LMFDB - Embedded newform 252.3.y.a.163.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [252,3,Mod(163,252)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 2])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("252.163"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	252.y (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.86650266188$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			163.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	252.163
Dual form			252.3.y.a.235.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} +4.00000 q^{4} +(-2.50000 + 4.33013i) q^{5} +(3.50000 + 6.06218i) q^{7} -8.00000 q^{8} +(5.00000 - 8.66025i) q^{10} +(4.50000 - 2.59808i) q^{11} -16.0000 q^{13} +(-7.00000 - 12.1244i) q^{14} +16.0000 q^{16} +(2.00000 + 3.46410i) q^{17} +(-24.0000 - 13.8564i) q^{19} +(-10.0000 + 17.3205i) q^{20} +(-9.00000 + 5.19615i) q^{22} +(18.0000 + 10.3923i) q^{23} +32.0000 q^{26} +(14.0000 + 24.2487i) q^{28} -37.0000 q^{29} +(-16.5000 + 9.52628i) q^{31} -32.0000 q^{32} +(-4.00000 - 6.92820i) q^{34} -35.0000 q^{35} +(-34.0000 + 58.8897i) q^{37} +(48.0000 + 27.7128i) q^{38} +(20.0000 - 34.6410i) q^{40} -40.0000 q^{41} -24.2487i q^{43} +(18.0000 - 10.3923i) q^{44} +(-36.0000 - 20.7846i) q^{46} +(-39.0000 - 22.5167i) q^{47} +(-24.5000 + 42.4352i) q^{49} -64.0000 q^{52} +(36.5000 + 63.2199i) q^{53} +25.9808i q^{55} +(-28.0000 - 48.4974i) q^{56} +74.0000 q^{58} +(-25.5000 + 14.7224i) q^{59} +(41.0000 - 71.0141i) q^{61} +(33.0000 - 19.0526i) q^{62} +64.0000 q^{64} +(40.0000 - 69.2820i) q^{65} +(69.0000 - 39.8372i) q^{67} +(8.00000 + 13.8564i) q^{68} +70.0000 q^{70} +72.7461i q^{71} +(47.0000 + 81.4064i) q^{73} +(68.0000 - 117.779i) q^{74} +(-96.0000 - 55.4256i) q^{76} +(31.5000 + 18.1865i) q^{77} +(-7.50000 - 4.33013i) q^{79} +(-40.0000 + 69.2820i) q^{80} +80.0000 q^{82} -133.368i q^{83} -20.0000 q^{85} +48.4974i q^{86} +(-36.0000 + 20.7846i) q^{88} +(29.0000 - 50.2295i) q^{89} +(-56.0000 - 96.9948i) q^{91} +(72.0000 + 41.5692i) q^{92} +(78.0000 + 45.0333i) q^{94} +(120.000 - 69.2820i) q^{95} +47.0000 q^{97} +(49.0000 - 84.8705i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} + 8 q^{4} - 5 q^{5} + 7 q^{7} - 16 q^{8} + 10 q^{10} + 9 q^{11} - 32 q^{13} - 14 q^{14} + 32 q^{16} + 4 q^{17} - 48 q^{19} - 20 q^{20} - 18 q^{22} + 36 q^{23} + 64 q^{26} + 28 q^{28} - 74 q^{29}+ \cdots + 98 q^{98}+O(q^{100}) $ 2 * q - 4 * q^2 + 8 * q^4 - 5 * q^5 + 7 * q^7 - 16 * q^8 + 10 * q^10 + 9 * q^11 - 32 * q^13 - 14 * q^14 + 32 * q^16 + 4 * q^17 - 48 * q^19 - 20 * q^20 - 18 * q^22 + 36 * q^23 + 64 * q^26 + 28 * q^28 - 74 * q^29 - 33 * q^31 - 64 * q^32 - 8 * q^34 - 70 * q^35 - 68 * q^37 + 96 * q^38 + 40 * q^40 - 80 * q^41 + 36 * q^44 - 72 * q^46 - 78 * q^47 - 49 * q^49 - 128 * q^52 + 73 * q^53 - 56 * q^56 + 148 * q^58 - 51 * q^59 + 82 * q^61 + 66 * q^62 + 128 * q^64 + 80 * q^65 + 138 * q^67 + 16 * q^68 + 140 * q^70 + 94 * q^73 + 136 * q^74 - 192 * q^76 + 63 * q^77 - 15 * q^79 - 80 * q^80 + 160 * q^82 - 40 * q^85 - 72 * q^88 + 58 * q^89 - 112 * q^91 + 144 * q^92 + 156 * q^94 + 240 * q^95 + 94 * q^97 + 98 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−2.00000			−1.00000
$2$	−2.00000			−1.00000
$3$		0			0
$3$		0			0
$4$	4.00000			1.00000
$5$	−2.50000	+	4.33013i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$5$	−2.50000	+	4.33013i	−0.500000	+	0.866025i	−1.00000			$\pi$
$6$		0			0
$7$	3.50000	+	6.06218i	0.500000	+	0.866025i
$7$	3.50000	+	6.06218i	0.500000	+	0.866025i
$8$	−8.00000			−1.00000
$9$		0			0
$10$	5.00000	−	8.66025i	0.500000	−	0.866025i
$11$	4.50000	−	2.59808i	0.409091	−	0.236189i	−0.281308	−	0.959617i	$-0.590768\pi$
$11$	4.50000	−	2.59808i	0.409091	−	0.236189i	0.690399	+	0.723429i	$0.257435\pi$
$12$		0			0
$13$	−16.0000			−1.23077			−0.615385	−	0.788227i	$-0.710999\pi$
$13$	−16.0000			−1.23077			−0.615385	+	0.788227i	$0.710999\pi$
$14$	−7.00000	−	12.1244i	−0.500000	−	0.866025i
$15$		0			0
$16$	16.0000			1.00000
