LMFDB - Embedded newform 288.2.bc.a.205.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(13,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 21, 8]))

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

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

chi := DirichletCharacter("288.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bc (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			205.30
Character	$\chi$	$=$	288.205
Dual form			288.2.bc.a.229.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.683019 + 1.23834i) q^{2} +(1.37019 - 1.05951i) q^{3} +(-1.06697 + 1.69162i) q^{4} +(-0.526137 - 0.403719i) q^{5} +(2.24791 + 0.973096i) q^{6} +(0.911495 + 3.40174i) q^{7} +(-2.82356 - 0.165864i) q^{8} +(0.754859 - 2.90348i) q^{9} +O(q^{10})$	\(q+(0.683019 + 1.23834i) q^{2} +(1.37019 - 1.05951i) q^{3} +(-1.06697 + 1.69162i) q^{4} +(-0.526137 - 0.403719i) q^{5} +(2.24791 + 0.973096i) q^{6} +(0.911495 + 3.40174i) q^{7} +(-2.82356 - 0.165864i) q^{8} +(0.754859 - 2.90348i) q^{9} +(0.140580 - 0.927284i) q^{10} +(5.10279 + 0.671795i) q^{11} +(0.330339 + 3.44831i) q^{12} +(0.389161 + 2.95597i) q^{13} +(-3.58995 + 3.45220i) q^{14} +(-1.14866 + 0.00427652i) q^{15} +(-1.72315 - 3.60981i) q^{16} -0.364422i q^{17} +(4.11108 - 1.04836i) q^{18} +(-4.46287 - 1.84858i) q^{19} +(1.24431 - 0.459267i) q^{20} +(4.85312 + 3.69531i) q^{21} +(2.65339 + 6.77783i) q^{22} +(1.33499 - 4.98224i) q^{23} +(-4.04456 + 2.76434i) q^{24} +(-1.18026 - 4.40481i) q^{25} +(-3.39469 + 2.50090i) q^{26} +(-2.04198 - 4.77811i) q^{27} +(-6.72699 - 2.08766i) q^{28} +(3.55450 + 4.63232i) q^{29} +(-0.789849 - 1.41950i) q^{30} +(-3.01601 - 5.22388i) q^{31} +(3.29323 - 4.59941i) q^{32} +(7.70358 - 4.48599i) q^{33} +(0.451278 - 0.248907i) q^{34} +(0.893778 - 2.15777i) q^{35} +(4.10617 + 4.37486i) q^{36} +(-7.56014 + 3.13151i) q^{37} +(-0.759053 - 6.78917i) q^{38} +(3.66512 + 3.63793i) q^{39} +(1.41862 + 1.22719i) q^{40} +(-0.884042 + 3.29929i) q^{41} +(-1.26127 + 8.53378i) q^{42} +(-9.64364 - 1.26961i) q^{43} +(-6.58094 + 7.91518i) q^{44} +(-1.56935 + 1.22288i) q^{45} +(7.08153 - 1.74980i) q^{46} +(-4.45774 - 2.57368i) q^{47} +(-6.18570 - 3.12044i) q^{48} +(-4.67887 + 2.70134i) q^{49} +(4.64850 - 4.47013i) q^{50} +(-0.386110 - 0.499328i) q^{51} +(-5.41559 - 2.49562i) q^{52} +(-3.65397 - 8.82145i) q^{53} +(4.52222 - 5.79220i) q^{54} +(-2.41355 - 2.41355i) q^{55} +(-2.00943 - 9.75621i) q^{56} +(-8.07359 + 2.19556i) q^{57} +(-3.30859 + 7.56564i) q^{58} +(2.32430 + 1.78350i) q^{59} +(1.21835 - 1.94765i) q^{60} +(6.44833 + 8.40362i) q^{61} +(4.40895 - 7.30285i) q^{62} +(10.5649 - 0.0786691i) q^{63} +(7.94498 + 0.936655i) q^{64} +(0.988629 - 1.71236i) q^{65} +(10.8169 + 6.47563i) q^{66} +(7.30385 - 0.961570i) q^{67} +(0.616463 + 0.388827i) q^{68} +(-3.44956 - 8.24107i) q^{69} +(3.28252 - 0.366998i) q^{70} +(5.87298 - 5.87298i) q^{71} +(-2.61297 + 8.07294i) q^{72} +(5.72879 + 5.72879i) q^{73} +(-9.04159 - 7.22313i) q^{74} +(-6.28415 - 4.78493i) q^{75} +(7.88885 - 5.57709i) q^{76} +(2.36589 + 17.9707i) q^{77} +(-2.00165 + 7.02343i) q^{78} +(4.12486 + 2.38149i) q^{79} +(-0.550739 + 2.59492i) q^{80} +(-7.86038 - 4.38343i) q^{81} +(-4.68946 + 1.15873i) q^{82} +(6.59994 - 5.06432i) q^{83} +(-11.4292 + 4.26685i) q^{84} +(-0.147124 + 0.191736i) q^{85} +(-5.01458 - 12.8093i) q^{86} +(9.77836 + 2.58112i) q^{87} +(-14.2966 - 2.74322i) q^{88} +(1.17717 - 1.17717i) q^{89} +(-2.58623 - 1.10814i) q^{90} +(-9.70073 + 4.01817i) q^{91} +(7.00366 + 7.57419i) q^{92} +(-9.66729 - 3.96222i) q^{93} +(0.142366 - 7.27806i) q^{94} +(1.60177 + 2.77435i) q^{95} +(-0.360779 - 9.79131i) q^{96} +(0.00601054 - 0.0104106i) q^{97} +(-6.54094 - 3.94896i) q^{98} +(5.80242 - 14.3087i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) $ 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.683019	+	1.23834i	0.482967	+	0.875638i
$2$	0.683019	+	1.23834i	0.482967	+	0.875638i
$3$	1.37019	−	1.05951i	0.791081	−	0.611711i
$3$	1.37019	−	1.05951i	0.791081	−	0.611711i
$4$	−1.06697	+	1.69162i	−0.533485	+	0.845809i
$5$	−0.526137	−	0.403719i	−0.235296	−	0.180549i	0.484383	−	0.874856i	$-0.339044\pi$
$5$	−0.526137	−	0.403719i	−0.235296	−	0.180549i	−0.719679	+	0.694307i	$0.755711\pi$
$6$	2.24791	+	0.973096i	0.917704	+	0.397265i
$7$	0.911495	+	3.40174i	0.344513	+	1.28574i	0.893181	+	0.449698i	$0.148468\pi$
$7$	0.911495	+	3.40174i	0.344513	+	1.28574i	−0.548668	+	0.836040i	$0.684865\pi$
$8$	−2.82356	−	0.165864i	−0.998279	−	0.0586419i
$9$	0.754859	−	2.90348i	0.251620	−	0.967826i
$10$	0.140580	−	0.927284i	0.0444553	−	0.293233i
$11$	5.10279	+	0.671795i	1.53855	+	0.202554i	0.851615	−	0.524167i	$-0.175623\pi$
$11$	5.10279	+	0.671795i	1.53855	+	0.202554i	0.686933	+	0.726721i	$0.258957\pi$
$12$	0.330339	+	3.44831i	0.0953606	+	0.995443i
$13$	0.389161	+	2.95597i	0.107934	+	0.819838i	0.956701	+	0.291072i	$0.0940119\pi$
$13$	0.389161	+	2.95597i	0.107934	+	0.819838i	−0.848767	+	0.528766i	$0.822655\pi$
$14$	−3.58995	+	3.45220i	−0.959454	+	0.922638i
$15$	−1.14866	+	0.00427652i	−0.296581	+	0.00110419i
$16$	−1.72315	−	3.60981i	−0.430787	−	0.902454i
$17$		−	0.364422i		−	0.0883853i	−0.999023	−	0.0441926i	$-0.985928\pi$
$17$		−	0.364422i		−	0.0883853i	0.999023	−	0.0441926i	$-0.0140715\pi$
$18$	4.11108	−	1.04836i	0.968990	−	0.247101i
$19$	−4.46287	−	1.84858i	−1.02385	−	0.424094i	−0.193363	−	0.981127i	$-0.561939\pi$
$19$	−4.46287	−	1.84858i	−1.02385	−	0.424094i	−0.830490	+	0.557034i	$0.811939\pi$
$20$	1.24431	−	0.459267i	0.278236	−	0.102695i
$21$	4.85312	+	3.69531i	1.05904	+	0.806382i
$22$	2.65339	+	6.77783i	0.565705	+	1.44504i
$23$	1.33499	−	4.98224i	0.278364	−	1.03887i	−0.675189	−	0.737645i	$-0.735938\pi$
$23$	1.33499	−	4.98224i	0.278364	−	1.03887i	0.953553	−	0.301224i	$-0.0973953\pi$
$24$	−4.04456	+	2.76434i	−0.825592	+	0.564268i
$25$	−1.18026	−	4.40481i	−0.236053	−	0.880961i
$26$	−3.39469	+	2.50090i	−0.665753	+	0.490466i
$27$	−2.04198	−	4.77811i	−0.392978	−	0.919548i
$28$	−6.72699	−	2.08766i	−1.27128	−	0.394531i
$29$	3.55450	+	4.63232i	0.660054	+	0.860199i	0.996678	−	0.0814397i	$-0.0259518\pi$
$29$	3.55450	+	4.63232i	0.660054	+	0.860199i	−0.336624	+	0.941639i	$0.609285\pi$
$30$	−0.789849	−	1.41950i	−0.144206	−	0.259165i
$31$	−3.01601	−	5.22388i	−0.541691	−	0.938236i	−0.998807	−	0.0488293i	$-0.984451\pi$
$31$	−3.01601	−	5.22388i	−0.541691	−	0.938236i	0.457116	−	0.889407i	$-0.348882\pi$
$32$	3.29323	−	4.59941i	0.582167	−	0.813069i
$33$	7.70358	−	4.48599i	1.34102	−	0.780910i
$34$	0.451278	−	0.248907i	0.0773935	−	0.0426872i
$35$	0.893778	−	2.15777i	0.151076	−	0.364730i
$36$	4.10617	+	4.37486i	0.684361	+	0.729143i
$37$	−7.56014	+	3.13151i	−1.24288	+	0.514817i	−0.904613	−	0.426234i	$-0.859840\pi$
$37$	−7.56014	+	3.13151i	−1.24288	+	0.514817i	−0.338265	+	0.941051i	$0.609840\pi$
$38$	−0.759053	−	6.78917i	−0.123135	−	1.10135i
$39$	3.66512	+	3.63793i	0.586888	+	0.582534i
$40$	1.41862	+	1.22719i	0.224303	+	0.194036i
$41$	−0.884042	+	3.29929i	−0.138064	+	0.515263i	0.861902	+	0.507074i	$0.169273\pi$
$41$	−0.884042	+	3.29929i	−0.138064	+	0.515263i	−0.999966	+	0.00818826i	$0.997394\pi$
$42$	−1.26127	+	8.53378i	−0.194618	+	1.31679i
$43$	−9.64364	−	1.26961i	−1.47064	−	0.193614i	−0.647768	−	0.761838i	$-0.724297\pi$
$43$	−9.64364	−	1.26961i	−1.47064	−	0.193614i	−0.822874	+	0.568224i	$0.807631\pi$
$44$	−6.58094	+	7.91518i	−0.992114	+	1.19326i
$45$	−1.56935	+	1.22288i	−0.233945	+	0.182296i
$46$	7.08153	−	1.74980i	1.04411	−	0.257993i
$47$	−4.45774	−	2.57368i	−0.650228	−	0.375409i	0.138316	−	0.990388i	$-0.455831\pi$
$47$	−4.45774	−	2.57368i	−0.650228	−	0.375409i	−0.788543	+	0.614979i	$0.789164\pi$
$48$	−6.18570	−	3.12044i	−0.892828	−	0.450397i
$49$	−4.67887	+	2.70134i	−0.668409	+	0.385906i
$50$	4.64850	−	4.47013i	0.657398	−	0.632172i
$51$	−0.386110	−	0.499328i	−0.0540662	−	0.0699199i
$52$	−5.41559	−	2.49562i	−0.751008	−	0.346080i
$53$	−3.65397	−	8.82145i	−0.501911	−	1.21172i	−0.948442	−	0.316952i	$-0.897341\pi$
$53$	−3.65397	−	8.82145i	−0.501911	−	1.21172i	0.446531	−	0.894768i	$-0.352659\pi$
$54$	4.52222	−	5.79220i	0.615396	−	0.788218i
$55$	−2.41355	−	2.41355i	−0.325443	−	0.325443i
$56$	−2.00943	−	9.75621i	−0.268522	−	1.30373i
$57$	−8.07359	+	2.19556i	−1.06937	+	0.290809i
$58$	−3.30859	+	7.56564i	−0.434439	+	0.993417i
$59$	2.32430	+	1.78350i	0.302598	+	0.232192i	0.748888	−	0.662697i	$-0.230588\pi$
$59$	2.32430	+	1.78350i	0.302598	+	0.232192i	−0.446290	+	0.894889i	$0.647255\pi$
$60$	1.21835	−	1.94765i	0.157288	−	0.251440i
$61$	6.44833	+	8.40362i	0.825624	+	1.07597i	0.995890	+	0.0905756i	$0.0288707\pi$
$61$	6.44833	+	8.40362i	0.825624	+	1.07597i	−0.170266	+	0.985398i	$0.554463\pi$
$62$	4.40895	−	7.30285i	0.559937	−	0.927463i
$63$	10.5649	−	0.0786691i	1.33106	−	0.00991137i
$64$	7.94498	+	0.936655i	0.993122	+	0.117082i
$65$	0.988629	−	1.71236i	0.122624	−	0.212392i
$66$	10.8169	+	6.47563i	1.33146	+	0.797095i
$67$	7.30385	−	0.961570i	0.892307	−	0.117474i	0.329590	−	0.944124i	$-0.393089\pi$
$67$	7.30385	−	0.961570i	0.892307	−	0.117474i	0.562717	+	0.826650i	$0.309756\pi$
$68$	0.616463	+	0.388827i	0.0747571	+	0.0471522i
$69$	−3.44956	−	8.24107i	−0.415279	−	0.992108i
$70$	3.28252	−	0.366998i	0.392336	−	0.0438646i
$71$	5.87298	−	5.87298i	0.696995	−	0.696995i	−0.266766	−	0.963761i	$-0.585955\pi$
$71$	5.87298	−	5.87298i	0.696995	−	0.696995i	0.963761	+	0.266766i	$0.0859552\pi$
$72$	−2.61297	+	8.07294i	−0.307942	+	0.951405i
