LMFDB - Embedded newform 600.2.d.f.349.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(349,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

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

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

chi := DirichletCharacter("600.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.d (of order $2$, degree $1$, not 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.6
Root			$-0.671462 + 1.24464i$ of defining polynomial
Character	$\chi$	$=$	600.349
Dual form			600.2.d.f.349.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24464 + 0.671462i) q^{2} +1.00000 q^{3} +(1.09828 + 1.67146i) q^{4} +(1.24464 + 0.671462i) q^{6} -4.68585i q^{7} +(0.244644 + 2.81783i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.24464 + 0.671462i) q^{2} +1.00000 q^{3} +(1.09828 + 1.67146i) q^{4} +(1.24464 + 0.671462i) q^{6} -4.68585i q^{7} +(0.244644 + 2.81783i) q^{8} +1.00000 q^{9} +2.29273i q^{11} +(1.09828 + 1.67146i) q^{12} +4.97858 q^{13} +(3.14637 - 5.83221i) q^{14} +(-1.58757 + 3.67146i) q^{16} +2.97858i q^{17} +(1.24464 + 0.671462i) q^{18} -2.68585i q^{19} -4.68585i q^{21} +(-1.53948 + 2.85363i) q^{22} +2.68585i q^{23} +(0.244644 + 2.81783i) q^{24} +(6.19656 + 3.34292i) q^{26} +1.00000 q^{27} +(7.83221 - 5.14637i) q^{28} -2.00000i q^{29} -6.97858 q^{31} +(-4.44120 + 3.50367i) q^{32} +2.29273i q^{33} +(-2.00000 + 3.70727i) q^{34} +(1.09828 + 1.67146i) q^{36} +4.39312 q^{37} +(1.80344 - 3.34292i) q^{38} +4.97858 q^{39} -11.3717 q^{41} +(3.14637 - 5.83221i) q^{42} -9.37169 q^{43} +(-3.83221 + 2.51806i) q^{44} +(-1.80344 + 3.34292i) q^{46} -7.27131i q^{47} +(-1.58757 + 3.67146i) q^{48} -14.9572 q^{49} +2.97858i q^{51} +(5.46787 + 8.32150i) q^{52} +2.00000 q^{53} +(1.24464 + 0.671462i) q^{54} +(13.2039 - 1.14637i) q^{56} -2.68585i q^{57} +(1.34292 - 2.48929i) q^{58} -1.70727i q^{59} +4.58546i q^{61} +(-8.68585 - 4.68585i) q^{62} -4.68585i q^{63} +(-7.88030 + 1.37873i) q^{64} +(-1.53948 + 2.85363i) q^{66} +4.00000 q^{67} +(-4.97858 + 3.27131i) q^{68} +2.68585i q^{69} +0.585462 q^{71} +(0.244644 + 2.81783i) q^{72} -6.00000i q^{73} +(5.46787 + 2.94981i) q^{74} +(4.48929 - 2.94981i) q^{76} +10.7434 q^{77} +(6.19656 + 3.34292i) q^{78} -1.02142 q^{79} +1.00000 q^{81} +(-14.1537 - 7.63565i) q^{82} +13.3717 q^{83} +(7.83221 - 5.14637i) q^{84} +(-11.6644 - 6.29273i) q^{86} -2.00000i q^{87} +(-6.46052 + 0.560904i) q^{88} -3.37169 q^{89} -23.3288i q^{91} +(-4.48929 + 2.94981i) q^{92} -6.97858 q^{93} +(4.88240 - 9.05019i) q^{94} +(-4.44120 + 3.50367i) q^{96} +3.95715i q^{97} +(-18.6163 - 10.0432i) q^{98} +2.29273i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} + 2 q^{4} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^3 + 2 * q^4 - 6 * q^8 + 6 * q^9	$ 6 q + 6 q^{3} + 2 q^{4} - 6 q^{8} + 6 q^{9} + 2 q^{12} + 16 q^{14} + 10 q^{16} + 12 q^{22} - 6 q^{24} + 28 q^{26} + 6 q^{27} + 20 q^{28} - 12 q^{31} - 10 q^{32} - 12 q^{34} + 2 q^{36} + 8 q^{37} + 20 q^{38} - 20 q^{41} + 16 q^{42} - 8 q^{43} + 4 q^{44} - 20 q^{46} + 10 q^{48} - 30 q^{49} - 12 q^{52} + 12 q^{53} + 4 q^{56} - 4 q^{58} - 28 q^{62} - 22 q^{64} + 12 q^{66} + 24 q^{67} - 8 q^{71} - 6 q^{72} - 12 q^{74} + 12 q^{76} - 32 q^{77} + 28 q^{78} - 36 q^{79} + 6 q^{81} - 16 q^{82} + 32 q^{83} + 20 q^{84} - 16 q^{86} - 60 q^{88} + 28 q^{89} - 12 q^{92} - 12 q^{93} - 4 q^{94} - 10 q^{96} - 56 q^{98}+O(q^{100}) $ 6 * q + 6 * q^3 + 2 * q^4 - 6 * q^8 + 6 * q^9 + 2 * q^12 + 16 * q^14 + 10 * q^16 + 12 * q^22 - 6 * q^24 + 28 * q^26 + 6 * q^27 + 20 * q^28 - 12 * q^31 - 10 * q^32 - 12 * q^34 + 2 * q^36 + 8 * q^37 + 20 * q^38 - 20 * q^41 + 16 * q^42 - 8 * q^43 + 4 * q^44 - 20 * q^46 + 10 * q^48 - 30 * q^49 - 12 * q^52 + 12 * q^53 + 4 * q^56 - 4 * q^58 - 28 * q^62 - 22 * q^64 + 12 * q^66 + 24 * q^67 - 8 * q^71 - 6 * q^72 - 12 * q^74 + 12 * q^76 - 32 * q^77 + 28 * q^78 - 36 * q^79 + 6 * q^81 - 16 * q^82 + 32 * q^83 + 20 * q^84 - 16 * q^86 - 60 * q^88 + 28 * q^89 - 12 * q^92 - 12 * q^93 - 4 * q^94 - 10 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$	1.24464	+	0.671462i	0.880096	+	0.474795i
$2$	1.24464	+	0.671462i	0.880096	+	0.474795i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	1.09828	+	1.67146i	0.549139	+	0.835731i
$5$		0			0
$5$		0			0
$6$	1.24464	+	0.671462i	0.508124	+	0.274123i
$7$		−	4.68585i		−	1.77108i	−0.464560	−	0.885542i	$-0.653787\pi$
$7$		−	4.68585i		−	1.77108i	0.464560	−	0.885542i	$-0.346213\pi$
$8$	0.244644	+	2.81783i	0.0864948	+	0.996252i
$9$	1.00000			0.333333
$10$		0			0
$11$			2.29273i			0.691284i	0.938366	+	0.345642i	$0.112339\pi$
$11$			2.29273i			0.691284i	−0.938366	+	0.345642i	$0.887661\pi$
$12$	1.09828	+	1.67146i	0.317046	+	0.482509i
$13$	4.97858			1.38081			0.690404	−	0.723424i	$-0.257433\pi$
$13$	4.97858			1.38081			0.690404	+	0.723424i	$0.257433\pi$
$14$	3.14637	−	5.83221i	0.840902	−	1.55872i
$15$		0			0
$16$	−1.58757	+	3.67146i	−0.396892	+	0.917865i
$17$			2.97858i			0.722411i	0.932486	+	0.361206i	$0.117635\pi$
$17$			2.97858i			0.722411i	−0.932486	+	0.361206i	$0.882365\pi$
$18$	1.24464	+	0.671462i	0.293365	+	0.158265i
$19$		−	2.68585i		−	0.616175i	−0.951358	−	0.308088i	$-0.900311\pi$
$19$		−	2.68585i		−	0.616175i	0.951358	−	0.308088i	$-0.0996890\pi$
$20$		0			0
$21$		−	4.68585i		−	1.02254i
$22$	−1.53948	+	2.85363i	−0.328218	+	0.608397i
$23$			2.68585i			0.560038i	0.959995	+	0.280019i	$0.0903407\pi$
$23$			2.68585i			0.560038i	−0.959995	+	0.280019i	$0.909659\pi$
$24$	0.244644	+	2.81783i	0.0499378	+	0.575187i
$25$		0			0
$26$	6.19656	+	3.34292i	1.21524	+	0.655601i
$27$	1.00000			0.192450
$28$	7.83221	−	5.14637i	1.48015	−	0.972572i
$29$		−	2.00000i		−	0.371391i	−0.982607	−	0.185695i	$-0.940546\pi$
$29$		−	2.00000i		−	0.371391i	0.982607	−	0.185695i	$-0.0594537\pi$
$30$		0			0
$31$	−6.97858			−1.25339			−0.626695	−	0.779265i	$-0.715593\pi$
$31$	−6.97858			−1.25339			−0.626695	+	0.779265i	$0.715593\pi$
$32$	−4.44120	+	3.50367i	−0.785101	+	0.619368i
$33$			2.29273i			0.399113i
$34$	−2.00000	+	3.70727i	−0.342997	+	0.635791i
$35$		0			0
$36$	1.09828	+	1.67146i	0.183046	+	0.278577i
$37$	4.39312			0.722224			0.361112	−	0.932523i	$-0.382397\pi$
$37$	4.39312			0.722224			0.361112	+	0.932523i	$0.382397\pi$
$38$	1.80344	−	3.34292i	0.292557	−	0.542294i
$39$	4.97858			0.797210
$40$		0			0
$41$	−11.3717			−1.77596			−0.887980	−	0.459882i	$-0.847892\pi$
$41$	−11.3717			−1.77596			−0.887980	+	0.459882i	$0.847892\pi$
$42$	3.14637	−	5.83221i	0.485495	−	0.899930i
$43$	−9.37169			−1.42917			−0.714585	−	0.699549i	$-0.753384\pi$
$43$	−9.37169			−1.42917			−0.714585	+	0.699549i	$0.753384\pi$
$44$	−3.83221	+	2.51806i	−0.577728	+	0.379611i
$45$		0			0
$46$	−1.80344	+	3.34292i	−0.265903	+	0.492887i
$47$		−	7.27131i		−	1.06063i	−0.847801	−	0.530315i	$-0.822074\pi$
$47$		−	7.27131i		−	1.06063i	0.847801	−	0.530315i	$-0.177926\pi$
$48$	−1.58757	+	3.67146i	−0.229146	+	0.529930i
$49$	−14.9572			−2.13674
$50$		0			0
$51$			2.97858i			0.417084i
$52$	5.46787	+	8.32150i	0.758257	+	1.15398i
$53$	2.00000			0.274721			0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000			0.274721			0.137361	+	0.990521i	$0.456138\pi$
$54$	1.24464	+	0.671462i	0.169375	+	0.0913743i
$55$		0			0
$56$	13.2039	−	1.14637i	1.76445	−	0.153190i
$57$		−	2.68585i		−	0.355749i
$58$	1.34292	−	2.48929i	0.176334	−	0.326860i
$59$		−	1.70727i		−	0.222267i	−0.993805	−	0.111134i	$-0.964552\pi$
$59$		−	1.70727i		−	0.222267i	0.993805	−	0.111134i	$-0.0354482\pi$
$60$		0			0
$61$			4.58546i			0.587108i	0.955942	+	0.293554i	$0.0948381\pi$
