LMFDB - Embedded newform 76.2.k.a.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.k (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:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.2
Character	$\chi$	$=$	76.71
Dual form			76.2.k.a.15.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06726 + 0.927872i) q^{2} +(0.361434 - 2.04979i) q^{3} +(0.278109 - 1.98057i) q^{4} +(-2.99965 - 2.51700i) q^{5} +(1.51620 + 2.52304i) q^{6} +(0.0108543 - 0.00626673i) q^{7} +(1.54090 + 2.37184i) q^{8} +(-1.25194 - 0.455671i) q^{9} +O(q^{10})$	\(q+(-1.06726 + 0.927872i) q^{2} +(0.361434 - 2.04979i) q^{3} +(0.278109 - 1.98057i) q^{4} +(-2.99965 - 2.51700i) q^{5} +(1.51620 + 2.52304i) q^{6} +(0.0108543 - 0.00626673i) q^{7} +(1.54090 + 2.37184i) q^{8} +(-1.25194 - 0.455671i) q^{9} +(5.53688 - 0.0969785i) q^{10} +(3.15988 + 1.82436i) q^{11} +(-3.95924 - 1.28591i) q^{12} +(3.04424 - 0.536781i) q^{13} +(-0.00576968 + 0.0167596i) q^{14} +(-6.24352 + 5.23893i) q^{15} +(-3.84531 - 1.10163i) q^{16} +(-2.82933 + 1.02979i) q^{17} +(1.75896 - 0.675323i) q^{18} +(3.96096 - 1.81957i) q^{19} +(-5.81933 + 5.24101i) q^{20} +(-0.00892239 - 0.0245141i) q^{21} +(-5.06520 + 0.984891i) q^{22} +(-2.50024 - 2.97967i) q^{23} +(5.41872 - 2.30126i) q^{24} +(1.79434 + 10.1762i) q^{25} +(-2.75094 + 3.39755i) q^{26} +(1.73560 - 3.00614i) q^{27} +(-0.00939301 - 0.0232405i) q^{28} +(-0.126343 + 0.347124i) q^{29} +(1.80243 - 11.3845i) q^{30} +(1.29454 + 2.24221i) q^{31} +(5.12613 - 2.39223i) q^{32} +(4.88165 - 5.81773i) q^{33} +(2.06413 - 3.72431i) q^{34} +(-0.0483324 - 0.00852231i) q^{35} +(-1.25066 + 2.35284i) q^{36} -2.87327i q^{37} +(-2.53906 + 5.61722i) q^{38} -6.43407i q^{39} +(1.34778 - 10.9931i) q^{40} +(7.88423 + 1.39020i) q^{41} +(0.0322685 + 0.0178842i) q^{42} +(-5.11775 + 6.09909i) q^{43} +(4.49206 - 5.75100i) q^{44} +(2.60847 + 4.51800i) q^{45} +(5.43318 + 0.860197i) q^{46} +(-2.68591 + 7.37948i) q^{47} +(-3.64794 + 7.48393i) q^{48} +(-3.49992 + 6.06204i) q^{49} +(-11.3573 - 9.19580i) q^{50} +(1.08825 + 6.17175i) q^{51} +(-0.216503 - 6.17861i) q^{52} +(-0.993871 - 1.18445i) q^{53} +(0.936972 + 4.81876i) q^{54} +(-4.88662 - 13.4259i) q^{55} +(0.0315890 + 0.0160883i) q^{56} +(-2.29812 - 8.77680i) q^{57} +(-0.187245 - 0.487703i) q^{58} +(3.93600 - 1.43259i) q^{59} +(8.63969 + 13.8227i) q^{60} +(-2.45324 + 2.05851i) q^{61} +(-3.46210 - 1.19186i) q^{62} +(-0.0164445 + 0.00289961i) q^{63} +(-3.25126 + 7.30953i) q^{64} +(-10.4827 - 6.05220i) q^{65} +(0.188087 + 10.7386i) q^{66} +(-8.76065 - 3.18861i) q^{67} +(1.25271 + 5.89008i) q^{68} +(-7.01139 + 4.04803i) q^{69} +(0.0594911 - 0.0357507i) q^{70} +(9.25916 + 7.76936i) q^{71} +(-0.848341 - 3.67156i) q^{72} +(0.801985 - 4.54828i) q^{73} +(2.66603 + 3.06655i) q^{74} +21.5077 q^{75} +(-2.50221 - 8.35099i) q^{76} +0.0457310 q^{77} +(5.96999 + 6.86686i) q^{78} +(-0.148866 + 0.844262i) q^{79} +(8.76178 + 12.9832i) q^{80} +(-8.59645 - 7.21328i) q^{81} +(-9.70450 + 5.83184i) q^{82} +(4.31582 - 2.49174i) q^{83} +(-0.0510332 + 0.0108538i) q^{84} +(11.0790 + 4.03242i) q^{85} +(-0.197183 - 11.2580i) q^{86} +(0.665868 + 0.384439i) q^{87} +(0.541968 + 10.3059i) q^{88} +(4.86849 - 0.858447i) q^{89} +(-6.97605 - 2.40158i) q^{90} +(0.0296792 - 0.0249038i) q^{91} +(-6.59679 + 4.12323i) q^{92} +(5.06396 - 1.84313i) q^{93} +(-3.98063 - 10.3680i) q^{94} +(-16.4613 - 4.51167i) q^{95} +(-3.05081 - 11.3722i) q^{96} +(-1.35020 - 3.70964i) q^{97} +(-1.88945 - 9.71728i) q^{98} +(-3.12469 - 3.72386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	−1.06726	+	0.927872i	−0.754670	+	0.656104i
$2$	−1.06726	+	0.927872i	−0.754670	+	0.656104i
$3$	0.361434	−	2.04979i	0.208674	−	1.18345i	−0.682878	−	0.730532i	$-0.739272\pi$
$3$	0.361434	−	2.04979i	0.208674	−	1.18345i	0.891553	−	0.452917i	$-0.149617\pi$
$4$	0.278109	−	1.98057i	0.139054	−	0.990285i
$5$	−2.99965	−	2.51700i	−1.34148	−	1.12564i	−0.981242	−	0.192779i	$-0.938250\pi$
$5$	−2.99965	−	2.51700i	−1.34148	−	1.12564i	−0.360241	−	0.932859i	$-0.617306\pi$
$6$	1.51620	+	2.52304i	0.618986	+	1.03003i
$7$	0.0108543	−	0.00626673i	0.00410253	−	0.00236860i	−0.497947	−	0.867207i	$-0.665913\pi$
$7$	0.0108543	−	0.00626673i	0.00410253	−	0.00236860i	0.502050	+	0.864839i	$0.332579\pi$
$8$	1.54090	+	2.37184i	0.544790	+	0.838573i
$9$	−1.25194	−	0.455671i	−0.417315	−	0.151890i
$10$	5.53688	−	0.0969785i	1.75091	−	0.0306673i
$11$	3.15988	+	1.82436i	0.952741	+	0.550065i	0.893931	−	0.448204i	$-0.147936\pi$
$11$	3.15988	+	1.82436i	0.952741	+	0.550065i	0.0588096	+	0.998269i	$0.481270\pi$
$12$	−3.95924	−	1.28591i	−1.14293	−	0.371211i
$13$	3.04424	−	0.536781i	0.844320	−	0.148876i	0.265276	−	0.964173i	$-0.414537\pi$
$13$	3.04424	−	0.536781i	0.844320	−	0.148876i	0.579044	+	0.815296i	$0.303426\pi$
$14$	−0.00576968	+	0.0167596i	−0.00154201	+	0.00447920i
$15$	−6.24352	+	5.23893i	−1.61207	+	1.35269i
$16$	−3.84531	−	1.10163i	−0.961328	−	0.275407i
$17$	−2.82933	+	1.02979i	−0.686213	+	0.249761i	−0.661513	−	0.749934i	$-0.730085\pi$
$17$	−2.82933	+	1.02979i	−0.686213	+	0.249761i	−0.0247002	+	0.999695i	$0.507863\pi$
$18$	1.75896	−	0.675323i	0.414591	−	0.159175i
$19$	3.96096	−	1.81957i	0.908706	−	0.417438i
$19$	3.96096	−	1.81957i	0.908706	−	0.417438i
$20$	−5.81933	+	5.24101i	−1.30124	+	1.17193i
$21$	−0.00892239	−	0.0245141i	−0.00194703	−	0.00534941i
$22$	−5.06520	+	0.984891i	−1.07991	+	0.209980i
$23$	−2.50024	−	2.97967i	−0.521337	−	0.621305i	0.439559	−	0.898214i	$-0.355135\pi$
$23$	−2.50024	−	2.97967i	−0.521337	−	0.621305i	−0.960896	+	0.276908i	$0.910690\pi$
$24$	5.41872	−	2.30126i	1.10609	−	0.469743i
$25$	1.79434	+	10.1762i	0.358868	+	2.03524i
$26$	−2.75094	+	3.39755i	−0.539505	+	0.666314i
$27$	1.73560	−	3.00614i	0.334016	−	0.578532i
$28$	−0.00939301	−	0.0232405i	−0.00177511	−	0.00439204i
$29$	−0.126343	+	0.347124i	−0.0234612	+	0.0644592i	−0.950870	−	0.309589i	$-0.899808\pi$
$29$	−0.126343	+	0.347124i	−0.0234612	+	0.0644592i	0.927409	+	0.374049i	$0.122031\pi$
$30$	1.80243	−	11.3845i	0.329077	−	2.07852i
$31$	1.29454	+	2.24221i	0.232506	+	0.402713i	0.958545	−	0.284941i	$-0.0919741\pi$
$31$	1.29454	+	2.24221i	0.232506	+	0.402713i	−0.726039	+	0.687654i	$0.758641\pi$
$32$	5.12613	−	2.39223i	0.906181	−	0.422890i
$33$	4.88165	−	5.81773i	0.849787	−	1.01274i
$34$	2.06413	−	3.72431i	0.353995	−	0.638715i
$35$	−0.0483324	−	0.00852231i	−0.00816967	−	0.00144053i
$36$	−1.25066	+	2.35284i	−0.208444	+	0.392140i
$37$		−	2.87327i		−	0.472363i	−0.971709	−	0.236182i	$-0.924104\pi$
$37$		−	2.87327i		−	0.472363i	0.971709	−	0.236182i	$-0.0758961\pi$
$38$	−2.53906	+	5.61722i	−0.411890	+	0.911233i
$39$		−	6.43407i		−	1.03028i
$40$	1.34778	−	10.9931i	0.213103	−	1.73817i
$41$	7.88423	+	1.39020i	1.23131	+	0.217113i	0.751188	−	0.660088i	$-0.229481\pi$
$41$	7.88423	+	1.39020i	1.23131	+	0.217113i	0.480122	+	0.877201i	$0.340592\pi$
$42$	0.0322685	+	0.0178842i	0.00497913	+	0.00275959i
$43$	−5.11775	+	6.09909i	−0.780449	+	0.930103i	−0.998954	−	0.0457330i	$-0.985438\pi$
$43$	−5.11775	+	6.09909i	−0.780449	+	0.930103i	0.218505	+	0.975836i	$0.429882\pi$
$44$	4.49206	−	5.75100i	0.677204	−	0.866996i
$45$	2.60847	+	4.51800i	0.388848	+	0.673504i
$46$	5.43318	+	0.860197i	0.801078	+	0.126829i
$47$	−2.68591	+	7.37948i	−0.391780	+	1.07641i	0.574408	+	0.818569i	$0.305232\pi$
$47$	−2.68591	+	7.37948i	−0.391780	+	1.07641i	−0.966188	+	0.257838i	$0.916990\pi$
$48$	−3.64794	+	7.48393i	−0.526534	+	1.08021i
$49$	−3.49992	+	6.06204i	−0.499989	+	0.866006i
$50$	−11.3573	−	9.19580i	−1.60616	−	1.30048i
$51$	1.08825	+	6.17175i	0.152385	+	0.864217i
$52$	−0.216503	−	6.17861i	−0.0300236	−	0.856819i
$53$	−0.993871	−	1.18445i	−0.136519	−	0.162697i	0.693454	−	0.720501i	$-0.256088\pi$
$53$	−0.993871	−	1.18445i	−0.136519	−	0.162697i	−0.829972	+	0.557805i	$0.811644\pi$
$54$	0.936972	+	4.81876i	0.127506	+	0.655750i
$55$	−4.88662	−	13.4259i	−0.658912	−	1.81034i
$56$	0.0315890	+	0.0160883i	0.00422126	+	0.00214988i
$57$	−2.29812	−	8.77680i	−0.304393	−	1.16252i
$58$	−0.187245	−	0.487703i	−0.0245865	−	0.0640385i
$59$	3.93600	−	1.43259i	0.512423	−	0.186507i	−0.0728499	−	0.997343i	$-0.523209\pi$
$59$	3.93600	−	1.43259i	0.512423	−	0.186507i	0.585273	+	0.810836i	$0.300987\pi$
$60$	8.63969	+	13.8227i	1.11538	+	1.78450i
$61$	−2.45324	+	2.05851i	−0.314105	+	0.263565i	−0.786186	−	0.617990i	$-0.787947\pi$
$61$	−2.45324	+	2.05851i	−0.314105	+	0.263565i	0.472081	+	0.881555i	$0.343503\pi$
$62$	−3.46210	−	1.19186i	−0.439687	−	0.151367i
$63$	−0.0164445	+	0.00289961i	−0.00207182	+	0.000365317i
$64$	−3.25126	+	7.30953i	−0.406408	+	0.913692i
$65$	−10.4827	−	6.05220i	−1.30022	−	0.750683i
$66$	0.188087	+	10.7386i	0.0231519	+	1.32183i
$67$	−8.76065	−	3.18861i	−1.07028	−	0.389551i	−0.254001	−	0.967204i	$-0.581747\pi$
$67$	−8.76065	−	3.18861i	−1.07028	−	0.389551i	−0.816283	+	0.577653i	$0.803969\pi$
$68$	1.25271	+	5.89008i	0.151914	+	0.714277i
$69$	−7.01139	+	4.04803i	−0.844073	+	0.487326i
$70$	0.0594911	−	0.0357507i	0.00711055	−	0.00427303i
$71$	9.25916	+	7.76936i	1.09886	+	0.922053i	0.997348	−	0.0727811i	$-0.0231874\pi$
$71$	9.25916	+	7.76936i	1.09886	+	0.922053i	0.101512	+	0.994834i	$0.467632\pi$
$72$	−0.848341	−	3.67156i	−0.0999780	−	0.432697i
$73$	0.801985	−	4.54828i	0.0938653	−	0.532336i	−0.901224	−	0.433354i	$-0.857330\pi$
$73$	0.801985	−	4.54828i	0.0938653	−	0.532336i	0.995089	−	0.0989826i	$-0.0315588\pi$
$74$	2.66603	+	3.06655i	0.309920	+	0.356479i