$73$	5.72879	+	5.72879i	0.670504	+	0.670504i	0.957832	−	0.287328i	$-0.0927669\pi$
$73$	5.72879	+	5.72879i	0.670504	+	0.670504i	−0.287328	+	0.957832i	$0.592767\pi$
$74$	−9.04159	−	7.22313i	−1.05106	−	0.839672i
$75$	−6.28415	−	4.78493i	−0.725631	−	0.552516i
$76$	7.88885	−	5.57709i	0.904913	−	0.639737i
$77$	2.36589	+	17.9707i	0.269618	+	2.04795i
$78$	−2.00165	+	7.02343i	−0.226642	+	0.795247i
$79$	4.12486	+	2.38149i	0.464083	+	0.267939i	0.713760	−	0.700391i	$-0.246991\pi$
$79$	4.12486	+	2.38149i	0.464083	+	0.267939i	−0.249676	+	0.968329i	$0.580324\pi$
$80$	−0.550739	+	2.59492i	−0.0615745	+	0.290121i
$81$	−7.86038	−	4.38343i	−0.873375	−	0.487048i
$82$	−4.68946	+	1.15873i	−0.517864	+	0.127961i
$83$	6.59994	−	5.06432i	0.724438	−	0.555881i	−0.179389	−	0.983778i	$-0.557412\pi$
$83$	6.59994	−	5.06432i	0.724438	−	0.555881i	0.903827	+	0.427897i	$0.140746\pi$
$84$	−11.4292	+	4.26685i	−1.24703	+	0.465551i
$85$	−0.147124	+	0.191736i	−0.0159578	+	0.0207967i
$86$	−5.01458	−	12.8093i	−0.540736	−	1.38126i
$87$	9.77836	+	2.58112i	1.04835	+	0.276725i
$88$	−14.2966	−	2.74322i	−1.52402	−	0.292428i
$89$	1.17717	−	1.17717i	0.124780	−	0.124780i	−0.641959	−	0.766739i	$-0.721878\pi$
$89$	1.17717	−	1.17717i	0.124780	−	0.124780i	0.766739	+	0.641959i	$0.221878\pi$
$90$	−2.58623	−	1.10814i	−0.272613	−	0.116808i
$91$	−9.70073	+	4.01817i	−1.01691	+	0.421219i
$92$	7.00366	+	7.57419i	0.730182	+	0.789664i
$93$	−9.66729	−	3.96222i	−1.00245	−	0.410863i
$94$	0.142366	−	7.27806i	0.0146839	−	0.750675i
$95$	1.60177	+	2.77435i	0.164338	+	0.284643i
$96$	−0.360779	−	9.79131i	−0.0368219	−	0.999322i
$97$	0.00601054	−	0.0104106i	0.000610278	−	0.00105703i	−0.865720	−	0.500528i	$-0.833139\pi$
$97$	0.00601054	−	0.0104106i	0.000610278	−	0.00105703i	0.866330	+	0.499471i	$0.166472\pi$
$98$	−6.54094	−	3.94896i	−0.660734	−	0.398905i
$99$	5.80242	−	14.3087i	0.583166	−	1.43808i
$100$	8.71056	+	2.70324i	0.871056	+	0.270324i
$101$	−1.96464	+	14.9229i	−0.195489	+	1.48489i	0.559326	+	0.828948i	$0.311060\pi$
$101$	−1.96464	+	14.9229i	−0.195489	+	1.48489i	−0.754815	+	0.655938i	$0.772273\pi$
$102$	0.354617	−	0.819186i	0.0351124	−	0.0811115i
$103$	5.91718	+	1.58550i	0.583037	+	0.156224i	0.538269	−	0.842773i	$-0.319078\pi$
$103$	5.91718	+	1.58550i	0.583037	+	0.156224i	0.0447682	+	0.998997i	$0.485745\pi$
$104$	−0.608529	−	8.41090i	−0.0596712	−	0.824757i
$105$	−1.06154	−	3.90353i	−0.103596	−	0.380946i
$106$	8.42823	−	10.5501i	0.818622	−	1.02471i
$107$	−6.78660	−	16.3843i	−0.656086	−	1.58393i	−0.803799	−	0.594901i	$-0.797191\pi$
$107$	−6.78660	−	16.3843i	−0.656086	−	1.58393i	0.147714	−	0.989030i	$-0.452809\pi$
$108$	10.2615	+	1.64386i	0.987410	+	0.158180i
$109$	−1.32634	−	0.549387i	−0.127040	−	0.0526217i	0.318258	−	0.948004i	$-0.396902\pi$
$109$	−1.32634	−	0.549387i	−0.127040	−	0.0526217i	−0.445298	+	0.895382i	$0.646902\pi$
$110$	1.34029	−	4.63729i	0.127792	−	0.442148i
$111$	−7.04097	+	12.3008i	−0.668299	+	1.16754i
$112$	10.7090	−	9.15204i	1.01191	−	0.864786i
$113$	−2.03598	+	1.17547i	−0.191529	+	0.110579i	−0.592698	−	0.805425i	$-0.701937\pi$
$113$	−2.03598	+	1.17547i	−0.191529	+	0.110579i	0.401169	+	0.916004i	$0.368604\pi$
$114$	−8.23327	−	8.49824i	−0.771116	−	0.795933i
$115$	−2.71381	+	2.08238i	−0.253064	+	0.194183i
$116$	−11.6287	+	1.07032i	−1.07969	+	0.0993764i
$117$	8.87635	+	1.10142i	0.820619	+	0.101826i
$118$	−0.621035	+	4.09643i	−0.0571709	+	0.377107i
$119$	1.23967	−	0.332169i	0.113640	−	0.0304498i
$120$	3.24401	+	0.178446i	0.296136	+	0.0162898i
$121$	14.9619	+	4.00904i	1.36018	+	0.364458i
$122$	−6.00221	+	13.7251i	−0.543415	+	1.24261i
$123$	2.28434	+	5.45732i	0.205972	+	0.492070i
$124$	12.0548	+	0.471788i	1.08255	+	0.0423679i
$125$	−2.42627	+	5.85752i	−0.217012	+	0.523913i
$126$	7.31347	+	13.0293i	0.651536	+	1.16074i
$127$	−6.25944			−0.555435			−0.277718	−	0.960663i	$-0.589578\pi$
$127$	−6.25944			−0.555435			−0.277718	+	0.960663i	$0.589578\pi$
$128$	4.26667	+	10.4783i	0.377124	+	0.926163i
$129$	−14.5588	+	8.47797i	−1.28183	+	0.746443i
$130$	2.79573	+	0.0546873i	0.245202	+	0.00479639i
$131$	−4.07654	+	0.536686i	−0.356169	+	0.0468905i	−0.306488	−	0.951875i	$-0.599154\pi$
$131$	−4.07654	+	0.536686i	−0.356169	+	0.0468905i	−0.0496810	+	0.998765i	$0.515820\pi$
$132$	−0.630911	+	17.8179i	−0.0549137	+	1.55085i
$133$	2.22052	−	16.8665i	0.192543	−	1.46251i
$134$	6.17942	+	8.38788i	0.533820	+	0.724602i
$135$	−0.854655	+	3.33832i	−0.0735570	+	0.287317i
$136$	−0.0604445	+	1.02897i	−0.00518308	+	0.0882332i
$137$	9.01232	−	2.41484i	0.769974	−	0.206314i	0.147614	−	0.989045i	$-0.452841\pi$
$137$	9.01232	−	2.41484i	0.769974	−	0.206314i	0.622360	+	0.782731i	$0.286174\pi$
$138$	7.84912	−	9.90054i	0.668162	−	0.842790i
$139$	−12.9755	+	16.9100i	−1.10057	+	1.43429i	−0.211000	+	0.977486i	$0.567672\pi$
$139$	−12.9755	+	16.9100i	−1.10057	+	1.43429i	−0.889568	+	0.456802i	$0.848995\pi$
$140$	2.69649	+	3.81421i	0.227895	+	0.322359i
$141$	−8.83481	+	1.19660i	−0.744025	+	0.100772i
$142$	11.2841	+	3.26139i	0.946941	+	0.273690i
$143$			15.3451i			1.28322i
$144$	−11.7818	+	2.27822i	−0.981813	+	0.189852i
$145$		−	3.87225i		−	0.321573i
$146$	−3.18132	+	11.0071i	−0.263288	+	0.910951i
$147$	−3.54884	+	8.65869i	−0.292703	+	0.714157i
$148$	2.76912	−	16.1301i	0.227620	−	1.32589i
$149$	−0.653845	+	0.852107i	−0.0535651	+	0.0698074i	−0.819368	−	0.573268i	$-0.805675\pi$
$149$	−0.653845	+	0.852107i	−0.0535651	+	0.0698074i	0.765803	+	0.643076i	$0.222342\pi$
$150$	1.63318	−	11.0501i	0.133348	−	0.902237i
$151$	−6.65612	+	1.78350i	−0.541667	+	0.145139i	−0.519271	−	0.854610i	$-0.673796\pi$
$151$	−6.65612	+	1.78350i	−0.541667	+	0.145139i	−0.0223966	+	0.999749i	$0.507130\pi$
$152$	12.2946	+	5.95981i	0.997221	+	0.483405i
$153$	−1.05809	−	0.275087i	−0.0855416	−	0.0222395i
$154$	−20.6379	+	15.2041i	−1.66305	+	1.22518i
$155$	−0.522146	+	3.96609i	−0.0419398	+	0.318564i
$156$	−10.0646	+	2.31842i	−0.805809	+	0.185622i
$157$	−6.86728	+	0.904094i	−0.548068	+	0.0721546i	−0.399475	−	0.916744i	$-0.630808\pi$
$157$	−6.86728	+	0.904094i	−0.548068	+	0.0721546i	−0.148593	+	0.988898i	$0.547474\pi$
$158$	−0.131735	+	6.73459i	−0.0104803	+	0.535775i
$159$	−14.3531	−	8.21567i	−1.13827	−	0.651545i
$160$	−3.58956	+	1.09038i	−0.283780	+	0.0862021i
$161$	18.1651			1.43161
$162$	0.0593921	−	12.7278i	0.00466628	−	0.999989i
$163$	−8.00966	+	19.3370i	−0.627365	+	1.51459i	0.215520	+	0.976499i	$0.430855\pi$
$163$	−8.00966	+	19.3370i	−0.627365	+	1.51459i	−0.842885	+	0.538094i	$0.819145\pi$
$164$	−4.63790	−	5.01571i	−0.362159	−	0.391661i
$165$	−5.86421	−	0.749838i	−0.456528	−	0.0583748i
$166$	10.7792	+	4.71395i	0.836631	+	0.365874i
$167$	2.77221	+	0.742811i	0.214520	+	0.0574804i	0.364478	−	0.931212i	$-0.381247\pi$
$167$	2.77221	+	0.742811i	0.214520	+	0.0574804i	−0.149958	+	0.988692i	$0.547914\pi$
$168$	−13.0902	−	11.2389i	−1.00993	−	0.867098i
$169$	3.97073	−	1.06395i	0.305441	−	0.0818427i
$170$	−0.337922	−	0.0512304i	−0.0259175	−	0.00392919i
$171$	−8.73615	+	11.5624i	−0.668070	+	0.884201i
$172$	12.4372	−	14.9587i	0.948326	−	1.14059i
$173$	−15.2398	+	11.6939i	−1.15866	+	0.889072i	−0.995237	−	0.0974841i	$-0.968920\pi$
$173$	−15.2398	+	11.6939i	−1.15866	+	0.889072i	−0.163424	+	0.986556i	$0.552254\pi$
$174$	3.48250	+	13.8719i	0.264007	+	1.05162i
$175$	13.9082	−	8.02992i	1.05136	−	0.607005i
$176$	−6.36780	−	19.5777i	−0.479991	−	1.47573i
$177$	5.07438	−	0.0188923i	0.381414	−	0.00142003i
$178$	2.26177	+	0.653708i	0.169527	+	0.0489975i
$179$	9.45002	+	3.91433i	0.706328	+	0.292571i	0.706784	−	0.707429i	$-0.250145\pi$
$179$	9.45002	+	3.91433i	0.706328	+	0.292571i	−0.000456333		1.00000i	$0.500145\pi$
$180$	−0.394192	−	3.95951i	−0.0293813	−	0.295125i
$181$	3.88557	+	9.38059i	0.288812	+	0.697254i	0.999983	−	0.00576488i	$-0.00183503\pi$
$181$	3.88557	+	9.38059i	0.288812	+	0.697254i	−0.711171	+	0.703019i	$0.751835\pi$
$182$	−11.6016	−	9.26831i	−0.859971	−	0.687013i
$183$	17.7392	+	4.68249i	1.31132	+	0.346140i
$184$	−4.59579	+	13.8462i	−0.338806	+	1.02076i
$185$	5.24192	+	1.40457i	0.385393	+	0.103266i
$186$	−1.69637	−	14.6777i	−0.124384	−	1.07622i
$187$	0.244817	−	1.85957i	0.0179028	−	0.135985i
$188$	9.10995	−	4.79476i	0.664412	−	0.349694i
$189$	14.3927	−	11.3015i	1.04691	−	0.822063i
$190$	−2.34155	+	3.87847i	−0.169874	+	0.281374i
$191$	8.97326	−	15.5421i	0.649283	−	1.12459i	−0.334012	−	0.942569i	$-0.608403\pi$
$191$	8.97326	−	15.5421i	0.649283	−	1.12459i	0.983295	−	0.182022i	$-0.0582641\pi$
$192$	11.8786	−	7.13442i	0.857261	−	0.514882i
$193$	2.28960	+	3.96571i	0.164809	+	0.285458i	0.936588	−	0.350434i	$-0.113966\pi$
$193$	2.28960	+	3.96571i	0.164809	+	0.285458i	−0.771778	+	0.635892i	$0.780632\pi$
$194$	0.0169971		0.000332481i	0.00122032		2.38707e-5i
$195$	−0.459653	−	3.39372i	−0.0329164	−	0.243030i
$196$	0.422566	−	10.7971i	0.0301833	−	0.771222i
$197$	−6.24771	+	2.58789i	−0.445131	+	0.184379i	−0.593978	−	0.804481i	$-0.702444\pi$
$197$	−6.24771	+	2.58789i	−0.445131	+	0.184379i	0.148848	+	0.988860i	$0.452444\pi$
$198$	21.6822	−	2.58776i	1.54089	−	0.183904i
$199$	−10.8310	+	10.8310i	−0.767787	+	0.767787i	−0.977716	−	0.209930i	$-0.932676\pi$
$199$	−10.8310	+	10.8310i	−0.767787	+	0.767787i	0.209930	+	0.977716i	$0.432676\pi$
$200$	2.60195	+	12.6330i	0.183985	+	0.893288i
$201$	8.98889	−	9.05607i	0.634027	−	0.638766i
$202$	−19.8215	+	7.75975i	−1.39464	+	0.545974i
$203$	−12.5180	+	16.3138i	−0.878595	+	1.14501i
$204$	1.25664	−	0.120383i	0.0879825	−	0.00842847i
