LMFDB - Embedded newform 285.2.i.d.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(106,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("285.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	285.121
Dual form			285.2.i.d.106.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20711 - 2.09077i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.20711 - 2.09077i) q^{6} -3.82843 q^{7} +4.41421 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.20711 - 2.09077i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.20711 - 2.09077i) q^{6} -3.82843 q^{7} +4.41421 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.20711 - 2.09077i) q^{10} +2.82843 q^{11} -3.82843 q^{12} +(-1.91421 + 3.31552i) q^{13} +(4.62132 + 8.00436i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(-1.50000 - 2.59808i) q^{16} +(3.41421 + 5.91359i) q^{17} +2.41421 q^{18} +(4.00000 + 1.73205i) q^{19} -3.82843 q^{20} +(-1.91421 - 3.31552i) q^{21} +(-3.41421 - 5.91359i) q^{22} +(-2.41421 + 4.18154i) q^{23} +(2.20711 + 3.82282i) q^{24} +(-0.500000 + 0.866025i) q^{25} +9.24264 q^{26} -1.00000 q^{27} +(7.32843 - 12.6932i) q^{28} +(0.828427 - 1.43488i) q^{29} +2.41421 q^{30} -5.00000 q^{31} +(0.792893 - 1.37333i) q^{32} +(1.41421 + 2.44949i) q^{33} +(8.24264 - 14.2767i) q^{34} +(-1.91421 - 3.31552i) q^{35} +(-1.91421 - 3.31552i) q^{36} -7.82843 q^{37} +(-1.20711 - 10.4539i) q^{38} -3.82843 q^{39} +(2.20711 + 3.82282i) q^{40} +(1.41421 + 2.44949i) q^{41} +(-4.62132 + 8.00436i) q^{42} +(-1.08579 - 1.88064i) q^{43} +(-5.41421 + 9.37769i) q^{44} -1.00000 q^{45} +11.6569 q^{46} +(4.41421 - 7.64564i) q^{47} +(1.50000 - 2.59808i) q^{48} +7.65685 q^{49} +2.41421 q^{50} +(-3.41421 + 5.91359i) q^{51} +(-7.32843 - 12.6932i) q^{52} +(1.00000 - 1.73205i) q^{53} +(1.20711 + 2.09077i) q^{54} +(1.41421 + 2.44949i) q^{55} -16.8995 q^{56} +(0.500000 + 4.33013i) q^{57} -4.00000 q^{58} +(-1.91421 - 3.31552i) q^{60} +(-7.15685 + 12.3960i) q^{61} +(6.03553 + 10.4539i) q^{62} +(1.91421 - 3.31552i) q^{63} -9.82843 q^{64} -3.82843 q^{65} +(3.41421 - 5.91359i) q^{66} +(5.74264 - 9.94655i) q^{67} -26.1421 q^{68} -4.82843 q^{69} +(-4.62132 + 8.00436i) q^{70} +(-5.00000 - 8.66025i) q^{71} +(-2.20711 + 3.82282i) q^{72} +(3.74264 + 6.48244i) q^{73} +(9.44975 + 16.3674i) q^{74} -1.00000 q^{75} +(-13.3995 + 9.94655i) q^{76} -10.8284 q^{77} +(4.62132 + 8.00436i) q^{78} +(7.32843 + 12.6932i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.41421 - 5.91359i) q^{82} -8.00000 q^{83} +14.6569 q^{84} +(-3.41421 + 5.91359i) q^{85} +(-2.62132 + 4.54026i) q^{86} +1.65685 q^{87} +12.4853 q^{88} +(2.24264 - 3.88437i) q^{89} +(1.20711 + 2.09077i) q^{90} +(7.32843 - 12.6932i) q^{91} +(-9.24264 - 16.0087i) q^{92} +(-2.50000 - 4.33013i) q^{93} -21.3137 q^{94} +(0.500000 + 4.33013i) q^{95} +1.58579 q^{96} +(3.00000 + 5.19615i) q^{97} +(-9.24264 - 16.0087i) q^{98} +(-1.41421 + 2.44949i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 12 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{12} - 2 q^{13} + 10 q^{14} - 2 q^{15} - 6 q^{16} + 8 q^{17} + 4 q^{18} + 16 q^{19} - 4 q^{20} - 2 q^{21} - 8 q^{22} - 4 q^{23} + 6 q^{24} - 2 q^{25} + 20 q^{26} - 4 q^{27} + 18 q^{28} - 8 q^{29} + 4 q^{30} - 20 q^{31} + 6 q^{32} + 16 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} - 2 q^{38} - 4 q^{39} + 6 q^{40} - 10 q^{42} - 10 q^{43} - 16 q^{44} - 4 q^{45} + 24 q^{46} + 12 q^{47} + 6 q^{48} + 8 q^{49} + 4 q^{50} - 8 q^{51} - 18 q^{52} + 4 q^{53} + 2 q^{54} - 28 q^{56} + 2 q^{57} - 16 q^{58} - 2 q^{60} - 6 q^{61} + 10 q^{62} + 2 q^{63} - 28 q^{64} - 4 q^{65} + 8 q^{66} + 6 q^{67} - 48 q^{68} - 8 q^{69} - 10 q^{70} - 20 q^{71} - 6 q^{72} - 2 q^{73} + 18 q^{74} - 4 q^{75} - 14 q^{76} - 32 q^{77} + 10 q^{78} + 18 q^{79} + 6 q^{80} - 2 q^{81} + 8 q^{82} - 32 q^{83} + 36 q^{84} - 8 q^{85} - 2 q^{86} - 16 q^{87} + 16 q^{88} - 8 q^{89} + 2 q^{90} + 18 q^{91} - 20 q^{92} - 10 q^{93} - 40 q^{94} + 2 q^{95} + 12 q^{96} + 12 q^{97} - 20 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 12 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^12 - 2 * q^13 + 10 * q^14 - 2 * q^15 - 6 * q^16 + 8 * q^17 + 4 * q^18 + 16 * q^19 - 4 * q^20 - 2 * q^21 - 8 * q^22 - 4 * q^23 + 6 * q^24 - 2 * q^25 + 20 * q^26 - 4 * q^27 + 18 * q^28 - 8 * q^29 + 4 * q^30 - 20 * q^31 + 6 * q^32 + 16 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 - 2 * q^38 - 4 * q^39 + 6 * q^40 - 10 * q^42 - 10 * q^43 - 16 * q^44 - 4 * q^45 + 24 * q^46 + 12 * q^47 + 6 * q^48 + 8 * q^49 + 4 * q^50 - 8 * q^51 - 18 * q^52 + 4 * q^53 + 2 * q^54 - 28 * q^56 + 2 * q^57 - 16 * q^58 - 2 * q^60 - 6 * q^61 + 10 * q^62 + 2 * q^63 - 28 * q^64 - 4 * q^65 + 8 * q^66 + 6 * q^67 - 48 * q^68 - 8 * q^69 - 10 * q^70 - 20 * q^71 - 6 * q^72 - 2 * q^73 + 18 * q^74 - 4 * q^75 - 14 * q^76 - 32 * q^77 + 10 * q^78 + 18 * q^79 + 6 * q^80 - 2 * q^81 + 8 * q^82 - 32 * q^83 + 36 * q^84 - 8 * q^85 - 2 * q^86 - 16 * q^87 + 16 * q^88 - 8 * q^89 + 2 * q^90 + 18 * q^91 - 20 * q^92 - 10 * q^93 - 40 * q^94 + 2 * q^95 + 12 * q^96 + 12 * q^97 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.20711	−	2.09077i	−0.853553	−	1.47840i	−0.877981	−	0.478696i	$-0.841110\pi$
$2$	−1.20711	−	2.09077i	−0.853553	−	1.47840i	0.0244272	−	0.999702i	$-0.492224\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.91421	+	3.31552i	−0.957107	+	1.65776i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	1.20711	−	2.09077i	0.492799	−	0.853553i
$7$	−3.82843			−1.44701			−0.723505	−	0.690319i	$-0.757470\pi$
$7$	−3.82843			−1.44701			−0.723505	+	0.690319i	$0.757470\pi$
$8$	4.41421			1.56066
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.20711	−	2.09077i	0.381721	−	0.661160i
$11$	2.82843			0.852803			0.426401	−	0.904534i	$-0.359781\pi$
$11$	2.82843			0.852803			0.426401	+	0.904534i	$0.359781\pi$
$12$	−3.82843			−1.10517
$13$	−1.91421	+	3.31552i	−0.530907	+	0.919558i	0.468442	+	0.883494i	$0.344815\pi$
$13$	−1.91421	+	3.31552i	−0.530907	+	0.919558i	−0.999349	+	0.0360643i	$0.988518\pi$
$14$	4.62132	+	8.00436i	1.23510	+	2.13926i
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$	−1.50000	−	2.59808i	−0.375000	−	0.649519i
$17$	3.41421	+	5.91359i	0.828068	+	1.43426i	0.899551	+	0.436815i	$0.143893\pi$
$17$	3.41421	+	5.91359i	0.828068	+	1.43426i	−0.0714831	+	0.997442i	$0.522773\pi$
$18$	2.41421			0.569036
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$20$	−3.82843			−0.856062
$21$	−1.91421	−	3.31552i	−0.417716	−	0.723505i
$22$	−3.41421	−	5.91359i	−0.727913	−	1.26078i
$23$	−2.41421	+	4.18154i	−0.503398	+	0.871911i	0.496594	+	0.867983i	$0.334584\pi$
$23$	−2.41421	+	4.18154i	−0.503398	+	0.871911i	−0.999992	+	0.00392850i	$0.998750\pi$
$24$	2.20711	+	3.82282i	0.450524	+	0.780330i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	9.24264			1.81263
$27$	−1.00000			−0.192450
$28$	7.32843	−	12.6932i	1.38494	−	2.39879i
$29$	0.828427	−	1.43488i	0.153835	−	0.266450i	−0.778799	−	0.627273i	$-0.784171\pi$
$29$	0.828427	−	1.43488i	0.153835	−	0.266450i	0.932634	+	0.360823i	$0.117504\pi$
