LMFDB - Embedded newform 81.2.g.a.40.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(4,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("81.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, 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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			40.7
Character	$\chi$	$=$	81.40
Dual form			81.2.g.a.79.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.137343 + 2.35809i) q^{2} +(1.64862 + 0.531080i) q^{3} +(-3.55525 + 0.415549i) q^{4} +(-2.58807 - 0.613384i) q^{5} +(-1.02591 + 3.96054i) q^{6} +(2.74329 - 3.68487i) q^{7} +(-0.647845 - 3.67411i) q^{8} +(2.43591 + 1.75110i) q^{9} +O(q^{10})$	\(q+(0.137343 + 2.35809i) q^{2} +(1.64862 + 0.531080i) q^{3} +(-3.55525 + 0.415549i) q^{4} +(-2.58807 - 0.613384i) q^{5} +(-1.02591 + 3.96054i) q^{6} +(2.74329 - 3.68487i) q^{7} +(-0.647845 - 3.67411i) q^{8} +(2.43591 + 1.75110i) q^{9} +(1.09096 - 6.18715i) q^{10} +(-0.332192 - 0.352103i) q^{11} +(-6.08194 - 1.20304i) q^{12} +(-3.89179 + 1.95453i) q^{13} +(9.06604 + 5.96283i) q^{14} +(-3.94100 - 2.38571i) q^{15} +(1.60898 - 0.381335i) q^{16} +(0.936739 - 0.340945i) q^{17} +(-3.79469 + 5.98459i) q^{18} +(0.818296 + 0.297835i) q^{19} +(9.45612 + 1.10526i) q^{20} +(6.47961 - 4.61806i) q^{21} +(0.784667 - 0.831698i) q^{22} +(-1.22578 - 1.64651i) q^{23} +(0.883194 - 6.40128i) q^{24} +(1.85371 + 0.930971i) q^{25} +(-5.14346 - 8.90874i) q^{26} +(3.08592 + 4.18056i) q^{27} +(-8.22182 + 14.2406i) q^{28} +(-0.693656 + 0.456225i) q^{29} +(5.08445 - 9.62088i) q^{30} +(1.58714 - 3.67940i) q^{31} +(-1.01980 - 3.40637i) q^{32} +(-0.360665 - 0.756906i) q^{33} +(0.932634 + 2.16209i) q^{34} +(-9.36007 + 7.85403i) q^{35} +(-9.38792 - 5.21335i) q^{36} +(0.840131 + 0.704953i) q^{37} +(-0.589935 + 1.97052i) q^{38} +(-7.45410 + 1.15543i) q^{39} +(-0.576973 + 9.90625i) q^{40} +(-0.0170132 + 0.292105i) q^{41} +(11.7797 + 14.6452i) q^{42} +(-3.21885 + 10.7517i) q^{43} +(1.32734 + 1.11377i) q^{44} +(-5.23021 - 6.02612i) q^{45} +(3.71426 - 3.11664i) q^{46} +(-1.59945 - 3.70793i) q^{47} +(2.85512 + 0.225819i) q^{48} +(-4.04505 - 13.5114i) q^{49} +(-1.94072 + 4.49909i) q^{50} +(1.72540 - 0.0646067i) q^{51} +(13.0241 - 8.56606i) q^{52} +(0.806764 - 1.39736i) q^{53} +(-9.43431 + 7.85105i) q^{54} +(0.643763 + 1.11503i) q^{55} +(-15.3159 - 7.69192i) q^{56} +(1.19089 + 0.925598i) q^{57} +(-1.17109 - 1.57304i) q^{58} +(-3.61650 + 3.83327i) q^{59} +(15.0026 + 6.84411i) q^{60} +(-4.00687 - 0.468336i) q^{61} +(8.89434 + 3.23728i) q^{62} +(13.1350 - 4.17225i) q^{63} +(11.0001 - 4.00372i) q^{64} +(11.2711 - 2.67130i) q^{65} +(1.73532 - 0.954435i) q^{66} +(12.0501 + 7.92548i) q^{67} +(-3.18866 + 1.60140i) q^{68} +(-1.14642 - 3.36546i) q^{69} +(-19.8061 - 20.9932i) q^{70} +(-2.20143 + 12.4849i) q^{71} +(4.85564 - 10.0842i) q^{72} +(1.00775 + 5.71524i) q^{73} +(-1.54696 + 2.07792i) q^{74} +(2.56166 + 2.51929i) q^{75} +(-3.03301 - 0.718836i) q^{76} +(-2.20876 + 0.258166i) q^{77} +(-3.74838 - 17.4187i) q^{78} +(0.376437 + 6.46317i) q^{79} -4.39806 q^{80} +(2.86731 + 8.53103i) q^{81} -0.691147 q^{82} +(-0.738471 - 12.6791i) q^{83} +(-21.1176 + 19.1109i) q^{84} +(-2.63348 + 0.307810i) q^{85} +(-25.7956 - 6.11366i) q^{86} +(-1.38587 + 0.383756i) q^{87} +(-1.07846 + 1.44862i) q^{88} +(-2.74643 - 15.5758i) q^{89} +(13.4918 - 13.1610i) q^{90} +(-3.47410 + 19.7026i) q^{91} +(5.04215 + 5.34437i) q^{92} +(4.57065 - 5.22305i) q^{93} +(8.52396 - 4.28089i) q^{94} +(-1.93512 - 1.27275i) q^{95} +(0.127788 - 6.15742i) q^{96} +(1.97203 - 0.467379i) q^{97} +(31.3056 - 11.3943i) q^{98} +(-0.192623 - 1.43939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{27}\right)$

Coefficient data

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

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

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

$2$	0.137343	+	2.35809i	0.0971162	+	1.66742i	0.597690	+	0.801727i	$0.296085\pi$
$2$	0.137343	+	2.35809i	0.0971162	+	1.66742i	−0.500574	+	0.865694i	$0.666878\pi$
$3$	1.64862	+	0.531080i	0.951832	+	0.306619i
$3$	1.64862	+	0.531080i	0.951832	+	0.306619i
$4$	−3.55525	+	0.415549i	−1.77762	+	0.207774i
$5$	−2.58807	−	0.613384i	−1.15742	−	0.274314i	−0.393315	−	0.919404i	$-0.628672\pi$
$5$	−2.58807	−	0.613384i	−1.15742	−	0.274314i	−0.764107	+	0.645090i	$0.776820\pi$
$6$	−1.02591	+	3.96054i	−0.418824	+	1.61688i
$7$	2.74329	−	3.68487i	1.03687	−	1.39275i	0.120360	−	0.992730i	$-0.461595\pi$
$7$	2.74329	−	3.68487i	1.03687	−	1.39275i	0.916506	−	0.400021i	$-0.130997\pi$
$8$	−0.647845	−	3.67411i	−0.229048	−	1.29899i
$9$	2.43591	+	1.75110i	0.811970	+	0.583700i
$10$	1.09096	−	6.18715i	0.344992	−	1.95655i
$11$	−0.332192	−	0.352103i	−0.100160	−	0.106163i	0.675354	−	0.737493i	$-0.263991\pi$
$11$	−0.332192	−	0.352103i	−0.100160	−	0.106163i	−0.775514	+	0.631330i	$0.782509\pi$
$12$	−6.08194	−	1.20304i	−1.75571	−	0.347286i
$13$	−3.89179	+	1.95453i	−1.07939	+	0.542089i	−0.897403	−	0.441212i	$-0.854549\pi$
$13$	−3.89179	+	1.95453i	−1.07939	+	0.542089i	−0.181985	+	0.983301i	$0.558252\pi$
$14$	9.06604	+	5.96283i	2.42300	+	1.59363i
$15$	−3.94100	−	2.38571i	−1.01756	−	0.615988i
$16$	1.60898	−	0.381335i	0.402245	−	0.0953339i
$17$	0.936739	−	0.340945i	0.227193	−	0.0826914i	−0.225916	−	0.974147i	$-0.572537\pi$
$17$	0.936739	−	0.340945i	0.227193	−	0.0826914i	0.453108	+	0.891456i	$0.350315\pi$
$18$	−3.79469	+	5.98459i	−0.894417	+	1.41058i
$19$	0.818296	+	0.297835i	0.187730	+	0.0683281i	0.434175	−	0.900829i	$-0.357040\pi$
$19$	0.818296	+	0.297835i	0.187730	+	0.0683281i	−0.246445	+	0.969157i	$0.579262\pi$
$20$	9.45612	+	1.10526i	2.11445	+	0.247144i
$21$	6.47961	−	4.61806i	1.41397	−	1.00774i
$22$	0.784667	−	0.831698i	0.167291	−	0.177319i
$23$	−1.22578	−	1.64651i	−0.255593	−	0.343321i	0.655743	−	0.754984i	$-0.272355\pi$
$23$	−1.22578	−	1.64651i	−0.255593	−	0.343321i	−0.911336	+	0.411663i	$0.864948\pi$
$24$	0.883194	−	6.40128i	0.180281	−	1.30666i
$25$	1.85371	+	0.930971i	0.370743	+	0.186194i
$26$	−5.14346	−	8.90874i	−1.00872	−	1.74715i
$27$	3.08592	+	4.18056i	0.593886	+	0.804549i
$28$	−8.22182	+	14.2406i	−1.55378	+	2.69122i
$29$	−0.693656	+	0.456225i	−0.128809	+	0.0847188i	−0.612278	−	0.790642i	$-0.709747\pi$
$29$	−0.693656	+	0.456225i	−0.128809	+	0.0847188i	0.483470	+	0.875361i	$0.339376\pi$
$30$	5.08445	−	9.62088i	0.928290	−	1.75653i
$31$	1.58714	−	3.67940i	0.285059	−	0.660840i	−0.714176	−	0.699967i	$-0.753198\pi$
$31$	1.58714	−	3.67940i	0.285059	−	0.660840i	0.999234	+	0.0391264i	$0.0124575\pi$
$32$	−1.01980	−	3.40637i	−0.180277	−	0.602167i
$33$	−0.360665	−	0.756906i	−0.0627837	−	0.131760i
$34$	0.932634	+	2.16209i	0.159945	+	0.370795i
$35$	−9.36007	+	7.85403i	−1.58214	+	1.32757i
$36$	−9.38792	−	5.21335i	−1.56465	−	0.868891i
$37$	0.840131	+	0.704953i	0.138117	+	0.115894i	0.709229	−	0.704979i	$-0.249043\pi$
$37$	0.840131	+	0.704953i	0.138117	+	0.115894i	−0.571112	+	0.820872i	$0.693488\pi$
$38$	−0.589935	+	1.97052i	−0.0957001	+	0.319661i
$39$	−7.45410	+	1.15543i	−1.19361	+	0.185017i
$40$	−0.576973	+	9.90625i	−0.0912275	+	1.56632i
$41$	−0.0170132	+	0.292105i	−0.00265702	+	0.0456192i	−0.999376	−	0.0353200i	$-0.988755\pi$
$41$	−0.0170132	+	0.292105i	−0.00265702	+	0.0456192i	0.996719	+	0.0809393i	$0.0257920\pi$
$42$	11.7797	+	14.6452i	1.81765	+	2.25981i
$43$	−3.21885	+	10.7517i	−0.490870	+	1.63962i	0.250203	+	0.968193i	$0.419503\pi$
$43$	−3.21885	+	10.7517i	−0.490870	+	1.63962i	−0.741072	+	0.671425i	$0.765682\pi$