$17$	2.00000	+	3.46410i	0.117647	+	0.203771i	0.918835	−	0.394642i	$-0.129132\pi$
$17$	2.00000	+	3.46410i	0.117647	+	0.203771i	−0.801188	+	0.598413i	$0.795798\pi$
$18$		0			0
$19$	−24.0000	−	13.8564i	−1.26316	−	0.729285i	−0.289474	−	0.957186i	$-0.593480\pi$
$19$	−24.0000	−	13.8564i	−1.26316	−	0.729285i	−0.973684	+	0.227901i	$0.926814\pi$
$20$	−10.0000	+	17.3205i	−0.500000	+	0.866025i
$21$		0			0
$22$	−9.00000	+	5.19615i	−0.409091	+	0.236189i
$23$	18.0000	+	10.3923i	0.782609	+	0.451839i	0.837354	−	0.546661i	$-0.184101\pi$
$23$	18.0000	+	10.3923i	0.782609	+	0.451839i	−0.0547453	+	0.998500i	$0.517435\pi$
$24$		0			0
$25$		0			0
$26$	32.0000			1.23077
$27$		0			0
$28$	14.0000	+	24.2487i	0.500000	+	0.866025i
$29$	−37.0000			−1.27586			−0.637931	−	0.770093i	$-0.720210\pi$
$29$	−37.0000			−1.27586			−0.637931	+	0.770093i	$0.720210\pi$
$30$		0			0
$31$	−16.5000	+	9.52628i	−0.532258	+	0.307299i	−0.741935	−	0.670471i	$-0.766092\pi$
$31$	−16.5000	+	9.52628i	−0.532258	+	0.307299i	0.209677	+	0.977771i	$0.432759\pi$
$32$	−32.0000			−1.00000
$33$		0			0
$34$	−4.00000	−	6.92820i	−0.117647	−	0.203771i
$35$	−35.0000			−1.00000
$36$		0			0
$37$	−34.0000	+	58.8897i	−0.918919	+	1.59161i	−0.117859	+	0.993030i	$0.537603\pi$
$37$	−34.0000	+	58.8897i	−0.918919	+	1.59161i	−0.801060	+	0.598584i	$0.795730\pi$
$38$	48.0000	+	27.7128i	1.26316	+	0.729285i
$39$		0			0
$40$	20.0000	−	34.6410i	0.500000	−	0.866025i
$41$	−40.0000			−0.975610			−0.487805	−	0.872953i	$-0.662202\pi$
$41$	−40.0000			−0.975610			−0.487805	+	0.872953i	$0.662202\pi$
$42$		0			0
$43$		−	24.2487i		−	0.563924i	−0.959426	−	0.281962i	$-0.909015\pi$
$43$		−	24.2487i		−	0.563924i	0.959426	−	0.281962i	$-0.0909851\pi$
$44$	18.0000	−	10.3923i	0.409091	−	0.236189i
$45$		0			0
$46$	−36.0000	−	20.7846i	−0.782609	−	0.451839i
$47$	−39.0000	−	22.5167i	−0.829787	−	0.479078i	0.0239926	−	0.999712i	$-0.492362\pi$
$47$	−39.0000	−	22.5167i	−0.829787	−	0.479078i	−0.853780	+	0.520634i	$0.825696\pi$
$48$		0			0
$49$	−24.5000	+	42.4352i	−0.500000	+	0.866025i
$50$		0			0
$51$		0			0
$52$	−64.0000			−1.23077
$53$	36.5000	+	63.2199i	0.688679	+	1.19283i	0.972265	+	0.233881i	$0.0751425\pi$
$53$	36.5000	+	63.2199i	0.688679	+	1.19283i	−0.283586	+	0.958947i	$0.591524\pi$
$54$		0			0
$55$			25.9808i			0.472377i
$56$	−28.0000	−	48.4974i	−0.500000	−	0.866025i
$57$		0			0
$58$	74.0000			1.27586
$59$	−25.5000	+	14.7224i	−0.432203	+	0.249533i	−0.700285	−	0.713863i	$-0.746944\pi$
$59$	−25.5000	+	14.7224i	−0.432203	+	0.249533i	0.268081	+	0.963396i	$0.413610\pi$
$60$		0			0
$61$	41.0000	−	71.0141i	0.672131	−	1.16417i	−0.305167	−	0.952299i	$-0.598712\pi$
$61$	41.0000	−	71.0141i	0.672131	−	1.16417i	0.977299	−	0.211867i	$-0.0679542\pi$
$62$	33.0000	−	19.0526i	0.532258	−	0.307299i
$63$		0			0
$64$	64.0000			1.00000
$65$	40.0000	−	69.2820i	0.615385	−	1.06588i
$66$		0			0
$67$	69.0000	−	39.8372i	1.02985	−	0.594585i	0.112909	−	0.993605i	$-0.463983\pi$
$67$	69.0000	−	39.8372i	1.02985	−	0.594585i	0.916942	+	0.399021i	$0.130650\pi$
$68$	8.00000	+	13.8564i	0.117647	+	0.203771i
$69$		0			0
$70$	70.0000			1.00000
$71$			72.7461i			1.02459i	0.858809	+	0.512297i	$0.171205\pi$
$71$			72.7461i			1.02459i	−0.858809	+	0.512297i	$0.828795\pi$
$72$		0			0
$73$	47.0000	+	81.4064i	0.643836	+	1.11516i	0.984569	+	0.174996i	$0.0559913\pi$
$73$	47.0000	+	81.4064i	0.643836	+	1.11516i	−0.340734	+	0.940160i	$0.610675\pi$
$74$	68.0000	−	117.779i	0.918919	−	1.59161i
$75$		0			0
$76$	−96.0000	−	55.4256i	−1.26316	−	0.729285i
$77$	31.5000	+	18.1865i	0.409091	+	0.236189i
$78$		0			0
$79$	−7.50000	−	4.33013i	−0.0949367	−	0.0548117i	0.451780	−	0.892129i	$-0.350789\pi$
$79$	−7.50000	−	4.33013i	−0.0949367	−	0.0548117i	−0.546717	+	0.837318i	$0.684123\pi$
$80$	−40.0000	+	69.2820i	−0.500000	+	0.866025i
$81$		0			0
$82$	80.0000			0.975610
$83$		−	133.368i		−	1.60684i	−0.595411	−	0.803421i	$-0.703011\pi$
$83$		−	133.368i		−	1.60684i	0.595411	−	0.803421i	$-0.296989\pi$
$84$		0			0
