LMFDB - Embedded newform 471.2.q.b.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(19,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 62]))

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

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

chi := DirichletCharacter("471.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.q (of order $39$, degree $24$, 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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	471.19
Dual form			471.2.q.b.124.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.670127 - 0.165171i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-1.34912 - 0.708075i) q^{4} +(2.10094 - 1.57875i) q^{5} +(0.478106 + 0.497761i) q^{6} +(2.63145 - 1.38109i) q^{7} +(1.82035 + 1.61269i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})$	\(q+(-0.670127 - 0.165171i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-1.34912 - 0.708075i) q^{4} +(2.10094 - 1.57875i) q^{5} +(0.478106 + 0.497761i) q^{6} +(2.63145 - 1.38109i) q^{7} +(1.82035 + 1.61269i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-1.66866 + 0.710950i) q^{10} +(0.499715 + 0.520258i) q^{11} +(0.761824 + 1.31952i) q^{12} +(0.101775 - 0.176280i) q^{13} +(-1.99152 + 0.490866i) q^{14} +(-2.61948 + 0.211467i) q^{15} +(0.777567 + 1.12650i) q^{16} +(2.67387 - 2.00928i) q^{17} +(-0.138054 - 0.676234i) q^{18} +(0.0989802 - 0.484837i) q^{19} +(-3.95230 + 0.642312i) q^{20} +(-2.96222 - 0.239135i) q^{21} +(-0.248941 - 0.431178i) q^{22} +(-2.00429 - 2.90371i) q^{23} +(-0.676614 - 2.33594i) q^{24} +(0.530398 - 1.83114i) q^{25} +(-0.0973190 + 0.101320i) q^{26} +(0.120537 - 0.992709i) q^{27} -4.52806 q^{28} +(0.528830 - 4.35531i) q^{29} +(1.79032 + 0.290955i) q^{30} +(1.93569 + 2.37079i) q^{31} +(-2.05977 - 5.43117i) q^{32} +(-0.144294 - 0.706798i) q^{33} +(-2.12371 + 0.904828i) q^{34} +(3.34811 - 7.05600i) q^{35} +(0.0613511 - 1.52241i) q^{36} +(-6.45905 - 4.85366i) q^{37} +(-0.146411 + 0.308554i) q^{38} +(-0.180235 + 0.0945948i) q^{39} +(6.37048 + 0.514278i) q^{40} +(5.99655 - 8.68750i) q^{41} +(1.94557 + 0.649525i) q^{42} +(-4.65987 + 2.94672i) q^{43} +(-0.305795 - 1.05573i) q^{44} +(2.32698 + 1.22130i) q^{45} +(0.863516 + 2.27690i) q^{46} +(-3.31826 - 1.41378i) q^{47} +(-0.0551160 - 1.36769i) q^{48} +(1.04065 - 1.50765i) q^{49} +(-0.657887 + 1.13949i) q^{50} +(-3.33382 + 0.269134i) q^{51} +(-0.262127 + 0.165759i) q^{52} +(3.33420 - 1.11312i) q^{53} +(-0.244742 + 0.645332i) q^{54} +(1.87123 + 0.304105i) q^{55} +(7.01742 + 1.72964i) q^{56} +(-0.342786 + 0.356878i) q^{57} +(-1.07376 + 2.83126i) q^{58} +(-4.27333 + 3.78584i) q^{59} +(3.68374 + 1.56950i) q^{60} +(-1.72242 + 8.43695i) q^{61} +(-0.905570 - 1.90845i) q^{62} +(2.37583 + 1.78532i) q^{63} +(0.153253 + 1.26215i) q^{64} +(-0.0644790 - 0.531033i) q^{65} +(-0.0200477 + 0.497477i) q^{66} +(8.90858 + 7.89232i) q^{67} +(-5.03010 + 0.817471i) q^{68} +(0.142069 + 3.52541i) q^{69} +(-3.40911 + 4.17540i) q^{70} +(4.29055 - 1.43240i) q^{71} +(-0.676614 + 2.33594i) q^{72} +(-2.87273 - 1.81660i) q^{73} +(3.52670 + 4.31942i) q^{74} +(-1.42697 + 1.26419i) q^{75} +(-0.476837 + 0.584019i) q^{76} +(2.03350 + 0.678881i) q^{77} +(0.136405 - 0.0336208i) q^{78} +(-13.8438 + 3.41219i) q^{79} +(3.41209 + 1.13912i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-5.45338 + 4.83127i) q^{82} +(-2.30698 - 2.82554i) q^{83} +(3.82707 + 2.42009i) q^{84} +(2.44548 - 8.44276i) q^{85} +(3.60942 - 1.20500i) q^{86} +(-2.77473 + 3.39842i) q^{87} +(0.0706409 + 1.75294i) q^{88} +(4.32315 - 0.702581i) q^{89} +(-1.35765 - 1.20277i) q^{90} +(0.0243578 - 0.604434i) q^{91} +(0.647986 + 5.33665i) q^{92} +(-0.368919 - 3.03832i) q^{93} +(1.99014 + 1.49549i) q^{94} +(-0.557487 - 1.17488i) q^{95} +(-1.16188 + 5.69125i) q^{96} +(8.46360 + 3.60600i) q^{97} +(-0.946392 + 0.838430i) q^{98} +(-0.255803 + 0.674498i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) $ 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{31}{39}\right)$

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 $

$2$	−0.670127	−	0.165171i	−0.473851	−	0.116794i	−0.00484429	−	0.999988i	$-0.501542\pi$
$2$	−0.670127	−	0.165171i	−0.473851	−	0.116794i	−0.469007	+	0.883194i	$0.655388\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	−1.34912	−	0.708075i	−0.674562	−	0.354037i
$5$	2.10094	−	1.57875i	0.939569	−	0.706040i	−0.0162896	−	0.999867i	$-0.505185\pi$
$5$	2.10094	−	1.57875i	0.939569	−	0.706040i	0.955859	+	0.293827i	$0.0949290\pi$
$6$	0.478106	+	0.497761i	0.195186	+	0.203210i
$7$	2.63145	−	1.38109i	0.994594	−	0.522003i	0.112790	−	0.993619i	$-0.464021\pi$
$7$	2.63145	−	1.38109i	0.994594	−	0.522003i	0.881804	+	0.471616i	$0.156329\pi$
$8$	1.82035	+	1.61269i	0.643590	+	0.570171i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	−1.66866	+	0.710950i	−0.527677	+	0.224822i
$11$	0.499715	+	0.520258i	0.150670	+	0.156864i	0.792260	−	0.610184i	$-0.208904\pi$
$11$	0.499715	+	0.520258i	0.150670	+	0.156864i	−0.641590	+	0.767048i	$0.721725\pi$
$12$	0.761824	+	1.31952i	0.219920	+	0.380912i
$13$	0.101775	−	0.176280i	0.0282274	−	0.0488914i	−0.851567	−	0.524246i	$-0.824347\pi$
$13$	0.101775	−	0.176280i	0.0282274	−	0.0488914i	0.879794	+	0.475355i	$0.157680\pi$
$14$	−1.99152	+	0.490866i	−0.532257	+	0.131189i
$15$	−2.61948	+	0.211467i	−0.676348	+	0.0546004i
$16$	0.777567	+	1.12650i	0.194392	+	0.281625i
$17$	2.67387	−	2.00928i	0.648509	−	0.487323i	−0.224855	−	0.974392i	$-0.572191\pi$
$17$	2.67387	−	2.00928i	0.648509	−	0.487323i	0.873363	+	0.487070i	$0.161934\pi$
$18$	−0.138054	−	0.676234i	−0.0325397	−	0.159390i
$19$	0.0989802	−	0.484837i	0.0227076	−	0.111229i	−0.966857	−	0.255318i	$-0.917820\pi$
$19$	0.0989802	−	0.484837i	0.0227076	−	0.111229i	0.989565	+	0.144089i	$0.0460250\pi$
$20$	−3.95230	+	0.642312i	−0.883762	+	0.143625i
$21$	−2.96222	−	0.239135i	−0.646409	−	0.0521836i
$22$	−0.248941	−	0.431178i	−0.0530743	−	0.0919274i
$23$	−2.00429	−	2.90371i	−0.417922	−	0.605465i	0.556320	−	0.830968i	$-0.312213\pi$
$23$	−2.00429	−	2.90371i	−0.417922	−	0.605465i	−0.974242	+	0.225503i	$0.927597\pi$
$24$	−0.676614	−	2.33594i	−0.138113	−	0.476822i
$25$	0.530398	−	1.83114i	0.106080	−	0.366229i
$26$	−0.0973190	+	0.101320i	−0.0190858	+	0.0198704i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	−4.52806			−0.855723
$29$	0.528830	−	4.35531i	0.0982013	−	0.808761i	−0.857512	−	0.514463i	$-0.827991\pi$
$29$	0.528830	−	4.35531i	0.0982013	−	0.808761i	0.955714	−	0.294298i	$-0.0950857\pi$
$30$	1.79032	+	0.290955i	0.326865	+	0.0531208i
$31$	1.93569	+	2.37079i	0.347660	+	0.425806i	0.918602	−	0.395185i	$-0.129319\pi$
$31$	1.93569	+	2.37079i	0.347660	+	0.425806i	−0.570942	+	0.820990i	$0.693422\pi$
$32$	−2.05977	−	5.43117i	−0.364120	−	0.960105i
$33$	−0.144294	−	0.706798i	−0.0251183	−	0.123038i
$34$	−2.12371	+	0.904828i	−0.364213	+	0.155177i
$35$	3.34811	−	7.05600i	0.565934	−	1.19268i
$36$	0.0613511	−	1.52241i	0.0102252	−	0.253735i
$37$	−6.45905	−	4.85366i	−1.06186	−	0.797937i	−0.0818034	−	0.996648i	$-0.526068\pi$
$37$	−6.45905	−	4.85366i	−1.06186	−	0.797937i	−0.980058	+	0.198711i	$0.936324\pi$
$38$	−0.146411	+	0.308554i	−0.0237509	+	0.0500540i
$39$	−0.180235	+	0.0945948i	−0.0288608	+	0.0151473i
$40$	6.37048	+	0.514278i	1.00726	+	0.0813146i
$41$	5.99655	−	8.68750i	0.936504	−	1.35676i	0.00230845	−	0.999997i	$-0.499265\pi$
$41$	5.99655	−	8.68750i	0.936504	−	1.35676i	0.934195	−	0.356762i	$-0.116119\pi$
$42$	1.94557	+	0.649525i	0.300207	+	0.100224i
$43$	−4.65987	+	2.94672i	−0.710623	+	0.449371i	−0.840255	−	0.542191i	$-0.817595\pi$
$43$	−4.65987	+	2.94672i	−0.710623	+	0.449371i	0.129632	+	0.991562i	$0.458620\pi$
$44$	−0.305795	−	1.05573i	−0.0461004	−	0.159157i
$45$	2.32698	+	1.22130i	0.346886	+	0.182060i
$46$	0.863516	+	2.27690i	0.127319	+	0.335711i
$47$	−3.31826	−	1.41378i	−0.484018	−	0.206221i	0.136152	−	0.990688i	$-0.456526\pi$
$47$	−3.31826	−	1.41378i	−0.484018	−	0.206221i	−0.620170	+	0.784467i	$0.712937\pi$
$48$	−0.0551160	−	1.36769i	−0.00795531	−	0.197409i
$49$	1.04065	−	1.50765i	0.148665	−	0.215378i
$50$	−0.657887	+	1.13949i	−0.0930392	+	0.161149i
$51$	−3.33382	+	0.269134i	−0.466828	+	0.0376863i
$52$	−0.262127	+	0.165759i	−0.0363505	+	0.0229867i
$53$	3.33420	−	1.11312i	0.457988	−	0.152899i	−0.0783074	−	0.996929i	$-0.524952\pi$
$53$	3.33420	−	1.11312i	0.457988	−	0.152899i	0.536295	+	0.844030i	$0.319823\pi$
$54$	−0.244742	+	0.645332i	−0.0333052	+	0.0878185i
$55$	1.87123	+	0.304105i	0.252317	+	0.0410055i
$56$	7.01742	+	1.72964i	0.937742	+	0.231133i
$57$	−0.342786	+	0.356878i	−0.0454031	+	0.0472696i
$58$	−1.07376	+	2.83126i	−0.140991	+	0.371763i
$59$	−4.27333	+	3.78584i	−0.556340	+	0.492874i	−0.893800	−	0.448465i	$-0.851971\pi$
$59$	−4.27333	+	3.78584i	−0.556340	+	0.492874i	0.337460	+	0.941340i	$0.390432\pi$
$60$	3.68374	+	1.56950i	0.475569	+	0.202621i
$61$	−1.72242	+	8.43695i	−0.220533	+	1.08024i	0.707205	+	0.707009i	$0.249956\pi$
$61$	−1.72242	+	8.43695i	−0.220533	+	1.08024i	−0.927738	+	0.373233i	$0.878249\pi$
$62$	−0.905570	−	1.90845i	−0.115008	−	0.242373i
$63$	2.37583	+	1.78532i	0.299326	+	0.224929i
$64$	0.153253	+	1.26215i	0.0191567	+	0.157769i
$65$	−0.0644790	−	0.531033i	−0.00799764	−	0.0658665i
$66$	−0.0200477	+	0.497477i	−0.00246770	+	0.0612352i
$67$	8.90858	+	7.89232i	1.08836	+	0.964200i	0.999493	−	0.0318438i	$-0.0101379\pi$
$67$	8.90858	+	7.89232i	1.08836	+	0.964200i	0.0888639	+	0.996044i	$0.471676\pi$
$68$	−5.03010	+	0.817471i	−0.609989	+	0.0991329i
$69$	0.142069	+	3.52541i	0.0171031	+	0.424409i
