LMFDB - Embedded newform 225.2.w.a.167.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.w (of order $60$, degree $16$, 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:	$448$
Relative dimension:	$28$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			167.5
Character	$\chi$	$=$	225.167
Dual form			225.2.w.a.128.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.113281 - 2.16152i) q^{2} +(0.935625 - 1.45760i) q^{3} +(-2.67031 + 0.280661i) q^{4} +(-0.996494 - 2.00175i) q^{5} +(-3.25663 - 1.85726i) q^{6} +(-0.983733 + 3.67134i) q^{7} +(0.231948 + 1.46446i) q^{8} +(-1.24921 - 2.72754i) q^{9} +O(q^{10})$	\(q+(-0.113281 - 2.16152i) q^{2} +(0.935625 - 1.45760i) q^{3} +(-2.67031 + 0.280661i) q^{4} +(-0.996494 - 2.00175i) q^{5} +(-3.25663 - 1.85726i) q^{6} +(-0.983733 + 3.67134i) q^{7} +(0.231948 + 1.46446i) q^{8} +(-1.24921 - 2.72754i) q^{9} +(-4.21395 + 2.38071i) q^{10} +(-0.855167 - 0.769996i) q^{11} +(-2.08932 + 4.15485i) q^{12} +(4.58443 + 0.240260i) q^{13} +(8.04713 + 1.71047i) q^{14} +(-3.85010 - 0.420393i) q^{15} +(-2.11349 + 0.449237i) q^{16} +(0.222002 - 0.0351616i) q^{17} +(-5.75413 + 3.00918i) q^{18} +(4.93421 - 6.79136i) q^{19} +(3.22276 + 5.06561i) q^{20} +(4.43095 + 4.86889i) q^{21} +(-1.56749 + 1.93569i) q^{22} +(-0.558183 - 0.859526i) q^{23} +(2.35162 + 1.03210i) q^{24} +(-3.01400 + 3.98946i) q^{25} -9.93658i q^{26} +(-5.14446 - 0.731098i) q^{27} +(1.59647 - 10.0797i) q^{28} +(7.73245 + 3.44271i) q^{29} +(-0.472549 + 8.36971i) q^{30} +(0.366699 - 0.163265i) q^{31} +(1.97797 + 7.38187i) q^{32} +(-1.92246 + 0.526067i) q^{33} +(-0.101151 - 0.475879i) q^{34} +(8.32938 - 1.68928i) q^{35} +(4.10130 + 6.93277i) q^{36} +(-2.61483 + 1.33232i) q^{37} +(-15.2386 - 9.89608i) q^{38} +(4.63951 - 6.45749i) q^{39} +(2.70035 - 1.92363i) q^{40} +(1.49808 - 1.34888i) q^{41} +(10.0223 - 10.1292i) q^{42} +(-3.34543 - 0.896406i) q^{43} +(2.49967 + 1.81612i) q^{44} +(-4.21502 + 5.21859i) q^{45} +(-1.79465 + 1.30389i) q^{46} +(-4.96935 + 1.90755i) q^{47} +(-1.32263 + 3.50095i) q^{48} +(-6.44883 - 3.72323i) q^{49} +(8.96475 + 6.06290i) q^{50} +(0.156459 - 0.356488i) q^{51} +(-12.3093 + 0.645103i) q^{52} +(7.49469 + 1.18704i) q^{53} +(-0.997518 + 11.2027i) q^{54} +(-0.689170 + 2.47913i) q^{55} +(-5.60471 - 0.589079i) q^{56} +(-5.28253 - 13.5463i) q^{57} +(6.56556 - 17.1039i) q^{58} +(-3.36933 - 3.74202i) q^{59} +(10.3989 + 0.0420082i) q^{60} +(7.40659 - 8.22585i) q^{61} +(-0.394441 - 0.774133i) q^{62} +(11.2426 - 1.90311i) q^{63} +(11.6221 - 3.77625i) q^{64} +(-4.08742 - 9.41630i) q^{65} +(1.35488 + 4.09586i) q^{66} +(11.9425 + 4.58430i) q^{67} +(-0.582945 + 0.156200i) q^{68} +(-1.77510 + 0.00941479i) q^{69} +(-4.59498 - 17.8128i) q^{70} +(-1.92420 - 2.64843i) q^{71} +(3.70463 - 2.46207i) q^{72} +(5.69206 + 2.90025i) q^{73} +(3.17605 + 5.50109i) q^{74} +(2.99508 + 8.12585i) q^{75} +(-11.2698 + 19.5199i) q^{76} +(3.66817 - 2.38214i) q^{77} +(-14.4836 - 9.29691i) q^{78} +(-3.96054 + 8.89551i) q^{79} +(3.00534 + 3.78302i) q^{80} +(-5.87894 + 6.81455i) q^{81} +(-3.08533 - 3.08533i) q^{82} +(-9.36596 + 7.58441i) q^{83} +(-13.1985 - 11.7578i) q^{84} +(-0.291608 - 0.409353i) q^{85} +(-1.55863 + 7.33278i) q^{86} +(12.2528 - 8.04976i) q^{87} +(0.929276 - 1.43096i) q^{88} +(-0.0846567 - 0.260547i) q^{89} +(11.7576 + 8.51969i) q^{90} +(-5.39193 + 16.5947i) q^{91} +(1.73176 + 2.13854i) q^{92} +(0.105117 - 0.687255i) q^{93} +(4.68615 + 10.5253i) q^{94} +(-18.5115 - 3.10950i) q^{95} +(12.6105 + 4.02357i) q^{96} +(1.76628 + 4.60131i) q^{97} +(-7.31733 + 14.3611i) q^{98} +(-1.03191 + 3.29439i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−0.113281	−	2.16152i	−0.0801015	−	1.52843i	−0.682886	−	0.730525i	$-0.739276\pi$
$2$	−0.113281	−	2.16152i	−0.0801015	−	1.52843i	0.602785	−	0.797904i	$-0.294058\pi$
$3$	0.935625	−	1.45760i	0.540183	−	0.841547i
$3$	0.935625	−	1.45760i	0.540183	−	0.841547i
$4$	−2.67031	+	0.280661i	−1.33516	+	0.140330i
$5$	−0.996494	−	2.00175i	−0.445646	−	0.895209i
$5$	−0.996494	−	2.00175i	−0.445646	−	0.895209i
$6$	−3.25663	−	1.85726i	−1.32951	−	0.758222i
$7$	−0.983733	+	3.67134i	−0.371816	+	1.38764i	0.486126	+	0.873889i	$0.338410\pi$
$7$	−0.983733	+	3.67134i	−0.371816	+	1.38764i	−0.857942	+	0.513747i	$0.828257\pi$
$8$	0.231948	+	1.46446i	0.0820060	+	0.517766i
$9$	−1.24921	−	2.72754i	−0.416404	−	0.909180i
$10$	−4.21395	+	2.38071i	−1.33257	+	0.752845i
$11$	−0.855167	−	0.769996i	−0.257843	−	0.232163i	0.530063	−	0.847958i	$-0.322168\pi$
$11$	−0.855167	−	0.769996i	−0.257843	−	0.232163i	−0.787906	+	0.615795i	$0.788835\pi$
$12$	−2.08932	+	4.15485i	−0.603134	+	1.19940i
$13$	4.58443	+	0.240260i	1.27149	+	0.0666361i	0.676107	−	0.736804i	$-0.263666\pi$
$13$	4.58443	+	0.240260i	1.27149	+	0.0666361i	0.595386	+	0.803440i	$0.296999\pi$
$14$	8.04713	+	1.71047i	2.15069	+	0.457142i
$15$	−3.85010	−	0.420393i	−0.994092	−	0.108545i
$16$	−2.11349	+	0.449237i	−0.528374	+	0.112309i
$17$	0.222002	−	0.0351616i	0.0538433	−	0.00852795i	−0.129455	−	0.991585i	$-0.541323\pi$
$17$	0.222002	−	0.0351616i	0.0538433	−	0.00852795i	0.183298	+	0.983057i	$0.441323\pi$
$18$	−5.75413	+	3.00918i	−1.35626	+	0.709270i
$19$	4.93421	−	6.79136i	1.13199	−	1.55804i	0.347742	−	0.937590i	$-0.386949\pi$
$19$	4.93421	−	6.79136i	1.13199	−	1.55804i	0.784243	−	0.620454i	$-0.213051\pi$
$20$	3.22276	+	5.06561i	0.720631	+	1.13271i
$21$	4.43095	+	4.86889i	0.966913	+	1.06248i
$22$	−1.56749	+	1.93569i	−0.334190	+	0.412691i
$23$	−0.558183	−	0.859526i	−0.116389	−	0.179224i	0.775675	−	0.631133i	$-0.217410\pi$
$23$	−0.558183	−	0.859526i	−0.116389	−	0.179224i	−0.892064	+	0.451909i	$0.850743\pi$
$24$	2.35162	+	1.03210i	0.480023	+	0.210676i
$25$	−3.01400	+	3.98946i	−0.602800	+	0.797893i
$26$		−	9.93658i		−	1.94872i
$27$	−5.14446	−	0.731098i	−0.990052	−	0.140700i
$28$	1.59647	−	10.0797i	0.301704	−	1.90489i
$29$	7.73245	+	3.44271i	1.43588	+	0.639295i	0.969456	−	0.245267i	$-0.0788755\pi$
$29$	7.73245	+	3.44271i	1.43588	+	0.639295i	0.466424	+	0.884561i	$0.345542\pi$
$30$	−0.472549	+	8.36971i	−0.0862752	+	1.52809i
$31$	0.366699	−	0.163265i	0.0658610	−	0.0293232i	−0.373542	−	0.927613i	$-0.621857\pi$
$31$	0.366699	−	0.163265i	0.0658610	−	0.0293232i	0.439403	+	0.898290i	$0.355190\pi$
$32$	1.97797	+	7.38187i	0.349658	+	1.30494i
$33$	−1.92246	+	0.526067i	−0.334658	+	0.0915765i
$34$	−0.101151	−	0.475879i	−0.0173473	−	0.0816126i
$35$	8.32938	−	1.68928i	1.40792	−	0.285541i
$36$	4.10130	+	6.93277i	0.683550	+	1.15546i
$37$	−2.61483	+	1.33232i	−0.429875	+	0.219032i	−0.655521	−	0.755177i	$-0.727551\pi$
$37$	−2.61483	+	1.33232i	−0.429875	+	0.219032i	0.225646	+	0.974209i	$0.427551\pi$
$38$	−15.2386	−	9.89608i	−2.47203	−	1.60536i
$39$	4.63951	−	6.45749i	0.742917	−	1.03403i
$40$	2.70035	−	1.92363i	0.426963	−	0.304153i
$41$	1.49808	−	1.34888i	0.233961	−	0.210659i	−0.543808	−	0.839210i	$-0.683018\pi$
$41$	1.49808	−	1.34888i	0.233961	−	0.210659i	0.777769	+	0.628550i	$0.216351\pi$
$42$	10.0223	−	10.1292i	1.54647	−	1.56296i
$43$	−3.34543	−	0.896406i	−0.510173	−	0.136701i	−0.00545592	−	0.999985i	$-0.501737\pi$
$43$	−3.34543	−	0.896406i	−0.510173	−	0.136701i	−0.504718	+	0.863285i	$0.668403\pi$
$44$	2.49967	+	1.81612i	0.376839	+	0.273790i
$45$	−4.21502	+	5.21859i	−0.628337	+	0.777941i
$46$	−1.79465	+	1.30389i	−0.264607	+	0.192249i
$47$	−4.96935	+	1.90755i	−0.724854	+	0.278245i	−0.692688	−	0.721237i	$-0.743574\pi$
$47$	−4.96935	+	1.90755i	−0.724854	+	0.278245i	−0.0321657	+	0.999483i	$0.510240\pi$
$48$	−1.32263	+	3.50095i	−0.190905	+	0.505319i
$49$	−6.44883	−	3.72323i	−0.921261	−	0.531890i
$50$	8.96475	+	6.06290i	1.26781	+	0.857424i
$51$	0.156459	−	0.356488i	0.0219086	−	0.0499184i
$52$	−12.3093	+	0.645103i	−1.70699	+	0.0894596i
$53$	7.49469	+	1.18704i	1.02948	+	0.163053i	0.648249	−	0.761429i	$-0.275502\pi$
$53$	7.49469	+	1.18704i	1.02948	+	0.163053i	0.381227	+	0.924482i	$0.375502\pi$
$54$	−0.997518	+	11.2027i	−0.135745	+	1.52449i
$55$	−0.689170	+	2.47913i	−0.0929276	+	0.334285i
$56$	−5.60471	−	0.589079i	−0.748961	−	0.0787190i
$57$	−5.28253	−	13.5463i	−0.699688	−	1.79425i
$58$	6.56556	−	17.1039i	0.862100	−	2.24585i
$59$	−3.36933	−	3.74202i	−0.438649	−	0.487169i	0.482766	−	0.875750i	$-0.339632\pi$
$59$	−3.36933	−	3.74202i	−0.438649	−	0.487169i	−0.921415	+	0.388580i	$0.872966\pi$
$60$	10.3989	+	0.0420082i	1.34250	+	0.00542324i
$61$	7.40659	−	8.22585i	0.948316	−	1.05321i	−0.0501989	−	0.998739i	$-0.515986\pi$
$61$	7.40659	−	8.22585i	0.948316	−	1.05321i	0.998515	−	0.0544728i	$-0.0173478\pi$
$62$	−0.394441	−	0.774133i	−0.0500940	−	0.0983150i
$63$	11.2426	−	1.90311i	1.41644	−	0.239770i
$64$	11.6221	−	3.77625i	1.45276	−	0.472031i
$65$	−4.08742	−	9.41630i	−0.506982	−	1.16795i
$66$	1.35488	+	4.09586i	0.166775	+	0.504166i
$67$	11.9425	+	4.58430i	1.45901	+	0.560062i	0.953135	−	0.302545i	$-0.0978361\pi$
$67$	11.9425	+	4.58430i	1.45901	+	0.560062i	0.505876	+	0.862606i	$0.331169\pi$
$68$	−0.582945	+	0.156200i	−0.0706925	+	0.0189420i
$69$	−1.77510	+	0.00941479i	−0.213697	+	0.00113341i
$70$	−4.59498	−	17.8128i	−0.549206	−	2.12904i
$71$	−1.92420	−	2.64843i	−0.228360	−	0.314311i	0.679426	−	0.733744i	$-0.262229\pi$
$71$	−1.92420	−	2.64843i	−0.228360	−	0.314311i	−0.907786	+	0.419433i	$0.862229\pi$
$72$	3.70463	−	2.46207i	0.436594	−	0.290158i
$73$	5.69206	+	2.90025i	0.666206	+	0.339449i	0.754174	−	0.656675i	$-0.228037\pi$
$73$	5.69206	+	2.90025i	0.666206	+	0.339449i	−0.0879685	+	0.996123i	$0.528037\pi$
$74$	3.17605	+	5.50109i	0.369209	+	0.639488i