$75$	21.5077			2.48349
$76$	−2.50221	−	8.35099i	−0.287023	−	0.957924i
$77$	0.0457310			0.00521154
$78$	5.96999	+	6.86686i	0.675969	+	0.777519i
$79$	−0.148866	+	0.844262i	−0.0167487	+	0.0949868i	−0.992036	−	0.125953i	$-0.959801\pi$
$79$	−0.148866	+	0.844262i	−0.0167487	+	0.0949868i	0.975288	+	0.220940i	$0.0709124\pi$
$80$	8.76178	+	12.9832i	0.979597	+	1.45156i
$81$	−8.59645	−	7.21328i	−0.955162	−	0.801476i
$82$	−9.70450	+	5.83184i	−1.07168	+	0.644019i
$83$	4.31582	−	2.49174i	0.473723	−	0.273504i	−0.244074	−	0.969757i	$-0.578484\pi$
$83$	4.31582	−	2.49174i	0.473723	−	0.273504i	0.717797	+	0.696253i	$0.245151\pi$
$84$	−0.0510332	+	0.0108538i	−0.00556818	+	0.00118425i
$85$	11.0790	+	4.03242i	1.20168	+	0.437377i
$86$	−0.197183	−	11.2580i	−0.0212628	−	1.21398i
$87$	0.665868	+	0.384439i	0.0713885	+	0.0412162i
$88$	0.541968	+	10.3059i	0.0577740	+	1.09861i
$89$	4.86849	−	0.858447i	0.516059	−	0.0909952i	0.0904478	−	0.995901i	$-0.471170\pi$
$89$	4.86849	−	0.858447i	0.516059	−	0.0909952i	0.425611	+	0.904906i	$0.360059\pi$
$90$	−6.97605	−	2.40158i	−0.735340	−	0.253149i
$91$	0.0296792	−	0.0249038i	0.00311122	−	0.00261063i
$92$	−6.59679	+	4.12323i	−0.687763	+	0.429877i
$93$	5.06396	−	1.84313i	0.525108	−	0.191124i
$94$	−3.98063	−	10.3680i	−0.410571	−	1.06938i
$95$	−16.4613	−	4.51167i	−1.68890	−	0.462888i
$96$	−3.05081	−	11.3722i	−0.311372	−	1.16067i
$97$	−1.35020	−	3.70964i	−0.137092	−	0.376657i	0.852081	−	0.523410i	$-0.175340\pi$
$97$	−1.35020	−	3.70964i	−0.137092	−	0.376657i	−0.989173	+	0.146752i	$0.953118\pi$
$98$	−1.88945	−	9.71728i	−0.190864	−	0.981594i
$99$	−3.12469	−	3.72386i	−0.314043	−	0.374262i
$100$	20.6537	−	0.723723i	2.06537	−	0.0723723i
$101$	−1.11341	−	6.31446i	−0.110788	−	0.628312i	−0.988750	−	0.149580i	$-0.952208\pi$
$101$	−1.11341	−	6.31446i	−0.110788	−	0.628312i	0.877961	−	0.478732i	$-0.158903\pi$
$102$	−6.88803	−	5.57714i	−0.682017	−	0.552219i
$103$	−1.81621	+	3.14577i	−0.178956	+	0.309962i	−0.941523	−	0.336948i	$-0.890605\pi$
$103$	−1.81621	+	3.14577i	−0.178956	+	0.309962i	0.762567	+	0.646909i	$0.223939\pi$
$104$	5.96402	+	6.39332i	0.584820	+	0.626917i
$105$	−0.0349380	+	0.0959913i	−0.00340960	+	0.00936779i
$106$	2.15974	+	0.341937i	0.209773	+	0.0332118i
$107$	−2.16098	−	3.74292i	−0.208909	−	0.361842i	0.742462	−	0.669888i	$-0.233658\pi$
$107$	−2.16098	−	3.74292i	−0.208909	−	0.361842i	−0.951371	+	0.308047i	$0.900325\pi$
$108$	−5.47119	−	4.27351i	−0.526465	−	0.411218i
$109$	−10.4560	+	12.4609i	−1.00150	+	1.19354i	−0.0204473	+	0.999791i	$0.506509\pi$
$109$	−10.4560	+	12.4609i	−1.00150	+	1.19354i	−0.981051	+	0.193748i	$0.937935\pi$
$110$	17.6728	+	9.79481i	1.68504	+	0.933899i
$111$	−5.88962	−	1.03850i	−0.559018	−	0.0985700i
$112$	−0.0486417	+	0.0121401i	−0.00459621	+	0.00114713i
$113$			5.68498i			0.534798i	0.963586	+	0.267399i	$0.0861642\pi$
$113$			5.68498i			0.534798i	−0.963586	+	0.267399i	$0.913836\pi$
$114$	10.5964	+	7.23481i	0.992448	+	0.677602i
$115$			15.2311i			1.42031i
$116$	0.652365	+	0.346769i	0.0605706	+	0.0321967i
$117$	−4.05581	−	0.715149i	−0.374960	−	0.0661156i
$118$	−2.87150	+	5.18105i	−0.264343	+	0.476954i
$119$	−0.0242569	+	0.0289083i	−0.00222363	+	0.00265002i
$120$	−22.0465	−	6.73597i	−2.01256	−	0.614907i
$121$	1.15658	+	2.00325i	0.105143	+	0.182114i
$122$	0.708220	−	4.47326i	0.0641192	−	0.404990i
$123$	5.69926	−	15.6586i	0.513885	−	1.41189i
$124$	4.80087	−	1.94035i	0.431131	−	0.174248i
$125$	10.4418	−	18.0857i	0.933940	−	1.61763i
$126$	0.0148602	−	0.0183531i	0.00132385	−	0.00163502i
$127$	1.92363	+	10.9095i	0.170695	+	0.968058i	0.942997	+	0.332802i	$0.107994\pi$
$127$	1.92363	+	10.9095i	0.170695	+	0.968058i	−0.772302	+	0.635256i	$0.780895\pi$
$128$	−3.31235	−	10.8180i	−0.292773	−	0.956182i
$129$	10.6522	+	12.6947i	0.937870	+	1.11771i
$130$	16.8035	−	3.26732i	1.47377	−	0.286563i
$131$	−4.88661	−	13.4259i	−0.426945	−	1.17302i	−0.947657	−	0.319290i	$-0.896556\pi$
$131$	−4.88661	−	13.4259i	−0.426945	−	1.17302i	0.520712	−	0.853733i	$-0.325667\pi$
$132$	−10.1648	−	11.2864i	−0.884731	−	0.982356i
$133$	0.0315906	−	0.0445723i	0.00273925	−	0.00386491i
$134$	12.3086	−	4.72566i	1.06330	−	0.408235i
$135$	−12.7727	+	4.64887i	−1.09929	+	0.400111i
$136$	−6.80221	−	5.12392i	−0.583285	−	0.439372i
$137$	1.69104	−	1.41895i	0.144475	−	0.121229i	−0.567686	−	0.823245i	$-0.692161\pi$
$137$	1.69104	−	1.41895i	0.144475	−	0.121229i	0.712161	+	0.702016i	$0.247717\pi$
$138$	3.72696	−	10.8260i	0.317260	−	0.921570i
$139$	−4.58434	+	0.808342i	−0.388838	+	0.0685627i	−0.364650	−	0.931145i	$-0.618811\pi$
$139$	−4.58434	+	0.808342i	−0.388838	+	0.0685627i	−0.0241886	+	0.999707i	$0.507700\pi$
$140$	−0.0303207	+	0.0933556i	−0.00256257	+	0.00788999i
$141$	14.1556	+	8.17276i	1.19212	+	0.688271i
$142$	−17.0909	+	0.299348i	−1.43424	+	0.0251208i
$143$	10.5987	+	3.85762i	0.886310	+	0.322590i
$144$	4.31214	+	3.13137i	0.359345	+	0.260948i
$145$	1.25270	−	0.723244i	0.104031	−	0.0600621i
$146$	3.36429	+	5.59836i	0.278431	+	0.463324i
$147$	11.1609	+	9.36515i	0.920540	+	0.772424i
$148$	−5.69072	−	0.799083i	−0.467774	−	0.0656842i
$149$	−3.23910	+	18.3698i	−0.265357	+	1.50491i	0.502659	+	0.864485i	$0.332355\pi$
$149$	−3.23910	+	18.3698i	−0.265357	+	1.50491i	−0.768016	+	0.640430i	$0.778756\pi$
$150$	−22.9544	+	19.9564i	−1.87422	+	1.62943i
$151$	11.9197			0.970010			0.485005	−	0.874511i	$-0.338818\pi$
$151$	11.9197			0.970010			0.485005	+	0.874511i	$0.338818\pi$
$152$	10.4192	+	6.59099i	0.845105	+	0.534600i
$153$	4.01141			0.324303
$154$	−0.0488071	+	0.0424325i	−0.00393299	+	0.00341931i
$155$	1.76048	−	9.98420i	0.141405	−	0.801950i
$156$	−12.7431	−	1.78937i	−1.02027	−	0.143264i
$157$	9.27872	+	7.78577i	0.740522	+	0.621372i	0.932978	−	0.359934i	$-0.117201\pi$
$157$	9.27872	+	7.78577i	0.740522	+	0.621372i	−0.192456	+	0.981306i	$0.561645\pi$
$158$	−0.624487	−	1.03918i	−0.0496815	−	0.0826727i
$159$	−2.78710	+	1.60913i	−0.221031	+	0.127612i
$160$	−21.3978	−	5.72666i	−1.69165	−	0.452732i
$161$	−0.0458112	−	0.0166739i	−0.00361043	−	0.00131409i
$162$	15.8677	−	0.277923i	1.24668	−	0.0218357i
$163$	3.89964	+	2.25146i	0.305443	+	0.176348i	0.644886	−	0.764279i	$-0.276905\pi$
$163$	3.89964	+	2.25146i	0.305443	+	0.176348i	−0.339442	+	0.940627i	$0.610238\pi$
$164$	4.94607	−	15.2286i	0.386223	−	1.18916i
$165$	−29.2865	+	5.16400i	−2.27995	+	0.402017i
$166$	−2.29411	+	6.66387i	−0.178057	+	0.517217i
$167$	0.466911	−	0.391785i	0.0361306	−	0.0303172i	−0.624544	−	0.780990i	$-0.714715\pi$
$167$	0.466911	−	0.391785i	0.0361306	−	0.0303172i	0.660674	+	0.750673i	$0.270271\pi$
$168$	0.0443950	−	0.0589362i	0.00342515	−	0.00454702i
$169$	−3.23675	+	1.17808i	−0.248981	+	0.0906217i
$170$	−15.5658	+	5.97621i	−1.19384	+	0.458355i
$171$	−5.78802	+	0.473108i	−0.442621	+	0.0361795i
$172$	10.6564	+	11.8323i	0.812542	+	0.902202i
$173$	−0.699568	−	1.92205i	−0.0531871	−	0.146130i	0.910254	−	0.414050i	$-0.135886\pi$
$173$	−0.699568	−	1.92205i	−0.0531871	−	0.146130i	−0.963441	+	0.267919i	$0.913664\pi$
$174$	−1.06737	+	0.207542i	−0.0809169	+	0.0157337i
$175$	0.0832478	+	0.0992109i	0.00629294	+	0.00749964i
$176$	−10.1410	−	10.4962i	−0.764405	−	0.791184i
$177$	−1.51390	−	8.58578i	−0.113792	−	0.645346i
$178$	−4.39944	+	5.43353i	−0.329752	+	0.407260i
$179$	−11.2319	+	19.4542i	−0.839510	+	1.45407i	0.0507946	+	0.998709i	$0.483825\pi$
$179$	−11.2319	+	19.4542i	−0.839510	+	1.45407i	−0.890305	+	0.455365i	$0.849509\pi$
$180$	9.67365	−	3.90976i	0.721032	−	0.291416i
$181$	8.67231	−	23.8270i	0.644607	−	1.77104i	0.00786332	−	0.999969i	$-0.497497\pi$
$181$	8.67231	−	23.8270i	0.644607	−	1.77104i	0.636744	−	0.771075i	$-0.280281\pi$
$182$	−0.00856803	+	0.0541174i	−0.000635104	+	0.00401145i
$183$	3.33284	+	5.77264i	0.246370	+	0.426726i
$184$	3.21469	−	10.5216i	0.236990	−	0.775660i
$185$	−7.23204	+	8.61881i	−0.531710	+	0.633668i
$186$	−3.69440	+	6.66581i	−0.270886	+	0.488761i
$187$	−10.8191	−	1.90769i	−0.791168	−	0.139504i
$188$	13.8686	+	7.37193i	1.01147	+	0.537653i
$189$		−	0.0435060i		−	0.00316460i
$190$	21.7549	−	10.4589i	1.57826	−	0.758765i
$191$		−	18.2562i		−	1.32097i	−0.750839	−	0.660485i	$-0.770351\pi$
$191$		−	18.2562i		−	1.32097i	0.750839	−	0.660485i	$-0.229649\pi$
$192$	13.8079	+	9.30634i	0.996501	+	0.671627i
$193$	−1.41653	−	0.249772i	−0.101964	−	0.0179790i	0.122433	−	0.992477i	$-0.460930\pi$
$193$	−1.41653	−	0.249772i	−0.101964	−	0.0179790i	−0.224397	+	0.974498i	$0.572041\pi$
$194$	4.88310	+	2.70636i	0.350586	+	0.194305i
$195$	−16.1946	+	19.3000i	−1.15972	+	1.38210i
$196$	11.0329	+	8.61774i	0.788067	+	0.615553i
$197$	1.84338	+	3.19283i	0.131335	+	0.227479i	0.924192	−	0.381929i	$-0.124740\pi$
$197$	1.84338	+	3.19283i	0.131335	+	0.227479i	−0.792856	+	0.609409i	$0.791407\pi$
$198$	6.79014	+	1.07504i	0.482554	+	0.0763995i
$199$	6.67292	−	18.3337i	0.473031	−	1.29964i	−0.442274	−	0.896880i	$-0.645828\pi$
$199$	6.67292	−	18.3337i	0.473031	−	1.29964i	0.915305	−	0.402762i	$-0.131950\pi$
$200$	−21.3715	+	19.9364i	−1.51119	+	1.40972i
$201$	−9.70240	+	16.8051i	−0.684355	+	1.18534i
$202$	7.04731	+	5.70610i	0.495847	+	0.401480i
$203$	0.000803969		0.00455953i	5.64276e−5		0.000320017i
$204$	12.5262	−	0.438929i	0.877011	−	0.0307312i
$205$	−20.1508	−	24.0148i	−1.40739	−	1.67726i
$206$	−0.980491	−	5.04258i	−0.0683141	−	0.351333i
$207$	1.77242	+	4.86968i	0.123192	+	0.338466i
$208$	−12.2974	−	1.28952i	−0.852670	−	0.0894125i
$209$	15.8357	+	1.47658i	1.09538	+	0.102137i