$70$	−3.40911	+	4.17540i	−0.407467	+	0.499056i
$71$	4.29055	−	1.43240i	0.509195	−	0.169994i	−0.0504503	−	0.998727i	$-0.516066\pi$
$71$	4.29055	−	1.43240i	0.509195	−	0.169994i	0.559645	+	0.828732i	$0.310937\pi$
$72$	−0.676614	+	2.33594i	−0.0797397	+	0.275293i
$73$	−2.87273	−	1.81660i	−0.336227	−	0.212617i	0.355673	−	0.934611i	$-0.384252\pi$
$73$	−2.87273	−	1.81660i	−0.336227	−	0.212617i	−0.691900	+	0.721993i	$0.743226\pi$
$74$	3.52670	+	4.31942i	0.409970	+	0.502123i
$75$	−1.42697	+	1.26419i	−0.164772	+	0.145976i
$76$	−0.476837	+	0.584019i	−0.0546970	+	0.0669916i
$77$	2.03350	+	0.678881i	0.231739	+	0.0773657i
$78$	0.136405	−	0.0336208i	0.0154448	−	0.00380681i
$79$	−13.8438	+	3.41219i	−1.55755	+	0.383901i	−0.921697	−	0.387910i	$-0.873197\pi$
$79$	−13.8438	+	3.41219i	−1.55755	+	0.383901i	−0.635851	+	0.771811i	$0.719351\pi$
$80$	3.41209	+	1.13912i	0.381483	+	0.127358i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	−5.45338	+	4.83127i	−0.602225	+	0.533525i
$83$	−2.30698	−	2.82554i	−0.253224	−	0.310143i	0.632312	−	0.774714i	$-0.282106\pi$
$83$	−2.30698	−	2.82554i	−0.253224	−	0.310143i	−0.885536	+	0.464571i	$0.846209\pi$
$84$	3.82707	+	2.42009i	0.417568	+	0.264054i
$85$	2.44548	−	8.44276i	0.265249	−	0.915746i
$86$	3.60942	−	1.20500i	0.389213	−	0.129939i
$87$	−2.77473	+	3.39842i	−0.297482	+	0.364349i
$88$	0.0706409	+	1.75294i	0.00753034	+	0.186864i
$89$	4.32315	−	0.702581i	0.458253	−	0.0744734i	0.0730971	−	0.997325i	$-0.476712\pi$
$89$	4.32315	−	0.702581i	0.458253	−	0.0744734i	0.385156	+	0.922851i	$0.374148\pi$
$90$	−1.35765	−	1.20277i	−0.143109	−	0.126784i
$91$	0.0243578	−	0.604434i	0.00255340	−	0.0633619i
$92$	0.647986	+	5.33665i	0.0675572	+	0.556384i
$93$	−0.368919	−	3.03832i	−0.0382551	−	0.315059i
$94$	1.99014	+	1.49549i	0.205267	+	0.154248i
$95$	−0.557487	−	1.17488i	−0.0571969	−	0.120540i
$96$	−1.16188	+	5.69125i	−0.118584	+	0.580861i
$97$	8.46360	+	3.60600i	0.859348	+	0.366134i	0.776264	−	0.630408i	$-0.217113\pi$
$97$	8.46360	+	3.60600i	0.859348	+	0.366134i	0.0830846	+	0.996542i	$0.473523\pi$
$98$	−0.946392	+	0.838430i	−0.0956000	+	0.0846942i
$99$	−0.255803	+	0.674498i	−0.0257092	+	0.0677896i
$100$	−2.01216	+	2.09488i	−0.201216	+	0.209488i
$101$	3.43462	+	0.846558i	0.341758	+	0.0842357i	0.406459	−	0.913669i	$-0.366763\pi$
$101$	3.43462	+	0.846558i	0.341758	+	0.0842357i	−0.0647015	+	0.997905i	$0.520610\pi$
$102$	2.27854	+	0.370298i	0.225609	+	0.0366650i
$103$	−1.97918	+	5.21868i	−0.195015	+	0.514212i	−0.996480	−	0.0838296i	$-0.973285\pi$
$103$	−1.97918	+	5.21868i	−0.195015	+	0.514212i	0.801465	+	0.598041i	$0.204054\pi$
$104$	0.469552	−	0.156759i	0.0460434	−	0.0153715i
$105$	−6.60098	+	4.17421i	−0.644190	+	0.407361i
$106$	−2.41819	+	0.195217i	−0.234876	+	0.0189611i
$107$	2.66099	−	4.60897i	0.257248	−	0.445566i	−0.708256	−	0.705956i	$-0.750518\pi$
$107$	2.66099	−	4.60897i	0.257248	−	0.445566i	0.965504	+	0.260390i	$0.0838510\pi$
$108$	−0.865531	+	1.25394i	−0.0832857	+	0.120660i
$109$	0.221870	+	5.50565i	0.0212513	+	0.527345i	0.974397	+	0.224834i	$0.0721840\pi$
$109$	0.221870	+	5.50565i	0.0212513	+	0.527345i	−0.953146	+	0.302511i	$0.902175\pi$
$110$	−1.20373	−	0.512863i	−0.114771	−	0.0488995i
$111$	2.86501	+	7.55441i	0.271935	+	0.717033i
$112$	3.60192	+	1.89044i	0.340350	+	0.178629i
$113$	−0.974101	−	3.36299i	−0.0916357	−	0.316363i	0.901586	−	0.432600i	$-0.142404\pi$
$113$	−0.974101	−	3.36299i	−0.0916357	−	0.316363i	−0.993221	+	0.116237i	$0.962917\pi$
$114$	0.288656	−	0.182535i	0.0270351	−	0.0170960i
$115$	−8.79513	−	2.93624i	−0.820150	−	0.273806i
$116$	−3.79734	+	5.50140i	−0.352574	+	0.510792i
$117$	0.202891	+	0.0163790i	0.0187573	+	0.00151424i
$118$	3.48899	−	1.83116i	0.321187	−	0.168572i
$119$	4.26115	−	8.98018i	0.390619	−	0.823212i
$120$	−5.10940	−	3.83947i	−0.466423	−	0.350494i
$121$	0.421972	−	10.4711i	0.0383611	−	0.951920i
$122$	2.54778	−	5.36934i	0.230665	−	0.486117i
$123$	−9.71140	+	4.13764i	−0.875647	+	0.373078i
$124$	−0.932787	−	4.56909i	−0.0837668	−	0.410317i
$125$	2.88292	+	7.60165i	0.257857	+	0.679912i
$126$	−1.29722	−	1.58881i	−0.115566	−	0.141542i
$127$	19.3045	+	3.13728i	1.71299	+	0.278389i	0.936226	−	0.351399i	$-0.114294\pi$
$127$	19.3045	+	3.13728i	1.71299	+	0.278389i	0.776768	+	0.629787i	$0.216858\pi$
$128$	−1.29454	+	10.6615i	−0.114422	+	0.942349i
$129$	5.51339			0.485427
$130$	−0.0445023	+	0.366510i	−0.00390311	+	0.0321450i
$131$	−8.11982	+	8.45363i	−0.709432	+	0.738597i	−0.974193	−	0.225717i	$-0.927528\pi$
$131$	−8.11982	+	8.45363i	−0.709432	+	0.738597i	0.264761	+	0.964314i	$0.414707\pi$
$132$	−0.305795	+	1.05573i	−0.0266161	+	0.0918893i
$133$	−0.409142	−	1.41252i	−0.0354772	−	0.122481i
$134$	−4.66630	−	6.76030i	−0.403107	−	0.584001i
$135$	−1.31400	−	2.27592i	−0.113091	−	0.195880i
$136$	8.10772	+	0.654523i	0.695231	+	0.0561249i
$137$	11.7941	−	1.91672i	1.00764	−	0.163757i	0.365877	−	0.930663i	$-0.380769\pi$
$137$	11.7941	−	1.91672i	1.00764	−	0.163757i	0.641759	+	0.766906i	$0.278205\pi$
$138$	0.487093	−	2.38594i	0.0414641	−	0.203104i
$139$	−0.145794	−	0.714148i	−0.0123661	−	0.0605732i	0.973139	−	0.230217i	$-0.0739435\pi$
$139$	−0.145794	−	0.714148i	−0.0123661	−	0.0605732i	−0.985505	+	0.169643i	$0.945738\pi$
$140$	−9.51319	+	7.14870i	−0.804011	+	0.604175i
$141$	2.04894	+	2.96841i	0.172552	+	0.249985i
$142$	−3.11181	+	0.251211i	−0.261137	+	0.0210812i
$143$	0.142570	−	0.0351403i	0.0119223	−	0.00293858i
$144$	−0.684400	+	1.18542i	−0.0570333	+	0.0987846i
$145$	−5.76492	−	9.98514i	−0.478751	−	0.829221i
$146$	1.62504	+	1.69185i	0.134489	+	0.140018i
$147$	−1.68534	+	0.718055i	−0.139004	+	0.0592242i
$148$	5.27730	+	11.1217i	0.433792	+	0.914196i
$149$	−8.32700	−	7.37708i	−0.682174	−	0.604354i	0.249185	−	0.968456i	$-0.419837\pi$
$149$	−8.32700	−	7.37708i	−0.682174	−	0.604354i	−0.931359	+	0.364102i	$0.881376\pi$
$150$	1.16506	−	0.611470i	0.0951267	−	0.0499263i
$151$	1.47860	+	1.53938i	0.120327	+	0.125273i	0.778641	−	0.627470i	$-0.215910\pi$
$151$	1.47860	+	1.53938i	0.120327	+	0.125273i	−0.658314	+	0.752743i	$0.728730\pi$
$152$	0.962069	−	0.722948i	0.0780341	−	0.0586388i
$153$	2.96155	+	1.55434i	0.239428	+	0.125661i
$154$	−1.25057	−	0.790812i	−0.100774	−	0.0637255i
$155$	7.80965	+	1.92491i	0.627286	+	0.154612i
$156$	0.310140			0.0248311
$157$	12.2592	+	2.59089i	0.978388	+	0.206776i
$157$	12.2592	+	2.59089i	0.978388	+	0.206776i
$158$	9.84070			0.782884
$159$	−3.41296	−	0.841219i	−0.270665	−	0.0667130i
$160$	−12.9019	−	8.15870i	−1.01999	−	0.645002i
$161$	−9.28446	−	4.87286i	−0.731718	−	0.384035i
$162$	0.551761	−	0.414622i	0.0433505	−	0.0325758i
$163$	−1.56758	−	1.63202i	−0.122782	−	0.127830i	0.656974	−	0.753914i	$-0.271836\pi$
$163$	−1.56758	−	1.63202i	−0.122782	−	0.127830i	−0.779756	+	0.626084i	$0.784657\pi$
$164$	−14.2415	+	7.47451i	−1.11207	+	0.583661i
$165$	−1.41901	−	1.25713i	−0.110470	−	0.0978678i
$166$	1.07927	+	2.27452i	0.0837677	+	0.176537i
$167$	−6.26434	+	2.66898i	−0.484749	+	0.206532i	−0.620493	−	0.784212i	$-0.713068\pi$
$167$	−6.26434	+	2.66898i	−0.484749	+	0.206532i	0.135745	+	0.990744i	$0.456657\pi$
$168$	−5.00662	−	5.21245i	−0.386269	−	0.402149i
$169$	6.47928	+	11.2224i	0.498406	+	0.863265i
$170$	−3.03328	+	5.25380i	−0.232642	+	0.402948i
$171$	0.480458	−	0.118422i	0.0367416	−	0.00905598i
$172$	8.37323	−	0.675957i	0.638453	−	0.0515413i
$173$	13.3587	+	19.3534i	1.01564	+	1.47141i	0.876655	+	0.481119i	$0.159770\pi$
$173$	13.3587	+	19.3534i	1.01564	+	1.47141i	0.138988	+	0.990294i	$0.455615\pi$
$174$	2.42074	−	1.81907i	0.183516	−	0.137903i
$175$	−1.13326	−	5.55109i	−0.0856666	−	0.419623i
$176$	−0.197509	+	0.967464i	−0.0148878	+	0.0729254i
$177$	5.63518	−	0.915806i	0.423566	−	0.0688362i
$178$	−3.01311	−	0.243243i	−0.225842	−	0.0182318i
$179$	1.19007	+	2.06126i	0.0889498	+	0.154066i	0.907067	−	0.420985i	$-0.138316\pi$
$179$	1.19007	+	2.06126i	0.0889498	+	0.154066i	−0.818118	+	0.575051i	$0.804982\pi$
$180$	−2.27462	−	3.29536i	−0.169540	−	0.245621i
$181$	−4.14278	−	14.3025i	−0.307930	−	1.06310i	−0.953997	−	0.299817i	$-0.903074\pi$
$181$	−4.14278	−	14.3025i	−0.307930	−	1.06310i	0.646066	−	0.763281i	$-0.276413\pi$
$182$	−0.116158	+	0.401024i	−0.00861021	+	0.0297259i
$183$	5.96503	−	6.21026i	0.440948	−	0.459075i
$184$	1.03428	−	8.51805i	0.0762480	−	0.627959i
$185$	−21.2328			−1.56107
$186$	−0.254622	+	2.09700i	−0.0186698	+	0.153759i
$187$	2.38152	+	0.387034i	0.174154	+	0.0283027i
$188$	3.47568	+	4.25694i	0.253490	+	0.310469i
$189$	−1.05383	−	2.77873i	−0.0766552	−	0.202123i
$190$	0.179531	+	0.879399i	0.0130245	+	0.0637983i
$191$	−10.5265	+	4.48493i	−0.761672	+	0.324518i	−0.737641	−	0.675193i	$-0.764060\pi$
$191$	−10.5265	+	4.48493i	−0.761672	+	0.324518i	−0.0240310	+	0.999711i	$0.507650\pi$
$192$	0.545050	−	1.14867i	0.0393356	−	0.0828981i
$193$	0.887396	−	22.0205i	0.0638762	−	1.58507i	−0.576557	−	0.817057i	$-0.695604\pi$
$193$	0.887396	−	22.0205i	0.0638762	−	1.58507i	0.640433	−	0.768014i	$-0.278755\pi$
$194$	−5.07608	−	3.81443i	−0.364441	−	0.273860i
$195$	−0.229322	+	0.483285i	−0.0164221	+	0.0346088i
$196$	−2.47150	+	1.29714i	−0.176536	+	0.0926531i
$197$	25.6862	+	2.07360i	1.83006	+	0.147738i	0.946942	−	0.321404i	$-0.104155\pi$
$197$	25.6862	+	2.07360i	1.83006	+	0.147738i	0.883123	+	0.469142i	$0.155437\pi$
$198$	0.282829	−	0.409748i	0.0200998	−	0.0291195i
$199$	3.11708	+	1.04063i	0.220964	+	0.0737686i	0.424994	−	0.905196i	$-0.360276\pi$
$199$	3.11708	+	1.04063i	0.220964	+	0.0737686i	−0.204031	+	0.978964i	$0.565404\pi$
$200$	3.91857	−	2.47796i	0.277085	−	0.175218i
$201$	−3.31127	−	11.4318i	−0.233559	−	0.806340i