$30$	2.41421			0.440773
$31$	−5.00000			−0.898027			−0.449013	−	0.893525i	$-0.648224\pi$
$31$	−5.00000			−0.898027			−0.449013	+	0.893525i	$0.648224\pi$
$32$	0.792893	−	1.37333i	0.140165	−	0.242773i
$33$	1.41421	+	2.44949i	0.246183	+	0.426401i
$34$	8.24264	−	14.2767i	1.41360	−	2.44843i
$35$	−1.91421	−	3.31552i	−0.323561	−	0.560424i
$36$	−1.91421	−	3.31552i	−0.319036	−	0.552586i
$37$	−7.82843			−1.28699			−0.643493	−	0.765452i	$-0.722515\pi$
$37$	−7.82843			−1.28699			−0.643493	+	0.765452i	$0.722515\pi$
$38$	−1.20711	−	10.4539i	−0.195819	−	1.69584i
$39$	−3.82843			−0.613039
$40$	2.20711	+	3.82282i	0.348974	+	0.604441i
$41$	1.41421	+	2.44949i	0.220863	+	0.382546i	0.955070	−	0.296379i	$-0.0957793\pi$
$41$	1.41421	+	2.44949i	0.220863	+	0.382546i	−0.734207	+	0.678925i	$0.762446\pi$
$42$	−4.62132	+	8.00436i	−0.713085	+	1.23510i
$43$	−1.08579	−	1.88064i	−0.165581	−	0.286794i	0.771281	−	0.636495i	$-0.219617\pi$
$43$	−1.08579	−	1.88064i	−0.165581	−	0.286794i	−0.936861	+	0.349701i	$0.886283\pi$
$44$	−5.41421	+	9.37769i	−0.816223	+	1.41374i
$45$	−1.00000			−0.149071
$46$	11.6569			1.71871
$47$	4.41421	−	7.64564i	0.643879	−	1.11523i	−0.340680	−	0.940179i	$-0.610657\pi$
$47$	4.41421	−	7.64564i	0.643879	−	1.11523i	0.984559	−	0.175052i	$-0.0560094\pi$
$48$	1.50000	−	2.59808i	0.216506	−	0.375000i
$49$	7.65685			1.09384
$50$	2.41421			0.341421
$51$	−3.41421	+	5.91359i	−0.478086	+	0.828068i
$52$	−7.32843	−	12.6932i	−1.01627	−	1.76023i
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	−0.789136	−	0.614218i	$-0.789471\pi$
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	0.926497	+	0.376303i	$0.122805\pi$
$54$	1.20711	+	2.09077i	0.164266	+	0.284518i
$55$	1.41421	+	2.44949i	0.190693	+	0.330289i
$56$	−16.8995			−2.25829
$57$	0.500000	+	4.33013i	0.0662266	+	0.573539i
$58$	−4.00000			−0.525226
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	−1.91421	−	3.31552i	−0.247124	−	0.428031i
$61$	−7.15685	+	12.3960i	−0.916341	+	1.58715i	−0.111416	+	0.993774i	$0.535539\pi$
$61$	−7.15685	+	12.3960i	−0.916341	+	1.58715i	−0.804926	+	0.593376i	$0.797795\pi$
$62$	6.03553	+	10.4539i	0.766514	+	1.32764i
$63$	1.91421	−	3.31552i	0.241168	−	0.417716i
$64$	−9.82843			−1.22855
$65$	−3.82843			−0.474858
$66$	3.41421	−	5.91359i	0.420261	−	0.727913i
$67$	5.74264	−	9.94655i	0.701575	−	1.21516i	−0.266338	−	0.963880i	$-0.585814\pi$
$67$	5.74264	−	9.94655i	0.701575	−	1.21516i	0.967913	−	0.251284i	$-0.0808529\pi$
$68$	−26.1421			−3.17020
$69$	−4.82843			−0.581274
$70$	−4.62132	+	8.00436i	−0.552353	+	0.956704i
$71$	−5.00000	−	8.66025i	−0.593391	−	1.02778i	−0.993772	−	0.111434i	$-0.964456\pi$
$71$	−5.00000	−	8.66025i	−0.593391	−	1.02778i	0.400381	−	0.916349i	$-0.368878\pi$
$72$	−2.20711	+	3.82282i	−0.260110	+	0.450524i
$73$	3.74264	+	6.48244i	0.438043	+	0.758713i	0.997539	−	0.0701207i	$-0.0223384\pi$
$73$	3.74264	+	6.48244i	0.438043	+	0.758713i	−0.559496	+	0.828833i	$0.689005\pi$
$74$	9.44975	+	16.3674i	1.09851	+	1.90268i
$75$	−1.00000			−0.115470
$76$	−13.3995	+	9.94655i	−1.53703	+	1.14095i
$77$	−10.8284			−1.23401
$78$	4.62132	+	8.00436i	0.523261	+	0.906315i
$79$	7.32843	+	12.6932i	0.824512	+	1.42810i	0.902291	+	0.431127i	$0.141884\pi$
$79$	7.32843	+	12.6932i	0.824512	+	1.42810i	−0.0777789	+	0.996971i	$0.524783\pi$
$80$	1.50000	−	2.59808i	0.167705	−	0.290474i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.41421	−	5.91359i	0.377037	−	0.653047i
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$	14.6569			1.59919
$85$	−3.41421	+	5.91359i	−0.370323	+	0.641419i
$86$	−2.62132	+	4.54026i	−0.282664	+	0.489589i
$87$	1.65685			0.177633
$88$	12.4853			1.33094
$89$	2.24264	−	3.88437i	0.237719	−	0.411742i	−0.722340	−	0.691538i	$-0.756933\pi$
$89$	2.24264	−	3.88437i	0.237719	−	0.411742i	0.960060	+	0.279796i	$0.0902668\pi$
$90$	1.20711	+	2.09077i	0.127240	+	0.220387i
$91$	7.32843	−	12.6932i	0.768228	−	1.33061i
$92$	−9.24264	−	16.0087i	−0.963612	−	1.66902i
$93$	−2.50000	−	4.33013i	−0.259238	−	0.449013i
$94$	−21.3137			−2.19834
$95$	0.500000	+	4.33013i	0.0512989	+	0.444262i
$96$	1.58579			0.161849
$97$	3.00000	+	5.19615i	0.304604	+	0.527589i	0.977173	−	0.212445i	$-0.0681426\pi$
$97$	3.00000	+	5.19615i	0.304604	+	0.527589i	−0.672569	+	0.740034i	$0.734809\pi$
$98$	−9.24264	−	16.0087i	−0.933648	−	1.61713i
$99$	−1.41421	+	2.44949i	−0.142134	+	0.246183i
$100$	−1.91421	−	3.31552i	−0.191421	−	0.331552i
$101$	8.07107	−	13.9795i	0.803101	−	1.39101i	−0.114464	−	0.993427i	$-0.536515\pi$
$101$	8.07107	−	13.9795i	0.803101	−	1.39101i	0.917565	−	0.397585i	$-0.130152\pi$
$102$	16.4853			1.63229
$103$	4.17157			0.411037			0.205519	−	0.978653i	$-0.434112\pi$
$103$	4.17157			0.411037			0.205519	+	0.978653i	$0.434112\pi$
$104$	−8.44975	+	14.6354i	−0.828566	+	1.43512i
$105$	1.91421	−	3.31552i	0.186808	−	0.323561i
$106$	−4.82843			−0.468978
$107$	14.0000			1.35343			0.676716	−	0.736245i	$-0.263403\pi$
$107$	14.0000			1.35343			0.676716	+	0.736245i	$0.263403\pi$
$108$	1.91421	−	3.31552i	0.184195	−	0.319036i
$109$	−2.65685	−	4.60181i	−0.254480	−	0.440773i	0.710274	−	0.703926i	$-0.248571\pi$
$109$	−2.65685	−	4.60181i	−0.254480	−	0.440773i	−0.964754	+	0.263152i	$0.915238\pi$
$110$	3.41421	−	5.91359i	0.325532	−	0.563839i
$111$	−3.91421	−	6.77962i	−0.371521	−	0.643493i
$112$	5.74264	+	9.94655i	0.542629	+	0.939860i
$113$	4.00000			0.376288			0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000			0.376288			0.188144	+	0.982141i	$0.439753\pi$
$114$	8.44975	−	6.27231i	0.791391	−	0.587456i
$115$	−4.82843			−0.450253
$116$	3.17157	+	5.49333i	0.294473	+	0.510042i
$117$	−1.91421	−	3.31552i	−0.176969	−	0.306519i
$118$		0			0
$119$	−13.0711	−	22.6398i	−1.19822	−	2.07538i
$120$	−2.20711	+	3.82282i	−0.201480	+	0.348974i
$121$	−3.00000			−0.272727
$122$	34.5563			3.12858
$123$	−1.41421	+	2.44949i	−0.127515	+	0.220863i
$124$	9.57107	−	16.5776i	0.859507	−	1.48871i
$125$	−1.00000			−0.0894427
$126$	−9.24264			−0.823400
$127$	10.4853	−	18.1610i	0.930418	−	1.61153i	0.147811	−	0.989016i	$-0.452777\pi$
$127$	10.4853	−	18.1610i	0.930418	−	1.61153i	0.782607	−	0.622516i	$-0.213889\pi$
$128$	10.2782	+	17.8023i	0.908471	+	1.57352i
$129$	1.08579	−	1.88064i	0.0955982	−	0.165581i
$130$	4.62132	+	8.00436i	0.405317	+	0.702029i
$131$	5.24264	+	9.08052i	0.458052	+	0.793369i	0.998858	−	0.0477784i	$-0.0152141\pi$
$131$	5.24264	+	9.08052i	0.458052	+	0.793369i	−0.540806	+	0.841147i	$0.681881\pi$
$132$	−10.8284			−0.942494
$133$	−15.3137	−	6.63103i	−1.32787	−	0.574983i
$134$	−27.7279			−2.39533
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	15.0711	+	26.1039i	1.29233	+	2.23839i
$137$	−3.24264	+	5.61642i	−0.277037	+	0.479843i	−0.970647	−	0.240508i	$-0.922686\pi$
$137$	−3.24264	+	5.61642i	−0.277037	+	0.479843i	0.693610	+	0.720351i	$0.256019\pi$
$138$	5.82843	+	10.0951i	0.496149	+	0.859355i
$139$	−3.15685	+	5.46783i	−0.267761	+	0.463775i	−0.968283	−	0.249855i	$-0.919617\pi$
$139$	−3.15685	+	5.46783i	−0.267761	+	0.463775i	0.700522	+	0.713630i	$0.252950\pi$
$140$	14.6569			1.23873
