LMFDB - Embedded newform 225.2.q.a.31.20

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			31.20
Character	$\chi$	$=$	225.31
Dual form			225.2.q.a.196.20

$q$-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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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	−0.391853	−	0.920028i	$-0.628166\pi$
$2$	0.797750	−	0.885991i	0.564095	−	0.626491i	0.955948	+	0.293537i	$0.0948325\pi$
$3$	−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	0.894268	−	0.447533i	$-0.147697\pi$
$7$	0.157578	+	0.272934i	0.0595591	+	0.103159i	−0.834708	+	0.550692i	$0.814364\pi$
$8$	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	−0.377210	−	0.926128i	$-0.623117\pi$
$11$	1.93450	−	2.14848i	0.583273	−	0.647790i	0.960483	+	0.278337i	$0.0897833\pi$
$12$	−0.516727	−	0.858705i	−0.149166	−	0.247887i
$13$	4.36810	+	4.85127i	1.21149	+	1.34550i	0.921455	+	0.388486i	$0.127002\pi$
$13$	4.36810	+	4.85127i	1.21149	+	1.34550i	0.290039	+	0.957015i	$0.406332\pi$
$14$	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	0.679933	−	0.733274i	$-0.262009\pi$
$17$	0.794350	+	0.577129i	0.192658	+	0.139974i	−0.487275	+	0.873249i	$0.662009\pi$
$18$	−0.502410	−	3.54119i	−0.118419	−	0.834668i
$19$	−5.88399	−	4.27497i	−1.34988	−	0.980746i	−0.999017	−	0.0443190i	$-0.985888\pi$
$19$	−5.88399	−	4.27497i	−1.34988	−	0.980746i	−0.350863	−	0.936427i	$-0.614112\pi$
$20$	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	0.339523	−	0.940598i	$-0.389734\pi$
$23$	1.28104	+	0.272294i	0.267116	+	0.0567773i	−0.0724063	+	0.997375i	$0.523068\pi$
$24$	−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	0.00682892	−	0.999977i	$-0.497826\pi$
$29$	−3.94048	−	1.75442i	−0.731729	−	0.325787i	−0.738558	+	0.674190i	$0.764493\pi$
$30$	2.79797	+	3.67317i	0.510837	+	0.670626i
$31$	−7.91741	+	3.52506i	−1.42201	+	0.633120i	−0.966396	−	0.257058i	$-0.917247\pi$
$31$	−7.91741	+	3.52506i	−1.42201	+	0.633120i	−0.455614	+	0.890178i	$0.650580\pi$
$32$	−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	−0.950447	−	0.310885i	$-0.899375\pi$
$37$	0.00738727	−	0.0227357i	0.00121446	−	0.00373772i	0.951662	+	0.307148i	$0.0993745\pi$
$38$	−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	0.933344	−	0.358983i	$-0.116876\pi$
$41$	3.06561	+	3.40470i	0.478767	+	0.531725i	−0.454577	+	0.890707i	$0.650210\pi$
$42$	−0.634018	+	0.146812i	−0.0978311	+	0.0226535i
$43$	−1.34599	−	2.33132i	−0.205261	−	0.355523i	0.744955	−	0.667115i	$-0.232471\pi$
$43$	−1.34599	−	2.33132i	−0.205261	−	0.355523i	−0.950216	+	0.311592i	$0.899138\pi$
$44$	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	0.0288398	−	0.999584i	$-0.490819\pi$
$47$	−4.76261	−	2.12045i	−0.694698	−	0.309300i	−0.723538	+	0.690284i	$0.757485\pi$
$48$	−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	−0.798478	−	0.602024i	$-0.794361\pi$
$53$	−3.44104	+	2.50006i	−0.472663	+	0.343410i	0.325815	+	0.945433i	$0.394361\pi$
$54$	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	0.925256	−	0.379342i	$-0.123850\pi$
$59$	3.46632	+	3.84974i	0.451276	+	0.501193i	−0.473980	+	0.880536i	$0.657183\pi$
$60$	−2.23342	−	0.183713i	−0.288333	−	0.0237172i
$61$	−4.95936	+	5.50792i	−0.634980	+	0.705217i	−0.971655	−	0.236404i	$-0.924031\pi$
$61$	−4.95936	+	5.50792i	−0.634980	+	0.705217i	0.336674	+	0.941621i	$0.390698\pi$
$62$	−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	−0.541081	−	0.840970i	$-0.681985\pi$
$67$	−2.27694	+	1.01376i	−0.278173	+	0.123851i	0.262908	+	0.964821i	$0.415318\pi$
$68$	−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	0.155999	−	0.987757i	$-0.450140\pi$
$71$	9.63629	−	7.00118i	1.14362	−	0.830887i	0.987619	+	0.156870i	$0.0501405\pi$
$72$	8.94593	−	2.24291i	1.05429	−	0.264330i
$73$	−0.283594	−	0.872814i	−0.0331922	−	0.102155i	0.933088	−	0.359649i	$-0.117103\pi$
$73$	−0.283594	−	0.872814i	−0.0331922	−	0.102155i	−0.966280	+	0.257493i	$0.917103\pi$
$74$	−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	−0.272503	−	0.962155i	$-0.587851\pi$
$79$	−10.3980	−	4.62948i	−1.16986	−	0.520857i	−0.897361	+	0.441298i	$0.854518\pi$
$80$	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	−0.776379	−	0.630266i	$-0.782946\pi$
$83$	1.03926	−	9.88793i	0.114074	−	1.08534i	0.890453	−	0.455075i	$-0.150388\pi$
$84$	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	0.923831	+	0.382800i	$0.125040\pi$
$89$	3.78718	+	11.6557i	0.401440	+	1.23551i	−0.522391	+	0.852706i	$0.674960\pi$
$90$	−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	0.0341407	−	0.999417i	$-0.489131\pi$
$97$	−6.75362	−	3.00691i	−0.685726	−	0.305305i	−0.719867	+	0.694112i	$0.755797\pi$
$98$	−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	−0.996107	−	0.0881544i	$-0.971903\pi$
$101$	−5.77262	−	9.99848i	−0.574397	−	0.994885i	0.421709	−	0.906731i	$-0.361430\pi$
$102$	−1.61847	+	1.22127i	−0.160253	+	0.120923i
$103$	1.71092	+	16.2783i	0.168582	+	1.60395i	0.672433	+	0.740158i	$0.265249\pi$