$202$	−2.16181	−	1.13460i	−0.152104	−	0.0798304i
$203$	−4.62349	−	12.1911i	−0.324505	−	0.855650i
$204$	4.68830	+	1.99750i	0.328247	+	0.139853i
$205$	−1.11704	−	27.7190i	−0.0780173	−	1.93598i
$206$	2.18828	−	3.17027i	0.152465	−	0.220883i
$207$	1.76413	−	3.05557i	0.122616	−	0.212377i
$208$	0.277717	−	0.0224196i	0.0192562	−	0.00155452i
$209$	0.301702	−	0.190785i	0.0208692	−	0.0131969i
$210$	5.11296	−	1.70696i	0.352828	−	0.117791i
$211$	−1.51687	+	3.99966i	−0.104426	+	0.275348i	−0.977038	−	0.213066i	$-0.931655\pi$
$211$	−1.51687	+	3.99966i	−0.104426	+	0.275348i	0.872612	+	0.488414i	$0.162424\pi$
$212$	−5.28642	−	0.859127i	−0.363073	−	0.0590051i
$213$	−4.39190	−	1.08251i	−0.300928	−	0.0741721i
$214$	−2.54447	+	2.64908i	−0.173937	+	0.181087i
$215$	−5.13795	+	13.5477i	−0.350405	+	0.923943i
$216$	1.82035	−	1.61269i	0.123859	−	0.109730i
$217$	8.36793	+	3.56524i	0.568052	+	0.242024i
$218$	0.760695	−	3.72613i	0.0515208	−	0.252365i
$219$	1.45709	+	3.07075i	0.0984609	+	0.207502i
$220$	−2.30919	−	1.73525i	−0.155686	−	0.116990i
$221$	−0.0820626	−	0.675846i	−0.00552013	−	0.0454623i
$222$	−0.672147	−	5.53563i	−0.0451116	−	0.371527i
$223$	−0.368307	+	9.13945i	−0.0246637	+	0.612023i	0.938844	+	0.344343i	$0.111898\pi$
$223$	−0.368307	+	9.13945i	−0.0246637	+	0.612023i	−0.963508	+	0.267680i	$0.913743\pi$
$224$	−12.9211	−	11.4471i	−0.863329	−	0.764843i
$225$	1.88173	−	0.305810i	0.125448	−	0.0203873i
$226$	0.0973020	+	2.41452i	0.00647243	+	0.160612i
$227$	−8.54084	+	10.4606i	−0.566875	+	0.694296i	−0.975898	−	0.218228i	$-0.929972\pi$
$227$	−8.54084	+	10.4606i	−0.566875	+	0.694296i	0.409022	+	0.912524i	$0.365870\pi$
$228$	0.715156	−	0.238754i	0.0473624	−	0.0158119i
$229$	−1.64951	+	5.69476i	−0.109002	+	0.376320i	−0.996409	−	0.0846669i	$-0.973017\pi$
$229$	−1.64951	+	5.69476i	−0.109002	+	0.376320i	0.887407	+	0.460987i	$0.152505\pi$
$230$	5.40887	+	3.42036i	0.356650	+	0.225532i
$231$	−1.35585	−	1.66062i	−0.0892086	−	0.109261i
$232$	7.98641	−	7.07534i	0.524334	−	0.464519i
$233$	−2.40130	+	2.94106i	−0.157315	+	0.192675i	−0.847248	−	0.531197i	$-0.821742\pi$
$233$	−2.40130	+	2.94106i	−0.157315	+	0.192675i	0.689934	+	0.723873i	$0.257640\pi$
$234$	−0.133257	−	0.0444878i	−0.00871130	−	0.00290826i
$235$	−9.20347	+	2.26845i	−0.600368	+	0.147978i
$236$	8.44591	−	2.08173i	0.549782	−	0.135509i
$237$	13.5243	+	4.51509i	0.878500	+	0.293286i
$238$	−4.33878	+	5.31404i	−0.281241	+	0.344458i
$239$	−13.7065	+	12.1429i	−0.886603	+	0.785462i	−0.977618	−	0.210388i	$-0.932527\pi$
$239$	−13.7065	+	12.1429i	−0.886603	+	0.785462i	0.0910151	+	0.995850i	$0.470989\pi$
$240$	−2.27504	−	2.78642i	−0.146853	−	0.179863i
$241$	0.332956	+	0.210549i	0.0214476	+	0.0135626i	0.545147	−	0.838341i	$-0.316474\pi$
$241$	0.332956	+	0.210549i	0.0214476	+	0.0135626i	−0.523699	+	0.851903i	$0.675448\pi$
$242$	−2.01230	+	6.94728i	−0.129356	+	0.446588i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	8.29775	−	10.1629i	0.531209	−	0.650613i
$245$	−0.193853	−	4.81042i	−0.0123848	−	0.307326i
$246$	7.19129	−	1.16870i	0.458500	−	0.0745135i
$247$	−0.0753934	−	0.0667928i	−0.00479717	−	0.00424992i
$248$	−0.299714	+	7.43732i	−0.0190318	+	0.472270i
$249$	0.439683	+	3.62112i	0.0278638	+	0.229479i
$250$	−0.676350	−	5.57025i	−0.0427762	−	0.352293i
$251$	−6.93725	−	5.21300i	−0.437875	−	0.329042i	0.358838	−	0.933400i	$-0.383173\pi$
$251$	−6.93725	−	5.21300i	−0.437875	−	0.329042i	−0.796713	+	0.604358i	$0.793430\pi$
$252$	−1.94115	−	4.09088i	−0.122281	−	0.257701i
$253$	0.509107	−	2.49377i	0.0320073	−	0.156782i
$254$	−12.4182	−	5.29092i	−0.779190	−	0.331982i
$255$	−6.57926	+	5.82872i	−0.412009	+	0.365008i
$256$	3.53018	−	9.30832i	0.220636	−	0.581770i
$257$	8.89091	−	9.25641i	0.554600	−	0.577399i	−0.383598	−	0.923500i	$-0.625315\pi$
$257$	8.89091	−	9.25641i	0.554600	−	0.577399i	0.938197	+	0.346101i	$0.112495\pi$
$258$	−3.69468	−	0.910656i	−0.230020	−	0.0566949i
$259$	−23.7000	−	3.85163i	−1.47265	−	0.239328i
$260$	−0.289021	+	0.762085i	−0.0179243	+	0.0472625i
$261$	4.16151	−	1.38932i	0.257591	−	0.0859966i
$262$	6.83761	−	4.32384i	0.422429	−	0.267128i
$263$	11.7769	−	0.950733i	0.726197	−	0.0586247i	0.288161	−	0.957582i	$-0.406956\pi$
$263$	11.7769	−	0.950733i	0.726197	−	0.0586247i	0.438036	+	0.898957i	$0.355674\pi$
$264$	0.877179	−	1.51932i	0.0539866	−	0.0935076i
$265$	5.24761	−	7.60248i	0.322358	−	0.467017i
$266$	0.0408688	+	1.01415i	0.00250583	+	0.0621815i
$267$	−4.02939	−	1.71676i	−0.246595	−	0.105064i
$268$	−6.43043	−	16.9557i	−0.392801	−	1.03573i
$269$	15.9322	+	8.36184i	0.971401	+	0.509830i	0.874269	−	0.485441i	$-0.161341\pi$
$269$	15.9322	+	8.36184i	0.971401	+	0.509830i	0.0971313	+	0.995272i	$0.469033\pi$
$270$	0.504632	+	1.74219i	0.0307109	+	0.106026i
$271$	−0.138066	+	0.0873075i	−0.00838690	+	0.00530355i	−0.538653	−	0.842528i	$-0.681066\pi$
$271$	−0.138066	+	0.0873075i	−0.00838690	+	0.00530355i	0.530266	+	0.847831i	$0.322092\pi$
$272$	4.34257	+	1.44976i	0.263307	+	0.0879047i
$273$	−0.343636	+	0.497843i	−0.0207978	+	0.0301308i
$274$	−8.22012	−	0.663597i	−0.496596	−	0.0400893i
$275$	1.21772	−	0.639106i	0.0734310	−	0.0385396i
$276$	2.30458	−	4.85681i	0.138720	−	0.292345i
$277$	−16.4602	−	12.3691i	−0.989001	−	0.743186i	−0.0224727	−	0.999747i	$-0.507154\pi$
$277$	−16.4602	−	12.3691i	−0.989001	−	0.743186i	−0.966528	+	0.256562i	$0.917410\pi$
$278$	−0.0202561	+	0.502651i	−0.00121488	+	0.0301470i
$279$	−1.31207	+	2.76514i	−0.0785518	+	0.165544i
$280$	17.4739	−	7.44491i	1.04426	−	0.444919i
$281$	−5.17230	−	25.3356i	−0.308554	−	1.51140i	−0.777904	−	0.628383i	$-0.783717\pi$
$281$	−5.17230	−	25.3356i	−0.308554	−	1.51140i	0.469350	−	0.883012i	$-0.344488\pi$
$282$	−0.882757	−	2.32764i	−0.0525674	−	0.138609i
$283$	−8.01837	−	9.82072i	−0.476643	−	0.583781i	0.479183	−	0.877715i	$-0.340933\pi$
$283$	−8.01837	−	9.82072i	−0.476643	−	0.583781i	−0.955826	+	0.293934i	$0.905036\pi$
$284$	−6.80273	−	1.10555i	−0.403668	−	0.0656024i
$285$	−0.156750	+	1.29095i	−0.00928508	+	0.0764695i
$286$	−0.101344			−0.00599261
$287$	3.78138	−	31.1425i	0.223208	−	1.83828i
$288$	4.02379	−	4.18921i	0.237104	−	0.246851i
$289$	−1.61734	+	5.58369i	−0.0951374	+	0.328452i
$290$	2.21397	+	7.64351i	0.130009	+	0.448843i
$291$	−5.22606	−	7.57126i	−0.306357	−	0.443835i
$292$	2.58937	+	4.48492i	0.151532	+	0.262460i
$293$	27.7425	+	2.23961i	1.62074	+	0.130839i	0.857220	−	0.514950i	$-0.172189\pi$
$293$	27.7425	+	2.23961i	1.62074	+	0.130839i	0.763516	+	0.645789i	$0.223472\pi$
$294$	1.24799	−	0.202819i	0.0727844	−	0.0118286i
$295$	−3.00110	+	14.7004i	−0.174731	+	0.855888i
$296$	−3.93028	−	19.2518i	−0.228443	−	1.11899i
$297$	0.576699	−	0.433361i	0.0334635	−	0.0251462i
$298$	4.36167	+	6.31896i	0.252665	+	0.366048i
$299$	−0.715854	+	0.0577897i	−0.0413989	+	0.00334206i
$300$	2.82030	−	0.695141i	0.162830	−	0.0401340i
$301$	−8.19251	+	14.1898i	−0.472208	+	0.817889i
$302$	−0.736586	−	1.27580i	−0.0423858	−	0.0734143i
$303$	−2.45045	−	2.55119i	−0.140775	−	0.146562i
$304$	0.623132	−	0.265492i	0.0357391	−	0.0152270i
$305$	9.70118	+	20.4448i	0.555488	+	1.17067i
$306$	−1.72788	−	1.53077i	−0.0987766	−	0.0875084i
$307$	−0.333883	+	0.175235i	−0.0190557	+	0.0100012i	−0.474224	−	0.880404i	$-0.657271\pi$
$307$	−0.333883	+	0.175235i	−0.0190557	+	0.0100012i	0.455168	+	0.890405i	$0.349579\pi$
$308$	−2.26274	−	2.35576i	−0.128932	−	0.134232i
$309$	4.46199	−	3.35297i	0.253834	−	0.190744i
$310$	−4.91552	−	2.57986i	−0.279183	−	0.146526i
$311$	9.75037	+	6.16576i	0.552893	+	0.349628i	0.781514	−	0.623887i	$-0.214447\pi$
$311$	9.75037	+	6.16576i	0.552893	+	0.349628i	−0.228622	+	0.973515i	$0.573422\pi$
$312$	−0.480643	−	0.118468i	−0.0272111	−	0.00670692i
$313$	−34.4518			−1.94733			−0.973667	−	0.227977i	$-0.926789\pi$
$313$	−34.4518			−1.94733			−0.973667	+	0.227977i	$0.926789\pi$
$314$	−7.78726	−	3.76109i	−0.439461	−	0.212251i
$315$	7.81006			0.440047
$316$	21.0931	+	5.19898i	1.18658	+	0.292465i
$317$	−26.7319	−	16.9042i	−1.50141	−	0.949437i	−0.996260	−	0.0864080i	$-0.972461\pi$
$317$	−26.7319	−	16.9042i	−1.50141	−	0.949437i	−0.505154	−	0.863029i	$-0.668564\pi$
$318$	2.14817	+	1.12745i	0.120463	+	0.0632241i
$319$	2.53015	−	1.90128i	0.141661	−	0.106452i
$320$	2.31461	+	2.40976i	0.129390	+	0.134710i
$321$	−4.71238	+	2.47325i	−0.263019	+	0.138043i
$322$	5.41691	+	4.79896i	0.301873	+	0.267436i
$323$	−0.709514	−	1.49527i	−0.0394784	−	0.0831990i
$324$	1.40172	−	0.597219i	0.0778736	−	0.0331788i
$325$	−0.268813	−	0.279864i	−0.0149111	−	0.0155241i
$326$	0.780914	+	1.35258i	0.0432508	+	0.0749126i
$327$	2.75506	−	4.77190i	0.152355	−	0.263887i
$328$	24.9260	−	6.14372i	1.37631	−	0.339230i
$329$	−10.6844	+	0.862533i	−0.589049	+	0.0475530i
$330$	0.743276	+	1.07682i	0.0409160	+	0.0592770i
$331$	−27.8512	+	20.9288i	−1.53084	+	1.15035i	−0.592034	+	0.805913i	$0.701675\pi$
$331$	−27.8512	+	20.9288i	−1.53084	+	1.15035i	−0.938808	+	0.344440i	$0.888069\pi$
$332$	1.11171	+	5.44551i	0.0610129	+	0.298861i
$333$	1.61610	−	7.91616i	0.0885615	−	0.433803i
$334$	4.63874	−	0.753869i	0.253821	−	0.0412499i
$335$	31.1764	+	2.51682i	1.70335	+	0.137509i
$336$	−2.03394	−	3.52288i	−0.110960	−	0.192189i
$337$	20.7138	+	30.0092i	1.12835	+	1.63470i	0.660291	+	0.751010i	$0.270433\pi$
$337$	20.7138	+	30.0092i	1.12835	+	1.63470i	0.468064	+	0.883695i	$0.344952\pi$
$338$	−2.48831	−	8.59066i	−0.135346	−	0.467270i
$339$	−0.974101	+	3.36299i	−0.0529059	+	0.182652i
$340$	−9.27736	+	9.65875i	−0.503135	+	0.523819i
$341$	−0.266130	+	2.19177i	−0.0144117	+	0.118691i
$342$	−0.341528			−0.0184677
