LMFDB - Embedded newform 354.2.e.b.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			289.1
Character	$\chi$	$=$	354.289
Dual form			354.2.e.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.370138 + 0.928977i) q^{2} +(0.994138 - 0.108119i) q^{3} +(-0.725995 + 0.687699i) q^{4} +(-2.09789 - 2.46983i) q^{5} +(0.468408 + 0.883512i) q^{6} +(3.22015 - 1.93750i) q^{7} +(-0.907575 - 0.419889i) q^{8} +(0.976621 - 0.214970i) q^{9} +O(q^{10})$	\(q+(0.370138 + 0.928977i) q^{2} +(0.994138 - 0.108119i) q^{3} +(-0.725995 + 0.687699i) q^{4} +(-2.09789 - 2.46983i) q^{5} +(0.468408 + 0.883512i) q^{6} +(3.22015 - 1.93750i) q^{7} +(-0.907575 - 0.419889i) q^{8} +(0.976621 - 0.214970i) q^{9} +(1.51790 - 2.86307i) q^{10} +(-0.0664190 - 1.22503i) q^{11} +(-0.647386 + 0.762162i) q^{12} +(3.78822 + 0.833851i) q^{13} +(2.99179 + 2.27430i) q^{14} +(-2.35263 - 2.22853i) q^{15} +(0.0541389 - 0.998533i) q^{16} +(1.60517 + 0.965800i) q^{17} +(0.561187 + 0.827689i) q^{18} +(-0.558798 - 2.01261i) q^{19} +(3.22155 + 0.350365i) q^{20} +(2.99179 - 2.27430i) q^{21} +(1.11344 - 0.515131i) q^{22} +(-1.75355 + 2.58629i) q^{23} +(-0.947653 - 0.319302i) q^{24} +(-0.889991 + 5.42870i) q^{25} +(0.627538 + 3.82781i) q^{26} +(0.947653 - 0.319302i) q^{27} +(-1.00540 + 3.62111i) q^{28} +(1.74335 - 4.37548i) q^{29} +(1.19945 - 3.01040i) q^{30} +(-1.92596 + 6.93668i) q^{31} +(0.947653 - 0.319302i) q^{32} +(-0.198478 - 1.21066i) q^{33} +(-0.303070 + 1.84865i) q^{34} +(-11.5408 - 3.88855i) q^{35} +(-0.561187 + 0.827689i) q^{36} +(-4.48315 + 2.07412i) q^{37} +(1.66283 - 1.26405i) q^{38} +(3.85617 + 0.419384i) q^{39} +(0.866939 + 3.12243i) q^{40} +(-2.48825 - 3.66990i) q^{41} +(3.22015 + 1.93750i) q^{42} +(0.269998 - 4.97982i) q^{43} +(0.890670 + 0.843688i) q^{44} +(-2.57978 - 1.96110i) q^{45} +(-3.05166 - 0.671721i) q^{46} +(-8.53306 + 10.0459i) q^{47} +(-0.0541389 - 0.998533i) q^{48} +(3.33661 - 6.29351i) q^{49} +(-5.37256 + 1.18259i) q^{50} +(1.70018 + 0.786589i) q^{51} +(-3.32367 + 1.99979i) q^{52} +(3.77351 + 7.11759i) q^{53} +(0.647386 + 0.762162i) q^{54} +(-2.88626 + 2.73401i) q^{55} +(-3.73607 + 0.406322i) q^{56} +(-0.773124 - 1.94039i) q^{57} +4.71000 q^{58} +(2.23996 - 7.34728i) q^{59} +3.24055 q^{60} +(3.52880 + 8.85663i) q^{61} +(-7.15688 + 0.778358i) q^{62} +(2.72836 - 2.58444i) q^{63} +(0.647386 + 0.762162i) q^{64} +(-5.88781 - 11.1056i) q^{65} +(1.05121 - 0.632495i) q^{66} +(10.9304 + 5.05696i) q^{67} +(-1.82953 + 0.402710i) q^{68} +(-1.46364 + 2.76072i) q^{69} +(-0.659320 - 12.1604i) q^{70} +(2.28511 - 2.69024i) q^{71} +(-0.976621 - 0.214970i) q^{72} +(-9.95742 - 7.56944i) q^{73} +(-3.58620 - 3.39703i) q^{74} +(-0.297827 + 5.49310i) q^{75} +(1.78975 + 1.07686i) q^{76} +(-2.58737 - 3.81609i) q^{77} +(1.03772 + 3.73753i) q^{78} +(8.31992 + 0.904846i) q^{79} +(-2.57978 + 1.96110i) q^{80} +(0.907575 - 0.419889i) q^{81} +(2.48825 - 3.66990i) q^{82} +(2.60163 + 0.876592i) q^{83} +(-0.607992 + 3.70859i) q^{84} +(-0.982115 - 5.99064i) q^{85} +(4.72607 - 1.59240i) q^{86} +(1.26006 - 4.53832i) q^{87} +(-0.454095 + 1.13969i) q^{88} +(-6.43106 + 16.1407i) q^{89} +(0.866939 - 3.12243i) q^{90} +(13.8142 - 4.65456i) q^{91} +(-0.505522 - 3.08355i) q^{92} +(-1.16468 + 7.10425i) q^{93} +(-12.4908 - 4.20865i) q^{94} +(-3.79850 + 5.60236i) q^{95} +(0.907575 - 0.419889i) q^{96} +(-3.99980 + 3.04057i) q^{97} +(7.08153 + 0.770163i) q^{98} +(-0.328211 - 1.18211i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 30 q^{11} + 2 q^{12} + 5 q^{13} + 28 q^{14} + 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 28 q^{21} - q^{22} - 2 q^{23} - 2 q^{24} + 64 q^{25} - 34 q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - 2 q^{30} + 2 q^{32} - q^{33} + 32 q^{34} - 87 q^{35} - 2 q^{36} + 47 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} + 3 q^{41} + q^{42} - 61 q^{43} + q^{44} - 2 q^{45} - 27 q^{46} + 50 q^{47} + 2 q^{48} - 45 q^{49} - 6 q^{50} + 3 q^{51} - 24 q^{52} - 27 q^{53} - 2 q^{54} - 95 q^{55} - q^{56} + 4 q^{57} + 50 q^{58} - 58 q^{59} + 2 q^{60} - 74 q^{61} - 29 q^{62} + q^{63} - 2 q^{64} - 17 q^{65} + q^{66} + 4 q^{67} - 32 q^{68} + 31 q^{69} - 58 q^{70} - 47 q^{71} + 2 q^{72} + 43 q^{73} - 18 q^{74} - 6 q^{75} - 33 q^{76} - 5 q^{77} + 5 q^{78} + 19 q^{79} - 2 q^{80} - 2 q^{81} - 3 q^{82} + 47 q^{83} - q^{84} - 149 q^{85} - 55 q^{86} + 21 q^{87} + 28 q^{88} + 36 q^{89} + 2 q^{90} + 175 q^{91} - 2 q^{92} - 29 q^{93} - 21 q^{94} + 50 q^{95} - 2 q^{96} + 10 q^{97} - 13 q^{98} + q^{99}+O(q^{100}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 30 * q^11 + 2 * q^12 + 5 * q^13 + 28 * q^14 + 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 28 * q^21 - q^22 - 2 * q^23 - 2 * q^24 + 64 * q^25 - 34 * q^26 + 2 * q^27 + q^28 + 8 * q^29 - 2 * q^30 + 2 * q^32 - q^33 + 32 * q^34 - 87 * q^35 - 2 * q^36 + 47 * q^37 + 4 * q^38 - 5 * q^39 + 2 * q^40 + 3 * q^41 + q^42 - 61 * q^43 + q^44 - 2 * q^45 - 27 * q^46 + 50 * q^47 + 2 * q^48 - 45 * q^49 - 6 * q^50 + 3 * q^51 - 24 * q^52 - 27 * q^53 - 2 * q^54 - 95 * q^55 - q^56 + 4 * q^57 + 50 * q^58 - 58 * q^59 + 2 * q^60 - 74 * q^61 - 29 * q^62 + q^63 - 2 * q^64 - 17 * q^65 + q^66 + 4 * q^67 - 32 * q^68 + 31 * q^69 - 58 * q^70 - 47 * q^71 + 2 * q^72 + 43 * q^73 - 18 * q^74 - 6 * q^75 - 33 * q^76 - 5 * q^77 + 5 * q^78 + 19 * q^79 - 2 * q^80 - 2 * q^81 - 3 * q^82 + 47 * q^83 - q^84 - 149 * q^85 - 55 * q^86 + 21 * q^87 + 28 * q^88 + 36 * q^89 + 2 * q^90 + 175 * q^91 - 2 * q^92 - 29 * q^93 - 21 * q^94 + 50 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{11}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	0.370138	+	0.928977i	0.261727	+	0.656886i
$2$	0.370138	+	0.928977i	0.261727	+	0.656886i
$3$	0.994138	−	0.108119i	0.573966	−	0.0624225i
$3$	0.994138	−	0.108119i	0.573966	−	0.0624225i
$4$	−0.725995	+	0.687699i	−0.362998	+	0.343850i
$5$	−2.09789	−	2.46983i	−0.938204	−	1.10454i	−0.994354	−	0.106117i	$-0.966158\pi$
$5$	−2.09789	−	2.46983i	−0.938204	−	1.10454i	0.0561494	−	0.998422i	$-0.482118\pi$
$6$	0.468408	+	0.883512i	0.191227	+	0.360692i
$7$	3.22015	−	1.93750i	1.21710	−	0.732307i	0.245609	−	0.969369i	$-0.421012\pi$
$7$	3.22015	−	1.93750i	1.21710	−	0.732307i	0.971494	+	0.237063i	$0.0761846\pi$
$8$	−0.907575	−	0.419889i	−0.320876	−	0.148453i
$9$	0.976621	−	0.214970i	0.325540	−	0.0716568i
$10$	1.51790	−	2.86307i	0.480003	−	0.905381i
$11$	−0.0664190	−	1.22503i	−0.0200261	−	0.369360i	−0.991320	−	0.131475i	$-0.958029\pi$
$11$	−0.0664190	−	1.22503i	−0.0200261	−	0.369360i	0.971293	−	0.237885i	$-0.0764540\pi$
$12$	−0.647386	+	0.762162i	−0.186884	+	0.220017i
$13$	3.78822	+	0.833851i	1.05066	+	0.231269i	0.706553	−	0.707660i	$-0.250249\pi$
$13$	3.78822	+	0.833851i	1.05066	+	0.231269i	0.344111	+	0.938929i	$0.388180\pi$
$14$	2.99179	+	2.27430i	0.799591	+	0.607833i
$15$	−2.35263	−	2.22853i	−0.607445	−	0.575403i
$16$	0.0541389	−	0.998533i	0.0135347	−	0.249633i
$17$	1.60517	+	0.965800i	0.389311	+	0.234241i	0.696730	−	0.717333i	$-0.254638\pi$
$17$	1.60517	+	0.965800i	0.389311	+	0.234241i	−0.307419	+	0.951574i	$0.599465\pi$
$18$	0.561187	+	0.827689i	0.132273	+	0.195088i
$19$	−0.558798	−	2.01261i	−0.128197	−	0.461724i	0.871386	−	0.490598i	$-0.163222\pi$
$19$	−0.558798	−	2.01261i	−0.128197	−	0.461724i	−0.999583	+	0.0288740i	$0.990808\pi$
$20$	3.22155	+	0.350365i	0.720362	+	0.0783440i
$21$	2.99179	−	2.27430i	0.652863	−	0.496294i
$22$	1.11344	−	0.515131i	0.237386	−	0.109826i
$23$	−1.75355	+	2.58629i	−0.365640	+	0.539279i	−0.965357	−	0.260934i	$-0.915970\pi$
$23$	−1.75355	+	2.58629i	−0.365640	+	0.539279i	0.599717	+	0.800212i	$0.295280\pi$
$24$	−0.947653	−	0.319302i	−0.193439	−	0.0651772i
$25$	−0.889991	+	5.42870i	−0.177998	+	1.08574i
$26$	0.627538	+	3.82781i	0.123070	+	0.750696i
$27$	0.947653	−	0.319302i	0.182376	−	0.0614496i
$28$	−1.00540	+	3.62111i	−0.190002	+	0.684326i
$29$	1.74335	−	4.37548i	0.323732	−	0.812506i	−0.673572	−	0.739122i	$-0.735241\pi$
$29$	1.74335	−	4.37548i	0.323732	−	0.812506i	0.997304	−	0.0733839i	$-0.0233798\pi$
$30$	1.19945	−	3.01040i	0.218989	−	0.549621i
$31$	−1.92596	+	6.93668i	−0.345913	+	1.24586i	0.562152	+	0.827034i	$0.309974\pi$
$31$	−1.92596	+	6.93668i	−0.345913	+	1.24586i	−0.908064	+	0.418830i	$0.862440\pi$
$32$	0.947653	−	0.319302i	0.167523	−	0.0564451i
$33$	−0.198478	−	1.21066i	−0.0345507	−	0.210750i
$34$	−0.303070	+	1.84865i	−0.0519761	+	0.317040i
$35$	−11.5408	−	3.88855i	−1.95075	−	0.657285i
$36$	−0.561187	+	0.827689i	−0.0935312	+	0.137948i
$37$	−4.48315	+	2.07412i	−0.737025	+	0.340984i	−0.752230	−	0.658901i	$-0.771022\pi$
$37$	−4.48315	+	2.07412i	−0.737025	+	0.340984i	0.0152055	+	0.999884i	$0.495160\pi$
$38$	1.66283	−	1.26405i	0.269747	−	0.205057i
$39$	3.85617	+	0.419384i	0.617482	+	0.0671552i
$40$	0.866939	+	3.12243i	0.137075	+	0.493700i
$41$	−2.48825	−	3.66990i	−0.388600	−	0.573142i	0.582196	−	0.813048i	$-0.302194\pi$
$41$	−2.48825	−	3.66990i	−0.388600	−	0.573142i	−0.970796	+	0.239906i	$0.922883\pi$
$42$	3.22015	+	1.93750i	0.496880	+	0.298963i
$43$	0.269998	−	4.97982i	0.0411743	−	0.759416i	−0.902934	−	0.429780i	$-0.858591\pi$
$43$	0.269998	−	4.97982i	0.0411743	−	0.759416i	0.944108	−	0.329636i	$-0.106926\pi$
$44$	0.890670	+	0.843688i	0.134274	+	0.127191i
$45$	−2.57978	−	1.96110i	−0.384571	−	0.292343i
$46$	−3.05166	−	0.671721i	−0.449942	−	0.0990398i
$47$	−8.53306	+	10.0459i	−1.24468	+	1.46534i	−0.412380	+	0.911012i	$0.635302\pi$
$47$	−8.53306	+	10.0459i	−1.24468	+	1.46534i	−0.832295	+	0.554333i	$0.812973\pi$
$48$	−0.0541389	−	0.998533i	−0.00781428	−	0.144126i
$49$	3.33661	−	6.29351i	0.476658	−	0.899073i
$50$	−5.37256	+	1.18259i	−0.759794	+	0.167243i
$51$	1.70018	+	0.786589i	0.238073	+	0.110144i
$52$	−3.32367	+	1.99979i	−0.460911	+	0.277321i
$53$	3.77351	+	7.11759i	0.518331	+	0.977676i	0.995121	+	0.0986591i	$0.0314553\pi$
$53$	3.77351	+	7.11759i	0.518331	+	0.977676i	−0.476790	+	0.879017i	$0.658200\pi$