$103$	1.71092	+	16.2783i	0.168582	+	1.60395i	−0.503851	+	0.863790i	$0.668084\pi$
$104$	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	−0.642112	−	0.766611i	$-0.721942\pi$
$109$	3.42411	−	10.5383i	0.327970	−	1.00939i	0.970082	−	0.242777i	$-0.0780584\pi$
$110$	−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	−0.999598	−	0.0283484i	$-0.990975\pi$
$113$	−9.81486	−	10.9005i	−0.923305	−	1.02543i	0.0762934	−	0.997085i	$-0.475691\pi$
$114$	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	0.905776	+	0.423757i	$0.139289\pi$
$127$	4.75644	+	14.6388i	0.422066	+	1.29899i	−0.483710	+	0.875228i	$0.660711\pi$
$128$	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	−0.269166	−	0.963094i	$-0.586748\pi$
$131$	3.04960	−	1.35777i	0.266445	−	0.118629i	0.535611	+	0.844465i	$0.320081\pi$
$132$	−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	0.158979	−	0.987282i	$-0.449180\pi$
$137$	8.26092	−	1.75591i	0.705778	−	0.150018i	0.546799	+	0.837264i	$0.315846\pi$
$138$	−1.30959	+	2.36621i	−0.111480	+	0.201425i
$139$	1.39912	+	0.297391i	0.118671	+	0.0252244i	0.266864	−	0.963734i	$-0.414012\pi$
$139$	1.39912	+	0.297391i	0.118671	+	0.0252244i	−0.148193	+	0.988958i	$0.547346\pi$
$140$	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	−0.0346486	−	0.999400i	$-0.511031\pi$
$149$	10.3534	−	17.9326i	0.848181	−	1.46909i	0.882830	−	0.469693i	$-0.155635\pi$
$150$	10.3211	−	0.280689i	0.842715	−	0.0229182i
$151$	10.6562	+	18.4570i	0.867186	+	1.50201i	0.864860	+	0.502014i	$0.167407\pi$
$151$	10.6562	+	18.4570i	0.867186	+	1.50201i	0.00232675	+	0.999997i	$0.499259\pi$
$152$	−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	0.440514	+	0.897746i	$0.354796\pi$
$157$	−6.98186	+	12.0929i	−0.557213	+	0.965122i	−0.997728	+	0.0673760i	$0.978537\pi$
$158$	−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	−0.958231	−	0.285997i	$-0.907675\pi$
$163$	−0.190245	+	0.585515i	−0.0149012	+	0.0458611i	0.943329	+	0.331858i	$0.107675\pi$
$164$	−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	−0.588633	−	0.808401i	$-0.700334\pi$
$167$	−4.93325	+	2.19642i	−0.381746	+	0.169964i	0.206887	+	0.978365i	$0.433667\pi$
$168$	−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	−0.752325	−	0.658792i	$-0.771068\pi$
$173$	−0.243366	+	0.270286i	−0.0185028	+	0.0205494i	0.733822	+	0.679341i	$0.237734\pi$
$174$	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	−0.0248313	−	0.999692i	$-0.507905\pi$
$179$	12.2855	−	8.92591i	0.918259	−	0.667154i	0.943090	+	0.332538i	$0.107905\pi$
$180$	3.63955	−	1.34885i	0.271276	−	0.100537i
$181$	0.0462635	+	0.0336124i	0.00343874	+	0.00249839i	0.589503	−	0.807766i	$-0.299324\pi$
$181$	0.0462635	+	0.0336124i	0.00343874	+	0.00249839i	−0.586065	+	0.810264i	$0.699324\pi$
$182$	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	−0.291938	−	0.956437i	$-0.594300\pi$
$191$	−2.34418	+	0.498271i	−0.169619	+	0.0360536i	0.122319	+	0.992491i	$0.460967\pi$
$192$	−10.3805	−	11.1172i	−0.749152	−	0.802313i
$193$	2.94773	−	5.10562i	0.212182	−	0.367511i	−0.740215	−	0.672370i	$-0.765276\pi$
$193$	2.94773	−	5.10562i	0.212182	−	0.367511i	0.952397	+	0.304860i	$0.0986095\pi$
$194$	−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	−0.942289	−	0.334801i	$-0.891331\pi$
$197$	−12.8434	+	9.33130i	−0.915057	+	0.664828i	0.0272318	+	0.999629i	$0.491331\pi$
$198$	−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	0.202923	−	0.979195i	$-0.434956\pi$
$211$	−0.144843	−	0.0307873i	−0.00997140	−	0.00211949i	−0.212895	+	0.977075i	$0.568289\pi$
$212$	−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	−0.778908	−	0.627139i	$-0.784226\pi$
$223$	−1.10187	+	1.22375i	−0.0737867	+	0.0819485i	0.705121	+	0.709087i	$0.250893\pi$
$224$	−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	−0.818960	−	0.573851i	$-0.805449\pi$
$227$	−2.45055	+	2.72161i	−0.162648	+	0.180639i	0.656312	+	0.754490i	$0.272116\pi$
$228$	−0.630521	+	7.26161i	−0.0417572	+	0.480912i
$229$	0.0884967	+	0.841990i	0.00584803	+	0.0556403i	0.997057	−	0.0766674i	$-0.0244280\pi$
$229$	0.0884967	+	0.841990i	0.00584803	+	0.0556403i	−0.991209	+	0.132308i	$0.957761\pi$
$230$	−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	0.843189	−	0.537617i	$-0.180675\pi$
$233$	9.04329	+	6.57033i	0.592445	+	0.430437i	−0.250744	+	0.968053i	$0.580675\pi$
$234$	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	0.693280	−	0.720669i	$-0.256165\pi$
$239$	15.9775	+	3.39613i	1.03350	+	0.219677i	0.340220	+	0.940346i	$0.389498\pi$
$240$	0.219972	+	9.71087i	0.0141992	+	0.626834i
$241$	−2.04979	+	0.435696i	−0.132038	+	0.0280656i	−0.273457	−	0.961884i	$-0.588167\pi$
$241$	−2.04979	+	0.435696i	−0.132038	+	0.0280656i	0.141418	+	0.989950i	$0.454834\pi$
$242$	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	−0.898226	−	0.439533i	$-0.855144\pi$
$257$	−1.09760	+	1.90109i	−0.0684661	+	0.118587i	0.829760	+	0.558120i	$0.188477\pi$
$258$	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	0.810454	−	0.585802i	$-0.199220\pi$
$263$	29.0145	−	6.16721i	1.78911	−	0.380287i	0.978654	+	0.205515i	$0.0658869\pi$