$343$	−1.85129	+	15.2468i	−0.0999605	+	0.823249i
$344$	−13.2347	−	2.15085i	−0.713568	−	0.115966i
$345$	5.86423	+	7.18238i	0.315720	+	0.386686i
$346$	−5.75540	−	15.1757i	−0.309412	−	0.815852i
$347$	5.96099	+	29.1989i	0.320003	+	1.56748i	0.748001	+	0.663698i	$0.231014\pi$
$347$	5.96099	+	29.1989i	0.320003	+	1.56748i	−0.427998	+	0.903780i	$0.640781\pi$
$348$	6.14979	−	2.62018i	0.329663	−	0.140456i
$349$	−8.71030	+	18.3566i	−0.466252	+	0.982605i	0.525059	+	0.851066i	$0.324043\pi$
$349$	−8.71030	+	18.3566i	−0.466252	+	0.982605i	−0.991311	+	0.131539i	$0.958008\pi$
$350$	−0.157451	+	3.90712i	−0.00841614	+	0.208844i
$351$	−0.162727	−	0.122282i	−0.00868574	−	0.00652691i
$352$	1.79631	−	3.78565i	0.0957439	−	0.201776i
$353$	−17.0014	+	8.92305i	−0.904896	+	0.474926i	−0.851921	−	0.523670i	$-0.824562\pi$
$353$	−17.0014	+	8.92305i	−0.904896	+	0.474926i	−0.0529744	+	0.998596i	$0.516870\pi$
$354$	−3.92755	−	0.317065i	−0.208747	−	0.0168518i
$355$	6.75279	−	9.78311i	0.358401	−	0.519233i
$356$	−6.32994	−	2.11325i	−0.335486	−	0.112002i
$357$	−8.40108	+	5.31252i	−0.444632	+	0.281168i
$358$	−0.457035	−	1.57787i	−0.0241551	−	0.0833930i
$359$	21.9370	+	11.5134i	1.15779	+	0.607655i	0.930543	−	0.366182i	$-0.119335\pi$
$359$	21.9370	+	11.5134i	1.15779	+	0.607655i	0.227247	+	0.973837i	$0.427027\pi$
$360$	2.26635	+	5.97588i	0.119447	+	0.314957i
$361$	17.2543	+	7.35139i	0.908123	+	0.386915i
$362$	0.413818	+	10.2688i	0.0217498	+	0.539715i
$363$	−5.95310	+	8.62456i	−0.312457	+	0.452672i
$364$	−0.460846	+	0.798208i	−0.0241549	+	0.0418375i
$365$	−8.90339	+	0.718756i	−0.466025	+	0.0376214i
$366$	−5.02309	+	3.17641i	−0.262561	+	0.166034i
$367$	27.5767	−	9.20645i	1.43949	−	0.480573i	0.513490	−	0.858095i	$-0.328352\pi$
$367$	27.5767	−	9.20645i	1.43949	−	0.480573i	0.926000	+	0.377523i	$0.123224\pi$
$368$	1.71256	−	4.51566i	0.0892735	−	0.235395i
$369$	10.4194	+	1.69332i	0.542412	+	0.0881506i
$370$	14.2287	+	3.50706i	0.739714	+	0.182323i
$371$	7.23646	−	7.53395i	0.375698	−	0.391143i
$372$	−1.65364	+	4.36030i	−0.0857373	+	0.226071i
$373$	−14.5849	+	12.9211i	−0.755179	+	0.669030i	−0.950155	−	0.311778i	$-0.899076\pi$
$373$	−14.5849	+	12.9211i	−0.755179	+	0.669030i	0.194976	+	0.980808i	$0.437537\pi$
$374$	−1.53199	−	0.652721i	−0.0792174	−	0.0337514i
$375$	1.62620	−	7.96566i	0.0839767	−	0.411345i
$376$	−3.76041	−	7.92489i	−0.193928	−	0.408695i
$377$	−0.713933	−	0.536486i	−0.0367694	−	0.0276304i
$378$	0.247236	+	2.03617i	0.0127164	+	0.104729i
$379$	1.07283	+	8.83556i	0.0551076	+	0.453852i	0.993978	+	0.109581i	$0.0349509\pi$
$379$	1.07283	+	8.83556i	0.0551076	+	0.453852i	−0.938870	+	0.344271i	$0.888126\pi$
$380$	−0.0797832	+	1.97980i	−0.00409279	+	0.101562i
$381$	−14.6392	−	12.9692i	−0.749987	−	0.664431i
$382$	7.79489	−	1.26679i	0.398821	−	0.0648147i
$383$	0.0694093	+	1.72237i	0.00354665	+	0.0880092i	0.999993	+	0.00377772i	$0.00120249\pi$
$383$	0.0694093	+	1.72237i	0.00354665	+	0.0880092i	−0.996446	+	0.0842315i	$0.973156\pi$
$384$	6.79232	−	8.31908i	0.346619	−	0.424531i
$385$	5.34404	−	1.78410i	0.272358	−	0.0909263i
$386$	−4.23183	+	14.6100i	−0.215394	+	0.743628i
$387$	−4.65987	−	2.94672i	−0.236874	−	0.149790i
$388$	−8.86512	−	10.8578i	−0.450058	−	0.551221i
$389$	−6.60713	+	5.85341i	−0.334995	+	0.296780i	−0.813804	−	0.581139i	$-0.802607\pi$
$389$	−6.60713	+	5.85341i	−0.334995	+	0.296780i	0.478809	+	0.877919i	$0.341069\pi$
$390$	0.233500	−	0.285985i	0.0118237	−	0.0144814i
$391$	−11.1936	−	3.73696i	−0.566083	−	0.188986i
$392$	4.32572	−	1.06619i	0.218482	−	0.0538510i
$393$	11.3810	−	2.80516i	0.574094	−	0.141501i
$394$	−16.8705	−	5.63220i	−0.849924	−	0.283746i
$395$	−23.6980	+	29.0248i	−1.19237	+	1.46039i
$396$	0.822706	−	0.728854i	0.0413425	−	0.0366263i
$397$	23.3932	+	28.6514i	1.17407	+	1.43797i	0.875254	+	0.483664i	$0.160694\pi$
$397$	23.3932	+	28.6514i	1.17407	+	1.43797i	0.298817	+	0.954311i	$0.403408\pi$
$398$	−1.91696	−	1.21221i	−0.0960883	−	0.0607626i
$399$	−0.409142	+	1.41252i	−0.0204827	+	0.0707146i
$400$	2.47520	−	0.826344i	0.123760	−	0.0413172i
$401$	−9.38340	+	11.4926i	−0.468585	+	0.573912i	−0.953785	−	0.300491i	$-0.902849\pi$
$401$	−9.38340	+	11.4926i	−0.468585	+	0.573912i	0.485200	+	0.874403i	$0.338747\pi$
$402$	0.330760	+	8.20772i	0.0164968	+	0.409364i
$403$	0.614928	−	0.0999356i	0.0306318	−	0.00497815i
$404$	−4.03430	−	3.57408i	−0.200714	−	0.177817i
$405$	−0.105819	+	2.62587i	−0.00525819	+	0.130481i
$406$	1.08470	+	8.93328i	0.0538326	+	0.443351i
$407$	−0.702526	−	5.78582i	−0.0348229	−	0.286793i
$408$	−6.50274	−	4.88650i	−0.321934	−	0.241918i
$409$	−8.46845	−	17.8469i	−0.418738	−	0.882471i	−0.997743	−	0.0671476i	$-0.978610\pi$
$409$	−8.46845	−	17.8469i	−0.418738	−	0.882471i	0.579005	−	0.815324i	$-0.303441\pi$
$410$	−3.82983	+	18.7598i	−0.189142	+	0.926478i
$411$	−10.9927	−	4.68353i	−0.542228	−	0.231022i
$412$	6.36538	−	5.63923i	0.313600	−	0.277825i
$413$	−6.01646	+	15.8641i	−0.296051	+	0.780621i
$414$	−1.68689	+	1.75624i	−0.0829060	+	0.0863143i
$415$	−9.30765	−	2.29413i	−0.456895	−	0.112614i
$416$	−1.16704	−	0.189663i	−0.0572190	−	0.00929899i
$417$	−0.258464	+	0.681513i	−0.0126570	+	0.0333738i
$418$	−0.233691	+	0.0780175i	−0.0114302	+	0.00381596i
$419$	−21.9086	+	13.8542i	−1.07030	+	0.676820i	−0.948834	−	0.315775i	$-0.897735\pi$
$419$	−21.9086	+	13.8542i	−1.07030	+	0.676820i	−0.121471	+	0.992595i	$0.538761\pi$
$420$	11.8612	−	0.957534i	0.578767	−	0.0467229i
$421$	−3.80637	+	6.59283i	−0.185511	+	0.321315i	−0.943749	−	0.330664i	$-0.892727\pi$
$421$	−3.80637	+	6.59283i	−0.185511	+	0.321315i	0.758238	+	0.651978i	$0.226061\pi$
$422$	1.67713	−	2.42974i	0.0816413	−	0.118278i
$423$	−0.145235	−	3.60396i	−0.00706155	−	0.175231i
$424$	7.86452	+	3.35076i	0.381935	+	0.162727i
$425$	−2.26107	−	5.96196i	−0.109678	−	0.289198i
$426$	2.76433	+	1.45083i	0.133932	+	0.0702931i
$427$	7.11975	+	24.5802i	0.344549	+	1.18952i
$428$	−6.85350	+	4.33389i	−0.331276	+	0.209487i
$429$	−0.139280	−	0.0464985i	−0.00672450	−	0.00224497i
$430$	5.68077	−	8.23002i	0.273951	−	0.396887i
$431$	2.72135	+	0.219690i	0.131083	+	0.0105821i	0.145834	−	0.989309i	$-0.453414\pi$
$431$	2.72135	+	0.219690i	0.131083	+	0.0105821i	−0.0147510	+	0.999891i	$0.504696\pi$
$432$	1.21201	−	0.636113i	0.0583129	−	0.0306050i
$433$	14.3039	−	30.1449i	0.687403	−	1.44867i	−0.196262	−	0.980551i	$-0.562880\pi$
$433$	14.3039	−	30.1449i	0.687403	−	1.44867i	0.883665	−	0.468120i	$-0.155068\pi$
$434$	−5.01870	−	3.77131i	−0.240905	−	0.181029i
$435$	−0.464260	+	11.5205i	−0.0222596	+	0.552365i
$436$	3.59908	−	7.58490i	0.172365	−	0.363251i
$437$	−1.60621	+	0.684342i	−0.0768354	+	0.0327365i
$438$	−0.469234	−	2.29846i	−0.0224209	−	0.109825i
$439$	4.12667	+	10.8811i	0.196955	+	0.519328i	0.996715	−	0.0809924i	$-0.0258089\pi$
$439$	4.12667	+	10.8811i	0.196955	+	0.519328i	−0.799760	+	0.600320i	$0.795040\pi$
$440$	2.91587	+	3.57129i	0.139008	+	0.170254i
$441$	1.80821	+	0.293862i	0.0861051	+	0.0139934i
$442$	−0.0566382	+	0.466457i	−0.00269400	+	0.0221871i
$443$	16.5952			0.788461			0.394230	−	0.919012i	$-0.371011\pi$
$443$	16.5952			0.788461			0.394230	+	0.919012i	$0.371011\pi$
$444$	1.48383	−	12.2205i	0.0704196	−	0.579958i
$445$	7.97348	−	8.30127i	0.377979	−	0.393518i
$446$	1.75639	−	6.06376i	0.0831674	−	0.287127i
$447$	3.09510	+	10.6855i	0.146393	+	0.505408i
$448$	2.14643	+	3.10964i	0.101409	+	0.146917i
$449$	−5.83132	−	10.1001i	−0.275197	−	0.476655i	0.694988	−	0.719022i	$-0.255410\pi$
$449$	−5.83132	−	10.1001i	−0.275197	−	0.476655i	−0.970185	+	0.242366i	$0.922076\pi$
$450$	−1.31151	−	0.105876i	−0.0618250	−	0.00499103i
$451$	7.51631	−	1.22152i	0.353929	−	0.0575191i
$452$	−1.06706	+	5.22682i	−0.0501904	+	0.245849i
$453$	−0.426948	−	2.09133i	−0.0200598	−	0.0982593i
$454$	7.45124	−	5.59925i	0.349704	−	0.262786i
$455$	−0.903078	−	1.30833i	−0.0423369	−	0.0613356i
$456$	−1.19952	+	0.0968354i	−0.0561728	+	0.00453474i
$457$	−6.93543	+	1.70943i	−0.324426	+	0.0799638i	−0.398165	−	0.917314i	$-0.630353\pi$
$457$	−6.93543	+	1.70943i	−0.324426	+	0.0799638i	0.0737393	+	0.997278i	$0.476507\pi$
$458$	2.04599	−	3.54376i	0.0956029	−	0.165589i
$459$	−1.67233	−	2.89657i	−0.0780578	−	0.135200i
$460$	9.78663	+	10.1890i	0.456304	+	0.475063i
$461$	−23.0860	+	9.83602i	−1.07522	+	0.458109i	−0.855686	−	0.517495i	$-0.826864\pi$
$461$	−23.0860	+	9.83602i	−1.07522	+	0.458109i	−0.219536	+	0.975605i	$0.570454\pi$
$462$	0.634307	+	1.33677i	0.0295106	+	0.0621923i
$463$	−1.99555	−	1.76791i	−0.0927413	−	0.0821616i	0.615478	−	0.788154i	$-0.288963\pi$
$463$	−1.99555	−	1.76791i	−0.0927413	−	0.0821616i	−0.708220	+	0.705992i	$0.750501\pi$
$464$	5.31746	−	2.79082i	0.246857	−	0.129560i
$465$	−5.57184	−	5.80090i	−0.258388	−	0.269010i
$466$	2.09496	−	1.57426i	0.0970470	−	0.0729261i
$467$	20.1381	+	10.5693i	0.931879	+	0.489088i	0.861118	−	0.508406i	$-0.169765\pi$
$467$	20.1381	+	10.5693i	0.931879	+	0.489088i	0.0707610	+	0.997493i	$0.477457\pi$
$468$	−0.262127	−	0.165759i	−0.0121168	−	0.00766222i
$469$	34.3425	+	8.46466i	1.58579	+	0.390862i
$470$	6.54218			0.301768
$471$	−8.97659	−	8.74190i	−0.413619	−	0.402806i
$472$	−13.8843			−0.639078
$473$	−3.86166	−	0.951814i	−0.177559	−	0.0437644i
$474$	−8.31726	−	5.25952i	−0.382024	−	0.241578i
$475$	−0.835308	−	0.438403i	−0.0383265	−	0.0201153i
$476$	−12.1074	+	9.09816i	−0.554944	+	0.417013i
$477$	2.43500	+	2.53510i	0.111491	+	0.116074i
$478$	11.1908	−	5.87338i	0.511855	−	0.268642i
$479$	−29.9065	−	26.4949i	−1.36646	−	1.21058i	−0.954073	−	0.299574i	$-0.903156\pi$
$479$	−29.9065	−	26.4949i	−1.36646	−	1.21058i	−0.412390	−	0.911007i	$-0.635306\pi$