$210$	−0.0517795	−	0.134866i	−0.00357312	−	0.00930664i
$211$	5.20674	−	1.89510i	0.358447	−	0.130464i	−0.156518	−	0.987675i	$-0.550027\pi$
$211$	5.20674	−	1.89510i	0.358447	−	0.130464i	0.514965	+	0.857211i	$0.327805\pi$
$212$	−2.62229	+	1.63903i	−0.180100	+	0.112569i
$213$	19.2722	−	16.1713i	1.32051	−	1.10804i
$214$	5.77928	+	1.98958i	0.395064	+	0.136005i
$215$	30.7029	−	5.41375i	2.09392	−	0.369214i
$216$	9.80447	−	0.515599i	0.667110	−	0.0350820i
$217$	0.0281026	+	0.0162251i	0.00190773	+	0.00110143i
$218$	−0.402861	−	23.0009i	−0.0272852	−	1.55782i
$219$	−9.03318	−	3.28781i	−0.610406	−	0.222170i
$220$	−27.9499	+	5.94444i	−1.88438	+	0.400774i
$221$	−8.06038	+	4.65366i	−0.542200	+	0.313039i
$222$	7.24938	−	4.35646i	0.486547	−	0.292386i
$223$	−1.81627	−	1.52403i	−0.121626	−	0.102057i	0.579946	−	0.814655i	$-0.303074\pi$
$223$	−1.81627	−	1.52403i	−0.121626	−	0.102057i	−0.701572	+	0.712598i	$0.747518\pi$
$224$	0.0406491	−	0.0580900i	0.00271598	−	0.00388130i
$225$	2.39059	−	13.5577i	0.159372	−	0.903846i
$226$	−5.27494	−	6.06738i	−0.350883	−	0.403596i
$227$	−24.6646			−1.63705			−0.818524	−	0.574472i	$-0.805207\pi$
$227$	−24.6646			−1.63705			−0.818524	+	0.574472i	$0.805207\pi$
$228$	−18.0222	+	2.11068i	−1.19355	+	0.139783i
$229$	−17.5053			−1.15678			−0.578392	−	0.815759i	$-0.696320\pi$
$229$	−17.5053			−1.15678			−0.578392	+	0.815759i	$0.696320\pi$
$230$	−14.1325	−	16.2556i	−0.931870	−	1.07186i
$231$	0.0165288	−	0.0937392i	0.00108751	−	0.00616759i
$232$	−1.01800	+	0.235217i	−0.0668352	+	0.0154428i
$233$	0.796913	+	0.668689i	0.0522075	+	0.0438073i	0.668518	−	0.743696i	$-0.266929\pi$
$233$	0.796913	+	0.668689i	0.0522075	+	0.0438073i	−0.616311	+	0.787503i	$0.711373\pi$
$234$	4.99219	−	3.00002i	0.326350	−	0.196117i
$235$	26.6310	−	15.3754i	1.73721	−	1.00298i
$236$	−1.74270	−	8.19394i	−0.113440	−	0.533380i
$237$	1.67676	+	0.610290i	0.108917	+	0.0396426i
$238$	−0.000934604	−	0.0533601i	−6.05814e−5	−	0.00345882i
$239$	5.03710	+	2.90817i	0.325823	+	0.188114i	0.653985	−	0.756508i	$-0.273096\pi$
$239$	5.03710	+	2.90817i	0.325823	+	0.188114i	−0.328162	+	0.944621i	$0.606429\pi$
$240$	29.7796	−	13.2673i	1.92227	−	0.856400i
$241$	10.6156	−	1.87182i	0.683813	−	0.120575i	0.179060	−	0.983838i	$-0.442695\pi$
$241$	10.6156	−	1.87182i	0.683813	−	0.120575i	0.504753	+	0.863264i	$0.331583\pi$
$242$	−3.09313	−	1.06484i	−0.198834	−	0.0684508i
$243$	−9.91553	+	8.32012i	−0.636081	+	0.533736i
$244$	3.39475	+	5.43129i	0.217327	+	0.347703i
$245$	25.7567	−	9.37468i	1.64554	−	0.598926i
$246$	8.44654	+	22.0000i	0.538532	+	1.40267i
$247$	11.0814	−	7.66537i	0.705091	−	0.487736i
$248$	−3.32341	+	6.52546i	−0.211037	+	0.414367i
$249$	−3.54767	−	9.74714i	−0.224824	−	0.617700i
$250$	5.63705	+	28.9908i	0.356518	+	1.83354i
$251$	−14.8164	−	17.6575i	−0.935205	−	1.11453i	−0.993224	−	0.116219i	$-0.962923\pi$
$251$	−14.8164	−	17.6575i	−0.935205	−	1.11453i	0.0580182	−	0.998316i	$-0.481522\pi$
$252$	0.00116952	+	0.0333759i	7.36728e−5	+	0.00210249i
$253$	−2.46448	−	13.9768i	−0.154941	−	0.878712i
$254$	−12.1756	−	9.85840i	−0.763965	−	0.618571i
$255$	12.2700	−	21.2522i	0.768374	−	1.33086i
$256$	13.5728	+	8.47220i	0.848302	+	0.529513i
$257$	−10.2488	+	28.1585i	−0.639305	+	1.75648i	0.0145929	+	0.999894i	$0.495355\pi$
$257$	−10.2488	+	28.1585i	−0.639305	+	1.75648i	−0.653898	+	0.756583i	$0.726867\pi$
$258$	−23.1478	−	3.66482i	−1.44112	−	0.228162i
$259$	−0.0180060	−	0.0311873i	−0.00111884	−	0.00193789i
$260$	−14.9021	+	19.0786i	−0.924192	+	1.18320i
$261$	0.316348	−	0.377009i	0.0195815	−	0.0233363i
$262$	17.6728	+	9.79480i	1.09183	+	0.605125i
$263$	28.4822	+	5.02219i	1.75629	+	0.309681i	0.956746	−	0.290925i	$-0.0939631\pi$
$263$	28.4822	+	5.02219i	1.75629	+	0.309681i	0.799545	+	0.600607i	$0.205074\pi$
$264$	21.3209	+	2.61398i	1.31221	+	0.160879i
$265$			6.05451i			0.371926i
$266$	0.00764185	+	0.0768825i	0.000468552	+	0.00471397i
$267$		−	10.2897i		−	0.629718i
$268$	−8.75169	+	16.4643i	−0.534594	+	1.00572i
$269$	−22.2457	−	3.92252i	−1.35634	−	0.239160i	−0.552258	−	0.833673i	$-0.686234\pi$
$269$	−22.2457	−	3.92252i	−1.35634	−	0.239160i	−0.804086	+	0.594513i	$0.797345\pi$
$270$	9.31825	−	16.8130i	0.567091	−	1.02320i
$271$	−11.2567	+	13.4152i	−0.683794	+	0.814914i	−0.990590	−	0.136861i	$-0.956299\pi$
$271$	−11.2567	+	13.4152i	−0.683794	+	0.814914i	0.306796	+	0.951775i	$0.400743\pi$
$272$	12.0141	−	0.843003i	0.728462	−	0.0511145i
$273$	−0.0403206	−	0.0698373i	−0.00244031	−	0.00422674i
$274$	−0.488183	+	3.08346i	−0.0294922	+	0.186279i
$275$	−12.8952	+	35.4292i	−0.777608	+	2.13646i
$276$	6.06748	+	15.0123i	0.365219	+	0.903637i
$277$	0.755353	−	1.30831i	0.0453848	−	0.0786087i	−0.842441	−	0.538789i	$-0.818882\pi$
$277$	0.755353	−	1.30831i	0.0453848	−	0.0786087i	0.887825	+	0.460180i	$0.152215\pi$
$278$	4.14266	−	5.11639i	0.248461	−	0.306861i
$279$	−0.598984	−	3.39701i	−0.0358602	−	0.203373i
$280$	−0.0542618	−	0.127769i	−0.00324276	−	0.00763565i
$281$	−10.9264	−	13.0216i	−0.651817	−	0.776805i	0.334370	−	0.942442i	$-0.391477\pi$
$281$	−10.9264	−	13.0216i	−0.651817	−	0.776805i	−0.986187	+	0.165637i	$0.947032\pi$
$282$	−22.6911	+	4.41211i	−1.35123	+	0.262737i
$283$	9.95447	+	27.3497i	0.591732	+	1.62577i	0.767290	+	0.641301i	$0.221605\pi$
$283$	9.95447	+	27.3497i	0.591732	+	1.62577i	−0.175558	+	0.984469i	$0.556173\pi$
$284$	17.9628	−	16.1777i	1.06590	−	0.959969i
$285$	−15.1977	+	32.1117i	−0.900234	+	1.90213i
$286$	−14.8910	+	5.71715i	−0.880524	+	0.338062i
$287$	0.0942898	−	0.0343187i	0.00556575	−	0.00202577i
$288$	−7.50770	+	0.659107i	−0.442396	+	0.0388382i
$289$	−6.07812	+	5.10015i	−0.357537	+	0.300009i
$290$	−0.665880	+	1.93423i	−0.0391018	+	0.113582i
$291$	−8.09202	+	1.42684i	−0.474362	+	0.0836429i
$292$	−8.78515	−	2.85330i	−0.514112	−	0.166977i
$293$	16.0206	+	9.24953i	0.935936	+	0.540363i	0.888684	−	0.458520i	$-0.151620\pi$
$293$	16.0206	+	9.24953i	0.935936	+	0.540363i	0.0472521	+	0.998883i	$0.484954\pi$
$294$	−20.6013	+	0.360833i	−1.20149	+	0.0210442i
$295$	−15.4124	−	5.60967i	−0.897347	−	0.326608i
$296$	6.81495	−	4.42742i	0.396111	−	0.257339i
$297$	10.9686	−	6.33271i	0.636461	−	0.367461i
$298$	−13.5879	−	22.6109i	−0.787124	−	1.30982i
$299$	−9.21077	−	7.72876i	−0.532673	−	0.446965i
$300$	5.98147	−	42.5975i	0.345341	−	2.45937i
$301$	−0.0173281	+	0.0982728i	−0.000998778	+	0.00566435i
$302$	−12.7215	+	11.0599i	−0.732038	+	0.636428i
$303$	−13.3458			−0.766694
$304$	−17.2356	+	2.63331i	−0.988529	+	0.151031i
$305$	12.5401			0.718045
$306$	−4.28124	+	3.72207i	−0.244742	+	0.212777i
$307$	2.03721	−	11.5536i	0.116270	−	0.659397i	−0.869844	−	0.493326i	$-0.835781\pi$
$307$	2.03721	−	11.5536i	0.116270	−	0.659397i	0.986114	−	0.166071i	$-0.0531081\pi$
$308$	0.0127182	−	0.0905735i	0.000724687	−	0.00516091i
$309$	5.79174	+	4.85984i	0.329480	+	0.276467i
$310$	7.38515	+	12.2893i	0.419448	+	0.697985i
$311$	−15.1860	+	8.76764i	−0.861119	+	0.497167i	−0.864387	−	0.502827i	$-0.832293\pi$
$311$	−15.1860	+	8.76764i	−0.861119	+	0.497167i	0.00326795	+	0.999995i	$0.498960\pi$
$312$	15.2606	−	9.91425i	0.863961	−	0.561284i
$313$	−17.7593	−	6.46387i	−1.00382	−	0.365359i	−0.212761	−	0.977104i	$-0.568246\pi$
$313$	−17.7593	−	6.46387i	−1.00382	−	0.365359i	−0.791055	+	0.611745i	$0.790468\pi$
$314$	−17.1270	+	0.299981i	−0.966535	+	0.0169289i
$315$	0.0566261	+	0.0326931i	0.00319052	+	0.00184205i
$316$	1.63072	+	0.529636i	0.0917350	+	0.0297944i
$317$	18.2177	−	3.21228i	1.02321	−	0.180420i	0.363228	−	0.931700i	$-0.381675\pi$
$317$	18.2177	−	3.21228i	1.02321	−	0.180420i	0.659983	+	0.751281i	$0.270564\pi$
$318$	1.48150	−	4.30344i	0.0830786	−	0.241325i
$319$	−1.03251	+	0.866376i	−0.0578093	+	0.0485077i
$320$	28.1508	−	13.7426i	1.57368	−	0.768234i
$321$	−8.45327	+	3.07674i	−0.471815	+	0.171727i
$322$	0.0643639	−	0.0247114i	0.00358686	−	0.00137711i
$323$	−9.33307	+	9.22712i	−0.519306	+	0.513411i
$324$	−16.6772	+	15.0198i	−0.926509	+	0.834433i
$325$	10.9248	+	30.0156i	0.605999	+	1.66497i
$326$	−6.25101	+	1.21546i	−0.346211	+	0.0673182i
$327$	21.7632	+	25.9364i	1.20351	+	1.43428i
$328$	8.85146	+	20.8423i	0.488740	+	1.15082i
$329$	0.0170915	+	0.0969308i	0.000942286	+	0.00534397i
$330$	26.4649	−	32.6854i	1.45685	−	1.79927i
$331$	−2.81137	+	4.86944i	−0.154527	+	0.267649i	−0.932887	−	0.360170i	$-0.882719\pi$
$331$	−2.81137	+	4.86944i	−0.154527	+	0.267649i	0.778360	+	0.627819i	$0.216052\pi$
$332$	−3.73480	−	9.24076i	−0.204974	−	0.507152i
$333$	−1.30927	+	3.59718i	−0.0717474	+	0.197124i
$334$	−0.134792	+	0.851371i	−0.00737547	+	0.0465850i
$335$	18.2531	+	31.6153i	0.997274	+	1.72733i
$336$	0.00730400	+	0.104093i	0.000398466	+	0.00567876i
$337$	11.9419	−	14.2318i	0.650515	−	0.775254i	−0.335476	−	0.942049i	$-0.608897\pi$
$337$	11.9419	−	14.2318i	0.650515	−	0.775254i	0.985992	+	0.166795i	$0.0533417\pi$
$338$	2.36136	−	4.26062i	0.128441	−	0.231747i
$339$	11.6530	+	2.05475i	0.632907	+	0.111599i
$340$	11.0676	−	20.8212i	0.600228	−	1.12919i
$341$			9.44683i			0.511574i
$342$	5.73837	−	5.87547i	0.310295	−	0.317709i
$343$			0.175466i			0.00947429i
$344$	−22.3520	−	2.74040i	−1.20514	−	0.147753i
$345$	31.2206	+	5.50504i	1.68086	+	0.296381i
$346$	2.53004	+	1.40222i	0.136016	+	0.0753840i
$347$	13.5612	−	16.1617i	0.728005	−	0.867603i	−0.267377	−	0.963592i	$-0.586157\pi$
$347$	13.5612	−	16.1617i	0.728005	−	0.867603i	0.995382	+	0.0959889i	$0.0306013\pi$
$348$	0.946591	−	1.21188i	0.0507426	−	0.0649636i