$75$	2.99508	+	8.12585i	0.345842	+	0.938293i
$76$	−11.2698	+	19.5199i	−1.29273	+	2.23908i
$77$	3.66817	−	2.38214i	0.418027	−	0.271470i
$78$	−14.4836	−	9.29691i	−1.63994	−	1.05267i
$79$	−3.96054	+	8.89551i	−0.445595	+	1.00082i	0.541502	+	0.840700i	$0.317856\pi$
$79$	−3.96054	+	8.89551i	−0.445595	+	1.00082i	−0.987097	+	0.160124i	$0.948811\pi$
$80$	3.00534	+	3.78302i	0.336008	+	0.422955i
$81$	−5.87894	+	6.81455i	−0.653215	+	0.757172i
$82$	−3.08533	−	3.08533i	−0.340718	−	0.340718i
$83$	−9.36596	+	7.58441i	−1.02805	+	0.832497i	−0.986021	−	0.166620i	$-0.946715\pi$
$83$	−9.36596	+	7.58441i	−1.02805	+	0.832497i	−0.0420268	+	0.999116i	$0.513381\pi$
$84$	−13.1985	−	11.7578i	−1.44008	−	1.28289i
$85$	−0.291608	−	0.409353i	−0.0316293	−	0.0444006i
$86$	−1.55863	+	7.33278i	−0.168071	+	0.790713i
$87$	12.2528	−	8.04976i	1.31363	−	0.863024i
$88$	0.929276	−	1.43096i	0.0990612	−	0.152541i
$89$	−0.0846567	−	0.260547i	−0.00897359	−	0.0276179i	0.946469	−	0.322793i	$-0.104622\pi$
$89$	−0.0846567	−	0.260547i	−0.00897359	−	0.0276179i	−0.955443	+	0.295175i	$0.904622\pi$
$90$	11.7576	+	8.51969i	1.23936	+	0.898055i
$91$	−5.39193	+	16.5947i	−0.565228	+	1.73959i
$92$	1.73176	+	2.13854i	0.180548	+	0.222958i
$93$	0.105117	−	0.687255i	0.0109001	−	0.0712651i
$94$	4.68615	+	10.5253i	0.483340	+	1.08560i
$95$	−18.5115	−	3.10950i	−1.89924	−	0.319028i
$96$	12.6105	+	4.02357i	1.28705	+	0.410654i
$97$	1.76628	+	4.60131i	0.179338	+	0.467193i	0.993553	−	0.113372i	$-0.0361652\pi$
$97$	1.76628	+	4.60131i	0.179338	+	0.467193i	−0.814214	+	0.580565i	$0.802832\pi$
$98$	−7.31733	+	14.3611i	−0.739162	+	1.45069i
$99$	−1.03191	+	3.29439i	−0.103711	+	0.331099i
$100$	6.92862	−	11.4990i	0.692862	−	1.14990i
$101$	−1.24967	+	0.721498i	−0.124347	+	0.0717917i	−0.560883	−	0.827895i	$-0.689538\pi$
$101$	−1.24967	+	0.721498i	−0.124347	+	0.0717917i	0.436536	+	0.899687i	$0.356205\pi$
$102$	−0.788282	−	0.297806i	−0.0780516	−	0.0294872i
$103$	11.1424	+	9.02290i	1.09789	+	0.889053i	0.994411	−	0.105579i	$-0.0336695\pi$
$103$	11.1424	+	9.02290i	1.09789	+	0.889053i	0.103478	+	0.994632i	$0.467003\pi$
$104$	0.711499	+	6.76946i	0.0697682	+	0.663800i
$105$	5.33088	−	13.7215i	0.520240	−	1.33908i
$106$	1.71682	−	16.3344i	0.166752	−	1.58654i
$107$	−9.54878	+	9.54878i	−0.923115	+	0.923115i	−0.997248	−	0.0741334i	$-0.976381\pi$
$107$	−9.54878	+	9.54878i	−0.923115	+	0.923115i	0.0741334	+	0.997248i	$0.476381\pi$
$108$	13.9425	+	0.508410i	1.34162	+	0.0489217i
$109$	−4.59978	−	1.49456i	−0.440579	−	0.143153i	0.0803239	−	0.996769i	$-0.474405\pi$
$109$	−4.59978	−	1.49456i	−0.440579	−	0.143153i	−0.520903	+	0.853616i	$0.674405\pi$
$110$	5.43676	+	1.20882i	0.518375	+	0.115256i
$111$	−0.504503	+	5.05793i	−0.0478853	+	0.480078i
$112$	0.429811	−	8.20128i	0.0406133	−	0.774948i
$113$	−0.296984	+	5.66680i	−0.0279379	+	0.533088i	0.948432	+	0.316981i	$0.102669\pi$
$113$	−0.296984	+	5.66680i	−0.0279379	+	0.533088i	−0.976370	+	0.216107i	$0.930664\pi$
$114$	−28.6822	+	12.9528i	−2.68633	+	1.21315i
$115$	−1.16433	+	1.97385i	−0.108574	+	0.184063i
$116$	−21.6143	−	7.02290i	−2.00683	−	0.652060i
$117$	−5.07161	−	12.8044i	−0.468871	−	1.18376i
$118$	−7.70678	+	7.70678i	−0.709467	+	0.709467i
$119$	−0.0893001	+	0.849633i	−0.00818612	+	0.0778858i
$120$	−0.277373	−	5.73584i	−0.0253206	−	0.523608i
$121$	−1.01140	−	9.62279i	−0.0919451	−	0.874799i
$122$	−18.6194	−	15.0777i	−1.68572	−	1.36507i
$123$	−0.564486	−	3.44565i	−0.0508980	−	0.310683i
$124$	−0.933377	+	0.538885i	−0.0838197	+	0.0483933i
$125$	10.9893	+	2.05779i	0.982916	+	0.184055i
$126$	−5.38720	−	24.0856i	−0.479930	−	2.14572i
$127$	−4.12284	+	8.09152i	−0.365842	+	0.718006i	−0.998402	−	0.0565052i	$-0.982004\pi$
$127$	−4.12284	+	8.09152i	−0.365842	+	0.718006i	0.632560	+	0.774512i	$0.282004\pi$
$128$	−4.00153	−	10.4243i	−0.353688	−	0.921390i
$129$	−4.43667	+	4.03761i	−0.390627	+	0.355492i
$130$	−19.8905	+	9.90174i	−1.74452	+	0.868440i
$131$	4.84435	+	10.8806i	0.423253	+	0.950642i	0.991777	+	0.127976i	$0.0408479\pi$
$131$	4.84435	+	10.8806i	0.423253	+	0.950642i	−0.568524	+	0.822667i	$0.692485\pi$
$132$	4.98593	−	1.94432i	0.433970	−	0.169232i
$133$	20.0794	+	24.7960i	1.74111	+	2.15009i
$134$	8.55623	−	26.3334i	0.739145	−	2.27486i
$135$	3.66295	+	11.0265i	0.315257	+	0.949006i
$136$	0.102986	+	0.316958i	0.00883096	+	0.0271789i
$137$	−1.39198	+	2.14347i	−0.118925	+	0.183129i	−0.893120	−	0.449819i	$-0.851488\pi$
$137$	−1.39198	+	2.14347i	−0.118925	+	0.183129i	0.774195	+	0.632948i	$0.218155\pi$
$138$	0.221434	+	3.83585i	0.0188498	+	0.326529i
$139$	−0.154718	+	0.727890i	−0.0131230	+	0.0617388i	−0.984222	−	0.176939i	$-0.943381\pi$
$139$	−0.154718	+	0.727890i	−0.0131230	+	0.0617388i	0.971099	+	0.238678i	$0.0767139\pi$
$140$	−21.7679	+	6.84864i	−1.83973	+	0.578816i
$141$	−1.86899	+	9.02809i	−0.157397	+	0.760302i
$142$	−5.50667	+	4.45921i	−0.462109	+	0.374209i
$143$	−3.73546	−	3.73546i	−0.312375	−	0.312375i
$144$	3.86551	+	5.20345i	0.322126	+	0.433620i
$145$	−0.813903	−	18.9091i	−0.0675910	−	1.57031i
$146$	5.62416	−	12.6321i	0.465459	−	1.04544i
$147$	−11.4607	+	5.91628i	−0.945261	+	0.487967i
$148$	6.60847	−	4.29159i	0.543213	−	0.352767i
$149$	5.45223	−	9.44355i	0.446664	−	0.773645i	−0.551502	−	0.834173i	$-0.685945\pi$
$149$	5.45223	−	9.44355i	0.446664	−	0.773645i	0.998166	+	0.0605281i	$0.0192785\pi$
$150$	17.2249	−	7.39444i	1.40641	−	0.603754i
$151$	7.72593	+	13.3817i	0.628727	+	1.08899i	0.987807	+	0.155681i	$0.0497571\pi$
$151$	7.72593	+	13.3817i	0.628727	+	1.08899i	−0.359080	+	0.933307i	$0.616910\pi$
$152$	11.0902	+	5.65072i	0.899531	+	0.458334i
$153$	−0.373232	−	0.561594i	−0.0301740	−	0.0454022i
$154$	−5.56459	−	7.65900i	−0.448407	−	0.617179i
$155$	−0.692228	−	0.571346i	−0.0556011	−	0.0458916i
$156$	−10.5766	+	18.5456i	−0.846804	+	1.48484i
$157$	−15.1756	+	4.06629i	−1.21114	+	0.324525i	−0.807211	−	0.590263i	$-0.799024\pi$
$157$	−15.1756	+	4.06629i	−1.21114	+	0.324525i	−0.403933	+	0.914788i	$0.632357\pi$
$158$	19.6765	+	7.55311i	1.56538	+	0.600893i
$159$	8.74246	−	9.81366i	0.693322	−	0.778274i
$160$	12.8056	−	11.3154i	1.01237	−	0.894559i
$161$	3.70471	−	1.20373i	0.291972	−	0.0948676i
$162$	15.3958	+	11.9355i	1.20961	+	0.937742i
$163$	−6.82341	−	13.3917i	−0.534451	−	1.04892i	−0.987527	−	0.157447i	$-0.949674\pi$
$163$	−6.82341	−	13.3917i	−0.534451	−	1.04892i	0.453077	−	0.891472i	$-0.350326\pi$
$164$	−3.62176	+	4.02237i	−0.282812	+	0.314094i
$165$	2.96878	+	3.32407i	0.231119	+	0.258778i
$166$	17.4549	+	19.3856i	1.35476	+	1.50461i
$167$	1.52782	−	3.98011i	0.118226	−	0.307990i	−0.861679	−	0.507454i	$-0.830587\pi$
$167$	1.52782	−	3.98011i	0.118226	−	0.307990i	0.979905	+	0.199464i	$0.0639200\pi$
$168$	−6.10255	+	7.61829i	−0.470822	+	0.587764i
$169$	8.03052	+	0.844041i	0.617732	+	0.0649263i
$170$	−0.851794	+	0.676690i	−0.0653296	+	0.0518997i
$171$	−24.6876	−	4.97440i	−1.88790	−	0.380402i
$172$	9.18492	+	1.45475i	0.700344	+	0.110924i
$173$	8.37979	−	0.439166i	0.637104	−	0.0333892i	0.268950	−	0.963154i	$-0.413323\pi$
$173$	8.37979	−	0.439166i	0.637104	−	0.0333892i	0.368154	+	0.929765i	$0.379990\pi$
$174$	−18.7877	−	25.5728i	−1.42430	−	1.93867i
$175$	−11.6817	−	14.9900i	−0.883054	−	1.13314i
$176$	2.15330	+	1.24321i	0.162311	+	0.0937105i
$177$	−8.60680	+	1.41002i	−0.646927	+	0.105983i
$178$	−0.553588	+	0.212502i	−0.0414932	+	0.0159277i
$179$	2.24873	−	1.63380i	0.168078	−	0.122116i	−0.500566	−	0.865698i	$-0.666875\pi$
$179$	2.24873	−	1.63380i	0.168078	−	0.122116i	0.668644	+	0.743582i	$0.266875\pi$
$180$	9.79075	−	15.1182i	0.729759	−	1.12685i
$181$	3.53173	+	2.56595i	0.262511	+	0.190726i	0.711253	−	0.702936i	$-0.248128\pi$
$181$	3.53173	+	2.56595i	0.262511	+	0.190726i	−0.448742	+	0.893661i	$0.648128\pi$
$182$	36.4806	+	9.77494i	2.70412	+	0.724566i
$183$	−5.06023	−	18.4922i	−0.374063	−	1.36698i
$184$	1.12927	−	1.01680i	0.0832512	−	0.0749597i
$185$	5.27263	+	3.90658i	0.387652	+	0.287217i
$186$	−1.49743	−	0.149361i	−0.109797	−	0.0109516i
$187$	−0.216923	−	0.140871i	−0.0158630	−	0.0103015i
$188$	12.7343	−	6.48846i	0.928746	−	0.473220i
$189$	7.74489	−	18.1679i	0.563357	−	1.32152i
$190$	−4.62427	+	40.3653i	−0.335479	+	2.92841i
$191$	−4.90169	−	23.0607i	−0.354674	−	1.66861i	−0.687933	−	0.725775i	$-0.741482\pi$
$191$	−4.90169	−	23.0607i	−0.354674	−	1.66861i	0.333259	−	0.942835i	$-0.391852\pi$
$192$	5.36966	−	20.4736i	0.387522	−	1.47755i
$193$	0.624853	+	2.33198i	0.0449779	+	0.167860i	0.984761	−	0.173910i	$-0.0556403\pi$
$193$	0.624853	+	2.33198i	0.0449779	+	0.167860i	−0.939784	+	0.341770i	$0.888974\pi$
$194$	9.74576	−	4.33909i	0.699705	−	0.311529i
$195$	−17.5495	−	2.85229i	−1.25675	−	0.204257i
$196$	18.2653	+	8.13225i	1.30467	+	0.580875i
$197$	0.974583	−	6.15327i	0.0694362	−	0.438403i	−0.928339	−	0.371735i	$-0.878763\pi$
$197$	0.974583	−	6.15327i	0.0694362	−	0.438403i	0.997775	−	0.0666681i	$-0.0212369\pi$
$198$	7.23780	+	1.85731i	0.514368	+	0.131993i
$199$			17.1858i			1.21827i	0.793068	+	0.609134i	$0.208483\pi$
$199$			17.1858i			1.21827i	−0.793068	+	0.609134i	$0.791517\pi$
$200$	−6.54151	−	3.48854i	−0.462555	−	0.246677i
$201$	17.8558	−	13.1183i	1.25945	−	0.925291i
$202$	1.70110	+	2.61946i	0.119689	+	0.184305i
$203$	−20.2460	+	25.0017i	−1.42099	+	1.75478i
$204$	−0.317741	+	0.995847i	−0.0222463	+	0.0697232i
$205$	−4.19294	−	1.65463i	−0.292848	−	0.115564i
$206$	18.2410	−	25.1066i	1.27091	−	1.74926i
$207$	−1.64710	+	2.59620i	−0.114482	+	0.180448i
$208$	−9.79711	+	1.55171i	−0.679307	+	0.107592i
