LMFDB - Embedded newform 462.2.y.b.235.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			235.2
Character	$\chi$	$=$	462.235
Dual form			462.2.y.b.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 + 0.994522i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.06629 + 0.474743i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-1.26472 + 2.32389i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.104528 + 0.994522i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.06629 + 0.474743i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-1.26472 + 2.32389i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-0.583600 + 1.01083i) q^{10} +(-2.83068 + 1.72836i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.534434 + 0.388289i) q^{13} +(-2.17896 - 1.50071i) q^{14} +(0.360685 + 1.11007i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.0238298 + 0.226726i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(-0.381789 + 0.0811518i) q^{19} +(-0.944285 - 0.686063i) q^{20} +(-2.57325 + 0.615116i) q^{21} +(-1.42300 - 2.99584i) q^{22} +(4.34784 + 7.53067i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-2.43406 - 2.70329i) q^{25} +(-0.442025 + 0.490919i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.72025 - 2.01016i) q^{28} +(0.834092 + 2.56707i) q^{29} +(-1.14169 + 0.242675i) q^{30} +(0.169662 - 0.0755383i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.17852 - 0.947110i) q^{33} -0.227975 q^{34} +(-2.45181 + 1.87753i) q^{35} +(0.309017 - 0.951057i) q^{36} +(2.59698 - 2.88424i) q^{37} +(-0.0407994 - 0.388181i) q^{38} +(0.0690511 + 0.656977i) q^{39} +(0.781010 - 0.867399i) q^{40} +(-0.155049 + 0.477191i) q^{41} +(-0.342768 - 2.62345i) q^{42} -4.81061 q^{43} +(3.12817 - 1.10206i) q^{44} +(-0.583600 + 1.01083i) q^{45} +(-7.94389 + 3.53685i) q^{46} +(1.13043 - 0.240281i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-3.80096 - 5.87816i) q^{49} +(2.94291 - 2.13815i) q^{50} +(-0.152545 + 0.169418i) q^{51} +(-0.442025 - 0.490919i) q^{52} +(8.54304 - 3.80361i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-3.83886 + 0.499086i) q^{55} +(1.81933 + 1.92094i) q^{56} +(-0.315775 - 0.229424i) q^{57} +(-2.64020 + 0.561191i) q^{58} +(10.2599 + 2.18080i) q^{59} +(-0.122006 - 1.16081i) q^{60} +(-8.69343 - 3.87056i) q^{61} +(0.0573900 + 0.176628i) q^{62} +(-2.17896 - 1.50071i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.385524 + 0.667748i) q^{65} +(1.27417 - 3.06211i) q^{66} +(2.15360 - 3.73015i) q^{67} +(0.0238298 - 0.226726i) q^{68} +(-2.68711 + 8.27008i) q^{69} +(-1.61096 - 2.63464i) q^{70} +(5.35911 - 3.89362i) q^{71} +(0.913545 + 0.406737i) q^{72} +(14.3285 + 3.04562i) q^{73} +(2.59698 + 2.88424i) q^{74} +(0.380237 - 3.61771i) q^{75} +0.390319 q^{76} +(-0.436493 - 8.76410i) q^{77} -0.660596 q^{78} +(-0.0118380 + 0.112631i) q^{79} +(0.781010 + 0.867399i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-0.458370 - 0.204079i) q^{82} +(-8.46595 + 6.15087i) q^{83} +(2.64491 - 0.0666648i) q^{84} +(-0.0822270 + 0.253069i) q^{85} +(0.502846 - 4.78426i) q^{86} +(-1.34959 + 2.33756i) q^{87} +(0.769038 + 3.22623i) q^{88} +(6.30388 + 10.9186i) q^{89} +(-0.944285 - 0.686063i) q^{90} +(-1.57825 + 0.750889i) q^{91} +(-2.68711 - 8.27008i) q^{92} +(0.169662 + 0.0755383i) q^{93} +(0.120802 + 1.14936i) q^{94} +(-0.445625 - 0.0947205i) q^{95} +(-0.978148 + 0.207912i) q^{96} +(6.08182 + 4.41870i) q^{97} +(6.24326 - 3.16570i) q^{98} +(-1.42300 - 2.99584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9} + 10 q^{10} - 2 q^{11} - 12 q^{12} + 10 q^{13} + 7 q^{14} + 20 q^{15} + 3 q^{16} + 8 q^{17} + 3 q^{18} + 7 q^{19} - 10 q^{20} + 8 q^{21} - 6 q^{22} + 24 q^{23} + 3 q^{24} + 8 q^{25} - 6 q^{27} - 2 q^{28} + 2 q^{29} - 10 q^{30} - 19 q^{31} - 12 q^{32} - 7 q^{33} + 24 q^{34} + 14 q^{35} - 6 q^{36} - q^{37} - 8 q^{38} - 5 q^{39} - 10 q^{40} + 16 q^{41} + 10 q^{42} - 68 q^{43} - 2 q^{44} + 10 q^{45} - 6 q^{46} + 25 q^{47} - 6 q^{48} - 21 q^{49} + 14 q^{50} - 2 q^{51} - 5 q^{53} - 12 q^{54} - 10 q^{55} - 10 q^{56} + 16 q^{57} - q^{58} - 36 q^{59} + 5 q^{60} - q^{61} - 52 q^{62} + 7 q^{63} - 6 q^{64} + 6 q^{65} + 8 q^{66} + 56 q^{67} + 8 q^{68} + 12 q^{69} - 17 q^{70} - 6 q^{71} + 3 q^{72} + 35 q^{73} - q^{74} - 7 q^{75} - 4 q^{76} + 38 q^{77} - 20 q^{78} - 3 q^{79} - 10 q^{80} + 3 q^{81} + 2 q^{82} - 28 q^{83} + 7 q^{84} - 80 q^{85} - 11 q^{86} + 4 q^{87} - 7 q^{88} - 6 q^{89} - 10 q^{90} - 24 q^{91} + 12 q^{92} - 19 q^{93} - 30 q^{94} - 44 q^{95} + 3 q^{96} - 8 q^{97} - 6 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9 + 10 * q^10 - 2 * q^11 - 12 * q^12 + 10 * q^13 + 7 * q^14 + 20 * q^15 + 3 * q^16 + 8 * q^17 + 3 * q^18 + 7 * q^19 - 10 * q^20 + 8 * q^21 - 6 * q^22 + 24 * q^23 + 3 * q^24 + 8 * q^25 - 6 * q^27 - 2 * q^28 + 2 * q^29 - 10 * q^30 - 19 * q^31 - 12 * q^32 - 7 * q^33 + 24 * q^34 + 14 * q^35 - 6 * q^36 - q^37 - 8 * q^38 - 5 * q^39 - 10 * q^40 + 16 * q^41 + 10 * q^42 - 68 * q^43 - 2 * q^44 + 10 * q^45 - 6 * q^46 + 25 * q^47 - 6 * q^48 - 21 * q^49 + 14 * q^50 - 2 * q^51 - 5 * q^53 - 12 * q^54 - 10 * q^55 - 10 * q^56 + 16 * q^57 - q^58 - 36 * q^59 + 5 * q^60 - q^61 - 52 * q^62 + 7 * q^63 - 6 * q^64 + 6 * q^65 + 8 * q^66 + 56 * q^67 + 8 * q^68 + 12 * q^69 - 17 * q^70 - 6 * q^71 + 3 * q^72 + 35 * q^73 - q^74 - 7 * q^75 - 4 * q^76 + 38 * q^77 - 20 * q^78 - 3 * q^79 - 10 * q^80 + 3 * q^81 + 2 * q^82 - 28 * q^83 + 7 * q^84 - 80 * q^85 - 11 * q^86 + 4 * q^87 - 7 * q^88 - 6 * q^89 - 10 * q^90 - 24 * q^91 + 12 * q^92 - 19 * q^93 - 30 * q^94 - 44 * q^95 + 3 * q^96 - 8 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	1.06629	+	0.474743i	0.476860	+	0.212312i	0.631069	−	0.775726i	$-0.282616\pi$
$5$	1.06629	+	0.474743i	0.476860	+	0.212312i	−0.154209	+	0.988038i	$0.549283\pi$
$6$	−0.809017	+	0.587785i	−0.330280	+	0.239962i
$7$	−1.26472	+	2.32389i	−0.478020	+	0.878349i
$7$	−1.26472	+	2.32389i	−0.478020	+	0.878349i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	−0.583600	+	1.01083i	−0.184551	+	0.319651i
$11$	−2.83068	+	1.72836i	−0.853483	+	0.521120i
$11$	−2.83068	+	1.72836i	−0.853483	+	0.521120i
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.534434	+	0.388289i	0.148225	+	0.107692i	0.659426	−	0.751769i	$-0.270799\pi$
$13$	0.534434	+	0.388289i	0.148225	+	0.107692i	−0.511201	+	0.859461i	$0.670799\pi$
$14$	−2.17896	−	1.50071i	−0.582352	−	0.401081i
$15$	0.360685	+	1.11007i	0.0931284	+	0.286620i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	0.0238298	+	0.226726i	0.00577958	+	0.0549891i	0.997032	−	0.0769940i	$-0.0245322\pi$
$17$	0.0238298	+	0.226726i	0.00577958	+	0.0549891i	−0.991252	+	0.131983i	$0.957866\pi$
$18$	−0.978148	−	0.207912i	−0.230552	−	0.0490053i
$19$	−0.381789	+	0.0811518i	−0.0875885	+	0.0186175i	−0.251497	−	0.967858i	$-0.580923\pi$
$19$	−0.381789	+	0.0811518i	−0.0875885	+	0.0186175i	0.163909	+	0.986475i	$0.447590\pi$
$20$	−0.944285	−	0.686063i	−0.211149	−	0.153408i
$21$	−2.57325	+	0.615116i	−0.561530	+	0.134229i
$22$	−1.42300	−	2.99584i	−0.303386	−	0.638715i
$23$	4.34784	+	7.53067i	0.906587	+	1.57025i	0.818773	+	0.574117i	$0.194655\pi$
$23$	4.34784	+	7.53067i	0.906587	+	1.57025i	0.0878135	+	0.996137i	$0.472012\pi$
$24$	0.913545	−	0.406737i	0.186477	−	0.0830248i
$25$	−2.43406	−	2.70329i	−0.486812	−	0.540659i
$26$	−0.442025	+	0.490919i	−0.0866883	+	0.0962771i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	1.72025	−	2.01016i	0.325097	−	0.379884i
$29$	0.834092	+	2.56707i	0.154887	+	0.476693i	0.998149	−	0.0608088i	$-0.0193680\pi$
$29$	0.834092	+	2.56707i	0.154887	+	0.476693i	−0.843262	+	0.537502i	$0.819368\pi$
$30$	−1.14169	+	0.242675i	−0.208444	+	0.0443061i
$31$	0.169662	−	0.0755383i	0.0304722	−	0.0135671i	−0.391444	−	0.920202i	$-0.628024\pi$
$31$	0.169662	−	0.0755383i	0.0304722	−	0.0135671i	0.421916	+	0.906635i	$0.361358\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−3.17852	−	0.947110i	−0.553309	−	0.164871i
$34$	−0.227975			−0.0390973
$35$	−2.45181	+	1.87753i	−0.414432	+	0.317360i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	2.59698	−	2.88424i	0.426942	−	0.474167i	−0.490841	−	0.871249i	$-0.663311\pi$
$37$	2.59698	−	2.88424i	0.426942	−	0.474167i	0.917783	+	0.397082i	$0.129977\pi$
$38$	−0.0407994	−	0.388181i	−0.00661854	−	0.0629712i
$39$	0.0690511	+	0.656977i	0.0110570	+	0.105201i
$40$	0.781010	−	0.867399i	0.123489	−	0.137148i
$41$	−0.155049	+	0.477191i	−0.0242145	+	0.0745247i	−0.962434	−	0.271517i	$-0.912475\pi$
$41$	−0.155049	+	0.477191i	−0.0242145	+	0.0745247i	0.938219	+	0.346042i	$0.112475\pi$
$42$	−0.342768	−	2.62345i	−0.0528903	−	0.404808i
$43$	−4.81061			−0.733611			−0.366806	−	0.930298i	$-0.619549\pi$
$43$	−4.81061			−0.733611			−0.366806	+	0.930298i	$0.619549\pi$
$44$	3.12817	−	1.10206i	0.471590	−	0.166142i
$45$	−0.583600	+	1.01083i	−0.0869980	+	0.150685i
$46$	−7.94389	+	3.53685i	−1.17126	+	0.521480i
$47$	1.13043	−	0.240281i	0.164890	−	0.0350485i	−0.124727	−	0.992191i	$-0.539805\pi$
$47$	1.13043	−	0.240281i	0.164890	−	0.0350485i	0.289617	+	0.957143i	$0.406472\pi$
$48$	0.309017	+	0.951057i	0.0446028	+	0.137273i
$49$	−3.80096	−	5.87816i	−0.542994	−	0.839737i
$50$	2.94291	−	2.13815i	0.416191	−	0.302380i
$51$	−0.152545	+	0.169418i	−0.0213605	+	0.0237233i
$52$	−0.442025	−	0.490919i	−0.0612979	−	0.0680782i
$53$	8.54304	−	3.80361i	1.17348	−	0.522466i	0.274982	−	0.961449i	$-0.411328\pi$
$53$	8.54304	−	3.80361i	1.17348	−	0.522466i	0.898495	+	0.438983i	$0.144661\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−3.83886	+	0.499086i	−0.517632	+	0.0672967i
$56$	1.81933	+	1.92094i	0.243119	+	0.256697i
$57$	−0.315775	−	0.229424i	−0.0418254	−	0.0303879i
$58$	−2.64020	+	0.561191i	−0.346675	+	0.0736880i
$59$	10.2599	+	2.18080i	1.33572	+	0.283916i	0.819765	−	0.572700i	$-0.194104\pi$
$59$	10.2599	+	2.18080i	1.33572	+	0.283916i	0.515955	+	0.856616i	$0.327437\pi$
$60$	−0.122006	−	1.16081i	−0.0157509	−	0.149860i