$85$	−20.0000			−0.235294
$86$			48.4974i			0.563924i
$87$		0			0
$88$	−36.0000	+	20.7846i	−0.409091	+	0.236189i
$89$	29.0000	−	50.2295i	0.325843	−	0.564376i	−0.655840	−	0.754900i	$-0.727685\pi$
$89$	29.0000	−	50.2295i	0.325843	−	0.564376i	0.981683	+	0.190524i	$0.0610187\pi$
$90$		0			0
$91$	−56.0000	−	96.9948i	−0.615385	−	1.06588i
$92$	72.0000	+	41.5692i	0.782609	+	0.451839i
$93$		0			0
$94$	78.0000	+	45.0333i	0.829787	+	0.479078i
$95$	120.000	−	69.2820i	1.26316	−	0.729285i
$96$		0			0
$97$	47.0000			0.484536			0.242268	−	0.970209i	$-0.422109\pi$
$97$	47.0000			0.484536			0.242268	+	0.970209i	$0.422109\pi$
$98$	49.0000	−	84.8705i	0.500000	−	0.866025i
$99$		0			0
$100$		0			0
$101$	65.0000	+	112.583i	0.643564	+	1.11469i	0.984631	+	0.174647i	$0.0558784\pi$
$101$	65.0000	+	112.583i	0.643564	+	1.11469i	−0.341067	+	0.940039i	$0.610788\pi$
$102$		0			0
$103$	18.0000	+	10.3923i	0.174757	+	0.100896i	0.584827	−	0.811158i	$-0.301162\pi$
$103$	18.0000	+	10.3923i	0.174757	+	0.100896i	−0.410070	+	0.912054i	$0.634496\pi$
$104$	128.000			1.23077
$105$		0			0
$106$	−73.0000	−	126.440i	−0.688679	−	1.19283i
$107$	70.5000	+	40.7032i	0.658879	+	0.380404i	0.791850	−	0.610716i	$-0.209118\pi$
$107$	70.5000	+	40.7032i	0.658879	+	0.380404i	−0.132971	+	0.991120i	$0.542452\pi$
$108$		0			0
$109$	−61.0000	−	105.655i	−0.559633	−	0.969313i	−0.997527	−	0.0702862i	$-0.977609\pi$
$109$	−61.0000	−	105.655i	−0.559633	−	0.969313i	0.437894	−	0.899027i	$-0.355725\pi$
$110$		−	51.9615i		−	0.472377i
$111$		0			0
$112$	56.0000	+	96.9948i	0.500000	+	0.866025i
$113$	−16.0000			−0.141593			−0.0707965	−	0.997491i	$-0.522554\pi$
$113$	−16.0000			−0.141593			−0.0707965	+	0.997491i	$0.522554\pi$
$114$		0			0
$115$	−90.0000	+	51.9615i	−0.782609	+	0.451839i
$116$	−148.000			−1.27586
$117$		0			0
$118$	51.0000	−	29.4449i	0.432203	−	0.249533i
$119$	−14.0000	+	24.2487i	−0.117647	+	0.203771i
$120$		0			0
$121$	−47.0000	+	81.4064i	−0.388430	+	0.672780i
$122$	−82.0000	+	142.028i	−0.672131	+	1.16417i
$123$		0			0
$124$	−66.0000	+	38.1051i	−0.532258	+	0.307299i
$125$	−125.000			−1.00000
$126$		0			0
$127$			109.119i			0.859206i	0.903018	+	0.429603i	$0.141347\pi$
$127$			109.119i			0.859206i	−0.903018	+	0.429603i	$0.858653\pi$
$128$	−128.000			−1.00000
$129$		0			0
$130$	−80.0000	+	138.564i	−0.615385	+	1.06588i
$131$	13.5000	+	7.79423i	0.103053	+	0.0594979i	0.550641	−	0.834742i	$-0.314383\pi$
$131$	13.5000	+	7.79423i	0.103053	+	0.0594979i	−0.447587	+	0.894240i	$0.647717\pi$
$132$		0			0
$133$		−	193.990i		−	1.45857i
$134$	−138.000	+	79.6743i	−1.02985	+	0.594585i
$135$		0			0
$136$	−16.0000	−	27.7128i	−0.117647	−	0.203771i
$137$	−37.0000	−	64.0859i	−0.270073	−	0.467780i	0.698807	−	0.715310i	$-0.253715\pi$
$137$	−37.0000	−	64.0859i	−0.270073	−	0.467780i	−0.968880	+	0.247530i	$0.920381\pi$
$138$		0			0
$139$			169.741i			1.22116i	0.791955	+	0.610579i	$0.209063\pi$
$139$			169.741i			1.22116i	−0.791955	+	0.610579i	$0.790937\pi$
$140$	−140.000			−1.00000
$141$		0			0
$142$		−	145.492i		−	1.02459i
$143$	−72.0000	+	41.5692i	−0.503497	+	0.290694i
$144$		0			0
$145$	92.5000	−	160.215i	0.637931	−	1.10493i
$146$	−94.0000	−	162.813i	−0.643836	−	1.11516i
$147$		0			0
$148$	−136.000	+	235.559i	−0.918919	+	1.59161i
$149$	83.0000	−	143.760i	0.557047	−	0.964834i	−0.440694	−	0.897657i	$-0.645268\pi$
$149$	83.0000	−	143.760i	0.557047	−	0.964834i	0.997741	−	0.0671763i	$-0.0213990\pi$
$150$		0			0
$151$	121.500	−	70.1481i	0.804636	−	0.464557i	−0.0404538	−	0.999181i	$-0.512880\pi$
$151$	121.500	−	70.1481i	0.804636	−	0.464557i	0.845090	+	0.534625i	$0.179547\pi$
$152$	192.000	+	110.851i	1.26316	+	0.729285i
$153$		0			0
$154$	−63.0000	−	36.3731i	−0.409091	−	0.236189i
$155$		−	95.2628i		−	0.614599i
$156$		0			0
$157$	26.0000	+	45.0333i	0.165605	+	0.286836i	0.936870	−	0.349678i	$-0.113709\pi$
$157$	26.0000	+	45.0333i	0.165605	+	0.286836i	−0.771265	+	0.636514i	$0.780376\pi$
$158$	15.0000	+	8.66025i	0.0949367	+	0.0548117i