$205$	1.79711	−	1.37897i	0.125516	−	0.0963117i
$206$	2.07815	+	8.41041i	0.144792	+	0.585981i
$207$	−13.4581	−	7.63699i	−0.935403	−	0.530808i
$208$	9.99992	−	6.49837i	0.693369	−	0.450581i
$209$	−21.5312	−	12.4311i	−1.48934	−	0.859874i
$210$	4.10885	−	3.98073i	0.283537	−	0.274697i
$211$	−3.39507	−	25.7881i	−0.233726	−	1.77533i	−0.558468	−	0.829526i	$-0.688611\pi$
$211$	−3.39507	−	25.7881i	−0.233726	−	1.77533i	0.324742	−	0.945803i	$-0.394723\pi$
$212$	18.8212	+	3.23111i	1.29265	+	0.221914i
$213$	1.82461	−	14.2696i	0.125020	−	0.977739i
$214$	15.6540	−	19.5949i	1.07008	−	1.33948i
$215$	4.56131	+	4.56131i	0.311079	+	0.311079i
$216$	4.97312	+	13.8300i	0.338378	+	0.941010i
$217$	15.0212	−	15.0212i	1.01971	−	1.01971i
$218$	−0.225586	−	2.01770i	−0.0152786	−	0.136656i
$219$	13.9193	+	1.77981i	0.940578	+	0.120269i
$220$	6.65799	−	1.50762i	0.448881	−	0.101644i
$221$	1.07722	−	0.141819i	0.0724616	−	0.00953975i
$222$	−20.0417	−	0.317397i	−1.34511	−	0.0213023i
$223$	7.49609	−	12.9836i	0.501976	−	0.869447i	−0.498022	−	0.867165i	$-0.665940\pi$
$223$	7.49609	−	12.9836i	0.501976	−	0.869447i	0.999997	−	0.00228276i	$-0.000726627\pi$
$224$	18.6478	+	7.01040i	1.24596	+	0.468402i
$225$	−13.6802	+	0.101866i	−0.912013	+	0.00679107i
$226$	−2.84624	−	1.71836i	−0.189329	−	0.114304i
$227$	15.9796	+	20.8251i	1.06061	+	1.38221i	0.919898	+	0.392158i	$0.128271\pi$
$227$	15.9796	+	20.8251i	1.06061	+	1.38221i	0.140709	+	0.990051i	$0.455062\pi$
$228$	4.90023	−	16.0000i	0.324526	−	1.05963i
$229$	−11.0776	−	8.50016i	−0.732030	−	0.561707i	0.174088	−	0.984730i	$-0.444302\pi$
$229$	−11.0776	−	8.50016i	−0.732030	−	0.561707i	−0.906119	+	0.423023i	$0.860969\pi$
$230$	−4.43228	−	1.93831i	−0.292256	−	0.127809i
$231$	22.2820	+	22.1167i	1.46604	+	1.45517i
$232$	−9.26801	−	13.6692i	−0.608475	−	0.897426i
$233$	−10.0276	−	10.0276i	−0.656932	−	0.656932i	0.297721	−	0.954653i	$-0.403773\pi$
$233$	−10.0276	−	10.0276i	−0.656932	−	0.656932i	−0.954653	+	0.297721i	$0.903773\pi$
$234$	4.69879	+	11.7442i	0.307169	+	0.767744i
$235$	1.30634	+	3.15378i	0.0852161	+	0.205730i
$236$	−5.49696	+	2.02889i	−0.357821	+	0.132069i
$237$	8.17508	−	1.10725i	0.531029	−	0.0719236i
$238$	1.25806	+	1.30825i	0.0815476	+	0.0848016i
$239$	−14.6640	+	8.46629i	−0.948538	+	0.547639i	−0.892627	−	0.450797i	$-0.851140\pi$
$239$	−14.6640	+	8.46629i	−0.948538	+	0.547639i	−0.0559118	+	0.998436i	$0.517807\pi$
$240$	1.99474	+	4.13906i	0.128760	+	0.267175i
$241$	9.10955	+	5.25940i	0.586798	+	0.338788i	0.763830	−	0.645417i	$-0.223316\pi$
$241$	9.10955	+	5.25940i	0.586798	+	0.338788i	−0.177032	+	0.984205i	$0.556650\pi$
$242$	5.25473	+	21.2662i	0.337787	+	1.36704i
$243$	−15.4145	+	2.32203i	−0.988843	+	0.148959i
$244$	−21.0959	+	1.94169i	−1.35053	+	0.124304i
$245$	3.55231	+	0.467670i	0.226949	+	0.0298784i
$246$	−5.19777	+	6.55624i	−0.331398	+	0.418011i
$247$	3.72758	−	13.9115i	0.237180	−	0.885168i
$248$	7.64942	+	15.2502i	0.485739	+	0.968387i
$249$	3.67748	−	13.9318i	0.233051	−	0.882894i
$250$	−8.91079	+	0.996258i	−0.563568	+	0.0630089i
$251$	1.80970	−	0.749602i	0.114227	−	0.0473144i	−0.324838	−	0.945770i	$-0.605310\pi$
$251$	1.80970	−	0.749602i	0.114227	−	0.0473144i	0.439065	+	0.898455i	$0.355310\pi$
$252$	−11.1394	+	17.9558i	−0.701716	+	1.13111i
$253$	10.1592	−	24.5265i	0.638703	−	1.54197i
$254$	−4.27531	−	7.75131i	−0.268257	−	0.486361i
$255$	0.00155846	+	0.418595i	9.75944e−5	+	0.0262134i
$256$	−10.0615	+	12.4405i	−0.628845	+	0.777531i
$257$	−7.85438	−	13.6042i	−0.489943	−	0.848606i	0.509990	−	0.860180i	$-0.329649\pi$
$257$	−7.85438	−	13.6042i	−0.489943	−	0.848606i	−0.999933	+	0.0115743i	$0.996316\pi$
$258$	−20.4426	−	12.2382i	−1.27270	−	0.761914i
$259$	−17.5436	−	22.8633i	−1.09011	−	1.42066i
$260$	1.84181	+	3.49942i	0.114224	+	0.217025i
$261$	16.1330	−	6.82367i	0.998606	−	0.422375i
$262$	−3.44895	−	4.68157i	−0.213077	−	0.289228i
$263$	−3.27241	−	12.2128i	−0.201786	−	0.753075i	−0.990405	−	0.138193i	$-0.955871\pi$
$263$	−3.27241	−	12.2128i	−0.201786	−	0.753075i	0.788620	−	0.614881i	$-0.210796\pi$
$264$	−22.4956	+	11.3887i	−1.38451	+	0.700926i
$265$	−1.63890	+	6.11647i	−0.100677	+	0.375732i
$266$	22.4031	−	8.77039i	1.37362	−	0.537747i
$267$	0.365722	−	2.86018i	0.0223818	−	0.175040i
$268$	−6.16638	+	13.3813i	−0.376672	+	0.817393i
$269$	1.03549	+	0.428914i	0.0631350	+	0.0261514i	0.414027	−	0.910264i	$-0.364122\pi$
$269$	1.03549	+	0.428914i	0.0631350	+	0.0261514i	−0.350892	+	0.936416i	$0.614122\pi$
$270$	−4.71772	+	1.22178i	−0.287112	+	0.0743554i
$271$		−	11.2278i		−	0.682043i	−0.940055	−	0.341022i	$-0.889227\pi$
$271$		−	11.2278i		−	0.682043i	0.940055	−	0.341022i	$-0.110773\pi$
$272$	−1.31549	+	0.627953i	−0.0797636	+	0.0380752i
$273$	−9.03456	+	15.7837i	−0.546797	+	0.955275i
$274$	9.14598	+	9.51093i	0.552529	+	0.574576i
$275$	−3.06351	−	23.2697i	−0.184737	−	1.40321i
$276$	17.6213	+	2.95763i	1.06068	+	0.178028i
$277$	−8.84144	−	1.16400i	−0.531231	−	0.0699378i	−0.139861	−	0.990171i	$-0.544665\pi$
$277$	−8.84144	−	1.16400i	−0.531231	−	0.0699378i	−0.391370	+	0.920233i	$0.627999\pi$
$278$	−29.8029	−	4.51823i	−1.78746	−	0.270985i
$279$	−17.4441	+	4.81362i	−1.04435	+	0.288184i
$280$	−2.88153	+	5.94435i	−0.172204	+	0.355243i
$281$	4.77995	+	17.8390i	0.285148	+	1.06419i	0.948731	+	0.316085i	$0.102368\pi$
$281$	4.77995	+	17.8390i	0.285148	+	1.06419i	−0.663583	+	0.748103i	$0.730965\pi$
$282$	−7.51614	−	10.1232i	−0.447580	−	0.602827i
$283$	20.3214	+	15.5932i	1.20798	+	0.926919i	0.998702	−	0.0509363i	$-0.0162206\pi$
$283$	20.3214	+	15.5932i	1.20798	+	0.926919i	0.209282	+	0.977855i	$0.432887\pi$
$284$	3.66855	+	16.2011i	0.217688	+	0.961361i
$285$	5.13420	+	2.10430i	0.304124	+	0.124648i
$286$	−19.0025	+	10.4810i	−1.12364	+	0.619755i
$287$	−12.0291			−0.710058
$288$	−10.8684	−	13.0337i	−0.640425	−	0.768021i
$289$	16.8672			0.992188
$290$	4.79516	−	2.64482i	0.281582	−	0.155309i
$291$	−0.00279454	−	0.0206327i	−0.000163819	−	0.00120951i
$292$	−15.8034	+	3.57848i	−0.924823	+	0.209415i
$293$	0.908240	+	0.696917i	0.0530599	+	0.0407143i	0.634951	−	0.772552i	$-0.281020\pi$
$293$	0.908240	+	0.696917i	0.0530599	+	0.0407143i	−0.581891	+	0.813267i	$0.697687\pi$
$294$	−13.1463	+	1.51938i	−0.766709	+	0.0886122i
$295$	−0.502867	−	1.87673i	−0.0292781	−	0.109267i
$296$	21.8659	−	7.58805i	1.27093	−	0.441046i
$297$	−7.20985	−	25.7535i	−0.418358	−	1.49437i
$298$	−1.50179	−	0.227677i	−0.0869962	−	0.0131890i
$299$	15.2469	+	2.00729i	0.881749	+	0.116084i
$300$	14.7993	−	5.52500i	0.854436	−	0.318986i
$301$	−4.47124	−	33.9624i	−0.257718	−	1.95756i
$302$	−6.75484	−	7.02437i	−0.388697	−	0.404207i
$303$	13.1191	+	22.5288i	0.753673	+	1.29425i
$304$	1.01715	+	19.2955i	0.0583377	+	1.10667i
$305$		−	7.02477i		−	0.402237i
$306$	−0.382045	−	1.49817i	−0.0218401	−	0.0856444i
$307$	0.619785	+	0.256723i	0.0353730	+	0.0146520i	0.400300	−	0.916384i	$-0.368906\pi$
$307$	0.619785	+	0.256723i	0.0353730	+	0.0146520i	−0.364927	+	0.931036i	$0.618906\pi$
$308$	−32.9239	−	15.1720i	−1.87602	−	0.864507i
$309$	9.78755	−	4.09689i	0.556794	−	0.233064i
$310$	−5.26801	+	2.06232i	−0.299203	+	0.117132i
$311$	−3.39980	+	12.6882i	−0.192785	+	0.719484i	0.800044	+	0.599941i	$0.204809\pi$
$311$	−3.39980	+	12.6882i	−0.192785	+	0.719484i	−0.992829	+	0.119543i	$0.961857\pi$
$312$	−9.74527	−	10.8798i	−0.551717	−	0.615948i
$313$	6.83546	+	25.5103i	0.386363	+	1.44193i	0.836007	+	0.548718i	$0.184884\pi$
$313$	6.83546	+	25.5103i	0.386363	+	1.44193i	−0.449644	+	0.893208i	$0.648449\pi$
$314$	−5.81006	−	7.88651i	−0.327880	−	0.445061i
$315$	−5.59037	−	4.22388i	−0.314981	−	0.237989i
$316$	−8.42968	+	4.43672i	−0.474207	+	0.249585i
$317$	10.5799	+	13.7879i	0.594224	+	0.774407i	0.989559	−	0.144129i	$-0.0460382\pi$
$317$	10.5799	+	13.7879i	0.594224	+	0.774407i	−0.395335	+	0.918537i	$0.629372\pi$
$318$	0.370350	−	23.3855i	0.0207682	−	1.31139i
$319$	15.0259	+	26.0256i	0.841288	+	1.45715i
$320$	−3.80200	−	3.70035i	−0.212538	−	0.206856i
$321$	−26.6584	−	15.2592i	−1.48792	−	0.851684i
$322$	12.4071	+	22.4946i	0.691423	+	1.25358i
$323$	−0.673663	+	1.62637i	−0.0374836	+	0.0904935i
$324$	15.8019	−	8.61977i	0.877883	−	0.478876i
$325$	12.5612	−	5.20300i	0.696768	−	0.288611i
$326$	−29.4166	+	3.28888i	−1.62923	+	0.182154i
$327$	−2.39942	+	0.652507i	−0.132688	+	0.0360837i
$328$	3.04338	−	9.16911i	0.168043	−	0.506280i
$329$	4.69178	−	17.5100i	0.258666	−	0.965356i
$330$	−3.07681	−	7.77404i	−0.169373	−	0.427947i
$331$	14.5022	+	1.90924i	0.797110	+	0.104942i	0.518070	−	0.855338i	$-0.326650\pi$
$331$	14.5022	+	1.90924i	0.797110	+	0.104942i	0.279040	+	0.960280i	$0.409984\pi$
$332$	1.52495	+	16.5681i	0.0836923	+	0.909291i
$333$	3.38544	+	24.3145i	0.185521	+	1.33243i
$334$	0.973618	+	3.94029i	0.0532740	+	0.215603i
$335$	−4.23103	−	2.44279i	−0.231166	−	0.133464i
$336$	4.97672	−	23.8864i	0.271502	−	1.30311i
$337$	−28.8231	+	16.6410i	−1.57010	+	0.906495i	−0.573940	+	0.818898i	$0.694586\pi$
$337$	−28.8231	+	16.6410i	−1.57010	+	0.906495i	−0.996156	+	0.0875974i	$0.972081\pi$
$338$	4.02962	+	4.19042i	0.219183	+	0.227929i
$339$	−1.54425	+	3.76777i	−0.0838723	+	0.204637i
$340$	−0.167367	−	0.453454i	−0.00907674	−	0.0245920i
$341$	−11.8807	−	28.6825i	−0.643374	−	1.55324i
$342$	−20.2852	−	2.92097i	−1.09690	−	0.157948i
$343$	3.97770	+	3.97770i	0.214776	+	0.214776i
$344$	27.0188	+	5.18435i	1.45676	+	0.279522i
$345$	−1.51213	+	5.72858i	−0.0814105	+	0.308417i
$346$	−24.8901	−	10.8849i	−1.33810	−	0.585175i