$61$	−8.69343	−	3.87056i	−1.11308	−	0.495575i	−0.233993	−	0.972238i	$-0.575179\pi$
$61$	−8.69343	−	3.87056i	−1.11308	−	0.495575i	−0.879086	+	0.476663i	$0.841846\pi$
$62$	0.0573900	+	0.176628i	0.00728854	+	0.0224318i
$63$	−2.17896	−	1.50071i	−0.274524	−	0.189071i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.385524	+	0.667748i	0.0478184	+	0.0828239i
$66$	1.27417	−	3.06211i	0.156839	−	0.376919i
$67$	2.15360	−	3.73015i	0.263104	−	0.455710i	−0.703961	−	0.710239i	$-0.748587\pi$
$67$	2.15360	−	3.73015i	0.263104	−	0.455710i	0.967065	+	0.254529i	$0.0819203\pi$
$68$	0.0238298	−	0.226726i	0.00288979	−	0.0274945i
$69$	−2.68711	+	8.27008i	−0.323490	+	0.995600i
$70$	−1.61096	−	2.63464i	−0.192546	−	0.314900i
$71$	5.35911	−	3.89362i	0.636009	−	0.462088i	−0.222468	−	0.974940i	$-0.571411\pi$
$71$	5.35911	−	3.89362i	0.636009	−	0.462088i	0.858477	+	0.512853i	$0.171411\pi$
$72$	0.913545	+	0.406737i	0.107662	+	0.0479344i
$73$	14.3285	+	3.04562i	1.67702	+	0.356462i	0.945567	−	0.325426i	$-0.105508\pi$
$73$	14.3285	+	3.04562i	1.67702	+	0.356462i	0.731456	+	0.681888i	$0.238841\pi$
$74$	2.59698	+	2.88424i	0.301893	+	0.335286i
$75$	0.380237	−	3.61771i	0.0439060	−	0.417738i
$76$	0.390319			0.0447726
$77$	−0.436493	−	8.76410i	−0.0497430	−	0.998762i
$78$	−0.660596			−0.0747978
$79$	−0.0118380	+	0.112631i	−0.00133188	+	0.0126720i	−0.995168	−	0.0981903i	$-0.968695\pi$
$79$	−0.0118380	+	0.112631i	−0.00133188	+	0.0126720i	0.993836	+	0.110862i	$0.0353613\pi$
$80$	0.781010	+	0.867399i	0.0873196	+	0.0969782i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−0.458370	−	0.204079i	−0.0506185	−	0.0225368i
$83$	−8.46595	+	6.15087i	−0.929258	+	0.675146i	−0.945811	−	0.324717i	$-0.894731\pi$
$83$	−8.46595	+	6.15087i	−0.929258	+	0.675146i	0.0165528	+	0.999863i	$0.494731\pi$
$84$	2.64491	−	0.0666648i	0.288583	−	0.00727373i
$85$	−0.0822270	+	0.253069i	−0.00891877	+	0.0274491i
$86$	0.502846	−	4.78426i	0.0542232	−	0.515900i
$87$	−1.34959	+	2.33756i	−0.144691	+	0.250613i
$88$	0.769038	+	3.22623i	0.0819797	+	0.343918i
$89$	6.30388	+	10.9186i	0.668210	+	1.15737i	0.978404	+	0.206701i	$0.0662727\pi$
$89$	6.30388	+	10.9186i	0.668210	+	1.15737i	−0.310194	+	0.950673i	$0.600394\pi$
$90$	−0.944285	−	0.686063i	−0.0995364	−	0.0723174i
$91$	−1.57825	+	0.750889i	−0.165446	+	0.0787145i
$92$	−2.68711	−	8.27008i	−0.280151	−	0.862215i
$93$	0.169662	+	0.0755383i	0.0175931	+	0.00783296i
$94$	0.120802	+	1.14936i	0.0124598	+	0.118547i
$95$	−0.445625	−	0.0947205i	−0.0457201	−	0.00971812i
$96$	−0.978148	+	0.207912i	−0.0998318	+	0.0212199i
$97$	6.08182	+	4.41870i	0.617515	+	0.448651i	0.852053	−	0.523456i	$-0.175358\pi$
$97$	6.08182	+	4.41870i	0.617515	+	0.448651i	−0.234538	+	0.972107i	$0.575358\pi$
$98$	6.24326	−	3.16570i	0.630665	−	0.319784i
$99$	−1.42300	−	2.99584i	−0.143017	−	0.301093i
$100$	1.81882	+	3.15029i	0.181882	+	0.315029i
$101$	2.09316	−	0.931937i	0.208278	−	0.0927312i	−0.299946	−	0.953956i	$-0.596969\pi$
$101$	2.09316	−	0.931937i	0.208278	−	0.0927312i	0.508224	+	0.861225i	$0.330302\pi$
$102$	−0.152545	−	0.169418i	−0.0151042	−	0.0167749i
$103$	7.88940	−	8.76207i	0.777366	−	0.863352i	−0.216230	−	0.976342i	$-0.569376\pi$
$103$	7.88940	−	8.76207i	0.777366	−	0.863352i	0.993596	+	0.112990i	$0.0360429\pi$
$104$	0.534434	−	0.388289i	0.0524055	−	0.0380748i
$105$	−3.03586	−	0.565742i	−0.296270	−	0.0552108i
$106$	2.88978	+	8.89383i	0.280680	+	0.863845i
$107$	14.8924	−	3.16547i	1.43970	−	0.306018i	0.579082	−	0.815269i	$-0.303411\pi$
$107$	14.8924	−	3.16547i	1.43970	−	0.306018i	0.860618	+	0.509251i	$0.170078\pi$
$108$	0.913545	−	0.406737i	0.0879060	−	0.0391383i
$109$	4.44483	−	7.69867i	0.425738	−	0.737399i	−0.570751	−	0.821123i	$-0.693348\pi$
$109$	4.44483	−	7.69867i	0.425738	−	0.737399i	0.996489	+	0.0837238i	$0.0266813\pi$
$110$	−0.0950815	−	3.87000i	−0.00906566	−	0.368990i
$111$	3.88113			0.368381
$112$	−2.10059	+	1.60857i	−0.198487	+	0.151996i
$113$	−3.01041	+	9.26509i	−0.283196	+	0.871586i	0.703738	+	0.710459i	$0.251513\pi$
$113$	−3.01041	+	9.26509i	−0.283196	+	0.871586i	−0.986934	+	0.161127i	$0.948487\pi$
$114$	0.261174	−	0.290063i	0.0244612	−	0.0271669i
$115$	1.06092	+	10.0940i	0.0989315	+	0.941270i
$116$	−0.282141	−	2.68439i	−0.0261961	−	0.249240i
$117$	−0.442025	+	0.490919i	−0.0408652	+	0.0453854i
$118$	−3.24130	+	9.97570i	−0.298386	+	0.918338i
$119$	−0.557024	−	0.231367i	−0.0510623	−	0.0212094i
$120$	1.16720			0.106550
$121$	5.02555	−	9.78488i	0.456868	−	0.889535i
$122$	4.75807	−	8.24122i	0.430775	−	0.746125i
$123$	−0.458370	+	0.204079i	−0.0413298	+	0.0184012i
$124$	−0.181660	+	0.0386129i	−0.0163135	+	0.00346754i
$125$	−3.11547	−	9.58842i	−0.278656	−	0.857615i
$126$	1.72025	−	2.01016i	0.153252	−	0.179079i
$127$	−2.65208	+	1.92685i	−0.235334	+	0.170980i	−0.699202	−	0.714924i	$-0.746461\pi$
$127$	−2.65208	+	1.92685i	−0.235334	+	0.170980i	0.463868	+	0.885904i	$0.346461\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	−3.21893	−	3.57498i	−0.283411	−	0.314759i
$130$	−0.704388	+	0.313614i	−0.0617789	+	0.0275057i
$131$	8.48170	+	14.6907i	0.741049	+	1.28354i	0.952018	+	0.306042i	$0.0990049\pi$
$131$	8.48170	+	14.6907i	0.741049	+	1.28354i	−0.210968	+	0.977493i	$0.567662\pi$
$132$	2.91215	+	1.58726i	0.253470	+	0.138154i
$133$	0.294269	−	0.989872i	0.0255164	−	0.0858328i
$134$	3.48460	+	2.53171i	0.301024	+	0.218707i
$135$	−1.14169	+	0.242675i	−0.0982614	+	0.0208861i
$136$	0.222993	+	0.0473986i	0.0191215	+	0.00406439i
$137$	−1.91926	−	18.2605i	−0.163973	−	1.56010i	−0.698911	−	0.715209i	$-0.746332\pi$
$137$	−1.91926	−	18.2605i	−0.163973	−	1.56010i	0.534938	−	0.844891i	$-0.320335\pi$
$138$	−7.94389	−	3.53685i	−0.676229	−	0.301077i
$139$	4.49686	+	13.8399i	0.381419	+	1.17389i	0.939045	+	0.343795i	$0.111712\pi$
$139$	4.49686	+	13.8399i	0.381419	+	1.17389i	−0.557626	+	0.830092i	$0.688288\pi$
$140$	2.78860	−	1.32674i	0.235679	−	0.112130i
$141$	0.934970	+	0.679295i	0.0787387	+	0.0572070i
$142$	3.31211	+	5.73674i	0.277946	+	0.481417i
$143$	−2.18392	−	0.175429i	−0.182628	−	0.0146701i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−0.329315	+	3.13323i	−0.0273482	+	0.260200i
$146$	−4.52667	+	13.9316i	−0.374630	+	1.15299i
$147$	1.82499	−	6.75792i	0.150522	−	0.557383i
$148$	−3.13990	+	2.28127i	−0.258098	+	0.187519i
$149$	−0.205724	−	0.0915944i	−0.0168536	−	0.00750371i	0.398293	−	0.917258i	$-0.369603\pi$
$149$	−0.205724	−	0.0915944i	−0.0168536	−	0.00750371i	−0.415146	+	0.909755i	$0.636270\pi$
$150$	3.55815	+	0.756308i	0.290522	+	0.0617523i
$151$	−9.86549	−	10.9567i	−0.802842	−	0.891646i	0.193143	−	0.981171i	$-0.438132\pi$
$151$	−9.86549	−	10.9567i	−0.802842	−	0.891646i	−0.995985	+	0.0895245i	$0.971465\pi$
$152$	−0.0407994	+	0.388181i	−0.00330927	+	0.0314856i
$153$	−0.227975			−0.0184307
$154$	8.76172	+	0.481996i	0.706039	+	0.0388404i
$155$	0.216770			0.0174114
$156$	0.0690511	−	0.656977i	0.00552851	−	0.0526003i
$157$	−1.95501	−	2.17125i	−0.156026	−	0.173285i	0.660064	−	0.751210i	$-0.270529\pi$
$157$	−1.95501	−	2.17125i	−0.156026	−	0.173285i	−0.816090	+	0.577925i	$0.803863\pi$
$158$	−0.110777	−	0.0235464i	−0.00881295	−	0.00187325i
$159$	8.54304	+	3.80361i	0.677508	+	0.301646i
$160$	−0.944285	+	0.686063i	−0.0746523	+	0.0542381i
$161$	−22.9993	+	0.579696i	−1.81260	+	0.0456864i
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	0.454597	−	4.32520i	0.0356068	−	0.338776i	−0.962187	−	0.272389i	$-0.912186\pi$
$163$	0.454597	−	4.32520i	0.0356068	−	0.338776i	0.997794	−	0.0663868i	$-0.0211471\pi$
$164$	0.250874	−	0.434527i	0.0195900	−	0.0339308i
$165$	−2.93959	−	2.51888i	−0.228847	−	0.196094i
$166$	−5.23224	−	9.06251i	−0.406101	−	0.703387i
$167$	−7.72274	−	5.61090i	−0.597603	−	0.434184i	0.247424	−	0.968907i	$-0.420416\pi$
$167$	−7.72274	−	5.61090i	−0.597603	−	0.434184i	−0.845027	+	0.534723i	$0.820416\pi$
$168$	−0.210169	+	2.63739i	−0.0162149	+	0.203479i
$169$	−3.88237	−	11.9487i	−0.298644	−	0.919131i
$170$	−0.243087	−	0.108229i	−0.0186439	−	0.00830082i
$171$	−0.0407994	−	0.388181i	−0.00312001	−	0.0296849i
$172$	4.70549	+	1.00018i	0.358790	+	0.0762632i
$173$	−7.52842	+	1.60022i	−0.572376	+	0.121662i	−0.485001	−	0.874513i	$-0.661181\pi$
$173$	−7.52842	+	1.60022i	−0.572376	+	0.121662i	−0.0873742	+	0.996176i	$0.527848\pi$
$174$	−2.18368	−	1.58654i	−0.165545	−	0.120275i
$175$	9.36057	−	2.23757i	0.707593	−	0.169145i
$176$	−3.28895	+	0.427592i	−0.247914	+	0.0322310i
$177$	5.24454	+	9.08380i	0.394203	+	0.682780i
$178$	−11.5178	+	5.12804i	−0.863293	+	0.384363i
$179$	6.93112	+	7.69779i	0.518056	+	0.575360i	0.944232	−	0.329281i	$-0.106806\pi$
$179$	6.93112	+	7.69779i	0.518056	+	0.575360i	−0.426176	+	0.904640i	$0.640140\pi$
$180$	0.781010	−	0.867399i	0.0582130	−	0.0646521i
$181$	3.12816	−	2.27274i	0.232514	−	0.168931i	−0.465428	−	0.885086i	$-0.654099\pi$
$181$	3.12816	−	2.27274i	0.232514	−	0.168931i	0.697942	+	0.716155i	$0.254099\pi$
$182$	−0.581803	−	1.64809i	−0.0431261	−	0.122165i
$183$	−2.94065	−	9.05039i	−0.217379	−	0.669024i
$184$	8.50565	−	1.80793i	0.627045	−	0.133283i
$185$	4.13842	−	1.84254i	0.304262	−	0.135466i
$186$	−0.0928590	+	0.160836i	−0.00680875	+	0.0117931i
$187$	−0.459318	−	0.600602i	−0.0335887	−	0.0439204i
$188$	−1.15569			−0.0842871
$189$	−0.342768	−	2.62345i	−0.0249327	−	0.190828i
$190$	0.140782	−	0.433283i	0.0102134	−	0.0314336i
$191$	3.05891	−	3.39727i	0.221335	−	0.245818i	−0.622243	−	0.782824i	$-0.713778\pi$
$191$	3.05891	−	3.39727i	0.221335	−	0.245818i	0.843578	+	0.537007i	$0.180445\pi$
$192$	−0.104528	−	0.994522i	−0.00754369	−	0.0717734i
$193$	−2.32827	−	22.1520i	−0.167593	−	1.59454i	−0.678302	−	0.734783i	$-0.737284\pi$
$193$	−2.32827	−	22.1520i	−0.167593	−	1.59454i	0.510710	−	0.859753i	$-0.329383\pi$
$194$	−5.03021	+	5.58662i	−0.361148	+	0.401096i
$195$	−0.238267	+	0.733311i	−0.0170627	+	0.0525135i
$196$	2.49576	+	6.53997i	0.178268	+	0.467141i
$197$	−6.40396			−0.456263			−0.228132	−	0.973630i	$-0.573262\pi$