$209$	−9.44889	+	2.00842i	−0.653594	+	0.138926i
$210$	−30.2632	−	9.96844i	−2.08836	−	0.687888i
$211$	−18.2552	−	3.88025i	−1.25674	−	0.267128i	−0.469032	−	0.883181i	$-0.655397\pi$
$211$	−18.2552	−	3.88025i	−1.25674	−	0.267128i	−0.787705	+	0.616053i	$0.788731\pi$
$212$	−20.3463	−	1.06630i	−1.39739	−	0.0732341i
$213$	−5.66068	+	0.326778i	−0.387864	+	0.0223905i
$214$	21.7216	+	19.5582i	1.48486	+	1.33697i
$215$	1.53932	+	7.58998i	0.104981	+	0.517632i
$216$	−0.122582	−	7.70345i	−0.00834066	−	0.524153i
$217$	0.238667	+	1.50688i	0.0162018	+	0.102294i
$218$	−2.70946	+	10.1118i	−0.183508	+	0.684860i
$219$	9.55305	−	5.58322i	0.645535	−	0.377279i
$220$	1.14450	−	6.81346i	0.0771624	−	0.459364i
$221$	1.02620	−	0.107858i	0.0690297	−	0.00725531i
$222$	10.9900	+	0.517528i	0.737600	+	0.0347342i
$223$	−1.28898	−	24.5951i	−0.0863162	−	1.64701i	−0.608047	−	0.793901i	$-0.708047\pi$
$223$	−1.28898	−	24.5951i	−0.0863162	−	1.64701i	0.521731	−	0.853110i	$-0.325287\pi$
$224$	−29.0471			−1.94079
$225$	14.6465	+	3.23711i	0.976436	+	0.215808i
$226$	12.2826			0.817024
$227$	−0.0774108	−	1.47709i	−0.00513793	−	0.0980376i	0.994857	−	0.101292i	$-0.0322975\pi$
$227$	−0.0774108	−	1.47709i	−0.00513793	−	0.0980376i	−0.999995	+	0.00325405i	$0.998964\pi$
$228$	17.9079	+	34.6902i	1.18598	+	2.29741i
$229$	−3.30637	+	0.347514i	−0.218491	+	0.0229644i	−0.213142	−	0.977021i	$-0.568370\pi$
$229$	−3.30637	+	0.347514i	−0.218491	+	0.0229644i	−0.00534979	+	0.999986i	$0.501703\pi$
$230$	4.39843	+	2.29313i	0.290024	+	0.151204i
$231$	−0.0401792	−	7.57553i	−0.00264360	−	0.498433i
$232$	−3.24819	+	12.1224i	−0.213254	+	0.795875i
$233$	−2.91976	−	18.4347i	−0.191280	−	1.20769i	−0.877239	−	0.480054i	$-0.840617\pi$
$233$	−2.91976	−	18.4347i	−0.191280	−	1.20769i	0.685959	−	0.727640i	$-0.259383\pi$
$234$	−27.1024	+	12.4129i	−1.77174	+	0.811456i
$235$	8.77037	+	8.04652i	0.572116	+	0.524897i
$236$	10.0474	+	9.04671i	0.654029	+	0.588891i
$237$	9.26055	+	14.0958i	0.601537	+	0.915618i
$238$	1.84662	+	0.0967772i	0.119699	+	0.00627313i
$239$	−2.63555	−	0.560204i	−0.170480	−	0.0362366i	0.121881	−	0.992545i	$-0.461107\pi$
$239$	−2.63555	−	0.560204i	−0.170480	−	0.0362366i	−0.292361	+	0.956308i	$0.594441\pi$
$240$	8.32602	−	0.841108i	0.537442	−	0.0542933i
$241$	2.69870	−	0.573627i	0.173839	−	0.0369506i	−0.120170	−	0.992753i	$-0.538344\pi$
$241$	2.69870	−	0.573627i	0.173839	−	0.0369506i	0.294009	+	0.955803i	$0.405011\pi$
$242$	−20.6853	+	3.27623i	−1.32970	+	0.210604i
$243$	4.43243	+	14.9450i	0.284340	+	0.958723i
$244$	−17.4692	+	24.0443i	−1.11835	+	1.53928i
$245$	−1.02676	+	16.6191i	−0.0655971	+	1.06176i
$246$	−7.38390	+	1.61048i	−0.470780	+	0.102680i
$247$	24.2522	−	29.9490i	1.54313	−	1.90561i
$248$	0.324150	+	0.499147i	0.0205836	+	0.0316959i
$249$	2.29203	+	20.7480i	0.145251	+	1.31485i
$250$	3.20309	−	23.9868i	0.202581	−	1.51706i
$251$			20.1332i			1.27079i	0.772185	+	0.635397i	$0.219164\pi$
$251$			20.1332i			1.27079i	−0.772185	+	0.635397i	$0.780836\pi$
$252$	−29.4871	+	8.23726i	−1.85751	+	0.518899i
$253$	−0.184492	+	1.16484i	−0.0115989	+	0.0732327i
$254$	17.9571	+	7.99500i	1.12673	+	0.501651i
$255$	−0.869511	+	0.0420477i	−0.0544509	+	0.00263313i
$256$	0.248274	−	0.110539i	0.0155171	−	0.00690868i
$257$	5.64157	+	21.0546i	0.351912	+	1.31335i	0.884327	+	0.466868i	$0.154618\pi$
$257$	5.64157	+	21.0546i	0.351912	+	1.31335i	−0.532415	+	0.846483i	$0.678716\pi$
$258$	9.22998	+	9.13259i	0.574634	+	0.568570i
$259$	−2.31911	−	10.9106i	−0.144103	−	0.677950i
$260$	13.5575	+	23.9973i	0.840799	+	1.48825i
$261$	−0.269348	−	25.3912i	−0.0166722	−	1.57168i
$262$	22.9699	−	11.7037i	1.41909	−	0.723060i
$263$	−16.4125	−	10.6584i	−1.01204	−	0.657227i	−0.0716879	−	0.997427i	$-0.522839\pi$
$263$	−16.4125	−	10.6584i	−1.01204	−	0.657227i	−0.940353	+	0.340200i	$0.889505\pi$
$264$	−1.21632	−	2.69336i	−0.0748592	−	0.165765i
$265$	−5.09226	−	16.1854i	−0.312815	−	0.994260i
$266$	51.3226	−	46.2111i	3.14679	−	2.83338i
$267$	−0.458980	−	0.120378i	−0.0280891	−	0.00736701i
$268$	−33.1769	−	8.88971i	−2.02660	−	0.543026i
$269$	−17.1255	−	12.4424i	−1.04416	−	0.758627i	−0.0730670	−	0.997327i	$-0.523279\pi$
$269$	−17.1255	−	12.4424i	−1.04416	−	0.758627i	−0.971093	+	0.238700i	$0.923279\pi$
$270$	23.4190	−	9.16664i	1.42524	−	0.557864i
$271$	12.7951	−	9.29620i	0.777248	−	0.564704i	−0.126904	−	0.991915i	$-0.540504\pi$
$271$	12.7951	−	9.29620i	0.777248	−	0.564704i	0.904152	+	0.427211i	$0.140504\pi$
$272$	−0.453403	+	0.174045i	−0.0274916	+	0.0105530i
$273$	19.1436	+	23.3857i	1.15862	+	1.41537i
$274$	4.79084	+	2.76599i	0.289425	+	0.167100i
$275$	5.64934	−	1.09089i	0.340668	−	0.0657832i
$276$	4.73742	−	0.523341i	0.285159	−	0.0315014i
$277$	6.66536	−	0.349317i	0.400483	−	0.0209884i	0.148968	−	0.988842i	$-0.452405\pi$
$277$	6.66536	−	0.349317i	0.400483	−	0.0209884i	0.251514	+	0.967854i	$0.419071\pi$
$278$	1.59088	+	0.251970i	0.0954145	+	0.0151122i
$279$	−0.903395	−	0.796232i	−0.0540849	−	0.0476692i
$280$	4.40588	+	11.8062i	0.263301	+	0.705558i
$281$	−16.5900	−	1.74368i	−0.989674	−	0.104019i	−0.404166	−	0.914686i	$-0.632438\pi$
$281$	−16.5900	−	1.74368i	−0.989674	−	0.104019i	−0.585508	+	0.810667i	$0.699105\pi$
$282$	19.7262	+	3.01716i	1.17468	+	0.179669i
$283$	−5.03954	+	13.1285i	−0.299570	+	0.780406i	0.698339	+	0.715767i	$0.253923\pi$
$283$	−5.03954	+	13.1285i	−0.299570	+	0.780406i	−0.997909	+	0.0646386i	$0.979411\pi$
$284$	5.88151	+	6.53208i	0.349004	+	0.387608i
$285$	−21.8522	+	24.0731i	−1.29441	+	1.42597i
$286$	−7.65113	+	8.49744i	−0.452421	+	0.502464i
$287$	3.47847	+	6.82689i	0.205328	+	0.402979i
$288$	17.6634	−	14.6165i	1.04083	−	0.861285i
$289$	−16.1199	+	5.23768i	−0.948230	+	0.308099i
$290$	−40.7802	+	3.90130i	−2.39470	+	0.229092i
$291$	8.35946	+	1.73057i	0.490040	+	0.101448i
$292$	−16.0136	−	6.14703i	−0.937123	−	0.359728i
$293$	−8.00619	+	2.14525i	−0.467726	+	0.125327i	−0.484982	−	0.874524i	$-0.661174\pi$
$293$	−8.00619	+	2.14525i	−0.467726	+	0.125327i	0.0172555	+	0.999851i	$0.494507\pi$
$294$	14.0865	+	24.1023i	0.821539	+	1.40568i
$295$	−4.13306	+	10.4734i	−0.240636	+	0.609788i
$296$	−2.55764	−	3.52029i	−0.148660	−	0.204613i
$297$	3.83643	+	4.58643i	0.222612	+	0.266132i
$298$	−21.0301	−	10.7154i	−1.21824	−	0.620724i
$299$	−2.35244	−	4.07455i	−0.136045	−	0.235637i
$300$	−10.2784	−	20.8579i	−0.593424	−	1.20423i
$301$	6.58202	−	11.4004i	0.379381	−	0.657108i
$302$	28.0497	−	18.2157i	1.61408	−	1.04819i
$303$	−0.117566	+	2.49658i	−0.00675399	+	0.143425i
$304$	−7.37749	+	16.5701i	−0.423128	+	0.950362i
$305$	−23.8467	−	6.62912i	−1.36546	−	0.379582i
$306$	−1.17162	+	0.870368i	−0.0669770	+	0.0497556i
$307$	−11.6622	−	11.6622i	−0.665597	−	0.665597i	0.291097	−	0.956694i	$-0.405980\pi$
$307$	−11.6622	−	11.6622i	−0.665597	−	0.665597i	−0.956694	+	0.291097i	$0.905980\pi$
$308$	−9.12659	+	7.39057i	−0.520036	+	0.421117i
$309$	23.5769	−	7.79908i	1.34124	−	0.443674i
$310$	−1.15656	+	1.56099i	−0.0656883	+	0.0886583i
$311$	−5.09104	+	23.9514i	−0.288686	+	1.35816i	0.559661	+	0.828722i	$0.310931\pi$
$311$	−5.09104	+	23.9514i	−0.288686	+	1.35816i	−0.848347	+	0.529440i	$0.822402\pi$
$312$	10.5329	+	5.29659i	0.596307	+	0.299860i
$313$	2.42977	−	3.74152i	0.137339	−	0.211483i	−0.763308	−	0.646034i	$-0.776426\pi$
$313$	2.42977	−	3.74152i	0.137339	−	0.211483i	0.900647	+	0.434551i	$0.143093\pi$
$314$	10.5085	+	32.3418i	0.593028	+	1.82515i
$315$	−15.0128	−	20.6084i	−0.845873	−	1.16115i
$316$	8.07924	−	24.8653i	0.454493	−	1.39879i
$317$	21.8856	+	27.0264i	1.22922	+	1.51796i	0.781665	+	0.623699i	$0.214371\pi$
$317$	21.8856	+	27.0264i	1.22922	+	1.51796i	0.447552	+	0.894258i	$0.352296\pi$
$318$	−22.2028	−	17.7853i	−1.24507	−	0.997352i
$319$	−3.96167	−	8.89805i	−0.221811	−	0.498195i
$320$	−19.1405	−	19.5015i	−1.06998	−	1.09017i
$321$	4.98425	+	22.8524i	0.278194	+	1.27550i
$322$	−3.02157	−	7.87147i	−0.168386	−	0.438660i
$323$	0.856608	−	1.68119i	0.0476629	−	0.0935438i
$324$	13.7860	−	19.8469i	0.765890	−	1.10261i
$325$	−14.7760	+	17.5653i	−0.819624	+	0.974347i
$326$	−28.1735	+	16.2660i	−1.56039	+	0.900890i
$327$	−6.48214	+	5.30630i	−0.358463	+	0.293439i
$328$	2.32286	+	1.88101i	0.128258	+	0.103861i
$329$	−2.11477	−	20.1207i	−0.116591	−	1.10929i
$330$	6.84875	−	6.79364i	0.377011	−	0.373978i
$331$	2.99319	−	28.4783i	0.164521	−	1.56531i	−0.531356	−	0.847149i	$-0.678317\pi$
$331$	2.99319	−	28.4783i	0.164521	−	1.56531i	0.695877	−	0.718161i	$-0.255016\pi$
$332$	22.8814	−	22.8814i	1.25578	−	1.25578i
$333$	6.90043	+	5.46769i	0.378141	+	0.299628i
$334$	−8.77618	−	2.85155i	−0.480211	−	0.156030i
$335$	−2.72403	−	28.4742i	−0.148829	−	1.55571i
$336$	−11.5521	−	8.29982i	−0.630217	−	0.452792i
$337$	−0.673586	+	12.8528i	−0.0366926	+	0.700136i	0.916915	+	0.399083i	$0.130671\pi$
$337$	−0.673586	+	12.8528i	−0.0366926	+	0.700136i	−0.953607	+	0.301053i	$0.902662\pi$
$338$	0.914713	−	17.4538i	0.0497538	−	0.949360i
$339$	7.98208	+	5.73488i	0.433527	+	0.311476i
$340$	0.893574	+	1.01126i	0.0484608	+	0.0548431i
$341$	−0.439302	−	0.142738i	−0.0237895	−	0.00772969i
$342$	−7.95567	+	53.9263i	−0.430193	+	2.91600i
$343$	1.19992	−	1.19992i	0.0647897	−	0.0647897i
$344$	0.536786	−	5.10718i	0.0289416	−	0.275361i
$345$	1.78772	+	3.54392i	0.0962476	+	0.190798i
$346$	−1.89854	−	18.0634i	−0.102066	−	0.971093i
$347$	−3.18395	−	2.57832i	−0.170924	−	0.138411i	0.540042	−	0.841638i	$-0.318408\pi$
$347$	−3.18395	−	2.57832i	−0.170924	−	0.138411i	−0.710965	+	0.703227i	$0.751742\pi$