$141$	8.82843			0.743488
$142$	−12.0711	+	20.9077i	−1.01298	+	1.75454i
$143$	−5.41421	+	9.37769i	−0.452759	+	0.784202i
$144$	3.00000			0.250000
$145$	1.65685			0.137594
$146$	9.03553	−	15.6500i	0.747786	−	1.29520i
$147$	3.82843	+	6.63103i	0.315763	+	0.546918i
$148$	14.9853	−	25.9553i	1.23178	−	2.13351i
$149$	3.41421	+	5.91359i	0.279703	+	0.484460i	0.971311	−	0.237813i	$-0.0764306\pi$
$149$	3.41421	+	5.91359i	0.279703	+	0.484460i	−0.691608	+	0.722273i	$0.743097\pi$
$150$	1.20711	+	2.09077i	0.0985599	+	0.170711i
$151$	21.6569			1.76241			0.881205	−	0.472735i	$-0.156733\pi$
$151$	21.6569			1.76241			0.881205	+	0.472735i	$0.156733\pi$
$152$	17.6569	+	7.64564i	1.43216	+	0.620143i
$153$	−6.82843			−0.552046
$154$	13.0711	+	22.6398i	1.05330	+	1.82436i
$155$	−2.50000	−	4.33013i	−0.200805	−	0.347804i
$156$	7.32843	−	12.6932i	0.586744	−	1.01627i
$157$	7.08579	+	12.2729i	0.565507	+	0.979487i	0.997002	+	0.0773721i	$0.0246529\pi$
$157$	7.08579	+	12.2729i	0.565507	+	0.979487i	−0.431495	+	0.902115i	$0.642014\pi$
$158$	17.6924	−	30.6441i	1.40753	−	2.43791i
$159$	2.00000			0.158610
$160$	1.58579			0.125367
$161$	9.24264	−	16.0087i	0.728422	−	1.26166i
$162$	−1.20711	+	2.09077i	−0.0948393	+	0.164266i
$163$	−13.1421			−1.02937			−0.514686	−	0.857379i	$-0.672091\pi$
$163$	−13.1421			−1.02937			−0.514686	+	0.857379i	$0.672091\pi$
$164$	−10.8284			−0.845558
$165$	−1.41421	+	2.44949i	−0.110096	+	0.190693i
$166$	9.65685	+	16.7262i	0.749517	+	1.29820i
$167$	−4.48528	+	7.76874i	−0.347081	+	0.601163i	−0.985730	−	0.168336i	$-0.946161\pi$
$167$	−4.48528	+	7.76874i	−0.347081	+	0.601163i	0.638648	+	0.769499i	$0.279494\pi$
$168$	−8.44975	−	14.6354i	−0.651912	−	1.12915i
$169$	−0.828427	−	1.43488i	−0.0637252	−	0.110375i
$170$	16.4853			1.26436
$171$	−3.50000	+	2.59808i	−0.267652	+	0.198680i
$172$	8.31371			0.633914
$173$	7.65685	+	13.2621i	0.582140	+	1.00830i	0.995225	+	0.0976036i	$0.0311177\pi$
$173$	7.65685	+	13.2621i	0.582140	+	1.00830i	−0.413086	+	0.910692i	$0.635549\pi$
$174$	−2.00000	−	3.46410i	−0.151620	−	0.262613i
$175$	1.91421	−	3.31552i	0.144701	−	0.250629i
$176$	−4.24264	−	7.34847i	−0.319801	−	0.553912i
$177$		0			0
$178$	−10.8284			−0.811625
$179$	−12.1421			−0.907546			−0.453773	−	0.891117i	$-0.649922\pi$
$179$	−12.1421			−0.907546			−0.453773	+	0.891117i	$0.649922\pi$
$180$	1.91421	−	3.31552i	0.142677	−	0.247124i
$181$	−1.34315	+	2.32640i	−0.0998352	+	0.172920i	−0.911616	−	0.411042i	$-0.865165\pi$
$181$	−1.34315	+	2.32640i	−0.0998352	+	0.172920i	0.811781	+	0.583962i	$0.198498\pi$
$182$	−35.3848			−2.62289
$183$	−14.3137			−1.05810
$184$	−10.6569	+	18.4582i	−0.785634	+	1.36076i
$185$	−3.91421	−	6.77962i	−0.287779	−	0.498447i
$186$	−6.03553	+	10.4539i	−0.442547	+	0.766514i
$187$	9.65685	+	16.7262i	0.706179	+	1.22314i
$188$	16.8995	+	29.2708i	1.23252	+	2.13479i
$189$	3.82843			0.278477
$190$	8.44975	−	6.27231i	0.613009	−	0.455041i
$191$	−11.1716			−0.808347			−0.404173	−	0.914682i	$-0.632441\pi$
$191$	−11.1716			−0.808347			−0.404173	+	0.914682i	$0.632441\pi$
$192$	−4.91421	−	8.51167i	−0.354653	−	0.614277i
$193$	−7.39949	−	12.8163i	−0.532627	−	0.922538i	−0.999274	−	0.0380938i	$-0.987871\pi$
$193$	−7.39949	−	12.8163i	−0.532627	−	0.922538i	0.466647	−	0.884444i	$-0.345462\pi$
$194$	7.24264	−	12.5446i	0.519991	−	0.900651i
$195$	−1.91421	−	3.31552i	−0.137080	−	0.237429i
$196$	−14.6569	+	25.3864i	−1.04692	+	1.81332i
$197$	6.34315			0.451930			0.225965	−	0.974135i	$-0.427446\pi$
$197$	6.34315			0.451930			0.225965	+	0.974135i	$0.427446\pi$
$198$	6.82843			0.485275
$199$	8.50000	−	14.7224i	0.602549	−	1.04365i	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	8.50000	−	14.7224i	0.602549	−	1.04365i	0.992434	−	0.122782i	$-0.0391815\pi$
$200$	−2.20711	+	3.82282i	−0.156066	+	0.270314i
$201$	11.4853			0.810109
$202$	−38.9706			−2.74196
$203$	−3.17157	+	5.49333i	−0.222601	+	0.385556i
$204$	−13.0711	−	22.6398i	−0.915158	−	1.58510i
$205$	−1.41421	+	2.44949i	−0.0987730	+	0.171080i
$206$	−5.03553	−	8.72180i	−0.350842	−	0.607677i
$207$	−2.41421	−	4.18154i	−0.167799	−	0.290637i
$208$	11.4853			0.796361
$209$	11.3137	+	4.89898i	0.782586	+	0.338869i
$210$	−9.24264			−0.637803
$211$	−11.1569	−	19.3242i	−0.768070	−	1.33034i	−0.938608	−	0.344984i	$-0.887884\pi$
$211$	−11.1569	−	19.3242i	−0.768070	−	1.33034i	0.170539	−	0.985351i	$-0.445449\pi$
$212$	3.82843	+	6.63103i	0.262937	+	0.455421i
$213$	5.00000	−	8.66025i	0.342594	−	0.593391i
$214$	−16.8995	−	29.2708i	−1.15523	−	2.00091i
$215$	1.08579	−	1.88064i	0.0740500	−	0.128258i
$216$	−4.41421			−0.300349
$217$	19.1421			1.29945
$218$	−6.41421	+	11.1097i	−0.434425	+	0.752447i
$219$	−3.74264	+	6.48244i	−0.252904	+	0.438043i
$220$	−10.8284			−0.730052
$221$	−26.1421			−1.75851
$222$	−9.44975	+	16.3674i	−0.634226	+	1.09851i
$223$	−0.0857864	−	0.148586i	−0.00574468	−	0.00995009i	0.863139	−	0.504967i	$-0.168495\pi$
$223$	−0.0857864	−	0.148586i	−0.00574468	−	0.00995009i	−0.868883	+	0.495017i	$0.835162\pi$
$224$	−3.03553	+	5.25770i	−0.202820	+	0.351295i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−4.82843	−	8.36308i	−0.321182	−	0.556304i
$227$	14.9706			0.993631			0.496816	−	0.867856i	$-0.334503\pi$
$227$	14.9706			0.993631			0.496816	+	0.867856i	$0.334503\pi$
$228$	−15.3137	−	6.63103i	−1.01418	−	0.439151i
$229$	6.65685			0.439897			0.219949	−	0.975511i	$-0.429411\pi$
$229$	6.65685			0.439897			0.219949	+	0.975511i	$0.429411\pi$
$230$	5.82843	+	10.0951i	0.384315	+	0.665653i
$231$	−5.41421	−	9.37769i	−0.356229	−	0.617007i
$232$	3.65685	−	6.33386i	0.240084	−	0.415838i
$233$	1.34315	+	2.32640i	0.0879924	+	0.152407i	0.906662	−	0.421857i	$-0.138622\pi$
$233$	1.34315	+	2.32640i	0.0879924	+	0.152407i	−0.818670	+	0.574264i	$0.805288\pi$
$234$	−4.62132	+	8.00436i	−0.302105	+	0.523261i
$235$	8.82843			0.575903
$236$		0			0
$237$	−7.32843	+	12.6932i	−0.476032	+	0.824512i
$238$	−31.5563	+	54.6572i	−2.04549	+	3.54290i
$239$	20.6274			1.33428			0.667138	−	0.744934i	$-0.267519\pi$
$239$	20.6274			1.33428			0.667138	+	0.744934i	$0.267519\pi$
$240$	3.00000			0.193649
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	−0.935242	−	0.354010i	$-0.884818\pi$
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	0.774202	+	0.632938i	$0.218151\pi$
$242$	3.62132	+	6.27231i	0.232787	+	0.403199i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−27.3995	−	47.4573i	−1.75407	−	3.03814i
$245$	3.82843	+	6.63103i	0.244589	+	0.423641i
$246$	6.82843			0.435365
$247$	−13.3995	+	9.94655i	−0.852589	+	0.632884i
$248$	−22.0711			−1.40151
$249$	−4.00000	−	6.92820i	−0.253490	−	0.439057i
$250$	1.20711	+	2.09077i	0.0763441	+	0.132232i
$251$	13.8284	−	23.9515i	0.872843	−	1.51181i	0.0137993	−	0.999905i	$-0.495607\pi$
$251$	13.8284	−	23.9515i	0.872843	−	1.51181i	0.859043	−	0.511903i	$-0.171059\pi$
$252$	7.32843	+	12.6932i	0.461648	+	0.799597i
$253$	−6.82843	+	11.8272i	−0.429300	+	0.743569i
$254$	−50.6274			−3.17665
$255$	−6.82843			−0.427613
$256$	14.9853	−	25.9553i	0.936580	−	1.62220i
$257$	5.58579	−	9.67487i	0.348432	−	0.603502i	−0.637539	−	0.770418i	$-0.720048\pi$