$349$	−7.02205	−	12.1625i	−0.375882	−	0.651046i	0.614577	−	0.788857i	$-0.289327\pi$
$349$	−7.02205	−	12.1625i	−0.375882	−	0.651046i	−0.990459	+	0.137811i	$0.955993\pi$
$350$	−0.180902	−	0.0286410i	−0.00966964	−	0.00153093i
$351$	3.66993	−	10.0830i	0.195886	−	0.538193i
$352$	20.5623	+	1.79276i	1.09597	+	0.0955542i
$353$	−5.54692	+	9.60756i	−0.295233	+	0.511359i	−0.975039	−	0.222033i	$-0.928731\pi$
$353$	−5.54692	+	9.60756i	−0.295233	+	0.511359i	0.679806	+	0.733392i	$0.262064\pi$
$354$	9.58223	+	7.75859i	0.509290	+	0.412364i
$355$	−8.21872	−	46.6107i	−0.436204	−	2.47384i
$356$	−0.346243	−	9.88113i	−0.0183508	−	0.523699i
$357$	0.0504888	+	0.0601702i	0.00267215	+	0.00318454i
$358$	−6.06360	−	31.1845i	−0.320471	−	1.64815i
$359$	−2.47546	−	6.80128i	−0.130650	−	0.358958i	0.857068	−	0.515203i	$-0.172283\pi$
$359$	−2.47546	−	6.80128i	−0.130650	−	0.358958i	−0.987718	+	0.156245i	$0.950061\pi$
$360$	−6.69660	+	13.1487i	−0.352942	+	0.692995i
$361$	12.3783	−	14.4145i	0.651492	−	0.758656i
$362$	12.8527	+	33.4765i	0.675524	+	1.75948i
$363$	4.52428	−	1.64670i	0.237463	−	0.0864295i
$364$	−0.0410696	−	0.0657076i	−0.00215263	−	0.00344402i
$365$	−13.8537	+	11.6247i	−0.725137	+	0.608462i
$366$	−8.91329	−	3.06850i	−0.465905	−	0.160393i
$367$	−11.9786	+	2.11215i	−0.625276	+	0.110253i	−0.477304	−	0.878738i	$-0.658386\pi$
$367$	−11.9786	+	2.11215i	−0.625276	+	0.110253i	−0.147973	+	0.988991i	$0.547275\pi$
$368$	6.33172	+	14.2121i	0.330064	+	0.740858i
$369$	−9.23715	−	5.33307i	−0.480867	−	0.277629i
$370$	−0.278646	−	15.9090i	−0.0144861	−	0.827068i
$371$	−0.0182104	−	0.00662804i	−0.000945436	−	0.000344111i
$372$	−2.24212	−	10.5421i	−0.116248	−	0.546583i
$373$	11.3195	−	6.53529i	0.586100	−	0.338385i	−0.177454	−	0.984129i	$-0.556786\pi$
$373$	11.3195	−	6.53529i	0.586100	−	0.338385i	0.763554	+	0.645744i	$0.223453\pi$
$374$	13.3169	−	8.00269i	0.688600	−	0.413809i
$375$	−33.2979	−	27.9403i	−1.71950	−	1.44283i
$376$	−21.6417	+	5.00047i	−1.11608	+	0.257880i
$377$	−0.198288	+	1.12455i	−0.0102123	+	0.0579170i
$378$	0.0403680	+	0.0464325i	0.00207631	+	0.00238823i
$379$	−1.20676			−0.0619869			−0.0309935	−	0.999520i	$-0.509867\pi$
$379$	−1.20676			−0.0619869			−0.0309935	+	0.999520i	$0.509867\pi$
$380$	−13.5137	+	31.3481i	−0.693240	+	1.60812i
$381$	23.0574			1.18127
$382$	16.9394	+	19.4842i	0.866694	+	0.996896i
$383$	−0.143101	+	0.811565i	−0.00731211	+	0.0414690i	−0.988246	−	0.152875i	$-0.951147\pi$
$383$	−0.143101	+	0.811565i	−0.00731211	+	0.0414690i	0.980933	+	0.194344i	$0.0622579\pi$
$384$	−23.3718	+	2.87965i	−1.19269	+	0.146952i
$385$	−0.137177	−	0.115105i	−0.00699119	−	0.00586631i
$386$	1.74357	−	1.04778i	0.0887452	−	0.0533308i
$387$	9.18631	−	5.30372i	0.466967	−	0.269603i
$388$	−7.72271	+	1.64248i	−0.392061	+	0.0833843i
$389$	−23.4630	−	8.53983i	−1.18962	−	0.432986i	−0.330030	−	0.943970i	$-0.607059\pi$
$389$	−23.4630	−	8.53983i	−1.18962	−	0.432986i	−0.859590	+	0.510984i	$0.829281\pi$
$390$	−0.623967	−	35.6247i	−0.0315958	−	1.80392i
$391$	10.1425	+	5.85575i	0.512926	+	0.296138i
$392$	−19.7712	+	1.03973i	−0.998598	+	0.0525144i
$393$	−29.2864	+	5.16399i	−1.47731	+	0.260489i
$394$	−4.92991	−	1.69717i	−0.248365	−	0.0855023i
$395$	2.57156	−	2.15779i	0.129389	−	0.108570i
$396$	−8.24438	+	5.15303i	−0.414295	+	0.258950i
$397$	8.73147	−	3.17800i	0.438220	−	0.159499i	−0.113482	−	0.993540i	$-0.536201\pi$
$397$	8.73147	−	3.17800i	0.438220	−	0.159499i	0.551703	+	0.834041i	$0.313978\pi$
$398$	9.88955	+	25.7585i	0.495718	+	1.29116i
$399$	−0.0799462	−	0.0808642i	−0.00400232	−	0.00404827i
$400$	4.31060	−	41.1074i	0.215530	−	2.05537i
$401$	−0.732427	−	2.01233i	−0.0365756	−	0.100491i	0.920061	−	0.391776i	$-0.128139\pi$
$401$	−0.732427	−	2.01233i	−0.0365756	−	0.100491i	−0.956636	+	0.291285i	$0.905917\pi$
$402$	−5.23790	−	26.9380i	−0.261243	−	1.34355i
$403$	5.14446	+	6.13093i	0.256264	+	0.305404i
$404$	−12.8159	+	0.449078i	−0.637613	+	0.0223425i
$405$	7.63048	+	43.2746i	0.379162	+	2.15033i
$406$	−0.00508871	−	0.00412025i	−0.000252548	−	0.000204485i
$407$	5.24189	−	9.07922i	0.259831	−	0.450040i
$408$	−12.9615	+	12.0912i	−0.641691	+	0.598602i
$409$	8.45981	−	23.2431i	0.418311	−	1.14930i	−0.534350	−	0.845264i	$-0.679443\pi$
$409$	8.45981	−	23.2431i	0.418311	−	1.14930i	0.952661	−	0.304036i	$-0.0983343\pi$
$410$	43.7888	+	6.93278i	2.16258	+	0.342386i
$411$	−2.29736	−	3.97914i	−0.113320	−	0.196276i
$412$	5.72531	+	4.47200i	0.282066	+	0.220319i
$413$	0.0337448	−	0.0402155i	0.00166047	−	0.00197888i
$414$	−6.41007	−	3.55266i	−0.315038	−	0.174604i
$415$	−19.2177	−	3.38859i	−0.943358	−	0.166339i
$416$	14.3211	−	10.0341i	0.702148	−	0.491963i
$417$			9.68911i			0.474478i
$418$	−18.2710	+	13.1176i	−0.893663	+	0.641603i
$419$			18.2597i			0.892044i	0.895022	+	0.446022i	$0.147160\pi$
$419$			18.2597i			0.892044i	−0.895022	+	0.446022i	$0.852840\pi$
$420$	0.180401	+	0.0958931i	0.00880266	+	0.00467910i
$421$	2.37505	+	0.418786i	0.115753	+	0.0204104i	0.231225	−	0.972900i	$-0.425727\pi$
$421$	2.37505	+	0.418786i	0.115753	+	0.0204104i	−0.115472	+	0.993311i	$0.536838\pi$
$422$	−3.79856	+	6.85376i	−0.184911	+	0.333636i
$423$	6.72522	−	8.01481i	0.326992	−	0.389693i
$424$	1.27787	−	4.18242i	0.0620590	−	0.203116i
$425$	−15.5562	−	26.9441i	−0.754585	−	1.30698i
$426$	−5.56365	+	35.1411i	−0.269560	+	1.70259i
$427$	−0.0137280	+	0.0377174i	−0.000664345	+	0.00182527i
$428$	−8.01410	+	3.23902i	−0.387376	+	0.156564i
$429$	11.7381	−	20.3309i	0.566719	−	0.981586i
$430$	−27.7448	+	34.2662i	−1.33798	+	1.65246i
$431$	4.29462	+	24.3560i	0.206864	+	1.17319i	0.894479	+	0.447111i	$0.147547\pi$
$431$	4.29462	+	24.3560i	0.206864	+	1.17319i	−0.687614	+	0.726076i	$0.741342\pi$
$432$	−9.98556	+	9.64757i	−0.480430	+	0.464169i
$433$	20.5038	+	24.4355i	0.985352	+	1.17430i	0.984693	+	0.174297i	$0.0557651\pi$
$433$	20.5038	+	24.4355i	0.985352	+	1.17430i	0.000658384		1.00000i	$0.499790\pi$
$434$	−0.0450477	+	0.00875919i	−0.00216236	+	0.000420455i
$435$	−1.02973	−	2.82917i	−0.0493720	−	0.135648i
$436$	21.7718	+	24.1742i	1.04268	+	1.15774i
$437$	−15.3251	−	7.25300i	−0.733098	−	0.346958i
$438$	12.6915	−	4.87267i	0.606422	−	0.232825i
$439$	−18.4899	+	6.72976i	−0.882473	+	0.321194i	−0.743207	−	0.669061i	$-0.766696\pi$
$439$	−18.4899	+	6.72976i	−0.882473	+	0.321194i	−0.139266	+	0.990255i	$0.544474\pi$
$440$	24.3143	−	32.2782i	1.15914	−	1.53880i
$441$	7.14400	−	5.99453i	0.340191	−	0.285454i
$442$	4.28456	−	12.4457i	0.203796	−	0.591981i
$443$	−5.11402	+	0.901740i	−0.242975	+	0.0428430i	−0.293809	−	0.955864i	$-0.594923\pi$
$443$	−5.11402	+	0.901740i	−0.242975	+	0.0428430i	0.0508345	+	0.998707i	$0.483812\pi$
$444$	−3.69478	+	11.3760i	−0.175346	+	0.539881i
$445$	−16.7645	−	9.67898i	−0.794712	−	0.458827i
$446$	3.35254	−	0.0587199i	0.158748	−	0.00278047i
$447$	36.4836	+	13.2790i	1.72562	+	0.628073i
$448$	0.0105167	+	0.0997146i	0.000496867	+	0.00471107i
$449$	13.6251	−	7.86644i	0.643007	−	0.371240i	−0.142765	−	0.989757i	$-0.545599\pi$
$449$	13.6251	−	7.86644i	0.643007	−	0.371240i	0.785772	+	0.618517i	$0.212266\pi$
$450$	10.0284	+	16.6878i	0.472743	+	0.786670i
$451$	22.3770	+	18.7766i	1.05369	+	0.884154i
$452$	11.2595	+	1.58104i	0.529603	+	0.0743660i
$453$	4.30818	−	24.4329i	0.202416	−	1.14796i
$454$	26.3237	−	22.8856i	1.23543	−	1.07407i
$455$	−0.151710			−0.00711227
$456$	17.2760	−	18.9749i	0.809023	−	0.888582i
$457$	−37.8299			−1.76961			−0.884803	−	0.465965i	$-0.845707\pi$
$457$	−37.8299			−1.76961			−0.884803	+	0.465965i	$0.845707\pi$
$458$	18.6828	−	16.2427i	0.872990	−	0.758971i
$459$	−1.81488	+	10.2927i	−0.0847111	+	0.480421i
$460$	30.1663	+	4.23590i	1.40651	+	0.197500i
$461$	−26.3446	−	22.1057i	−1.22699	−	1.02957i	−0.998429	−	0.0560360i	$-0.982154\pi$
$461$	−26.3446	−	22.1057i	−1.22699	−	1.02957i	−0.228560	−	0.973530i	$-0.573402\pi$
$462$	0.0693374	+	0.115381i	0.00322587	+	0.00536802i
$463$	−5.85991	+	3.38322i	−0.272333	+	0.157232i	−0.629948	−	0.776638i	$-0.716924\pi$
$463$	−5.85991	+	3.38322i	−0.272333	+	0.157232i	0.357614	+	0.933869i	$0.383590\pi$
$464$	0.868228	−	1.19562i	0.0403065	−	0.0555051i
$465$	−19.8293	−	7.21726i	−0.919560	−	0.334692i
$466$	−1.47097	+	0.0257642i	−0.0681416	+	0.00119350i
$467$	−34.2890	−	19.7968i	−1.58671	−	0.916086i	−0.993845	−	0.110783i	$-0.964664\pi$
$467$	−34.2890	−	19.7968i	−1.58671	−	0.916086i	−0.592863	−	0.805303i	$-0.702002\pi$
$468$	−2.54436	+	7.83393i	−0.117613	+	0.362124i
$469$	−0.115073	+	0.0202904i	−0.00531357	+	0.000936925i
$470$	−14.1559	+	41.1197i	−0.652963	+	1.89671i
$471$	19.3129	−	16.2054i	0.889890	−	0.746706i
$472$	9.46284	+	7.12810i	0.435563	+	0.328097i
$473$	−27.2984	+	9.93581i	−1.25518	+	0.456849i
$474$	−2.35581	+	0.904475i	−0.108206	+	0.0415439i
$475$	25.6236	+	37.0426i	1.17569	+	1.69963i
$476$	0.0505088	+	0.0560822i	0.00231507	+	0.00257052i
$477$	0.704553	+	1.93574i	0.0322593	+	0.0886316i
$478$	−8.07433	+	1.56999i	−0.369311	+	0.0718098i
$479$	−3.80512	−	4.53476i	−0.173860	−	0.207199i	0.672077	−	0.740482i	$-0.265403\pi$
$479$	−3.80512	−	4.53476i	−0.173860	−	0.207199i	−0.845937	+	0.533283i	$0.820958\pi$
$480$	−19.4724	+	41.7914i	−0.888789	+	1.90751i
$481$	−1.54232	−	8.74693i	−0.0703237	−	0.398826i
$482$	−9.59288	+	11.8477i	−0.436944	+	0.539647i
$483$	−0.0507358	+	0.0878770i	−0.00230856	+	0.00399854i
$484$	4.28923	−	1.73356i	0.194965	−	0.0787982i
$485$	−5.28706	+	14.5261i	−0.240073	+	0.659596i
$486$	2.86250	−	18.0801i	0.129845	−	0.820130i