$61$			4.58546i			0.587108i	−0.955942	+	0.293554i	$0.905162\pi$
$62$	−8.68585	−	4.68585i	−1.10310	−	0.595103i
$63$		−	4.68585i		−	0.590361i
$64$	−7.88030	+	1.37873i	−0.985037	+	0.172341i
$65$		0			0
$66$	−1.53948	+	2.85363i	−0.189497	+	0.351258i
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	−4.97858	+	3.27131i	−0.603741	+	0.396704i
$69$			2.68585i			0.323338i
$70$		0			0
$71$	0.585462			0.0694816			0.0347408	−	0.999396i	$-0.488939\pi$
$71$	0.585462			0.0694816			0.0347408	+	0.999396i	$0.488939\pi$
$72$	0.244644	+	2.81783i	0.0288316	+	0.332084i
$73$		−	6.00000i		−	0.702247i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$		−	6.00000i		−	0.702247i	0.936329	−	0.351123i	$-0.114200\pi$
$74$	5.46787	+	2.94981i	0.635626	+	0.342908i
$75$		0			0
$76$	4.48929	−	2.94981i	0.514957	−	0.338366i
$77$	10.7434			1.22432
$78$	6.19656	+	3.34292i	0.701622	+	0.378512i
$79$	−1.02142			−0.114919			−0.0574595	−	0.998348i	$-0.518300\pi$
$79$	−1.02142			−0.114919			−0.0574595	+	0.998348i	$0.518300\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	−14.1537	−	7.63565i	−1.56302	−	0.843217i
$83$	13.3717			1.46773			0.733867	−	0.679293i	$-0.237714\pi$
$83$	13.3717			1.46773			0.733867	+	0.679293i	$0.237714\pi$
$84$	7.83221	−	5.14637i	0.854564	−	0.561515i
$85$		0			0
$86$	−11.6644	−	6.29273i	−1.25781	−	0.678563i
$87$		−	2.00000i		−	0.214423i
$88$	−6.46052	+	0.560904i	−0.688694	+	0.0597925i
$89$	−3.37169			−0.357399			−0.178699	−	0.983904i	$-0.557189\pi$
$89$	−3.37169			−0.357399			−0.178699	+	0.983904i	$0.557189\pi$
$90$		0			0
$91$		−	23.3288i		−	2.44553i
$92$	−4.48929	+	2.94981i	−0.468041	+	0.307539i
$93$	−6.97858			−0.723645
$94$	4.88240	−	9.05019i	0.503581	−	0.933456i
$95$		0			0
$96$	−4.44120	+	3.50367i	−0.453278	+	0.357592i
$97$			3.95715i			0.401788i	0.979613	+	0.200894i	$0.0643847\pi$
$97$			3.95715i			0.401788i	−0.979613	+	0.200894i	$0.935615\pi$
$98$	−18.6163	−	10.0432i	−1.88053	−	1.01451i
$99$			2.29273i			0.230428i
$100$		0			0
$101$		−	2.00000i		−	0.199007i	−0.995037	−	0.0995037i	$-0.968274\pi$
$101$		−	2.00000i		−	0.199007i	0.995037	−	0.0995037i	$-0.0317255\pi$
$102$	−2.00000	+	3.70727i	−0.198030	+	0.367074i
$103$		−	14.6430i		−	1.44282i	−0.692509	−	0.721409i	$-0.743495\pi$
$103$		−	14.6430i		−	1.44282i	0.692509	−	0.721409i	$-0.256505\pi$
$104$	1.21798	+	14.0288i	0.119433	+	1.37563i
$105$		0			0
$106$	2.48929	+	1.34292i	0.241781	+	0.130436i
$107$	−11.3288			−1.09520			−0.547600	−	0.836740i	$-0.684459\pi$
$107$	−11.3288			−1.09520			−0.547600	+	0.836740i	$0.684459\pi$
$108$	1.09828	+	1.67146i	0.105682	+	0.160836i
$109$			9.37169i			0.897645i	0.893621	+	0.448823i	$0.148157\pi$
$109$			9.37169i			0.897645i	−0.893621	+	0.448823i	$0.851843\pi$
$110$		0			0
$111$	4.39312			0.416976
$112$	17.2039	+	7.43910i	1.62562	+	0.702929i
$113$			19.7648i			1.85932i	0.368423	+	0.929658i	$0.379898\pi$
$113$			19.7648i			1.85932i	−0.368423	+	0.929658i	$0.620102\pi$
$114$	1.80344	−	3.34292i	0.168908	−	0.313093i
$115$		0			0
$116$	3.34292	−	2.19656i	0.310383	−	0.203945i
$117$	4.97858			0.460270
$118$	1.14637	−	2.12494i	0.105531	−	0.195617i
$119$	13.9572			1.27945
$120$		0			0
$121$	5.74338			0.522126
$122$	−3.07896	+	5.70727i	−0.278756	+	0.516712i
$123$	−11.3717			−1.02535
$124$	−7.66442	−	11.6644i	−0.688286	−	1.04750i
$125$		0			0
$126$	3.14637	−	5.83221i	0.280301	−	0.519575i
$127$		−	6.64300i		−	0.589471i	−0.955579	−	0.294735i	$-0.904768\pi$
$127$		−	6.64300i		−	0.589471i	0.955579	−	0.294735i	$-0.0952315\pi$
$128$	−10.7339	−	3.57529i	−0.948755	−	0.316014i
$129$	−9.37169			−0.825132
$130$		0			0
$131$			7.07896i			0.618492i	0.950982	+	0.309246i	$0.100077\pi$
$131$			7.07896i			0.618492i	−0.950982	+	0.309246i	$0.899923\pi$
$132$	−3.83221	+	2.51806i	−0.333551	+	0.219169i
$133$	−12.5855			−1.09130
$134$	4.97858	+	2.68585i	0.430084	+	0.232022i
$135$		0			0
$136$	−8.39312	+	0.728692i	−0.719704	+	0.0624848i
$137$			14.9786i			1.27971i	0.768497	+	0.639853i	$0.221005\pi$
$137$			14.9786i			1.27971i	−0.768497	+	0.639853i	$0.778995\pi$
$138$	−1.80344	+	3.34292i	−0.153519	+	0.284569i
$139$		−	4.64300i		−	0.393814i	−0.980422	−	0.196907i	$-0.936910\pi$
$139$		−	4.64300i		−	0.393814i	0.980422	−	0.196907i	$-0.0630897\pi$
$140$		0			0
$141$		−	7.27131i		−	0.612355i
$142$	0.728692	+	0.393115i	0.0611505	+	0.0329895i
$143$			11.4145i			0.954532i
$144$	−1.58757	+	3.67146i	−0.132297	+	0.305955i
$145$		0			0
$146$	4.02877	−	7.46787i	0.333423	−	0.618045i
$147$	−14.9572			−1.23365
$148$	4.82487	+	7.34292i	0.396601	+	0.603585i
$149$		−	2.00000i		−	0.163846i	−0.996639	−	0.0819232i	$-0.973894\pi$
$149$		−	2.00000i		−	0.163846i	0.996639	−	0.0819232i	$-0.0261062\pi$
$150$		0			0
$151$	−8.35027			−0.679535			−0.339768	−	0.940509i	$-0.610348\pi$
$151$	−8.35027			−0.679535			−0.339768	+	0.940509i	$0.610348\pi$
$152$	7.56825	−	0.657077i	0.613866	−	0.0532960i
$153$			2.97858i			0.240804i
$154$	13.3717	+	7.21377i	1.07752	+	0.581302i
$155$		0			0
$156$	5.46787	+	8.32150i	0.437780	+	0.666253i
$157$	−22.3503			−1.78375			−0.891873	−	0.452286i	$-0.850609\pi$
$157$	−22.3503			−1.78375			−0.891873	+	0.452286i	$0.850609\pi$
$158$	−1.27131	−	0.685846i	−0.101140	−	0.0545630i
$159$	2.00000			0.158610
$160$		0			0
$161$	12.5855			0.991873
$162$	1.24464	+	0.671462i	0.0977885	+	0.0527550i
$163$	1.37169			0.107439			0.0537196	−	0.998556i	$-0.482892\pi$
$163$	1.37169			0.107439			0.0537196	+	0.998556i	$0.482892\pi$
$164$	−12.4893	−	19.0073i	−0.975250	−	1.48422i
$165$		0			0
$166$	16.6430	+	8.97858i	1.29175	+	0.696873i
$167$		−	11.2713i		−	0.872200i	−0.899898	−	0.436100i	$-0.856359\pi$
$167$		−	11.2713i		−	0.872200i	0.899898	−	0.436100i	$-0.143641\pi$
$168$	13.2039	−	1.14637i	1.01870	−	0.0884440i
$169$	11.7862			0.906633
$170$		0			0
$171$		−	2.68585i		−	0.205392i
$172$	−10.2927	−	15.6644i	−0.784813	−	1.19440i
$173$	10.7862			0.820062			0.410031	−	0.912072i	$-0.365518\pi$
$173$	10.7862			0.820062			0.410031	+	0.912072i	$0.365518\pi$
$174$	1.34292	−	2.48929i	0.101807	−	0.188712i
$175$		0			0
$176$	−8.41767	−	3.63986i	−0.634506	−	0.274365i
$177$		−	1.70727i		−	0.128326i
$178$	−4.19656	−	2.26396i	−0.314545	−	0.169691i
$179$		−	3.66442i		−	0.273892i	−0.990579	−	0.136946i	$-0.956271\pi$
$179$		−	3.66442i		−	0.273892i	0.990579	−	0.136946i	$-0.0437287\pi$
$180$		0			0
$181$		−	6.62831i		−	0.492678i	−0.969184	−	0.246339i	$-0.920772\pi$
$181$		−	6.62831i		−	0.492678i	0.969184	−	0.246339i	$-0.0792277\pi$
$182$	15.6644	−	29.0361i	1.16112	−	2.15230i
$183$			4.58546i			0.338967i
$184$	−7.56825	+	0.657077i	−0.557939	+	0.0484404i
$185$		0			0
$186$	−8.68585	−	4.68585i	−0.636877	−	0.343583i
$187$	−6.82908			−0.499392
$188$	12.1537	−	7.98592i	0.886401	−	0.582433i
$189$		−	4.68585i		−	0.340845i
$190$		0			0
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$	−7.88030	+	1.37873i	−0.568712	+	0.0995013i
$193$			1.21377i			0.0873690i	0.999045	+	0.0436845i	$0.0139096\pi$
$193$			1.21377i			0.0873690i	−0.999045	+	0.0436845i	$0.986090\pi$
$194$	−2.65708	+	4.92525i	−0.190767	+	0.353612i
$195$		0			0
$196$	−16.4271	−	25.0003i	−1.17337	−	1.78574i
$197$	23.9572			1.70688			0.853438	−	0.521194i	$-0.174513\pi$
$197$	23.9572			1.70688			0.853438	+	0.521194i	$0.174513\pi$
$198$	−1.53948	+	2.85363i	−0.109406	+	0.202799i
$199$	−0.350269			−0.0248299			−0.0124150	−	0.999923i	$-0.503952\pi$
$199$	−0.350269			−0.0248299			−0.0124150	+	0.999923i	$0.503952\pi$
$200$		0			0
$201$	4.00000			0.282138
$202$	1.34292	−	2.48929i	0.0944877	−	0.175146i