$347$	−18.7227	−	14.3664i	−1.00509	−	0.771230i	−0.0314898	−	0.999504i	$-0.510025\pi$
$347$	−18.7227	−	14.3664i	−1.00509	−	0.771230i	−0.973597	+	0.228274i	$0.926692\pi$
$348$	−14.7995	+	13.7873i	−0.793336	+	0.739075i
$349$	8.63989	+	11.2597i	0.462483	+	0.602719i	0.965130	−	0.261773i	$-0.0843071\pi$
$349$	8.63989	+	11.2597i	0.462483	+	0.602719i	−0.502647	+	0.864492i	$0.667640\pi$
$350$	19.4433	+	11.7385i	1.03929	+	0.627450i
$351$	13.3293	−	7.89547i	0.711465	−	0.421429i
$352$	19.8945	−	21.2575i	1.06038	−	1.13303i
$353$	5.11951	−	8.86725i	0.272484	−	0.471956i	−0.697013	−	0.717058i	$-0.745488\pi$
$353$	5.11951	−	8.86725i	0.272484	−	0.471956i	0.969497	+	0.245102i	$0.0788215\pi$
$354$	3.48929	+	6.27090i	0.185454	+	0.333295i
$355$	−5.46103	+	0.718958i	−0.289841	+	0.0381583i
$356$	0.735319	+	3.24733i	0.0389718	+	0.172108i
$357$	1.34665	−	1.76858i	0.0712723	−	0.0936033i
$358$	1.60728	+	14.3759i	0.0849472	+	0.759790i
$359$	7.16055	−	7.16055i	0.377919	−	0.377919i	−0.492432	−	0.870351i	$-0.663892\pi$
$359$	7.16055	−	7.16055i	0.377919	−	0.377919i	0.870351	+	0.492432i	$0.163892\pi$
$360$	4.63398	−	3.19257i	0.244232	−	0.168263i
$361$	3.06494	+	3.06494i	0.161312	+	0.161312i
$362$	−8.96244	+	11.2188i	−0.471055	+	0.589646i
$363$	24.7484	−	10.3592i	1.29895	−	0.543718i
$364$	3.55317	−	20.6972i	0.186237	−	1.08483i
$365$	−0.701306	−	5.32695i	−0.0367081	−	0.278825i
$366$	6.31770	+	25.1654i	0.330232	+	1.31542i
$367$	−11.9247	−	6.88475i	−0.622466	−	0.359381i	0.155362	−	0.987858i	$-0.450345\pi$
$367$	−11.9247	−	6.88475i	−0.622466	−	0.359381i	−0.777829	+	0.628476i	$0.783679\pi$
$368$	−20.2853	+	3.76608i	−1.05745	+	0.196321i
$369$	8.91209	+	5.05730i	0.463945	+	0.263272i
$370$	1.84100	+	7.45062i	0.0957088	+	0.387339i
$371$	26.6778	−	20.4706i	1.38504	−	1.06278i
$372$	17.0173	−	12.1258i	0.882305	−	0.628693i
$373$	−2.62505	+	3.42103i	−0.135920	+	0.177134i	−0.856354	−	0.516389i	$-0.827276\pi$
$373$	−2.62505	+	3.42103i	−0.135920	+	0.177134i	0.720434	+	0.693523i	$0.243943\pi$
$374$	2.46999	−	0.966953i	0.127720	−	0.0499999i
$375$	2.88168	+	10.5966i	0.148809	+	0.547206i
$376$	12.1598	+	8.00631i	0.627094	+	0.412894i
$377$	−12.3097	+	12.3097i	−0.633982	+	0.633982i
$378$	23.8256	+	10.1039i	1.22545	+	0.519687i
$379$	19.5152	−	8.08347i	1.00243	−	0.415220i	0.179742	−	0.983714i	$-0.442474\pi$
$379$	19.5152	−	8.08347i	1.00243	−	0.415220i	0.822688	+	0.568494i	$0.192474\pi$
$380$	−6.40219	−	0.250562i	−0.328425	−	0.0128536i
$381$	−8.57664	+	6.63197i	−0.439395	+	0.339766i
$382$	25.3754	+	0.496368i	1.29832	+	0.0253964i
$383$	−18.6303	−	32.2686i	−0.951962	−	1.64885i	−0.741171	−	0.671316i	$-0.765729\pi$
$383$	−18.6303	−	32.2686i	−0.951962	−	1.64885i	−0.210791	−	0.977531i	$-0.567604\pi$
$384$	16.9481	+	9.83674i	0.864880	+	0.501979i
$385$	6.01034	−	10.4102i	0.306315	−	0.530553i
$386$	−3.34705	+	5.54396i	−0.170361	+	0.282180i
$387$	−10.9659	+	27.0417i	−0.557426	+	1.37461i
$388$	0.0111976	+	0.0212753i	0.000568473	+	0.00108009i
$389$	2.28752	−	17.3755i	0.115982	−	0.880972i	−0.830229	−	0.557422i	$-0.811790\pi$
$389$	2.28752	−	17.3755i	0.115982	−	0.880972i	0.946211	−	0.323549i	$-0.104876\pi$
$390$	3.88863	−	2.88718i	0.196909	−	0.146198i
$391$	−1.81564	−	0.486498i	−0.0918207	−	0.0246033i
$392$	13.6591	−	6.85135i	0.689889	−	0.346046i
$393$	−5.01702	+	5.05451i	−0.253075	+	0.254966i
$394$	−7.47198	−	5.96921i	−0.376433	−	0.300724i
$395$	−1.20879	−	2.91828i	−0.0608208	−	0.146834i
$396$	18.0139	+	25.0825i	0.905232	+	1.26044i
$397$	−15.8643	−	6.57122i	−0.796208	−	0.329800i	−0.0527716	−	0.998607i	$-0.516806\pi$
$397$	−15.8643	−	6.57122i	−0.796208	−	0.329800i	−0.743437	+	0.668806i	$0.766806\pi$
$398$	−20.8102	−	6.01466i	−1.04312	−	0.301488i
$399$	−14.8278	−	25.4631i	−0.742317	−	1.27475i
$400$	−13.8668	+	11.8507i	−0.693338	+	0.592533i
$401$	−10.2206	+	5.90086i	−0.510392	+	0.294675i	−0.732995	−	0.680234i	$-0.761878\pi$
$401$	−10.2206	+	5.90086i	−0.510392	+	0.294675i	0.222603	+	0.974909i	$0.428545\pi$
$402$	17.3541	+	4.94583i	0.865542	+	0.246676i
$403$	14.2679	−	10.9482i	0.710735	−	0.545366i
$404$	−23.1477	−	19.2457i	−1.15164	−	0.957511i
$405$	2.36596	+	5.47967i	0.117565	+	0.272287i
$406$	−28.7521	−	4.35894i	−1.42694	−	0.216330i
$407$	−40.6815	+	10.9006i	−2.01651	+	0.540321i
$408$	1.00738	+	1.47392i	0.0498730	+	0.0729702i
$409$	28.8411	+	7.72795i	1.42610	+	0.382123i	0.887644	−	0.460531i	$-0.152341\pi$
$409$	28.8411	+	7.72795i	1.42610	+	0.382123i	0.538457	+	0.842653i	$0.319007\pi$
$410$	2.93510	+	1.28357i	0.144954	+	0.0633911i
$411$	9.79006	−	12.8575i	0.482908	−	0.634213i
$412$	−8.99553	+	8.31793i	−0.443178	+	0.409795i
$413$	−3.94842	+	9.53232i	−0.194289	+	0.469055i
$414$	0.265055	−	21.8819i	0.0130268	−	1.07544i
$415$	−5.51703			−0.270821
$416$	14.8773	+	7.94478i	0.729421	+	0.389525i
$417$	0.137447	+	36.9177i	0.00673082	+	1.80787i
$418$	0.687639	−	35.1536i	0.0336335	−	1.71942i
$419$	21.2173	−	2.79331i	1.03653	−	0.136462i	0.406994	−	0.913431i	$-0.366577\pi$
$419$	21.2173	−	2.79331i	1.03653	−	0.136462i	0.629539	+	0.776968i	$0.283244\pi$
$420$	7.73592	+	2.36923i	0.377474	+	0.115607i
$421$	−1.82883	+	13.8913i	−0.0891317	+	0.677022i	0.887300	+	0.461194i	$0.152579\pi$
$421$	−1.82883	+	13.8913i	−0.0891317	+	0.677022i	−0.976431	+	0.215829i	$0.930755\pi$
$422$	29.6156	−	21.8180i	1.44166	−	1.06209i
$423$	−10.8376	+	11.0002i	−0.526941	+	0.534847i
$424$	8.85403	+	25.5140i	0.429990	+	1.23907i
$425$	−1.60521	+	0.430114i	−0.0778640	+	0.0208636i
$426$	18.9169	−	7.48694i	0.916527	−	0.362743i
$427$	−22.7094	+	29.5954i	−1.09898	+	1.43222i
$428$	34.9571	+	6.00123i	1.68972	+	0.290080i
$429$	16.2584	+	21.0258i	0.784961	+	1.01513i
$430$	−2.53299	+	8.76391i	−0.122152	+	0.422633i
$431$		−	18.2965i		−	0.881310i	−0.897677	−	0.440655i	$-0.854746\pi$
$431$		−	18.2965i		−	0.881310i	0.897677	−	0.440655i	$-0.145254\pi$
$432$	−13.7295	+	15.6045i	−0.660559	+	0.750774i
$433$		−	25.3301i		−	1.21729i	−0.793443	−	0.608644i	$-0.791714\pi$
$433$		−	25.3301i		−	1.21729i	0.793443	−	0.608644i	$-0.208286\pi$
$434$	28.8612	+	8.34160i	1.38538	+	0.400410i
$435$	−4.10271	−	5.30573i	−0.196710	−	0.254390i
$436$	2.34452	−	1.65748i	0.112282	−	0.0793788i
$437$	−15.1680	+	19.7673i	−0.725582	+	0.945596i
$438$	7.30312	+	18.4525i	0.348957	+	0.881692i
$439$	5.33132	−	1.42852i	0.254450	−	0.0681796i	−0.129339	−	0.991600i	$-0.541286\pi$
$439$	5.33132	−	1.42852i	0.254450	−	0.0681796i	0.383789	+	0.923421i	$0.374619\pi$
$440$	6.41447	+	7.21512i	0.305798	+	0.343967i
$441$	4.31141	+	15.6241i	0.205305	+	0.744006i
$442$	0.911381	+	1.23710i	0.0433500	+	0.0588428i
$443$	−3.55957	+	27.0376i	−0.169120	+	1.28460i	0.670699	+	0.741730i	$0.265994\pi$
$443$	−3.55957	+	27.0376i	−0.169120	+	1.28460i	−0.839819	+	0.542866i	$0.817339\pi$
$444$	−13.2958	−	25.0353i	−0.630993	−	1.18812i
$445$	−1.09460	+	0.144107i	−0.0518890	+	0.00683132i
$446$	21.1981	+	0.414656i	1.00376	+	0.0196345i
$447$	0.00692606	+	1.86031i	0.000327591	+	0.0879896i
$448$	4.05554	+	27.8805i	0.191606	+	1.31723i
$449$	19.5429			0.922287			0.461144	−	0.887325i	$-0.347439\pi$
$449$	19.5429			0.922287			0.461144	+	0.887325i	$0.347439\pi$
$450$	−9.46998	−	16.8712i	−0.446419	−	0.795314i
$451$	−6.72753	+	16.2417i	−0.316787	+	0.764791i
$452$	0.183877	−	4.69829i	0.00864884	−	0.220989i
$453$	−7.23052	+	9.49599i	−0.339720	+	0.446161i
$454$	−14.8741	+	34.0122i	−0.698077	+	1.59627i
$455$	6.72612	+	1.80226i	0.315326	+	0.0844912i
$456$	23.1604	−	4.86018i	1.08459	−	0.227599i
$457$	−19.3015	+	5.17182i	−0.902886	+	0.241928i	−0.680255	−	0.732975i	$-0.738131\pi$
$457$	−19.3015	+	5.17182i	−0.902886	+	0.241928i	−0.222631	+	0.974903i	$0.571464\pi$
$458$	2.95986	−	19.5236i	0.138305	−	0.912280i
$459$	−1.74125	+	0.744140i	−0.0812745	+	0.0347335i
$460$	−0.627038	−	6.81257i	−0.0292358	−	0.317638i
$461$	22.6154	−	17.3534i	1.05331	−	0.808230i	0.0713710	−	0.997450i	$-0.477263\pi$
$461$	22.6154	−	17.3534i	1.05331	−	0.808230i	0.981935	+	0.189220i	$0.0605959\pi$
$462$	−12.1689	+	42.6987i	−0.566150	+	1.98652i
$463$	27.8633	−	16.0869i	1.29492	−	0.747620i	0.315394	−	0.948961i	$-0.397863\pi$
$463$	27.8633	−	16.0869i	1.29492	−	0.747620i	0.979521	+	0.201341i	$0.0645300\pi$
$464$	10.5969	−	20.8133i	0.491947	−	0.966231i
$465$	3.48669	+	5.98754i	0.161691	+	0.277665i
$466$	5.56855	−	19.2667i	0.257958	−	0.892511i
$467$	24.3959	+	10.1051i	1.12891	+	0.467609i	0.867409	−	0.497595i	$-0.165783\pi$
$467$	24.3959	+	10.1051i	1.12891	+	0.467609i	0.261498	+	0.965204i	$0.415783\pi$
$468$	−11.3340	+	13.8402i	−0.523914	+	0.639765i
$469$	9.92844	+	23.9694i	0.458453	+	1.10680i
$470$	−3.01320	+	3.77178i	−0.138988	+	0.173979i
$471$	−8.45160	+	8.51476i	−0.389429	+	0.392340i
$472$	−6.26698	−	5.42133i	−0.288461	−	0.249537i
$473$	−48.3565	−	12.9571i	−2.22344	−	0.595768i
$474$	6.95489	+	9.36726i	0.319449	+	0.430252i
$475$	−2.87528	+	21.8399i	−0.131927	+	1.00208i
$476$	−0.760788	+	2.45146i	−0.0348707	+	0.112363i
$477$	−28.3711	+	3.95026i	−1.29902	+	0.180870i
$478$	−20.5000	−	12.3764i	−0.937647	−	0.566085i
$479$	−15.7051	+	27.2021i	−0.717586	+	1.24289i	0.244368	+	0.969683i	$0.421419\pi$
$479$	−15.7051	+	27.2021i	−0.717586	+	1.24289i	−0.961954	+	0.273212i	$0.911914\pi$
$480$	−3.76312	+	5.29722i	−0.171762	+	0.241784i
$481$	−12.1988	−	21.1289i	−0.556215	−	0.963393i
$482$	−0.290931	+	14.8730i	−0.0132515	+	0.677446i
$483$	24.8898	−	19.2462i	1.13252	−	0.875734i
$484$	−22.7457	+	21.0324i	−1.03390	+	0.956017i
$485$	−0.00736530	+	0.00305081i	−0.000334441	+	0.000138530i
$486$	−13.4039	−	17.5024i	−0.608013	−	0.793927i