$54$	0.647386	+	0.762162i	0.0880981	+	0.103717i
$55$	−2.88626	+	2.73401i	−0.389184	+	0.368654i
$56$	−3.73607	+	0.406322i	−0.499253	+	0.0542970i
$57$	−0.773124	−	1.94039i	−0.102403	−	0.257011i
$58$	4.71000			0.618453
$59$	2.23996	−	7.34728i	0.291618	−	0.956535i
$59$	2.23996	−	7.34728i	0.291618	−	0.956535i
$60$	3.24055			0.418353
$61$	3.52880	+	8.85663i	0.451817	+	1.13397i	0.961791	+	0.273785i	$0.0882757\pi$
$61$	3.52880	+	8.85663i	0.451817	+	1.13397i	−0.509974	+	0.860190i	$0.670345\pi$
$62$	−7.15688	+	0.778358i	−0.908925	+	0.0988516i
$63$	2.72836	−	2.58444i	0.343741	−	0.325609i
$64$	0.647386	+	0.762162i	0.0809233	+	0.0952703i
$65$	−5.88781	−	11.1056i	−0.730292	−	1.37748i
$66$	1.05121	−	0.632495i	0.129396	−	0.0778548i
$67$	10.9304	+	5.05696i	1.33537	+	0.617806i	0.952087	−	0.305826i	$-0.0989327\pi$
$67$	10.9304	+	5.05696i	1.33537	+	0.617806i	0.383279	+	0.923633i	$0.374795\pi$
$68$	−1.82953	+	0.402710i	−0.221863	+	0.0488357i
$69$	−1.46364	+	2.76072i	−0.176202	+	0.332352i
$70$	−0.659320	−	12.1604i	−0.0788038	−	1.45345i
$71$	2.28511	−	2.69024i	0.271192	−	0.319272i	−0.609660	−	0.792663i	$-0.708694\pi$
$71$	2.28511	−	2.69024i	0.271192	−	0.319272i	0.880853	+	0.473390i	$0.156970\pi$
$72$	−0.976621	−	0.214970i	−0.115096	−	0.0253345i
$73$	−9.95742	−	7.56944i	−1.16543	−	0.885936i	−0.170385	−	0.985378i	$-0.554501\pi$
$73$	−9.95742	−	7.56944i	−1.16543	−	0.885936i	−0.995043	+	0.0994419i	$0.968294\pi$
$74$	−3.58620	−	3.39703i	−0.416887	−	0.394896i
$75$	−0.297827	+	5.49310i	−0.0343902	+	0.634289i
$76$	1.78975	+	1.07686i	0.205299	+	0.123524i
$77$	−2.58737	−	3.81609i	−0.294858	−	0.434883i
$78$	1.03772	+	3.73753i	0.117499	+	0.423191i
$79$	8.31992	+	0.904846i	0.936065	+	0.101803i	0.563420	−	0.826171i	$-0.309485\pi$
$79$	8.31992	+	0.904846i	0.936065	+	0.101803i	0.372645	+	0.927974i	$0.378451\pi$
$80$	−2.57978	+	1.96110i	−0.288428	+	0.219257i
$81$	0.907575	−	0.419889i	0.100842	−	0.0466543i
$82$	2.48825	−	3.66990i	0.274782	−	0.405273i
$83$	2.60163	+	0.876592i	0.285566	+	0.0962185i	0.458440	−	0.888726i	$-0.348409\pi$
$83$	2.60163	+	0.876592i	0.285566	+	0.0962185i	−0.172873	+	0.984944i	$0.555305\pi$
$84$	−0.607992	+	3.70859i	−0.0663374	+	0.404640i
$85$	−0.982115	−	5.99064i	−0.106525	−	0.649776i
$86$	4.72607	−	1.59240i	0.509626	−	0.171713i
$87$	1.26006	−	4.53832i	0.135092	−	0.486559i
$88$	−0.454095	+	1.13969i	−0.0484067	+	0.121492i
$89$	−6.43106	+	16.1407i	−0.681691	+	1.71091i	0.0213569	+	0.999772i	$0.493201\pi$
$89$	−6.43106	+	16.1407i	−0.681691	+	1.71091i	−0.703048	+	0.711143i	$0.748178\pi$
$90$	0.866939	−	3.12243i	0.0913834	−	0.329133i
$91$	13.8142	−	4.65456i	1.44813	−	0.487931i
$92$	−0.505522	−	3.08355i	−0.0527043	−	0.321482i
$93$	−1.16468	+	7.10425i	−0.120772	+	0.736676i
$94$	−12.4908	−	4.20865i	−1.28833	−	0.434089i
$95$	−3.79850	+	5.60236i	−0.389717	+	0.574790i
$96$	0.907575	−	0.419889i	0.0926290	−	0.0428548i
$97$	−3.99980	+	3.04057i	−0.406118	+	0.308723i	−0.788216	−	0.615399i	$-0.788995\pi$
$97$	−3.99980	+	3.04057i	−0.406118	+	0.308723i	0.382098	+	0.924122i	$0.375202\pi$
$98$	7.08153	+	0.770163i	0.715342	+	0.0777982i
$99$	−0.328211	−	1.18211i	−0.0329864	−	0.118806i
$100$	−3.08719	−	4.55326i	−0.308719	−	0.455326i
$101$	−11.0086	−	6.62366i	−1.09540	−	0.659079i	−0.151215	−	0.988501i	$-0.548319\pi$
$101$	−11.0086	−	6.62366i	−1.09540	−	0.659079i	−0.944183	+	0.329422i	$0.893146\pi$
$102$	−0.101420	+	1.87058i	−0.0100421	+	0.185215i
$103$	−5.41983	−	5.13394i	−0.534032	−	0.505862i	0.372481	−	0.928040i	$-0.378507\pi$
$103$	−5.41983	−	5.13394i	−0.534032	−	0.505862i	−0.906513	+	0.422178i	$0.861266\pi$
$104$	−3.08797	−	2.34742i	−0.302801	−	0.230183i
$105$	−11.8936	−	2.61798i	−1.16069	−	0.255488i
$106$	−5.21536	+	6.13999i	−0.506560	+	0.596369i
$107$	0.873381	+	16.1086i	0.0844329	+	1.55727i	0.667351	+	0.744743i	$0.267428\pi$
$107$	0.873381	+	16.1086i	0.0844329	+	1.55727i	−0.582918	+	0.812531i	$0.698089\pi$
$108$	−0.468408	+	0.883512i	−0.0450726	+	0.0850160i
$109$	−18.9110	+	4.16262i	−1.81134	+	0.398707i	−0.986111	−	0.166086i	$-0.946887\pi$
$109$	−18.9110	+	4.16262i	−1.81134	+	0.398707i	−0.825233	+	0.564793i	$0.808956\pi$
$110$	−3.60815	−	1.66931i	−0.344024	−	0.159162i
$111$	−4.23261	+	2.54668i	−0.401742	+	0.241720i
$112$	−1.76032	−	3.32032i	−0.166335	−	0.313741i
$113$	−2.59897	−	3.05975i	−0.244491	−	0.287837i	0.626205	−	0.779658i	$-0.284607\pi$
$113$	−2.59897	−	3.05975i	−0.244491	−	0.287837i	−0.870696	+	0.491821i	$0.836331\pi$
$114$	1.51642	−	1.43643i	0.142026	−	0.134534i
$115$	10.0664	−	1.09479i	0.938700	−	0.102090i
$116$	1.74335	+	4.37548i	0.161866	+	0.406253i
$117$	3.87891			0.358606
$118$	7.65455	−	0.638636i	0.704658	−	0.0587912i
$119$	7.04014			0.645368
$120$	1.19945	+	3.01040i	0.109494	+	0.274810i
$121$	9.43924	−	1.02658i	0.858113	−	0.0933254i
$122$	−6.92146	+	6.55635i	−0.626639	+	0.593584i
$123$	−2.87045	−	3.37936i	−0.258820	−	0.304707i
$124$	−3.37211	−	6.36048i	−0.302825	−	0.571188i
$125$	1.39160	−	0.837298i	0.124468	−	0.0748902i
$126$	3.41076	+	1.57798i	0.303854	+	0.140578i
$127$	−12.2964	+	2.70664i	−1.09113	+	0.240176i	−0.723866	−	0.689941i	$-0.757636\pi$
$127$	−12.2964	+	2.70664i	−1.09113	+	0.240176i	−0.367264	+	0.930117i	$0.619705\pi$
$128$	−0.468408	+	0.883512i	−0.0414018	+	0.0780922i
$129$	−0.269998	−	4.97982i	−0.0237720	−	0.438449i
$130$	8.13752	−	9.58023i	0.713708	−	0.840242i
$131$	13.4090	+	2.95154i	1.17155	+	0.257877i	0.757783	−	0.652507i	$-0.226283\pi$
$131$	13.4090	+	2.95154i	1.17155	+	0.257877i	0.413765	+	0.910384i	$0.364214\pi$
$132$	0.976668	+	0.742444i	0.0850080	+	0.0646214i
$133$	−5.69884	−	5.39823i	−0.494153	−	0.468086i
$134$	−0.652025	+	12.0259i	−0.0563264	+	1.03888i
$135$	−2.77669	−	1.67068i	−0.238979	−	0.143789i
$136$	−1.05129	−	1.55053i	−0.0901470	−	0.132957i
$137$	2.00567	+	7.22375i	0.171356	+	0.617167i	0.998478	+	0.0551457i	$0.0175623\pi$
$137$	2.00567	+	7.22375i	0.171356	+	0.617167i	−0.827123	+	0.562021i	$0.810024\pi$
$138$	−3.10640	−	0.337841i	−0.264434	−	0.0287589i
$139$	13.8772	−	10.5492i	1.17705	−	0.894770i	0.180993	−	0.983484i	$-0.442069\pi$
$139$	13.8772	−	10.5492i	1.17705	−	0.894770i	0.996057	+	0.0887146i	$0.0282759\pi$
$140$	11.0527	−	5.11354i	0.934126	−	0.432173i
$141$	−7.39689	+	10.9096i	−0.622930	+	0.918754i
$142$	3.34497	+	1.12705i	0.280704	+	0.0945802i
$143$	0.769880	−	4.69606i	0.0643806	−	0.392704i
$144$	−0.161782	−	0.986827i	−0.0134818	−	0.0822355i
$145$	−14.4640	+	4.87349i	−1.20117	+	0.404722i
$146$	3.34621	−	12.0520i	0.276934	−	0.997427i
$147$	2.63660	−	6.61737i	0.217463	−	0.545791i
$148$	1.82837	−	4.58886i	0.150291	−	0.377202i
$149$	4.14247	−	14.9198i	0.339365	−	1.22228i	−0.575258	−	0.817972i	$-0.695098\pi$
$149$	4.14247	−	14.9198i	0.339365	−	1.22228i	0.914623	−	0.404309i	$-0.132488\pi$
$150$	−5.21320	+	1.75653i	−0.425656	+	0.143420i
$151$	1.69701	+	10.3513i	0.138101	+	0.842378i	0.961478	+	0.274883i	$0.0886391\pi$
$151$	1.69701	+	10.3513i	0.138101	+	0.842378i	−0.823377	+	0.567495i	$0.807913\pi$
$152$	−0.337921	+	2.06123i	−0.0274090	+	0.167188i
$153$	1.77526	+	0.598156i	0.143521	+	0.0483580i
$154$	2.58737	−	3.81609i	0.208496	−	0.307509i
$155$	21.1728	−	9.79560i	1.70064	−	0.786801i
$156$	−3.08797	+	2.34742i	−0.247236	+	0.187944i
$157$	11.8532	+	1.28911i	0.945989	+	0.102882i	0.568092	−	0.822965i	$-0.307682\pi$
$157$	11.8532	+	1.28911i	0.945989	+	0.102882i	0.377897	+	0.925848i	$0.376647\pi$
$158$	2.23894	+	8.06393i	0.178121	+	0.641532i
$159$	4.52093	+	6.66788i	0.358533	+	0.528797i
$160$	−2.77669	−	1.67068i	−0.219517	−	0.132079i
$161$	−0.635752	+	11.7257i	−0.0501042	+	0.924118i
$162$	0.725995	+	0.687699i	0.0570396	+	0.0540308i
$163$	6.86279	+	5.21696i	0.537535	+	0.408624i	0.838410	−	0.545040i	$-0.183486\pi$
$163$	6.86279	+	5.21696i	0.537535	+	0.408624i	−0.300875	+	0.953664i	$0.597279\pi$
$164$	4.33025	+	0.953160i	0.338136	+	0.0744293i
$165$	−2.57374	+	3.03005i	−0.200366	+	0.235889i
$166$	0.148630	+	2.74132i	0.0115359	+	0.212768i
$167$	−2.74596	+	5.17942i	−0.212488	+	0.400796i	−0.966729	−	0.255802i	$-0.917660\pi$
$167$	−2.74596	+	5.17942i	−0.212488	+	0.400796i	0.754241	+	0.656598i	$0.228005\pi$
$168$	−3.67023	+	0.807880i	−0.283165	+	0.0623293i
$169$	1.85686	+	0.859075i	0.142835	+	0.0660827i
$170$	5.20164	−	3.12973i	0.398948	−	0.240039i
$171$	−0.978385	−	1.84543i	−0.0748190	−	0.141124i
$172$	3.22860	+	3.80101i	0.246179	+	0.289824i
$173$	13.6322	−	12.9131i	1.03644	−	0.981764i	0.0365897	−	0.999330i	$-0.488351\pi$
$173$	13.6322	−	12.9131i	1.03644	−	0.981764i	0.999846	+	0.0175667i	$0.00559193\pi$
$174$	4.68239	−	0.509240i	0.354971	−	0.0386054i
$175$	7.65221	+	19.2056i	0.578453	+	1.45181i
$176$	−1.22683			−0.0924755
$177$	1.43245	−	7.54640i	0.107670	−	0.567222i
$178$	−17.3747			−1.30229
$179$	−0.542688	−	1.36204i	−0.0405624	−	0.101804i	0.907300	−	0.420484i	$-0.138140\pi$
$179$	−0.542688	−	1.36204i	−0.0405624	−	0.101804i	−0.947862	+	0.318680i	$0.896760\pi$
$180$	3.22155	−	0.350365i	0.240121	−	0.0261147i
$181$	−2.59747	+	2.46045i	−0.193068	+	0.182884i	−0.778127	−	0.628107i	$-0.783830\pi$
$181$	−2.59747	+	2.46045i	−0.193068	+	0.182884i	0.585059	+	0.810991i	$0.301071\pi$
$182$	9.43716	+	11.1103i	0.699529	+	0.823549i
$183$	4.46569	+	8.42318i	0.330113	+	0.622659i
$184$	2.67743	−	1.61096i	0.197383	−	0.118761i
$185$	14.5279	+	6.72130i	1.06811	+	0.494160i
$186$	−7.03078	+	1.54759i	−0.515521	+	0.113475i
$187$	1.07652	−	2.03053i	0.0787227	−	0.148487i
$188$	−0.713594	−	13.1615i	−0.0520442	−	0.959898i
$189$	2.43294	−	2.86428i	0.176970	−	0.208346i
$190$	−6.61043	−	1.45507i	−0.479571	−	0.105562i
$191$	9.12038	+	6.93314i	0.659928	+	0.501664i	0.880708	−	0.473659i	$-0.157067\pi$
$191$	9.12038	+	6.93314i	0.659928	+	0.501664i	−0.220780	+	0.975324i	$0.570860\pi$
$192$	0.725995	+	0.687699i	0.0523942	+	0.0496304i
$193$	0.352965	−	6.51005i	0.0254070	−	0.468604i	−0.957952	−	0.286929i	$-0.907365\pi$