$203$	−9.37169			−0.657764
$204$	−4.97858	+	3.27131i	−0.348570	+	0.229037i
$205$		0			0
$206$	9.83221	−	18.2253i	0.685043	−	1.26982i
$207$			2.68585i			0.186679i
$208$	−7.90383	+	18.2787i	−0.548032	+	1.26740i
$209$	6.15792			0.425952
$210$		0			0
$211$			14.1004i			0.970710i	0.874317	+	0.485355i	$0.161310\pi$
$211$			14.1004i			0.970710i	−0.874317	+	0.485355i	$0.838690\pi$
$212$	2.19656	+	3.34292i	0.150860	+	0.229593i
$213$	0.585462			0.0401152
$214$	−14.1004	−	7.60688i	−0.963882	−	0.519996i
$215$		0			0
$216$	0.244644	+	2.81783i	0.0166459	+	0.191729i
$217$			32.7005i			2.21986i
$218$	−6.29273	+	11.6644i	−0.426198	+	0.790014i
$219$		−	6.00000i		−	0.405442i
$220$		0			0
$221$			14.8291i			0.997512i
$222$	5.46787	+	2.94981i	0.366979	+	0.197978i
$223$		−	6.72869i		−	0.450587i	−0.974291	−	0.225293i	$-0.927666\pi$
$223$		−	6.72869i		−	0.450587i	0.974291	−	0.225293i	$-0.0723340\pi$
$224$	16.4177	+	20.8108i	1.09695	+	1.39048i
$225$		0			0
$226$	−13.2713	+	24.6002i	−0.882794	+	1.63638i
$227$	9.95715			0.660880			0.330440	−	0.943827i	$-0.392803\pi$
$227$	9.95715			0.660880			0.330440	+	0.943827i	$0.392803\pi$
$228$	4.48929	−	2.94981i	0.297310	−	0.195356i
$229$			11.3288i			0.748631i	0.927301	+	0.374316i	$0.122122\pi$
$229$			11.3288i			0.748631i	−0.927301	+	0.374316i	$0.877878\pi$
$230$		0			0
$231$	10.7434			0.706863
$232$	5.63565	−	0.489289i	0.369999	−	0.0321234i
$233$		−	18.9786i		−	1.24333i	−0.783284	−	0.621664i	$-0.786457\pi$
$233$		−	18.9786i		−	1.24333i	0.783284	−	0.621664i	$-0.213543\pi$
$234$	6.19656	+	3.34292i	0.405082	+	0.218534i
$235$		0			0
$236$	2.85363	−	1.87506i	0.185756	−	0.122056i
$237$	−1.02142			−0.0663485
$238$	17.3717	+	9.37169i	1.12604	+	0.607477i
$239$	−2.62831			−0.170011			−0.0850055	−	0.996380i	$-0.527091\pi$
$239$	−2.62831			−0.170011			−0.0850055	+	0.996380i	$0.527091\pi$
$240$		0			0
$241$	10.7862			0.694802			0.347401	−	0.937717i	$-0.387064\pi$
$241$	10.7862			0.694802			0.347401	+	0.937717i	$0.387064\pi$
$242$	7.14847	+	3.85646i	0.459521	+	0.247903i
$243$	1.00000			0.0641500
$244$	−7.66442	+	5.03612i	−0.490664	+	0.322404i
$245$		0			0
$246$	−14.1537	−	7.63565i	−0.902408	−	0.486832i
$247$		−	13.3717i		−	0.850820i
$248$	−1.70727	−	19.6644i	−0.108412	−	1.24869i
$249$	13.3717			0.847397
$250$		0			0
$251$			30.9933i			1.95628i	0.207952	+	0.978139i	$0.433320\pi$
$251$			30.9933i			1.95628i	−0.207952	+	0.978139i	$0.566680\pi$
$252$	7.83221	−	5.14637i	0.493383	−	0.324191i
$253$	−6.15792			−0.387145
$254$	4.46052	−	8.26817i	0.279878	−	0.518791i
$255$		0			0
$256$	−10.9593	−	11.6574i	−0.684954	−	0.728587i
$257$		−	20.9357i		−	1.30594i	−0.757386	−	0.652968i	$-0.773524\pi$
$257$		−	20.9357i		−	1.30594i	0.757386	−	0.652968i	$-0.226476\pi$
$258$	−11.6644	−	6.29273i	−0.726195	−	0.391768i
$259$		−	20.5855i		−	1.27912i
$260$		0			0
$261$		−	2.00000i		−	0.123797i
$262$	−4.75325	+	8.81079i	−0.293657	+	0.544332i
$263$		−	19.2713i		−	1.18832i	−0.804347	−	0.594160i	$-0.797485\pi$
$263$		−	19.2713i		−	1.18832i	0.804347	−	0.594160i	$-0.202515\pi$
$264$	−6.46052	+	0.560904i	−0.397617	+	0.0345212i
$265$		0			0
$266$	−15.6644	−	8.45065i	−0.960447	−	0.518143i
$267$	−3.37169			−0.206344
$268$	4.39312	+	6.68585i	0.268352	+	0.408403i
$269$			24.7434i			1.50863i	0.656512	+	0.754315i	$0.272031\pi$
$269$			24.7434i			1.50863i	−0.656512	+	0.754315i	$0.727969\pi$
$270$		0			0
$271$	27.5640			1.67440			0.837198	−	0.546900i	$-0.184192\pi$
$271$	27.5640			1.67440			0.837198	+	0.546900i	$0.184192\pi$
$272$	−10.9357	−	4.72869i	−0.663076	−	0.286719i
$273$		−	23.3288i		−	1.41193i
$274$	−10.0575	+	18.6430i	−0.607598	+	1.12626i
$275$		0			0
$276$	−4.48929	+	2.94981i	−0.270223	+	0.177558i
$277$	−20.3074			−1.22015			−0.610077	−	0.792342i	$-0.708862\pi$
$277$	−20.3074			−1.22015			−0.610077	+	0.792342i	$0.708862\pi$
$278$	3.11760	−	5.77888i	0.186981	−	0.346594i
$279$	−6.97858			−0.417796
$280$		0			0
$281$	−10.7862			−0.643453			−0.321726	−	0.946833i	$-0.604263\pi$
$281$	−10.7862			−0.643453			−0.321726	+	0.946833i	$0.604263\pi$
$282$	4.88240	−	9.05019i	0.290743	−	0.538931i
$283$	20.0000			1.18888			0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000			1.18888			0.594438	+	0.804141i	$0.297374\pi$
$284$	0.643000	+	0.978577i	0.0381551	+	0.0580679i
$285$		0			0
$286$	−7.66442	+	14.2070i	−0.453207	+	0.840080i
$287$			53.2860i			3.14537i
$288$	−4.44120	+	3.50367i	−0.261700	+	0.206456i
$289$	8.12808			0.478122
$290$		0			0
$291$			3.95715i			0.231972i
$292$	10.0288	−	6.58967i	0.586889	−	0.385631i
$293$	21.9143			1.28025			0.640124	−	0.768272i	$-0.278883\pi$
$293$	21.9143			1.28025			0.640124	+	0.768272i	$0.278883\pi$
$294$	−18.6163	−	10.0432i	−1.08573	−	0.585729i
$295$		0			0
$296$	1.07475	+	12.3790i	0.0624686	+	0.719517i
$297$			2.29273i			0.133038i
$298$	1.34292	−	2.48929i	0.0777934	−	0.144201i
$299$			13.3717i			0.773305i
$300$		0			0
$301$			43.9143i			2.53118i
$302$	−10.3931	−	5.60688i	−0.598057	−	0.322640i
$303$		−	2.00000i		−	0.114897i
$304$	9.86098	+	4.26396i	0.565566	+	0.244555i
$305$		0			0
$306$	−2.00000	+	3.70727i	−0.114332	+	0.211930i
$307$	26.5426			1.51487			0.757434	−	0.652912i	$-0.226453\pi$
$307$	26.5426			1.51487			0.757434	+	0.652912i	$0.226453\pi$
$308$	11.7992	+	17.9572i	0.672324	+	1.02320i
$309$		−	14.6430i		−	0.833011i
$310$		0			0
$311$	12.2008			0.691842			0.345921	−	0.938264i	$-0.387566\pi$
$311$	12.2008			0.691842			0.345921	+	0.938264i	$0.387566\pi$
$312$	1.21798	+	14.0288i	0.0689546	+	0.794223i
$313$			15.9572i			0.901952i	0.892536	+	0.450976i	$0.148924\pi$
$313$			15.9572i			0.901952i	−0.892536	+	0.450976i	$0.851076\pi$
$314$	−27.8181	−	15.0073i	−1.56987	−	0.846914i
$315$		0			0
$316$	−1.12181	−	1.70727i	−0.0631066	−	0.0960414i
$317$	−33.5296			−1.88321			−0.941605	−	0.336718i	$-0.890683\pi$
$317$	−33.5296			−1.88321			−0.941605	+	0.336718i	$0.890683\pi$
$318$	2.48929	+	1.34292i	0.139592	+	0.0753074i
$319$	4.58546			0.256737
$320$		0			0
$321$	−11.3288			−0.632315
$322$	15.6644	+	8.45065i	0.872944	+	0.470937i
$323$	8.00000			0.445132
$324$	1.09828	+	1.67146i	0.0610155	+	0.0928590i
$325$		0			0
$326$	1.70727	+	0.921039i	0.0945569	+	0.0510116i
$327$			9.37169i			0.518256i
$328$	−2.78202	−	32.0435i	−0.153611	−	1.76930i
$329$	−34.0722			−1.87846
$330$		0			0
$331$		−	19.8568i		−	1.09143i	−0.837972	−	0.545713i	$-0.816259\pi$
$331$		−	19.8568i		−	1.09143i	0.837972	−	0.545713i	$-0.183741\pi$
$332$	14.6858	+	22.3503i	0.805991	+	1.22663i
$333$	4.39312			0.240741
$334$	7.56825	−	14.0288i	0.414116	−	0.767620i
$335$		0			0
$336$	17.2039	+	7.43910i	0.938550	+	0.405836i
$337$		−	7.17092i		−	0.390625i	−0.980741	−	0.195313i	$-0.937428\pi$
$337$		−	7.17092i		−	0.390625i	0.980741	−	0.195313i	$-0.0625721\pi$
$338$	14.6697	+	7.91400i	0.797925	+	0.430465i
$339$			19.7648i			1.07348i
$340$		0			0
$341$		−	16.0000i		−	0.866449i
$342$	1.80344	−	3.34292i	0.0975190	−	0.180765i
$343$			37.2860i			2.01325i
$344$	−2.29273	−	26.4078i	−0.123616	−	1.42381i
$345$		0			0
$346$	13.4250	+	7.24254i	0.721734	+	0.389361i
$347$	0.786230			0.0422071			0.0211035	−	0.999777i	$-0.493282\pi$
$347$	0.786230			0.0422071			0.0211035	+	0.999777i	$0.493282\pi$
$348$	3.34292	−	2.19656i	0.179199	−	0.117748i
$349$		−	6.15792i		−	0.329626i	−0.986325	−	0.164813i	$-0.947298\pi$
$349$		−	6.15792i		−	0.329626i	0.986325	−	0.164813i	$-0.0527021\pi$
$350$		0			0
$351$	4.97858			0.265737
$352$	−8.03298	−	10.1825i	−0.428159	−	0.542728i
$353$			21.7220i			1.15614i	0.815986	+	0.578072i	$0.196195\pi$