$44$	1.32734	+	1.11377i	0.200104	+	0.167907i
$45$	−5.23021	−	6.02612i	−0.779674	−	0.898321i
$46$	3.71426	−	3.11664i	0.547638	−	0.459523i
$47$	−1.59945	−	3.70793i	−0.233303	−	0.540857i	0.760839	−	0.648941i	$-0.224788\pi$
$47$	−1.59945	−	3.70793i	−0.233303	−	0.540857i	−0.994142	+	0.108084i	$0.965529\pi$
$48$	2.85512	+	0.225819i	0.412101	+	0.0325941i
$49$	−4.04505	−	13.5114i	−0.577865	−	1.93020i
$50$	−1.94072	+	4.49909i	−0.274459	+	0.636267i
$51$	1.72540	−	0.0646067i	0.241604	−	0.00904675i
$52$	13.0241	−	8.56606i	1.80611	−	1.18790i
$53$	0.806764	−	1.39736i	0.110818	−	0.191942i	−0.805283	−	0.592891i	$-0.797986\pi$
$53$	0.806764	−	1.39736i	0.110818	−	0.191942i	0.916100	+	0.400950i	$0.131320\pi$
$54$	−9.43431	+	7.85105i	−1.28385	+	1.06839i
$55$	0.643763	+	1.11503i	0.0868050	+	0.150351i
$56$	−15.3159	−	7.69192i	−2.04667	−	1.02788i
$57$	1.19089	+	0.925598i	0.157737	+	0.122598i
$58$	−1.17109	−	1.57304i	−0.153771	−	0.206551i
$59$	−3.61650	+	3.83327i	−0.470828	+	0.499049i	−0.918649	−	0.395075i	$-0.870719\pi$
$59$	−3.61650	+	3.83327i	−0.470828	+	0.499049i	0.447821	+	0.894123i	$0.352200\pi$
$60$	15.0026	+	6.84411i	1.93683	+	0.883571i
$61$	−4.00687	−	0.468336i	−0.513027	−	0.0599643i	−0.144359	−	0.989525i	$-0.546112\pi$
$61$	−4.00687	−	0.468336i	−0.513027	−	0.0599643i	−0.368668	+	0.929561i	$0.620186\pi$
$62$	8.89434	+	3.23728i	1.12958	+	0.411134i
$63$	13.1350	−	4.17225i	1.65485	−	0.525654i
$64$	11.0001	−	4.00372i	1.37502	−	0.500465i
$65$	11.2711	−	2.67130i	1.39801	−	0.331334i
$66$	1.73532	−	0.954435i	0.213603	−	0.117483i
$67$	12.0501	+	7.92548i	1.47215	+	0.968251i	0.996044	+	0.0888660i	$0.0283243\pi$
$67$	12.0501	+	7.92548i	1.47215	+	0.968251i	0.476111	+	0.879385i	$0.342046\pi$
$68$	−3.18866	+	1.60140i	−0.386682	+	0.194199i
$69$	−1.14642	−	3.36546i	−0.138013	−	0.405153i
$70$	−19.8061	−	20.9932i	−2.36728	−	2.50917i
$71$	−2.20143	+	12.4849i	−0.261261	+	1.48169i	0.518213	+	0.855252i	$0.326597\pi$
$71$	−2.20143	+	12.4849i	−0.261261	+	1.48169i	−0.779474	+	0.626434i	$0.784514\pi$
$72$	4.85564	−	10.0842i	0.572243	−	1.18844i
$73$	1.00775	+	5.71524i	0.117948	+	0.668918i	0.985248	+	0.171132i	$0.0547425\pi$
$73$	1.00775	+	5.71524i	0.117948	+	0.668918i	−0.867300	+	0.497786i	$0.834146\pi$
$74$	−1.54696	+	2.07792i	−0.179830	+	0.241554i
$75$	2.56166	+	2.51929i	0.295795	+	0.290902i
$76$	−3.03301	−	0.718836i	−0.347910	−	0.0824561i
$77$	−2.20876	+	0.258166i	−0.251711	+	0.0294208i
$78$	−3.74838	−	17.4187i	−0.424420	−	1.97228i
$79$	0.376437	+	6.46317i	0.0423525	+	0.727164i	0.950922	+	0.309430i	$0.100138\pi$
$79$	0.376437	+	6.46317i	0.0423525	+	0.727164i	−0.908570	+	0.417733i	$0.862825\pi$
$80$	−4.39806			−0.491718
$81$	2.86731	+	8.53103i	0.318590	+	0.947893i
$82$	−0.691147			−0.0763245
$83$	−0.738471	−	12.6791i	−0.0810577	−	1.39171i	−0.756355	−	0.654162i	$-0.773022\pi$
$83$	−0.738471	−	12.6791i	−0.0810577	−	1.39171i	0.675297	−	0.737546i	$-0.264015\pi$
$84$	−21.1176	+	19.1109i	−2.30411	+	2.08517i
$85$	−2.63348	+	0.307810i	−0.285641	+	0.0333866i
$86$	−25.7956	−	6.11366i	−2.78161	−	0.659253i
$87$	−1.38587	+	0.383756i	−0.148581	+	0.0411429i
$88$	−1.07846	+	1.44862i	−0.114964	+	0.154423i
$89$	−2.74643	−	15.5758i	−0.291121	−	1.65103i	−0.682563	−	0.730827i	$-0.739135\pi$
$89$	−2.74643	−	15.5758i	−0.291121	−	1.65103i	0.391442	−	0.920203i	$-0.371976\pi$
$90$	13.4918	−	13.1610i	1.42216	−	1.38729i
$91$	−3.47410	+	19.7026i	−0.364184	+	2.06539i
$92$	5.04215	+	5.34437i	0.525681	+	0.557189i
$93$	4.57065	−	5.22305i	0.473954	−	0.541605i
$94$	8.52396	−	4.28089i	0.879179	−	0.441540i
$95$	−1.93512	−	1.27275i	−0.198539	−	0.130581i
$96$	0.127788	−	6.15742i	0.0130423	−	0.628439i
$97$	1.97203	−	0.467379i	0.200229	−	0.0474551i	−0.129278	−	0.991608i	$-0.541266\pi$
$97$	1.97203	−	0.467379i	0.200229	−	0.0474551i	0.329506	+	0.944153i	$0.393118\pi$
$98$	31.3056	−	11.3943i	3.16234	−	1.15100i
$99$	−0.192623	−	1.43939i	−0.0193593	−	0.144664i
$100$	−6.97727	−	2.53952i	−0.697727	−	0.253952i
$101$	7.17078	+	0.838144i	0.713519	+	0.0833984i	0.465105	−	0.885256i	$-0.346017\pi$
$101$	7.17078	+	0.838144i	0.713519	+	0.0833984i	0.248414	+	0.968654i	$0.420091\pi$
$102$	0.389320	+	4.05977i	0.0385484	+	0.401977i
$103$	−3.01030	+	3.19073i	−0.296614	+	0.314392i	−0.858491	−	0.512828i	$-0.828598\pi$
$103$	−3.01030	+	3.19073i	−0.296614	+	0.314392i	0.561878	+	0.827220i	$0.310079\pi$
$104$	9.70244	+	13.0326i	0.951402	+	1.27795i
$105$	−19.6023	+	7.97739i	−1.91299	+	0.778513i
$106$	3.40589	+	1.71050i	0.330810	+	0.166139i
$107$	3.17835	+	5.50506i	0.307263	+	0.532194i	0.977763	−	0.209715i	$-0.0672537\pi$
$107$	3.17835	+	5.50506i	0.307263	+	0.532194i	−0.670500	+	0.741910i	$0.733920\pi$
$108$	−12.7084	−	13.5806i	−1.22287	−	1.30679i
$109$	4.40215	−	7.62475i	0.421649	−	0.730318i	−0.574452	−	0.818539i	$-0.694785\pi$
$109$	4.40215	−	7.62475i	0.421649	−	0.730318i	0.996101	+	0.0882203i	$0.0281179\pi$
$110$	−2.54092	+	1.67119i	−0.242268	+	0.159342i
$111$	1.01067	+	1.60838i	0.0959287	+	0.152660i
$112$	3.00872	−	6.97501i	0.284298	−	0.659076i
$113$	5.08089	+	16.9714i	0.477970	+	1.59653i	0.768622	+	0.639703i	$0.220943\pi$
$113$	5.08089	+	16.9714i	0.477970	+	1.59653i	−0.290652	+	0.956829i	$0.593872\pi$
$114$	−2.01908	+	2.93534i	−0.189104	+	0.274920i
$115$	2.16246	+	5.01316i	0.201651	+	0.467479i
$116$	2.27653	−	1.91024i	0.211371	−	0.177361i
$117$	−12.9026	−	2.05385i	−1.19285	−	0.189878i
$118$	−9.53588	−	8.00156i	−0.877849	−	0.736603i
$119$	1.31340	−	4.38708i	0.120400	−	0.402163i
$120$	−6.21222	+	16.0252i	−0.567095	+	1.46290i
$121$	0.625968	−	10.7475i	0.0569062	−	0.977042i
$122$	0.554063	−	9.51289i	0.0501625	−	0.861256i
$123$	−0.183180	+	0.472536i	−0.0165167	+	0.0426071i
$124$	−4.11370	+	13.7407i	−0.369421	+	1.23395i
$125$	5.96099	+	5.00187i	0.533167	+	0.447381i
$126$	11.6425	+	30.4004i	1.03720	+	2.70829i
$127$	4.25250	−	3.56827i	0.377349	−	0.316633i	−0.434312	−	0.900763i	$-0.643008\pi$
$127$	4.25250	−	3.56827i	0.377349	−	0.316633i	0.811660	+	0.584130i	$0.198564\pi$
$128$	8.13520	+	18.8595i	0.719057	+	1.66696i
$129$	−11.0167	+	16.0160i	−0.969964	+	1.41013i
$130$	7.84717	+	26.2114i	0.688243	+	2.29889i
$131$	7.28767	−	16.8947i	0.636726	−	1.47610i	−0.227901	−	0.973684i	$-0.573186\pi$
$131$	7.28767	−	16.8947i	0.636726	−	1.47610i	0.864627	−	0.502414i	$-0.167554\pi$
$132$	1.59678	+	2.54111i	0.138982	+	0.221175i
$133$	3.34231	−	2.19827i	0.289815	−	0.190614i
$134$	−17.0340	+	29.5037i	−1.47151	+	2.54873i
$135$	−5.42229	−	12.7125i	−0.466677	−	1.09411i
$136$	−1.85953	−	3.22081i	−0.159454	−	0.276182i
$137$	5.10519	+	2.56392i	0.436166	+	0.219051i	0.653313	−	0.757088i	$-0.273379\pi$
$137$	5.10519	+	2.56392i	0.436166	+	0.219051i	−0.217147	+	0.976139i	$0.569675\pi$
$138$	7.77859	−	3.16559i	0.662158	−	0.269473i
$139$	−5.72886	−	7.69519i	−0.485915	−	0.652697i	0.489776	−	0.871848i	$-0.337079\pi$
$139$	−5.72886	−	7.69519i	−0.485915	−	0.652697i	−0.975691	+	0.219151i	$0.929671\pi$
$140$	30.0136	−	31.8126i	2.53661	−	2.68865i
$141$	−0.667675	−	6.96241i	−0.0562283	−	0.586341i
$142$	−29.7429	−	3.47644i	−2.49597	−	0.291737i
$143$	1.98102	+	0.721031i	0.165661	+	0.0602957i
$144$	4.58709	+	1.88859i	0.382257	+	0.157382i
$145$	2.07507	−	0.755265i	0.172325	−	0.0627213i
$146$	−13.3386	+	3.16132i	−1.10391	+	0.261632i
$147$	0.506874	−	24.4235i	0.0418062	−	2.01441i
$148$	−3.27981	−	2.15717i	−0.269599	−	0.177318i
$149$	14.7208	−	7.39306i	1.20597	−	0.605663i	0.271757	−	0.962366i	$-0.412395\pi$
$149$	14.7208	−	7.39306i	1.20597	−	0.605663i	0.934218	+	0.356703i	$0.116099\pi$
