	1.53947i	0.0269213	−	0.0589495i
$683$	6.71569	+	4.31591i	0.256969	+	0.165144i	0.662782	−	0.748812i	$-0.269375\pi$
$683$	6.71569	+	4.31591i	0.256969	+	0.165144i	−0.405814	+	0.913956i	$0.633012\pi$
$684$	0.728850	−	0.214010i	0.0278683	−	0.00818287i
$685$	5.86239	+	6.76556i	0.223990	+	0.258499i
$686$	−0.213744	−	0.0627609i	−0.00816079	−	0.00239622i
$687$	−8.93387	−	19.5624i	−0.340848	−	0.746354i
$688$	5.12394	−	35.6378i	0.195349	−	1.35868i
$689$	32.6540			1.24402
$690$	1.30755	+	0.391978i	0.0497774	+	0.0149224i
$691$	47.1939			1.79534			0.897671	−	0.440667i	$-0.145258\pi$
$691$	47.1939			1.79534			0.897671	+	0.440667i	$0.145258\pi$
$692$	1.17200	−	8.15145i	0.0445528	−	0.309872i
$693$	−0.0534573	−	0.117055i	−0.00203068	−	0.00444656i
$694$	6.08163	+	1.78573i	0.230855	+	0.0677853i
$695$	1.06959	+	1.23438i	0.0405720	+	0.0468226i
$696$	−1.85735	+	0.545366i	−0.0704025	+	0.0206720i
$697$	−25.6346	−	16.4744i	−0.970982	−	0.624012i
$698$	−0.606690	+	1.32847i	−0.0229636	+	0.0502832i
$699$	10.6920	−	12.3392i	0.404408	−	0.466712i
$700$	0.390932	−	0.251237i	0.0147759	−	0.00949586i
$701$	0.571838	+	3.97722i	0.0215980	+	0.150218i	0.997767	−	0.0667957i	$-0.0212776\pi$
$701$	0.571838	+	3.97722i	0.0215980	+	0.150218i	−0.976169	+	0.217013i	$0.930368\pi$
$702$	0.145796	+	1.01403i	0.00550272	+	0.0382723i
$703$	1.09123	−	0.701291i	0.0411565	−	0.0264497i
$704$	−8.37453	+	9.66472i	−0.315627	+	0.364253i
$705$	−6.09871	+	13.3543i	−0.229691	+	0.502953i
$706$	3.12441	+	2.00793i	0.117589	+	0.0755696i
$707$	0.616672	−	0.181071i	0.0231923	−	0.00680989i
$708$	8.90335	+	10.2750i	0.334608	+	0.386158i
$709$	2.22562	+	0.653500i	0.0835848	+	0.0245427i	0.323258	−	0.946311i	$-0.395222\pi$
$709$	2.22562	+	0.653500i	0.0835848	+	0.0245427i	−0.239673	+	0.970854i	$0.577040\pi$
$710$	−1.45035	−	3.17582i	−0.0544306	−	0.119186i
$711$	−1.40991	+	9.80613i	−0.0528757	+	0.367759i
$712$	−13.3022			−0.498520
$713$	2.65540	−	17.7551i	0.0994454	−	0.664932i
$714$	0.108480			0.00405976
$715$	−1.41871	+	9.86735i	−0.0530568	+	0.369018i
$716$	−10.9217	−	23.9152i	−0.408164	−	0.893754i
$717$	0.902020	+	0.264857i	0.0336866	+	0.00989126i
$718$	−3.44749	−	3.97862i	−0.128659	−	0.148481i
$719$	−29.4341	+	8.64262i	−1.09770	+	0.322315i	−0.779940	−	0.625854i	$-0.784750\pi$
$719$	−29.4341	+	8.64262i	−1.09770	+	0.322315i	−0.317765	+	0.948170i	$0.602932\pi$
$720$	3.71361	+	2.38659i	0.138398	+	0.0889430i
$721$	−0.0984704	+	0.215620i	−0.00366723	+	0.00803011i
$722$	−2.91871	+	3.36837i	−0.108623	+	0.125358i
$723$	6.63577	−	4.26455i	0.246787	−	0.158600i
$724$	5.34287	+	37.1604i	0.198566	+	1.38106i
$725$	−1.04894	−	7.29556i	−0.0389568	−	0.270950i
$726$	−1.46118	+	0.939040i	−0.0542293	+	0.0348511i
$727$	0.588728	−	0.679428i	0.0218347	−	0.0251986i	−0.744727	−	0.667369i	$-0.767420\pi$
$727$	0.588728	−	0.679428i	0.0218347	−	0.0251986i	0.766562	+	0.642170i	$0.221966\pi$
$728$	−0.112979	+	0.247389i	−0.00418726	+	0.00916883i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	1.32181	−	0.388117i	0.0489222	−	0.0143649i
$731$	43.8133	+	50.5633i	1.62049	+	1.87015i
$732$	15.9339	+	4.67862i	0.588935	+	0.172927i
$733$	−20.2719	−	44.3893i	−0.748760	−	1.63956i	−0.768582	−	0.639752i	$-0.779037\pi$
$733$	−20.2719	−	44.3893i	−0.748760	−	1.63956i	0.0198219	−	0.999804i	$-0.493690\pi$
$734$	0.0889514	−	0.618671i	0.00328326	−	0.0228356i