$480$	6.54405	+	13.7913i	0.298694	+	0.629484i
$481$	−1.51298	+	0.644620i	−0.0689859	+	0.0293921i
$482$	−0.188346	−	0.196089i	−0.00857894	−	0.00893163i
$483$	5.24276	+	9.08072i	0.238554	+	0.413187i
$484$	−7.98362	+	13.8280i	−0.362892	+	0.628547i
$485$	23.4745	−	5.78595i	1.06592	−	0.262726i
$486$	−0.687944	+	0.0555366i	−0.0312058	+	0.00251919i
$487$	3.77609	+	5.47061i	0.171111	+	0.247897i	0.899152	−	0.437637i	$-0.144184\pi$
$487$	3.77609	+	5.47061i	0.171111	+	0.247897i	−0.728041	+	0.685534i	$0.759569\pi$
$488$	−16.7416	+	12.5805i	−0.757855	+	0.569491i
$489$	0.452642	+	2.21719i	0.0204692	+	0.100265i
$490$	−0.664638	+	3.25561i	−0.0300253	+	0.147073i
$491$	38.8391	−	6.31197i	1.75278	−	0.284855i	0.802594	−	0.596526i	$-0.203453\pi$
$491$	38.8391	−	6.31197i	1.75278	−	0.284855i	0.950190	+	0.311671i	$0.100889\pi$
$492$	16.0316	+	1.29421i	0.722762	+	0.0583474i
$493$	−7.33703	−	12.7081i	−0.330443	−	0.572344i
$494$	0.0394909	+	0.0572125i	0.00177678	+	0.00257411i
$495$	0.527439	+	1.82093i	0.0237066	+	0.0818448i
$496$	−1.16556	+	4.02400i	−0.0523354	+	0.180683i
$497$	9.31210	−	9.69492i	0.417705	−	0.434877i
$498$	0.303462	−	2.49923i	0.0135984	−	0.111993i
$499$	−18.5129			−0.828752			−0.414376	−	0.910106i	$-0.636000\pi$
$499$	−18.5129			−0.828752			−0.414376	+	0.910106i	$0.636000\pi$
$500$	1.49311	−	12.2969i	0.0667740	−	0.549933i
$501$	6.72104	+	1.09227i	0.300274	+	0.0487992i
$502$	3.78780	+	4.63921i	0.169058	+	0.207058i
$503$	2.63203	+	6.94010i	0.117357	+	0.309444i	0.980804	−	0.194994i	$-0.0624689\pi$
$503$	2.63203	+	6.94010i	0.117357	+	0.309444i	−0.863448	+	0.504438i	$0.831700\pi$
$504$	1.44567	+	7.08138i	0.0643954	+	0.315430i
$505$	8.55244	−	3.64385i	0.380579	−	0.162149i
$506$	−0.753067	+	1.58705i	−0.0334779	+	0.0705532i
$507$	0.521789	−	12.9481i	0.0231735	−	0.575043i
$508$	−23.8227	−	17.9016i	−1.05696	−	0.794254i
$509$	−1.15255	+	2.42894i	−0.0510857	+	0.107661i	−0.927388	−	0.374101i	$-0.877951\pi$
$509$	−1.15255	+	2.42894i	−0.0510857	+	0.107661i	0.876302	+	0.481761i	$0.160003\pi$
$510$	5.37168	−	2.81927i	0.237862	−	0.124840i
$511$	−10.0683	−	0.812799i	−0.445396	−	0.0359561i
$512$	8.29863	−	12.0226i	0.366751	−	0.531331i
$513$	−0.469371	−	0.156699i	−0.0207232	−	0.00691844i
$514$	−7.48693	+	4.73445i	−0.330234	+	0.208828i
$515$	4.08086	+	14.0888i	0.179824	+	0.620826i
$516$	−7.43825	−	3.90389i	−0.327451	−	0.171859i
$517$	−0.922654	−	2.43284i	−0.0405783	−	0.106996i
$518$	15.2458	+	6.49564i	0.669864	+	0.285402i
$519$	−0.946900	−	23.4971i	−0.0415643	−	1.03141i
$520$	0.739016	−	1.07065i	0.0324080	−	0.0469511i
$521$	0.971274	−	1.68230i	0.0425523	−	0.0737027i	−0.843965	−	0.536398i	$-0.819784\pi$
$521$	0.971274	−	1.68230i	0.0425523	−	0.0737027i	0.886517	+	0.462696i	$0.153118\pi$
$522$	−3.01822	+	0.243656i	−0.132104	+	0.0106645i
$523$	11.7897	−	7.45536i	0.515528	−	0.326000i	−0.251240	−	0.967925i	$-0.580838\pi$
$523$	11.7897	−	7.45536i	0.515528	−	0.326000i	0.766768	+	0.641925i	$0.221864\pi$
$524$	16.9404	−	5.65555i	0.740047	−	0.247064i
$525$	−2.00904	+	5.29742i	−0.0876819	+	0.231198i
$526$	−8.04908	−	1.30810i	−0.350957	−	0.0570360i
$527$	9.93935	+	2.44983i	0.432965	+	0.106716i
$528$	0.684009	−	0.712129i	0.0297677	−	0.0309914i
$529$	3.74155	−	9.86565i	0.162676	−	0.428941i
$530$	−4.77228	+	4.22787i	−0.207295	+	0.183647i
$531$	−5.25226	−	2.23778i	−0.227929	−	0.0971114i
$532$	−0.448188	+	2.19537i	−0.0194314	+	0.0951815i
$533$	−0.921134	−	1.94125i	−0.0398987	−	0.0840848i
$534$	2.41664	+	1.81599i	0.104578	+	0.0785856i
$535$	−1.68585	−	13.8842i	−0.0728856	−	0.600267i
$536$	3.48888	+	28.7335i	0.150697	+	1.24110i
$537$	0.0958383	−	2.37820i	0.00413573	−	0.102627i
$538$	−9.29543	−	8.23503i	−0.400754	−	0.355037i
$539$	1.30440	−	0.211985i	0.0561844	−	0.00913085i
$540$	0.161231	+	4.00091i	0.00693828	+	0.172172i
$541$	−22.3026	+	27.3157i	−0.958864	+	1.17440i	0.0257529	+	0.999668i	$0.491802\pi$
$541$	−22.3026	+	27.3157i	−0.958864	+	1.17440i	−0.984617	+	0.174727i	$0.944096\pi$
$542$	0.106942	−	0.0357026i	0.00459357	−	0.00153356i
$543$	−4.14278	+	14.3025i	−0.177784	+	0.613780i
$544$	−16.4203	−	10.3836i	−0.704016	−	0.445193i
$545$	9.15820	+	11.2168i	0.392294	+	0.480473i
$546$	0.312509	−	0.276859i	0.0133742	−	0.0118485i
$547$	16.2266	−	19.8739i	0.693798	−	0.849749i	−0.300785	−	0.953692i	$-0.597249\pi$
$547$	16.2266	−	19.8739i	0.693798	−	0.849749i	0.994583	+	0.103943i	$0.0331461\pi$
$548$	−17.2688	−	5.76519i	−0.737689	−	0.246277i
$549$	−8.36076	+	2.06074i	−0.356828	+	0.0879503i
$550$	−0.921586	+	0.227151i	−0.0392966	+	0.00968574i
$551$	−2.05927	−	0.687486i	−0.0877279	−	0.0292879i
$552$	−5.42677	+	6.64658i	−0.230979	+	0.282897i
$553$	−31.7167	+	28.0985i	−1.34873	+	1.19487i
$554$	8.98744	+	11.0076i	0.381840	+	0.467669i
$555$	17.9458	+	11.3482i	0.761755	+	0.481705i
$556$	−0.308975	+	1.06671i	−0.0131035	+	0.0452385i
$557$	−12.6387	+	4.21940i	−0.535517	+	0.178782i	−0.571548	−	0.820569i	$-0.693657\pi$
$557$	−12.6387	+	4.21940i	−0.535517	+	0.178782i	0.0360306	+	0.999351i	$0.488529\pi$
$558$	1.33598	−	1.63628i	0.0565564	−	0.0692691i
$559$	0.0451887	+	1.12135i	0.00191128	+	0.0474279i
$560$	10.5520	−	1.71486i	0.445902	−	0.0724661i
$561$	−1.80598	−	1.59996i	−0.0762485	−	0.0675503i
$562$	−0.718621	+	17.8324i	−0.0303132	+	0.752214i
$563$	−1.44650	−	11.9130i	−0.0609626	−	0.502072i	−0.990925	−	0.134417i	$-0.957084\pi$
$563$	−1.44650	−	11.9130i	−0.0609626	−	0.502072i	0.929962	−	0.367655i	$-0.119839\pi$
$564$	−0.662424	−	5.45555i	−0.0278931	−	0.229720i
$565$	−7.35586	−	5.52757i	−0.309463	−	0.232547i
$566$	3.75122	+	7.90554i	0.157676	+	0.332295i
$567$	−0.594448	+	2.91180i	−0.0249645	+	0.122284i
$568$	10.1203	+	4.31186i	0.424639	+	0.180922i
$569$	9.34990	−	8.28329i	0.391968	−	0.347254i	−0.444004	−	0.896025i	$-0.646443\pi$
$569$	9.34990	−	8.28329i	0.391968	−	0.347254i	0.835973	+	0.548771i	$0.184904\pi$
$570$	0.318271	−	0.839212i	0.0133309	−	0.0351507i
$571$	−6.19512	+	6.44981i	−0.259258	+	0.269916i	−0.838092	−	0.545530i	$-0.816329\pi$
$571$	−6.19512	+	6.44981i	−0.259258	+	0.269916i	0.578834	+	0.815446i	$0.303508\pi$
$572$	−0.217226	−	0.0535415i	−0.00908269	−	0.00223868i
$573$	11.2939	+	1.83545i	0.471812	+	0.0766768i
$574$	−7.67786	+	20.2448i	−0.320468	+	0.845004i
$575$	−6.38018	+	2.13002i	−0.266072	+	0.0888278i
$576$	−1.07460	+	0.679533i	−0.0447748	+	0.0283139i
$577$	0.736365	−	0.0594456i	0.0306553	−	0.00247475i	−0.0651294	−	0.997877i	$-0.520746\pi$
$577$	0.736365	−	0.0594456i	0.0306553	−	0.00247475i	0.0957847	+	0.995402i	$0.469464\pi$
$578$	2.00609	−	3.47465i	0.0834422	−	0.144526i
$579$	−12.5192	+	18.1372i	−0.520281	+	0.753758i
$580$	0.707369	+	17.5532i	0.0293719	+	0.728856i
$581$	−9.97302	−	4.24911i	−0.413750	−	0.176283i
$582$	2.25157	+	5.93690i	0.0933306	+	0.246093i
$583$	2.24526	+	1.17840i	0.0929892	+	0.0488045i
$584$	−2.29975	−	7.93966i	−0.0951643	−	0.328545i
$585$	0.452120	−	0.285903i	0.0186929	−	0.0118207i
$586$	−18.2211	−	6.08310i	−0.752707	−	0.251290i
$587$	2.61578	−	3.78961i	0.107965	−	0.156414i	−0.765277	−	0.643701i	$-0.777398\pi$
$587$	2.61578	−	3.78961i	0.107965	−	0.156414i	0.873242	+	0.487287i	$0.162013\pi$
$588$	2.78217	+	0.224600i	0.114735	+	0.00926233i
$589$	1.34104	−	0.703832i	0.0552566	−	0.0290009i
$590$	4.43920	−	9.35541i	0.182759	−	0.385156i
$591$	−20.6014	−	15.4810i	−0.847430	−	0.636802i
$592$	0.445306	−	11.0502i	0.0183020	−	0.454159i
$593$	3.95034	−	8.32516i	0.162221	−	0.341873i	−0.806022	−	0.591886i	$-0.798384\pi$
$593$	3.95034	−	8.32516i	0.162221	−	0.341873i	0.968243	+	0.250013i	$0.0804348\pi$
$594$	−0.458040	+	0.195153i	−0.0187936	+	0.00800722i
$595$	−5.22508	−	25.5941i	−0.214207	−	1.04926i
$596$	6.01063	+	15.8487i	0.246205	+	0.649189i
$597$	−2.07834	−	2.54550i	−0.0850608	−	0.104181i
$598$	0.489258	+	0.0795122i	0.0200073	+	0.00325150i
$599$	1.83726	−	15.1312i	0.0750682	−	0.618243i	−0.905819	−	0.423665i	$-0.860743\pi$
$599$	1.83726	−	15.1312i	0.0750682	−	0.618243i	0.980887	−	0.194578i	$-0.0623336\pi$
$600$	−4.63632			−0.189277
$601$	3.08432	−	25.4017i	0.125812	−	1.03616i	−0.783891	−	0.620898i	$-0.786768\pi$
$601$	3.08432	−	25.4017i	0.125812	−	1.03616i	0.909704	−	0.415258i	$-0.136309\pi$
$602$	7.83378	−	8.15583i	0.319281	−	0.332407i
$603$	−3.31127	+	11.4318i	−0.134845	+	0.465541i
$604$	−0.904813	−	3.12378i	−0.0368163	−	0.127105i
$605$	−15.6448	−	22.6654i	−0.636051	−	0.921479i
$606$	1.22073	+	2.11437i	0.0495888	+	0.0858902i
$607$	19.6353	+	1.58512i	0.796971	+	0.0643381i	0.472242	−	0.881469i	$-0.343445\pi$
$607$	19.6353	+	1.58512i	0.796971	+	0.0643381i	0.324729	+	0.945807i	$0.394727\pi$
$608$	−2.83711	+	0.461075i	−0.115060	+	0.0186991i
$609$	−2.60802	+	12.7749i	−0.105682	+	0.517666i
$610$	−3.12413	−	15.3030i	−0.126492	−	0.619599i
$611$	−0.586939	+	0.441056i	−0.0237450	+	0.0178432i
$612$	−2.89491	−	4.19400i	−0.117020	−	0.169533i
$613$	−6.33913	+	0.511747i	−0.256035	+	0.0206693i	−0.207818	−	0.978168i	$-0.566636\pi$
$613$	−6.33913	+	0.511747i	−0.256035	+	0.0206693i	−0.0482174	+	0.998837i	$0.515354\pi$
$614$	0.252688	−	0.0622820i	0.0101977	−	0.00251350i
$615$	−13.8707	+	24.0248i	−0.559322	+	0.968775i
$616$	2.60685	+	4.51520i	0.105033	+	0.181922i
$617$	−0.147767	−	0.153842i	−0.00594887	−	0.00619343i	0.718221	−	0.695815i	$-0.244957\pi$
$617$	−0.147767	−	0.153842i	−0.00594887	−	0.00619343i	−0.724170	+	0.689621i	$0.757777\pi$
$618$	−3.54392	+	1.50992i	−0.142557	+	0.0607380i
$619$	6.93481	+	14.6148i	0.278734	+	0.587419i	0.993742	−	0.111697i	$-0.0356286\pi$
$619$	6.93481	+	14.6148i	0.278734	+	0.587419i	−0.715009	+	0.699116i	$0.753577\pi$