$264$	−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	−0.250210	−	0.968192i	$-0.580500\pi$
$269$	−20.4742	−	14.8754i	−1.24833	−	0.906968i	−0.998124	+	0.0612238i	$0.980500\pi$
$270$	13.8378	+	0.634991i	0.842140	+	0.0386443i
$271$	−15.2201	+	11.0580i	−0.924555	+	0.671728i	−0.944654	−	0.328070i	$-0.893602\pi$
$271$	−15.2201	+	11.0580i	−0.924555	+	0.671728i	0.0200987	+	0.999798i	$0.493602\pi$
$272$	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	−0.0898796	−	0.995953i	$-0.528648\pi$
$277$	15.1456	−	16.8209i	0.910012	−	1.01067i	0.999892	−	0.0147182i	$-0.00468511\pi$
$278$	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	−0.991209	−	0.132304i	$-0.957763\pi$
$281$	0.0980168	−	0.932568i	0.00584719	−	0.0556323i	0.997056	+	0.0766714i	$0.0244292\pi$
$282$	7.05744	−	8.12940i	0.420265	−	0.484099i
$283$	10.5924	−	4.71605i	0.629653	−	0.280340i	−0.0669940	−	0.997753i	$-0.521341\pi$
$283$	10.5924	−	4.71605i	0.629653	−	0.280340i	0.696648	+	0.717414i	$0.254674\pi$
$284$	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	−0.278435	−	0.960455i	$-0.589816\pi$
$293$	11.8547	−	20.5330i	0.692561	−	1.19955i	0.970996	−	0.239096i	$-0.0768509\pi$
$294$	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	0.583207	−	0.812324i	$-0.301798\pi$
$311$	13.8540	+	2.94477i	0.785590	+	0.166982i	0.202384	+	0.979306i	$0.435131\pi$
$312$	−17.9224	−	29.7838i	−1.01466	−	1.68617i
$313$	−2.73979	+	0.582360i	−0.154862	+	0.0329169i	−0.284690	−	0.958620i	$-0.591891\pi$
$313$	−2.73979	+	0.582360i	−0.154862	+	0.0329169i	0.129828	+	0.991537i	$0.458557\pi$
$314$	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	0.455805	+	0.890080i	$0.349351\pi$
$317$	−3.11752	+	29.6613i	−0.175098	+	1.66594i	−0.630902	+	0.775862i	$0.717315\pi$
$318$	−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	−0.765458	−	0.643486i	$-0.777487\pi$
$331$	2.12974	−	20.2631i	0.117061	−	1.11376i	0.882519	−	0.470277i	$-0.155846\pi$
$332$	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	0.997099	+	0.0761198i	$0.0242532\pi$
$337$	17.7807	+	19.7475i	0.968576	+	1.07571i	−0.0285223	+	0.999593i	$0.509080\pi$
$338$	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	−0.888260	−	0.459341i	$-0.848086\pi$
$347$	−2.14059	−	20.3664i	−0.114913	−	1.09332i	0.773347	−	0.633983i	$-0.218581\pi$
$348$	0.529629	+	4.29027i	0.0283911	+	0.229982i
$349$	2.88806	+	5.00227i	0.154594	+	0.267766i	0.932911	−	0.360106i	$-0.117260\pi$
$349$	2.88806	+	5.00227i	0.154594	+	0.267766i	−0.778317	+	0.627872i	$0.783926\pi$
$350$	−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	0.714408	−	0.699729i	$-0.246696\pi$
$353$	12.6340	+	5.62502i	0.672440	+	0.299390i	−0.0419678	+	0.999119i	$0.513363\pi$
$354$	−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	−0.946793	−	0.321843i	$-0.895698\pi$
$359$	0.158269	−	0.487102i	0.00835313	−	0.0257083i	0.955146	+	0.296135i	$0.0956977\pi$
$360$	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	−0.801955	−	0.597385i	$-0.796207\pi$
$367$	2.04367	−	19.4442i	0.106679	−	1.01498i	0.908633	−	0.417595i	$-0.137127\pi$
$368$	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	−0.468587	−	0.883417i	$-0.655237\pi$
$373$	−24.2570	−	5.15599i	−1.25598	−	0.266967i	−0.787394	+	0.616450i	$0.788570\pi$
$374$	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	−0.125550	−	0.992087i	$-0.540070\pi$
$379$	15.1691	−	11.0210i	0.779184	−	0.566110i	0.904734	+	0.425977i	$0.140070\pi$
$380$	−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	−0.274770	−	0.961510i	$-0.588602\pi$
$383$	5.00833	−	2.22985i	0.255914	−	0.113940i	0.530684	+	0.847570i	$0.321935\pi$
$384$	−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	−0.769157	−	0.639060i	$-0.779324\pi$
$389$	−1.04925	+	1.16531i	−0.0531990	+	0.0590835i	0.715958	+	0.698143i	$0.245990\pi$
$390$	−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	−0.373599	−	0.927590i	$-0.621876\pi$
$397$	7.83333	−	5.69125i	0.393143	−	0.285635i	0.766742	+	0.641955i	$0.221876\pi$
$398$	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	−0.878367	−	0.477988i	$-0.841366\pi$
$401$	−0.505309	+	0.875221i	−0.0252339	+	0.0437064i	0.853133	+	0.521694i	$0.174700\pi$
$402$	−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	0.861028	−	0.508557i	$-0.169821\pi$
$409$	5.36444	+	5.95782i	0.265255	+	0.294595i	−0.595773	+	0.803153i	$0.703154\pi$
$410$	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	0.236711	−	0.971580i	$-0.423931\pi$
$419$	22.8670	−	10.1810i	1.11713	−	0.497377i	0.880415	+	0.474204i	$0.157264\pi$
$420$	−0.301797	−	0.638525i	−0.0147262	−	0.0311568i
$421$	30.1379	+	13.4182i	1.46883	+	0.653965i	0.976318	−	0.216340i	$-0.0694120\pi$
$421$	30.1379	+	13.4182i	1.46883	+	0.653965i	0.492512	+	0.870305i	$0.336079\pi$
$422$	−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	0.695516	−	0.718511i	$-0.255176\pi$
$431$	4.71468	+	3.42542i	0.227098	+	0.164997i	−0.468418	+	0.883507i	$0.655176\pi$
$432$	−0.656483	+	13.0153i	−0.0315851	+	0.626198i