$257$	5.58579	−	9.67487i	0.348432	−	0.603502i	0.985971	+	0.166916i	$0.0533810\pi$
$258$	−5.24264			−0.326393
$259$	29.9706			1.86228
$260$	7.32843	−	12.6932i	0.454490	−	0.787199i
$261$	0.828427	+	1.43488i	0.0512784	+	0.0888167i
$262$	12.6569	−	21.9223i	0.781943	−	1.35437i
$263$	6.89949	+	11.9503i	0.425441	+	0.736886i	0.996462	−	0.0840503i	$-0.0267856\pi$
$263$	6.89949	+	11.9503i	0.425441	+	0.736886i	−0.571020	+	0.820936i	$0.693452\pi$
$264$	6.24264	+	10.8126i	0.384208	+	0.665468i
$265$	2.00000			0.122859
$266$	4.62132	+	40.0218i	0.283351	+	2.45389i
$267$	4.48528			0.274495
$268$	21.9853	+	38.0796i	1.34296	+	2.32608i
$269$	4.82843	+	8.36308i	0.294394	+	0.509906i	0.974844	−	0.222889i	$-0.0715487\pi$
$269$	4.82843	+	8.36308i	0.294394	+	0.509906i	−0.680449	+	0.732795i	$0.738215\pi$
$270$	−1.20711	+	2.09077i	−0.0734622	+	0.127240i
$271$	−1.17157	−	2.02922i	−0.0711680	−	0.123267i	0.828245	−	0.560365i	$-0.189339\pi$
$271$	−1.17157	−	2.02922i	−0.0711680	−	0.123267i	−0.899413	+	0.437099i	$0.856006\pi$
$272$	10.2426	−	17.7408i	0.621051	−	1.07569i
$273$	14.6569			0.887073
$274$	15.6569			0.945865
$275$	−1.41421	+	2.44949i	−0.0852803	+	0.147710i
$276$	9.24264	−	16.0087i	0.556342	−	0.963612i
$277$	6.00000			0.360505			0.180253	−	0.983620i	$-0.442309\pi$
$277$	6.00000			0.360505			0.180253	+	0.983620i	$0.442309\pi$
$278$	15.2426			0.914193
$279$	2.50000	−	4.33013i	0.149671	−	0.259238i
$280$	−8.44975	−	14.6354i	−0.504969	−	0.874632i
$281$	−13.4853	+	23.3572i	−0.804464	+	1.39337i	0.112188	+	0.993687i	$0.464214\pi$
$281$	−13.4853	+	23.3572i	−0.804464	+	1.39337i	−0.916652	+	0.399686i	$0.869119\pi$
$282$	−10.6569	−	18.4582i	−0.634606	−	1.09917i
$283$	−6.48528	−	11.2328i	−0.385510	−	0.667723i	0.606330	−	0.795213i	$-0.292641\pi$
$283$	−6.48528	−	11.2328i	−0.385510	−	0.667723i	−0.991840	+	0.127490i	$0.959308\pi$
$284$	38.2843			2.27175
$285$	−3.50000	+	2.59808i	−0.207322	+	0.153897i
$286$	26.1421			1.54582
$287$	−5.41421	−	9.37769i	−0.319591	−	0.553548i
$288$	0.792893	+	1.37333i	0.0467217	+	0.0809243i
$289$	−14.8137	+	25.6581i	−0.871395	+	1.50930i
$290$	−2.00000	−	3.46410i	−0.117444	−	0.203419i
$291$	−3.00000	+	5.19615i	−0.175863	+	0.304604i
$292$	−28.6569			−1.67702
$293$	17.3137			1.01148			0.505739	−	0.862687i	$-0.331220\pi$
$293$	17.3137			1.01148			0.505739	+	0.862687i	$0.331220\pi$
$294$	9.24264	−	16.0087i	0.539042	−	0.933648i
$295$		0			0
$296$	−34.5563			−2.00855
$297$	−2.82843			−0.164122
$298$	8.24264	−	14.2767i	0.477483	−	0.827025i
$299$	−9.24264	−	16.0087i	−0.534516	−	0.925808i
$300$	1.91421	−	3.31552i	0.110517	−	0.191421i
$301$	4.15685	+	7.19988i	0.239597	+	0.414994i
$302$	−26.1421	−	45.2795i	−1.50431	−	2.60554i
$303$	16.1421			0.927341
$304$	−1.50000	−	12.9904i	−0.0860309	−	0.745049i
$305$	−14.3137			−0.819601
$306$	8.24264	+	14.2767i	0.471200	+	0.816143i
$307$	3.17157	+	5.49333i	0.181011	+	0.313521i	0.942225	−	0.334980i	$-0.108730\pi$
$307$	3.17157	+	5.49333i	0.181011	+	0.313521i	−0.761214	+	0.648501i	$0.775396\pi$
$308$	20.7279	−	35.9018i	1.18108	−	2.04570i
$309$	2.08579	+	3.61269i	0.118656	+	0.205519i
$310$	−6.03553	+	10.4539i	−0.342795	+	0.593739i
$311$	−4.00000			−0.226819			−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000			−0.226819			−0.113410	+	0.993548i	$0.536177\pi$
$312$	−16.8995			−0.956746
$313$	3.00000	−	5.19615i	0.169570	−	0.293704i	−0.768699	−	0.639611i	$-0.779095\pi$
$313$	3.00000	−	5.19615i	0.169570	−	0.293704i	0.938269	+	0.345907i	$0.112429\pi$
$314$	17.1066	−	29.6295i	0.965381	−	1.67209i
$315$	3.82843			0.215707
$316$	−56.1127			−3.15659
$317$	8.65685	−	14.9941i	0.486217	−	0.842153i	−0.513657	−	0.857996i	$-0.671710\pi$
$317$	8.65685	−	14.9941i	0.486217	−	0.842153i	0.999875	+	0.0158423i	$0.00504299\pi$
$318$	−2.41421	−	4.18154i	−0.135382	−	0.234489i
$319$	2.34315	−	4.05845i	0.131191	−	0.227229i
$320$	−4.91421	−	8.51167i	−0.274713	−	0.475817i
$321$	7.00000	+	12.1244i	0.390702	+	0.676716i
$322$	−44.6274			−2.48699
$323$	3.41421	+	29.5680i	0.189972	+	1.64521i
$324$	3.82843			0.212690
$325$	−1.91421	−	3.31552i	−0.106181	−	0.183912i
$326$	15.8640	+	27.4772i	0.878624	+	1.52182i
$327$	2.65685	−	4.60181i	0.146924	−	0.254480i
$328$	6.24264	+	10.8126i	0.344692	+	0.597024i
$329$	−16.8995	+	29.2708i	−0.931699	+	1.61375i
$330$	6.82843			0.375893
$331$	−16.6569			−0.915544			−0.457772	−	0.889070i	$-0.651352\pi$
$331$	−16.6569			−0.915544			−0.457772	+	0.889070i	$0.651352\pi$
$332$	15.3137	−	26.5241i	0.840449	−	1.45570i
$333$	3.91421	−	6.77962i	0.214498	−	0.371521i
$334$	21.6569			1.18501
$335$	11.4853			0.627508
$336$	−5.74264	+	9.94655i	−0.313287	+	0.542629i
$337$	−0.257359	−	0.445759i	−0.0140193	−	0.0242821i	0.858931	−	0.512092i	$-0.171129\pi$
$337$	−0.257359	−	0.445759i	−0.0140193	−	0.0242821i	−0.872950	+	0.487810i	$0.837796\pi$
$338$	−2.00000	+	3.46410i	−0.108786	+	0.188422i
$339$	2.00000	+	3.46410i	0.108625	+	0.188144i
$340$	−13.0711	−	22.6398i	−0.708878	−	1.22781i
$341$	−14.1421			−0.765840
$342$	9.65685	+	4.18154i	0.522183	+	0.226112i
$343$	−2.51472			−0.135782
$344$	−4.79289	−	8.30153i	−0.258415	−	0.447589i
$345$	−2.41421	−	4.18154i	−0.129977	−	0.225127i
$346$	18.4853	−	32.0174i	0.993775	−	1.72127i
$347$	−7.72792	−	13.3852i	−0.414857	−	0.718553i	0.580557	−	0.814220i	$-0.302835\pi$
$347$	−7.72792	−	13.3852i	−0.414857	−	0.718553i	−0.995413	+	0.0956671i	$0.969502\pi$
$348$	−3.17157	+	5.49333i	−0.170014	+	0.294473i
$349$	13.6274			0.729459			0.364729	−	0.931114i	$-0.381161\pi$
$349$	13.6274			0.729459			0.364729	+	0.931114i	$0.381161\pi$
$350$	−9.24264			−0.494040
$351$	1.91421	−	3.31552i	0.102173	−	0.176969i
$352$	2.24264	−	3.88437i	0.119533	−	0.207037i
$353$	21.3137			1.13441			0.567207	−	0.823575i	$-0.308024\pi$
$353$	21.3137			1.13441			0.567207	+	0.823575i	$0.308024\pi$
$354$		0			0
$355$	5.00000	−	8.66025i	0.265372	−	0.459639i
$356$	8.58579	+	14.8710i	0.455046	+	0.788162i
$357$	13.0711	−	22.6398i	0.691794	−	1.19822i
$358$	14.6569	+	25.3864i	0.774639	+	1.34171i
$359$	−7.41421	−	12.8418i	−0.391307	−	0.677764i	0.601315	−	0.799012i	$-0.294644\pi$
$359$	−7.41421	−	12.8418i	−0.391307	−	0.677764i	−0.992622	+	0.121248i	$0.961310\pi$
$360$	−4.41421			−0.232649
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$	6.48528			0.340859
$363$	−1.50000	−	2.59808i	−0.0787296	−	0.136364i
$364$	28.0563	+	48.5950i	1.47055	+	2.54707i
$365$	−3.74264	+	6.48244i	−0.195899	+	0.339307i
$366$	17.2782	+	29.9267i	0.903145	+	1.56429i
$367$	−14.0563	+	24.3463i	−0.733735	+	1.27087i	0.221540	+	0.975151i	$0.428892\pi$
$367$	−14.0563	+	24.3463i	−0.733735	+	1.27087i	−0.955276	+	0.295716i	$0.904442\pi$
$368$	14.4853			0.755097
$369$	−2.82843			−0.147242
$370$	−9.44975	+	16.3674i	−0.491269	+	0.850903i
$371$	−3.82843	+	6.63103i	−0.198762	+	0.344266i
$372$	19.1421			0.992473
$373$	−0.343146			−0.0177674			−0.00888371	−	0.999961i	$-0.502828\pi$
$373$	−0.343146			−0.0177674			−0.00888371	+	0.999961i	$0.502828\pi$