$353$			21.7220i			1.15614i	−0.815986	+	0.578072i	$0.803805\pi$
$354$	1.14637	−	2.12494i	0.0609286	−	0.112939i
$355$		0			0
$356$	−3.70306	−	5.63565i	−0.196262	−	0.298689i
$357$	13.9572			0.738691
$358$	2.46052	−	4.56090i	0.130042	−	0.241051i
$359$	−0.585462			−0.0308995			−0.0154498	−	0.999881i	$-0.504918\pi$
$359$	−0.585462			−0.0308995			−0.0154498	+	0.999881i	$0.504918\pi$
$360$		0			0
$361$	11.7862			0.620328
$362$	4.45065	−	8.24989i	0.233921	−	0.433604i
$363$	5.74338			0.301450
$364$	38.9933	−	25.6216i	2.04380	−	1.34294i
$365$		0			0
$366$	−3.07896	+	5.70727i	−0.160940	+	0.298324i
$367$			0.485078i			0.0253209i	0.999920	+	0.0126604i	$0.00403005\pi$
$367$			0.485078i			0.0253209i	−0.999920	+	0.0126604i	$0.995970\pi$
$368$	−9.86098	−	4.26396i	−0.514039	−	0.222274i
$369$	−11.3717			−0.591987
$370$		0			0
$371$		−	9.37169i		−	0.486554i
$372$	−7.66442	−	11.6644i	−0.397382	−	0.604772i
$373$	12.3931			0.641691			0.320846	−	0.947132i	$-0.396033\pi$
$373$	12.3931			0.641691			0.320846	+	0.947132i	$0.396033\pi$
$374$	−8.49977	−	4.58546i	−0.439513	−	0.237109i
$375$		0			0
$376$	20.4893	−	1.77888i	1.05665	−	0.0917389i
$377$		−	9.95715i		−	0.512820i
$378$	3.14637	−	5.83221i	0.161832	−	0.299977i
$379$			26.0147i			1.33629i	0.744033	+	0.668143i	$0.232910\pi$
$379$			26.0147i			1.33629i	−0.744033	+	0.668143i	$0.767090\pi$
$380$		0			0
$381$		−	6.64300i		−	0.340331i
$382$	−9.95715	−	5.37169i	−0.509452	−	0.274840i
$383$			6.68585i			0.341631i	0.985303	+	0.170815i	$0.0546402\pi$
$383$			6.68585i			0.341631i	−0.985303	+	0.170815i	$0.945360\pi$
$384$	−10.7339	−	3.57529i	−0.547764	−	0.182451i
$385$		0			0
$386$	−0.815000	+	1.51071i	−0.0414824	+	0.0768932i
$387$	−9.37169			−0.476390
$388$	−6.61423	+	4.34606i	−0.335787	+	0.220638i
$389$		−	29.9143i		−	1.51672i	−0.651838	−	0.758358i	$-0.726002\pi$
$389$		−	29.9143i		−	1.51672i	0.651838	−	0.758358i	$-0.273998\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$	−3.65918	−	42.1467i	−0.184817	−	2.12873i
$393$			7.07896i			0.357086i
$394$	29.8181	+	16.0863i	1.50222	+	0.810416i
$395$		0			0
$396$	−3.83221	+	2.51806i	−0.192576	+	0.126537i
$397$	9.76481			0.490082			0.245041	−	0.969513i	$-0.421199\pi$
$397$	9.76481			0.490082			0.245041	+	0.969513i	$0.421199\pi$
$398$	−0.435961	−	0.235192i	−0.0218527	−	0.0117891i
$399$	−12.5855			−0.630061
$400$		0			0
$401$	−6.58546			−0.328862			−0.164431	−	0.986389i	$-0.552579\pi$
$401$	−6.58546			−0.328862			−0.164431	+	0.986389i	$0.552579\pi$
$402$	4.97858	+	2.68585i	0.248309	+	0.133958i
$403$	−34.7434			−1.73069
$404$	3.34292	−	2.19656i	0.166317	−	0.109283i
$405$		0			0
$406$	−11.6644	−	6.29273i	−0.578896	−	0.312303i
$407$			10.0722i			0.499262i
$408$	−8.39312	+	0.728692i	−0.415521	+	0.0360756i
$409$	25.9143			1.28138			0.640690	−	0.767800i	$-0.278648\pi$
$409$	25.9143			1.28138			0.640690	+	0.767800i	$0.278648\pi$
$410$		0			0
$411$			14.9786i			0.738839i
$412$	24.4752	−	16.0821i	1.20581	−	0.792308i
$413$	−8.00000			−0.393654
$414$	−1.80344	+	3.34292i	−0.0886344	+	0.164296i
$415$		0			0
$416$	−22.1109	+	17.4433i	−1.08407	+	0.855229i
$417$		−	4.64300i		−	0.227369i
$418$	7.66442	+	4.13481i	0.374879	+	0.202240i
$419$			12.2499i			0.598446i	0.954183	+	0.299223i	$0.0967275\pi$
$419$			12.2499i			0.598446i	−0.954183	+	0.299223i	$0.903273\pi$
$420$		0			0
$421$		−	4.67115i		−	0.227658i	−0.993500	−	0.113829i	$-0.963688\pi$
$421$		−	4.67115i		−	0.227658i	0.993500	−	0.113829i	$-0.0363116\pi$
$422$	−9.46787	+	17.5500i	−0.460888	+	0.854319i
$423$		−	7.27131i		−	0.353543i
$424$	0.489289	+	5.63565i	0.0237620	+	0.273692i
$425$		0			0
$426$	0.728692	+	0.393115i	0.0353052	+	0.0190465i
$427$	21.4868			1.03982
$428$	−12.4422	−	18.9357i	−0.601418	−	0.915293i
$429$			11.4145i			0.551099i
$430$		0			0
$431$	0.585462			0.0282007			0.0141004	−	0.999901i	$-0.495512\pi$
$431$	0.585462			0.0282007			0.0141004	+	0.999901i	$0.495512\pi$
$432$	−1.58757	+	3.67146i	−0.0763819	+	0.176643i
$433$		−	21.9143i		−	1.05313i	−0.850133	−	0.526567i	$-0.823479\pi$
$433$		−	21.9143i		−	1.05313i	0.850133	−	0.526567i	$-0.176521\pi$
$434$	−21.9572	+	40.7005i	−1.05398	+	1.95369i
$435$		0			0
$436$	−15.6644	+	10.2927i	−0.750190	+	0.492932i
$437$	7.21377			0.345081
$438$	4.02877	−	7.46787i	0.192502	−	0.356828i
$439$	2.39312			0.114217			0.0571086	−	0.998368i	$-0.481812\pi$
$439$	2.39312			0.114217			0.0571086	+	0.998368i	$0.481812\pi$
$440$		0			0
$441$	−14.9572			−0.712245
$442$	−9.95715	+	18.4569i	−0.473614	+	0.877906i
$443$	20.7005			0.983512			0.491756	−	0.870733i	$-0.336355\pi$
$443$	20.7005			0.983512			0.491756	+	0.870733i	$0.336355\pi$
$444$	4.82487	+	7.34292i	0.228978	+	0.348480i
$445$		0			0
$446$	4.51806	−	8.37483i	0.213936	−	0.396560i
$447$		−	2.00000i		−	0.0945968i
$448$	6.46052	+	36.9259i	0.305231	+	1.74458i
$449$	37.9143			1.78929			0.894643	−	0.446781i	$-0.147430\pi$
$449$	37.9143			1.78929			0.894643	+	0.446781i	$0.147430\pi$
$450$		0			0
$451$		−	26.0722i		−	1.22769i
$452$	−33.0361	+	21.7073i	−1.55389	+	1.02102i
$453$	−8.35027			−0.392330
$454$	12.3931	+	6.68585i	0.581638	+	0.313782i
$455$		0			0
$456$	7.56825	−	0.657077i	0.354416	−	0.0307704i
$457$		−	38.7005i		−	1.81033i	−0.425055	−	0.905167i	$-0.639745\pi$
$457$		−	38.7005i		−	1.81033i	0.425055	−	0.905167i	$-0.360255\pi$
$458$	−7.60688	+	14.1004i	−0.355446	+	0.658868i
$459$			2.97858i			0.139028i
$460$		0			0
$461$		−	4.74338i		−	0.220921i	−0.993880	−	0.110461i	$-0.964767\pi$
$461$		−	4.74338i		−	0.220921i	0.993880	−	0.110461i	$-0.0352326\pi$
$462$	13.3717	+	7.21377i	0.622107	+	0.335615i
$463$			15.3142i			0.711709i	0.934541	+	0.355855i	$0.115810\pi$
$463$			15.3142i			0.711709i	−0.934541	+	0.355855i	$0.884190\pi$
$464$	7.34292	+	3.17513i	0.340887	+	0.147402i
$465$		0			0
$466$	12.7434	−	23.6216i	0.590326	−	1.09425i
$467$	−30.5426			−1.41334			−0.706672	−	0.707541i	$-0.749804\pi$
$467$	−30.5426			−1.41334			−0.706672	+	0.707541i	$0.749804\pi$
$468$	5.46787	+	8.32150i	0.252752	+	0.384661i
$469$		−	18.7434i		−	0.865489i
$470$		0			0
$471$	−22.3503			−1.02985
$472$	4.81079	−	0.417674i	0.221435	−	0.0192250i
$473$		−	21.4868i		−	0.987963i
$474$	−1.27131	−	0.685846i	−0.0583931	−	0.0315020i
$475$		0			0
$476$	15.3288	+	23.3288i	0.702597	+	1.06928i
$477$	2.00000			0.0915737
$478$	−3.27131	−	1.76481i	−0.149626	−	0.0807204i
$479$	−3.32885			−0.152099			−0.0760494	−	0.997104i	$-0.524231\pi$
$479$	−3.32885			−0.152099			−0.0760494	+	0.997104i	$0.524231\pi$
$480$		0			0
$481$	21.8715			0.997253
$482$	13.4250	+	7.24254i	0.611493	+	0.329889i
$483$	12.5855			0.572658
$484$	6.30784	+	9.59985i	0.286720	+	0.436357i
$485$		0			0
$486$	1.24464	+	0.671462i	0.0564582	+	0.0304581i
$487$			12.1004i			0.548321i	0.961684	+	0.274160i	$0.0883999\pi$
$487$			12.1004i			0.548321i	−0.961684	+	0.274160i	$0.911600\pi$
$488$	−12.9210	+	1.12181i	−0.584908	+	0.0507818i
$489$	1.37169			0.0620301
$490$		0			0
$491$			14.2927i			0.645022i	0.946566	+	0.322511i	$0.104527\pi$
$491$			14.2927i			0.645022i	−0.946566	+	0.322511i	$0.895473\pi$
$492$	−12.4893	−	19.0073i	−0.563061	−	0.856917i
$493$	5.95715			0.268297
$494$	8.97858	−	16.6430i	0.403965	−	0.748804i
$495$		0			0
$496$	11.0790	−	25.6216i	0.497460	−	1.15044i
$497$		−	2.74338i		−	0.123058i
$498$	16.6430	+	8.97858i	0.745791	+	0.402340i
$499$			9.22846i			0.413123i	0.978434	+	0.206561i	$0.0662273\pi$
$499$			9.22846i			0.413123i	−0.978434	+	0.206561i	$0.933773\pi$
$500$		0			0
$501$		−	11.2713i		−	0.503565i
$502$	−20.8108	+	38.5756i	−0.928831	+	1.72171i
