LMFDB - Embedded newform 225.2.q.a.196.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			196.20
Character	$\chi$	$=$	225.196
Dual form			225.2.q.a.31.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.797750 + 0.885991i) q^{2} +(-1.56929 - 0.733023i) q^{3} +(0.0604816 - 0.575444i) q^{4} +(1.30610 + 1.81497i) q^{5} +(-0.602450 - 1.97515i) q^{6} +(0.157578 - 0.272934i) q^{7} +(2.48714 - 1.80701i) q^{8} +(1.92535 + 2.30066i) q^{9} +O(q^{10})$	\(q+(0.797750 + 0.885991i) q^{2} +(-1.56929 - 0.733023i) q^{3} +(0.0604816 - 0.575444i) q^{4} +(1.30610 + 1.81497i) q^{5} +(-0.602450 - 1.97515i) q^{6} +(0.157578 - 0.272934i) q^{7} +(2.48714 - 1.80701i) q^{8} +(1.92535 + 2.30066i) q^{9} +(-0.566103 + 2.60508i) q^{10} +(1.93450 + 2.14848i) q^{11} +(-0.516727 + 0.858705i) q^{12} +(4.36810 - 4.85127i) q^{13} +(0.367525 - 0.0781199i) q^{14} +(-0.719240 - 3.80561i) q^{15} +(2.45317 + 0.521438i) q^{16} +(0.794350 - 0.577129i) q^{17} +(-0.502410 + 3.54119i) q^{18} +(-5.88399 + 4.27497i) q^{19} +(1.12341 - 0.641816i) q^{20} +(-0.447354 + 0.312804i) q^{21} +(-0.360286 + 3.42790i) q^{22} +(1.28104 - 0.272294i) q^{23} +(-5.22763 + 1.01260i) q^{24} +(-1.58820 + 4.74106i) q^{25} +7.78284 q^{26} +(-1.33501 - 5.02173i) q^{27} +(-0.147528 - 0.107185i) q^{28} +(-3.94048 + 1.75442i) q^{29} +(2.79797 - 3.67317i) q^{30} +(-7.91741 - 3.52506i) q^{31} +(-1.57924 - 2.73533i) q^{32} +(-1.46091 - 4.78962i) q^{33} +(1.14502 + 0.243382i) q^{34} +(0.701179 - 0.0704794i) q^{35} +(1.44035 - 0.968786i) q^{36} +(0.00738727 + 0.0227357i) q^{37} +(-8.48155 - 1.80281i) q^{38} +(-10.4109 + 4.41114i) q^{39} +(6.52812 + 2.15393i) q^{40} +(3.06561 - 3.40470i) q^{41} +(-0.634018 - 0.146812i) q^{42} +(-1.34599 + 2.33132i) q^{43} +(1.35333 - 0.983252i) q^{44} +(-1.66091 + 6.49934i) q^{45} +(1.26320 + 0.917772i) q^{46} +(-4.76261 + 2.12045i) q^{47} +(-3.46752 - 2.61652i) q^{48} +(3.45034 + 5.97616i) q^{49} +(-5.46752 + 2.37504i) q^{50} +(-1.66962 + 0.323407i) q^{51} +(-2.52745 - 2.80701i) q^{52} +(-3.44104 - 2.50006i) q^{53} +(3.38421 - 5.18889i) q^{54} +(-1.37277 + 6.31717i) q^{55} +(-0.101275 - 0.963571i) q^{56} +(12.3674 - 2.39557i) q^{57} +(-4.69792 - 2.09165i) q^{58} +(3.46632 - 3.84974i) q^{59} +(-2.23342 + 0.183713i) q^{60} +(-4.95936 - 5.50792i) q^{61} +(-3.19295 - 9.82688i) q^{62} +(0.931321 - 0.162961i) q^{63} +(2.71365 - 8.35176i) q^{64} +(14.5101 + 1.59172i) q^{65} +(3.07812 - 5.11527i) q^{66} +(-2.27694 - 1.01376i) q^{67} +(-0.284062 - 0.492010i) q^{68} +(-2.20993 - 0.511726i) q^{69} +(0.621810 + 0.565014i) q^{70} +(9.63629 + 7.00118i) q^{71} +(8.94593 + 2.24291i) q^{72} +(-0.283594 + 0.872814i) q^{73} +(-0.0142504 + 0.0246825i) q^{74} +(5.96766 - 6.27591i) q^{75} +(2.10413 + 3.64447i) q^{76} +(0.891228 - 0.189436i) q^{77} +(-12.2135 - 5.70500i) q^{78} +(-10.3980 + 4.62948i) q^{79} +(2.25770 + 5.13348i) q^{80} +(-1.58603 + 8.85915i) q^{81} +5.46212 q^{82} +(1.03926 + 9.88793i) q^{83} +(0.152945 + 0.276346i) q^{84} +(2.08497 + 0.687930i) q^{85} +(-3.13929 + 0.667278i) q^{86} +(7.46979 + 0.135276i) q^{87} +(8.69369 + 1.84790i) q^{88} +(3.78718 - 11.6557i) q^{89} +(-7.08335 + 3.71330i) q^{90} +(-0.635757 - 1.95666i) q^{91} +(-0.0792106 - 0.753639i) q^{92} +(9.84078 + 11.3355i) q^{93} +(-5.67808 - 2.52804i) q^{94} +(-15.4440 - 5.09571i) q^{95} +(0.473233 + 5.45015i) q^{96} +(-6.75362 + 3.00691i) q^{97} +(-2.54232 + 7.82445i) q^{98} +(-1.21831 + 8.58719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.797750	+	0.885991i	0.564095	+	0.626491i	0.955948	−	0.293537i	$-0.0948325\pi$
$2$	0.797750	+	0.885991i	0.564095	+	0.626491i	−0.391853	+	0.920028i	$0.628166\pi$
$3$	−1.56929	−	0.733023i	−0.906031	−	0.423211i
$3$	−1.56929	−	0.733023i	−0.906031	−	0.423211i
$4$	0.0604816	−	0.575444i	0.0302408	−	0.287722i
$5$	1.30610	+	1.81497i	0.584106	+	0.811678i
$5$	1.30610	+	1.81497i	0.584106	+	0.811678i
$6$	−0.602450	−	1.97515i	−0.245949	−	0.806351i
$7$	0.157578	−	0.272934i	0.0595591	−	0.103159i	−0.834708	−	0.550692i	$-0.814364\pi$
$7$	0.157578	−	0.272934i	0.0595591	−	0.103159i	0.894268	+	0.447533i	$0.147697\pi$
$8$	2.48714	−	1.80701i	0.879336	−	0.638875i
$9$	1.92535	+	2.30066i	0.641784	+	0.766885i
$10$	−0.566103	+	2.60508i	−0.179017	+	0.823800i
$11$	1.93450	+	2.14848i	0.583273	+	0.647790i	0.960483	−	0.278337i	$-0.0897833\pi$
$11$	1.93450	+	2.14848i	0.583273	+	0.647790i	−0.377210	+	0.926128i	$0.623117\pi$
$12$	−0.516727	+	0.858705i	−0.149166	+	0.247887i
$13$	4.36810	−	4.85127i	1.21149	−	1.34550i	0.290039	−	0.957015i	$-0.406332\pi$
$13$	4.36810	−	4.85127i	1.21149	−	1.34550i	0.921455	−	0.388486i	$-0.127002\pi$
$14$	0.367525	−	0.0781199i	0.0982253	−	0.0208784i
$15$	−0.719240	−	3.80561i	−0.185707	−	0.982605i
$16$	2.45317	+	0.521438i	0.613293	+	0.130359i
$17$	0.794350	−	0.577129i	0.192658	−	0.139974i	−0.487275	−	0.873249i	$-0.662009\pi$
$17$	0.794350	−	0.577129i	0.192658	−	0.139974i	0.679933	+	0.733274i	$0.262009\pi$
$18$	−0.502410	+	3.54119i	−0.118419	+	0.834668i
$19$	−5.88399	+	4.27497i	−1.34988	+	0.980746i	−0.350863	+	0.936427i	$0.614112\pi$
$19$	−5.88399	+	4.27497i	−1.34988	+	0.980746i	−0.999017	+	0.0443190i	$0.985888\pi$
$20$	1.12341	−	0.641816i	0.251201	−	0.143514i
$21$	−0.447354	+	0.312804i	−0.0976206	+	0.0682595i
$22$	−0.360286	+	3.42790i	−0.0768133	+	0.730830i
$23$	1.28104	−	0.272294i	0.267116	−	0.0567773i	−0.0724063	−	0.997375i	$-0.523068\pi$
$23$	1.28104	−	0.272294i	0.267116	−	0.0567773i	0.339523	+	0.940598i	$0.389734\pi$
$24$	−5.22763	+	1.01260i	−1.06709	+	0.206696i
$25$	−1.58820	+	4.74106i	−0.317641	+	0.948211i
$26$	7.78284			1.52634
$27$	−1.33501	−	5.02173i	−0.256922	−	0.966432i
$28$	−0.147528	−	0.107185i	−0.0278801	−	0.0202561i
$29$	−3.94048	+	1.75442i	−0.731729	+	0.325787i	−0.738558	−	0.674190i	$-0.764493\pi$
$29$	−3.94048	+	1.75442i	−0.731729	+	0.325787i	0.00682892	+	0.999977i	$0.497826\pi$
$30$	2.79797	−	3.67317i	0.510837	−	0.670626i
$31$	−7.91741	−	3.52506i	−1.42201	−	0.633120i	−0.455614	−	0.890178i	$-0.650580\pi$
$31$	−7.91741	−	3.52506i	−1.42201	−	0.633120i	−0.966396	+	0.257058i	$0.917247\pi$
$32$	−1.57924	−	2.73533i	−0.279173	−	0.483542i
$33$	−1.46091	−	4.78962i	−0.254311	−	0.833766i
$34$	1.14502	+	0.243382i	0.196370	+	0.0417397i
$35$	0.701179	−	0.0704794i	0.118521	−	0.0119132i
$36$	1.44035	−	0.968786i	0.240058	−	0.161464i
$37$	0.00738727	+	0.0227357i	0.00121446	+	0.00373772i	0.951662	−	0.307148i	$-0.0993745\pi$
$37$	0.00738727	+	0.0227357i	0.00121446	+	0.00373772i	−0.950447	+	0.310885i	$0.899375\pi$
$38$	−8.48155	−	1.80281i	−1.37589	−	0.292454i
$39$	−10.4109	+	4.41114i	−1.66708	+	0.706347i
$40$	6.52812	+	2.15393i	1.03219	+	0.340567i
$41$	3.06561	−	3.40470i	0.478767	−	0.531725i	−0.454577	−	0.890707i	$-0.650210\pi$
$41$	3.06561	−	3.40470i	0.478767	−	0.531725i	0.933344	+	0.358983i	$0.116876\pi$
$42$	−0.634018	−	0.146812i	−0.0978311	−	0.0226535i
$43$	−1.34599	+	2.33132i	−0.205261	+	0.355523i	−0.950216	−	0.311592i	$-0.899138\pi$
$43$	−1.34599	+	2.33132i	−0.205261	+	0.355523i	0.744955	+	0.667115i	$0.232471\pi$
$44$	1.35333	−	0.983252i	0.204022	−	0.148231i
$45$	−1.66091	+	6.49934i	−0.247593	+	0.968864i
$46$	1.26320	+	0.917772i	0.186249	+	0.135318i
$47$	−4.76261	+	2.12045i	−0.694698	+	0.309300i	−0.723538	−	0.690284i	$-0.757485\pi$
$47$	−4.76261	+	2.12045i	−0.694698	+	0.309300i	0.0288398	+	0.999584i	$0.490819\pi$
$48$	−3.46752	−	2.61652i	−0.500493	−	0.377662i
$49$	3.45034	+	5.97616i	0.492905	+	0.853737i
$50$	−5.46752	+	2.37504i	−0.773225	+	0.335882i
