LMFDB - Embedded newform 12.3.d.a.7.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [12,3,Mod(7,12)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("12.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(12, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	12.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.326976317232$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.2
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.3.d.a.7.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.73205i) q^{2} -1.73205i q^{3} +(-2.00000 - 3.46410i) q^{4} -2.00000 q^{5} +(3.00000 + 1.73205i) q^{6} +6.92820i q^{7} +8.00000 q^{8} -3.00000 q^{9} +(2.00000 - 3.46410i) q^{10} -6.92820i q^{11} +(-6.00000 + 3.46410i) q^{12} +2.00000 q^{13} +(-12.0000 - 6.92820i) q^{14} +3.46410i q^{15} +(-8.00000 + 13.8564i) q^{16} +10.0000 q^{17} +(3.00000 - 5.19615i) q^{18} -20.7846i q^{19} +(4.00000 + 6.92820i) q^{20} +12.0000 q^{21} +(12.0000 + 6.92820i) q^{22} +27.7128i q^{23} -13.8564i q^{24} -21.0000 q^{25} +(-2.00000 + 3.46410i) q^{26} +5.19615i q^{27} +(24.0000 - 13.8564i) q^{28} -26.0000 q^{29} +(-6.00000 - 3.46410i) q^{30} -6.92820i q^{31} +(-16.0000 - 27.7128i) q^{32} -12.0000 q^{33} +(-10.0000 + 17.3205i) q^{34} -13.8564i q^{35} +(6.00000 + 10.3923i) q^{36} +26.0000 q^{37} +(36.0000 + 20.7846i) q^{38} -3.46410i q^{39} -16.0000 q^{40} +58.0000 q^{41} +(-12.0000 + 20.7846i) q^{42} +48.4974i q^{43} +(-24.0000 + 13.8564i) q^{44} +6.00000 q^{45} +(-48.0000 - 27.7128i) q^{46} -69.2820i q^{47} +(24.0000 + 13.8564i) q^{48} +1.00000 q^{49} +(21.0000 - 36.3731i) q^{50} -17.3205i q^{51} +(-4.00000 - 6.92820i) q^{52} -74.0000 q^{53} +(-9.00000 - 5.19615i) q^{54} +13.8564i q^{55} +55.4256i q^{56} -36.0000 q^{57} +(26.0000 - 45.0333i) q^{58} +90.0666i q^{59} +(12.0000 - 6.92820i) q^{60} +26.0000 q^{61} +(12.0000 + 6.92820i) q^{62} -20.7846i q^{63} +64.0000 q^{64} -4.00000 q^{65} +(12.0000 - 20.7846i) q^{66} -6.92820i q^{67} +(-20.0000 - 34.6410i) q^{68} +48.0000 q^{69} +(24.0000 + 13.8564i) q^{70} -24.0000 q^{72} -46.0000 q^{73} +(-26.0000 + 45.0333i) q^{74} +36.3731i q^{75} +(-72.0000 + 41.5692i) q^{76} +48.0000 q^{77} +(6.00000 + 3.46410i) q^{78} -117.779i q^{79} +(16.0000 - 27.7128i) q^{80} +9.00000 q^{81} +(-58.0000 + 100.459i) q^{82} -48.4974i q^{83} +(-24.0000 - 41.5692i) q^{84} -20.0000 q^{85} +(-84.0000 - 48.4974i) q^{86} +45.0333i q^{87} -55.4256i q^{88} +82.0000 q^{89} +(-6.00000 + 10.3923i) q^{90} +13.8564i q^{91} +(96.0000 - 55.4256i) q^{92} -12.0000 q^{93} +(120.000 + 69.2820i) q^{94} +41.5692i q^{95} +(-48.0000 + 27.7128i) q^{96} +2.00000 q^{97} +(-1.00000 + 1.73205i) q^{98} +20.7846i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 6 q^{6} + 16 q^{8} - 6 q^{9} + 4 q^{10} - 12 q^{12} + 4 q^{13} - 24 q^{14} - 16 q^{16} + 20 q^{17} + 6 q^{18} + 8 q^{20} + 24 q^{21} + 24 q^{22} - 42 q^{25} - 4 q^{26}+ \cdots - 2 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 6 * q^6 + 16 * q^8 - 6 * q^9 + 4 * q^10 - 12 * q^12 + 4 * q^13 - 24 * q^14 - 16 * q^16 + 20 * q^17 + 6 * q^18 + 8 * q^20 + 24 * q^21 + 24 * q^22 - 42 * q^25 - 4 * q^26 + 48 * q^28 - 52 * q^29 - 12 * q^30 - 32 * q^32 - 24 * q^33 - 20 * q^34 + 12 * q^36 + 52 * q^37 + 72 * q^38 - 32 * q^40 + 116 * q^41 - 24 * q^42 - 48 * q^44 + 12 * q^45 - 96 * q^46 + 48 * q^48 + 2 * q^49 + 42 * q^50 - 8 * q^52 - 148 * q^53 - 18 * q^54 - 72 * q^57 + 52 * q^58 + 24 * q^60 + 52 * q^61 + 24 * q^62 + 128 * q^64 - 8 * q^65 + 24 * q^66 - 40 * q^68 + 96 * q^69 + 48 * q^70 - 48 * q^72 - 92 * q^73 - 52 * q^74 - 144 * q^76 + 96 * q^77 + 12 * q^78 + 32 * q^80 + 18 * q^81 - 116 * q^82 - 48 * q^84 - 40 * q^85 - 168 * q^86 + 164 * q^89 - 12 * q^90 + 192 * q^92 - 24 * q^93 + 240 * q^94 - 96 * q^96 + 4 * q^97 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$1$	$-1$

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 $

$2$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$2$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$5$	−2.00000			−0.400000			−0.200000	−	0.979796i	$-0.564094\pi$
$5$	−2.00000			−0.400000			−0.200000	+	0.979796i	$0.564094\pi$
$6$	3.00000	+	1.73205i	0.500000	+	0.288675i
$7$			6.92820i			0.989743i	0.868966	+	0.494872i	$0.164785\pi$
$7$			6.92820i			0.989743i	−0.868966	+	0.494872i	$0.835215\pi$
$8$	8.00000			1.00000
$9$	−3.00000			−0.333333
$10$	2.00000	−	3.46410i	0.200000	−	0.346410i
$11$		−	6.92820i		−	0.629837i	−0.949119	−	0.314918i	$-0.898023\pi$
$11$		−	6.92820i		−	0.629837i	0.949119	−	0.314918i	$-0.101977\pi$
$12$	−6.00000	+	3.46410i	−0.500000	+	0.288675i
$13$	2.00000			0.153846			0.0769231	−	0.997037i	$-0.475490\pi$
$13$	2.00000			0.153846			0.0769231	+	0.997037i	$0.475490\pi$
$14$	−12.0000	−	6.92820i	−0.857143	−	0.494872i
$15$			3.46410i			0.230940i
$16$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$17$	10.0000			0.588235			0.294118	−	0.955769i	$-0.404974\pi$
$17$	10.0000			0.588235			0.294118	+	0.955769i	$0.404974\pi$
$18$	3.00000	−	5.19615i	0.166667	−	0.288675i
$19$		−	20.7846i		−	1.09393i	−0.837157	−	0.546963i	$-0.815784\pi$
$19$		−	20.7846i		−	1.09393i	0.837157	−	0.546963i	$-0.184216\pi$
$20$	4.00000	+	6.92820i	0.200000	+	0.346410i
$21$	12.0000			0.571429
$22$	12.0000	+	6.92820i	0.545455	+	0.314918i
$23$			27.7128i			1.20490i	0.798155	+	0.602452i	$0.205810\pi$
$23$			27.7128i			1.20490i	−0.798155	+	0.602452i	$0.794190\pi$
$24$		−	13.8564i		−	0.577350i
$25$	−21.0000			−0.840000
$26$	−2.00000	+	3.46410i	−0.0769231	+	0.133235i
$27$			5.19615i			0.192450i
$28$	24.0000	−	13.8564i	0.857143	−	0.494872i
$29$	−26.0000			−0.896552			−0.448276	−	0.893895i	$-0.647962\pi$
$29$	−26.0000			−0.896552			−0.448276	+	0.893895i	$0.647962\pi$
$30$	−6.00000	−	3.46410i	−0.200000	−	0.115470i
$31$		−	6.92820i		−	0.223490i	−0.993737	−	0.111745i	$-0.964356\pi$
$31$		−	6.92820i		−	0.223490i	0.993737	−	0.111745i	$-0.0356441\pi$
$32$	−16.0000	−	27.7128i	−0.500000	−	0.866025i
$33$	−12.0000			−0.363636
$34$	−10.0000	+	17.3205i	−0.294118	+	0.509427i
$35$		−	13.8564i		−	0.395897i
$36$	6.00000	+	10.3923i	0.166667	+	0.288675i
$37$	26.0000			0.702703			0.351351	−	0.936244i	$-0.385722\pi$
$37$	26.0000			0.702703			0.351351	+	0.936244i	$0.385722\pi$
$38$	36.0000	+	20.7846i	0.947368	+	0.546963i
$39$		−	3.46410i		−	0.0888231i
$40$	−16.0000			−0.400000
$41$	58.0000			1.41463			0.707317	−	0.706896i	$-0.249905\pi$
$41$	58.0000			1.41463			0.707317	+	0.706896i	$0.249905\pi$
$42$	−12.0000	+	20.7846i	−0.285714	+	0.494872i
$43$			48.4974i			1.12785i	0.825827	+	0.563924i	$0.190709\pi$
$43$			48.4974i			1.12785i	−0.825827	+	0.563924i	$0.809291\pi$
$44$	−24.0000	+	13.8564i	−0.545455	+	0.314918i
$45$	6.00000			0.133333
$46$	−48.0000	−	27.7128i	−1.04348	−	0.602452i
$47$		−	69.2820i		−	1.47409i	−0.675846	−	0.737043i	$-0.736222\pi$
$47$		−	69.2820i		−	1.47409i	0.675846	−	0.737043i	$-0.263778\pi$
$48$	24.0000	+	13.8564i	0.500000	+	0.288675i
$49$	1.00000			0.0204082
$50$	21.0000	−	36.3731i	0.420000	−	0.727461i
$51$		−	17.3205i		−	0.339618i
$52$	−4.00000	−	6.92820i	−0.0769231	−	0.133235i
$53$	−74.0000			−1.39623			−0.698113	−	0.715987i	$-0.745977\pi$
$53$	−74.0000			−1.39623			−0.698113	+	0.715987i	$0.745977\pi$
$54$	−9.00000	−	5.19615i	−0.166667	−	0.0962250i
$55$			13.8564i			0.251935i
$56$			55.4256i			0.989743i
$57$	−36.0000			−0.631579
$58$	26.0000	−	45.0333i	0.448276	−	0.776437i
$59$			90.0666i			1.52655i	0.646072	+	0.763277i	$0.276411\pi$
$59$			90.0666i			1.52655i	−0.646072	+	0.763277i	$0.723589\pi$
$60$	12.0000	−	6.92820i	0.200000	−	0.115470i
$61$	26.0000			0.426230			0.213115	−	0.977027i	$-0.431639\pi$
$61$	26.0000			0.426230			0.213115	+	0.977027i	$0.431639\pi$
$62$	12.0000	+	6.92820i	0.193548	+	0.111745i
$63$		−	20.7846i		−	0.329914i
$64$	64.0000			1.00000
$65$	−4.00000			−0.0615385
$66$	12.0000	−	20.7846i	0.181818	−	0.314918i
$67$		−	6.92820i		−	0.103406i	−0.998663	−	0.0517030i	$-0.983535\pi$