$197$	−6.40396			−0.456263			−0.228132	+	0.973630i	$0.573262\pi$
$198$	3.12817	−	1.10206i	0.222310	−	0.0783199i
$199$	−11.7977	+	20.4342i	−0.836314	+	1.44854i	0.0566413	+	0.998395i	$0.481961\pi$
$199$	−11.7977	+	20.4342i	−0.836314	+	1.44854i	−0.892956	+	0.450144i	$0.851372\pi$
$200$	−3.32315	+	1.47956i	−0.234982	+	0.104621i
$201$	4.21308	−	0.895518i	0.297168	−	0.0631650i
$202$	0.708036	+	2.17911i	0.0498173	+	0.153322i
$203$	−7.02050	−	1.30829i	−0.492742	−	0.0918241i
$204$	0.184435	−	0.134000i	0.0129131	−	0.00938188i
$205$	−0.391870	+	0.435216i	−0.0273694	+	0.0303968i
$206$	7.88940	+	8.76207i	0.549681	+	0.610482i
$207$	−7.94389	+	3.53685i	−0.552139	+	0.245828i
$208$	0.330298	+	0.572093i	0.0229021	+	0.0396675i
$209$	0.940466	−	0.889584i	0.0650534	−	0.0615338i
$210$	0.879977	−	2.96009i	0.0607242	−	0.204266i
$211$	0.344508	+	0.250300i	0.0237169	+	0.0172313i	0.599581	−	0.800314i	$-0.295334\pi$
$211$	0.344508	+	0.250300i	0.0237169	+	0.0172313i	−0.575864	+	0.817546i	$0.695334\pi$
$212$	−9.14717	+	1.94429i	−0.628230	+	0.133535i
$213$	6.47946	+	1.37725i	0.443966	+	0.0943678i
$214$	1.59145	+	15.1417i	0.108790	+	1.03506i
$215$	−5.12951	−	2.28380i	−0.349830	−	0.155754i
$216$	0.309017	+	0.951057i	0.0210259	+	0.0647112i
$217$	−0.0390321	+	0.489811i	−0.00264967	+	0.0332505i
$218$	7.19189	+	5.22521i	0.487096	+	0.353896i
$219$	7.32430	+	12.6861i	0.494930	+	0.857245i
$220$	3.85874	+	0.309965i	0.260156	+	0.0208978i
$221$	−0.0752996	+	0.130423i	−0.00506520	+	0.00877318i
$222$	−0.405689	+	3.85987i	−0.0272280	+	0.259058i
$223$	−4.02306	+	12.3817i	−0.269404	+	0.829140i	0.721242	+	0.692683i	$0.243571\pi$
$223$	−4.02306	+	12.3817i	−0.269404	+	0.829140i	−0.990646	+	0.136457i	$0.956429\pi$
$224$	−1.38019	−	2.25723i	−0.0922178	−	0.150817i
$225$	2.94291	−	2.13815i	0.196194	−	0.142543i
$226$	−8.89966	−	3.96238i	−0.591997	−	0.263574i
$227$	−16.9031	−	3.59286i	−1.12190	−	0.238467i	−0.390623	−	0.920551i	$-0.627740\pi$
$227$	−16.9031	−	3.59286i	−1.12190	−	0.238467i	−0.731274	+	0.682084i	$0.761074\pi$
$228$	0.261174	+	0.290063i	0.0172967	+	0.0192099i
$229$	1.08683	−	10.3405i	0.0718199	−	0.683321i	−0.898083	−	0.439827i	$-0.855040\pi$
$229$	1.08683	−	10.3405i	0.0718199	−	0.683321i	0.969902	−	0.243494i	$-0.0782936\pi$
$230$	−10.1496			−0.669245
$231$	6.22093	−	6.18871i	0.409307	−	0.407187i
$232$	2.69918			0.177210
$233$	0.543050	−	5.16678i	0.0355764	−	0.338487i	−0.962227	−	0.272247i	$-0.912233\pi$
$233$	0.543050	−	5.16678i	0.0355764	−	0.338487i	0.997804	−	0.0662396i	$-0.0211002\pi$
$234$	−0.442025	−	0.490919i	−0.0288961	−	0.0320924i
$235$	1.31944	+	0.280456i	0.0860708	+	0.0182949i
$236$	−9.58224	−	4.26629i	−0.623751	−	0.277712i
$237$	−0.0916227	+	0.0665678i	−0.00595153	+	0.00432404i
$238$	0.288324	−	0.529788i	0.0186893	−	0.0343411i
$239$	−3.25939	+	10.0314i	−0.210832	+	0.648875i	0.788591	+	0.614918i	$0.210811\pi$
$239$	−3.25939	+	10.0314i	−0.210832	+	0.648875i	−0.999423	+	0.0339572i	$0.989189\pi$
$240$	−0.122006	+	1.16081i	−0.00787544	+	0.0749298i
$241$	−12.4228	+	21.5169i	−0.800222	+	1.38603i	0.119247	+	0.992865i	$0.461952\pi$
$241$	−12.4228	+	21.5169i	−0.800222	+	1.38603i	−0.919470	+	0.393161i	$0.871381\pi$
$242$	9.20596	+	6.02081i	0.591782	+	0.387033i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	7.69872	+	5.59345i	0.492860	+	0.358084i
$245$	−1.26231	−	8.07231i	−0.0806459	−	0.515721i
$246$	−0.155049	−	0.477191i	−0.00988554	−	0.0304246i
$247$	−0.235551	−	0.104874i	−0.0149878	−	0.00667299i
$248$	−0.0194128	−	0.184701i	−0.00123271	−	0.0117285i
$249$	−10.2358	−	2.17569i	−0.648668	−	0.137879i
$250$	9.86155	−	2.09614i	0.623699	−	0.132571i
$251$	−22.9297	−	16.6594i	−1.44731	−	1.05153i	−0.986450	−	0.164060i	$-0.947541\pi$
$251$	−22.9297	−	16.6594i	−1.44731	−	1.05153i	−0.460860	−	0.887473i	$-0.652459\pi$
$252$	1.81933	+	1.92094i	0.114607	+	0.121008i
$253$	−25.3231	−	13.8023i	−1.59205	−	0.867745i
$254$	−1.63907	−	2.83896i	−0.102845	−	0.178132i
$255$	−0.243087	+	0.108229i	−0.0152227	+	0.00677759i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	−14.1196	+	15.6814i	−0.880755	+	0.978177i	−0.999892	−	0.0147006i	$-0.995320\pi$
$257$	−14.1196	+	15.6814i	−0.880755	+	0.978177i	0.119137	+	0.992878i	$0.461987\pi$
$258$	3.89186	−	2.82761i	0.242297	−	0.176039i
$259$	3.41821	+	9.68288i	0.212397	+	0.601665i
$260$	−0.238267	−	0.733311i	−0.0147767	−	0.0454780i
$261$	−2.64020	+	0.561191i	−0.163424	+	0.0347369i
$262$	−15.4968	+	6.89964i	−0.957398	+	0.426261i
$263$	8.70300	−	15.0740i	0.536650	−	0.929505i	−0.462432	−	0.886655i	$-0.653023\pi$
$263$	8.70300	−	15.0740i	0.536650	−	0.929505i	0.999082	−	0.0428501i	$-0.0136438\pi$
$264$	−1.88297	+	2.73028i	−0.115889	+	0.168037i
$265$	10.9151			0.670510
$266$	0.953690	+	0.396127i	0.0584745	+	0.0242881i
$267$	−3.89601	+	11.9907i	−0.238432	+	0.733819i
$268$	−2.88208	+	3.20088i	−0.176051	+	0.195525i
$269$	0.530904	+	5.05121i	0.0323698	+	0.307978i	0.998713	+	0.0507210i	$0.0161519\pi$
$269$	0.530904	+	5.05121i	0.0323698	+	0.307978i	−0.966343	+	0.257257i	$0.917181\pi$
$270$	−0.122006	−	1.16081i	−0.00742503	−	0.0706445i
$271$	−19.6163	+	21.7861i	−1.19160	+	1.32341i	−0.257554	+	0.966264i	$0.582916\pi$
$271$	−19.6163	+	21.7861i	−1.19160	+	1.32341i	−0.934049	+	0.357145i	$0.883750\pi$
$272$	−0.0704480	+	0.216817i	−0.00427154	+	0.0131464i
$273$	−1.61408	−	0.670427i	−0.0976883	−	0.0405761i
$274$	18.3611			1.10923
$275$	11.5623	+	3.44525i	0.697234	+	0.207756i
$276$	4.34784	−	7.53067i	0.261709	−	0.453293i
$277$	−7.49645	+	3.33764i	−0.450418	+	0.200539i	−0.619393	−	0.785081i	$-0.712621\pi$
$277$	−7.49645	+	3.33764i	−0.450418	+	0.200539i	0.168974	+	0.985620i	$0.445954\pi$
$278$	−14.2342	+	3.02556i	−0.853708	+	0.181461i
$279$	0.0573900	+	0.176628i	0.00343585	+	0.0105745i
$280$	1.02798	+	2.91200i	0.0614337	+	0.174025i
$281$	−25.6785	+	18.6565i	−1.53185	+	1.11295i	−0.576648	+	0.816993i	$0.695640\pi$
$281$	−25.6785	+	18.6565i	−1.53185	+	1.11295i	−0.955200	+	0.295960i	$0.904360\pi$
$282$	−0.773305	+	0.858842i	−0.0460496	+	0.0511433i
$283$	−15.8065	−	17.5549i	−0.939601	−	1.04353i	−0.998974	−	0.0452965i	$-0.985577\pi$
$283$	−15.8065	−	17.5549i	−0.939601	−	1.04353i	0.0593729	−	0.998236i	$-0.481090\pi$
$284$	−6.05153	+	2.69431i	−0.359092	+	0.159878i
$285$	−0.227790	−	0.394544i	−0.0134931	−	0.0233708i
$286$	0.402750	−	2.15361i	0.0238151	−	0.127346i
$287$	−0.912847	−	0.963830i	−0.0538836	−	0.0568931i
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	16.5777	−	3.52369i	0.975157	−	0.207276i
$290$	−3.08164	−	0.655023i	−0.180960	−	0.0384643i
$291$	0.785797	+	7.47636i	0.0460642	+	0.438272i
$292$	−13.3822	−	5.95812i	−0.783132	−	0.348673i
$293$	1.82266	+	5.60958i	0.106481	+	0.327715i	0.990075	−	0.140538i	$-0.0448834\pi$
$293$	1.82266	+	5.60958i	0.106481	+	0.327715i	−0.883594	+	0.468254i	$0.844883\pi$
$294$	6.53013	+	2.52138i	0.380845	+	0.147050i
$295$	9.90468	+	7.19617i	0.576673	+	0.418977i
$296$	−1.94057	−	3.36116i	−0.112793	−	0.195363i
$297$	1.27417	−	3.06211i	0.0739347	−	0.177681i
$298$	0.112597	−	0.195023i	0.00652255	−	0.0112974i
$299$	−0.600446	+	5.71286i	−0.0347247	+	0.330383i
$300$	−1.12409	+	3.45960i	−0.0648996	+	0.199740i
$301$	6.08408	−	11.1793i	0.350681	−	0.644366i
$302$	11.9279	−	8.66615i	0.686375	−	0.498681i
$303$	2.09316	+	0.931937i	0.120249	+	0.0535384i
$304$	−0.381789	−	0.0811518i	−0.0218971	−	0.00465438i
$305$	−7.43220	−	8.25429i	−0.425567	−	0.472640i
$306$	0.0238298	−	0.226726i	0.00136226	−	0.0129610i
$307$	23.1916			1.32362			0.661809	−	0.749673i	$-0.269789\pi$
$307$	23.1916			1.32362			0.661809	+	0.749673i	$0.269789\pi$
$308$	−1.39520	+	8.66334i	−0.0794992	+	0.493639i
$309$	11.7905			0.670739
$310$	−0.0226587	+	0.215583i	−0.00128692	+	0.0122443i
$311$	−0.265085	−	0.294406i	−0.0150316	−	0.0166943i	0.735582	−	0.677436i	$-0.236909\pi$
$311$	−0.265085	−	0.294406i	−0.0150316	−	0.0166943i	−0.750614	+	0.660741i	$0.770242\pi$
$312$	0.646161	+	0.137346i	0.0365816	+	0.00777567i
$313$	7.40282	+	3.29595i	0.418432	+	0.186298i	0.605143	−	0.796117i	$-0.293116\pi$
$313$	7.40282	+	3.29595i	0.418432	+	0.186298i	−0.186711	+	0.982415i	$0.559783\pi$
$314$	2.36371	−	1.71734i	0.133392	−	0.0969150i
$315$	−1.61096	−	2.63464i	−0.0907672	−	0.148445i
$316$	0.0349967	−	0.107709i	0.00196872	−	0.00605910i
$317$	3.13092	−	29.7887i	0.175850	−	1.67310i	−0.449902	−	0.893078i	$-0.648541\pi$
$317$	3.13092	−	29.7887i	0.175850	−	1.67310i	0.625752	−	0.780022i	$-0.284792\pi$
$318$	−4.67576	+	8.09866i	−0.262204	+	0.454150i
$319$	−6.79788	−	5.82496i	−0.380608	−	0.326135i
$320$	−0.583600	−	1.01083i	−0.0326243	−	0.0565069i
$321$	12.3173	+	8.94908i	0.687487	+	0.499489i
$322$	1.82756	−	22.9339i	0.101846	−	1.27806i
$323$	−0.0274972	−	0.0846276i	−0.00152998	−	0.00470881i
$324$	0.913545	+	0.406737i	0.0507525	+	0.0225965i
$325$	−0.251183	−	2.38985i	−0.0139331	−	0.132565i
$326$	4.25399	+	0.904213i	0.235607	+	0.0500797i
$327$	8.69540	−	1.84826i	0.480857	−	0.102209i
$328$	0.405923	+	0.294920i	0.0224133	+	0.0162842i
$329$	−0.871296	+	2.93089i	−0.0480361	+	0.161585i
$330$	2.81235	−	2.66019i	0.154815	−	0.146439i
$331$	13.8246	+	23.9449i	0.759868	+	1.31613i	0.942918	+	0.333026i	$0.108070\pi$
$331$	13.8246	+	23.9449i	0.759868	+	1.31613i	−0.183050	+	0.983104i	$0.558597\pi$
$332$	9.55978	−	4.25629i	0.524661	−	0.233594i
$333$	2.59698	+	2.88424i	0.142314	+	0.158056i
$334$	6.38741	−	7.09393i	0.349503	−	0.388163i
$335$	4.06723	−	2.95502i	0.222217	−	0.161450i
$336$	−2.60097	−	0.484700i	−0.141895	−	0.0264425i
$337$	5.12692	+	15.7790i	0.279281	+	0.859540i	0.988055	+	0.154103i	$0.0492489\pi$
$337$	5.12692	+	15.7790i	0.279281	+	0.859540i	−0.708773	+	0.705436i	$0.750751\pi$
$338$	12.2891	−	2.61212i	0.668437	−	0.142081i
$339$	−8.89966	+	3.96238i	−0.483363	+	0.215207i
$340$	0.133046	−	0.230443i	0.00721544	−	0.0124975i
$341$	−0.349702	+	0.507062i	−0.0189374	+	0.0274589i
$342$	0.390319			0.0211060
$343$	18.4674	−	1.39878i	0.997144	−	0.0755268i