$51$	−1.66962	+	0.323407i	−0.233793	+	0.0452860i
$52$	−2.52745	−	2.80701i	−0.350494	−	0.389263i
$53$	−3.44104	−	2.50006i	−0.472663	−	0.343410i	0.325815	−	0.945433i	$-0.394361\pi$
$53$	−3.44104	−	2.50006i	−0.472663	−	0.343410i	−0.798478	+	0.602024i	$0.794361\pi$
$54$	3.38421	−	5.18889i	0.460532	−	0.706118i
$55$	−1.37277	+	6.31717i	−0.185104	+	0.851808i
$56$	−0.101275	−	0.963571i	−0.0135335	−	0.128763i
$57$	12.3674	−	2.39557i	1.63810	−	0.317301i
$58$	−4.69792	−	2.09165i	−0.616867	−	0.274647i
$59$	3.46632	−	3.84974i	0.451276	−	0.501193i	−0.473980	−	0.880536i	$-0.657183\pi$
$59$	3.46632	−	3.84974i	0.451276	−	0.501193i	0.925256	+	0.379342i	$0.123850\pi$
$60$	−2.23342	+	0.183713i	−0.288333	+	0.0237172i
$61$	−4.95936	−	5.50792i	−0.634980	−	0.705217i	0.336674	−	0.941621i	$-0.390698\pi$
$61$	−4.95936	−	5.50792i	−0.634980	−	0.705217i	−0.971655	+	0.236404i	$0.924031\pi$
$62$	−3.19295	−	9.82688i	−0.405505	−	1.24801i
$63$	0.931321	−	0.162961i	0.117335	−	0.0205311i
$64$	2.71365	−	8.35176i	0.339207	−	1.04397i
$65$	14.5101	+	1.59172i	1.79975	+	0.197428i
$66$	3.07812	−	5.11527i	0.378891	−	0.629646i
$67$	−2.27694	−	1.01376i	−0.278173	−	0.123851i	0.262908	−	0.964821i	$-0.415318\pi$
$67$	−2.27694	−	1.01376i	−0.278173	−	0.123851i	−0.541081	+	0.840970i	$0.681985\pi$
$68$	−0.284062	−	0.492010i	−0.0344476	−	0.0596649i
$69$	−2.20993	−	0.511726i	−0.266044	−	0.0616046i
$70$	0.621810	+	0.565014i	0.0743205	+	0.0675321i
$71$	9.63629	+	7.00118i	1.14362	+	0.830887i	0.987619	−	0.156870i	$-0.0501405\pi$
$71$	9.63629	+	7.00118i	1.14362	+	0.830887i	0.155999	+	0.987757i	$0.450140\pi$
$72$	8.94593	+	2.24291i	1.05429	+	0.264330i
$73$	−0.283594	+	0.872814i	−0.0331922	+	0.102155i	−0.966280	−	0.257493i	$-0.917103\pi$
$73$	−0.283594	+	0.872814i	−0.0331922	+	0.102155i	0.933088	+	0.359649i	$0.117103\pi$
$74$	−0.0142504	+	0.0246825i	−0.00165658	+	0.00286928i
$75$	5.96766	−	6.27591i	0.689086	−	0.724679i
$76$	2.10413	+	3.64447i	0.241361	+	0.418049i
$77$	0.891228	−	0.189436i	0.101565	−	0.0215883i
$78$	−12.2135	−	5.70500i	−1.38291	−	0.645964i
$79$	−10.3980	+	4.62948i	−1.16986	+	0.520857i	−0.897361	−	0.441298i	$-0.854518\pi$
$79$	−10.3980	+	4.62948i	−1.16986	+	0.520857i	−0.272503	+	0.962155i	$0.587851\pi$
$80$	2.25770	+	5.13348i	0.252418	+	0.573940i
$81$	−1.58603	+	8.85915i	−0.176225	+	0.984350i
$82$	5.46212			0.603191
$83$	1.03926	+	9.88793i	0.114074	+	1.08534i	0.890453	+	0.455075i	$0.150388\pi$
$83$	1.03926	+	9.88793i	0.114074	+	1.08534i	−0.776379	+	0.630266i	$0.782946\pi$
$84$	0.152945	+	0.276346i	0.0166876	+	0.0301518i
$85$	2.08497	+	0.687930i	0.226147	+	0.0746165i
$86$	−3.13929	+	0.667278i	−0.338519	+	0.0719544i
$87$	7.46979	+	0.135276i	0.800846	+	0.0145031i
$88$	8.69369	+	1.84790i	0.926750	+	0.196987i
$89$	3.78718	−	11.6557i	0.401440	−	1.23551i	−0.522391	−	0.852706i	$-0.674960\pi$
$89$	3.78718	−	11.6557i	0.401440	−	1.23551i	0.923831	−	0.382800i	$-0.125040\pi$
$90$	−7.08335	+	3.71330i	−0.746650	+	0.391416i
$91$	−0.635757	−	1.95666i	−0.0666455	−	0.205114i
$92$	−0.0792106	−	0.753639i	−0.00825828	−	0.0785723i
$93$	9.84078	+	11.3355i	1.02044	+	1.17544i
$94$	−5.67808	−	2.52804i	−0.585649	−	0.260748i
$95$	−15.4440	−	5.09571i	−1.58452	−	0.522809i
$96$	0.473233	+	5.45015i	0.0482991	+	0.556254i
$97$	−6.75362	+	3.00691i	−0.685726	+	0.305305i	−0.719867	−	0.694112i	$-0.755797\pi$
$97$	−6.75362	+	3.00691i	−0.685726	+	0.305305i	0.0341407	+	0.999417i	$0.489131\pi$
$98$	−2.54232	+	7.82445i	−0.256813	+	0.790389i
$99$	−1.21831	+	8.58719i	−0.122445	+	0.863045i
$100$	2.63216	+	1.20067i	0.263216	+	0.120067i
$101$	−5.77262	+	9.99848i	−0.574397	+	0.994885i	0.421709	+	0.906731i	$0.361430\pi$
$101$	−5.77262	+	9.99848i	−0.574397	+	0.994885i	−0.996107	+	0.0881544i	$0.971903\pi$
$102$	−1.61847	−	1.22127i	−0.160253	−	0.120923i
$103$	1.71092	−	16.2783i	0.168582	−	1.60395i	−0.503851	−	0.863790i	$-0.668084\pi$
$103$	1.71092	−	16.2783i	0.168582	−	1.60395i	0.672433	−	0.740158i	$-0.265249\pi$
$104$	2.09778	−	19.9590i	0.205704	−	1.95714i
$105$	−1.15202	−	0.403378i	−0.112425	−	0.0393657i
$106$	−0.530057	−	5.04315i	−0.0514837	−	0.489834i
$107$	−10.1611			−0.982314			−0.491157	−	0.871071i	$-0.663426\pi$
$107$	−10.1611			−0.982314			−0.491157	+	0.871071i	$0.663426\pi$
$108$	−2.97047	+	0.464500i	−0.285833	+	0.0446965i
$109$	3.42411	+	10.5383i	0.327970	+	1.00939i	0.970082	+	0.242777i	$0.0780584\pi$
$109$	3.42411	+	10.5383i	0.327970	+	1.00939i	−0.642112	+	0.766611i	$0.721942\pi$
$110$	−6.69209	+	3.82327i	−0.638065	+	0.364534i
$111$	0.00507301	−	0.0410940i	0.000481508	−	0.00390047i
$112$	0.528885	−	0.587387i	0.0499750	−	0.0555028i
$113$	−9.81486	+	10.9005i	−0.923305	+	1.02543i	0.0762934	+	0.997085i	$0.475691\pi$
$113$	−9.81486	+	10.9005i	−0.923305	+	1.02543i	−0.999598	+	0.0283484i	$0.990975\pi$
$114$	11.9885	+	9.04630i	1.12283	+	0.847264i
$115$	2.16738	+	1.96941i	0.202109	+	0.183648i
$116$	0.771242	+	2.37364i	0.0716080	+	0.220387i
$117$	19.5712	+	0.709090i	1.80936	+	0.0655554i
$118$	6.17609			0.568555
$119$	−0.0323456	−	0.307748i	−0.00296512	−	0.0282112i
$120$	−8.66564	−	8.16541i	−0.791061	−	0.745397i
$121$	0.276140	−	2.62729i	0.0251036	−	0.238845i
$122$	0.923645	−	8.78789i	0.0836229	−	0.795618i
$123$	−7.30655	+	3.09581i	−0.658810	+	0.279140i
$124$	−2.50733	+	4.34283i	−0.225165	+	0.389998i
$125$	−10.6792	+	3.30976i	−0.955178	+	0.296034i
$126$	0.887343	+	0.695141i	0.0790508	+	0.0619281i
$127$	4.75644	−	14.6388i	0.422066	−	1.29899i	−0.483710	−	0.875228i	$-0.660711\pi$
$127$	4.75644	−	14.6388i	0.422066	−	1.29899i	0.905776	−	0.423757i	$-0.139289\pi$
$128$	3.79357	−	1.68900i	0.335307	−	0.149288i
$129$	3.82116	−	2.67188i	0.336435	−	0.235246i
$130$	10.1652	+	14.1256i	0.891544	+	1.23890i
$131$	3.04960	+	1.35777i	0.266445	+	0.118629i	0.535611	−	0.844465i	$-0.320081\pi$
$131$	3.04960	+	1.35777i	0.266445	+	0.118629i	−0.269166	+	0.963094i	$0.586748\pi$
$132$	−2.84452	+	0.550987i	−0.247583	+	0.0479572i
$133$	0.239594	+	2.27959i	0.0207754	+	0.197665i
$134$	−0.918249	−	2.82608i	−0.0793247	−	0.244136i
$135$	7.37061	−	8.98187i	0.634361	−	0.773037i
$136$	0.932779	−	2.87080i	0.0799851	−	0.246169i
$137$	8.26092	+	1.75591i	0.705778	+	0.150018i	0.546799	−	0.837264i	$-0.315846\pi$
$137$	8.26092	+	1.75591i	0.705778	+	0.150018i	0.158979	+	0.987282i	$0.449180\pi$
$138$	−1.30959	−	2.36621i	−0.111480	−	0.201425i
$139$	1.39912	−	0.297391i	0.118671	−	0.0252244i	−0.148193	−	0.988958i	$-0.547346\pi$
$139$	1.39912	−	0.297391i	0.118671	−	0.0252244i	0.266864	+	0.963734i	$0.414012\pi$
$140$	0.00185147	−	0.407752i	0.000156477	−	0.0344613i
$141$	9.02827	+	0.163499i	0.760317	+	0.0137691i
$142$	1.48437	+	14.1229i	0.124566	+	1.18516i
$143$	18.8729			1.57823
$144$	3.52358	+	6.64786i	0.293631	+	0.553988i
$145$	−8.33087	−	4.86040i	−0.691841	−	0.403634i
$146$	−0.999543	+	0.445025i	−0.0827228	+	0.0368305i
$147$	−1.03392	−	11.9075i	−0.0852764	−	0.982116i
$148$	0.0135299	−	0.00287587i	0.00111215	−	0.000236395i
$149$	10.3534	+	17.9326i	0.848181	+	1.46909i	0.882830	+	0.469693i	$0.155635\pi$
$149$	10.3534	+	17.9326i	0.848181	+	1.46909i	−0.0346486	+	0.999400i	$0.511031\pi$
$150$	10.3211	+	0.280689i	0.842715	+	0.0229182i
$151$	10.6562	−	18.4570i	0.867186	−	1.50201i	0.00232675	−	0.999997i	$-0.499259\pi$
$151$	10.6562	−	18.4570i	0.867186	−	1.50201i	0.864860	−	0.502014i	$-0.167407\pi$
$152$	−6.90938	+	21.2649i	−0.560425	+	1.72481i
$153$	2.85718	+	0.716348i	0.230989	+	0.0579133i
$154$	0.878816	+	0.638497i	0.0708170	+	0.0514516i