$620$	−9.17320	−	8.12675i	−0.368405	−	0.326378i
$621$	−3.12413	+	1.63967i	−0.125367	+	0.0657976i
$622$	−5.51558	−	5.74233i	−0.221155	−	0.230246i
$623$	10.4058	−	7.81947i	0.416900	−	0.313280i
$624$	−0.246706	−	0.129481i	−0.00987615	−	0.00518340i
$625$	26.1144	+	16.5137i	1.04458	+	0.660550i
$626$	23.0871	+	5.69046i	0.922747	+	0.227437i
$627$	−0.356964			−0.0142558
$628$	−14.7046	−	12.1758i	−0.586777	−	0.485869i
$629$	−27.0230			−1.07748
$630$	−5.23373	−	1.29000i	−0.208517	−	0.0513948i
$631$	−24.1927	−	15.2986i	−0.963098	−	0.609026i	−0.0423160	−	0.999104i	$-0.513474\pi$
$631$	−24.1927	−	15.2986i	−0.963098	−	0.609026i	−0.920782	+	0.390078i	$0.872448\pi$
$632$	−30.7033	−	16.1143i	−1.22131	−	0.640994i
$633$	3.41973	−	2.56976i	0.135922	−	0.102139i
$634$	15.1217	+	15.7433i	0.600559	+	0.625248i
$635$	45.5105	−	23.8858i	1.80603	−	0.947877i
$636$	4.00886	+	3.55154i	0.158962	+	0.140828i
$637$	−0.159856	−	0.336889i	−0.00633371	−	0.0133480i
$638$	−2.00956	+	0.856194i	−0.0795593	+	0.0338970i
$639$	3.13343	+	3.26224i	0.123956	+	0.129052i
$640$	14.1121	+	24.4429i	0.557829	+	0.966189i
$641$	11.5345	−	19.9783i	0.455585	−	0.789096i	−0.543137	−	0.839644i	$-0.682763\pi$
$641$	11.5345	−	19.9783i	0.455585	−	0.789096i	0.998722	+	0.0505480i	$0.0160968\pi$
$642$	3.56640	−	0.879040i	0.140755	−	0.0346929i
$643$	−40.1726	+	3.24307i	−1.58425	+	0.127894i	−0.840970	−	0.541082i	$-0.818015\pi$
$643$	−40.1726	+	3.24307i	−1.58425	+	0.127894i	−0.743284	+	0.668976i	$0.766733\pi$
$644$	9.07553	+	13.1482i	0.357626	+	0.518111i
$645$	11.5833	−	8.70429i	0.456092	−	0.342731i
$646$	0.228489	+	1.11921i	0.00898977	+	0.0440348i
$647$	6.41759	−	31.4354i	0.252301	−	1.23585i	−0.634215	−	0.773157i	$-0.718677\pi$
$647$	6.41759	−	31.4354i	0.252301	−	1.23585i	0.886516	−	0.462697i	$-0.153118\pi$
$648$	−2.40047	+	0.390114i	−0.0942993	+	0.0153251i
$649$	−4.10506	−	0.331395i	−0.161138	−	0.0130084i
$650$	0.133913	+	0.231945i	0.00525252	+	0.00909763i
$651$	−5.16699	−	7.48568i	−0.202510	−	0.293387i
$652$	0.959264	+	3.31176i	0.0375677	+	0.129699i
$653$	−5.57137	+	19.2346i	−0.218025	+	0.752708i	0.774703	+	0.632325i	$0.217899\pi$
$653$	−5.57137	+	19.2346i	−0.218025	+	0.752708i	−0.992728	+	0.120383i	$0.961588\pi$
$654$	−2.63442	+	2.74272i	−0.103014	+	0.107249i
$655$	−3.71306	+	30.5798i	−0.145081	+	1.19485i
$656$	14.4492			0.564146
$657$	0.409693	−	3.37413i	0.0159837	−	0.131637i
$658$	7.30236	+	1.18675i	0.284676	+	0.0462643i
$659$	−22.7872	−	27.9093i	−0.887665	−	1.08719i	−0.995662	−	0.0930408i	$-0.970341\pi$
$659$	−22.7872	−	27.9093i	−0.887665	−	1.08719i	0.107998	−	0.994151i	$-0.465556\pi$
$660$	1.02428	+	2.70080i	0.0398699	+	0.105128i
$661$	−0.248401	−	1.21675i	−0.00966167	−	0.0473260i	0.974674	−	0.223630i	$-0.0717908\pi$
$661$	−0.248401	−	1.21675i	−0.00966167	−	0.0473260i	−0.984336	+	0.176304i	$0.943586\pi$
$662$	22.1207	−	9.42475i	0.859746	−	0.366303i
$663$	−0.291858	+	0.615078i	−0.0113348	+	0.0238877i
$664$	0.357203	−	8.86390i	0.0138622	−	0.343986i
$665$	−3.08961	−	2.32169i	−0.119810	−	0.0900314i
$666$	−2.39051	+	5.03790i	−0.0926305	+	0.195215i
$667$	−13.7065	+	7.19372i	−0.530717	+	0.278542i
$668$	10.3412	+	0.834828i	0.400113	+	0.0323005i
$669$	5.19601	−	7.52773i	0.200889	−	0.291039i
$670$	−20.4765	−	6.83605i	−0.791075	−	0.264100i
$671$	−5.25011	+	3.31997i	−0.202678	+	0.128166i
$672$	4.80272	+	16.5809i	0.185269	+	0.639622i
$673$	30.6151	+	16.0680i	1.18012	+	0.619377i	0.936560	−	0.350508i	$-0.113991\pi$
$673$	30.6151	+	16.0680i	1.18012	+	0.619377i	0.243564	+	0.969885i	$0.421683\pi$
$674$	−8.92425	−	23.5313i	−0.343749	−	0.906392i
$675$	−1.75386	−	0.747250i	−0.0675062	−	0.0287617i
$676$	−0.795023	−	19.7283i	−0.0305778	−	0.758780i
$677$	−25.1242	+	36.3987i	−0.965601	+	1.39891i	−0.0491387	+	0.998792i	$0.515648\pi$
$677$	−25.1242	+	36.3987i	−0.965601	+	1.39891i	−0.916462	+	0.400122i	$0.868968\pi$
$678$	1.20824	−	2.09274i	0.0464022	−	0.0803710i
$679$	27.2517	−	2.19999i	1.04583	−	0.0844278i
$680$	18.0672	−	11.4250i	0.692844	−	0.438128i
$681$	12.8095	−	4.27643i	0.490860	−	0.163873i
$682$	0.540359	−	1.42481i	0.0206914	−	0.0545588i
$683$	23.5291	+	3.82385i	0.900315	+	0.146315i	0.592915	−	0.805265i	$-0.297977\pi$
$683$	23.5291	+	3.82385i	0.900315	+	0.146315i	0.307400	+	0.951580i	$0.400541\pi$
$684$	−0.732049	−	0.180434i	−0.0279906	−	0.00689906i
$685$	21.7526	−	22.6469i	0.831125	−	0.865292i
$686$	3.75894	−	9.91150i	0.143517	−	0.378423i
$687$	4.43780	−	3.93155i	0.169313	−	0.149998i
$688$	−6.94284	−	2.95807i	−0.264693	−	0.112775i
$689$	0.143119	−	0.701042i	0.00545239	−	0.0267076i
$690$	−2.74346	−	5.78171i	−0.104442	−	0.220106i
$691$	−27.5733	−	20.7200i	−1.04894	−	0.788226i	−0.0710748	−	0.997471i	$-0.522643\pi$
$691$	−27.5733	−	20.7200i	−1.04894	−	0.788226i	−0.977863	+	0.209245i	$0.932899\pi$
$692$	−4.31887	−	35.5691i	−0.164179	−	1.35213i
$693$	0.258410	+	2.12820i	0.00981617	+	0.0808435i
$694$	0.828199	−	20.5515i	0.0314380	−	0.780126i
$695$	−1.43377	−	1.27021i	−0.0543860	−	0.0481818i
$696$	−10.5316	+	1.71155i	−0.399198	+	0.0648760i
$697$	−1.42165	−	35.2780i	−0.0538490	−	1.33625i
$698$	8.86899	−	10.8625i	0.335696	−	0.411153i
$699$	3.60145	−	1.20234i	0.136219	−	0.0454767i
$700$	−2.40167	+	8.29154i	−0.0907747	+	0.313391i
$701$	−21.1810	−	13.3940i	−0.799994	−	0.505886i	0.0708252	−	0.997489i	$-0.477437\pi$
$701$	−21.1810	−	13.3940i	−0.799994	−	0.505886i	−0.870819	+	0.491603i	$0.836411\pi$
$702$	0.0888505	+	0.108822i	0.00335345	+	0.00410723i
$703$	−2.99255	+	2.65117i	−0.112866	+	0.0999908i
$704$	−0.580063	+	0.710449i	−0.0218620	+	0.0267760i
$705$	8.99110	+	3.00167i	0.338624	+	0.113049i
$706$	12.8670	−	3.17142i	0.484254	−	0.119358i
$707$	10.2072	−	2.51585i	0.383881	−	0.0946182i
$708$	−8.25101	−	2.75459i	−0.310092	−	0.103524i
$709$	12.3857	−	15.1697i	0.465154	−	0.569710i	−0.487750	−	0.872983i	$-0.662182\pi$
$709$	12.3857	−	15.1697i	0.465154	−	0.569710i	0.952903	+	0.303274i	$0.0980797\pi$
$710$	−6.14112	+	5.44056i	−0.230472	+	0.204180i
$711$	−9.01748	−	11.0444i	−0.338182	−	0.414197i
$712$	9.00269	+	5.69295i	0.337390	+	0.213352i
$713$	3.00440	−	10.3724i	0.112516	−	0.388450i
$714$	6.50727	−	2.17244i	0.243528	−	0.0813017i
$715$	0.244053	−	0.298911i	0.00912706	−	0.0111786i
$716$	−0.146024	−	3.62354i	−0.00545717	−	0.135418i
$717$	18.0746	−	2.93741i	0.675009	−	0.109700i
$718$	−12.7989	−	11.3388i	−0.477650	−	0.423161i
$719$	1.02259	−	25.3753i	0.0381362	−	0.946340i	−0.860982	−	0.508635i	$-0.830150\pi$
$719$	1.02259	−	25.3753i	0.0381362	−	0.946340i	0.899119	−	0.437705i	$-0.144209\pi$
$720$	0.433596	+	3.57098i	0.0161592	+	0.133083i
$721$	1.99935	+	16.4661i	0.0744596	+	0.613230i
$722$	−10.3484	−	7.77629i	−0.385126	−	0.289404i
$723$	−0.168880	−	0.355908i	−0.00628072	−	0.0132363i
$724$	−4.53814	+	22.2293i	−0.168659	+	0.826144i
$725$	−7.69471	−	3.27841i	−0.285774	−	0.121757i
$726$	5.41386	−	4.79627i	0.200927	−	0.178006i
$727$	−12.3319	+	32.5165i	−0.457364	+	1.20597i	0.485926	+	0.874000i	$0.338482\pi$
$727$	−12.3319	+	32.5165i	−0.457364	+	1.20597i	−0.943290	+	0.331970i	$0.892287\pi$
$728$	1.01910	−	1.06100i	0.0377705	−	0.0393232i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	6.08512	+	0.988929i	0.225221	+	0.0366019i
$731$	−6.53908	+	17.2421i	−0.241857	+	0.637723i
$732$	−12.4449	+	4.15472i	−0.459976	+	0.153563i
$733$	38.7944	−	24.5321i	1.43290	−	0.906113i	0.432915	−	0.901435i	$-0.357485\pi$
$733$	38.7944	−	24.5321i	1.43290	−	0.906113i	0.999989	−	0.00467837i	$-0.00148918\pi$
$734$	−20.0005	+	1.61461i	−0.738233	+	0.0595963i
$735$	−2.40716	+	4.16933i	−0.0887895	+	0.153788i
$736$	−11.6422	+	16.8666i	−0.429136	+	0.621711i
$737$	0.345709	+	8.57867i	0.0127343	+	0.315999i
$738$	−6.70264	−	2.85573i	−0.246727	−	0.105121i
$739$	−11.7029	−	30.8581i	−0.430499	−	1.13513i	−0.958300	−	0.285764i	$-0.907753\pi$
$739$	−11.7029	−	30.8581i	−0.430499	−	1.13513i	0.527801	−	0.849368i	$-0.323017\pi$
$740$	28.6457	+	15.0344i	1.05304	+	0.552676i
$741$	0.0280233	+	0.0967478i	0.00102946	+	0.00355412i
$742$	−6.09374	+	3.85345i	−0.223708	+	0.141465i
$743$	2.76561	+	0.923296i	0.101460	+	0.0338724i	0.366945	−	0.930243i	$-0.380404\pi$
$743$	2.76561	+	0.923296i	0.101460	+	0.0338724i	−0.265485	+	0.964115i	$0.585532\pi$
$744$	4.22831	−	6.12576i	0.155017	−	0.224581i
$745$	−29.1411	−	2.35251i	−1.06765	−	0.0861895i
$746$	11.9080	−	6.24978i	0.435981	−	0.228821i
$747$	1.56375	−	3.29553i	0.0572145	−	0.120577i
$748$	−2.93891	−	2.20845i	−0.107457	−	0.0807489i
$749$	0.636853	−	15.8033i	0.0232701	−	0.577441i
$750$	−2.40546	+	5.06940i	−0.0878350	+	0.185108i
$751$	30.2640	−	12.8943i	1.10435	−	0.470520i	0.238662	−	0.971103i	$-0.423291\pi$
$751$	30.2640	−	12.8943i	1.10435	−	0.470520i	0.865689	+	0.500583i	$0.166881\pi$
$752$	−0.987547	−	4.83733i	−0.0360121	−	0.176399i
$753$	3.07712	+	8.11370i	0.112137	+	0.295680i
$754$	0.389814	+	0.477435i	0.0141962	+	0.0173872i
$755$	5.53675	+	0.899810i	0.201503	+	0.0327474i
$756$	−0.545798	+	4.49505i	−0.0198505	+	0.163483i
$757$	8.18047			0.297324			0.148662	−	0.988888i	$-0.452503\pi$
$757$	8.18047			0.297324			0.148662	+	0.988888i	$0.452503\pi$
$758$	0.740449	−	6.09815i	0.0268943	−	0.221495i
$759$	−1.76313	+	1.83561i	−0.0639975	+	0.0666285i
$760$	0.879892	−	3.03774i	0.0319171	−	0.110190i
$761$	2.12544	+	7.33786i	0.0770471	+	0.265997i	0.989789	−	0.142539i	$-0.0455266\pi$
$761$	2.12544	+	7.33786i	0.0770471	+	0.265997i	−0.912742	+	0.408536i	$0.866039\pi$
$762$	7.66796	+	11.1090i	0.277781	+	0.402435i
$763$	8.18764	+	14.1814i	0.296412	+	0.513401i
$764$	17.3772	+	1.40284i	0.628686	+	0.0507528i
$765$	8.67598	−	1.40998i	0.313681	−	0.0509781i