$374$	23.3137	−	40.3805i	1.20552	−	2.08803i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	19.4853	−	33.7495i	1.00488	−	1.74050i
$377$	3.17157	+	5.49333i	0.163344	+	0.282921i
$378$	−4.62132	−	8.00436i	−0.237695	−	0.411700i
$379$	24.3137			1.24891			0.624456	−	0.781060i	$-0.285321\pi$
$379$	24.3137			1.24891			0.624456	+	0.781060i	$0.285321\pi$
$380$	−15.3137	−	6.63103i	−0.785577	−	0.340165i
$381$	20.9706			1.07435
$382$	13.4853	+	23.3572i	0.689967	+	1.19506i
$383$	−16.9706	−	29.3939i	−0.867155	−	1.50196i	−0.864891	−	0.501960i	$-0.832613\pi$
$383$	−16.9706	−	29.3939i	−0.867155	−	1.50196i	−0.00226413	−	0.999997i	$-0.500721\pi$
$384$	−10.2782	+	17.8023i	−0.524506	+	0.908471i
$385$	−5.41421	−	9.37769i	−0.275934	−	0.477931i
$386$	−17.8640	+	30.9413i	−0.909252	+	1.57487i
$387$	2.17157			0.110387
$388$	−22.9706			−1.16615
$389$	−17.7279	+	30.7057i	−0.898841	+	1.55684i	−0.0698641	+	0.997557i	$0.522257\pi$
$389$	−17.7279	+	30.7057i	−0.898841	+	1.55684i	−0.828977	+	0.559282i	$0.811077\pi$
$390$	−4.62132	+	8.00436i	−0.234010	+	0.405317i
$391$	−32.9706			−1.66739
$392$	33.7990			1.70711
$393$	−5.24264	+	9.08052i	−0.264456	+	0.458052i
$394$	−7.65685	−	13.2621i	−0.385747	−	0.668133i
$395$	−7.32843	+	12.6932i	−0.368733	+	0.638665i
$396$	−5.41421	−	9.37769i	−0.272074	−	0.471247i
$397$	9.08579	+	15.7370i	0.456003	+	0.789820i	0.998745	−	0.0500794i	$-0.0159475\pi$
$397$	9.08579	+	15.7370i	0.456003	+	0.789820i	−0.542743	+	0.839899i	$0.682614\pi$
$398$	−41.0416			−2.05723
$399$	−1.91421	−	16.5776i	−0.0958305	−	0.829917i
$400$	3.00000			0.150000
$401$	−11.3137	−	19.5959i	−0.564980	−	0.978573i	−0.997052	−	0.0767343i	$-0.975551\pi$
$401$	−11.3137	−	19.5959i	−0.564980	−	0.978573i	0.432072	−	0.901839i	$-0.357783\pi$
$402$	−13.8640	−	24.0131i	−0.691472	−	1.19766i
$403$	9.57107	−	16.5776i	0.476769	−	0.825788i
$404$	30.8995	+	53.5195i	1.53731	+	2.66269i
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$	15.3137			0.760007
$407$	−22.1421			−1.09754
$408$	−15.0711	+	26.1039i	−0.746129	+	1.29233i
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	−0.930614	−	0.366002i	$-0.880726\pi$
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	0.782274	+	0.622935i	$0.214060\pi$
$410$	6.82843			0.337232
$411$	−6.48528			−0.319895
$412$	−7.98528	+	13.8309i	−0.393407	+	0.681400i
$413$		0			0
$414$	−5.82843	+	10.0951i	−0.286452	+	0.496149i
$415$	−4.00000	−	6.92820i	−0.196352	−	0.340092i
$416$	3.03553	+	5.25770i	0.148829	+	0.257780i
$417$	−6.31371			−0.309184
$418$	−3.41421	−	29.5680i	−0.166995	−	1.44622i
$419$	−19.3137			−0.943536			−0.471768	−	0.881723i	$-0.656384\pi$
$419$	−19.3137			−0.943536			−0.471768	+	0.881723i	$0.656384\pi$
$420$	7.32843	+	12.6932i	0.357591	+	0.619365i
$421$	−1.82843	−	3.16693i	−0.0891121	−	0.154347i	0.818024	−	0.575184i	$-0.195070\pi$
$421$	−1.82843	−	3.16693i	−0.0891121	−	0.154347i	−0.907136	+	0.420837i	$0.861736\pi$
$422$	−26.9350	+	46.6528i	−1.31118	+	2.27102i
$423$	4.41421	+	7.64564i	0.214626	+	0.371744i
$424$	4.41421	−	7.64564i	0.214373	−	0.371305i
$425$	−6.82843			−0.331227
$426$	−24.1421			−1.16969
$427$	27.3995	−	47.4573i	1.32595	−	2.29662i
$428$	−26.7990	+	46.4172i	−1.29538	+	2.24366i
$429$	−10.8284			−0.522801
$430$	−5.24264			−0.252823
$431$	−7.24264	+	12.5446i	−0.348866	+	0.604253i	−0.986048	−	0.166460i	$-0.946766\pi$
$431$	−7.24264	+	12.5446i	−0.348866	+	0.604253i	0.637183	+	0.770713i	$0.280100\pi$
$432$	1.50000	+	2.59808i	0.0721688	+	0.125000i
$433$	17.0858	−	29.5935i	0.821090	−	1.42217i	−0.0837804	−	0.996484i	$-0.526699\pi$
$433$	17.0858	−	29.5935i	0.821090	−	1.42217i	0.904871	−	0.425686i	$-0.139967\pi$
$434$	−23.1066	−	40.0218i	−1.10915	−	1.92111i
$435$	0.828427	+	1.43488i	0.0397200	+	0.0687971i
$436$	20.3431			0.974260
$437$	−16.8995	+	12.5446i	−0.808412	+	0.600091i
$438$	18.0711			0.863469
$439$	−8.50000	−	14.7224i	−0.405683	−	0.702663i	0.588718	−	0.808339i	$-0.299633\pi$
$439$	−8.50000	−	14.7224i	−0.405683	−	0.702663i	−0.994401	+	0.105675i	$0.966300\pi$
$440$	6.24264	+	10.8126i	0.297606	+	0.515469i
$441$	−3.82843	+	6.63103i	−0.182306	+	0.315763i
$442$	31.5563	+	54.6572i	1.50098	+	2.59978i
$443$	5.07107	−	8.78335i	0.240934	−	0.417309i	−0.720047	−	0.693925i	$-0.755880\pi$
$443$	5.07107	−	8.78335i	0.240934	−	0.417309i	0.960981	+	0.276616i	$0.0892130\pi$
$444$	29.9706			1.42234
$445$	4.48528			0.212623
$446$	−0.207107	+	0.358719i	−0.00980679	+	0.0169859i
$447$	−3.41421	+	5.91359i	−0.161487	+	0.279703i
$448$	37.6274			1.77773
$449$	18.8284			0.888568			0.444284	−	0.895886i	$-0.353458\pi$
$449$	18.8284			0.888568			0.444284	+	0.895886i	$0.353458\pi$
$450$	−1.20711	+	2.09077i	−0.0569036	+	0.0985599i
$451$	4.00000	+	6.92820i	0.188353	+	0.326236i
$452$	−7.65685	+	13.2621i	−0.360148	+	0.623795i
$453$	10.8284	+	18.7554i	0.508764	+	0.881205i
$454$	−18.0711	−	31.3000i	−0.848117	−	1.46898i
$455$	14.6569			0.687124
$456$	2.20711	+	19.1141i	0.103357	+	0.895100i
$457$	−9.82843			−0.459754			−0.229877	−	0.973220i	$-0.573832\pi$
$457$	−9.82843			−0.459754			−0.229877	+	0.973220i	$0.573832\pi$
$458$	−8.03553	−	13.9180i	−0.375476	−	0.650343i
$459$	−3.41421	−	5.91359i	−0.159362	−	0.276023i
$460$	9.24264	−	16.0087i	0.430940	−	0.746411i
$461$	−0.928932	−	1.60896i	−0.0432647	−	0.0749366i	0.843582	−	0.537000i	$-0.180443\pi$
$461$	−0.928932	−	1.60896i	−0.0432647	−	0.0749366i	−0.886847	+	0.462064i	$0.847109\pi$
$462$	−13.0711	+	22.6398i	−0.608121	+	1.05330i
$463$	16.7990			0.780715			0.390358	−	0.920663i	$-0.372351\pi$
$463$	16.7990			0.780715			0.390358	+	0.920663i	$0.372351\pi$
$464$	−4.97056			−0.230753
$465$	2.50000	−	4.33013i	0.115935	−	0.200805i
$466$	3.24264	−	5.61642i	0.150212	−	0.260176i
$467$	−15.7990			−0.731090			−0.365545	−	0.930794i	$-0.619117\pi$
$467$	−15.7990			−0.731090			−0.365545	+	0.930794i	$0.619117\pi$
$468$	14.6569			0.677513
$469$	−21.9853	+	38.0796i	−1.01519	+	1.75835i
$470$	−10.6569	−	18.4582i	−0.491564	−	0.851414i
$471$	−7.08579	+	12.2729i	−0.326496	+	0.565507i
$472$		0			0
$473$	−3.07107	−	5.31925i	−0.141208	−	0.244579i
$474$	35.3848			1.62528
$475$	−3.50000	+	2.59808i	−0.160591	+	0.119208i
$476$	100.083			4.58731
$477$	1.00000	+	1.73205i	0.0457869	+	0.0793052i
$478$	−24.8995	−	43.1272i	−1.13888	−	1.97259i
$479$	7.24264	−	12.5446i	0.330925	−	0.573178i	−0.651769	−	0.758418i	$-0.725973\pi$
$479$	7.24264	−	12.5446i	0.330925	−	0.573178i	0.982693	+	0.185239i	$0.0593061\pi$
$480$	0.792893	+	1.37333i	0.0361905	+	0.0626837i
$481$	14.9853	−	25.9553i	0.683270	−	1.18346i
$482$	12.0711			0.549822
$483$	18.4853			0.841109
$484$	5.74264	−	9.94655i	0.261029	−	0.452116i
$485$	−3.00000	+	5.19615i	−0.136223	+	0.235945i
$486$	−2.41421			−0.109511
$487$	−17.6569			−0.800108			−0.400054	−	0.916491i	$-0.631009\pi$
$487$	−17.6569			−0.800108			−0.400054	+	0.916491i	$0.631009\pi$
$488$	−31.5919	+	54.7187i	−1.43010	+	2.47700i
$489$	−6.57107	−	11.3814i	−0.297154	−	0.514686i
$490$	9.24264	−	16.0087i	0.417540	−	0.723200i
$491$	−6.17157	−	10.6895i	−0.278519	−	0.482409i	0.692498	−	0.721420i	$-0.256510\pi$
$491$	−6.17157	−	10.6895i	−0.278519	−	0.482409i	−0.971017	+	0.239011i	$0.923177\pi$