$67$		−	6.92820i		−	0.103406i	0.998663	−	0.0517030i	$-0.0164649\pi$
$68$	−20.0000	−	34.6410i	−0.294118	−	0.509427i
$69$	48.0000			0.695652
$70$	24.0000	+	13.8564i	0.342857	+	0.197949i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−24.0000			−0.333333
$73$	−46.0000			−0.630137			−0.315068	−	0.949069i	$-0.602027\pi$
$73$	−46.0000			−0.630137			−0.315068	+	0.949069i	$0.602027\pi$
$74$	−26.0000	+	45.0333i	−0.351351	+	0.608558i
$75$			36.3731i			0.484974i
$76$	−72.0000	+	41.5692i	−0.947368	+	0.546963i
$77$	48.0000			0.623377
$78$	6.00000	+	3.46410i	0.0769231	+	0.0444116i
$79$		−	117.779i		−	1.49088i	−0.666573	−	0.745440i	$-0.732240\pi$
$79$		−	117.779i		−	1.49088i	0.666573	−	0.745440i	$-0.267760\pi$
$80$	16.0000	−	27.7128i	0.200000	−	0.346410i
$81$	9.00000			0.111111
$82$	−58.0000	+	100.459i	−0.707317	+	1.22511i
$83$		−	48.4974i		−	0.584306i	−0.956372	−	0.292153i	$-0.905628\pi$
$83$		−	48.4974i		−	0.584306i	0.956372	−	0.292153i	$-0.0943717\pi$
$84$	−24.0000	−	41.5692i	−0.285714	−	0.494872i
$85$	−20.0000			−0.235294
$86$	−84.0000	−	48.4974i	−0.976744	−	0.563924i
$87$			45.0333i			0.517624i
$88$		−	55.4256i		−	0.629837i
$89$	82.0000			0.921348			0.460674	−	0.887569i	$-0.347608\pi$
$89$	82.0000			0.921348			0.460674	+	0.887569i	$0.347608\pi$
$90$	−6.00000	+	10.3923i	−0.0666667	+	0.115470i
$91$			13.8564i			0.152268i
$92$	96.0000	−	55.4256i	1.04348	−	0.602452i
$93$	−12.0000			−0.129032
$94$	120.000	+	69.2820i	1.27660	+	0.737043i
$95$			41.5692i			0.437571i
$96$	−48.0000	+	27.7128i	−0.500000	+	0.288675i
$97$	2.00000			0.0206186			0.0103093	−	0.999947i	$-0.496718\pi$
$97$	2.00000			0.0206186			0.0103093	+	0.999947i	$0.496718\pi$
$98$	−1.00000	+	1.73205i	−0.0102041	+	0.0176740i
$99$			20.7846i			0.209946i
$100$	42.0000	+	72.7461i	0.420000	+	0.727461i
$101$	−74.0000			−0.732673			−0.366337	−	0.930482i	$-0.619388\pi$
$101$	−74.0000			−0.732673			−0.366337	+	0.930482i	$0.619388\pi$
$102$	30.0000	+	17.3205i	0.294118	+	0.169809i
$103$			76.2102i			0.739905i	0.929051	+	0.369953i	$0.120626\pi$
$103$			76.2102i			0.739905i	−0.929051	+	0.369953i	$0.879374\pi$
$104$	16.0000			0.153846
$105$	−24.0000			−0.228571
$106$	74.0000	−	128.172i	0.698113	−	1.20917i
$107$		−	20.7846i		−	0.194249i	−0.995272	−	0.0971243i	$-0.969036\pi$
$107$		−	20.7846i		−	0.194249i	0.995272	−	0.0971243i	$-0.0309645\pi$
$108$	18.0000	−	10.3923i	0.166667	−	0.0962250i
$109$	−46.0000			−0.422018			−0.211009	−	0.977484i	$-0.567675\pi$
$109$	−46.0000			−0.422018			−0.211009	+	0.977484i	$0.567675\pi$
$110$	−24.0000	−	13.8564i	−0.218182	−	0.125967i
$111$		−	45.0333i		−	0.405706i
$112$	−96.0000	−	55.4256i	−0.857143	−	0.494872i
$113$	−110.000			−0.973451			−0.486726	−	0.873555i	$-0.661809\pi$
$113$	−110.000			−0.973451			−0.486726	+	0.873555i	$0.661809\pi$
$114$	36.0000	−	62.3538i	0.315789	−	0.546963i
$115$		−	55.4256i		−	0.481962i
$116$	52.0000	+	90.0666i	0.448276	+	0.776437i
$117$	−6.00000			−0.0512821
$118$	−156.000	−	90.0666i	−1.32203	−	0.763277i
$119$			69.2820i			0.582202i
$120$			27.7128i			0.230940i
$121$	73.0000			0.603306
$122$	−26.0000	+	45.0333i	−0.213115	+	0.369126i
$123$		−	100.459i		−	0.816739i
$124$	−24.0000	+	13.8564i	−0.193548	+	0.111745i
$125$	92.0000			0.736000
$126$	36.0000	+	20.7846i	0.285714	+	0.164957i
$127$			145.492i			1.14561i	0.819692	+	0.572804i	$0.194144\pi$
$127$			145.492i			1.14561i	−0.819692	+	0.572804i	$0.805856\pi$
$128$	−64.0000	+	110.851i	−0.500000	+	0.866025i
$129$	84.0000			0.651163
$130$	4.00000	−	6.92820i	0.0307692	−	0.0532939i
$131$		−	117.779i		−	0.899080i	−0.893260	−	0.449540i	$-0.851588\pi$
$131$		−	117.779i		−	0.899080i	0.893260	−	0.449540i	$-0.148412\pi$
$132$	24.0000	+	41.5692i	0.181818	+	0.314918i
$133$	144.000			1.08271
$134$	12.0000	+	6.92820i	0.0895522	+	0.0517030i
$135$		−	10.3923i		−	0.0769800i
$136$	80.0000			0.588235
$137$	10.0000			0.0729927			0.0364964	−	0.999334i	$-0.488380\pi$
$137$	10.0000			0.0729927			0.0364964	+	0.999334i	$0.488380\pi$
$138$	−48.0000	+	83.1384i	−0.347826	+	0.602452i
$139$		−	48.4974i		−	0.348902i	−0.984666	−	0.174451i	$-0.944185\pi$
$139$		−	48.4974i		−	0.348902i	0.984666	−	0.174451i	$-0.0558151\pi$
$140$	−48.0000	+	27.7128i	−0.342857	+	0.197949i
$141$	−120.000			−0.851064
$142$		0			0
$143$		−	13.8564i		−	0.0968979i
$144$	24.0000	−	41.5692i	0.166667	−	0.288675i
$145$	52.0000			0.358621
$146$	46.0000	−	79.6743i	0.315068	−	0.545715i
$147$		−	1.73205i		−	0.0117827i
$148$	−52.0000	−	90.0666i	−0.351351	−	0.608558i
$149$	−2.00000			−0.0134228			−0.00671141	−	0.999977i	$-0.502136\pi$
$149$	−2.00000			−0.0134228			−0.00671141	+	0.999977i	$0.502136\pi$
$150$	−63.0000	−	36.3731i	−0.420000	−	0.242487i
$151$			90.0666i			0.596468i	0.954493	+	0.298234i	$0.0963975\pi$
$151$			90.0666i			0.596468i	−0.954493	+	0.298234i	$0.903602\pi$
$152$		−	166.277i		−	1.09393i
$153$	−30.0000			−0.196078
$154$	−48.0000	+	83.1384i	−0.311688	+	0.539860i
$155$			13.8564i			0.0893962i
$156$	−12.0000	+	6.92820i	−0.0769231	+	0.0444116i
$157$	−214.000			−1.36306			−0.681529	−	0.731791i	$-0.738685\pi$
$157$	−214.000			−1.36306			−0.681529	+	0.731791i	$0.738685\pi$
$158$	204.000	+	117.779i	1.29114	+	0.745440i
$159$			128.172i			0.806112i
$160$	32.0000	+	55.4256i	0.200000	+	0.346410i
$161$	−192.000			−1.19255
$162$	−9.00000	+	15.5885i	−0.0555556	+	0.0962250i
$163$		−	20.7846i		−	0.127513i	−0.997965	−	0.0637565i	$-0.979692\pi$
$163$		−	20.7846i		−	0.127513i	0.997965	−	0.0637565i	$-0.0203081\pi$
$164$	−116.000	−	200.918i	−0.707317	−	1.22511i
$165$	24.0000			0.145455
$166$	84.0000	+	48.4974i	0.506024	+	0.292153i
$167$		−	96.9948i		−	0.580807i	−0.956904	−	0.290404i	$-0.906210\pi$
$167$		−	96.9948i		−	0.580807i	0.956904	−	0.290404i	$-0.0937896\pi$
$168$	96.0000			0.571429
$169$	−165.000			−0.976331
$170$	20.0000	−	34.6410i	0.117647	−	0.203771i
$171$			62.3538i			0.364642i
$172$	168.000	−	96.9948i	0.976744	−	0.563924i
$173$	334.000			1.93064			0.965318	−	0.261077i	$-0.0840777\pi$
$173$	334.000			1.93064			0.965318	+	0.261077i	$0.0840777\pi$
$174$	−78.0000	−	45.0333i	−0.448276	−	0.258812i
$175$		−	145.492i		−	0.831384i
$176$	96.0000	+	55.4256i	0.545455	+	0.314918i
$177$	156.000			0.881356
$178$	−82.0000	+	142.028i	−0.460674	+	0.797911i
$179$			187.061i			1.04504i	0.852628	+	0.522518i	$0.175007\pi$
$179$			187.061i			1.04504i	−0.852628	+	0.522518i	$0.824993\pi$
$180$	−12.0000	−	20.7846i	−0.0666667	−	0.115470i
$181$	2.00000			0.0110497			0.00552486	−	0.999985i	$-0.498241\pi$
$181$	2.00000			0.0110497			0.00552486	+	0.999985i	$0.498241\pi$
$182$	−24.0000	−	13.8564i	−0.131868	−	0.0761341i
$183$		−	45.0333i		−	0.246084i
$184$			221.703i			1.20490i
$185$	−52.0000			−0.281081
$186$	12.0000	−	20.7846i	0.0645161	−	0.111745i
$187$		−	69.2820i		−	0.370492i
$188$	−240.000	+	138.564i	−1.27660	+	0.737043i
$189$	−36.0000			−0.190476
$190$	−72.0000	−	41.5692i	−0.378947	−	0.218785i
$191$			221.703i			1.16075i	0.814351	+	0.580373i	$0.197093\pi$
$191$			221.703i			1.16075i	−0.814351	+	0.580373i	$0.802907\pi$
$192$		−	110.851i		−	0.577350i
$193$	290.000			1.50259			0.751295	−	0.659966i	$-0.229429\pi$
$193$	290.000			1.50259			0.751295	+	0.659966i	$0.229429\pi$
$194$	−2.00000	+	3.46410i	−0.0103093	+	0.0178562i
$195$			6.92820i			0.0355292i
$196$	−2.00000	−	3.46410i	−0.0102041	−	0.0176740i
$197$	−26.0000			−0.131980			−0.0659898	−	0.997820i	$-0.521020\pi$
$197$	−26.0000			−0.131980			−0.0659898	+	0.997820i	$0.521020\pi$
$198$	−36.0000	−	20.7846i	−0.181818	−	0.104973i
$199$		−	394.908i		−	1.98446i	−0.124416	−	0.992230i	$-0.539706\pi$
$199$		−	394.908i		−	1.98446i	0.124416	−	0.992230i	$-0.460294\pi$
$200$	−168.000			−0.840000
$201$	−12.0000			−0.0597015
$202$	74.0000	−	128.172i	0.366337	−	0.634514i
$203$		−	180.133i		−	0.887356i
$204$	−60.0000	+	34.6410i	−0.294118	+	0.169809i
$205$	−116.000			−0.565854
$206$	−132.000	−	76.2102i	−0.640777	−	0.369953i
$207$		−	83.1384i		−	0.401635i