$348$	−30.4594	+	24.9342i	−1.63280	+	1.33661i
$349$	15.3233	−	8.84692i	0.820239	−	0.473565i	−0.0302601	−	0.999542i	$-0.509634\pi$
$349$	15.3233	−	8.84692i	0.820239	−	0.473565i	0.850499	+	0.525977i	$0.176300\pi$
$350$	−31.0779	+	26.9484i	−1.66118	+	1.44045i
$351$	−23.4088	−	4.58768i	−1.24947	−	0.244872i
$352$	3.99252	−	7.83576i	0.212802	−	0.417647i
$353$	−6.07156	−	15.8169i	−0.323156	−	0.841851i	−0.994881	−	0.101051i	$-0.967780\pi$
$353$	−6.07156	−	15.8169i	−0.323156	−	0.841851i	0.671725	−	0.740801i	$-0.265554\pi$
$354$	4.02277	+	18.4441i	0.213808	+	0.980292i
$355$	−3.38404	+	6.49090i	−0.179606	+	0.344501i
$356$	0.299185	+	0.671980i	0.0158568	+	0.0356149i
$357$	1.15488	+	0.925102i	0.0611226	+	0.0489616i
$358$	−3.78624	−	4.67561i	−0.200109	−	0.247114i
$359$	−5.70211	+	17.5493i	−0.300946	+	0.926216i	0.680213	+	0.733014i	$0.261887\pi$
$359$	−5.70211	+	17.5493i	−0.300946	+	0.926216i	−0.981159	+	0.193202i	$0.938113\pi$
$360$	−8.62009	−	4.96229i	−0.454319	−	0.261536i
$361$	−15.9048	−	48.9499i	−0.837093	−	2.57631i
$362$	5.14629	−	7.92459i	0.270483	−	0.416507i
$363$	−14.9725	−	7.52911i	−0.785852	−	0.395176i
$364$	9.74066	−	45.8262i	0.510549	−	2.40195i
$365$	0.133467	−	14.2842i	0.00698596	−	0.747667i
$366$	−39.3980	+	13.0326i	−2.05937	+	0.681226i
$367$	−12.4799	+	10.1060i	−0.651443	+	0.527528i	−0.897100	−	0.441829i	$-0.854330\pi$
$367$	−12.4799	+	10.1060i	−0.651443	+	0.527528i	0.245656	+	0.969357i	$0.420997\pi$
$368$	1.56585	+	1.56585i	0.0816254	+	0.0816254i
$369$	−5.55053	−	2.40104i	−0.288949	−	0.124993i
$370$	7.84688	−	11.8395i	0.407940	−	0.615504i
$371$	−11.7308	+	26.3478i	−0.609033	+	1.36791i
$372$	−0.0878098	+	1.86469i	−0.00455272	+	0.0966795i
$373$	0.105114	−	0.0682618i	0.00544259	−	0.00353446i	−0.541915	−	0.840433i	$-0.682300\pi$
$373$	0.105114	−	0.0682618i	0.00544259	−	0.00353446i	0.547357	+	0.836899i	$0.315634\pi$
$374$	−0.279924	+	0.484842i	−0.0144745	+	0.0250706i
$375$	13.2813	−	14.0928i	0.685845	−	0.727747i
$376$	−3.94617	−	6.83497i	−0.203508	−	0.352487i
$377$	34.6217	+	17.6407i	1.78311	+	0.908540i
$378$	−40.1476	−	14.6827i	−2.06497	−	0.755196i
$379$	−4.49310	−	6.18422i	−0.230795	−	0.317662i	0.677875	−	0.735177i	$-0.262901\pi$
$379$	−4.49310	−	6.18422i	−0.230795	−	0.317662i	−0.908670	+	0.417515i	$0.862901\pi$
$380$	50.3042	+	3.10788i	2.58055	+	0.159431i
$381$	7.93680	+	13.5801i	0.406614	+	0.695729i
$382$	−49.2909	+	13.2075i	−2.52194	+	0.675752i
$383$	−23.5201	−	9.02851i	−1.20182	−	0.461335i	−0.326647	−	0.945146i	$-0.605919\pi$
$383$	−23.5201	−	9.02851i	−1.20182	−	0.461335i	−0.875172	+	0.483811i	$0.839252\pi$
$384$	−18.9385	−	3.92063i	−0.966449	−	0.200074i
$385$	−8.42376	−	4.96897i	−0.429315	−	0.253242i
$386$	4.96985	−	1.61480i	0.252959	−	0.0821913i
$387$	1.73417	+	10.2446i	0.0881529	+	0.520762i
$388$	−6.00792	−	11.7912i	−0.305006	−	0.598608i
$389$	15.4141	−	17.1190i	0.781524	−	0.867970i	−0.212497	−	0.977162i	$-0.568160\pi$
$389$	15.4141	−	17.1190i	0.781524	−	0.867970i	0.994021	+	0.109192i	$0.0348262\pi$
$390$	−4.17727	+	38.2568i	−0.211524	+	1.93721i
$391$	−0.154140	−	0.171190i	−0.00779519	−	0.00865743i
$392$	3.95674	−	10.3077i	0.199846	−	0.520616i
$393$	20.3921	+	3.11901i	1.02864	+	0.157333i
$394$	−13.4109	−	1.40954i	−0.675629	−	0.0710115i
$395$	21.7532	−	0.936325i	1.09452	−	0.0471116i
$396$	1.83091	−	9.08666i	0.0920067	−	0.456622i
$397$	7.13931	+	1.13076i	0.358312	+	0.0567510i	0.332995	−	0.942929i	$-0.391941\pi$
$397$	7.13931	+	1.13076i	0.358312	+	0.0567510i	0.0253163	+	0.999679i	$0.491941\pi$
$398$	37.1475	−	1.94682i	1.86203	−	0.0975851i
$399$	54.9296	−	6.06805i	2.74992	−	0.303783i
$400$	4.57785	−	9.78571i	0.228893	−	0.489285i
$401$	25.2877	+	14.5998i	1.26281	+	0.729082i	0.973617	−	0.228190i	$-0.0732808\pi$
$401$	25.2877	+	14.5998i	1.26281	+	0.729082i	0.289190	+	0.957272i	$0.406614\pi$
$402$	−30.3782	−	37.1097i	−1.51512	−	1.85086i
$403$	1.72033	−	0.660373i	0.0856958	−	0.0328955i
$404$	3.13451	−	2.27736i	0.155948	−	0.113303i
$405$	19.4993	+	4.97750i	0.968930	+	0.247334i
$406$	56.3353	+	40.9300i	2.79588	+	2.03132i
$407$	3.26200	+	0.874050i	0.161691	+	0.0433250i
$408$	0.558354	+	0.146441i	0.0276427	+	0.00724991i
$409$	−16.7269	+	15.0610i	−0.827091	+	0.744716i	−0.969500	−	0.245091i	$-0.921182\pi$
$409$	−16.7269	+	15.0610i	−0.827091	+	0.744716i	0.142409	+	0.989808i	$0.454515\pi$
$410$	−3.10154	+	9.25058i	−0.153174	+	0.456853i
$411$	1.82195	+	4.03444i	0.0898700	+	0.199004i
$412$	−32.2859	−	20.9667i	−1.59061	−	1.03296i
$413$	17.0527	−	8.68880i	0.839110	−	0.427548i
$414$	5.79832	+	3.26615i	0.284972	+	0.160523i
$415$	24.5152	+	11.1905i	1.20340	+	0.549320i
$416$	7.29428	+	34.3169i	0.357632	+	1.68252i
$417$	0.916217	+	0.906549i	0.0448673	+	0.0443939i
$418$	5.41163	+	20.1965i	0.264692	+	0.987843i
$419$	−5.65519	+	2.51785i	−0.276274	+	0.123005i	−0.540197	−	0.841539i	$-0.681650\pi$
$419$	−5.65519	+	2.51785i	−0.276274	+	0.123005i	0.263923	+	0.964544i	$0.414984\pi$
$420$	−10.3840	+	38.1368i	−0.506688	+	1.86088i
$421$	−23.6927	−	10.5487i	−1.15471	−	0.514112i	−0.262147	−	0.965028i	$-0.584431\pi$
$421$	−23.6927	−	10.5487i	−1.15471	−	0.514112i	−0.892566	+	0.450916i	$0.851097\pi$
$422$	−6.31931	+	39.8985i	−0.307619	+	1.94223i
$423$	11.4107	+	11.1712i	0.554807	+	0.543160i
$424$			11.2510i			0.546398i
$425$	−0.528837	+	0.991645i	−0.0256524	+	0.0481018i
$426$	1.34758	+	12.1987i	0.0652907	+	0.591028i
$427$	22.9138	+	35.2841i	1.10888	+	1.70752i
$428$	22.8182	−	28.1782i	1.10296	−	1.36204i
$429$	−8.93980	+	1.94983i	−0.431618	+	0.0941385i
$430$	16.2315	−	4.18708i	0.782754	−	0.201919i
$431$	−12.2660	+	16.8827i	−0.590832	+	0.813210i	−0.994831	−	0.101549i	$-0.967620\pi$
$431$	−12.2660	+	16.8827i	−0.590832	+	0.813210i	0.403999	+	0.914760i	$0.367620\pi$
$432$	11.2012	−	0.765911i	0.538919	−	0.0368499i
$433$	4.49113	−	0.711326i	0.215830	−	0.0341841i	−0.0475829	−	0.998867i	$-0.515152\pi$
$433$	4.49113	−	0.711326i	0.215830	−	0.0341841i	0.263413	+	0.964683i	$0.415152\pi$
$434$	3.23013	−	0.686585i	0.155051	−	0.0329571i
$435$	−28.3234	−	16.5054i	−1.35800	−	0.791375i
$436$	12.7023	+	2.69996i	0.608330	+	0.129304i
$437$	−8.59154	−	0.450263i	−0.410989	−	0.0215390i
$438$	−13.1504	−	20.0167i	−0.628352	−	0.956434i
$439$	8.94461	+	8.05376i	0.426903	+	0.384385i	0.854387	−	0.519638i	$-0.173933\pi$
$439$	8.94461	+	8.05376i	0.426903	+	0.384385i	−0.427484	+	0.904023i	$0.640600\pi$
$440$	−3.79044	−	0.434235i	−0.180702	−	0.0207013i
$441$	−2.09931	+	22.2405i	−0.0999670	+	1.05907i
$442$	−0.349386	−	2.20594i	−0.0166186	−	0.104926i
$443$	7.41998	−	27.6917i	0.352534	−	1.31567i	−0.531026	−	0.847356i	$-0.678193\pi$
$443$	7.41998	−	27.6917i	0.352534	−	1.31567i	0.883560	−	0.468319i	$-0.155140\pi$
$444$	−0.0723857	−	13.6478i	−0.00343527	−	0.647698i
$445$	−0.437189	+	0.429095i	−0.0207247	+	0.0203410i
$446$	−53.0169	+	5.57231i	−2.51043	+	0.263856i
$447$	−8.66369	−	16.7828i	−0.409779	−	0.793800i
$448$	2.43086	+	46.3835i	0.114847	+	2.19142i
$449$	5.85036			0.276096			0.138048	−	0.990426i	$-0.455917\pi$
$449$	5.85036			0.276096			0.138048	+	0.990426i	$0.455917\pi$
$450$	5.33793	−	32.0255i	0.251632	−	1.50970i
$451$	−2.31974			−0.109232
$452$	−0.797409	−	15.2155i	−0.0375070	−	0.715675i
$453$	26.7338	+	1.25892i	1.25606	+	0.0591491i
$454$	−3.18399	+	0.334651i	−0.149432	+	0.0157059i
$455$	38.5914	−	5.74319i	1.80919	−	0.269245i
$456$	18.6127	−	10.8781i	0.871622	−	0.509414i
$457$	4.65241	−	17.3630i	0.217631	−	0.812208i	−0.767593	−	0.640937i	$-0.778546\pi$
$457$	4.65241	−	17.3630i	0.217631	−	0.812208i	0.985224	−	0.171271i	$-0.0547874\pi$
$458$	1.12571	+	7.10744i	0.0526009	+	0.332109i
$459$	−1.16779	+	0.0185826i	−0.0545076	+	0.000867360i
$460$	2.55514	−	5.59759i	0.119134	−	0.260989i
$461$	−3.65707	−	3.29284i	−0.170327	−	0.153363i	0.579559	−	0.814930i	$-0.303225\pi$
$461$	−3.65707	−	3.29284i	−0.170327	−	0.153363i	−0.749886	+	0.661567i	$0.769892\pi$
$462$	−16.3701	+	0.945010i	−0.761608	+	0.0439658i
$463$	15.5143	+	0.813069i	0.721010	+	0.0377865i	0.409312	−	0.912395i	$-0.365769\pi$
$463$	15.5143	+	0.813069i	0.721010	+	0.0377865i	0.311698	+	0.950181i	$0.399102\pi$
$464$	−17.8891	−	3.80244i	−0.830479	−	0.176524i
$465$	−1.48046	+	0.474428i	−0.0686548	+	0.0220011i
$466$	−39.5162	+	8.39943i	−1.83055	+	0.389096i
$467$	−15.8493	+	2.51028i	−0.733417	+	0.116162i	−0.511961	−	0.859009i	$-0.671081\pi$
$467$	−15.8493	+	2.51028i	−0.733417	+	0.116162i	−0.221456	+	0.975170i	$0.571081\pi$
$468$	17.1365	+	32.7682i	0.792133	+	1.51471i
$469$	−28.5788	+	39.3353i	−1.31965	+	1.81634i
$470$	16.3992	−	19.8689i	0.756440	−	0.916483i
$471$	−8.27163	+	25.9245i	−0.381137	+	1.19454i
$472$	4.69853	−	5.80221i	0.216268	−	0.267068i
$473$	2.17067	+	3.34255i	0.0998077	+	0.153690i
$474$	29.4193	−	21.6137i	1.35127	−	0.992749i
$475$	12.2222	+	40.1540i	0.560791	+	1.84239i
$476$		−	2.29385i		−	0.105138i
$477$	−6.12476	−	21.9249i	−0.280433	−	1.00387i
$478$	−0.912338	+	5.76028i	−0.0417294	+	0.263469i
$479$	31.7786	+	14.1487i	1.45200	+	0.646472i	0.972887	−	0.231281i	$-0.0742918\pi$
$479$	31.7786	+	14.1487i	1.45200	+	0.646472i	0.479113	+	0.877753i	$0.340958\pi$
$480$	−4.51208	−	29.2525i	−0.205947	−	1.33519i
$481$	−12.3076	+	5.47970i	−0.561179	+	0.249853i
$482$	−1.54562	−	5.76833i	−0.0704011	−	0.262740i
$483$	1.71166	−	6.52625i	0.0778830	−	0.296954i
$484$	5.40148	+	25.4120i	0.245522	+	1.15509i
$485$	7.45059	−	8.12083i	0.338314	−	0.368748i
$486$	31.8019	−	11.2738i	1.44256	−	0.511389i
$487$	−0.699020	+	0.356169i	−0.0316756	+	0.0161395i	−0.469757	−	0.882796i	$-0.655658\pi$