$155$	−3.94307	−	18.9739i	−0.316715	−	1.52402i
$156$	1.90869	+	6.25770i	0.152818	+	0.501017i
$157$	−6.98186	−	12.0929i	−0.557213	−	0.965122i	−0.997728	−	0.0673760i	$-0.978537\pi$
$157$	−6.98186	−	12.0929i	−0.557213	−	0.965122i	0.440514	−	0.897746i	$-0.354796\pi$
$158$	−12.3967	−	5.51935i	−0.986226	−	0.439096i
$159$	3.56739	+	6.44568i	0.282912	+	0.511176i
$160$	2.90188	−	6.43889i	0.229414	−	0.509039i
$161$	0.127547	−	0.392548i	0.0100521	−	0.0309371i
$162$	−9.11438	+	5.66218i	−0.716094	+	0.444863i
$163$	−0.190245	−	0.585515i	−0.0149012	−	0.0458611i	0.943329	−	0.331858i	$-0.107675\pi$
$163$	−0.190245	−	0.585515i	−0.0149012	−	0.0458611i	−0.958231	+	0.285997i	$0.907675\pi$
$164$	−1.77380	−	1.97001i	−0.138511	−	0.153832i
$165$	6.78491	−	8.90722i	0.528204	−	0.693426i
$166$	−7.93155	+	8.80888i	−0.615608	+	0.683702i
$167$	−4.93325	−	2.19642i	−0.381746	−	0.169964i	0.206887	−	0.978365i	$-0.433667\pi$
$167$	−4.93325	−	2.19642i	−0.381746	−	0.169964i	−0.588633	+	0.808401i	$0.700334\pi$
$168$	−0.547389	+	1.58636i	−0.0422320	+	0.122390i
$169$	−3.09563	−	29.4529i	−0.238125	−	2.26561i
$170$	1.05378	+	2.39606i	0.0808216	+	0.183769i
$171$	−21.1640	−	5.30621i	−1.61845	−	0.405776i
$172$	1.26014	+	0.915544i	0.0960846	+	0.0698096i
$173$	−0.243366	−	0.270286i	−0.0185028	−	0.0205494i	0.733822	−	0.679341i	$-0.237734\pi$
$173$	−0.243366	−	0.270286i	−0.0185028	−	0.0205494i	−0.752325	+	0.658792i	$0.771068\pi$
$174$	5.83918	+	6.72609i	0.442667	+	0.509903i
$175$	1.04373	+	1.18056i	0.0788984	+	0.0892422i
$176$	3.62536	+	6.27931i	0.273272	+	0.473321i
$177$	−8.26161	+	3.50047i	−0.620981	+	0.263111i
$178$	13.3481	−	5.94296i	1.00048	−	0.445444i
$179$	12.2855	+	8.92591i	0.918259	+	0.667154i	0.943090	−	0.332538i	$-0.107905\pi$
$179$	12.2855	+	8.92591i	0.918259	+	0.667154i	−0.0248313	+	0.999692i	$0.507905\pi$
$180$	3.63955	+	1.34885i	0.271276	+	0.100537i
$181$	0.0462635	−	0.0336124i	0.00343874	−	0.00249839i	−0.586065	−	0.810264i	$-0.699324\pi$
$181$	0.0462635	−	0.0336124i	0.00343874	−	0.00249839i	0.589503	+	0.807766i	$0.299324\pi$
$182$	1.22641	−	2.12420i	0.0909074	−	0.157456i
$183$	3.74524	+	12.2789i	0.276856	+	0.907680i
$184$	2.69410	−	2.99210i	0.198611	−	0.220580i
$185$	−0.0316160	+	0.0431027i	−0.00232445	+	0.00316898i
$186$	−2.19267	+	17.7617i	−0.160774	+	1.30235i
$187$	2.77662	+	0.590188i	0.203046	+	0.0431588i
$188$	0.932151	+	2.86887i	0.0679841	+	0.209234i
$189$	−1.58097	−	0.426948i	−0.114999	−	0.0310559i
$190$	−7.80571	−	17.7484i	−0.566286	−	1.28760i
$191$	−2.34418	−	0.498271i	−0.169619	−	0.0360536i	0.122319	−	0.992491i	$-0.460967\pi$
$191$	−2.34418	−	0.498271i	−0.169619	−	0.0360536i	−0.291938	+	0.956437i	$0.594300\pi$
$192$	−10.3805	+	11.1172i	−0.749152	+	0.802313i
$193$	2.94773	+	5.10562i	0.212182	+	0.367511i	0.952397	−	0.304860i	$-0.0986095\pi$
$193$	2.94773	+	5.10562i	0.212182	+	0.367511i	−0.740215	+	0.672370i	$0.765276\pi$
$194$	−8.05179	−	3.58489i	−0.578085	−	0.257380i
$195$	−21.6038	−	13.1341i	−1.54708	−	0.940552i
$196$	3.64763	−	1.62403i	0.260545	−	0.116002i
$197$	−12.8434	−	9.33130i	−0.915057	−	0.664828i	0.0272318	−	0.999629i	$-0.491331\pi$
$197$	−12.8434	−	9.33130i	−0.915057	−	0.664828i	−0.942289	+	0.334801i	$0.891331\pi$
$198$	−8.58009	+	5.77102i	−0.609760	+	0.410128i
$199$	4.61006			0.326798			0.163399	−	0.986560i	$-0.447754\pi$
$199$	4.61006			0.326798			0.163399	+	0.986560i	$0.447754\pi$
$200$	4.61706	+	14.6616i	0.326475	+	1.03673i
$201$	2.83008	+	3.25994i	0.199618	+	0.229938i
$202$	−13.4637	+	2.86179i	−0.947301	+	0.201355i
$203$	−0.142096	+	1.35195i	−0.00997316	+	0.0948882i
$204$	0.0851214	+	0.980330i	0.00595969	+	0.0686369i
$205$	10.1834	+	1.11709i	0.711240	+	0.0780211i
$206$	15.7873	−	11.4702i	1.09995	−	0.799164i
$207$	3.09292	+	2.42298i	0.214973	+	0.168409i
$208$	13.2453	−	9.62331i	0.918400	−	0.667256i
$209$	−20.5673	−	4.37170i	−1.42267	−	0.302397i
$210$	−0.561633	−	1.34247i	−0.0387564	−	0.0926394i
$211$	−0.144843	+	0.0307873i	−0.00997140	+	0.00211949i	−0.212895	−	0.977075i	$-0.568289\pi$
$211$	−0.144843	+	0.0307873i	−0.00997140	+	0.00211949i	0.202923	+	0.979195i	$0.434956\pi$
$212$	−1.64676	+	1.82892i	−0.113100	+	0.125611i
$213$	−9.99013	−	18.0505i	−0.684512	−	1.23680i
$214$	−8.10605	−	9.00268i	−0.554118	−	0.615410i
$215$	−5.98927	+	0.602015i	−0.408465	+	0.0410571i
$216$	−12.3947	−	10.0774i	−0.843351	−	0.685678i
$217$	−2.20972	+	1.60546i	−0.150006	+	0.108986i
$218$	−6.60528	+	11.4407i	−0.447366	+	0.774861i
$219$	1.08484	−	1.16182i	0.0733064	−	0.0785084i
$220$	3.55215	+	1.17202i	0.239486	+	0.0790178i
$221$	0.669994	−	6.37456i	0.0450686	−	0.428800i
$222$	0.0404559	−	0.0282881i	0.00271522	−	0.00189857i
$223$	−1.10187	−	1.22375i	−0.0737867	−	0.0819485i	0.705121	−	0.709087i	$-0.250893\pi$
$223$	−1.10187	−	1.22375i	−0.0737867	−	0.0819485i	−0.778908	+	0.627139i	$0.784226\pi$
$224$	−0.995419			−0.0665092
$225$	−13.9654	+	5.47430i	−0.931026	+	0.364953i
$226$	−17.4876			−1.16326
$227$	−2.45055	−	2.72161i	−0.162648	−	0.180639i	0.656312	−	0.754490i	$-0.272116\pi$
$227$	−2.45055	−	2.72161i	−0.162648	−	0.180639i	−0.818960	+	0.573851i	$0.805449\pi$
$228$	−0.630521	−	7.26161i	−0.0417572	−	0.480912i
$229$	0.0884967	−	0.841990i	0.00584803	−	0.0556403i	−0.991209	−	0.132308i	$-0.957761\pi$
$229$	0.0884967	−	0.841990i	0.00584803	−	0.0556403i	0.997057	+	0.0766674i	$0.0244280\pi$
$230$	−0.0158532	+	3.49138i	−0.00104533	+	0.230214i
$231$	−1.53746	−	0.356010i	−0.101157	−	0.0234237i
$232$	−6.63027	+	11.4840i	−0.435299	+	0.753960i
$233$	9.04329	−	6.57033i	0.592445	−	0.430437i	−0.250744	−	0.968053i	$-0.580675\pi$
$233$	9.04329	−	6.57033i	0.592445	−	0.430437i	0.843189	+	0.537617i	$0.180675\pi$
$234$	14.9847	+	17.9056i	0.979582	+	1.17053i
$235$	−10.0690	−	5.87446i	−0.656829	−	0.383207i
$236$	−2.00566	−	2.22751i	−0.130557	−	0.144999i
$237$	19.7110	+	0.356959i	1.28037	+	0.0231870i
$238$	0.246858	−	0.274164i	0.0160015	−	0.0177714i
$239$	15.9775	−	3.39613i	1.03350	−	0.219677i	0.340220	−	0.940346i	$-0.389498\pi$
$239$	15.9775	−	3.39613i	1.03350	−	0.219677i	0.693280	+	0.720669i	$0.256165\pi$
$240$	0.219972	−	9.71087i	0.0141992	−	0.626834i
$241$	−2.04979	−	0.435696i	−0.132038	−	0.0280656i	0.141418	−	0.989950i	$-0.454834\pi$
$241$	−2.04979	−	0.435696i	−0.132038	−	0.0280656i	−0.273457	+	0.961884i	$0.588167\pi$
$242$	2.54805	−	1.85127i	0.163795	−	0.119004i
$243$	8.98290	−	12.7400i	0.576254	−	0.817271i
$244$	−3.46945	+	2.52070i	−0.222109	+	0.161372i
$245$	−6.34004	+	14.0677i	−0.405050	+	0.898753i
$246$	−8.57166	−	4.00386i	−0.546509	−	0.255277i
$247$	−4.96285	+	47.2184i	−0.315779	+	3.00443i
$248$	−26.0615	+	5.53955i	−1.65491	+	0.351762i
$249$	5.61718	−	16.2789i	0.355974	−	1.03163i
$250$	−11.4518	−	6.82133i	−0.724273	−	0.431419i
$251$	−15.8673			−1.00154			−0.500769	−	0.865581i	$-0.666949\pi$
$251$	−15.8673			−1.00154			−0.500769	+	0.865581i	$0.666949\pi$
$252$	−0.0374469	−	0.545779i	−0.00235893	−	0.0343809i
$253$	3.06320	+	2.22554i	0.192582	+	0.139919i
$254$	16.7643	−	7.46396i	1.05189	−	0.468330i
$255$	−2.76766	−	2.60789i	−0.173317	−	0.163313i
$256$	−11.5220	−	5.12990i	−0.720122	−	0.320619i
$257$	−1.09760	−	1.90109i	−0.0684661	−	0.118587i	0.829760	−	0.558120i	$-0.188477\pi$
$257$	−1.09760	−	1.90109i	−0.0684661	−	0.118587i	−0.898226	+	0.439533i	$0.855144\pi$
$258$	5.41560	+	1.25402i	0.337160	+	0.0780721i
$259$	0.00736942	+	0.00156642i	0.000457913	+	9.73325e-5i
$260$	1.79354	−	8.25347i	0.111230	−	0.511858i
$261$	−11.6231	−	5.68782i	−0.719453	−	0.352067i