$735$	8.41986			0.310571
$736$	5.51159	−	11.8902i	0.203160	−	0.438279i
$737$	−4.77337			−0.175829
$738$	−0.150473	+	1.04656i	−0.00553899	+	0.0385245i
$739$	19.5814	+	42.8773i	0.720313	+	1.57727i	0.813465	+	0.581614i	$0.197579\pi$
$739$	19.5814	+	42.8773i	0.720313	+	1.57727i	−0.0931513	+	0.995652i	$0.529694\pi$
$740$	7.45332	+	2.18849i	0.273990	+	0.0804506i
$741$	−1.10850	−	1.27928i	−0.0407217	−	0.0469954i
$742$	−0.115117	+	0.0338014i	−0.00422608	+	0.00124089i
$743$	−42.6984	−	27.4406i	−1.56645	−	1.00670i	−0.980539	−	0.196325i	$-0.937099\pi$
$743$	−42.6984	−	27.4406i	−1.56645	−	1.00670i	−0.585914	−	0.810373i	$-0.699265\pi$
$744$	−1.45038	+	3.17589i	−0.0531735	+	0.116434i
$745$	16.8343	−	19.4279i	0.616762	−	0.711782i
$746$	3.17250	−	2.03884i	0.116153	−	0.0746473i
$747$	1.83440	+	12.7585i	0.0671172	+	0.466811i
$748$	−3.60496	−	25.0730i	−0.131810	−	0.916761i
$749$	−0.709398	+	0.455902i	−0.0259208	+	0.0166583i
$750$	1.59390	−	1.83946i	0.0582011	−	0.0671676i
$751$	−5.13134	+	11.2361i	−0.187245	+	0.410010i	−0.979852	−	0.199723i	$-0.935996\pi$
$751$	−5.13134	+	11.2361i	−0.187245	+	0.410010i	0.792607	+	0.609733i	$0.208723\pi$
$752$	37.6336	+	24.1857i	1.37236	+	0.881961i
$753$	−13.5379	+	3.97509i	−0.493349	+	0.144860i
$754$	1.39238	+	1.60689i	0.0507075	+	0.0585196i
$755$	16.7919	+	4.93055i	0.611120	+	0.179441i
$756$	0.0543586	+	0.119029i	0.00197700	+	0.00432903i
$757$	1.48950	−	10.3597i	0.0541366	−	0.376528i	−0.944684	−	0.327981i	$-0.893632\pi$
$757$	1.48950	−	10.3597i	0.0541366	−	0.376528i	0.998821	−	0.0485473i	$-0.0154592\pi$
$758$	−5.09186			−0.184945
$759$	6.04345	−	6.89530i	0.219363	−	0.250284i
$760$	0.438640			0.0159112
$761$	2.94582	−	20.4886i	0.106786	−	0.742712i	−0.864126	−	0.503275i	$-0.832128\pi$
$761$	2.94582	−	20.4886i	0.106786	−	0.742712i	0.970912	−	0.239437i	$-0.0769627\pi$
$762$	−0.435068	−	0.952666i	−0.0157608	−	0.0345114i
$763$	−0.0959716	−	0.0281798i	−0.00347441	−	0.00102018i
$764$	18.0716	+	20.8558i	0.653808	+	0.754535i
$765$	−7.87071	+	2.31105i	−0.284566	+	0.0835561i
$766$	0.230633	+	0.148219i	0.00833312	+	0.00535537i
$767$	12.5857	−	27.5588i	0.454442	−	0.995090i
$768$	7.66935	−	8.85090i	0.276744	−	0.319379i
$769$	11.7277	−	7.53694i	0.422912	−	0.271789i	−0.311827	−	0.950139i	$-0.600941\pi$
$769$	11.7277	−	7.53694i	0.422912	−	0.271789i	0.734739	+	0.678350i	$0.237305\pi$
$770$	−0.00521261	−	0.0362545i	−0.000187849	−	0.00130652i
$771$	−1.20975	−	8.41401i	−0.0435681	−	0.303023i
$772$	−34.8773	+	22.4143i	−1.25526	+	0.806708i
$773$	−35.1110	+	40.5203i	−1.26286	+	1.45741i	−0.431070	+	0.902319i	$0.641864\pi$
$773$	−35.1110	+	40.5203i	−1.26286	+	1.45741i	−0.831787	+	0.555096i	$0.812682\pi$
$774$	0.964379	−	2.11169i	0.0346639	−	0.0759033i
$775$	−11.1835	−	7.18719i	−0.401722	−	0.258171i
$776$	16.3368	−	4.79693i	0.586458	−	0.172200i
$777$	0.146328	+	0.168872i	0.00524950	+	0.00605824i
$778$	−3.18225	−	0.934392i	−0.114089	−	0.0334996i
$779$	−0.725741	−	1.58915i	−0.0260024	−	0.0569372i
$780$	1.44263	−	10.0337i	0.0516545	−	0.359265i
$781$	−23.4510			−0.839144
$782$	3.17104	+	7.04888i	0.113396	+	0.252067i
$783$	2.07545			0.0741707
$784$	3.65131	−	25.3954i	0.130404	−	0.906978i
$785$	0.0188386	+	0.0412508i	0.000672379	+	0.00147230i
$786$	2.80957	+	0.824963i	0.100214	+	0.0294255i