$487$	−0.699020	+	0.356169i	−0.0316756	+	0.0161395i	0.438081	+	0.898936i	$0.355658\pi$
$488$	13.7644	+	8.93870i	0.623085	+	0.404636i
$489$	−25.9039	−	2.58378i	−1.17142	−	0.116843i
$490$	36.0389	+	0.336736i	1.62807	+	0.0152122i
$491$	−13.1759	+	11.8636i	−0.594620	+	0.535399i	−0.910558	−	0.413381i	$-0.864348\pi$
$491$	−13.1759	+	11.8636i	−0.594620	+	0.535399i	0.315938	+	0.948780i	$0.397681\pi$
$492$	2.47441	+	9.04251i	0.111555	+	0.407668i
$493$	1.83767	+	0.492402i	0.0827644	+	0.0221767i
$494$	−67.4828	−	49.0292i	−3.03620	−	2.20593i
$495$	7.62284	−	1.21722i	0.342621	−	0.0547099i
$496$	−0.701671	+	0.509794i	−0.0315059	+	0.0228904i
$497$	11.6162	−	4.45903i	0.521057	−	0.200015i
$498$	44.5877	−	7.30462i	1.99802	−	0.327328i
$499$	8.31356	+	4.79984i	0.372166	+	0.214870i	0.674404	−	0.738362i	$-0.264400\pi$
$499$	8.31356	+	4.79984i	0.372166	+	0.214870i	−0.302238	+	0.953232i	$0.597734\pi$
$500$	−29.9225	−	2.41067i	−1.33817	−	0.107808i
$501$	−4.37195	−	5.95085i	−0.195324	−	0.265864i
$502$	43.5183	−	2.28070i	1.94232	−	0.101793i
$503$	22.6324	+	3.58462i	1.00913	+	0.159830i	0.639047	−	0.769168i	$-0.279329\pi$
$503$	22.6324	+	3.58462i	1.00913	+	0.159830i	0.370083	+	0.928999i	$0.379329\pi$
$504$	5.39474	+	16.0230i	0.240301	+	0.713719i
$505$	2.68955	+	1.78256i	0.119683	+	0.0793228i
$506$	2.53872	+	0.266831i	0.112860	+	0.0118621i
$507$	8.74383	−	10.9156i	0.388327	−	0.484779i
$508$	8.73828	−	22.7640i	0.387698	−	1.00999i
$509$	2.40476	+	2.67076i	0.106589	+	0.118379i	0.794079	−	0.607815i	$-0.207954\pi$
$509$	2.40476	+	2.67076i	0.106589	+	0.118379i	−0.687489	+	0.726194i	$0.741287\pi$
$510$	0.189386	+	1.87470i	0.00838615	+	0.0830133i
$511$	−16.2473	+	18.0444i	−0.718737	+	0.798238i
$512$	−10.4055	−	20.4220i	−0.459865	−	0.902535i
$513$	−30.3490	+	31.3305i	−1.33994	+	1.38327i
$514$	44.8710	−	14.5795i	1.97918	−	0.643073i
$515$	6.95829	−	31.2955i	0.306619	−	1.37904i
$516$	10.7141	−	12.0269i	0.471662	−	0.529454i
$517$	5.71843	+	2.19510i	0.251496	+	0.0965404i
$518$	−23.3207	+	6.24878i	−1.02465	+	0.274555i
$519$	7.20021	−	12.6253i	0.316054	−	0.554189i
$520$	12.8418	−	8.16997i	0.563148	−	0.358277i
$521$	10.7490	+	14.7947i	0.470920	+	0.648166i	0.976728	−	0.214480i	$-0.0688056\pi$
$521$	10.7490	+	14.7947i	0.470920	+	0.648166i	−0.505808	+	0.862646i	$0.668806\pi$
$522$	−54.8532	+	3.45854i	−2.40086	+	0.151376i
$523$	33.5336	+	17.0862i	1.46632	+	0.747127i	0.991148	−	0.132765i	$-0.0423856\pi$
$523$	33.5336	+	17.0862i	1.46632	+	0.747127i	0.475173	+	0.879893i	$0.342386\pi$
$524$	−15.9897	−	27.6949i	−0.698513	−	1.20986i
$525$	−32.7791	+	3.00229i	−1.43060	+	0.131031i
$526$	−21.1792	+	36.6835i	−0.923459	+	1.59948i
$527$	0.0756671	−	0.0491388i	0.00329611	−	0.00214052i
$528$	3.82679	−	1.97548i	0.166540	−	0.0859718i
$529$	8.92773	−	20.0520i	0.388162	−	0.871826i
$530$	−34.4082	+	12.8405i	−1.49460	+	0.557757i
$531$	−5.99749	+	13.8645i	−0.260269	+	0.601670i
$532$	−60.5776	−	60.5776i	−2.62637	−	2.62637i
$533$	7.19192	−	5.82390i	0.311517	−	0.252261i
$534$	−0.208206	+	1.00573i	−0.00900997	+	0.0435223i
$535$	28.6296	+	9.59895i	1.23776	+	0.414999i
$536$	−3.94350	+	18.5527i	−0.170333	+	0.801354i
$537$	−0.277461	−	4.80638i	−0.0119733	−	0.207411i
$538$	−24.9546	+	38.4267i	−1.07587	+	1.65669i
$539$	2.64795	+	8.14956i	0.114055	+	0.351026i
$540$	−12.8759	−	28.4160i	−0.554091	−	1.22283i
$541$	9.55655	−	29.4121i	0.410868	−	1.26452i	−0.505026	−	0.863104i	$-0.668517\pi$
$541$	9.55655	−	29.4121i	0.410868	−	1.26452i	0.915895	−	0.401419i	$-0.131483\pi$
$542$	−21.5434	−	26.6039i	−0.925368	−	1.14273i
$543$	7.04451	−	2.74709i	0.302309	−	0.117889i
$544$	0.698670	+	1.56924i	0.0299552	+	0.0672806i
$545$	1.59192	+	10.6969i	0.0681904	+	0.458206i
$546$	48.3801	−	44.0285i	2.07048	−	1.88425i
$547$	−0.654870	−	1.70600i	−0.0280002	−	0.0729431i	0.918868	−	0.394566i	$-0.129105\pi$
$547$	−0.654870	−	1.70600i	−0.0280002	−	0.0729431i	−0.946868	+	0.321623i	$0.895772\pi$
$548$	3.11544	−	6.11439i	0.133085	−	0.261194i
$549$	−31.6887	−	9.92593i	−1.35244	−	0.423628i
$550$	−2.99795	−	12.0876i	−0.127833	−	0.515418i
$551$	61.5342	−	35.5268i	2.62144	−	1.51349i
$552$	−0.425518	−	2.59738i	−0.0181112	−	0.110552i
$553$	−28.7623	−	23.2913i	−1.22310	−	0.990446i
$554$	−1.51011	−	14.3678i	−0.0641586	−	0.610428i
$555$	10.6274	−	4.03031i	0.451110	−	0.171077i
$556$	0.208854	−	1.98711i	0.00885739	−	0.0842724i
$557$	1.54187	−	1.54187i	0.0653311	−	0.0653311i	−0.673686	−	0.739017i	$-0.735290\pi$
$557$	1.54187	−	1.54187i	0.0653311	−	0.0653311i	0.739017	+	0.673686i	$0.235290\pi$
$558$	−1.61874	+	2.04291i	−0.0685267	+	0.0864832i
$559$	−15.1215	−	4.91328i	−0.639573	−	0.207810i
$560$	−16.8452	+	7.31216i	−0.711840	+	0.308995i
$561$	−0.408293	+	0.184385i	−0.0172381	+	0.00778473i
$562$	−1.88967	+	36.0571i	−0.0797111	+	1.52098i
$563$	0.384996	−	7.34617i	0.0162257	−	0.309604i	−0.978445	−	0.206505i	$-0.933791\pi$
$563$	0.384996	−	7.34617i	0.0162257	−	0.309604i	0.994671	−	0.103099i	$-0.0328758\pi$
$564$	2.45695	−	24.6324i	0.103456	−	1.03721i
$565$	11.6395	−	5.05245i	0.489676	−	0.212558i
$566$	28.9484	+	9.40589i	1.21679	+	0.395359i
$567$	−19.2352	−	28.2873i	−0.807803	−	1.18795i
$568$	3.43221	−	3.43221i	0.144012	−	0.144012i
$569$	−3.87342	+	36.8531i	−0.162382	+	1.54496i	0.545184	+	0.838316i	$0.316460\pi$
$569$	−3.87342	+	36.8531i	−0.162382	+	1.54496i	−0.707566	+	0.706647i	$0.750207\pi$
$570$	54.5100	+	44.5071i	2.28317	+	1.86420i
$571$	0.741883	+	7.05855i	0.0310469	+	0.295391i	0.999017	+	0.0443262i	$0.0141141\pi$
$571$	0.741883	+	7.05855i	0.0310469	+	0.295391i	−0.967970	+	0.251065i	$0.919219\pi$
$572$	11.0232	+	8.92644i	0.460904	+	0.373233i
$573$	−38.1994	−	14.4314i	−1.59580	−	0.602880i
$574$	14.3624	−	8.29216i	0.599477	−	0.346108i
$575$	5.11141	+	0.363761i	0.213160	+	0.0151699i
$576$	−24.8183	−	26.9824i	−1.03410	−	1.12427i
$577$	1.79070	−	3.51444i	0.0745477	−	0.146308i	−0.850725	−	0.525612i	$-0.823836\pi$
$577$	1.79070	−	3.51444i	0.0745477	−	0.146308i	0.925272	+	0.379304i	$0.123836\pi$
$578$	13.1474	+	34.2503i	0.546861	+	1.42462i
$579$	3.98373	+	1.27107i	0.165558	+	0.0528240i
$580$	7.48041	+	50.2646i	0.310607	+	2.08712i
$581$	−18.6313	−	41.8467i	−0.772958	−	1.73609i
$582$	2.79370	−	18.2652i	0.115803	−	0.757118i
$583$	−5.49520	−	6.78601i	−0.227588	−	0.281048i
$584$	−2.92705	+	9.00852i	−0.121122	+	0.372775i
$585$	−20.5773	+	22.9116i	−0.850766	+	0.947276i
$586$	5.54396	+	17.0625i	0.229019	+	0.704847i
$587$	−4.23426	+	6.52018i	−0.174766	+	0.269117i	−0.915189	−	0.403025i	$-0.867959\pi$
$587$	−4.23426	+	6.52018i	−0.174766	+	0.269117i	0.740423	+	0.672142i	$0.234625\pi$
$588$	28.9431	−	19.0149i	1.19359	−	0.784160i
$589$	0.700579	−	3.29596i	0.0288668	−	0.135808i
$590$	23.1068	+	7.74728i	0.951292	+	0.318950i
$591$	−8.05719	−	7.17771i	−0.331428	−	0.295252i
$592$	4.92789	−	3.99053i	0.202535	−	0.164010i
$593$	−22.7004	−	22.7004i	−0.932193	−	0.932193i	0.0656493	−	0.997843i	$-0.479088\pi$
$593$	−22.7004	−	22.7004i	−0.932193	−	0.932193i	−0.997843	+	0.0656493i	$0.979088\pi$
$594$	9.47908	−	8.81210i	0.388931	−	0.361565i
$595$	1.78974	−	0.667898i	0.0733722	−	0.0273812i
$596$	−11.9087	+	26.7474i	−0.487800	+	1.09562i
$597$	25.0500	+	16.0794i	1.02523	+	0.658088i
$598$	−8.54075	+	5.54643i	−0.349257	+	0.226810i
$599$	−4.83995	+	8.38304i	−0.197755	+	0.342522i	−0.947800	−	0.318865i	$-0.896698\pi$
$599$	−4.83995	+	8.38304i	−0.197755	+	0.342522i	0.750045	+	0.661387i	$0.230032\pi$
$600$	−11.2053	+	6.27096i	−0.457455	+	0.256011i
$601$	−9.15566	−	15.8581i	−0.373467	−	0.646864i	0.616629	−	0.787254i	$-0.288498\pi$
$601$	−9.15566	−	15.8581i	−0.373467	−	0.646864i	−0.990096	+	0.140390i	$0.955164\pi$
$602$	−25.3878	−	12.9357i	−1.03473	−	0.527222i
$603$	−2.41487	−	38.3005i	−0.0983412	−	1.55972i
$604$	−24.3863	−	33.5649i	−0.992266	−	1.36574i
$605$	−18.2546	+	11.6136i	−0.742153	+	0.472161i
$606$	5.40973	−	0.0286922i	0.219755	−	0.00116554i
$607$	1.81525	−	0.486396i	0.0736789	−	0.0197422i	−0.221791	−	0.975094i	$-0.571190\pi$
$607$	1.81525	−	0.486396i	0.0736789	−	0.0197422i	0.295470	+	0.955352i	$0.404524\pi$
$608$	59.8926	+	22.9906i	2.42897	+	0.932392i
$609$	17.4999	+	52.9029i	0.709133	+	2.14373i
$610$	−11.6276	+	52.2962i	−0.470789	+	2.11741i
$611$	−23.2400	+	7.55112i	−0.940188	+	0.305486i
$612$	1.15426	+	1.39488i	0.0466583	+	0.0563846i
$613$	−13.9149	−	27.3095i	−0.562017	−	1.10302i	−0.980815	−	0.194940i	$-0.937549\pi$
$613$	−13.9149	−	27.3095i	−0.562017	−	1.10302i	0.418799	−	0.908079i	$-0.362451\pi$
$614$	−23.8870	+	26.5292i	−0.964001	+	1.07063i
$615$	−6.33481	+	4.56353i	−0.255444	+	0.184019i
$616$	4.33938	+	4.81937i	0.174839	+	0.194178i
$617$	14.4764	−	37.7122i	0.582796	−	1.51824i	−0.252029	−	0.967720i	$-0.581098\pi$
$617$	14.4764	−	37.7122i	0.582796	−	1.51824i	0.834825	−	0.550516i	$-0.185569\pi$
$618$	−19.5287	−	50.0785i	−0.785560	−	2.01445i
$619$	−21.5139	−	2.26121i	−0.864718	−	0.0908855i	−0.338225	−	0.941065i	$-0.609827\pi$
$619$	−21.5139	−	2.26121i	−0.864718	−	0.0908855i	−0.526493	+	0.850180i	$0.676493\pi$
$620$	2.00882	+	1.33139i	0.0806761	+	0.0534699i
$621$	2.24315	+	4.82989i	0.0900146	+	0.193817i
$622$	52.3483	+	8.29116i	2.09898	+	0.332445i
$623$	1.03983	−	0.0544954i	0.0416601	−	0.00218331i
$624$	−6.90464	+	15.7321i	−0.276407	+	0.629788i
$625$	−6.83163	−	24.0485i	−0.273265	−	0.961939i
$626$	−8.36263	−	4.82816i	−0.334238	−	0.192972i
$627$	−5.91313	+	15.6519i	−0.236148	+	0.625075i
$628$	39.3823	−	15.1174i	1.57152	−	0.603252i