$193$	0.352965	−	6.51005i	0.0254070	−	0.468604i	0.983359	−	0.181675i	$-0.0581517\pi$
$194$	−4.30509	−	2.59029i	−0.309088	−	0.185972i
$195$	−7.05402	−	10.4039i	−0.505149	−	0.745038i
$196$	1.90568	+	6.86364i	0.136120	+	0.490260i
$197$	14.9424	+	1.62508i	1.06460	+	0.115782i	0.623614	−	0.781732i	$-0.285664\pi$
$197$	14.9424	+	1.62508i	1.06460	+	0.115782i	0.440985	+	0.897514i	$0.354629\pi$
$198$	0.976668	−	0.742444i	0.0694088	−	0.0527632i
$199$	−5.86659	+	2.71417i	−0.415872	+	0.192403i	−0.616656	−	0.787233i	$-0.711513\pi$
$199$	−5.86659	+	2.71417i	−0.415872	+	0.192403i	0.200784	+	0.979635i	$0.435651\pi$
$200$	3.08719	−	4.55326i	0.218297	−	0.321964i
$201$	11.4131	+	3.84553i	0.805020	+	0.271243i
$202$	2.07852	−	12.6784i	0.146244	−	0.892050i
$203$	−2.86364	−	17.4674i	−0.200988	−	1.22597i
$204$	−1.77526	+	0.598156i	−0.124293	+	0.0418793i
$205$	−3.84393	+	13.8446i	−0.268472	+	0.966949i
$206$	2.76322	−	6.93516i	0.192523	−	0.483196i
$207$	−1.15658	+	2.90279i	−0.0803875	+	0.201758i
$208$	1.03772	−	3.73753i	0.0719529	−	0.259151i
$209$	−2.42838	+	0.818218i	−0.167975	+	0.0565973i
$210$	−1.97023	−	12.0179i	−0.135959	−	0.829312i
$211$	−2.53183	+	15.4435i	−0.174298	+	1.06317i	0.744260	+	0.667889i	$0.232802\pi$
$211$	−2.53183	+	15.4435i	−0.174298	+	1.06317i	−0.918559	+	0.395284i	$0.870646\pi$
$212$	−7.63431	−	2.57230i	−0.524327	−	0.176666i
$213$	1.98085	−	2.92153i	0.135725	−	0.200180i
$214$	−14.6412	+	6.77375i	−1.00085	+	0.463044i
$215$	−12.8657	+	9.78026i	−0.877434	+	0.667008i
$216$	−0.994138	−	0.108119i	−0.0676425	−	0.00735657i
$217$	7.23794	+	26.0687i	0.491343	+	1.76966i
$218$	−10.8667	−	16.0271i	−0.735983	−	1.08549i
$219$	−10.7175	−	6.44848i	−0.724218	−	0.435748i
$220$	0.215234	−	3.96976i	0.0145111	−	0.267641i
$221$	5.27542	+	4.99714i	0.354863	+	0.336144i
$222$	−3.93246	−	2.98938i	−0.263929	−	0.200634i
$223$	13.0558	+	2.87380i	0.874282	+	0.192444i	0.629374	−	0.777103i	$-0.283311\pi$
$223$	13.0558	+	2.87380i	0.874282	+	0.192444i	0.244908	+	0.969546i	$0.421242\pi$
$224$	2.43294	−	2.86428i	0.162558	−	0.191378i
$225$	0.297827	+	5.49310i	0.0198552	+	0.366207i
$226$	1.88045	−	3.54691i	0.125086	−	0.235937i
$227$	−12.8504	+	2.82859i	−0.852911	+	0.187740i	−0.619848	−	0.784722i	$-0.712806\pi$
$227$	−12.8504	+	2.82859i	−0.852911	+	0.187740i	−0.233063	+	0.972462i	$0.574875\pi$
$228$	1.89569	+	0.877040i	0.125545	+	0.0580834i
$229$	−19.3693	+	11.6541i	−1.27996	+	0.770127i	−0.982795	−	0.184698i	$-0.940869\pi$
$229$	−19.3693	+	11.6541i	−1.27996	+	0.770127i	−0.297166	+	0.954826i	$0.596042\pi$
$230$	4.74301	+	8.94626i	0.312745	+	0.589899i
$231$	−2.98479	−	3.51397i	−0.196385	−	0.231202i
$232$	−3.41944	+	3.23906i	−0.224497	+	0.212655i
$233$	−2.14712	+	0.233514i	−0.140663	+	0.0152980i	−0.178179	−	0.983998i	$-0.557021\pi$
$233$	−2.14712	+	0.233514i	−0.140663	+	0.0152980i	0.0375168	+	0.999296i	$0.488055\pi$
$234$	1.43573	+	3.60342i	0.0938568	+	0.235563i
$235$	42.7130			2.78629
$236$	3.42652	+	6.87452i	0.223047	+	0.447493i
$237$	8.36898			0.543624
$238$	2.60582	+	6.54012i	0.168910	+	0.423933i
$239$	8.12099	−	0.883211i	0.525303	−	0.0571302i	0.158374	−	0.987379i	$-0.449375\pi$
$239$	8.12099	−	0.883211i	0.525303	−	0.0571302i	0.366929	+	0.930249i	$0.380409\pi$
$240$	−2.35263	+	2.22853i	−0.151861	+	0.143851i
$241$	−18.5983	−	21.8956i	−1.19802	−	1.41042i	−0.888097	−	0.459657i	$-0.847972\pi$
$241$	−18.5983	−	21.8956i	−1.19802	−	1.41042i	−0.309923	−	0.950762i	$-0.600303\pi$
$242$	4.44749	+	8.38886i	0.285895	+	0.539256i
$243$	0.856857	−	0.515554i	0.0549674	−	0.0330728i
$244$	−8.65259	−	4.00312i	−0.553925	−	0.256273i
$245$	−22.5437	+	4.96224i	−1.44026	+	0.317026i
$246$	2.07688	−	3.91742i	0.132417	−	0.249765i
$247$	−0.438636	−	8.09017i	−0.0279098	−	0.514765i
$248$	4.66059	−	5.48687i	0.295948	−	0.348417i
$249$	2.68116	+	0.590168i	0.169912	+	0.0374004i
$250$	1.29291	+	0.982848i	0.0817711	+	0.0621608i
$251$	−17.1254	−	16.2220i	−1.08094	−	1.02392i	−0.999629	−	0.0272358i	$-0.991330\pi$
$251$	−17.1254	−	16.2220i	−1.08094	−	1.02392i	−0.0813147	−	0.996688i	$-0.525912\pi$
$252$	−0.203459	+	3.75258i	−0.0128167	+	0.236391i
$253$	3.28474	+	1.97637i	0.206510	+	0.124253i
$254$	−7.06578	−	10.4212i	−0.443346	−	0.653887i
$255$	−1.62406	−	5.84933i	−0.101703	−	0.366299i
$256$	−0.994138	−	0.108119i	−0.0621336	−	0.00675744i
$257$	14.5187	−	11.0369i	0.905655	−	0.688461i	−0.0449088	−	0.998991i	$-0.514300\pi$
$257$	14.5187	−	11.0369i	0.905655	−	0.688461i	0.950563	+	0.310530i	$0.100507\pi$
$258$	4.52620	−	2.09404i	0.281789	−	0.130369i
$259$	−10.4178	+	15.3651i	−0.647330	+	0.954740i
$260$	11.9118	+	4.01356i	0.738740	+	0.248910i
$261$	0.761993	−	4.64795i	0.0471662	−	0.287701i
$262$	2.22126	+	13.5491i	0.137230	+	0.837066i
$263$	22.4789	−	7.57402i	1.38611	−	0.467034i	0.475285	−	0.879832i	$-0.342345\pi$
$263$	22.4789	−	7.57402i	1.38611	−	0.467034i	0.910823	+	0.412798i	$0.135448\pi$
$264$	−0.328211	+	1.18211i	−0.0202000	+	0.0727537i
$265$	9.66281	−	24.2518i	0.593581	−	1.48978i
$266$	2.90547	−	7.29219i	0.178146	−	0.447113i
$267$	−4.64824	+	16.7414i	−0.284468	+	1.02456i
$268$	−11.4131	+	3.84553i	−0.697167	+	0.234903i
$269$	−0.595654	−	3.63333i	−0.0363177	−	0.221528i	0.962432	−	0.271524i	$-0.0875275\pi$
$269$	−0.595654	−	3.63333i	−0.0363177	−	0.221528i	−0.998749	+	0.0499957i	$0.984079\pi$
$270$	0.524263	−	3.19786i	0.0319056	−	0.194616i
$271$	−22.0944	−	7.44448i	−1.34214	−	0.452220i	−0.445620	−	0.895222i	$-0.647017\pi$
$271$	−22.0944	−	7.44448i	−1.34214	−	0.452220i	−0.896521	+	0.443002i	$0.853913\pi$
$272$	1.05129	−	1.55053i	0.0637436	−	0.0940147i
$273$	13.2300	−	6.12086i	0.800717	−	0.370451i
$274$	−5.96833	+	4.53700i	−0.360560	+	0.274090i
$275$	6.70942	+	0.729693i	0.404593	+	0.0440022i
$276$	−0.835949	−	3.01082i	−0.0503182	−	0.181230i
$277$	−14.0507	−	20.7232i	−0.844225	−	1.24514i	−0.967527	−	0.252770i	$-0.918659\pi$
$277$	−14.0507	−	20.7232i	−0.844225	−	1.24514i	0.123301	−	0.992369i	$-0.460652\pi$
$278$	14.9364	+	8.98695i	0.895827	+	0.539002i
$279$	−0.389751	+	7.18853i	−0.0233338	+	0.430366i
$280$	8.84139	+	8.37501i	0.528374	+	0.500503i
$281$	4.29491	+	3.26490i	0.256213	+	0.194768i	0.725394	−	0.688334i	$-0.241658\pi$
$281$	4.29491	+	3.26490i	0.256213	+	0.194768i	−0.469181	+	0.883102i	$0.655451\pi$
$282$	−12.8726	−	2.83348i	−0.766554	−	0.168731i
$283$	16.0004	−	18.8371i	0.951126	−	1.11975i	−0.0415734	−	0.999135i	$-0.513237\pi$
$283$	16.0004	−	18.8371i	0.951126	−	1.11975i	0.992699	−	0.120616i	$-0.0384871\pi$
$284$	0.191097	+	3.52457i	0.0113395	+	0.209145i
$285$	−3.17051	+	5.98021i	−0.187805	+	0.354237i
$286$	4.64749	−	1.02299i	0.274812	−	0.0604907i
$287$	−15.1230	−	6.99664i	−0.892682	−	0.412999i
$288$	0.856857	−	0.515554i	0.0504908	−	0.0303793i
$289$	−6.31914	−	11.9192i	−0.371714	−	0.701127i
$290$	−9.88105	−	11.6329i	−0.580235	−	0.683105i
$291$	−3.64761	+	3.45520i	−0.213826	+	0.202547i
$292$	12.4345	−	1.35234i	0.727677	−	0.0791396i
$293$	−5.93315	−	14.8911i	−0.346618	−	0.869946i	−0.994160	−	0.107916i	$-0.965582\pi$
$293$	−5.93315	−	14.8911i	−0.346618	−	0.869946i	0.647542	−	0.762030i	$-0.275797\pi$
$294$	7.12329			0.415438
$295$	−22.8457	+	9.88146i	−1.33013	+	0.575321i
$296$	4.93969			0.287114
$297$	−0.454095	−	1.13969i	−0.0263493	−	0.0661317i
$298$	15.3935	−	1.67414i	0.891720	−	0.0969804i
$299$	−8.79942	+	8.33525i	−0.508883	+	0.482040i
$300$	−3.56138	−	4.19278i	−0.205617	−	0.242071i
$301$	−8.77897	−	16.5589i	−0.506012	−	0.954439i
$302$	−8.98800	+	5.40790i	−0.517201	+	0.311190i
$303$	−11.6602	−	5.39459i	−0.669862	−	0.309911i
$304$	−2.03991	+	0.449018i	−0.116997	+	0.0257530i
$305$	14.4713	−	27.2957i	0.828623	−	1.56295i
$306$	0.101420	+	1.87058i	0.00579778	+	0.106934i
$307$	8.49456	−	10.0006i	0.484810	−	0.570763i	−0.464312	−	0.885672i	$-0.653698\pi$
$307$	8.49456	−	10.0006i	0.484810	−	0.570763i	0.949122	+	0.314909i	$0.101974\pi$
$308$	4.50274	+	0.991128i	0.256567	+	0.0564748i
$309$	−5.94314	−	4.51786i	−0.338093	−	0.257012i
$310$	16.9368	+	16.0433i	0.961943	+	0.911201i
$311$	0.102305	−	1.88691i	0.00580120	−	0.106997i	−0.994199	−	0.107560i	$-0.965696\pi$
$311$	0.102305	−	1.88691i	0.00580120	−	0.106997i	1.00000		0.000562764i	$0.000179133\pi$
$312$	−3.32367	−	1.99979i	−0.188166	−	0.113216i
$313$	−9.08705	−	13.4024i	−0.513630	−	0.757548i	0.479119	−	0.877750i	$-0.340956\pi$
$313$	−9.08705	−	13.4024i	−0.513630	−	0.757548i	−0.992749	+	0.120202i	$0.961646\pi$
$314$	3.18977	+	11.4885i	0.180009	+	0.648334i
$315$	−12.1069	−	1.31671i	−0.682147	−	0.0741880i
$316$	−6.66249	+	5.06469i	−0.374794	+	0.284911i
$317$	−22.4022	+	10.3644i	−1.25823	+	0.582120i	−0.931756	−	0.363085i	$-0.881723\pi$
$317$	−22.4022	+	10.3644i	−1.25823	+	0.582120i	−0.326476	+	0.945205i	$0.605861\pi$
$318$	−4.52093	+	6.66788i	−0.253521	+	0.373916i
$319$	−5.47587	−	1.84503i	−0.306590	−	0.103302i
$320$	0.524263	−	3.19786i	0.0293072	−	0.178766i
$321$	2.60990	+	15.9197i	0.145671	+	0.888552i
$322$	−11.1283	+	3.74955i	−0.620154	+	0.208954i
$323$	1.04681	−	3.77027i	0.0582461	−	0.209783i
$324$	−0.370138	+	0.928977i	−0.0205632	+	0.0516098i
$325$	−7.89822	+	19.8230i	−0.438114	+	1.09958i
$326$	−2.30625	+	8.30637i	−0.127731	+	0.460047i
$327$	−18.3501	+	6.18286i	−1.01476	+	0.341913i
$328$	0.717327	+	4.37550i	0.0396078	+	0.241597i
$329$	−8.01382	+	48.8821i	−0.441816	+	2.69496i
$330$	−3.76748	−	1.26941i	−0.207393	−	0.0698789i
$331$	−20.3444	+	30.0058i	−1.11823	+	1.64927i	−0.488055	+	0.872813i	$0.662293\pi$
$331$	−20.3444	+	30.0058i	−1.11823	+	1.64927i	−0.630175	+	0.776453i	$0.717017\pi$
$332$	−2.49161	+	1.15274i	−0.136745	+	0.0632648i
$333$	−3.93246	+	2.98938i	−0.215497	+	0.163817i
$334$	−5.82795	−	0.633827i	−0.318891	−	0.0346815i
$335$	−10.4410	−	37.6052i	−0.570455	−	2.05459i
$336$	−2.10899	−	3.11053i	−0.115055	−	0.169694i
$337$	−8.89466	−	5.35174i	−0.484523	−	0.291528i	0.252257	−	0.967660i	$-0.418827\pi$
$337$	−8.89466	−	5.35174i	−0.484523	−	0.291528i	−0.736780	+	0.676132i	$0.763655\pi$
