LMFDB - Embedded newform 756.2.bt.a.103.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(103,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14, 15]))

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

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

chi := DirichletCharacter("756.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bt (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.7
Character	$\chi$	$=$	756.103
Dual form			756.2.bt.a.367.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39958 + 0.202941i) q^{2} +(-1.70851 - 0.284574i) q^{3} +(1.91763 - 0.568062i) q^{4} +(2.54587 + 0.448906i) q^{5} +(2.44895 + 0.0515557i) q^{6} +(2.36953 - 1.17699i) q^{7} +(-2.56859 + 1.18421i) q^{8} +(2.83804 + 0.972395i) q^{9} +O(q^{10})$	\(q+(-1.39958 + 0.202941i) q^{2} +(-1.70851 - 0.284574i) q^{3} +(1.91763 - 0.568062i) q^{4} +(2.54587 + 0.448906i) q^{5} +(2.44895 + 0.0515557i) q^{6} +(2.36953 - 1.17699i) q^{7} +(-2.56859 + 1.18421i) q^{8} +(2.83804 + 0.972395i) q^{9} +(-3.65425 - 0.111617i) q^{10} +(4.78431 - 0.843602i) q^{11} +(-3.43795 + 0.424835i) q^{12} +(0.792083 - 0.943968i) q^{13} +(-3.07748 + 2.12817i) q^{14} +(-4.22191 - 1.49145i) q^{15} +(3.35461 - 2.17867i) q^{16} -0.0599377i q^{17} +(-4.16939 - 0.784989i) q^{18} +4.40303 q^{19} +(5.13705 - 0.585378i) q^{20} +(-4.38332 + 1.33660i) q^{21} +(-6.52480 + 2.15162i) q^{22} +(-2.92206 + 3.48237i) q^{23} +(4.72546 - 1.29229i) q^{24} +(1.58149 + 0.575617i) q^{25} +(-0.917011 + 1.48190i) q^{26} +(-4.57210 - 2.46898i) q^{27} +(3.87528 - 3.60308i) q^{28} +(-6.55090 + 5.49686i) q^{29} +(6.21157 + 1.23060i) q^{30} +(-1.82718 + 0.665039i) q^{31} +(-4.25290 + 3.73000i) q^{32} +(-8.41412 + 0.0798188i) q^{33} +(0.0121638 + 0.0838875i) q^{34} +(6.56089 - 1.93278i) q^{35} +(5.99468 + 0.252514i) q^{36} +(-4.75666 - 8.23877i) q^{37} +(-6.16238 + 0.893555i) q^{38} +(-1.62191 + 1.38738i) q^{39} +(-7.07090 + 1.86180i) q^{40} +(2.90388 - 3.46071i) q^{41} +(5.86354 - 2.76023i) q^{42} +(1.57470 - 4.32646i) q^{43} +(8.69531 - 4.33550i) q^{44} +(6.78877 + 3.74961i) q^{45} +(3.38293 - 5.46685i) q^{46} +(3.91794 + 1.42601i) q^{47} +(-6.35139 + 2.76765i) q^{48} +(4.22937 - 5.57785i) q^{49} +(-2.33024 - 0.484671i) q^{50} +(-0.0170567 + 0.102404i) q^{51} +(0.982690 - 2.26013i) q^{52} +(4.96662 + 8.60244i) q^{53} +(6.90007 + 2.52766i) q^{54} +12.5589 q^{55} +(-4.69254 + 5.82924i) q^{56} +(-7.52264 - 1.25299i) q^{57} +(8.05296 - 9.02272i) q^{58} +(9.05014 + 7.59397i) q^{59} +(-8.94330 - 0.461743i) q^{60} +(-0.894724 + 2.45823i) q^{61} +(2.42231 - 1.30158i) q^{62} +(7.86932 - 1.03623i) q^{63} +(5.19529 - 6.08350i) q^{64} +(2.44030 - 2.04765i) q^{65} +(11.7600 - 1.81928i) q^{66} +(-6.30892 - 1.11243i) q^{67} +(-0.0340484 - 0.114938i) q^{68} +(5.98337 - 5.11814i) q^{69} +(-8.79023 + 4.03655i) q^{70} +(-5.47210 - 3.15932i) q^{71} +(-8.44127 + 0.863152i) q^{72} +(7.66637 + 4.42618i) q^{73} +(8.32929 + 10.5655i) q^{74} +(-2.53820 - 1.43350i) q^{75} +(8.44339 - 2.50120i) q^{76} +(10.3437 - 7.63005i) q^{77} +(1.98844 - 2.27089i) q^{78} +(4.82129 - 0.850124i) q^{79} +(9.51843 - 4.04070i) q^{80} +(7.10889 + 5.51939i) q^{81} +(-3.36188 + 5.43284i) q^{82} +(-5.66393 + 4.75260i) q^{83} +(-7.64631 + 5.05311i) q^{84} +(0.0269064 - 0.152594i) q^{85} +(-1.32590 + 6.37478i) q^{86} +(12.7566 - 7.52725i) q^{87} +(-11.2899 + 7.83250i) q^{88} -12.4302i q^{89} +(-10.2623 - 3.87015i) q^{90} +(0.765822 - 3.16904i) q^{91} +(-3.62522 + 8.33781i) q^{92} +(3.31101 - 0.616261i) q^{93} +(-5.77286 - 1.20071i) q^{94} +(11.2096 + 1.97655i) q^{95} +(8.32759 - 5.16249i) q^{96} +(-4.05259 + 11.1344i) q^{97} +(-4.78735 + 8.66494i) q^{98} +(14.3983 + 2.25806i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.39958	+	0.202941i	−0.989650	+	0.143501i
$2$	−1.39958	+	0.202941i	−0.989650	+	0.143501i
$3$	−1.70851	−	0.284574i	−0.986411	−	0.164299i
$3$	−1.70851	−	0.284574i	−0.986411	−	0.164299i
$4$	1.91763	−	0.568062i	0.958815	−	0.284031i
$5$	2.54587	+	0.448906i	1.13855	+	0.200757i	0.710971	−	0.703221i	$-0.248256\pi$
$5$	2.54587	+	0.448906i	1.13855	+	0.200757i	0.427578	+	0.903978i	$0.359367\pi$
$6$	2.44895	+	0.0515557i	0.999778	+	0.0210475i
$7$	2.36953	−	1.17699i	0.895599	−	0.444862i
$7$	2.36953	−	1.17699i	0.895599	−	0.444862i
$8$	−2.56859	+	1.18421i	−0.908133	+	0.418682i
$9$	2.83804	+	0.972395i	0.946012	+	0.324132i
$10$	−3.65425	−	0.111617i	−1.15557	−	0.0352965i
$11$	4.78431	−	0.843602i	1.44252	−	0.254356i	0.603027	−	0.797721i	$-0.293961\pi$
$11$	4.78431	−	0.843602i	1.44252	−	0.254356i	0.839496	+	0.543365i	$0.182850\pi$
$12$	−3.43795	+	0.424835i	−0.992451	+	0.122639i
$13$	0.792083	−	0.943968i	0.219684	−	0.261810i	−0.644935	−	0.764238i	$-0.723115\pi$
$13$	0.792083	−	0.943968i	0.219684	−	0.261810i	0.864619	+	0.502428i	$0.167560\pi$
$14$	−3.07748	+	2.12817i	−0.822492	+	0.568777i
$15$	−4.22191	−	1.49145i	−1.09009	−	0.385091i
$16$	3.35461	−	2.17867i	0.838653	−	0.544666i
$17$		−	0.0599377i		−	0.0145370i	−0.999974	−	0.00726852i	$-0.997686\pi$
$17$		−	0.0599377i		−	0.0145370i	0.999974	−	0.00726852i	$-0.00231366\pi$
$18$	−4.16939	−	0.784989i	−0.982734	−	0.185024i
$19$	4.40303			1.01013			0.505063	−	0.863083i	$-0.331469\pi$
$19$	4.40303			1.01013			0.505063	+	0.863083i	$0.331469\pi$
$20$	5.13705	−	0.585378i	1.14868	−	0.130895i
$21$	−4.38332	+	1.33660i	−0.956519	+	0.291671i
$22$	−6.52480	+	2.15162i	−1.39109	+	0.458726i
$23$	−2.92206	+	3.48237i	−0.609291	+	0.726125i	−0.979190	−	0.202947i	$-0.934948\pi$
$23$	−2.92206	+	3.48237i	−0.609291	+	0.726125i	0.369898	+	0.929072i	$0.379392\pi$
$24$	4.72546	−	1.29229i	0.964581	−	0.263787i
$25$	1.58149	+	0.575617i	0.316299	+	0.115123i
$26$	−0.917011	+	1.48190i	−0.179841	+	0.290625i
$27$	−4.57210	−	2.46898i	−0.879902	−	0.475155i
$28$	3.87528	−	3.60308i	0.732359	−	0.680918i
$29$	−6.55090	+	5.49686i	−1.21647	+	1.02074i	−0.217471	+	0.976067i	$0.569781\pi$
$29$	−6.55090	+	5.49686i	−1.21647	+	1.02074i	−0.999002	+	0.0446746i	$0.985775\pi$
$30$	6.21157	+	1.23060i	1.13407	+	0.224676i
$31$	−1.82718	+	0.665039i	−0.328171	+	0.119445i	−0.500851	−	0.865533i	$-0.666980\pi$
$31$	−1.82718	+	0.665039i	−0.328171	+	0.119445i	0.172680	+	0.984978i	$0.444757\pi$
$32$	−4.25290	+	3.73000i	−0.751813	+	0.659377i
$33$	−8.41412	+	0.0798188i	−1.46471	+	0.0138947i
$34$	0.0121638	+	0.0838875i	0.00208607	+	0.0143866i
$35$	6.56089	−	1.93278i	1.10899	−	0.326700i
$36$	5.99468	+	0.252514i	0.999114	+	0.0420857i
$37$	−4.75666	−	8.23877i	−0.781990	−	1.35445i	−0.930781	−	0.365577i	$-0.880872\pi$
$37$	−4.75666	−	8.23877i	−0.781990	−	1.35445i	0.148792	−	0.988869i	$-0.452462\pi$
$38$	−6.16238	+	0.893555i	−0.999671	+	0.144954i
$39$	−1.62191	+	1.38738i	−0.259714	+	0.222158i
$40$	−7.07090	+	1.86180i	−1.11801	+	0.294376i
$41$	2.90388	−	3.46071i	0.453510	−	0.540472i	−0.490041	−	0.871699i	$-0.663018\pi$
$41$	2.90388	−	3.46071i	0.453510	−	0.540472i	0.943551	+	0.331227i	$0.107463\pi$
$42$	5.86354	−	2.76023i	0.904764	−	0.425913i
$43$	1.57470	−	4.32646i	0.240140	−	0.659779i	−0.759814	−	0.650141i	$-0.774710\pi$
$43$	1.57470	−	4.32646i	0.240140	−	0.659779i	0.999954	−	0.00963807i	$-0.00306794\pi$
$44$	8.69531	−	4.33550i	1.31087	−	0.653601i
$45$	6.78877	+	3.74961i	1.01201	+	0.558959i
$46$	3.38293	−	5.46685i	0.498786	−	0.806044i
$47$	3.91794	+	1.42601i	0.571491	+	0.208006i	0.611569	−	0.791191i	$-0.290539\pi$
$47$	3.91794	+	1.42601i	0.571491	+	0.208006i	−0.0400786	+	0.999197i	$0.512761\pi$
$48$	−6.35139	+	2.76765i	−0.916744	+	0.399475i
$49$	4.22937	−	5.57785i	0.604196	−	0.796836i
$50$	−2.33024	−	0.484671i	−0.329546	−	0.0685428i
$51$	−0.0170567	+	0.102404i	−0.00238841	+	0.0143395i
$52$	0.982690	−	2.26013i	0.136275	−	0.313424i
$53$	4.96662	+	8.60244i	0.682218	+	1.18164i	0.974302	+	0.225244i	$0.0723179\pi$
$53$	4.96662	+	8.60244i	0.682218	+	1.18164i	−0.292084	+	0.956393i	$0.594349\pi$
$54$	6.90007	+	2.52766i	0.938980	+	0.343971i
$55$	12.5589			1.69345
$56$	−4.69254	+	5.82924i	−0.627067	+	0.778965i
$57$	−7.52264	−	1.25299i	−0.996398	−	0.165962i
$58$	8.05296	−	9.02272i	1.05740	−	1.18474i
$59$	9.05014	+	7.59397i	1.17823	+	0.988650i	0.999989	+	0.00466282i	$0.00148423\pi$
$59$	9.05014	+	7.59397i	1.17823	+	0.988650i	0.178238	+	0.983987i	$0.442960\pi$
$60$	−8.94330	−	0.461743i	−1.15458	−	0.0596107i
$61$	−0.894724	+	2.45823i	−0.114558	+	0.314745i	−0.983700	−	0.179817i	$-0.942449\pi$
$61$	−0.894724	+	2.45823i	−0.114558	+	0.314745i	0.869142	+	0.494562i	$0.164672\pi$
$62$	2.42231	−	1.30158i	0.307634	−	0.165301i
$63$	7.86932	−	1.03623i	0.991441	−	0.130553i
$64$	5.19529	−	6.08350i	0.649411	−	0.760438i
$65$	2.44030	−	2.04765i	0.302682	−	0.253980i
$66$	11.7600	−	1.81928i	1.44756	−	0.223938i
$67$	−6.30892	−	1.11243i	−0.770757	−	0.135905i	−0.225578	−	0.974225i	$-0.572427\pi$
$67$	−6.30892	−	1.11243i	−0.770757	−	0.135905i	−0.545179	+	0.838320i	$0.683538\pi$
$68$	−0.0340484	−	0.114938i	−0.00412897	−	0.0139383i
$69$	5.98337	−	5.11814i	0.720313	−	0.616152i
$70$	−8.79023	+	4.03655i	−1.05063	+	0.482460i
$71$	−5.47210	−	3.15932i	−0.649418	−	0.374942i	0.138815	−	0.990318i	$-0.455671\pi$
$71$	−5.47210	−	3.15932i	−0.649418	−	0.374942i	−0.788233	+	0.615376i	$0.789004\pi$
$72$	−8.44127	+	0.863152i	−0.994813	+	0.101723i
$73$	7.66637	+	4.42618i	0.897281	+	0.518045i	0.876317	−	0.481735i	$-0.159993\pi$
$73$	7.66637	+	4.42618i	0.897281	+	0.518045i	0.0209640	+	0.999780i	$0.493326\pi$
$74$	8.32929	+	10.5655i	0.968260	+	1.22821i