$262$	1.22985	+	3.78508i	0.0759801	+	0.233843i
$263$	29.0145	+	6.16721i	1.78911	+	0.380287i	0.978654	−	0.205515i	$-0.0658869\pi$
$263$	29.0145	+	6.16721i	1.78911	+	0.380287i	0.810454	+	0.585802i	$0.199220\pi$
$264$	−12.2884	−	9.27257i	−0.756297	−	0.570687i
$265$	0.0431849	−	9.51070i	0.00265283	−	0.584237i
$266$	−1.82856	+	2.03082i	−0.112116	+	0.124517i
$267$	−14.4871	+	15.5152i	−0.886597	+	0.949512i
$268$	−0.721076	+	1.24894i	−0.0440467	+	0.0762912i
$269$	−20.4742	+	14.8754i	−1.24833	+	0.906968i	−0.998124	−	0.0612238i	$-0.980500\pi$
$269$	−20.4742	+	14.8754i	−1.24833	+	0.906968i	−0.250210	+	0.968192i	$0.580500\pi$
$270$	13.8378	−	0.634991i	0.842140	−	0.0386443i
$271$	−15.2201	−	11.0580i	−0.924555	−	0.671728i	0.0200987	−	0.999798i	$-0.493602\pi$
$271$	−15.2201	−	11.0580i	−0.924555	−	0.671728i	−0.944654	+	0.328070i	$0.893602\pi$
$272$	2.24961	−	1.00159i	0.136403	−	0.0607305i
$273$	−0.436589	+	3.53659i	−0.0264235	+	0.214044i
$274$	5.03443	+	8.71989i	0.304141	+	0.526788i
$275$	−13.2584	+	5.75934i	−0.799513	+	0.347301i
$276$	−0.428130	+	1.24074i	−0.0257704	+	0.0746839i
$277$	15.1456	+	16.8209i	0.910012	+	1.01067i	0.999892	+	0.0147182i	$0.00468511\pi$
$277$	15.1456	+	16.8209i	0.910012	+	1.01067i	−0.0898796	+	0.995953i	$0.528648\pi$
$278$	1.37963	+	1.00236i	0.0827447	+	0.0601176i
$279$	−7.13387	−	25.0022i	−0.427094	−	1.49684i
$280$	1.61657	−	1.44233i	0.0966087	−	0.0861958i
$281$	0.0980168	+	0.932568i	0.00584719	+	0.0556323i	0.997056	−	0.0766714i	$-0.0244292\pi$
$281$	0.0980168	+	0.932568i	0.00584719	+	0.0556323i	−0.991209	+	0.132304i	$0.957763\pi$
$282$	7.05744	+	8.12940i	0.420265	+	0.484099i
$283$	10.5924	+	4.71605i	0.629653	+	0.280340i	0.696648	−	0.717414i	$-0.254674\pi$
$283$	10.5924	+	4.71605i	0.629653	+	0.280340i	−0.0669940	+	0.997753i	$0.521341\pi$
$284$	4.61161	−	5.12171i	0.273648	−	0.303917i
$285$	20.5009	+	19.3175i	1.21437	+	1.14427i
$286$	15.0559	+	16.7213i	0.890273	+	0.988748i
$287$	−0.446185	−	1.37322i	−0.0263375	−	0.0810583i
$288$	3.25245	−	8.89977i	0.191652	−	0.524424i
$289$	−4.95538	+	15.2511i	−0.291493	+	0.897122i
$290$	−2.33968	−	11.2585i	−0.137391	−	0.661120i
$291$	12.8025	+	0.231850i	0.750498	+	0.0135913i
$292$	0.485103	+	0.215982i	0.0283885	+	0.0126394i
$293$	11.8547	+	20.5330i	0.692561	+	1.19955i	0.970996	+	0.239096i	$0.0768509\pi$
$293$	11.8547	+	20.5330i	0.692561	+	1.19955i	−0.278435	+	0.960455i	$0.589816\pi$
$294$	9.72515	−	10.4153i	0.567182	−	0.607431i
$295$	11.5145	+	1.26311i	0.670400	+	0.0735411i
$296$	0.0594568	+	0.0431979i	0.00345586	+	0.00251083i
$297$	8.20650	−	12.5828i	0.476189	−	0.730125i
$298$	−7.62869	+	23.4787i	−0.441918	+	1.36008i
$299$	4.27476	−	7.40411i	0.247216	−	0.428190i
$300$	−3.25050	−	3.81363i	−0.187668	−	0.220180i
$301$	0.424198	+	0.734732i	0.0244504	+	0.0423493i
$302$	24.8537	−	5.28282i	1.43017	−	0.303992i
$303$	16.3880	−	11.4591i	0.941469	−	0.658306i
$304$	−16.6636	+	7.41911i	−0.955722	+	0.425515i
$305$	3.51928	−	16.1950i	0.201513	−	0.927321i
$306$	1.64464	+	3.10290i	0.0940176	+	0.177381i
$307$	−12.6269			−0.720652			−0.360326	−	0.932826i	$-0.617335\pi$
$307$	−12.6269			−0.720652			−0.360326	+	0.932826i	$0.617335\pi$
$308$	−0.0551071	−	0.524309i	−0.00314002	−	0.0298753i
$309$	−14.6173	+	24.2913i	−0.831549	+	1.38188i
$310$	13.6651	−	18.6300i	0.776128	−	1.05811i
$311$	13.8540	−	2.94477i	0.785590	−	0.166982i	0.202384	−	0.979306i	$-0.435131\pi$
$311$	13.8540	−	2.94477i	0.785590	−	0.166982i	0.583207	+	0.812324i	$0.301798\pi$
$312$	−17.9224	+	29.7838i	−1.01466	+	1.68617i
$313$	−2.73979	−	0.582360i	−0.154862	−	0.0329169i	0.129828	−	0.991537i	$-0.458557\pi$
$313$	−2.73979	−	0.582360i	−0.154862	−	0.0329169i	−0.284690	+	0.958620i	$0.591891\pi$
$314$	5.14446	−	15.8330i	0.290319	−	0.893509i
$315$	1.51217	+	1.47747i	0.0852009	+	0.0832462i
$316$	2.03512	+	6.26345i	0.114484	+	0.352347i
$317$	−3.11752	−	29.6613i	−0.175098	−	1.66594i	−0.630902	−	0.775862i	$-0.717315\pi$
$317$	−3.11752	−	29.6613i	−0.175098	−	1.66594i	0.455805	−	0.890080i	$-0.349351\pi$
$318$	−2.86494	+	8.30272i	−0.160658	+	0.465594i
$319$	−11.3922	−	5.07212i	−0.637839	−	0.283984i
$320$	18.7025	−	5.98305i	1.04550	−	0.334463i
$321$	15.9458	+	7.44835i	0.890007	+	0.415726i
$322$	0.449545	−	0.200150i	0.0250522	−	0.0111539i
$323$	−2.20674	+	6.79164i	−0.122786	+	0.377897i
$324$	5.00202	+	1.44849i	0.277890	+	0.0804715i
$325$	16.0627	+	28.4142i	0.890998	+	1.57614i
$326$	0.366993	−	0.635650i	0.0203259	−	0.0352054i
$327$	2.35141	−	19.0477i	0.130033	−	1.05334i
$328$	1.47225	−	14.0075i	0.0812916	−	0.773437i
$329$	−0.171742	+	1.63402i	−0.00946844	+	0.0900862i
$330$	13.3044	−	1.09437i	0.732382	−	0.0602430i
$331$	2.12974	+	20.2631i	0.117061	+	1.11376i	0.882519	+	0.470277i	$0.155846\pi$
$331$	2.12974	+	20.2631i	0.117061	+	1.11376i	−0.765458	+	0.643486i	$0.777487\pi$
$332$	5.75281			0.315726
$333$	−0.0380839	+	0.0607698i	−0.00208698	+	0.00333017i
$334$	−1.98949	−	6.12301i	−0.108860	−	0.335036i
$335$	−1.13398	−	5.45665i	−0.0619557	−	0.298129i
$336$	−1.26054	+	0.534096i	−0.0687683	+	0.0291373i
$337$	17.7807	−	19.7475i	0.968576	−	1.07571i	−0.0285223	−	0.999593i	$-0.509080\pi$
$337$	17.7807	−	19.7475i	0.968576	−	1.07571i	0.997099	−	0.0761198i	$-0.0242532\pi$
$338$	23.6255	−	26.2388i	1.28506	−	1.42720i
$339$	23.3927	−	9.91156i	1.27052	−	0.538322i
$340$	0.521967	−	1.15818i	0.0283077	−	0.0628109i
$341$	−7.74271	−	23.8296i	−0.419291	−	1.29045i
$342$	−12.1823	−	22.9842i	−0.658745	−	1.24284i
$343$	4.38089			0.236546
$344$	0.865065	+	8.23054i	0.0466412	+	0.443761i
$345$	−1.95763	−	4.67932i	−0.105395	−	0.251926i
$346$	0.0453252	−	0.431241i	0.00243670	−	0.0231837i
$347$	−2.14059	+	20.3664i	−0.114913	+	1.09332i	0.773347	+	0.633983i	$0.218581\pi$
$347$	−2.14059	+	20.3664i	−0.114913	+	1.09332i	−0.888260	+	0.459341i	$0.848086\pi$
$348$	0.529629	−	4.29027i	0.0283911	−	0.229982i
$349$	2.88806	−	5.00227i	0.154594	−	0.267766i	−0.778317	−	0.627872i	$-0.783926\pi$
$349$	2.88806	−	5.00227i	0.154594	−	0.267766i	0.932911	+	0.360106i	$0.117260\pi$
$350$	−0.213335	+	1.86653i	−0.0114032	+	0.0997701i
$351$	−30.1932	−	15.4589i	−1.61159	−	0.825138i
$352$	2.82175	−	8.68445i	0.150400	−	0.462883i
$353$	12.6340	−	5.62502i	0.672440	−	0.299390i	−0.0419678	−	0.999119i	$-0.513363\pi$
$353$	12.6340	−	5.62502i	0.672440	−	0.299390i	0.714408	+	0.699729i	$0.246696\pi$
$354$	−9.69209	−	4.52722i	−0.515129	−	0.240619i
$355$	−0.120935	+	26.6338i	−0.00641857	+	1.41357i
$356$	−6.47817	−	2.88427i	−0.343342	−	0.152866i
$357$	−0.174827	+	0.506657i	−0.00925281	+	0.0268151i
$358$	1.89245	+	18.0055i	0.100019	+	0.951618i
$359$	0.158269	+	0.487102i	0.00835313	+	0.0257083i	0.955146	−	0.296135i	$-0.0956977\pi$
$359$	0.158269	+	0.487102i	0.00835313	+	0.0257083i	−0.946793	+	0.321843i	$0.895698\pi$
$360$	7.61347	+	19.1660i	0.401265	+	1.01014i
$361$	10.4747	−	32.2377i	0.551299	−	1.69672i
$362$	0.0666870	+	0.0141748i	0.00350499	+	0.000745008i
$363$	−2.35921	+	3.92057i	−0.123826	+	0.205777i
$364$	−1.16440	+	0.247501i	−0.0610311	+	0.0129726i
$365$	−1.95453	+	0.625268i	−0.102305	+	0.0327280i
$366$	−7.89120	+	13.1137i	−0.412480	+	0.685465i
$367$	2.04367	+	19.4442i	0.106679	+	1.01498i	0.908633	+	0.417595i	$0.137127\pi$
$367$	2.04367	+	19.4442i	0.106679	+	1.01498i	−0.801955	+	0.597385i	$0.796207\pi$
$368$	3.28461			0.171222
$369$	13.7354	+	0.497651i	0.715037	+	0.0259067i
$370$	−0.0634103	+	0.00637373i	−0.00329655	+	0.000331354i
$371$	−1.22458	+	0.545220i	−0.0635773	+	0.0283064i