$150$	−5.58888	+	6.38662i	−0.456330	+	0.521465i
$151$	−8.07578	−	8.55982i	−0.657197	−	0.696588i	0.309965	−	0.950748i	$-0.399683\pi$
$151$	−8.07578	−	8.55982i	−0.657197	−	0.696588i	−0.967162	+	0.254159i	$0.918201\pi$
$152$	0.564151	−	3.19946i	0.0457587	−	0.259511i
$153$	2.87884	+	0.809811i	0.232740	+	0.0654694i
$154$	−0.912137	−	5.17298i	−0.0735021	−	0.416851i
$155$	−6.36452	+	8.54903i	−0.511210	+	0.686675i
$156$	26.0210	−	7.20538i	2.08335	−	0.576892i
$157$	−13.1785	−	3.12336i	−1.05176	−	0.249271i	−0.331844	−	0.943334i	$-0.607671\pi$
$157$	−13.1785	−	3.12336i	−1.05176	−	0.249271i	−0.719914	+	0.694063i	$0.755819\pi$
$158$	−15.1890	+	1.77534i	−1.20837	+	0.141239i
$159$	2.07216	−	1.87526i	0.164333	−	0.148717i
$160$	0.549903	+	9.44147i	0.0434736	+	0.746414i
$161$	−9.42984			−0.743176
$162$	−19.7231	+	7.93304i	−1.54960	+	0.623279i
$163$	−13.5555			−1.06175			−0.530874	−	0.847451i	$-0.678136\pi$
$163$	−13.5555			−1.06175			−0.530874	+	0.847451i	$0.678136\pi$
$164$	−0.0608979	−	1.04558i	−0.00475533	−	0.0816458i
$165$	0.469152	+	2.18015i	0.0365234	+	0.169725i
$166$	29.7969	−	3.48276i	2.31269	−	0.270315i
$167$	10.7746	+	2.55363i	0.833765	+	0.197606i	0.625261	−	0.780416i	$-0.284992\pi$
$167$	10.7746	+	2.55363i	0.833765	+	0.197606i	0.208504	+	0.978022i	$0.433141\pi$
$168$	−21.1651	−	20.8150i	−1.63292	−	1.60591i
$169$	3.56276	−	4.78562i	0.274059	−	0.368125i
$170$	−1.08753	−	6.16770i	−0.0834099	−	0.473041i
$171$	1.47175	+	2.15842i	0.112548	+	0.165058i
$172$	6.97594	−	39.5625i	0.531910	−	3.01661i
$173$	−8.89736	−	9.43065i	−0.676454	−	0.716999i	0.294664	−	0.955601i	$-0.404792\pi$
$173$	−8.89736	−	9.43065i	−0.676454	−	0.716999i	−0.971117	+	0.238602i	$0.923311\pi$
$174$	−1.09527	−	3.21529i	−0.0830321	−	0.243751i
$175$	8.51578	−	4.27679i	0.643733	−	0.323295i
$176$	−0.668760	−	0.439851i	−0.0504097	−	0.0331550i
$177$	−7.99801	+	4.39896i	−0.601167	+	0.330646i
$178$	36.3519	−	8.61555i	2.72469	−	0.645763i
$179$	−23.7701	+	8.65162i	−1.77666	+	0.646652i	−0.776806	+	0.629740i	$0.783161\pi$
$179$	−23.7701	+	8.65162i	−1.77666	+	0.646652i	−0.999857	+	0.0169124i	$0.994616\pi$
$180$	21.0988	+	19.2509i	1.57261	+	1.43488i
$181$	10.2266	+	3.72217i	0.760135	+	0.276667i	0.692864	−	0.721068i	$-0.256348\pi$
$181$	10.2266	+	3.72217i	0.760135	+	0.276667i	0.0672712	+	0.997735i	$0.478571\pi$
$182$	−46.9376	−	5.48622i	−3.47925	−	0.406666i
$183$	−6.35709	−	2.90008i	−0.469930	−	0.214380i
$184$	−5.25534	+	5.57034i	−0.387429	+	0.410651i
$185$	−1.74191	−	2.33979i	−0.128068	−	0.172025i
$186$	12.9442	+	10.0606i	0.949112	+	0.737682i
$187$	−0.431225	−	0.216570i	−0.0315343	−	0.0158371i
$188$	7.22725	+	12.5180i	0.527101	+	0.912966i
$189$	23.8704	+	0.0972510i	1.73632	+	0.00707397i
$190$	2.73548	−	4.73799i	0.198453	−	0.343730i
$191$	−9.87188	+	6.49284i	−0.714304	+	0.469805i	−0.853923	−	0.520400i	$-0.825783\pi$
$191$	−9.87188	+	6.49284i	−0.714304	+	0.469805i	0.139618	+	0.990205i	$0.455412\pi$
$192$	20.2613	−	0.758677i	1.46224	−	0.0547528i
$193$	−3.41083	+	7.90719i	−0.245517	+	0.569172i	−0.995760	−	0.0919899i	$-0.970677\pi$
$193$	−3.41083	+	7.90719i	−0.245517	+	0.569172i	0.750243	+	0.661162i	$0.229937\pi$
$194$	1.37296	+	4.58602i	0.0985731	+	0.329257i
$195$	20.0005	+	1.58189i	1.43226	+	0.113281i
$196$	19.9958	+	46.3555i	1.42827	+	3.31111i
$197$	11.2572	−	9.44590i	0.802041	−	0.672992i	−0.146653	−	0.989188i	$-0.546850\pi$
$197$	11.2572	−	9.44590i	0.802041	−	0.672992i	0.948694	+	0.316196i	$0.102406\pi$
$198$	3.36776	−	0.651912i	0.239336	−	0.0463294i
$199$	−10.9420	−	9.18142i	−0.775657	−	0.650853i	0.166494	−	0.986042i	$-0.446755\pi$
$199$	−10.9420	−	9.18142i	−0.775657	−	0.650853i	−0.942151	+	0.335189i	$0.891200\pi$
$200$	2.21957	−	7.41388i	0.156947	−	0.524241i
$201$	15.6570	+	19.4657i	1.10436	+	1.37300i
$202$	−0.991561	+	17.0244i	−0.0697660	+	1.19784i
$203$	−0.221767	+	3.80759i	−0.0155650	+	0.267240i
$204$	−6.10737	+	0.946679i	−0.427601	+	0.0662808i
$205$	0.223204	−	0.745554i	0.0155893	−	0.0520718i
$206$	−7.93747	−	6.66033i	−0.553030	−	0.464047i
$207$	−0.102690	−	6.15721i	−0.00713745	−	0.427955i
$208$	−5.51648	+	4.62888i	−0.382499	+	0.320955i
$209$	−0.166963	−	0.387063i	−0.0115491	−	0.0267737i
$210$	−21.5036	−	45.1284i	−1.48389	−	3.11416i
$211$	−0.797451	−	2.66367i	−0.0548988	−	0.183375i	0.926142	−	0.377174i	$-0.123104\pi$
$211$	−0.797451	−	2.66367i	−0.0548988	−	0.183375i	−0.981041	+	0.193799i	$0.937919\pi$
$212$	−2.28757	+	5.30319i	−0.157111	+	0.364225i
$213$	−10.2598	+	19.4138i	−0.702990	+	1.33021i
$214$	−12.5449	+	8.25091i	−0.857552	+	0.564021i
$215$	14.9255	−	25.8518i	1.01791	−	1.76308i
$216$	13.3607	−	14.0464i	0.909077	−	0.955735i
$217$	−9.20416	−	15.9421i	−0.624819	−	1.08222i
$218$	18.5844	+	9.33346i	1.25870	+	0.632141i
$219$	−1.37385	+	9.95747i	−0.0928359	+	0.672863i
$220$	−2.75208	−	3.69669i	−0.185545	−	0.249231i
$221$	−2.97920	+	3.15777i	−0.200403	+	0.212415i
$222$	−3.65389	+	2.60415i	−0.245233	+	0.174779i
$223$	23.6785	+	2.76762i	1.58563	+	0.185333i	0.862746	−	0.505637i	$-0.168743\pi$
$223$	23.6785	+	2.76762i	1.58563	+	0.185333i	0.722883	+	0.690971i	$0.242817\pi$
$224$	−15.3497	−	5.58682i	−1.02559	−	0.373285i
$225$	2.88526	+	5.51380i	0.192351	+	0.367587i
$226$	−39.3222	+	14.3121i	−2.61567	+	0.952027i
$227$	3.27522	−	0.776241i	0.217384	−	0.0515209i	−0.120481	−	0.992716i	$-0.538444\pi$
$227$	3.27522	−	0.776241i	0.217384	−	0.0515209i	0.337865	+	0.941195i	$0.390295\pi$
$228$	−4.61852	−	2.79586i	−0.305869	−	0.185160i
$229$	−7.70783	−	5.06952i	−0.509348	−	0.335003i	0.268684	−	0.963228i	$-0.413411\pi$
$229$	−7.70783	−	5.06952i	−0.509348	−	0.335003i	−0.778032	+	0.628225i	$0.783782\pi$
$230$	−11.5245	+	5.78781i	−0.759901	+	0.381637i
$231$	−3.77851	−	0.747406i	−0.248608	−	0.0491757i
$232$	2.12560	+	2.25301i	0.139553	+	0.147917i
$233$	−0.733258	+	4.15851i	−0.0480373	+	0.272433i	−0.999360	−	0.0357624i	$-0.988614\pi$
$233$	−0.733258	+	4.15851i	−0.0480373	+	0.272433i	0.951323	+	0.308196i	$0.0997252\pi$
$234$	3.07107	−	30.7076i	0.200762	−	2.00742i
$235$	1.86509	+	10.5775i	0.121665	+	0.689998i
$236$	11.2646	−	15.1310i	0.733265	−	0.984946i
$237$	−2.81186	+	10.8552i	−0.182650	+	0.705124i
$238$	10.5255	+	2.49459i	0.682267	+	0.161700i
$239$	4.48188	−	0.523857i	0.289909	−	0.0338855i	0.0301045	−	0.999547i	$-0.490416\pi$
$239$	4.48188	−	0.523857i	0.289909	−	0.0338855i	0.259804	+	0.965661i	$0.416342\pi$
$240$	−7.25074	−	2.33572i	−0.468034	−	0.150770i
$241$	−0.489698	−	8.40779i	−0.0315442	−	0.541593i	−0.976651	−	0.214832i	$-0.931080\pi$
$241$	−0.489698	−	8.40779i	−0.0315442	−	0.541593i	0.945107	−	0.326761i	$-0.105957\pi$
$242$	25.4294			1.63467
$243$	0.196446	+	15.5872i	0.0126020	+	0.999921i
$244$	14.4400			0.924428
$245$	2.18120	+	37.4497i	0.139352	+	2.39257i
$246$	−1.13944	−	0.367054i	−0.0726481	−	0.0234025i
$247$	−3.76676	+	0.440271i	−0.239673	+	0.0280138i
$248$	−14.5468	−	3.44764i	−0.923720	−	0.218926i
$249$	5.51613	−	21.2952i	0.349570	−	1.34953i
$250$	−10.9761	+	14.7435i	−0.694192	+	0.932462i
$251$	1.59517	+	9.04665i	0.100686	+	0.571020i	0.992856	+	0.119319i	$0.0380713\pi$
$251$	1.59517	+	9.04665i	0.100686	+	0.571020i	−0.892170	+	0.451700i	$0.850818\pi$
$252$	−44.9643	+	20.2916i	−2.83248	+	1.27825i
$253$	−0.172546	+	0.978558i	−0.0108479	+	0.0615214i
$254$	8.99836	+	9.53770i	0.564607	+	0.598449i
$255$	−4.50508	−	0.891125i	−0.282119	−	0.0558044i
$256$	−22.4332	+	11.2664i	−1.40207	+	0.704148i
$257$	6.87814	+	4.52382i	0.429046	+	0.282188i	0.745609	−	0.666383i	$-0.232158\pi$