$75$	−2.53820	−	1.43350i	−0.293086	−	0.165526i
$76$	8.44339	−	2.50120i	0.968524	−	0.286907i
$77$	10.3437	−	7.63005i	1.17877	−	0.869524i
$78$	1.98844	−	2.27089i	0.225146	−	0.257128i
$79$	4.82129	−	0.850124i	0.542438	−	0.0956464i	0.104286	−	0.994547i	$-0.466744\pi$
$79$	4.82129	−	0.850124i	0.542438	−	0.0956464i	0.438152	+	0.898901i	$0.355633\pi$
$80$	9.51843	−	4.04070i	1.06419	−	0.451764i
$81$	7.10889	+	5.51939i	0.789877	+	0.613265i
$82$	−3.36188	+	5.43284i	−0.371258	+	0.599957i
$83$	−5.66393	+	4.75260i	−0.621697	+	0.521666i	−0.898336	−	0.439308i	$-0.855224\pi$
$83$	−5.66393	+	4.75260i	−0.621697	+	0.521666i	0.276640	+	0.960974i	$0.410779\pi$
$84$	−7.64631	+	5.05311i	−0.834281	+	0.551340i
$85$	0.0269064	−	0.152594i	0.00291841	−	0.0165511i
$86$	−1.32590	+	6.37478i	−0.142976	+	0.687411i
$87$	12.7566	−	7.52725i	1.36765	−	0.807006i
$88$	−11.2899	+	7.83250i	−1.20351	+	0.834947i
$89$		−	12.4302i		−	1.31760i	−0.752319	−	0.658799i	$-0.771065\pi$
$89$		−	12.4302i		−	1.31760i	0.752319	−	0.658799i	$-0.228935\pi$
$90$	−10.2623	−	3.87015i	−1.08175	−	0.407949i
$91$	0.765822	−	3.16904i	0.0802799	−	0.332206i
$92$	−3.62522	+	8.33781i	−0.377956	+	0.869277i
$93$	3.31101	−	0.616261i	0.343336	−	0.0639033i
$94$	−5.77286	−	1.20071i	−0.595425	−	0.123843i
$95$	11.2096	+	1.97655i	1.15008	+	0.202790i
$96$	8.32759	−	5.16249i	0.849931	−	0.526894i
$97$	−4.05259	+	11.1344i	−0.411478	+	1.13053i	0.544927	+	0.838484i	$0.316557\pi$
$97$	−4.05259	+	11.1344i	−0.411478	+	1.13053i	−0.956405	+	0.292044i	$0.905665\pi$
$98$	−4.78735	+	8.66494i	−0.483596	+	0.875292i
$99$	14.3983	+	2.25806i	1.44709	+	0.226944i
$100$	3.35971	+	0.205433i	0.335971	+	0.0205433i
$101$	−5.77977	−	6.88806i	−0.575108	−	0.685387i	0.397563	−	0.917575i	$-0.369856\pi$
$101$	−5.77977	−	6.88806i	−0.575108	−	0.685387i	−0.972671	+	0.232188i	$0.925412\pi$
$102$	0.00309013	−	0.146784i	0.000305969	−	0.0145338i
$103$	3.05760	−	17.3405i	0.301275	−	1.70861i	−0.339267	−	0.940690i	$-0.610179\pi$
$103$	3.05760	−	17.3405i	0.301275	−	1.70861i	0.640542	−	0.767923i	$-0.278710\pi$
$104$	−0.916677	+	3.36266i	−0.0898876	+	0.329736i
$105$	−11.7594	+	1.43513i	−1.14760	+	0.140054i
$106$	−8.69696	−	11.0319i	−0.844723	−	1.07151i
$107$	−14.4034	−	8.31581i	−1.39243	−	0.803919i	−0.398846	−	0.917018i	$-0.630589\pi$
$107$	−14.4034	−	8.31581i	−1.39243	−	0.803919i	−0.993584	+	0.113099i	$0.963922\pi$
$108$	−10.1701	−	2.13735i	−0.978622	−	0.205667i
$109$	4.44317	+	7.69579i	0.425578	+	0.737123i	0.996474	−	0.0838993i	$-0.0267374\pi$
$109$	4.44317	+	7.69579i	0.425578	+	0.737123i	−0.570896	+	0.821022i	$0.693404\pi$
$110$	−17.5772	+	2.54872i	−1.67592	+	0.243011i
$111$	5.78228	+	15.4297i	0.548829	+	1.46452i
$112$	5.38458	−	9.11078i	0.508795	−	0.860888i
$113$	11.0320	−	4.01532i	1.03780	−	0.377730i	0.233756	−	0.972295i	$-0.424898\pi$
$113$	11.0320	−	4.01532i	1.03780	−	0.377730i	0.804047	+	0.594566i	$0.202676\pi$
$114$	10.7828	+	0.227002i	1.00990	+	0.0212606i
$115$	−9.00245	+	7.55395i	−0.839483	+	0.704410i
$116$	−9.43965	+	14.2623i	−0.876450	+	1.32422i
$117$	3.16587	−	1.90880i	0.292685	−	0.176468i
$118$	−14.2075	−	8.79170i	−1.30791	−	0.809341i
$119$	−0.0705464	−	0.142024i	−0.00646698	−	0.0130194i
$120$	12.6105	−	1.16872i	1.15118	−	0.106689i
$121$	11.8413	−	4.30988i	1.07648	−	0.391808i
$122$	0.753359	−	3.62206i	0.0682059	−	0.327926i
$123$	−5.94615	+	5.08630i	−0.536146	+	0.458616i
$124$	−3.12607	+	2.31325i	−0.280730	+	0.207736i
$125$	−7.42613	−	4.28748i	−0.664213	−	0.383484i
$126$	−10.8034	+	3.04729i	−0.962446	+	0.271474i
$127$	−3.23384	+	1.86706i	−0.286956	+	0.165674i	−0.636568	−	0.771220i	$-0.719647\pi$
$127$	−3.23384	+	1.86706i	−0.286956	+	0.165674i	0.349612	+	0.936895i	$0.386313\pi$
$128$	−6.03661	+	9.56866i	−0.533566	+	0.845758i
$129$	−3.92160	+	6.94370i	−0.345277	+	0.611358i
$130$	−2.99983	+	3.36108i	−0.263103	+	0.294786i
$131$	5.37315	+	4.50861i	0.469454	+	0.393919i	0.846596	−	0.532237i	$-0.178648\pi$
$131$	5.37315	+	4.50861i	0.469454	+	0.393919i	−0.377141	+	0.926156i	$0.623093\pi$
$132$	−16.0898	+	4.93280i	−1.40044	+	0.429346i
$133$	10.4331	−	5.18235i	0.904667	−	0.449366i
$134$	9.05557	+	0.276599i	0.782282	+	0.0238945i
$135$	−10.5317	−	8.33816i	−0.906421	−	0.717635i
$136$	0.0709790	+	0.153955i	0.00608640	+	0.0132016i
$137$	−4.24773	−	1.54605i	−0.362908	−	0.132088i	0.154129	−	0.988051i	$-0.450743\pi$
$137$	−4.24773	−	1.54605i	−0.362908	−	0.132088i	−0.517037	+	0.855963i	$0.672965\pi$
$138$	−7.33550	+	8.37750i	−0.624439	+	0.713140i
$139$	−0.0677038	+	0.383967i	−0.00574256	+	0.0325677i	−0.987544	−	0.157341i	$-0.949708\pi$
$139$	−0.0677038	+	0.383967i	−0.00574256	+	0.0325677i	0.981802	+	0.189908i	$0.0608191\pi$
$140$	11.4834	−	7.43335i	0.970526	−	0.628233i
$141$	−6.28805	−	3.55131i	−0.529549	−	0.299074i
$142$	8.29977	+	3.31119i	0.696501	+	0.277869i
$143$	2.99323	−	5.18443i	0.250307	−	0.433544i
$144$	11.6390	−	2.92112i	0.969919	−	0.243427i
$145$	−19.1454	+	11.0536i	−1.58993	+	0.917949i
$146$	−11.6279	−	4.63896i	−0.962334	−	0.383923i
$147$	−8.81324	+	8.32627i	−0.726904	+	0.686739i
$148$	−13.8016	−	13.0968i	−1.13449	−	1.07655i
$149$	−12.3239	+	4.48553i	−1.00961	+	0.367469i	−0.793284	−	0.608852i	$-0.791630\pi$
$149$	−12.3239	+	4.48553i	−1.00961	+	0.367469i	−0.216328	+	0.976321i	$0.569408\pi$
$150$	3.84332	+	1.49119i	0.313806	+	0.121755i
$151$	−4.09975	+	0.722896i	−0.333633	+	0.0588285i	−0.337955	−	0.941162i	$-0.609735\pi$
$151$	−4.09975	+	0.722896i	−0.333633	+	0.0588285i	0.00432240	+	0.999991i	$0.498624\pi$
$152$	−11.3096	+	5.21412i	−0.917328	+	0.422921i
$153$	0.0582832	−	0.170105i	0.00471192	−	0.0137522i
$154$	−12.9283	+	12.7780i	−1.04179	+	1.02968i
$155$	−4.95031	+	0.872873i	−0.397618	+	0.0701109i
$156$	−2.32211	+	3.58182i	−0.185918	+	0.286775i
$157$	−7.65810	+	9.12656i	−0.611183	+	0.728379i	−0.979528	−	0.201310i	$-0.935480\pi$
$157$	−7.65810	+	9.12656i	−0.611183	+	0.728379i	0.368345	+	0.929689i	$0.379925\pi$
$158$	−6.57524	+	2.16825i	−0.523098	+	0.172497i
$159$	−6.03751	−	16.1108i	−0.478806	−	1.27767i
$160$	−12.5018	+	7.58695i	−0.988351	+	0.599801i
$161$	−2.82518	+	11.6908i	−0.222655	+	0.921367i
$162$	−11.0696	−	6.28212i	−0.869706	−	0.493570i
$163$	0.476024	+	0.274833i	0.0372851	+	0.0215266i	0.518527	−	0.855061i	$-0.326481\pi$
$163$	0.476024	+	0.274833i	0.0372851	+	0.0215266i	−0.481242	+	0.876588i	$0.659814\pi$
$164$	3.60267	−	8.28595i	0.281321	−	0.647024i
$165$	−21.4571	−	3.57394i	−1.67043	−	0.278231i
$166$	6.96261	−	7.80107i	0.540403	−	0.605480i
$167$	19.3610	−	7.04681i	1.49820	−	0.545299i	0.542603	−	0.839989i	$-0.317439\pi$
$167$	19.3610	−	7.04681i	1.49820	−	0.545299i	0.955593	+	0.294690i	$0.0952165\pi$
$168$	9.67612	−	8.62396i	0.746529	−	0.665353i
$169$	1.99375	+	11.3071i	0.153365	+	0.869777i
$170$	−0.00669010	+	0.219027i	−0.000513107	+	0.0167986i
$171$	12.4960	+	4.28149i	0.955591	+	0.327414i
$172$	0.562000	−	9.19108i	0.0428521	−	0.700813i
$173$	−1.90285	−	2.26773i	−0.144671	−	0.172412i	0.688843	−	0.724911i	$-0.258119\pi$
$173$	−1.90285	−	2.26773i	−0.144671	−	0.172412i	−0.833514	+	0.552498i	$0.813675\pi$
$174$	−16.3262	+	13.1238i	−1.23769	+	0.994912i
$175$	4.42490	−	0.497467i	0.334491	−	0.0376050i
$176$	14.2116	−	13.2534i	1.07124	−	0.999010i
$177$	−13.3012	−	15.5498i	−0.999782	−	1.16880i
$178$	2.52259	+	17.3970i	0.189076	+	1.30396i
$179$			15.9855i			1.19481i	0.801938	+	0.597407i	$0.203802\pi$
$179$			15.9855i			1.19481i	−0.801938	+	0.597407i	$0.796198\pi$
$180$	15.1484	+	3.33392i	1.12909	+	0.248496i
$181$	0.805751	−	0.465201i	0.0598910	−	0.0345781i	−0.469755	−	0.882797i	$-0.655658\pi$
$181$	0.805751	−	0.465201i	0.0598910	−	0.0345781i	0.529647	+	0.848218i	$0.322325\pi$
$182$	−0.428699	+	4.59073i	−0.0317773	+	0.340288i
$183$	2.22820	−	3.94531i	0.164713	−	0.291646i
$184$	3.38170	−	12.4051i	0.249302	−	0.914517i
$185$	−8.41141	−	23.1102i	−0.618419	−	1.69909i
$186$	−4.50895	+	1.53444i	−0.330612	+	0.112511i
$187$	−0.0505636	−	0.286761i	−0.00369758	−	0.0209700i
$188$	8.32323	+	0.508934i	0.607034	+	0.0371178i
$189$	−13.7397	−	0.468989i	−0.999418	−	0.0341139i
$190$	−16.0898	−	0.491456i	−1.16728	−	0.0356539i
$191$	−19.4328	+	3.42652i	−1.40611	+	0.247934i	−0.824650	−	0.565644i	$-0.808628\pi$
$191$	−19.4328	+	3.42652i	−1.40611	+	0.247934i	−0.581456	+	0.813578i	$0.697517\pi$
$192$	−10.6074	+	8.91530i	−0.765525	+	0.643407i
$193$	3.33919	−	1.21537i	0.240360	−	0.0874839i	−0.219031	−	0.975718i	$-0.570290\pi$
$193$	3.33919	−	1.21537i	0.240360	−	0.0874839i	0.459392	+	0.888234i	$0.348068\pi$
$194$	3.41229	−	16.4059i	0.244988	−	1.17787i
$195$	−4.75199	+	2.80400i	−0.340297	+	0.200798i
$196$	4.94180	−	13.0988i	0.352986	−	0.935629i
$197$	5.52957	+	9.57750i	0.393966	+	0.682369i	0.992969	−	0.118378i	$-0.0377695\pi$
$197$	5.52957	+	9.57750i	0.393966	+	0.682369i	−0.599003	+	0.800747i	$0.704436\pi$
$198$	−20.6098	−	0.238324i	−1.46468	−	0.0169369i
$199$	23.8480			1.69054			0.845271	−	0.534338i	$-0.179439\pi$
$199$	23.8480			1.69054			0.845271	+	0.534338i	$0.179439\pi$
$200$	−4.74386	+	0.394302i	−0.335442	+	0.0278813i
$201$	10.4623	+	3.69596i	0.737954	+	0.260693i
$202$	9.48709	+	8.46741i	0.667510	+	0.595765i
$203$	−9.05281	+	20.7354i	−0.635382	+	1.45534i
$204$	0.0254636	+	0.206063i	0.00178281	+	0.0144273i
$205$	8.94645	−	7.50696i	0.624847	−	0.524309i
$206$	−0.760252	+	24.8899i	−0.0529693	+	1.73416i
$207$	−11.6791	+	7.04170i	−0.811757	+	0.489432i
$208$	0.600540	−	4.89233i	0.0416400	−	0.339222i
$209$	21.0655	−	3.71441i	1.45713	−	0.256931i