$487$	−9.55411	−	16.5482i	−0.432938	−	0.749871i	0.564187	−	0.825647i	$-0.309190\pi$
$487$	−9.55411	−	16.5482i	−0.432938	−	0.749871i	−0.997125	+	0.0757763i	$0.975857\pi$
$488$	−8.66264	−	2.64673i	−0.392139	−	0.119812i
$489$	6.02449	−	7.17970i	0.272437	−	0.324677i
$490$	−18.7907	+	33.9042i	−0.848879	+	1.53164i
$491$	−10.3208	−	1.81983i	−0.465771	−	0.0821279i	−0.0641624	−	0.997939i	$-0.520438\pi$
$491$	−10.3208	−	1.81983i	−0.465771	−	0.0821279i	−0.401608	+	0.915812i	$0.631549\pi$
$492$	−29.4279	−	15.6426i	−1.32671	−	0.705222i
$493$		−	1.11223i		−	0.0500925i
$494$	−4.71429	+	18.4631i	−0.212106	+	0.830693i
$495$			19.0351i			0.855566i
$496$	−2.50783	−	10.0481i	−0.112605	−	0.451173i
$497$	0.149190	+	0.0263062i	0.00669209	+	0.00118000i
$498$	12.8304	+	7.11100i	0.574944	+	0.318652i
$499$	25.8797	−	30.8423i	1.15854	−	1.38069i	0.247232	−	0.968956i	$-0.420479\pi$
$499$	25.8797	−	30.8423i	1.15854	−	1.38069i	0.911304	−	0.411733i	$-0.135077\pi$
$500$	−32.9160	−	25.7104i	−1.47205	−	1.14981i
$501$	−0.634321	−	1.09868i	−0.0283394	−	0.0490852i
$502$	32.1970	+	5.09753i	1.43702	+	0.227514i
$503$	9.52283	−	26.1638i	0.424602	−	1.16658i	−0.524443	−	0.851445i	$-0.675727\pi$
$503$	9.52283	−	26.1638i	0.424602	−	1.16658i	0.949045	−	0.315139i	$-0.102051\pi$
$504$	−0.0322168	−	0.0345358i	−0.00143505	−	0.00153835i
$505$	−12.5537	+	21.7436i	−0.558631	+	0.967578i
$506$	15.5989	+	12.6302i	0.693456	+	0.561481i
$507$	1.24495	+	7.06048i	0.0552903	+	0.313567i
$508$	22.1419	−	0.775871i	0.982389	−	0.0344237i
$509$	17.9851	+	21.4337i	0.797173	+	0.950034i	0.999572	−	0.0292691i	$-0.00931798\pi$
$509$	17.9851	+	21.4337i	0.797173	+	0.950034i	−0.202398	+	0.979303i	$0.564874\pi$
$510$	6.62400	+	34.0666i	0.293316	+	1.50850i
$511$	−0.0197979	−	0.0543942i	−0.000875806	−	0.00240626i
$512$	−22.3469	+	3.55176i	−0.987604	+	0.156967i
$513$	1.40474	−	15.0652i	0.0620209	−	0.665146i
$514$	−15.1892	−	39.5621i	−0.669967	−	1.74501i
$515$	13.3659	−	4.86479i	0.588972	−	0.214368i
$516$	28.1053	−	17.5668i	1.23727	−	0.773336i
$517$	−21.9500	+	18.4182i	−0.965359	+	0.810033i
$518$	0.0481551	+	0.0165779i	0.00211581	+	0.000728390i
$519$	−4.19265	+	0.739277i	−0.184037	+	0.0324507i
$520$	−1.79795	−	34.1892i	−0.0788451	−	1.49930i
$521$	−0.104545	−	0.0603592i	−0.00458021	−	0.00264439i	0.497708	−	0.867345i	$-0.334175\pi$
$521$	−0.104545	−	0.0603592i	−0.00458021	−	0.00264439i	−0.502288	+	0.864700i	$0.667508\pi$
$522$	0.0121887	+	0.695899i	0.000533484	+	0.0304587i
$523$	−16.0259	−	5.83294i	−0.700763	−	0.255057i	−0.0330262	−	0.999454i	$-0.510514\pi$
$523$	−16.0259	−	5.83294i	−0.700763	−	0.255057i	−0.667737	+	0.744398i	$0.732737\pi$
$524$	−27.9499	+	5.94443i	−1.22100	+	0.259684i
$525$	0.233451	−	0.134783i	0.0101886	−	0.00588240i
$526$	−35.0580	+	21.0679i	−1.52860	+	0.918602i
$527$	−5.97169	−	5.01084i	−0.260131	−	0.218276i
$528$	−25.1804	+	16.9932i	−1.09584	+	0.739534i
$529$	1.36667	−	7.75075i	0.0594203	−	0.336989i
$530$	−5.61781	−	6.46177i	−0.244022	−	0.280681i
$531$	−5.58044			−0.242171
$532$	−0.0794930	−	0.0749634i	−0.00344646	−	0.00325007i
$533$	24.7477			1.07194
$534$	9.54750	+	10.9818i	0.413161	+	0.475230i
$535$	−2.93878	+	16.6666i	−0.127054	+	0.720561i
$536$	−5.93638	−	25.6922i	−0.256412	−	1.10973i
$537$	35.8175	+	30.0545i	1.54564	+	1.29695i
$538$	27.3816	−	16.4548i	1.18051	−	0.709416i
$539$	−22.1187	+	12.7702i	−0.952719	+	0.550053i
$540$	5.65521	+	26.5900i	0.243362	+	1.14425i
$541$	36.3211	+	13.2198i	1.56157	+	0.568364i	0.971095	−	0.238694i	$-0.0767193\pi$
$541$	36.3211	+	13.2198i	1.56157	+	0.568364i	0.590472	+	0.807058i	$0.298942\pi$
$542$	−0.433712	−	24.7623i	−0.0186295	−	1.06363i
$543$	−45.7059	−	26.3883i	−1.96143	−	1.13243i
$544$	−12.0400	+	12.0472i	−0.516212	+	0.516521i
$545$	62.7284	−	11.0607i	2.68699	−	0.473788i
$546$	0.107833	+	0.0371226i	0.00461482	+	0.00158870i
$547$	30.4952	−	25.5886i	1.30388	−	1.09409i	0.314422	−	0.949283i	$-0.398189\pi$
$547$	30.4952	−	25.5886i	1.30388	−	1.09409i	0.989460	−	0.144804i	$-0.0462552\pi$
$548$	−2.34004	−	3.74384i	−0.0999613	−	0.159929i
$549$	4.00932	−	1.45927i	0.171113	−	0.0622802i
$550$	−19.1112	−	49.7774i	−0.814903	−	2.12251i
$551$	0.131177	+	1.60483i	0.00558835	+	0.0683681i
$552$	−20.4051	−	10.3923i	−0.868500	−	0.442326i
$553$	0.00367492	+	0.0100968i	0.000156273	+	0.000429358i
$554$	0.407782	+	2.09718i	0.0173250	+	0.0891008i
$555$	15.0529	+	17.9393i	0.638960	+	0.761482i
$556$	0.326034	+	9.30441i	0.0138269	+	0.394595i
$557$	−2.60992	−	14.8016i	−0.110586	−	0.627163i	−0.988841	−	0.148972i	$-0.952404\pi$
$557$	−2.60992	−	14.8016i	−0.110586	−	0.627163i	0.878256	−	0.478191i	$-0.158707\pi$
$558$	3.79126	+	3.06972i	0.160497	+	0.129952i
$559$	−12.3058	+	21.3142i	−0.520478	+	0.901495i
$560$	0.176465	+	0.0860152i	0.00745700	+	0.00363481i
$561$	−7.82076	+	21.4873i	−0.330193	+	0.907197i
$562$	23.7438	+	3.75919i	1.00157	+	0.158572i
$563$	−12.7286	−	22.0466i	−0.536448	−	0.929155i	−0.999092	−	0.0426108i	$-0.986432\pi$
$563$	−12.7286	−	22.0466i	−0.536448	−	0.929155i	0.462644	−	0.886544i	$-0.346901\pi$
$564$	20.1235	−	25.7633i	0.847353	−	1.08483i
$565$	14.3091	−	17.0530i	0.601989	−	0.717423i
$566$	−36.0010	−	19.9529i	−1.51324	−	0.838682i
$567$	−0.138512	−	0.0244234i	−0.00581696	−	0.00102569i
$568$	−4.16026	+	33.9331i	−0.174561	+	1.42380i
$569$		−	5.45023i		−	0.228485i	−0.993453	−	0.114243i	$-0.963556\pi$
$569$		−	5.45023i		−	0.228485i	0.993453	−	0.114243i	$-0.0364441\pi$
$570$	−13.5755	−	48.3732i	−0.568617	−	2.02613i
$571$			23.3280i			0.976248i	0.872774	+	0.488124i	$0.162319\pi$
$571$			23.3280i			0.976248i	−0.872774	+	0.488124i	$0.837681\pi$
$572$	10.5879	−	19.9187i	0.442701	−	0.832841i
$573$	−37.4214	−	6.59840i	−1.56330	−	0.275652i
$574$	−0.0687888	+	0.124116i	−0.00287119	+	0.00518050i
$575$	25.8355	−	30.7896i	1.07742	−	1.28401i
$576$	7.40114	−	7.66963i	0.308381	−	0.319568i
$577$	9.14162	+	15.8338i	0.380571	+	0.659168i	0.991144	−	0.132792i	$-0.0423942\pi$
$577$	9.14162	+	15.8338i	0.380571	+	0.659168i	−0.610573	+	0.791960i	$0.709061\pi$
$578$	1.75468	−	11.0829i	0.0729852	−	0.460989i
$579$	−1.02396	+	2.81332i	−0.0425545	+	0.116917i
$580$	−1.08405	−	2.68219i	−0.0450127	−	0.111372i
$581$	0.0312301	−	0.0540921i	0.00129564	−	0.00224412i
$582$	7.31240	−	9.03117i	0.303109	−	0.374354i
$583$	−0.979656	−	5.55590i	−0.0405732	−	0.230102i
$584$	12.0236	−	5.10626i	0.497540	−	0.211299i
$585$	10.3660	+	12.3537i	0.428581	+	0.510762i
$586$	−25.6806	+	4.99341i	−1.06086	+	0.206276i
$587$	10.3417	+	28.4136i	0.426849	+	1.17276i	0.947715	+	0.319118i	$0.103387\pi$
$587$	10.3417	+	28.4136i	0.426849	+	1.17276i	−0.520866	+	0.853638i	$0.674391\pi$
$588$	21.6523	−	19.5005i	0.892925	−	0.804187i
$589$	9.20747	+	6.52579i	0.379387	+	0.268890i
$590$	21.6542	−	8.31376i	0.891490	−	0.342272i
$591$	7.21090	−	2.62455i	0.296617	−	0.107960i
$592$	−3.16528	+	11.0486i	−0.130092	+	0.454096i
$593$	−12.2887	+	10.3114i	−0.504635	+	0.423439i	−0.859237	−	0.511578i	$-0.829061\pi$
$593$	−12.2887	+	10.3114i	−0.504635	+	0.423439i	0.354601	+	0.935018i	$0.384617\pi$
$594$	−5.83043	+	16.9361i	−0.239226	+	0.694897i
$595$	0.145525	−	0.0256599i	0.00596592	−	0.00105195i
$596$	35.4819	+	11.5241i	1.45339	+	0.472044i
$597$	−35.1685	−	20.3046i	−1.43935	−	0.831010i
$598$	17.0016	−	0.297784i	0.695248	−	0.0121773i
$599$	7.44486	+	2.70971i	0.304189	+	0.110716i	0.489605	−	0.871944i	$-0.337141\pi$
$599$	7.44486	+	2.70971i	0.304189	+	0.110716i	−0.185416	+	0.982660i	$0.559363\pi$
$600$	33.1411	+	51.0128i	1.35298	+	2.08259i
$601$	−8.01633	+	4.62823i	−0.326993	+	0.188789i	−0.654505	−	0.756058i	$-0.727123\pi$
$601$	−8.01633	+	4.62823i	−0.326993	+	0.188789i	0.327512	+	0.944847i	$0.393790\pi$
$602$	−0.0726908	−	0.120961i	−0.00296266	−	0.00493002i
$603$	9.51489	+	7.98394i	0.387476	+	0.325131i
$604$	3.31497	−	23.6078i	0.134884	−	0.960586i
$605$	1.57286	−	8.92016i	0.0639461	−	0.362656i
$606$	14.2435	−	12.3832i	0.578601	−	0.503031i
$607$	−10.8462			−0.440232			−0.220116	−	0.975474i	$-0.570644\pi$
$607$	−10.8462			−0.440232			−0.220116	+	0.975474i	$0.570644\pi$
$608$	15.9516	−	18.8029i	0.646922	−	0.762556i
$609$	0.00963669			0.000390498
$610$	−13.3836	+	11.6356i	−0.541887	+	0.471112i
$611$	−4.21539	+	23.9066i	−0.170536	+	0.967159i
$612$	1.11561	−	7.94488i	0.0450958	−	0.321153i
$613$	−0.997329	−	0.836858i	−0.0402817	−	0.0338004i	0.622425	−	0.782680i	$-0.286148\pi$
$613$	−0.997329	−	0.836858i	−0.0402817	−	0.0338004i	−0.662706	+	0.748879i	$0.730592\pi$
$614$	8.54599	+	14.2210i	0.344888	+	0.573912i
$615$	−56.5085	+	32.6252i	−2.27864	+	1.31558i
$616$	0.0704669	+	0.108467i	0.00283919	+	0.00437025i
$617$	42.4866	+	15.4639i	1.71045	+	0.622551i	0.996945	−	0.0781039i	$-0.0248866\pi$
$617$	42.4866	+	15.4639i	1.71045	+	0.622551i	0.713500	+	0.700655i	$0.247109\pi$
$618$	−10.6906	+	0.187247i	−0.430040	+	0.00753217i
$619$	3.83161	+	2.21218i	0.154005	+	0.0889151i	0.575022	−	0.818138i	$-0.304993\pi$
$619$	3.83161	+	2.21218i	0.154005	+	0.0889151i	−0.421017	+	0.907053i	$0.638327\pi$
$620$	−19.2848	−	6.26345i	−0.774496	−	0.251546i
$621$	−13.2967	+	2.34457i	−0.533580	+	0.0940845i
$622$	8.07224	−	23.4480i	0.323667	−	0.940181i
$623$	0.0474644	−	0.0398273i	0.00190162	−	0.00159565i
$624$	−7.08795	+	24.7410i	−0.283745	+	0.990433i
$625$	−28.2932	+	10.2979i	−1.13173	+	0.411915i
$626$	24.9515	−	9.57972i	0.997264	−	0.382882i
$627$	8.75026	−	31.9263i	0.349452	−	1.27501i
$628$	18.0007	−	16.2119i	0.718308	−	0.646923i
$629$	2.95887	+	8.12944i	0.117978	+	0.324142i