$787$	22.9101	+	26.4396i	0.816655	+	0.942470i	0.999170	−	0.0407327i	$-0.0129692\pi$
$787$	22.9101	+	26.4396i	0.816655	+	0.942470i	−0.182515	+	0.983203i	$0.558424\pi$
$788$	6.74192	−	1.97961i	0.240171	−	0.0705206i
$789$	15.1341	+	9.72607i	0.538787	+	0.346257i
$790$	−1.17139	+	2.56500i	−0.0416763	+	0.0912585i
$791$	0.310158	−	0.357942i	0.0110280	−	0.0127269i
$792$	−1.50009	+	0.964049i	−0.0533034	+	0.0342560i
$793$	−5.26649	−	36.6292i	−0.187018	−	1.30074i
$794$	0.117075	+	0.814274i	0.00415484	+	0.0288975i
$795$	7.63217	−	4.90490i	0.270685	−	0.173959i
$796$	28.3329	−	32.6979i	1.00423	−	1.15895i
$797$	−8.39904	+	18.3913i	−0.297509	+	0.651454i	−0.998067	−	0.0621411i	$-0.980207\pi$
$797$	−8.39904	+	18.3913i	−0.297509	+	0.651454i	0.700558	+	0.713595i	$0.252934\pi$
$798$	0.00523208	+	0.00336246i	0.000185214	+	0.000119030i
$799$	−79.7617	+	23.4201i	−2.82176	+	0.828545i
$800$	−6.35518	−	7.33427i	−0.224690	−	0.259306i
$801$	13.6844	+	4.01811i	0.483516	+	0.141973i
$802$	2.00396	+	4.38806i	0.0707623	+	0.154948i
$803$	1.31689	−	9.15915i	0.0464719	−	0.323219i
$804$	4.85385			0.171182
$805$	−0.159399	−	0.354327i	−0.00561808	−	0.0124884i
$806$	3.83493			0.135080
$807$	−3.42183	+	23.7993i	−0.120454	+	0.837777i
$808$	−3.69964	−	8.10109i	−0.130153	−	0.284995i
$809$	−40.0292	−	11.7536i	−1.40735	−	0.413236i	−0.512150	−	0.858896i	$-0.671151\pi$
$809$	−40.0292	−	11.7536i	−1.40735	−	0.413236i	−0.895202	+	0.445660i	$0.852969\pi$
$810$	0.186393	+	0.215109i	0.00654918	+	0.00755815i
$811$	−46.7854	+	13.7374i	−1.64286	+	0.482387i	−0.967028	−	0.254670i	$-0.918033\pi$
$811$	−46.7854	+	13.7374i	−1.64286	+	0.482387i	−0.675830	+	0.737057i	$0.736215\pi$
$812$	0.228468	+	0.146828i	0.00801767	+	0.00515264i
$813$	−0.917640	+	2.00935i	−0.0321830	+	0.0704710i
$814$	−0.982880	+	1.13430i	−0.0344499	+	0.0397573i
$815$	0.662438	−	0.425723i	0.0232042	−	0.0149124i
$816$	3.55726	+	24.7413i	0.124529	+	0.866118i
$817$	0.545891	+	3.79676i	0.0190983	+	0.132832i
$818$	−5.05549	+	3.24897i	−0.176761	+	0.113597i
$819$	0.190952	−	0.220371i	0.00667242	−	0.00770038i
$820$	4.34610	−	9.51664i	0.151772	−	0.332335i
$821$	33.2207	+	21.3497i	1.15941	+	0.745108i	0.971491	−	0.237076i	$-0.0761891\pi$
$821$	33.2207	+	21.3497i	1.15941	+	0.745108i	0.187920	+	0.982184i	$0.439825\pi$
$822$	1.68761	−	0.495527i	0.0588622	−	0.0172835i
$823$	−6.67740	−	7.70613i	−0.232760	−	0.268619i	0.627339	−	0.778746i	$-0.284144\pi$
$823$	−6.67740	−	7.70613i	−0.232760	−	0.268619i	−0.860099	+	0.510127i	$0.829598\pi$
$824$	3.15159	+	0.925392i	0.109791	+	0.0322376i
$825$	−2.82048	−	6.17599i	−0.0981965	−	0.215020i
$826$	−0.0158418	+	0.110182i	−0.000551208	+	0.00383374i
$827$	7.61698			0.264868			0.132434	−	0.991192i	$-0.457721\pi$
$827$	7.61698			0.264868			0.132434	+	0.991192i	$0.457721\pi$
$828$	−6.14534	+	7.01155i	−0.213565	+	0.243668i
$829$	−23.4293			−0.813734			−0.406867	−	0.913487i	$-0.633379\pi$
$829$	−23.4293			−0.813734			−0.406867	+	0.913487i	$0.633379\pi$
$830$	−0.522125	+	3.63146i	−0.0181232	+	0.126050i
$831$	0.822678	+	1.80141i	0.0285384	+	0.0624904i
$832$	−27.8038	−	8.16393i	−0.963923	−	0.283033i
$833$	31.2212	+	36.0312i	1.08175	+	1.24841i
$834$	0.307905	−	0.0904090i	0.0106619	−	0.00313061i
$835$	−7.87504	−	5.06098i	−0.272527	−	0.175142i
$836$	0.603297	−	1.32104i	0.0208655	−	0.0456890i
$837$	2.45138	−	2.82904i	0.0847321	−	0.0977860i