$210$	16.1669	−	4.39503i	1.11562	−	0.303286i
$211$	−7.84154	−	21.5445i	−0.539834	−	1.48318i	−0.847035	−	0.531537i	$-0.821615\pi$
$211$	−7.84154	−	21.5445i	−0.539834	−	1.48318i	0.307201	−	0.951645i	$-0.400608\pi$
$212$	14.4109	+	13.6750i	0.989743	+	0.939200i
$213$	8.45009	+	6.95495i	0.578991	+	0.476545i
$214$	21.8463	+	8.71558i	1.49338	+	0.595784i
$215$	5.95117	−	10.3077i	0.405866	−	0.702981i
$216$	14.6676	+	0.927454i	0.998007	+	0.0631053i
$217$	−3.54681	+	3.72641i	−0.240773	+	0.252965i
$218$	−7.78034	−	9.86915i	−0.526951	−	0.668423i
$219$	−11.8385	−	9.74384i	−0.799973	−	0.658428i
$220$	24.0834	−	7.13426i	1.62370	−	0.480992i
$221$	−0.0565793	−	0.0474757i	−0.00380593	−	0.00319356i
$222$	−11.2240	−	20.4215i	−0.753309	−	1.37060i
$223$	−1.86997	−	10.6051i	−0.125223	−	0.710172i	−0.981175	−	0.193119i	$-0.938140\pi$
$223$	−1.86997	−	10.6051i	−0.125223	−	0.710172i	0.855953	−	0.517054i	$-0.172971\pi$
$224$	−5.68719	+	13.8440i	−0.379991	+	0.924990i
$225$	3.92861	+	3.17146i	0.261907	+	0.211431i
$226$	−14.6253	+	7.85859i	−0.972858	+	0.522746i
$227$	4.44938	+	25.2337i	0.295316	+	1.67482i	0.665916	+	0.746027i	$0.268041\pi$
$227$	4.44938	+	25.2337i	0.295316	+	1.67482i	−0.370600	+	0.928793i	$0.620848\pi$
$228$	−15.1374	+	1.87056i	−1.00250	+	0.123881i
$229$	4.80815	+	13.2103i	0.317732	+	0.872961i	0.991036	+	0.133595i	$0.0426522\pi$
$229$	4.80815	+	13.2103i	0.317732	+	0.872961i	−0.673304	+	0.739365i	$0.735126\pi$
$230$	11.0666	−	12.3993i	0.729711	−	0.817586i
$231$	−19.8436	+	10.0925i	−1.30561	+	0.664038i
$232$	10.3171	−	21.8768i	0.677352	−	1.43628i
$233$	−9.81411	−	16.9985i	−0.642943	−	1.11361i	−0.984772	−	0.173849i	$-0.944380\pi$
$233$	−9.81411	−	16.9985i	−0.642943	−	1.11361i	0.341829	−	0.939762i	$-0.388954\pi$
$234$	−4.04350	+	3.31399i	−0.264332	+	0.216642i
$235$	9.33444	+	5.38924i	0.608912	+	0.351555i
$236$	21.6687	+	9.42138i	1.41051	+	0.613280i
$237$	−8.47917	+	0.0804359i	−0.550781	+	0.00522487i
$238$	0.127558	+	0.184457i	0.00826833	+	0.0119566i
$239$	−2.79000	−	0.491951i	−0.180470	−	0.0318217i	0.0826828	−	0.996576i	$-0.473651\pi$
$239$	−2.79000	−	0.491951i	−0.180470	−	0.0318217i	−0.263153	+	0.964754i	$0.584762\pi$
$240$	−17.4122	+	4.19490i	−1.12396	+	0.270780i
$241$	−1.03273	+	2.83740i	−0.0665239	+	0.182773i	−0.968500	−	0.249012i	$-0.919894\pi$
$241$	−1.03273	+	2.83740i	−0.0665239	+	0.182773i	0.901976	+	0.431785i	$0.142116\pi$
$242$	−15.6982	+	8.43510i	−1.00912	+	0.542229i
$243$	−10.5750	−	11.4529i	−0.678385	−	0.734707i
$244$	−0.319320	+	5.22224i	−0.0204424	+	0.334320i
$245$	13.2714	−	12.3019i	0.847877	−	0.785941i
$246$	7.28987	−	8.32538i	0.464785	−	0.530807i
$247$	3.48757	−	4.15632i	0.221909	−	0.264460i
$248$	3.90572	−	3.87198i	0.248014	−	0.245871i
$249$	11.0294	−	6.50808i	0.698957	−	0.412433i
$250$	11.2635	+	4.49359i	0.712369	+	0.284200i
$251$	−8.25980	−	14.3064i	−0.521354	−	0.903011i	−0.999692	−	0.0248353i	$-0.992094\pi$
$251$	−8.25980	−	14.3064i	−0.521354	−	0.903011i	0.478338	−	0.878176i	$-0.341239\pi$
$252$	14.5018	−	6.45737i	0.913528	−	0.406776i
$253$	−11.0423	+	19.1258i	−0.694222	+	1.20243i
$254$	4.14710	−	3.26936i	0.260212	−	0.205138i
$255$	−0.0893942	+	0.253052i	−0.00559808	+	0.0158467i
$256$	6.50683	−	14.6172i	0.406677	−	0.913572i
$257$	−6.63937	−	18.2415i	−0.414152	−	1.13787i	−0.954962	−	0.296729i	$-0.904104\pi$
$257$	−6.63937	−	18.2415i	−0.414152	−	1.13787i	0.540809	−	0.841145i	$-0.318118\pi$
$258$	4.07942	−	10.5141i	0.253973	−	0.654579i
$259$	−20.9680	−	13.9235i	−1.30289	−	0.865163i
$260$	3.51639	−	5.31288i	0.218077	−	0.329491i
$261$	−23.9368	+	9.23022i	−1.48165	+	0.571336i
$262$	−8.43512	−	5.21971i	−0.521123	−	0.322475i
$263$	−12.5845	−	14.9976i	−0.775993	−	0.924792i	0.222752	−	0.974875i	$-0.428496\pi$
$263$	−12.5845	−	14.9976i	−0.775993	−	0.924792i	−0.998745	+	0.0500830i	$0.984051\pi$
$264$	21.5179	−	10.1691i	1.32433	−	0.625866i
$265$	8.78271	+	24.1303i	0.539517	+	1.48231i
$266$	−13.5503	+	9.37040i	−0.830820	+	0.574536i
$267$	−3.53730	+	21.2371i	−0.216479	+	1.29969i
$268$	−12.7301	+	1.45062i	−0.777615	+	0.0886109i
$269$	15.3137	−	8.84137i	0.933693	−	0.539068i	0.0457154	−	0.998955i	$-0.485443\pi$
$269$	15.3137	−	8.84137i	0.933693	−	0.539068i	0.887978	+	0.459887i	$0.152110\pi$
$270$	16.4320	+	9.53259i	1.00002	+	0.580135i
$271$	−4.49163	+	7.77973i	−0.272847	+	0.472585i	−0.969590	−	0.244736i	$-0.921299\pi$
$271$	−4.49163	+	7.77973i	−0.272847	+	0.472585i	0.696743	+	0.717321i	$0.254632\pi$
$272$	−0.130584	−	0.201068i	−0.00791784	−	0.0121915i
$273$	−2.21024	+	5.19641i	−0.133770	+	0.314501i
$274$	6.25879	+	1.30178i	0.378107	+	0.0786432i
$275$	8.05195	+	1.41978i	0.485551	+	0.0856157i
$276$	8.56646	−	13.2136i	0.515640	−	0.795367i
$277$	−20.6166	+	17.2994i	−1.23873	+	1.03942i	−0.241110	+	0.970498i	$0.577511\pi$
$277$	−20.6166	+	17.2994i	−1.23873	+	1.03942i	−0.997622	+	0.0689213i	$0.978044\pi$
$278$	0.0168341	−	0.551131i	0.00100964	−	0.0330547i
$279$	−5.83228	+	0.110663i	−0.349170	+	0.00662525i
$280$	−14.5634	+	12.7340i	−0.870330	+	0.761002i
$281$	−14.8390	−	5.40094i	−0.885218	−	0.322193i	−0.140905	−	0.990023i	$-0.545001\pi$
$281$	−14.8390	−	5.40094i	−0.885218	−	0.322193i	−0.744314	+	0.667830i	$0.767223\pi$
$282$	9.52131	+	3.69423i	0.566986	+	0.219988i
$283$	−3.42862	+	19.4447i	−0.203810	+	1.15587i	0.695491	+	0.718535i	$0.255187\pi$
$283$	−3.42862	+	19.4447i	−0.203810	+	1.15587i	−0.899301	+	0.437330i	$0.855924\pi$
$284$	−12.2881	−	2.94991i	−0.729167	−	0.175045i
$285$	−18.5892	−	6.56691i	−1.10113	−	0.388990i
$286$	−3.13713	+	7.86346i	−0.185502	+	0.464976i
$287$	2.80760	−	11.6181i	0.165728	−	0.685796i
$288$	−15.6969	+	6.45037i	−0.924949	+	0.380092i
$289$	16.9964			0.999789
$290$	24.5522	−	19.3557i	1.44175	−	1.13661i
$291$	10.0925	−	17.8700i	0.591631	−	1.04756i
$292$	17.2156	+	4.13281i	1.00747	+	0.241854i
$293$	14.7760	+	2.60541i	0.863224	+	0.152210i	0.587694	−	0.809083i	$-0.300036\pi$
$293$	14.7760	+	2.60541i	0.863224	+	0.152210i	0.275529	+	0.961293i	$0.411147\pi$
$294$	10.6451	−	13.4418i	0.620833	−	0.783943i
$295$	19.6315	+	23.3959i	1.14299	+	1.36216i
$296$	21.9743	+	15.5291i	1.27723	+	0.902612i
$297$	−23.9572	−	7.95532i	−1.39014	−	0.461615i
$298$	16.3379	−	8.77886i	0.946431	−	0.508546i
$299$	0.972735	+	5.51666i	0.0562547	+	0.319036i
$300$	−5.68165	−	1.30707i	−0.328030	−	0.0754637i
$301$	−1.36091	−	12.1051i	−0.0784415	−	0.697727i
$302$	5.59121	−	1.84375i	0.321738	−	0.106096i
$303$	7.91465	+	13.4131i	0.454685	+	0.770563i
$304$	14.7705	−	9.59274i	0.847144	−	0.550181i
$305$	−3.38137	+	5.85670i	−0.193617	+	0.335354i
$306$	−0.0470505	+	0.249904i	−0.00268970	+	0.0142860i
$307$	−1.53497	+	2.65865i	−0.0876055	+	0.151737i	−0.906498	−	0.422209i	$-0.861255\pi$
$307$	−1.53497	+	2.65865i	−0.0876055	+	0.151737i	0.818893	+	0.573946i	$0.194588\pi$
$308$	15.5010	−	20.5074i	0.883250	−	1.16852i
$309$	−10.1586	+	28.7564i	−0.577903	+	1.63590i
$310$	6.75120	−	2.22627i	0.383442	−	0.126444i
$311$	2.48909	−	14.1163i	0.141143	−	0.800465i	−0.829240	−	0.558893i	$-0.811226\pi$
$311$	2.48909	−	14.1163i	0.141143	−	0.800465i	0.970383	−	0.241571i	$-0.0776628\pi$
$312$	2.52308	−	5.48428i	0.142841	−	0.310486i
$313$	15.7394	+	18.7575i	0.889642	+	1.06023i	0.997813	+	0.0661021i	$0.0210563\pi$
$313$	15.7394	+	18.7575i	0.889642	+	1.06023i	−0.108170	+	0.994132i	$0.534499\pi$
$314$	8.86594	−	14.3275i	0.500334	−	0.808546i
$315$	20.4995	+	0.894478i	1.15501	+	0.0503981i
$316$	8.76253	−	4.36902i	0.492931	−	0.245776i
$317$	−9.59675	−	3.49293i	−0.539007	−	0.196183i	0.0581485	−	0.998308i	$-0.481480\pi$
$317$	−9.59675	−	3.49293i	−0.539007	−	0.196183i	−0.597156	+	0.802125i	$0.703703\pi$
$318$	11.7195	+	21.3230i	0.657197	+	1.19573i
$319$	−26.7044	+	31.8250i	−1.49516	+	1.78186i
$320$	15.9575	−	13.1556i	0.892050	−	0.735422i
$321$	22.2419	+	18.3065i	1.24142	+	1.02177i
$322$	1.58151	−	16.9356i	0.0881339	−	0.943783i
$323$		−	0.263908i		−	0.0146842i
$324$	16.7676	+	6.54585i	0.931532	+	0.363658i
$325$	1.79604	−	1.03694i	0.0996263	−	0.0575193i
$326$	−0.722007	−	0.288045i	−0.0399883	−	0.0159533i
$327$	−5.40119	−	14.4128i	−0.298687	−	0.797028i
$328$	−3.36066	+	12.3279i	−0.185561	+	0.680697i
$329$	10.9621	−	1.23241i	0.604360	−	0.0679449i
$330$	30.7562	+	0.647485i	1.69307	+	0.0356429i
$331$	−9.35227	+	25.6951i	−0.514047	+	1.41233i	0.362937	+	0.931814i	$0.381774\pi$
$331$	−9.35227	+	25.6951i	−0.514047	+	1.41233i	−0.876984	+	0.480519i	$0.840448\pi$
$332$	−8.16155	+	12.3312i	−0.447923	+	0.676762i
$333$	−5.48822	−	28.0073i	−0.300753	−	1.53479i
$334$	−25.6671	+	13.7917i	−1.40444	+	0.754647i
$335$	−15.5623	−	5.66423i	−0.850261	−	0.309470i
$336$	−11.7923	+	14.0336i	−0.643324	+	0.765594i
$337$	−0.445510	−	0.373827i	−0.0242685	−	0.0203637i	0.630573	−	0.776130i	$-0.282820\pi$
$337$	−0.445510	−	0.373827i	−0.0242685	−	0.0203637i	−0.654841	+	0.755766i	$0.727265\pi$
$338$	−5.08507	−	15.4205i	−0.276591	−	0.838767i
$339$	−19.9910	+	3.72081i	−1.08576	+	0.202087i
$340$	−0.0350862	−	0.307903i	−0.00190282	−	0.0166984i
$341$	−8.18076	+	4.72316i	−0.443013	+	0.255774i
$342$	−18.3580	−	3.45633i	−0.992685	−	0.186897i
$343$	3.45653	−	18.1948i	0.186635	−	0.982429i
$344$	1.07868	+	12.9777i	0.0581586	+	0.699709i
$345$	17.5305	−	10.3442i	0.943808	−	0.556911i
$346$	3.12340	+	2.78769i	0.167915	+	0.149867i
$347$	−2.23384	−	6.13743i	−0.119919	−	0.329474i	0.865181	−	0.501461i	$-0.167204\pi$
$347$	−2.23384	−	6.13743i	−0.119919	−	0.329474i	−0.985099	+	0.171986i	$0.944982\pi$