$492$	−5.41421	−	9.37769i	−0.244092	−	0.422779i
$493$	11.3137			0.509544
$494$	36.9706	+	16.0087i	1.66338	+	0.720267i
$495$	−2.82843			−0.127128
$496$	7.50000	+	12.9904i	0.336760	+	0.583285i
$497$	19.1421	+	33.1552i	0.858642	+	1.48721i
$498$	−9.65685	+	16.7262i	−0.432734	+	0.749517i
$499$	9.32843	+	16.1573i	0.417598	+	0.723301i	0.995697	−	0.0926657i	$-0.0295388\pi$
$499$	9.32843	+	16.1573i	0.417598	+	0.723301i	−0.578100	+	0.815966i	$0.696205\pi$
$500$	1.91421	−	3.31552i	0.0856062	−	0.148274i
$501$	−8.97056			−0.400775
$502$	−66.7696			−2.98007
$503$	−21.0711	+	36.4962i	−0.939512	+	1.62728i	−0.173130	+	0.984899i	$0.555388\pi$
$503$	−21.0711	+	36.4962i	−0.939512	+	1.62728i	−0.766383	+	0.642384i	$0.777945\pi$
$504$	8.44975	−	14.6354i	0.376382	−	0.651912i
$505$	16.1421			0.718316
$506$	32.9706			1.46572
$507$	0.828427	−	1.43488i	0.0367917	−	0.0637252i
$508$	40.1421	+	69.5282i	1.78102	+	3.08482i
$509$	14.5563	−	25.2123i	0.645199	−	1.11752i	−0.339057	−	0.940766i	$-0.610108\pi$
$509$	14.5563	−	25.2123i	0.645199	−	1.11752i	0.984256	−	0.176751i	$-0.0565588\pi$
$510$	8.24264	+	14.2767i	0.364990	+	0.632182i
$511$	−14.3284	−	24.8176i	−0.633852	−	1.09786i
$512$	−31.2426			−1.38074
$513$	−4.00000	−	1.73205i	−0.176604	−	0.0764719i
$514$	−26.9706			−1.18962
$515$	2.08579	+	3.61269i	0.0919107	+	0.159194i
$516$	4.15685	+	7.19988i	0.182995	+	0.316957i
$517$	12.4853	−	21.6251i	0.549102	−	0.951073i
$518$	−36.1777	−	62.6616i	−1.58956	−	2.75319i
$519$	−7.65685	+	13.2621i	−0.336099	+	0.582140i
$520$	−16.8995			−0.741092
$521$	17.6569			0.773561			0.386780	−	0.922172i	$-0.373587\pi$
$521$	17.6569			0.773561			0.386780	+	0.922172i	$0.373587\pi$
$522$	2.00000	−	3.46410i	0.0875376	−	0.151620i
$523$	−21.8848	+	37.9055i	−0.956954	+	1.65749i	−0.227124	+	0.973866i	$0.572932\pi$
$523$	−21.8848	+	37.9055i	−0.956954	+	1.65749i	−0.729831	+	0.683628i	$0.760401\pi$
$524$	−40.1421			−1.75362
$525$	3.82843			0.167086
$526$	16.6569	−	28.8505i	0.726273	−	1.25794i
$527$	−17.0711	−	29.5680i	−0.743627	−	1.28800i
$528$	4.24264	−	7.34847i	0.184637	−	0.319801i
$529$	−0.156854	−	0.271680i	−0.00681975	−	0.0118122i
$530$	−2.41421	−	4.18154i	−0.104867	−	0.181635i
$531$		0			0
$532$	51.2990	−	38.0796i	2.22409	−	1.65096i
$533$	−10.8284			−0.469031
$534$	−5.41421	−	9.37769i	−0.234296	−	0.405812i
$535$	7.00000	+	12.1244i	0.302636	+	0.524182i
$536$	25.3492	−	43.9062i	1.09492	−	1.89646i
$537$	−6.07107	−	10.5154i	−0.261986	−	0.453773i
$538$	11.6569	−	20.1903i	0.502563	−	0.870464i
$539$	21.6569			0.932827
$540$	3.82843			0.164749
$541$	3.15685	−	5.46783i	0.135724	−	0.235080i	−0.790150	−	0.612914i	$-0.789997\pi$
$541$	3.15685	−	5.46783i	0.135724	−	0.235080i	0.925874	+	0.377833i	$0.123331\pi$
$542$	−2.82843	+	4.89898i	−0.121491	+	0.210429i
$543$	−2.68629			−0.115280
$544$	10.8284			0.464265
$545$	2.65685	−	4.60181i	0.113807	−	0.197120i
$546$	−17.6924	−	30.6441i	−0.757164	−	1.31145i
$547$	−7.57107	+	13.1135i	−0.323715	+	0.560692i	−0.981252	−	0.192731i	$-0.938265\pi$
$547$	−7.57107	+	13.1135i	−0.323715	+	0.560692i	0.657536	+	0.753423i	$0.271599\pi$
$548$	−12.4142	−	21.5020i	−0.530309	−	0.918522i
$549$	−7.15685	−	12.3960i	−0.305447	−	0.529050i
$550$	6.82843			0.291165
$551$	5.79899	−	4.30463i	0.247045	−	0.183384i
$552$	−21.3137			−0.907172
$553$	−28.0563	−	48.5950i	−1.19308	−	2.06647i
$554$	−7.24264	−	12.5446i	−0.307710	−	0.532970i
$555$	3.91421	−	6.77962i	0.166149	−	0.287779i
$556$	−12.0858	−	20.9332i	−0.512552	−	0.887765i
$557$	21.4853	−	37.2136i	0.910361	−	1.57679i	0.0968052	−	0.995303i	$-0.469138\pi$
$557$	21.4853	−	37.2136i	0.910361	−	1.57679i	0.813555	−	0.581487i	$-0.197529\pi$
$558$	−12.0711			−0.511009
$559$	8.31371			0.351632
$560$	−5.74264	+	9.94655i	−0.242671	+	0.420318i
$561$	−9.65685	+	16.7262i	−0.407713	+	0.706179i
$562$	65.1127			2.74661
$563$	16.1421			0.680310			0.340155	−	0.940369i	$-0.389520\pi$
$563$	16.1421			0.680310			0.340155	+	0.940369i	$0.389520\pi$
$564$	−16.8995	+	29.2708i	−0.711597	+	1.23252i
$565$	2.00000	+	3.46410i	0.0841406	+	0.145736i
$566$	−15.6569	+	27.1185i	−0.658107	+	1.13987i
$567$	1.91421	+	3.31552i	0.0803894	+	0.139239i
$568$	−22.0711	−	38.2282i	−0.926081	−	1.60402i
$569$	−28.9706			−1.21451			−0.607255	−	0.794507i	$-0.707729\pi$
$569$	−28.9706			−1.21451			−0.607255	+	0.794507i	$0.707729\pi$
$570$	9.65685	+	4.18154i	0.404481	+	0.175145i
$571$	−8.31371			−0.347918			−0.173959	−	0.984753i	$-0.555656\pi$
$571$	−8.31371			−0.347918			−0.173959	+	0.984753i	$0.555656\pi$
$572$	−20.7279	−	35.9018i	−0.866678	−	1.50113i
$573$	−5.58579	−	9.67487i	−0.233350	−	0.404173i
$574$	−13.0711	+	22.6398i	−0.545576	+	0.944965i
$575$	−2.41421	−	4.18154i	−0.100680	−	0.174382i
$576$	4.91421	−	8.51167i	0.204759	−	0.354653i
$577$	−47.6569			−1.98398			−0.991990	−	0.126313i	$-0.959686\pi$
$577$	−47.6569			−1.98398			−0.991990	+	0.126313i	$0.959686\pi$
$578$	71.5269			2.97513
$579$	7.39949	−	12.8163i	0.307513	−	0.532627i
$580$	−3.17157	+	5.49333i	−0.131692	+	0.228098i
$581$	30.6274			1.27064
$582$	14.4853			0.600434
$583$	2.82843	−	4.89898i	0.117141	−	0.202895i
$584$	16.5208	+	28.6149i	0.683636	+	1.18409i
$585$	1.91421	−	3.31552i	0.0791430	−	0.137080i
$586$	−20.8995	−	36.1990i	−0.863350	−	1.49537i
$587$	17.3137	+	29.9882i	0.714613	+	1.23775i	0.963109	+	0.269113i	$0.0867306\pi$
$587$	17.3137	+	29.9882i	0.714613	+	1.23775i	−0.248495	+	0.968633i	$0.579936\pi$
$588$	−29.3137			−1.20888
$589$	−20.0000	−	8.66025i	−0.824086	−	0.356840i
$590$		0			0
$591$	3.17157	+	5.49333i	0.130461	+	0.225965i
$592$	11.7426	+	20.3389i	0.482620	+	0.835922i
$593$	19.0711	−	33.0321i	0.783155	−	1.35646i	−0.146940	−	0.989145i	$-0.546943\pi$
$593$	19.0711	−	33.0321i	0.783155	−	1.35646i	0.930095	−	0.367319i	$-0.119724\pi$
$594$	3.41421	+	5.91359i	0.140087	+	0.242638i
$595$	13.0711	−	22.6398i	0.535862	−	0.928139i
$596$	−26.1421			−1.07082
$597$	17.0000			0.695764
$598$	−22.3137	+	38.6485i	−0.912475	+	1.58045i
$599$	−8.48528	+	14.6969i	−0.346699	+	0.600501i	−0.985661	−	0.168738i	$-0.946031\pi$
$599$	−8.48528	+	14.6969i	−0.346699	+	0.600501i	0.638962	+	0.769238i	$0.279364\pi$
$600$	−4.41421			−0.180210
$601$	−46.6569			−1.90317			−0.951586	−	0.307381i	$-0.900547\pi$
$601$	−46.6569			−1.90317			−0.951586	+	0.307381i	$0.900547\pi$
$602$	10.0355	−	17.3821i	0.409018	−	0.708440i
$603$	5.74264	+	9.94655i	0.233858	+	0.405055i
$604$	−41.4558	+	71.8036i	−1.68681	+	2.92165i
$605$	−1.50000	−	2.59808i	−0.0609837	−	0.105627i
$606$	−19.4853	−	33.7495i	−0.791535	−	1.37098i
$607$	−11.8284			−0.480101			−0.240051	−	0.970760i	$-0.577164\pi$
$607$	−11.8284			−0.480101			−0.240051	+	0.970760i	$0.577164\pi$
$608$	5.55025	−	4.11999i	0.225092	−	0.167088i
$609$	−6.34315			−0.257037
$610$	17.2782	+	29.9267i	0.699573	+	1.21170i
$611$	16.8995	+	29.2708i	0.683680	+	1.18417i
$612$	13.0711	−	22.6398i	0.528367	−	0.915158i
$613$	22.7990	+	39.4890i	0.920843	+	1.59495i	0.798115	+	0.602506i	$0.205831\pi$
$613$	22.7990	+	39.4890i	0.920843	+	1.59495i	0.122728	+	0.992440i	$0.460836\pi$