$630$	−0.0907701	+	0.0176496i	−0.00361637	+	0.000703176i
$631$	−16.8681	−	20.1027i	−0.671510	−	0.800275i	0.317479	−	0.948265i	$-0.397164\pi$
$631$	−16.8681	−	20.1027i	−0.671510	−	0.800275i	−0.988989	+	0.147991i	$0.952719\pi$
$632$	−2.23184	+	0.947834i	−0.0887779	+	0.0377028i
$633$	−2.00267	−	11.3577i	−0.0795990	−	0.451428i
$634$	−16.4626	+	20.3321i	−0.653813	+	0.807490i
$635$	21.6889	−	37.5663i	0.860699	−	1.49077i
$636$	2.41188	+	5.96755i	0.0956373	+	0.236629i
$637$	−7.40060	+	20.3330i	−0.293223	+	0.805622i
$638$	0.298072	−	1.88269i	0.0118008	−	0.0745363i
$639$	−8.05169	−	13.9459i	−0.318520	−	0.551693i
$640$	−17.2930	+	40.7873i	−0.683565	+	1.61226i
$641$	−12.9356	+	15.4160i	−0.510925	+	0.608897i	−0.958410	−	0.285395i	$-0.907875\pi$
$641$	−12.9356	+	15.4160i	−0.510925	+	0.608897i	0.447485	+	0.894291i	$0.352320\pi$
$642$	6.16706	−	11.1272i	0.243394	−	0.439157i
$643$	−13.0933	−	2.30869i	−0.516348	−	0.0910460i	−0.0905990	−	0.995887i	$-0.528878\pi$
$643$	−13.0933	−	2.30869i	−0.516348	−	0.0910460i	−0.425749	+	0.904841i	$0.639989\pi$
$644$	−0.0457643	+	0.0860950i	−0.00180337	+	0.00339262i
$645$		−	64.8913i		−	2.55509i
$646$	1.39928	−	18.5077i	0.0550539	−	0.728175i
$647$			1.02886i			0.0404485i	0.999795	+	0.0202243i	$0.00643802\pi$
$647$			1.02886i			0.0404485i	−0.999795	+	0.0202243i	$0.993562\pi$
$648$	3.86250	−	31.5044i	0.151733	−	1.23761i
$649$	15.0509	+	2.65387i	0.590798	+	0.104174i
$650$	−39.5103	−	21.8978i	−1.54972	−	0.858904i
$651$	0.0434153	−	0.0517403i	0.00170158	−	0.00202786i
$652$	5.54369	−	7.09736i	0.217108	−	0.277954i
$653$	16.8522	+	29.1890i	0.659479	+	1.14225i	0.980751	+	0.195265i	$0.0625566\pi$
$653$	16.8522	+	29.1890i	0.659479	+	1.14225i	−0.321271	+	0.946987i	$0.604110\pi$
$654$	−47.2927	−	7.48752i	−1.84929	−	0.292785i
$655$	−19.1348	+	52.5725i	−0.747659	+	2.05418i
$656$	−28.7858	−	14.0313i	−1.12390	−	0.547828i
$657$	−3.07656	+	5.32876i	−0.120028	+	0.207895i
$658$	−0.108181	−	0.0875921i	−0.00421732	−	0.00341470i
$659$	3.56241	+	20.2034i	0.138772	+	0.787015i	0.972159	+	0.234324i	$0.0752877\pi$
$659$	3.56241	+	20.2034i	0.138772	+	0.787015i	−0.833387	+	0.552690i	$0.813601\pi$
$660$	2.08283	+	59.4401i	0.0810740	+	2.31370i
$661$	−6.85599	−	8.17065i	−0.266667	−	0.317802i	0.616049	−	0.787708i	$-0.288732\pi$
$661$	−6.85599	−	8.17065i	−0.266667	−	0.317802i	−0.882716	+	0.469906i	$0.844288\pi$
$662$	−1.51774	−	7.80558i	−0.0589885	−	0.303372i
$663$	6.62575	+	18.2041i	0.257323	+	0.706989i
$664$	12.5603	+	6.39692i	0.487432	+	0.248249i
$665$	−0.206949	+	0.0541876i	−0.00802516	+	0.00210131i
$666$	−1.94039	−	5.05398i	−0.0751885	−	0.195838i
$667$	1.35020	−	0.491434i	0.0522801	−	0.0190284i
$668$	−0.646105	−	1.03371i	−0.0249985	−	0.0399954i
$669$	−3.78041	+	3.17214i	−0.146159	+	0.122642i
$670$	−48.8158	−	16.8054i	−1.88592	−	0.649248i
$671$	−11.5074	+	2.02907i	−0.444238	+	0.0783312i
$672$	−0.104381	−	0.104318i	−0.00402657	−	0.00402415i
$673$	9.63086	+	5.56038i	0.371243	+	0.214337i	0.674001	−	0.738730i	$-0.264574\pi$
$673$	9.63086	+	5.56038i	0.371243	+	0.214337i	−0.302759	+	0.953067i	$0.597908\pi$
$674$	0.460113	+	26.2696i	0.0177229	+	1.01187i
$675$	33.7054	+	12.2678i	1.29732	+	0.472186i
$676$	1.43310	+	6.73825i	0.0551194	+	0.259163i
$677$	35.8298	−	20.6863i	1.37705	−	0.795040i	0.385246	−	0.922814i	$-0.374117\pi$
$677$	35.8298	−	20.6863i	1.37705	−	0.795040i	0.991803	+	0.127774i	$0.0407833\pi$
$678$	−14.3434	+	8.61957i	−0.550856	+	0.331033i
$679$	−0.0379028	−	0.0318042i	−0.00145458	−	0.00122053i
$680$	7.50733	+	32.4911i	0.287893	+	1.24598i
$681$	−8.91464	+	50.5574i	−0.341610	+	1.93736i
$682$	−8.76544	−	10.0823i	−0.335646	−	0.386070i
$683$	9.92340			0.379708			0.189854	−	0.981812i	$-0.439199\pi$
$683$	9.92340			0.379708			0.189854	+	0.981812i	$0.439199\pi$
$684$	−0.672676	+	11.5952i	−0.0257204	+	0.443352i
$685$	−8.64402			−0.330271
$686$	−0.162810	−	0.187269i	−0.00621612	−	0.00714997i
$687$	−6.32702	+	35.8823i	−0.241391	+	1.36900i
$688$	26.3983	−	17.8151i	1.00642	−	0.679193i
$689$	−3.66137	−	3.07226i	−0.139487	−	0.117044i
$690$	−38.4286	+	23.0934i	−1.46295	+	0.879151i
$691$	33.6096	−	19.4045i	1.27857	−	0.738182i	0.301984	−	0.953313i	$-0.402351\pi$
$691$	33.6096	−	19.4045i	1.27857	−	0.738182i	0.976585	+	0.215130i	$0.0690177\pi$
$692$	−4.00130	+	0.851004i	−0.152107	+	0.0323503i
$693$	−0.0572527	−	0.0208383i	−0.00217485	−	0.000791581i
$694$	0.522506	+	29.8319i	0.0198341	+	1.13240i
$695$	15.7860	+	9.11405i	0.598797	+	0.345716i
$696$	0.114206	+	2.17171i	0.00432898	+	0.0823186i
$697$	−23.7387	+	4.18578i	−0.899168	+	0.158548i
$698$	18.7797	+	6.46510i	0.710821	+	0.244708i
$699$	1.65871	−	1.39182i	0.0627381	−	0.0526435i
$700$	0.219646	−	0.137287i	0.00830184	−	0.00518895i
$701$	−9.41264	+	3.42592i	−0.355511	+	0.129395i	−0.513601	−	0.858029i	$-0.671689\pi$
$701$	−9.41264	+	3.42592i	−0.355511	+	0.129395i	0.158090	+	0.987425i	$0.449466\pi$
$702$	5.43899	+	14.1665i	0.205281	+	0.534680i
$703$	−5.22812	−	11.3809i	−0.197182	−	0.429239i
$704$	−23.6088	+	17.1658i	−0.889792	+	0.646960i
$705$	−21.8911	−	60.1452i	−0.824465	−	2.26520i
$706$	−2.99454	−	15.4006i	−0.112701	−	0.579611i
$707$	−0.0516562	−	0.0615615i	−0.00194273	−	0.00231526i
$708$	−17.4258	+	0.610613i	−0.654900	+	0.0229482i
$709$	8.31894	+	47.1790i	0.312424	+	1.77185i	0.586313	+	0.810085i	$0.300579\pi$
$709$	8.31894	+	47.1790i	0.312424	+	1.77185i	−0.273889	+	0.961761i	$0.588310\pi$
$710$	52.0203	+	42.1200i	1.95229	+	1.58074i
$711$	0.571077	−	0.989135i	0.0214171	−	0.0370955i
$712$	9.53795	+	10.2245i	0.357450	+	0.383180i
$713$	3.44439	−	9.46338i	0.128993	−	0.354406i
$714$	−0.109715	−	0.0173704i	−0.00410598	−	0.000650071i
$715$	−22.0828	−	38.2485i	−0.825850	−	1.43041i
$716$	35.4067	+	27.6559i	1.32321	+	1.03355i
$717$	7.78173	−	9.27390i	0.290614	−	0.346340i
$718$	8.95269	+	4.96185i	0.334111	+	0.185175i
$719$	33.5360	+	5.91330i	1.25068	+	0.220529i	0.759487	−	0.650522i	$-0.225450\pi$
$719$	33.5360	+	5.91330i	1.25068	+	0.220529i	0.491193	+	0.871051i	$0.336561\pi$
$720$	−5.05322	−	20.2467i	−0.188322	−	0.754549i
$721$			0.0455268i			0.00169550i
$722$	0.163799	+	26.8696i	0.00609597	+	0.999981i
$723$		−	22.4364i		−	0.834419i
$724$	−44.7791	−	23.8026i	−1.66420	−	0.884616i
$725$	−3.75911	−	0.662832i	−0.139610	−	0.0246170i
$726$	−3.30068	+	5.95542i	−0.122500	+	0.221026i
$727$	1.87961	−	2.24003i	0.0697107	−	0.0830780i	−0.730062	−	0.683381i	$-0.760509\pi$
$727$	1.87961	−	2.24003i	0.0697107	−	0.0830780i	0.799773	+	0.600303i	$0.204953\pi$
$728$	0.104800	+	0.0320201i	0.00388416	+	0.00118674i
$729$	−3.36209	−	5.82332i	−0.124522	−	0.215678i
$730$	3.99941	−	25.2611i	0.148025	−	0.934954i
$731$	8.19900	−	22.5266i	0.303251	−	0.833175i
$732$	12.3600	−	4.99549i	0.456839	−	0.184639i
$733$	16.3253	−	28.2763i	0.602989	−	1.04441i	−0.389377	−	0.921078i	$-0.627310\pi$
$733$	16.3253	−	28.2763i	0.602989	−	1.04441i	0.992366	−	0.123329i	$-0.0393570\pi$
$734$	10.8245	−	13.3688i	0.399540	−	0.493451i
$735$	−9.90681	−	56.1843i	−0.365418	−	2.07239i
$736$	−19.9446	−	9.29306i	−0.735169	−	0.342547i
$737$	−21.8654	−	26.0582i	−0.805424	−	0.959867i
$738$	14.8069	−	2.87909i	0.545049	−	0.105981i
$739$	8.80642	+	24.1954i	0.323949	+	0.890044i	0.989609	+	0.143788i	$0.0459282\pi$
$739$	8.80642	+	24.1954i	0.323949	+	0.890044i	−0.665659	+	0.746256i	$0.731850\pi$
$740$	15.0589	+	16.7205i	0.553575	+	0.614659i
$741$	−11.7072	−	25.4851i	−0.430076	−	0.936218i
$742$	0.0255853	−	0.00982303i	0.000939265	−	0.000360615i
$743$	−6.00559	+	2.18585i	−0.220324	+	0.0801912i	−0.449824	−	0.893117i	$-0.648513\pi$
$743$	−6.00559	+	2.18585i	−0.220324	+	0.0801912i	0.229500	+	0.973309i	$0.426291\pi$
$744$	12.1747	+	9.17083i	0.446345	+	0.336219i
$745$	55.9531	−	46.9502i	2.04996	−	1.72012i
$746$	−6.01695	+	17.4779i	−0.220296	+	0.639911i
$747$	−6.53858	+	1.15293i	−0.239234	+	0.0421834i
$748$	−6.78719	+	20.8974i	−0.248164	+	0.764083i
$749$	−0.0469117	−	0.0270845i	−0.00171412	−	0.000989646i
$750$	61.4626	−	1.07652i	2.24430	−	0.0393090i
$751$	13.2775	+	4.83260i	0.484501	+	0.176344i	0.572710	−	0.819758i	$-0.305892\pi$
$751$	13.2775	+	4.83260i	0.484501	+	0.176344i	−0.0882089	+	0.996102i	$0.528114\pi$
$752$	18.4576	−	25.4175i	0.673079	−	0.926882i
$753$	−41.5495	+	23.9886i	−1.51415	+	0.874194i
$754$	−0.831808	−	1.38417i	−0.0302927	−	0.0504086i
$755$	−35.7549	−	30.0019i	−1.30125	−	1.09188i
$756$	−0.0861667	−	0.0120994i	−0.00313385	−	0.000440051i
$757$	−8.05808	+	45.6996i	−0.292876	+	1.66098i	0.382837	+	0.923816i	$0.374947\pi$
$757$	−8.05808	+	45.6996i	−0.292876	+	1.66098i	−0.675713	+	0.737165i	$0.736164\pi$
$758$	1.28793	−	1.11971i	0.0467797	−	0.0406699i
$759$	−29.5403			−1.07224
$760$	−14.6643	−	45.9957i	−0.531929	−	1.66844i
$761$	−21.5443			−0.780979			−0.390489	−	0.920607i	$-0.627694\pi$
$761$	−21.5443			−0.780979			−0.390489	+	0.920607i	$0.627694\pi$
$762$	−24.6084	+	21.3943i	−0.891467	+	0.775035i
$763$	−0.0354027	+	0.200779i	−0.00128167	+	0.00726869i
$764$	−36.1576	−	5.07720i	−1.30814	−	0.183687i
$765$	−12.0328	−	10.0967i	−0.435047	−	0.365048i
$766$	−0.600301	−	0.998933i	−0.0216898	−	0.0360929i
$767$	11.2131	−	6.47391i	0.404883	−	0.233759i
$768$	22.2720	−	24.7594i	0.803670	−	0.893427i
$769$	−15.8951	−	5.78536i	−0.573193	−	0.208625i	0.0391282	−	0.999234i	$-0.487542\pi$
$769$	−15.8951	−	5.78536i	−0.573193	−	0.208625i	−0.612321	+	0.790609i	$0.709764\pi$
$770$	0.253207	−	0.00443493i	0.00912495	−	0.000159824i