$348$	20.1864	−	21.6810i	1.08211	−	1.16222i
$349$	−0.151883	−	0.181007i	−0.00813013	−	0.00968911i	0.761964	−	0.647619i	$-0.224235\pi$
$349$	−0.151883	−	0.181007i	−0.00813013	−	0.00968911i	−0.770094	+	0.637930i	$0.779791\pi$
$350$	−6.09203	+	1.59424i	−0.325633	+	0.0852155i
$351$	−5.95212	+	2.36028i	−0.317701	+	0.125982i
$352$	−17.2005	+	21.4332i	−0.916791	+	1.14239i
$353$	5.98911	−	16.4549i	0.318768	−	0.875809i	−0.672038	−	0.740517i	$-0.734581\pi$
$353$	5.98911	−	16.4549i	0.318768	−	0.875809i	0.990806	−	0.135292i	$-0.0431971\pi$
$354$	21.7718	+	19.0638i	1.15716	+	1.01323i
$355$	−12.5130	−	10.4997i	−0.664123	−	0.557265i
$356$	−7.06112	−	23.8365i	−0.374239	−	1.26333i
$357$	0.0801130	+	0.262726i	0.00424003	+	0.0139049i
$358$	−3.24411	−	22.3729i	−0.171457	−	1.18245i
$359$		−	12.9346i		−	0.682663i	−0.939943	−	0.341332i	$-0.889122\pi$
$359$		−	12.9346i		−	0.682663i	0.939943	−	0.341332i	$-0.110878\pi$
$360$	−21.8779	−	1.59186i	−1.15307	−	0.0838985i
$361$	0.386714			0.0203534
$362$	−1.03330	+	0.814604i	−0.0543092	+	0.0428146i
$363$	−21.4575	+	3.99377i	−1.12623	+	0.209619i
$364$	−0.331648	−	6.51208i	−0.0173831	−	0.341326i
$365$	17.5307	+	14.7100i	0.917598	+	0.769956i
$366$	−2.31787	+	5.97395i	−0.121157	+	0.312264i
$367$	5.61935	+	31.8689i	0.293328	+	1.66355i	0.673921	+	0.738803i	$0.264609\pi$
$367$	5.61935	+	31.8689i	0.293328	+	1.66355i	−0.380594	+	0.924742i	$0.624280\pi$
$368$	−2.21544	+	18.0482i	−0.115488	+	0.940827i
$369$	11.6065	−	6.99790i	0.604210	−	0.364296i
$370$	16.4624	+	30.6374i	0.855840	+	1.59276i
$371$	21.8936	+	14.5381i	1.13666	+	0.754780i
$372$	5.99922	−	3.06262i	0.311045	−	0.158790i
$373$	0.701346	−	3.97753i	0.0363143	−	0.205949i	−0.961252	−	0.275671i	$-0.911100\pi$
$373$	0.701346	−	3.97753i	0.0363143	−	0.205949i	0.997566	+	0.0697220i	$0.0222112\pi$
$374$	0.128963	+	0.391082i	0.00666852	+	0.0202224i
$375$	11.4675	+	9.43850i	0.592181	+	0.487402i
$376$	−11.7523	+	0.976829i	−0.606078	+	0.0503761i
$377$			10.5378i			0.542725i
$378$	19.3250	−	2.13196i	0.993970	−	0.109656i
$379$		−	24.9867i		−	1.28348i	−0.766922	−	0.641740i	$-0.778213\pi$
$379$		−	24.9867i		−	1.28348i	0.766922	−	0.641740i	$-0.221787\pi$
$380$	22.6186	−	2.57744i	1.16031	−	0.132220i
$381$	6.05637	−	2.26963i	0.310277	−	0.116276i
$382$	26.5023	−	8.73937i	1.35597	−	0.447145i
$383$	−6.56171	+	37.2133i	−0.335288	+	1.90151i	0.0890861	+	0.996024i	$0.471605\pi$
$383$	−6.56171	+	37.2133i	−0.335288	+	1.90151i	−0.424374	+	0.905487i	$0.639506\pi$
$384$	13.0366	−	14.6303i	0.665272	−	0.746601i
$385$	29.7588	−	14.7818i	1.51665	−	0.753350i
$386$	−4.42680	+	2.37865i	−0.225318	+	0.121070i
$387$	8.67609	−	10.7474i	0.441031	−	0.546322i
$388$	−1.44634	+	23.6538i	−0.0734268	+	1.20084i
$389$	−2.21450	−	12.5591i	−0.112280	−	0.636770i	−0.988061	−	0.154062i	$-0.950764\pi$
$389$	−2.21450	−	12.5591i	−0.112280	−	0.636770i	0.875782	−	0.482708i	$-0.160347\pi$
$390$	6.08172	−	4.88878i	0.307960	−	0.247553i
$391$	0.208726	+	0.175142i	0.0105557	+	0.00885729i
$392$	−4.25815	+	19.3357i	−0.215069	+	0.976599i
$393$	−7.89707	−	9.23208i	−0.398355	−	0.465697i
$394$	−9.68273	−	12.2823i	−0.487809	−	0.618772i
$395$	12.6560			0.636794
$396$	28.8934	−	3.84902i	1.45195	−	0.193421i
$397$		−	12.3161i		−	0.618129i	−0.951041	−	0.309065i	$-0.899984\pi$
$397$		−	12.3161i		−	0.618129i	0.951041	−	0.309065i	$-0.100016\pi$
$398$	−33.3771	+	4.83973i	−1.67304	+	0.242594i
$399$	−19.2999	+	5.88512i	−0.966204	+	0.294624i
$400$	6.55938	−	1.51458i	0.327969	−	0.0757289i
$401$	18.7586	+	15.7403i	0.936760	+	0.786035i	0.977019	−	0.213154i	$-0.0683736\pi$
$401$	18.7586	+	15.7403i	0.936760	+	0.786035i	−0.0402582	+	0.999189i	$0.512818\pi$
$402$	−15.3929	−	3.04955i	−0.767726	−	0.152098i
$403$	−0.819502	+	2.25156i	−0.0408223	+	0.112158i
$404$	−14.9963	−	9.92548i	−0.746094	−	0.493811i
$405$	15.6207	+	17.2429i	0.776197	+	0.856806i
$406$	8.46205	−	30.8579i	0.419964	−	1.53145i
$407$	−29.7076	−	35.4041i	−1.47255	−	1.75492i
$408$	−0.0774569	−	0.283233i	−0.00383469	−	0.0140221i
$409$	−10.0896	−	27.7209i	−0.498898	−	1.37071i	−0.892341	−	0.451362i	$-0.850938\pi$
$409$	−10.0896	−	27.7209i	−0.498898	−	1.37071i	0.393443	−	0.919349i	$-0.371284\pi$
$410$	−10.9978	+	12.3222i	−0.543141	+	0.608548i
$411$	6.81735	+	3.85024i	0.336275	+	0.189918i
$412$	−3.98715	−	34.9896i	−0.196433	−	1.72382i
$413$	30.3826	+	7.34219i	1.49503	+	0.361286i
$414$	14.9168	−	12.2256i	0.733122	−	0.600854i
$415$	−16.5531	+	9.55695i	−0.812561	+	0.469132i
$416$	0.152350	+	6.96906i	0.00746960	+	0.341686i
$417$	0.224940	−	0.636746i	0.0110153	−	0.0311816i
$418$	−28.7289	+	9.47364i	−1.40518	+	0.463371i
$419$	−29.2791	−	24.5681i	−1.43038	−	1.20023i	−0.945490	−	0.325652i	$-0.894416\pi$
$419$	−29.2791	−	24.5681i	−1.43038	−	1.20023i	−0.484887	−	0.874577i	$-0.661139\pi$
$420$	−21.7349	+	9.43210i	−1.06056	+	0.460240i
$421$	26.3095	+	9.57587i	1.28225	+	0.466699i	0.891174	−	0.453661i	$-0.149882\pi$
$421$	26.3095	+	9.57587i	1.28225	+	0.466699i	0.391072	+	0.920360i	$0.372104\pi$
$422$	15.3471	+	28.5618i	0.747085	+	1.39036i
$423$	9.73261	+	7.85687i	0.473216	+	0.382014i
$424$	−22.9443	−	16.2146i	−1.11427	−	0.787451i
$425$	0.0345012	−	0.0947912i	0.00167355	−	0.00459805i
$426$	−13.2380	−	8.01912i	−0.641383	−	0.388527i
$427$	0.773250	+	6.87795i	0.0374202	+	0.332847i
$428$	−32.3443	−	7.76462i	−1.56342	−	0.375317i
$429$	−6.58933	+	8.00588i	−0.318136	+	0.386528i
$430$	−6.23726	+	15.6342i	−0.300787	+	0.753948i
$431$	−7.61842	+	4.39850i	−0.366966	+	0.211868i	−0.672132	−	0.740431i	$-0.734621\pi$
$431$	−7.61842	+	4.39850i	−0.366966	+	0.211868i	0.305166	+	0.952299i	$0.401288\pi$
$432$	−20.7167	+	1.67862i	−0.996733	+	0.0807625i
$433$		−	14.8237i		−	0.712382i	−0.934413	−	0.356191i	$-0.884075\pi$
$433$		−	14.8237i		−	0.712382i	0.934413	−	0.356191i	$-0.115925\pi$
$434$	4.20780	−	5.93519i	0.201981	−	0.284898i
$435$	35.8556	−	13.4369i	1.71915	−	0.644251i
$436$	12.8920	+	12.2337i	0.617417	+	0.585887i
$437$	−12.8659	+	15.3330i	−0.615461	+	0.733477i
$438$	18.5463	+	11.2347i	0.886179	+	0.536816i
$439$	−1.66223	−	0.605001i	−0.0793338	−	0.0288751i	0.302048	−	0.953293i	$-0.402330\pi$
$439$	−1.66223	−	0.605001i	−0.0793338	−	0.0288751i	−0.381382	+	0.924417i	$0.624552\pi$
$440$	−32.2587	+	14.8724i	−1.53788	+	0.709016i
$441$	17.4270	−	11.7175i	0.829856	−	0.557977i
$442$	0.0888218	+	0.0549636i	0.00422482	+	0.00261435i
$443$	4.25659	+	5.07280i	0.202237	+	0.241016i	0.857625	−	0.514276i	$-0.171939\pi$
$443$	4.25659	+	5.07280i	0.202237	+	0.241016i	−0.655388	+	0.755292i	$0.727495\pi$
$444$	19.8533	+	26.3037i	0.942195	+	1.24832i
$445$	5.57999	−	31.6457i	0.264517	−	1.50015i
$446$	4.76938	+	14.4632i	0.225837	+	0.684853i
$447$	22.3320	−	4.15653i	1.05627	−	0.196597i
$448$	5.15015	−	20.5299i	0.243322	−	0.969946i
$449$	2.76145	−	4.78298i	0.130321	−	0.225723i	−0.793479	−	0.608597i	$-0.791733\pi$
$449$	2.76145	−	4.78298i	0.130321	−	0.225723i	0.923800	+	0.382875i	$0.125066\pi$
$450$	−6.14201	−	3.64143i	−0.289537	−	0.171659i
$451$	10.9736	−	19.0068i	0.516726	−	0.894996i
$452$	18.8743	−	13.9668i	0.887775	−	0.656941i
$453$	7.21019	−	0.0683980i	0.338764	−	0.00321362i
$454$	−11.3482	−	34.4135i	−0.532597	−	1.61511i
$455$	3.37229	−	7.72419i	0.158095	−	0.362116i
$456$	20.8064	−	5.68999i	0.974348	−	0.266458i
$457$	−0.173230	−	0.982434i	−0.00810334	−	0.0459563i	0.980488	−	0.196579i	$-0.0629832\pi$
$457$	−0.173230	−	0.982434i	−0.00810334	−	0.0459563i	−0.988591	+	0.150623i	$0.951872\pi$
$458$	−9.41028	−	17.5130i	−0.439714	−	0.818331i
$459$	−0.147985	+	0.274042i	−0.00690735	+	0.0127912i
$460$	−12.9723	+	19.5996i	−0.604835	+	0.913838i
$461$	−4.10028	−	4.88652i	−0.190969	−	0.227588i	0.662061	−	0.749450i	$-0.269682\pi$
$461$	−4.10028	−	4.88652i	−0.190969	−	0.227588i	−0.853030	+	0.521862i	$0.825238\pi$
$462$	25.7244	−	18.1523i	1.19681	−	0.844522i
$463$	−16.1074	−	2.84018i	−0.748577	−	0.131994i	−0.213670	−	0.976906i	$-0.568542\pi$
$463$	−16.1074	−	2.84018i	−0.748577	−	0.131994i	−0.534906	+	0.844912i	$0.679653\pi$
$464$	−9.99991	+	32.7121i	−0.464234	+	1.51862i
$465$	8.70607	−	0.0825883i	0.403734	−	0.00382994i
$466$	17.1853	+	21.7991i	0.796093	+	1.00982i
$467$	5.54548			0.256614			0.128307	−	0.991734i	$-0.459046\pi$
$467$	5.54548			0.256614			0.128307	+	0.991734i	$0.459046\pi$
$468$	4.98665	−	5.45878i	0.230508	−	0.252332i
$469$	−16.2585	+	4.78962i	−0.750748	+	0.221164i
$470$	−14.1580	−	5.64832i	−0.653058	−	0.260538i
$471$	15.6811	−	13.4136i	0.722549	−	0.618064i
$472$	−32.2389	−	8.78849i	−1.48392	−	0.404523i
$473$	3.88405	−	22.0275i	0.178589	−	1.01283i
$474$	11.8509	−	1.83334i	0.544331	−	0.0842083i
$475$	6.96338	+	2.53446i	0.319502	+	0.116289i
$476$	−0.215961	−	0.232276i	−0.00989853	−	0.0106463i
$477$	5.73048	+	29.2436i	0.262381	+	1.33897i
$478$	4.00465	+	0.122320i	0.183168	+	0.00559480i
$479$	−26.8958	+	22.5682i	−1.22890	+	1.03117i	−0.230589	+	0.973051i	$0.574065\pi$
$479$	−26.8958	+	22.5682i	−1.22890	+	1.03117i	−0.998310	+	0.0581170i	$0.981490\pi$
$480$	23.5185	−	9.40474i	1.07347	−	0.429266i
$481$	−11.5448	−	2.03566i	−0.526398	−	0.0928181i
$482$	0.869560	−	4.18074i	0.0396074	−	0.190428i
$483$	8.15376	−	19.1700i	0.371009	−	0.872265i
$484$	20.2590	−	14.9914i	0.920862	−	0.681426i
$485$	−15.3157	+	26.5276i	−0.695450	+	1.20455i
$486$	17.1248	+	13.8832i	0.776794	+	0.629754i
$487$	−29.4287	+	16.9907i	−1.33354	+	0.769922i	−0.985841	−	0.167683i	$-0.946371\pi$