$208$	−16.0000	+	27.7128i	−0.0769231	+	0.133235i
$209$	−144.000			−0.688995
$210$	24.0000	−	41.5692i	0.114286	−	0.197949i
$211$			242.487i			1.14923i	0.818425	+	0.574614i	$0.194848\pi$
$211$			242.487i			1.14923i	−0.818425	+	0.574614i	$0.805152\pi$
$212$	148.000	+	256.344i	0.698113	+	1.20917i
$213$		0			0
$214$	36.0000	+	20.7846i	0.168224	+	0.0971243i
$215$		−	96.9948i		−	0.451139i
$216$			41.5692i			0.192450i
$217$	48.0000			0.221198
$218$	46.0000	−	79.6743i	0.211009	−	0.365479i
$219$			79.6743i			0.363810i
$220$	48.0000	−	27.7128i	0.218182	−	0.125967i
$221$	20.0000			0.0904977
$222$	78.0000	+	45.0333i	0.351351	+	0.202853i
$223$			339.482i			1.52234i	0.648552	+	0.761170i	$0.275375\pi$
$223$			339.482i			1.52234i	−0.648552	+	0.761170i	$0.724625\pi$
$224$	192.000	−	110.851i	0.857143	−	0.494872i
$225$	63.0000			0.280000
$226$	110.000	−	190.526i	0.486726	−	0.843034i
$227$			284.056i			1.25135i	0.780084	+	0.625675i	$0.215176\pi$
$227$			284.056i			1.25135i	−0.780084	+	0.625675i	$0.784824\pi$
$228$	72.0000	+	124.708i	0.315789	+	0.546963i
$229$	−142.000			−0.620087			−0.310044	−	0.950722i	$-0.600344\pi$
$229$	−142.000			−0.620087			−0.310044	+	0.950722i	$0.600344\pi$
$230$	96.0000	+	55.4256i	0.417391	+	0.240981i
$231$		−	83.1384i		−	0.359907i
$232$	−208.000			−0.896552
$233$	82.0000			0.351931			0.175966	−	0.984396i	$-0.443695\pi$
$233$	82.0000			0.351931			0.175966	+	0.984396i	$0.443695\pi$
$234$	6.00000	−	10.3923i	0.0256410	−	0.0444116i
$235$			138.564i			0.589634i
$236$	312.000	−	180.133i	1.32203	−	0.763277i
$237$	−204.000			−0.860759
$238$	−120.000	−	69.2820i	−0.504202	−	0.291101i
$239$		−	387.979i		−	1.62334i	−0.584113	−	0.811672i	$-0.698558\pi$
$239$		−	387.979i		−	1.62334i	0.584113	−	0.811672i	$-0.301442\pi$
$240$	−48.0000	−	27.7128i	−0.200000	−	0.115470i
$241$	−46.0000			−0.190871			−0.0954357	−	0.995436i	$-0.530424\pi$
$241$	−46.0000			−0.190871			−0.0954357	+	0.995436i	$0.530424\pi$
$242$	−73.0000	+	126.440i	−0.301653	+	0.522478i
$243$		−	15.5885i		−	0.0641500i
$244$	−52.0000	−	90.0666i	−0.213115	−	0.369126i
$245$	−2.00000			−0.00816327
$246$	174.000	+	100.459i	0.707317	+	0.408370i
$247$		−	41.5692i		−	0.168296i
$248$		−	55.4256i		−	0.223490i
$249$	−84.0000			−0.337349
$250$	−92.0000	+	159.349i	−0.368000	+	0.637395i
$251$		−	145.492i		−	0.579650i	−0.957080	−	0.289825i	$-0.906403\pi$
$251$		−	145.492i		−	0.579650i	0.957080	−	0.289825i	$-0.0935972\pi$
$252$	−72.0000	+	41.5692i	−0.285714	+	0.164957i
$253$	192.000			0.758893
$254$	−252.000	−	145.492i	−0.992126	−	0.572804i
$255$			34.6410i			0.135847i
$256$	−128.000	−	221.703i	−0.500000	−	0.866025i
$257$	−254.000			−0.988327			−0.494163	−	0.869369i	$-0.664526\pi$
$257$	−254.000			−0.988327			−0.494163	+	0.869369i	$0.664526\pi$
$258$	−84.0000	+	145.492i	−0.325581	+	0.563924i
$259$			180.133i			0.695495i
$260$	8.00000	+	13.8564i	0.0307692	+	0.0532939i
$261$	78.0000			0.298851
$262$	204.000	+	117.779i	0.778626	+	0.449540i
$263$		−	152.420i		−	0.579546i	−0.957095	−	0.289773i	$-0.906420\pi$
$263$		−	152.420i		−	0.579546i	0.957095	−	0.289773i	$-0.0935797\pi$
$264$	−96.0000			−0.363636
$265$	148.000			0.558491
$266$	−144.000	+	249.415i	−0.541353	+	0.937652i
$267$		−	142.028i		−	0.531941i
$268$	−24.0000	+	13.8564i	−0.0895522	+	0.0517030i
$269$	262.000			0.973978			0.486989	−	0.873408i	$-0.338095\pi$
$269$	262.000			0.973978			0.486989	+	0.873408i	$0.338095\pi$
$270$	18.0000	+	10.3923i	0.0666667	+	0.0384900i
$271$		−	20.7846i		−	0.0766960i	−0.999264	−	0.0383480i	$-0.987790\pi$
$271$		−	20.7846i		−	0.0766960i	0.999264	−	0.0383480i	$-0.0122095\pi$
$272$	−80.0000	+	138.564i	−0.294118	+	0.509427i
$273$	24.0000			0.0879121
$274$	−10.0000	+	17.3205i	−0.0364964	+	0.0632135i
$275$			145.492i			0.529063i
$276$	−96.0000	−	166.277i	−0.347826	−	0.602452i
$277$	290.000			1.04693			0.523466	−	0.852047i	$-0.324639\pi$
$277$	290.000			1.04693			0.523466	+	0.852047i	$0.324639\pi$
$278$	84.0000	+	48.4974i	0.302158	+	0.174451i
$279$			20.7846i			0.0744968i
$280$		−	110.851i		−	0.395897i
$281$	226.000			0.804270			0.402135	−	0.915580i	$-0.368268\pi$
$281$	226.000			0.804270			0.402135	+	0.915580i	$0.368268\pi$
$282$	120.000	−	207.846i	0.425532	−	0.737043i
$283$		−	297.913i		−	1.05270i	−0.850269	−	0.526348i	$-0.823561\pi$
$283$		−	297.913i		−	1.05270i	0.850269	−	0.526348i	$-0.176439\pi$
$284$		0			0
$285$	72.0000			0.252632
$286$	24.0000	+	13.8564i	0.0839161	+	0.0484490i
$287$			401.836i			1.40012i
$288$	48.0000	+	83.1384i	0.166667	+	0.288675i
$289$	−189.000			−0.653979
$290$	−52.0000	+	90.0666i	−0.179310	+	0.310575i
$291$		−	3.46410i		−	0.0119041i
$292$	92.0000	+	159.349i	0.315068	+	0.545715i
$293$	−362.000			−1.23549			−0.617747	−	0.786377i	$-0.711955\pi$
$293$	−362.000			−1.23549			−0.617747	+	0.786377i	$0.711955\pi$
$294$	3.00000	+	1.73205i	0.0102041	+	0.00589133i
$295$		−	180.133i		−	0.610621i
$296$	208.000			0.702703
$297$	36.0000			0.121212
$298$	2.00000	−	3.46410i	0.00671141	−	0.0116245i
$299$			55.4256i			0.185370i
$300$	126.000	−	72.7461i	0.420000	−	0.242487i
$301$	−336.000			−1.11628
$302$	−156.000	−	90.0666i	−0.516556	−	0.298234i
$303$			128.172i			0.423009i
$304$	288.000	+	166.277i	0.947368	+	0.546963i
$305$	−52.0000			−0.170492
$306$	30.0000	−	51.9615i	0.0980392	−	0.169809i
$307$		−	145.492i		−	0.473916i	−0.971520	−	0.236958i	$-0.923850\pi$
$307$		−	145.492i		−	0.473916i	0.971520	−	0.236958i	$-0.0761504\pi$
$308$	−96.0000	−	166.277i	−0.311688	−	0.539860i
$309$	132.000			0.427184
$310$	−24.0000	−	13.8564i	−0.0774194	−	0.0446981i
$311$			235.559i			0.757424i	0.925515	+	0.378712i	$0.123633\pi$
$311$			235.559i			0.757424i	−0.925515	+	0.378712i	$0.876367\pi$
$312$		−	27.7128i		−	0.0888231i
$313$	−478.000			−1.52716			−0.763578	−	0.645715i	$-0.776559\pi$
$313$	−478.000			−1.52716			−0.763578	+	0.645715i	$0.776559\pi$
$314$	214.000	−	370.659i	0.681529	−	1.18044i
$315$			41.5692i			0.131966i
$316$	−408.000	+	235.559i	−1.29114	+	0.745440i
$317$	−170.000			−0.536278			−0.268139	−	0.963380i	$-0.586409\pi$
$317$	−170.000			−0.536278			−0.268139	+	0.963380i	$0.586409\pi$
$318$	−222.000	−	128.172i	−0.698113	−	0.403056i
$319$			180.133i			0.564681i
$320$	−128.000			−0.400000
$321$	−36.0000			−0.112150
$322$	192.000	−	332.554i	0.596273	−	1.03278i
$323$		−	207.846i		−	0.643486i
$324$	−18.0000	−	31.1769i	−0.0555556	−	0.0962250i
$325$	−42.0000			−0.129231
$326$	36.0000	+	20.7846i	0.110429	+	0.0637565i
$327$			79.6743i			0.243652i
$328$	464.000			1.41463
$329$	480.000			1.45897
$330$	−24.0000	+	41.5692i	−0.0727273	+	0.125967i
$331$		−	408.764i		−	1.23494i	−0.786596	−	0.617468i	$-0.788158\pi$
$331$		−	408.764i		−	1.23494i	0.786596	−	0.617468i	$-0.211842\pi$
$332$	−168.000	+	96.9948i	−0.506024	+	0.292153i
$333$	−78.0000			−0.234234
$334$	168.000	+	96.9948i	0.502994	+	0.290404i
$335$			13.8564i			0.0413624i
$336$	−96.0000	+	166.277i	−0.285714	+	0.494872i
$337$	338.000			1.00297			0.501484	−	0.865167i	$-0.332788\pi$
$337$	338.000			1.00297			0.501484	+	0.865167i	$0.332788\pi$
$338$	165.000	−	285.788i	0.488166	−	0.845528i
$339$			190.526i			0.562022i
$340$	40.0000	+	69.2820i	0.117647	+	0.203771i
$341$	−48.0000			−0.140762
$342$	−108.000	−	62.3538i	−0.315789	−	0.182321i
$343$			346.410i			1.00994i
$344$			387.979i			1.12785i
$345$	−96.0000			−0.278261
$346$	−334.000	+	578.505i	−0.965318	+	1.67198i
$347$		−	200.918i		−	0.579014i	−0.957176	−	0.289507i	$-0.906509\pi$
$347$		−	200.918i		−	0.579014i	0.957176	−	0.289507i	$-0.0934914\pi$
$348$	156.000	−	90.0666i	0.448276	−	0.258812i
$349$	506.000			1.44986			0.724928	−	0.688824i	$-0.241873\pi$
$349$	506.000			1.44986			0.724928	+	0.688824i	$0.241873\pi$
$350$	252.000	+	145.492i	0.720000	+	0.415692i
$351$			10.3923i			0.0296077i
$352$	−192.000	+	110.851i	−0.545455	+	0.314918i
$353$	178.000			0.504249			0.252125	−	0.967695i	$-0.418871\pi$
$353$	178.000			0.504249			0.252125	+	0.967695i	$0.418871\pi$