$433$	−1.68629	−	1.22516i	−0.0810381	−	0.0588776i	0.546529	−	0.837440i	$-0.315949\pi$
$433$	−1.68629	−	1.22516i	−0.0810381	−	0.0588776i	−0.627567	+	0.778563i	$0.715949\pi$
$434$	−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	−0.259807	−	0.965661i	$-0.583659\pi$
$439$	15.2474	−	16.9340i	0.727721	−	0.808216i	0.987528	+	0.157445i	$0.0503256\pi$
$440$	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	0.952932	−	0.303184i	$-0.0980495\pi$
$443$	4.50211	+	7.79787i	0.213901	+	0.370488i	−0.739031	+	0.673672i	$0.764716\pi$
$444$	−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	0.998835	−	0.0482552i	$-0.0153661\pi$
$457$	9.78295	+	16.9446i	0.457627	+	0.792634i	−0.541208	+	0.840889i	$0.682033\pi$
$458$	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	−0.799639	−	0.600482i	$-0.794976\pi$
$461$	−2.55207	+	2.83436i	−0.118862	+	0.132009i	0.680777	+	0.732491i	$0.261642\pi$
$462$	−0.911085	+	1.64618i	−0.0423875	+	0.0765873i
$463$	6.05576	+	6.72560i	0.281435	+	0.312565i	0.867243	−	0.497884i	$-0.165890\pi$
$463$	6.05576	+	6.72560i	0.281435	+	0.312565i	−0.585808	+	0.810450i	$0.699223\pi$
$464$	−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	0.988759	−	0.149515i	$-0.0477713\pi$
$467$	24.8972	+	18.0889i	1.15211	+	0.837053i	0.163346	+	0.986569i	$0.447771\pi$
$468$	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	0.647331	−	0.762209i	$-0.275885\pi$
$479$	11.2505	+	5.00905i	0.514049	+	0.228870i	−0.133282	+	0.991078i	$0.542552\pi$
$480$	−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	−0.910252	−	0.414054i	$-0.864113\pi$
$487$	1.53444	−	4.72251i	0.0695320	−	0.213997i	0.979784	+	0.200056i	$0.0641125\pi$
$488$	−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	0.383090	−	0.923711i	$-0.374860\pi$
$491$	−12.7546	−	14.1654i	−0.575605	−	0.639274i	−0.958695	+	0.284437i	$0.908193\pi$
$492$	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	−0.916709	−	0.399557i	$-0.869164\pi$
$499$	−2.50922	+	4.34610i	−0.112328	+	0.194558i	0.804380	+	0.594115i	$0.202497\pi$
$500$	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	−0.703226	−	0.710966i	$-0.748258\pi$
$503$	−5.48055	+	3.98186i	−0.244366	+	0.177542i	0.458860	+	0.888508i	$0.348258\pi$
$504$	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	0.577405	−	0.816458i	$-0.304065\pi$
$509$	−6.65406	−	7.39008i	−0.294936	−	0.327559i	−0.872341	+	0.488899i	$0.837399\pi$
$510$	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	−0.194072	−	0.980987i	$-0.562170\pi$
$521$	15.4969	−	11.2591i	0.678930	−	0.493272i	0.873003	+	0.487715i	$0.162170\pi$
$522$	−4.23299	+	14.8354i	−0.185273	+	0.649330i
$523$	0.0808887	+	0.248950i	0.00353702	+	0.0108858i	0.952809	−	0.303569i	$-0.0981783\pi$
$523$	0.0808887	+	0.248950i	0.00353702	+	0.0108858i	−0.949272	+	0.314455i	$0.898178\pi$
$524$	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	−0.722683	−	0.691180i	$-0.757091\pi$
$541$	6.23922	−	19.2023i	0.268245	−	0.825573i	0.990928	−	0.134394i	$-0.0429087\pi$
$542$	−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	0.254708	−	0.967018i	$-0.418021\pi$
$547$	−6.86422	−	3.05615i	−0.293493	−	0.130671i	−0.548201	+	0.836346i	$0.684687\pi$
$548$	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	0.780047	−	0.625721i	$-0.215195\pi$
$563$	1.80844	+	2.00848i	0.0762167	+	0.0846473i	−0.703830	+	0.710368i	$0.748528\pi$
$564$	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	−0.347877	−	0.937540i	$-0.613097\pi$
$569$	4.46837	−	42.5137i	0.187324	−	1.78227i	0.535201	−	0.844725i	$-0.320236\pi$
$570$	−0.760528	−	33.5741i	−0.0318550	−	1.40627i
$571$	−3.16839	−	30.1452i	−0.132593	−	1.26154i	−0.835194	−	0.549955i	$-0.814645\pi$
$571$	−3.16839	−	30.1452i	−0.132593	−	1.26154i	0.702601	−	0.711584i	$-0.252022\pi$
$572$	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	0.821707	+	0.569910i	$0.193022\pi$
$577$	11.8163	+	36.3667i	0.491917	+	1.51396i	−0.329790	+	0.944054i	$0.606978\pi$
$578$	−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	−0.569539	−	0.821964i	$-0.692878\pi$
$587$	−18.3047	+	3.89078i	−0.755515	+	0.160590i	−0.185976	+	0.982554i	$0.559545\pi$
$588$	−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	−0.168757	+	0.985658i	$0.553975\pi$
$599$	−22.9566	+	39.7621i	−0.937983	+	1.62463i	−0.769226	+	0.638977i	$0.779358\pi$
$600$	3.50176	+	26.3927i	0.142959	+	1.07748i
$601$	13.8303	+	23.9548i	0.564150	+	0.977136i	0.997128	+	0.0757320i	$0.0241293\pi$
$601$	13.8303	+	23.9548i	0.564150	+	0.977136i	−0.432978	+	0.901404i	$0.642537\pi$
$602$	−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	−0.979532	−	0.201287i	$-0.935488\pi$
$607$	−7.77177	+	13.4611i	−0.315446	+	0.546369i	0.664086	+	0.747656i	$0.268821\pi$
$608$	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	0.243359	+	0.969936i	$0.421751\pi$
$613$	−12.9646	+	39.9011i	−0.523637	+	1.61159i	−0.766996	+	0.641652i	$0.778249\pi$
$614$	−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	−0.569979	−	0.821659i	$-0.693049\pi$