$838$	−0.345885	+	0.222287i	−0.0119484	+	0.00767876i
$839$	0.100107	+	0.696262i	0.00345609	+	0.0240376i	0.991477	−	0.130286i	$-0.0415894\pi$
$839$	0.100107	+	0.696262i	0.00345609	+	0.0240376i	−0.988020	+	0.154323i	$0.950680\pi$
$840$	0.0107535	+	0.0747920i	0.000371030	+	0.00258057i
$841$	−20.7726	+	13.3498i	−0.716298	+	0.460337i
$842$	−3.68797	+	4.25614i	−0.127096	+	0.146676i
$843$	−5.43288	+	11.8964i	−0.187118	+	0.409732i
$844$	−26.1924	−	16.8328i	−0.901579	−	0.579409i
$845$	−6.66070	+	1.95576i	−0.229135	+	0.0672801i
$846$	1.88890	+	2.17991i	0.0649418	+	0.0749468i
$847$	0.474348	+	0.139281i	0.0162988	+	0.00478576i
$848$	−11.4841	−	25.1467i	−0.394365	−	0.863540i
$849$	−0.173389	+	1.20595i	−0.00595070	+	0.0413881i
$850$	5.72354			0.196316
$851$	−6.69565	+	14.4446i	−0.229524	+	0.495155i
$852$	23.8464			0.816965
$853$	−2.37445	+	16.5147i	−0.0812996	+	0.565451i	0.907935	+	0.419111i	$0.137658\pi$
$853$	−2.37445	+	16.5147i	−0.0812996	+	0.565451i	−0.989234	+	0.146340i	$0.953251\pi$
$854$	0.0564826	+	0.123680i	0.00193279	+	0.00423223i
$855$	−0.451245	−	0.132498i	−0.0154323	−	0.00453132i
$856$	7.65204	+	8.83092i	0.261541	+	0.301835i
$857$	−11.9531	+	3.50976i	−0.408311	+	0.119891i	−0.479437	−	0.877576i	$-0.659159\pi$
$857$	−11.9531	+	3.50976i	−0.408311	+	0.119891i	0.0711256	+	0.997467i	$0.477341\pi$
$858$	1.64769	+	1.05891i	0.0562512	+	0.0361504i
$859$	−5.22305	+	11.4369i	−0.178208	+	0.390221i	−0.977565	−	0.210636i	$-0.932447\pi$
$859$	−5.22305	+	11.4369i	−0.178208	+	0.390221i	0.799357	+	0.600857i	$0.205174\pi$
$860$	−15.0426	+	17.3601i	−0.512949	+	0.591975i
$861$	0.253172	−	0.162704i	0.00862808	−	0.00554493i
$862$	−0.487116	−	3.38797i	−0.0165912	−	0.115395i
$863$	−6.18253	−	43.0004i	−0.210456	−	1.46375i	−0.771639	−	0.636060i	$-0.780563\pi$
$863$	−6.18253	−	43.0004i	−0.210456	−	1.46375i	0.561184	−	0.827691i	$-0.310346\pi$
$864$	2.29889	−	1.47740i	0.0782097	−	0.0502623i
$865$	−3.33888	+	3.85328i	−0.113525	+	0.131015i
$866$	−2.93606	+	6.42908i	−0.0997714	+	0.218469i
$867$	−24.7734	−	15.9209i	−0.841347	−	0.540701i
$868$	0.469991	−	0.138002i	0.0159525	−	0.00468409i
$869$	12.4034	+	14.3143i	0.420758	+	0.485581i
$870$	0.566807	+	0.166430i	0.0192166	+	0.00564249i
$871$	−4.49323	−	9.83879i	−0.152247	−	0.333375i
$872$	−0.197250	+	1.37190i	−0.00667972	+	0.0464585i
$873$	−18.2553			−0.617847
$874$	−0.0655456	+	0.438264i	−0.00221711	+	0.0148245i
$875$	−0.692776			−0.0234201
$876$	−1.33909	+	9.31357i	−0.0452436	+	0.314676i
$877$	−0.0764685	−	0.167443i	−0.00258216	−	0.00565414i	0.908337	−	0.418240i	$-0.137353\pi$
$877$	−0.0764685	−	0.167443i	−0.00258216	−	0.00565414i	−0.910919	+	0.412586i	$0.864626\pi$
$878$	−1.92039	−	0.563878i	−0.0648101	−	0.0190300i
$879$	−14.4127	−	16.6331i	−0.486128	−	0.561022i
$880$	8.09773	−	2.37771i	0.272974	−	0.0801525i
$881$	5.59422	+	3.59519i	0.188474	+	0.121125i	0.631475	−	0.775396i	$-0.282450\pi$
$881$	5.59422	+	3.59519i	0.188474	+	0.121125i	−0.443001	+	0.896521i	$0.646086\pi$
$882$	0.687213	−	1.50479i	0.0231397	−	0.0506688i
$883$	25.2932	−	29.1899i	0.851185	−	0.982320i	−0.148794	−	0.988868i	$-0.547539\pi$
$883$	25.2932	−	29.1899i	0.851185	−	0.982320i	0.999979	+	0.00654850i	$0.00208447\pi$
$884$	48.2868	−	31.0320i	1.62406	−	1.04372i
$885$	−1.19792	−	8.33173i	−0.0402677	−	0.280068i