$503$		−	14.1004i		−	0.628705i	−0.949306	−	0.314353i	$-0.898213\pi$
$503$		−	14.1004i		−	0.628705i	0.949306	−	0.314353i	$-0.101787\pi$
$504$	13.2039	−	1.14637i	0.588149	−	0.0510632i
$505$		0			0
$506$	−7.66442	−	4.13481i	−0.340725	−	0.183815i
$507$	11.7862			0.523445
$508$	11.1035	−	7.29587i	0.492639	−	0.323702i
$509$		−	43.4011i		−	1.92372i	−0.273544	−	0.961859i	$-0.588196\pi$
$509$		−	43.4011i		−	1.92372i	0.273544	−	0.961859i	$-0.411804\pi$
$510$		0			0
$511$	−28.1151			−1.24374
$512$	−5.81289	−	21.8680i	−0.256896	−	0.966439i
$513$		−	2.68585i		−	0.118583i
$514$	14.0575	−	26.0575i	0.620051	−	1.14935i
$515$		0			0
$516$	−10.2927	−	15.6644i	−0.453112	−	0.689588i
$517$	16.6712			0.733196
$518$	13.8223	−	25.6216i	0.607319	−	1.12575i
$519$	10.7862			0.473463
$520$		0			0
$521$	10.0000			0.438108			0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000			0.438108			0.219054	+	0.975713i	$0.429703\pi$
$522$	1.34292	−	2.48929i	0.0587781	−	0.108953i
$523$	13.5725			0.593482			0.296741	−	0.954958i	$-0.404100\pi$
$523$	13.5725			0.593482			0.296741	+	0.954958i	$0.404100\pi$
$524$	−11.8322	+	7.77467i	−0.516893	+	0.339638i
$525$		0			0
$526$	12.9399	−	23.9859i	0.564208	−	1.04584i
$527$		−	20.7862i		−	0.905462i
$528$	−8.41767	−	3.63986i	−0.366332	−	0.158405i
$529$	15.7862			0.686358
$530$		0			0
$531$		−	1.70727i		−	0.0740892i
$532$	−13.8223	−	21.0361i	−0.599275	−	0.912031i
$533$	−56.6148			−2.45226
$534$	−4.19656	−	2.26396i	−0.181603	−	0.0979712i
$535$		0			0
$536$	0.978577	+	11.2713i	0.0422681	+	0.486846i
$537$		−	3.66442i		−	0.158132i
$538$	−16.6142	+	30.7967i	−0.716290	+	1.32774i
$539$		−	34.2927i		−	1.47709i
$540$		0			0
$541$			37.2860i			1.60305i	0.597961	+	0.801525i	$0.295978\pi$
$541$			37.2860i			1.60305i	−0.597961	+	0.801525i	$0.704022\pi$
$542$	34.3074	+	18.5082i	1.47363	+	0.794995i
$543$		−	6.62831i		−	0.284448i
$544$	−10.4360	−	13.2285i	−0.447438	−	0.567166i
$545$		0			0
$546$	15.6644	−	29.0361i	0.670375	−	1.24263i
$547$	0.200768			0.00858424			0.00429212	−	0.999991i	$-0.498634\pi$
$547$	0.200768			0.00858424			0.00429212	+	0.999991i	$0.498634\pi$
$548$	−25.0361	+	16.4507i	−1.06949	+	0.702737i
$549$			4.58546i			0.195703i
$550$		0			0
$551$	−5.37169			−0.228842
$552$	−7.56825	+	0.657077i	−0.322126	+	0.0279671i
$553$			4.78623i			0.203531i
$554$	−25.2755	−	13.6357i	−1.07385	−	0.579323i
$555$		0			0
$556$	7.76060	−	5.09931i	0.329123	−	0.216259i
$557$	−9.21377			−0.390400			−0.195200	−	0.980763i	$-0.562536\pi$
$557$	−9.21377			−0.390400			−0.195200	+	0.980763i	$0.562536\pi$
$558$	−8.68585	−	4.68585i	−0.367701	−	0.198368i
$559$	−46.6577			−1.97341
$560$		0			0
$561$	−6.82908			−0.288324
$562$	−13.4250	−	7.24254i	−0.566300	−	0.305508i
$563$	−36.7005			−1.54674			−0.773372	−	0.633953i	$-0.781431\pi$
$563$	−36.7005			−1.54674			−0.773372	+	0.633953i	$0.781431\pi$
$564$	12.1537	−	7.98592i	0.511764	−	0.336268i
$565$		0			0
$566$	24.8929	+	13.4292i	1.04633	+	0.564473i
$567$		−	4.68585i		−	0.196787i
$568$	0.143230	+	1.64973i	0.00600979	+	0.0692212i
$569$	−13.4145			−0.562367			−0.281183	−	0.959654i	$-0.590727\pi$
$569$	−13.4145			−0.562367			−0.281183	+	0.959654i	$0.590727\pi$
$570$		0			0
$571$		−	18.6858i		−	0.781978i	−0.920395	−	0.390989i	$-0.872133\pi$
$571$		−	18.6858i		−	0.781978i	0.920395	−	0.390989i	$-0.127867\pi$
$572$	−19.0790	+	12.5363i	−0.797731	+	0.524171i
$573$	−8.00000			−0.334205
$574$	−35.7795	+	66.3221i	−1.49341	+	2.76823i
$575$		0			0
$576$	−7.88030	+	1.37873i	−0.328346	+	0.0574471i
$577$			2.78623i			0.115992i	0.998317	+	0.0579961i	$0.0184711\pi$
$577$			2.78623i			0.115992i	−0.998317	+	0.0579961i	$0.981529\pi$
$578$	10.1166	+	5.45769i	0.420794	+	0.227010i
$579$			1.21377i			0.0504425i
$580$		0			0
$581$		−	62.6577i		−	2.59948i
$582$	−2.65708	+	4.92525i	−0.110139	+	0.204158i
$583$			4.58546i			0.189910i
$584$	16.9070	−	1.46787i	0.699615	−	0.0607407i
$585$		0			0
$586$	27.2755	+	14.7146i	1.12674	+	0.607855i
$587$	27.3288			1.12798			0.563991	−	0.825781i	$-0.309265\pi$
$587$	27.3288			1.12798			0.563991	+	0.825781i	$0.309265\pi$
$588$	−16.4271	−	25.0003i	−0.677443	−	1.03100i
$589$			18.7434i			0.772308i
$590$		0			0
$591$	23.9572			0.985466
$592$	−6.97437	+	16.1292i	−0.286645	+	0.662904i
$593$		−	6.97858i		−	0.286576i	−0.989681	−	0.143288i	$-0.954233\pi$
$593$		−	6.97858i		−	0.286576i	0.989681	−	0.143288i	$-0.0457675\pi$
$594$	−1.53948	+	2.85363i	−0.0631657	+	0.117086i
$595$		0			0
$596$	3.34292	−	2.19656i	0.136931	−	0.0899745i
$597$	−0.350269			−0.0143356
$598$	−8.97858	+	16.6430i	−0.367161	+	0.680583i
$599$	−36.4998			−1.49134			−0.745670	−	0.666315i	$-0.767870\pi$
$599$	−36.4998			−1.49134			−0.745670	+	0.666315i	$0.767870\pi$
$600$		0			0
$601$	−15.5725			−0.635214			−0.317607	−	0.948222i	$-0.602879\pi$
$601$	−15.5725			−0.635214			−0.317607	+	0.948222i	$0.602879\pi$
$602$	−29.4868	+	54.6577i	−1.20179	+	2.22768i
$603$	4.00000			0.162893
$604$	−9.17092	−	13.9572i	−0.373160	−	0.567909i
$605$		0			0
$606$	1.34292	−	2.48929i	0.0545525	−	0.101120i
$607$			31.2285i			1.26752i	0.773528	+	0.633762i	$0.218490\pi$
$607$			31.2285i			1.26752i	−0.773528	+	0.633762i	$0.781510\pi$
$608$	9.41033	+	11.9284i	0.381639	+	0.483760i
$609$	−9.37169			−0.379760
$610$		0			0
$611$		−	36.2008i		−	1.46453i
$612$	−4.97858	+	3.27131i	−0.201247	+	0.132235i
$613$	−0.978577			−0.0395244			−0.0197622	−	0.999805i	$-0.506291\pi$
$613$	−0.978577			−0.0395244			−0.0197622	+	0.999805i	$0.506291\pi$
$614$	33.0361	+	17.8223i	1.33323	+	0.719251i
$615$		0			0
$616$	2.62831	+	30.2730i	0.105898	+	1.21973i
$617$		−	32.9357i		−	1.32594i	−0.748645	−	0.662971i	$-0.769295\pi$
$617$		−	32.9357i		−	1.32594i	0.748645	−	0.662971i	$-0.230705\pi$
$618$	9.83221	−	18.2253i	0.395510	−	0.733130i
$619$			3.35700i			0.134929i	0.997722	+	0.0674646i	$0.0214910\pi$
$619$			3.35700i			0.134929i	−0.997722	+	0.0674646i	$0.978509\pi$
$620$		0			0
$621$			2.68585i			0.107779i
$622$	15.1856	+	8.19235i	0.608888	+	0.328483i
$623$			15.7992i			0.632983i
$624$	−7.90383	+	18.2787i	−0.316406	+	0.731732i
$625$		0			0
$626$	−10.7146	+	19.8610i	−0.428242	+	0.793804i
$627$	6.15792			0.245924
$628$	−24.5468	−	37.3576i	−0.979525	−	1.49073i
$629$			13.0852i			0.521742i
$630$		0			0
$631$	−27.7648			−1.10530			−0.552650	−	0.833414i	$-0.686383\pi$
$631$	−27.7648			−1.10530			−0.552650	+	0.833414i	$0.686383\pi$
$632$	−0.249885	−	2.87819i	−0.00993990	−	0.114488i
$633$			14.1004i			0.560440i
$634$	−41.7324	−	22.5138i	−1.65741	−	0.894139i
$635$		0			0
$636$	2.19656	+	3.34292i	0.0870992	+	0.132556i
$637$	−74.4653			−2.95042
$638$	5.70727	+	3.07896i	0.225953	+	0.121897i
$639$	0.585462			0.0231605
$640$		0			0
$641$	−21.1281			−0.834509			−0.417254	−	0.908790i	$-0.637008\pi$
$641$	−21.1281			−0.834509			−0.417254	+	0.908790i	$0.637008\pi$
$642$	−14.1004	−	7.60688i	−0.556498	−	0.300220i
$643$	−29.2860			−1.15493			−0.577464	−	0.816416i	$-0.695957\pi$
$643$	−29.2860			−1.15493			−0.577464	+	0.816416i	$0.695957\pi$
$644$	13.8223	+	21.0361i	0.544677	+	0.828939i
$645$		0			0
$646$	9.95715	+	5.37169i	0.391759	+	0.211346i
$647$		−	15.6728i		−	0.616163i	−0.951360	−	0.308082i	$-0.900313\pi$
$647$		−	15.6728i		−	0.616163i	0.951360	−	0.308082i	$-0.0996870\pi$
$648$	0.244644	+	2.81783i	0.00961054	+	0.110695i
$649$	3.91431			0.153650
$650$		0			0
$651$			32.7005i			1.28164i
$652$	1.50650	+	2.29273i	0.0589991	+	0.0897903i
$653$	−17.5296			−0.685987			−0.342993	−	0.939338i	$-0.611441\pi$
$653$	−17.5296			−0.685987			−0.342993	+	0.939338i	$0.611441\pi$