$159$		0			0
$160$	80.0000	−	138.564i	0.500000	−	0.866025i
$161$			145.492i			0.903679i
$162$		0			0
$163$	66.0000	+	38.1051i	0.404908	+	0.233774i	0.688600	−	0.725142i	$-0.258226\pi$
$163$	66.0000	+	38.1051i	0.404908	+	0.233774i	−0.283692	+	0.958916i	$0.591559\pi$
$164$	−160.000			−0.975610
$165$		0			0
$166$			266.736i			1.60684i
$167$			169.741i			1.01641i	0.861235	+	0.508207i	$0.169691\pi$
$167$			169.741i			1.01641i	−0.861235	+	0.508207i	$0.830309\pi$
$168$		0			0
$169$	87.0000			0.514793
$170$	40.0000			0.235294
$171$		0			0
$172$		−	96.9948i		−	0.563924i
$173$	−13.0000	+	22.5167i	−0.0751445	+	0.130154i	−0.901149	−	0.433509i	$-0.857275\pi$
$173$	−13.0000	+	22.5167i	−0.0751445	+	0.130154i	0.826005	+	0.563663i	$0.190608\pi$
$174$		0			0
$175$		0			0
$176$	72.0000	−	41.5692i	0.409091	−	0.236189i
$177$		0			0
$178$	−58.0000	+	100.459i	−0.325843	+	0.564376i
$179$	−258.000	+	148.956i	−1.44134	+	0.832158i	−0.997939	−	0.0641646i	$-0.979562\pi$
$179$	−258.000	+	148.956i	−1.44134	+	0.832158i	−0.443401	+	0.896323i	$0.646228\pi$
$180$		0			0
$181$	−16.0000			−0.0883978			−0.0441989	−	0.999023i	$-0.514074\pi$
$181$	−16.0000			−0.0883978			−0.0441989	+	0.999023i	$0.514074\pi$
$182$	112.000	+	193.990i	0.615385	+	1.06588i
$183$		0			0
$184$	−144.000	−	83.1384i	−0.782609	−	0.451839i
$185$	−170.000	−	294.449i	−0.918919	−	1.59161i
$186$		0			0
$187$	18.0000	+	10.3923i	0.0962567	+	0.0555738i
$188$	−156.000	−	90.0666i	−0.829787	−	0.479078i
$189$		0			0
$190$	−240.000	+	138.564i	−1.26316	+	0.729285i
$191$	312.000	+	180.133i	1.63351	+	0.943106i	0.983000	+	0.183607i	$0.0587773\pi$
$191$	312.000	+	180.133i	1.63351	+	0.943106i	0.650508	+	0.759499i	$0.274556\pi$
$192$		0			0
$193$	75.5000	+	130.770i	0.391192	+	0.677564i	0.992607	−	0.121373i	$-0.0387296\pi$
$193$	75.5000	+	130.770i	0.391192	+	0.677564i	−0.601415	+	0.798937i	$0.705396\pi$
$194$	−94.0000			−0.484536
$195$		0			0
$196$	−98.0000	+	169.741i	−0.500000	+	0.866025i
$197$	278.000			1.41117			0.705584	−	0.708627i	$-0.250685\pi$
$197$	278.000			1.41117			0.705584	+	0.708627i	$0.250685\pi$
$198$		0			0
$199$	120.000	−	69.2820i	0.603015	−	0.348151i	−0.167212	−	0.985921i	$-0.553476\pi$
$199$	120.000	−	69.2820i	0.603015	−	0.348151i	0.770227	+	0.637770i	$0.220143\pi$
$200$		0			0
$201$		0			0
$202$	−130.000	−	225.167i	−0.643564	−	1.11469i
$203$	−129.500	−	224.301i	−0.637931	−	1.10493i
$204$		0			0
$205$	100.000	−	173.205i	0.487805	−	0.844903i
$206$	−36.0000	−	20.7846i	−0.174757	−	0.100896i
$207$		0			0
$208$	−256.000			−1.23077
$209$	−144.000			−0.688995
$210$		0			0
$211$		−	121.244i		−	0.574614i	−0.957839	−	0.287307i	$-0.907240\pi$
$211$		−	121.244i		−	0.574614i	0.957839	−	0.287307i	$-0.0927600\pi$
$212$	146.000	+	252.879i	0.688679	+	1.19283i
$213$		0			0
$214$	−141.000	−	81.4064i	−0.658879	−	0.380404i
$215$	105.000	+	60.6218i	0.488372	+	0.281962i
$216$		0			0
$217$	−115.500	−	66.6840i	−0.532258	−	0.307299i
$218$	122.000	+	211.310i	0.559633	+	0.969313i
$219$		0			0
$220$			103.923i			0.472377i
$221$	−32.0000	−	55.4256i	−0.144796	−	0.250795i
$222$		0			0
$223$			12.1244i			0.0543693i	0.999630	+	0.0271847i	$0.00865421\pi$
$223$			12.1244i			0.0543693i	−0.999630	+	0.0271847i	$0.991346\pi$
$224$	−112.000	−	193.990i	−0.500000	−	0.866025i
$225$		0			0
$226$	32.0000			0.141593
$227$	−130.500	+	75.3442i	−0.574890	+	0.331913i	−0.759100	−	0.650974i	$-0.774361\pi$
$227$	−130.500	+	75.3442i	−0.574890	+	0.331913i	0.184210	+	0.982887i	$0.441027\pi$
$228$		0			0
$229$	−106.000	+	183.597i	−0.462882	+	0.801735i	−0.999103	−	0.0423423i	$-0.986518\pi$
$229$	−106.000	+	183.597i	−0.462882	+	0.801735i	0.536221	+	0.844078i	$0.319851\pi$
$230$	180.000	−	103.923i	0.782609	−	0.451839i
$231$		0			0
$232$	296.000			1.27586
$233$	−106.000	+	183.597i	−0.454936	+	0.787972i	−0.998685	−	0.0512764i	$-0.983671\pi$
$233$	−106.000	+	183.597i	−0.454936	+	0.787972i	0.543749	+	0.839248i	$0.317004\pi$
$234$		0			0
$235$	195.000	−	112.583i	0.829787	−	0.479078i