$614$	7.65685	−	13.2621i	0.309005	−	0.535213i
$615$	−2.82843			−0.114053
$616$	−47.7990			−1.92588
$617$	−7.17157	+	12.4215i	−0.288717	+	0.500072i	−0.973504	−	0.228671i	$-0.926562\pi$
$617$	−7.17157	+	12.4215i	−0.288717	+	0.500072i	0.684787	+	0.728743i	$0.259895\pi$
$618$	5.03553	−	8.72180i	0.202559	−	0.350842i
$619$	38.3137			1.53996			0.769979	−	0.638069i	$-0.220267\pi$
$619$	38.3137			1.53996			0.769979	+	0.638069i	$0.220267\pi$
$620$	19.1421			0.768767
$621$	2.41421	−	4.18154i	0.0968791	−	0.167799i
$622$	4.82843	+	8.36308i	0.193602	+	0.335329i
$623$	−8.58579	+	14.8710i	−0.343982	+	0.595795i
$624$	5.74264	+	9.94655i	0.229890	+	0.398180i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−14.4853			−0.578948
$627$	1.41421	+	12.2474i	0.0564782	+	0.489116i
$628$	−54.2548			−2.16500
$629$	−26.7279	−	46.2941i	−1.06571	−	1.84587i
$630$	−4.62132	−	8.00436i	−0.184118	−	0.318901i
$631$	−21.6421	+	37.4853i	−0.861560	+	1.49227i	0.00886314	+	0.999961i	$0.497179\pi$
$631$	−21.6421	+	37.4853i	−0.861560	+	1.49227i	−0.870423	+	0.492305i	$0.836155\pi$
$632$	32.3492	+	56.0305i	1.28678	+	2.22877i
$633$	11.1569	−	19.3242i	0.443445	−	0.768070i
$634$	−41.7990			−1.66005
$635$	20.9706			0.832191
$636$	−3.82843	+	6.63103i	−0.151807	+	0.262937i
$637$	−14.6569	+	25.3864i	−0.580726	+	1.00585i
$638$	−11.3137			−0.447914
$639$	10.0000			0.395594
$640$	−10.2782	+	17.8023i	−0.406281	+	0.703699i
$641$	0.0710678	+	0.123093i	0.00280701	+	0.00486188i	0.867425	−	0.497567i	$-0.165773\pi$
$641$	0.0710678	+	0.123093i	0.00280701	+	0.00486188i	−0.864618	+	0.502429i	$0.832440\pi$
$642$	16.8995	−	29.2708i	0.666970	−	1.15523i
$643$	−0.0857864	−	0.148586i	−0.00338309	−	0.00585968i	0.864329	−	0.502927i	$-0.167744\pi$
$643$	−0.0857864	−	0.148586i	−0.00338309	−	0.00585968i	−0.867712	+	0.497067i	$0.834410\pi$
$644$	35.3848	+	61.2882i	1.39436	+	2.41509i
$645$	2.17157			0.0855056
$646$	57.6985	−	42.8300i	2.27012	−	1.68512i
$647$	24.2843			0.954713			0.477357	−	0.878710i	$-0.341595\pi$
$647$	24.2843			0.954713			0.477357	+	0.878710i	$0.341595\pi$
$648$	−2.20711	−	3.82282i	−0.0867033	−	0.150175i
$649$		0			0
$650$	−4.62132	+	8.00436i	−0.181263	+	0.313957i
$651$	9.57107	+	16.5776i	0.375120	+	0.649726i
$652$	25.1569	−	43.5729i	0.985218	−	1.70645i
$653$	−27.9411			−1.09342			−0.546710	−	0.837322i	$-0.684120\pi$
$653$	−27.9411			−1.09342			−0.546710	+	0.837322i	$0.684120\pi$
$654$	−12.8284			−0.501631
$655$	−5.24264	+	9.08052i	−0.204847	+	0.354805i
$656$	4.24264	−	7.34847i	0.165647	−	0.286910i
$657$	−7.48528			−0.292029
$658$	81.5980			3.18102
$659$	−12.2426	+	21.2049i	−0.476906	+	0.826025i	−0.999650	−	0.0264649i	$-0.991575\pi$
$659$	−12.2426	+	21.2049i	−0.476906	+	0.826025i	0.522744	+	0.852490i	$0.324908\pi$
$660$	−5.41421	−	9.37769i	−0.210748	−	0.365026i
$661$	−13.4853	+	23.3572i	−0.524517	+	0.908489i	0.475076	+	0.879945i	$0.342421\pi$
$661$	−13.4853	+	23.3572i	−0.524517	+	0.908489i	−0.999593	+	0.0285447i	$0.990913\pi$
$662$	20.1066	+	34.8257i	0.781465	+	1.35354i
$663$	−13.0711	−	22.6398i	−0.507638	−	0.879255i
$664$	−35.3137			−1.37044
$665$	−1.91421	−	16.5776i	−0.0742300	−	0.642851i
$666$	−18.8995			−0.732341
$667$	4.00000	+	6.92820i	0.154881	+	0.268261i
$668$	−17.1716	−	29.7420i	−0.664388	−	1.15075i
$669$	0.0857864	−	0.148586i	0.00331670	−	0.00574468i
$670$	−13.8640	−	24.0131i	−0.535612	−	0.927706i
$671$	−20.2426	+	35.0613i	−0.781458	+	1.35353i
$672$	−6.07107			−0.234197
$673$	−18.1716			−0.700463			−0.350231	−	0.936663i	$-0.613897\pi$
$673$	−18.1716			−0.700463			−0.350231	+	0.936663i	$0.613897\pi$
$674$	−0.621320	+	1.07616i	−0.0239324	+	0.0414521i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	6.34315			0.243967
$677$	27.4558			1.05521			0.527607	−	0.849489i	$-0.323089\pi$
$677$	27.4558			1.05521			0.527607	+	0.849489i	$0.323089\pi$
$678$	4.82843	−	8.36308i	0.185435	−	0.321182i
$679$	−11.4853	−	19.8931i	−0.440765	−	0.763427i
$680$	−15.0711	+	26.1039i	−0.577949	+	1.00104i
$681$	7.48528	+	12.9649i	0.286837	+	0.496816i
$682$	17.0711	+	29.5680i	0.653685	+	1.13222i
$683$	15.8579			0.606784			0.303392	−	0.952866i	$-0.401881\pi$
$683$	15.8579			0.606784			0.303392	+	0.952866i	$0.401881\pi$
$684$	−1.91421	−	16.5776i	−0.0731918	−	0.633859i
$685$	−6.48528			−0.247790
$686$	3.03553	+	5.25770i	0.115897	+	0.200740i
$687$	3.32843	+	5.76500i	0.126987	+	0.219949i
$688$	−3.25736	+	5.64191i	−0.124186	+	0.215096i
$689$	3.82843	+	6.63103i	0.145851	+	0.252622i
$690$	−5.82843	+	10.0951i	−0.221884	+	0.384315i
$691$	8.68629			0.330442			0.165221	−	0.986257i	$-0.447166\pi$
$691$	8.68629			0.330442			0.165221	+	0.986257i	$0.447166\pi$
$692$	−58.6274			−2.22868
$693$	5.41421	−	9.37769i	0.205669	−	0.356229i
$694$	−18.6569	+	32.3146i	−0.708205	+	1.22665i
$695$	−6.31371			−0.239493
$696$	7.31371			0.277225
$697$	−9.65685	+	16.7262i	−0.365779	+	0.633549i
$698$	−16.4497	−	28.4918i	−0.622632	−	1.07843i
$699$	−1.34315	+	2.32640i	−0.0508024	+	0.0879924i
$700$	7.32843	+	12.6932i	0.276989	+	0.479758i
$701$	−1.92893	−	3.34101i	−0.0728548	−	0.126188i	0.827297	−	0.561765i	$-0.189878\pi$
$701$	−1.92893	−	3.34101i	−0.0728548	−	0.126188i	−0.900151	+	0.435577i	$0.856544\pi$
$702$	−9.24264			−0.348841
$703$	−31.3137	−	13.5592i	−1.18102	−	0.511396i
$704$	−27.7990			−1.04771
$705$	4.41421	+	7.64564i	0.166249	+	0.287952i
$706$	−25.7279	−	44.5621i	−0.968283	−	1.67712i
$707$	−30.8995	+	53.5195i	−1.16210	+	2.01281i
$708$		0			0
$709$	6.81371	−	11.8017i	0.255894	−	0.443222i	−0.709244	−	0.704963i	$-0.750963\pi$
$709$	6.81371	−	11.8017i	0.255894	−	0.443222i	0.965138	+	0.261742i	$0.0842968\pi$
$710$	−24.1421			−0.906038
$711$	−14.6569			−0.549675
$712$	9.89949	−	17.1464i	0.370999	−	0.642590i
$713$	12.0711	−	20.9077i	0.452065	−	0.783000i
$714$	−63.1127			−2.36193
$715$	−10.8284			−0.404960
$716$	23.2426	−	40.2574i	0.868618	−	1.50449i
$717$	10.3137	+	17.8639i	0.385173	+	0.667138i
$718$	−17.8995	+	31.0028i	−0.668003	+	1.15702i
$719$	14.4142	+	24.9662i	0.537559	+	0.931080i	0.999035	+	0.0439272i	$0.0139870\pi$
$719$	14.4142	+	24.9662i	0.537559	+	0.931080i	−0.461475	+	0.887153i	$0.652680\pi$
$720$	1.50000	+	2.59808i	0.0559017	+	0.0968246i
$721$	−15.9706			−0.594775
$722$	13.2782	−	43.9062i	0.494162	−	1.63402i
$723$	−5.00000			−0.185952
$724$	−5.14214	−	8.90644i	−0.191106	−	0.331005i
$725$	0.828427	+	1.43488i	0.0307670	+	0.0532900i
$726$	−3.62132	+	6.27231i	−0.134400	+	0.232787i
$727$	−20.9142	−	36.2245i	−0.775665	−	1.34349i	−0.934420	−	0.356174i	$-0.884081\pi$
$727$	−20.9142	−	36.2245i	−0.775665	−	1.34349i	0.158755	−	0.987318i	$-0.449252\pi$
$728$	32.3492	−	56.0305i	1.19894	−	2.07663i
$729$	1.00000			0.0370370
$730$	18.0711			0.668840
$731$	7.41421	−	12.8418i	0.274225	−	0.474971i
$732$	27.3995	−	47.4573i	1.01271	−	1.75407i
$733$	−7.65685			−0.282812			−0.141406	−	0.989952i	$-0.545162\pi$
$733$	−7.65685			−0.282812			−0.141406	+	0.989952i	$0.545162\pi$
$734$	67.8701			2.50513
$735$	−3.82843	+	6.63103i	−0.141214	+	0.244589i
$736$	3.82843	+	6.63103i	0.141118	+	0.244423i
$737$	16.2426	−	28.1331i	0.598305	−	1.03630i