$338$	−0.110766	+	2.04296i	−0.00602487	+	0.111122i
$339$	−2.91455	−	2.76081i	−0.158297	−	0.149947i
$340$	4.83277	+	3.67377i	0.262094	+	0.199238i
$341$	8.62554	+	1.89862i	0.467099	+	0.102816i
$342$	1.35222	−	1.59196i	0.0731199	−	0.0860834i
$343$	−0.0250837	−	0.462641i	−0.00135439	−	0.0249803i
$344$	−2.33602	+	4.40619i	−0.125950	+	0.237566i
$345$	9.88906	−	2.17675i	0.532409	−	0.117192i
$346$	17.0417	+	7.88435i	0.916170	+	0.423865i
$347$	−1.73613	+	1.04460i	−0.0932004	+	0.0560768i	−0.561391	−	0.827551i	$-0.689734\pi$
$347$	−1.73613	+	1.04460i	−0.0932004	+	0.0560768i	0.468191	+	0.883627i	$0.344906\pi$
$348$	2.20620	+	4.16134i	0.118265	+	0.223071i
$349$	−6.83591	−	8.04785i	−0.365918	−	0.430792i	0.548133	−	0.836391i	$-0.315339\pi$
$349$	−6.83591	−	8.04785i	−0.365918	−	0.430792i	−0.914051	+	0.405599i	$0.867063\pi$
$350$	−15.0092	+	14.2175i	−0.802275	+	0.759955i
$351$	3.85617	−	0.419384i	0.205827	−	0.0223851i
$352$	−0.454095	−	1.13969i	−0.0242034	−	0.0607458i
$353$	21.2043			1.12859			0.564296	−	0.825572i	$-0.309148\pi$
$353$	21.2043			1.12859			0.564296	+	0.825572i	$0.309148\pi$
$354$	7.54063	−	1.46249i	0.400780	−	0.0777307i
$355$	−11.4383			−0.607083
$356$	−6.43106	−	16.1407i	−0.340845	−	0.855457i
$357$	6.99887	−	0.761173i	0.370419	−	0.0402855i
$358$	1.06444	−	1.00829i	0.0562572	−	0.0532897i
$359$	16.1271	+	18.9863i	0.851156	+	1.00206i	0.999913	+	0.0131842i	$0.00419677\pi$
$359$	16.1271	+	18.9863i	0.851156	+	1.00206i	−0.148757	+	0.988874i	$0.547527\pi$
$360$	1.51790	+	2.86307i	0.0800004	+	0.150897i
$361$	12.5419	−	7.54624i	0.660103	−	0.397171i
$362$	−3.24713	−	1.50228i	−0.170665	−	0.0789581i
$363$	9.27291	−	2.04112i	0.486702	−	0.107131i
$364$	−6.82814	+	12.8792i	−0.357892	+	0.675056i
$365$	2.19438	+	40.4729i	0.114859	+	2.11845i
$366$	−6.17202	+	7.26626i	−0.322616	+	0.379813i
$367$	11.2671	+	2.48008i	0.588139	+	0.129459i	0.499063	−	0.866566i	$-0.333678\pi$
$367$	11.2671	+	2.48008i	0.588139	+	0.129459i	0.0890760	+	0.996025i	$0.471609\pi$
$368$	2.48756	+	1.89100i	0.129673	+	0.0985749i
$369$	−3.21900	−	3.04920i	−0.167574	−	0.158735i
$370$	−0.866620	+	15.9839i	−0.0450534	+	0.830961i
$371$	25.9416	+	15.6085i	1.34682	+	0.810355i
$372$	−4.04003	−	5.95860i	−0.209466	−	0.308939i
$373$	−1.77033	−	6.37617i	−0.0916644	−	0.330145i	0.903473	−	0.428646i	$-0.141009\pi$
$373$	−1.77033	−	6.37617i	−0.0916644	−	0.330145i	−0.995137	+	0.0985005i	$0.968595\pi$
$374$	2.28477	+	0.248484i	0.118143	+	0.0128488i
$375$	1.29291	−	0.982848i	0.0667658	−	0.0507540i
$376$	11.9626	−	5.53447i	0.616922	−	0.285419i
$377$	10.2527	−	15.1216i	0.528041	−	0.778802i
$378$	3.56137	+	1.19997i	0.183177	+	0.0617196i
$379$	5.14689	−	31.3946i	0.264378	−	1.61263i	−0.436740	−	0.899588i	$-0.643867\pi$
$379$	5.14689	−	31.3946i	0.264378	−	1.61263i	0.701118	−	0.713045i	$-0.252685\pi$
$380$	−1.09505	−	6.67951i	−0.0561749	−	0.342652i
$381$	−11.9317	+	4.02025i	−0.611279	+	0.205964i
$382$	−3.06492	+	11.0388i	−0.156815	+	0.564796i
$383$	−11.9697	+	30.0417i	−0.611624	+	1.53506i	0.217537	+	0.976052i	$0.430198\pi$
$383$	−11.9697	+	30.0417i	−0.611624	+	1.53506i	−0.829161	+	0.559010i	$0.811181\pi$
$384$	−0.370138	+	0.928977i	−0.0188885	+	0.0474066i
$385$	−3.99705	+	14.3961i	−0.203709	+	0.733692i
$386$	6.17833	−	2.08172i	0.314469	−	0.105957i
$387$	−0.806829	−	4.92144i	−0.0410134	−	0.250171i
$388$	0.812838	−	4.95809i	0.0412656	−	0.251709i
$389$	−9.02159	−	3.03973i	−0.457413	−	0.154120i	0.0811568	−	0.996701i	$-0.474139\pi$
$389$	−9.02159	−	3.03973i	−0.457413	−	0.154120i	−0.538570	+	0.842581i	$0.681035\pi$
$390$	7.05402	−	10.4039i	0.357194	−	0.526822i
$391$	−5.31259	+	2.45786i	−0.268669	+	0.124300i
$392$	−5.67080	+	4.31083i	−0.286419	+	0.217730i
$393$	13.6495	+	1.48447i	0.688526	+	0.0748817i
$394$	4.02108	+	14.4826i	0.202579	+	0.729624i
$395$	−15.2195	−	22.4470i	−0.765774	−	1.12943i
$396$	1.05121	+	0.632495i	0.0528255	+	0.0317841i
$397$	1.12518	−	20.7527i	0.0564712	−	1.04155i	−0.823740	−	0.566967i	$-0.808117\pi$
$397$	1.12518	−	20.7527i	0.0564712	−	1.04155i	0.880211	−	0.474582i	$-0.157401\pi$
$398$	−4.69285	−	4.44531i	−0.235232	−	0.222823i
$399$	−6.24909	−	4.75043i	−0.312846	−	0.237819i
$400$	5.37256	+	1.18259i	0.268628	+	0.0591295i
$401$	−7.82987	+	9.21804i	−0.391005	+	0.460327i	−0.922081	−	0.386998i	$-0.873512\pi$
$401$	−7.82987	+	9.21804i	−0.391005	+	0.460327i	0.531076	+	0.847324i	$0.321788\pi$
$402$	0.652025	+	12.0259i	0.0325201	+	0.599797i
$403$	−13.0801	+	24.6717i	−0.651568	+	1.22899i
$404$	12.5473	−	2.76187i	0.624251	−	0.137408i
$405$	−2.94104	−	1.36067i	−0.146142	−	0.0676123i
$406$	15.1669	−	9.12562i	0.752721	−	0.452897i
$407$	2.83862	+	5.35421i	0.140705	+	0.265398i
$408$	−1.21277	−	1.42778i	−0.0600408	−	0.0706855i
$409$	−11.1794	+	10.5897i	−0.552788	+	0.523629i	−0.912306	−	0.409510i	$-0.865700\pi$
$409$	−11.1794	+	10.5897i	−0.552788	+	0.523629i	0.359518	+	0.933138i	$0.382941\pi$
$410$	−14.2841	+	1.55349i	−0.705441	+	0.0767213i
$411$	2.77493	+	6.96456i	0.136877	+	0.343536i
$412$	7.46538			0.367793
$413$	−7.02235	−	27.9993i	−0.345547	−	1.37776i
$414$	−3.12471			−0.153571
$415$	−3.29291	−	8.26457i	−0.161642	−	0.405692i
$416$	3.85617	−	0.419384i	0.189064	−	0.0205620i
$417$	12.6553	−	11.9877i	0.619732	−	0.587042i
$418$	−1.65894	−	1.95306i	−0.0811416	−	0.0955273i
$419$	8.68419	+	16.3801i	0.424250	+	0.800221i	0.999847	−	0.0175131i	$-0.00557487\pi$
$419$	8.68419	+	16.3801i	0.424250	+	0.800221i	−0.575596	+	0.817734i	$0.695230\pi$
$420$	10.4351	−	6.27857i	0.509179	−	0.306363i
$421$	−16.5650	−	7.66379i	−0.807329	−	0.373510i	−0.0275935	−	0.999619i	$-0.508784\pi$
$421$	−16.5650	−	7.66379i	−0.807329	−	0.373510i	−0.779736	+	0.626109i	$0.784646\pi$
$422$	−15.2838	+	3.36421i	−0.744002	+	0.163767i
$423$	−6.17399	+	11.6454i	−0.300190	+	0.566218i
$424$	−0.436144	−	8.04420i	−0.0211810	−	0.390661i
$425$	−6.67163	+	7.85445i	−0.323622	+	0.380997i
$426$	3.44722	+	0.758791i	0.167018	+	0.0367635i
$427$	28.5230	+	21.6826i	1.38032	+	1.04930i
$428$	−11.7119	−	11.0941i	−0.566117	−	0.536255i
$429$	0.257634	−	4.75177i	0.0124387	−	0.229418i
$430$	−13.8477	−	8.33190i	−0.667797	−	0.401800i
$431$	−13.2528	−	19.5464i	−0.638365	−	0.941518i	−0.999958	−	0.00918200i	$-0.997077\pi$
$431$	−13.2528	−	19.5464i	−0.638365	−	0.941518i	0.361593	−	0.932336i	$-0.382233\pi$
$432$	−0.267528	−	0.963550i	−0.0128715	−	0.0463588i
$433$	−38.7785	−	4.21741i	−1.86357	−	0.202676i	−0.894100	−	0.447867i	$-0.852184\pi$
$433$	−38.7785	−	4.21741i	−1.86357	−	0.202676i	−0.969475	+	0.245191i	$0.921149\pi$
$434$	−21.5382	+	16.3729i	−1.03387	+	0.785924i
$435$	−13.8523	+	6.40876i	−0.664167	+	0.307277i
$436$	10.8667	−	16.0271i	0.520419	−	0.767560i
$437$	6.18507	+	2.08399i	0.295872	+	0.0996909i
$438$	2.02355	−	12.3431i	0.0966888	−	0.589776i
$439$	−3.88076	−	23.6716i	−0.185218	−	1.12978i	−0.901760	−	0.432238i	$-0.857724\pi$
$439$	−3.88076	−	23.6716i	−0.185218	−	1.12978i	0.716541	−	0.697545i	$-0.245724\pi$
$440$	3.76748	−	1.26941i	0.179608	−	0.0605169i
$441$	1.90568	−	6.86364i	0.0907467	−	0.326840i
$442$	−2.68960	+	6.75038i	−0.127931	+	0.321083i
$443$	10.9021	−	27.3622i	0.517975	−	1.30002i	−0.404703	−	0.914448i	$-0.632625\pi$
$443$	10.9021	−	27.3622i	0.517975	−	1.30002i	0.922678	−	0.385571i	$-0.125996\pi$
$444$	1.32151	−	4.75964i	0.0627160	−	0.225883i
$445$	53.3564	−	17.9779i	2.52934	−	0.852233i
$446$	2.16276	+	13.1922i	0.102410	+	0.624671i
$447$	2.50507	−	15.2803i	0.118486	−	0.722731i
$448$	3.56137	+	1.19997i	0.168259	+	0.0566931i
$449$	10.1638	−	14.9904i	0.479657	−	0.707441i	−0.508470	−	0.861080i	$-0.669789\pi$
$449$	10.1638	−	14.9904i	0.479657	−	0.707441i	0.988127	+	0.153638i	$0.0490991\pi$
$450$	−4.99273	+	2.30988i	−0.235359	+	0.108889i
$451$	−4.33046	+	3.29193i	−0.203913	+	0.155011i
$452$	3.99103	+	0.434050i	0.187722	+	0.0204160i
$453$	2.80624	+	10.1072i	0.131849	+	0.474875i
$454$	−7.38411	−	10.8908i	−0.346554	−	0.511128i
$455$	−40.4767	−	24.3540i	−1.89758	−	1.14173i
$456$	−0.113082	+	2.08568i	−0.00529556	+	0.0976709i
$457$	−6.50037	−	6.15747i	−0.304074	−	0.288035i	0.520413	−	0.853915i	$-0.325778\pi$
$457$	−6.50037	−	6.15747i	−0.304074	−	0.288035i	−0.824488	+	0.565880i	$0.808537\pi$
$458$	−17.9958	−	13.6800i	−0.840887	−	0.639225i
$459$	1.82953	+	0.402710i	0.0853951	+	0.0187969i
$460$	−6.55530	+	7.71749i	−0.305642	+	0.359830i
$461$	1.28987	+	23.7902i	0.0600750	+	1.10802i	0.860786	+	0.508968i	$0.169973\pi$
$461$	1.28987	+	23.7902i	0.0600750	+	1.10802i	−0.800711	+	0.599051i	$0.795545\pi$
$462$	2.15961	−	4.07346i	0.100474	−	0.189514i
$463$	4.70491	−	1.03563i	0.218656	−	0.0481298i	−0.104291	−	0.994547i	$-0.533257\pi$
$463$	4.70491	−	1.03563i	0.218656	−	0.0481298i	0.322947	+	0.946417i	$0.395326\pi$
$464$	−4.27468	−	1.97768i	−0.198447	−	0.0918113i
$465$	19.9896	−	12.0274i	0.926997	−	0.557755i
$466$	−1.01166	−	1.90819i	−0.0468643	−	0.0883954i
$467$	2.21589	+	2.60874i	0.102539	+	0.120718i	0.811038	−	0.584994i	$-0.198903\pi$
$467$	2.21589	+	2.60874i	0.102539	+	0.120718i	−0.708499	+	0.705712i	$0.750627\pi$
$468$	−2.81607	+	2.66753i	−0.130173	+	0.123306i
$469$	44.9956	−	4.89356i	2.07770	−	0.225964i
$470$	15.8097	+	39.6794i	0.729248	+	1.83027i
$471$	11.9231			0.549387
$472$	−5.11798	+	5.72768i	−0.235574	+	0.263638i
$473$	−6.11835			−0.281322
$474$	3.09768	+	7.77459i	0.142281	+	0.357099i
$475$	11.4232	−	1.24235i	0.524131	−	0.0570027i
$476$	−5.11111	+	4.84150i	−0.234267	+	0.221910i
$477$	5.21536	+	6.13999i	0.238795	+	0.281131i
$478$	3.82637	+	7.21730i	0.175014	+	0.330112i
$479$	−0.132562	+	0.0797599i	−0.00605691	+	0.00364432i	−0.518579	−	0.855030i	$-0.673539\pi$
$479$	−0.132562	+	0.0797599i	−0.00605691	+	0.00364432i	0.512522	+	0.858674i	$0.328711\pi$
$480$	−2.94104	−	1.36067i	−0.134240	−	0.0621059i
$481$	−18.7127	+	4.11897i	−0.853224	+	0.187809i
$482$	13.4566	−	25.3818i	0.612929	−	1.15611i
$483$	0.635752	+	11.7257i	0.0289277	+	0.533540i
$484$	−6.14687	+	7.23665i	−0.279403	+	0.328939i