$257$	6.87814	+	4.52382i	0.429046	+	0.282188i	−0.316563	+	0.948571i	$0.602529\pi$
$258$	−39.2803	−	23.7786i	−2.44548	−	1.48039i
$259$	4.90238	−	1.16189i	0.304619	−	0.0721961i
$260$	−38.9615	+	14.1808i	−2.41629	+	0.879457i
$261$	−2.48858	−	0.103338i	−0.154039	−	0.00639647i
$262$	40.8401	+	14.8646i	2.52311	+	0.918338i
$263$	−0.428165	−	0.0500453i	−0.0264018	−	0.00308592i	0.102882	−	0.994694i	$-0.467194\pi$
$263$	−0.428165	−	0.0500453i	−0.0264018	−	0.00308592i	−0.129284	+	0.991608i	$0.541268\pi$
$264$	−2.54730	+	1.81548i	−0.156776	+	0.111735i
$265$	−2.94508	+	3.12160i	−0.180915	+	0.191758i
$266$	5.64276	+	7.57954i	0.345980	+	0.464731i
$267$	3.74415	−	27.1371i	0.229138	−	1.66077i
$268$	−46.1345	−	23.1696i	−2.81811	−	1.41531i
$269$	−5.33884	−	9.24714i	−0.325515	−	0.563808i	0.656102	−	0.754673i	$-0.272204\pi$
$269$	−5.33884	−	9.24714i	−0.325515	−	0.563808i	−0.981616	+	0.190864i	$0.938871\pi$
$270$	29.2324	−	14.5322i	1.77903	−	0.884403i
$271$	7.65288	−	13.2552i	0.464880	−	0.805195i	−0.534316	−	0.845285i	$-0.679431\pi$
$271$	7.65288	−	13.2552i	0.464880	−	0.805195i	0.999196	+	0.0400894i	$0.0127643\pi$
$272$	1.37718	−	0.905786i	0.0835039	−	0.0549214i
$273$	−16.1911	+	30.6371i	−0.979931	+	1.85424i
$274$	−5.34479	+	12.3906i	−0.322891	+	0.748545i
$275$	−0.287992	−	0.961960i	−0.0173666	−	0.0580084i
$276$	5.47432	+	11.4886i	0.329515	+	0.691534i
$277$	−4.91956	−	11.4048i	−0.295588	−	0.685249i	0.704104	−	0.710097i	$-0.251349\pi$
$277$	−4.91956	−	11.4048i	−0.295588	−	0.685249i	−0.999691	+	0.0248481i	$0.992090\pi$
$278$	17.3591	−	14.5660i	1.04113	−	0.873613i
$279$	10.3091	−	6.18345i	0.617191	−	0.370194i
$280$	34.9205	+	29.3018i	2.08690	+	1.75112i
$281$	9.00948	−	30.0938i	0.537460	−	1.79524i	−0.0659631	−	0.997822i	$-0.521012\pi$
$281$	9.00948	−	30.0938i	0.537460	−	1.79524i	0.603424	−	0.797421i	$-0.293803\pi$
$282$	16.3263	−	2.53068i	0.972216	−	0.150700i
$283$	0.0341306	−	0.586000i	0.00202886	−	0.0348341i	−0.997142	−	0.0755530i	$-0.975928\pi$
$283$	0.0341306	−	0.586000i	0.00202886	−	0.0348341i	0.999171	+	0.0407189i	$0.0129648\pi$
$284$	2.63852	−	45.3017i	0.156568	−	2.68816i
$285$	−2.51435	−	3.12599i	−0.148937	−	0.185167i
$286$	−1.42818	+	4.77045i	−0.0844499	+	0.282082i
$287$	1.02970	+	0.864021i	0.0607813	+	0.0510015i
$288$	3.48075	−	10.0834i	0.205105	−	0.594169i
$289$	−12.2615	+	10.2886i	−0.721266	+	0.605214i
$290$	2.06598	+	4.78948i	0.121318	+	0.281248i
$291$	3.49934	+	0.276772i	0.205135	+	0.0162246i
$292$	−5.95776	−	19.9003i	−0.348652	−	1.16458i
$293$	−11.8644	+	27.5047i	−0.693123	+	1.60684i	0.0980029	+	0.995186i	$0.468755\pi$
$293$	−11.8644	+	27.5047i	−0.693123	+	1.60684i	−0.791126	+	0.611653i	$0.790505\pi$
$294$	57.6623	−	2.15914i	3.36294	−	0.125924i
$295$	11.7110	−	7.70246i	0.681842	−	0.448455i
$296$	2.04580	−	3.54343i	0.118910	−	0.205958i
$297$	0.446870	−	2.47531i	0.0259300	−	0.143632i
$298$	19.4553	+	33.6976i	1.12702	+	1.95205i
$299$	7.98862	+	4.01204i	0.461994	+	0.232022i
$300$	−10.1542	−	7.89220i	−0.586253	−	0.455656i
$301$	30.7884	+	41.3561i	1.77462	+	2.38372i
$302$	19.0757	−	20.2190i	1.09768	−	1.16347i
$303$	11.3768	+	5.19003i	0.653579	+	0.298160i
$304$	1.43020	+	0.167166i	0.0820274	+	0.00958763i
$305$	10.0828	+	3.66984i	0.577340	+	0.210135i
$306$	−1.51422	+	6.89978i	−0.0865621	+	0.394434i
$307$	2.24152	−	0.815848i	0.127930	−	0.0465629i	−0.277262	−	0.960794i	$-0.589427\pi$
$307$	2.24152	−	0.815848i	0.127930	−	0.0465629i	0.405192	+	0.914232i	$0.367205\pi$
$308$	7.74539	−	1.83569i	0.441334	−	0.104598i
$309$	−6.65738	+	3.66160i	−0.378725	+	0.208301i
$310$	−21.0335	−	13.8340i	−1.19462	−	0.785716i
$311$	−23.8757	+	11.9908i	−1.35387	+	0.679938i	−0.969922	−	0.243418i	$-0.921731\pi$
$311$	−23.8757	+	11.9908i	−1.35387	+	0.679938i	−0.383946	+	0.923356i	$0.625435\pi$
$312$	9.07428	+	26.6386i	0.513730	+	1.50812i
$313$	−4.80971	−	5.09800i	−0.271861	−	0.288156i	0.577031	−	0.816722i	$-0.304211\pi$
$313$	−4.80971	−	5.09800i	−0.271861	−	0.288156i	−0.848892	+	0.528567i	$0.822730\pi$
$314$	5.55519	−	31.5050i	0.313497	−	1.77793i
$315$	−36.5535	+	2.74130i	−2.05955	+	0.154455i
$316$	−4.02409	−	22.8217i	−0.226373	−	1.28382i
$317$	−8.40999	+	11.2966i	−0.472352	+	0.634479i	−0.972899	−	0.231231i	$-0.925725\pi$
$317$	−8.40999	+	11.2966i	−0.472352	+	0.634479i	0.500547	+	0.865709i	$0.333132\pi$
$318$	4.70662	+	4.62877i	0.263934	+	0.259569i
$319$	0.391065	+	0.0926842i	0.0218955	+	0.00518932i
$320$	−30.9249	+	3.61461i	−1.72876	+	0.202063i
$321$	2.31627	+	10.7637i	0.129282	+	0.600772i
$322$	−1.29512	−	22.2364i	−0.0721744	−	1.23919i
$323$	0.868075			0.0483010
$324$	−13.7390	−	29.1384i	−0.763280	−	1.61880i
$325$	−9.03387			−0.501109
$326$	−1.86175	−	31.9650i	−0.103113	−	1.77038i
$327$	11.3068	−	10.2324i	0.625269	−	0.565855i
$328$	1.08425	−	0.126731i	0.0598677	−	0.00699753i
$329$	−18.0510	−	4.27817i	−0.995184	−	0.235863i
$330$	−5.07656	+	1.40573i	−0.279455	+	0.0773830i
$331$	17.4259	−	23.4070i	0.957812	−	1.28657i	−0.000248497	−	1.00000i	$-0.500079\pi$
$331$	17.4259	−	23.4070i	0.957812	−	1.28657i	0.958061	−	0.286565i	$-0.0925135\pi$
$332$	7.89421	+	44.7703i	0.433251	+	2.45709i
$333$	0.812039	+	3.18835i	0.0444995	+	0.174721i
$334$	−4.54187	+	25.7582i	−0.248520	+	1.40943i
$335$	−26.3252	−	27.9031i	−1.43830	−	1.52451i
$336$	8.66453	−	9.90128i	0.472689	−	0.540159i
$337$	0.636967	−	0.319897i	0.0346978	−	0.0174259i	−0.431366	−	0.902177i	$-0.641968\pi$
$337$	0.636967	−	0.319897i	0.0346978	−	0.0174259i	0.466064	+	0.884751i	$0.345672\pi$
$338$	11.7742	+	7.74404i	0.640435	+	0.421220i
$339$	−0.636672	+	30.6777i	−0.0345793	+	1.66619i
$340$	9.23476	−	2.18868i	0.500825	−	0.118698i
$341$	−1.82276	+	0.663432i	−0.0987082	+	0.0359269i
$342$	−4.88760	+	3.76697i	−0.264291	+	0.203695i
$343$	−30.6666	−	11.1617i	−1.65584	−	0.602678i
$344$	41.5883	+	4.86097i	2.24229	+	0.262086i
$345$	0.902702	+	9.41324i	0.0485999	+	0.506792i
$346$	21.0163	−	22.2760i	1.12984	−	1.19757i
$347$	8.24305	+	11.0723i	0.442510	+	0.594394i	0.966289	−	0.257460i	$-0.0828856\pi$
$347$	8.24305	+	11.0723i	0.442510	+	0.594394i	−0.523779	+	0.851854i	$0.675478\pi$
$348$	4.76763	−	1.94024i	0.255572	−	0.104008i
$349$	−15.5123	−	7.79057i	−0.830355	−	0.417020i	−0.0177553	−	0.999842i	$-0.505652\pi$
$349$	−15.5123	−	7.79057i	−0.830355	−	0.417020i	−0.812599	+	0.582823i	$0.801948\pi$
$350$	11.2546	+	19.4936i	0.601585	+	1.04198i
$351$	−20.1808	−	10.2383i	−1.07717	−	0.546482i
$352$	−0.860625	+	1.49065i	−0.0458714	+	0.0794517i
$353$	8.77742	−	5.77300i	0.467175	−	0.307266i	−0.294008	−	0.955803i	$-0.594989\pi$
$353$	8.77742	−	5.77300i	0.467175	−	0.307266i	0.761183	+	0.648537i	$0.224619\pi$
$354$	−11.4716	−	18.2559i	−0.609709	−	0.970288i
$355$	13.3555	−	30.9615i	0.708836	−	1.64327i
$356$	16.2367	+	54.2344i	0.860545	+	2.87442i
$357$	4.49520	−	6.53511i	0.237911	−	0.345875i
$358$	−23.6660	−	54.8638i	−1.25078	−	2.89964i
$359$	−1.97814	+	1.65986i	−0.104402	+	0.0876039i	−0.693495	−	0.720462i	$-0.743930\pi$
$359$	−1.97814	+	1.65986i	−0.104402	+	0.0876039i	0.589092	+	0.808066i	$0.299485\pi$
$360$	−18.7523	+	23.1204i	−0.988331	+	1.21855i
$361$	−13.9739	−	11.7255i	−0.735471	−	0.617133i
$362$	−7.37266	+	24.6264i	−0.387498	+	1.29433i
$363$	6.73974	−	17.3861i	0.353745	−	0.912531i
$364$	4.16389	−	71.4912i	0.218247	−	3.74716i
$365$	0.897507	−	15.4096i	0.0469776	−	0.806575i
$366$	5.96554	−	15.3889i	0.311824	−	0.804391i
$367$	−6.33974	+	21.1762i	−0.330932	+	1.10539i	0.617012	+	0.786953i	$0.288343\pi$
$367$	−6.33974	+	21.1762i	−0.330932	+	1.10539i	−0.947944	+	0.318436i	$0.896842\pi$