$354$	−156.000	+	270.200i	−0.440678	+	0.763277i
$355$		0			0
$356$	−164.000	−	284.056i	−0.460674	−	0.797911i
$357$	120.000			0.336134
$358$	−324.000	−	187.061i	−0.905028	−	0.522518i
$359$		−	166.277i		−	0.463167i	−0.972815	−	0.231583i	$-0.925609\pi$
$359$		−	166.277i		−	0.463167i	0.972815	−	0.231583i	$-0.0743906\pi$
$360$	48.0000			0.133333
$361$	−71.0000			−0.196676
$362$	−2.00000	+	3.46410i	−0.00552486	+	0.00956934i
$363$		−	126.440i		−	0.348319i
$364$	48.0000	−	27.7128i	0.131868	−	0.0761341i
$365$	92.0000			0.252055
$366$	78.0000	+	45.0333i	0.213115	+	0.123042i
$367$		−	200.918i		−	0.547460i	−0.961807	−	0.273730i	$-0.911742\pi$
$367$		−	200.918i		−	0.547460i	0.961807	−	0.273730i	$-0.0882575\pi$
$368$	−384.000	−	221.703i	−1.04348	−	0.602452i
$369$	−174.000			−0.471545
$370$	52.0000	−	90.0666i	0.140541	−	0.243423i
$371$		−	512.687i		−	1.38191i
$372$	24.0000	+	41.5692i	0.0645161	+	0.111745i
$373$	−310.000			−0.831099			−0.415550	−	0.909571i	$-0.636411\pi$
$373$	−310.000			−0.831099			−0.415550	+	0.909571i	$0.636411\pi$
$374$	120.000	+	69.2820i	0.320856	+	0.185246i
$375$		−	159.349i		−	0.424930i
$376$		−	554.256i		−	1.47409i
$377$	−52.0000			−0.137931
$378$	36.0000	−	62.3538i	0.0952381	−	0.164957i
$379$			436.477i			1.15165i	0.817572	+	0.575827i	$0.195320\pi$
$379$			436.477i			1.15165i	−0.817572	+	0.575827i	$0.804680\pi$
$380$	144.000	−	83.1384i	0.378947	−	0.218785i
$381$	252.000			0.661417
$382$	−384.000	−	221.703i	−1.00524	−	0.580373i
$383$			609.682i			1.59186i	0.605390	+	0.795929i	$0.293017\pi$
$383$			609.682i			1.59186i	−0.605390	+	0.795929i	$0.706983\pi$
$384$	192.000	+	110.851i	0.500000	+	0.288675i
$385$	−96.0000			−0.249351
$386$	−290.000	+	502.295i	−0.751295	+	1.30128i
$387$		−	145.492i		−	0.375949i
$388$	−4.00000	−	6.92820i	−0.0103093	−	0.0178562i
$389$	−578.000			−1.48586			−0.742931	−	0.669368i	$-0.766565\pi$
$389$	−578.000			−1.48586			−0.742931	+	0.669368i	$0.766565\pi$
$390$	−12.0000	−	6.92820i	−0.0307692	−	0.0177646i
$391$			277.128i			0.708768i
$392$	8.00000			0.0204082
$393$	−204.000			−0.519084
$394$	26.0000	−	45.0333i	0.0659898	−	0.114298i
$395$			235.559i			0.596352i
$396$	72.0000	−	41.5692i	0.181818	−	0.104973i
$397$	26.0000			0.0654912			0.0327456	−	0.999464i	$-0.489575\pi$
$397$	26.0000			0.0654912			0.0327456	+	0.999464i	$0.489575\pi$
$398$	684.000	+	394.908i	1.71859	+	0.992230i
$399$		−	249.415i		−	0.625101i
$400$	168.000	−	290.985i	0.420000	−	0.727461i
$401$	250.000			0.623441			0.311721	−	0.950174i	$-0.399095\pi$
$401$	250.000			0.623441			0.311721	+	0.950174i	$0.399095\pi$
$402$	12.0000	−	20.7846i	0.0298507	−	0.0517030i
$403$		−	13.8564i		−	0.0343831i
$404$	148.000	+	256.344i	0.366337	+	0.634514i
$405$	−18.0000			−0.0444444
$406$	312.000	+	180.133i	0.768473	+	0.443678i
$407$		−	180.133i		−	0.442588i
$408$		−	138.564i		−	0.339618i
$409$	290.000			0.709046			0.354523	−	0.935047i	$-0.384643\pi$
$409$	290.000			0.709046			0.354523	+	0.935047i	$0.384643\pi$
$410$	116.000	−	200.918i	0.282927	−	0.490044i
$411$		−	17.3205i		−	0.0421424i
$412$	264.000	−	152.420i	0.640777	−	0.369953i
$413$	−624.000			−1.51090
$414$	144.000	+	83.1384i	0.347826	+	0.200817i
$415$			96.9948i			0.233723i
$416$	−32.0000	−	55.4256i	−0.0769231	−	0.133235i
$417$	−84.0000			−0.201439
$418$	144.000	−	249.415i	0.344498	−	0.596687i
$419$			339.482i			0.810219i	0.914268	+	0.405110i	$0.132767\pi$
$419$			339.482i			0.810219i	−0.914268	+	0.405110i	$0.867233\pi$
$420$	48.0000	+	83.1384i	0.114286	+	0.197949i
$421$	674.000			1.60095			0.800475	−	0.599366i	$-0.204581\pi$
$421$	674.000			1.60095			0.800475	+	0.599366i	$0.204581\pi$
$422$	−420.000	−	242.487i	−0.995261	−	0.574614i
$423$			207.846i			0.491362i
$424$	−592.000			−1.39623
$425$	−210.000			−0.494118
$426$		0			0
$427$			180.133i			0.421858i
$428$	−72.0000	+	41.5692i	−0.168224	+	0.0971243i
$429$	−24.0000			−0.0559441
$430$	168.000	+	96.9948i	0.390698	+	0.225569i
$431$		−	540.400i		−	1.25383i	−0.779088	−	0.626914i	$-0.784318\pi$
$431$		−	540.400i		−	1.25383i	0.779088	−	0.626914i	$-0.215682\pi$
$432$	−72.0000	−	41.5692i	−0.166667	−	0.0962250i
$433$	−334.000			−0.771363			−0.385681	−	0.922632i	$-0.626034\pi$
$433$	−334.000			−0.771363			−0.385681	+	0.922632i	$0.626034\pi$
$434$	−48.0000	+	83.1384i	−0.110599	+	0.191563i
$435$		−	90.0666i		−	0.207050i
$436$	92.0000	+	159.349i	0.211009	+	0.365479i
$437$	576.000			1.31808
$438$	−138.000	−	79.6743i	−0.315068	−	0.181905i
$439$		−	117.779i		−	0.268290i	−0.990962	−	0.134145i	$-0.957171\pi$
$439$		−	117.779i		−	0.268290i	0.990962	−	0.134145i	$-0.0428288\pi$
$440$			110.851i			0.251935i
$441$	−3.00000			−0.00680272
$442$	−20.0000	+	34.6410i	−0.0452489	+	0.0783733i
$443$			76.2102i			0.172032i	0.996294	+	0.0860161i	$0.0274136\pi$
$443$			76.2102i			0.172032i	−0.996294	+	0.0860161i	$0.972586\pi$
$444$	−156.000	+	90.0666i	−0.351351	+	0.202853i
$445$	−164.000			−0.368539
$446$	−588.000	−	339.482i	−1.31839	−	0.761170i
$447$			3.46410i			0.00774967i
$448$			443.405i			0.989743i
$449$	394.000			0.877506			0.438753	−	0.898608i	$-0.355420\pi$
$449$	394.000			0.877506			0.438753	+	0.898608i	$0.355420\pi$
$450$	−63.0000	+	109.119i	−0.140000	+	0.242487i
$451$		−	401.836i		−	0.890988i
$452$	220.000	+	381.051i	0.486726	+	0.843034i
$453$	156.000			0.344371
$454$	−492.000	−	284.056i	−1.08370	−	0.625675i
$455$		−	27.7128i		−	0.0609073i
$456$	−288.000			−0.631579
$457$	−478.000			−1.04595			−0.522976	−	0.852347i	$-0.675178\pi$
$457$	−478.000			−1.04595			−0.522976	+	0.852347i	$0.675178\pi$
$458$	142.000	−	245.951i	0.310044	−	0.537011i
$459$			51.9615i			0.113206i
$460$	−192.000	+	110.851i	−0.417391	+	0.240981i
$461$	142.000			0.308026			0.154013	−	0.988069i	$-0.450780\pi$
$461$	142.000			0.308026			0.154013	+	0.988069i	$0.450780\pi$
$462$	144.000	+	83.1384i	0.311688	+	0.179953i
$463$		−	630.466i		−	1.36170i	−0.732423	−	0.680849i	$-0.761611\pi$
$463$		−	630.466i		−	1.36170i	0.732423	−	0.680849i	$-0.238389\pi$
$464$	208.000	−	360.267i	0.448276	−	0.776437i
$465$	24.0000			0.0516129
$466$	−82.0000	+	142.028i	−0.175966	+	0.304781i
$467$		−	20.7846i		−	0.0445067i	−0.999752	−	0.0222533i	$-0.992916\pi$
$467$		−	20.7846i		−	0.0445067i	0.999752	−	0.0222533i	$-0.00708404\pi$
$468$	12.0000	+	20.7846i	0.0256410	+	0.0444116i
$469$	48.0000			0.102345
$470$	−240.000	−	138.564i	−0.510638	−	0.294817i
$471$			370.659i			0.786962i
$472$			720.533i			1.52655i
$473$	336.000			0.710359
$474$	204.000	−	353.338i	0.430380	−	0.745440i
$475$			436.477i			0.918899i
$476$	240.000	−	138.564i	0.504202	−	0.291101i
$477$	222.000			0.465409
$478$	672.000	+	387.979i	1.40586	+	0.811672i
$479$		−	734.390i		−	1.53317i	−0.642141	−	0.766586i	$-0.721954\pi$
$479$		−	734.390i		−	1.53317i	0.642141	−	0.766586i	$-0.278046\pi$
$480$	96.0000	−	55.4256i	0.200000	−	0.115470i
$481$	52.0000			0.108108
$482$	46.0000	−	79.6743i	0.0954357	−	0.165299i
$483$			332.554i			0.688517i
$484$	−146.000	−	252.879i	−0.301653	−	0.522478i
$485$	−4.00000			−0.00824742
$486$	27.0000	+	15.5885i	0.0555556	+	0.0320750i
$487$		−	103.923i		−	0.213394i	−0.994292	−	0.106697i	$-0.965972\pi$
$487$		−	103.923i		−	0.213394i	0.994292	−	0.106697i	$-0.0340275\pi$
$488$	208.000			0.426230
$489$	−36.0000			−0.0736196
$490$	2.00000	−	3.46410i	0.00408163	−	0.00706960i
$491$			921.451i			1.87668i	0.345711	+	0.938341i	$0.387638\pi$
$491$			921.451i			1.87668i	−0.345711	+	0.938341i	$0.612362\pi$
$492$	−348.000	+	200.918i	−0.707317	+	0.408370i
$493$	−260.000			−0.527383
$494$	72.0000	+	41.5692i	0.145749	+	0.0841482i
$495$		−	41.5692i		−	0.0839782i
$496$	96.0000	+	55.4256i	0.193548	+	0.111745i
$497$		0			0
$498$	84.0000	−	145.492i	0.168675	−	0.292153i
$499$			76.2102i			0.152726i	0.997080	+	0.0763630i	$0.0243308\pi$
$499$			76.2102i			0.152726i	−0.997080	+	0.0763630i	$0.975669\pi$
$500$	−184.000	−	318.697i	−0.368000	−	0.637395i
$501$	−168.000			−0.335329