$617$	−8.46425	+	3.76852i	−0.340758	+	0.151715i	0.229221	+	0.973374i	$0.426382\pi$
$618$	−33.1828	−	6.42755i	−1.33481	−	0.258554i
$619$	−1.08260	+	10.3002i	−0.0435132	+	0.414001i	0.950984	+	0.309240i	$0.100074\pi$
$619$	−1.08260	+	10.3002i	−0.0435132	+	0.414001i	−0.994497	+	0.104761i	$0.966592\pi$
$620$	−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	0.992188	−	0.124749i	$-0.0398126\pi$
$631$	29.6450	+	21.5383i	1.18015	+	0.857428i	0.187960	+	0.982177i	$0.439813\pi$
$632$	−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	0.331261	−	0.943539i	$-0.392526\pi$
$641$	25.7650	−	5.47651i	1.01766	−	0.216309i	0.686394	+	0.727230i	$0.259193\pi$
$642$	6.12158	−	20.0698i	0.241600	−	0.792090i
$643$	24.3415	−	42.1606i	0.959934	−	1.66265i	0.237282	−	0.971441i	$-0.423743\pi$
$643$	24.3415	−	42.1606i	0.959934	−	1.66265i	0.722651	−	0.691213i	$-0.242923\pi$
$644$	−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	−0.359199	−	0.933261i	$-0.616950\pi$
$647$	10.6167	−	7.71348i	0.417386	−	0.303248i	0.776585	+	0.630012i	$0.216950\pi$
$648$	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	0.421835	+	0.906673i	$0.361386\pi$
$653$	5.05266	+	48.0729i	0.197726	+	1.88124i	−0.224109	+	0.974564i	$0.571947\pi$
$654$	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	−0.740263	−	0.672318i	$-0.765299\pi$
$659$	−29.3437	+	6.23721i	−1.14307	+	0.242967i	−0.402807	+	0.915285i	$0.631966\pi$
$660$	−4.71525	+	4.44306i	−0.183541	+	0.172946i
$661$	−11.7271	−	2.49266i	−0.456130	−	0.0969533i	−0.0258835	−	0.999665i	$-0.508240\pi$
$661$	−11.7271	−	2.49266i	−0.456130	−	0.0969533i	−0.430246	+	0.902712i	$0.641573\pi$
$662$	−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	−0.978231	−	0.207521i	$-0.933460\pi$
$673$	−17.3708	+	19.2922i	−0.669593	+	0.743659i	0.308637	+	0.951180i	$0.400127\pi$
$674$	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	0.0184004	−	0.999831i	$-0.494143\pi$
$677$	26.3010	−	29.2103i	1.01083	−	1.12264i	0.992430	−	0.122810i	$-0.0391907\pi$
$678$	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	−0.0446482	−	0.999003i	$-0.514217\pi$
$683$	−26.3578	−	19.1501i	−1.00855	−	0.732757i	−0.963905	+	0.266246i	$0.914217\pi$
$684$	−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	−0.781643	−	0.623726i	$-0.785618\pi$
$691$	−32.6488	+	6.93971i	−1.24202	+	0.263999i	−0.460375	+	0.887725i	$0.652285\pi$
$692$	−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	−0.153766	−	0.988107i	$-0.549140\pi$
$709$	2.86671	−	0.609338i	0.107661	−	0.0228842i	0.261427	+	0.965223i	$0.415807\pi$
$710$	−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	0.816536	−	0.577295i	$-0.195892\pi$
$719$	13.9385	+	10.1269i	0.519820	+	0.377671i	−0.296716	+	0.954966i	$0.595892\pi$
$720$	−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	−0.745296	−	0.666733i	$-0.767692\pi$
$727$	−0.116229	+	0.129085i	−0.00431069	+	0.00478751i	0.740986	+	0.671521i	$0.234359\pi$
$728$	−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	−0.811104	+	0.584902i	$0.801133\pi$
$733$	−48.4219	+	21.5588i	−1.78851	+	0.796294i	−0.977401	+	0.211392i	$0.932200\pi$
$734$	−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	0.923675	−	0.383177i	$-0.125170\pi$
$739$	−1.32714	−	4.08451i	−0.0488195	−	0.150251i	−0.972494	+	0.232926i	$0.925170\pi$
$740$	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	0.441327	+	0.897346i	$0.354508\pi$
$743$	−15.1680	+	26.2718i	−0.556461	+	0.963820i	−0.997788	+	0.0664731i	$0.978825\pi$
$744$	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	−0.495324	−	0.868708i	$-0.664951\pi$
$751$	13.8299	−	23.9541i	0.504661	−	0.874099i	0.999985	−	0.00539081i	$-0.00171596\pi$
$752$	−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	0.522843	−	0.852429i	$-0.324872\pi$
$761$	18.0350	+	3.83346i	0.653769	+	0.138963i	0.130926	+	0.991392i	$0.458205\pi$
$762$	−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
$767$	−3.53488	+	33.6321i	−0.127637	+	1.21438i
$768$	14.3210	−	16.4962i	0.516763	−	0.595255i
$769$	−15.0205	+	6.68758i	−0.541655	+	0.241160i	−0.659280	−	0.751898i	$-0.729139\pi$
$769$	−15.0205	+	6.68758i	−0.541655	+	0.241160i	0.117625	+	0.993058i	$0.462472\pi$
$770$	−0.0110291	−	2.42896i	−0.000397461	−	0.0875337i
$771$	0.328903	−	3.78793i	0.0118452	−	0.136419i
$772$	3.11629	+	1.38746i	0.112158	+	0.0499358i
$773$	11.8001	+	36.3171i	0.424421	+	1.30623i	0.903547	+	0.428489i	$0.140954\pi$
$773$	11.8001	+	36.3171i	0.424421	+	1.30623i	−0.479126	+	0.877746i	$0.659046\pi$
$774$	−7.57943	+	5.93769i	−0.272437	+	0.213426i
$775$	29.2870	+	31.9384i	1.05202	+	1.14726i
$776$	−11.3637	−	19.6825i	−0.407932	−	0.706559i
$777$	−0.0104165	+	0.00786012i	−0.000373691	+	0.000281980i
$778$	0.195415	+	1.85925i	0.00700597	+	0.0666573i
$779$	−3.48301	−	33.1386i	−0.124792	−	1.18731i
$780$	−8.86457	−	11.6374i	−0.317402	−	0.416686i
$781$	3.59952	−	34.2471i	0.128801	−	1.22546i
$782$	1.53310			0.0548235
$783$	14.0708	−	17.4459i	0.502848	−	0.623465i
$784$	5.34808	−	16.4597i	0.191003	−	0.587846i