$368$	−2.60013	−	2.18177i	−0.135541	−	0.113732i
$369$	−0.552948	+	0.681751i	−0.0287853	+	0.0354905i
$370$	5.27820	−	4.42894i	0.274401	−	0.230249i
$371$	−2.93590	−	6.80617i	−0.152424	−	0.353359i
$372$	−14.0793	+	20.4685i	−0.729980	+	1.06124i
$373$	2.97446	+	9.93538i	0.154012	+	0.514435i	0.999818	−	0.0190547i	$-0.00606566\pi$
$373$	2.97446	+	9.93538i	0.154012	+	0.514435i	−0.845807	+	0.533489i	$0.820880\pi$
$374$	0.451465	−	1.04661i	0.0233447	−	0.0541190i
$375$	7.17103	+	11.4119i	0.370311	+	0.589310i
$376$	−12.5872	+	8.27871i	−0.649133	+	0.426942i
$377$	1.80786	−	3.13130i	0.0931094	−	0.161270i
$378$	3.04911	+	56.3019i	0.156829	+	2.89586i
$379$	3.96481	+	6.86725i	0.203658	+	0.352747i	0.949704	−	0.313148i	$-0.101383\pi$
$379$	3.96481	+	6.86725i	0.203658	+	0.352747i	−0.746046	+	0.665894i	$0.768050\pi$
$380$	7.40872	+	3.72080i	0.380059	+	0.190873i
$381$	8.90581	−	3.62432i	0.456258	−	0.185679i
$382$	−16.6665	−	22.3870i	−0.852734	−	1.14542i
$383$	−3.01103	+	3.19151i	−0.153856	+	0.163078i	−0.799717	−	0.600377i	$-0.795017\pi$
$383$	−3.01103	+	3.19151i	−0.153856	+	0.163078i	0.645861	+	0.763455i	$0.276499\pi$
$384$	3.39597	+	35.4126i	0.173300	+	1.80714i
$385$	5.87477	+	0.686663i	0.299406	+	0.0349956i
$386$	−19.1143	−	6.95704i	−0.972893	−	0.354104i
$387$	−26.6681	+	20.5536i	−1.35562	+	1.04480i
$388$	−6.81682	+	2.48112i	−0.346071	+	0.125960i
$389$	−3.02216	+	0.716264i	−0.153229	+	0.0363160i	−0.306515	−	0.951866i	$-0.599163\pi$
$389$	−3.02216	+	0.716264i	−0.153229	+	0.0363160i	0.153285	+	0.988182i	$0.451015\pi$
$390$	−0.983307	+	47.3801i	−0.0497917	+	2.39919i
$391$	−1.70961	−	1.12443i	−0.0864585	−	0.0568646i
$392$	−47.0219	+	23.6153i	−2.37496	+	1.19275i
$393$	20.9870	−	23.9827i	1.05866	−	1.20977i
$394$	23.8204	+	25.2481i	1.20005	+	1.27198i
$395$	2.99016	−	16.9581i	0.150451	−	0.853252i
$396$	1.28296	+	5.03735i	0.0644711	+	0.253136i
$397$	4.18830	+	23.7530i	0.210205	+	1.19213i	0.889037	+	0.457836i	$0.151375\pi$
$397$	4.18830	+	23.7530i	0.210205	+	1.19213i	−0.678832	+	0.734294i	$0.737514\pi$
$398$	20.1478	−	27.0632i	1.00992	−	1.35655i
$399$	6.67766	−	1.84908i	0.334301	−	0.0925700i
$400$	3.33760	+	0.791027i	0.166880	+	0.0395513i
$401$	29.9880	−	3.50510i	1.49753	−	0.175036i	0.672489	−	0.740107i	$-0.265225\pi$
$401$	29.9880	−	3.50510i	1.49753	−	0.175036i	0.825042	+	0.565071i	$0.191151\pi$
$402$	−43.7514	+	39.5941i	−2.18212	+	1.97477i
$403$	1.01469	+	17.4216i	0.0505453	+	0.867830i
$404$	−25.8422			−1.28570
$405$	−2.18799	−	23.8377i	−0.108722	−	1.18450i
$406$	−9.00910			−0.447114
$407$	−0.0308686	−	0.529993i	−0.00153010	−	0.0262708i
$408$	−1.35516	−	6.29745i	−0.0670906	−	0.311770i
$409$	−4.91901	+	0.574949i	−0.243229	+	0.0284294i	−0.236834	−	0.971550i	$-0.576110\pi$
$409$	−4.91901	+	0.574949i	−0.243229	+	0.0284294i	−0.00639520	+	0.999980i	$0.502036\pi$
$410$	1.78874	+	0.423939i	0.0883395	+	0.0209369i
$411$	7.05488	+	6.93820i	0.347991	+	0.342236i
$412$	9.37645	−	12.5948i	0.461945	−	0.620499i
$413$	4.20401	+	23.8421i	0.206866	+	1.17319i
$414$	14.5051	−	1.08780i	0.712889	−	0.0534625i
$415$	−5.86592	+	33.2673i	−0.287947	+	1.63303i
$416$	10.6267	+	11.2636i	0.521017	+	0.552246i
$417$	−5.35796	−	15.7289i	−0.262380	−	0.770249i
$418$	0.889798	−	0.446873i	0.0435214	−	0.0218573i
$419$	20.9288	+	13.7651i	1.02244	+	0.672470i	0.945854	−	0.324593i	$-0.105227\pi$
$419$	20.9288	+	13.7651i	1.02244	+	0.672470i	0.0765867	+	0.997063i	$0.475598\pi$
$420$	66.3761	−	36.5073i	3.23882	−	1.78137i
$421$	−30.4178	+	7.20915i	−1.48247	+	0.351352i	−0.890640	−	0.454709i	$-0.849743\pi$
$421$	−30.4178	+	7.20915i	−1.48247	+	0.351352i	−0.591832	+	0.806061i	$0.701595\pi$
$422$	6.17165	−	2.24630i	0.300431	−	0.109348i
$423$	2.59685	−	11.8330i	0.126263	−	0.575339i
$424$	−5.65670	−	2.05887i	−0.274714	−	0.0999876i
$425$	2.05386	+	0.240062i	0.0996267	+	0.0116447i
$426$	−47.1885	−	21.5272i	−2.28629	−	1.04299i
$427$	−12.7178	+	13.4800i	−0.615456	+	0.652345i
$428$	−13.5874	−	18.2511i	−0.656773	−	0.882199i
$429$	2.88302	+	2.24079i	0.139194	+	0.108186i
$430$	63.0107	+	31.6452i	3.03865	+	1.52607i
$431$	−0.627551	−	1.08695i	−0.0302281	−	0.0523566i	0.850516	−	0.525950i	$-0.176290\pi$
$431$	−0.627551	−	1.08695i	−0.0302281	−	0.0523566i	−0.880744	+	0.473593i	$0.842957\pi$
$432$	6.55938	+	5.54967i	0.315588	+	0.267009i
$433$	16.4409	−	28.4764i	0.790097	−	1.36849i	−0.135809	−	0.990735i	$-0.543363\pi$
$433$	16.4409	−	28.4764i	0.790097	−	1.36849i	0.925906	−	0.377753i	$-0.123303\pi$
$434$	36.3287	−	23.8938i	1.74383	−	1.14694i
$435$	3.82212	−	0.143117i	0.183256	−	0.00686195i
$436$	−12.4823	+	28.9372i	−0.597792	+	1.38584i
$437$	−0.512662	−	1.71241i	−0.0245240	−	0.0819157i
$438$	−23.6693	−	1.87206i	−1.13096	−	0.0894506i
$439$	10.1626	+	23.5595i	0.485033	+	1.12443i	0.968487	+	0.249063i	$0.0801227\pi$
$439$	10.1626	+	23.5595i	0.485033	+	1.12443i	−0.483454	+	0.875370i	$0.660618\pi$
$440$	3.67969	−	3.08762i	0.175422	−	0.147197i
$441$	13.8064	−	39.9959i	0.657450	−	1.90457i
$442$	−7.85548	−	6.59153i	−0.373647	−	0.313527i
$443$	−5.58222	+	18.6459i	−0.265219	+	0.885894i	0.716827	+	0.697251i	$0.245594\pi$
$443$	−5.58222	+	18.6459i	−0.265219	+	0.885894i	−0.982046	+	0.188642i	$0.939591\pi$
$444$	−4.26154	−	5.29819i	−0.202244	−	0.251441i
$445$	−2.44598	+	41.9959i	−0.115951	+	1.99079i
$446$	−3.27422	+	56.2161i	−0.155039	+	2.66191i
$447$	28.1953	−	4.37045i	1.33359	−	0.206715i
$448$	15.4233	−	51.5175i	0.728683	−	2.43397i
$449$	−1.02554	−	0.860532i	−0.0483983	−	0.0406110i	0.618268	−	0.785968i	$-0.287835\pi$
$449$	−1.02554	−	0.860532i	−0.0483983	−	0.0406110i	−0.666666	+	0.745357i	$0.732279\pi$
$450$	−12.6058	+	7.56098i	−0.594241	+	0.356428i
$451$	0.108503	−	0.0910448i	0.00510920	−	0.00428713i
$452$	−25.1163	−	58.2260i	−1.18137	−	2.73872i
$453$	−8.76796	−	18.4008i	−0.411955	−	0.864545i
$454$	2.28027	+	7.61664i	0.107019	+	0.357467i
$455$	21.0765	−	48.8608i	0.988080	−	2.29063i
$456$	2.62924	−	4.97509i	0.123125	−	0.232980i
$457$	−16.5667	+	10.8961i	−0.774955	+	0.509696i	−0.874317	−	0.485355i	$-0.838690\pi$
$457$	−16.5667	+	10.8961i	−0.774955	+	0.509696i	0.0993618	+	0.995051i	$0.468320\pi$
$458$	10.8958	−	18.8720i	0.509126	−	0.881832i
$459$	4.31605	+	2.86397i	0.201456	+	0.133678i
$460$	−9.77130	−	16.9244i	−0.455589	−	0.789104i
$461$	−27.7646	−	13.9439i	−1.29313	−	0.649432i	−0.336756	−	0.941592i	$-0.609330\pi$
$461$	−27.7646	−	13.9439i	−1.29313	−	0.649432i	−0.956370	+	0.292159i	$0.905626\pi$
$462$	1.24350	−	9.01271i	0.0578527	−	0.419309i
$463$	2.51984	+	3.38473i	0.117107	+	0.157302i	0.856811	−	0.515630i	$-0.172442\pi$
$463$	2.51984	+	3.38473i	0.117107	+	0.157302i	−0.739705	+	0.672932i	$0.765035\pi$
$464$	−0.942104	+	0.998572i	−0.0437361	+	0.0463575i
$465$	−15.0329	+	10.7141i	−0.697134	+	0.496853i
$466$	−9.90685	−	1.15795i	−0.458926	−	0.0536408i
$467$	−27.5275	−	10.0192i	−1.27382	−	0.463633i	−0.385438	−	0.922734i	$-0.625950\pi$
$467$	−27.5275	−	10.0192i	−1.27382	−	0.463633i	−0.888384	+	0.459100i	$0.848172\pi$
$468$	46.7254	+	1.94027i	2.15988	+	0.0896892i
$469$	62.2613	−	22.6613i	2.87496	−	1.04640i
$470$	−24.6865	+	5.85080i	−1.13870	+	0.269877i
$471$	−20.0676	−	12.1481i	−0.924666	−	0.559753i
$472$	16.4268	+	10.8041i	0.756104	+	0.497297i
$473$	4.85498	−	2.43826i	0.223232	−	0.112112i
$474$	−25.9838	−	5.13971i	−1.19348	−	0.236075i
$475$	1.23961	+	1.31391i	0.0568773	+	0.0602864i
$476$	−2.84643	+	16.1429i	−0.130466	+	0.739910i
$477$	4.41211	−	1.99111i	0.202017	−	0.0911666i
$478$	1.85086	+	10.4967i	0.0846562	+	0.480109i