$738$	3.41421	+	5.91359i	0.125679	+	0.217682i
$739$	−1.81371	−	3.14144i	−0.0667183	−	0.115560i	0.830737	−	0.556666i	$-0.187920\pi$
$739$	−1.81371	−	3.14144i	−0.0667183	−	0.115560i	−0.897455	+	0.441106i	$0.854586\pi$
$740$	29.9706			1.10174
$741$	−15.3137	−	6.63103i	−0.562563	−	0.243597i
$742$	18.4853			0.678616
$743$	−2.92893	−	5.07306i	−0.107452	−	0.186112i	0.807285	−	0.590161i	$-0.200936\pi$
$743$	−2.92893	−	5.07306i	−0.107452	−	0.186112i	−0.914737	+	0.404049i	$0.867603\pi$
$744$	−11.0355	−	19.1141i	−0.404582	−	0.700757i
$745$	−3.41421	+	5.91359i	−0.125087	+	0.216657i
$746$	0.414214	+	0.717439i	0.0151654	+	0.0262673i
$747$	4.00000	−	6.92820i	0.146352	−	0.253490i
$748$	−73.9411			−2.70356
$749$	−53.5980			−1.95843
$750$	−1.20711	+	2.09077i	−0.0440773	+	0.0763441i
$751$	−1.84315	+	3.19242i	−0.0672573	+	0.116493i	−0.897693	−	0.440621i	$-0.854758\pi$
$751$	−1.84315	+	3.19242i	−0.0672573	+	0.116493i	0.830436	+	0.557114i	$0.188092\pi$
$752$	−26.4853			−0.965819
$753$	27.6569			1.00787
$754$	7.65685	−	13.2621i	0.278846	−	0.482976i
$755$	10.8284	+	18.7554i	0.394087	+	0.682578i
$756$	−7.32843	+	12.6932i	−0.266532	+	0.461648i
$757$	2.42893	+	4.20703i	0.0882810	+	0.152907i	0.906785	−	0.421594i	$-0.138529\pi$
$757$	2.42893	+	4.20703i	0.0882810	+	0.152907i	−0.818504	+	0.574501i	$0.805196\pi$
$758$	−29.3492	−	50.8344i	−1.06601	−	1.84639i
$759$	−13.6569			−0.495712
$760$	2.20711	+	19.1141i	0.0800602	+	0.693341i
$761$	−27.5980			−1.00043			−0.500213	−	0.865902i	$-0.666745\pi$
$761$	−27.5980			−1.00043			−0.500213	+	0.865902i	$0.666745\pi$
$762$	−25.3137	−	43.8446i	−0.917019	−	1.58832i
$763$	10.1716	+	17.6177i	0.368236	+	0.637803i
$764$	21.3848	−	37.0395i	0.773674	−	1.34004i
$765$	−3.41421	−	5.91359i	−0.123441	−	0.213806i
$766$	−40.9706	+	70.9631i	−1.48033	+	2.56400i
$767$		0			0
$768$	29.9706			1.08147
$769$	4.15685	−	7.19988i	0.149900	−	0.259634i	−0.781290	−	0.624168i	$-0.785438\pi$
$769$	4.15685	−	7.19988i	0.149900	−	0.259634i	0.931190	+	0.364533i	$0.118771\pi$
$770$	−13.0711	+	22.6398i	−0.471049	+	0.815880i
$771$	11.1716			0.402334

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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20711 - 2.09077i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.20711 - 2.09077i) q^{6} -3.82843 q^{7} +4.41421 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.20711 - 2.09077i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.20711 - 2.09077i) q^{6} -3.82843 q^{7} +4.41421 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.20711 - 2.09077i) q^{10} +2.82843 q^{11} -3.82843 q^{12} +(-1.91421 + 3.31552i) q^{13} +(4.62132 + 8.00436i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(-1.50000 - 2.59808i) q^{16} +(3.41421 + 5.91359i) q^{17} +2.41421 q^{18} +(4.00000 + 1.73205i) q^{19} -3.82843 q^{20} +(-1.91421 - 3.31552i) q^{21} +(-3.41421 - 5.91359i) q^{22} +(-2.41421 + 4.18154i) q^{23} +(2.20711 + 3.82282i) q^{24} +(-0.500000 + 0.866025i) q^{25} +9.24264 q^{26} -1.00000 q^{27} +(7.32843 - 12.6932i) q^{28} +(0.828427 - 1.43488i) q^{29} +2.41421 q^{30} -5.00000 q^{31} +(0.792893 - 1.37333i) q^{32} +(1.41421 + 2.44949i) q^{33} +(8.24264 - 14.2767i) q^{34} +(-1.91421 - 3.31552i) q^{35} +(-1.91421 - 3.31552i) q^{36} -7.82843 q^{37} +(-1.20711 - 10.4539i) q^{38} -3.82843 q^{39} +(2.20711 + 3.82282i) q^{40} +(1.41421 + 2.44949i) q^{41} +(-4.62132 + 8.00436i) q^{42} +(-1.08579 - 1.88064i) q^{43} +(-5.41421 + 9.37769i) q^{44} -1.00000 q^{45} +11.6569 q^{46} +(4.41421 - 7.64564i) q^{47} +(1.50000 - 2.59808i) q^{48} +7.65685 q^{49} +2.41421 q^{50} +(-3.41421 + 5.91359i) q^{51} +(-7.32843 - 12.6932i) q^{52} +(1.00000 - 1.73205i) q^{53} +(1.20711 + 2.09077i) q^{54} +(1.41421 + 2.44949i) q^{55} -16.8995 q^{56} +(0.500000 + 4.33013i) q^{57} -4.00000 q^{58} +(-1.91421 - 3.31552i) q^{60} +(-7.15685 + 12.3960i) q^{61} +(6.03553 + 10.4539i) q^{62} +(1.91421 - 3.31552i) q^{63} -9.82843 q^{64} -3.82843 q^{65} +(3.41421 - 5.91359i) q^{66} +(5.74264 - 9.94655i) q^{67} -26.1421 q^{68} -4.82843 q^{69} +(-4.62132 + 8.00436i) q^{70} +(-5.00000 - 8.66025i) q^{71} +(-2.20711 + 3.82282i) q^{72} +(3.74264 + 6.48244i) q^{73} +(9.44975 + 16.3674i) q^{74} -1.00000 q^{75} +(-13.3995 + 9.94655i) q^{76} -10.8284 q^{77} +(4.62132 + 8.00436i) q^{78} +(7.32843 + 12.6932i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.41421 - 5.91359i) q^{82} -8.00000 q^{83} +14.6569 q^{84} +(-3.41421 + 5.91359i) q^{85} +(-2.62132 + 4.54026i) q^{86} +1.65685 q^{87} +12.4853 q^{88} +(2.24264 - 3.88437i) q^{89} +(1.20711 + 2.09077i) q^{90} +(7.32843 - 12.6932i) q^{91} +(-9.24264 - 16.0087i) q^{92} +(-2.50000 - 4.33013i) q^{93} -21.3137 q^{94} +(0.500000 + 4.33013i) q^{95} +1.58579 q^{96} +(3.00000 + 5.19615i) q^{97} +(-9.24264 - 16.0087i) q^{98} +(-1.41421 + 2.44949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 12 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{12} - 2 q^{13} + 10 q^{14} - 2 q^{15} - 6 q^{16} + 8 q^{17} + 4 q^{18} + 16 q^{19} - 4 q^{20} - 2 q^{21} - 8 q^{22} - 4 q^{23} + 6 q^{24} - 2 q^{25} + 20 q^{26} - 4 q^{27} + 18 q^{28} - 8 q^{29} + 4 q^{30} - 20 q^{31} + 6 q^{32} + 16 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} - 2 q^{38} - 4 q^{39} + 6 q^{40} - 10 q^{42} - 10 q^{43} - 16 q^{44} - 4 q^{45} + 24 q^{46} + 12 q^{47} + 6 q^{48} + 8 q^{49} + 4 q^{50} - 8 q^{51} - 18 q^{52} + 4 q^{53} + 2 q^{54} - 28 q^{56} + 2 q^{57} - 16 q^{58} - 2 q^{60} - 6 q^{61} + 10 q^{62} + 2 q^{63} - 28 q^{64} - 4 q^{65} + 8 q^{66} + 6 q^{67} - 48 q^{68} - 8 q^{69} - 10 q^{70} - 20 q^{71} - 6 q^{72} - 2 q^{73} + 18 q^{74} - 4 q^{75} - 14 q^{76} - 32 q^{77} + 10 q^{78} + 18 q^{79} + 6 q^{80} - 2 q^{81} + 8 q^{82} - 32 q^{83} + 36 q^{84} - 8 q^{85} - 2 q^{86} - 16 q^{87} + 16 q^{88} - 8 q^{89} + 2 q^{90} + 18 q^{91} - 20 q^{92} - 10 q^{93} - 40 q^{94} + 2 q^{95} + 12 q^{96} + 12 q^{97} - 20 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 12 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^12 - 2 * q^13 + 10 * q^14 - 2 * q^15 - 6 * q^16 + 8 * q^17 + 4 * q^18 + 16 * q^19 - 4 * q^20 - 2 * q^21 - 8 * q^22 - 4 * q^23 + 6 * q^24 - 2 * q^25 + 20 * q^26 - 4 * q^27 + 18 * q^28 - 8 * q^29 + 4 * q^30 - 20 * q^31 + 6 * q^32 + 16 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 - 2 * q^38 - 4 * q^39 + 6 * q^40 - 10 * q^42 - 10 * q^43 - 16 * q^44 - 4 * q^45 + 24 * q^46 + 12 * q^47 + 6 * q^48 + 8 * q^49 + 4 * q^50 - 8 * q^51 - 18 * q^52 + 4 * q^53 + 2 * q^54 - 28 * q^56 + 2 * q^57 - 16 * q^58 - 2 * q^60 - 6 * q^61 + 10 * q^62 + 2 * q^63 - 28 * q^64 - 4 * q^65 + 8 * q^66 + 6 * q^67 - 48 * q^68 - 8 * q^69 - 10 * q^70 - 20 * q^71 - 6 * q^72 - 2 * q^73 + 18 * q^74 - 4 * q^75 - 14 * q^76 - 32 * q^77 + 10 * q^78 + 18 * q^79 + 6 * q^80 - 2 * q^81 + 8 * q^82 - 32 * q^83 + 36 * q^84 - 8 * q^85 - 2 * q^86 - 16 * q^87 + 16 * q^88 - 8 * q^89 + 2 * q^90 + 18 * q^91 - 20 * q^92 - 10 * q^93 - 40 * q^94 + 2 * q^95 + 12 * q^96 + 12 * q^97 - 20 * q^98

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