$502$	252.000	+	145.492i	0.501992	+	0.289825i
$503$			581.969i			1.15700i	0.815684	+	0.578498i	$0.196361\pi$
$503$			581.969i			1.15700i	−0.815684	+	0.578498i	$0.803639\pi$
$504$		−	166.277i		−	0.329914i
$505$	148.000			0.293069
$506$	−192.000	+	332.554i	−0.379447	+	0.657221i
$507$			285.788i			0.563685i
$508$	504.000	−	290.985i	0.992126	−	0.572804i
$509$	−842.000			−1.65422			−0.827112	−	0.562037i	$-0.810018\pi$
$509$	−842.000			−1.65422			−0.827112	+	0.562037i	$0.810018\pi$
$510$	−60.0000	−	34.6410i	−0.117647	−	0.0679236i
$511$		−	318.697i		−	0.623674i
$512$	512.000			1.00000
$513$	108.000			0.210526
$514$	254.000	−	439.941i	0.494163	−	0.855916i
$515$		−	152.420i		−	0.295962i
$516$	−168.000	−	290.985i	−0.325581	−	0.563924i
$517$	−480.000			−0.928433
$518$	−312.000	−	180.133i	−0.602317	−	0.347748i
$519$		−	578.505i		−	1.11465i
$520$	−32.0000			−0.0615385
$521$	−326.000			−0.625720			−0.312860	−	0.949799i	$-0.601287\pi$
$521$	−326.000			−0.625720			−0.312860	+	0.949799i	$0.601287\pi$
$522$	−78.0000	+	135.100i	−0.149425	+	0.258812i
$523$		−	311.769i		−	0.596117i	−0.954548	−	0.298058i	$-0.903661\pi$
$523$		−	311.769i		−	0.596117i	0.954548	−	0.298058i	$-0.0963390\pi$
$524$	−408.000	+	235.559i	−0.778626	+	0.449540i
$525$	−252.000			−0.480000
$526$	264.000	+	152.420i	0.501901	+	0.289773i
$527$		−	69.2820i		−	0.131465i
$528$	96.0000	−	166.277i	0.181818	−	0.314918i
$529$	−239.000			−0.451796
$530$	−148.000	+	256.344i	−0.279245	+	0.483667i
$531$		−	270.200i		−	0.508851i
$532$	−288.000	−	498.831i	−0.541353	−	0.937652i
$533$	116.000			0.217636
$534$	246.000	+	142.028i	0.460674	+	0.265970i
$535$			41.5692i			0.0776995i
$536$		−	55.4256i		−	0.103406i
$537$	324.000			0.603352
$538$	−262.000	+	453.797i	−0.486989	+	0.843489i
$539$		−	6.92820i		−	0.0128538i
$540$	−36.0000	+	20.7846i	−0.0666667	+	0.0384900i
$541$	530.000			0.979667			0.489834	−	0.871816i	$-0.337058\pi$
$541$	530.000			0.979667			0.489834	+	0.871816i	$0.337058\pi$
$542$	36.0000	+	20.7846i	0.0664207	+	0.0383480i
$543$		−	3.46410i		−	0.00637956i
$544$	−160.000	−	277.128i	−0.294118	−	0.509427i
$545$	92.0000			0.168807
$546$	−24.0000	+	41.5692i	−0.0439560	+	0.0761341i
$547$			339.482i			0.620625i	0.950635	+	0.310313i	$0.100434\pi$
$547$			339.482i			0.620625i	−0.950635	+	0.310313i	$0.899566\pi$
$548$	−20.0000	−	34.6410i	−0.0364964	−	0.0632135i
$549$	−78.0000			−0.142077
$550$	−252.000	−	145.492i	−0.458182	−	0.264531i
$551$			540.400i			0.980762i
$552$	384.000			0.695652
$553$	816.000			1.47559
$554$	−290.000	+	502.295i	−0.523466	+	0.906669i
$555$			90.0666i			0.162282i
$556$	−168.000	+	96.9948i	−0.302158	+	0.174451i
$557$	766.000			1.37522			0.687612	−	0.726078i	$-0.258659\pi$
$557$	766.000			1.37522			0.687612	+	0.726078i	$0.258659\pi$
$558$	−36.0000	−	20.7846i	−0.0645161	−	0.0372484i
$559$			96.9948i			0.173515i
$560$	192.000	+	110.851i	0.342857	+	0.197949i
$561$	−120.000			−0.213904
$562$	−226.000	+	391.443i	−0.402135	+	0.696519i
$563$		−	491.902i		−	0.873717i	−0.899530	−	0.436858i	$-0.856091\pi$
$563$		−	491.902i		−	0.873717i	0.899530	−	0.436858i	$-0.143909\pi$
$564$	240.000	+	415.692i	0.425532	+	0.737043i
$565$	220.000			0.389381
$566$	516.000	+	297.913i	0.911661	+	0.526348i
$567$			62.3538i			0.109971i
$568$		0			0
$569$	−422.000			−0.741652			−0.370826	−	0.928702i	$-0.620925\pi$
$569$	−422.000			−0.741652			−0.370826	+	0.928702i	$0.620925\pi$
$570$	−72.0000	+	124.708i	−0.126316	+	0.218785i
$571$			284.056i			0.497472i	0.968571	+	0.248736i	$0.0800151\pi$
$571$			284.056i			0.497472i	−0.968571	+	0.248736i	$0.919985\pi$
$572$	−48.0000	+	27.7128i	−0.0839161	+	0.0484490i
$573$	384.000			0.670157
$574$	−696.000	−	401.836i	−1.21254	−	0.700062i
$575$		−	581.969i		−	1.01212i
$576$	−192.000			−0.333333
$577$	−46.0000			−0.0797227			−0.0398614	−	0.999205i	$-0.512692\pi$
$577$	−46.0000			−0.0797227			−0.0398614	+	0.999205i	$0.512692\pi$
$578$	189.000	−	327.358i	0.326990	−	0.566363i
$579$		−	502.295i		−	0.867521i
$580$	−104.000	−	180.133i	−0.179310	−	0.310575i
$581$	336.000			0.578313
$582$	6.00000	+	3.46410i	0.0103093	+	0.00595206i
$583$			512.687i			0.879395i
$584$	−368.000			−0.630137
$585$	12.0000			0.0205128
$586$	362.000	−	627.002i	0.617747	−	1.06997i
$587$		−	630.466i		−	1.07405i	−0.843567	−	0.537024i	$-0.819548\pi$
$587$		−	630.466i		−	1.07405i	0.843567	−	0.537024i	$-0.180452\pi$
$588$	−6.00000	+	3.46410i	−0.0102041	+	0.00589133i
$589$	−144.000			−0.244482
$590$	312.000	+	180.133i	0.528814	+	0.305311i
$591$			45.0333i			0.0761985i
$592$	−208.000	+	360.267i	−0.351351	+	0.608558i
$593$	82.0000			0.138280			0.0691400	−	0.997607i	$-0.477974\pi$
$593$	82.0000			0.138280			0.0691400	+	0.997607i	$0.477974\pi$
$594$	−36.0000	+	62.3538i	−0.0606061	+	0.104973i
$595$		−	138.564i		−	0.232881i
$596$	4.00000	+	6.92820i	0.00671141	+	0.0116245i
$597$	−684.000			−1.14573
$598$	−96.0000	−	55.4256i	−0.160535	−	0.0926850i
$599$		−	55.4256i		−	0.0925303i	−0.998929	−	0.0462651i	$-0.985268\pi$
$599$		−	55.4256i		−	0.0925303i	0.998929	−	0.0462651i	$-0.0147319\pi$
$600$			290.985i			0.484974i
$601$	−334.000			−0.555740			−0.277870	−	0.960619i	$-0.589629\pi$
$601$	−334.000			−0.555740			−0.277870	+	0.960619i	$0.589629\pi$
$602$	336.000	−	581.969i	0.558140	−	0.966726i
$603$			20.7846i			0.0344687i
$604$	312.000	−	180.133i	0.516556	−	0.298234i
$605$	−146.000			−0.241322
$606$	−222.000	−	128.172i	−0.366337	−	0.211505i
$607$			367.195i			0.604934i	0.953160	+	0.302467i	$0.0978102\pi$
$607$			367.195i			0.604934i	−0.953160	+	0.302467i	$0.902190\pi$
$608$	−576.000	+	332.554i	−0.947368	+	0.546963i
$609$	−312.000			−0.512315
$610$	52.0000	−	90.0666i	0.0852459	−	0.147650i
$611$		−	138.564i		−	0.226782i
$612$	60.0000	+	103.923i	0.0980392	+	0.169809i
$613$	−214.000			−0.349103			−0.174551	−	0.984648i	$-0.555848\pi$
$613$	−214.000			−0.349103			−0.174551	+	0.984648i	$0.555848\pi$
$614$	252.000	+	145.492i	0.410423	+	0.236958i
$615$			200.918i			0.326696i
$616$	384.000			0.623377
$617$	−1118.00			−1.81199			−0.905997	−	0.423285i	$-0.860877\pi$
$617$	−1118.00			−1.81199			−0.905997	+	0.423285i	$0.860877\pi$
$618$	−132.000	+	228.631i	−0.213592	+	0.369953i
$619$			672.036i			1.08568i	0.839836	+	0.542840i	$0.182651\pi$
$619$			672.036i			1.08568i	−0.839836	+	0.542840i	$0.817349\pi$
$620$	48.0000	−	27.7128i	0.0774194	−	0.0446981i
$621$	−144.000			−0.231884
$622$	−408.000	−	235.559i	−0.655949	−	0.378712i
$623$			568.113i			0.911898i
$624$	48.0000	+	27.7128i	0.0769231	+	0.0444116i
$625$	341.000			0.545600
$626$	478.000	−	827.920i	0.763578	−	1.32256i
$627$			249.415i			0.397792i
$628$	428.000	+	741.318i	0.681529	+	1.18044i
$629$	260.000			0.413355
$630$	−72.0000	−	41.5692i	−0.114286	−	0.0659829i
$631$			145.492i			0.230574i	0.993332	+	0.115287i	$0.0367788\pi$
$631$			145.492i			0.230574i	−0.993332	+	0.115287i	$0.963221\pi$
$632$		−	942.236i		−	1.49088i
$633$	420.000			0.663507
$634$	170.000	−	294.449i	0.268139	−	0.464430i
$635$		−	290.985i		−	0.458243i
$636$	444.000	−	256.344i	0.698113	−	0.403056i
$637$	2.00000			0.00313972
$638$	−312.000	−	180.133i	−0.489028	−	0.282341i
$639$		0			0
$640$	128.000	−	221.703i	0.200000	−	0.346410i
$641$	10.0000			0.0156006			0.00780031	−	0.999970i	$-0.497517\pi$
$641$	10.0000			0.0156006			0.00780031	+	0.999970i	$0.497517\pi$
$642$	36.0000	−	62.3538i	0.0560748	−	0.0971243i
$643$		−	1212.44i		−	1.88559i	−0.333370	−	0.942796i	$-0.608186\pi$
$643$		−	1212.44i		−	1.88559i	0.333370	−	0.942796i	$-0.391814\pi$
$644$	384.000	+	665.108i	0.596273	+	1.03278i
$645$	−168.000			−0.260465
$646$	360.000	+	207.846i	0.557276	+	0.321743i
$647$			332.554i			0.513993i	0.966412	+	0.256997i	$0.0827330\pi$
$647$			332.554i			0.513993i	−0.966412	+	0.256997i	$0.917267\pi$
$648$	72.0000			0.111111
$649$	624.000			0.961479
$650$	42.0000	−	72.7461i	0.0646154	−	0.111917i
$651$		−	83.1384i		−	0.127709i