$487$	−29.4287	+	16.9907i	−1.33354	+	0.769922i	−0.347703	+	0.937605i	$0.613038\pi$
$488$	−0.612892	−	7.37373i	−0.0277443	−	0.333793i
$489$	−0.735083	−	0.605019i	−0.0332416	−	0.0273599i
$490$	−16.0777	+	19.9108i	−0.726319	+	0.899478i
$491$	6.11890	+	16.8115i	0.276142	+	0.758694i	0.997791	+	0.0664345i	$0.0211623\pi$
$491$	6.11890	+	16.8115i	0.276142	+	0.758694i	−0.721649	+	0.692259i	$0.756615\pi$
$492$	−8.51317	+	13.1314i	−0.383803	+	0.592010i
$493$	0.329469	+	0.392646i	0.0148386	+	0.0176839i
$494$	−4.03763	+	6.52486i	−0.181662	+	0.293567i
$495$	35.6427	+	12.2123i	1.60202	+	0.548900i
$496$	−4.68058	+	6.21176i	−0.210164	+	0.278916i
$497$	−16.6848	−	1.04548i	−0.748416	−	0.0468960i
$498$	−14.1157	+	11.3469i	−0.632539	+	0.508465i
$499$	−5.46809	−	15.0235i	−0.244786	−	0.672543i	−0.999857	−	0.0169005i	$-0.994620\pi$
$499$	−5.46809	−	15.0235i	−0.244786	−	0.672543i	0.755072	−	0.655642i	$-0.227602\pi$
$500$	−16.6761	−	4.00330i	−0.745779	−	0.179033i
$501$	−35.0838	+	6.52996i	−1.56743	+	0.291737i
$502$	14.4636	+	18.3466i	0.645541	+	0.818851i
$503$	4.17222	−	7.22650i	0.186030	−	0.322214i	−0.757893	−	0.652379i	$-0.773771\pi$
$503$	4.17222	−	7.22650i	0.186030	−	0.322214i	0.943923	+	0.330165i	$0.107104\pi$
$504$	−18.9859	+	11.9806i	−0.845700	+	0.533658i
$505$	−11.6225	−	20.1307i	−0.517193	−	0.895804i
$506$	11.5731	−	29.0090i	0.514488	−	1.28961i
$507$	−0.188642	−	19.8857i	−0.00837787	−	0.883155i
$508$	−5.14070	+	5.41734i	−0.228082	+	0.240356i
$509$	−13.4351	+	16.0113i	−0.595500	+	0.709689i	−0.976653	−	0.214823i	$-0.931083\pi$
$509$	−13.4351	+	16.0113i	−0.595500	+	0.709689i	0.381153	+	0.924512i	$0.375527\pi$
$510$	0.0737595	−	0.372307i	0.00326613	−	0.0164860i
$511$	23.3753	+	1.46471i	1.03406	+	0.0647948i
$512$	−6.14039	+	21.7783i	−0.271370	+	0.962475i
$513$	−20.1311	−	10.8710i	−0.888811	−	0.479967i
$514$	12.9943	+	24.1830i	0.573152	+	1.06667i
$515$	15.5685	−	42.7742i	0.686032	−	1.88486i
$516$	−3.57572	+	15.5432i	−0.157412	+	0.684249i
$517$	19.9476	+	3.51731i	0.877296	+	0.154691i
$518$	32.1720	+	15.2317i	1.41356	+	0.669243i
$519$	2.60571	+	4.41594i	0.114378	+	0.193838i
$520$	−3.84326	+	8.14940i	−0.168538	+	0.357375i
$521$	3.73580	+	2.15686i	0.163668	+	0.0944939i	0.579597	−	0.814903i	$-0.303210\pi$
$521$	3.73580	+	2.15686i	0.163668	+	0.0944939i	−0.415929	+	0.909397i	$0.636543\pi$
$522$	31.6282	−	17.7762i	1.38433	−	0.778041i
$523$	5.50012	+	9.52649i	0.240503	+	0.416564i	0.960858	−	0.277042i	$-0.0893541\pi$
$523$	5.50012	+	9.52649i	0.240503	+	0.416564i	−0.720354	+	0.693606i	$0.756021\pi$
$524$	12.8649	+	5.59356i	0.562005	+	0.244356i
$525$	−7.70157	−	0.409281i	−0.336124	−	0.0178625i
$526$	20.6566	+	18.4364i	0.900670	+	0.803865i
$527$	0.0398609	+	0.109517i	0.00173637	+	0.00477064i
$528$	−28.0522	+	18.5993i	−1.22082	+	0.809431i
$529$	0.405408	+	2.29918i	0.0176264	+	0.0999645i
$530$	−17.1891	−	31.9898i	−0.746646	−	1.38955i
$531$	18.3003	+	30.3523i	0.794164	+	1.31718i
$532$	17.0630	−	15.8645i	0.739775	−	0.687813i
$533$	−0.966684	−	5.48234i	−0.0418717	−	0.237466i
$534$	0.640847	−	30.4409i	0.0277322	−	1.31731i
$535$	−32.9362	−	27.6368i	−1.42396	−	1.19484i
$536$	17.5224	−	4.61371i	0.756851	−	0.199282i
$537$	4.54905	−	27.3115i	0.196306	−	1.17858i
$538$	−19.6384	+	15.4820i	−0.846673	+	0.667474i
$539$	15.5291	−	30.2541i	0.668886	−	1.30313i
$540$	−24.9324	−	10.0069i	−1.07292	−	0.430627i
$541$	−6.97108	+	12.0743i	−0.299710	+	0.519113i	−0.976070	−	0.217459i	$-0.930223\pi$
$541$	−6.97108	+	12.0743i	−0.299710	+	0.519113i	0.676359	+	0.736572i	$0.263557\pi$
$542$	4.70756	−	11.7999i	0.202207	−	0.506848i
$543$	−1.50902	+	0.565506i	−0.0647583	+	0.0242682i
$544$	0.223568	+	0.254909i	0.00958538	+	0.0109291i
$545$	7.85705	+	21.5871i	0.336559	+	0.924689i
$546$	2.03884	−	7.72133i	0.0872542	−	0.330442i
$547$	−28.7302	+	5.06592i	−1.22842	+	0.216603i	−0.749945	−	0.661500i	$-0.769920\pi$
$547$	−28.7302	+	5.06592i	−1.22842	+	0.216603i	−0.478472	+	0.878103i	$0.658809\pi$
$548$	−9.02384	−	0.551773i	−0.385479	−	0.0235706i
$549$	−4.92963	+	6.10653i	−0.210392	+	0.260620i
$550$	−11.5575	−	0.353018i	−0.492811	−	0.0150527i
$551$	−28.8439	+	24.2029i	−1.22879	+	1.03108i
$552$	−9.30784	+	20.2320i	−0.396168	+	0.861130i
$553$	10.4236	−	7.68903i	0.443257	−	0.326971i
$554$	25.3438	−	28.3958i	1.07675	−	1.20642i
$555$	7.79447	+	41.8777i	0.330857	+	1.77761i
$556$	0.0882864	+	0.774767i	0.00374418	+	0.0328574i
$557$	−18.8322			−0.797948			−0.398974	−	0.916962i	$-0.630634\pi$
$557$	−18.8322			−0.797948			−0.398974	+	0.916962i	$0.630634\pi$
$558$	8.14027	−	1.33849i	0.344605	−	0.0566628i
$559$	−2.83674	−	4.91338i	−0.119981	−	0.207814i
$560$	17.7984	−	20.7777i	0.752118	−	0.878019i
$561$	0.00478416	+	0.504323i	0.000201987	+	0.0212925i
$562$	21.8643	+	4.54760i	0.922291	+	0.191829i
$563$	21.3762	−	7.78029i	0.900899	−	0.327900i	0.150286	−	0.988643i	$-0.451981\pi$
$563$	21.3762	−	7.78029i	0.900899	−	0.327900i	0.750613	+	0.660742i	$0.229758\pi$
$564$	−14.0755	−	3.23809i	−0.592686	−	0.136348i
$565$	29.8886	−	5.27017i	1.25742	−	0.221718i
$566$	0.852503	−	27.9101i	0.0358334	−	1.17315i
$567$	23.3410	+	4.71124i	0.980232	+	0.197853i
$568$	17.7969	+	1.63486i	0.746740	+	0.0685973i
$569$	5.77744	+	32.7655i	0.242203	+	1.37360i	0.826900	+	0.562349i	$0.190102\pi$
$569$	5.77744	+	32.7655i	0.242203	+	1.37360i	−0.584697	+	0.811251i	$0.698787\pi$
$570$	27.3497	+	5.41838i	1.14555	+	0.226951i
$571$	0.144178	+	0.396125i	0.00603365	+	0.0165773i	0.942673	−	0.333718i	$-0.108303\pi$
$571$	0.144178	+	0.396125i	0.00603365	+	0.0165773i	−0.936639	+	0.350296i	$0.886081\pi$
$572$	2.79484	−	11.6422i	0.116858	−	0.486784i
$573$	34.1762	−	0.324206i	1.42773	−	0.0135439i
$574$	−1.57167	+	16.8302i	−0.0656002	+	0.702480i
$575$	−6.62573	+	3.82537i	−0.276312	+	0.159529i
$576$	20.6600	−	12.2133i	0.860832	−	0.508889i
$577$		−	43.6807i		−	1.81845i	−0.416303	−	0.909226i	$-0.636674\pi$
$577$		−	43.6807i		−	1.81845i	0.416303	−	0.909226i	$-0.363326\pi$
$578$	−23.7878	+	3.44926i	−0.989441	+	0.143470i
$579$	−6.05091	+	1.12622i	−0.251467	+	0.0468042i
$580$	−30.4346	+	32.0724i	−1.26373	+	1.33173i
$581$	−7.82708	+	17.9279i	−0.324722	+	0.743773i
$582$	−10.4986	+	27.0586i	−0.435182	+	1.12162i
$583$	31.0189	+	36.9669i	1.28467	+	1.53101i
$584$	−24.9333	−	2.29043i	−1.03175	−	0.0947787i
$585$	8.91678	−	3.43838i	0.368663	−	0.142159i
$586$	−21.2089	−	0.647817i	−0.876132	−	0.0267611i
$587$	0.664898	+	3.77083i	0.0274433	+	0.155639i	0.995450	−	0.0952859i	$-0.0303765\pi$
$587$	0.664898	+	3.77083i	0.0274433	+	0.155639i	−0.968007	+	0.250925i	$0.919265\pi$
$588$	−12.1707	+	20.9732i	−0.501911	+	0.864919i
$589$	−8.04514	+	2.92819i	−0.331494	+	0.120654i
$590$	−32.2238	−	28.7604i	−1.32663	−	1.18405i
$591$	−6.72185	−	17.9369i	−0.276500	−	0.737824i
$592$	−33.9063	−	17.2747i	−1.39354	−	0.709986i
$593$	23.4815	+	13.5570i	0.964269	+	0.556721i	0.897484	−	0.441046i	$-0.145392\pi$
$593$	23.4815	+	13.5570i	0.964269	+	0.556721i	0.0667851	+	0.997767i	$0.478726\pi$
$594$	35.1444	+	6.27220i	1.44199	+	0.257351i
$595$	−0.115847	−	0.393245i	−0.00474924	−	0.0161215i
$596$	−21.0846	+	15.6023i	−0.863659	+	0.639096i
$597$	−40.7447	−	6.78652i	−1.66757	−	0.277754i
$598$	−2.48097	−	7.52358i	−0.101454	−	0.307662i
$599$	11.6191	−	13.8471i	0.474744	−	0.565777i	−0.474526	−	0.880242i	$-0.657380\pi$
$599$	11.6191	−	13.8471i	0.474744	−	0.565777i	0.949269	+	0.314464i	$0.101825\pi$
$600$	8.21716	+	0.676308i	0.335464	+	0.0276101i
$601$	−17.3731	+	3.06334i	−0.708663	+	0.124956i	−0.516350	−	0.856377i	$-0.672710\pi$
$601$	−17.3731	+	3.06334i	−0.708663	+	0.124956i	−0.192312	+	0.981334i	$0.561599\pi$
$602$	4.36132	+	16.6658i	0.177754	+	0.679249i
$603$	−16.8232	−	9.29189i	−0.685094	−	0.378395i
$604$	−7.45115	+	3.71516i	−0.303183	+	0.151168i
$605$	32.0812	−	5.65678i	1.30429	−	0.229981i
$606$	−13.7992	−	17.1665i	−0.560555	−	0.697340i
$607$	4.10750	−	1.49501i	0.166718	−	0.0606805i	−0.257313	−	0.966328i	$-0.582837\pi$
$607$	4.10750	−	1.49501i	0.166718	−	0.0606805i	0.424031	+	0.905648i	$0.360615\pi$
$608$	−18.7256	+	16.4233i	−0.759425	+	0.666053i
$609$	21.3676	−	32.8505i	0.865858	−	1.33117i
$610$	3.54392	−	8.88313i	0.143489	−	0.359667i
$611$	4.44945	−	2.56889i	0.180005	−	0.103926i
$612$	0.0151351	−	0.359308i	0.000611802	−	0.0145242i
$613$	−21.6500	+	37.4989i	−0.874435	+	1.51457i	−0.0170707	+	0.999854i	$0.505434\pi$
$613$	−21.6500	+	37.4989i	−0.874435	+	1.51457i	−0.857364	+	0.514711i	$0.827899\pi$
$614$	1.60876	−	4.03249i	0.0649244	−	0.162738i
$615$	−17.4214	+	10.2798i	−0.702499	+	0.414522i
$616$	−17.5330	+	31.8475i	−0.706425	+	1.28317i
$617$	3.31278	−	18.7877i	0.133367	−	0.756364i	−0.842615	−	0.538516i	$-0.818985\pi$
$617$	3.31278	−	18.7877i	0.133367	−	0.756364i	0.975983	−	0.217848i	$-0.0699037\pi$
$618$	8.38191	−	42.3084i	0.337170	−	1.70189i
$619$	−23.1618	−	8.43022i	−0.930953	−	0.338839i	−0.168366	−	0.985725i	$-0.553849\pi$
$619$	−23.1618	−	8.43022i	−0.930953	−	0.338839i	−0.762587	+	0.646886i	$0.776071\pi$
$620$	−8.99702	+	4.48593i	−0.361329	+	0.180159i
$621$	21.9579	−	8.70727i	0.881139	−	0.349411i
$622$	−0.618896	+	20.2620i	−0.0248155	+	0.812434i
$623$	−14.6303	−	29.4537i	−0.586149	−	1.18004i
$624$	−2.41826	+	8.18771i	−0.0968078	+	0.327771i
$625$	−23.4276	−	19.6581i	−0.937102	−	0.786322i
$626$	−25.8351	−	23.0583i	−1.03258	−	0.921597i
$627$	−37.0477	+	0.351445i	−1.47954	+	0.0140354i
$628$	−9.50094	+	21.8516i	−0.379129	+	0.871976i
$629$	−0.493813	+	0.285103i	−0.0196896	+	0.0113678i