$372$	7.11813	−	4.97723i	0.369058	−	0.258057i
$373$	−24.2570	+	5.15599i	−1.25598	+	0.266967i	−0.787394	−	0.616450i	$-0.788570\pi$
$373$	−24.2570	+	5.15599i	−1.25598	+	0.266967i	−0.468587	+	0.883417i	$0.655237\pi$
$374$	1.69214	+	2.93088i	0.0874987	+	0.151552i
$375$	19.1849	+	2.63414i	0.990705	+	0.136026i
$376$	−8.01359	+	13.8800i	−0.413270	+	0.715804i
$377$	−8.70129	+	26.7798i	−0.448139	+	1.37923i
$378$	−0.882946	−	1.74132i	−0.0454138	−	0.0895639i
$379$	15.1691	+	11.0210i	0.779184	+	0.566110i	0.904734	−	0.425977i	$-0.140070\pi$
$379$	15.1691	+	11.0210i	0.779184	+	0.566110i	−0.125550	+	0.992087i	$0.540070\pi$
$380$	−3.86637	+	8.57897i	−0.198341	+	0.440092i
$381$	−18.1948	+	19.4860i	−0.932150	+	0.998298i
$382$	−1.42861	−	2.47442i	−0.0730938	−	0.126602i
$383$	5.00833	+	2.22985i	0.255914	+	0.113940i	0.530684	−	0.847570i	$-0.321935\pi$
$383$	5.00833	+	2.22985i	0.255914	+	0.113940i	−0.274770	+	0.961510i	$0.588602\pi$
$384$	−7.19129	−	0.130232i	−0.366979	−	0.00664587i
$385$	1.50785	+	1.37013i	0.0768473	+	0.0698280i
$386$	−2.17198	+	6.68468i	−0.110551	+	0.340241i
$387$	−7.95507	+	1.39196i	−0.404379	+	0.0707574i
$388$	1.32184	+	4.06819i	0.0671061	+	0.206531i
$389$	−1.04925	−	1.16531i	−0.0531990	−	0.0590835i	0.715958	−	0.698143i	$-0.245990\pi$
$389$	−1.04925	−	1.16531i	−0.0531990	−	0.0590835i	−0.769157	+	0.639060i	$0.779324\pi$
$390$	−5.59773	−	29.6185i	−0.283452	−	1.49979i
$391$	0.860448	−	0.955625i	0.0435148	−	0.0483280i
$392$	19.3805	+	8.62874i	0.978861	+	0.435817i
$393$	−3.79043	−	4.36616i	−0.191202	−	0.220244i
$394$	−1.97840	−	18.8232i	−0.0996704	−	0.948300i
$395$	−21.9831	−	12.8254i	−1.10609	−	0.645317i
$396$	4.86776	+	1.22044i	0.244614	+	0.0613294i
$397$	7.83333	+	5.69125i	0.393143	+	0.285635i	0.766742	−	0.641955i	$-0.221876\pi$
$397$	7.83333	+	5.69125i	0.393143	+	0.285635i	−0.373599	+	0.927590i	$0.621876\pi$
$398$	3.67768	+	4.08447i	0.184345	+	0.204736i
$399$	1.29500	−	3.75296i	0.0648309	−	0.187883i
$400$	−6.36831	+	10.8025i	−0.318415	+	0.540124i
$401$	−0.505309	−	0.875221i	−0.0252339	−	0.0437064i	0.853133	−	0.521694i	$-0.174700\pi$
$401$	−0.505309	−	0.875221i	−0.0252339	−	0.0437064i	−0.878367	+	0.477988i	$0.841366\pi$
$402$	−0.630582	+	5.10804i	−0.0314506	+	0.254766i
$403$	−51.6851	+	23.0117i	−2.57462	+	1.14629i
$404$	5.40443	+	3.92655i	0.268880	+	0.195353i
$405$	−18.1506	+	8.69235i	−0.901909	+	0.431926i
$406$	−1.31117	+	0.952622i	−0.0650724	+	0.0472779i
$407$	−0.0345565	+	0.0598535i	−0.00171290	+	0.00296683i
$408$	−3.56816	+	3.82137i	−0.176650	+	0.189186i
$409$	5.36444	−	5.95782i	0.265255	−	0.294595i	−0.595773	−	0.803153i	$-0.703154\pi$
$409$	5.36444	−	5.95782i	0.265255	−	0.294595i	0.861028	+	0.508557i	$0.169821\pi$
$410$	7.13408	+	9.91357i	0.352327	+	0.489596i
$411$	−11.6767	−	8.81099i	−0.575968	−	0.434614i
$412$	−9.26377	−	1.96908i	−0.456393	−	0.0970094i
$413$	−0.504507	−	1.55271i	−0.0248251	−	0.0764040i
$414$	0.320639	+	4.67323i	0.0157585	+	0.229677i
$415$	−16.5889	+	14.8009i	−0.814316	+	0.726546i
$416$	−20.1681	−	4.28687i	−0.988823	−	0.210181i
$417$	−2.41361	−	0.558891i	−0.118195	−	0.0273690i
$418$	−12.5342	−	21.7099i	−0.613070	−	1.06187i
$419$	22.8670	+	10.1810i	1.11713	+	0.497377i	0.880415	−	0.474204i	$-0.157264\pi$
$419$	22.8670	+	10.1810i	1.11713	+	0.497377i	0.236711	+	0.971580i	$0.423931\pi$
$420$	−0.301797	+	0.638525i	−0.0147262	+	0.0311568i
$421$	30.1379	−	13.4182i	1.46883	−	0.653965i	0.492512	−	0.870305i	$-0.336079\pi$
$421$	30.1379	−	13.4182i	1.46883	−	0.653965i	0.976318	+	0.216340i	$0.0694120\pi$
$422$	−0.142826	−	0.103769i	−0.00695265	−	0.00505140i
$423$	−14.0481	−	6.87451i	−0.683044	−	0.334250i
$424$	−13.0760			−0.635026
$425$	1.47461	+	4.68265i	0.0715291	+	0.227142i
$426$	8.02298	−	23.2510i	0.388714	−	1.12651i
$427$	−2.28479	+	0.485646i	−0.110569	+	0.0235021i
$428$	−0.614562	+	5.84717i	−0.0297060	+	0.282633i
$429$	−29.6171	−	13.8343i	−1.42993	−	0.667926i
$430$	−5.31132	−	4.82618i	−0.256135	−	0.232739i
$431$	4.71468	−	3.42542i	0.227098	−	0.164997i	−0.468418	−	0.883507i	$-0.655176\pi$
$431$	4.71468	−	3.42542i	0.227098	−	0.164997i	0.695516	+	0.718511i	$0.255176\pi$
$432$	−0.656483	−	13.0153i	−0.0315851	−	0.626198i
$433$	−1.68629	+	1.22516i	−0.0810381	+	0.0588776i	−0.627567	−	0.778563i	$-0.715949\pi$
$433$	−1.68629	+	1.22516i	−0.0810381	+	0.0588776i	0.546529	+	0.837440i	$0.315949\pi$
$434$	−3.18523	−	0.677041i	−0.152896	−	0.0324990i
$435$	9.51078	+	13.7341i	0.456007	+	0.658500i
$436$	6.27131	−	1.33301i	0.300341	−	0.0638395i
$437$	−6.37361	+	7.07861i	−0.304891	+	0.338616i
$438$	1.89479	+	0.0343140i	0.0905365	+	0.00163959i
$439$	15.2474	+	16.9340i	0.727721	+	0.808216i	0.987528	−	0.157445i	$-0.0503256\pi$
$439$	15.2474	+	16.9340i	0.727721	+	0.808216i	−0.259807	+	0.965661i	$0.583659\pi$
$440$	8.00095	+	18.1923i	0.381430	+	0.867284i
$441$	−7.10597	+	19.4443i	−0.338379	+	0.925917i
$442$	6.18230	−	4.49170i	0.294062	−	0.213648i
$443$	4.50211	−	7.79787i	0.213901	−	0.370488i	−0.739031	−	0.673672i	$-0.764716\pi$
$443$	4.50211	−	7.79787i	0.213901	−	0.370488i	0.952932	+	0.303184i	$0.0980495\pi$
$444$	−0.0233405	−	0.00540466i	−0.00110769	−	0.000256494i
$445$	26.1012	−	8.34996i	1.23732	−	0.395826i
$446$	0.205216	−	1.95250i	0.00971724	−	0.0924534i
$447$	−3.10247	−	35.7307i	−0.146742	−	1.69000i
$448$	−1.85187	−	2.05671i	−0.0874925	−	0.0971702i
$449$	−2.14345			−0.101156			−0.0505779	−	0.998720i	$-0.516106\pi$
$449$	−2.14345			−0.101156			−0.0505779	+	0.998720i	$0.516106\pi$
$450$	−15.9911	−	8.00609i	−0.753826	−	0.377411i
$451$	13.2453			0.623698
$452$	5.67902	+	6.30719i	0.267118	+	0.296665i
$453$	−30.2521	+	21.1532i	−1.42137	+	0.993865i
$454$	0.456397	−	4.34233i	0.0214198	−	0.203795i
$455$	2.72091	−	3.70947i	0.127558	−	0.173903i
$456$	26.4305	−	28.3061i	1.23772	−	1.32555i
$457$	9.78295	−	16.9446i	0.457627	−	0.792634i	−0.541208	−	0.840889i	$-0.682033\pi$
$457$	9.78295	−	16.9446i	0.457627	−	0.792634i	0.998835	+	0.0482552i	$0.0153661\pi$
$458$	0.816594	−	0.593290i	0.0381569	−	0.0277226i
$459$	−3.95865	−	3.21854i	−0.184774	−	0.150228i
$460$	1.26437	−	1.12809i	0.0589516	−	0.0525976i
$461$	−2.55207	−	2.83436i	−0.118862	−	0.132009i	0.680777	−	0.732491i	$-0.261642\pi$
$461$	−2.55207	−	2.83436i	−0.118862	−	0.132009i	−0.799639	+	0.600482i	$0.794976\pi$
$462$	−0.911085	−	1.64618i	−0.0423875	−	0.0765873i
$463$	6.05576	−	6.72560i	0.281435	−	0.312565i	−0.585808	−	0.810450i	$-0.699223\pi$
$463$	6.05576	−	6.72560i	0.281435	−	0.312565i	0.867243	+	0.497884i	$0.165890\pi$
$464$	−10.5815	+	2.24917i	−0.491234	+	0.104415i
$465$	−7.72050	+	32.6660i	−0.358030	+	1.51485i
$466$	13.0355	+	2.77079i	0.603860	+	0.128354i
$467$	24.8972	−	18.0889i	1.15211	−	0.837053i	0.163346	−	0.986569i	$-0.447771\pi$
$467$	24.8972	−	18.0889i	1.15211	−	0.837053i	0.988759	+	0.149515i	$0.0477713\pi$
$468$	1.59174	−	11.2193i	0.0735783	−	0.518611i
$469$	−0.635487	+	0.461708i	−0.0293441	+	0.0213197i
$470$	−2.82782	−	13.6074i	−0.130438	−	0.627662i
$471$	2.09217	+	24.0952i	0.0964021	+	1.11025i
$472$	1.66469	−	15.8385i	0.0766238	−	0.729027i
$473$	−7.61260	+	1.61811i	−0.350028	+	0.0744007i
$474$	15.4082	+	17.7485i	0.707721	+	0.815216i
$475$	−10.9229	−	34.6859i	−0.501177	−	1.59150i
$476$	−0.179048			−0.00820666
$477$	−0.873437	−	12.7301i	−0.0399919	−	0.582873i
$478$	15.7550	+	11.4467i	0.720617	+	0.523559i
$479$	11.2505	−	5.00905i	0.514049	−	0.228870i	−0.133282	−	0.991078i	$-0.542552\pi$
$479$	11.2505	−	5.00905i	0.514049	−	0.228870i	0.647331	+	0.762209i	$0.275885\pi$