$487$	5.85560	−	5.85560i	0.265343	−	0.265343i	−0.561878	−	0.827220i	$-0.689921\pi$
$487$	5.85560	−	5.85560i	0.265343	−	0.265343i	0.827220	+	0.561878i	$0.189921\pi$
$488$	−16.8134	−	24.7977i	−0.761106	−	1.12254i
$489$	9.51308	+	34.9818i	0.430196	+	1.58193i
$490$	1.84716	+	4.71839i	0.0834461	+	0.213155i
$491$	13.9023	−	18.1179i	0.627404	−	0.817649i	−0.366204	−	0.930535i	$-0.619343\pi$
$491$	13.9023	−	18.1179i	0.627404	−	0.817649i	0.993608	+	0.112886i	$0.0360094\pi$
$492$	−11.6690	−	1.95857i	−0.526080	−	0.0882993i
$493$	1.68812	−	1.29534i	0.0760289	−	0.0583391i
$494$	19.7732	−	4.88581i	0.889637	−	0.219823i
$495$	−8.82957	+	5.18580i	−0.396860	+	0.233084i
$496$	−13.6602	+	19.8887i	−0.613361	+	0.893031i
$497$	25.3316	+	14.6252i	1.13628	+	0.656030i
$498$	19.7641	−	4.96173i	0.885652	−	0.222340i
$499$	1.26745	+	9.62721i	0.0567387	+	0.430973i	0.996113	+	0.0880806i	$0.0280733\pi$
$499$	1.26745	+	9.62721i	0.0567387	+	0.430973i	−0.939375	+	0.342892i	$0.888593\pi$
$500$	−7.31994	−	10.3541i	−0.327358	−	0.463050i
$501$	4.58548	−	1.91940i	0.204864	−	0.0857525i
$502$	2.16432	+	1.72903i	0.0965983	+	0.0771704i
$503$	−19.8682	−	19.8682i	−0.885879	−	0.885879i	0.108245	−	0.994124i	$-0.465477\pi$
$503$	−19.8682	−	19.8682i	−0.885879	−	0.885879i	−0.994124	+	0.108245i	$0.965477\pi$
$504$	−29.8438	−	1.53022i	−1.32935	−	0.0681614i
$505$	7.05834	−	7.05834i	0.314092	−	0.314092i
$506$	37.3110	−	4.17151i	1.65868	−	0.185446i
$507$	4.31340	−	5.66487i	0.191565	−	0.251586i
$508$	6.67864	−	10.5886i	0.296317	−	0.469792i
$509$	4.39242	−	0.578273i	0.194690	−	0.0256315i	−0.0325503	−	0.999470i	$-0.510363\pi$
$509$	4.39242	−	0.578273i	0.194690	−	0.0256315i	0.227241	+	0.973839i	$0.427030\pi$
$510$	−0.517298	+	0.287838i	−0.0229064	+	0.0127457i
$511$	−14.2661	+	24.7097i	−0.631096	+	1.09309i
$512$	−22.2778	−	3.96249i	−0.984547	−	0.175119i
$513$	0.280345	+	25.0988i	0.0123775	+	1.10814i
$514$	11.4819	−	19.0183i	0.506446	−	0.838862i
$515$	−2.47315	−	3.22307i	−0.108980	−	0.142025i
$516$	1.19234	−	33.6737i	0.0524900	−	1.48240i
$517$	−21.0179	−	16.1276i	−0.924366	−	0.709291i
$518$	16.3299	−	37.3410i	0.717495	−	1.64067i
$519$	−8.49161	+	32.1697i	−0.372740	+	1.41209i
$520$	−3.07547	+	4.67096i	−0.134868	+	0.204835i
$521$	2.21180	+	2.21180i	0.0969006	+	0.0969006i	0.753895	−	0.656995i	$-0.228173\pi$
$521$	2.21180	+	2.21180i	0.0969006	+	0.0969006i	−0.656995	+	0.753895i	$0.728173\pi$
$522$	19.4692	+	15.3174i	0.852142	+	0.670425i
$523$	5.64862	+	13.6370i	0.246997	+	0.596303i	0.997946	−	0.0640565i	$-0.0204038\pi$
$523$	5.64862	+	13.6370i	0.246997	+	0.596303i	−0.750949	+	0.660360i	$0.770404\pi$
$524$	3.44168	−	7.46858i	0.150350	−	0.326266i
$525$	10.5491	−	25.7385i	0.460402	−	1.12332i
$526$	12.8885	−	12.3939i	0.561965	−	0.540402i
$527$	−1.90369	+	1.09910i	−0.0829263	+	0.0478775i
$528$	−29.4680	−	20.0785i	−1.28243	−	0.873803i
$529$	−3.12194	−	1.80245i	−0.135736	−	0.0783674i
$530$	−8.69367	+	2.14814i	−0.377629	+	0.0933094i
$531$	6.93286	−	5.40226i	0.300861	−	0.234438i
$532$	26.1625	+	21.7524i	1.13429	+	0.943084i
$533$	−10.0966	−	1.32925i	−0.437334	−	0.0575761i
$534$	3.79167	−	1.50067i	0.164082	−	0.0649404i
$535$	−3.04397	+	11.3603i	−0.131602	+	0.491147i
$536$	−20.7823	+	1.50360i	−0.897661	+	0.0649458i
$537$	17.0956	−	4.64905i	0.737731	−	0.200621i
$538$	0.176118	+	1.57525i	0.00759299	+	0.0679137i
$539$	−25.6900	+	10.6411i	−1.10655	+	0.458347i
$540$	−4.73528	−	5.00764i	−0.203774	−	0.215495i
$541$	6.82229	−	16.4705i	0.293313	−	0.708120i	−0.706687	−	0.707526i	$-0.749811\pi$
$541$	6.82229	−	16.4705i	0.293313	−	0.708120i	1.00000		0.000593663i	$-0.000188969\pi$
$542$	13.9039	−	7.66883i	0.597223	−	0.329405i
$543$	15.2628	+	8.73641i	0.654992	+	0.374915i
$544$	−1.67613	−	1.20013i	−0.0718633	−	0.0514550i
$545$	0.476037	+	0.824520i	0.0203912	+	0.0353186i
$546$	−25.7164	−	0.407265i	−1.10056	−	0.0174293i
$547$	−3.77777	−	4.92329i	−0.161526	−	0.210505i	0.705578	−	0.708633i	$-0.250688\pi$
$547$	−3.77777	−	4.92329i	−0.161526	−	0.210505i	−0.867104	+	0.498128i	$0.834021\pi$
$548$	−5.53088	+	17.8220i	−0.236268	+	0.761317i
$549$	29.2673	−	12.3790i	1.24910	−	0.528324i
$550$	26.7233	−	19.6873i	1.13949	−	0.839469i
$551$	−7.30006	−	27.2442i	−0.310993	−	1.16064i
$552$	8.37315	+	23.8413i	0.356385	+	1.01475i
$553$	−4.34143	+	16.2025i	−0.184617	+	0.688998i
$554$	−4.59745	−	11.7437i	−0.195327	−	0.498944i
$555$	8.67060	−	3.62936i	0.368046	−	0.154058i
$556$	−14.7608	−	39.9921i	−0.625998	−	1.69604i
$557$	−4.90627	−	2.03224i	−0.207885	−	0.0861089i	0.276311	−	0.961068i	$-0.410888\pi$
$557$	−4.90627	−	2.03224i	−0.207885	−	0.0861089i	−0.484196	+	0.874959i	$0.660888\pi$
$558$	−17.8755	−	18.3139i	−0.756732	−	0.775289i
$559$		−	29.0004i		−	1.22659i
$560$	−9.32926	+	0.491787i	−0.394233	+	0.0207818i
$561$	−1.63479	−	2.80735i	−0.0690209	−	0.118526i
$562$	−18.8260	+	18.1036i	−0.794126	+	0.763654i
$563$	4.16537	+	31.6391i	0.175549	+	1.33343i	0.821569	+	0.570109i	$0.193099\pi$
$563$	4.16537	+	31.6391i	0.175549	+	1.33343i	−0.646020	+	0.763321i	$0.723568\pi$
$564$	7.40228	−	16.2219i	0.311692	−	0.683064i
$565$	1.54576	+	0.203503i	0.0650307	+	0.00856146i
$566$	−5.42974	+	35.8153i	−0.228229	+	1.50543i
$567$	7.74662	−	30.7345i	0.325328	−	1.29073i
$568$	−17.5568	+	15.6086i	−0.736669	+	0.654922i
$569$	−2.31938	−	8.65606i	−0.0972336	−	0.362881i	0.900115	−	0.435652i	$-0.143482\pi$
$569$	−2.31938	−	8.65606i	−0.0972336	−	0.362881i	−0.997349	+	0.0727715i	$0.976816\pi$
$570$	0.900924	+	7.79516i	0.0377356	+	0.326504i
$571$	−18.5366	−	14.2236i	−0.775732	−	0.595240i	0.143183	−	0.989696i	$-0.454266\pi$
$571$	−18.5366	−	14.2236i	−0.775732	−	0.595240i	−0.918915	+	0.394456i	$0.870933\pi$
$572$	−25.9581	−	16.3728i	−1.08536	−	0.684580i
$573$	−4.17202	−	30.8030i	−0.174289	−	1.28682i
$574$	−8.21613	−	14.8962i	−0.342935	−	0.621754i
$575$	−23.5214			−0.980912
$576$	8.71689	−	22.3610i	0.363204	−	0.931710i
$577$	−37.3273			−1.55396			−0.776978	−	0.629528i	$-0.783248\pi$
$577$	−37.3273			−1.55396			−0.776978	+	0.629528i	$0.783248\pi$
$578$	11.5206	+	20.8873i	0.479194	+	0.868798i
$579$	7.33893	+	3.00792i	0.304995	+	0.125005i
$580$	6.55037	+	4.13158i	0.271989	+	0.171554i
$581$	23.2433	+	17.8352i	0.964296	+	0.739930i
$582$	0.0236416	−	0.0175531i	0.000979976	−	0.000727600i
$583$	−12.7192	−	47.4687i	−0.526776	−	1.96595i
$584$	−15.2254	−	17.1258i	−0.630031	−	0.708670i
$585$	−4.22551	−	4.16305i	−0.174703	−	0.172121i
$586$	−0.242675	+	1.60072i	−0.0100248	+	0.0661250i
$587$	−3.95447	−	0.520616i	−0.163218	−	0.0214881i	0.0484740	−	0.998824i	$-0.484564\pi$
$587$	−3.95447	−	0.520616i	−0.163218	−	0.0214881i	−0.211692	+	0.977336i	$0.567898\pi$
$588$	−10.8607	−	15.2418i	−0.447888	−	0.628563i
$589$	3.80329	+	28.8888i	0.156712	+	1.19034i
$590$	1.98056	−	1.90456i	0.0815383	−	0.0784095i
$591$	−5.81867	+	10.1654i	−0.239348	+	0.418150i
$592$	24.3314	+	21.8946i	1.00001	+	0.899864i
$593$			15.9184i			0.653691i	0.945078	+	0.326845i	$0.105986\pi$
$593$			15.9184i			0.653691i	−0.945078	+	0.326845i	$0.894014\pi$
$594$	26.9671	−	26.5184i	1.10647	−	1.08806i
$595$	−0.786339	−	0.325712i	−0.0322367	−	0.0133529i
$596$	−0.743808	−	2.01523i	−0.0304675	−	0.0825470i
$597$	−3.36495	+	26.3161i	−0.137718	+	1.07705i
$598$	7.92819	+	20.2518i	0.324208	+	0.828158i
$599$	0.282184	−	1.05313i	0.0115297	−	0.0430296i	−0.959921	−	0.280270i	$-0.909576\pi$
$599$	0.282184	−	1.05313i	0.0115297	−	0.0430296i	0.971451	+	0.237240i	$0.0762428\pi$
$600$	16.9500	+	14.5528i	0.691981	+	0.594117i
$601$	3.38870	+	12.6468i	0.138228	+	0.515874i	0.999964	+	0.00851666i	$0.00271097\pi$
$601$	3.38870	+	12.6468i	0.138228	+	0.515874i	−0.861736	+	0.507358i	$0.830622\pi$
$602$	39.0031	−	28.7339i	1.58965	−	1.17111i
$603$	2.72148	−	21.9324i	0.110827	−	0.893157i
$604$	4.08488	−	13.1626i	0.166211	−	0.535577i
$605$	−6.25350	−	8.14972i	−0.254241	−	0.331333i
$606$	−18.9378	+	31.6335i	−0.769294	+	1.28503i
$607$	−12.8234	−	22.2108i	−0.520486	−	0.901508i	−0.999716	−	0.0238187i	$-0.992418\pi$
$607$	−12.8234	−	22.2108i	−0.520486	−	0.901508i	0.479231	−	0.877689i	$-0.340916\pi$
$608$	−23.1997	+	14.4388i	−0.940871	+	0.585570i
$609$	0.132601	+	35.6162i	0.00537328	+	1.44324i
$610$	8.69905	−	4.79805i	0.352214	−	0.194267i
$611$	5.87293	−	14.1785i	0.237593	−	0.573601i
$612$	1.59429	−	1.49638i	0.0644455	−	0.0604874i
$613$	3.23462	−	1.33982i	0.130645	−	0.0541149i	−0.316403	−	0.948625i	$-0.602475\pi$
$613$	3.23462	−	1.33982i	0.130645	−	0.0541149i	0.447048	+	0.894510i	$0.352475\pi$
$614$	0.105414	+	0.942851i	0.00425417	+	0.0380504i
$615$	1.00135	−	3.79353i	0.0403783	−	0.152970i
$616$	−3.69953	−	51.1338i	−0.149058	−	2.06024i
$617$	5.45373	−	20.3536i	0.219559	−	0.819405i	−0.764953	−	0.644086i	$-0.777238\pi$
$617$	5.45373	−	20.3536i	0.219559	−	0.819405i	0.984512	−	0.175319i	$-0.0560956\pi$
$618$	11.7584	+	9.32205i	0.472993	+	0.374988i
$619$	−9.37900	−	1.23477i	−0.376974	−	0.0496296i	−0.0603413	−	0.998178i	$-0.519219\pi$
$619$	−9.37900	−	1.23477i	−0.376974	−	0.0496296i	−0.316633	+	0.948548i	$0.602552\pi$
$620$	−6.15200	−	5.11498i	−0.247070	−	0.205422i
$621$	−26.5317	+	3.79489i	−1.06468	+	0.152284i
$622$	−18.0345	+	4.45619i	−0.723117	+	0.178677i
$623$	5.07743	+	2.93145i	0.203423	+	0.117446i
$624$	6.81670	−	19.4991i	0.272886	−	0.780588i
$625$	−16.1049	+	9.29815i	−0.644195	+	0.371926i
$626$	−26.9216	+	25.8886i	−1.07601	+	1.03472i
$627$	−42.6728	+	5.77969i	−1.70419	+	0.230818i
$628$	5.79780	−	12.5815i	0.231357	−	0.502055i