$785$	12.8293	+	28.4664i	0.457896	+	1.01601i
$786$	0.844562	+	6.84139i	0.0301245	+	0.244024i
$787$	−8.48025	−	9.41827i	−0.302288	−	0.335725i	0.572794	−	0.819699i	$-0.305860\pi$
$787$	−8.48025	−	9.41827i	−0.302288	−	0.335725i	−0.875082	+	0.483974i	$0.839193\pi$
$788$	−6.14644	−	6.82631i	−0.218958	−	0.243177i
$789$	−41.0114	+	30.9464i	−1.46005	+	1.10172i
$790$	−6.17385	+	29.7083i	−0.219656	+	1.05698i
$791$	1.42851	−	4.39650i	0.0507919	−	0.156321i
$792$	12.4870	−	23.5590i	0.443708	−	0.837134i
$793$	−48.3834			−1.71814
$794$	1.20664	−	11.4805i	0.0428222	−	0.407426i
$795$	−7.03933	−	14.8934i	−0.249659	−	0.528214i
$796$	0.278824	+	2.65283i	0.00988265	+	0.0940271i
$797$	−2.19931	−	20.9250i	−0.0779034	−	0.741202i	−0.961843	−	0.273601i	$-0.911785\pi$
$797$	−2.19931	−	20.9250i	−0.0779034	−	0.741202i	0.883940	−	0.467601i	$-0.154881\pi$
$798$	4.35818	+	1.84657i	0.154278	+	0.0653679i
$799$	−2.55941	−	4.43302i	−0.0905452	−	0.156829i
$800$	15.4765	+	3.14302i	0.547177	+	0.111122i
$801$	34.1075	+	13.7284i	1.20513	+	0.485070i
$802$	0.372328	+	1.14591i	0.0131473	+	0.0404634i
$803$	−2.42383	−	1.07916i	−0.0855352	−	0.0380827i
$804$	2.04708	+	1.43139i	0.0721950	+	0.0504811i
$805$	0.879051	+	0.281215i	0.0309825	+	0.00991151i
$806$	−61.6200	+	27.4350i	−2.17047	+	0.966356i
$807$	43.0340	+	8.33574i	1.51487	+	0.293432i
$808$	3.71005	−	35.2988i	0.130519	−	1.24181i
$809$	−11.6292	+	35.7910i	−0.408861	+	1.25834i	0.508767	+	0.860904i	$0.330102\pi$
$809$	−11.6292	+	35.7910i	−0.408861	+	1.25834i	−0.917628	+	0.397441i	$0.869898\pi$
$810$	−22.1810	+	9.14692i	−0.779360	+	0.321390i
$811$	8.42021	+	25.9147i	0.295673	+	0.909989i	0.982994	+	0.183636i	$0.0587866\pi$
$811$	8.42021	+	25.9147i	0.295673	+	0.909989i	−0.687321	+	0.726354i	$0.741213\pi$
$812$	0.769377	−	0.163536i	0.0269998	−	0.00573899i
$813$	15.7790	−	28.5100i	0.553392	−	0.999889i
$814$	−0.0805971	−	0.0171314i	−0.00282493	−	0.000600457i
$815$	0.814210	+	1.11003i	0.0285205	+	0.0388826i
$816$	−4.26449	+	0.0772285i	−0.149287	+	0.00270354i
$817$	−2.04654	+	19.4715i	−0.0715994	+	0.681223i
$818$	9.55806			0.334190
$819$	3.27754	+	5.22992i	0.114527	+	0.182748i
$820$	1.25873	+	5.79242i	0.0439568	+	0.202280i
$821$	−18.4249	−	8.20330i	−0.643034	−	0.286297i	0.0591972	−	0.998246i	$-0.481146\pi$
$821$	−18.4249	−	8.20330i	−0.643034	−	0.286297i	−0.702231	+	0.711949i	$0.747813\pi$
$822$	−1.50861	+	17.3744i	−0.0526187	+	0.606002i
$823$	47.1257	+	10.0169i	1.64270	+	0.349166i	0.934256	−	0.356602i	$-0.116065\pi$
$823$	47.1257	+	10.0169i	1.64270	+	0.349166i	0.708442	+	0.705769i	$0.249398\pi$
$824$	−25.1598	+	43.5780i	−0.876483	+	1.51811i
$825$	25.0281	−	0.680655i	0.871366	−	0.0236974i
$826$	0.973219	+	1.68566i	0.0338626	+	0.0586518i
$827$	−6.10623	−	18.7930i	−0.212334	−	0.653498i	−0.999332	−	0.0365422i	$-0.988366\pi$
$827$	−6.10623	−	18.7930i	−0.212334	−	0.653498i	0.786998	−	0.616956i	$-0.211634\pi$
$828$	1.58135	+	1.63326i	0.0549559	+	0.0567596i
$829$	21.1194	−	15.3441i	0.733507	−	0.532924i	−0.157164	−	0.987573i	$-0.550235\pi$
$829$	21.1194	−	15.3441i	0.733507	−	0.532924i	0.890671	+	0.454648i	$0.150235\pi$
$830$	−26.3472	+	2.89022i	−0.914525	+	0.100321i
$831$	−11.4378	+	37.4990i	−0.396772	+	1.30083i
$832$	−28.6631	+	49.6460i	−0.993716	+	1.72117i
$833$	6.18979	−	2.75587i	0.214463	−	0.0954853i
$834$	−1.43029	+	2.58430i	−0.0495269	+	0.0894869i
$835$	−2.45688	+	11.8224i	−0.0850239	+	0.409132i
$836$	−3.75961	−	11.5709i	−0.130029	−	0.400188i
$837$	−7.13209	−	44.4651i	−0.246521	−	1.53694i
$838$	9.22184	−	28.3819i	0.318563	−	0.980436i
$839$	−1.99630	+	2.21712i	−0.0689201	+	0.0765435i	−0.776619	−	0.629971i	$-0.783067\pi$
$839$	−1.99630	+	2.21712i	−0.0689201	+	0.0765435i	0.707699	+	0.706514i	$0.249733\pi$
$840$	−3.59414	−	1.07845i	−0.124009	−	0.0372102i
$841$	−6.95536	−	7.72471i	−0.239840	−	0.266369i
$842$	35.9310	−	15.9975i	1.23826	−	0.551310i
$843$	0.529777	+	1.53532i	0.0182465	+	0.0528792i
$844$	0.00895605	−	0.0852111i	0.000308280	−	0.00293309i
$845$	49.4129	+	44.0869i	1.69985	+	1.51664i
$846$	−5.11615	+	17.9307i	−0.175897	+	0.616469i
$847$	−0.673564	+	0.489373i	−0.0231439	+	0.0168150i
$848$	−7.13783	+	7.92737i	−0.245114	+	0.272227i
$849$	−13.1656	+	15.1653i	−0.451843	+	0.520473i
$850$	−2.97242	−	5.04208i	−0.101953	−	0.172942i
$851$	0.0156542	−	0.0271139i	0.000536620	−	0.000929453i
$852$	−10.9913	−	4.65704i	−0.376555	−	0.159547i
$853$	24.8916	+	11.0825i	0.852274	+	0.379457i	0.785911	−	0.618339i	$-0.212194\pi$
$853$	24.8916	+	11.0825i	0.852274	+	0.379457i	0.0663620	+	0.997796i	$0.478861\pi$
$854$	−2.25297	+	1.63688i	−0.0770950	+	0.0560128i
$855$	−18.0117	+	45.3424i	−0.615988	+	1.55068i
$856$	−25.2722	−	18.3613i	−0.863784	−	0.627576i
$857$	−25.6908	−	44.4978i	−0.877582	−	1.52002i	−0.853986	−	0.520296i	$-0.825822\pi$
$857$	−25.6908	−	44.4978i	−0.877582	−	1.52002i	−0.0235962	−	0.999722i	$-0.507512\pi$
$858$	−11.3700	+	37.2768i	−0.388166	+	1.27261i
$859$	32.3856	+	35.9678i	1.10498	+	1.22721i	0.971723	+	0.236125i	$0.0758774\pi$