$480$	−9.27375	+	7.97734i	−0.423287	+	0.364114i
$481$	0.142565	+	0.0634742i	0.00650042	+	0.00289417i
$482$	−1.24920	−	2.16367i	−0.0568993	−	0.0985524i
$483$	−0.487905	+	0.522528i	−0.0222005	+	0.0237759i
$484$	−1.49516	−	0.317806i	−0.0679618	−	0.0144457i
$485$	−14.2783	−	8.33027i	−0.648346	−	0.378258i
$486$	18.4536	−	2.20456i	0.837074	−	0.100001i
$487$	1.53444	+	4.72251i	0.0695320	+	0.213997i	0.979784	−	0.200056i	$-0.0641125\pi$
$487$	1.53444	+	4.72251i	0.0695320	+	0.213997i	−0.910252	+	0.414054i	$0.864113\pi$
$488$	−22.2875	−	4.73735i	−1.00891	−	0.214450i
$489$	−0.130646	+	1.05830i	−0.00590800	+	0.0478579i
$490$	−17.5216	+	5.60530i	−0.791547	+	0.253221i
$491$	−12.7546	+	14.1654i	−0.575605	+	0.639274i	−0.958695	−	0.284437i	$-0.908193\pi$
$491$	−12.7546	+	14.1654i	−0.575605	+	0.639274i	0.383090	+	0.923711i	$0.374860\pi$
$492$	1.33955	+	4.39175i	0.0603917	+	0.197996i
$493$	−2.11760	+	3.66778i	−0.0953718	+	0.165189i
$494$	−45.7942	+	33.2714i	−2.06038	+	1.49695i
$495$	−17.1767	+	9.00453i	−0.772035	+	0.404724i
$496$	−17.5847	−	12.7760i	−0.789576	−	0.573660i
$497$	3.42933	−	1.52684i	0.153827	−	0.0684880i
$498$	18.9040	−	8.00969i	0.847110	−	0.358923i
$499$	−2.50922	−	4.34610i	−0.112328	−	0.194558i	0.804380	−	0.594115i	$-0.202497\pi$
$499$	−2.50922	−	4.34610i	−0.112328	−	0.194558i	−0.916709	+	0.399557i	$0.869164\pi$
$500$	1.25868	+	6.34547i	0.0562900	+	0.283778i
$501$	6.13167	+	7.06301i	0.273943	+	0.315552i
$502$	−12.6582	−	14.0583i	−0.564962	−	0.627453i
$503$	−5.48055	−	3.98186i	−0.244366	−	0.177542i	0.458860	−	0.888508i	$-0.348258\pi$
$503$	−5.48055	−	3.98186i	−0.244366	−	0.177542i	−0.703226	+	0.710966i	$0.748258\pi$
$504$	2.02185	−	2.08821i	0.0900605	−	0.0930164i
$505$	−25.6865	+	2.58190i	−1.14304	+	0.114893i
$506$	0.471854	+	4.48939i	0.0209765	+	0.199578i
$507$	−16.7317	+	48.4894i	−0.743083	+	2.15349i
$508$	−8.13615	−	3.62245i	−0.360983	−	0.160720i
$509$	−6.65406	+	7.39008i	−0.294936	+	0.327559i	−0.872341	−	0.488899i	$-0.837399\pi$
$509$	−6.65406	+	7.39008i	−0.294936	+	0.327559i	0.577405	+	0.816458i	$0.304065\pi$
$510$	0.102673	−	4.53257i	0.00454642	−	0.200705i
$511$	0.193532	+	0.214939i	0.00856136	+	0.00950835i
$512$	−7.21302	−	22.1994i	−0.318774	−	0.981084i
$513$	29.3229	+	23.8407i	1.29464	+	1.05259i
$514$	0.808743	−	2.48906i	0.0356721	−	0.109788i
$515$	31.7792	−	18.1558i	1.40036	−	0.800041i
$516$	−1.30641	−	2.36047i	−0.0575115	−	0.103914i
$517$	−13.7690	−	6.13035i	−0.605560	−	0.269613i
$518$	0.00449112	+	0.00777885i	0.000197329	+	0.000341783i
$519$	0.183787	+	0.602550i	0.00806736	+	0.0264490i
$520$	38.9648	−	22.2611i	1.70872	−	0.976212i
$521$	15.4969	+	11.2591i	0.678930	+	0.493272i	0.873003	−	0.487715i	$-0.162170\pi$
$521$	15.4969	+	11.2591i	0.678930	+	0.493272i	−0.194072	+	0.980987i	$0.562170\pi$
$522$	−4.23299	−	14.8354i	−0.185273	−	0.649330i
$523$	0.0808887	−	0.248950i	0.00353702	−	0.0108858i	−0.949272	−	0.314455i	$-0.898178\pi$
$523$	0.0808887	−	0.248950i	0.00353702	−	0.0108858i	0.952809	+	0.303569i	$0.0981783\pi$
$524$	0.965764	−	1.67275i	0.0421896	−	0.0730745i
$525$	−0.772533	−	2.61773i	−0.0337161	−	0.114247i
$526$	17.6822	+	30.6265i	0.770980	+	1.33538i
$527$	−8.32361	+	1.76924i	−0.362582	+	0.0770692i
$528$	−1.08637	−	12.5115i	−0.0472781	−	0.544495i
$529$	−19.4446	+	8.65730i	−0.845418	+	0.376404i
$530$	8.46084	−	7.54890i	0.367516	−	0.327903i
$531$	15.5308	+	0.562700i	0.673980	+	0.0244191i
$532$	1.32626			0.0575009
$533$	−3.12624	−	29.7442i	−0.135412	−	1.28836i
$534$	−25.3034	−	0.458236i	−1.09498	−	0.0198298i
$535$	−13.2715	−	18.4421i	−0.573775	−	0.797322i
$536$	−7.49495	+	1.59310i	−0.323733	+	0.0688115i
$537$	−12.7366	−	23.0129i	−0.549624	−	0.993080i
$538$	−29.5128	−	6.27313i	−1.27239	−	0.270454i
$539$	−6.16497	+	18.9738i	−0.265544	+	0.817261i
$540$	−4.72278	−	4.78462i	−0.203236	−	0.205897i
$541$	6.23922	+	19.2023i	0.268245	+	0.825573i	0.990928	+	0.134394i	$0.0429087\pi$
$541$	6.23922	+	19.2023i	0.268245	+	0.825573i	−0.722683	+	0.691180i	$0.757091\pi$
$542$	−2.34450	−	22.3064i	−0.100705	−	0.958143i
$543$	−0.0972395	+	0.0188354i	−0.00417295	+	0.000808305i
$544$	−2.83311	−	1.26138i	−0.121468	−	0.0540813i
$545$	−14.6545	+	19.9787i	−0.627729	+	0.855795i
$546$	−3.48168	+	2.43451i	−0.149002	+	0.104187i
$547$	−6.86422	+	3.05615i	−0.293493	+	0.130671i	−0.548201	−	0.836346i	$-0.684687\pi$
$547$	−6.86422	+	3.05615i	−0.293493	+	0.130671i	0.254708	+	0.967018i	$0.418021\pi$
$548$	1.51006	−	4.64750i	0.0645067	−	0.198531i
$549$	3.12332	−	22.0145i	0.133300	−	0.939554i
$550$	−15.6796	−	7.15234i	−0.668582	−	0.304977i
$551$	15.6857	−	27.1684i	0.668233	−	1.15741i
$552$	−6.42110	+	2.72064i	−0.273300	+	0.115798i
$553$	−0.374956	+	3.56747i	−0.0159447	+	0.151704i
$554$	−2.82076	+	26.8378i	−0.119843	+	1.14023i
$555$	0.0812100	−	0.0444655i	0.00344717	−	0.00188746i
$556$	−0.0865112	−	0.823099i	−0.00366889	−	0.0349072i
$557$	17.2753			0.731980			0.365990	−	0.930619i	$-0.380730\pi$
$557$	17.2753			0.731980			0.365990	+	0.930619i	$0.380730\pi$
$558$	16.4607	−	26.2661i	0.696837	−	1.11193i
$559$	5.43045	+	16.7132i	0.229684	+	0.706894i
$560$	1.75686	+	0.192723i	0.0742411	+	0.00814404i
$561$	−3.92470	−	2.96150i	−0.165701	−	0.125035i
$562$	−0.748054	+	0.830798i	−0.0315548	+	0.0350451i
$563$	1.80844	−	2.00848i	0.0762167	−	0.0846473i	−0.703830	−	0.710368i	$-0.748528\pi$
$563$	1.80844	−	2.00848i	0.0762167	−	0.0846473i	0.780047	+	0.625721i	$0.215195\pi$
$564$	0.640129	−	5.18538i	0.0269543	−	0.218344i
$565$	−32.6033	−	3.57649i	−1.37163	−	0.150464i
$566$	4.27172	+	13.1470i	0.179554	+	0.552610i
$567$	2.16804	+	1.82889i	0.0910490	+	0.0768063i
$568$	36.6180			1.53646
$569$	4.46837	+	42.5137i	0.187324	+	1.78227i	0.535201	+	0.844725i	$0.320236\pi$
$569$	4.46837	+	42.5137i	0.187324	+	1.78227i	−0.347877	+	0.937540i	$0.613097\pi$
$570$	−0.760528	+	33.5741i	−0.0318550	+	1.40627i
$571$	−3.16839	+	30.1452i	−0.132593	+	1.26154i	0.702601	+	0.711584i	$0.252022\pi$
$571$	−3.16839	+	30.1452i	−0.132593	+	1.26154i	−0.835194	+	0.549955i	$0.814645\pi$
$572$	1.14147	−	10.8603i	0.0477271	−	0.454093i
$573$	3.31346	+	2.50027i	0.138422	+	0.104450i
$574$	0.860713	−	1.49080i	0.0359255	−	0.0622247i
$575$	−0.743598	+	6.50596i	−0.0310102	+	0.271317i
$576$	24.4393	−	9.83692i	1.01830	−	0.409872i
$577$	11.8163	−	36.3667i	0.491917	−	1.51396i	−0.329790	−	0.944054i	$-0.606978\pi$
$577$	11.8163	−	36.3667i	0.491917	−	1.51396i	0.821707	−	0.569910i	$-0.193022\pi$
$578$	−17.4655	+	7.77613i	−0.726468	+	0.323444i
$579$	−0.883312	−	10.1730i	−0.0367092	−	0.422774i
$580$	−3.30075	+	4.49999i	−0.137056	+	0.186852i
$581$	2.86252	+	1.27448i	0.118757	+	0.0528741i
$582$	10.0078	+	11.5279i	0.414837	+	0.477847i
$583$	−1.28536	−	12.2294i	−0.0532340	−	0.506488i
$584$	0.871846	+	2.68327i	0.0360773	+	0.111034i
$585$	24.2750	+	36.4473i	1.00365	+	1.50691i
$586$	−8.73494	+	26.8834i	−0.360837	+	1.11054i
$587$	−18.3047	−	3.89078i	−0.755515	−	0.160590i	−0.185976	−	0.982554i	$-0.559545\pi$
$587$	−18.3047	−	3.89078i	−0.755515	−	0.160590i	−0.569539	+	0.821964i	$0.692878\pi$
$588$	−6.91465	−	0.125222i	−0.285155	−	0.00516407i
$589$	61.6556	−	13.1053i	2.54047	−	0.539994i
$590$	8.06659	+	11.2094i	0.332096	+	0.461484i
$591$	13.3150	+	24.0581i	0.547707	+	0.989617i
$592$	0.00626701	+	0.0596266i	0.000257572	+	0.00245064i
$593$	−42.4830			−1.74457			−0.872284	−	0.489000i	$-0.837362\pi$
$593$	−42.4830			−1.74457			−0.872284	+	0.489000i	$0.837362\pi$
$594$	17.6949	−	2.76701i	0.726033	−	0.113532i