$629$	1.14119	+	2.75508i	0.0455022	+	0.109852i
$630$	1.41227	−	9.80776i	0.0562662	−	0.390750i
$631$	2.19037	+	2.19037i	0.0871974	+	0.0871974i	0.749360	−	0.662163i	$-0.230361\pi$
$631$	2.19037	+	2.19037i	0.0871974	+	0.0871974i	−0.662163	+	0.749360i	$0.730361\pi$
$632$	−11.2518	−	7.40845i	−0.447572	−	0.294692i
$633$	−31.9748	−	31.7376i	−1.27088	−	1.26146i
$634$	−9.84791	+	22.5189i	−0.391110	+	0.894339i
$635$	3.29332	+	2.52705i	0.130691	+	0.100283i
$636$	29.2121	−	15.5141i	1.15834	−	0.615174i
$637$	−9.80592	−	12.7793i	−0.388525	−	0.506335i
$638$	−21.9656	+	36.3831i	−0.869626	+	1.44042i
$639$	−12.6188	−	21.4854i	−0.499192	−	0.849948i
$640$	1.98545	−	7.23557i	0.0784818	−	0.286011i
$641$	0.687774	−	1.19126i	0.0271654	−	0.0470519i	−0.852123	−	0.523341i	$-0.824685\pi$
$641$	0.687774	−	1.19126i	0.0271654	−	0.0470519i	0.879289	+	0.476290i	$0.158019\pi$
$642$	0.687861	−	43.4344i	0.0271477	−	1.71422i
$643$	36.1711	−	4.76202i	1.42645	−	0.187796i	0.622559	−	0.782573i	$-0.286093\pi$
$643$	36.1711	−	4.76202i	1.42645	−	0.187796i	0.803891	+	0.594777i	$0.202760\pi$
$644$	−19.3817	+	30.7285i	−0.763745	+	1.21087i
$645$	11.0826	+	1.41710i	0.436379	+	0.0557983i
$646$	−2.47412	+	0.276615i	−0.0973430	+	0.0108833i
$647$	−1.20432	+	1.20432i	−0.0473466	+	0.0473466i	−0.730384	−	0.683037i	$-0.760659\pi$
$647$	−1.20432	+	1.20432i	−0.0473466	+	0.0473466i	0.683037	+	0.730384i	$0.260659\pi$
$648$	21.4672	+	13.6806i	0.843311	+	0.537426i
$649$	10.6623	+	10.6623i	0.418530	+	0.418530i
$650$	15.0226	+	12.0012i	0.589234	+	0.470727i
$651$	4.66678	−	36.4972i	0.182905	−	1.43044i
$652$	−24.1648	−	34.1813i	−0.946367	−	1.33864i
$653$	4.54597	+	34.5301i	0.177898	+	1.35127i	0.814540	+	0.580108i	$0.196990\pi$
$653$	4.54597	+	34.5301i	0.177898	+	1.35127i	−0.636642	+	0.771159i	$0.719677\pi$
$654$	−2.44688	−	2.52562i	−0.0956804	−	0.0987597i
$655$	2.36149	+	1.36340i	0.0922709	+	0.0532726i
$656$	13.4332	−	2.49394i	0.524477	−	0.0973720i
$657$	20.9579	−	12.3090i	0.817644	−	0.480220i
$658$	24.8879	−	6.14962i	0.970230	−	0.239737i
$659$	−18.5413	+	14.2272i	−0.722265	+	0.554214i	−0.903168	−	0.429287i	$-0.858765\pi$
$659$	−18.5413	+	14.2272i	−0.722265	+	0.554214i	0.180903	+	0.983501i	$0.442098\pi$
$660$	7.52538	−	9.11996i	0.292925	−	0.354994i
$661$	−7.01686	+	9.14455i	−0.272924	+	0.355682i	−0.909626	−	0.415429i	$-0.863632\pi$
$661$	−7.01686	+	9.14455i	−0.272924	+	0.355682i	0.636702	+	0.771110i	$0.280298\pi$
$662$	7.54095	+	19.2626i	0.293087	+	0.748664i
$663$	1.32574	−	1.33565i	0.0514875	−	0.0518723i
$664$	−19.4753	+	13.2047i	−0.755789	+	0.512442i
$665$	−7.97763	+	7.97763i	−0.309359	+	0.309359i
$666$	−27.7973	+	20.7996i	−1.07712	+	0.805969i
$667$	27.8245	−	11.5253i	1.07737	−	0.446261i
$668$	−4.21442	+	3.89696i	−0.163061	+	0.150778i
$669$	−3.48523	−	25.7323i	−0.134747	−	0.994868i
$670$	0.135126	−	6.90792i	0.00522036	−	0.266876i
$671$	27.2589	+	47.2138i	1.05232	+	1.82267i
$672$	32.9787	−	10.1520i	1.27218	−	0.391622i
$673$	−21.3364	+	36.9557i	−0.822458	+	1.42454i	0.0813884	+	0.996682i	$0.474065\pi$
$673$	−21.3364	+	36.9557i	−0.822458	+	1.42454i	−0.903847	+	0.427857i	$0.859269\pi$
$674$	−40.2940	−	24.3267i	−1.55207	−	0.937028i
$675$	−18.6366	+	14.6339i	−0.717322	+	0.563261i
$676$	−2.43685	+	7.85218i	−0.0937250	+	0.302007i
$677$	4.87762	−	37.0492i	0.187462	−	1.42392i	−0.596253	−	0.802797i	$-0.703344\pi$
$677$	4.87762	−	37.0492i	0.187462	−	1.42392i	0.783715	−	0.621120i	$-0.213322\pi$
$678$	−5.72053	+	0.661149i	−0.219696	+	0.0253913i
$679$	0.0408926	+	0.0109571i	0.00156931	+	0.000420497i
$680$	0.447215	−	0.516975i	0.0171499	−	0.0198251i
$681$	43.9597	+	11.6037i	1.68454	+	0.444655i
$682$	27.4039	−	34.3030i	1.04935	−	1.31353i
$683$	1.78395	+	4.30684i	0.0682611	+	0.164797i	0.954328	−	0.298760i	$-0.0965730\pi$
$683$	1.78395	+	4.30684i	0.0682611	+	0.164797i	−0.886067	+	0.463557i	$0.846573\pi$
$684$	−10.2380	−	27.1150i	−0.391460	−	1.03677i
$685$	−5.71663	−	2.36791i	−0.218421	−	0.0904730i
$686$	−2.20890	+	7.64259i	−0.0843362	+	0.291796i
$687$	−24.1845	+	0.0900407i	−0.922698	+	0.00343527i
$688$	12.0344	+	36.9995i	0.458806	+	1.41059i
$689$	24.6540	−	14.2340i	0.939241	−	0.542271i
$690$	−8.12675	+	2.04020i	−0.309380	+	0.0776690i
$691$	−7.76824	+	5.96078i	−0.295518	+	0.226759i	−0.745869	−	0.666093i	$-0.767965\pi$
$691$	−7.76824	+	5.96078i	−0.295518	+	0.226759i	0.450351	+	0.892851i	$0.351299\pi$
$692$	−3.52122	−	38.2570i	−0.133857	−	1.45431i
$693$	53.9635	+	6.69604i	2.04990	+	0.254362i
$694$	5.00256	−	32.9976i	0.189895	−	1.25257i
$695$	13.6538	−	3.65852i	0.517918	−	0.138776i
$696$	−27.1817	−	8.90983i	−1.03032	−	0.337726i
$697$	1.20233	+	0.322164i	0.0455416	+	0.0122028i
$698$	−8.04215	+	18.3897i	−0.304400	+	0.696061i
$699$	−24.3642	−	3.11537i	−0.921539	−	0.117834i
$700$	−1.25610	+	32.0951i	−0.0474763	+	1.21308i
$701$	1.53880	−	3.71500i	0.0581197	−	0.140313i	−0.892152	−	0.451735i	$-0.850805\pi$
$701$	1.53880	−	3.71500i	0.0581197	−	0.140313i	0.950272	+	0.311422i	$0.100805\pi$
$702$	18.8814	+	11.1134i	0.712633	+	0.419449i
$703$	39.5288			1.49086
$704$	39.9123	+	10.1169i	1.50425	+	0.381297i
$705$	5.13141	+	2.93720i	0.193260	+	0.110621i
$706$	14.4774	+	0.283192i	0.544864	+	0.0106581i
$707$	−52.5547	+	6.91896i	−1.97652	+	0.260214i
$708$	−5.38225	+	8.60407i	−0.202277	+	0.323361i
$709$	−4.54255	+	34.5041i	−0.170599	+	1.29583i	0.665147	+	0.746712i	$0.268369\pi$
$709$	−4.54255	+	34.5041i	−0.170599	+	1.29583i	−0.835746	+	0.549116i	$0.814965\pi$
$710$	−4.62030	−	6.27155i	−0.173397	−	0.235367i
$711$	10.0283	−	10.1788i	0.376091	−	0.381734i
$712$	−3.51907	+	3.12856i	−0.131883	+	0.117248i
$713$	−30.0529	+	8.05266i	−1.12549	+	0.301575i
$714$	3.10989	+	0.459634i	0.116385	+	0.0172014i
$715$	6.19511	−	8.07363i	0.231684	−	0.301937i
$716$	−16.7044	+	11.8094i	−0.624274	+	0.441337i
$717$	−11.1224	+	27.1372i	−0.415374	+	1.01346i
$718$	13.7580	+	3.97640i	0.513443	+	0.148398i
$719$			48.6842i			1.81562i	0.419386	+	0.907808i	$0.362245\pi$
$719$			48.6842i			1.81562i	−0.419386	+	0.907808i	$0.637755\pi$
$720$	7.11858	+	3.55786i	0.265294	+	0.132594i
$721$			21.5739i			0.803455i
$722$	−1.70202	+	5.88884i	−0.0633427	+	0.219160i
$723$	18.0543	−	2.44530i	0.671445	−	0.0909418i
$724$	−20.0142	−	3.43591i	−0.743821	−	0.127695i
$725$	16.2092	−	21.1242i	0.601995	−	0.784535i
$726$	29.7319	+	23.5713i	1.10345	+	0.874815i
$727$	19.8906	−	5.32966i	0.737701	−	0.197666i	0.129645	−	0.991560i	$-0.458616\pi$
$727$	19.8906	−	5.32966i	0.737701	−	0.197666i	0.608056	+	0.793894i	$0.291950\pi$
$728$	28.0571	−	9.73655i	1.03986	−	0.360861i
$729$	−18.6607	+	19.5136i	−0.691136	+	0.722725i
$730$	6.11757	−	4.50686i	0.226421	−	0.166806i
$731$	−0.462673	+	3.51435i	−0.0171126	+	0.129983i
$732$	−26.8482	+	25.0119i	−0.992338	+	0.924467i
$733$	−15.6428	+	2.05941i	−0.577780	+	0.0760662i	−0.413752	−	0.910389i	$-0.635782\pi$
$733$	−15.6428	+	2.05941i	−0.577780	+	0.0760662i	−0.164028	+	0.986456i	$0.552449\pi$
$734$	0.380839	−	19.4693i	0.0140570	−	0.718625i
$735$	5.36285	−	3.12292i	0.197812	−	0.115191i
$736$	−18.5190	−	22.5478i	−0.682618	−	0.831124i
$737$	37.9160			1.39665
$738$	−0.175523	+	14.4904i	−0.00646107	+	0.533400i
$739$	0.521486	−	1.25898i	0.0191832	−	0.0463123i	−0.913998	−	0.405719i	$-0.867021\pi$
$739$	0.521486	−	1.25898i	0.0191832	−	0.0463123i	0.933181	+	0.359407i	$0.117021\pi$
$740$	−7.96896	+	7.36869i	−0.292945	+	0.270878i
$741$	−9.63194	−	23.0109i	−0.353838	−	0.845325i
$742$	43.5709	+	19.0544i	1.59954	+	0.699507i
$743$	46.2290	+	12.3870i	1.69598	+	0.454436i	0.971922	−	0.235304i	$-0.0756085\pi$
$743$	46.2290	+	12.3870i	1.69598	+	0.454436i	0.724057	+	0.689740i	$0.242275\pi$
$744$	26.6390	+	12.7910i	0.976632	+	0.468942i
$745$	0.688024	−	0.184355i	0.0252072	−	0.00675426i
$746$	−6.02936	−	0.914074i	−0.220750	−	0.0334666i
$747$	−9.72211	−	22.9856i	−0.355713	−	0.841001i
$748$	2.88447	+	2.39824i	0.105467	+	0.0876883i
$749$	49.5493	−	38.0205i	1.81049	−	1.38924i
$750$	−11.1539	+	10.8062i	−0.407285	+	0.394586i
$751$	23.6971	−	13.6815i	0.864721	−	0.499247i	−0.000869577	−	1.00000i	$-0.500277\pi$
$751$	23.6971	−	13.6815i	0.864721	−	0.499247i	0.865590	+	0.500753i	$0.166943\pi$
$752$	−1.60915	+	20.5264i	−0.0586796	+	0.748522i
$753$	1.68542	−	2.94450i	0.0614202	−	0.107304i
$754$	−23.6514	−	6.83584i	−0.861332	−	0.248946i
$755$	4.22206	+	1.74884i	0.153657	+	0.0636466i
$756$	3.76129	+	36.4053i	0.136797	+	1.32405i
$757$	−10.1539	−	24.5137i	−0.369050	−	0.890966i	−0.993907	−	0.110226i	$-0.964843\pi$
$757$	−10.1539	−	24.5137i	−0.369050	−	0.890966i	0.624856	−	0.780740i	$-0.285157\pi$
$758$	23.3394	+	18.6453i	0.847724	+	0.677228i
$759$	−12.0661	−	44.3698i	−0.437971	−	1.61052i
$760$	−4.06254	−	8.09923i	−0.147364	−	0.293790i
$761$	5.59207	+	1.49839i	0.202712	+	0.0543166i	0.358746	−	0.933435i	$-0.383204\pi$
$761$	5.59207	+	1.49839i	0.202712	+	0.0543166i	−0.156034	+	0.987752i	$0.549871\pi$
$762$	−14.0706	−	6.09104i	−0.509725	−	0.220655i
$763$	0.659925	−	5.01262i	0.0238909	−	0.181469i
$764$	16.7172	+	31.7624i	0.604806	+	1.14912i
$765$	0.445643	+	0.571905i	0.0161122	+	0.0206773i
$766$	27.2346	−	45.1106i	0.984027	−	1.62991i
$767$	−4.36744	+	7.56462i	−0.157699	+	0.273143i
$768$	−0.605347	+	27.7062i	−0.0218436	+	0.999761i
$769$	−23.5101	−	40.7207i	−0.847795	−	1.46842i	−0.883171	−	0.469050i	$-0.844596\pi$
$769$	−23.5101	−	40.7207i	−0.847795	−	1.46842i	0.0353762	−	0.999374i	$-0.488737\pi$
$770$	16.9965	+	0.332469i	0.612513	+	0.0119814i
$771$	−25.1759	−	10.3185i	−0.906686	−	0.371613i