$652$	−72.0000	+	41.5692i	−0.110429	+	0.0637565i
$653$	670.000			1.02603			0.513017	−	0.858379i	$-0.328528\pi$
$653$	670.000			1.02603			0.513017	+	0.858379i	$0.328528\pi$
$654$	−138.000	−	79.6743i	−0.211009	−	0.121826i
$655$			235.559i			0.359632i
$656$	−464.000	+	803.672i	−0.707317	+	1.22511i
$657$	138.000			0.210046
$658$	−480.000	+	831.384i	−0.729483	+	1.26350i
$659$			824.456i			1.25107i	0.780195	+	0.625536i	$0.215120\pi$
$659$			824.456i			1.25107i	−0.780195	+	0.625536i	$0.784880\pi$
$660$	−48.0000	−	83.1384i	−0.0727273	−	0.125967i
$661$	−1222.00			−1.84871			−0.924357	−	0.381529i	$-0.875398\pi$
$661$	−1222.00			−1.84871			−0.924357	+	0.381529i	$0.875398\pi$
$662$	708.000	+	408.764i	1.06949	+	0.617468i
$663$		−	34.6410i		−	0.0522489i
$664$		−	387.979i		−	0.584306i
$665$	−288.000			−0.433083
$666$	78.0000	−	135.100i	0.117117	−	0.202853i
$667$		−	720.533i		−	1.08026i
$668$	−336.000	+	193.990i	−0.502994	+	0.290404i
$669$	588.000			0.878924
$670$	−24.0000	−	13.8564i	−0.0358209	−	0.0206812i
$671$		−	180.133i		−	0.268455i
$672$	−192.000	−	332.554i	−0.285714	−	0.494872i
$673$	−334.000			−0.496285			−0.248143	−	0.968724i	$-0.579820\pi$
$673$	−334.000			−0.496285			−0.248143	+	0.968724i	$0.579820\pi$
$674$	−338.000	+	585.433i	−0.501484	+	0.868595i
$675$		−	109.119i		−	0.161658i
$676$	330.000	+	571.577i	0.488166	+	0.845528i
$677$	1006.00			1.48597			0.742984	−	0.669309i	$-0.233410\pi$
$677$	1006.00			1.48597			0.742984	+	0.669309i	$0.233410\pi$
$678$	−330.000	−	190.526i	−0.486726	−	0.281011i
$679$			13.8564i			0.0204071i
$680$	−160.000			−0.235294
$681$	492.000			0.722467
$682$	48.0000	−	83.1384i	0.0703812	−	0.121904i
$683$			187.061i			0.273882i	0.990579	+	0.136941i	$0.0437271\pi$
$683$			187.061i			0.273882i	−0.990579	+	0.136941i	$0.956273\pi$
$684$	216.000	−	124.708i	0.315789	−	0.182321i
$685$	−20.0000			−0.0291971
$686$	−600.000	−	346.410i	−0.874636	−	0.504971i
$687$			245.951i			0.358008i
$688$	−672.000	−	387.979i	−0.976744	−	0.563924i
$689$	−148.000			−0.214804
$690$	96.0000	−	166.277i	0.139130	−	0.240981i
$691$		−	990.733i		−	1.43377i	−0.697193	−	0.716884i	$-0.745568\pi$
$691$		−	990.733i		−	1.43377i	0.697193	−	0.716884i	$-0.254432\pi$
$692$	−668.000	−	1157.01i	−0.965318	−	1.67198i
$693$	−144.000			−0.207792
$694$	348.000	+	200.918i	0.501441	+	0.289507i
$695$			96.9948i			0.139561i
$696$			360.267i			0.517624i
$697$	580.000			0.832138
$698$	−506.000	+	876.418i	−0.724928	+	1.25561i
$699$		−	142.028i		−	0.203188i
$700$	−504.000	+	290.985i	−0.720000	+	0.415692i
$701$	−1034.00			−1.47504			−0.737518	−	0.675328i	$-0.764002\pi$
$701$	−1034.00			−1.47504			−0.737518	+	0.675328i	$0.764002\pi$
$702$	−18.0000	−	10.3923i	−0.0256410	−	0.0148039i
$703$		−	540.400i		−	0.768705i
$704$		−	443.405i		−	0.629837i
$705$	240.000			0.340426
$706$	−178.000	+	308.305i	−0.252125	+	0.436693i
$707$		−	512.687i		−	0.725158i
$708$	−312.000	−	540.400i	−0.440678	−	0.763277i
$709$	530.000			0.747532			0.373766	−	0.927523i	$-0.378066\pi$
$709$	530.000			0.747532			0.373766	+	0.927523i	$0.378066\pi$
$710$		0			0
$711$			353.338i			0.496960i
$712$	656.000			0.921348
$713$	192.000			0.269285
$714$	−120.000	+	207.846i	−0.168067	+	0.291101i
$715$			27.7128i			0.0387592i
$716$	648.000	−	374.123i	0.905028	−	0.522518i
$717$	−672.000			−0.937238
$718$	288.000	+	166.277i	0.401114	+	0.231583i
$719$			706.677i			0.982861i	0.870917	+	0.491430i	$0.163526\pi$
$719$			706.677i			0.982861i	−0.870917	+	0.491430i	$0.836474\pi$
$720$	−48.0000	+	83.1384i	−0.0666667	+	0.115470i
$721$	−528.000			−0.732316
$722$	71.0000	−	122.976i	0.0983380	−	0.170326i
$723$			79.6743i			0.110200i
$724$	−4.00000	−	6.92820i	−0.00552486	−	0.00956934i
$725$	546.000			0.753103
$726$	219.000	+	126.440i	0.301653	+	0.174159i
$727$		−	242.487i		−	0.333545i	−0.985995	−	0.166772i	$-0.946665\pi$
$727$		−	242.487i		−	0.333545i	0.985995	−	0.166772i	$-0.0533345\pi$
$728$			110.851i			0.152268i
$729$	−27.0000			−0.0370370
$730$	−92.0000	+	159.349i	−0.126027	+	0.218286i
$731$			484.974i			0.663439i
$732$	−156.000	+	90.0666i	−0.213115	+	0.123042i
$733$	194.000			0.264666			0.132333	−	0.991205i	$-0.457753\pi$
$733$	194.000			0.264666			0.132333	+	0.991205i	$0.457753\pi$
$734$	348.000	+	200.918i	0.474114	+	0.273730i
$735$			3.46410i			0.00471306i
$736$	768.000	−	443.405i	1.04348	−	0.602452i
$737$	−48.0000			−0.0651289
$738$	174.000	−	301.377i	0.235772	−	0.408370i
$739$			1351.00i			1.82815i	0.405550	+	0.914073i	$0.367080\pi$
$739$			1351.00i			1.82815i	−0.405550	+	0.914073i	$0.632920\pi$
$740$	104.000	+	180.133i	0.140541	+	0.243423i
$741$	−72.0000			−0.0971660
$742$	888.000	+	512.687i	1.19677	+	0.690953i
$743$		−	678.964i		−	0.913814i	−0.889514	−	0.456907i	$-0.848957\pi$
$743$		−	678.964i		−	0.913814i	0.889514	−	0.456907i	$-0.151043\pi$
$744$	−96.0000			−0.129032
$745$	4.00000			0.00536913
$746$	310.000	−	536.936i	0.415550	−	0.719753i
$747$			145.492i			0.194769i
$748$	−240.000	+	138.564i	−0.320856	+	0.185246i
$749$	144.000			0.192256
$750$	276.000	+	159.349i	0.368000	+	0.212465i
$751$			658.179i			0.876404i	0.898877	+	0.438202i	$0.144385\pi$
$751$			658.179i			0.876404i	−0.898877	+	0.438202i	$0.855615\pi$
$752$	960.000	+	554.256i	1.27660	+	0.737043i
$753$	−252.000			−0.334661
$754$	52.0000	−	90.0666i	0.0689655	−	0.119452i
$755$		−	180.133i		−	0.238587i
$756$	72.0000	+	124.708i	0.0952381	+	0.164957i
$757$	−1006.00			−1.32893			−0.664465	−	0.747319i	$-0.731341\pi$
$757$	−1006.00			−1.32893			−0.664465	+	0.747319i	$0.731341\pi$
$758$	−756.000	−	436.477i	−0.997361	−	0.575827i
$759$		−	332.554i		−	0.438147i
$760$			332.554i			0.437571i
$761$	−758.000			−0.996058			−0.498029	−	0.867160i	$-0.665943\pi$
$761$	−758.000			−0.996058			−0.498029	+	0.867160i	$0.665943\pi$
$762$	−252.000	+	436.477i	−0.330709	+	0.572804i
$763$		−	318.697i		−	0.417690i
$764$	768.000	−	443.405i	1.00524	−	0.580373i
$765$	60.0000			0.0784314
$766$	−1056.00	−	609.682i	−1.37859	−	0.795929i
$767$			180.133i			0.234854i
$768$	−384.000	+	221.703i	−0.500000	+	0.288675i
$769$	2.00000			0.00260078			0.00130039	−	0.999999i	$-0.499586\pi$
$769$	2.00000			0.00260078			0.00130039	+	0.999999i	$0.499586\pi$
$770$	96.0000	−	166.277i	0.124675	−	0.215944i
$771$			439.941i			0.570611i
$772$	−580.000	−	1004.59i	−0.751295	−	1.30128i
$773$	262.000			0.338939			0.169470	−	0.985535i	$-0.445795\pi$
$773$	262.000			0.338939			0.169470	+	0.985535i	$0.445795\pi$
$774$	252.000	+	145.492i	0.325581	+	0.187975i
$775$			145.492i			0.187732i
$776$	16.0000			0.0206186
$777$	312.000			0.401544
$778$	578.000	−	1001.13i	0.742931	−	1.28679i
$779$		−	1205.51i		−	1.54751i
$780$	24.0000	−	13.8564i	0.0307692	−	0.0177646i
$781$		0			0
$782$	−480.000	−	277.128i	−0.613811	−	0.354384i
$783$		−	135.100i		−	0.172541i
$784$	−8.00000	+	13.8564i	−0.0102041	+	0.0176740i
$785$	428.000			0.545223
$786$	204.000	−	353.338i	0.259542	−	0.449540i
$787$			1447.99i			1.83989i	0.392046	+	0.919946i	$0.371767\pi$
$787$			1447.99i			1.83989i	−0.392046	+	0.919946i	$0.628233\pi$
$788$	52.0000	+	90.0666i	0.0659898	+	0.114298i
$789$	−264.000			−0.334601
$790$	−408.000	−	235.559i	−0.516456	−	0.298176i
$791$		−	762.102i		−	0.963467i
$792$			166.277i			0.209946i
$793$	52.0000			0.0655738
$794$	−26.0000	+	45.0333i	−0.0327456	+	0.0567170i
$795$		−	256.344i		−	0.322445i
$796$	−1368.00	+	789.815i	−1.71859	+	0.992230i
$797$	−866.000			−1.08657			−0.543287	−	0.839547i	$-0.682821\pi$
$797$	−866.000			−1.08657			−0.543287	+	0.839547i	$0.682821\pi$
$798$	432.000	+	249.415i	0.541353	+	0.312551i
$799$		−	692.820i		−	0.867109i
$800$	336.000	+	581.969i	0.420000	+	0.727461i
$801$	−246.000			−0.307116
$802$	−250.000	+	433.013i	−0.311721	+	0.539916i
$803$			318.697i			0.396883i
$804$	24.0000	+	41.5692i	0.0298507	+	0.0517030i
$805$	384.000			0.477019
$806$	24.0000	+	13.8564i	0.0297767	+	0.0171916i
$807$		−	453.797i		−	0.562326i
$808$	−592.000			−0.732673