$595$	0.516306	−	0.460656i	0.0211665	−	0.0188851i
$596$	10.9454	−	4.87320i	0.448340	−	0.199614i
$597$	−7.23453	−	3.37928i	−0.296089	−	0.138305i
$598$	9.97017	−	2.11922i	0.407710	−	0.0866615i
$599$	−22.9566	−	39.7621i	−0.937983	−	1.62463i	−0.769226	−	0.638977i	$-0.779358\pi$
$599$	−22.9566	−	39.7621i	−0.937983	−	1.62463i	−0.168757	−	0.985658i	$-0.553975\pi$
$600$	3.50176	−	26.3927i	0.142959	−	1.07748i
$601$	13.8303	−	23.9548i	0.564150	−	0.977136i	−0.432978	−	0.901404i	$-0.642537\pi$
$601$	13.8303	−	23.9548i	0.564150	−	0.977136i	0.997128	−	0.0757320i	$-0.0241293\pi$
$602$	−0.312563	+	0.961968i	−0.0127391	+	0.0392069i
$603$	−2.05161	−	7.19031i	−0.0835479	−	0.292812i
$604$	−9.97648	−	7.24834i	−0.405937	−	0.294931i
$605$	5.12911	−	2.93032i	0.208528	−	0.119135i
$606$	23.2262	+	5.37820i	0.943500	+	0.218474i
$607$	−7.77177	−	13.4611i	−0.315446	−	0.546369i	0.664086	−	0.747656i	$-0.268821\pi$
$607$	−7.77177	−	13.4611i	−0.315446	−	0.546369i	−0.979532	+	0.201287i	$0.935488\pi$
$608$	20.9857	+	9.34344i	0.851083	+	0.378926i
$609$	1.21400	−	2.01744i	0.0491938	−	0.0817509i
$610$	17.1561	−	9.80148i	0.694630	−	0.396850i
$611$	−10.5167	+	32.3671i	−0.425460	+	1.30943i
$612$	0.585025	−	1.60082i	0.0236482	−	0.0647093i
$613$	−12.9646	−	39.9011i	−0.523637	−	1.61159i	−0.766996	−	0.641652i	$-0.778249\pi$
$613$	−12.9646	−	39.9011i	−0.523637	−	1.61159i	0.243359	−	0.969936i	$-0.421751\pi$
$614$	−10.0731	−	11.1873i	−0.406516	−	0.451482i
$615$	−15.1619	−	9.21772i	−0.611386	−	0.371694i
$616$	1.87429	−	2.08161i	0.0755174	−	0.0838706i
$617$	−8.46425	−	3.76852i	−0.340758	−	0.151715i	0.229221	−	0.973374i	$-0.426382\pi$
$617$	−8.46425	−	3.76852i	−0.340758	−	0.151715i	−0.569979	+	0.821659i	$0.693049\pi$
$618$	−33.1828	+	6.42755i	−1.33481	+	0.258554i
$619$	−1.08260	−	10.3002i	−0.0435132	−	0.414001i	−0.994497	−	0.104761i	$-0.966592\pi$
$619$	−1.08260	−	10.3002i	−0.0435132	−	0.414001i	0.950984	−	0.309240i	$-0.100074\pi$
$620$	−11.1569	+	1.12144i	−0.448073	+	0.0450383i
$621$	−3.07759	−	6.06954i	−0.123500	−	0.243562i
$622$	13.6611	+	9.92537i	0.547760	+	0.397971i
$623$	−2.58447	−	2.87034i	−0.103545	−	0.114998i
$624$	−27.8399	+	5.39263i	−1.11449	+	0.215878i
$625$	−19.9552	−	15.0595i	−0.798208	−	0.602381i
$626$	−1.66970	−	2.89201i	−0.0667347	−	0.115588i
$627$	29.0715	+	21.9368i	1.16100	+	0.876070i
$628$	−7.38109	+	3.28627i	−0.294537	+	0.131136i
$629$	0.0189895	+	0.0137967i	0.000757161	+	0.000550110i
$630$	−0.102698	+	2.51842i	−0.00409157	+	0.100336i
$631$	29.6450	−	21.5383i	1.18015	−	0.857428i	0.187960	−	0.982177i	$-0.439813\pi$
$631$	29.6450	−	21.5383i	1.18015	−	0.857428i	0.992188	+	0.124749i	$0.0398126\pi$
$632$	−17.4957	+	30.3034i	−0.695941	+	1.20541i
$633$	0.249869	+	0.0578590i	0.00993139	+	0.00229969i
$634$	23.7926	−	26.4244i	0.944925	−	1.04945i
$635$	32.7814	−	10.4870i	1.30089	−	0.416163i
$636$	3.92489	−	1.66299i	0.155632	−	0.0659418i
$637$	44.0634	+	9.36597i	1.74586	+	0.371093i
$638$	−4.59425	−	14.1397i	−0.181888	−	0.559794i
$639$	2.44598	+	35.6495i	0.0967613	+	1.41027i
$640$	8.02026	+	4.67918i	0.317029	+	0.184961i
$641$	25.7650	+	5.47651i	1.01766	+	0.216309i	0.686394	−	0.727230i	$-0.259193\pi$
$641$	25.7650	+	5.47651i	1.01766	+	0.216309i	0.331261	+	0.943539i	$0.392526\pi$
$642$	6.12158	+	20.0698i	0.241600	+	0.792090i
$643$	24.3415	+	42.1606i	0.959934	+	1.66265i	0.722651	+	0.691213i	$0.242923\pi$
$643$	24.3415	+	42.1606i	0.959934	+	1.66265i	0.237282	+	0.971441i	$0.423743\pi$
$644$	−0.218175	−	0.0971380i	−0.00859732	−	0.00382777i
$645$	9.84020	+	3.44554i	0.387457	+	0.135668i
$646$	−7.77776	+	3.46288i	−0.306012	+	0.136245i
$647$	10.6167	+	7.71348i	0.417386	+	0.303248i	0.776585	−	0.630012i	$-0.216950\pi$
$647$	10.6167	+	7.71348i	0.417386	+	0.303248i	−0.359199	+	0.933261i	$0.616950\pi$
$648$	12.0639	+	24.8999i	0.473915	+	0.978161i
$649$	14.9767			0.587885
$650$	−12.3607	+	36.8989i	−0.484828	+	1.44729i
$651$	4.64454	−	0.899653i	0.182034	−	0.0352602i
$652$	−0.348437	+	0.0740627i	−0.0136459	+	0.00290052i
$653$	5.05266	−	48.0729i	0.197726	−	1.88124i	−0.224109	−	0.974564i	$-0.571947\pi$
$653$	5.05266	−	48.0729i	0.197726	−	1.88124i	0.421835	−	0.906673i	$-0.361386\pi$
$654$	18.7519	−	13.1119i	0.733257	−	0.512717i
$655$	1.51878	+	7.30830i	0.0593435	+	0.285559i
$656$	9.29580	−	6.75379i	0.362940	−	0.263691i
$657$	−2.55406	+	1.02802i	−0.0996435	+	0.0401070i
$658$	−1.58473	+	1.15137i	−0.0617792	+	0.0448853i
$659$	−29.3437	−	6.23721i	−1.14307	−	0.242967i	−0.402807	−	0.915285i	$-0.631966\pi$
$659$	−29.3437	−	6.23721i	−1.14307	−	0.242967i	−0.740263	+	0.672318i	$0.765299\pi$
$660$	−4.71525	−	4.44306i	−0.183541	−	0.172946i
$661$	−11.7271	+	2.49266i	−0.456130	+	0.0969533i	−0.430246	−	0.902712i	$-0.641573\pi$
$661$	−11.7271	+	2.49266i	−0.456130	+	0.0969533i	−0.0258835	+	0.999665i	$0.508240\pi$
$662$	−16.2540	+	18.0519i	−0.631729	+	0.701606i
$663$	−5.72412	+	9.51243i	−0.222306	+	0.369432i
$664$	20.4524	+	22.7147i	0.793707	+	0.881501i
$665$	−3.82444	+	3.41222i	−0.148305	+	0.132320i
$666$	−0.0842229	+	0.0147371i	−0.00326357	+	0.000571053i
$667$	−4.57022	+	3.32046i	−0.176959	+	0.128569i
$668$	−1.56229	+	2.70596i	−0.0604468	+	0.104697i
$669$	0.832119	+	2.72812i	0.0321716	+	0.105475i
$670$	3.92992	−	5.35774i	0.151826	−	0.206987i
$671$	2.23978	−	21.3101i	0.0864659	−	0.822668i
$672$	1.56210	+	0.729665i	0.0602594	+	0.0281474i
$673$	−17.3708	−	19.2922i	−0.669593	−	0.743659i	0.308637	−	0.951180i	$-0.400127\pi$
$673$	−17.3708	−	19.2922i	−0.669593	−	0.743659i	−0.978231	+	0.207521i	$0.933460\pi$
$674$	31.6806			1.22029
$675$	25.9286	+	1.64619i	0.997991	+	0.0633619i
$676$	−17.1357			−0.659067
$677$	26.3010	+	29.2103i	1.01083	+	1.12264i	0.992430	+	0.122810i	$0.0391907\pi$
$677$	26.3010	+	29.2103i	1.01083	+	1.12264i	0.0184004	+	0.999831i	$0.494143\pi$
$678$	27.4431	+	12.8188i	1.05395	+	0.492303i
$679$	−0.243539	+	2.31712i	−0.00934616	+	0.0889227i
$680$	6.42871	−	2.05659i	0.246530	−	0.0788666i
$681$	1.85062	+	6.06730i	0.0709159	+	0.232500i
$682$	14.9361	−	25.8700i	0.571932	−	0.990615i
$683$	−26.3578	+	19.1501i	−1.00855	+	0.732757i	−0.963905	−	0.266246i	$-0.914217\pi$
$683$	−26.3578	+	19.1501i	−1.00855	+	0.732757i	−0.0446482	+	0.999003i	$0.514217\pi$
$684$	−4.33346	+	11.8578i	−0.165694	+	0.453393i
$685$	7.60267	+	17.2867i	0.290483	+	0.660491i
$686$	3.49486	+	3.88143i	0.133434	+	0.148194i
$687$	−0.756076	+	1.25646i	−0.0288461	+	0.0479369i
$688$	−4.51758	+	5.01729i	−0.172231	+	0.191282i
$689$	−27.1593	+	5.77288i	−1.03469	+	0.219929i
$690$	2.58414	−	5.46737i	0.0983764	−	0.208139i
$691$	−32.6488	−	6.93971i	−1.24202	−	0.263999i	−0.460375	−	0.887725i	$-0.652285\pi$
$691$	−32.6488	−	6.93971i	−1.24202	−	0.263999i	−0.781643	+	0.623726i	$0.785618\pi$
$692$	−0.170254	+	0.123696i	−0.00647207	+	0.00470223i
$693$	2.15176	+	1.68568i	0.0817384	+	0.0640335i
$694$	−19.7521	+	14.3507i	−0.749779	+	0.544746i
$695$	2.36714	+	2.15092i	0.0897907	+	0.0815892i
$696$	18.8229	−	13.1616i	0.713479	−	0.498888i
$697$	0.470212	−	4.47377i	0.0178106	−	0.169456i
$698$	6.73592	−	1.43176i	0.254958	−	0.0541931i
$699$	−19.0078	+	3.68183i	−0.718940	+	0.139260i
$700$	0.742475	−	0.529205i	0.0280629	−	0.0200021i
$701$	−47.0156			−1.77575			−0.887877	−	0.460081i	$-0.847820\pi$
$701$	−47.0156			−1.77575			−0.887877	+	0.460081i	$0.847820\pi$
$702$	−10.3901	−	39.0833i	−0.392151	−	1.47510i
$703$	−0.140661	−	0.102196i	−0.00530513	−	0.00385441i
$704$	23.1931	−	10.3262i	0.874124	−	0.389185i