$479$	−15.2629	+	20.5016i	−0.697379	+	0.936742i	−0.999865	−	0.0164116i	$-0.994776\pi$
$479$	−15.2629	+	20.5016i	−0.697379	+	0.936742i	0.302487	+	0.953154i	$0.402183\pi$
$480$	−4.10759	+	15.8575i	−0.187485	+	0.723790i
$481$	−4.64746	−	1.10147i	−0.211906	−	0.0502226i
$482$	19.7591	−	2.30950i	0.900001	−	0.105195i
$483$	−15.5462	−	5.00800i	−0.707379	−	0.227872i
$484$	2.24062	+	38.4700i	0.101846	+	1.74863i
$485$	−5.39043			−0.244767
$486$	−36.7291	+	2.60403i	−1.66606	+	0.118121i
$487$	−3.18751			−0.144440			−0.0722199	−	0.997389i	$-0.523008\pi$
$487$	−3.18751			−0.144440			−0.0722199	+	0.997389i	$0.523008\pi$
$488$	0.875113	+	15.0251i	0.0396145	+	0.680155i
$489$	−22.3479	−	7.19904i	−1.01061	−	0.325552i
$490$	−88.0102	+	10.2869i	−3.97589	+	0.464715i
$491$	16.2621	+	3.85419i	0.733898	+	0.173937i	0.580538	−	0.814233i	$-0.302842\pi$
$491$	16.2621	+	3.85419i	0.733898	+	0.173937i	0.153360	+	0.988170i	$0.450990\pi$
$492$	0.454887	−	1.75610i	0.0205079	−	0.0791712i
$493$	−0.494227	+	0.663862i	−0.0222589	+	0.0298988i
$494$	−1.55554	−	8.82189i	−0.0699869	−	0.396916i
$495$	−0.384380	+	3.84340i	−0.0172766	+	0.172748i
$496$	1.15059	−	6.52532i	0.0516630	−	0.292995i
$497$	39.9662	+	42.3617i	1.79273	+	1.90018i
$498$	50.9735	+	10.0828i	2.28418	+	0.451820i
$499$	16.3966	−	8.23468i	0.734012	−	0.368635i	−0.0421976	−	0.999109i	$-0.513436\pi$
$499$	16.3966	−	8.23468i	0.734012	−	0.368635i	0.776210	+	0.630474i	$0.217140\pi$
$500$	−23.2713	−	15.3058i	−1.04072	−	0.684495i
$501$	16.4071	+	9.93215i	0.733015	+	0.443736i
$502$	−21.1137	+	5.00405i	−0.942352	+	0.223342i
$503$	21.3376	−	7.76624i	0.951395	−	0.346280i	0.180739	−	0.983531i	$-0.442151\pi$
$503$	21.3376	−	7.76624i	0.951395	−	0.346280i	0.770656	+	0.637251i	$0.219929\pi$
$504$	−23.8388	−	45.5564i	−1.06186	−	2.02924i
$505$	−18.0444	−	6.56762i	−0.802965	−	0.292255i
$506$	−2.33123	−	0.272481i	−0.103636	−	0.0121133i
$507$	8.41520	−	5.99757i	0.373732	−	0.266362i
$508$	−13.6359	+	14.4532i	−0.604995	+	0.641257i
$509$	−15.8074	−	21.2330i	−0.700650	−	0.941136i	0.299265	−	0.954170i	$-0.403259\pi$
$509$	−15.8074	−	21.2330i	−0.700650	−	0.941136i	−0.999915	+	0.0130337i	$0.995851\pi$
$510$	1.48261	−	10.7458i	0.0656511	−	0.475831i
$511$	23.8245	+	11.9651i	1.05393	+	0.529305i
$512$	−9.10887	−	15.7770i	−0.402559	−	0.697253i
$513$	1.28008	+	4.34003i	0.0565168	+	0.191617i
$514$	−9.72291	+	16.8406i	−0.428859	+	0.742806i
$515$	9.74802	−	6.41137i	0.429549	−	0.282519i
$516$	32.5115	−	61.5188i	1.43124	−	2.70822i
$517$	−0.774251	+	1.79492i	−0.0340515	+	0.0789403i
$518$	3.41314	+	11.4007i	0.149965	+	0.500917i
$519$	−9.65996	−	20.2728i	−0.424025	−	0.889876i
$520$	−17.1166	−	39.6807i	−0.750612	−	1.74011i
$521$	26.2017	−	21.9858i	1.14792	−	0.963216i	0.148247	−	0.988950i	$-0.452637\pi$
$521$	26.2017	−	21.9858i	1.14792	−	0.963216i	0.999669	+	0.0257345i	$0.00819245\pi$
$522$	−0.0981082	−	5.88248i	−0.00429408	−	0.257469i
$523$	17.6317	+	14.7948i	0.770982	+	0.646931i	0.940960	−	0.338517i	$-0.109925\pi$
$523$	17.6317	+	14.7948i	0.770982	+	0.646931i	−0.169978	+	0.985448i	$0.554370\pi$
$524$	−18.8889	+	63.0932i	−0.825164	+	2.75624i
$525$	16.3106	−	2.52825i	0.711854	−	0.110342i
$526$	0.0592058	−	1.01652i	0.00258149	−	0.0443226i
$527$	0.232261	−	3.98777i	0.0101175	−	0.173710i
$528$	−0.868937	−	1.08031i	−0.0378156	−	0.0470146i
$529$	5.38802	−	17.9972i	0.234262	−	0.782489i
$530$	−7.76550	−	6.51603i	−0.337312	−	0.283038i
$531$	−15.5219	+	3.00464i	−0.673593	+	0.130390i
$532$	−10.9692	+	9.20428i	−0.475576	+	0.399056i
$533$	−0.504717	−	1.17007i	−0.0218617	−	0.0506812i
$534$	64.5060	+	5.10195i	2.79145	+	0.220783i
$535$	−4.84908	−	16.1970i	−0.209644	−	0.700259i
$536$	21.3125	−	49.4079i	0.920560	−	2.13410i
$537$	−43.7827	+	1.63942i	−1.88936	+	0.0707463i
$538$	21.0723	−	13.8595i	0.908493	−	0.597525i
$539$	−3.41368	+	5.91266i	−0.147038	+	0.254676i
$540$	24.5602	+	42.9427i	1.05690	+	1.84796i
$541$	14.1264	+	24.4676i	0.607340	+	1.05194i	0.991677	+	0.128751i	$0.0410970\pi$
$541$	14.1264	+	24.4676i	0.607340	+	1.05194i	−0.384336	+	0.923193i	$0.625570\pi$
$542$	32.3080	+	16.2257i	1.38775	+	0.696953i
$543$	14.8830	+	11.5676i	0.638690	+	0.496412i
$544$	−2.11667	−	2.84319i	−0.0907516	−	0.121901i
$545$	−16.0700	+	17.0332i	−0.688362	+	0.729622i
$546$	−74.4687	−	33.9723i	−3.18697	−	1.45388i
$547$	−18.0438	−	2.10902i	−0.771497	−	0.0901751i	−0.278769	−	0.960358i	$-0.589926\pi$
$547$	−18.0438	−	2.10902i	−0.771497	−	0.0901751i	−0.492728	+	0.870183i	$0.664000\pi$
$548$	−19.2156	−	6.99392i	−0.820851	−	0.298765i
$549$	−8.94027	−	8.15725i	−0.381562	−	0.348143i
$550$	2.22883	−	0.811229i	0.0950378	−	0.0345909i
$551$	−0.703495	+	0.166731i	−0.0299699	+	0.00710300i
$552$	−11.6224	+	6.39237i	−0.494681	+	0.272078i
$553$	24.8487	+	16.3432i	1.05667	+	0.694984i
$554$	26.2179	−	13.1671i	1.11389	−	0.559418i
$555$	−1.62914	−	4.78253i	−0.0691530	−	0.203007i
$556$	23.5652	+	24.9777i	0.999387	+	1.05929i
$557$	1.02531	−	5.81482i	0.0434438	−	0.246382i	−0.955350	−	0.295475i	$-0.904522\pi$
$557$	1.02531	−	5.81482i	0.0434438	−	0.246382i	0.998794	+	0.0490932i	$0.0156331\pi$
$558$	15.9970	+	23.4606i	0.677208	+	0.993166i
$559$	−8.48744	−	48.1347i	−0.358980	−	2.03588i
$560$	−12.0652	+	16.2063i	−0.509846	+	0.684842i
$561$	−0.595912	−	0.586056i	−0.0251594	−	0.0247433i
$562$	72.2012	+	17.1120i	3.04562	+	0.721826i
$563$	−22.9360	+	2.68083i	−0.966637	+	0.112984i	−0.584740	−	0.811221i	$-0.698803\pi$
$563$	−22.9360	+	2.68083i	−0.966637	+	0.112984i	−0.381898	+	0.924205i	$0.624729\pi$
$564$	5.26697	+	24.4756i	0.221779	+	1.03061i
$565$	−2.73975	−	47.0397i	−0.115262	−	1.97897i
$566$	1.38653			0.0582802
$567$	39.3016	+	12.8374i	1.65051	+	0.539121i
$568$	47.2971			1.98454
$569$	0.532209	+	9.13768i	0.0223114	+	0.383071i	0.990918	+	0.134471i	$0.0429335\pi$
$569$	0.532209	+	9.13768i	0.0223114	+	0.383071i	−0.968606	+	0.248600i	$0.920029\pi$
$570$	7.02602	−	6.35840i	0.294288	−	0.266324i
$571$	−11.3000	+	1.32078i	−0.472889	+	0.0552728i	−0.349200	−	0.937048i	$-0.613547\pi$
$571$	−11.3000	+	1.32078i	−0.472889	+	0.0552728i	−0.123689	+	0.992321i	$0.539473\pi$
$572$	−7.34263	−	1.74023i	−0.307011	−	0.0727629i
$573$	−19.7232	+	5.46148i	−0.823949	+	0.228157i
$574$	−1.89602	+	2.54679i	−0.0791382	+	0.106301i
$575$	−0.739396	−	4.19332i	−0.0308349	−	0.174874i
$576$	33.8062	+	9.50961i	1.40859	+	0.396234i
$577$	−3.91622	+	22.2100i	−0.163034	+	0.924613i	0.788034	+	0.615632i	$0.211099\pi$
$577$	−3.91622	+	22.2100i	−0.163034	+	0.924613i	−0.951068	+	0.308981i	$0.900012\pi$
$578$	−25.9456	−	27.5007i	−1.07919	−	1.14388i
$579$	−9.82252	+	11.2246i	−0.408210	+	0.466476i
$580$	−7.06354	+	3.54744i	−0.293298	+	0.147300i
$581$	−48.7466	−	32.0611i	−2.02235	−	1.33012i
$582$	−0.172042	+	8.28977i	−0.00713138	+	0.343622i
$583$	−0.760014	+	0.180127i	−0.0314766	+	0.00746008i
$584$	20.3456	−	7.40518i	0.841906	−	0.306429i
$585$	32.1331	+	13.2298i	1.32854	+	0.546984i
$586$	−66.4879	−	24.1996i	−2.74659	−	0.999677i
$587$	25.0889	+	2.93247i	1.03553	+	0.121036i	0.616837	−	0.787091i	$-0.288414\pi$
$587$	25.0889	+	2.93247i	1.03553	+	0.121036i	0.418694	+	0.908127i	$0.362488\pi$
$588$	8.34708	+	87.0420i	0.344228	+	3.58955i
$589$	2.39460	−	2.53813i	0.0986680	−	0.104582i
$590$	19.7715	+	26.5578i	0.813981	+	1.09337i
$591$	23.5754	−	9.59426i	0.969761	−	0.394655i
$592$	1.62058	+	0.813885i	0.0666053	+	0.0334505i
$593$	−13.0866	−	22.6667i	−0.537404	−	0.930811i	−0.999043	−	0.0437427i	$-0.986072\pi$