$630$	−28.8721	+	2.90829i	−1.15029	+	0.115869i
$631$	22.8170	+	13.1734i	0.908330	+	0.524425i	0.879894	−	0.475171i	$-0.157614\pi$
$631$	22.8170	+	13.1734i	0.908330	+	0.524425i	0.0284367	+	0.999596i	$0.490947\pi$
$632$	−11.3772	+	7.89305i	−0.452560	+	0.313969i
$633$	7.26640	+	39.0405i	0.288813	+	1.55172i
$634$	14.1402	+	2.94105i	0.561581	+	0.116804i
$635$	−9.07107	+	3.30160i	−0.359974	+	0.131020i
$636$	−20.7296	−	27.4648i	−0.821983	−	1.08905i
$637$	−1.91530	−	8.41051i	−0.0758870	−	0.333236i
$638$	30.9162	−	49.9610i	1.22399	−	1.97797i
$639$	−12.4579	−	14.2873i	−0.492827	−	0.565197i
$640$	−19.6639	+	21.6507i	−0.777283	+	0.855821i
$641$	−15.2164	+	12.7681i	−0.601011	+	0.504308i	−0.891770	−	0.452488i	$-0.850536\pi$
$641$	−15.2164	+	12.7681i	−0.601011	+	0.504308i	0.290760	+	0.956796i	$0.406092\pi$
$642$	−34.8444	−	21.1076i	−1.37520	−	0.833049i
$643$	20.1894	−	7.34833i	0.796191	−	0.289790i	0.0882836	−	0.996095i	$-0.471862\pi$
$643$	20.1894	−	7.34833i	0.796191	−	0.289790i	0.707907	+	0.706306i	$0.249640\pi$
$644$	1.22348	+	24.0236i	0.0482118	+	0.946662i
$645$	−13.1010	+	15.9173i	−0.515850	+	0.626745i
$646$	0.0535576	+	0.369359i	0.00210720	+	0.0145323i
$647$	1.58489	+	2.74511i	0.0623086	+	0.107922i	0.895497	−	0.445068i	$-0.146820\pi$
$647$	1.58489	+	2.74511i	0.0623086	+	0.107922i	−0.833188	+	0.552989i	$0.813487\pi$
$648$	−24.7959	−	5.75859i	−0.974077	−	0.226219i
$649$	49.7049	+	28.6971i	1.95109	+	1.12646i
$650$	−2.30326	+	1.81577i	−0.0903412	+	0.0712204i
$651$	7.12022	−	5.35729i	0.279063	−	0.209969i
$652$	1.06896	+	0.256616i	0.0418637	+	0.0100499i
$653$	5.49945	−	31.1889i	0.215210	−	1.22052i	−0.665332	−	0.746548i	$-0.731710\pi$
$653$	5.49945	−	31.1889i	0.215210	−	1.22052i	0.880542	−	0.473968i	$-0.157179\pi$
$654$	10.4843	+	19.0757i	0.409969	+	0.745917i
$655$	11.6554	+	13.8904i	0.455415	+	0.542743i
$656$	2.20166	−	17.9359i	0.0859603	−	0.700280i
$657$	17.4534	+	20.0164i	0.680924	+	0.780915i
$658$	−15.0922	+	3.94951i	−0.588355	+	0.153968i
$659$	−13.8360	+	38.0141i	−0.538974	+	1.48082i	0.309146	+	0.951015i	$0.399957\pi$
$659$	−13.8360	+	38.0141i	−0.538974	+	1.48082i	−0.848120	+	0.529805i	$0.822265\pi$
$660$	−43.1770	+	5.33548i	−1.68066	+	0.207683i
$661$	−13.2184	−	2.33076i	−0.514136	−	0.0906560i	−0.0894400	−	0.995992i	$-0.528508\pi$
$661$	−13.2184	−	2.33076i	−0.514136	−	0.0906560i	−0.424696	+	0.905336i	$0.639619\pi$
$662$	7.87463	−	37.8603i	0.306056	−	1.47148i
$663$	0.0831561	+	0.0972138i	0.00322952	+	0.00377547i
$664$	8.92021	−	18.9148i	0.346171	−	0.734035i
$665$	28.8878	−	8.51010i	1.12022	−	0.330008i
$666$	13.3650	+	38.0846i	0.517883	+	1.47575i
$667$		−	38.8748i		−	1.50524i
$668$	33.1241	−	24.5114i	1.28161	−	0.948375i
$669$	0.176930	+	18.6512i	0.00684052	+	0.721096i
$670$	22.9302	+	4.76929i	0.885870	+	0.184254i
$671$	−2.20686	+	12.5157i	−0.0851949	+	0.483165i
$672$	13.6563	−	22.0342i	0.526802	−	0.849988i
$673$	−23.9861	+	20.1267i	−0.924596	+	0.775828i	−0.974839	−	0.222909i	$-0.928445\pi$
$673$	−23.9861	+	20.1267i	−0.924596	+	0.775828i	0.0502431	+	0.998737i	$0.484000\pi$
$674$	0.699390	+	0.432788i	0.0269395	+	0.0166704i
$675$	−5.80957	−	6.53646i	−0.223611	−	0.251589i
$676$	10.2464	+	20.5503i	0.394092	+	0.790395i
$677$	−47.7708	+	8.42328i	−1.83598	+	0.323733i	−0.980863	−	0.194701i	$-0.937626\pi$
$677$	−47.7708	+	8.42328i	−1.83598	+	0.323733i	−0.855118	+	0.518434i	$0.826515\pi$
$678$	27.2238	−	9.26455i	1.04552	−	0.355803i
$679$	3.50238	+	31.1532i	0.134409	+	1.19555i
$680$	0.111592	+	0.423814i	0.00427936	+	0.0162525i
$681$	−0.420986	−	44.3783i	−0.0161322	−	1.70058i
$682$	10.4911	−	8.27064i	0.401724	−	0.316699i
$683$	33.2735	+	19.2105i	1.27318	+	0.735069i	0.975584	−	0.219625i	$-0.0704832\pi$
$683$	33.2735	+	19.2105i	1.27318	+	0.735069i	0.297592	+	0.954693i	$0.403817\pi$
$684$	26.3948	+	1.11183i	1.00923	+	0.0425119i
$685$	−10.1202	−	5.84288i	−0.386672	−	0.223245i
$686$	−1.14520	+	26.1666i	−0.0437239	+	0.999044i
$687$	−4.45549	−	23.9382i	−0.169988	−	0.913300i
$688$	−4.14340	−	17.9443i	−0.157965	−	0.684122i
$689$	12.0544	+	2.12552i	0.459236	+	0.0809757i
$690$	−22.4360	+	18.0351i	−0.854123	+	0.686585i
$691$	−5.31144	+	4.45683i	−0.202057	+	0.169546i	−0.738201	−	0.674580i	$-0.764325\pi$
$691$	−5.31144	+	4.45683i	−0.202057	+	0.169546i	0.536145	+	0.844126i	$0.319880\pi$
$692$	−4.93717	−	3.26773i	−0.187683	−	0.124220i
$693$	36.7751	−	11.5962i	1.39697	−	0.440504i
$694$	4.37196	+	8.13646i	0.165958	+	0.308856i
$695$	−0.344731	+	0.947139i	−0.0130764	+	0.0359270i
$696$	−23.8525	+	34.4409i	−0.904127	+	1.30548i
$697$	−0.207427	−	0.174052i	−0.00785686	−	0.00659269i
$698$	0.249306	+	0.222511i	0.00943637	+	0.00842215i
$699$	11.9302	+	31.8351i	0.451242	+	1.20411i
$700$	8.20273	−	3.46758i	0.310034	−	0.131062i
$701$	−45.7626			−1.72843			−0.864214	−	0.503124i	$-0.832184\pi$
$701$	−45.7626			−1.72843			−0.864214	+	0.503124i	$0.832184\pi$
$702$	7.85146	−	4.51132i	0.296334	−	0.170269i
$703$	−20.9437	−	36.2756i	−0.789908	−	1.36816i
$704$	19.7238	−	33.4881i	0.743368	−	1.26213i
$705$	−14.4144	−	11.8639i	−0.542877	−	0.446821i
$706$	−5.04284	+	24.2454i	−0.189790	+	0.912488i
$707$	−21.8025	−	9.51872i	−0.819969	−	0.357988i
$708$	−34.3401	−	22.2629i	−1.29058	−	0.836690i
$709$	−9.61271	−	3.49874i	−0.361013	−	0.131398i	0.155144	−	0.987892i	$-0.450416\pi$
$709$	−9.61271	−	3.49874i	−0.361013	−	0.131398i	−0.516157	+	0.856494i	$0.672638\pi$
$710$	19.6438	+	12.1557i	0.737217	+	0.456195i
$711$	14.5097	+	2.27552i	0.544155	+	0.0853387i
$712$	14.7200	+	31.9280i	0.551654	+	1.19655i
$713$	3.02321	−	8.30620i	0.113220	−	0.311070i
$714$	−0.165442	−	0.351447i	−0.00619152	−	0.0131526i
$715$	9.94772	−	11.8552i	0.372024	−	0.443361i
$716$	9.08076	+	30.6543i	0.339364	+	1.14560i
$717$	4.62675	+	1.63446i	0.172789	+	0.0610402i
$718$	2.62496	+	18.1030i	0.0979626	+	0.675598i
$719$	−2.77701	−	4.80992i	−0.103565	−	0.179380i	0.809586	−	0.587001i	$-0.199692\pi$
$719$	−2.77701	−	4.80992i	−0.103565	−	0.179380i	−0.913151	+	0.407621i	$0.866358\pi$
$720$	30.9428	−	2.21198i	1.15317	−	0.0824356i
$721$	−13.1646	−	44.6877i	−0.490276	−	1.66426i
$722$	−0.541236	+	0.0784800i	−0.0201427	+	0.00292072i
$723$	2.57188	−	4.55385i	0.0956493	−	0.169359i
$724$	1.28087	−	1.34980i	0.0476032	−	0.0501649i
$725$	−13.5243	+	4.92245i	−0.502280	+	0.182815i
$726$	29.2209	−	9.94419i	1.08449	−	0.369064i
$727$	−0.385871	+	0.323784i	−0.0143112	+	0.0120085i	−0.649915	−	0.760007i	$-0.725196\pi$
$727$	−0.385871	+	0.323784i	−0.0143112	+	0.0120085i	0.635604	+	0.772015i	$0.280751\pi$
$728$	1.78573	+	9.04685i	0.0661837	+	0.335299i
$729$	14.8083	+	22.5769i	0.548455	+	0.836180i
$730$	−27.5208	−	17.0301i	−1.01859	−	0.630311i
$731$	−0.259318	−	0.0943841i	−0.00959123	−	0.00349092i
$732$	2.03167	−	8.83140i	0.0750928	−	0.326418i
$733$	−31.9637	+	38.0928i	−1.18061	+	1.40699i	−0.287123	+	0.957894i	$0.592699\pi$
$733$	−31.9637	+	38.0928i	−1.18061	+	1.40699i	−0.893483	+	0.449098i	$0.851746\pi$
$734$	−14.3322	−	43.4626i	−0.529012	−	1.60424i
$735$	−26.1751	+	17.2413i	−0.965484	+	0.635955i
$736$	−0.562033	−	25.7094i	−0.0207168	−	0.947662i
$737$	−31.1223			−1.14640
$738$	−14.8240	+	12.1495i	−0.545680	+	0.447230i
$739$			17.4442i			0.641695i	0.947131	+	0.320847i	$0.103968\pi$
$739$			17.4442i			0.641695i	−0.947131	+	0.320847i	$0.896032\pi$
$740$	−29.2580	−	39.5385i	−1.07555	−	1.45347i
$741$	−7.14134	+	6.10866i	−0.262344	+	0.224407i
$742$	−33.5921	−	15.9041i	−1.23321	−	0.583856i
$743$	1.21953	−	1.45338i	0.0447402	−	0.0533193i	−0.743210	−	0.669058i	$-0.766698\pi$
$743$	1.21953	−	1.45338i	0.0447402	−	0.0533193i	0.787950	+	0.615739i	$0.211142\pi$
$744$	−7.77485	+	5.50386i	−0.285040	+	0.201781i
$745$	−33.3886	+	5.88732i	−1.22327	+	0.215695i
$746$	−0.174385	+	5.70919i	−0.00638468	+	0.209028i
$747$	−20.6958	+	7.98047i	−0.757221	+	0.291990i
$748$	−0.259860	−	0.521177i	−0.00950143	−	0.0190561i
$749$	−43.9170	−	2.75185i	−1.60469	−	0.100551i
$750$	−17.9652	−	10.8827i	−0.655995	−	0.397379i
$751$	29.2282	+	5.15373i	1.06655	+	0.188062i	0.679263	−	0.733895i	$-0.262300\pi$
$751$	29.2282	+	5.15373i	1.06655	+	0.188062i	0.387291	+	0.921958i	$0.373411\pi$
$752$	16.2500	−	3.75216i	0.592576	−	0.136827i
$753$	10.0408	+	26.7932i	0.365905	+	0.976398i
$754$	−2.13855	−	14.7485i	−0.0778814	−	0.537108i
$755$	−10.7620			−0.391668
$756$	−26.6141	+	6.90567i	−0.967946	+	0.251157i
$757$	−52.2311			−1.89837			−0.949186	−	0.314716i	$-0.898091\pi$
$757$	−52.2311			−1.89837			−0.949186	+	0.314716i	$0.898091\pi$
$758$	5.07081	+	34.9708i	0.184180	+	1.27020i
$759$	24.3086	−	29.5343i	0.882346	−	1.07203i
$760$	−31.1334	+	8.19756i	−1.12933	+	0.297357i
$761$	−31.4342	−	5.54270i	−1.13949	−	0.200923i	−0.428107	−	0.903728i	$-0.640819\pi$
$761$	−31.4342	−	5.54270i	−1.13949	−	0.200923i	−0.711382	+	0.702806i	$0.751930\pi$
$762$	−8.01575	+	4.40560i	−0.290380	+	0.159598i
$763$	19.5861	+	13.0058i	0.709065	+	0.470843i
$764$	−35.3184	+	17.6098i	−1.27777	+	0.637101i
$765$	0.224743	−	0.406903i	0.00812560	−	0.0147116i
$766$	1.63152	−	53.4145i	0.0589494	−	1.92994i
$767$	14.3369	−	2.52799i	0.517676	−	0.0912803i
$768$	−15.2767	+	23.1219i	−0.551249	+	0.834341i
$769$	22.8846	−	27.2728i	0.825239	−	0.983482i	−0.174760	−	0.984611i	$-0.555915\pi$
$769$	22.8846	−	27.2728i	0.825239	−	0.983482i	0.999999	+	0.00112896i	$0.000359360\pi$
$770$	−38.6499	+	26.7275i	−1.39285	+	0.963194i
$771$	6.15240	+	33.0553i	0.221573	+	1.19046i
$772$	5.71293	−	4.22749i	0.205613	−	0.152151i