$809$	10.0000			0.0123609			0.00618047	−	0.999981i	$-0.498033\pi$
$809$	10.0000			0.0123609			0.00618047	+	0.999981i	$0.498033\pi$
$810$	18.0000	−	31.1769i	0.0222222	−	0.0384900i
$811$			436.477i			0.538196i	0.963113	+	0.269098i	$0.0867255\pi$
$811$			436.477i			0.538196i	−0.963113	+	0.269098i	$0.913274\pi$
$812$	−624.000	+	360.267i	−0.768473	+	0.443678i
$813$	−36.0000			−0.0442804
$814$	312.000	+	180.133i	0.383292	+	0.221294i
$815$			41.5692i			0.0510052i
$816$	240.000	+	138.564i	0.294118	+	0.169809i
$817$	1008.00			1.23378
$818$	−290.000	+	502.295i	−0.354523	+	0.614052i
$819$		−	41.5692i		−	0.0507561i
$820$	232.000	+	401.836i	0.282927	+	0.490044i
$821$	838.000			1.02071			0.510353	−	0.859965i	$-0.329515\pi$
$821$	838.000			1.02071			0.510353	+	0.859965i	$0.329515\pi$
$822$	30.0000	+	17.3205i	0.0364964	+	0.0210712i
$823$		−	879.882i		−	1.06912i	−0.845132	−	0.534558i	$-0.820478\pi$
$823$		−	879.882i		−	1.06912i	0.845132	−	0.534558i	$-0.179522\pi$
$824$			609.682i			0.739905i
$825$	252.000			0.305455
$826$	624.000	−	1080.80i	0.755448	−	1.30847i
$827$			727.461i			0.879639i	0.898086	+	0.439819i	$0.144958\pi$
$827$			727.461i			0.879639i	−0.898086	+	0.439819i	$0.855042\pi$
$828$	−288.000	+	166.277i	−0.347826	+	0.200817i
$829$	1298.00			1.56574			0.782871	−	0.622184i	$-0.213754\pi$
$829$	1298.00			1.56574			0.782871	+	0.622184i	$0.213754\pi$
$830$	−168.000	−	96.9948i	−0.202410	−	0.116861i
$831$		−	502.295i		−	0.604446i
$832$	128.000			0.153846
$833$	10.0000			0.0120048
$834$	84.0000	−	145.492i	0.100719	−	0.174451i
$835$			193.990i			0.232323i
$836$	288.000	+	498.831i	0.344498	+	0.596687i
$837$	36.0000			0.0430108
$838$	−588.000	−	339.482i	−0.701671	−	0.405110i
$839$		−	193.990i		−	0.231215i	−0.993295	−	0.115608i	$-0.963118\pi$
$839$		−	193.990i		−	0.231215i	0.993295	−	0.115608i	$-0.0368815\pi$
$840$	−192.000			−0.228571
$841$	−165.000			−0.196195
$842$	−674.000	+	1167.40i	−0.800475	+	1.38646i
$843$		−	391.443i		−	0.464346i
$844$	840.000	−	484.974i	0.995261	−	0.574614i
$845$	330.000			0.390533
$846$	−360.000	−	207.846i	−0.425532	−	0.245681i
$847$			505.759i			0.597118i
$848$	592.000	−	1025.37i	0.698113	−	1.20917i
$849$	−516.000			−0.607774
$850$	210.000	−	363.731i	0.247059	−	0.427918i
$851$			720.533i			0.846690i
$852$		0			0
$853$	506.000			0.593200			0.296600	−	0.955002i	$-0.404147\pi$
$853$	506.000			0.593200			0.296600	+	0.955002i	$0.404147\pi$
$854$	−312.000	−	180.133i	−0.365340	−	0.210929i
$855$		−	124.708i		−	0.145857i
$856$		−	166.277i		−	0.194249i
$857$	−998.000			−1.16453			−0.582264	−	0.813000i	$-0.697833\pi$
$857$	−998.000			−1.16453			−0.582264	+	0.813000i	$0.697833\pi$
$858$	24.0000	−	41.5692i	0.0279720	−	0.0484490i
$859$		−	505.759i		−	0.588776i	−0.955686	−	0.294388i	$-0.904884\pi$
$859$		−	505.759i		−	0.588776i	0.955686	−	0.294388i	$-0.0951158\pi$
$860$	−336.000	+	193.990i	−0.390698	+	0.225569i
$861$	696.000			0.808362
$862$	936.000	+	540.400i	1.08585	+	0.626914i
$863$		−	166.277i		−	0.192673i	−0.995349	−	0.0963365i	$-0.969287\pi$
$863$		−	166.277i		−	0.192673i	0.995349	−	0.0963365i	$-0.0307125\pi$
$864$	144.000	−	83.1384i	0.166667	−	0.0962250i
$865$	−668.000			−0.772254
$866$	334.000	−	578.505i	0.385681	−	0.668020i
$867$			327.358i			0.377575i
$868$	−96.0000	−	166.277i	−0.110599	−	0.191563i
$869$	−816.000			−0.939010
$870$	156.000	+	90.0666i	0.179310	+	0.103525i
$871$		−	13.8564i		−	0.0159086i
$872$	−368.000			−0.422018
$873$	−6.00000			−0.00687285
$874$	−576.000	+	997.661i	−0.659039	+	1.14149i
$875$			637.395i			0.728451i
$876$	276.000	−	159.349i	0.315068	−	0.181905i
$877$	−646.000			−0.736602			−0.368301	−	0.929707i	$-0.620060\pi$
$877$	−646.000			−0.736602			−0.368301	+	0.929707i	$0.620060\pi$
$878$	204.000	+	117.779i	0.232346	+	0.134145i
$879$			627.002i			0.713313i
$880$	−192.000	−	110.851i	−0.218182	−	0.125967i
$881$	898.000			1.01930			0.509648	−	0.860383i	$-0.329776\pi$
$881$	898.000			1.01930			0.509648	+	0.860383i	$0.329776\pi$
$882$	3.00000	−	5.19615i	0.00340136	−	0.00589133i
$883$			727.461i			0.823852i	0.911217	+	0.411926i	$0.135144\pi$
$883$			727.461i			0.823852i	−0.911217	+	0.411926i	$0.864856\pi$
$884$	−40.0000	−	69.2820i	−0.0452489	−	0.0783733i
$885$	−312.000			−0.352542
$886$	−132.000	−	76.2102i	−0.148984	−	0.0860161i
$887$		−	845.241i		−	0.952921i	−0.879196	−	0.476460i	$-0.841920\pi$
$887$		−	845.241i		−	0.952921i	0.879196	−	0.476460i	$-0.158080\pi$
$888$		−	360.267i		−	0.405706i
$889$	−1008.00			−1.13386
$890$	164.000	−	284.056i	0.184270	−	0.319164i
$891$		−	62.3538i		−	0.0699819i
$892$	1176.00	−	678.964i	1.31839	−	0.761170i
$893$	−1440.00			−1.61254
$894$	−6.00000	−	3.46410i	−0.00671141	−	0.00387483i
$895$		−	374.123i		−	0.418014i
$896$	−768.000	−	443.405i	−0.857143	−	0.494872i
$897$	96.0000			0.107023
$898$	−394.000	+	682.428i	−0.438753	+	0.759942i
$899$			180.133i			0.200371i
$900$	−126.000	−	218.238i	−0.140000	−	0.242487i
$901$	−740.000			−0.821310
$902$	696.000	+	401.836i	0.771619	+	0.445494i
$903$			581.969i			0.644484i
$904$	−880.000			−0.973451
$905$	−4.00000			−0.00441989
$906$	−156.000	+	270.200i	−0.172185	+	0.298234i
$907$		−	1364.86i		−	1.50480i	−0.658705	−	0.752401i	$-0.728895\pi$
$907$		−	1364.86i		−	1.50480i	0.658705	−	0.752401i	$-0.271105\pi$
$908$	984.000	−	568.113i	1.08370	−	0.625675i
$909$	222.000			0.244224
$910$	48.0000	+	27.7128i	0.0527473	+	0.0304536i
$911$			387.979i			0.425883i	0.977065	+	0.212941i	$0.0683044\pi$
$911$			387.979i			0.425883i	−0.977065	+	0.212941i	$0.931696\pi$
$912$	288.000	−	498.831i	0.315789	−	0.546963i
$913$	−336.000			−0.368018
$914$	478.000	−	827.920i	0.522976	−	0.905821i
$915$			90.0666i			0.0984335i
$916$	284.000	+	491.902i	0.310044	+	0.537011i
$917$	816.000			0.889858
$918$	−90.0000	−	51.9615i	−0.0980392	−	0.0566030i
$919$		−	602.754i		−	0.655880i	−0.944699	−	0.327940i	$-0.893646\pi$
$919$		−	602.754i		−	0.655880i	0.944699	−	0.327940i	$-0.106354\pi$
$920$		−	443.405i		−	0.481962i
$921$	−252.000			−0.273616
$922$	−142.000	+	245.951i	−0.154013	+	0.266758i
$923$		0			0
$924$	−288.000	+	166.277i	−0.311688	+	0.179953i
$925$	−546.000			−0.590270
$926$	1092.00	+	630.466i	1.17927	+	0.680849i
$927$		−	228.631i		−	0.246635i
$928$	416.000	+	720.533i	0.448276	+	0.776437i
$929$	1594.00			1.71582			0.857912	−	0.513797i	$-0.171762\pi$
$929$	1594.00			1.71582			0.857912	+	0.513797i	$0.171762\pi$
$930$	−24.0000	+	41.5692i	−0.0258065	+	0.0446981i
$931$		−	20.7846i		−	0.0223250i
$932$	−164.000	−	284.056i	−0.175966	−	0.304781i
$933$	408.000			0.437299
$934$	36.0000	+	20.7846i	0.0385439	+	0.0222533i
$935$			138.564i			0.148197i
$936$	−48.0000			−0.0512821
$937$	674.000			0.719317			0.359658	−	0.933084i	$-0.382893\pi$
$937$	674.000			0.719317			0.359658	+	0.933084i	$0.382893\pi$
$938$	−48.0000	+	83.1384i	−0.0511727	+	0.0886337i
$939$			827.920i			0.881704i
$940$	480.000	−	277.128i	0.510638	−	0.294817i
$941$	430.000			0.456961			0.228480	−	0.973549i	$-0.426624\pi$
$941$	430.000			0.456961			0.228480	+	0.973549i	$0.426624\pi$
$942$	−642.000	−	370.659i	−0.681529	−	0.393481i
$943$			1607.34i			1.70450i
$944$	−1248.00	−	720.533i	−1.32203	−	0.763277i
$945$	72.0000			0.0761905
$946$	−336.000	+	581.969i	−0.355180	+	0.615189i
$947$			76.2102i			0.0804754i	0.999190	+	0.0402377i	$0.0128115\pi$
$947$			76.2102i			0.0804754i	−0.999190	+	0.0402377i	$0.987188\pi$
$948$	408.000	+	706.677i	0.430380	+	0.745440i
$949$	−92.0000			−0.0969442
$950$	−756.000	−	436.477i	−0.795789	−	0.459449i
$951$			294.449i			0.309620i
$952$			554.256i			0.582202i
$953$	730.000			0.766002			0.383001	−	0.923748i	$-0.374891\pi$
$953$	730.000			0.766002			0.383001	+	0.923748i	$0.374891\pi$
$954$	−222.000	+	384.515i	−0.232704	+	0.403056i
$955$		−	443.405i		−	0.464298i
$956$	−1344.00	+	775.959i	−1.40586	+	0.811672i
$957$	312.000			0.326019
$958$	1272.00	+	734.390i	1.32777	+	0.766586i
$959$			69.2820i			0.0722440i