$772$	−9.15141	−	0.358159i	−0.329366	−	0.0128904i
$773$	−42.6292	+	17.6576i	−1.53326	+	0.635099i	−0.980195	−	0.198036i	$-0.936544\pi$
$773$	−42.6292	+	17.6576i	−1.53326	+	0.635099i	−0.553070	+	0.833135i	$0.686544\pi$
$774$	−40.9767	+	4.89054i	−1.47288	+	0.175787i
$775$	−19.4505	+	19.4505i	−0.698682	+	0.698682i
$776$	−0.0186978	+	0.0283979i	−0.000671214	+	0.00101942i
$777$	−48.2621	−	12.7394i	−1.73139	−	0.457024i
$778$	23.0792	−	9.03504i	0.827428	−	0.323922i
$779$	10.0444	−	13.0901i	0.359877	−	0.469001i
$780$	6.23132	+	2.84345i	0.223117	+	0.101812i
$781$	33.9140	−	26.0231i	1.21354	−	0.931181i
$782$	−0.637664	−	2.58066i	−0.0228028	−	0.0922843i
$783$	14.8755	−	26.4429i	0.531607	−	0.944991i
$784$	17.8137	+	12.2350i	0.636205	+	0.436965i
$785$	3.97813	+	2.29677i	0.141985	+	0.0819753i
$786$	−9.68592	−	2.76044i	−0.345485	−	0.0984617i
$787$	−5.21244	−	39.5924i	−0.185803	−	1.41132i	−0.789327	−	0.613972i	$-0.789571\pi$
$787$	−5.21244	−	39.5924i	−0.185803	−	1.41132i	0.603524	−	0.797345i	$-0.293763\pi$
$788$	2.28840	−	13.3299i	0.0815210	−	0.474859i
$789$	−17.4235	−	13.2667i	−0.620293	−	0.472309i
$790$	2.78819	−	3.49013i	0.0991994	−	0.124173i
$791$	−5.85444	−	5.85444i	−0.208160	−	0.208160i
$792$	−18.7568	+	39.4391i	−0.666494	+	1.40141i
$793$	−22.3314	+	22.3314i	−0.793012	+	0.793012i
$794$	−2.69823	−	24.1337i	−0.0957568	−	0.856473i
$795$	4.23487	+	10.1172i	0.150195	+	0.358819i
$796$	−6.76554	−	29.8782i	−0.239798	−	1.05900i
$797$	−24.7257	+	3.25520i	−0.875830	+	0.115305i	−0.555019	−	0.831838i	$-0.687289\pi$
$797$	−24.7257	+	3.25520i	−0.875830	+	0.115305i	−0.320811	+	0.947143i	$0.603956\pi$
$798$	21.4043	−	35.7536i	0.757703	−	1.26566i
$799$	−0.937903	+	1.62450i	−0.0331806	+	0.0574706i
$800$	−24.1464	−	9.07753i	−0.853705	−	0.320939i
$801$	−2.52930	−	4.30649i	−0.0893683	−	0.152162i
$802$	−14.2881	−	8.62616i	−0.504531	−	0.304600i
$803$	25.3842	+	33.0814i	0.895790	+	1.16742i
$804$	5.72854	+	24.8683i	0.202030	+	0.877038i
$805$	−9.55735	−	7.33361i	−0.336852	−	0.258476i
$806$	23.3028	+	10.1907i	0.820805	+	0.358953i
$807$	1.87326	−	0.509422i	0.0659420	−	0.0179325i
$808$	8.02246	−	41.8099i	0.282229	−	1.47087i
$809$	38.0030	+	38.0030i	1.33611	+	1.33611i	0.899789	+	0.436325i	$0.143720\pi$
$809$	38.0030	+	38.0030i	1.33611	+	1.33611i	0.436325	+	0.899789i	$0.356280\pi$
$810$	−5.16970	+	6.67258i	−0.181645	+	0.234450i
$811$	2.57804	+	6.22395i	0.0905273	+	0.218552i	0.962658	−	0.270721i	$-0.0872621\pi$
$811$	2.57804	+	6.22395i	0.0905273	+	0.218552i	−0.872131	+	0.489273i	$0.837262\pi$
$812$	−14.2404	−	38.5821i	−0.499740	−	1.35397i
$813$	−11.8961	−	15.3843i	−0.417213	−	0.539552i
$814$	−41.2848	−	42.9322i	−1.44703	−	1.50477i
$815$	12.0209	−	6.94027i	0.421074	−	0.243107i
$816$	−1.13716	+	2.25420i	−0.0398085	+	0.0789129i
$817$	40.6913	+	23.4932i	1.42361	+	0.821922i
$818$	10.1292	+	40.9934i	0.354159	+	1.43330i
$819$	4.34400	+	31.1990i	0.151792	+	1.09018i
$820$	0.415231	+	4.51136i	0.0145005	+	0.157543i
$821$	−38.5054	−	5.06934i	−1.34385	−	0.176921i	−0.575946	−	0.817488i	$-0.695366\pi$
$821$	−38.5054	−	5.06934i	−1.34385	−	0.176921i	−0.767903	+	0.640567i	$0.778700\pi$
$822$	22.6087	+	3.34151i	0.788570	+	0.116549i
$823$	−4.52971	+	16.9051i	−0.157896	+	0.589275i	0.840944	+	0.541122i	$0.182000\pi$
$823$	−4.52971	+	16.9051i	−0.157896	+	0.589275i	−0.998840	+	0.0481532i	$0.984666\pi$
$824$	−16.4445	−	5.45821i	−0.572873	−	0.190146i
$825$	−28.8522	−	28.6381i	−1.00450	−	0.997051i
$826$	−14.5011	+	1.62127i	−0.504558	+	0.0564113i
$827$	6.40373	−	2.65251i	0.222679	−	0.0922368i	−0.268555	−	0.963264i	$-0.586546\pi$
$827$	6.40373	−	2.65251i	0.222679	−	0.0922368i	0.491234	+	0.871028i	$0.336546\pi$
$828$	27.2783	−	14.6175i	0.947986	−	0.507994i
$829$	−7.76228	+	18.7398i	−0.269595	+	0.650860i	−0.999464	−	0.0327264i	$-0.989581\pi$
$829$	−7.76228	+	18.7398i	−0.269595	+	0.650860i	0.729869	+	0.683587i	$0.239581\pi$
$830$	−3.76824	−	6.83196i	−0.130797	−	0.237141i
$831$	−13.3478	+	7.77273i	−0.463028	+	0.269633i
$832$	0.323150	+	23.8496i	0.0112032	+	0.826837i
$833$	0.984429	+	1.70508i	0.0341084	+	0.0590775i
$834$	−45.6228	+	25.3857i	−1.57979	+	0.879035i
$835$	−1.15867	−	1.51001i	−0.0400976	−	0.0522562i
$836$	44.0018	−	23.1590i	1.52183	−	0.800972i
$837$	−18.8017	+	25.0778i	−0.649880	+	0.866817i
$838$	17.9509	+	24.3664i	0.620103	+	0.841722i
$839$	−11.7000	−	43.6649i	−0.403928	−	1.50748i	−0.806024	−	0.591883i	$-0.798385\pi$
$839$	−11.7000	−	43.6649i	−0.403928	−	1.50748i	0.402096	−	0.915598i	$-0.368282\pi$
$840$	2.34987	+	11.1979i	0.0810781	+	0.386365i
$841$	−1.31812	+	4.91929i	−0.0454524	+	0.169631i
$842$	−18.4513	+	7.22333i	−0.635875	+	0.248933i
$843$	25.4502	+	19.3785i	0.876550	+	0.667431i
$844$	47.2461	+	21.7720i	1.62628	+	0.749424i
$845$	−2.51869	−	1.04327i	−0.0866455	−	0.0358897i
$846$	−21.0242	−	5.90727i	−0.722828	−	0.203096i
$847$			54.5509i			1.87439i
$848$	−25.5475	+	28.3908i	−0.877304	+	0.974945i
$849$	44.3655	−	0.165176i	1.52262	−	0.00566882i
$850$	−1.62901	−	1.69402i	−0.0558747	−	0.0581043i
$851$	5.50925	+	41.8469i	0.188855	+	1.43449i
$852$	22.1920	+	18.3118i	0.760284	+	0.627353i
$853$	−15.4839	−	2.03850i	−0.530160	−	0.0697969i	−0.139306	−	0.990249i	$-0.544487\pi$
$853$	−15.4839	−	2.03850i	−0.530160	−	0.0697969i	−0.390854	+	0.920453i	$0.627820\pi$
$854$	−52.1601	−	7.90768i	−1.78488	−	0.270595i
$855$	9.26439	−	2.55647i	0.316835	−	0.0874294i
$856$	16.4448	+	47.3877i	0.562072	+	1.61968i
$857$	6.36520	+	23.7553i	0.217431	+	0.811464i	0.985297	+	0.170853i	$0.0546523\pi$
$857$	6.36520	+	23.7553i	0.217431	+	0.811464i	−0.767865	+	0.640611i	$0.778681\pi$
$858$	−14.9323	+	34.4944i	−0.509779	+	1.17762i
$859$	−7.35907	−	5.64681i	−0.251088	−	0.192667i	0.475547	−	0.879690i	$-0.342250\pi$
$859$	−7.35907	−	5.64681i	−0.251088	−	0.192667i	−0.726635	+	0.687024i	$0.758917\pi$
$860$	−12.5828	+	2.84921i	−0.429069	+	0.0971574i
$861$	−16.4823	+	12.7451i	−0.561714	+	0.434350i
$862$	22.6572	−	12.4968i	0.771709	−	0.425644i
$863$	20.8415			0.709454			0.354727	−	0.934970i	$-0.384574\pi$
$863$	20.8415			0.709454			0.354727	+	0.934970i	$0.384574\pi$
$864$	−28.7012	−	6.34354i	−0.976435	−	0.215812i
$865$	12.7393			0.433148
$866$	31.3673	−	17.3009i	1.06590	−	0.587910i
$867$	23.1113	−	17.8710i	0.784902	−	0.606932i
$868$	9.38298	+	41.4374i	0.318479	+	1.40648i
$869$	19.4484	+	14.9233i	0.659743	+	0.506238i
$870$	3.76807	−	8.70446i	0.127750	−	0.295109i
$871$	5.68474	+	21.2157i	0.192620	+	0.718868i
$872$	3.65387	+	1.77122i	0.123736	+	0.0599810i
$873$	−0.0256897	−	0.0253100i	−0.000869465	−	0.000856612i
$874$	−34.8386	−	5.28167i	−1.17843	−	0.178655i
$875$	−22.1373	−	2.91443i	−0.748378	−	0.0985258i
$876$	−17.8622	+	21.6471i	−0.603509	+	0.731389i
$877$	−3.95256	−	30.0227i	−0.133469	−	1.01379i	−0.918801	−	0.394720i	$-0.870841\pi$
$877$	−3.95256	−	30.0227i	−0.133469	−	1.01379i	0.785333	−	0.619074i	$-0.212492\pi$
$878$	5.41039	+	5.62627i	0.182592	+	0.189878i
$879$	1.98286	−	0.00738231i	0.0668801	−	0.000248999i
$880$	−4.55356	+	12.8714i	−0.153500	+	0.433893i
$881$		−	33.1137i		−	1.11563i	−0.829966	−	0.557814i	$-0.811640\pi$
$881$		−	33.1137i		−	1.11563i	0.829966	−	0.557814i	$-0.188360\pi$
$882$	−16.4032	+	16.0106i	−0.552324	+	0.539104i
$883$	7.72620	+	3.20030i	0.260007	+	0.107699i	0.508879	−	0.860838i	$-0.330060\pi$
$883$	7.72620	+	3.20030i	0.260007	+	0.107699i	−0.248872	+	0.968536i	$0.580060\pi$
$884$	−0.909458	+	1.97356i	−0.0305884	+	0.0663780i
$885$	−2.67744	−	2.03868i	−0.0900013	−	0.0685296i
$886$	−35.9130	+	14.0592i	−1.20652	+	0.472330i
$887$	7.20893	−	26.9041i	0.242052	−	0.903351i	−0.732790	−	0.680455i	$-0.761782\pi$
$887$	7.20893	−	26.9041i	0.242052	−	0.903351i	0.974842	−	0.222896i	$-0.0715512\pi$
$888$	21.9209	−	33.5643i	0.735616	−	1.12635i
$889$	−5.70545	−	21.2930i	−0.191354	−	0.714145i
$890$	−0.926086	−	1.25706i	−0.0310425	−	0.0421367i
$891$	−37.1651	−	27.6483i	−1.24508	−	0.926252i
$892$	13.9652	+	26.5337i	0.467590	+	0.888413i
$893$	15.1367	+	19.7265i	0.506529	+	0.660121i
$894$	−2.29896	+	1.27920i	−0.0768889	+	0.0427830i
$895$	−3.39172	−	5.87462i	−0.113373	−	0.196367i
$896$	−31.7556	+	24.0651i	−1.06088	+	0.803958i
$897$	23.0179	−	13.4039i	0.768545	−	0.447543i
$898$	13.3482	+	24.2008i	0.445435	+	0.807590i
$899$	13.4783	−	32.5394i	0.449525	−	1.08525i
$900$	14.4240	−	23.2504i	0.480801	−	0.775012i
$901$	−3.21473	+	1.33158i	−0.107098	+	0.0443615i
$902$	−24.7077	+	2.76241i	−0.822678	+	0.0919783i
$903$	−42.1102	−	41.7978i	−1.40134	−	1.39094i
$904$	5.94367	−	2.98132i	0.197684	−	0.0991572i
$905$	1.74278	−	6.50415i	0.0579320	−	0.216205i
$906$	−16.6979	−	2.46790i	−0.554749	−	0.0819905i
$907$	29.6142	+	3.89879i	0.983325	+	0.129457i	0.605008	−	0.796219i	$-0.293170\pi$
$907$	29.6142	+	3.89879i	0.983325	+	0.129457i	0.378316	+	0.925676i	$0.376503\pi$
$908$	−52.2779	+	4.81173i	−1.73490	+	0.159683i
$909$	41.8454	+	16.9690i	1.38792	+	0.562826i
$910$	2.36226	+	9.56020i	0.0783082	+	0.316918i
$911$	3.23823	+	1.86959i	0.107287	+	0.0619423i	0.552683	−	0.833391i	$-0.313604\pi$
$911$	3.23823	+	1.86959i	0.107287	+	0.0619423i	−0.445396	+	0.895334i	$0.646937\pi$
$912$	21.8376	+	25.3609i	0.723114	+	0.839783i
$913$	37.0803	−	21.4083i	1.22718	−	0.708512i
$914$	−19.5878	−	20.3694i	−0.647906	−	0.673759i
$915$	−7.44284	−	9.62529i	−0.246053	−	0.318202i
$916$	26.1985	−	9.66970i	0.865624	−	0.319496i
$917$	−5.54141	−	13.3782i	−0.182994	−	0.441785i
$918$	−2.11080	−	1.64799i	−0.0696669	−	0.0543919i