$485$	15.9008	+	3.50003i	0.722018	+	0.158928i
$486$	0.796093	+	0.605174i	0.0361115	+	0.0274513i
$487$	15.5602	+	14.7394i	0.705101	+	0.667907i	0.953721	−	0.300694i	$-0.0972183\pi$
$487$	15.5602	+	14.7394i	0.705101	+	0.667907i	−0.248620	+	0.968601i	$0.579977\pi$
$488$	0.516147	−	9.51976i	0.0233649	−	0.430939i
$489$	7.38661	+	4.44438i	0.334034	+	0.200982i
$490$	−12.9541	−	19.1059i	−0.585206	−	0.863115i
$491$	2.35930	+	8.49744i	0.106474	+	0.383484i	0.997516	−	0.0704358i	$-0.0224390\pi$
$491$	2.35930	+	8.49744i	0.106474	+	0.383484i	−0.891042	+	0.453920i	$0.850025\pi$
$492$	4.40792	+	0.479390i	0.198724	+	0.0216126i
$493$	7.02421	−	5.33967i	0.316355	−	0.240487i
$494$	7.35322	−	3.40196i	0.330837	−	0.153062i
$495$	−2.23105	+	3.29055i	−0.100278	+	0.147899i
$496$	6.82224	+	2.29868i	0.306327	+	0.103214i
$497$	2.14606	−	13.0904i	0.0962638	−	0.587183i
$498$	0.444147	+	2.70918i	0.0199027	+	0.121401i
$499$	10.6628	−	3.59273i	0.477334	−	0.160833i	−0.0703422	−	0.997523i	$-0.522409\pi$
$499$	10.6628	−	3.59273i	0.477334	−	0.160833i	0.547676	+	0.836690i	$0.315513\pi$
$500$	−0.434486	+	1.56488i	−0.0194308	+	0.0699834i
$501$	−2.16987	+	5.44595i	−0.0969424	+	0.243307i
$502$	8.73112	−	21.9135i	0.389689	−	0.978045i
$503$	7.65579	−	27.5737i	0.341355	−	1.22945i	−0.571308	−	0.820736i	$-0.693564\pi$
$503$	7.65579	−	27.5737i	0.341355	−	1.22945i	0.912663	−	0.408713i	$-0.134022\pi$
$504$	−3.56137	+	1.19997i	−0.158636	+	0.0534507i
$505$	6.73555	+	41.0851i	0.299728	+	1.82826i
$506$	−0.620188	+	3.78298i	−0.0275707	+	0.168174i
$507$	1.93886	+	0.653277i	0.0861077	+	0.0290130i
$508$	7.06578	−	10.4212i	0.313493	−	0.462368i
$509$	−15.6893	+	7.25866i	−0.695417	+	0.321734i	−0.735560	−	0.677460i	$-0.763081\pi$
$509$	−15.6893	+	7.25866i	−0.695417	+	0.321734i	0.0401426	+	0.999194i	$0.487219\pi$
$510$	4.83277	−	3.67377i	0.213999	−	0.162677i
$511$	−46.7302	−	5.08222i	−2.06722	−	0.224824i
$512$	−0.267528	−	0.963550i	−0.0118232	−	0.0425833i
$513$	−1.17218	−	1.72883i	−0.0517528	−	0.0763297i
$514$	15.6269	+	9.40241i	0.689274	+	0.414723i
$515$	−1.30973	+	24.1565i	−0.0577134	+	1.06446i
$516$	3.62064	+	3.42965i	0.159390	+	0.150982i
$517$	12.8733	+	9.78599i	0.566165	+	0.430388i
$518$	−18.1298	−	3.99068i	−0.796579	−	0.175340i
$519$	12.1561	−	14.3113i	0.533594	−	0.628196i
$520$	0.680516	+	12.5514i	0.0298426	+	0.550414i
$521$	−12.8423	+	24.2232i	−0.562632	+	1.06124i	0.425110	+	0.905142i	$0.360235\pi$
$521$	−12.8423	+	24.2232i	−0.562632	+	1.06124i	−0.987742	+	0.156095i	$0.950109\pi$
$522$	4.59988	−	1.01251i	0.201331	−	0.0443164i
$523$	−18.0479	−	8.34984i	−0.789179	−	0.365113i	−0.0164627	−	0.999864i	$-0.505240\pi$
$523$	−18.0479	−	8.34984i	−0.789179	−	0.365113i	−0.772717	+	0.634751i	$0.781103\pi$
$524$	−11.7646	+	7.07854i	−0.513940	+	0.309227i
$525$	9.68385	+	18.2657i	0.422638	+	0.797179i
$526$	15.3564	+	18.0789i	0.669570	+	0.788279i
$527$	−9.79094	+	9.27447i	−0.426500	+	0.404002i
$528$	−1.21963	+	0.132643i	−0.0530778	+	0.00577256i
$529$	4.89921	+	12.2961i	0.213009	+	0.534613i
$530$	26.1059			1.13397
$531$	0.608145	−	7.65703i	0.0263913	−	0.332287i
$532$	7.84970			0.340328
$533$	−6.36592	−	15.9772i	−0.275738	−	0.692051i
$534$	−17.2729	+	1.87854i	−0.747471	+	0.0812924i
$535$	37.9531	−	35.9511i	1.64086	−	1.55430i
$536$	−7.79684	−	9.17915i	−0.336772	−	0.396479i
$537$	−0.686769	−	1.29538i	−0.0296363	−	0.0558999i
$538$	3.15480	−	1.89818i	0.136013	−	0.0818364i
$539$	−7.93133	−	3.66943i	−0.341627	−	0.158053i
$540$	3.16479	−	0.696623i	0.136191	−	0.0299779i
$541$	−7.04708	+	13.2922i	−0.302978	+	0.571477i	−0.987519	−	0.157497i	$-0.949658\pi$
$541$	−7.04708	+	13.2922i	−0.302978	+	0.571477i	0.684542	+	0.728974i	$0.260002\pi$
$542$	−1.26224	−	23.2807i	−0.0542180	−	0.999991i
$543$	−2.31622	+	2.72687i	−0.0993986	+	0.117021i
$544$	1.82953	+	0.402710i	0.0784404	+	0.0172660i
$545$	49.9541	+	37.9741i	2.13980	+	1.62663i
$546$	10.5831	+	10.0248i	0.452914	+	0.429023i
$547$	1.21458	−	22.4015i	0.0519315	−	0.957821i	−0.850227	−	0.526416i	$-0.823535\pi$
$547$	1.21458	−	22.4015i	0.0519315	−	0.957821i	0.902159	−	0.431404i	$-0.141982\pi$
$548$	−6.42388	−	3.86512i	−0.274414	−	0.165110i
$549$	5.35021	+	7.89098i	0.228342	+	0.336779i
$550$	1.80554	+	6.50298i	0.0769887	+	0.277288i
$551$	−9.78030	−	1.06367i	−0.416655	−	0.0453139i
$552$	2.48756	−	1.89100i	0.105878	−	0.0804861i
$553$	28.5446	−	13.2061i	1.21384	−	0.561581i
$554$	14.0507	−	20.7232i	0.596957	−	0.880446i
$555$	15.1694	+	5.11117i	0.643905	+	0.216957i
$556$	−2.82013	+	17.2020i	−0.119600	+	0.729528i
$557$	0.660723	+	4.03023i	0.0279957	+	0.170766i	0.997124	−	0.0757920i	$-0.0241485\pi$
$557$	0.660723	+	4.03023i	0.0279957	+	0.170766i	−0.969128	+	0.246559i	$0.920700\pi$
$558$	−6.82224	+	2.29868i	−0.288808	+	0.0973109i
$559$	5.17524	−	18.6395i	0.218889	−	0.788369i
$560$	−4.50765	+	11.3134i	−0.190483	+	0.478077i
$561$	0.850668	−	2.13502i	0.0359152	−	0.0901404i
$562$	−1.44331	+	5.19834i	−0.0608824	+	0.219279i
$563$	15.6846	−	5.28477i	0.661029	−	0.222727i	0.0312626	−	0.999511i	$-0.490047\pi$
$563$	15.6846	−	5.28477i	0.661029	−	0.222727i	0.629766	+	0.776785i	$0.283151\pi$
$564$	−2.13241	−	13.0072i	−0.0897909	−	0.547700i
$565$	−2.10469	+	12.8380i	−0.0885448	+	0.540099i
$566$	23.4216	+	7.89167i	0.984484	+	0.331711i
$567$	2.10899	−	3.11053i	0.0885695	−	0.130630i
$568$	−3.20351	+	1.48210i	−0.134416	+	0.0621876i
$569$	5.05562	−	3.84318i	0.211943	−	0.161115i	−0.493817	−	0.869566i	$-0.664399\pi$
$569$	5.05562	−	3.84318i	0.211943	−	0.161115i	0.705760	+	0.708451i	$0.250606\pi$
$570$	−6.72900	−	0.731823i	−0.281847	−	0.0306527i
$571$	−2.38502	−	8.59006i	−0.0998099	−	0.359483i	0.896732	−	0.442574i	$-0.145935\pi$
$571$	−2.38502	−	8.59006i	−0.0998099	−	0.359483i	−0.996542	+	0.0830910i	$0.973521\pi$
$572$	2.67055	+	3.93877i	0.111661	+	0.164688i
$573$	9.81652	+	5.90641i	0.410091	+	0.246744i
$574$	0.902120	−	16.6386i	0.0376538	−	0.694483i
$575$	−12.4796	−	11.8213i	−0.520434	−	0.492981i
$576$	0.796093	+	0.605174i	0.0331705	+	0.0252156i
$577$	−8.61347	−	1.89597i	−0.358584	−	0.0789302i	0.0320250	−	0.999487i	$-0.489804\pi$
$577$	−8.61347	−	1.89597i	−0.358584	−	0.0789302i	−0.390609	+	0.920557i	$0.627735\pi$
$578$	8.73366	−	10.2821i	0.363272	−	0.427677i
$579$	−0.352965	−	6.51005i	−0.0146687	−	0.270549i
$580$	7.14931	−	13.4850i	0.296859	−	0.559935i
$581$	10.0761	−	2.21791i	0.418025	−	0.0920143i
$582$	−4.55991	−	2.10964i	−0.189015	−	0.0874474i
$583$	8.46861	−	5.09539i	0.350734	−	0.211030i
$584$	5.85879	+	11.0508i	0.242438	+	0.457287i
$585$	−8.13752	−	9.58023i	−0.336445	−	0.396094i
$586$	11.6374	−	11.0235i	0.480736	−	0.455377i
$587$	−0.0426618	+	0.00463975i	−0.00176084	+	0.000191503i	−0.108999	−	0.994042i	$-0.534765\pi$
$587$	−0.0426618	+	0.00463975i	−0.00176084	+	0.000191503i	0.107239	+	0.994233i	$0.465799\pi$
$588$	2.63660	+	6.61737i	0.108732	+	0.272896i
$589$	15.0370			0.619591
$590$	−17.6357	−	17.5656i	−0.726051	−	0.723165i
$591$	15.0305			0.618271
$592$	1.82837	+	4.58886i	0.0751455	+	0.188601i
$593$	−36.7267	+	3.99427i	−1.50818	+	0.164025i	−0.824546	−	0.565795i	$-0.808569\pi$
$593$	−36.7267	+	3.99427i	−1.50818	+	0.164025i	−0.683639	+	0.729820i	$0.739604\pi$
$594$	0.890670	−	0.843688i	0.0365446	−	0.0346169i
$595$	−14.7694	−	17.3879i	−0.605487	−	0.712835i
$596$	7.25295	+	13.6805i	0.297092	+	0.560376i
$597$	−5.53875	+	3.33255i	−0.226686	+	0.136392i
$598$	−11.0003	−	5.08926i	−0.449834	−	0.208115i
$599$	−22.2842	+	4.90512i	−0.910507	+	0.200418i	−0.645439	−	0.763812i	$-0.723326\pi$
$599$	−22.2842	+	4.90512i	−0.910507	+	0.200418i	−0.265068	+	0.964230i	$0.585394\pi$
$600$	2.57680	−	4.86035i	0.105197	−	0.198423i
$601$	1.19645	+	22.0673i	0.0488044	+	0.900144i	0.915752	+	0.401744i	$0.131596\pi$
$601$	1.19645	+	22.0673i	0.0488044	+	0.900144i	−0.866948	+	0.498399i	$0.833921\pi$
$602$	12.1334	−	14.2845i	0.494520	−	0.582194i
$603$	11.7620	+	2.58901i	0.478985	+	0.105433i
$604$	−8.35061	−	6.34797i	−0.339782	−	0.258295i
$605$	−22.3379	−	21.1596i	−0.908166	−	0.860261i
$606$	0.695558	−	12.8288i	0.0282551	−	0.521135i
$607$	−9.36261	−	5.63330i	−0.380017	−	0.228649i	0.312710	−	0.949849i	$-0.398763\pi$
$607$	−9.36261	−	5.63330i	−0.380017	−	0.228649i	−0.692727	+	0.721200i	$0.743591\pi$
$608$	−1.17218	−	1.72883i	−0.0475380	−	0.0701133i
$609$	−4.73542	−	17.0554i	−0.191889	−	0.691121i
$610$	30.7135	+	3.34029i	1.24355	+	0.135244i
$611$	−40.7019	+	30.9408i	−1.64662	+	1.25173i
$612$	−1.70018	+	0.786589i	−0.0687259	+	0.0317960i
$613$	8.18248	−	12.0683i	0.330487	−	0.487432i	−0.625750	−	0.780023i	$-0.715207\pi$
$613$	8.18248	−	12.0683i	0.330487	−	0.487432i	0.956238	+	0.292591i	$0.0945174\pi$
$614$	12.4345	+	4.18966i	0.501814	+	0.169081i
$615$	−2.32454	+	14.1790i	−0.0937343	+	0.571754i
$616$	0.745901	+	4.54979i	0.0300532	+	0.183316i
$617$	21.7811	−	7.33890i	0.876873	−	0.295453i	0.155364	−	0.987857i	$-0.450345\pi$
$617$	21.7811	−	7.33890i	0.876873	−	0.295453i	0.721510	+	0.692404i	$0.243449\pi$
$618$	1.99720	−	7.19327i	0.0803392	−	0.289356i
$619$	12.6882	−	31.8451i	0.509983	−	1.27996i	−0.418375	−	0.908274i	$-0.637400\pi$
$619$	12.6882	−	31.8451i	0.509983	−	1.27996i	0.928358	−	0.371687i	$-0.121220\pi$
$620$	−8.63496	+	21.6721i	−0.346788	+	0.870373i
$621$	−0.835949	+	3.01082i	−0.0335455	+	0.120820i
$622$	1.79076	−	0.603378i	0.0718030	−	0.0241932i
$623$	10.5637	+	64.4358i	0.423226	+	2.58157i
$624$	0.627538	−	3.82781i	0.0251216	−	0.153235i
$625$	21.0786	+	7.10221i	0.843145	+	0.284089i
$626$	9.08705	−	13.4024i	0.363191	−	0.535667i
$627$	−2.32568	+	1.07598i	−0.0928789	+	0.0429704i
$628$	−9.49190	+	7.21555i	−0.378768	+	0.287932i
$629$	−9.19941	−	1.00050i	−0.366805	−	0.0398924i
$630$	−3.25804	−	11.7344i	−0.129803	−	0.467510i
$631$	16.7230	+	24.6646i	0.665734	+	0.981883i	0.999234	+	0.0391335i	$0.0124598\pi$
$631$	16.7230	+	24.6646i	0.665734	+	0.981883i	−0.333500	+	0.942750i	$0.608230\pi$
$632$	−7.17102	−	4.31466i	−0.285248	−	0.171628i