$236$	−102.000	+	58.8897i	−0.432203	+	0.249533i
$237$		0			0
$238$	28.0000	−	48.4974i	0.117647	−	0.203771i
$239$		−	48.4974i		−	0.202918i	−0.994840	−	0.101459i	$-0.967649\pi$
$239$		−	48.4974i		−	0.202918i	0.994840	−	0.101459i	$-0.0323511\pi$
$240$		0			0
$241$	−5.50000	−	9.52628i	−0.0228216	−	0.0395281i	0.854389	−	0.519634i	$-0.173932\pi$
$241$	−5.50000	−	9.52628i	−0.0228216	−	0.0395281i	−0.877211	+	0.480106i	$0.840598\pi$
$242$	94.0000	−	162.813i	0.388430	−	0.672780i
$243$		0			0
$244$	164.000	−	284.056i	0.672131	−	1.16417i
$245$	−122.500	−	212.176i	−0.500000	−	0.866025i
$246$		0			0
$247$	384.000	+	221.703i	1.55466	+	0.897581i
$248$	132.000	−	76.2102i	0.532258	−	0.307299i
$249$		0			0
$250$	250.000			1.00000
$251$		−	36.3731i		−	0.144913i	−0.997372	−	0.0724563i	$-0.976916\pi$
$251$		−	36.3731i		−	0.144913i	0.997372	−	0.0724563i	$-0.0230838\pi$
$252$		0			0
$253$	108.000			0.426877
$254$		−	218.238i		−	0.859206i
$255$		0			0
$256$	256.000			1.00000
$257$	29.0000	−	50.2295i	0.112840	−	0.195445i	−0.804074	−	0.594529i	$-0.797338\pi$
$257$	29.0000	−	50.2295i	0.112840	−	0.195445i	0.916914	+	0.399084i	$0.130672\pi$
$258$		0			0
$259$	−476.000			−1.83784
$260$	160.000	−	277.128i	0.615385	−	1.06588i
$261$		0			0
$262$	−27.0000	−	15.5885i	−0.103053	−	0.0594979i
$263$	351.000	−	202.650i	1.33460	−	0.770532i	0.348600	−	0.937272i	$-0.386657\pi$
$263$	351.000	−	202.650i	1.33460	−	0.770532i	0.986001	+	0.166740i	$0.0533239\pi$
$264$		0			0
$265$	−365.000			−1.37736
$266$			387.979i			1.45857i
$267$		0			0
$268$	276.000	−	159.349i	1.02985	−	0.594585i
$269$	222.500	+	385.381i	0.827138	+	1.43264i	0.900275	+	0.435322i	$0.143366\pi$
$269$	222.500	+	385.381i	0.827138	+	1.43264i	−0.0731371	+	0.997322i	$0.523301\pi$
$270$		0			0
$271$	−307.500	−	177.535i	−1.13469	−	0.655111i	−0.189577	−	0.981866i	$-0.560712\pi$
$271$	−307.500	−	177.535i	−1.13469	−	0.655111i	−0.945109	+	0.326754i	$0.894045\pi$
$272$	32.0000	+	55.4256i	0.117647	+	0.203771i
$273$		0			0
$274$	74.0000	+	128.172i	0.270073	+	0.467780i
$275$		0			0
$276$		0			0
$277$	128.000	+	221.703i	0.462094	+	0.800370i	0.999065	−	0.0432305i	$-0.0137650\pi$
$277$	128.000	+	221.703i	0.462094	+	0.800370i	−0.536971	+	0.843601i	$0.680432\pi$
$278$		−	339.482i		−	1.22116i
$279$		0			0
$280$	280.000			1.00000
$281$	278.000			0.989324			0.494662	−	0.869085i	$-0.335292\pi$
$281$	278.000			0.989324			0.494662	+	0.869085i	$0.335292\pi$
$282$		0			0
$283$	15.0000	−	8.66025i	0.0530035	−	0.0306016i	−0.473264	−	0.880921i	$-0.656924\pi$
$283$	15.0000	−	8.66025i	0.0530035	−	0.0306016i	0.526268	+	0.850319i	$0.323591\pi$
$284$			290.985i			1.02459i
$285$		0			0
$286$	144.000	−	83.1384i	0.503497	−	0.290694i
$287$	−140.000	−	242.487i	−0.487805	−	0.844903i
$288$		0			0
$289$	136.500	−	236.425i	0.472318	−	0.818079i
$290$	−185.000	+	320.429i	−0.637931	+	1.10493i
$291$		0			0
$292$	188.000	+	325.626i	0.643836	+	1.11516i
$293$	−61.0000			−0.208191			−0.104096	−	0.994567i	$-0.533195\pi$
$293$	−61.0000			−0.208191			−0.104096	+	0.994567i	$0.533195\pi$
$294$		0			0
$295$		−	147.224i		−	0.499065i
$296$	272.000	−	471.118i	0.918919	−	1.59161i
$297$		0			0
$298$	−166.000	+	287.520i	−0.557047	+	0.964834i
$299$	−288.000	−	166.277i	−0.963211	−	0.556110i
$300$		0			0
$301$	147.000	−	84.8705i	0.488372	−	0.281962i
$302$	−243.000	+	140.296i	−0.804636	+	0.464557i
$303$		0			0
$304$	−384.000	−	221.703i	−1.26316	−	0.729285i
$305$	205.000	+	355.070i	0.672131	+	1.16417i
$306$		0			0
$307$			436.477i			1.42175i	0.703319	+	0.710874i	$0.251701\pi$
$307$			436.477i			1.42175i	−0.703319	+	0.710874i	$0.748299\pi$
$308$	126.000	+	72.7461i	0.409091	+	0.236189i
$309$		0			0
$310$			190.526i			0.614599i
$311$	132.000	−	76.2102i	0.424437	−	0.245049i	−0.272537	−	0.962145i	$-0.587863\pi$
$311$	132.000	−	76.2102i	0.424437	−	0.245049i	0.696974	+	0.717096i	$0.254529\pi$
$312$		0			0
$313$	−116.500	+	201.784i	−0.372204	+	0.644677i	−0.989904	−	0.141737i	$-0.954731\pi$