$859$	32.3856	+	35.9678i	1.10498	+	1.22721i	0.133259	+	0.991081i	$0.457456\pi$
$860$	−0.0158147	−	3.48290i	−0.000539276	−	0.118766i
$861$	−0.306405	−	2.48204i	−0.0104423	−	0.0845877i
$862$	6.79603	−	1.44454i	0.231474	−	0.0492012i
$863$	0.728582	−	2.24234i	0.0248012	−	0.0763303i	−0.937890	−	0.346933i	$-0.887223\pi$
$863$	0.728582	−	2.24234i	0.0248012	−	0.0763303i	0.962691	+	0.270603i	$0.0872230\pi$
$864$	−11.6278	−	11.5822i	−0.395585	−	0.394035i
$865$	0.172699	+	0.794722i	0.00587193	+	0.0270214i
$866$	−2.43072	+	0.516667i	−0.0825994	+	0.0175570i
$867$	18.9558	+	20.3010i	0.643774	+	0.689458i
$868$	0.790204	−	1.36867i	0.0268213	−	0.0464558i
$869$	−30.0612	+	13.3841i	−1.01976	+	0.454025i
$870$	−4.58107	−	19.3829i	−0.155313	−	0.657140i
$871$	−14.8640	−	6.61786i	−0.503646	−	0.224238i
$872$	27.5591	−	20.0229i	0.933269	−	0.678060i
$873$	−19.9210	+	9.74840i	−0.674222	+	0.329933i
$874$	−11.3561			−0.384127
$875$	−0.779469	−	3.43626i	−0.0263509	−	0.116167i
$876$	−0.602949	+	0.694531i	−0.0203718	+	0.0234660i
$877$	−26.8040	−	5.69737i	−0.905107	−	0.192386i	−0.268233	−	0.963354i	$-0.586440\pi$
$877$	−26.8040	−	5.69737i	−0.905107	−	0.192386i	−0.636874	+	0.770968i	$0.719773\pi$
$878$	−2.83973	−	27.0182i	−0.0958362	−	0.911821i
$879$	−3.55237	+	40.9121i	−0.119818	+	1.37993i
$880$	−6.66165	−	14.7813i	−0.224564	−	0.498278i
$881$	−34.8348	−	25.3090i	−1.17362	−	0.852682i	−0.182179	−	0.983265i	$-0.558315\pi$
$881$	−34.8348	−	25.3090i	−1.17362	−	0.852682i	−0.991437	+	0.130584i	$0.958315\pi$
$882$	−22.8962	−	9.21584i	−0.770956	−	0.310313i
$883$	11.2465	+	8.17107i	0.378475	+	0.274979i	0.760717	−	0.649084i	$-0.224848\pi$
$883$	11.2465	+	8.17107i	0.378475	+	0.274979i	−0.382241	+	0.924063i	$0.624848\pi$
$884$	−3.62768	+	0.771088i	−0.122012	+	0.0259345i
$885$	−17.1437	+	10.4226i	−0.576280	+	0.350351i
$886$	10.5004	+	2.23193i	0.352768	+	0.0749832i
$887$	−3.84956	−	4.27536i	−0.129255	−	0.143553i	0.675043	−	0.737779i	$-0.264125\pi$
$887$	−3.84956	−	4.27536i	−0.129255	−	0.143553i	−0.804298	+	0.594226i	$0.797459\pi$
$888$	−0.0616400	+	0.111373i	−0.00206850	+	0.00373745i
$889$	−3.24592	+	3.60496i	−0.108865	+	0.120906i
$890$	28.2202	−	16.4643i	0.945944	−	0.551883i
$891$	−22.1018	−	13.7305i	−0.740440	−	0.459988i
$892$	−0.770844	−	0.560051i	−0.0258098	−	0.0187519i
$893$	18.9583	+	32.8368i	0.634416	+	1.09884i
$894$	29.1821	+	31.2529i	0.975995	+	1.04525i
$895$	−0.154182	−	33.9558i	−0.00515374	−	1.13502i
$896$	0.136798	+	1.30154i	0.00457009	+	0.0434815i
$897$	−12.1357	−	8.48570i	−0.405200	−	0.283329i
$898$	−1.70994	+	1.89908i	−0.0570614	+	0.0633731i
$899$	37.3829			1.24679
$900$	2.30550	−	8.36740i	0.0768501	−	0.278913i
$901$	−4.17624			−0.139131
$902$	10.5665	−	11.7352i	0.351825	−	0.390741i
$903$	−0.127114	+	1.46396i	−0.00423010	+	0.0487174i
$904$	−4.71357	−	44.8467i	−0.156771	−	1.49158i
$905$	0.121430	−	0.0400655i	0.00403647	−	0.00133182i
$906$	−42.8752	+	9.92807i	−1.42443	+	0.329838i
$907$	−9.88602	−	17.1231i	−0.328260	−	0.568563i	0.653907	−	0.756575i	$-0.273129\pi$
$907$	−9.88602	−	17.1231i	−0.328260	−	0.568563i	−0.982167	+	0.188012i	$0.939796\pi$
$908$	−1.71435	−	1.24555i	−0.0568926	−	0.0413349i
$909$	−34.1174	−	5.96978i	−1.13160	−	0.198005i
$910$	5.45716	+	0.548530i	0.180903	+	0.0181836i
$911$	−14.1994	+	15.7700i	−0.470448	+	0.522485i	−0.930937	−	0.365180i	$-0.881007\pi$
$911$	−14.1994	+	15.7700i	−0.470448	+	0.522485i	0.460489	+	0.887665i	$0.347674\pi$
$912$	31.5884	−	0.572056i	1.04600	−	0.0189427i
$913$	−19.2335	−	21.3610i	−0.636537	−	0.706947i
$914$	22.8171	+	4.84992i	0.754723	+	0.160421i
$915$	−17.3941	−	22.8349i	−0.575030	−	0.754899i
$916$	−0.479166	+	0.101850i	−0.0158321	+	0.00336521i
$917$	0.851132	+	0.618383i	0.0281068	+	0.0204208i
$918$	−0.306415	+	6.07491i	−0.0101132	+	0.200502i
$919$	−0.706640	−	0.513404i	−0.0233099	−	0.0169356i	0.576069	−	0.817401i	$-0.304586\pi$
$919$	−0.706640	−	0.513404i	−0.0233099	−	0.0169356i	−0.599379	+	0.800465i	$0.704586\pi$
$920$	8.94932	−	0.981715i	0.295050	−	0.0323662i
$921$	19.8152	−	9.25578i	0.652933	−	0.304988i
$922$	0.475304	+	4.52222i	0.0156533	+	0.148931i
$923$	76.0569	+	16.1664i	2.50344	+	0.532124i
$924$	−0.297852	−	0.863189i	−0.00979860	−	0.0283968i
$925$	−0.119524	+	0.00108546i	−0.00392991	+	3.56896e-5i
$926$	10.7898			0.354575
$927$	40.7449	+	27.4052i	1.33824	+	0.900106i
$928$	11.0219	−	8.00787i	0.361811	−	0.262871i
$929$	11.8209	+	5.26300i	0.387831	+	0.172673i	0.591383	−	0.806391i	$-0.298582\pi$
$929$	11.8209	+	5.26300i	0.387831	+	0.172673i	−0.203552	+	0.979064i	$0.565249\pi$
$930$	−35.1008	−	19.2190i	−1.15100	−	0.630216i
$931$	−45.8497	+	20.4136i	−1.50266	+	0.669029i
$932$	−3.23391	+	5.60129i	−0.105930	+	0.183476i
$933$	−23.8996	+	5.53414i	−0.782438	+	0.181179i
$934$	35.8883	−	7.62830i	1.17430	−	0.249606i
$935$	2.55537	−	5.81031i	0.0835694	−	0.190017i
$936$	49.9577	+	33.6019i	1.63292	+	1.09831i
$937$	−0.517445	+	1.59253i	−0.0169042	+	0.0520257i	−0.959153	−	0.282889i	$-0.908707\pi$
$937$	−0.517445	+	1.59253i	−0.0169042	+	0.0520257i	0.942249	+	0.334914i	$0.108707\pi$