$886$	−0.228409	−	1.58862i	−0.00767355	−	0.0533707i
$887$	−39.7373	+	25.5376i	−1.33425	+	0.857469i	−0.996486	−	0.0837624i	$-0.973306\pi$
$887$	−39.7373	+	25.5376i	−1.33425	+	0.857469i	−0.337762	+	0.941231i	$0.609670\pi$
$888$	2.02765	−	2.34004i	0.0680436	−	0.0785265i
$889$	−0.123833	+	0.271157i	−0.00415323	+	0.00909431i
$890$	3.41501	+	2.19469i	0.114471	+	0.0735663i
$891$	1.83440	−	0.538629i	0.0614547	−	0.0180447i
$892$	16.2653	+	18.7712i	0.544604	+	0.628507i
$893$	−4.57291	−	1.34273i	−0.153027	−	0.0449327i
$894$	−2.09814	−	4.59428i	−0.0701722	−	0.153656i
$895$	−2.31651	+	16.1117i	−0.0774322	+	0.538553i
$896$	0.474338			0.0158465
$897$	19.9012	+	5.96603i	0.664483	+	0.199200i
$898$	6.54242			0.218323
$899$	1.10567	−	7.69009i	0.0368761	−	0.256479i
$900$	2.86803	+	6.28012i	0.0956011	+	0.209337i
$901$	49.2901	+	14.4729i	1.64209	+	0.482161i
$902$	1.32376	+	1.52770i	0.0440765	+	0.0508670i
$903$	−0.633997	+	0.186158i	−0.0210981	+	0.00619496i
$904$	−5.52111	−	3.54820i	−0.183629	−	0.118012i
$905$	9.65563	−	21.1429i	0.320964	−	0.702813i
$906$	2.25171	−	2.59861i	0.0748080	−	0.0863330i
$907$	21.9279	−	14.0922i	0.728104	−	0.467924i	−0.123343	−	0.992364i	$-0.539362\pi$
$907$	21.9279	−	14.0922i	0.728104	−	0.467924i	0.851447	+	0.524440i	$0.175725\pi$
$908$	0.894663	+	6.22252i	0.0296904	+	0.206502i
$909$	1.35891	+	9.45142i	0.0450722	+	0.313484i
$910$	0.0698205	−	0.0448709i	0.00231453	−	0.00148746i
$911$	−10.1815	+	11.7501i	−0.337328	+	0.389297i	−0.898917	−	0.438119i	$-0.855645\pi$
$911$	−10.1815	+	11.7501i	−0.337328	+	0.389297i	0.561589	+	0.827416i	$0.310190\pi$
$912$	−0.595314	+	1.30356i	−0.0197128	+	0.0431651i
$913$	20.7312	+	13.3231i	0.686101	+	0.440930i
$914$	−6.22463	+	1.82771i	−0.205892	+	0.0604554i
$915$	−6.73293	−	7.77021i	−0.222584	−	0.256875i
$916$	40.1156	+	11.7790i	1.32546	+	0.389189i
$917$	−0.346226	−	0.758129i	−0.0114334	−	0.0250356i
$918$	−0.229365	+	1.59527i	−0.00757017	+	0.0526517i
$919$	−47.5604			−1.56887			−0.784437	−	0.620209i	$-0.787048\pi$
$919$	−47.5604			−1.56887			−0.784437	+	0.620209i	$0.787048\pi$
$920$	−4.54554	+	2.88504i	−0.149862	+	0.0951169i
$921$	22.3621			0.736856
$922$	−0.684078	+	4.75787i	−0.0225289	+	0.156692i
$923$	−22.0747	−	48.3369i	−0.726599	−	1.59103i
$924$	0.240038	+	0.0704816i	0.00789668	+	0.00231867i
$925$	7.72048	+	8.90991i	0.253848	+	0.292956i
$926$	−5.85898	+	1.72035i	−0.192538	+	0.0565342i
$927$	−2.96263	−	1.90397i	−0.0973056	−	0.0625345i
$928$	2.35606	−	5.15905i	0.0773414	−	0.169354i
$929$	39.4515	−	45.5294i	1.29436	−	1.49377i	0.531772	−	0.846887i	$-0.321526\pi$
$929$	39.4515	−	45.5294i	1.29436	−	1.49377i	0.762588	−	0.646884i	$-0.223928\pi$
$930$	0.896331	−	0.576037i	0.0293919	−	0.0188890i
$931$	0.389000	+	2.70556i	0.0127490	+	0.0886710i
$932$	4.51724	+	31.4181i	0.147967	+	1.02913i
$933$	−9.71424	+	6.24296i	−0.318030	+	0.204385i
$934$	1.31388	−	1.51630i	0.0429914	−	0.0496147i
$935$	−6.51488	+	14.2656i	−0.213059	+	0.466535i
$936$	−3.39913	−	2.18449i	−0.111104	−	0.0714023i
$937$	7.68089	−	2.25531i	0.250924	−	0.0736779i	−0.153852	−	0.988094i	$-0.549168\pi$
$937$	7.68089	−	2.25531i	0.250924	−	0.0736779i	0.404776	+	0.914416i	$0.367350\pi$
$938$	0.0260247	+	0.0300341i	0.000849738	+	0.000980650i
$939$	1.96882	+	0.578097i	0.0642499	+	0.0188655i
$940$	−11.8564	−	25.9618i	−0.386712	−	0.846782i