$773$			3.87773i			0.139472i	0.997565	+	0.0697360i	$0.0222157\pi$
$773$			3.87773i			0.139472i	−0.997565	+	0.0697360i	$0.977784\pi$
$774$	−9.96177	+	16.8026i	−0.358068	+	0.603956i
$775$	−3.27248			−0.117551
$776$	−2.77605	−	33.3988i	−0.0996545	−	1.19895i
$777$	31.8619	+	29.7554i	1.14304	+	1.06747i
$778$	5.64811	+	17.1280i	0.202495	+	0.614067i
$779$	12.7859	−	15.2376i	0.458102	−	0.545945i
$780$	−7.51971	+	8.07645i	−0.269249	+	0.289183i
$781$	−28.8454	−	10.4989i	−1.03217	−	0.375679i
$782$	−0.327671	−	0.202765i	−0.0117175	−	0.00725087i
$783$	43.5231	−	8.95817i	1.55539	−	0.320139i
$784$	2.03561	−	27.9259i	0.0727003	−	0.997354i
$785$	−23.5935	+	19.7973i	−0.842089	+	0.706596i
$786$	12.9261	+	11.3184i	0.461059	+	0.403713i
$787$	−34.7877	+	12.6617i	−1.24005	+	0.451341i	−0.877027	−	0.480440i	$-0.840477\pi$
$787$	−34.7877	+	12.6617i	−1.24005	+	0.451341i	−0.363021	+	0.931781i	$0.618255\pi$
$788$	16.0443	+	15.2250i	0.571554	+	0.542367i
$789$	17.2328	+	29.2048i	0.613505	+	1.03972i
$790$	−17.7131	+	2.56842i	−0.630203	+	0.0913804i
$791$	21.4147	−	22.4990i	0.761418	−	0.799974i
$792$	−39.6575	+	11.2507i	−1.40917	+	0.399775i
$793$	1.61180	+	2.79171i	0.0572366	+	0.0991367i
$794$	2.49945	+	17.2374i	0.0887020	+	0.611732i
$795$	−8.13853	−	43.7262i	−0.288644	−	1.55081i
$796$	45.7317	−	13.5472i	1.62092	−	0.480166i
$797$	−16.8845	+	20.1221i	−0.598078	+	0.712761i	−0.977137	−	0.212611i	$-0.931803\pi$
$797$	−16.8845	+	20.1221i	−0.598078	+	0.712761i	0.379059	+	0.925373i	$0.376248\pi$
$798$	25.8174	−	12.1534i	0.913925	−	0.430226i
$799$	0.0854721	−	0.234833i	0.00302378	−	0.00830778i
$800$	−8.87298	+	3.45093i	−0.313707	+	0.122009i
$801$	12.0871	−	35.2773i	0.427075	−	1.24646i
$802$	−29.4485	−	18.2229i	−1.03986	−	0.643474i
$803$	40.4122	+	14.7088i	1.42612	+	0.519064i
$804$	22.1624	+	1.14424i	0.781606	+	0.0403543i
$805$	−12.4406	+	28.4952i	−0.438475	+	1.00432i
$806$	0.690023	−	3.31755i	0.0243050	−	0.116856i
$807$	−28.6797	+	10.7477i	−1.00957	+	0.378338i
$808$	23.0028	+	10.8481i	0.809234	+	0.381635i
$809$	−13.6005	−	23.5568i	−0.478169	−	0.828213i	0.521518	−	0.853241i	$-0.325366\pi$
$809$	−13.6005	−	23.5568i	−0.478169	−	0.828213i	−0.999687	+	0.0250272i	$0.992033\pi$
$810$	−25.3616	−	20.9627i	−0.891116	−	0.736553i
$811$	27.5108			0.966036			0.483018	−	0.875610i	$-0.339541\pi$
$811$	27.5108			0.966036			0.483018	+	0.875610i	$0.339541\pi$
$812$	−5.58096	+	44.9053i	−0.195853	+	1.57587i
$813$	9.88792	−	12.0136i	0.346784	−	0.421335i
$814$	48.7629	+	43.5219i	1.70914	+	1.52544i
$815$	1.08852	+	0.913379i	0.0381293	+	0.0319943i
$816$	0.165886	+	0.380688i	0.00580719	+	0.0133267i
$817$	6.93347	−	19.0496i	0.242571	−	0.666460i
$818$	19.7469	+	36.7500i	0.690433	+	1.28493i
$819$	5.25499	−	8.24916i	0.183624	−	0.288249i
$820$	12.8916	−	19.4777i	0.450193	−	0.680191i
$821$	−14.7479	+	12.3749i	−0.514704	+	0.431888i	−0.862781	−	0.505578i	$-0.831279\pi$
$821$	−14.7479	+	12.3749i	−0.514704	+	0.431888i	0.348077	+	0.937466i	$0.386835\pi$
$822$	−10.3228	−	4.00519i	−0.360048	−	0.139697i
$823$	8.83133	+	1.55720i	0.307841	+	0.0542807i	0.325435	−	0.945565i	$-0.394489\pi$
$823$	8.83133	+	1.55720i	0.307841	+	0.0542807i	−0.0175937	+	0.999845i	$0.505601\pi$
$824$	12.6811	+	48.1615i	0.441768	+	1.67779i
$825$	−13.3528	−	4.71708i	−0.464886	−	0.164228i
$826$	−44.0129	−	4.11008i	−1.53140	−	0.143008i
$827$	−0.278766	−	0.160945i	−0.00969363	−	0.00559662i	0.495145	−	0.868810i	$-0.335115\pi$
$827$	−0.278766	−	0.160945i	−0.00969363	−	0.00559662i	−0.504839	+	0.863214i	$0.668448\pi$
$828$	−18.3962	+	20.1379i	−0.639311	+	0.699839i
$829$	14.2326	+	8.21721i	0.494320	+	0.285396i	0.726365	−	0.687309i	$-0.241208\pi$
$829$	14.2326	+	8.21721i	0.494320	+	0.285396i	−0.232045	+	0.972705i	$0.574542\pi$
$830$	21.2279	−	16.7350i	0.736830	−	0.580880i
$831$	40.1467	−	23.6893i	1.39267	−	0.821772i
$832$	−1.62753	−	9.72282i	−0.0564245	−	0.337078i
$833$	−0.334324	−	0.253499i	−0.0115836	−	0.00878321i
$834$	−0.185599	+	0.936825i	−0.00642676	+	0.0324396i
$835$	52.4539	−	9.24904i	1.81524	−	0.320076i
$836$	38.2858	−	19.0894i	1.32414	−	0.660219i
$837$	9.99602	+	1.47064i	0.345513	+	0.0508329i
$838$	45.9642	+	28.4430i	1.58781	+	0.982546i
$839$	−10.7835	+	9.04843i	−0.372288	+	0.312386i	−0.809666	−	0.586891i	$-0.800352\pi$
$839$	−10.7835	+	9.04843i	−0.372288	+	0.312386i	0.437378	+	0.899278i	$0.355907\pi$
$840$	28.5055	−	17.6119i	0.983534	−	0.607667i
$841$	7.66306	−	43.4594i	0.264244	−	1.49860i
$842$	−38.7655	−	8.06290i	−1.33595	−	0.277866i
$843$	23.8156	+	13.4504i	0.820253	+	0.463255i
$844$	−27.2758	−	36.8598i	−0.938871	−	1.26877i
$845$			29.6815i			1.02107i
$846$	−15.2160	−	9.02115i	−0.523137	−	0.310153i
$847$	22.9857	−	24.1496i	0.789797	−	0.829789i
$848$	35.4029	+	18.0372i	1.21574	+	0.619401i
$849$	11.3913	−	32.2458i	0.390948	−	1.10667i
$850$	−0.0290501	+	0.139669i	−0.000996409	+	0.00479062i
$851$	42.5897	+	7.50971i	1.45996	+	0.257430i
$852$	20.1550	+	8.53684i	0.690499	+	0.292467i
$853$	6.03557	−	16.5826i	0.206654	−	0.567777i	−0.792457	−	0.609928i	$-0.791199\pi$
$853$	6.03557	−	16.5826i	0.206654	−	0.567777i	0.999111	+	0.0421501i	$0.0134208\pi$
$854$	−2.47804	−	9.46929i	−0.0847967	−	0.324033i
$855$	29.8912	+	16.5097i	1.02226	+	0.564618i
$856$	46.8441	+	4.30321i	1.60110	+	0.147081i
$857$	18.2378	+	21.7350i	0.622993	+	0.742454i	0.981582	−	0.191042i	$-0.0611865\pi$
$857$	18.2378	+	21.7350i	0.622993	+	0.742454i	−0.358589	+	0.933495i	$0.616742\pi$
$858$	7.59756	−	12.5421i	0.259376	−	0.428180i
$859$	1.05611	−	5.98949i	0.0360340	−	0.204359i	−0.961476	−	0.274890i	$-0.911358\pi$
$859$	1.05611	−	5.98949i	0.0360340	−	0.204359i	0.997510	+	0.0705315i	$0.0224695\pi$
$860$	5.55671	−	23.1470i	0.189482	−	0.789308i
$861$	−8.10304	+	19.0507i	−0.276151	+	0.649247i
$862$	9.76993	−	7.70212i	0.332765	−	0.262335i
$863$	13.7216	+	7.92218i	0.467089	+	0.269674i	0.715020	−	0.699104i	$-0.246417\pi$
$863$	13.7216	+	7.92218i	0.467089	+	0.269674i	−0.247931	+	0.968778i	$0.579751\pi$
$864$	28.6540	−	6.55362i	0.974828	−	0.222959i
$865$	−3.82642	−	6.62755i	−0.130102	−	0.225344i
$866$	3.00833	+	20.7469i	0.102227	+	0.705009i
$867$	−29.0386	−	4.83673i	−0.986202	−	0.164264i
$868$	−4.68465	+	9.16069i	−0.159007	+	0.310934i
$869$	22.3494	−	8.13451i	0.758151	−	0.275944i
$870$	−47.4558	+	26.0826i	−1.60890	+	0.884282i
$871$	−6.04729	+	5.07428i	−0.204904	+	0.171935i
$872$	−20.5261	−	14.5057i	−0.695102	−	0.491224i
$873$	−22.3284	+	27.6591i	−0.755703	+	0.936119i
$874$	14.8952	−	24.0707i	0.503836	−	0.814205i
$875$	−22.6428	−	1.41881i	−0.765466	−	0.0479644i
$876$	−28.2370	−	11.9601i	−0.954041	−	0.404093i
$877$	24.9366	−	9.07620i	0.842051	−	0.306481i	0.115256	−	0.993336i	$-0.463231\pi$
$877$	24.9366	−	9.07620i	0.842051	−	0.306481i	0.726795	+	0.686855i	$0.241009\pi$
$878$	2.44919	+	0.509412i	0.0826563	+	0.0171918i
$879$	−24.5036	−	8.65624i	−0.826485	−	0.291968i
$880$	42.1304	−	27.3617i	1.42021	−	0.922364i
$881$	−7.88922	−	4.55484i	−0.265795	−	0.153457i	0.361180	−	0.932496i	$-0.382374\pi$
$881$	−7.88922	−	4.55484i	−0.265795	−	0.153457i	−0.626975	+	0.779039i	$0.715707\pi$
$882$	−22.0124	+	19.9362i	−0.741197	+	0.671287i
$883$	30.3011	−	17.4943i	1.01971	−	0.588731i	0.105691	−	0.994399i	$-0.466294\pi$
$883$	30.3011	−	17.4943i	1.01971	−	0.588731i	0.914020	+	0.405668i	$0.132961\pi$
$884$	−0.135467	−	0.0589002i	−0.00455626	−	0.00198103i
$885$	−26.8829	−	45.5589i	−0.903658	−	1.53145i
$886$	−6.98690	−	6.23594i	−0.234729	−	0.209501i
$887$	−2.61375	−	2.19320i	−0.0877612	−	0.0736404i	0.597852	−	0.801607i	$-0.296021\pi$
$887$	−2.61375	−	2.19320i	−0.0877612	−	0.0736404i	−0.685613	+	0.727966i	$0.740466\pi$
$888$	−33.1243	−	32.7850i	−1.11158	−	1.10019i
$889$	−5.46516	+	8.23025i	−0.183296	+	0.276034i
$890$	−1.38743	+	45.4230i	−0.0465066	+	1.52258i
$891$	38.6673	+	20.4094i	1.29540	+	0.683739i
$892$	−9.61029	−	19.2745i	−0.321776	−	0.645357i
$893$	17.2508	+	6.27879i	0.577277	+	0.210112i
$894$	−30.4118	+	10.3495i	−1.01712	+	0.346138i
$895$	−7.17600	+	40.6971i	−0.239867	+	1.36035i
$896$	−3.04168	+	29.7783i	−0.101616	+	0.994824i
$897$	−0.0920369	−	9.70210i	−0.00307302	−	0.323944i
$898$	−2.89421	+	7.25456i	−0.0965809	+	0.242088i
$899$	8.31405	−	14.4004i	0.277289	−	0.480279i
$900$	9.33521	+	3.84999i	0.311174	+	0.128333i
$901$	0.515611	−	0.297688i	0.0171775	−	0.00991743i
$902$	−11.5011	+	28.8285i	−0.382946	+	0.959884i
$903$	−1.11966	+	21.0690i	−0.0372599	+	0.701133i
$904$	−23.5817	+	23.3779i	−0.784315	+	0.777538i
$905$	2.26017	−	0.822636i	0.0751307	−	0.0273453i
$906$	−10.0773	+	1.55897i	−0.334797	+	0.0517933i
$907$	29.3477	−	5.17479i	0.974474	−	0.171826i	0.336331	−	0.941744i	$-0.390814\pi$
$907$	29.3477	−	5.17479i	0.974474	−	0.171826i	0.638143	+	0.769918i	$0.279703\pi$
$908$	22.8666	+	45.8614i	0.758854	+	1.52196i
$909$	−9.70527	−	25.1688i	−0.321903	−	0.834795i
$910$	−3.15222	+	11.4950i	−0.104495	+	0.381055i
$911$	20.3254	−	3.58391i	0.673410	−	0.118740i	0.173521	−	0.984830i	$-0.444485\pi$
$911$	20.3254	−	3.58391i	0.673410	−	0.118740i	0.499888	+	0.866090i	$0.333374\pi$
$912$	−27.9654	+	12.1860i	−0.926026	+	0.403520i
$913$	−23.0887	+	27.5160i	−0.764123	+	0.910647i
$914$	0.441824	+	1.33984i	0.0146142	+	0.0443179i
$915$	7.44378	−	9.04401i	0.246084	−	0.298986i
$916$	16.7245	+	22.6011i	0.552594	+	0.746762i
$917$	18.0385	+	4.35913i	0.595683	+	0.143951i
$918$	0.151502	−	0.413574i	0.00500032	−	0.0136500i
$919$	−28.9973	−	16.7416i	−0.956531	−	0.552254i	−0.0614276	−	0.998112i	$-0.519565\pi$