$938$	−0.916030	+	0.194708i	−0.0299094	+	0.00635745i
$939$	3.87264	−	2.92222i	0.126379	−	0.0953631i
$940$	−3.98941	−	5.43885i	−0.130120	−	0.177396i
$941$	−6.72992	−	7.47433i	−0.219389	−	0.243656i	0.623396	−	0.781906i	$-0.285752\pi$
$941$	−6.72992	−	7.47433i	−0.219389	−	0.243656i	−0.842785	+	0.538250i	$0.819086\pi$
$942$	−19.6791	−	21.0756i	−0.641181	−	0.686680i
$943$	3.00010	+	5.19632i	0.0976966	+	0.169216i
$944$	10.5109	+	7.63660i	0.342100	+	0.248550i
$945$	−1.29001	+	3.42704i	−0.0419640	+	0.111482i
$946$	−7.50659	+	5.45386i	−0.244060	+	0.177320i
$947$	−37.3142	−	16.6134i	−1.21255	−	0.539862i	−0.302019	−	0.953302i	$-0.597660\pi$
$947$	−37.3142	−	16.6134i	−1.21255	−	0.539862i	−0.910531	+	0.413440i	$0.864327\pi$
$948$	1.39756	+	11.3210i	0.0453907	+	0.367688i
$949$	2.99549	−	5.18833i	0.0972376	−	0.168420i
$950$	22.0176	+	37.3482i	0.714347	+	1.21174i
$951$	−16.8501	−	48.8324i	−0.546402	−	1.58350i
$952$	−0.636552	+	0.706963i	−0.0206308	+	0.0229128i
$953$	−28.0837	+	20.4040i	−0.909720	+	0.660951i	−0.940944	−	0.338562i	$-0.890060\pi$
$953$	−28.0837	+	20.4040i	−0.909720	+	0.660951i	0.0312237	+	0.999512i	$0.490060\pi$
$954$	10.5820	+	10.9293i	0.342605	+	0.353850i
$955$	−2.15739	+	4.90540i	−0.0698114	+	0.158735i
$956$	−0.987935	+	9.39958i	−0.0319521	+	0.304004i
$957$	14.1597	−	16.3104i	0.457717	−	0.527239i
$958$	13.4131	−	5.97189i	0.433357	−	0.192943i
$959$	1.78099	+	1.97799i	0.0575112	+	0.0638727i
$960$	−33.7353	+	4.32019i	−1.08880	+	0.139434i
$961$	29.5164	−	32.7812i	0.952141	−	1.05746i
$962$	0.0574940	−	0.176948i	0.00185368	−	0.00570504i
$963$	−19.5638	+	23.3773i	−0.630434	+	0.753322i
$964$	−0.374693	−	1.15319i	−0.0120680	−	0.0371416i
$965$	−5.41650	−	12.0185i	−0.174363	−	0.386889i
$966$	−0.852182	+	0.0154327i	−0.0274185	+	0.000496540i
$967$	−19.2260	+	8.55999i	−0.618268	+	0.275271i	−0.691876	−	0.722017i	$-0.743215\pi$
$967$	−19.2260	+	8.55999i	−0.618268	+	0.275271i	0.0736078	+	0.997287i	$0.476549\pi$
$968$	−4.06075	+	7.03343i	−0.130517	+	0.226063i
$969$	8.44145	+	9.04048i	0.271178	+	0.290422i
$970$	−4.01000	+	19.2960i	−0.128753	+	0.619556i
$971$	27.0192	−	19.6306i	0.867089	−	0.629977i	−0.0627155	−	0.998031i	$-0.519976\pi$
$971$	27.0192	−	19.6306i	0.867089	−	0.629977i	0.929804	+	0.368055i	$0.119976\pi$
$972$	−6.78785	+	5.93970i	−0.217721	+	0.190516i
$973$	0.139302	+	0.428728i	0.00446583	+	0.0137444i
$974$	−2.96001	−	5.12688i	−0.0948448	−	0.164276i
$975$	−4.37877	+	56.3646i	−0.140233	+	1.80511i
$976$	−9.29412	+	16.0979i	−0.297497	+	0.515281i
$977$	−7.57062	−	1.60918i	−0.242206	−	0.0514824i	0.0852093	−	0.996363i	$-0.472844\pi$
$977$	−7.57062	−	1.60918i	−0.242206	−	0.0514824i	−0.327415	+	0.944881i	$0.606177\pi$
$978$	−1.04187	−	0.728506i	−0.0333152	−	0.0232951i
$979$	32.3684	+	14.4113i	1.03450	+	0.460588i
$980$	7.71173	−	4.49918i	0.246342	−	0.143721i
$981$	−17.6524	−	28.1677i	−0.563599	−	0.899325i
$982$	−22.7253			−0.725195
$983$	5.02975	−	47.8549i	0.160424	−	1.52633i	−0.557479	−	0.830191i	$-0.688231\pi$
$983$	5.02975	−	47.8549i	0.160424	−	1.52633i	0.717903	−	0.696143i	$-0.245102\pi$
$984$	−12.5783	−	20.9027i	−0.400980	−	0.666355i
$985$	0.161185	+	35.4980i	0.00513577	+	1.13106i
$986$	−4.93894	−	1.04980i	−0.157288	−	0.0334326i
$987$	1.46729	+	2.43836i	0.0467042	+	0.0776137i
$988$	26.8714	−	5.71169i	0.854892	−	0.181713i
$989$	−1.08947	−	3.35303i	−0.0346430	−	0.106620i
$990$	−21.6807	+	8.03504i	−0.689056	+	0.255370i
$991$	−15.7450	+	48.4581i	−0.500157	+	1.53932i	0.308607	+	0.951190i	$0.400137\pi$
$991$	−15.7450	+	48.4581i	−0.500157	+	1.53932i	−0.808763	+	0.588134i	$0.799863\pi$
$992$	2.86132	−	27.2237i	0.0908471	−	0.864352i
$993$	11.5112	+	33.3599i	0.365296	+	1.05865i
$994$	4.08851	−	1.82032i	0.129680	−	0.0577372i
$995$	6.02120	−	8.36710i	0.190885	−	0.265255i
$996$	−9.02784	+	4.21694i	−0.286058	+	0.133619i
$997$	13.8124	+	6.14967i	0.437443	+	0.194762i	0.613629	−	0.789595i	$-0.289709\pi$
$997$	13.8124	+	6.14967i	0.437443	+	0.194762i	−0.176186	+	0.984357i	$0.556376\pi$
$998$	1.84887	+	5.69025i	0.0585251	+	0.180122i
$999$	0.104310	+	0.0674492i	0.00330024	+	0.00213400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.31.20	✓	224
3.2	odd	2		675.2.r.a.631.9		224
9.2	odd	6		675.2.r.a.181.20		224
9.7	even	3	inner	225.2.q.a.106.9	yes	224
25.21	even	5	inner	225.2.q.a.121.9	yes	224
75.71	odd	10		675.2.r.a.496.20		224
225.146	odd	30		675.2.r.a.46.9		224
225.196	even	15	inner	225.2.q.a.196.20	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.20	✓	224	1.1	even	1	trivial
225.2.q.a.106.9	yes	224	9.7	even	3	inner
225.2.q.a.121.9	yes	224	25.21	even	5	inner
225.2.q.a.196.20	yes	224	225.196	even	15	inner
675.2.r.a.46.9		224	225.146	odd	30
675.2.r.a.181.20		224	9.2	odd	6
675.2.r.a.496.20		224	75.71	odd	10
675.2.r.a.631.9		224	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
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

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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