$941$	3.71648	−	25.8487i	0.121154	−	0.842644i	−0.835098	−	0.550100i	$-0.814589\pi$
$941$	3.71648	−	25.8487i	0.121154	−	0.842644i	0.956252	−	0.292543i	$-0.0945015\pi$
$942$	0.00890987			0.000290299
$943$	17.9729	+	11.6947i	0.585278	+	0.380831i
$944$	−25.6491			−0.834807
$945$	0.0115295	−	0.0801894i	0.000375055	−	0.00260856i
$946$	−1.84374	−	4.03723i	−0.0599452	−	0.131262i
$947$	20.3667	+	5.98019i	0.661827	+	0.194330i	0.595361	−	0.803459i	$-0.297009\pi$
$947$	20.3667	+	5.98019i	0.661827	+	0.194330i	0.0664667	+	0.997789i	$0.478827\pi$
$948$	−12.6126	−	14.5557i	−0.409637	−	0.472746i
$949$	20.1183	−	5.90726i	0.653067	−	0.191758i
$950$	0.276052	+	0.177408i	0.00895630	+	0.00575587i
$951$	−7.22320	+	15.8166i	−0.234228	+	0.512889i
$952$	−0.280184	+	0.323350i	−0.00908082	+	0.0104798i
$953$	−20.6366	+	13.2623i	−0.668485	+	0.429609i	−0.830379	−	0.557199i	$-0.811876\pi$
$953$	−20.6366	+	13.2623i	−0.668485	+	0.429609i	0.161894	+	0.986808i	$0.448240\pi$
$954$	−0.253674	−	1.76434i	−0.00821300	−	0.0571227i
$955$	−2.43149	−	16.9114i	−0.0786812	−	0.547239i
$956$	−1.53750	+	0.988091i	−0.0497263	+	0.0319571i
$957$	2.59845	−	2.99877i	0.0839960	−	0.0969366i
$958$	1.77309	−	3.88253i	0.0572861	−	0.125439i
$959$	−0.421151	−	0.270657i	−0.0135997	−	0.00873997i
$960$	−7.72482	+	2.26821i	−0.249318	+	0.0732062i
$961$	11.1243	+	12.8381i	0.358848	+	0.414133i
$962$	−3.26321	−	0.958164i	−0.105210	−	0.0308924i
$963$	−5.20442	−	11.3961i	−0.167710	−	0.367234i
$964$	−2.18237	+	15.1787i	−0.0702894	+	0.488874i
$965$	25.6679			0.826279
$966$	−0.0763347		0.000431852i	−0.00245603		1.38946e-5i
$967$	51.2304			1.64746			0.823729	−	0.566983i	$-0.191890\pi$
$967$	51.2304			1.64746			0.823729	+	0.566983i	$0.191890\pi$
$968$	0.974925	−	6.78075i	0.0313353	−	0.217942i
$969$	−1.10624	−	2.42233i	−0.0355375	−	0.0778164i
$970$	−4.98552	−	1.46388i	−0.160075	−	0.0470024i
$971$	6.86019	+	7.91708i	0.220154	+	0.254071i	0.855073	−	0.518507i	$-0.173512\pi$
$971$	6.86019	+	7.91708i	0.220154	+	0.254071i	−0.634919	+	0.772579i	$0.718967\pi$
$972$	−1.86533	+	0.547710i	−0.0598305	+	0.0175678i
$973$	−0.0768390	−	0.0493814i	−0.00246335	−	0.00158310i
$974$	3.30550	−	7.23804i	0.105915	−	0.231922i
$975$	10.0749	−	11.6271i	0.322655	−	0.372364i
$976$	−26.3557	+	16.9378i	−0.843627	+	0.542166i
$977$	1.07038	+	7.44463i	0.0342443	+	0.238175i	0.999754	−	0.0221938i	$-0.00706507\pi$
$977$	1.07038	+	7.44463i	0.0342443	+	0.238175i	−0.965509	+	0.260368i	$0.916156\pi$
$978$	−0.0220177	−	0.153137i	−0.000704050	−	0.00489677i
$979$	22.9385	−	14.7417i	0.733117	−	0.471145i
$980$	−10.7193	+	12.3708i	−0.342416	+	0.395169i
$981$	0.617321	−	1.35174i	0.0197095	−	0.0431578i
$982$	−6.32180	−	4.06277i	−0.201737	−	0.129648i
$983$	48.4074	−	14.2137i	1.54396	−	0.453346i	0.604668	−	0.796478i	$-0.293306\pi$
$983$	48.4074	−	14.2137i	1.54396	−	0.453346i	0.939287	+	0.343131i	$0.111488\pi$
$984$	−2.73088	−	3.15161i	−0.0870574	−	0.100470i
$985$	−4.17405	−	1.22561i	−0.132996	−	0.0390513i
$986$	1.38954	+	3.04267i	0.0442521	+	0.0968985i
$987$	0.116840	−	0.812639i	0.00371905	−	0.0258666i
$988$	3.29079			0.104694
$989$	−30.6291	−	35.7546i	−0.973949	−	1.13693i
$990$	0.544168			0.0172948
$991$	−3.18763	+	22.1705i	−0.101258	+	0.704268i	0.874437	+	0.485138i	$0.161231\pi$
$991$	−3.18763	+	22.1705i	−0.101258	+	0.704268i	−0.975696	+	0.219129i	$0.929678\pi$