$629$	−0.533650	+	0.387719i	−0.0212780	+	0.0154594i
$630$	−42.8450	+	34.7850i	−1.70699	+	1.38587i
$631$	8.29682	+	6.02799i	0.330291	+	0.239971i	0.740554	−	0.671997i	$-0.234563\pi$
$631$	8.29682	+	6.02799i	0.330291	+	0.239971i	−0.410263	+	0.911967i	$0.634563\pi$
$632$	−13.9458	−	3.73676i	−0.554734	−	0.148640i
$633$	−22.7359	+	22.9783i	−0.903669	+	0.913306i
$634$	55.9391	−	50.3678i	2.22163	−	2.00036i
$635$	20.3056	+	0.189729i	0.805802	+	0.00752916i
$636$	−20.5908	+	28.6592i	−0.816477	+	1.13641i
$637$	−28.6697	−	18.6183i	−1.13593	−	0.737684i
$638$	−18.7846	+	9.57121i	−0.743688	+	0.378928i
$639$	−4.81996	+	8.55677i	−0.190675	+	0.338501i
$640$	−16.8794	+	18.3978i	−0.667217	+	0.727238i
$641$	5.91928	+	27.8480i	0.233798	+	1.09993i	0.925793	+	0.378030i	$0.123398\pi$
$641$	5.91928	+	27.8480i	0.233798	+	1.09993i	−0.691996	+	0.721902i	$0.743268\pi$
$642$	48.8314	−	13.3623i	1.92722	−	0.527368i
$643$	−1.12044	−	4.18152i	−0.0441857	−	0.164903i	0.940308	−	0.340326i	$-0.110537\pi$
$643$	−1.12044	−	4.18152i	−0.0441857	−	0.164903i	−0.984493	+	0.175423i	$0.943871\pi$
$644$	−9.55489	+	4.25411i	−0.376516	+	0.167636i
$645$	12.5034	+	4.85765i	0.492321	+	0.191270i
$646$	−3.73096	−	1.66113i	−0.146793	−	0.0653564i
$647$	1.20130	−	7.58468i	0.0472278	−	0.298185i	−0.952757	−	0.303734i	$-0.901767\pi$
$647$	1.20130	−	7.58468i	0.0472278	−	0.298185i	0.999985	+	0.00554960i	$0.00176650\pi$
$648$	−11.3433	−	7.02886i	−0.445605	−	0.276120i
$649$			5.79442i			0.227451i
$650$	39.6416	+	29.9488i	1.55487	+	1.17469i
$651$	2.41974	+	1.06200i	0.0948371	+	0.0416229i
$652$	21.9791	+	33.8449i	0.860770	+	1.32547i
$653$	−30.2023	+	37.2968i	−1.18191	+	1.45954i	−0.323757	+	0.946140i	$0.604946\pi$
$653$	−30.2023	+	37.2968i	−1.18191	+	1.45954i	−0.858152	+	0.513396i	$0.828387\pi$
$654$	12.2040	+	13.4102i	0.477214	+	0.524380i
$655$	16.9529	−	20.5396i	0.662403	−	0.802550i
$656$	−2.56022	+	3.52383i	−0.0999596	+	0.137583i
$657$	0.799954	−	19.1484i	0.0312092	−	0.747048i
$658$	−43.2518	+	6.85041i	−1.68613	+	0.267057i
$659$	−30.6970	+	6.52486i	−1.19579	+	0.254172i	−0.762443	−	0.647056i	$-0.776000\pi$
$659$	−30.6970	+	6.52486i	−1.19579	+	0.254172i	−0.433345	+	0.901228i	$0.642667\pi$
$660$	−8.86050	−	8.04308i	−0.344894	−	0.313076i
$661$	46.7880	+	9.94509i	1.81984	+	0.386819i	0.986210	−	0.165502i	$-0.0529243\pi$
$661$	46.7880	+	9.94509i	1.81984	+	0.386819i	0.833632	+	0.552321i	$0.186258\pi$
$662$	−61.8957	−	3.24381i	−2.40564	−	0.126074i
$663$	0.802924	−	1.59671i	0.0311830	−	0.0620109i
$664$	−13.2795	−	11.9569i	−0.515344	−	0.464018i
$665$	29.6264	−	64.9031i	1.14886	−	2.51683i
$666$	11.0369	−	15.5348i	0.427670	−	0.601963i
$667$	−1.35702	−	8.56790i	−0.0525441	−	0.331750i
$668$	−2.96270	+	11.0569i	−0.114630	+	0.427806i
$669$	−37.0559	−	21.1330i	−1.43266	−	0.817049i
$670$	−61.2390	+	9.11362i	−2.36587	+	0.352090i
$671$	−12.6677	+	1.33143i	−0.489033	+	0.0513994i
$672$	−27.1772	+	42.3392i	−1.04838	+	1.63327i
$673$	0.232865	+	4.44333i	0.00897628	+	0.171278i	0.999439	+	0.0334956i	$0.0106640\pi$
$673$	0.232865	+	4.44333i	0.00897628	+	0.171278i	−0.990463	+	0.137782i	$0.956003\pi$
$674$	27.8579			1.07305
$675$	18.4221	−	18.3201i	0.709067	−	0.705141i
$676$	−21.6809			−0.833879
$677$	0.291644	+	5.56489i	0.0112088	+	0.213876i	0.998492	+	0.0549031i	$0.0174850\pi$
$677$	0.291644	+	5.56489i	0.0112088	+	0.213876i	−0.987283	+	0.158973i	$0.949182\pi$
$678$	11.4919	−	17.9031i	0.441343	−	0.687565i
$679$	−18.6305	+	1.95815i	−0.714974	+	0.0751468i
$680$	0.531845	−	0.521998i	0.0203953	−	0.0200177i
$681$	−2.22543	−	1.26916i	−0.0852787	−	0.0486345i
$682$	−0.258767	+	0.965731i	−0.00990870	+	0.0369798i
$683$	−3.59928	−	22.7250i	−0.137723	−	0.869547i	−0.955710	−	0.294311i	$-0.904910\pi$
$683$	−3.59928	−	22.7250i	−0.137723	−	0.869547i	0.817987	−	0.575237i	$-0.195090\pi$
$684$	67.3196	+	6.35437i	2.57403	+	0.242965i
$685$	5.67778	+	0.650449i	0.216937	+	0.0248524i
$686$	−2.72959	−	2.45773i	−0.104216	−	0.0938367i
$687$	−2.58699	+	5.14452i	−0.0986998	+	0.196276i
$688$	7.47325	+	0.391656i	0.284915	+	0.0149318i
$689$	34.0737	+	7.24259i	1.29811	+	0.275921i
$690$	7.45775	−	4.26566i	0.283912	−	0.162391i
$691$	−13.7162	+	2.91546i	−0.521788	+	0.110909i	−0.461274	−	0.887258i	$-0.652607\pi$
$691$	−13.7162	+	2.91546i	−0.521788	+	0.110909i	−0.0605143	+	0.998167i	$0.519274\pi$
$692$	−22.2534	+	3.52459i	−0.845947	+	0.133985i
$693$	−11.0797	−	7.02929i	−0.420883	−	0.267021i
$694$	−5.21241	+	7.17427i	−0.197860	+	0.272332i
$695$	1.61123	−	0.415632i	0.0611174	−	0.0157658i
$696$	14.6306	+	16.0766i	0.554570	+	0.609382i
$697$	0.285147	−	0.352128i	0.0108007	−	0.0133378i
$698$	−20.8587	−	32.1195i	−0.789513	−	1.21574i
$699$	−29.6022	−	12.9921i	−1.11966	−	0.491405i
$700$	35.4009	+	36.7493i	1.33803	+	1.38899i
$701$			10.4999i			0.396575i	0.980144	+	0.198287i	$0.0635379\pi$
$701$			10.4999i			0.396575i	−0.980144	+	0.198287i	$0.936462\pi$
$702$	−7.26462	+	51.1184i	−0.274185	+	1.92934i
$703$	−3.85384	+	24.3322i	−0.145350	+	0.917705i
$704$	−12.8465	−	5.71965i	−0.484172	−	0.215567i
$705$	19.9344	−	5.25519i	0.750773	−	0.197922i
$706$	−33.5009	+	14.9156i	−1.26082	+	0.561355i
$707$	−1.41952	−	5.29773i	−0.0533866	−	0.199242i
$708$	22.5871	−	6.18077i	0.848875	−	0.232288i
$709$	4.82664	+	22.7076i	0.181268	+	0.852801i	0.970950	+	0.239284i	$0.0769125\pi$
$709$	4.82664	+	22.7076i	0.181268	+	0.852801i	−0.789681	+	0.613517i	$0.789754\pi$
$710$	14.4136	+	6.57939i	0.540932	+	0.246920i
$711$	29.2104	−	0.309862i	1.09548	−	0.0116207i
$712$	0.361925	−	0.184410i	0.0135637	−	0.00691105i
$713$	−0.345015	−	0.224055i	−0.0129209	−	0.00839094i
$714$	1.86881	−	2.60109i	0.0699383	−	0.0973433i
$715$	−3.75509	+	11.1998i	−0.140432	+	0.418849i
$716$	−5.54627	+	4.99388i	−0.207274	+	0.186630i
$717$	−3.28245	+	3.31745i	−0.122585	+	0.123892i
$718$	38.5792	+	10.3373i	1.43976	+	0.385783i
$719$	35.8526	+	26.0484i	1.33708	+	0.971443i	0.999546	+	0.0301283i	$0.00959158\pi$
$719$	35.8526	+	26.0484i	1.33708	+	0.971443i	0.337530	+	0.941315i	$0.390408\pi$
$720$	6.56403	−	12.9230i	0.244627	−	0.481611i
$721$	−44.0872	+	32.0313i	−1.64189	+	1.19291i
$722$	−104.005	+	39.9236i	−3.87065	+	1.48580i
$723$	1.68885	−	4.47034i	0.0628091	−	0.166254i
$724$	−10.1510	−	5.86067i	−0.377258	−	0.217810i
$725$	−37.0401	+	20.4720i	−1.37564	+	0.760311i
$726$	−14.5783	+	33.2163i	−0.541050	+	1.23277i
$727$	−37.9719	+	1.99002i	−1.40830	+	0.0738059i	−0.741261	−	0.671217i	$-0.765772\pi$
$727$	−37.9719	+	1.99002i	−1.40830	+	0.0738059i	−0.667039	+	0.745023i	$0.732439\pi$
$728$	−25.5529	−	4.04718i	−0.947054	−	0.149999i
$729$	25.9310	+	7.52222i	0.960407	+	0.278601i
$730$	−30.8907	+	1.32963i	−1.14332	+	0.0492118i
$731$	−0.774211	−	0.0813728i	−0.0286352	−	0.00300968i
$732$	18.7024	+	47.9596i	0.691261	+	1.77264i
$733$	−9.72980	+	25.3470i	−0.359378	+	0.936212i	0.628054	+	0.778170i	$0.283852\pi$
$733$	−9.72980	+	25.3470i	−0.359378	+	0.936212i	−0.987432	+	0.158043i	$0.949482\pi$
$734$	23.2581	+	25.8307i	0.858471	+	0.953429i
$735$	23.2634	+	17.0459i	0.858084	+	0.628746i
$736$	5.24084	−	5.82054i	0.193180	−	0.214548i
$737$	−6.68296	−	13.1160i	−0.246170	−	0.483136i
$738$	−4.56113	+	12.2696i	−0.167897	+	0.451650i
$739$	13.9701	−	4.53917i	0.513900	−	0.166976i	−0.0405753	−	0.999176i	$-0.512919\pi$
$739$	13.9701	−	4.53917i	0.513900	−	0.166976i	0.554475	+	0.832200i	$0.312919\pi$
$740$	−15.1760	−	8.95195i	−0.557881	−	0.329080i
$741$	−20.9628	−	63.3712i	−0.770087	−	2.32800i
$742$	58.2803	+	22.3717i	2.13954	+	0.821292i
$743$	35.5286	−	9.51985i	1.30342	−	0.349249i	0.460675	−	0.887569i	$-0.347607\pi$
$743$	35.5286	−	9.51985i	1.30342	−	0.349249i	0.842741	+	0.538319i	$0.180941\pi$
$744$	1.03084	−	0.00546739i	0.0377925	−	0.000200444i
$745$	−24.3367	−	1.50356i	−0.891629	−	0.0550863i
$746$	−0.159457	−	0.219474i	−0.00583813	−	0.00803550i
$747$	32.3868	+	16.0715i	1.18497	+	0.588025i
$748$	0.618789	+	0.315289i	0.0226252	+	0.0115281i
$749$	−25.6634	−	44.4502i	−0.937719	−	1.62418i
$750$	−31.9664	−	27.1115i	−1.16725	−	0.989972i
$751$	12.5734	−	21.7778i	0.458810	−	0.794682i	−0.540089	−	0.841608i	$-0.681609\pi$
$751$	12.5734	−	21.7778i	0.458810	−	0.794682i	0.998898	+	0.0469263i	$0.0149426\pi$
$752$	9.64574	−	6.26402i	0.351744	−	0.228425i
$753$	29.3462	+	18.8371i	1.06943	+	0.686462i
$754$	34.2087	−	76.8341i	1.24581	−	2.79813i
$755$	19.0880	−	28.8002i	0.694682	−	1.04815i
$756$	−15.5822	+	50.6875i	−0.566720	+	1.84349i
$757$	20.9425	+	20.9425i	0.761168	+	0.761168i	0.976534	−	0.215365i	$-0.0690943\pi$
$757$	20.9425	+	20.9425i	0.761168	+	0.761168i	−0.215365	+	0.976534i	$0.569094\pi$
$758$	−12.8584	+	10.4125i	−0.467037	+	0.378199i
$759$	1.52525	+	1.35877i	0.0553632	+	0.0493201i
$760$	0.260041	−	27.8306i	0.00943266	−	1.00952i
$761$	5.81279	−	27.3470i	0.210713	−	0.991329i	−0.737904	−	0.674905i	$-0.764185\pi$
$761$	5.81279	−	27.3470i	0.210713	−	0.991329i	0.948618	−	0.316424i	$-0.102482\pi$
$762$	28.4546	−	18.6939i	1.03080	−	0.677210i
$763$	10.0120	−	15.4171i	0.362458	−	0.558136i
$764$	19.5613	+	60.2034i	0.707702	+	2.17808i
$765$	−0.752247	+	1.30674i	−0.0271975	+	0.0472454i
$766$	−16.8510	+	51.8620i	−0.608850	+	1.87385i
$767$	−14.5474	−	17.9645i	−0.525276	−	0.648662i
$768$	0.0711699	−	0.465308i	0.00256812	−	0.0167904i
$769$	−5.74230	−	12.8974i	−0.207072	−	0.465092i	0.779916	−	0.625884i	$-0.215262\pi$
$769$	−5.74230	−	12.8974i	−0.207072	−	0.465092i	−0.986988	+	0.160792i	$0.948595\pi$
$770$	−9.78631	+	18.7711i	−0.352674	+	0.676462i
$771$	35.9677	+	11.4761i	1.29534	+	0.413300i