$771$	54.0148	+	31.1854i	1.94529	+	1.12312i
$772$	−0.888640	+	2.73607i	−0.0319829	+	0.0984733i
$773$	−42.1912	+	7.43944i	−1.51751	+	0.267578i	−0.869454	−	0.494014i	$-0.835529\pi$
$773$	−42.1912	+	7.43944i	−1.51751	+	0.267578i	−0.648057	+	0.761592i	$0.724418\pi$
$774$	−4.88306	+	14.1842i	−0.175518	+	0.509840i
$775$	−20.4944	+	17.1968i	−0.736179	+	0.617727i
$776$	6.71817	−	8.91865i	0.241168	−	0.320161i
$777$	−0.0704356	+	0.0256365i	−0.00252686	+	0.000919704i
$778$	32.9651	−	12.6564i	1.18186	−	0.453753i
$779$	33.7587	−	8.83937i	1.20953	−	0.316703i
$780$	33.7210	+	37.4420i	1.20741	+	1.34064i
$781$	15.0838	+	41.4423i	0.539740	+	1.48292i
$782$	−16.2581	+	3.16126i	−0.581388	+	0.113046i
$783$	0.824223	+	0.982271i	0.0294553	+	0.0351035i
$784$	20.1364	−	19.4548i	0.719157	−	0.694815i
$785$	−8.23608	−	46.7091i	−0.293958	−	1.66712i
$786$	26.4649	−	32.6854i	0.943971	−	1.16585i
$787$	−8.04667	+	13.9372i	−0.286833	+	0.496809i	−0.973052	−	0.230586i	$-0.925936\pi$
$787$	−8.04667	+	13.9372i	−0.286833	+	0.496809i	0.686219	+	0.727395i	$0.259269\pi$
$788$	6.83627	−	2.76299i	0.243532	−	0.0984273i
$789$	20.5889	−	56.5676i	0.732984	−	2.01386i
$790$	−0.742378	+	4.68901i	−0.0264126	+	0.166827i
$791$	0.0356262	+	0.0617064i	0.00126672	+	0.00219403i
$792$	4.01758	−	13.1494i	0.142759	−	0.467243i
$793$	−6.36326	+	7.58344i	−0.225966	+	0.269296i
$794$	−6.37002	+	11.4935i	−0.226064	+	0.407887i
$795$	12.4105	+	2.18831i	0.440155	+	0.0776112i
$796$	−34.4554	−	18.3150i	−1.22124	−	0.649156i
$797$		−	32.8715i		−	1.16437i	−0.813057	−	0.582183i	$-0.802199\pi$
$797$		−	32.8715i		−	1.16437i	0.813057	−	0.582183i	$-0.197801\pi$
$798$	0.160355	+	0.0121237i	0.00567652	+	0.000429176i
$799$		−	23.6449i		−	0.836497i
$800$	33.5418	+	47.8722i	1.18588	+	1.69254i
$801$	−6.48625	−	1.14370i	−0.229180	−	0.0404107i
$802$	2.64887	+	1.46809i	0.0935350	+	0.0518400i
$803$	10.8319	−	12.9089i	0.382249	−	0.455547i
$804$	30.5852	+	23.8899i	1.07866	+	0.842532i
$805$	0.0954491	+	0.165323i	0.00336414	+	0.00582686i
$806$	−11.1792	−	1.76993i	−0.393771	−	0.0623431i
$807$	−16.0807	+	44.1814i	−0.566068	+	1.55526i
$808$	13.2612	−	12.3708i	0.466529	−	0.435202i
$809$	20.3941	−	35.3237i	0.717020	−	1.24191i	−0.245156	−	0.969484i	$-0.578839\pi$
$809$	20.3941	−	35.3237i	0.717020	−	1.24191i	0.962175	−	0.272431i	$-0.0878276\pi$
$810$	−48.2970	−	39.1054i	−1.69698	−	1.37402i
$811$	−0.919587	−	5.21523i	−0.0322911	−	0.183132i	0.964396	−	0.264462i	$-0.0851943\pi$
$811$	−0.919587	−	5.21523i	−0.0322911	−	0.183132i	−0.996687	+	0.0813301i	$0.974083\pi$
$812$	0.00925407		0.000324270i	0.000324754		1.13796e-5i
$813$	23.4298	+	27.9226i	0.821719	+	0.979287i
$814$	2.82986	+	14.5537i	0.0991867	+	0.510108i
$815$	−6.03062	−	16.5690i	−0.211243	−	0.580386i
$816$	2.61432	−	24.9311i	0.0915196	−	0.872764i
$817$	−9.17345	+	33.4703i	−0.320938	+	1.17098i
$818$	12.5378	+	32.6562i	0.438374	+	1.14180i
$819$	−0.0485046	+	0.0176542i	−0.00169489	+	0.000616889i
$820$	−53.1670	+	33.2313i	−1.85667	+	1.16049i
$821$	−13.1364	+	11.0227i	−0.458463	+	0.384696i	−0.842565	−	0.538595i	$-0.818955\pi$
$821$	−13.1364	+	11.0227i	−0.458463	+	0.384696i	0.384102	+	0.923291i	$0.374511\pi$
$822$	6.14401	+	2.11514i	0.214297	+	0.0737740i
$823$	−50.5398	+	8.91153i	−1.76171	+	0.310636i	−0.958506	−	0.285072i	$-0.907982\pi$
$823$	−50.5398	+	8.91153i	−1.76171	+	0.310636i	−0.803201	+	0.595709i	$0.796871\pi$
$824$	−10.2599	+	0.539547i	−0.357419	+	0.0187960i
$825$	67.9618	+	39.2377i	2.36613	+	1.36608i
$826$	0.00130017	+	0.0742315i	4.52386e−5	+	0.00258284i
$827$	−34.3316	−	12.4957i	−1.19383	−	0.434517i	−0.332761	−	0.943011i	$-0.607980\pi$
$827$	−34.3316	−	12.4957i	−1.19383	−	0.434517i	−0.861066	+	0.508494i	$0.830203\pi$
$828$	10.1377	−	2.15610i	0.352308	−	0.0749295i
$829$	0.294740	−	0.170168i	0.0102367	−	0.00591018i	−0.494873	−	0.868965i	$-0.664785\pi$
$829$	0.294740	−	0.170168i	0.0102367	−	0.00591018i	0.505110	+	0.863055i	$0.331452\pi$
$830$	23.6545	−	14.2150i	0.821060	−	0.493410i
$831$	−2.40876	−	2.02119i	−0.0835588	−	0.0701142i
$832$	−5.97400	+	23.9972i	−0.207111	+	0.831952i
$833$	3.65979	−	20.7557i	0.126804	−	0.719142i
$834$	−8.99025	−	10.3408i	−0.311307	−	0.358074i
$835$	−2.38669			−0.0825949
$836$	7.32853	−	30.9531i	0.253462	−	1.07053i
$837$	8.98720			0.310643
$838$	−16.9426	−	19.4879i	−0.585274	−	0.673199i
$839$	0.678584	−	3.84844i	0.0234273	−	0.132863i	−0.970851	−	0.239684i	$-0.922956\pi$
$839$	0.678584	−	3.84844i	0.0234273	−	0.132863i	0.994278	+	0.106821i	$0.0340672\pi$
$840$	−0.281512	+	0.0650455i	−0.00971308	+	0.00224428i
$841$	22.1108	+	18.5531i	0.762440	+	0.639763i
$842$	−2.92339	+	1.75679i	−0.100747	+	0.0605429i
$843$	−30.6408	+	17.6905i	−1.05533	+	0.609293i
$844$	−2.30533	−	10.8394i	−0.0793529	−	0.373106i
$845$	12.6744	+	4.61309i	0.436011	+	0.158695i
$846$	0.259119	+	14.7941i	0.00890868	+	0.508631i
$847$	0.0251077	+	0.0144959i	0.000862709	+	0.000498085i
$848$	2.51692	+	5.64945i	0.0864315	+	0.194003i
$849$	59.6591	−	10.5195i	2.04750	−	0.361029i
$850$	41.6032	+	14.3223i	1.42698	+	0.491252i
$851$	−8.56143	+	7.18389i	−0.293482	+	0.246261i
$852$	−26.6686	−	42.6672i	−0.913650	−	1.46176i
$853$	−39.7032	+	14.4508i	−1.35941	+	0.494785i	−0.915872	−	0.401470i	$-0.868499\pi$
$853$	−39.7032	+	14.4508i	−1.35941	+	0.494785i	−0.443539	+	0.896255i	$0.646277\pi$
$854$	−0.0203455	−	0.0529923i	−0.000696208	−	0.00181336i
$855$	18.5528	+	13.1493i	0.634494	+	0.449697i
$856$	5.54777	−	10.8930i	0.189619	−	0.372313i
$857$	−12.7400	−	35.0028i	−0.435189	−	1.19567i	−0.942587	−	0.333961i	$-0.891615\pi$
$857$	−12.7400	−	35.0028i	−0.435189	−	1.19567i	0.507398	−	0.861712i	$-0.330608\pi$
$858$	6.33686	+	32.5899i	0.216337	+	1.11260i
$859$	24.2289	+	28.8748i	0.826678	+	0.985197i	1.00000		0.000331301i	$0.000105456\pi$
$859$	24.2289	+	28.8748i	0.826678	+	0.985197i	−0.173322	+	0.984865i	$0.555450\pi$
$860$	−2.18356	−	62.3148i	−0.0744588	−	2.12492i
$861$	−0.0362667	−	0.205679i	−0.00123597	−	0.00700951i
$862$	−27.1827	−	22.0094i	−0.925847	−	0.749644i
$863$	5.22567	−	9.05113i	0.177884	−	0.308104i	−0.763272	−	0.646078i	$-0.776408\pi$
$863$	5.22567	−	9.05113i	0.177884	−	0.308104i	0.941156	+	0.337974i	$0.109742\pi$
$864$	1.70553	−	19.5618i	0.0580233	−	0.665507i
$865$	−2.73934	+	7.52628i	−0.0931404	+	0.255901i
$866$	−44.5561	−	7.05425i	−1.51408	−	0.239713i
$867$	8.25742	+	14.3023i	0.280437	+	0.485731i
$868$	0.0399504	−	0.0511469i	0.00135601	−	0.00173604i
$869$	−2.01064	+	2.39618i	−0.0682062	+	0.0812849i
$870$	3.72411	+	2.06401i	0.126259	+	0.0699767i
$871$	−28.3811	−	5.00435i	−0.961656	−	0.169566i
$872$	−45.6669	−	5.59885i	−1.54648	−	0.189601i
$873$			5.25952i			0.178008i
$874$	23.0858	−	6.47884i	0.780888	−	0.219150i
$875$		−	0.261743i		−	0.00884852i
$876$	−9.02394	+	16.9765i	−0.304891	+	0.573582i
$877$	2.79895	+	0.493531i	0.0945139	+	0.0166653i	0.220705	−	0.975341i	$-0.429164\pi$
$877$	2.79895	+	0.493531i	0.0945139	+	0.0166653i	−0.126191	+	0.992006i	$0.540275\pi$
$878$	13.4892	−	24.3387i	0.455239	−	0.821390i
$879$	24.7500	−	29.4959i	0.834798	−	0.994873i
$880$	4.00026	+	57.0099i	0.134849	+	1.92180i
$881$	−1.49413	−	2.58791i	−0.0503385	−	0.0871888i	0.839758	−	0.542961i	$-0.182697\pi$
$881$	−1.49413	−	2.58791i	−0.0503385	−	0.0871888i	−0.890097	+	0.455772i	$0.849363\pi$
$882$	−2.06239	+	13.0265i	−0.0694443	+	0.438624i
$883$	−4.43210	+	12.1771i	−0.149152	+	0.409792i	−0.991658	−	0.128895i	$-0.958857\pi$
$883$	−4.43210	+	12.1771i	−0.149152	+	0.409792i	0.842506	+	0.538687i	$0.181079\pi$
$884$	6.97524	+	17.2584i	0.234603	+	0.580462i
$885$	−17.0692	+	29.5648i	−0.573777	+	0.993810i
$886$	4.62132	−	5.70755i	0.155256	−	0.191749i
$887$	9.42179	+	53.4336i	0.316353	+	1.79413i	0.564532	+	0.825411i	$0.309057\pi$
$887$	9.42179	+	53.4336i	0.316353	+	1.79413i	−0.248179	+	0.968714i	$0.579832\pi$
$888$	−6.61215	−	15.5695i	−0.221889	−	0.522477i
$889$	0.0892463	+	0.106360i	0.00299322	+	0.00356718i
$890$	26.8730	−	5.22525i	0.900784	−	0.175151i
$891$	−14.0042	−	38.4762i	−0.469158	−	1.28900i
$892$	−3.52357	+	3.17340i	−0.117978	+	0.106253i
$893$	2.78869	+	34.1170i	0.0933201	+	1.14168i
$894$	−51.2589	+	19.6800i	−1.71435	+	0.658197i
$895$	82.6580	−	30.0850i	2.76295	−	1.00563i
$896$	−0.103746	−	0.0966637i	−0.00346592	−	0.00322931i
$897$	−19.1714	+	16.0868i	−0.640116	+	0.537121i
$898$	−7.24251	+	21.0379i	−0.241686	+	0.702043i
$899$	−0.941879	+	0.166079i	−0.0314134	+	0.00553904i
$900$	−26.1871	−	8.50523i	−0.872903	−	0.283508i
$901$	4.03173	+	2.32772i	0.134316	+	0.0775475i
$902$	−41.3045	+	0.723449i	−1.37529	+	0.0240882i
$903$	0.195176	+	0.0710383i	0.00649505	+	0.00236401i
$904$	−13.4839	+	8.75998i	−0.448467	+	0.291353i
$905$	−85.9864	+	49.6443i	−2.85829	+	1.65023i
$906$	18.0726	+	30.0738i	0.600423	+	0.999135i
$907$	−38.9250	−	32.6620i	−1.29248	−	1.08452i	−0.991392	−	0.130927i	$-0.958205\pi$
$907$	−38.9250	−	32.6620i	−1.29248	−	1.08452i	−0.301092	−	0.953595i	$-0.597351\pi$
$908$	−6.85945	+	48.8500i	−0.227639	+	1.62114i
$909$	−1.48339	+	8.41270i	−0.0492008	+	0.279032i
$910$	0.161915	−	0.140767i	0.00536742	−	0.00466639i
$911$	−35.5696			−1.17847			−0.589236	−	0.807961i	$-0.700571\pi$
$911$	−35.5696			−1.17847			−0.589236	+	0.807961i	$0.700571\pi$
$912$	−0.831788	+	36.2812i	−0.0275432	+	1.20139i
$913$	18.1833			0.601780
$914$	40.3745	−	35.1012i	1.33547	−	1.16105i
$915$	4.53243	−	25.7047i	0.149837	−	0.849770i
$916$	−4.86838	+	34.6705i	−0.160856	+	1.14555i
$917$	−0.137177	−	0.115105i	−0.00452998	−	0.00380110i