$633$	−0.847255	+	15.6267i	−0.0336754	+	0.621105i
$634$	−17.9201	−	16.9749i	−0.711700	−	0.674158i
$635$	32.4814	+	24.6917i	1.28899	+	0.979862i
$636$	−7.86767	−	1.73181i	−0.311974	−	0.0686706i
$637$	17.8877	−	21.0590i	0.708735	−	0.834388i
$638$	−0.312833	−	5.76987i	−0.0123852	−	0.228431i
$639$	1.65336	−	3.11857i	0.0654060	−	0.123369i
$640$	3.16479	−	0.696623i	0.125099	−	0.0275364i
$641$	−5.76531	−	2.66731i	−0.227716	−	0.105353i	0.302714	−	0.953081i	$-0.402107\pi$
$641$	−5.76531	−	2.66731i	−0.227716	−	0.105353i	−0.530430	+	0.847729i	$0.677969\pi$
$642$	−13.8230	+	8.31703i	−0.545551	+	0.328247i
$643$	−11.4782	−	21.6502i	−0.452656	−	0.853801i	−0.999859	−	0.0168002i	$-0.994652\pi$
$643$	−11.4782	−	21.6502i	−0.452656	−	0.853801i	0.547202	−	0.837000i	$-0.315693\pi$
$644$	−7.60224	−	8.95005i	−0.299570	−	0.352681i
$645$	−11.7329	+	11.1140i	−0.461981	+	0.437612i
$646$	3.88996	−	0.423058i	0.153048	−	0.0166450i
$647$	0.774651	+	1.94423i	0.0304547	+	0.0764355i	0.943418	−	0.331607i	$-0.107591\pi$
$647$	0.774651	+	1.94423i	0.0304547	+	0.0764355i	−0.912963	+	0.408043i	$0.866212\pi$
$648$	−1.00000			−0.0392837
$649$	−9.14940	−	2.25602i	−0.359145	−	0.0885564i
$650$	−21.3386			−0.836967
$651$	10.0140	+	25.1333i	0.392481	+	0.985053i
$652$	−8.57005	+	0.932050i	−0.335629	+	0.0365019i
$653$	12.9661	−	12.2822i	0.507405	−	0.480639i	−0.390640	−	0.920543i	$-0.627746\pi$
$653$	12.9661	−	12.2822i	0.507405	−	0.480639i	0.898045	+	0.439904i	$0.144988\pi$
$654$	−12.5358	−	14.7583i	−0.490188	−	0.577094i
$655$	−20.8407	−	39.3098i	−0.814315	−	1.53596i
$656$	−3.79923	+	2.28592i	−0.148335	+	0.0892502i
$657$	−11.3518	−	5.25192i	−0.442877	−	0.204897i
$658$	−48.3766	+	10.6485i	−1.88592	+	0.415121i
$659$	11.2486	−	21.2172i	0.438184	−	0.826503i	−0.561815	−	0.827263i	$-0.689897\pi$
$659$	11.2486	−	21.2172i	0.438184	−	0.826503i	1.00000		0.000759319i	$0.000241699\pi$
$660$	−0.215234	−	3.96976i	−0.00837798	−	0.154523i
$661$	−27.0952	+	31.8990i	−1.05388	+	1.24073i	−0.0841764	+	0.996451i	$0.526826\pi$
$661$	−27.0952	+	31.8990i	−1.05388	+	1.24073i	−0.969706	+	0.244275i	$0.921450\pi$
$662$	−35.4049	−	7.79321i	−1.37605	−	0.302892i
$663$	5.78478	+	4.39748i	0.224662	+	0.170784i
$664$	−1.99311	−	1.88797i	−0.0773476	−	0.0732675i
$665$	−1.37715	+	25.4000i	−0.0534036	+	0.984971i
$666$	−4.23261	−	2.54668i	−0.164010	−	0.0986818i
$667$	8.25920	+	12.1814i	0.319798	+	0.471666i
$668$	−1.56833	−	5.64863i	−0.0606807	−	0.218552i
$669$	13.2900	+	1.44537i	0.513821	+	0.0558814i
$670$	31.0698	−	23.6186i	1.20033	−	0.912467i
$671$	10.6152	−	4.91113i	0.409796	−	0.189592i
$672$	2.10899	−	3.11053i	0.0813562	−	0.119991i
$673$	45.8819	+	15.4594i	1.76862	+	0.595916i	0.999088	−	0.0426964i	$-0.0135948\pi$
$673$	45.8819	+	15.4594i	1.76862	+	0.595916i	0.769528	+	0.638613i	$0.220491\pi$
$674$	1.67939	−	10.2438i	0.0646876	−	0.394577i
$675$	0.889991	+	5.42870i	0.0342558	+	0.208951i
$676$	−1.93886	+	0.653277i	−0.0745714	+	0.0251260i
$677$	−2.57475	+	9.27340i	−0.0989555	+	0.356406i	−0.996406	−	0.0847105i	$-0.973003\pi$
$677$	−2.57475	+	9.27340i	−0.0989555	+	0.356406i	0.897450	+	0.441116i	$0.145417\pi$
$678$	1.48594	−	3.72943i	0.0570673	−	0.143228i
$679$	−6.98885	+	17.5407i	−0.268207	+	0.673150i
$680$	−1.62406	+	5.84933i	−0.0622798	+	0.224312i
$681$	−12.4692	+	4.20138i	−0.477822	+	0.160997i
$682$	1.42886	+	8.71568i	0.0547140	+	0.333741i
$683$	1.68089	−	10.2530i	0.0643176	−	0.392320i	−0.934975	−	0.354714i	$-0.884578\pi$
$683$	1.68089	−	10.2530i	0.0643176	−	0.392320i	0.999293	−	0.0376065i	$-0.0119733\pi$
$684$	1.97940	+	0.666939i	0.0756844	+	0.0255010i
$685$	13.6337	−	20.1083i	0.520919	−	0.768298i
$686$	0.420499	−	0.194543i	0.0160547	−	0.00742770i
$687$	−17.9958	+	13.6800i	−0.686581	+	0.521925i
$688$	−4.95790	−	0.539204i	−0.189018	−	0.0205570i
$689$	8.35988	+	30.1096i	0.318486	+	1.14708i
$690$	5.68246	+	8.38101i	0.216328	+	0.319059i
$691$	3.74609	+	2.25395i	0.142508	+	0.0857442i	0.585022	−	0.811017i	$-0.301086\pi$
$691$	3.74609	+	2.25395i	0.142508	+	0.0857442i	−0.442514	+	0.896761i	$0.645913\pi$
$692$	−1.01658	+	18.7497i	−0.0386445	+	0.712756i
$693$	−3.34722	−	3.17066i	−0.127151	−	0.120443i
$694$	−1.61301	−	1.22618i	−0.0612292	−	0.0465452i
$695$	−55.1675	−	12.1433i	−2.09262	−	0.460621i
$696$	−3.04919	+	3.58978i	−0.115579	+	0.136070i
$697$	−0.449687	−	8.29398i	−0.0170331	−	0.314157i
$698$	4.94604	−	9.32922i	0.187210	−	0.353116i
$699$	−2.10929	+	0.464290i	−0.0797806	+	0.0175610i
$700$	−18.7632	−	8.68076i	−0.709181	−	0.328102i
$701$	−11.4383	+	6.88218i	−0.432018	+	0.259936i	−0.714912	−	0.699215i	$-0.753533\pi$
$701$	−11.4383	+	6.88218i	−0.432018	+	0.259936i	0.282894	+	0.959151i	$0.408706\pi$
$702$	1.81692	+	3.42707i	0.0685750	+	0.129346i
$703$	6.67957	+	7.86380i	0.251925	+	0.296589i
$704$	0.890670	−	0.843688i	0.0335684	−	0.0317977i
$705$	42.4626	−	4.61809i	1.59924	−	0.173927i
$706$	7.84853	+	19.6983i	0.295383	+	0.741356i
$707$	−48.2828			−1.81586
$708$	4.14970	+	6.46375i	0.155955	+	0.242922i
$709$	25.3156			0.950748			0.475374	−	0.879784i	$-0.342313\pi$
$709$	25.3156			0.950748			0.475374	+	0.879784i	$0.342313\pi$
$710$	−4.23376	−	10.6259i	−0.158890	−	0.398784i
$711$	8.31992	−	0.904846i	0.312022	−	0.0339344i
$712$	12.6140	−	11.9486i	0.472729	−	0.447793i
$713$	−14.5630	−	17.1449i	−0.545389	−	0.642081i
$714$	3.29766	+	6.22005i	0.123412	+	0.232779i
$715$	−13.2136	+	7.95034i	−0.494160	+	0.297326i
$716$	1.33067	+	0.615631i	0.0497293	+	0.0230072i
$717$	7.97789	−	1.75607i	0.297940	−	0.0655815i
$718$	−11.6686	+	22.0092i	−0.435467	+	0.821378i
$719$	1.65470	+	30.5192i	0.0617099	+	1.13817i	0.851349	+	0.524600i	$0.175785\pi$
$719$	1.65470	+	30.5192i	0.0617099	+	1.13817i	−0.789639	+	0.613572i	$0.789732\pi$
$720$	−2.09789	+	2.46983i	−0.0781837	+	0.0920449i
$721$	−27.3997	−	6.03113i	−1.02042	−	0.224611i
$722$	11.6525	+	8.85803i	0.433662	+	0.329662i
$723$	−20.8566	−	19.7564i	−0.775664	−	0.734748i
$724$	0.193698	−	3.57256i	0.00719874	−	0.132773i
$725$	22.2016	+	13.3583i	0.824547	+	0.496113i
$726$	5.32841	+	7.85882i	0.197756	+	0.291668i
$727$	9.61046	+	34.6137i	0.356432	+	1.28375i	0.896842	+	0.442351i	$0.145855\pi$
$727$	9.61046	+	34.6137i	0.356432	+	1.28375i	−0.540410	+	0.841402i	$0.681731\pi$
$728$	−14.4919	−	1.57609i	−0.537104	−	0.0584136i
$729$	0.796093	−	0.605174i	0.0294849	−	0.0224139i
$730$	−36.7862	+	17.0191i	−1.36152	+	0.629905i
$731$	5.24291	−	7.73271i	0.193916	−	0.286005i
$732$	−9.03468	−	3.04414i	−0.333932	−	0.112515i
$733$	3.92941	−	23.9684i	0.145136	−	0.885291i	−0.809413	−	0.587239i	$-0.800215\pi$
$733$	3.92941	−	23.9684i	0.145136	−	0.885291i	0.954550	−	0.298052i	$-0.0963369\pi$
$734$	1.86645	+	11.3849i	0.0688921	+	0.420223i
$735$	−21.8750	+	7.37056i	−0.806873	+	0.271867i
$736$	−0.835949	+	3.01082i	−0.0308135	+	0.110980i
$737$	5.46893	−	13.7260i	0.201450	−	0.505602i
$738$	1.64116	−	4.11900i	0.0604119	−	0.151623i
$739$	4.09891	−	14.7629i	0.150781	−	0.543063i	−0.849109	−	0.528218i	$-0.822861\pi$
$739$	4.09891	−	14.7629i	0.150781	−	0.543063i	0.999890	−	0.0148456i	$-0.00472568\pi$
$740$	−15.1694	+	5.11117i	−0.557638	+	0.187890i
$741$	−1.31077	−	7.99532i	−0.0481522	−	0.293715i
$742$	−4.89800	+	29.8765i	−0.179811	+	1.09680i
$743$	−38.9274	−	13.1162i	−1.42811	−	0.481186i	−0.504130	−	0.863628i	$-0.668187\pi$
$743$	−38.9274	−	13.1162i	−1.42811	−	0.481186i	−0.923980	+	0.382442i	$0.875083\pi$
$744$	4.04003	−	5.95860i	0.148115	−	0.218453i
$745$	−45.5398	+	21.0690i	−1.66845	+	0.771907i
$746$	5.26804	−	4.00466i	0.192877	−	0.146621i
$747$	2.72925	+	0.296824i	0.0998581	+	0.0108602i
$748$	0.614846	+	2.21447i	0.0224810	+	0.0809692i
$749$	34.0228	+	50.1799i	1.24317	+	1.83353i
$750$	1.39160	+	0.837298i	0.0508140	+	0.0305738i
$751$	−2.44706	+	45.1334i	−0.0892946	+	1.64694i	0.520122	+	0.854092i	$0.325886\pi$
$751$	−2.44706	+	45.1334i	−0.0892946	+	1.64694i	−0.609417	+	0.792850i	$0.708596\pi$
$752$	9.56919	+	9.06442i	0.348953	+	0.330545i
$753$	−18.7789	−	14.2753i	−0.684341	−	0.520222i
$754$	17.8425	+	3.92744i	0.649786	+	0.143029i
$755$	22.0058	−	25.9072i	0.800873	−	0.942860i
$756$	0.203459	+	3.75258i	0.00739974	+	0.136480i
$757$	−24.2707	+	45.7794i	−0.882134	+	1.66388i	−0.143631	+	0.989631i	$0.545878\pi$
$757$	−24.2707	+	45.7794i	−0.882134	+	1.66388i	−0.738503	+	0.674250i	$0.764467\pi$
$758$	31.0699	−	6.83901i	1.12851	−	0.248404i
$759$	3.47917	+	1.60964i	0.126286	+	0.0584261i
$760$	5.79979	−	3.48962i	0.210381	−	0.126582i
$761$	−6.58444	−	12.4196i	−0.238686	−	0.450209i	0.735012	−	0.678054i	$-0.237177\pi$
$761$	−6.58444	−	12.4196i	−0.238686	−	0.450209i	−0.973697	+	0.227846i	$0.926832\pi$
$762$	−8.15109	−	9.59621i	−0.295283	−	0.347634i
$763$	−52.8312	+	50.0443i	−1.91262	+	1.81173i
$764$	−11.3893	+	1.23866i	−0.412049	+	0.0448131i
$765$	−2.24696	−	5.63945i	−0.0812391	−	0.203895i
$766$	−32.3385			−1.16844
$767$	14.6120	−	25.9654i	0.527610	−	0.937555i
$768$	−1.00000			−0.0360844
$769$	−3.90765	−	9.80747i	−0.140914	−	0.353666i	0.841534	−	0.540204i	$-0.181653\pi$
$769$	−3.90765	−	9.80747i	−0.140914	−	0.353666i	−0.982448	+	0.186537i	$0.940273\pi$
$770$	−14.8531	+	1.61537i	−0.535268	+	0.0582139i
$771$	13.2403	−	12.5419i	0.476839	−	0.451686i
$772$	4.22071	+	4.96900i	0.151907	+	0.178838i
$773$	−3.17328	−	5.98543i	−0.114135	−	0.215281i	0.819863	−	0.572560i	$-0.194050\pi$
$773$	−3.17328	−	5.98543i	−0.114135	−	0.215281i	−0.933998	+	0.357279i	$0.883705\pi$
$774$	4.27326	−	2.57114i	0.153599	−	0.0924176i
$775$	−35.9431	−	16.6290i	−1.29111	−	0.597333i
$776$	4.90682	−	1.08007i	0.176144	−	0.0387723i
$777$	−8.69546	+	16.4014i	−0.311948	+	0.588396i
$778$	−0.515399	−	9.50597i	−0.0184779	−	0.340805i
$779$	−5.99564	+	7.05862i	−0.214816	+	0.252901i
$780$	12.2759	+	2.70214i	0.439549	+	0.0967521i
$781$	−3.44739	−	2.62064i	−0.123357	−	0.0937738i
$782$	−4.24969	−	4.02552i	−0.151969	−	0.143952i
$783$	0.254994	−	4.70309i	0.00911274	−	0.168075i