$772$	−2.32305	−	6.05174i	−0.0836083	−	0.217807i
$773$	−20.6705	+	40.5681i	−0.743465	+	1.45913i	0.139761	+	0.990185i	$0.455367\pi$
$773$	−20.6705	+	40.5681i	−0.743465	+	1.45913i	−0.883226	+	0.468947i	$0.844633\pi$
$774$	21.9475	−	4.90897i	0.788886	−	0.176449i
$775$	−0.453890	+	1.95501i	−0.0163042	+	0.0702260i
$776$	−6.32876	+	3.65391i	−0.227189	+	0.131168i
$777$	−18.0731	−	6.82785i	−0.648369	−	0.244948i
$778$	−38.7493	−	31.3786i	−1.38923	−	1.12498i
$779$	−1.76886	−	16.8296i	−0.0633762	−	0.602984i
$780$	47.6632	+	2.69103i	1.70662	+	0.0963545i
$781$	−0.393770	+	3.74647i	−0.0140902	+	0.134059i
$782$	−0.352569	+	0.352569i	−0.0126079	+	0.0126079i
$783$	−37.2623	−	23.3641i	−1.33165	−	0.834963i
$784$	15.3022	+	4.97198i	0.546506	+	0.177571i
$785$	23.2621	+	26.3257i	0.830259	+	0.939604i
$786$	4.43179	−	44.4313i	0.158077	−	1.58481i
$787$	2.03654	−	38.8596i	0.0725949	−	1.38519i	−0.683126	−	0.730300i	$-0.739380\pi$
$787$	2.03654	−	38.8596i	0.0725949	−	1.38519i	0.755721	−	0.654894i	$-0.227287\pi$
$788$	−0.875455	+	16.7047i	−0.0311868	+	0.595080i
$789$	−30.8918	+	13.9507i	−1.09978	+	0.496657i
$790$	−4.48811	−	46.9141i	−0.159680	−	1.66913i
$791$	−20.5126	−	6.66495i	−0.729344	−	0.236978i
$792$	−5.06386	−	0.747065i	−0.179937	−	0.0265458i
$793$	35.9313	−	35.9313i	1.27596	−	1.27596i
$794$	1.63541	−	15.5599i	0.0580385	−	0.552199i
$795$	−28.3563	−	7.72095i	−1.00569	−	0.273834i
$796$	−4.82337	−	45.8913i	−0.170960	−	1.62658i
$797$	35.8670	+	29.0445i	1.27047	+	1.02881i	0.997772	+	0.0667103i	$0.0212503\pi$
$797$	35.8670	+	29.0445i	1.27047	+	1.02881i	0.272701	+	0.962099i	$0.412083\pi$
$798$	−19.3387	−	118.044i	−0.684583	−	4.17872i
$799$	−1.03613	+	0.598211i	−0.0366557	+	0.0211632i
$800$	−35.4113	−	14.3579i	−1.25198	−	0.507629i
$801$	−0.604897	+	0.556382i	−0.0213730	+	0.0196588i
$802$	28.6933	−	56.3138i	1.01320	−	1.98851i
$803$	−2.63448	−	6.86307i	−0.0929690	−	0.242192i
$804$	−43.9988	+	40.0413i	−1.55172	+	1.41215i
$805$	−6.10130	−	6.21639i	−0.215043	−	0.219099i
$806$	−1.62229	−	3.64373i	−0.0571428	−	0.128345i
$807$	−34.1591	+	13.3208i	−1.20246	+	0.468913i
$808$	−1.34647	−	1.66275i	−0.0473685	−	0.0584952i
$809$	−6.68210	+	20.5654i	−0.234930	+	0.723041i	0.762201	+	0.647341i	$0.224119\pi$
$809$	−6.68210	+	20.5654i	−0.234930	+	0.723041i	−0.997131	+	0.0756996i	$0.975881\pi$
$810$	8.55009	−	42.7122i	0.300419	−	1.50075i
$811$	−0.735337	−	2.26313i	−0.0258212	−	0.0794694i	0.937316	−	0.348482i	$-0.113303\pi$
$811$	−0.735337	−	2.26313i	−0.0258212	−	0.0794694i	−0.963137	+	0.269012i	$0.913303\pi$
$812$	47.0461	−	72.4447i	1.65100	−	2.54231i
$813$	−1.57873	−	27.3479i	−0.0553686	−	0.959134i
$814$	1.51976	−	7.14990i	0.0532675	−	0.250604i
$815$	−20.0073	+	27.0035i	−0.700826	+	0.945891i
$816$	−0.170527	+	0.823723i	−0.00596963	+	0.0288361i
$817$	−22.5949	+	18.2970i	−0.790494	+	0.640130i
$818$	34.4495	+	34.4495i	1.20450	+	1.20450i
$819$	51.9982	−	6.02355i	1.81697	−	0.210480i
$820$	11.6608	+	3.24158i	0.407214	+	0.113201i
$821$	13.7768	−	30.9433i	0.480814	−	1.07993i	−0.496481	−	0.868047i	$-0.665375\pi$
$821$	13.7768	−	30.9433i	0.480814	−	1.07993i	0.977296	−	0.211880i	$-0.0679584\pi$
$822$	8.51414	−	4.39521i	0.296965	−	0.153300i
$823$	−28.2925	+	18.3734i	−0.986216	+	0.640456i	−0.933659	−	0.358162i	$-0.883404\pi$
$823$	−28.2925	+	18.3734i	−0.986216	+	0.640456i	−0.0525563	+	0.998618i	$0.516737\pi$
$824$	−10.6293	+	18.4104i	−0.370288	+	0.641357i
$825$	3.69558	−	9.25517i	0.128664	−	0.322224i
$826$	−20.7128	−	35.8756i	−0.720690	−	1.24827i
$827$	−37.5943	−	19.1553i	−1.30728	−	0.666094i	−0.345117	−	0.938560i	$-0.612161\pi$
$827$	−37.5943	−	19.1553i	−1.30728	−	0.666094i	−0.962165	+	0.272466i	$0.912161\pi$
$828$	3.66962	−	7.39492i	0.127528	−	0.256991i
$829$	−5.59854	−	7.70573i	−0.194445	−	0.267631i	0.700651	−	0.713504i	$-0.252893\pi$
$829$	−5.59854	−	7.70573i	−0.194445	−	0.267631i	−0.895096	+	0.445873i	$0.852893\pi$
$830$	21.4114	−	54.2579i	0.743201	−	1.88332i
$831$	5.72712	−	10.0423i	0.198671	−	0.348363i
$832$	54.1880	−	14.5196i	1.87863	−	0.503378i
$833$	−1.56257	−	0.599813i	−0.0541397	−	0.0207823i
$834$	1.85574	−	2.08312i	0.0642589	−	0.0721325i
$835$	−9.48965	+	0.907843i	−0.328403	+	0.0314172i
$836$	24.6678	−	8.01505i	0.853153	−	0.277206i
$837$	−2.00583	+	0.571817i	−0.0693316	+	0.0197649i
$838$	6.08302	+	11.9386i	0.210134	+	0.412412i
$839$	−17.3472	+	19.2660i	−0.598893	+	0.665138i	−0.964023	−	0.265819i	$-0.914358\pi$
$839$	−17.3472	+	19.2660i	−0.598893	+	0.665138i	0.365130	+	0.930956i	$0.381024\pi$
$840$	21.3311	+	4.62420i	0.735992	+	0.159550i
$841$	28.5337	+	31.6899i	0.983922	+	1.09276i
$842$	−20.1173	+	52.4074i	−0.693289	+	1.80608i
$843$	−18.0636	+	22.5502i	−0.622142	+	0.776668i
$844$	49.8360	+	5.23797i	1.71542	+	0.180298i
$845$	−6.31280	−	16.9162i	−0.217167	−	0.581934i
$846$	22.8541	−	25.9300i	0.785740	−	0.891491i
$847$	36.3235	+	5.75307i	1.24809	+	0.197678i
$848$	−16.3733	+	0.858086i	−0.562260	+	0.0294668i
$849$	14.4210	+	19.6290i	0.494926	+	0.673664i
$850$	2.20337	+	1.03076i	0.0755750	+	0.0353548i
$851$	2.60472	+	1.50383i	0.0892885	+	0.0515508i
$852$	15.0241	−	2.46133i	0.514716	−	0.0843238i
$853$	−36.1582	+	13.8798i	−1.23803	+	0.475236i	−0.887280	−	0.461232i	$-0.847408\pi$
$853$	−36.1582	+	13.8798i	−1.23803	+	0.475236i	−0.350753	+	0.936468i	$0.614074\pi$
$854$	73.6718	−	53.5257i	2.52100	−	1.83161i
$855$	14.6435	+	54.3753i	0.500797	+	1.85959i
$856$	−16.1986	−	11.7690i	−0.553658	−	0.402256i
$857$	2.45870	+	0.658807i	0.0839877	+	0.0225044i	0.300568	−	0.953760i	$-0.402824\pi$
$857$	2.45870	+	0.658807i	0.0839877	+	0.0225044i	−0.216580	+	0.976265i	$0.569490\pi$
$858$	5.22731	+	19.1027i	0.178457	+	0.652156i
$859$	3.22266	−	2.90169i	0.109956	−	0.0990045i	−0.612319	−	0.790611i	$-0.709763\pi$
$859$	3.22266	−	2.90169i	0.109956	−	0.0990045i	0.722275	+	0.691606i	$0.243097\pi$
$860$	−6.24068	−	19.8356i	−0.212805	−	0.676387i
$861$	13.2054	+	1.31717i	0.450040	+	0.0448892i
$862$	37.8818	+	24.6007i	1.29026	+	0.837905i
$863$	−21.9053	+	11.1613i	−0.745665	+	0.379935i	−0.785167	−	0.619284i	$-0.787423\pi$
$863$	−21.9053	+	11.1613i	−0.745665	+	0.379935i	0.0395017	+	0.999220i	$0.487423\pi$
$864$	−4.77870	−	39.4218i	−0.162575	−	1.34116i
$865$	−9.22951	−	16.3366i	−0.313813	−	0.555461i
$866$	−2.04631	−	9.62711i	−0.0695363	−	0.327143i
$867$	−7.44774	+	28.3969i	−0.252938	+	0.964410i
$868$	−1.06024	−	3.95686i	−0.0359868	−	0.134305i
$869$	10.2364	−	4.55755i	0.347247	−	0.154604i
$870$	−32.4684	+	63.0915i	−1.10078	+	2.13900i
$871$	53.6483	+	23.8857i	1.81780	+	0.809337i
$872$	1.12182	−	7.08286i	0.0379895	−	0.239856i
$873$	10.3438	−	10.5656i	0.350085	−	0.357592i
$874$			18.6218i			0.629892i
$875$	−18.3654	+	38.3213i	−0.620865	+	1.29550i
$876$	−23.9426	+	17.5901i	−0.808946	+	0.594314i
$877$	18.4722	+	28.4447i	0.623762	+	0.960510i	0.999430	+	0.0337554i	$0.0107467\pi$
$877$	18.4722	+	28.4447i	0.623762	+	0.960510i	−0.375668	+	0.926754i	$0.622587\pi$
$878$	16.3952	−	20.2463i	0.553310	−	0.683280i
$879$	−4.36386	+	13.6770i	−0.147189	+	0.461313i
$880$	0.342840	−	5.54922i	0.0115571	−	0.187064i
$881$	15.5295	−	21.3745i	0.523202	−	0.720126i	−0.462873	−	0.886425i	$-0.653181\pi$
$881$	15.5295	−	21.3745i	0.523202	−	0.720126i	0.986075	+	0.166298i	$0.0531815\pi$
$882$	48.3113	+	2.01828i	1.62672	+	0.0679591i
$883$	29.9681	−	4.74648i	1.00851	−	0.159732i	0.369742	−	0.929135i	$-0.379446\pi$
$883$	29.9681	−	4.74648i	1.00851	−	0.159732i	0.638764	+	0.769403i	$0.279446\pi$
$884$	−2.71000	+	0.576028i	−0.0911472	+	0.0193739i
$885$	11.3991	+	15.8236i	0.383177	+	0.531904i
$886$	−60.6969	−	12.9015i	−2.03915	−	0.433435i
$887$	−10.6573	−	0.558526i	−0.357837	−	0.0187535i	−0.127430	−	0.991848i	$-0.540673\pi$
$887$	−10.6573	−	0.558526i	−0.357837	−	0.0187535i	−0.230408	+	0.973094i	$0.574006\pi$
$888$	−7.52417	+	0.434353i	−0.252495	+	0.0145759i
$889$	−25.6510	−	23.0962i	−0.860305	−	0.774622i
$890$	0.977023	+	0.896386i	0.0327499	+	0.0300469i
$891$	10.2747	−	1.30082i	0.344214	−	0.0435791i
$892$	10.3449	+	65.3149i	0.346371	+	2.18690i
$893$	−11.5649	+	43.1609i	−0.387005	+	1.44432i
$894$	−35.2950	+	20.6280i	−1.18044	+	0.689902i
$895$	−5.51131	−	2.87333i	−0.184223	−	0.0960447i
$896$	42.2077	−	4.43621i	1.41006	−	0.148203i
$897$	−8.14008	−	0.383323i	−0.271789	−	0.0127988i
$898$	−0.662733	−	12.6457i	−0.0221157	−	0.421992i
$899$	3.39755			0.113315
$900$	−40.0193	−	4.53339i	−1.33398	−	0.151113i
$901$	1.70557			0.0568209
$902$	0.262781	+	5.01417i	0.00874967	+	0.166954i
$903$	−10.4589	−	20.2605i	−0.348052	−	0.674226i
$904$	−8.36770	+	0.879481i	−0.278306	+	0.0292511i
$905$	1.61704	−	9.62659i	0.0537523	−	0.319999i
$906$	−0.307241	−	57.9283i	−0.0102074	−	1.92454i
$907$	−0.433717	+	1.61866i	−0.0144014	+	0.0537466i	−0.972753	−	0.231846i	$-0.925524\pi$
$907$	−0.433717	+	1.61866i	−0.0144014	+	0.0537466i	0.958351	+	0.285592i	$0.0921903\pi$
$908$	0.621271	+	3.92255i	0.0206176	+	0.130174i
$909$	3.52902	+	2.50722i	0.117050	+	0.0831593i
$910$	−16.7857	−	82.7656i	−0.556440	−	2.74365i
$911$	−10.6293	−	9.57071i	−0.352166	−	0.317092i	0.473993	−	0.880529i	$-0.342812\pi$
$911$	−10.6293	−	9.57071i	−0.352166	−	0.317092i	−0.826159	+	0.563437i	$0.809479\pi$
$912$	17.2501	+	26.2569i	0.571207	+	0.869452i
$913$	13.8494	+	0.725818i	0.458349	+	0.0240211i
$914$	−38.0576	−	8.08940i	−1.25883	−	0.267574i
$915$	−31.9742	+	28.5567i	−1.05703	+	0.944054i
$916$	8.73151	−	1.85594i	0.288497	−	0.0613220i
$917$	−44.7119	+	7.08167i	−1.47652	+	0.233857i