$919$	−28.9973	−	16.7416i	−0.956531	−	0.552254i	−0.895104	+	0.445858i	$0.852899\pi$
$920$	14.1781	−	30.0638i	0.467438	−	0.991174i
$921$	3.37910	−	4.10553i	0.111345	−	0.135282i
$922$	6.73032	+	6.00694i	0.221651	+	0.197828i
$923$	−7.31665	+	2.66304i	−0.240830	+	0.0876551i
$924$	−32.3195	+	30.6261i	−1.06323	+	1.00752i
$925$	−2.78025	−	15.7676i	−0.0914141	−	0.518435i
$926$	23.1200	+	0.706191i	0.759770	+	0.0232069i
$927$	25.5394	−	46.2399i	0.838825	−	1.51872i
$928$	7.35704	−	47.8124i	0.241507	−	1.56952i
$929$	13.5422	+	16.1389i	0.444304	+	0.529501i	0.940992	−	0.338428i	$-0.109895\pi$
$929$	13.5422	+	16.1389i	0.444304	+	0.529501i	−0.496688	+	0.867929i	$0.665451\pi$
$930$	−12.1680	+	1.88240i	−0.399006	+	0.0617264i
$931$	18.6221	−	24.5595i	0.610313	−	0.804904i
$932$	−28.4760	−	27.0219i	−0.932764	−	0.885131i
$933$	−8.26979	+	23.4096i	−0.270741	+	0.766397i
$934$	−7.76133	+	1.12540i	−0.253958	+	0.0368243i
$935$		−	0.752754i		−	0.0246177i
$936$	−5.87139	+	8.65197i	−0.191913	+	0.282798i
$937$	24.2699	−	14.0122i	0.792863	−	0.457760i	−0.0481063	−	0.998842i	$-0.515319\pi$
$937$	24.2699	−	14.0122i	0.792863	−	0.457760i	0.840970	+	0.541082i	$0.181985\pi$
$938$	21.7830	−	10.0029i	0.711241	−	0.326608i
$939$	−21.5531	−	36.5264i	−0.703358	−	1.19199i
$940$	20.9614	+	5.03203i	0.683686	+	0.164127i
$941$	1.22302	+	3.36022i	0.0398694	+	0.109540i	0.958030	−	0.286669i	$-0.0925479\pi$
$941$	1.22302	+	3.36022i	0.0398694	+	0.109540i	−0.918160	+	0.396209i	$0.870326\pi$
$942$	−19.2248	+	21.9557i	−0.626378	+	0.715354i
$943$	3.56618	+	20.2248i	0.116131	+	0.658610i
$944$	46.9044	+	5.75758i	1.52661	+	0.187393i
$945$	−34.7691	−	7.36184i	−1.13104	−	0.239481i
$946$	−0.965742	+	31.6175i	−0.0313990	+	1.02797i
$947$	11.3590	−	2.00291i	0.369119	−	0.0650857i	0.0139882	−	0.999902i	$-0.495547\pi$
$947$	11.3590	−	2.00291i	0.369119	−	0.0650857i	0.355131	+	0.934816i	$0.384436\pi$
$948$	−16.2142	+	4.97094i	−0.526613	+	0.161449i
$949$	10.2506	−	3.73090i	0.332748	−	0.121110i
$950$	−10.2601	−	2.13402i	−0.332882	−	0.0692368i
$951$	15.4022	+	8.69870i	0.499450	+	0.282075i
$952$	0.349391	+	0.281260i	0.0113238	+	0.00911570i
$953$	5.14234	+	8.90679i	0.166577	+	0.288519i	0.937214	−	0.348755i	$-0.113395\pi$
$953$	5.14234	+	8.90679i	0.166577	+	0.288519i	−0.770637	+	0.637274i	$0.780062\pi$
$954$	−13.9550	−	39.7657i	−0.451808	−	1.28746i
$955$	−51.0115			−1.65069
$956$	−5.62964	+	0.641509i	−0.182076	+	0.0207479i
$957$	54.6813	−	46.7741i	1.76760	−	1.51199i
$958$	33.0627	−	37.0442i	1.06821	−	1.19684i
$959$	−11.8848	+	1.33615i	−0.383781	+	0.0431464i
$960$	−31.0073	+	17.9355i	−1.00076	+	0.578866i
$961$	−20.8511	+	17.4961i	−0.672615	+	0.564391i
$962$	16.5710	+	0.506153i	0.534269	+	0.0163190i
$963$	−32.7911	−	37.6064i	−1.05668	−	1.21185i
$964$	−0.368573	+	6.02774i	−0.0118709	+	0.194140i
$965$	9.04674	−	1.59518i	0.291225	−	0.0513508i
$966$	−7.52144	+	28.4846i	−0.241998	+	0.916477i
$967$	0.503492	+	1.38333i	0.0161912	+	0.0444850i	0.947525	−	0.319682i	$-0.103576\pi$
$967$	0.503492	+	1.38333i	0.0161912	+	0.0444850i	−0.931334	+	0.364167i	$0.881354\pi$
$968$	−25.3116	+	25.0929i	−0.813547	+	0.806517i
$969$	−0.0751012	+	0.450890i	−0.00241260	+	0.0144847i
$970$	16.0520	−	40.2355i	0.515398	−	1.29188i
$971$	−0.475696	+	0.823929i	−0.0152658	+	0.0264412i	−0.873557	−	0.486721i	$-0.838193\pi$
$971$	−0.475696	+	0.823929i	−0.0152658	+	0.0264412i	0.858292	+	0.513162i	$0.171526\pi$
$972$	−26.7849	−	15.9553i	−0.859125	−	0.511766i
$973$	0.291501	+	0.989510i	0.00934509	+	0.0317222i
$974$	37.7397	−	29.7521i	1.20926	−	0.953318i
$975$	−3.36364	+	1.26053i	−0.107723	+	0.0403692i
$976$	2.35422	+	10.1957i	0.0753567	+	0.326357i
$977$	2.47042	+	2.07293i	0.0790357	+	0.0663188i	0.681450	−	0.731865i	$-0.261350\pi$
$977$	2.47042	+	2.07293i	0.0790357	+	0.0663188i	−0.602414	+	0.798184i	$0.705794\pi$
$978$	1.15159	+	0.697592i	0.0368237	+	0.0223065i
$979$	−10.4861	−	59.4698i	−0.335138	−	1.90066i
$980$	18.4613	−	31.1295i	0.589726	−	0.994395i
$981$	5.12651	+	26.1614i	0.163677	+	0.835271i
$982$	−11.9756	−	22.2873i	−0.382157	−	0.711215i
$983$	1.24257	+	7.04698i	0.0396319	+	0.224764i	0.998190	−	0.0601320i	$-0.0191522\pi$
$983$	1.24257	+	7.04698i	0.0396319	+	0.224764i	−0.958559	+	0.284896i	$0.908041\pi$
$984$	9.24994	−	20.1061i	0.294877	−	0.640959i
$985$	9.77820	+	26.8654i	0.311559	+	0.856002i
$986$	−0.540802	−	0.482676i	−0.0172226	−	0.0153715i
$987$	−19.0796	−	1.01394i	−0.607311	−	0.0322740i
$988$	4.32682	−	9.95144i	0.137654	−	0.316598i
$989$	10.4650	+	18.1259i	0.332767	+	0.576369i
$990$	−52.3631	−	9.85863i	−1.66421	−	0.313328i
$991$	14.4075	+	8.31818i	0.457670	+	0.264236i	0.711064	−	0.703127i	$-0.248214\pi$
$991$	14.4075	+	8.31818i	0.457670	+	0.264236i	−0.253394	+	0.967363i	$0.581547\pi$
$992$	5.29021	−	9.64372i	0.167964	−	0.306188i
$993$	23.2906	−	41.2391i	0.739106	−	1.30868i
$994$	23.5638	−	1.92280i	0.747400	−	0.0609876i
$995$	60.7141	+	10.7055i	1.92477	+	0.339388i
$996$	17.4532	−	18.7454i	0.553027	−	0.593972i
$997$	−3.22162	+	8.85133i	−0.102030	+	0.280324i	−0.980196	−	0.198032i	$-0.936545\pi$
$997$	−3.22162	+	8.85133i	−0.102030	+	0.280324i	0.878166	+	0.478356i	$0.158767\pi$
$998$	10.7019	+	19.9168i	0.338762	+	0.630455i
$999$	1.40657	+	49.4126i	0.0445018	+	1.56335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bt.a.103.7	✓	840
4.3	odd	2	inner	756.2.bt.a.103.130	yes	840
7.3	odd	6		756.2.cd.a.535.88	yes	840
27.16	even	9		756.2.cd.a.691.57	yes	840
28.3	even	6		756.2.cd.a.535.57	yes	840
108.43	odd	18		756.2.cd.a.691.88	yes	840
189.178	odd	18	inner	756.2.bt.a.367.130	yes	840
756.367	even	18	inner	756.2.bt.a.367.7	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bt.a.103.7	✓	840	1.1	even	1	trivial
756.2.bt.a.103.130	yes	840	4.3	odd	2	inner
756.2.bt.a.367.7	yes	840	756.367	even	18	inner
756.2.bt.a.367.130	yes	840	189.178	odd	18	inner
756.2.cd.a.535.57	yes	840	28.3	even	6
756.2.cd.a.535.88	yes	840	7.3	odd	6
756.2.cd.a.691.57	yes	840	27.16	even	9
756.2.cd.a.691.88	yes	840	108.43	odd	18

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bt (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39958 + 0.202941i) q^{2} +(-1.70851 - 0.284574i) q^{3} +(1.91763 - 0.568062i) q^{4} +(2.54587 + 0.448906i) q^{5} +(2.44895 + 0.0515557i) q^{6} +(2.36953 - 1.17699i) q^{7} +(-2.56859 + 1.18421i) q^{8} +(2.83804 + 0.972395i) q^{9} +O(q^{10})\)	\(q+(-1.39958 + 0.202941i) q^{2} +(-1.70851 - 0.284574i) q^{3} +(1.91763 - 0.568062i) q^{4} +(2.54587 + 0.448906i) q^{5} +(2.44895 + 0.0515557i) q^{6} +(2.36953 - 1.17699i) q^{7} +(-2.56859 + 1.18421i) q^{8} +(2.83804 + 0.972395i) q^{9} +(-3.65425 - 0.111617i) q^{10} +(4.78431 - 0.843602i) q^{11} +(-3.43795 + 0.424835i) q^{12} +(0.792083 - 0.943968i) q^{13} +(-3.07748 + 2.12817i) q^{14} +(-4.22191 - 1.49145i) q^{15} +(3.35461 - 2.17867i) q^{16} -0.0599377i q^{17} +(-4.16939 - 0.784989i) q^{18} +4.40303 q^{19} +(5.13705 - 0.585378i) q^{20} +(-4.38332 + 1.33660i) q^{21} +(-6.52480 + 2.15162i) q^{22} +(-2.92206 + 3.48237i) q^{23} +(4.72546 - 1.29229i) q^{24} +(1.58149 + 0.575617i) q^{25} +(-0.917011 + 1.48190i) q^{26} +(-4.57210 - 2.46898i) q^{27} +(3.87528 - 3.60308i) q^{28} +(-6.55090 + 5.49686i) q^{29} +(6.21157 + 1.23060i) q^{30} +(-1.82718 + 0.665039i) q^{31} +(-4.25290 + 3.73000i) q^{32} +(-8.41412 + 0.0798188i) q^{33} +(0.0121638 + 0.0838875i) q^{34} +(6.56089 - 1.93278i) q^{35} +(5.99468 + 0.252514i) q^{36} +(-4.75666 - 8.23877i) q^{37} +(-6.16238 + 0.893555i) q^{38} +(-1.62191 + 1.38738i) q^{39} +(-7.07090 + 1.86180i) q^{40} +(2.90388 - 3.46071i) q^{41} +(5.86354 - 2.76023i) q^{42} +(1.57470 - 4.32646i) q^{43} +(8.69531 - 4.33550i) q^{44} +(6.78877 + 3.74961i) q^{45} +(3.38293 - 5.46685i) q^{46} +(3.91794 + 1.42601i) q^{47} +(-6.35139 + 2.76765i) q^{48} +(4.22937 - 5.57785i) q^{49} +(-2.33024 - 0.484671i) q^{50} +(-0.0170567 + 0.102404i) q^{51} +(0.982690 - 2.26013i) q^{52} +(4.96662 + 8.60244i) q^{53} +(6.90007 + 2.52766i) q^{54} +12.5589 q^{55} +(-4.69254 + 5.82924i) q^{56} +(-7.52264 - 1.25299i) q^{57} +(8.05296 - 9.02272i) q^{58} +(9.05014 + 7.59397i) q^{59} +(-8.94330 - 0.461743i) q^{60} +(-0.894724 + 2.45823i) q^{61} +(2.42231 - 1.30158i) q^{62} +(7.86932 - 1.03623i) q^{63} +(5.19529 - 6.08350i) q^{64} +(2.44030 - 2.04765i) q^{65} +(11.7600 - 1.81928i) q^{66} +(-6.30892 - 1.11243i) q^{67} +(-0.0340484 - 0.114938i) q^{68} +(5.98337 - 5.11814i) q^{69} +(-8.79023 + 4.03655i) q^{70} +(-5.47210 - 3.15932i) q^{71} +(-8.44127 + 0.863152i) q^{72} +(7.66637 + 4.42618i) q^{73} +(8.32929 + 10.5655i) q^{74} +(-2.53820 - 1.43350i) q^{75} +(8.44339 - 2.50120i) q^{76} +(10.3437 - 7.63005i) q^{77} +(1.98844 - 2.27089i) q^{78} +(4.82129 - 0.850124i) q^{79} +(9.51843 - 4.04070i) q^{80} +(7.10889 + 5.51939i) q^{81} +(-3.36188 + 5.43284i) q^{82} +(-5.66393 + 4.75260i) q^{83} +(-7.64631 + 5.05311i) q^{84} +(0.0269064 - 0.152594i) q^{85} +(-1.32590 + 6.37478i) q^{86} +(12.7566 - 7.52725i) q^{87} +(-11.2899 + 7.83250i) q^{88} -12.4302i q^{89} +(-10.2623 - 3.87015i) q^{90} +(0.765822 - 3.16904i) q^{91} +(-3.62522 + 8.33781i) q^{92} +(3.31101 - 0.616261i) q^{93} +(-5.77286 - 1.20071i) q^{94} +(11.2096 + 1.97655i) q^{95} +(8.32759 - 5.16249i) q^{96} +(-4.05259 + 11.1344i) q^{97} +(-4.78735 + 8.66494i) q^{98} +(14.3983 + 2.25806i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Introduction

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