$705$	11.4951	+	16.5995i	0.432930	+	0.625175i
$706$	15.0625	+	6.70626i	0.566885	+	0.252393i
$707$	1.81928	+	3.15109i	0.0684211	+	0.118509i
$708$	1.51465	+	4.96581i	0.0569240	+	0.186627i
$709$	2.86671	+	0.609338i	0.107661	+	0.0228842i	0.261427	−	0.965223i	$-0.415807\pi$
$709$	2.86671	+	0.609338i	0.107661	+	0.0228842i	−0.153766	+	0.988107i	$0.549140\pi$
$710$	−23.6938	+	21.1400i	−0.889212	+	0.793369i
$711$	−30.6706	−	15.0088i	−1.15024	−	0.562873i
$712$	−11.6428	−	35.8329i	−0.436333	−	1.34289i
$713$	−11.1024	−	2.35989i	−0.415789	−	0.0883786i
$714$	−0.588361	+	0.249290i	−0.0220189	+	0.00932946i
$715$	24.6499	+	34.2537i	0.921855	+	1.28102i
$716$	5.87941	−	6.52975i	0.219724	−	0.244028i
$717$	−27.5628	−	6.38238i	−1.02935	−	0.238354i
$718$	−0.305309	+	0.528811i	−0.0113940	+	0.0197351i
$719$	13.9385	−	10.1269i	0.519820	−	0.377671i	−0.296716	−	0.954966i	$-0.595892\pi$
$719$	13.9385	−	10.1269i	0.519820	−	0.377671i	0.816536	+	0.577295i	$0.195892\pi$
$720$	−7.46349	+	15.0779i	−0.278148	+	0.561922i
$721$	−4.17330	−	3.03208i	−0.155422	−	0.112920i
$722$	36.9185	−	16.4372i	1.37397	−	0.611729i
$723$	2.89734	+	2.18628i	0.107753	+	0.0813084i
$724$	−0.0165440	−	0.0286550i	−0.000614851	−	0.00106495i
$725$	−2.05949	−	21.4684i	−0.0764875	−	0.797317i
$726$	−5.35565	+	1.03740i	−0.198767	+	0.0385014i
$727$	−0.116229	−	0.129085i	−0.00431069	−	0.00478751i	0.740986	−	0.671521i	$-0.234359\pi$
$727$	−0.116229	−	0.129085i	−0.00431069	−	0.00478751i	−0.745296	+	0.666733i	$0.767692\pi$
$728$	−5.11692	−	3.71766i	−0.189646	−	0.137786i
$729$	−23.4355	+	13.4081i	−0.867982	+	0.496596i
$730$	−2.11321	−	1.23289i	−0.0782134	−	0.0456313i
$731$	0.276287	+	2.62869i	0.0102188	+	0.0972257i
$732$	7.29232	−	1.41253i	0.269532	−	0.0522087i
$733$	−48.4219	−	21.5588i	−1.78851	−	0.796294i	−0.977401	−	0.211392i	$-0.932200\pi$
$733$	−48.4219	−	21.5588i	−1.78851	−	0.796294i	−0.811104	−	0.584902i	$-0.801133\pi$
$734$	−15.5971	+	17.3223i	−0.575698	+	0.639378i
$735$	20.2613	−	17.4289i	0.747351	−	0.642876i
$736$	−2.76790	−	3.07406i	−0.102026	−	0.113311i
$737$	−2.22670	−	6.85308i	−0.0820216	−	0.252436i
$738$	10.5165	+	12.5665i	0.387118	+	0.462578i
$739$	−1.32714	+	4.08451i	−0.0488195	+	0.150251i	−0.972494	−	0.232926i	$-0.925170\pi$
$739$	−1.32714	+	4.08451i	−0.0488195	+	0.150251i	0.923675	+	0.383177i	$0.125170\pi$
$740$	0.0228910	+	0.0208002i	0.000841491	+	0.000764629i
$741$	42.4003	−	70.4615i	1.55761	−	2.58847i
$742$	−1.45997	−	0.650022i	−0.0535973	−	0.0238631i
$743$	−15.1680	−	26.2718i	−0.556461	−	0.963820i	−0.997788	−	0.0664731i	$-0.978825\pi$
$743$	−15.1680	−	26.2718i	−0.556461	−	0.963820i	0.441327	−	0.897346i	$-0.354508\pi$
$744$	44.9588	+	10.4105i	1.64827	+	0.381669i
$745$	−19.0245	+	42.2127i	−0.697002	+	1.54656i
$746$	−23.9192	−	17.3783i	−0.875745	−	0.636266i
$747$	−20.7478	+	21.4288i	−0.759121	+	0.784037i
$748$	0.507554	−	1.56209i	0.0185580	−	0.0571157i
$749$	−1.60118	+	2.77332i	−0.0585057	+	0.101335i
$750$	12.9710	+	19.0991i	0.473632	+	0.697399i
$751$	13.8299	+	23.9541i	0.504661	+	0.874099i	0.999985	+	0.00539081i	$0.00171596\pi$
$751$	13.8299	+	23.9541i	0.504661	+	0.874099i	−0.495324	+	0.868708i	$0.664951\pi$
$752$	−12.7892	+	2.71843i	−0.466374	+	0.0991308i
$753$	24.9005	+	11.6311i	0.907424	+	0.423862i
$754$	−30.6681	+	13.6543i	−1.11687	+	0.497262i
$755$	47.4169	−	4.76614i	1.72568	−	0.173457i
$756$	−0.341304	+	0.883937i	−0.0124131	+	0.0321485i
$757$	31.2908			1.13729			0.568643	−	0.822585i	$-0.307469\pi$
$757$	31.2908			1.13729			0.568643	+	0.822585i	$0.307469\pi$
$758$	2.33664	+	22.2317i	0.0848707	+	0.807491i
$759$	−3.17567	−	5.73792i	−0.115270	−	0.208273i
$760$	−47.6194	+	15.2338i	−1.72734	+	0.552587i
$761$	18.0350	−	3.83346i	0.653769	−	0.138963i	0.130926	−	0.991392i	$-0.458205\pi$
$761$	18.0350	−	3.83346i	0.653769	−	0.138963i	0.522843	+	0.852429i	$0.324872\pi$
$762$	−31.7794	−	0.575514i	−1.15125	−	0.0208487i
$763$	3.41583	+	0.726057i	0.123661	+	0.0262850i
$764$	−0.428507	+	1.31881i	−0.0155028	+	0.0477128i
$765$	2.43161	+	6.12130i	0.0879152	+	0.221316i
$766$	2.01977	+	6.21620i	0.0729771	+	0.224601i

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.797750 + 0.885991i) q^{2} +(-1.56929 - 0.733023i) q^{3} +(0.0604816 - 0.575444i) q^{4} +(1.30610 + 1.81497i) q^{5} +(-0.602450 - 1.97515i) q^{6} +(0.157578 - 0.272934i) q^{7} +(2.48714 - 1.80701i) q^{8} +(1.92535 + 2.30066i) q^{9} +O(q^{10})\)	\(q+(0.797750 + 0.885991i) q^{2} +(-1.56929 - 0.733023i) q^{3} +(0.0604816 - 0.575444i) q^{4} +(1.30610 + 1.81497i) q^{5} +(-0.602450 - 1.97515i) q^{6} +(0.157578 - 0.272934i) q^{7} +(2.48714 - 1.80701i) q^{8} +(1.92535 + 2.30066i) q^{9} +(-0.566103 + 2.60508i) q^{10} +(1.93450 + 2.14848i) q^{11} +(-0.516727 + 0.858705i) q^{12} +(4.36810 - 4.85127i) q^{13} +(0.367525 - 0.0781199i) q^{14} +(-0.719240 - 3.80561i) q^{15} +(2.45317 + 0.521438i) q^{16} +(0.794350 - 0.577129i) q^{17} +(-0.502410 + 3.54119i) q^{18} +(-5.88399 + 4.27497i) q^{19} +(1.12341 - 0.641816i) q^{20} +(-0.447354 + 0.312804i) q^{21} +(-0.360286 + 3.42790i) q^{22} +(1.28104 - 0.272294i) q^{23} +(-5.22763 + 1.01260i) q^{24} +(-1.58820 + 4.74106i) q^{25} +7.78284 q^{26} +(-1.33501 - 5.02173i) q^{27} +(-0.147528 - 0.107185i) q^{28} +(-3.94048 + 1.75442i) q^{29} +(2.79797 - 3.67317i) q^{30} +(-7.91741 - 3.52506i) q^{31} +(-1.57924 - 2.73533i) q^{32} +(-1.46091 - 4.78962i) q^{33} +(1.14502 + 0.243382i) q^{34} +(0.701179 - 0.0704794i) q^{35} +(1.44035 - 0.968786i) q^{36} +(0.00738727 + 0.0227357i) q^{37} +(-8.48155 - 1.80281i) q^{38} +(-10.4109 + 4.41114i) q^{39} +(6.52812 + 2.15393i) q^{40} +(3.06561 - 3.40470i) q^{41} +(-0.634018 - 0.146812i) q^{42} +(-1.34599 + 2.33132i) q^{43} +(1.35333 - 0.983252i) q^{44} +(-1.66091 + 6.49934i) q^{45} +(1.26320 + 0.917772i) q^{46} +(-4.76261 + 2.12045i) q^{47} +(-3.46752 - 2.61652i) q^{48} +(3.45034 + 5.97616i) q^{49} +(-5.46752 + 2.37504i) q^{50} +(-1.66962 + 0.323407i) q^{51} +(-2.52745 - 2.80701i) q^{52} +(-3.44104 - 2.50006i) q^{53} +(3.38421 - 5.18889i) q^{54} +(-1.37277 + 6.31717i) q^{55} +(-0.101275 - 0.963571i) q^{56} +(12.3674 - 2.39557i) q^{57} +(-4.69792 - 2.09165i) q^{58} +(3.46632 - 3.84974i) q^{59} +(-2.23342 + 0.183713i) q^{60} +(-4.95936 - 5.50792i) q^{61} +(-3.19295 - 9.82688i) q^{62} +(0.931321 - 0.162961i) q^{63} +(2.71365 - 8.35176i) q^{64} +(14.5101 + 1.59172i) q^{65} +(3.07812 - 5.11527i) q^{66} +(-2.27694 - 1.01376i) q^{67} +(-0.284062 - 0.492010i) q^{68} +(-2.20993 - 0.511726i) q^{69} +(0.621810 + 0.565014i) q^{70} +(9.63629 + 7.00118i) q^{71} +(8.94593 + 2.24291i) q^{72} +(-0.283594 + 0.872814i) q^{73} +(-0.0142504 + 0.0246825i) q^{74} +(5.96766 - 6.27591i) q^{75} +(2.10413 + 3.64447i) q^{76} +(0.891228 - 0.189436i) q^{77} +(-12.2135 - 5.70500i) q^{78} +(-10.3980 + 4.62948i) q^{79} +(2.25770 + 5.13348i) q^{80} +(-1.58603 + 8.85915i) q^{81} +5.46212 q^{82} +(1.03926 + 9.88793i) q^{83} +(0.152945 + 0.276346i) q^{84} +(2.08497 + 0.687930i) q^{85} +(-3.13929 + 0.667278i) q^{86} +(7.46979 + 0.135276i) q^{87} +(8.69369 + 1.84790i) q^{88} +(3.78718 - 11.6557i) q^{89} +(-7.08335 + 3.71330i) q^{90} +(-0.635757 - 1.95666i) q^{91} +(-0.0792106 - 0.753639i) q^{92} +(9.84078 + 11.3355i) q^{93} +(-5.67808 - 2.52804i) q^{94} +(-15.4440 - 5.09571i) q^{95} +(0.473233 + 5.45015i) q^{96} +(-6.75362 + 3.00691i) q^{97} +(-2.54232 + 7.82445i) q^{98} +(-1.21831 + 8.58719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

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