$918$	0.172454	+	2.52209i	0.00569184	+	0.0832415i
$919$	8.43579	−	11.6109i	0.278271	−	0.383007i	−0.646889	−	0.762584i	$-0.723930\pi$
$919$	8.43579	−	11.6109i	0.278271	−	0.383007i	0.925160	+	0.379577i	$0.123930\pi$
$920$	−3.16070	−	1.24729i	−0.104205	−	0.0411218i
$921$	−27.9103	+	6.08741i	−0.919675	+	0.200587i
$922$	−6.70328	+	8.27786i	−0.220761	+	0.272617i
$923$	−8.18504	−	12.6039i	−0.269414	−	0.414861i
$924$	2.23345	+	20.2177i	0.0734750	+	0.665115i
$925$	2.56584	−	14.4474i	0.0843643	−	0.475027i
$926$		−	33.6266i		−	1.10504i
$927$	10.6912	−	41.6627i	0.351144	−	1.36838i
$928$	−10.1191	+	63.8895i	−0.332176	+	2.09727i
$929$	12.0276	+	5.35503i	0.394613	+	0.175693i	0.594443	−	0.804138i	$-0.297373\pi$
$929$	12.0276	+	5.35503i	0.394613	+	0.175693i	−0.199831	+	0.979830i	$0.564039\pi$
$930$	1.19319	+	3.14631i	0.0391264	+	0.103172i
$931$	−57.1057	+	25.4251i	−1.87156	+	0.833273i
$932$	12.9706	+	48.4068i	0.424865	+	1.58562i
$933$	30.1484	+	29.8303i	0.987014	+	0.976600i
$934$	7.22144	+	33.9742i	0.236293	+	1.11167i
$935$	−0.0658268	+	0.574603i	−0.00215276	+	0.0187915i
$936$	17.5751	−	10.3971i	0.574462	−	0.339841i
$937$	−21.1664	+	10.7848i	−0.691475	+	0.352324i	−0.764156	−	0.645031i	$-0.776844\pi$
$937$	−21.1664	+	10.7848i	−0.691475	+	0.352324i	0.0726812	+	0.997355i	$0.476844\pi$
$938$	88.2617	+	57.3178i	2.88185	+	1.87149i
$939$	−3.18029	−	7.04230i	−0.103785	−	0.229817i
$940$	−25.6780	−	19.0252i	−0.837523	−	0.620534i
$941$	−21.5036	+	19.3620i	−0.700999	+	0.631182i	−0.940532	−	0.339706i	$-0.889672\pi$
$941$	−21.5036	+	19.3620i	−0.700999	+	0.631182i	0.239533	+	0.970888i	$0.423006\pi$
$942$	56.9735	+	14.9426i	1.85630	+	0.486856i
$943$	−1.99560	−	0.534718i	−0.0649855	−	0.0174128i
$944$	8.80211	+	6.39510i	0.286484	+	0.208143i
$945$	−44.0852	+	2.60086i	−1.43409	+	0.0846059i
$946$	6.97910	−	5.07061i	0.226910	−	0.164860i
$947$	−12.4183	+	4.76695i	−0.403541	+	0.154905i	−0.551669	−	0.834063i	$-0.686009\pi$
$947$	−12.4183	+	4.76695i	−0.403541	+	0.154905i	0.148127	+	0.988968i	$0.452675\pi$
$948$	−28.6847	−	35.0410i	−0.931635	−	1.13808i
$949$	25.3981	+	14.6636i	0.824456	+	0.476000i
$950$	85.4093	−	30.9672i	2.77104	−	1.00471i
$951$	59.8705	−	6.61388i	1.94143	−	0.214470i
$952$	−1.26497	+	0.0662942i	−0.0409979	+	0.00214861i
$953$	35.2767	+	5.58728i	1.14272	+	0.180990i	0.698965	−	0.715156i	$-0.253644\pi$
$953$	35.2767	+	5.58728i	1.14272	+	0.180990i	0.443760	+	0.896146i	$0.353644\pi$
$954$	−46.6975	+	15.7225i	−1.51189	+	0.509034i
$955$	−41.2771	+	32.7918i	−1.33570	+	1.06112i
$956$	7.19498	+	0.756223i	0.232702	+	0.0244580i
$957$	−16.6765	−	2.55070i	−0.539073	−	0.0824524i
$958$	26.9829	−	70.2929i	0.871779	−	2.27106i
$959$	−6.50005	−	7.21904i	−0.209898	−	0.233115i
$960$	−46.3338	+	9.65309i	−1.49542	+	0.311552i
$961$	−20.6352	+	22.9178i	−0.665653	+	0.739282i
$962$	13.2387	+	25.9824i	0.426833	+	0.837708i
$963$	37.9731	+	14.1162i	1.22367	+	0.454889i
$964$	−7.04538	+	2.28918i	−0.226916	+	0.0737296i
$965$	4.04538	−	3.57460i	0.130225	−	0.115071i
$966$	−14.3005	−	2.96049i	−0.460112	−	0.0952521i
$967$	13.4581	+	5.16608i	0.432783	+	0.166130i	0.565000	−	0.825091i	$-0.308876\pi$
$967$	13.4581	+	5.16608i	0.432783	+	0.166130i	−0.132217	+	0.991221i	$0.542210\pi$
$968$	13.8576	−	3.71314i	0.445401	−	0.119345i
$969$	−1.64904	−	2.82155i	−0.0529748	−	0.0906414i
$970$	−18.3974	−	15.1847i	−0.590704	−	0.487551i
$971$	24.1952	+	33.3018i	0.776461	+	1.06871i	0.995664	+	0.0930274i	$0.0296544\pi$
$971$	24.1952	+	33.3018i	0.776461	+	1.06871i	−0.219203	+	0.975679i	$0.570346\pi$
$972$	−16.0304	−	38.6638i	−0.514176	−	1.24014i
$973$	−2.52013	−	1.28407i	−0.0807917	−	0.0411654i
$974$	0.849053	+	1.47060i	0.0272054	+	0.0471211i
$975$	11.7784	+	37.9720i	0.377212	+	1.21608i
$976$	−11.9584	+	20.7126i	−0.382780	+	0.662994i
$977$	37.8608	−	24.5871i	1.21127	−	0.786610i	0.228884	−	0.973454i	$-0.426492\pi$
$977$	37.8608	−	24.5871i	1.21127	−	0.786610i	0.982390	+	0.186843i	$0.0598256\pi$
$978$	−2.65049	+	56.2847i	−0.0847534	+	1.79978i
$979$	−0.128224	+	0.287996i	−0.00409806	+	0.00920440i
$980$	−1.92258	−	44.6664i	−0.0614144	−	1.42681i
$981$	1.66963	+	14.4131i	0.0533072	+	0.460175i
$982$	27.1361	+	27.1361i	0.865948	+	0.865948i
$983$	38.4753	−	31.1567i	1.22717	−	0.993745i	0.227372	−	0.973808i	$-0.426987\pi$
$983$	38.4753	−	31.1567i	1.22717	−	0.993745i	0.999801	−	0.0199369i	$-0.00634652\pi$
$984$	4.91509	−	1.62588i	0.156687	−	0.0518311i
$985$	−13.2885	+	4.18083i	−0.423406	+	0.133212i
$986$	0.856166	−	4.02794i	0.0272659	−	0.128276i
$987$	−31.3066	−	15.7429i	−0.996500	−	0.501103i
$988$	−56.3555	+	86.7798i	−1.79291	+	2.76083i
$989$	1.09688	+	3.37584i	0.0348787	+	0.107346i
$990$	−3.49457	−	16.3391i	−0.111065	−	0.519289i
$991$	5.65328	−	17.3990i	0.179582	−	0.552698i	−0.820231	−	0.572033i	$-0.806155\pi$
$991$	5.65328	−	17.3990i	0.179582	−	0.552698i	0.999813	+	0.0193353i	$0.00615499\pi$
$992$	1.93052	+	2.38399i	0.0612939	+	0.0756917i
$993$	−38.7096	−	31.0079i	−1.22841	−	0.984006i
$994$	−10.9542	−	24.6035i	−0.347446	−	0.780376i
$995$	34.4016	−	17.1255i	1.09060	−	0.542916i
$996$	−11.9436	−	54.7604i	−0.378447	−	1.73515i
$997$	−1.92463	−	5.01383i	−0.0609537	−	0.158790i	0.899721	−	0.436465i	$-0.143770\pi$
$997$	−1.92463	−	5.01383i	−0.0609537	−	0.158790i	−0.960675	+	0.277675i	$0.910436\pi$
$998$	9.43320	−	18.5137i	0.298603	−	0.586041i
$999$	14.4259	−	4.94238i	0.456417	−	0.156370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.w.a.167.5	yes	448
3.2	odd	2		675.2.bd.a.17.24		448
9.2	odd	6	inner	225.2.w.a.92.24	✓	448
9.7	even	3		675.2.bd.a.467.5		448
25.3	odd	20	inner	225.2.w.a.203.24	yes	448
75.53	even	20		675.2.bd.a.503.5		448
225.128	even	60	inner	225.2.w.a.128.5	yes	448
225.178	odd	60		675.2.bd.a.278.24		448

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.w.a.92.24	✓	448	9.2	odd	6	inner
225.2.w.a.128.5	yes	448	225.128	even	60	inner
225.2.w.a.167.5	yes	448	1.1	even	1	trivial
225.2.w.a.203.24	yes	448	25.3	odd	20	inner
675.2.bd.a.17.24		448	3.2	odd	2
675.2.bd.a.278.24		448	225.178	odd	60
675.2.bd.a.467.5		448	9.7	even	3
675.2.bd.a.503.5		448	75.53	even	20

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.w (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.113281 - 2.16152i) q^{2} +(0.935625 - 1.45760i) q^{3} +(-2.67031 + 0.280661i) q^{4} +(-0.996494 - 2.00175i) q^{5} +(-3.25663 - 1.85726i) q^{6} +(-0.983733 + 3.67134i) q^{7} +(0.231948 + 1.46446i) q^{8} +(-1.24921 - 2.72754i) q^{9} +O(q^{10})\)	\(q+(-0.113281 - 2.16152i) q^{2} +(0.935625 - 1.45760i) q^{3} +(-2.67031 + 0.280661i) q^{4} +(-0.996494 - 2.00175i) q^{5} +(-3.25663 - 1.85726i) q^{6} +(-0.983733 + 3.67134i) q^{7} +(0.231948 + 1.46446i) q^{8} +(-1.24921 - 2.72754i) q^{9} +(-4.21395 + 2.38071i) q^{10} +(-0.855167 - 0.769996i) q^{11} +(-2.08932 + 4.15485i) q^{12} +(4.58443 + 0.240260i) q^{13} +(8.04713 + 1.71047i) q^{14} +(-3.85010 - 0.420393i) q^{15} +(-2.11349 + 0.449237i) q^{16} +(0.222002 - 0.0351616i) q^{17} +(-5.75413 + 3.00918i) q^{18} +(4.93421 - 6.79136i) q^{19} +(3.22276 + 5.06561i) q^{20} +(4.43095 + 4.86889i) q^{21} +(-1.56749 + 1.93569i) q^{22} +(-0.558183 - 0.859526i) q^{23} +(2.35162 + 1.03210i) q^{24} +(-3.01400 + 3.98946i) q^{25} -9.93658i q^{26} +(-5.14446 - 0.731098i) q^{27} +(1.59647 - 10.0797i) q^{28} +(7.73245 + 3.44271i) q^{29} +(-0.472549 + 8.36971i) q^{30} +(0.366699 - 0.163265i) q^{31} +(1.97797 + 7.38187i) q^{32} +(-1.92246 + 0.526067i) q^{33} +(-0.101151 - 0.475879i) q^{34} +(8.32938 - 1.68928i) q^{35} +(4.10130 + 6.93277i) q^{36} +(-2.61483 + 1.33232i) q^{37} +(-15.2386 - 9.89608i) q^{38} +(4.63951 - 6.45749i) q^{39} +(2.70035 - 1.92363i) q^{40} +(1.49808 - 1.34888i) q^{41} +(10.0223 - 10.1292i) q^{42} +(-3.34543 - 0.896406i) q^{43} +(2.49967 + 1.81612i) q^{44} +(-4.21502 + 5.21859i) q^{45} +(-1.79465 + 1.30389i) q^{46} +(-4.96935 + 1.90755i) q^{47} +(-1.32263 + 3.50095i) q^{48} +(-6.44883 - 3.72323i) q^{49} +(8.96475 + 6.06290i) q^{50} +(0.156459 - 0.356488i) q^{51} +(-12.3093 + 0.645103i) q^{52} +(7.49469 + 1.18704i) q^{53} +(-0.997518 + 11.2027i) q^{54} +(-0.689170 + 2.47913i) q^{55} +(-5.60471 - 0.589079i) q^{56} +(-5.28253 - 13.5463i) q^{57} +(6.56556 - 17.1039i) q^{58} +(-3.36933 - 3.74202i) q^{59} +(10.3989 + 0.0420082i) q^{60} +(7.40659 - 8.22585i) q^{61} +(-0.394441 - 0.774133i) q^{62} +(11.2426 - 1.90311i) q^{63} +(11.6221 - 3.77625i) q^{64} +(-4.08742 - 9.41630i) q^{65} +(1.35488 + 4.09586i) q^{66} +(11.9425 + 4.58430i) q^{67} +(-0.582945 + 0.156200i) q^{68} +(-1.77510 + 0.00941479i) q^{69} +(-4.59498 - 17.8128i) q^{70} +(-1.92420 - 2.64843i) q^{71} +(3.70463 - 2.46207i) q^{72} +(5.69206 + 2.90025i) q^{73} +(3.17605 + 5.50109i) q^{74} +(2.99508 + 8.12585i) q^{75} +(-11.2698 + 19.5199i) q^{76} +(3.66817 - 2.38214i) q^{77} +(-14.4836 - 9.29691i) q^{78} +(-3.96054 + 8.89551i) q^{79} +(3.00534 + 3.78302i) q^{80} +(-5.87894 + 6.81455i) q^{81} +(-3.08533 - 3.08533i) q^{82} +(-9.36596 + 7.58441i) q^{83} +(-13.1985 - 11.7578i) q^{84} +(-0.291608 - 0.409353i) q^{85} +(-1.55863 + 7.33278i) q^{86} +(12.2528 - 8.04976i) q^{87} +(0.929276 - 1.43096i) q^{88} +(-0.0846567 - 0.260547i) q^{89} +(11.7576 + 8.51969i) q^{90} +(-5.39193 + 16.5947i) q^{91} +(1.73176 + 2.13854i) q^{92} +(0.105117 - 0.687255i) q^{93} +(4.68615 + 10.5253i) q^{94} +(-18.5115 - 3.10950i) q^{95} +(12.6105 + 4.02357i) q^{96} +(1.76628 + 4.60131i) q^{97} +(-7.31733 + 14.3611i) q^{98} +(-1.03191 + 3.29439i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more