$313$	−116.500	+	201.784i	−0.372204	+	0.644677i	0.617700	+	0.786414i	$0.288065\pi$
$314$	−52.0000	−	90.0666i	−0.165605	−	0.286836i
$315$		0			0
$316$	−30.0000	−	17.3205i	−0.0949367	−	0.0548117i
$317$	−53.5000	+	92.6647i	−0.168770	+	0.292318i	−0.937988	−	0.346669i	$-0.887313\pi$
$317$	−53.5000	+	92.6647i	−0.168770	+	0.292318i	0.769218	+	0.638987i	$0.220646\pi$
$318$		0			0
$319$	−166.500	+	96.1288i	−0.521944	+	0.301344i
$320$	−160.000	+	277.128i	−0.500000	+	0.866025i
$321$		0			0
$322$		−	290.985i		−	0.903679i
$323$		−	110.851i		−	0.343193i
$324$		0			0
$325$		0			0
$326$	−132.000	−	76.2102i	−0.404908	−	0.233774i
$327$		0			0
$328$	320.000			0.975610
$329$		−	315.233i		−	0.958156i
$330$		0			0
$331$	−354.000	−	204.382i	−1.06949	−	0.617468i	−0.141445	−	0.989946i	$-0.545175\pi$
$331$	−354.000	−	204.382i	−1.06949	−	0.617468i	−0.928041	+	0.372478i	$0.878508\pi$
$332$		−	533.472i		−	1.60684i
$333$		0			0
$334$		−	339.482i		−	1.01641i
$335$			398.372i			1.18917i
$336$		0			0
$337$	149.000			0.442136			0.221068	−	0.975258i	$-0.429046\pi$
$337$	149.000			0.442136			0.221068	+	0.975258i	$0.429046\pi$
$338$	−174.000			−0.514793
$339$		0			0
$340$	−80.0000			−0.235294
$341$	−49.5000	+	85.7365i	−0.145161	+	0.251427i
$342$		0			0
$343$	−343.000			−1.00000
$344$			193.990i			0.563924i
$345$		0			0
$346$	26.0000	−	45.0333i	0.0751445	−	0.130154i
$347$	330.000	−	190.526i	0.951009	−	0.549065i	0.0576145	−	0.998339i	$-0.481651\pi$
$347$	330.000	−	190.526i	0.951009	−	0.549065i	0.893394	+	0.449274i	$0.148317\pi$
$348$		0			0
$349$	−394.000			−1.12894			−0.564470	−	0.825454i	$-0.690919\pi$
$349$	−394.000			−1.12894			−0.564470	+	0.825454i	$0.690919\pi$
$350$		0			0
$351$		0			0
$352$	−144.000	+	83.1384i	−0.409091	+	0.236189i
$353$	128.000	+	221.703i	0.362606	+	0.628052i	0.988389	−	0.151945i	$-0.0485537\pi$
$353$	128.000	+	221.703i	0.362606	+	0.628052i	−0.625783	+	0.779997i	$0.715220\pi$
$354$		0			0
$355$	−315.000	−	181.865i	−0.887324	−	0.512297i
$356$	116.000	−	200.918i	0.325843	−	0.564376i
$357$		0			0
$358$	516.000	−	297.913i	1.44134	−	0.832158i
$359$	−339.000	−	195.722i	−0.944290	−	0.545186i	−0.0529873	−	0.998595i	$-0.516874\pi$
$359$	−339.000	−	195.722i	−0.944290	−	0.545186i	−0.891302	+	0.453409i	$0.850208\pi$
$360$		0			0
$361$	203.500	+	352.472i	0.563712	+	0.976378i
$362$	32.0000			0.0883978
$363$		0			0
$364$	−224.000	−	387.979i	−0.615385	−	1.06588i
$365$	−470.000			−1.28767
$366$		0			0
$367$	256.500	−	148.090i	0.698910	−	0.403516i	−0.108031	−	0.994147i	$-0.534455\pi$
$367$	256.500	−	148.090i	0.698910	−	0.403516i	0.806941	+	0.590632i	$0.201121\pi$
$368$	288.000	+	166.277i	0.782609	+	0.451839i
$369$		0			0
$370$	340.000	+	588.897i	0.918919	+	1.59161i
$371$	−255.500	+	442.539i	−0.688679	+	1.19283i
$372$		0			0
$373$	−328.000	+	568.113i	−0.879357	+	1.52309i	−0.0273083	+	0.999627i	$0.508694\pi$
$373$	−328.000	+	568.113i	−0.879357	+	1.52309i	−0.852048	+	0.523463i	$0.824640\pi$
$374$	−36.0000	−	20.7846i	−0.0962567	−	0.0555738i
$375$		0			0
$376$	312.000	+	180.133i	0.829787	+	0.479078i
$377$	592.000			1.57029
$378$		0			0
$379$		−	290.985i		−	0.767769i	−0.923381	−	0.383885i	$-0.874586\pi$
$379$		−	290.985i		−	0.767769i	0.923381	−	0.383885i	$-0.125414\pi$
$380$	480.000	−	277.128i	1.26316	−	0.729285i
$381$		0			0
$382$	−624.000	−	360.267i	−1.63351	−	0.943106i
$383$	171.000	+	98.7269i	0.446475	+	0.257773i	0.706340	−	0.707872i	$-0.250345\pi$
$383$	171.000	+	98.7269i	0.446475	+	0.257773i	−0.259865	+	0.965645i	$0.583678\pi$
$384$		0			0
$385$	−157.500	+	90.9327i	−0.409091	+	0.236189i
$386$	−151.000	−	261.540i	−0.391192	−	0.677564i
$387$		0			0
$388$	188.000			0.484536
$389$	−205.000	−	355.070i	−0.526992	−	0.912777i	−0.999505	−	0.0314537i	$-0.989986\pi$
$389$	−205.000	−	355.070i	−0.526992	−	0.912777i	0.472513	−	0.881324i	$-0.343347\pi$
$390$		0			0
$391$			83.1384i			0.212630i
$392$	196.000	−	339.482i	0.500000	−	0.866025i
$393$		0			0
$394$	−556.000			−1.41117