$593$	−13.0866	−	22.6667i	−0.537404	−	0.930811i	0.461639	−	0.887068i	$-0.347262\pi$
$594$	5.89838	+	0.713793i	0.242014	+	0.0292873i
$595$	−6.09015	+	10.5485i	−0.249672	+	0.432444i
$596$	−49.2639	+	32.4014i	−2.01793	+	1.32721i
$597$	−13.1631	−	20.9478i	−0.538731	−	0.857334i
$598$	−8.36356	+	19.3889i	−0.342011	+	0.792872i
$599$	4.02015	+	13.4282i	0.164259	+	0.548663i	1.00000		0.000460948i	$-0.000146724\pi$
$599$	4.02015	+	13.4282i	0.164259	+	0.548663i	−0.835741	+	0.549124i	$0.814962\pi$
$600$	7.59659	−	11.0439i	0.310130	−	0.450866i
$601$	−5.40023	−	12.5191i	−0.220280	−	0.510667i	0.771861	−	0.635791i	$-0.219326\pi$
$601$	−5.40023	−	12.5191i	−0.220280	−	0.510667i	−0.992141	+	0.125125i	$0.960067\pi$
$602$	−93.2927	+	78.2819i	−3.80233	+	3.19053i
$603$	15.4747	+	40.4067i	0.630177	+	1.64549i
$604$	32.2684	+	27.0764i	1.31298	+	1.10172i
$605$	−8.21237	+	27.4312i	−0.333880	+	1.11524i
$606$	−10.6760	+	27.5403i	−0.433685	+	1.11875i
$607$	−1.23913	+	21.2751i	−0.0502948	+	0.863529i	0.874963	+	0.484190i	$0.160886\pi$
$607$	−1.23913	+	21.2751i	−0.0502948	+	0.863529i	−0.925258	+	0.379339i	$0.876151\pi$
$608$	0.180039	−	3.09115i	0.00730155	−	0.125363i
$609$	−2.38774	+	6.15950i	−0.0967562	+	0.249596i
$610$	−7.26901	+	24.2802i	−0.294314	+	0.983076i
$611$	13.4720	+	11.3043i	0.545017	+	0.457324i
$612$	−10.5715	−	1.68278i	−0.427328	−	0.0680224i
$613$	19.6311	−	16.4725i	0.792894	−	0.665317i	−0.153566	−	0.988138i	$-0.549076\pi$
$613$	19.6311	−	16.4725i	0.792894	−	0.665317i	0.946460	+	0.322821i	$0.104631\pi$
$614$	2.23170	+	5.17366i	0.0900641	+	0.208792i
$615$	0.763928	−	1.11060i	0.0308046	−	0.0447836i
$616$	2.37946	+	7.94796i	0.0958713	+	0.320233i
$617$	−4.68084	+	10.8514i	−0.188443	+	0.436861i	−0.986079	−	0.166279i	$-0.946825\pi$
$617$	−4.68084	+	10.8514i	−0.188443	+	0.436861i	0.797635	+	0.603140i	$0.206084\pi$
$618$	−9.54873	−	15.1958i	−0.384106	−	0.611265i
$619$	−25.2667	+	16.6182i	−1.01556	+	0.667941i	−0.944153	−	0.329506i	$-0.893118\pi$
$619$	−25.2667	+	16.6182i	−1.01556	+	0.667941i	−0.0714021	+	0.997448i	$0.522747\pi$
$620$	19.0749	−	33.0387i	0.766066	−	1.32687i
$621$	3.10067	−	10.2054i	0.124426	−	0.409530i
$622$	−31.5546	−	54.6542i	−1.26523	−	2.19143i
$623$	−64.9290	−	32.6086i	−2.60133	−	1.30644i
$624$	−11.5529	+	4.70158i	−0.462486	+	0.188214i
$625$	−18.5530	−	24.9210i	−0.742121	−	0.996841i
$626$	11.3609	−	12.0419i	0.454075	−	0.481291i
$627$	−0.0696971	−	0.726791i	−0.00278344	−	0.0290252i
$628$	48.1507	+	5.62801i	1.92142	+	0.224582i
$629$	1.02733	+	0.373919i	0.0409625	+	0.0149091i
$630$	−11.4846	−	85.8199i	−0.457557	−	3.41914i
$631$	−0.842816	+	0.306760i	−0.0335520	+	0.0122119i	−0.358742	−	0.933437i	$-0.616794\pi$
$631$	−0.842816	+	0.306760i	−0.0335520	+	0.0122119i	0.325190	+	0.945649i	$0.394572\pi$
$632$	23.5025	−	5.57020i	0.934881	−	0.221571i
$633$	0.0999262	−	4.81490i	0.00397171	−	0.191375i
$634$	−27.7934	−	18.2800i	−1.10382	−	0.725991i
$635$	−13.1945	+	6.62653i	−0.523608	+	0.262966i
$636$	−6.58776	+	7.52808i	−0.261222	+	0.298508i
$637$	42.1509	+	44.6774i	1.67008	+	1.77018i
$638$	−0.164847	+	0.934896i	−0.00652637	+	0.0370129i
$639$	−27.2248	+	26.5572i	−1.07700	+	1.05059i
$640$	−9.48635	−	53.7998i	−0.374981	−	2.12662i
$641$	3.82175	−	5.13350i	0.150950	−	0.202761i	−0.720216	−	0.693750i	$-0.755957\pi$
$641$	3.82175	−	5.13350i	0.150950	−	0.202761i	0.871166	+	0.490989i	$0.163365\pi$
$642$	−25.0637	+	6.94029i	−0.989185	+	0.273912i
$643$	−14.5692	−	3.45295i	−0.574552	−	0.136171i	−0.0669396	−	0.997757i	$-0.521323\pi$
$643$	−14.5692	−	3.45295i	−0.574552	−	0.136171i	−0.507612	+	0.861586i	$0.669472\pi$
$644$	33.5254	−	3.91856i	1.32109	−	0.154413i
$645$	38.3359	−	34.6932i	1.50948	−	1.36604i
$646$	0.119224	+	2.04700i	0.00469081	+	0.0805381i
$647$	6.78181			0.266620			0.133310	−	0.991074i	$-0.457439\pi$
$647$	6.78181			0.266620			0.133310	+	0.991074i	$0.457439\pi$
$648$	29.4864	−	16.0616i	1.15834	−	0.630959i
$649$	2.55108			0.100139
$650$	−1.24074	−	21.3027i	−0.0486658	−	0.835560i
$651$	−6.70767	−	31.1706i	−0.262894	−	1.22167i
$652$	48.1931	−	5.63296i	1.88739	−	0.220604i
$653$	−34.7762	−	8.24211i	−1.36090	−	0.322539i	−0.515598	−	0.856831i	$-0.672430\pi$
$653$	−34.7762	−	8.24211i	−1.36090	−	0.322539i	−0.845300	+	0.534292i	$0.820578\pi$
$654$	25.6819	+	25.2572i	1.00424	+	0.987633i
$655$	−29.2240	+	39.2546i	−1.14187	+	1.53380i
$656$	0.0840162	+	0.476480i	0.00328028	+	0.0186034i
$657$	−7.55316	+	15.6865i	−0.294677	+	0.611988i
$658$	7.60912	−	43.1535i	0.296634	−	1.68230i
$659$	9.20156	+	9.75309i	0.358442	+	0.379926i	0.881351	−	0.472462i	$-0.156635\pi$
$659$	9.20156	+	9.75309i	0.358442	+	0.379926i	−0.522909	+	0.852389i	$0.675153\pi$
$660$	−2.57391	−	7.55602i	−0.100189	−	0.294118i
$661$	−7.10524	+	3.56839i	−0.276362	+	0.138794i	−0.581582	−	0.813488i	$-0.697566\pi$
$661$	−7.10524	+	3.56839i	−0.276362	+	0.138794i	0.305220	+	0.952282i	$0.401270\pi$
$662$	57.5891	+	37.8770i	2.23826	+	1.47213i
$663$	−6.58861	+	3.62378i	−0.255880	+	0.140736i
$664$	−46.1059	+	10.9273i	−1.78925	+	0.424061i
$665$	−9.99851	+	3.63916i	−0.387726	+	0.141121i
$666$	−7.40690	+	2.35276i	−0.287011	+	0.0911675i
$667$	1.60145	+	0.582879i	0.0620083	+	0.0225692i
$668$	−39.3676	−	4.60141i	−1.52318	−	0.178034i
$669$	37.5671	+	17.1379i	1.45243	+	0.662590i
$670$	62.1823	−	65.9094i	2.40231	−	2.54630i
$671$	1.16615	+	1.56641i	0.0450187	+	0.0604706i
$672$	−22.3387	−	17.3624i	−0.861736	−	0.669771i
$673$	−26.4238	−	13.2705i	−1.01856	−	0.511541i	−0.140497	−	0.990081i	$-0.544870\pi$
$673$	−26.4238	−	13.2705i	−1.01856	−	0.511541i	−0.878066	+	0.478540i	$0.841166\pi$
$674$	0.841829	+	1.45809i	0.0324260	+	0.0561635i
$675$	1.82844	+	10.6225i	0.0703766	+	0.408859i
$676$	−10.6778	+	18.4946i	−0.410686	+	0.711329i
$677$	21.6796	−	14.2589i	0.833214	−	0.548014i	−0.0597126	−	0.998216i	$-0.519018\pi$
$677$	21.6796	−	14.2589i	0.833214	−	0.548014i	0.892927	+	0.450202i	$0.148648\pi$
$678$	−72.4283	+	2.71204i	−2.78159	+	0.104155i
$679$	3.68760	−	8.54882i	0.141517	−	0.328074i
$680$	2.83701	+	9.47629i	0.108795	+	0.363399i
$681$	5.81184	+	0.459673i	0.222710	+	0.0176147i
$682$	−1.81478	−	4.20712i	−0.0694914	−	0.161099i
$683$	−11.3957	+	9.56212i	−0.436044	+	0.365885i	−0.834227	−	0.551422i	$-0.814086\pi$
$683$	−11.3957	+	9.56212i	−0.436044	+	0.365885i	0.398182	+	0.917306i	$0.369641\pi$
$684$	−6.12938	−	7.06211i	−0.234363	−	0.270027i
$685$	−11.6399	−	9.76706i	−0.444739	−	0.373180i
$686$	22.1085	−	73.8477i	0.844108	−	2.81952i
$687$	−10.0150	−	12.4512i	−0.382095	−	0.475043i
$688$	−1.07906	+	18.5267i	−0.0411388	+	0.706325i
$689$	−0.408580	+	7.01506i	−0.0155657	+	0.267252i
$690$	−22.0733	+	3.42150i	−0.840316	+	0.130254i
$691$	6.11101	−	20.4122i	0.232474	−	0.776516i	−0.759548	−	0.650451i	$-0.774580\pi$
$691$	6.11101	−	20.4122i	0.232474	−	0.776516i	0.992022	−	0.126065i	$-0.0402348\pi$
$692$	35.5512	+	29.8310i	1.35145	+	1.13400i
$693$	−5.83240	−	3.23888i	−0.221555	−	0.123035i
$694$	−24.9774	+	20.9586i	−0.948130	+	0.795576i
$695$	10.1066	+	23.4297i	0.383365	+	0.888739i
$696$	2.30779	+	4.84322i	0.0874765	+	0.183582i
$697$	0.0836550	+	0.279427i	0.00316866	+	0.0105841i
$698$	16.2404	−	37.6494i	0.614707	−	1.42505i
$699$	−3.41737	+	6.46640i	−0.129257	+	0.244582i
$700$	−28.4985	+	18.7437i	−1.07714	+	0.708447i
$701$	−11.9432	+	20.6862i	−0.451088	+	0.781308i	−0.998454	−	0.0555858i	$-0.982297\pi$
$701$	−11.9432	+	20.6862i	−0.451088	+	0.781308i	0.547366	+	0.836894i	$0.315631\pi$
$702$	21.3712	−	48.9942i	0.806605	−	1.84917i
$703$	0.477515	+	0.827081i	0.0180098	+	0.0311939i