$654$	−6.29273	+	11.6644i	−0.246065	+	0.456115i
$655$		0			0
$656$	18.0533	−	41.7507i	0.704864	−	1.63009i
$657$		−	6.00000i		−	0.234082i
$658$	−42.4078	−	22.8782i	−1.65323	−	0.891885i
$659$			23.8652i			0.929656i	0.885401	+	0.464828i	$0.153884\pi$
$659$			23.8652i			0.929656i	−0.885401	+	0.464828i	$0.846116\pi$
$660$		0			0
$661$		−	30.1579i		−	1.17301i	−0.809947	−	0.586504i	$-0.800504\pi$
$661$		−	30.1579i		−	1.17301i	0.809947	−	0.586504i	$-0.199496\pi$
$662$	13.3331	−	24.7146i	0.518204	−	0.960561i
$663$			14.8291i			0.575914i
$664$	3.27131	+	37.6791i	0.126951	+	1.46223i
$665$		0			0
$666$	5.46787	+	2.94981i	0.211875	+	0.114303i
$667$	5.37169			0.207993
$668$	18.8396	−	12.3790i	0.728924	−	0.478959i
$669$		−	6.72869i		−	0.260146i
$670$		0			0
$671$	−10.5132			−0.405859
$672$	16.4177	+	20.8108i	0.633326	+	0.802794i
$673$		−	18.0000i		−	0.693849i	−0.937893	−	0.346925i	$-0.887226\pi$
$673$		−	18.0000i		−	0.693849i	0.937893	−	0.346925i	$-0.112774\pi$
$674$	4.81500	−	8.92525i	0.185467	−	0.343788i
$675$		0			0
$676$	12.9446	+	19.7002i	0.497868	+	0.757701i
$677$	9.61531			0.369546			0.184773	−	0.982781i	$-0.440845\pi$
$677$	9.61531			0.369546			0.184773	+	0.982781i	$0.440845\pi$
$678$	−13.2713	+	24.6002i	−0.509682	+	0.944763i
$679$	18.5426			0.711600
$680$		0			0
$681$	9.95715			0.381559
$682$	10.7434	−	19.9143i	0.411385	−	0.762558i
$683$	−18.6283			−0.712792			−0.356396	−	0.934335i	$-0.615995\pi$
$683$	−18.6283			−0.712792			−0.356396	+	0.934335i	$0.615995\pi$
$684$	4.48929	−	2.94981i	0.171652	−	0.112789i
$685$		0			0
$686$	−25.0361	+	46.4078i	−0.955883	+	1.77186i
$687$			11.3288i			0.432222i
$688$	14.8782	−	34.4078i	0.567226	−	1.31179i
$689$	9.95715			0.379337
$690$		0			0
$691$		−	13.4292i		−	0.510872i	−0.966826	−	0.255436i	$-0.917781\pi$
$691$		−	13.4292i		−	0.510872i	0.966826	−	0.255436i	$-0.0822190\pi$
$692$	11.8463	+	18.0288i	0.450328	+	0.685351i
$693$	10.7434			0.408107
$694$	0.978577	+	0.527923i	0.0371463	+	0.0200397i
$695$		0			0
$696$	5.63565	−	0.489289i	0.213619	−	0.0185464i
$697$		−	33.8715i		−	1.28297i
$698$	4.13481	−	7.66442i	0.156505	−	0.290103i
$699$		−	18.9786i		−	0.717836i
$700$		0			0
$701$			19.1709i			0.724076i	0.932163	+	0.362038i	$0.117919\pi$
$701$			19.1709i			0.724076i	−0.932163	+	0.362038i	$0.882081\pi$
$702$	6.19656	+	3.34292i	0.233874	+	0.126171i
$703$		−	11.7992i		−	0.445016i
$704$	−3.16106	−	18.0674i	−0.119137	−	0.680941i
$705$		0			0
$706$	−14.5855	+	27.0361i	−0.548931	+	1.01752i
$707$	−9.37169			−0.352459
$708$	2.85363	−	1.87506i	0.107246	−	0.0704690i
$709$		−	15.4145i		−	0.578905i	−0.957192	−	0.289453i	$-0.906527\pi$
$709$		−	15.4145i		−	0.578905i	0.957192	−	0.289453i	$-0.0934732\pi$
$710$		0			0
$711$	−1.02142			−0.0383063
$712$	−0.824865	−	9.50085i	−0.0309131	−	0.356059i
$713$		−	18.7434i		−	0.701945i
$714$	17.3717	+	9.37169i	0.650119	+	0.350727i
$715$		0			0
$716$	6.12494	−	4.02456i	0.228900	−	0.150405i
$717$	−2.62831			−0.0981559
$718$	−0.728692	−	0.393115i	−0.0271945	−	0.0146709i
$719$	−20.7862			−0.775196			−0.387598	−	0.921829i	$-0.626695\pi$
$719$	−20.7862			−0.775196			−0.387598	+	0.921829i	$0.626695\pi$
$720$		0			0
$721$	−68.6148			−2.55535
$722$	14.6697	+	7.91400i	0.545948	+	0.294529i
$723$	10.7862			0.401144
$724$	11.0790	−	7.27973i	0.411746	−	0.270549i
$725$		0			0
$726$	7.14847	+	3.85646i	0.265305	+	0.143127i
$727$		−	12.3012i		−	0.456224i	−0.973635	−	0.228112i	$-0.926745\pi$
$727$		−	12.3012i		−	0.456224i	0.973635	−	0.228112i	$-0.0732553\pi$
$728$	65.7367	−	5.70727i	2.43636	−	0.211525i
$729$	1.00000			0.0370370
$730$		0			0
$731$		−	27.9143i		−	1.03245i
$732$	−7.66442	+	5.03612i	−0.283285	+	0.186140i
$733$	35.9227			1.32684			0.663418	−	0.748249i	$-0.269105\pi$
$733$	35.9227			1.32684			0.663418	+	0.748249i	$0.269105\pi$
$734$	−0.325711	+	0.603749i	−0.0120222	+	0.0222848i
$735$		0			0
$736$	−9.41033	−	11.9284i	−0.346869	−	0.439686i
$737$			9.17092i			0.337815i
$738$	−14.1537	−	7.63565i	−0.521005	−	0.281072i
$739$		−	29.0277i		−	1.06780i	−0.845547	−	0.533900i	$-0.820726\pi$
$739$		−	29.0277i		−	1.06780i	0.845547	−	0.533900i	$-0.179274\pi$
$740$		0			0
$741$		−	13.3717i		−	0.491221i
$742$	6.29273	−	11.6644i	0.231013	−	0.428214i
$743$			2.60015i			0.0953904i	0.998862	+	0.0476952i	$0.0151876\pi$
$743$			2.60015i			0.0953904i	−0.998862	+	0.0476952i	$0.984812\pi$
$744$	−1.70727	−	19.6644i	−0.0625915	−	0.720933i
$745$		0			0
$746$	15.4250	+	8.32150i	0.564750	+	0.304672i
$747$	13.3717			0.489245
$748$	−7.50023	−	11.4145i	−0.274236	−	0.417357i
$749$			53.0852i			1.93969i
$750$		0			0
$751$	−10.8929			−0.397487			−0.198744	−	0.980052i	$-0.563686\pi$
$751$	−10.8929			−0.397487			−0.198744	+	0.980052i	$0.563686\pi$
$752$	26.6963	+	11.5437i	0.973515	+	0.420955i
$753$			30.9933i			1.12946i
$754$	6.68585	−	12.3931i	0.243484	−	0.451331i
$755$		0			0
$756$	7.83221	−	5.14637i	0.284855	−	0.187172i
$757$	34.3503			1.24848			0.624241	−	0.781232i	$-0.285408\pi$
$757$	34.3503			1.24848			0.624241	+	0.781232i	$0.285408\pi$
$758$	−17.4679	+	32.3790i	−0.634461	+	1.17606i
$759$	−6.15792			−0.223518
$760$		0			0
$761$	−19.0852			−0.691839			−0.345920	−	0.938264i	$-0.612433\pi$
$761$	−19.0852			−0.691839			−0.345920	+	0.938264i	$0.612433\pi$
$762$	4.46052	−	8.26817i	0.161588	−	0.299524i
$763$	43.9143			1.58980
$764$	−8.78623	−	13.3717i	−0.317875	−	0.483771i
$765$		0			0
$766$	−4.48929	+	8.32150i	−0.162205	+	0.300668i
$767$		−	8.49977i		−	0.306909i
$768$	−10.9593	−	11.6574i	−0.395458	−	0.420650i
$769$	−31.8715			−1.14931			−0.574657	−	0.818394i	$-0.694865\pi$
$769$	−31.8715			−1.14931			−0.574657	+	0.818394i	$0.694865\pi$
$770$		0			0
$771$		−	20.9357i		−	0.753982i
$772$	−2.02877	+	1.33306i	−0.0730170	+	0.0479778i
$773$	11.9572			0.430069			0.215034	−	0.976606i	$-0.431014\pi$
$773$	11.9572			0.430069			0.215034	+	0.976606i	$0.431014\pi$
$774$	−11.6644	−	6.29273i	−0.419269	−	0.226188i
$775$		0			0
$776$	−11.1506	+	0.968095i	−0.400282	+	0.0347526i
$777$		−	20.5855i		−	0.738499i
$778$	20.0863	−	37.2327i	0.720129	−	1.33486i
$779$			30.5426i			1.09430i
$780$		0			0
$781$			1.34231i			0.0480315i
$782$	−9.95715	−	5.37169i	−0.356067	−	0.192091i
$783$		−	2.00000i		−	0.0714742i
$784$	23.7455	−	54.9146i	0.848053	−	1.96124i
$785$		0			0
$786$	−4.75325	+	8.81079i	−0.169543	+	0.314270i
$787$	33.0852			1.17936			0.589681	−	0.807637i	$-0.299254\pi$
$787$	33.0852			1.17936			0.589681	+	0.807637i	$0.299254\pi$
$788$	26.3116	+	40.0435i	0.937313	+	1.42649i
$789$		−	19.2713i		−	0.686077i
$790$		0			0
$791$	92.6148			3.29300
$792$	−6.46052	+	0.560904i	−0.229565	+	0.0199308i
$793$			22.8291i			0.810684i
$794$	12.1537	+	6.55669i	0.431319	+	0.232688i
$795$		0			0
$796$	−0.384694	−	0.585462i	−0.0136351	−	0.0207511i
$797$	−10.0000			−0.354218			−0.177109	−	0.984191i	$-0.556675\pi$
$797$	−10.0000			−0.354218			−0.177109	+	0.984191i	$0.556675\pi$
$798$	−15.6644	−	8.45065i	−0.554515	−	0.299150i
$799$	21.6582			0.766210
$800$		0			0
$801$	−3.37169			−0.119133
$802$	−8.19656	−	4.42188i	−0.289431	−	0.156142i
$803$	13.7564			0.485452
$804$	4.39312	+	6.68585i	0.154933	+	0.235792i
$805$		0			0
$806$	−43.2432	−	23.3288i	−1.52318	−	0.821724i
$807$			24.7434i			0.871008i
$808$	5.63565	−	0.489289i	0.198262	−	0.0172131i
$809$	30.6148			1.07636			0.538180	−	0.842830i	$-0.319112\pi$
$809$	30.6148			1.07636			0.538180	+	0.842830i	$0.319112\pi$
$810$		0			0
$811$			53.9290i			1.89370i	0.321670	+	0.946852i	$0.395756\pi$
$811$			53.9290i			1.89370i	−0.321670	+	0.946852i	$0.604244\pi$
$812$	−10.2927	−	15.6644i	−0.361204	−	0.549713i