$919$	−19.7686	−	19.7686i	−0.652106	−	0.652106i	0.301394	−	0.953500i	$-0.402548\pi$
$919$	−19.7686	−	19.7686i	−0.652106	−	0.652106i	−0.953500	+	0.301394i	$0.902548\pi$
$920$	8.00800	−	5.42960i	0.264016	−	0.179009i
$921$	1.12123	−	0.304910i	0.0369457	−	0.0100471i
$922$	36.9362	+	16.1529i	1.21643	+	0.531966i
$923$	19.6459	+	15.0748i	0.646652	+	0.496194i
$924$	−61.1871	+	14.0948i	−2.01291	+	0.463683i
$925$	22.7167	+	29.6049i	0.746919	+	0.973404i
$926$	38.9521	+	23.5165i	1.28005	+	0.772802i
$927$	9.07011	−	15.9836i	0.297902	−	0.524970i
$928$	33.0117	−	1.09332i	1.08366	−	0.0358901i
$929$	0.818762	−	1.41814i	0.0268627	−	0.0465276i	−0.852282	−	0.523083i	$-0.824782\pi$
$929$	0.818762	−	1.41814i	0.0268627	−	0.0465276i	0.879144	+	0.476556i	$0.158115\pi$
$930$	−5.03313	+	8.40731i	−0.165043	+	0.275687i
$931$	25.8748	−	3.40649i	0.848013	−	0.111643i
$932$	27.6621	−	6.26374i	0.906102	−	0.205176i
$933$	8.78498	+	20.9875i	0.287607	+	0.687099i
$934$	4.14930	+	37.1124i	0.135769	+	1.21435i
$935$	−0.879549	+	0.879549i	−0.0287643	+	0.0287643i
$936$	−24.8802	−	4.58219i	−0.813236	−	0.149774i
$937$	−34.2841	−	34.2841i	−1.12001	−	1.12001i	−0.991739	−	0.128273i	$-0.959057\pi$
$937$	−34.2841	−	34.2841i	−1.12001	−	1.12001i	−0.128273	−	0.991739i	$-0.540943\pi$
$938$	−22.9009	+	28.6663i	−0.747741	+	0.935988i
$939$	36.3944	+	27.7117i	1.18769	+	0.904338i
$940$	−6.72881	−	1.15516i	−0.219470	−	0.0376773i
$941$	−1.17410	−	8.91816i	−0.0382745	−	0.290724i	−0.999868	−	0.0162462i	$-0.994828\pi$
$941$	−1.17410	−	8.91816i	−0.0382745	−	0.290724i	0.961594	−	0.274478i	$-0.0885049\pi$
$942$	−16.3168	−	4.65020i	−0.531629	−	0.151512i
$943$	15.2577	+	8.80902i	0.496858	+	0.286861i
$944$	2.43298	−	11.4635i	0.0791868	−	0.373106i
$945$	−12.1351	+	0.135545i	−0.394756	+	0.00440927i
$946$	−16.9831	−	68.7317i	−0.552169	−	2.23466i
$947$	−10.3095	+	7.91078i	−0.335015	+	0.257066i	−0.762545	−	0.646935i	$-0.776050\pi$
$947$	−10.3095	+	7.91078i	−0.335015	+	0.257066i	0.427530	+	0.904001i	$0.359384\pi$
$948$	−6.84953	+	15.0105i	−0.222462	+	0.487519i
$949$	−14.7047	+	19.1635i	−0.477335	+	0.622075i
$950$	−29.0091	+	11.3565i	−0.941179	+	0.368453i
$951$	29.1050	+	7.68263i	0.943793	+	0.249126i
$952$	−3.55538	+	0.732281i	−0.115230	+	0.0237334i
$953$	28.2602	−	28.2602i	0.915437	−	0.915437i	−0.0812562	−	0.996693i	$-0.525893\pi$
$953$	28.2602	−	28.2602i	0.915437	−	0.915437i	0.996693	+	0.0812562i	$0.0258932\pi$
$954$	−24.2698	−	32.4350i	−0.785763	−	1.05012i
$955$	−10.9958	+	4.55462i	−0.355817	+	0.147384i
$956$	1.32437	−	33.8393i	0.0428331	−	1.09444i
$957$	48.1629	+	19.7400i	1.55688	+	0.638102i
$958$	−44.4123	−	0.868749i	−1.43490	−	0.0280680i
$959$	16.4294	+	28.4565i	0.530532	+	0.918908i
$960$	−9.13004	−	1.04192i	−0.294671	−	0.0336277i
$961$	−2.69260	+	4.66373i	−0.0868582	+	0.150443i
$962$	17.8327	−	29.5376i	0.574950	−	0.952331i
$963$	−52.6944	+	7.33692i	−1.69805	+	0.236429i
$964$	−18.6165	+	9.79826i	−0.599598	+	0.315581i
$965$	0.396388	−	3.01086i	0.0127602	−	0.0969231i
$966$	40.8335	+	17.6764i	1.31380	+	0.568730i
$967$	−32.1519	−	8.61509i	−1.03394	−	0.277043i	−0.298338	−	0.954460i	$-0.596432\pi$
$967$	−32.1519	−	8.61509i	−1.03394	−	0.277043i	−0.735599	+	0.677418i	$0.763099\pi$
$968$	−41.5810	−	13.8014i	−1.33646	−	0.443594i
$969$	0.800111	+	2.94219i	0.0257033	+	0.0945169i
$970$	−0.00880858	−	0.00703699i	−0.000282826	−	0.000225944i
$971$	−15.4074	−	37.1968i	−0.494448	−	1.19370i	−0.952435	−	0.304743i	$-0.901429\pi$
$971$	−15.4074	−	37.1968i	−0.494448	−	1.19370i	0.457987	−	0.888959i	$-0.348571\pi$
$972$	12.5189	−	28.5531i	0.401543	−	0.915840i
$973$	−69.3506	−	28.7260i	−2.22328	−	0.920913i
$974$	11.2507	+	3.25174i	0.360496	+	0.104192i
$975$	11.6986	−	20.4378i	0.374654	−	0.654535i
$976$	19.2241	−	37.7580i	0.615348	−	1.20860i
$977$	31.2571	−	18.0463i	1.00000	−	0.577352i	0.0917535	−	0.995782i	$-0.470753\pi$
$977$	31.2571	−	18.0463i	1.00000	−	0.577352i	0.908249	+	0.418430i	$0.137419\pi$
$978$	−36.8218	+	35.6737i	−1.17743	+	1.14072i
$979$	6.79768	−	5.21604i	0.217255	−	0.166705i
$980$	−4.58133	+	5.51016i	−0.146345	+	0.176016i
$981$	−2.59633	+	3.43628i	−0.0828945	+	0.109712i
$982$	31.9317	+	4.84097i	1.01898	+	0.154481i
$983$	0.923447	−	0.247437i	0.0294534	−	0.00789201i	−0.244062	−	0.969760i	$-0.578480\pi$
$983$	0.923447	−	0.247437i	0.0294534	−	0.00789201i	0.273516	+	0.961868i	$0.411813\pi$
$984$	−5.54479	−	15.7880i	−0.176761	−	0.503302i
$985$	4.33193	+	1.16074i	0.138027	+	0.0369841i
$986$	2.75708	+	1.20572i	0.0878034	+	0.0383980i
$987$	−12.1234	−	28.9631i	−0.385893	−	0.921904i
$988$	19.5557	+	21.1488i	0.622151	+	0.672833i
$989$	−19.1996	+	46.3520i	−0.610513	+	1.47391i
$990$	−12.4525	−	7.39201i	−0.395768	−	0.234934i
$991$	42.0988			1.33731			0.668657	−	0.743571i	$-0.266869\pi$
$991$	42.0988			1.33731			0.668657	+	0.743571i	$0.266869\pi$
$992$	−33.9592	−	3.33158i	−1.07821	−	0.105778i
$993$	21.8936	−	12.7492i	0.694773	−	0.404584i
$994$	−0.809012	+	41.3584i	−0.0256603	+	1.31181i
$995$	10.0712	−	1.32590i	0.319280	−	0.0420339i
$996$	19.6436	+	21.0857i	0.622430	+	0.668128i
$997$	−0.935630	+	7.10681i	−0.0296317	+	0.225075i	−0.999853	−	0.0171451i	$-0.994542\pi$
$997$	−0.935630	+	7.10681i	−0.0296317	+	0.225075i	0.970221	+	0.242220i	$0.0778756\pi$
$998$	−11.0561	+	8.14509i	−0.349974	+	0.257828i
$999$	30.4003	+	29.7287i	0.961823	+	0.940574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bc.a.205.30	yes	368
3.2	odd	2		864.2.bk.a.397.17		368
9.4	even	3	inner	288.2.bc.a.13.1	✓	368
9.5	odd	6		864.2.bk.a.685.46		368
32.5	even	8	inner	288.2.bc.a.133.1	yes	368
96.5	odd	8		864.2.bk.a.613.46		368
288.5	odd	24		864.2.bk.a.37.17		368
288.229	even	24	inner	288.2.bc.a.229.30	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.1	✓	368	9.4	even	3	inner
288.2.bc.a.133.1	yes	368	32.5	even	8	inner
288.2.bc.a.205.30	yes	368	1.1	even	1	trivial
288.2.bc.a.229.30	yes	368	288.229	even	24	inner
864.2.bk.a.37.17		368	288.5	odd	24
864.2.bk.a.397.17		368	3.2	odd	2
864.2.bk.a.613.46		368	96.5	odd	8
864.2.bk.a.685.46		368	9.5	odd	6

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bc (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.683019 + 1.23834i) q^{2} +(1.37019 - 1.05951i) q^{3} +(-1.06697 + 1.69162i) q^{4} +(-0.526137 - 0.403719i) q^{5} +(2.24791 + 0.973096i) q^{6} +(0.911495 + 3.40174i) q^{7} +(-2.82356 - 0.165864i) q^{8} +(0.754859 - 2.90348i) q^{9} +O(q^{10})\)	\(q+(0.683019 + 1.23834i) q^{2} +(1.37019 - 1.05951i) q^{3} +(-1.06697 + 1.69162i) q^{4} +(-0.526137 - 0.403719i) q^{5} +(2.24791 + 0.973096i) q^{6} +(0.911495 + 3.40174i) q^{7} +(-2.82356 - 0.165864i) q^{8} +(0.754859 - 2.90348i) q^{9} +(0.140580 - 0.927284i) q^{10} +(5.10279 + 0.671795i) q^{11} +(0.330339 + 3.44831i) q^{12} +(0.389161 + 2.95597i) q^{13} +(-3.58995 + 3.45220i) q^{14} +(-1.14866 + 0.00427652i) q^{15} +(-1.72315 - 3.60981i) q^{16} -0.364422i q^{17} +(4.11108 - 1.04836i) q^{18} +(-4.46287 - 1.84858i) q^{19} +(1.24431 - 0.459267i) q^{20} +(4.85312 + 3.69531i) q^{21} +(2.65339 + 6.77783i) q^{22} +(1.33499 - 4.98224i) q^{23} +(-4.04456 + 2.76434i) q^{24} +(-1.18026 - 4.40481i) q^{25} +(-3.39469 + 2.50090i) q^{26} +(-2.04198 - 4.77811i) q^{27} +(-6.72699 - 2.08766i) q^{28} +(3.55450 + 4.63232i) q^{29} +(-0.789849 - 1.41950i) q^{30} +(-3.01601 - 5.22388i) q^{31} +(3.29323 - 4.59941i) q^{32} +(7.70358 - 4.48599i) q^{33} +(0.451278 - 0.248907i) q^{34} +(0.893778 - 2.15777i) q^{35} +(4.10617 + 4.37486i) q^{36} +(-7.56014 + 3.13151i) q^{37} +(-0.759053 - 6.78917i) q^{38} +(3.66512 + 3.63793i) q^{39} +(1.41862 + 1.22719i) q^{40} +(-0.884042 + 3.29929i) q^{41} +(-1.26127 + 8.53378i) q^{42} +(-9.64364 - 1.26961i) q^{43} +(-6.58094 + 7.91518i) q^{44} +(-1.56935 + 1.22288i) q^{45} +(7.08153 - 1.74980i) q^{46} +(-4.45774 - 2.57368i) q^{47} +(-6.18570 - 3.12044i) q^{48} +(-4.67887 + 2.70134i) q^{49} +(4.64850 - 4.47013i) q^{50} +(-0.386110 - 0.499328i) q^{51} +(-5.41559 - 2.49562i) q^{52} +(-3.65397 - 8.82145i) q^{53} +(4.52222 - 5.79220i) q^{54} +(-2.41355 - 2.41355i) q^{55} +(-2.00943 - 9.75621i) q^{56} +(-8.07359 + 2.19556i) q^{57} +(-3.30859 + 7.56564i) q^{58} +(2.32430 + 1.78350i) q^{59} +(1.21835 - 1.94765i) q^{60} +(6.44833 + 8.40362i) q^{61} +(4.40895 - 7.30285i) q^{62} +(10.5649 - 0.0786691i) q^{63} +(7.94498 + 0.936655i) q^{64} +(0.988629 - 1.71236i) q^{65} +(10.8169 + 6.47563i) q^{66} +(7.30385 - 0.961570i) q^{67} +(0.616463 + 0.388827i) q^{68} +(-3.44956 - 8.24107i) q^{69} +(3.28252 - 0.366998i) q^{70} +(5.87298 - 5.87298i) q^{71} +(-2.61297 + 8.07294i) q^{72} +(5.72879 + 5.72879i) q^{73} +(-9.04159 - 7.22313i) q^{74} +(-6.28415 - 4.78493i) q^{75} +(7.88885 - 5.57709i) q^{76} +(2.36589 + 17.9707i) q^{77} +(-2.00165 + 7.02343i) q^{78} +(4.12486 + 2.38149i) q^{79} +(-0.550739 + 2.59492i) q^{80} +(-7.86038 - 4.38343i) q^{81} +(-4.68946 + 1.15873i) q^{82} +(6.59994 - 5.06432i) q^{83} +(-11.4292 + 4.26685i) q^{84} +(-0.147124 + 0.191736i) q^{85} +(-5.01458 - 12.8093i) q^{86} +(9.77836 + 2.58112i) q^{87} +(-14.2966 - 2.74322i) q^{88} +(1.17717 - 1.17717i) q^{89} +(-2.58623 - 1.10814i) q^{90} +(-9.70073 + 4.01817i) q^{91} +(7.00366 + 7.57419i) q^{92} +(-9.66729 - 3.96222i) q^{93} +(0.142366 - 7.27806i) q^{94} +(1.60177 + 2.77435i) q^{95} +(-0.360779 - 9.79131i) q^{96} +(0.00601054 - 0.0104106i) q^{97} +(-6.54094 - 3.94896i) q^{98} +(5.80242 - 14.3087i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Introduction

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