$344$	−1.48656	+	4.57516i	−0.0801499	+	0.246676i
$345$	−6.79141	+	7.54262i	−0.365637	+	0.406081i
$346$	−0.804515	−	7.65445i	−0.0432510	−	0.411506i
$347$	0.0930001	+	0.884837i	0.00499251	+	0.0475005i	0.996735	−	0.0807484i	$-0.0257310\pi$
$347$	0.0930001	+	0.884837i	0.00499251	+	0.0475005i	−0.991742	+	0.128249i	$0.959064\pi$
$348$	1.80610	−	2.00588i	0.0968173	−	0.107527i
$349$	10.5609	−	32.5030i	0.565310	−	1.73984i	−0.101719	−	0.994813i	$-0.532434\pi$
$349$	10.5609	−	32.5030i	0.565310	−	1.73984i	0.667029	−	0.745032i	$-0.267566\pi$
$350$	1.24687	+	9.54319i	0.0666479	+	0.510105i
$351$	−0.660596			−0.0352600
$352$	−0.0814611	−	3.31562i	−0.00434189	−	0.176723i
$353$	2.46648	−	4.27206i	0.131277	−	0.227379i	−0.792892	−	0.609362i	$-0.791426\pi$
$353$	2.46648	−	4.27206i	0.131277	−	0.227379i	0.924169	+	0.381983i	$0.124759\pi$
$354$	−9.58224	+	4.26629i	−0.509291	+	0.226751i
$355$	7.56284	−	1.60753i	0.401394	−	0.0853189i
$356$	−3.89601	−	11.9907i	−0.206488	−	0.635506i
$357$	−0.200783	−	0.568765i	−0.0106266	−	0.0301022i
$358$	−8.38012	+	6.08851i	−0.442903	+	0.321788i
$359$	−0.0821762	+	0.0912660i	−0.00433710	+	0.00481683i	−0.745309	−	0.666719i	$-0.767698\pi$
$359$	−0.0821762	+	0.0912660i	−0.00433710	+	0.00481683i	0.740972	+	0.671536i	$0.234365\pi$
$360$	0.781010	+	0.867399i	0.0411628	+	0.0457160i
$361$	−17.2182	+	7.66603i	−0.906220	+	0.403475i
$362$	1.93331	+	3.34859i	0.101612	+	0.175998i
$363$	10.6343	−	2.81265i	0.558158	−	0.147626i
$364$	1.69988	−	0.406343i	0.0890980	−	0.0212982i
$365$	13.8325	+	10.0499i	0.724024	+	0.526034i
$366$	9.30819	−	1.97852i	0.486547	−	0.103419i
$367$	7.93819	+	1.68731i	0.414370	+	0.0880770i	0.410379	−	0.911915i	$-0.365396\pi$
$367$	7.93819	+	1.68731i	0.414370	+	0.0880770i	0.00399077	+	0.999992i	$0.498730\pi$
$368$	0.908945	+	8.64804i	0.0473821	+	0.450810i
$369$	−0.458370	−	0.204079i	−0.0238618	−	0.0106239i
$370$	1.39987	+	4.30834i	0.0727756	+	0.223980i
$371$	−1.96540	+	24.6636i	−0.102038	+	1.28047i
$372$	−0.150249	−	0.109162i	−0.00779005	−	0.00565980i
$373$	−12.8019	−	22.1736i	−0.662860	−	1.14811i	−0.979861	−	0.199681i	$-0.936009\pi$
$373$	−12.8019	−	22.1736i	−0.662860	−	1.14811i	0.317001	−	0.948425i	$-0.397324\pi$
$374$	0.645324	−	0.394022i	0.0333689	−	0.0203744i
$375$	5.04093	−	8.73115i	0.260313	−	0.450875i
$376$	0.120802	−	1.14936i	0.00622989	−	0.0592735i
$377$	−0.550998	+	1.69580i	−0.0283779	+	0.0873381i
$378$	2.64491	−	0.0666648i	0.136040	−	0.00342887i
$379$	6.44330	−	4.68133i	0.330970	−	0.240464i	−0.409872	−	0.912143i	$-0.634427\pi$
$379$	6.44330	−	4.68133i	0.330970	−	0.240464i	0.740842	+	0.671679i	$0.234427\pi$
$380$	0.416193	+	0.185301i	0.0213503	+	0.00950575i
$381$	−3.20651	−	0.681565i	−0.164275	−	0.0349176i
$382$	3.05891	+	3.39727i	0.156508	+	0.173819i
$383$	3.35589	−	31.9292i	0.171478	−	1.63150i	−0.483139	−	0.875544i	$-0.660503\pi$
$383$	3.35589	−	31.9292i	0.171478	−	1.63150i	0.654617	−	0.755961i	$-0.272830\pi$
$384$	1.00000			0.0510310
$385$	3.69527	−	9.55231i	0.188328	−	0.486831i
$386$	22.2740			1.13372
$387$	0.502846	−	4.78426i	0.0255611	−	0.243197i
$388$	−5.03021	−	5.58662i	−0.255370	−	0.283618i
$389$	17.4942	+	3.71851i	0.886993	+	0.188536i	0.628809	−	0.777560i	$-0.283543\pi$
$389$	17.4942	+	3.71851i	0.886993	+	0.188536i	0.258184	+	0.966096i	$0.416876\pi$
$390$	−0.704388	−	0.313614i	−0.0356681	−	0.0158804i
$391$	−1.60379	+	1.16522i	−0.0811071	+	0.0589278i
$392$	−6.76502	+	1.79847i	−0.341685	+	0.0908366i
$393$	−5.24198	+	16.1331i	−0.264423	+	0.813810i
$394$	0.669396	−	6.36888i	0.0337237	−	0.320859i
$395$	−0.0660938	+	0.114478i	−0.00332554	+	0.00576001i
$396$	0.769038	+	3.22623i	0.0386456	+	0.162124i
$397$	0.841641	+	1.45776i	0.0422407	+	0.0731631i	0.886373	−	0.462972i	$-0.153217\pi$
$397$	0.841641	+	1.45776i	0.0422407	+	0.0731631i	−0.844132	+	0.536135i	$0.819884\pi$
$398$	−19.0890	−	13.8690i	−0.956846	−	0.695190i
$399$	0.932523	−	0.443669i	0.0466845	−	0.0222112i
$400$	−1.12409	−	3.45960i	−0.0562047	−	0.172980i
$401$	−18.8714	−	8.40208i	−0.942391	−	0.419580i	−0.122738	−	0.992439i	$-0.539167\pi$
$401$	−18.8714	−	8.40208i	−0.942391	−	0.419580i	−0.819654	+	0.572860i	$0.805834\pi$
$402$	0.450226	+	4.28361i	0.0224552	+	0.213647i
$403$	0.120004	+	0.0255076i	0.00597781	+	0.00127062i
$404$	−2.24118	+	0.476378i	−0.111503	+	0.0237007i
$405$	−0.944285	−	0.686063i	−0.0469219	−	0.0340908i
$406$	2.03497	−	6.84528i	0.100994	−	0.339726i
$407$	−2.36623	+	12.6529i	−0.117290	+	0.627181i
$408$	0.113987	+	0.197432i	0.00564321	+	0.00977433i
$409$	32.4675	−	14.4555i	1.60542	−	0.714777i	0.608522	−	0.793537i	$-0.291763\pi$
$409$	32.4675	−	14.4555i	1.60542	−	0.714777i	0.996894	+	0.0787599i	$0.0250960\pi$
$410$	−0.391870	−	0.435216i	−0.0193531	−	0.0214938i
$411$	12.2860	−	13.6449i	0.606022	−	0.673056i
$412$	−9.53873	+	6.93030i	−0.469940	+	0.341431i
$413$	−18.0438	+	21.0847i	−0.887878	+	1.03751i
$414$	−2.68711	−	8.27008i	−0.132064	−	0.406452i
$415$	−11.9472	+	2.53947i	−0.586467	+	0.124657i
$416$	−0.603485	+	0.268689i	−0.0295883	+	0.0131735i
$417$	−7.27608	+	12.6025i	−0.356311	+	0.617149i
$418$	0.786406	+	1.02830i	0.0384644	+	0.0502958i
$419$	0.118769			0.00580225			0.00290113	−	0.999996i	$-0.499077\pi$
$419$	0.118769			0.00580225			0.00290113	+	0.999996i	$0.499077\pi$
$420$	2.85189	+	1.18457i	0.139158	+	0.0578011i
$421$	7.11399	−	21.8946i	0.346715	−	1.06708i	−0.613945	−	0.789349i	$-0.710418\pi$
$421$	7.11399	−	21.8946i	0.346715	−	1.06708i	0.960659	−	0.277729i	$-0.0895818\pi$
$422$	−0.284939	+	0.316457i	−0.0138706	+	0.0154049i
$423$	0.120802	+	1.14936i	0.00587360	+	0.0558836i
$424$	−0.977501	−	9.30030i	−0.0474716	−	0.451662i
$425$	0.554903	−	0.616282i	0.0269168	−	0.0298941i
$426$	−2.04700	+	6.30001i	−0.0991773	+	0.305236i
$427$	19.9895	−	15.3074i	0.967362	−	0.740777i
$428$	−15.2251			−0.735932
$429$	−1.33095	−	1.74035i	−0.0642591	−	0.0840249i
$430$	2.80747	−	4.86269i	0.135388	−	0.234500i
$431$	17.3888	−	7.74201i	0.837590	−	0.372919i	0.0573156	−	0.998356i	$-0.481746\pi$
$431$	17.3888	−	7.74201i	0.837590	−	0.372919i	0.780275	+	0.625437i	$0.215079\pi$
$432$	−0.978148	+	0.207912i	−0.0470611	+	0.0100032i
$433$	3.61593	+	11.1287i	0.173771	+	0.534811i	0.999575	−	0.0291454i	$-0.00927859\pi$
$433$	3.61593	+	11.1287i	0.173771	+	0.534811i	−0.825805	+	0.563956i	$0.809279\pi$
$434$	−0.483048	−	0.0900175i	−0.0231870	−	0.00432098i
$435$	−2.54880	+	1.85181i	−0.122205	+	0.0887874i
$436$	−5.94834	+	6.60631i	−0.284874	+	0.316385i
$437$	−2.27109	−	2.52230i	−0.108641	−	0.120658i
$438$	−13.3822	+	5.95812i	−0.639425	+	0.284690i
$439$	15.4915	+	26.8320i	0.739368	+	1.28062i	0.952780	+	0.303661i	$0.0982091\pi$
$439$	15.4915	+	26.8320i	0.739368	+	1.28062i	−0.213412	+	0.976962i	$0.568458\pi$
$440$	−0.711614	+	3.80520i	−0.0339249	+	0.181406i
$441$	6.24326	−	3.16570i	0.297298	−	0.150748i
$442$	−0.121837	−	0.0885199i	−0.00579521	−	0.00421046i
$443$	−12.5976	+	2.67770i	−0.598530	+	0.127221i	−0.497207	−	0.867632i	$-0.665641\pi$
$443$	−12.5976	+	2.67770i	−0.598530	+	0.127221i	−0.101323	+	0.994854i	$0.532308\pi$
$444$	−3.79632	−	0.806933i	−0.180165	−	0.0382953i
$445$	1.53822	+	14.6352i	0.0729186	+	0.693774i
$446$	−11.8933	−	5.29526i	−0.563166	−	0.250738i
$447$	−0.0695886	−	0.214172i	−0.00329143	−	0.0101300i
$448$	2.38913	−	1.13668i	0.112876	−	0.0537033i
$449$	30.1442	+	21.9010i	1.42259	+	1.03357i	0.991337	+	0.131344i	$0.0419294\pi$
$449$	30.1442	+	21.9010i	1.42259	+	1.03357i	0.431256	+	0.902230i	$0.358071\pi$
$450$	1.81882	+	3.15029i	0.0857400	+	0.148506i
$451$	−0.385863	−	1.61876i	−0.0181696	−	0.0762242i
$452$	4.87095	−	8.43673i	0.229110	−	0.396830i
$453$	1.54114	−	14.6630i	0.0724091	−	0.688926i
$454$	5.34003	−	16.4349i	0.250620	−	0.771329i
$455$	−2.03935	+	0.0514018i	−0.0956064	+	0.00240975i
$456$	−0.315775	+	0.229424i	−0.0147875	+	0.0107437i
$457$	10.7956	+	4.80650i	0.504996	+	0.224839i	0.643390	−	0.765539i	$-0.277527\pi$
$457$	10.7956	+	4.80650i	0.504996	+	0.224839i	−0.138394	+	0.990377i	$0.544194\pi$
$458$	10.1703	+	2.16176i	0.475225	+	0.101012i
$459$	−0.152545	−	0.169418i	−0.00712018	−	0.00790776i
$460$	1.06092	−	10.0940i	0.0494657	−	0.470635i
$461$	−15.8039			−0.736062			−0.368031	−	0.929813i	$-0.619968\pi$
$461$	−15.8039			−0.736062			−0.368031	+	0.929813i	$0.619968\pi$
$462$	5.50454	+	6.83374i	0.256094	+	0.317934i
$463$	−37.1337			−1.72575			−0.862875	−	0.505418i	$-0.831338\pi$
$463$	−37.1337			−1.72575			−0.862875	+	0.505418i	$0.831338\pi$
$464$	−0.282141	+	2.68439i	−0.0130981	+	0.124620i
$465$	0.145048	+	0.161092i	0.00672642	+	0.00747044i
$466$	5.08171	+	1.08015i	0.235406	+	0.0500370i
$467$	0.983797	+	0.438015i	0.0455247	+	0.0202689i	0.429373	−	0.903127i	$-0.358735\pi$
$467$	0.983797	+	0.438015i	0.0455247	+	0.0202689i	−0.383848	+	0.923396i	$0.625401\pi$
$468$	0.534434	−	0.388289i	0.0247042	−	0.0179487i
$469$	5.94476	+	9.72234i	0.274503	+	0.448936i
$470$	−0.416839	+	1.28290i	−0.0192273	+	0.0591756i
$471$	0.305402	−	2.90571i	0.0140722	−	0.133888i
$472$	5.24454	−	9.08380i	0.241399	−	0.418116i
$473$	13.6173	−	8.31446i	0.626125	−	0.382299i
$474$	−0.0566259	−	0.0980790i	−0.00260091	−	0.00450492i
$475$	1.14867	+	0.834561i	0.0527048	+	0.0382923i
$476$	0.496748	+	0.342123i	0.0227684	+	0.0156812i
$477$	2.88978	+	8.89383i	0.132314	+	0.407221i
$478$	−9.63572	−	4.29010i	−0.440728	−	0.196225i
$479$	−0.126338	−	1.20202i	−0.00577251	−	0.0549218i	0.991256	−	0.131949i	$-0.0421237\pi$
$479$	−0.126338	−	1.20202i	−0.00577251	−	0.0549218i	−0.997029	+	0.0770277i	$0.975457\pi$
$480$	−1.14169	−	0.242675i	−0.0521110	−	0.0110765i
$481$	2.50783	−	0.533057i	0.114347	−	0.0243053i
$482$	−20.1005	−	14.6039i	−0.915553	−	0.665188i
$483$	−15.8203	−	16.7039i	−0.719850	−	0.760054i
$484$	−6.95012	+	8.52619i	−0.315914	+	0.387554i
$485$	4.38724	+	7.59892i	0.199214	+	0.345049i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	6.94002	+	7.70767i	0.314482	+	0.349268i	0.879576	−	0.475759i	$-0.157827\pi$