$992$	−4.24946	−	9.30503i	−0.134921	−	0.295435i
$993$	7.49599	+	2.20102i	0.237878	+	0.0698473i
$994$	0.127857	+	0.147555i	0.00405537	+	0.00468014i
$995$	−25.7015	+	7.54664i	−0.814792	+	0.239244i
$996$	−21.0807	−	13.5477i	−0.667967	−	0.429276i
$997$	9.72175	−	21.2877i	0.307891	−	0.674187i	−0.690920	−	0.722931i	$-0.742795\pi$
$997$	9.72175	−	21.2877i	0.307891	−	0.674187i	0.998811	+	0.0487438i	$0.0155218\pi$
$998$	−2.49655	+	2.88117i	−0.0790268	+	0.0912018i
$999$	−2.79276	+	1.79480i	−0.0883590	+	0.0567849i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.a.31.1	✓	10
3.2	odd	2		207.2.i.b.100.1		10
23.3	even	11	inner	69.2.e.a.49.1	yes	10
23.7	odd	22		1587.2.a.p.1.4		5
23.16	even	11		1587.2.a.o.1.4		5
69.26	odd	22		207.2.i.b.118.1		10
69.53	even	22		4761.2.a.bq.1.2		5
69.62	odd	22		4761.2.a.br.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.a.31.1	✓	10	1.1	even	1	trivial
69.2.e.a.49.1	yes	10	23.3	even	11	inner
207.2.i.b.100.1		10	3.2	odd	2
207.2.i.b.118.1		10	69.26	odd	22
1587.2.a.o.1.4		5	23.16	even	11
1587.2.a.p.1.4		5	23.7	odd	22
4761.2.a.bq.1.2		5	69.53	even	22
4761.2.a.br.1.2		5	69.62	odd	22

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0336545 - 0.234072i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(1.86533 + 0.547710i) q^{4} +(-0.788201 - 0.909632i) q^{5} +(-0.226900 + 0.0666238i) q^{6} +(0.0566239 + 0.0363899i) q^{7} +(0.387454 - 0.848406i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.0336545 - 0.234072i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(1.86533 + 0.547710i) q^{4} +(-0.788201 - 0.909632i) q^{5} +(-0.226900 + 0.0666238i) q^{6} +(0.0566239 + 0.0363899i) q^{7} +(0.387454 - 0.848406i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.239446 + 0.153882i) q^{10} +(0.272084 + 1.89238i) q^{11} +(-0.276671 - 1.92429i) q^{12} +(-3.64444 + 2.34214i) q^{13} +(0.0104235 - 0.0120294i) q^{14} +(-0.500000 + 1.09485i) q^{15} +(3.08538 + 1.98285i) q^{16} +(-6.53922 + 1.92009i) q^{17} +(0.154861 + 0.178719i) q^{18} +(-0.374908 - 0.110083i) q^{19} +(-0.972039 - 2.12847i) q^{20} +(0.00957906 - 0.0666238i) q^{21} +0.452111 q^{22} +(4.60914 - 1.32509i) q^{23} -0.932691 q^{24} +(0.505404 - 3.51516i) q^{25} +(0.425577 + 0.931884i) q^{26} +(0.959493 + 0.281733i) q^{27} +(0.0856910 + 0.0988927i) q^{28} +(1.99138 - 0.584723i) q^{29} +(0.239446 + 0.153882i) q^{30} +(1.55505 - 3.40508i) q^{31} +(1.78953 - 2.06523i) q^{32} +(1.60835 - 1.03362i) q^{33} +(0.229365 + 1.59527i) q^{34} +(-0.0115295 - 0.0801894i) q^{35} +(-1.63546 + 1.05105i) q^{36} +(-2.17398 + 2.50891i) q^{37} +(-0.0383846 + 0.0840506i) q^{38} +(3.64444 + 2.34214i) q^{39} +(-1.07713 + 0.316273i) q^{40} +(2.92796 + 3.37905i) q^{41} +(-0.0152724 - 0.00448438i) q^{42} +(-4.07807 - 8.92974i) q^{43} +(-0.528952 + 3.67894i) q^{44} +1.20362 q^{45} +(-0.155048 - 1.12346i) q^{46} +12.1974 q^{47} +(0.521953 - 3.63026i) q^{48} +(-2.90602 - 6.36330i) q^{49} +(-0.805791 - 0.236602i) q^{50} +(4.46306 + 5.15065i) q^{51} +(-8.08089 + 2.37276i) q^{52} +(-6.34104 - 4.07514i) q^{53} +(0.0982369 - 0.215109i) q^{54} +(1.50692 - 1.73907i) q^{55} +(0.0528126 - 0.0339406i) q^{56} +(0.0556075 + 0.386758i) q^{57} +(-0.0698483 - 0.485806i) q^{58} +(-5.88325 + 3.78094i) q^{59} +(-1.53232 + 1.76840i) q^{60} +(-3.54854 + 7.77021i) q^{61} +(-0.744699 - 