$784$	−6.10364	−	3.67244i	−0.217987	−	0.131158i
$785$	−21.6828	−	31.9798i	−0.773893	−	1.14141i
$786$	3.67316	+	13.2295i	0.131017	+	0.471881i
$787$	−8.00730	−	0.870847i	−0.285429	−	0.0310423i	−0.0357156	−	0.999362i	$-0.511371\pi$
$787$	−8.00730	−	0.870847i	−0.285429	−	0.0310423i	−0.249714	+	0.968320i	$0.580337\pi$
$788$	−11.9657	+	9.09606i	−0.426259	+	0.324034i
$789$	21.5282	−	9.96002i	0.766425	−	0.354586i
$790$	15.2195	−	22.4470i	0.541484	−	0.798629i
$791$	−14.2973	−	4.81734i	−0.508355	−	0.171285i
$792$	−0.198478	+	1.21066i	−0.00705262	+	0.0430191i
$793$	5.98279	+	36.4934i	0.212455	+	1.29592i
$794$	19.6953	−	6.63611i	0.698959	−	0.235507i
$795$	6.98408	−	25.1544i	0.247700	−	0.892134i
$796$	2.39258	−	6.00493i	0.0848029	−	0.212839i
$797$	9.88412	−	24.8073i	0.350114	−	0.878719i	−0.643455	−	0.765484i	$-0.722499\pi$
$797$	9.88412	−	24.8073i	0.350114	−	0.878719i	0.993568	−	0.113235i	$-0.0361212\pi$
$798$	2.10002	−	7.56358i	0.0743398	−	0.267748i
$799$	−23.3994	+	7.88416i	−0.827810	+	0.278922i
$800$	0.889991	+	5.42870i	0.0314659	+	0.191934i
$801$	−2.81092	+	17.1459i	−0.0993190	+	0.605819i
$802$	−11.4615	−	3.86182i	−0.404719	−	0.136366i
$803$	−8.61140	+	12.7009i	−0.303890	+	0.448204i
$804$	−10.9304	+	5.05696i	−0.385487	+	0.178345i
$805$	30.2943	−	23.0291i	1.06773	−	0.811670i
$806$	−27.7609	−	3.01918i	−0.977837	−	0.106346i
$807$	−0.984994	−	3.54763i	−0.0346734	−	0.124882i
$808$	7.20994	+	10.6339i	0.253645	+	0.374098i
$809$	−18.4837	−	11.1213i	−0.649851	−	0.391003i	0.152123	−	0.988362i	$-0.451389\pi$
$809$	−18.4837	−	11.1213i	−0.649851	−	0.391003i	−0.801974	+	0.597359i	$0.796217\pi$
$810$	0.175440	−	3.23580i	0.00616433	−	0.113694i
$811$	23.5032	+	22.2634i	0.825309	+	0.781774i	0.978462	−	0.206429i	$-0.0661842\pi$
$811$	23.5032	+	22.2634i	0.825309	+	0.781774i	−0.153153	+	0.988202i	$0.548943\pi$
$812$	14.0913	+	10.7120i	0.494509	+	0.375916i
$813$	−22.7698	−	5.01201i	−0.798572	−	0.175779i
$814$	−3.92326	+	4.61881i	−0.137510	+	0.161889i
$815$	−1.51240	−	27.8945i	−0.0529769	−	0.977101i
$816$	0.877481	−	1.65511i	0.0307180	−	0.0579403i
$817$	−10.1733	+	2.23931i	−0.355919	+	0.0783437i
$818$	−13.9756	−	6.46578i	−0.488644	−	0.226071i
$819$	12.4907	−	7.51540i	0.436460	−	0.262609i
$820$	−6.73024	−	12.6946i	−0.235030	−	0.443314i
$821$	−5.95549	−	7.01135i	−0.207848	−	0.244698i	0.648354	−	0.761339i	$-0.275458\pi$
$821$	−5.95549	−	7.01135i	−0.207848	−	0.244698i	−0.856202	+	0.516642i	$0.827182\pi$
$822$	−5.44280	+	5.15570i	−0.189840	+	0.179826i
$823$	−29.3033	+	3.18693i	−1.02145	+	0.111089i	−0.603485	−	0.797374i	$-0.706222\pi$
$823$	−29.3033	+	3.18693i	−1.02145	+	0.111089i	−0.417964	+	0.908464i	$0.637256\pi$
$824$	2.76322	+	6.93516i	0.0962614	+	0.241598i
$825$	6.74898			0.234969
$826$	23.4115	−	16.8872i	0.814589	−	0.587581i
$827$	23.8687			0.829998			0.414999	−	0.909822i	$-0.363782\pi$
$827$	23.8687			0.829998			0.414999	+	0.909822i	$0.363782\pi$
$828$	−1.15658	−	2.90279i	−0.0401938	−	0.100879i
$829$	17.2195	−	1.87273i	0.598057	−	0.0650426i	0.195917	−	0.980621i	$-0.437232\pi$
$829$	17.2195	−	1.87273i	0.598057	−	0.0650426i	0.402141	+	0.915578i	$0.368266\pi$
$830$	6.45877	−	6.11807i	0.224187	−	0.212361i
$831$	−16.2089	−	19.0826i	−0.562281	−	0.661968i
$832$	1.81692	+	3.42707i	0.0629902	+	0.118812i
$833$	11.4341	−	6.87967i	0.396168	−	0.238366i
$834$	15.8205	+	7.31936i	0.547820	+	0.253449i
$835$	18.5530	−	4.08382i	0.642052	−	0.141326i
$836$	1.20031	−	2.26402i	0.0415135	−	0.0783028i
$837$	0.389751	+	7.18853i	0.0134718	+	0.248472i
$838$	−12.0024	+	14.1303i	−0.414616	+	0.488123i
$839$	37.9194	+	8.34670i	1.30912	+	0.288160i	0.814103	−	0.580721i	$-0.197229\pi$
$839$	37.9194	+	8.34670i	1.30912	+	0.288160i	0.495021	+	0.868881i	$0.335160\pi$
$840$	9.69506	+	7.36999i	0.334511	+	0.254289i
$841$	4.94834	+	4.68732i	0.170632	+	0.161632i
$842$	0.988140	−	18.2252i	0.0340535	−	0.628081i
$843$	4.62273	+	2.78140i	0.159215	+	0.0957967i
$844$	−8.78238	−	12.9530i	−0.302302	−	0.445862i
$845$	−1.77372	−	6.38836i	−0.0610178	−	0.219766i
$846$	−13.1035	−	1.42509i	−0.450508	−	0.0489957i
$847$	28.4068	−	21.5943i	0.976068	−	0.741988i
$848$	7.31145	−	3.38263i	0.251076	−	0.116160i
$849$	13.8700	−	20.4567i	0.476016	−	0.702071i
$850$	−9.76603	−	3.29056i	−0.334972	−	0.112865i
$851$	2.49713	−	15.2318i	0.0856004	−	0.522139i
$852$	0.571049	+	3.48325i	0.0195638	+	0.119334i
$853$	14.6093	−	4.92245i	0.500213	−	0.168541i	−0.0578740	−	0.998324i	$-0.518432\pi$
$853$	14.6093	−	4.92245i	0.500213	−	0.168541i	0.558087	+	0.829783i	$0.311536\pi$
$854$	−9.58520	+	34.5228i	−0.327999	+	1.18134i
$855$	−2.50535	+	6.28795i	−0.0856810	+	0.215043i
$856$	5.97115	−	14.9865i	0.204090	−	0.512227i
$857$	7.36982	−	26.5437i	0.251748	−	0.906716i	−0.724358	−	0.689424i	$-0.757864\pi$
$857$	7.36982	−	26.5437i	0.251748	−	0.906716i	0.976107	−	0.217292i	$-0.0697224\pi$
$858$	4.50965	−	1.51948i	0.153957	−	0.0518741i
$859$	−1.42566	−	8.69613i	−0.0486428	−	0.296708i	0.951290	−	0.308297i	$-0.0997592\pi$
$859$	−1.42566	−	8.69613i	−0.0486428	−	0.296708i	−0.999933	+	0.0115894i	$0.996311\pi$
$860$	2.61457	−	15.9482i	0.0891561	−	0.543828i
$861$	−15.7908	−	5.32054i	−0.538149	−	0.181324i
$862$	13.2528	−	19.5464i	0.451392	−	0.665754i
$863$	−25.2254	+	11.6705i	−0.858683	+	0.397269i	−0.799275	−	0.600965i	$-0.794783\pi$
$863$	−25.2254	+	11.6705i	−0.858683	+	0.397269i	−0.0594072	+	0.998234i	$0.518921\pi$
$864$	0.796093	−	0.605174i	0.0270836	−	0.0205884i
$865$	−60.4919	−	6.57889i	−2.05678	−	0.223689i
$866$	−10.4355	−	37.5853i	−0.354613	−	1.27720i
$867$	−7.57078	−	11.1661i	−0.257117	−	0.379219i
$868$	−23.1821	−	13.9482i	−0.786853	−	0.473434i
$869$	0.555860	−	10.2522i	0.0188563	−	0.347783i
$870$	−11.0809	−	10.4963i	−0.375676	−	0.355859i
$871$	37.1902	+	28.2713i	1.26014	+	0.957936i
$872$	18.9110	+	4.16262i	0.640407	+	0.140964i
$873$	−3.25265	+	3.82932i	−0.110086	+	0.129603i
$874$	0.353350	+	6.51715i	0.0119522	+	0.220446i
$875$	2.85890	−	5.39245i	0.0966483	−	0.182298i
$876$	12.2154	−	2.68882i	0.412721	−	0.0908469i
$877$	17.7744	+	8.22331i	0.600199	+	0.277681i	0.696370	−	0.717683i	$-0.254797\pi$
$877$	17.7744	+	8.22331i	0.600199	+	0.277681i	−0.0961710	+	0.995365i	$0.530660\pi$
$878$	20.5539	−	12.3669i	0.693661	−	0.417362i
$879$	−7.50837	−	14.1623i	−0.253251	−	0.477682i
$880$	2.57374	+	3.03005i	0.0867609	+	0.102143i
$881$	34.3896	−	32.5755i	1.15861	−	1.09750i	0.164813	−	0.986325i	$-0.447298\pi$
$881$	34.3896	−	32.5755i	1.15861	−	1.09750i	0.993801	−	0.111172i	$-0.0354606\pi$
$882$	7.08153	−	0.770163i	0.238447	−	0.0259327i
$883$	12.9929	+	32.6096i	0.437244	+	1.09740i	0.968239	+	0.250025i	$0.0804390\pi$
$883$	12.9929	+	32.6096i	0.437244	+	1.09740i	−0.530995	+	0.847375i	$0.678182\pi$
$884$	−7.26646			−0.244398
$885$	−21.6434	+	12.2936i	−0.727535	+	0.413245i
$886$	29.4542			0.989532
$887$	2.37986	+	5.97299i	0.0799078	+	0.200553i	0.963503	−	0.267699i	$-0.0862632\pi$
$887$	2.37986	+	5.97299i	0.0799078	+	0.200553i	−0.883595	+	0.468252i	$0.844884\pi$
$888$	4.91074	−	0.534075i	0.164794	−	0.0179224i
$889$	−34.3522	+	32.5401i	−1.15213	+	1.09136i
$890$	36.4503	+	42.9126i	1.22182	+	1.43843i
$891$	−0.574656	−	1.08392i	−0.0192517	−	0.0363125i
$892$	−11.4548	+	6.89211i	−0.383534	+	0.230765i
$893$	24.9867	+	11.5601i	0.836149	+	0.386844i
$894$	15.1222	−	3.32865i	0.505763	−	0.111327i
$895$	−2.22551	+	4.19776i	−0.0743906	+	0.140316i
$896$	0.203459	+	3.75258i	0.00679710	+	0.125365i
$897$	−7.84664	+	9.23777i	−0.261992	+	0.308440i
$898$	17.6877	+	3.89337i	0.590248	+	0.129923i
$899$	26.9937	+	20.5200i	0.900289	+	0.684382i
$900$	−3.99383	−	3.78315i	−0.133128	−	0.126105i
$901$	−0.817040	+	15.0694i	−0.0272195	+	0.502035i
$902$	−4.66100	−	2.80443i	−0.155194	−	0.0933772i
$903$	−10.5178	−	15.5127i	−0.350012	−	0.516229i
$904$	1.07401	+	3.86823i	0.0357210	+	0.128655i
$905$	11.5261	+	1.25354i	0.383140	+	0.0416690i
$906$	−8.35061	+	6.34797i	−0.277431	+	0.210897i
$907$	−2.46436	+	1.14014i	−0.0818278	+	0.0378576i	−0.460376	−	0.887724i	$-0.652285\pi$
$907$	−2.46436	+	1.14014i	−0.0818278	+	0.0378576i	0.378548	+	0.925582i	$0.376423\pi$
$908$	7.38411	−	10.8908i	0.245050	−	0.361422i
$909$	−12.1751	−	4.10228i	−0.403824	−	0.136064i
$910$	7.64235	−	46.6163i	0.253341	−	1.54531i
$911$	8.50510	+	51.8788i	0.281787	+	1.71882i	0.625908	+	0.779897i	$0.284729\pi$
$911$	8.50510	+	51.8788i	0.281787	+	1.71882i	−0.344121	+	0.938925i	$0.611823\pi$
$912$	−1.97940	+	0.666939i	−0.0655446	+	0.0220846i
$913$	0.901051	−	3.24529i	0.0298205	−	0.107404i
$914$	3.31412	−	8.31781i	0.109621	−	0.275129i
$915$	11.4353	−	28.7004i	0.378038	−	0.948804i
$916$	6.04750	−	21.7811i	0.199815	−	0.719669i
$917$	48.8975	−	16.4755i	1.61474	−	0.544069i
$918$	0.303070	+	1.84865i	0.0100028	+	0.0610145i
$919$	−3.64777	+	22.2504i	−0.120329	+	0.733973i	0.855886	+	0.517165i	$0.173013\pi$
$919$	−3.64777	+	22.2504i	−0.120329	+	0.733973i	−0.976214	+	0.216808i	$0.930436\pi$
$920$	−9.59574	−	3.23318i	−0.316362	−	0.106595i
$921$	7.36351	−	10.8604i	0.242636	−	0.357861i
$922$	−21.6231	+	10.0039i	−0.712119	+	0.329461i
$923$	10.8998	−	8.28578i	0.358770	−	0.272730i
$924$	4.58350	+	0.498486i	0.150786	+	0.0163990i
$925$	−7.26984	−	26.1836i	−0.239031	−	0.860912i
$926$	2.70354	+	3.98743i	0.0888440	+	0.131035i
$927$	−6.39677	−	3.84881i	−0.210097	−	0.126411i
$928$	0.254994	−	4.70309i	0.00837059	−	0.154386i
$929$	−10.3690	−	9.82208i	−0.340197	−	0.322252i	0.498459	−	0.866913i	$-0.333900\pi$
$929$	−10.3690	−	9.82208i	−0.340197	−	0.322252i	−0.838656	+	0.544662i	$0.816658\pi$
$930$	18.5721	+	14.1181i	0.609002	+	0.462951i
$931$	−14.5309	−	3.19848i	−0.476230	−	0.104826i
$932$	1.39821	−	1.64610i	0.0458000	−	0.0539200i
$933$	−0.102305	−	1.88691i	−0.00334932	−	0.0617746i
$934$	−1.60328	+	3.02410i	−0.0524609	+	0.0989517i
$935$	−7.27346	+	1.60101i	−0.237868	+	0.0523586i
$936$	−3.52040	−	1.62871i	−0.115068	−	0.0532361i