$395$	37.5000	−	21.6506i	0.0949367	−	0.0548117i
$396$		0			0
$397$	−106.000	+	183.597i	−0.267003	+	0.462462i	−0.968086	−	0.250617i	$-0.919367\pi$
$397$	−106.000	+	183.597i	−0.267003	+	0.462462i	0.701084	+	0.713079i	$0.252700\pi$
$398$	−240.000	+	138.564i	−0.603015	+	0.348151i
$399$		0			0
$400$		0			0
$401$	−232.000	+	401.836i	−0.578554	+	1.00208i	0.417092	+	0.908864i	$0.363049\pi$
$401$	−232.000	+	401.836i	−0.578554	+	1.00208i	−0.995646	+	0.0932200i	$0.970284\pi$
$402$		0			0
$403$	264.000	−	152.420i	0.655087	−	0.378215i
$404$	260.000	+	450.333i	0.643564	+	1.11469i
$405$		0			0
$406$	259.000	+	448.601i	0.637931	+	1.10493i
$407$			353.338i			0.868153i
$408$		0			0
$409$	−257.500	−	446.003i	−0.629584	−	1.09047i	−0.987635	−	0.156770i	$-0.949892\pi$
$409$	−257.500	−	446.003i	−0.629584	−	1.09047i	0.358051	−	0.933702i	$-0.383441\pi$
$410$	−200.000	+	346.410i	−0.487805	+	0.844903i
$411$		0			0
$412$	72.0000	+	41.5692i	0.174757	+	0.100896i
$413$	−178.500	−	103.057i	−0.432203	−	0.249533i
$414$		0			0
$415$	577.500	+	333.420i	1.39157	+	0.803421i
$416$	512.000			1.23077
$417$		0			0
$418$	288.000			0.688995
$419$			96.9948i			0.231491i	0.993279	+	0.115746i	$0.0369257\pi$
$419$			96.9948i			0.231491i	−0.993279	+	0.115746i	$0.963074\pi$
$420$		0			0
$421$	170.000			0.403800			0.201900	−	0.979406i	$-0.435288\pi$
$421$	170.000			0.403800			0.201900	+	0.979406i	$0.435288\pi$
$422$			242.487i			0.574614i
$423$		0			0
$424$	−292.000	−	505.759i	−0.688679	−	1.19283i
$425$		0			0
$426$		0			0
$427$	574.000			1.34426
$428$	282.000	+	162.813i	0.658879	+	0.380404i
$429$		0			0
$430$	−210.000	−	121.244i	−0.488372	−	0.281962i
$431$	−6.00000	+	3.46410i	−0.0139211	+	0.00803736i	−0.506944	−	0.861979i	$-0.669225\pi$
$431$	−6.00000	+	3.46410i	−0.0139211	+	0.00803736i	0.493023	+	0.870016i	$0.335892\pi$
$432$		0			0
$433$	−226.000			−0.521940			−0.260970	−	0.965347i	$-0.584042\pi$
$433$	−226.000			−0.521940			−0.260970	+	0.965347i	$0.584042\pi$
$434$	231.000	+	133.368i	0.532258	+	0.307299i
$435$		0			0
$436$	−244.000	−	422.620i	−0.559633	−	0.969313i
$437$	−288.000	−	498.831i	−0.659039	−	1.14149i
$438$		0			0
$439$	154.500	+	89.2006i	0.351936	+	0.203190i	0.665538	−	0.746364i	$-0.268202\pi$
$439$	154.500	+	89.2006i	0.351936	+	0.203190i	−0.313602	+	0.949555i	$0.601536\pi$
$440$		−	207.846i		−	0.472377i
$441$		0			0
$442$	64.0000	+	110.851i	0.144796	+	0.250795i
$443$	−538.500	−	310.903i	−1.21558	−	0.701813i	−0.251607	−	0.967829i	$-0.580959\pi$
$443$	−538.500	−	310.903i	−1.21558	−	0.701813i	−0.963968	+	0.266017i	$0.914292\pi$
$444$		0			0
$445$	145.000	+	251.147i	0.325843	+	0.564376i
$446$		−	24.2487i		−	0.0543693i
$447$		0			0
$448$	224.000	+	387.979i	0.500000	+	0.866025i
$449$	−520.000			−1.15813			−0.579065	−	0.815282i	$-0.696582\pi$
$449$	−520.000			−1.15813			−0.579065	+	0.815282i	$0.696582\pi$
$450$		0			0
$451$	−180.000	+	103.923i	−0.399113	+	0.230428i
$452$	−64.0000			−0.141593
$453$		0			0
$454$	261.000	−	150.688i	0.574890	−	0.331913i
$455$	560.000			1.23077
$456$		0			0
$457$	18.5000	−	32.0429i	0.0404814	−	0.0701158i	−0.845075	−	0.534648i	$-0.820444\pi$
$457$	18.5000	−	32.0429i	0.0404814	−	0.0701158i	0.885556	+	0.464532i	$0.153778\pi$
$458$	212.000	−	367.195i	0.462882	−	0.801735i
$459$		0			0
$460$	−360.000	+	207.846i	−0.782609	+	0.451839i
$461$	−250.000			−0.542299			−0.271150	−	0.962537i	$-0.587404\pi$
$461$	−250.000			−0.542299			−0.271150	+	0.962537i	$0.587404\pi$
$462$		0			0
$463$		−	339.482i		−	0.733222i	−0.930374	−	0.366611i	$-0.880518\pi$
$463$		−	339.482i		−	0.733222i	0.930374	−	0.366611i	$-0.119482\pi$
$464$	−592.000			−1.27586
$465$		0			0
$466$	212.000	−	367.195i	0.454936	−	0.787972i
$467$	−690.000	−	398.372i	−1.47752	−	0.853044i	−0.477839	−	0.878448i	$-0.658580\pi$
$467$	−690.000	−	398.372i	−1.47752	−	0.853044i	−0.999677	+	0.0254033i	$0.991913\pi$
$468$		0			0
$469$	483.000	+	278.860i	1.02985	+	0.594585i
$470$	−390.000	+	225.167i	−0.829787	+	0.479078i