$487$	6.94002	+	7.70767i	0.314482	+	0.349268i	−0.565093	+	0.825027i	$0.691160\pi$
$488$	−6.36754	+	7.07187i	−0.288245	+	0.320129i
$489$	3.51844	−	2.55629i	0.159109	−	0.115600i
$490$	8.16003	−	0.411608i	0.368633	−	0.0185945i
$491$	−2.36489	−	7.27839i	−0.106726	−	0.328469i	0.883406	−	0.468609i	$-0.155245\pi$
$491$	−2.36489	−	7.27839i	−0.106726	−	0.328469i	−0.990132	+	0.140140i	$0.955245\pi$
$492$	0.490784	−	0.104319i	0.0221262	−	0.00470308i
$493$	−0.562145	+	0.250283i	−0.0253177	+	0.0112722i
$494$	0.128922	−	0.223299i	0.00580045	−	0.0100467i
$495$	−0.0950815	−	3.87000i	−0.00427359	−	0.173944i
$496$	0.185718			0.00833898
$497$	2.27057	+	17.3783i	0.101849	+	0.779525i
$498$	3.23370	−	9.95232i	0.144906	−	0.445974i
$499$	−7.81871	+	8.68355i	−0.350013	+	0.388729i	−0.892284	−	0.451475i	$-0.850898\pi$
$499$	−7.81871	+	8.68355i	−0.350013	+	0.388729i	0.542271	+	0.840204i	$0.317565\pi$
$500$	1.05384	+	10.0266i	0.0471292	+	0.448405i
$501$	−0.997811	−	9.49353i	−0.0445789	−	0.424140i
$502$	18.9650	−	21.0627i	0.846447	−	0.940075i
$503$	1.07850	−	3.31929i	0.0480881	−	0.148000i	−0.924129	−	0.382080i	$-0.875208\pi$
$503$	1.07850	−	3.31929i	0.0480881	−	0.148000i	0.972217	+	0.234080i	$0.0752078\pi$
$504$	−2.10059	+	1.60857i	−0.0935679	+	0.0716515i
$505$	2.67435			0.119007
$506$	16.3737	−	23.7416i	0.727900	−	1.05544i
$507$	6.28181	−	10.8804i	0.278985	−	0.483216i
$508$	2.99474	−	1.33334i	0.132870	−	0.0591575i
$509$	26.0800	−	5.54348i	1.15598	−	0.245711i	0.410257	−	0.911970i	$-0.365439\pi$
$509$	26.0800	−	5.54348i	1.15598	−	0.245711i	0.745720	+	0.666259i	$0.232106\pi$
$510$	−0.0822270	−	0.253069i	−0.00364107	−	0.0112061i
$511$	−25.1993	+	29.4460i	−1.11475	+	1.30262i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	0.261174	−	0.290063i	0.0115311	−	0.0128066i
$514$	−14.1196	−	15.6814i	−0.622788	−	0.691676i
$515$	12.5721	−	5.59747i	0.553994	−	0.246654i
$516$	2.40530	+	4.16611i	0.105888	+	0.183403i
$517$	−2.78460	+	2.63395i	−0.122467	+	0.115841i
$518$	−9.98714	+	2.38735i	−0.438810	+	0.104894i
$519$	−6.22669	−	4.52396i	−0.273321	−	0.198580i
$520$	0.754199	−	0.160310i	0.0330738	−	0.00703006i
$521$	−5.50297	−	1.16969i	−0.241089	−	0.0512451i	0.0857821	−	0.996314i	$-0.472661\pi$
$521$	−5.50297	−	1.16969i	−0.241089	−	0.0512451i	−0.326872	+	0.945069i	$0.605994\pi$
$522$	−0.282141	−	2.68439i	−0.0123490	−	0.117493i
$523$	−6.36511	−	2.83393i	−0.278327	−	0.123919i	0.262826	−	0.964843i	$-0.415345\pi$
$523$	−6.36511	−	2.83393i	−0.278327	−	0.123919i	−0.541153	+	0.840924i	$0.682012\pi$
$524$	−5.24198	−	16.1331i	−0.228997	−	0.704780i
$525$	7.92629	+	5.45903i	0.345932	+	0.238252i
$526$	14.0818	+	10.2310i	0.613993	+	0.446092i
$527$	0.0211695	+	0.0366666i	0.000922157	+	0.00159722i
$528$	−2.51850	−	2.15805i	−0.109604	−	0.0939170i
$529$	−26.3074	+	45.5657i	−1.14380	+	1.98112i
$530$	−1.14094	+	10.8553i	−0.0495593	+	0.471525i
$531$	−3.24130	+	9.97570i	−0.140661	+	0.432909i
$532$	−0.493645	+	0.907059i	−0.0214022	+	0.0393260i
$533$	−0.268151	+	0.194823i	−0.0116149	+	0.00843872i
$534$	−11.5178	−	5.12804i	−0.498423	−	0.221912i
$535$	17.3824	+	3.69474i	0.751506	+	0.159738i
$536$	−2.88208	−	3.20088i	−0.124487	−	0.138257i
$537$	−1.08275	+	10.3016i	−0.0467240	+	0.444549i
$538$	−5.07903			−0.218973
$539$	20.9189	+	10.0698i	0.901040	+	0.433737i
$540$	1.16720			0.0502283
$541$	2.02070	−	19.2257i	0.0868767	−	0.826576i	−0.861143	−	0.508363i	$-0.830251\pi$
$541$	2.02070	−	19.2257i	0.0868767	−	0.826576i	0.948019	−	0.318213i	$-0.103083\pi$
$542$	−19.6163	−	21.7861i	−0.842590	−	0.935791i
$543$	3.78212	+	0.803915i	0.162306	+	0.0344993i
$544$	−0.208265	−	0.0927256i	−0.00892929	−	0.00397558i
$545$	8.39438	−	6.09887i	0.359576	−	0.261247i
$546$	0.835471	−	1.53515i	0.0357548	−	0.0656986i
$547$	−3.81872	+	11.7528i	−0.163276	+	0.502513i	−0.998905	−	0.0467814i	$-0.985104\pi$
$547$	−3.81872	+	11.7528i	−0.163276	+	0.502513i	0.835629	+	0.549295i	$0.185104\pi$
$548$	−1.91926	+	18.2605i	−0.0819866	+	0.780050i
$549$	4.75807	−	8.24122i	0.203070	−	0.351727i
$550$	−4.63497	+	11.1388i	−0.197636	+	0.474962i
$551$	−0.526770	−	0.912393i	−0.0224412	−	0.0388692i
$552$	7.03495	+	5.11119i	0.299427	+	0.217547i
$553$	−0.246772	−	0.169958i	−0.0104938	−	0.00722734i
$554$	−2.53576	−	7.80426i	−0.107734	−	0.331571i
$555$	4.13842	+	1.84254i	0.175666	+	0.0782115i
$556$	−1.52111	−	14.4724i	−0.0645096	−	0.613768i
$557$	−19.6903	−	4.18531i	−0.834306	−	0.177337i	−0.229097	−	0.973404i	$-0.573577\pi$
$557$	−19.6903	−	4.18531i	−0.834306	−	0.177337i	−0.605209	+	0.796066i	$0.706911\pi$
$558$	−0.181660	+	0.0386129i	−0.00769026	+	0.00163462i
$559$	−2.57095	−	1.86791i	−0.108740	−	0.0790040i
$560$	−3.00350	+	0.717964i	−0.126921	+	0.0303395i
$561$	0.138991	−	0.743221i	0.00586819	−	0.0313788i
$562$	−15.8702	−	27.4879i	−0.669442	−	1.15951i
$563$	19.5196	−	8.69069i	0.822653	−	0.366269i	0.0481510	−	0.998840i	$-0.484667\pi$
$563$	19.5196	−	8.69069i	0.822653	−	0.366269i	0.774502	+	0.632571i	$0.218000\pi$
$564$	−0.773305	−	0.858842i	−0.0325620	−	0.0361638i
$565$	−7.60851	+	8.45011i	−0.320093	+	0.355499i
$566$	19.1110	−	13.8850i	0.803295	−	0.583628i
$567$	1.72025	−	2.01016i	0.0722437	−	0.0844188i
$568$	−2.04700	−	6.30001i	−0.0858901	−	0.264342i
$569$	−5.26543	+	1.11920i	−0.220739	+	0.0469194i	−0.316953	−	0.948441i	$-0.602660\pi$
$569$	−5.26543	+	1.11920i	−0.220739	+	0.0469194i	0.0962147	+	0.995361i	$0.469326\pi$
$570$	0.416193	−	0.185301i	0.0174324	−	0.00776142i
$571$	21.2456	−	36.7984i	0.889099	−	1.53997i	0.0481573	−	0.998840i	$-0.484665\pi$
$571$	21.2456	−	36.7984i	0.889099	−	1.53997i	0.840942	−	0.541125i	$-0.182002\pi$
$572$	2.09972	+	0.625657i	0.0877936	+	0.0261600i
$573$	4.57148			0.190976
$574$	1.05397	−	0.807098i	0.0439918	−	0.0336876i
$575$	9.77475	−	30.0836i	0.407635	−	1.25457i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	1.38541	+	13.1813i	0.0576755	+	0.548746i	0.984763	+	0.173901i	$0.0556374\pi$
$577$	1.38541	+	13.1813i	0.0576755	+	0.548746i	−0.927088	+	0.374845i	$0.877696\pi$
$578$	1.77155	+	16.8552i	0.0736868	+	0.701083i
$579$	14.9042	−	16.5528i	0.619399	−	0.687912i
$580$	0.973553	−	2.99629i	0.0404246	−	0.124414i
$581$	−3.58689	−	27.4531i	−0.148809	−	1.13895i
$582$	−7.51754			−0.311612
$583$	−17.6087	+	25.5323i	−0.729276	+	1.05744i
$584$	7.32430	−	12.6861i	0.303082	−	0.524953i
$585$	−0.704388	+	0.313614i	−0.0291229	+	0.0129663i
$586$	−5.76937	+	1.22632i	−0.238330	+	0.0506587i
$587$	−13.5226	−	41.6184i	−0.558139	−	1.71778i	−0.687506	−	0.726178i	$-0.741295\pi$
$587$	−13.5226	−	41.6184i	−0.558139	−	1.71778i	0.129367	−	0.991597i	$-0.458705\pi$
$588$	−3.19016	+	6.23080i	−0.131560	+	0.256954i
$589$	−0.0586450	+	0.0426081i	−0.00241642	+	0.00175564i
$590$	−8.19207	+	9.09821i	−0.337262	+	0.374568i
$591$	−4.28508	−	4.75907i	−0.176265	−	0.195762i
$592$	3.54559	−	1.57860i	0.145723	−	0.0648800i
$593$	13.8966	+	24.0695i	0.570663	+	0.988418i	0.996498	+	0.0836168i	$0.0266472\pi$
$593$	13.8966	+	24.0695i	0.570663	+	0.988418i	−0.425835	+	0.904801i	$0.640019\pi$
$594$	2.91215	+	1.58726i	0.119487	+	0.0651263i
$595$	−0.484110	−	0.511148i	−0.0198466	−	0.0209550i
$596$	0.182185	+	0.132365i	0.00746260	+	0.00542190i
$597$	−23.0797	+	4.90575i	−0.944590	+	0.200779i
$598$	−5.61880	−	1.19431i	−0.229770	−	0.0488391i
$599$	0.290187	+	2.76095i	0.0118567	+	0.112809i	0.998849	−	0.0479556i	$-0.0152706\pi$
$599$	0.290187	+	2.76095i	0.0118567	+	0.112809i	−0.986993	+	0.160765i	$0.948604\pi$
$600$	−3.32315	−	1.47956i	−0.135667	−	0.0604029i
$601$	6.47701	+	19.9342i	0.264203	+	0.813133i	0.991876	+	0.127209i	$0.0406018\pi$
$601$	6.47701	+	19.9342i	0.264203	+	0.813133i	−0.727673	+	0.685924i	$0.759398\pi$
$602$	10.4821	+	7.21931i	0.427220	+	0.294237i
$603$	3.48460	+	2.53171i	0.141904	+	0.103099i
$604$	7.37187	+	12.7685i	0.299957	+	0.519541i
$605$	10.0040	−	8.04769i	0.406721	−	0.327185i
$606$	−1.14563	+	1.98428i	−0.0465379	+	0.0806060i
$607$	1.16890	−	11.1213i	0.0474441	−	0.451401i	−0.944851	−	0.327501i	$-0.893793\pi$
$607$	1.16890	−	11.1213i	0.0474441	−	0.451401i	0.992295	−	0.123899i	$-0.0395399\pi$
$608$	0.120615	−	0.371215i	0.00489159	−	0.0150548i
$609$	−3.72538	−	6.09266i	−0.150960	−	0.246887i
$610$	8.98595	−	6.52868i	0.363831	−	0.264338i
$611$	0.697439	+	0.310520i	0.0282154	+	0.0125623i
$612$	0.222993	+	0.0473986i	0.00901395	+	0.00191597i
$613$	−2.12373	−	2.35864i	−0.0857767	−	0.0952647i	0.698728	−	0.715387i	$-0.253750\pi$
$613$	−2.12373	−	2.35864i	−0.0857767	−	0.0952647i	−0.784505	+	0.620122i	$0.787083\pi$
$614$	−2.42419	+	23.0646i	−0.0978322	+	0.930812i
$615$	−0.585641			−0.0236153
$616$	−8.47004	−	2.29313i	−0.341268	−	0.0923927i
$617$	18.5959			0.748643			0.374322	−	0.927299i	$-0.377876\pi$
$617$	18.5959			0.748643			0.374322	+	0.927299i	$0.377876\pi$
$618$	−1.23245	+	11.7259i	−0.0495762	+	0.471686i
$619$	−23.5334	−	26.1365i	−0.945889	−	1.05052i	−0.998652	−	0.0519088i	$-0.983469\pi$
$619$	−23.5334	−	26.1365i	−0.945889	−	1.05052i	0.0527631	−	0.998607i	$-0.483197\pi$
$620$	−0.212033	−	0.0450690i	−0.00851546	−	0.00181002i
$621$	−7.94389	−	3.53685i	−0.318777	−	0.141929i
$622$	0.320502	−	0.232859i	0.0128510	−	0.00933678i
$623$	−33.3464	+	0.840495i	−1.33600	+	0.0336737i
$624$	−0.204135	+	0.628264i	−0.00817196	+	0.0251507i
$625$	−0.671141	+	6.38548i	−0.0268456	+	0.255419i
$626$	−4.05170	+	7.01774i	−0.161938	+	0.280485i
$627$	1.29038	+	0.103654i	0.0515330	+	0.00413954i
$628$	1.46086	+	2.53028i	0.0582945	+	0.100969i
$629$	0.715818	+	0.520072i	0.0285415	+	0.0207366i
$630$	2.78860	−	1.32674i	0.111100	−	0.0528585i
$631$	−12.0708	−	37.1502i	−0.480533	−	1.47893i	−0.838348	−	0.545135i	$-0.816478\pi$
$631$	−12.0708	−	37.1502i	−0.480533	−	1.47893i	0.357816	−	0.933792i	$-0.383522\pi$
$632$	0.103461	+	0.0460637i	0.00411545	+	0.00183231i
$633$	0.0445119	+	0.423502i	0.00176919	+	0.0168327i
$634$	29.2982	+	6.22753i	1.16358	+	0.247327i
$635$	−3.74264	+	0.795524i	−0.148522	+	0.0315694i