$813$	27.5640			0.966713
$814$	−6.76312	+	12.5363i	−0.237047	+	0.439399i
$815$		0			0
$816$	−10.9357	−	4.72869i	−0.382827	−	0.165537i
$817$			25.1709i			0.880619i
$818$	32.2541	+	17.4005i	1.12774	+	0.608393i
$819$		−	23.3288i		−	0.815176i
$820$		0			0
$821$			12.6577i			0.441757i	0.975301	+	0.220878i	$0.0708924\pi$
$821$			12.6577i			0.441757i	−0.975301	+	0.220878i	$0.929108\pi$
$822$	−10.0575	+	18.6430i	−0.350797	+	0.650249i
$823$		−	19.8139i		−	0.690670i	−0.938479	−	0.345335i	$-0.887765\pi$
$823$		−	19.8139i		−	0.690670i	0.938479	−	0.345335i	$-0.112235\pi$
$824$	41.2614	−	3.58233i	1.43741	−	0.124796i
$825$		0			0
$826$	−9.95715	−	5.37169i	−0.346454	−	0.186905i
$827$	20.0000			0.695468			0.347734	−	0.937593i	$-0.386951\pi$
$827$	20.0000			0.695468			0.347734	+	0.937593i	$0.386951\pi$
$828$	−4.48929	+	2.94981i	−0.156014	+	0.102513i
$829$			41.3717i			1.43690i	0.695580	+	0.718449i	$0.255148\pi$
$829$			41.3717i			1.43690i	−0.695580	+	0.718449i	$0.744852\pi$
$830$		0			0
$831$	−20.3074			−0.704457
$832$	−39.2327	+	6.86412i	−1.36015	+	0.237970i
$833$		−	44.5510i		−	1.54360i
$834$	3.11760	−	5.77888i	0.107954	−	0.200106i
$835$		0			0
$836$	6.76312	+	10.2927i	0.233907	+	0.355982i
$837$	−6.97858			−0.241215
$838$	−8.22533	+	15.2467i	−0.284139	+	0.526690i
$839$	−20.9013			−0.721593			−0.360797	−	0.932645i	$-0.617495\pi$
$839$	−20.9013			−0.721593			−0.360797	+	0.932645i	$0.617495\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$	3.13650	−	5.81392i	0.108091	−	0.200361i
$843$	−10.7862			−0.371498
$844$	−23.5682	+	15.4862i	−0.811253	+	0.533055i
$845$		0			0
$846$	4.88240	−	9.05019i	0.167860	−	0.311152i
$847$		−	26.9126i		−	0.924728i
$848$	−3.17513	+	7.34292i	−0.109035	+	0.252157i
$849$	20.0000			0.686398
$850$		0			0
$851$			11.7992i			0.404472i
$852$	0.643000	+	0.978577i	0.0220288	+	0.0335255i
$853$	−6.63673			−0.227237			−0.113619	−	0.993524i	$-0.536244\pi$
$853$	−6.63673			−0.227237			−0.113619	+	0.993524i	$0.536244\pi$
$854$	26.7434	+	14.4275i	0.915140	+	0.493700i
$855$		0			0
$856$	−2.77154	−	31.9227i	−0.0947292	−	1.09110i
$857$		−	9.80765i		−	0.335023i	−0.985870	−	0.167512i	$-0.946427\pi$
$857$		−	9.80765i		−	0.335023i	0.985870	−	0.167512i	$-0.0535731\pi$
$858$	−7.66442	+	14.2070i	−0.261659	+	0.485020i
$859$		−	39.3864i		−	1.34385i	−0.740621	−	0.671923i	$-0.765469\pi$
$859$		−	39.3864i		−	1.34385i	0.740621	−	0.671923i	$-0.234531\pi$
$860$		0			0
$861$			53.2860i			1.81598i
$862$	0.728692	+	0.393115i	0.0248193	+	0.0133896i
$863$			7.07054i			0.240684i	0.992732	+	0.120342i	$0.0383991\pi$
$863$			7.07054i			0.240684i	−0.992732	+	0.120342i	$0.961601\pi$
$864$	−4.44120	+	3.50367i	−0.151093	+	0.119197i
$865$		0			0
$866$	14.7146	−	27.2755i	0.500023	−	0.926860i
$867$	8.12808			0.276044
$868$	−54.6577	+	35.9143i	−1.85520	+	1.21901i
$869$		−	2.34185i		−	0.0794417i
$870$		0			0
$871$	19.9143			0.674771
$872$	−26.4078	+	2.29273i	−0.894281	+	0.0776417i
$873$			3.95715i			0.133929i
$874$	8.97858	+	4.84377i	0.303705	+	0.163843i
$875$		0			0
$876$	10.0288	−	6.58967i	0.338841	−	0.222644i
$877$	23.1365			0.781264			0.390632	−	0.920547i	$-0.372256\pi$
$877$	23.1365			0.781264			0.390632	+	0.920547i	$0.372256\pi$
$878$	2.97858	+	1.60688i	0.100522	+	0.0542297i
$879$	21.9143			0.739151
$880$		0			0
$881$	28.4569			0.958738			0.479369	−	0.877613i	$-0.340866\pi$
$881$	28.4569			0.958738			0.479369	+	0.877613i	$0.340866\pi$
$882$	−18.6163	−	10.0432i	−0.626845	−	0.338171i
$883$	41.2003			1.38650			0.693250	−	0.720697i	$-0.256178\pi$
$883$	41.2003			1.38650			0.693250	+	0.720697i	$0.256178\pi$
$884$	−24.7862	+	16.2865i	−0.833651	+	0.547773i
$885$		0			0
$886$	25.7648	+	13.8996i	0.865586	+	0.466967i
$887$			3.55777i			0.119458i	0.998215	+	0.0597291i	$0.0190237\pi$
$887$			3.55777i			0.119458i	−0.998215	+	0.0597291i	$0.980976\pi$
$888$	1.07475	+	12.3790i	0.0360663	+	0.415413i
$889$	−31.1281			−1.04400
$890$		0			0
$891$			2.29273i			0.0768094i
$892$	11.2467	−	7.38998i	0.376569	−	0.247435i
$893$	−19.5296			−0.653534
$894$	1.34292	−	2.48929i	0.0449141	−	0.0832543i
$895$		0			0
$896$	−16.7533	+	50.2976i	−0.559687	+	1.68032i
$897$			13.3717i			0.446468i
$898$	47.1898	+	25.4580i	1.57474	+	0.849544i
$899$			13.9572i			0.465497i
$900$		0			0
$901$			5.95715i			0.198462i
$902$	17.5065	−	32.4507i	0.582903	−	1.08049i
$903$			43.9143i			1.46138i
$904$	−55.6938	+	4.83535i	−1.85235	+	0.160821i
$905$		0			0
$906$	−10.3931	−	5.60688i	−0.345288	−	0.186276i
$907$	−50.6577			−1.68206			−0.841031	−	0.540988i	$-0.818051\pi$
$907$	−50.6577			−1.68206			−0.841031	+	0.540988i	$0.818051\pi$
$908$	10.9357	+	16.6430i	0.362915	+	0.552317i
$909$		−	2.00000i		−	0.0663358i
$910$		0			0
$911$	−26.4569			−0.876557			−0.438279	−	0.898839i	$-0.644412\pi$
$911$	−26.4569			−0.876557			−0.438279	+	0.898839i	$0.644412\pi$
$912$	9.86098	+	4.26396i	0.326530	+	0.141194i
$913$			30.6577i			1.01462i
$914$	25.9859	−	48.1684i	0.859538	−	1.59327i
$915$		0			0
$916$	−18.9357	+	12.4422i	−0.625654	+	0.411103i
$917$	33.1709			1.09540
$918$	−2.00000	+	3.70727i	−0.0660098	+	0.122358i
$919$	−29.8077			−0.983264			−0.491632	−	0.870803i	$-0.663599\pi$
$919$	−29.8077			−0.983264			−0.491632	+	0.870803i	$0.663599\pi$
$920$		0			0
$921$	26.5426			0.874609
$922$	3.18500	−	5.90383i	0.104892	−	0.194432i
$923$	2.91477			0.0959407
$924$	11.7992	+	17.9572i	0.388166	+	0.590747i
$925$		0			0
$926$	−10.2829	+	19.0607i	−0.337916	+	0.626373i
$927$		−	14.6430i		−	0.480939i
$928$	7.00735	+	8.88240i	0.230027	+	0.291579i
$929$	8.82908			0.289673			0.144836	−	0.989456i	$-0.453734\pi$
$929$	8.82908			0.289673			0.144836	+	0.989456i	$0.453734\pi$
$930$		0			0
$931$			40.1726i			1.31660i
$932$	31.7220	−	20.8438i	1.03909	−	0.682760i
$933$	12.2008			0.399435
$934$	−38.0147	−	20.5082i	−1.24388	−	0.671049i
$935$		0			0
$936$	1.21798	+	14.0288i	0.0398109	+	0.458545i
$937$			42.2302i			1.37960i	0.724000	+	0.689799i	$0.242301\pi$
$937$			42.2302i			1.37960i	−0.724000	+	0.689799i	$0.757699\pi$
$938$	12.5855	−	23.3288i	0.410930	−	0.761714i
$939$			15.9572i			0.520742i
$940$		0			0
$941$			32.7434i			1.06740i	0.845673	+	0.533702i	$0.179200\pi$
$941$			32.7434i			1.06740i	−0.845673	+	0.533702i	$0.820800\pi$
$942$	−27.8181	−	15.0073i	−0.906364	−	0.488966i
$943$		−	30.5426i		−	0.994604i
$944$	6.26817	+	2.71040i	0.204012	+	0.0882162i
$945$		0			0
$946$	14.4275	−	26.7434i	0.469080	−	0.869502i
$947$	−15.9143			−0.517146			−0.258573	−	0.965992i	$-0.583252\pi$
$947$	−15.9143			−0.517146			−0.258573	+	0.965992i	$0.583252\pi$
$948$	−1.12181	−	1.70727i	−0.0364346	−	0.0554495i
$949$		−	29.8715i		−	0.969669i
$950$		0			0
$951$	−33.5296			−1.08727
$952$	3.41454	+	39.3288i	0.110666	+	1.27466i
$953$			55.6791i			1.80362i	0.432129	+	0.901812i	$0.357762\pi$
$953$			55.6791i			1.80362i	−0.432129	+	0.901812i	$0.642238\pi$
$954$	2.48929	+	1.34292i	0.0805937	+	0.0434787i
$955$		0			0
$956$	−2.88661	−	4.39312i	−0.0933598	−	0.142083i
$957$	4.58546			0.148227
$958$	−4.14323	−	2.23519i	−0.133862	−	0.0722158i
$959$	70.1873			2.26647
$960$		0			0
$961$	17.7005			0.570985
$962$	27.2222	+	14.6858i	0.877679	+	0.473491i
$963$	−11.3288			−0.365067
$964$	11.8463	+	18.0288i	0.381543	+	0.580668i
$965$		0			0
$966$	15.6644	+	8.45065i	0.503995	+	0.271895i
$967$			54.7581i			1.76090i	0.474138	+	0.880451i	$0.342760\pi$
$967$			54.7581i			1.76090i	−0.474138	+	0.880451i	$0.657240\pi$
$968$	1.40509	+	16.1839i	0.0451612	+	0.520169i
$969$	8.00000			0.256997
$970$		0			0