$766$	0.237974	−	1.16567i	0.00859835	−	0.0421175i
$767$	0.232449	+	1.13861i	0.00839324	+	0.0411128i
$768$	−7.95865	+	5.98054i	−0.287183	+	0.215804i
$769$	28.8501	+	41.7966i	1.04036	+	1.50722i	0.850895	+	0.525336i	$0.176061\pi$
$769$	28.8501	+	41.7966i	1.04036	+	1.50722i	0.189467	+	0.981887i	$0.439324\pi$
$770$	−3.87587	+	0.312893i	−0.139677	+	0.0112759i
$771$	−12.4617	+	3.07154i	−0.448799	+	0.110619i
$772$	−16.7894	+	29.0800i	−0.604263	+	1.04661i
$773$	−15.8933	−	27.5280i	−0.571642	−	0.990114i	−0.996398	−	0.0848055i	$-0.972973\pi$
$773$	−15.8933	−	27.5280i	−0.571642	−	0.990114i	0.424755	−	0.905308i	$-0.360360\pi$
$774$	2.63599	+	2.74435i	0.0947486	+	0.0986438i
$775$	5.36794	−	2.28706i	0.192822	−	0.0821538i
$776$	9.59134	+	20.2133i	0.344309	+	0.725616i
$777$	17.9724	+	15.9222i	0.644758	+	0.571206i
$778$	5.39444	−	2.83122i	0.193400	−	0.101504i
$779$	−3.61848	−	3.76724i	−0.129646	−	0.134975i
$780$	0.651586	−	0.489635i	0.0233305	−	0.0175317i
$781$	2.88927	+	1.51641i	0.103386	+	0.0542612i
$782$	6.88387	+	4.35310i	0.246167	+	0.155666i
$783$	−4.25981	−	1.04995i	−0.152233	−	0.0375221i
$784$	2.50755			0.0895552
$785$	29.8462	−	13.9109i	1.06526	−	0.496502i
$786$	−8.09003			−0.288562
$787$	−42.4828	−	10.4711i	−1.51435	−	0.373254i	−0.607367	−	0.794422i	$-0.707774\pi$
$787$	−42.4828	−	10.4711i	−1.51435	−	0.373254i	−0.906983	+	0.421168i	$0.861620\pi$
$788$	−33.1856	−	20.9853i	−1.18219	−	0.747570i
$789$	−10.4619	−	5.49082i	−0.372453	−	0.195478i
$790$	20.6747	−	15.5360i	0.735573	−	0.552748i
$791$	−7.20789	−	7.50421i	−0.256283	−	0.266819i
$792$	−1.55341	+	0.815291i	−0.0551979	+	0.0289701i
$793$	1.31197	+	1.16230i	0.0465894	+	0.0412746i
$794$	−10.9440	−	23.0640i	−0.388388	−	0.818511i
$795$	−8.49850	+	3.62087i	−0.301411	+	0.128419i
$796$	−3.46848	−	3.61107i	−0.122937	−	0.127991i
$797$	−15.0047	−	25.9888i	−0.531492	−	0.920572i	−0.999324	−	0.0367543i	$-0.988298\pi$
$797$	−15.0047	−	25.9888i	−0.531492	−	0.920572i	0.467832	−	0.883817i	$-0.345035\pi$
$798$	0.507486	−	0.878992i	0.0179648	−	0.0311160i
$799$	−11.7133	+	2.88706i	−0.414386	+	0.102137i
$800$	−11.0378	+	0.891061i	−0.390244	+	0.0315037i
$801$	2.48805	+	3.60456i	0.0879109	+	0.127361i
$802$	8.18632	−	6.15162i	0.289069	−	0.217221i
$803$	−0.490442	−	2.40234i	−0.0173073	−	0.0847768i
$804$	−3.62728	+	17.7676i	−0.127924	+	0.626615i
$805$	−27.1991	+	4.42029i	−0.958644	+	0.155795i
$806$	−0.428587	−	0.0345991i	−0.0150963	−	0.00121870i
$807$	−8.99658	−	15.5825i	−0.316695	−	0.548531i
$808$	4.88697	+	7.08000i	0.171923	+	0.249074i
$809$	−1.14888	−	3.96639i	−0.0403925	−	0.139451i	0.937788	−	0.347209i	$-0.112871\pi$
$809$	−1.14888	−	3.96639i	−0.0403925	−	0.139451i	−0.978180	+	0.207758i	$0.933383\pi$
$810$	0.504632	−	1.74219i	0.0177310	−	0.0612144i
$811$	15.5483	−	16.1875i	0.545976	−	0.568421i	−0.389852	−	0.920877i	$-0.627474\pi$
$811$	15.5483	−	16.1875i	0.545976	−	0.568421i	0.935828	+	0.352456i	$0.114653\pi$
$812$	−2.39458	+	19.7211i	−0.0840332	+	0.692076i
$813$	0.163355			0.00572910
$814$	−0.484871	+	3.99327i	−0.0169947	+	0.139964i
$815$	−5.86995	−	0.953960i	−0.205616	−	0.0334158i
$816$	−2.89545	−	3.54628i	−0.101361	−	0.124145i
$817$	0.967445	+	2.55094i	0.0338466	+	0.0892462i
$818$	2.72714	+	13.3584i	0.0953523	+	0.467066i
$819$	0.556518	−	0.237110i	0.0194463	−	0.00828530i
$820$	−18.1201	+	38.1873i	−0.632781	+	1.33356i
$821$	−0.239408	+	5.94086i	−0.00835541	+	0.207337i	0.989619	+	0.143717i	$0.0459056\pi$
$821$	−0.239408	+	5.94086i	−0.00835541	+	0.207337i	−0.997974	+	0.0636200i	$0.979735\pi$
$822$	6.59289	+	4.95424i	0.229954	+	0.172799i
$823$	−12.7541	+	26.8788i	−0.444581	+	0.936935i	0.550213	+	0.835025i	$0.314547\pi$
$823$	−12.7541	+	26.8788i	−0.444581	+	0.936935i	−0.994794	+	0.101910i	$0.967505\pi$
$824$	−12.0189	+	6.30801i	−0.418698	+	0.219750i
$825$	−1.37078	−	0.110661i	−0.0477245	−	0.00385272i
$826$	6.65209	−	9.63721i	0.231456	−	0.335322i
$827$	−0.514765	−	0.171854i	−0.0179001	−	0.00597594i	0.307704	−	0.951482i	$-0.400439\pi$
$827$	−0.514765	−	0.171854i	−0.0179001	−	0.00597594i	−0.325604	+	0.945506i	$0.605568\pi$
$828$	−4.54361	+	2.87320i	−0.157901	+	0.0998507i
$829$	−5.74675	−	19.8401i	−0.199593	−	0.689075i	−0.996395	−	0.0848346i	$-0.972964\pi$
$829$	−5.74675	−	19.8401i	−0.199593	−	0.689075i	0.796802	−	0.604240i	$-0.206523\pi$
$830$	5.85838	+	3.07472i	0.203347	+	0.106725i
$831$	7.30119	+	19.2517i	0.253276	+	0.667833i
$832$	0.238090	+	0.101441i	0.00825430	+	0.00351683i
$833$	−0.246717	−	6.12223i	−0.00854825	−	0.212123i
$834$	0.285770	−	0.414009i	0.00989541	−	0.0143360i
$835$	−8.94733	+	15.4972i	−0.309635	+	0.536303i
$836$	−0.542123	+	0.0437647i	−0.0187497	+	0.00151363i
$837$	2.58682	−	1.63581i	0.0894136	−	0.0565418i
$838$	16.9699	−	5.66537i	0.586214	−	0.195707i
$839$	−16.8754	+	44.4968i	−0.582604	+	1.53620i	0.241875	+	0.970307i	$0.422238\pi$
$839$	−16.8754	+	44.4968i	−0.582604	+	1.53620i	−0.824479	+	0.565893i	$0.808532\pi$
$840$	−18.7478	−	3.04681i	−0.646860	−	0.105125i
$841$	9.46824	+	2.33371i	0.326491	+	0.0804729i
$842$	3.63970	−	3.78933i	0.125432	−	0.130589i
$843$	−9.16944	+	24.1778i	−0.315812	+	0.832728i
$844$	4.87851	−	4.32198i	0.167925	−	0.148769i
$845$	31.3301	+	13.3485i	1.07779	+	0.459202i
$846$	−0.497946	+	2.43910i	−0.0171197	+	0.0838580i
$847$	−13.3512	−	28.1370i	−0.458751	−	0.966798i
$848$	3.84649	+	2.89045i	0.132089	+	0.0992585i
$849$	1.52821	+	12.5859i	0.0524479	+	0.431948i
$850$	0.530461	+	4.36874i	0.0181946	+	0.149846i
$851$	−1.14784	+	28.4833i	−0.0393474	+	0.976396i
$852$	5.15872	+	4.57023i	0.176735	+	0.156573i
$853$	−10.0941	+	1.64046i	−0.345617	+	0.0561682i	−0.330742	−	0.943721i	$-0.607299\pi$
$853$	−10.0941	+	1.64046i	−0.345617	+	0.0561682i	−0.0148748	+	0.999889i	$0.504735\pi$
$854$	−0.711184	−	17.6479i	−0.0243362	−	0.603897i
$855$	0.822454	−	1.00732i	0.0281273	−	0.0344497i
$856$	12.2768	−	4.09859i	0.419611	−	0.140087i
$857$	−4.09984	+	14.1543i	−0.140048	+	0.483502i	−0.999622	−	0.0275104i	$-0.991242\pi$
$857$	−4.09984	+	14.1543i	−0.140048	+	0.483502i	0.859574	+	0.511012i	$0.170729\pi$
$858$	0.0856551	+	0.0541650i	0.00292422	+	0.00184916i
$859$	−12.1531	−	14.8849i	−0.414660	−	0.507866i	0.524470	−	0.851429i	$-0.324264\pi$
$859$	−12.1531	−	14.8849i	−0.414660	−	0.507866i	−0.939130	+	0.343563i	$0.888366\pi$
$860$	16.5245	−	14.6394i	0.563480	−	0.499200i
$861$	−19.8406	+	24.3003i	−0.676165	+	0.828152i
$862$	−1.78736	−	0.596710i	−0.0608779	−	0.0203240i
$863$	12.5296	−	3.08827i	0.426512	−	0.105126i	−0.0202157	−	0.999796i	$-0.506435\pi$
$863$	12.5296	−	3.08827i	0.426512	−	0.105126i	0.446728	+	0.894670i	$0.352589\pi$
$864$	−5.63985	+	1.39010i	−0.191872	+	0.0472921i
$865$	58.6201	+	19.5703i	1.99314	+	0.665409i
$866$	−14.5645	+	17.8383i	−0.494923	+	0.606170i
$867$	4.35125	−	3.85487i	0.147776	−	0.130918i
$868$	−8.76491	−	10.7351i	−0.297501	−	0.364372i
$869$	−8.69317	−	5.49723i	−0.294896	−	0.186481i
$870$	2.21397	−	7.64351i	0.0750606	−	0.259139i
$871$	2.29794	−	0.767163i	0.0778626	−	0.0259943i
$872$	−8.47501	+	10.3800i	−0.287000	+	0.351511i
$873$	0.370437	+	9.19231i	0.0125374	+	0.311113i
$874$	1.18940	−	0.193296i	0.0402320	−	0.00653834i
$875$	18.0848	+	16.0218i	0.611379	+	0.541634i
$876$	0.208527	−	5.17454i	0.00704547	−	0.174832i
$877$	6.09711	+	50.2142i	0.205885	+	1.69561i	0.619367	+	0.785102i	$0.287389\pi$
$877$	6.09711	+	50.2142i	0.205885	+	1.69561i	−0.413482	+	0.910512i	$0.635688\pi$
$878$	−0.968140	−	7.97335i	−0.0326731	−	0.269087i
$879$	−22.2507	−	16.7203i	−0.750498	−	0.563963i
$880$	1.11243	+	2.34440i	0.0375001	+	0.0790298i
$881$	1.42947	−	7.00199i	0.0481599	−	0.235903i	−0.948585	−	0.316522i	$-0.897485\pi$
$881$	1.42947	−	7.00199i	0.0481599	−	0.235903i	0.996745	+	0.0806195i	$0.0256899\pi$
$882$	−1.16319	−	0.495589i	−0.0391667	−	0.0166874i
$883$	0.799885	−	0.708637i	0.0269183	−	0.0238475i	−0.649556	−	0.760313i	$-0.725045\pi$
$883$	0.799885	−	0.708637i	0.0269183	−	0.0238475i	0.676475	+	0.736466i	$0.263507\pi$
$884$	−0.367837	+	0.969906i	−0.0123717	+	0.0326215i
$885$	10.3933	−	10.8206i	0.349368	−	0.363731i
$886$	−11.1209	−	2.74105i	−0.373613	−	0.0920874i
$887$	−43.4826	−	7.06661i	−1.46000	−	0.237274i	−0.622033	−	0.782991i	$-0.713693\pi$
$887$	−43.4826	−	7.06661i	−1.46000	−	0.237274i	−0.837969	+	0.545717i	$0.816257\pi$
$888$	−6.96759	+	18.3720i	−0.233817	+	0.616525i
$889$	55.1315	−	18.4056i	1.84905	−	0.617304i
$890$	−6.71438	+	4.24592i	−0.225067	+	0.142323i
$891$	−0.719037	+	0.0580467i	−0.0240886	+	0.00194464i
$892$	6.96830	−	12.0695i	0.233316	−	0.404115i
$893$	−1.01389	+	1.46888i	−0.0339287	+	0.0491542i
$894$	−0.309166	−	7.67189i	−0.0103401	−	0.256586i
$895$	5.75448	+	2.45175i	0.192351	+	0.0819531i
$896$	11.3179	+	29.8430i	0.378106	+	0.996983i
$897$	0.635919	+	0.333756i	0.0212327	+	0.0111438i
$898$	2.23947	+	7.73155i	0.0747321	+	0.258005i
$899$	11.3492	−	7.17677i	0.378516	−	0.239359i
$900$	−2.75522	−	0.919827i	−0.0918406	−	0.0306609i
$901$	6.67865	−	9.67569i	0.222498	−	0.322344i
$902$	−5.23864	−	0.422907i	−0.174428	−	0.0140813i
$903$	14.5082	−	7.61450i	0.482803	−	0.253395i
$904$	3.65025	−	7.69273i	0.121405	−	0.255856i
$905$	−31.2839	−	23.5083i	−1.03991	−	0.781443i
$906$	−0.0593187	+	1.47198i	−0.00197073	+	0.0489032i
$907$	16.1450	−	34.0250i	0.536087	−	1.12978i	−0.437025	−	0.899449i	$-0.643968\pi$
$907$	16.1450	−	34.0250i	0.536087	−	1.12978i	0.973112	−	0.230331i	$-0.0739808\pi$
$908$	18.9295	−	8.06513i	0.628199	−	0.267651i
$909$	0.707573	+	3.46592i	0.0234687	+	0.114957i
$910$	0.389077	+	1.02591i	0.0128978	+	0.0340087i