$636$	−7.56554	−	5.49669i	−0.299993	−	0.217958i
$637$	0.251064	−	4.61735i	0.00994752	−	0.182946i
$638$	6.50362	−	6.15176i	0.257481	−	0.243551i
$639$	3.31211	+	5.73674i	0.131025	+	0.226942i
$640$	1.06629	−	0.474743i	0.0421489	−	0.0187659i
$641$	27.7606	+	30.8313i	1.09648	+	1.21776i	0.974300	+	0.225255i	$0.0723215\pi$
$641$	27.7606	+	30.8313i	1.09648	+	1.21776i	0.122179	+	0.992508i	$0.461012\pi$
$642$	−10.1876	+	11.3144i	−0.402071	+	0.446545i
$643$	−19.6055	+	14.2443i	−0.773167	+	0.561738i	−0.902920	−	0.429808i	$-0.858581\pi$
$643$	−19.6055	+	14.2443i	−0.773167	+	0.561738i	0.129754	+	0.991546i	$0.458581\pi$
$644$	22.6172	+	4.21479i	0.891243	+	0.166086i
$645$	−1.73511	−	5.34013i	−0.0683201	−	0.210267i
$646$	0.0870383	−	0.0185006i	0.00342447	−	0.000727895i
$647$	−34.7212	+	15.4589i	−1.36503	+	0.607750i	−0.952875	−	0.303364i	$-0.901890\pi$
$647$	−34.7212	+	15.4589i	−1.36503	+	0.607750i	−0.412155	+	0.911114i	$0.635224\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−32.8116	+	11.5596i	−1.28797	+	0.453753i
$650$	2.40301			0.0942539
$651$	−0.390118	+	0.298741i	−0.0152899	+	0.0117086i
$652$	−1.34392	+	4.13617i	−0.0526321	+	0.161985i
$653$	−23.9073	+	26.5517i	−0.935563	+	1.03905i	0.0635931	+	0.997976i	$0.479744\pi$
$653$	−23.9073	+	26.5517i	−0.935563	+	1.03905i	−0.999156	+	0.0410721i	$0.986923\pi$
$654$	0.929223	+	8.84096i	0.0363355	+	0.345709i
$655$	2.06963	+	19.6912i	0.0808672	+	0.769400i
$656$	−0.335735	+	0.372871i	−0.0131082	+	0.0145582i
$657$	−4.52667	+	13.9316i	−0.176602	+	0.543525i
$658$	−2.82376	−	1.17288i	−0.110082	−	0.0457238i
$659$	17.5078			0.682006			0.341003	−	0.940062i	$-0.389233\pi$
$659$	17.5078			0.682006			0.341003	+	0.940062i	$0.389233\pi$
$660$	2.35165	+	3.07501i	0.0915379	+	0.119695i
$661$	−24.1011	+	41.7443i	−0.937424	+	1.62367i	−0.167171	+	0.985928i	$0.553463\pi$
$661$	−24.1011	+	41.7443i	−0.937424	+	1.62367i	−0.770253	+	0.637738i	$0.779870\pi$
$662$	−25.2588	+	11.2459i	−0.981710	+	0.437085i
$663$	−0.147308	+	0.0313113i	−0.00572098	+	0.00121603i
$664$	3.23370	+	9.95232i	0.125492	+	0.386225i
$665$	0.783712	−	0.915789i	0.0303910	−	0.0355128i
$666$	−3.13990	+	2.28127i	−0.121669	+	0.0883975i
$667$	−15.7053	+	17.4425i	−0.608111	+	0.675376i
$668$	6.38741	+	7.09393i	0.247136	+	0.274472i
$669$	−11.8933	+	5.29526i	−0.459823	+	0.204727i
$670$	2.51369	+	4.35383i	0.0971122	+	0.168203i
$671$	31.2981	−	4.06903i	1.20825	−	0.157083i
$672$	0.753921	−	2.53606i	0.0290831	−	0.0978307i
$673$	−4.55728	−	3.31106i	−0.175670	−	0.127632i	0.496476	−	0.868051i	$-0.334627\pi$
$673$	−4.55728	−	3.31106i	−0.175670	−	0.127632i	−0.672146	+	0.740419i	$0.734627\pi$
$674$	−16.2285	+	3.44948i	−0.625099	+	0.132869i
$675$	3.55815	+	0.756308i	0.136953	+	0.0291103i
$676$	1.31326	+	12.4948i	0.0505098	+	0.480569i
$677$	15.2733	+	6.80011i	0.587000	+	0.261349i	0.678674	−	0.734440i	$-0.262555\pi$
$677$	15.2733	+	6.80011i	0.587000	+	0.261349i	−0.0916735	+	0.995789i	$0.529222\pi$
$678$	−3.01041	−	9.26509i	−0.115614	−	0.355824i
$679$	−17.9604	+	8.54506i	−0.689256	+	0.327929i
$680$	0.215273	+	0.156405i	0.00825534	+	0.00599786i
$681$	−8.64035	−	14.9655i	−0.331099	−	0.573480i
$682$	−0.467730	−	0.400788i	−0.0179103	−	0.0153470i
$683$	7.96506	−	13.7959i	0.304775	−	0.527885i	−0.672436	−	0.740155i	$-0.734752\pi$
$683$	7.96506	−	13.7959i	0.304775	−	0.527885i	0.977211	+	0.212270i	$0.0680855\pi$
$684$	−0.0407994	+	0.388181i	−0.00156000	+	0.0148425i
$685$	6.62257	−	20.3822i	0.253035	−	0.778762i
$686$	−0.539251	+	18.5124i	−0.0205887	+	0.706807i
$687$	8.41174	−	6.11148i	0.320928	−	0.233168i
$688$	−4.39471	−	1.95665i	−0.167547	−	0.0745966i
$689$	6.04259	+	1.28439i	0.230204	+	0.0489314i
$690$	−6.79141	−	7.54262i	−0.258544	−	0.287143i
$691$	−3.50291	+	33.3280i	−0.133257	+	1.26786i	0.699667	+	0.714469i	$0.253332\pi$
$691$	−3.50291	+	33.3280i	−0.133257	+	1.26786i	−0.832924	+	0.553387i	$0.813335\pi$
$692$	7.69661			0.292581
$693$	8.76172	+	0.481996i	0.332830	+	0.0183095i
$694$	−0.889711			−0.0337730
$695$	−1.77545	+	16.8922i	−0.0673465	+	0.640759i
$696$	1.80610	+	2.00588i	0.0684602	+	0.0760327i
$697$	−0.111886	−	0.0237821i	−0.00423799	−	0.000900813i
$698$	31.2210	+	13.9005i	1.18173	+	0.526141i
$699$	4.20303	−	3.05368i	0.158973	−	0.115501i
$700$	−9.62124	+	0.242503i	−0.363649	+	0.00916574i
$701$	2.00987	−	6.18575i	0.0759119	−	0.233633i	−0.905899	−	0.423493i	$-0.860804\pi$
$701$	2.00987	−	6.18575i	0.0759119	−	0.233633i	0.981811	+	0.189861i	$0.0608037\pi$
$702$	0.0690511	−	0.656977i	0.00260617	−	0.0247960i
$703$	−0.757439	+	1.31192i	−0.0285674	+	0.0494801i
$704$	3.30598	+	0.265562i	0.124599	+	0.0100088i
$705$	0.674459	+	1.16820i	0.0254016	+	0.0439969i
$706$	3.99084	+	2.89952i	0.150197	+	0.109125i
$707$	−0.481550	+	6.04293i	−0.0181106	+	0.227268i
$708$	−3.24130	−	9.97570i	−0.121816	−	0.374910i
$709$	11.3011	+	5.03157i	0.424421	+	0.188964i	0.607821	−	0.794074i	$-0.292044\pi$
$709$	11.3011	+	5.03157i	0.424421	+	0.188964i	−0.183400	+	0.983038i	$0.558710\pi$
$710$	0.808193	+	7.68944i	0.0303309	+	0.288580i
$711$	−0.110777	−	0.0235464i	−0.00415446	−	0.000883058i
$712$	12.3323	−	2.62130i	0.462171	−	0.0982375i
$713$	1.30652	+	0.949239i	0.0489294	+	0.0355493i
$714$	0.586636	−	0.140231i	0.0219543	−	0.00524801i
$715$	−2.24541	−	1.22386i	−0.0839734	−	0.0457697i
$716$	−5.17920	−	8.97063i	−0.193556	−	0.335248i
$717$	−9.63572	+	4.29010i	−0.359853	+	0.160217i
$718$	−0.0821762	−	0.0912660i	−0.00306679	−	0.00340602i
$719$	16.9072	−	18.7773i	0.630531	−	0.700275i	−0.340225	−	0.940344i	$-0.610503\pi$
$719$	16.9072	−	18.7773i	0.630531	−	0.700275i	0.970756	+	0.240069i	$0.0771700\pi$
$720$	−0.944285	+	0.686063i	−0.0351914	+	0.0255681i
$721$	10.3842	+	29.4157i	0.386728	+	1.09550i
$722$	−5.82424	−	17.9252i	−0.216756	−	0.667106i
$723$	−24.3026	+	5.16569i	−0.903825	+	0.192114i
$724$	−3.53233	+	1.57269i	−0.131278	+	0.0584487i
$725$	4.90932	−	8.50320i	0.182328	−	0.315801i
$726$	1.68566	+	10.8701i	0.0625605	+	0.403426i
$727$	−41.2773			−1.53089			−0.765446	−	0.643500i	$-0.777482\pi$
$727$	−41.2773			−1.53089			−0.765446	+	0.643500i	$0.777482\pi$
$728$	0.226431	+	1.73304i	0.00839210	+	0.0642309i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−11.4407	+	12.7062i	−0.423439	+	0.470277i
$731$	−0.114636	−	1.09069i	−0.00423997	−	0.0403406i
$732$	0.994708	+	9.46401i	0.0367655	+	0.349800i
$733$	28.0612	−	31.1652i	1.03647	−	1.15111i	0.0481261	−	0.998841i	$-0.484675\pi$
$733$	28.0612	−	31.1652i	1.03647	−	1.15111i	0.988339	−	0.152270i	$-0.0486583\pi$
$734$	−2.50784	+	7.71833i	−0.0925659	+	0.284889i
$735$	5.15424	−	6.33950i	0.190117	−	0.233836i
$736$	−8.69567			−0.320527
$737$	0.350870	+	14.2811i	0.0129244	+	0.526050i
$738$	0.250874	−	0.434527i	0.00923480	−	0.0159951i
$739$	−24.7463	+	11.0178i	−0.910308	+	0.405295i	−0.807813	−	0.589438i	$-0.799349\pi$
$739$	−24.7463	+	11.0178i	−0.910308	+	0.405295i	−0.102495	+	0.994734i	$0.532682\pi$
$740$	−4.43107	+	0.941853i	−0.162889	+	0.0346232i
$741$	−0.0796779	−	0.245223i	−0.00292704	−	0.00900850i
$742$	−24.3231	−	4.53268i	−0.892928	−	0.166400i
$743$	16.0554	−	11.6649i	0.589014	−	0.427944i	−0.252948	−	0.967480i	$-0.581400\pi$
$743$	16.0554	−	11.6649i	0.589014	−	0.427944i	0.841963	+	0.539536i	$0.181400\pi$
$744$	0.124270	−	0.138015i	0.00455594	−	0.00505989i
$745$	−0.175878	−	0.195333i	−0.00644368	−	0.00715643i
$746$	23.3903	−	10.4140i	0.856380	−	0.381285i
$747$	−5.23224	−	9.06251i	−0.191438	−	0.331580i
$748$	0.324409	+	0.682975i	0.0118616	+	0.0249721i
$749$	−11.4785	+	38.6117i	−0.419415	+	1.41084i
$750$	8.15640	+	5.92597i	0.297830	+	0.216386i
$751$	−50.8984	+	10.8188i	−1.85731	+	0.394783i	−0.993952	−	0.109811i	$-0.964975\pi$
$751$	−50.8984	+	10.8188i	−1.85731	+	0.394783i	−0.863356	+	0.504595i	$0.831642\pi$
$752$	1.13043	+	0.240281i	0.0412226	+	0.00876214i
$753$	−2.96262	−	28.1874i	−0.107964	−	1.02721i
$754$	−1.62891	−	0.725239i	−0.0593215	−	0.0264116i
$755$	−5.31784	−	16.3666i	−0.193536	−	0.595643i
$756$	−0.210169	+	2.63739i	−0.00764377	+	0.0959210i
$757$	13.5842	+	9.86948i	0.493725	+	0.358713i	0.806615	−	0.591077i	$-0.201297\pi$
$757$	13.5842	+	9.86948i	0.493725	+	0.358713i	−0.312890	+	0.949789i	$0.601297\pi$
$758$	3.98218	+	6.89733i	0.144639	+	0.250522i
$759$	−6.68730	−	28.0543i	−0.242734	−	1.01831i
$760$	−0.227790	+	0.394544i	−0.00826282	+	0.0143116i
$761$	−4.13506	+	39.3424i	−0.149896	+	1.42616i	0.618298	+	0.785944i	$0.287823\pi$
$761$	−4.13506	+	39.3424i	−0.149896	+	1.42616i	−0.768193	+	0.640218i	$0.778844\pi$
$762$	1.01300	−	3.11770i	0.0366972	−	0.112942i
$763$	12.2694	+	20.0660i	0.444183	+	0.726438i
$764$	−3.69840	+	2.68705i	−0.133803	+	0.0972139i
$765$	−0.243087	−	0.108229i	−0.00878884	−	0.00391304i
$766$	31.4035	+	6.67502i	1.13465	+	0.241178i
$767$	4.63643	+	5.14928i	0.167412	+	0.185930i
$768$	−0.104528	+	0.994522i	−0.00377185	+	0.0358867i
$769$	35.0363			1.26344			0.631721	−	0.775196i	$-0.282349\pi$
$769$	35.0363			1.26344			0.631721	+	0.775196i	$0.282349\pi$
$770$	9.11372	+	4.67352i	0.328436	+	0.168422i
$771$	−21.1014			−0.759947
$772$	−2.32827	+	22.1520i	−0.0837963	+	0.797268i
$773$	7.77376	+	8.63364i	0.279603	+	0.310530i	0.866545	−	0.499098i	$-0.166335\pi$
$773$	7.77376	+	8.63364i	0.279603	+	0.310530i	−0.586943	+	0.809628i	$0.699669\pi$
$774$	4.70549	+	1.00018i	0.169135	+	0.0359508i
$775$	−0.617169	−	0.274781i	−0.0221694	−	0.00987043i
$776$	6.08182	−	4.41870i	0.218324	−	0.158622i
$777$	−4.90855	+	9.01933i	−0.176093	+	0.323567i
$778$	−5.52679	+	17.0097i	−0.198145	+	0.609828i
$779$	0.0204710	−	0.194769i	0.000733451	−	0.00697832i
$780$	0.385524	−	0.667748i	0.0138040	−	0.0239092i
$781$	−8.44037	+	20.2841i	−0.302020	+	0.725821i
$782$	−0.991196	−	1.71680i	−0.0354451	−	0.0613927i
$783$	−2.18368	−	1.58654i	−0.0780384	−	0.0566982i
$784$	−1.08148	−	6.91595i	−0.0386244	−	0.246998i
$785$	−1.05382	−	3.24331i	−0.0376123	−	0.115759i
$786$	−15.4968	−	6.89964i	−0.552754	−	0.246102i