$960$			221.703i			0.230940i
$961$	913.000			0.950052
$962$	−52.0000	+	90.0666i	−0.0540541	+	0.0936244i
$963$			62.3538i			0.0647496i
$964$	92.0000	+	159.349i	0.0954357	+	0.165299i
$965$	−580.000			−0.601036
$966$	−576.000	−	332.554i	−0.596273	−	0.344259i
$967$		−	921.451i		−	0.952897i	−0.879202	−	0.476448i	$-0.841924\pi$
$967$		−	921.451i		−	0.952897i	0.879202	−	0.476448i	$-0.158076\pi$
$968$	584.000			0.603306
$969$	−360.000			−0.371517
$970$	4.00000	−	6.92820i	0.00412371	−	0.00714248i
$971$		−	1475.71i		−	1.51978i	−0.650051	−	0.759890i	$-0.725253\pi$
$971$		−	1475.71i		−	1.51978i	0.650051	−	0.759890i	$-0.274747\pi$
$972$	−54.0000	+	31.1769i	−0.0555556	+	0.0320750i
$973$	336.000			0.345324
$974$	180.000	+	103.923i	0.184805	+	0.106697i
$975$			72.7461i			0.0746114i
$976$	−208.000	+	360.267i	−0.213115	+	0.369126i
$977$	346.000			0.354145			0.177073	−	0.984198i	$-0.443337\pi$
$977$	346.000			0.354145			0.177073	+	0.984198i	$0.443337\pi$
$978$	36.0000	−	62.3538i	0.0368098	−	0.0637565i
$979$		−	568.113i		−	0.580299i
$980$	4.00000	+	6.92820i	0.00408163	+	0.00706960i
$981$	138.000			0.140673
$982$	−1596.00	−	921.451i	−1.62525	−	0.938341i
$983$		−	734.390i		−	0.747090i	−0.927612	−	0.373545i	$-0.878142\pi$
$983$		−	734.390i		−	0.747090i	0.927612	−	0.373545i	$-0.121858\pi$
$984$		−	803.672i		−	0.816739i
$985$	52.0000			0.0527919
$986$	260.000	−	450.333i	0.263692	−	0.456727i
$987$		−	831.384i		−	0.842335i
$988$	−144.000	+	83.1384i	−0.145749	+	0.0841482i
$989$	−1344.00			−1.35895
$990$	72.0000	+	41.5692i	0.0727273	+	0.0419891i
$991$		−	976.877i		−	0.985748i	−0.870101	−	0.492874i	$-0.835946\pi$
$991$		−	976.877i		−	0.985748i	0.870101	−	0.492874i	$-0.164054\pi$
$992$	−192.000	+	110.851i	−0.193548	+	0.111745i
$993$	−708.000			−0.712991
$994$		0			0
$995$			789.815i			0.793784i
$996$	168.000	+	290.985i	0.168675	+	0.292153i
$997$	458.000			0.459378			0.229689	−	0.973264i	$-0.426229\pi$
$997$	458.000			0.459378			0.229689	+	0.973264i	$0.426229\pi$
$998$	−132.000	−	76.2102i	−0.132265	−	0.0763630i
$999$			135.100i			0.135235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.3.d.a.7.2	yes	2
3.2	odd	2		36.3.d.c.19.1		2
4.3	odd	2	inner	12.3.d.a.7.1	✓	2
5.2	odd	4		300.3.f.a.199.1		4
5.3	odd	4		300.3.f.a.199.4		4
5.4	even	2		300.3.c.b.151.1		2
7.6	odd	2		588.3.g.b.295.2		2
8.3	odd	2		192.3.g.b.127.1		2
8.5	even	2		192.3.g.b.127.2		2
9.2	odd	6		324.3.f.a.271.1		2
9.4	even	3		324.3.f.d.55.1		2
9.5	odd	6		324.3.f.g.55.1		2
9.7	even	3		324.3.f.j.271.1		2
12.11	even	2		36.3.d.c.19.2		2
15.2	even	4		900.3.f.c.199.4		4
15.8	even	4		900.3.f.c.199.1		4
15.14	odd	2		900.3.c.e.451.2		2
16.3	odd	4		768.3.b.c.127.2		4
16.5	even	4		768.3.b.c.127.1		4
16.11	odd	4		768.3.b.c.127.3		4
16.13	even	4		768.3.b.c.127.4		4
20.3	even	4		300.3.f.a.199.2		4
20.7	even	4		300.3.f.a.199.3		4
20.19	odd	2		300.3.c.b.151.2		2
24.5	odd	2		576.3.g.e.127.2		2
24.11	even	2		576.3.g.e.127.1		2
28.27	even	2		588.3.g.b.295.1		2
36.7	odd	6		324.3.f.d.271.1		2
36.11	even	6		324.3.f.g.271.1		2
36.23	even	6		324.3.f.a.55.1		2
36.31	odd	6		324.3.f.j.55.1		2
48.5	odd	4		2304.3.b.l.127.3		4
48.11	even	4		2304.3.b.l.127.4		4
48.29	odd	4		2304.3.b.l.127.1		4
48.35	even	4		2304.3.b.l.127.2		4
60.23	odd	4		900.3.f.c.199.3		4
60.47	odd	4		900.3.f.c.199.2		4
60.59	even	2		900.3.c.e.451.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.3.d.a.7.1	✓	2	4.3	odd	2	inner
12.3.d.a.7.2	yes	2	1.1	even	1	trivial
36.3.d.c.19.1		2	3.2	odd	2
36.3.d.c.19.2		2	12.11	even	2
192.3.g.b.127.1		2	8.3	odd	2
192.3.g.b.127.2		2	8.5	even	2
300.3.c.b.151.1		2	5.4	even	2
300.3.c.b.151.2		2	20.19	odd	2
300.3.f.a.199.1		4	5.2	odd	4
300.3.f.a.199.2		4	20.3	even	4
300.3.f.a.199.3		4	20.7	even	4
300.3.f.a.199.4		4	5.3	odd	4
324.3.f.a.55.1		2	36.23	even	6
324.3.f.a.271.1		2	9.2	odd	6
324.3.f.d.55.1		2	9.4	even	3
324.3.f.d.271.1		2	36.7	odd	6
324.3.f.g.55.1		2	9.5	odd	6
324.3.f.g.271.1		2	36.11	even	6
324.3.f.j.55.1		2	36.31	odd	6
324.3.f.j.271.1		2	9.7	even	3
576.3.g.e.127.1		2	24.11	even	2
576.3.g.e.127.2		2	24.5	odd	2
588.3.g.b.295.1		2	28.27	even	2
588.3.g.b.295.2		2	7.6	odd	2
768.3.b.c.127.1		4	16.5	even	4
768.3.b.c.127.2		4	16.3	odd	4
768.3.b.c.127.3		4	16.11	odd	4
768.3.b.c.127.4		4	16.13	even	4
900.3.c.e.451.1		2	60.59	even	2
900.3.c.e.451.2		2	15.14	odd	2
900.3.f.c.199.1		4	15.8	even	4
900.3.f.c.199.2		4	60.47	odd	4
900.3.f.c.199.3		4	60.23	odd	4
900.3.f.c.199.4		4	15.2	even	4
2304.3.b.l.127.1		4	48.29	odd	4
2304.3.b.l.127.2		4	48.35	even	4
2304.3.b.l.127.3		4	48.5	odd	4
2304.3.b.l.127.4		4	48.11	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} -1.73205i q^{3} +(-2.00000 - 3.46410i) q^{4} -2.00000 q^{5} +(3.00000 + 1.73205i) q^{6} +6.92820i q^{7} +8.00000 q^{8} -3.00000 q^{9} +(2.00000 - 3.46410i) q^{10} -6.92820i q^{11} +(-6.00000 + 3.46410i) q^{12} +2.00000 q^{13} +(-12.0000 - 6.92820i) q^{14} +3.46410i q^{15} +(-8.00000 + 13.8564i) q^{16} +10.0000 q^{17} +(3.00000 - 5.19615i) q^{18} -20.7846i q^{19} +(4.00000 + 6.92820i) q^{20} +12.0000 q^{21} +(12.0000 + 6.92820i) q^{22} +27.7128i q^{23} -13.8564i q^{24} -21.0000 q^{25} +(-2.00000 + 3.46410i) q^{26} +5.19615i q^{27} +(24.0000 - 13.8564i) q^{28} -26.0000 q^{29} +(-6.00000 - 3.46410i) q^{30} -6.92820i q^{31} +(-16.0000 - 27.7128i) q^{32} -12.0000 q^{33} +(-10.0000 + 17.3205i) q^{34} -13.8564i q^{35} +(6.00000 + 10.3923i) q^{36} +26.0000 q^{37} +(36.0000 + 20.7846i) q^{38} -3.46410i q^{39} -16.0000 q^{40} +58.0000 q^{41} +(-12.0000 + 20.7846i) q^{42} +48.4974i q^{43} +(-24.0000 + 13.8564i) q^{44} +6.00000 q^{45} +(-48.0000 - 27.7128i) q^{46} -69.2820i q^{47} +(24.0000 + 13.8564i) q^{48} +1.00000 q^{49} +(21.0000 - 36.3731i) q^{50} -17.3205i q^{51} +(-4.00000 - 6.92820i) q^{52} -74.0000 q^{53} +(-9.00000 - 5.19615i) q^{54} +13.8564i q^{55} +55.4256i q^{56} -36.0000 q^{57} +(26.0000 - 45.0333i) q^{58} +90.0666i q^{59} +(12.0000 - 6.92820i) q^{60} +26.0000 q^{61} +(12.0000 + 6.92820i) q^{62} -20.7846i q^{63} +64.0000 q^{64} -4.00000 q^{65} +(12.0000 - 20.7846i) q^{66} -6.92820i q^{67} +(-20.0000 - 34.6410i) q^{68} +48.0000 q^{69} +(24.0000 + 13.8564i) q^{70} -24.0000 q^{72} -46.0000 q^{73} +(-26.0000 + 45.0333i) q^{74} +36.3731i q^{75} +(-72.0000 + 41.5692i) q^{76} +48.0000 q^{77} +(6.00000 + 3.46410i) q^{78} -117.779i q^{79} +(16.0000 - 27.7128i) q^{80} +9.00000 q^{81} +(-58.0000 + 100.459i) q^{82} -48.4974i q^{83} +(-24.0000 - 41.5692i) q^{84} -20.0000 q^{85} +(-84.0000 - 48.4974i) q^{86} +45.0333i q^{87} -55.4256i q^{88} +82.0000 q^{89} +(-6.00000 + 10.3923i) q^{90} +13.8564i q^{91} +(96.0000 - 55.4256i) q^{92} -12.0000 q^{93} +(120.000 + 69.2820i) q^{94} +41.5692i q^{95} +(-48.0000 + 27.7128i) q^{96} +2.00000 q^{97} +(-1.00000 + 1.73205i) q^{98} +20.7846i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 6 q^{6} + 16 q^{8} - 6 q^{9} + 4 q^{10} - 12 q^{12} + 4 q^{13} - 24 q^{14} - 16 q^{16} + 20 q^{17} + 6 q^{18} + 8 q^{20} + 24 q^{21} + 24 q^{22} - 42 q^{25} - 4 q^{26}+ \cdots - 2 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 6 * q^6 + 16 * q^8 - 6 * q^9 + 4 * q^10 - 12 * q^12 + 4 * q^13 - 24 * q^14 - 16 * q^16 + 20 * q^17 + 6 * q^18 + 8 * q^20 + 24 * q^21 + 24 * q^22 - 42 * q^25 - 4 * q^26 + 48 * q^28 - 52 * q^29 - 12 * q^30 - 32 * q^32 - 24 * q^33 - 20 * q^34 + 12 * q^36 + 52 * q^37 + 72 * q^38 - 32 * q^40 + 116 * q^41 - 24 * q^42 - 48 * q^44 + 12 * q^45 - 96 * q^46 + 48 * q^48 + 2 * q^49 + 42 * q^50 - 8 * q^52 - 148 * q^53 - 18 * q^54 - 72 * q^57 + 52 * q^58 + 24 * q^60 + 52 * q^61 + 24 * q^62 + 128 * q^64 - 8 * q^65 + 24 * q^66 - 40 * q^68 + 96 * q^69 + 48 * q^70 - 48 * q^72 - 92 * q^73 - 52 * q^74 - 144 * q^76 + 96 * q^77 + 12 * q^78 + 32 * q^80 + 18 * q^81 - 116 * q^82 - 48 * q^84 - 40 * q^85 - 168 * q^86 + 164 * q^89 - 12 * q^90 + 192 * q^92 - 24 * q^93 + 240 * q^94 - 96 * q^96 + 4 * q^97 - 2 * q^98

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