$911$	9.70600	+	11.8877i	0.321574	+	0.393857i	0.909941	−	0.414737i	$-0.136126\pi$
$911$	9.70600	+	11.8877i	0.321574	+	0.393857i	−0.588367	+	0.808594i	$0.700229\pi$
$912$	−0.668562	−	0.108652i	−0.0221383	−	0.00359782i
$913$	0.317177	−	2.61219i	0.0104970	−	0.0864508i
$914$	4.92997			0.163069
$915$	2.72771	−	22.4647i	0.0901753	−	0.742660i
$916$	6.25770	−	6.51496i	0.206760	−	0.215260i
$917$	−9.69166	+	33.4595i	−0.320047	+	1.10493i
$918$	0.642246	+	2.21729i	0.0211973	+	0.0731814i
$919$	−14.2692	−	20.6726i	−0.470699	−	0.681925i	0.513681	−	0.857981i	$-0.328281\pi$
$919$	−14.2692	−	20.6726i	−0.470699	−	0.681925i	−0.984380	+	0.176056i	$0.943666\pi$
$920$	−11.2749	−	19.5288i	−0.371724	−	0.643845i
$921$	0.375852	+	0.0303419i	0.0123847	+	0.000999800i
$922$	17.0952	−	2.77824i	0.563000	−	0.0914963i
$923$	0.184170	−	0.902123i	0.00606202	−	0.0296937i
$924$	0.653371	+	3.20042i	0.0214943	+	0.105286i
$925$	−12.3136	+	9.25309i	−0.404869	+	0.304240i
$926$	1.04527	+	1.51433i	0.0343496	+	0.0497640i
$927$	−5.56328	+	0.449114i	−0.182722	+	0.0147508i
$928$	−24.7437	+	6.09878i	−0.812253	+	0.200202i
$929$	−4.02708	+	6.97511i	−0.132124	+	0.228846i	−0.924495	−	0.381194i	$-0.875513\pi$
$929$	−4.02708	+	6.97511i	−0.132124	+	0.228846i	0.792371	+	0.610040i	$0.208846\pi$
$930$	2.77570	+	4.80765i	0.0910188	+	0.157649i
$931$	−0.627960	−	0.653775i	−0.0205805	−	0.0214266i
$932$	5.32214	−	2.26755i	0.174333	−	0.0742762i
$933$	−4.94553	−	10.4225i	−0.161909	−	0.341217i
$934$	−11.7493	−	10.4090i	−0.384450	−	0.340593i
$935$	5.61446	−	2.94669i	0.183612	−	0.0963672i
$936$	0.342918	+	0.357015i	0.0112086	+	0.0116694i
$937$	−29.6982	+	22.3167i	−0.970196	+	0.729055i	−0.962603	−	0.270916i	$-0.912673\pi$
$937$	−29.6982	+	22.3167i	−0.970196	+	0.729055i	−0.00759342	+	0.999971i	$0.502417\pi$
$938$	−21.6157	−	11.3448i	−0.705778	−	0.370421i
$939$	29.1184	+	18.4133i	0.950242	+	0.600896i
$940$	14.0229	+	3.45632i	0.457375	+	0.112733i
$941$	15.8608			0.517046			0.258523	−	0.966005i	$-0.416764\pi$
$941$	15.8608			0.517046			0.258523	+	0.966005i	$0.416764\pi$
$942$	4.57154	+	7.34086i	0.148949	+	0.239178i
$943$	−37.2448			−1.21286
$944$	−7.58755	−	1.87016i	−0.246954	−	0.0608686i
$945$	−6.60098	−	4.17421i	−0.214730	−	0.135787i
$946$	2.43059	+	1.27567i	0.0790253	+	0.0414757i
$947$	23.1906	−	17.4266i	0.753592	−	0.566288i	−0.153035	−	0.988221i	$-0.548905\pi$
$947$	23.1906	−	17.4266i	0.753592	−	0.566288i	0.906627	+	0.421933i	$0.138648\pi$
$948$	−15.0490	−	15.6676i	−0.488768	−	0.508862i
$949$	−0.612604	+	0.321519i	−0.0198860	+	0.0104370i
$950$	0.487351	+	0.431755i	0.0158117	+	0.0140080i
$951$	13.5588	+	28.5746i	0.439675	+	0.926595i
$952$	22.2390	−	9.47515i	0.720770	−	0.307091i
$953$	13.9666	+	14.5408i	0.452423	+	0.471022i	0.907877	−	0.419237i	$-0.137702\pi$
$953$	13.9666	+	14.5408i	0.452423	+	0.471022i	−0.455454	+	0.890260i	$0.650523\pi$
$954$	−1.21303	−	2.10103i	−0.0392733	−	0.0680234i
$955$	−15.0350	+	26.0414i	−0.486521	+	0.842678i
$956$	27.0899	−	6.67707i	0.876151	−	0.215952i
$957$	−3.15463	+	0.254668i	−0.101975	+	0.00823225i
$958$	15.6650	+	22.6946i	0.506112	+	0.733230i
$959$	28.3883	−	21.3324i	0.916707	−	0.688861i
$960$	−0.668348	−	3.27379i	−0.0215708	−	0.105661i
$961$	4.32705	−	21.1953i	0.139582	−	0.683720i
$962$	1.12036	−	0.182076i	0.0361219	−	0.00587037i
$963$	5.30472	+	0.428242i	0.170942	+	0.0137999i
$964$	−0.300115	−	0.519814i	−0.00966605	−	0.0167421i
$965$	−32.9006	−	47.6648i	−1.05911	−	1.53438i
$966$	−2.01344	−	6.95119i	−0.0647813	−	0.223651i
$967$	1.30788	−	4.51532i	0.0420586	−	0.145203i	−0.936741	−	0.350023i	$-0.886174\pi$
$967$	1.30788	−	4.51532i	0.0420586	−	0.145203i	0.978800	+	0.204820i	$0.0656609\pi$
$968$	17.6548	−	18.3806i	0.567446	−	0.590774i
$969$	−0.199496	+	1.64300i	−0.00640874	+	0.0527807i
$970$	−16.6866			−0.535774
$971$	−1.15727	+	9.53101i	−0.0371387	+	0.305865i	0.962289	+	0.272030i	$0.0876950\pi$
$971$	−1.15727	+	9.53101i	−0.0371387	+	0.305865i	−0.999427	+	0.0338346i	$0.989228\pi$
$972$	−1.50392	−	0.244410i	−0.0482382	−	0.00783947i
$973$	−1.36995	−	1.67789i	−0.0439187	−	0.0537906i
$974$	−1.62687	−	4.28971i	−0.0521283	−	0.137451i
$975$	0.0776204	+	0.380210i	0.00248584	+	0.0121765i
$976$	−10.8435	+	4.61999i	−0.347093	+	0.147882i
$977$	18.1151	−	38.1767i	0.579552	−	1.22138i	−0.376017	−	0.926613i	$-0.622707\pi$
$977$	18.1151	−	38.1767i	0.579552	−	1.22138i	0.955569	−	0.294767i	$-0.0952422\pi$
$978$	0.0628885	−	1.56056i	0.00201095	−	0.0499012i
$979$	2.52587	+	1.89807i	0.0807270	+	0.0606624i
$980$	−3.14460	+	6.62711i	−0.100451	+	0.211695i
$981$	−4.87897	+	2.56068i	−0.155773	+	0.0817562i
$982$	−27.0697	−	2.18529i	−0.863828	−	0.0697354i
$983$	8.15217	−	11.8105i	0.260014	−	0.376695i	−0.671135	−	0.741336i	$-0.734193\pi$
$983$	8.15217	−	11.8105i	0.260014	−	0.376695i	0.931148	+	0.364640i	$0.118808\pi$
$984$	−24.3508	−	8.12951i	−0.776277	−	0.259159i
$985$	57.2388	−	36.1956i	1.82378	−	1.15329i
$986$	2.81772	+	9.72791i	0.0897346	+	0.309800i
$987$	9.49133	+	4.98143i	0.302112	+	0.158561i
$988$	0.0544208	+	0.143496i	0.00173136	+	0.00456521i
$989$	17.8961	+	7.62483i	0.569064	+	0.242455i
$990$	−0.0526853	−	1.30737i	−0.00167445	−	0.0415511i
$991$	−32.3972	+	46.9354i	−1.02913	+	1.49095i	−0.165900	+	0.986143i	$0.553053\pi$
$991$	−32.3972	+	46.9354i	−1.02913	+	1.49095i	−0.863230	+	0.504810i	$0.831562\pi$
$992$	8.88908	−	15.3963i	0.282229	−	0.488834i
$993$	34.7253	−	2.80332i	1.10198	−	0.0889606i
$994$	−7.84161	+	4.95874i	−0.248721	+	0.157282i
$995$	8.19170	−	2.73479i	0.259694	−	0.0866987i
$996$	1.97083	−	5.19666i	0.0624483	−	0.164663i
$997$	−18.3818	−	2.98733i	−0.582156	−	0.0946096i	−0.137801	−	0.990460i	$-0.544003\pi$
$997$	−18.3818	−	2.98733i	−0.582156	−	0.0946096i	−0.444356	+	0.895850i	$0.646567\pi$
$998$	12.4060	+	3.05780i	0.392705	+	0.0967931i
$999$	−5.59683	+	5.82691i	−0.177076	+	0.184355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.q.b.19.6	✓	336
157.124	even	39	inner	471.2.q.b.124.6	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.q.b.19.6	✓	336	1.1	even	1	trivial
471.2.q.b.124.6	yes	336	157.124	even	39	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.670127 - 0.165171i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-1.34912 - 0.708075i) q^{4} +(2.10094 - 1.57875i) q^{5} +(0.478106 + 0.497761i) q^{6} +(2.63145 - 1.38109i) q^{7} +(1.82035 + 1.61269i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\)	\(q+(-0.670127 - 0.165171i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-1.34912 - 0.708075i) q^{4} +(2.10094 - 1.57875i) q^{5} +(0.478106 + 0.497761i) q^{6} +(2.63145 - 1.38109i) q^{7} +(1.82035 + 1.61269i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-1.66866 + 0.710950i) q^{10} +(0.499715 + 0.520258i) q^{11} +(0.761824 + 1.31952i) q^{12} +(0.101775 - 0.176280i) q^{13} +(-1.99152 + 0.490866i) q^{14} +(-2.61948 + 0.211467i) q^{15} +(0.777567 + 1.12650i) q^{16} +(2.67387 - 2.00928i) q^{17} +(-0.138054 - 0.676234i) q^{18} +(0.0989802 - 0.484837i) q^{19} +(-3.95230 + 0.642312i) q^{20} +(-2.96222 - 0.239135i) q^{21} +(-0.248941 - 0.431178i) q^{22} +(-2.00429 - 2.90371i) q^{23} +(-0.676614 - 2.33594i) q^{24} +(0.530398 - 1.83114i) q^{25} +(-0.0973190 + 0.101320i) q^{26} +(0.120537 - 0.992709i) q^{27} -4.52806 q^{28} +(0.528830 - 4.35531i) q^{29} +(1.79032 + 0.290955i) q^{30} +(1.93569 + 2.37079i) q^{31} +(-2.05977 - 5.43117i) q^{32} +(-0.144294 - 0.706798i) q^{33} +(-2.12371 + 0.904828i) q^{34} +(3.34811 - 7.05600i) q^{35} +(0.0613511 - 1.52241i) q^{36} +(-6.45905 - 4.85366i) q^{37} +(-0.146411 + 0.308554i) q^{38} +(-0.180235 + 0.0945948i) q^{39} +(6.37048 + 0.514278i) q^{40} +(5.99655 - 8.68750i) q^{41} +(1.94557 + 0.649525i) q^{42} +(-4.65987 + 2.94672i) q^{43} +(-0.305795 - 1.05573i) q^{44} +(2.32698 + 1.22130i) q^{45} +(0.863516 + 2.27690i) q^{46} +(-3.31826 - 1.41378i) q^{47} +(-0.0551160 - 1.36769i) q^{48} +(1.04065 - 1.50765i) q^{49} +(-0.657887 + 1.13949i) q^{50} +(-3.33382 + 0.269134i) q^{51} +(-0.262127 + 0.165759i) q^{52} +(3.33420 - 1.11312i) q^{53} +(-0.244742 + 0.645332i) q^{54} +(1.87123 + 0.304105i) q^{55} +(7.01742 + 1.72964i) q^{56} +(-0.342786 + 0.356878i) q^{57} +(-1.07376 + 2.83126i) q^{58} +(-4.27333 + 3.78584i) q^{59} +(3.68374 + 1.56950i) q^{60} +(-1.72242 + 8.43695i) q^{61} +(-0.905570 - 1.90845i) q^{62} +(2.37583 + 1.78532i) q^{63} +(0.153253 + 1.26215i) q^{64} +(-0.0644790 - 0.531033i) q^{65} +(-0.0200477 + 0.497477i) q^{66} +(8.90858 + 7.89232i) q^{67} +(-5.03010 + 0.817471i) q^{68} +(0.142069 + 3.52541i) q^{69} +(-3.40911 + 4.17540i) q^{70} +(4.29055 - 1.43240i) q^{71} +(-0.676614 + 2.33594i) q^{72} +(-2.87273 - 1.81660i) q^{73} +(3.52670 + 4.31942i) q^{74} +(-1.42697 + 1.26419i) q^{75} +(-0.476837 + 0.584019i) q^{76} +(2.03350 + 0.678881i) q^{77} +(0.136405 - 0.0336208i) q^{78} +(-13.8438 + 3.41219i) q^{79} +(3.41209 + 1.13912i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-5.45338 + 4.83127i) q^{82} +(-2.30698 - 2.82554i) q^{83} +(3.82707 + 2.42009i) q^{84} +(2.44548 - 8.44276i) q^{85} +(3.60942 - 1.20500i) q^{86} +(-2.77473 + 3.39842i) q^{87} +(0.0706409 + 1.75294i) q^{88} +(4.32315 - 0.702581i) q^{89} +(-1.35765 - 1.20277i) q^{90} +(0.0243578 - 0.604434i) q^{91} +(0.647986 + 5.33665i) q^{92} +(-0.368919 - 3.03832i) q^{93} +(1.99014 + 1.49549i) q^{94} +(-0.557487 - 1.17488i) q^{95} +(-1.16188 + 5.69125i) q^{96} +(8.46360 + 3.60600i) q^{97} +(-0.946392 + 0.838430i) q^{98} +(-0.255803 + 0.674498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Introduction

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