$787$	−2.78031	−	26.4529i	−0.0991074	−	0.942944i	−0.925218	−	0.379436i	$-0.876118\pi$
$787$	−2.78031	−	26.4529i	−0.0991074	−	0.942944i	0.826111	−	0.563508i	$-0.190549\pi$
$788$	6.26402	+	1.33146i	0.223146	+	0.0474312i
$789$	17.0256	−	3.61891i	0.606129	−	0.128837i
$790$	−0.106942	−	0.0776979i	−0.00380483	−	0.00276437i
$791$	−17.7237	−	18.7136i	−0.630184	−	0.665380i
$792$	−3.28895	+	0.427592i	−0.116868	+	0.0151938i
$793$	−3.14316	−	5.44412i	−0.111617	−	0.193326i
$794$	−1.53775	+	0.684652i	−0.0545729	+	0.0242974i
$795$	7.30363	+	8.11151i	0.259033	+	0.287686i
$796$	15.7884	−	17.5348i	0.559604	−	0.621503i
$797$	−4.05308	+	2.94473i	−0.143567	+	0.104308i	−0.657251	−	0.753672i	$-0.728281\pi$
$797$	−4.05308	+	2.94473i	−0.143567	+	0.104308i	0.513683	+	0.857980i	$0.328281\pi$
$798$	0.343763	+	0.973790i	0.0121691	+	0.0344718i
$799$	0.0814158	+	0.250572i	0.00288028	+	0.00886460i
$800$	3.55815	−	0.756308i	0.125800	−	0.0267395i
$801$	−11.5178	+	5.12804i	−0.406960	+	0.181190i
$802$	10.3286	−	17.8897i	0.364717	−	0.631709i
$803$	−45.8234	+	16.1436i	−1.61707	+	0.569696i
$804$	−4.30721			−0.151903
$805$	−24.7991	−	10.3006i	−0.874055	−	0.363050i
$806$	−0.0379116	+	0.116680i	−0.00133538	+	0.00410988i
$807$	−3.39854	+	3.77446i	−0.119634	+	0.132867i
$808$	−0.239501	−	2.27870i	−0.00842562	−	0.0801644i
$809$	2.28444	+	21.7350i	0.0803166	+	0.764161i	0.958357	+	0.285574i	$0.0921843\pi$
$809$	2.28444	+	21.7350i	0.0803166	+	0.764161i	−0.878040	+	0.478587i	$0.841149\pi$
$810$	0.781010	−	0.867399i	0.0274419	−	0.0304773i
$811$	10.7419	−	33.0601i	0.377198	−	1.16090i	−0.564785	−	0.825238i	$-0.691041\pi$
$811$	10.7419	−	33.0601i	0.377198	−	1.16090i	0.941983	−	0.335659i	$-0.108959\pi$
$812$	6.59507	+	2.73935i	0.231442	+	0.0961322i
$813$	−29.3160			−1.02816
$814$	−12.3363	−	3.67586i	−0.432385	−	0.128839i
$815$	2.53809	−	4.39611i	0.0889055	−	0.153989i
$816$	−0.208265	+	0.0927256i	−0.00729074	+	0.00324605i
$817$	1.83664	−	0.390390i	0.0642559	−	0.0136580i
$818$	10.9825	+	33.8007i	0.383994	+	1.18181i
$819$	−0.581803	−	1.64809i	−0.0203299	−	0.0575891i
$820$	0.473793	−	0.344231i	0.0165456	−	0.0120211i
$821$	31.5203	−	35.0068i	1.10007	−	1.22175i	0.126833	−	0.991924i	$-0.459519\pi$
$821$	31.5203	−	35.0068i	1.10007	−	1.22175i	0.973233	−	0.229822i	$-0.0738145\pi$
$822$	12.2860	+	13.6449i	0.428522	+	0.475922i
$823$	−0.548287	+	0.244113i	−0.0191121	+	0.00850924i	−0.416270	−	0.909241i	$-0.636663\pi$
$823$	−0.548287	+	0.244113i	−0.0191121	+	0.00850924i	0.397158	+	0.917750i	$0.369996\pi$
$824$	−5.89526	−	10.2109i	−0.205371	−	0.355713i
$825$	5.17638	+	10.8978i	0.180218	+	0.379413i
$826$	−19.0831	−	20.1489i	−0.663986	−	0.701071i
$827$	−32.7651	−	23.8052i	−1.13935	−	0.827789i	−0.152325	−	0.988330i	$-0.548676\pi$
$827$	−32.7651	−	23.8052i	−1.13935	−	0.827789i	−0.987029	+	0.160541i	$0.948676\pi$
$828$	8.50565	−	1.80793i	0.295592	−	0.0628300i
$829$	11.9800	+	2.54644i	0.416084	+	0.0884414i	0.411197	−	0.911547i	$-0.365111\pi$
$829$	11.9800	+	2.54644i	0.416084	+	0.0884414i	0.00488730	+	0.999988i	$0.498444\pi$
$830$	−1.27673	−	12.1472i	−0.0443158	−	0.421637i
$831$	−7.49645	−	3.33764i	−0.260049	−	0.115781i
$832$	−0.204135	−	0.628264i	−0.00707712	−	0.0217811i
$833$	1.24215	−	1.00185i	0.0430381	−	0.0347120i
$834$	−11.7729	−	8.55354i	−0.407664	−	0.296185i
$835$	−5.57095	−	9.64917i	−0.192791	−	0.333923i
$836$	−1.10487	+	0.674611i	−0.0382127	+	0.0233319i
$837$	−0.0928590	+	0.160836i	−0.00320968	+	0.00555932i
$838$	−0.0124148	+	0.118118i	−0.000428861	+	0.00408034i
$839$	11.6227	−	35.7711i	0.401261	−	1.23496i	−0.522716	−	0.852507i	$-0.675081\pi$
$839$	11.6227	−	35.7711i	0.401261	−	1.23496i	0.923977	−	0.382448i	$-0.124919\pi$
$840$	−1.47618	+	2.71245i	−0.0509332	+	0.0935884i
$841$	17.5673	−	12.7634i	0.605770	−	0.440118i
$842$	21.0311	+	9.36363i	0.724778	+	0.322692i
$843$	−31.0467	−	6.59918i	−1.06931	−	0.227288i
$844$	−0.284939	−	0.316457i	−0.00980801	−	0.0108929i
$845$	1.53283	−	14.5839i	0.0527310	−	0.501702i
$846$	−1.15569			−0.0397333
$847$	16.3831	+	24.0540i	0.562930	+	0.826505i
$848$	9.35153			0.321133
$849$	2.46922	−	23.4931i	0.0847435	−	0.806281i
$850$	0.554903	+	0.616282i	0.0190330	+	0.0211383i
$851$	33.0116	+	7.01682i	1.13162	+	0.240534i
$852$	−6.05153	−	2.69431i	−0.207322	−	0.0923056i
$853$	28.8074	−	20.9298i	0.986346	−	0.716622i	0.0272283	−	0.999629i	$-0.491332\pi$
$853$	28.8074	−	20.9298i	0.986346	−	0.716622i	0.959118	+	0.283007i	$0.0913319\pi$
$854$	13.1341	+	21.4801i	0.449439	+	0.735034i
$855$	0.140782	−	0.433283i	0.00481465	−	0.0148180i
$856$	1.59145	−	15.1417i	0.0543948	−	0.517532i
$857$	−5.57201	+	9.65101i	−0.190336	+	0.329672i	−0.945362	−	0.326023i	$-0.894291\pi$
$857$	−5.57201	+	9.65101i	−0.190336	+	0.329672i	0.755025	+	0.655696i	$0.227625\pi$
$858$	1.86994	−	1.14175i	0.0638387	−	0.0389786i
$859$	−18.2148	−	31.5490i	−0.621482	−	1.07644i	−0.989210	−	0.146506i	$-0.953197\pi$
$859$	−18.2148	−	31.5490i	−0.621482	−	1.07644i	0.367727	−	0.929934i	$-0.380136\pi$
$860$	4.54259	+	3.30038i	0.154901	+	0.112542i
$861$	0.105452	−	1.32331i	0.00359379	−	0.0450981i
$862$	5.88197	+	18.1028i	0.200341	+	0.616585i
$863$	−38.6591	−	17.2121i	−1.31597	−	0.585908i	−0.375828	−	0.926689i	$-0.622642\pi$
$863$	−38.6591	−	17.2121i	−1.31597	−	0.585908i	−0.940143	+	0.340781i	$0.889308\pi$
$864$	−0.104528	−	0.994522i	−0.00355613	−	0.0338343i
$865$	−8.78718	−	1.86777i	−0.298773	−	0.0635062i
$866$	−11.4457	+	2.43286i	−0.388941	+	0.0826719i
$867$	13.7112	+	9.96180i	0.465658	+	0.338320i
$868$	0.140017	−	0.470992i	0.00475247	−	0.0159865i
$869$	−0.161158	−	0.339284i	−0.00546691	−	0.0115094i
$870$	−1.57524	−	2.72840i	−0.0534057	−	0.0925014i
$871$	2.59933	−	1.15730i	0.0880750	−	0.0392135i
$872$	−5.94834	−	6.60631i	−0.201436	−	0.223718i
$873$	−5.03021	+	5.58662i	−0.170247	+	0.189078i
$874$	2.74587	−	1.99499i	0.0928805	−	0.0674816i
$875$	26.2227	+	4.88668i	0.886488	+	0.165200i
$876$	−4.52667	−	13.9316i	−0.152942	−	0.470707i
$877$	27.3566	−	5.81483i	0.923767	−	0.196353i	0.278611	−	0.960404i	$-0.410126\pi$
$877$	27.3566	−	5.81483i	0.923767	−	0.196353i	0.645156	+	0.764051i	$0.276793\pi$
$878$	−28.3044	+	12.6019i	−0.955226	+	0.425294i
$879$	−2.94913	+	5.10804i	−0.0994717	+	0.172290i
$880$	−3.70997	−	1.10547i	−0.125063	−	0.0372653i
$881$	−5.99256			−0.201894			−0.100947	−	0.994892i	$-0.532187\pi$
$881$	−5.99256			−0.201894			−0.100947	+	0.994892i	$0.532187\pi$
$882$	2.49576	+	6.53997i	0.0840365	+	0.220212i
$883$	8.02286	−	24.6918i	0.269991	−	0.830946i	−0.720511	−	0.693444i	$-0.756093\pi$
$883$	8.02286	−	24.6918i	0.269991	−	0.830946i	0.990501	−	0.137502i	$-0.0439075\pi$
$884$	0.100770	−	0.111917i	0.00338928	−	0.00376417i
$885$	1.27973	+	12.1758i	0.0430175	+	0.409285i
$886$	−1.34623	−	12.8085i	−0.0452273	−	0.430309i
$887$	27.7112	−	30.7764i	0.930451	−	1.03337i	−0.0689095	−	0.997623i	$-0.521952\pi$
$887$	27.7112	−	30.7764i	0.930451	−	1.03337i	0.999361	−	0.0357479i	$-0.0113813\pi$
$888$	1.19934	−	3.69118i	0.0402471	−	0.123868i
$889$	−1.12364	−	8.60007i	−0.0376858	−	0.288437i
$890$	−14.7158			−0.493275
$891$	3.12817	−	1.10206i	0.104798	−	0.0369203i
$892$	6.50944	−	11.2747i	0.217952	−	0.377504i
$893$	−0.412088	+	0.183473i	−0.0137900	+	0.00613970i
$894$	0.220272	−	0.0468203i	0.00736701	−	0.00156591i
$895$	3.73612	+	11.4986i	0.124885	+	0.384355i
$896$	0.880725	+	2.49486i	0.0294229	+	0.0833474i
$897$	−4.64726	+	3.37643i	−0.155167	+	0.112736i
$898$	−24.9320	+	27.6898i	−0.831991	+	0.924020i
$899$	0.335426	+	0.372528i	0.0111871	+	0.0124245i
$900$	−3.32315	+	1.47956i	−0.110772	+	0.0493187i
$901$	1.06596	+	1.84629i	0.0355121	+	0.0615088i
$902$	1.65022	−	0.214543i	0.0549464	−	0.00714351i
$903$	12.3789	−	2.95908i	0.411945	−	0.0984721i
$904$	7.88136	+	5.72614i	0.262130	+	0.190449i
$905$	4.41449	−	0.938330i	0.146743	−	0.0311911i
$906$	14.4216	+	3.06540i	0.479124	+	0.101841i
$907$	−2.82742	−	26.9011i	−0.0938831	−	0.893238i	−0.935539	−	0.353224i	$-0.885085\pi$
$907$	−2.82742	−	26.9011i	−0.0938831	−	0.893238i	0.841656	−	0.540014i	$-0.181581\pi$
$908$	15.7867	+	7.02870i	0.523900	+	0.233255i
$909$	0.708036	+	2.17911i	0.0234841	+	0.0722766i
$910$	0.162050	−	2.03356i	0.00537192	−	0.0674117i
$911$	40.2538	+	29.2461i	1.33367	+	0.968966i	0.999651	+	0.0263989i	$0.00840401\pi$
$911$	40.2538	+	29.2461i	1.33367	+	0.968966i	0.334016	+	0.942567i	$0.391596\pi$
$912$	−0.195159	−	0.338026i	−0.00646237	−	0.0111932i
$913$	13.3335	−	32.0434i	0.441275	−	1.06048i
$914$	−5.90861	+	10.2340i	−0.195440	+	0.338511i
$915$	1.16102	−	11.0464i	0.0383823	−	0.365183i
$916$	−3.21300	+	9.88859i	−0.106160	+	0.326728i
$917$	−44.8667	+	1.13086i	−1.48163	+	0.0373444i
$918$	0.184435	−	0.134000i	0.00608727	−	0.00442266i
$919$	31.4467	+	14.0010i	1.03733	+	0.461850i	0.853492	−	0.521106i	$-0.174480\pi$
$919$	31.4467	+	14.0010i	1.03733	+	0.461850i	0.183840	+	0.982956i	$0.441147\pi$
$920$	9.92780	+	2.11022i	0.327310	+	0.0695719i
$921$	15.5182	+	17.2348i	0.511343	+	0.567904i
$922$	1.65196	−	15.7173i	0.0544044	−	0.517623i
$923$	4.37593			0.144036
$924$	−7.37169	+	4.76006i	−0.242511	+	0.156595i
$925$	−14.1182			−0.464203
$926$	3.88153	−	36.9303i	0.127555	−	1.21360i
$927$	7.88940	+	8.76207i	0.259122	+	0.287784i
$928$	−2.64020	−	0.561191i	−0.0866687	−	0.0184220i
$929$	32.8209	+	14.6128i	1.07682	+	0.479430i	0.866999	−	0.498310i	$-0.166046\pi$
$929$	32.8209	+	14.6128i	1.07682	+	0.479430i	0.209819	+	0.977740i	$0.432713\pi$
$930$	−0.175371	+	0.127414i	−0.00575063	+	0.00417808i
$931$	1.92819	+	1.93576i	0.0631938	+	0.0634421i
$932$	−1.60542	+	4.94096i	−0.0525872	+	0.161847i
$933$	0.0414103	−	0.393993i	0.00135571	−	0.0128987i
$934$	−0.538450	+	0.932623i	−0.0176186	+	0.0305164i
$935$	−0.204635	−	0.858475i	−0.00669228	−	0.0280751i
$936$	0.330298	+	0.572093i	0.0107961	+	0.0186994i
$937$	−14.0782	−	10.2284i	−0.459915	−	0.334148i	0.333583	−	0.942721i	$-0.391742\pi$
$937$	−14.0782	−	10.2284i	−0.459915	−	0.334148i	−0.793498	+	0.608573i	$0.791742\pi$