$918$	−7.61332	−	12.6690i	−0.251277	−	0.418139i
$919$	42.9006	−	24.7687i	1.41516	−	0.817043i	0.419292	−	0.907851i	$-0.362278\pi$
$919$	42.9006	−	24.7687i	1.41516	−	0.817043i	0.995868	+	0.0908078i	$0.0289449\pi$
$920$	−36.1258	+	23.4696i	−1.19103	+	0.773769i
$921$	−22.9461	−	8.35171i	−0.756101	−	0.275198i
$922$	48.6279	−	0.851719i	1.60147	−	0.0280499i
$923$	32.3575	+	18.6816i	1.06506	+	0.614913i
$924$	−0.181060	−	0.0588061i	−0.00595645	−	0.00193458i
$925$	29.2391	−	5.15563i	0.961374	−	0.169516i
$926$	3.11488	−	9.04804i	0.102361	−	0.297337i
$927$	3.70723	−	3.11073i	0.121761	−	0.102170i
$928$	0.182749	+	2.08164i	0.00599903	+	0.0683333i
$929$	0.176709	−	0.0643169i	0.00579764	−	0.00211017i	−0.339120	−	0.940743i	$-0.610129\pi$
$929$	0.176709	−	0.0643169i	0.00579764	−	0.00211017i	0.344917	+	0.938633i	$0.387907\pi$
$930$	27.8598	−	10.6963i	0.913558	−	0.350745i
$931$	−2.83273	+	30.3798i	−0.0928391	+	0.995659i
$932$	1.54601	−	1.39237i	0.0506414	−	0.0456087i
$933$	12.4831	+	34.2971i	0.408679	+	1.12284i
$934$	54.9644	−	10.6874i	1.79849	−	0.349703i
$935$	27.6517	+	32.9540i	0.904308	+	1.07771i
$936$	−4.55338	−	10.7217i	−0.148832	−	0.350450i
$937$	−9.10768	−	51.6522i	−0.297535	−	1.68740i	−0.656717	−	0.754137i	$-0.728055\pi$
$937$	−9.10768	−	51.6522i	−0.297535	−	1.68740i	0.359182	−	0.933268i	$-0.383056\pi$
$938$	0.103986	−	0.128428i	0.00339527	−	0.00419332i
$939$	−19.6684	+	34.0667i	−0.641855	+	1.11172i
$940$	−23.0457	−	57.0205i	−0.751669	−	1.85980i
$941$	−3.40150	+	9.34555i	−0.110886	+	0.304656i	−0.982707	−	0.185168i	$-0.940717\pi$
$941$	−3.40150	+	9.34555i	−0.110886	+	0.304656i	0.871821	+	0.489825i	$0.162939\pi$
$942$	−5.57540	+	35.2153i	−0.181656	+	1.14738i
$943$	−15.5702	−	26.9683i	−0.507034	−	0.878209i
$944$	−16.7133	+	1.17274i	−0.543972	+	0.0381693i
$945$	−0.109505	+	0.130503i	−0.00356219	+	0.00424526i
$946$	19.9155	−	35.9336i	0.647509	−	1.16830i
$947$	−4.29338	−	0.757039i	−0.139516	−	0.0246005i	0.103454	−	0.994634i	$-0.467011\pi$
$947$	−4.29338	−	0.757039i	−0.139516	−	0.0246005i	−0.242970	+	0.970034i	$0.578122\pi$
$948$	1.67504	−	3.15121i	0.0544028	−	0.102346i
$949$		−	14.2765i		−	0.463436i
$950$	−61.7180	−	15.7588i	−2.00240	−	0.511284i
$951$		−	38.5037i		−	1.24857i
$952$	−0.105943	−	0.0129889i	−0.00343364	−	0.000420972i
$953$	6.29014	+	1.10912i	0.203758	+	0.0359280i	0.274595	−	0.961560i	$-0.411456\pi$
$953$	6.29014	+	1.10912i	0.203758	+	0.0359280i	−0.0708377	+	0.997488i	$0.522567\pi$
$954$	−2.54807	−	1.41222i	−0.0824967	−	0.0457222i
$955$	−45.9508	+	54.7621i	−1.48693	+	1.77206i
$956$	7.16069	−	9.16754i	0.231593	−	0.296499i
$957$	1.40271	+	2.42956i	0.0453432	+	0.0785367i
$958$	8.26875	+	1.30913i	0.267151	+	0.0422962i
$959$	0.00946284	−	0.0259990i	0.000305571	−	0.000839550i
$960$	−17.9948	−	62.6703i	−0.580781	−	2.02268i
$961$	12.1483	−	21.0415i	0.391882	−	0.678759i
$962$	9.76209	+	7.90422i	0.314743	+	0.254842i
$963$	0.999884	+	5.67062i	0.0322208	+	0.182733i
$964$	−0.754974	−	21.5456i	−0.0243161	−	0.693936i
$965$	3.62041	+	4.31464i	0.116545	+	0.138893i
$966$	−0.0273900	−	0.140864i	−0.000881259	−	0.00453223i
$967$	14.2587	+	39.1755i	0.458529	+	1.25980i	0.926580	+	0.376097i	$0.122734\pi$
$967$	14.2587	+	39.1755i	0.458529	+	1.25980i	−0.468051	+	0.883702i	$0.655044\pi$
$968$	−2.96923	+	5.83003i	−0.0954345	+	0.187384i
$969$	15.5404	+	22.4659i	0.499230	+	0.721708i
$970$	−7.83565	−	20.4089i	−0.251587	−	0.655290i
$971$	−40.8739	+	14.8769i	−1.31170	+	0.477421i	−0.900791	−	0.434253i	$-0.857012\pi$
$971$	−40.8739	+	14.8769i	−1.31170	+	0.477421i	−0.410913	+	0.911674i	$0.634790\pi$
$972$	13.7210	+	21.9523i	0.440100	+	0.704120i
$973$	−0.0446941	+	0.0375028i	−0.00143283	+	0.00120228i
$974$	25.5514	+	8.79633i	0.818719	+	0.281853i
$975$	65.4745	−	11.5449i	2.09686	−	0.369733i
$976$	11.7012	−	5.21306i	0.374545	−	0.166866i
$977$	8.59156	+	4.96034i	0.274868	+	0.158695i	0.631098	−	0.775703i	$-0.282605\pi$
$977$	8.59156	+	4.96034i	0.274868	+	0.158695i	−0.356230	+	0.934398i	$0.615938\pi$
$978$	0.232120	+	13.2526i	0.00742237	+	0.423771i
$979$	16.9500	+	6.16929i	0.541724	+	0.197171i
$980$	−11.4040	−	53.6201i	−0.364288	−	1.71283i
$981$	18.7683	−	10.8359i	0.599227	−	0.345964i
$982$	12.7036	−	7.63412i	0.405388	−	0.243615i
$983$	5.76120	+	4.83422i	0.183754	+	0.154188i	0.730025	−	0.683421i	$-0.239509\pi$
$983$	5.76120	+	4.83422i	0.183754	+	0.154188i	−0.546271	+	0.837609i	$0.683953\pi$
$984$	45.9217	−	10.6106i	1.46393	−	0.338252i
$985$	2.50687	−	14.2171i	0.0798754	−	0.452996i
$986$	1.03201	+	1.18705i	0.0328659	+	0.0378033i
$987$	0.204866			0.00652095
$988$	−12.1000	−	24.0793i	−0.384951	−	0.766063i
$989$	30.9689			0.984755
$990$	−17.6622	−	20.3155i	−0.561341	−	0.645670i
$991$	6.13760	−	34.8080i	0.194967	−	1.10571i	−0.717498	−	0.696560i	$-0.754713\pi$
$991$	6.13760	−	34.8080i	0.194967	−	1.10571i	0.912466	−	0.409154i	$-0.134176\pi$
$992$	11.9999	+	8.39703i	0.380996	+	0.266606i
$993$	8.96523	+	7.52272i	0.284503	+	0.238726i
$994$	−0.183634	+	0.110353i	−0.00582452	+	0.00350020i
$995$	−66.1624	+	38.1989i	−2.09749	+	1.21099i
$996$	−20.2915	+	4.31564i	−0.642962	+	0.136746i
$997$	10.1997	+	3.71239i	0.323028	+	0.117573i	0.498444	−	0.866922i	$-0.333905\pi$
$997$	10.1997	+	3.71239i	0.323028	+	0.117573i	−0.175416	+	0.984494i	$0.556127\pi$
$998$	0.997130	+	56.9300i	0.0315636	+	1.80209i
$999$	−8.63747	−	4.98685i	−0.273278	−	0.157777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.71.2	yes	48
3.2	odd	2		684.2.cf.a.451.7		48
4.3	odd	2	inner	76.2.k.a.71.8	yes	48
12.11	even	2		684.2.cf.a.451.1		48
19.15	odd	18	inner	76.2.k.a.15.8	yes	48
57.53	even	18		684.2.cf.a.91.1		48
76.15	even	18	inner	76.2.k.a.15.2	✓	48
228.167	odd	18		684.2.cf.a.91.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.15.2	✓	48	76.15	even	18	inner
76.2.k.a.15.8	yes	48	19.15	odd	18	inner
76.2.k.a.71.2	yes	48	1.1	even	1	trivial
76.2.k.a.71.8	yes	48	4.3	odd	2	inner
684.2.cf.a.91.1		48	57.53	even	18
684.2.cf.a.91.7		48	228.167	odd	18
684.2.cf.a.451.1		48	12.11	even	2
684.2.cf.a.451.7		48	3.2	odd	2

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06726 + 0.927872i) q^{2} +(0.361434 - 2.04979i) q^{3} +(0.278109 - 1.98057i) q^{4} +(-2.99965 - 2.51700i) q^{5} +(1.51620 + 2.52304i) q^{6} +(0.0108543 - 0.00626673i) q^{7} +(1.54090 + 2.37184i) q^{8} +(-1.25194 - 0.455671i) q^{9} +O(q^{10})\)	\(q+(-1.06726 + 0.927872i) q^{2} +(0.361434 - 2.04979i) q^{3} +(0.278109 - 1.98057i) q^{4} +(-2.99965 - 2.51700i) q^{5} +(1.51620 + 2.52304i) q^{6} +(0.0108543 - 0.00626673i) q^{7} +(1.54090 + 2.37184i) q^{8} +(-1.25194 - 0.455671i) q^{9} +(5.53688 - 0.0969785i) q^{10} +(3.15988 + 1.82436i) q^{11} +(-3.95924 - 1.28591i) q^{12} +(3.04424 - 0.536781i) q^{13} +(-0.00576968 + 0.0167596i) q^{14} +(-6.24352 + 5.23893i) q^{15} +(-3.84531 - 1.10163i) q^{16} +(-2.82933 + 1.02979i) q^{17} +(1.75896 - 0.675323i) q^{18} +(3.96096 - 1.81957i) q^{19} +(-5.81933 + 5.24101i) q^{20} +(-0.00892239 - 0.0245141i) q^{21} +(-5.06520 + 0.984891i) q^{22} +(-2.50024 - 2.97967i) q^{23} +(5.41872 - 2.30126i) q^{24} +(1.79434 + 10.1762i) q^{25} +(-2.75094 + 3.39755i) q^{26} +(1.73560 - 3.00614i) q^{27} +(-0.00939301 - 0.0232405i) q^{28} +(-0.126343 + 0.347124i) q^{29} +(1.80243 - 11.3845i) q^{30} +(1.29454 + 2.24221i) q^{31} +(5.12613 - 2.39223i) q^{32} +(4.88165 - 5.81773i) q^{33} +(2.06413 - 3.72431i) q^{34} +(-0.0483324 - 0.00852231i) q^{35} +(-1.25066 + 2.35284i) q^{36} -2.87327i q^{37} +(-2.53906 + 5.61722i) q^{38} -6.43407i q^{39} +(1.34778 - 10.9931i) q^{40} +(7.88423 + 1.39020i) q^{41} +(0.0322685 + 0.0178842i) q^{42} +(-5.11775 + 6.09909i) q^{43} +(4.49206 - 5.75100i) q^{44} +(2.60847 + 4.51800i) q^{45} +(5.43318 + 0.860197i) q^{46} +(-2.68591 + 7.37948i) q^{47} +(-3.64794 + 7.48393i) q^{48} +(-3.49992 + 6.06204i) q^{49} +(-11.3573 - 9.19580i) q^{50} +(1.08825 + 6.17175i) q^{51} +(-0.216503 - 6.17861i) q^{52} +(-0.993871 - 1.18445i) q^{53} +(0.936972 + 4.81876i) q^{54} +(-4.88662 - 13.4259i) q^{55} +(0.0315890 + 0.0160883i) q^{56} +(-2.29812 - 8.77680i) q^{57} +(-0.187245 - 0.487703i) q^{58} +(3.93600 - 1.43259i) q^{59} +(8.63969 + 13.8227i) q^{60} +(-2.45324 + 2.05851i) q^{61} +(-3.46210 - 1.19186i) q^{62} +(-0.0164445 + 0.00289961i) q^{63} +(-3.25126 + 7.30953i) q^{64} +(-10.4827 - 6.05220i) q^{65} +(0.188087 + 10.7386i) q^{66} +(-8.76065 - 3.18861i) q^{67} +(1.25271 + 5.89008i) q^{68} +(-7.01139 + 4.04803i) q^{69} +(0.0594911 - 0.0357507i) q^{70} +(9.25916 + 7.76936i) q^{71} +(-0.848341 - 3.67156i) q^{72} +(0.801985 - 4.54828i) q^{73} +(2.66603 + 3.06655i) q^{74} +21.5077 q^{75} +(-2.50221 - 8.35099i) q^{76} +0.0457310 q^{77} +(5.96999 + 6.86686i) q^{78} +(-0.148866 + 0.844262i) q^{79} +(8.76178 + 12.9832i) q^{80} +(-8.59645 - 7.21328i) q^{81} +(-9.70450 + 5.83184i) q^{82} +(4.31582 - 2.49174i) q^{83} +(-0.0510332 + 0.0108538i) q^{84} +(11.0790 + 4.03242i) q^{85} +(-0.197183 - 11.2580i) q^{86} +(0.665868 + 0.384439i) q^{87} +(0.541968 + 10.3059i) q^{88} +(4.86849 - 0.858447i) q^{89} +(-6.97605 - 2.40158i) q^{90} +(0.0296792 - 0.0249038i) q^{91} +(-6.59679 + 4.12323i) q^{92} +(5.06396 - 1.84313i) q^{93} +(-3.98063 - 10.3680i) q^{94} +(-16.4613 - 4.51167i) q^{95} +(-3.05081 - 11.3722i) q^{96} +(-1.35020 - 3.70964i) q^{97} +(-1.88945 - 9.71728i) q^{98} +(-3.12469 - 3.72386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Introduction

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