$704$	−5.06388	−	2.54318i	−0.190852	−	0.0958496i
$705$	−2.54264	+	18.4288i	−0.0957615	+	0.694067i
$706$	14.8188	+	19.9051i	0.557712	+	0.749137i
$707$	22.7600	−	24.1241i	0.855976	−	0.907282i
$708$	26.6069	−	18.9629i	0.999949	−	0.712671i
$709$	30.2611	+	3.53701i	1.13648	+	0.132835i	0.663456	−	0.748215i	$-0.269089\pi$
$709$	30.2611	+	3.53701i	1.13648	+	0.132835i	0.473023	+	0.881050i	$0.343163\pi$
$710$	74.8443	+	27.2411i	2.80886	+	1.02234i
$711$	−10.4007	+	16.4029i	−0.390056	+	0.615156i
$712$	−55.4479	+	20.1814i	−2.07800	+	0.756329i
$713$	−8.00365	+	1.89690i	−0.299739	+	0.0710395i
$714$	16.0278	+	9.70252i	0.599824	+	0.363108i
$715$	−4.68475	−	3.08121i	−0.175200	−	0.115231i
$716$	80.9135	−	40.6363i	3.02388	−	1.51865i
$717$	7.66714	+	1.51659i	0.286335	+	0.0566382i
$718$	−4.18578	−	4.43666i	−0.156212	−	0.165575i
$719$	−7.27531	+	41.2603i	−0.271323	+	1.53875i	0.479081	+	0.877771i	$0.340970\pi$
$719$	−7.27531	+	41.2603i	−0.271323	+	1.53875i	−0.750404	+	0.660979i	$0.770141\pi$
$720$	−10.7133	−	7.70144i	−0.399260	−	0.287016i
$721$	3.49933	+	19.8457i	0.130322	+	0.739091i
$722$	25.7306	−	34.5622i	0.957595	−	1.28627i
$723$	3.65788	−	14.1213i	0.136038	−	0.525178i
$724$	−37.9047	−	8.98359i	−1.40872	−	0.333872i
$725$	−1.71057	+	0.199937i	−0.0635290	+	0.00742548i
$726$	41.9235	+	13.5051i	1.55593	+	0.501220i
$727$	1.20396	+	20.6712i	0.0446524	+	0.766653i	0.944107	+	0.329639i	$0.106927\pi$
$727$	1.20396	+	20.6712i	0.0446524	+	0.766653i	−0.899455	+	0.437014i	$0.856036\pi$
$728$	74.6402			2.76635
$729$	−7.95419	+	25.8018i	−0.294600	+	0.955621i
$730$	36.4605			1.34946
$731$	0.650520	+	11.1690i	0.0240603	+	0.413100i
$732$	23.8062	+	7.66880i	0.879901	+	0.283447i
$733$	39.8603	−	4.65900i	1.47227	−	0.172084i	0.658198	−	0.752845i	$-0.271319\pi$
$733$	39.8603	−	4.65900i	1.47227	−	0.172084i	0.814074	+	0.580761i	$0.197245\pi$
$734$	−50.8061	−	12.0413i	−1.87529	−	0.444452i
$735$	−16.2928	+	62.8988i	−0.600969	+	2.32006i
$736$	−4.35857	+	5.85457i	−0.160659	+	0.215802i
$737$	−1.21236	−	6.87566i	−0.0446580	−	0.253268i
$738$	−1.68357	−	1.21027i	−0.0619732	−	0.0445506i
$739$	5.98018	−	33.9153i	0.219985	−	1.24759i	−0.652060	−	0.758168i	$-0.726095\pi$
$739$	5.98018	−	33.9153i	0.219985	−	1.24759i	0.872044	−	0.489427i	$-0.162794\pi$
$740$	7.16522	+	7.59469i	0.263399	+	0.279186i
$741$	−6.44378	−	1.27461i	−0.236718	−	0.0468239i
$742$	15.6463	−	7.85789i	0.574395	−	0.288472i
$743$	−10.1980	−	6.70731i	−0.374127	−	0.246068i	0.348495	−	0.937311i	$-0.386693\pi$
$743$	−10.1980	−	6.70731i	−0.374127	−	0.246068i	−0.722622	+	0.691243i	$0.757063\pi$
$744$	−22.1511	−	13.4093i	−0.812100	−	0.491611i
$745$	−42.6333	+	10.1043i	−1.56196	+	0.370192i
$746$	−23.0200	+	8.37859i	−0.842822	+	0.306762i
$747$	20.4034	−	32.1782i	0.746523	−	1.17734i
$748$	1.62311	+	0.590763i	0.0593467	+	0.0216004i
$749$	29.0046	+	3.39015i	1.05980	+	0.123873i
$750$	−25.9255	+	18.4773i	−0.946665	+	0.674695i
$751$	27.2113	−	28.8423i	0.992956	−	1.05247i	−0.00566603	−	0.999984i	$-0.501804\pi$
$751$	27.2113	−	28.8423i	0.992956	−	1.05247i	0.998622	−	0.0524875i	$-0.0167150\pi$
$752$	−3.98744	−	5.35606i	−0.145407	−	0.195316i
$753$	−2.17466	+	15.7617i	−0.0792491	+	0.574387i
$754$	7.63218	+	3.83303i	0.277948	+	0.139591i
$755$	15.6502	+	27.1070i	0.569570	+	0.986525i
$756$	−84.9056	+	9.57357i	−3.08799	+	0.348187i
$757$	−9.73596	+	16.8632i	−0.353859	+	0.612902i	−0.986922	−	0.161198i	$-0.948464\pi$
$757$	−9.73596	+	16.8632i	−0.353859	+	0.612902i	0.633063	+	0.774101i	$0.281798\pi$
$758$	−15.6490	+	10.2925i	−0.568399	+	0.373842i
$759$	−0.804156	+	1.52164i	−0.0291890	+	0.0552319i
$760$	−3.42256	+	7.93440i	−0.124149	+	0.287811i
$761$	−1.63523	−	5.46204i	−0.0592769	−	0.197999i	0.923222	−	0.384267i	$-0.125546\pi$
$761$	−1.63523	−	5.46204i	−0.0592769	−	0.197999i	−0.982499	+	0.186268i	$0.940361\pi$
$762$	9.76961	+	20.5029i	0.353916	+	0.742742i
$763$	−16.0199	−	37.1382i	−0.579958	−	1.34449i
$764$	32.3989	−	27.1859i	1.17215	−	0.983551i
$765$	−6.95392	−	3.86169i	−0.251420	−	0.139620i
$766$	−7.93940	−	6.66195i	−0.286862	−	0.240706i
$767$	6.58242	−	21.9868i	0.237677	−	0.793898i
$768$	−42.9672	+

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.137343 + 2.35809i) q^{2} +(1.64862 + 0.531080i) q^{3} +(-3.55525 + 0.415549i) q^{4} +(-2.58807 - 0.613384i) q^{5} +(-1.02591 + 3.96054i) q^{6} +(2.74329 - 3.68487i) q^{7} +(-0.647845 - 3.67411i) q^{8} +(2.43591 + 1.75110i) q^{9} +O(q^{10})\)	\(q+(0.137343 + 2.35809i) q^{2} +(1.64862 + 0.531080i) q^{3} +(-3.55525 + 0.415549i) q^{4} +(-2.58807 - 0.613384i) q^{5} +(-1.02591 + 3.96054i) q^{6} +(2.74329 - 3.68487i) q^{7} +(-0.647845 - 3.67411i) q^{8} +(2.43591 + 1.75110i) q^{9} +(1.09096 - 6.18715i) q^{10} +(-0.332192 - 0.352103i) q^{11} +(-6.08194 - 1.20304i) q^{12} +(-3.89179 + 1.95453i) q^{13} +(9.06604 + 5.96283i) q^{14} +(-3.94100 - 2.38571i) q^{15} +(1.60898 - 0.381335i) q^{16} +(0.936739 - 0.340945i) q^{17} +(-3.79469 + 5.98459i) q^{18} +(0.818296 + 0.297835i) q^{19} +(9.45612 + 1.10526i) q^{20} +(6.47961 - 4.61806i) q^{21} +(0.784667 - 0.831698i) q^{22} +(-1.22578 - 1.64651i) q^{23} +(0.883194 - 6.40128i) q^{24} +(1.85371 + 0.930971i) q^{25} +(-5.14346 - 8.90874i) q^{26} +(3.08592 + 4.18056i) q^{27} +(-8.22182 + 14.2406i) q^{28} +(-0.693656 + 0.456225i) q^{29} +(5.08445 - 9.62088i) q^{30} +(1.58714 - 3.67940i) q^{31} +(-1.01980 - 3.40637i) q^{32} +(-0.360665 - 0.756906i) q^{33} +(0.932634 + 2.16209i) q^{34} +(-9.36007 + 7.85403i) q^{35} +(-9.38792 - 5.21335i) q^{36} +(0.840131 + 0.704953i) q^{37} +(-0.589935 + 1.97052i) q^{38} +(-7.45410 + 1.15543i) q^{39} +(-0.576973 + 9.90625i) q^{40} +(-0.0170132 + 0.292105i) q^{41} +(11.7797 + 14.6452i) q^{42} +(-3.21885 + 10.7517i) q^{43} +(1.32734 + 1.11377i) q^{44} +(-5.23021 - 6.02612i) q^{45} +(3.71426 - 3.11664i) q^{46} +(-1.59945 - 3.70793i) q^{47} +(2.85512 + 0.225819i) q^{48} +(-4.04505 - 13.5114i) q^{49} +(-1.94072 + 4.49909i) q^{50} +(1.72540 - 0.0646067i) q^{51} +(13.0241 - 8.56606i) q^{52} +(0.806764 - 1.39736i) q^{53} +(-9.43431 + 7.85105i) q^{54} +(0.643763 + 1.11503i) q^{55} +(-15.3159 - 7.69192i) q^{56} +(1.19089 + 0.925598i) q^{57} +(-1.17109 - 1.57304i) q^{58} +(-3.61650 + 3.83327i) q^{59} +(15.0026 + 6.84411i) q^{60} +(-4.00687 - 0.468336i) q^{61} +(8.89434 + 3.23728i) q^{62} +(13.1350 - 4.17225i) q^{63} +(11.0001 - 4.00372i) q^{64} +(11.2711 - 2.67130i) q^{65} +(1.73532 - 0.954435i) q^{66} +(12.0501 + 7.92548i) q^{67} +(-3.18866 + 1.60140i) q^{68} +(-1.14642 - 3.36546i) q^{69} +(-19.8061 - 20.9932i) q^{70} +(-2.20143 + 12.4849i) q^{71} +(4.85564 - 10.0842i) q^{72} +(1.00775 + 5.71524i) q^{73} +(-1.54696 + 2.07792i) q^{74} +(2.56166 + 2.51929i) q^{75} +(-3.03301 - 0.718836i) q^{76} +(-2.20876 + 0.258166i) q^{77} +(-3.74838 - 17.4187i) q^{78} +(0.376437 + 6.46317i) q^{79} -4.39806 q^{80} +(2.86731 + 8.53103i) q^{81} -0.691147 q^{82} +(-0.738471 - 12.6791i) q^{83} +(-21.1176 + 19.1109i) q^{84} +(-2.63348 + 0.307810i) q^{85} +(-25.7956 - 6.11366i) q^{86} +(-1.38587 + 0.383756i) q^{87} +(-1.07846 + 1.44862i) q^{88} +(-2.74643 - 15.5758i) q^{89} +(13.4918 - 13.1610i) q^{90} +(-3.47410 + 19.7026i) q^{91} +(5.04215 + 5.34437i) q^{92} +(4.57065 - 5.22305i) q^{93} +(8.52396 - 4.28089i) q^{94} +(-1.93512 - 1.27275i) q^{95} +(0.127788 - 6.15742i) q^{96} +(1.97203 - 0.467379i) q^{97} +(31.3056 - 11.3943i) q^{98} +(-0.192623 - 1.43939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

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