$938$	−10.2905	+	4.89593i	−0.335996	+	0.159858i
$939$	2.50409	+	7.70678i	0.0817178	+	0.251501i
$940$	−1.23230	−	0.548654i	−0.0401931	−	0.0178951i
$941$	−3.71523	−	35.3481i	−0.121113	−	1.15231i	−0.871184	−	0.490957i	$-0.836647\pi$
$941$	−3.71523	−	35.3481i	−0.121113	−	1.15231i	0.750071	−	0.661357i	$-0.230019\pi$
$942$	2.85786	+	0.607458i	0.0931142	+	0.0197920i
$943$	−4.26769	+	0.907126i	−0.138975	+	0.0295401i
$944$	8.48584	+	6.16532i	0.276190	+	0.200664i
$945$	0.879977	−	2.96009i	0.0286256	−	0.0962918i
$946$	6.84552	+	14.4118i	0.222567	+	0.468569i
$947$	−12.0438	−	20.8605i	−0.391372	−	0.677876i	0.601259	−	0.799054i	$-0.294666\pi$
$947$	−12.0438	−	20.8605i	−0.391372	−	0.677876i	−0.992631	+	0.121178i	$0.961333\pi$
$948$	0.103461	−	0.0460637i	0.00336025	−	0.00149608i
$949$	6.47505	+	7.19127i	0.210189	+	0.233439i
$950$	−0.950058	+	1.05515i	−0.0308240	+	0.0342335i
$951$	24.2323	−	17.6058i	0.785786	−	0.570907i
$952$	−0.392173	+	0.458265i	−0.0127104	+	0.0148525i
$953$	−17.4242	−	53.6261i	−0.564425	−	1.73712i	−0.669654	−	0.742673i	$-0.733558\pi$
$953$	−17.4242	−	53.6261i	−0.564425	−	1.73712i	0.105229	−	0.994448i	$-0.466442\pi$
$954$	−9.14717	+	1.94429i	−0.296151	+	0.0629488i
$955$	4.87452	−	2.17028i	0.157736	−	0.0702286i
$956$	5.27380	−	9.13450i	0.170567	−	0.295431i
$957$	−0.219878	−	8.94947i	−0.00710765	−	0.289295i
$958$	1.20864			0.0390495
$959$	44.8628	+	18.6343i	1.44869	+	0.601733i
$960$	0.360685	−	1.11007i	0.0116411	−	0.0358275i
$961$	−20.7200	+	23.0119i	−0.668386	+	0.742318i
$962$	0.267996	+	2.54982i	0.00864055	+	0.0822094i
$963$	1.59145	+	15.1417i	0.0512839	+	0.487934i
$964$	16.6249	−	18.4639i	0.535453	−	0.594681i
$965$	8.03391	−	24.7258i	0.258621	−	0.795952i
$966$	18.2661	−	13.9876i	0.587701	−	0.450044i
$967$	12.4643			0.400826			0.200413	−	0.979711i	$-0.435772\pi$
$967$	12.4643			0.400826			0.200413	+	0.979711i	$0.435772\pi$
$968$	−7.75299	−	7.80327i	−0.249191	−	0.250807i
$969$	0.0444914	−	0.0770613i	0.00142927	−	0.00247557i
$970$	−8.01588	+	3.56890i	−0.257375	+	0.114591i
$971$	2.33940	−	0.497255i	0.0750749	−	0.0159577i	−0.170221	−	0.985406i	$-0.554448\pi$
$971$	2.33940	−	0.497255i	0.0750749	−	0.0159577i	0.245296	+	0.969448i	$0.421115\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	−37.8498	−	7.05343i	−1.21341	−	0.226123i
$974$	−8.39087	+	6.09633i	−0.268861	+	0.195339i
$975$	1.60793	−	1.78579i	0.0514949	−	0.0571909i
$976$	−6.36754	−	7.07187i	−0.203820	−	0.226365i
$977$	−29.3711	+	13.0769i	−0.939666	+	0.418366i	−0.818656	−	0.574285i	$-0.805280\pi$
$977$	−29.3711	+	13.0769i	−0.939666	+	0.418366i	−0.121011	+	0.992651i	$0.538614\pi$
$978$	2.17451	+	3.76637i	0.0695332	+	0.120435i
$979$	−36.7157	−	20.0119i	−1.17344	−	0.639582i
$980$	−0.443603	+	8.15836i	−0.0141704	+	0.260609i
$981$	7.19189	+	5.22521i	0.229619	+	0.166828i
$982$	7.48572	−	1.59114i	0.238879	−	0.0507753i
$983$	21.9915	+	4.67444i	0.701421	+	0.149092i	0.544798	−	0.838567i	$-0.316606\pi$
$983$	21.9915	+	4.67444i	0.701421	+	0.149092i	0.156622	+	0.987659i	$0.449940\pi$
$984$	0.0524469	+	0.498999i	0.00167195	+	0.0159075i
$985$	−6.82848	−	3.04024i	−0.217574	−	0.0968700i
$986$	−0.190152	−	0.585227i	−0.00605567	−	0.0186374i
$987$	−2.76109	+	1.31365i	−0.0878864	+	0.0418139i
$988$	0.208599	+	0.151556i	0.00663643	+	0.00482165i
$989$	−20.9157	−	36.2271i	−0.665082	−	1.15196i
$990$	3.85874	+	0.309965i	0.122639	+	0.00985132i
$991$	9.51399	−	16.4787i	0.302222	−	0.523464i	−0.674417	−	0.738351i	$-0.735605\pi$
$991$	9.51399	−	16.4787i	0.302222	−	0.523464i	0.976639	+	0.214887i	$0.0689383\pi$
$992$	−0.0194128	+	0.184701i	−0.000616357	+	0.00586425i
$993$	−8.54406	+	26.2959i	−0.271138	+	0.834476i
$994$	−17.5205	+	0.441602i	−0.555716	+	0.0140068i
$995$	−22.2807	+	16.1879i	−0.706347	+	0.513191i
$996$	9.55978	+	4.25629i	0.302913	+	0.134866i
$997$	51.2143	+	10.8859i	1.62197	+	0.344761i	0.927229	−	0.374496i	$-0.122184\pi$
$997$	51.2143	+	10.8859i	1.62197	+	0.344761i	0.694744	+	0.719257i	$0.255517\pi$
$998$	−7.81871	−	8.68355i	−0.247497	−	0.274873i
$999$	−0.405689	+	3.85987i	−0.0128354	+	0.122121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.b.235.2	yes	24
7.2	even	3	inner	462.2.y.b.37.2	yes	24
11.3	even	5	inner	462.2.y.b.25.2	✓	24
77.58	even	15	inner	462.2.y.b.289.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.b.25.2	✓	24	11.3	even	5	inner
462.2.y.b.37.2	yes	24	7.2	even	3	inner
462.2.y.b.235.2	yes	24	1.1	even	1	trivial
462.2.y.b.289.2	yes	24	77.58	even	15	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.06629 + 0.474743i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-1.26472 + 2.32389i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.104528 + 0.994522i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.06629 + 0.474743i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-1.26472 + 2.32389i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-0.583600 + 1.01083i) q^{10} +(-2.83068 + 1.72836i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.534434 + 0.388289i) q^{13} +(-2.17896 - 1.50071i) q^{14} +(0.360685 + 1.11007i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.0238298 + 0.226726i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(-0.381789 + 0.0811518i) q^{19} +(-0.944285 - 0.686063i) q^{20} +(-2.57325 + 0.615116i) q^{21} +(-1.42300 - 2.99584i) q^{22} +(4.34784 + 7.53067i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-2.43406 - 2.70329i) q^{25} +(-0.442025 + 0.490919i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.72025 - 2.01016i) q^{28} +(0.834092 + 2.56707i) q^{29} +(-1.14169 + 0.242675i) q^{30} +(0.169662 - 0.0755383i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.17852 - 0.947110i) q^{33} -0.227975 q^{34} +(-2.45181 + 1.87753i) q^{35} +(0.309017 - 0.951057i) q^{36} +(2.59698 - 2.88424i) q^{37} +(-0.0407994 - 0.388181i) q^{38} +(0.0690511 + 0.656977i) q^{39} +(0.781010 - 0.867399i) q^{40} +(-0.155049 + 0.477191i) q^{41} +(-0.342768 - 2.62345i) q^{42} -4.81061 q^{43} +(3.12817 - 1.10206i) q^{44} +(-0.583600 + 1.01083i) q^{45} +(-7.94389 + 3.53685i) q^{46} +(1.13043 - 0.240281i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-3.80096 - 5.87816i) q^{49} +(2.94291 - 2.13815i) q^{50} +(-0.152545 + 0.169418i) q^{51} +(-0.442025 - 0.490919i) q^{52} +(8.54304 - 3.80361i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-3.83886 + 0.499086i) q^{55} +(1.81933 + 1.92094i) q^{56} +(-0.315775 - 0.229424i) q^{57} +(-2.64020 + 0.561191i) q^{58} +(10.2599 + 2.18080i) q^{59} +(-0.122006 - 1.16081i) q^{60} +(-8.69343 - 3.87056i) q^{61} +(0.0573900 + 0.176628i) q^{62} +(-2.17896 - 1.50071i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.385524 + 0.667748i) q^{65} +(1.27417 - 3.06211i) q^{66} +(2.15360 - 3.73015i) q^{67} +(0.0238298 - 0.226726i) q^{68} +(-2.68711 + 8.27008i) q^{69} +(-1.61096 - 2.63464i) q^{70} +(5.35911 - 3.89362i) q^{71} +(0.913545 + 0.406737i) q^{72} +(14.3285 + 3.04562i) q^{73} +(2.59698 + 2.88424i) q^{74} +(0.380237 - 3.61771i) q^{75} +0.390319 q^{76} +(-0.436493 - 8.76410i) q^{77} -0.660596 q^{78} +(-0.0118380 + 0.112631i) q^{79} +(0.781010 + 0.867399i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-0.458370 - 0.204079i) q^{82} +(-8.46595 + 6.15087i) q^{83} +(2.64491 - 0.0666648i) q^{84} +(-0.0822270 + 0.253069i) q^{85} +(0.502846 - 4.78426i) q^{86} +(-1.34959 + 2.33756i) q^{87} +(0.769038 + 3.22623i) q^{88} +(6.30388 + 10.9186i) q^{89} +(-0.944285 - 0.686063i) q^{90} +(-1.57825 + 0.750889i) q^{91} +(-2.68711 - 8.27008i) q^{92} +(0.169662 + 0.0755383i) q^{93} +(0.120802 + 1.14936i) q^{94} +(-0.445625 - 0.0947205i) q^{95} +(-0.978148 + 0.207912i) q^{96} +(6.08182 + 4.41870i) q^{97} +(6.24326 - 3.16570i) q^{98} +(-1.42300 - 2.99584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9} + 10 q^{10} - 2 q^{11} - 12 q^{12} + 10 q^{13} + 7 q^{14} + 20 q^{15} + 3 q^{16} + 8 q^{17} + 3 q^{18} + 7 q^{19} - 10 q^{20} + 8 q^{21} - 6 q^{22} + 24 q^{23} + 3 q^{24} + 8 q^{25} - 6 q^{27} - 2 q^{28} + 2 q^{29} - 10 q^{30} - 19 q^{31} - 12 q^{32} - 7 q^{33} + 24 q^{34} + 14 q^{35} - 6 q^{36} - q^{37} - 8 q^{38} - 5 q^{39} - 10 q^{40} + 16 q^{41} + 10 q^{42} - 68 q^{43} - 2 q^{44} + 10 q^{45} - 6 q^{46} + 25 q^{47} - 6 q^{48} - 21 q^{49} + 14 q^{50} - 2 q^{51} - 5 q^{53} - 12 q^{54} - 10 q^{55} - 10 q^{56} + 16 q^{57} - q^{58} - 36 q^{59} + 5 q^{60} - q^{61} - 52 q^{62} + 7 q^{63} - 6 q^{64} + 6 q^{65} + 8 q^{66} + 56 q^{67} + 8 q^{68} + 12 q^{69} - 17 q^{70} - 6 q^{71} + 3 q^{72} + 35 q^{73} - q^{74} - 7 q^{75} - 4 q^{76} + 38 q^{77} - 20 q^{78} - 3 q^{79} - 10 q^{80} + 3 q^{81} + 2 q^{82} - 28 q^{83} + 7 q^{84} - 80 q^{85} - 11 q^{86} + 4 q^{87} - 7 q^{88} - 6 q^{89} - 10 q^{90} - 24 q^{91} + 12 q^{92} - 19 q^{93} - 30 q^{94} - 44 q^{95} + 3 q^{96} - 8 q^{97} - 6 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9 + 10 * q^10 - 2 * q^11 - 12 * q^12 + 10 * q^13 + 7 * q^14 + 20 * q^15 + 3 * q^16 + 8 * q^17 + 3 * q^18 + 7 * q^19 - 10 * q^20 + 8 * q^21 - 6 * q^22 + 24 * q^23 + 3 * q^24 + 8 * q^25 - 6 * q^27 - 2 * q^28 + 2 * q^29 - 10 * q^30 - 19 * q^31 - 12 * q^32 - 7 * q^33 + 24 * q^34 + 14 * q^35 - 6 * q^36 - q^37 - 8 * q^38 - 5 * q^39 - 10 * q^40 + 16 * q^41 + 10 * q^42 - 68 * q^43 - 2 * q^44 + 10 * q^45 - 6 * q^46 + 25 * q^47 - 6 * q^48 - 21 * q^49 + 14 * q^50 - 2 * q^51 - 5 * q^53 - 12 * q^54 - 10 * q^55 - 10 * q^56 + 16 * q^57 - q^58 - 36 * q^59 + 5 * q^60 - q^61 - 52 * q^62 + 7 * q^63 - 6 * q^64 + 6 * q^65 + 8 * q^66 + 56 * q^67 + 8 * q^68 + 12 * q^69 - 17 * q^70 - 6 * q^71 + 3 * q^72 + 35 * q^73 - q^74 - 7 * q^75 - 4 * q^76 + 38 * q^77 - 20 * q^78 - 3 * q^79 - 10 * q^80 + 3 * q^81 + 2 * q^82 - 28 * q^83 + 7 * q^84 - 80 * q^85 - 11 * q^86 + 4 * q^87 - 7 * q^88 - 6 * q^89 - 10 * q^90 - 24 * q^91 + 12 * q^92 - 19 * q^93 - 30 * q^94 - 44 * q^95 + 3 * q^96 - 8 * q^97 - 6 * q^99

Introduction

L-functions

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