$937$	−35.9512	+	21.6311i	−1.17447	+	0.706657i	−0.962676	−	0.270657i	$-0.912759\pi$
$937$	−35.9512	+	21.6311i	−1.17447	+	0.706657i	−0.211797	+	0.977314i	$0.567932\pi$
$938$	21.2006	+	39.9885i	0.692223	+	1.30567i
$939$	−10.4828	−	12.3413i	−0.342094	−	0.402745i
$940$	−31.0095	+	29.3737i	−1.01142	+	0.958065i
$941$	58.7473	−	6.38915i	1.91511	−	0.208280i	0.928493	−	0.371350i	$-0.121105\pi$
$941$	58.7473	−	6.38915i	1.91511	−	0.208280i	0.986615	+	0.163070i	$0.0521395\pi$
$942$	4.41319	+	11.0763i	0.143790	+	0.360885i
$943$	13.8547			0.451171
$944$	−7.21524	−	2.63445i	−0.234836	−	0.0857441i
$945$	−12.1783			−0.396160
$946$	−2.26463	−	5.68380i	−0.0736296	−	0.184796i
$947$	17.3818	−	1.89039i	0.564834	−	0.0614294i	0.178752	−	0.983894i	$-0.442794\pi$
$947$	17.3818	−	1.89039i	0.564834	−	0.0614294i	0.386081	+	0.922465i	$0.373828\pi$
$948$	−6.07584	+	5.75534i	−0.197334	+	0.186925i
$949$	−31.4092	−	36.9777i	−1.01959	−	1.20035i
$950$	5.38226	+	10.1520i	0.174624	+	0.329375i
$951$	−21.1503	+	12.7257i	−0.685845	+	0.412659i
$952$	−6.38946	−	2.95608i	−0.207083	−	0.0958070i
$953$	15.7448	−	3.46569i	0.510023	−	0.112265i	0.0474991	−	0.998871i	$-0.484875\pi$
$953$	15.7448	−	3.46569i	0.510023	−	0.112265i	0.462524	+	0.886607i	$0.346944\pi$
$954$	−3.77351	+	7.11759i	−0.122172	+	0.230441i
$955$	−2.00991	−	37.0707i	−0.0650393	−	1.19958i
$956$	−5.28842	+	6.22601i	−0.171040	+	0.201363i
$957$	−5.64325	−	1.24217i	−0.182420	−	0.0401538i
$958$	−0.123161	−	0.0936248i	−0.00397916	−	0.00302488i
$959$	20.4546	+	19.3756i	0.660513	+	0.625671i
$960$	0.175440	−	3.23580i	0.00566230	−	0.104435i
$961$	−17.8456	−	10.7374i	−0.575665	−	0.346366i
$962$	−10.7527	−	15.8590i	−0.346681	−	0.511316i
$963$	4.31583	+	15.5442i	0.139076	+	0.500905i
$964$	28.5598	+	3.10607i	0.919850	+	0.100040i
$965$	−16.8192	+	12.7856i	−0.541428	+	0.411583i
$966$	−10.6576	+	4.93074i	−0.342904	+	0.158644i
$967$	−10.9586	+	16.1627i	−0.352403	+	0.519756i	−0.962034	−	0.272930i	$-0.912007\pi$
$967$	−10.9586	+	16.1627i	−0.352403	+	0.519756i	0.609631	+	0.792686i	$0.291318\pi$
$968$	−8.99787	−	3.03174i	−0.289202	−	0.0974437i
$969$	0.633036	−	3.86135i	0.0203360	−	0.124044i
$970$	2.63404	+	16.0670i	0.0845741	+	0.515879i
$971$	−48.3306	+	16.2845i	−1.55100	+	0.522594i	−0.959016	−	0.283353i	$-0.908553\pi$
$971$	−48.3306	+	16.2845i	−1.55100	+	0.522594i	−0.591988	+	0.805947i	$0.701657\pi$
$972$	−0.267528	+	0.963550i	−0.00858098	+	0.0309059i
$973$	24.2477	−	60.8571i	0.777345	−	1.95099i
$974$	−7.93315	+	19.9107i	−0.254195	+	0.637980i
$975$	−5.70867	+	20.5608i	−0.182824	+	0.658472i
$976$	9.03468	−	3.04414i	0.289193	−	0.0974405i
$977$	−1.09225	−	6.66244i	−0.0349442	−	0.213150i	0.963583	−	0.267411i	$-0.0861681\pi$
$977$	−1.09225	−	6.66244i	−0.0349442	−	0.213150i	−0.998527	+	0.0542606i	$0.982720\pi$
$978$	−1.39466	+	8.50703i	−0.0445962	+	0.272025i
$979$	20.2000	+	6.80617i	0.645594	+	0.217526i
$980$	12.9541	−	19.1059i	0.413803	−	0.610314i
$981$	−17.5740	+	8.13061i	−0.561095	+	0.259590i
$982$	−7.02066	+	5.33696i	−0.224038	+	0.170309i
$983$	−39.3086	−	4.27507i	−1.25375	−	0.136353i	−0.542960	−	0.839759i	$-0.682696\pi$
$983$	−39.3086	−	4.27507i	−1.25375	−	0.136353i	−0.710789	+	0.703405i	$0.751662\pi$
$984$	1.18620	+	4.27230i	0.0378146	+	0.136196i
$985$	−27.3338	−	40.3143i	−0.870926	−	1.28452i
$986$	7.56036	+	4.54891i	0.240771	+	0.144867i
$987$	−2.68175	+	49.4620i	−0.0853611	+	1.57439i
$988$	5.88205	+	5.57178i	0.187133	+	0.177262i
$989$	12.4058	+	9.43065i	0.394482	+	0.299877i
$990$	−3.88265	−	0.854635i	−0.123399	−	0.0271621i
$991$	22.3985	−	26.3696i	0.711512	−	0.837657i	−0.281012	−	0.959704i	$-0.590670\pi$
$991$	22.3985	−	26.3696i	0.711512	−	0.837657i	0.992524	+	0.122047i	$0.0389459\pi$
$992$	0.389751	+	7.18853i	0.0123746	+	0.228236i
$993$	−16.9810	+	32.0295i	−0.538874	+	1.01643i
$994$	12.9550	−	2.85161i	0.410907	−	0.0904475i
$995$	19.0110	+	8.79542i	0.602689	+	0.278834i
$996$	−2.35237	+	1.41537i	−0.0745376	+	0.0448478i
$997$	11.8442	+	22.3406i	0.375111	+	0.707534i	0.997149	−	0.0754526i	$-0.0240402\pi$
$997$	11.8442	+	22.3406i	0.375111	+	0.707534i	−0.622039	+	0.782987i	$0.713695\pi$
$998$	7.28428	+	8.57572i	0.230580	+	0.271460i
$999$	−3.58620	+	3.39703i	−0.113462	+	0.107477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.b.289.1	yes	56
59.49	even	29	inner	354.2.e.b.49.1	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.b.49.1	✓	56	59.49	even	29	inner
354.2.e.b.289.1	yes	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.370138 + 0.928977i) q^{2} +(0.994138 - 0.108119i) q^{3} +(-0.725995 + 0.687699i) q^{4} +(-2.09789 - 2.46983i) q^{5} +(0.468408 + 0.883512i) q^{6} +(3.22015 - 1.93750i) q^{7} +(-0.907575 - 0.419889i) q^{8} +(0.976621 - 0.214970i) q^{9} +O(q^{10})\)	\(q+(0.370138 + 0.928977i) q^{2} +(0.994138 - 0.108119i) q^{3} +(-0.725995 + 0.687699i) q^{4} +(-2.09789 - 2.46983i) q^{5} +(0.468408 + 0.883512i) q^{6} +(3.22015 - 1.93750i) q^{7} +(-0.907575 - 0.419889i) q^{8} +(0.976621 - 0.214970i) q^{9} +(1.51790 - 2.86307i) q^{10} +(-0.0664190 - 1.22503i) q^{11} +(-0.647386 + 0.762162i) q^{12} +(3.78822 + 0.833851i) q^{13} +(2.99179 + 2.27430i) q^{14} +(-2.35263 - 2.22853i) q^{15} +(0.0541389 - 0.998533i) q^{16} +(1.60517 + 0.965800i) q^{17} +(0.561187 + 0.827689i) q^{18} +(-0.558798 - 2.01261i) q^{19} +(3.22155 + 0.350365i) q^{20} +(2.99179 - 2.27430i) q^{21} +(1.11344 - 0.515131i) q^{22} +(-1.75355 + 2.58629i) q^{23} +(-0.947653 - 0.319302i) q^{24} +(-0.889991 + 5.42870i) q^{25} +(0.627538 + 3.82781i) q^{26} +(0.947653 - 0.319302i) q^{27} +(-1.00540 + 3.62111i) q^{28} +(1.74335 - 4.37548i) q^{29} +(1.19945 - 3.01040i) q^{30} +(-1.92596 + 6.93668i) q^{31} +(0.947653 - 0.319302i) q^{32} +(-0.198478 - 1.21066i) q^{33} +(-0.303070 + 1.84865i) q^{34} +(-11.5408 - 3.88855i) q^{35} +(-0.561187 + 0.827689i) q^{36} +(-4.48315 + 2.07412i) q^{37} +(1.66283 - 1.26405i) q^{38} +(3.85617 + 0.419384i) q^{39} +(0.866939 + 3.12243i) q^{40} +(-2.48825 - 3.66990i) q^{41} +(3.22015 + 1.93750i) q^{42} +(0.269998 - 4.97982i) q^{43} +(0.890670 + 0.843688i) q^{44} +(-2.57978 - 1.96110i) q^{45} +(-3.05166 - 0.671721i) q^{46} +(-8.53306 + 10.0459i) q^{47} +(-0.0541389 - 0.998533i) q^{48} +(3.33661 - 6.29351i) q^{49} +(-5.37256 + 1.18259i) q^{50} +(1.70018 + 0.786589i) q^{51} +(-3.32367 + 1.99979i) q^{52} +(3.77351 + 7.11759i) q^{53} +(0.647386 + 0.762162i) q^{54} +(-2.88626 + 2.73401i) q^{55} +(-3.73607 + 0.406322i) q^{56} +(-0.773124 - 1.94039i) q^{57} +4.71000 q^{58} +(2.23996 - 7.34728i) q^{59} +3.24055 q^{60} +(3.52880 + 8.85663i) q^{61} +(-7.15688 + 0.778358i) q^{62} +(2.72836 - 2.58444i) q^{63} +(0.647386 + 0.762162i) q^{64} +(-5.88781 - 11.1056i) q^{65} +(1.05121 - 0.632495i) q^{66} +(10.9304 + 5.05696i) q^{67} +(-1.82953 + 0.402710i) q^{68} +(-1.46364 + 2.76072i) q^{69} +(-0.659320 - 12.1604i) q^{70} +(2.28511 - 2.69024i) q^{71} +(-0.976621 - 0.214970i) q^{72} +(-9.95742 - 7.56944i) q^{73} +(-3.58620 - 3.39703i) q^{74} +(-0.297827 + 5.49310i) q^{75} +(1.78975 + 1.07686i) q^{76} +(-2.58737 - 3.81609i) q^{77} +(1.03772 + 3.73753i) q^{78} +(8.31992 + 0.904846i) q^{79} +(-2.57978 + 1.96110i) q^{80} +(0.907575 - 0.419889i) q^{81} +(2.48825 - 3.66990i) q^{82} +(2.60163 + 0.876592i) q^{83} +(-0.607992 + 3.70859i) q^{84} +(-0.982115 - 5.99064i) q^{85} +(4.72607 - 1.59240i) q^{86} +(1.26006 - 4.53832i) q^{87} +(-0.454095 + 1.13969i) q^{88} +(-6.43106 + 16.1407i) q^{89} +(0.866939 - 3.12243i) q^{90} +(13.8142 - 4.65456i) q^{91} +(-0.505522 - 3.08355i) q^{92} +(-1.16468 + 7.10425i) q^{93} +(-12.4908 - 4.20865i) q^{94} +(-3.79850 + 5.60236i) q^{95} +(0.907575 - 0.419889i) q^{96} +(-3.99980 + 3.04057i) q^{97} +(7.08153 + 0.770163i) q^{98} +(-0.328211 - 1.18211i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 30 q^{11} + 2 q^{12} + 5 q^{13} + 28 q^{14} + 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 28 q^{21} - q^{22} - 2 q^{23} - 2 q^{24} + 64 q^{25} - 34 q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - 2 q^{30} + 2 q^{32} - q^{33} + 32 q^{34} - 87 q^{35} - 2 q^{36} + 47 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} + 3 q^{41} + q^{42} - 61 q^{43} + q^{44} - 2 q^{45} - 27 q^{46} + 50 q^{47} + 2 q^{48} - 45 q^{49} - 6 q^{50} + 3 q^{51} - 24 q^{52} - 27 q^{53} - 2 q^{54} - 95 q^{55} - q^{56} + 4 q^{57} + 50 q^{58} - 58 q^{59} + 2 q^{60} - 74 q^{61} - 29 q^{62} + q^{63} - 2 q^{64} - 17 q^{65} + q^{66} + 4 q^{67} - 32 q^{68} + 31 q^{69} - 58 q^{70} - 47 q^{71} + 2 q^{72} + 43 q^{73} - 18 q^{74} - 6 q^{75} - 33 q^{76} - 5 q^{77} + 5 q^{78} + 19 q^{79} - 2 q^{80} - 2 q^{81} - 3 q^{82} + 47 q^{83} - q^{84} - 149 q^{85} - 55 q^{86} + 21 q^{87} + 28 q^{88} + 36 q^{89} + 2 q^{90} + 175 q^{91} - 2 q^{92} - 29 q^{93} - 21 q^{94} + 50 q^{95} - 2 q^{96} + 10 q^{97} - 13 q^{98} + q^{99}+O(q^{100}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 30 * q^11 + 2 * q^12 + 5 * q^13 + 28 * q^14 + 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 28 * q^21 - q^22 - 2 * q^23 - 2 * q^24 + 64 * q^25 - 34 * q^26 + 2 * q^27 + q^28 + 8 * q^29 - 2 * q^30 + 2 * q^32 - q^33 + 32 * q^34 - 87 * q^35 - 2 * q^36 + 47 * q^37 + 4 * q^38 - 5 * q^39 + 2 * q^40 + 3 * q^41 + q^42 - 61 * q^43 + q^44 - 2 * q^45 - 27 * q^46 + 50 * q^47 + 2 * q^48 - 45 * q^49 - 6 * q^50 + 3 * q^51 - 24 * q^52 - 27 * q^53 - 2 * q^54 - 95 * q^55 - q^56 + 4 * q^57 + 50 * q^58 - 58 * q^59 + 2 * q^60 - 74 * q^61 - 29 * q^62 + q^63 - 2 * q^64 - 17 * q^65 + q^66 + 4 * q^67 - 32 * q^68 + 31 * q^69 - 58 * q^70 - 47 * q^71 + 2 * q^72 + 43 * q^73 - 18 * q^74 - 6 * q^75 - 33 * q^76 - 5 * q^77 + 5 * q^78 + 19 * q^79 - 2 * q^80 - 2 * q^81 - 3 * q^82 + 47 * q^83 - q^84 - 149 * q^85 - 55 * q^86 + 21 * q^87 + 28 * q^88 + 36 * q^89 + 2 * q^90 + 175 * q^91 - 2 * q^92 - 29 * q^93 - 21 * q^94 + 50 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + q^99

Introduction

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