$971$		−	30.3221i		−	0.973083i	−0.873657	−	0.486542i	$-0.838258\pi$
$971$		−	30.3221i		−	0.973083i	0.873657	−	0.486542i	$-0.161742\pi$
$972$	1.09828	+	1.67146i	0.0352273	+	0.0536122i
$973$	−21.7564			−0.697478
$974$	−8.12494	+	15.0607i	−0.260340	+	0.482575i
$975$		0			0
$976$	−16.8353	−	7.27973i	−0.538886	−	0.233018i
$977$			29.7220i			0.950890i	0.879746	+	0.475445i	$0.157713\pi$
$977$			29.7220i			0.950890i	−0.879746	+	0.475445i	$0.842287\pi$
$978$	1.70727	+	0.921039i	0.0545924	+	0.0294516i
$979$		−	7.73038i		−	0.247064i
$980$		0			0
$981$			9.37169i			0.299215i
$982$	−9.59702	+	17.7894i	−0.306253	+	0.567681i
$983$		−	49.5443i		−	1.58022i	−0.612966	−	0.790109i	$-0.710024\pi$
$983$		−	49.5443i		−	1.58022i	0.612966	−	0.790109i	$-0.289976\pi$
$984$	−2.78202	−	32.0435i	−0.0886875	−	1.02151i
$985$		0			0
$986$	7.41454	+	4.00000i	0.236127	+	0.127386i
$987$	−34.0722			−1.08453
$988$	22.3503	−	14.6858i	0.711057	−	0.467219i
$989$		−	25.1709i		−	0.800389i
$990$		0			0
$991$	19.0937			0.606530			0.303265	−	0.952906i	$-0.401923\pi$
$991$	19.0937			0.606530			0.303265	+	0.952906i	$0.401923\pi$
$992$	30.9933	−	24.4507i	0.984037	−	0.776309i
$993$		−	19.8568i		−	0.630136i
$994$	1.84208	−	3.41454i	0.0584271	−	0.108303i
$995$		0			0
$996$	14.6858	+	22.3503i	0.465339	+	0.708195i
$997$	38.8500			1.23039			0.615197	−	0.788374i	$-0.289077\pi$
$997$	38.8500			1.23039			0.615197	+	0.788374i	$0.289077\pi$
$998$	−6.19656	+	11.4862i	−0.196149	+	0.363588i
$999$	4.39312			0.138992

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.d.f.349.6		6
3.2	odd	2		1800.2.d.r.1549.1		6
4.3	odd	2		2400.2.d.e.49.6		6
5.2	odd	4		120.2.k.b.61.2	yes	6
5.3	odd	4		600.2.k.c.301.5		6
5.4	even	2		600.2.d.e.349.1		6
8.3	odd	2		2400.2.d.f.49.6		6
8.5	even	2		600.2.d.e.349.2		6
12.11	even	2		7200.2.d.r.2449.6		6
15.2	even	4		360.2.k.f.181.5		6
15.8	even	4		1800.2.k.p.901.2		6
15.14	odd	2		1800.2.d.q.1549.6		6
20.3	even	4		2400.2.k.c.1201.3		6
20.7	even	4		480.2.k.b.241.4		6
20.19	odd	2		2400.2.d.f.49.1		6
24.5	odd	2		1800.2.d.q.1549.5		6
24.11	even	2		7200.2.d.q.2449.6		6
40.3	even	4		2400.2.k.c.1201.6		6
40.13	odd	4		600.2.k.c.301.6		6
40.19	odd	2		2400.2.d.e.49.1		6
40.27	even	4		480.2.k.b.241.1		6
40.29	even	2	inner	600.2.d.f.349.5		6
40.37	odd	4		120.2.k.b.61.1	✓	6
60.23	odd	4		7200.2.k.p.3601.6		6
60.47	odd	4		1440.2.k.f.721.4		6
60.59	even	2		7200.2.d.q.2449.1		6
80.27	even	4		3840.2.a.br.1.3		3
80.37	odd	4		3840.2.a.bp.1.1		3
80.67	even	4		3840.2.a.bo.1.3		3
80.77	odd	4		3840.2.a.bq.1.1		3
120.29	odd	2		1800.2.d.r.1549.2		6
120.53	even	4		1800.2.k.p.901.1		6
120.59	even	2		7200.2.d.r.2449.1		6
120.77	even	4		360.2.k.f.181.6		6
120.83	odd	4		7200.2.k.p.3601.5		6
120.107	odd	4		1440.2.k.f.721.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.k.b.61.1	✓	6	40.37	odd	4
120.2.k.b.61.2	yes	6	5.2	odd	4
360.2.k.f.181.5		6	15.2	even	4
360.2.k.f.181.6		6	120.77	even	4
480.2.k.b.241.1		6	40.27	even	4
480.2.k.b.241.4		6	20.7	even	4
600.2.d.e.349.1		6	5.4	even	2
600.2.d.e.349.2		6	8.5	even	2
600.2.d.f.349.5		6	40.29	even	2	inner
600.2.d.f.349.6		6	1.1	even	1	trivial
600.2.k.c.301.5		6	5.3	odd	4
600.2.k.c.301.6		6	40.13	odd	4
1440.2.k.f.721.1		6	120.107	odd	4
1440.2.k.f.721.4		6	60.47	odd	4
1800.2.d.q.1549.5		6	24.5	odd	2
1800.2.d.q.1549.6		6	15.14	odd	2
1800.2.d.r.1549.1		6	3.2	odd	2
1800.2.d.r.1549.2		6	120.29	odd	2
1800.2.k.p.901.1		6	120.53	even	4
1800.2.k.p.901.2		6	15.8	even	4
2400.2.d.e.49.1		6	40.19	odd	2
2400.2.d.e.49.6		6	4.3	odd	2
2400.2.d.f.49.1		6	20.19	odd	2
2400.2.d.f.49.6		6	8.3	odd	2
2400.2.k.c.1201.3		6	20.3	even	4
2400.2.k.c.1201.6		6	40.3	even	4
3840.2.a.bo.1.3		3	80.67	even	4
3840.2.a.bp.1.1		3	80.37	odd	4
3840.2.a.bq.1.1		3	80.77	odd	4
3840.2.a.br.1.3		3	80.27	even	4
7200.2.d.q.2449.1		6	60.59	even	2
7200.2.d.q.2449.6		6	24.11	even	2
7200.2.d.r.2449.1		6	120.59	even	2
7200.2.d.r.2449.6		6	12.11	even	2
7200.2.k.p.3601.5		6	120.83	odd	4
7200.2.k.p.3601.6		6	60.23	odd	4

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.24464 + 0.671462i) q^{2} +1.00000 q^{3} +(1.09828 + 1.67146i) q^{4} +(1.24464 + 0.671462i) q^{6} -4.68585i q^{7} +(0.244644 + 2.81783i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.24464 + 0.671462i) q^{2} +1.00000 q^{3} +(1.09828 + 1.67146i) q^{4} +(1.24464 + 0.671462i) q^{6} -4.68585i q^{7} +(0.244644 + 2.81783i) q^{8} +1.00000 q^{9} +2.29273i q^{11} +(1.09828 + 1.67146i) q^{12} +4.97858 q^{13} +(3.14637 - 5.83221i) q^{14} +(-1.58757 + 3.67146i) q^{16} +2.97858i q^{17} +(1.24464 + 0.671462i) q^{18} -2.68585i q^{19} -4.68585i q^{21} +(-1.53948 + 2.85363i) q^{22} +2.68585i q^{23} +(0.244644 + 2.81783i) q^{24} +(6.19656 + 3.34292i) q^{26} +1.00000 q^{27} +(7.83221 - 5.14637i) q^{28} -2.00000i q^{29} -6.97858 q^{31} +(-4.44120 + 3.50367i) q^{32} +2.29273i q^{33} +(-2.00000 + 3.70727i) q^{34} +(1.09828 + 1.67146i) q^{36} +4.39312 q^{37} +(1.80344 - 3.34292i) q^{38} +4.97858 q^{39} -11.3717 q^{41} +(3.14637 - 5.83221i) q^{42} -9.37169 q^{43} +(-3.83221 + 2.51806i) q^{44} +(-1.80344 + 3.34292i) q^{46} -7.27131i q^{47} +(-1.58757 + 3.67146i) q^{48} -14.9572 q^{49} +2.97858i q^{51} +(5.46787 + 8.32150i) q^{52} +2.00000 q^{53} +(1.24464 + 0.671462i) q^{54} +(13.2039 - 1.14637i) q^{56} -2.68585i q^{57} +(1.34292 - 2.48929i) q^{58} -1.70727i q^{59} +4.58546i q^{61} +(-8.68585 - 4.68585i) q^{62} -4.68585i q^{63} +(-7.88030 + 1.37873i) q^{64} +(-1.53948 + 2.85363i) q^{66} +4.00000 q^{67} +(-4.97858 + 3.27131i) q^{68} +2.68585i q^{69} +0.585462 q^{71} +(0.244644 + 2.81783i) q^{72} -6.00000i q^{73} +(5.46787 + 2.94981i) q^{74} +(4.48929 - 2.94981i) q^{76} +10.7434 q^{77} +(6.19656 + 3.34292i) q^{78} -1.02142 q^{79} +1.00000 q^{81} +(-14.1537 - 7.63565i) q^{82} +13.3717 q^{83} +(7.83221 - 5.14637i) q^{84} +(-11.6644 - 6.29273i) q^{86} -2.00000i q^{87} +(-6.46052 + 0.560904i) q^{88} -3.37169 q^{89} -23.3288i q^{91} +(-4.48929 + 2.94981i) q^{92} -6.97858 q^{93} +(4.88240 - 9.05019i) q^{94} +(-4.44120 + 3.50367i) q^{96} +3.95715i q^{97} +(-18.6163 - 10.0432i) q^{98} +2.29273i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} + 2 q^{4} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^3 + 2 * q^4 - 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{3} + 2 q^{4} - 6 q^{8} + 6 q^{9} + 2 q^{12} + 16 q^{14} + 10 q^{16} + 12 q^{22} - 6 q^{24} + 28 q^{26} + 6 q^{27} + 20 q^{28} - 12 q^{31} - 10 q^{32} - 12 q^{34} + 2 q^{36} + 8 q^{37} + 20 q^{38} - 20 q^{41} + 16 q^{42} - 8 q^{43} + 4 q^{44} - 20 q^{46} + 10 q^{48} - 30 q^{49} - 12 q^{52} + 12 q^{53} + 4 q^{56} - 4 q^{58} - 28 q^{62} - 22 q^{64} + 12 q^{66} + 24 q^{67} - 8 q^{71} - 6 q^{72} - 12 q^{74} + 12 q^{76} - 32 q^{77} + 28 q^{78} - 36 q^{79} + 6 q^{81} - 16 q^{82} + 32 q^{83} + 20 q^{84} - 16 q^{86} - 60 q^{88} + 28 q^{89} - 12 q^{92} - 12 q^{93} - 4 q^{94} - 10 q^{96} - 56 q^{98}+O(q^{100}) \) 6 * q + 6 * q^3 + 2 * q^4 - 6 * q^8 + 6 * q^9 + 2 * q^12 + 16 * q^14 + 10 * q^16 + 12 * q^22 - 6 * q^24 + 28 * q^26 + 6 * q^27 + 20 * q^28 - 12 * q^31 - 10 * q^32 - 12 * q^34 + 2 * q^36 + 8 * q^37 + 20 * q^38 - 20 * q^41 + 16 * q^42 - 8 * q^43 + 4 * q^44 - 20 * q^46 + 10 * q^48 - 30 * q^49 - 12 * q^52 + 12 * q^53 + 4 * q^56 - 4 * q^58 - 28 * q^62 - 22 * q^64 + 12 * q^66 + 24 * q^67 - 8 * q^71 - 6 * q^72 - 12 * q^74 + 12 * q^76 - 32 * q^77 + 28 * q^78 - 36 * q^79 + 6 * q^81 - 16 * q^82 + 32 * q^83 + 20 * q^84 - 16 * q^86 - 60 * q^88 + 28 * q^89 - 12 * q^92 - 12 * q^93 - 4 * q^94 - 10 * q^96 - 56 * q^98

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