0.478589i) q^{62} +(-0.0645824 + 0.0189631i) q^{63} +(4.38034 + 5.05518i) q^{64} +(5.00303 + 1.46902i) q^{65} +(-0.187814 - 0.411254i) q^{66} +(-0.355322 + 2.47132i) q^{67} -13.2494 q^{68} +(-3.12005 - 3.64216i) q^{69} -0.0191581 q^{70} +(-1.74566 + 12.1413i) q^{71} +(0.387454 + 0.848406i) q^{72} +(-4.64395 - 1.36359i) q^{73} +(0.514101 + 0.593304i) q^{74} +(-3.40746 + 1.00052i) q^{75} +(-0.639033 - 0.410682i) q^{76} +(-0.0534573 + 0.117055i) q^{77} +(0.670880 - 0.774237i) q^{78} +(8.33427 - 5.35611i) q^{79} +(-0.628231 - 4.36944i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(0.889479 - 0.571633i) q^{82} +(8.44098 - 9.74141i) q^{83} +(0.0543586 - 0.119029i) q^{84} +(6.90079 + 4.43487i) q^{85} +(-2.22745 + 0.654037i) q^{86} +(-1.35913 - 1.56852i) q^{87} +(1.71093 + 0.502374i) q^{88} +(-5.92471 - 12.9733i) q^{89} +(0.0405070 - 0.281733i) q^{90} -0.291592 q^{91} +(9.32332 + 0.0527453i) q^{92} -3.74336 q^{93} +(0.410498 - 2.85507i) q^{94} +(0.195368 + 0.427796i) q^{95} +(-2.62200 - 0.769888i) q^{96} +(11.9547 + 13.7964i) q^{97} +(-1.58727 + 0.466065i) q^{98} +(-1.60835 - 1.03362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9} - 2 q^{10} + 7 q^{11} + 14 q^{12} - 30 q^{13} + q^{14} - 5 q^{15} + 12 q^{16} - 2 q^{17} - 4 q^{18} + 10 q^{19} + 4 q^{20} - 3 q^{21} + 6 q^{22} - q^{23} - 18 q^{24} + 24 q^{25} + q^{26} + q^{27} + 9 q^{28} - 14 q^{29} + 2 q^{30} - 28 q^{31} + 23 q^{32} - 7 q^{33} - 8 q^{34} - 4 q^{35} - 3 q^{36} + 19 q^{37} - 15 q^{38} + 30 q^{39} - 13 q^{40} + 19 q^{41} + 21 q^{42} - 24 q^{43} + 54 q^{44} - 6 q^{45} + 18 q^{46} + 26 q^{47} + 10 q^{48} - 13 q^{49} - 36 q^{50} + 24 q^{51} - 57 q^{52} - q^{53} + 4 q^{54} - 24 q^{55} - 10 q^{56} + q^{57} + 10 q^{58} + 2 q^{59} + 7 q^{60} + 30 q^{61} - 24 q^{62} - 8 q^{63} + 13 q^{64} - 4 q^{65} - 28 q^{66} + 4 q^{67} - 50 q^{68} + q^{69} + 6 q^{70} - 14 q^{71} - 15 q^{72} - 26 q^{73} - 12 q^{74} - 13 q^{75} + 19 q^{76} - 43 q^{77} + 10 q^{78} + 20 q^{79} - 5 q^{80} - q^{81} + 10 q^{82} + 18 q^{83} - 42 q^{84} + 21 q^{85} + 14 q^{86} - 8 q^{87} - 38 q^{88} - 5 q^{89} + 9 q^{90} + 46 q^{91} + 52 q^{92} - 16 q^{93} - 6 q^{94} + 5 q^{95} - q^{96} + 15 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9 - 2 * q^10 + 7 * q^11 + 14 * q^12 - 30 * q^13 + q^14 - 5 * q^15 + 12 * q^16 - 2 * q^17 - 4 * q^18 + 10 * q^19 + 4 * q^20 - 3 * q^21 + 6 * q^22 - q^23 - 18 * q^24 + 24 * q^25 + q^26 + q^27 + 9 * q^28 - 14 * q^29 + 2 * q^30 - 28 * q^31 + 23 * q^32 - 7 * q^33 - 8 * q^34 - 4 * q^35 - 3 * q^36 + 19 * q^37 - 15 * q^38 + 30 * q^39 - 13 * q^40 + 19 * q^41 + 21 * q^42 - 24 * q^43 + 54 * q^44 - 6 * q^45 + 18 * q^46 + 26 * q^47 + 10 * q^48 - 13 * q^49 - 36 * q^50 + 24 * q^51 - 57 * q^52 - q^53 + 4 * q^54 - 24 * q^55 - 10 * q^56 + q^57 + 10 * q^58 + 2 * q^59 + 7 * q^60 + 30 * q^61 - 24 * q^62 - 8 * q^63 + 13 * q^64 - 4 * q^65 - 28 * q^66 + 4 * q^67 - 50 * q^68 + q^69 + 6 * q^70 - 14 * q^71 - 15 * q^72 - 26 * q^73 - 12 * q^74 - 13 * q^75 + 19 * q^76 - 43 * q^77 + 10 * q^78 + 20 * q^79 - 5 * q^80 - q^81 + 10 * q^82 + 18 * q^83 - 42 * q^84 + 21 * q^85 + 14 * q^86 - 8 * q^87 - 38 * q^88 - 5 * q^89 + 9 * q^90 + 46 * q^91 + 52 * q^92 - 16 * q^93 - 6 * q^94 + 5 * q^95 - q^96 + 15 * q^97 + 58 * q^98 + 7 * q^99

Introduction

L-functions

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