$471$		0			0
$472$	204.000	−	117.779i	0.432203	−	0.249533i
$473$	−63.0000	−	109.119i	−0.133192	−	0.230696i
$474$		0			0
$475$		0			0
$476$	−56.0000	+	96.9948i	−0.117647	+	0.203771i
$477$		0			0
$478$			96.9948i			0.202918i
$479$	153.000	−	88.3346i	0.319415	−	0.184415i	−0.331717	−	0.943379i	$-0.607628\pi$
$479$	153.000	−	88.3346i	0.319415	−	0.184415i	0.651132	+	0.758965i	$0.274294\pi$
$480$		0			0
$481$	544.000	−	942.236i	1.13098	−	1.95891i
$482$	11.0000	+	19.0526i	0.0228216	+	0.0395281i
$483$		0			0
$484$	−188.000	+	325.626i	−0.388430	+	0.672780i
$485$	−117.500	+	203.516i	−0.242268	+	0.419621i
$486$		0			0
$487$	268.500	−	155.019i	0.551335	−	0.318313i	−0.198325	−	0.980136i	$-0.563550\pi$
$487$	268.500	−	155.019i	0.551335	−	0.318313i	0.749660	+	0.661823i	$0.230217\pi$
$488$	−328.000	+	568.113i	−0.672131	+	1.16417i
$489$		0			0
$490$	245.000	+	424.352i	0.500000	+	0.866025i
$491$		−	230.363i		−	0.469171i	−0.972096	−	0.234585i	$-0.924627\pi$
$491$		−	230.363i		−	0.469171i	0.972096	−	0.234585i	$-0.0753732\pi$
$492$		0			0
$493$	−74.0000	−	128.172i	−0.150101	−	0.259983i
$494$	−768.000	−	443.405i	−1.55466	−	0.897581i
$495$		0			0
$496$	−264.000	+	152.420i	−0.532258	+	0.307299i
$497$	−441.000	+	254.611i	−0.887324	+	0.512297i
$498$		0			0
$499$	−207.000	−	119.512i	−0.414830	−	0.239502i	0.278033	−	0.960571i	$-0.410318\pi$
$499$	−207.000	−	119.512i	−0.414830	−	0.239502i	−0.692863	+	0.721069i	$0.743651\pi$
$500$	−500.000			−1.00000
$501$		0			0
$502$			72.7461i			0.144913i
$503$			872.954i			1.73549i	0.497006	+	0.867747i	$0.334433\pi$
$503$			872.954i			1.73549i	−0.497006	+	0.867747i	$0.665567\pi$
$504$		0			0
$505$	−650.000			−1.28713
$506$	−216.000			−0.426877
$507$		0			0
$508$			436.477i			0.859206i
$509$	270.500	−	468.520i	0.531434	−	0.920471i	−0.467893	−	0.883785i	$-0.654987\pi$
$509$	270.500	−	468.520i	0.531434	−	0.920471i	0.999327	−	0.0366857i	$-0.0116800\pi$
$510$		0			0
$511$	−329.000	+	569.845i	−0.643836	+	1.11516i
$512$	−512.000			−1.00000
$513$		0			0
$514$	−58.0000	+	100.459i	−0.112840	+	0.195445i
$515$	−90.0000	+	51.9615i	−0.174757	+	0.100896i
$516$		0			0
$517$	−234.000			−0.452611
$518$	952.000			1.83784
$519$		0			0
$520$	−320.000	+	554.256i	−0.615385	+	1.06588i
$521$	275.000	+	476.314i	0.527831	+	0.914230i	0.999474	+	0.0324405i	$0.0103279\pi$
$521$	275.000	+	476.314i	0.527831	+	0.914230i	−0.471643	+	0.881790i	$0.656339\pi$
$522$		0			0
$523$	−528.000	−	304.841i	−1.00956	−	0.582870i	−0.0984974	−	0.995137i	$-0.531404\pi$
$523$	−528.000	−	304.841i	−1.00956	−	0.582870i	−0.911063	+	0.412267i	$0.864737\pi$
$524$	54.0000	+	31.1769i	0.103053	+	0.0594979i
$525$		0			0
$526$	−702.000	+	405.300i	−1.33460	+	0.770532i
$527$	−66.0000	−	38.1051i	−0.125237	−	0.0723057i
$528$		0			0
$529$	−48.5000	−	84.0045i	−0.0916824	−	0.158799i
$530$	730.000			1.37736
$531$		0			0
$532$		−	775.959i		−	1.45857i
$533$	640.000			1.20075
$534$		0			0
$535$	−352.500	+	203.516i	−0.658879	+	0.380404i
$536$	−552.000	+	318.697i	−1.02985	+	0.594585i
$537$		0			0
$538$	−445.000	−	770.763i	−0.827138	−	1.43264i
$539$			254.611i			0.472377i
$540$		0			0
$541$	155.000	−	268.468i	0.286506	−	0.496244i	−0.686467	−	0.727161i	$-0.740839\pi$
$541$	155.000	−	268.468i	0.286506	−	0.496244i	0.972973	+	0.230917i	$0.0741727\pi$
$542$	615.000	+	355.070i	1.13469	+	0.655111i
$543$		0			0
$544$	−64.0000	−	110.851i	−0.117647	−	0.203771i
$545$	610.000			1.11927
$546$		0			0
$547$			630.466i			1.15259i	0.817242	+	0.576295i	$0.195502\pi$
$547$			630.466i			1.15259i	−0.817242	+	0.576295i	$0.804498\pi$
$548$	−148.000	−	256.344i	−0.270073	−	0.467780i
$549$		0			0
$550$		0			0
$551$	888.000	+	512.687i	1.61162	+	0.930466i
$552$		0			0
$553$		−	60.6218i		−	0.109623i
$554$	−256.000	−	443.405i	−0.462094	−	0.800370i
$555$		0			0
$556$			678.964i			1.22116i
$557$	267.500	+	463.324i	0.480251	+	0.831820i	0.999743	−	0.0226556i	$-0.00721212\pi$
$557$	267.500	+	463.324i	0.480251	+	0.831820i	−0.519492	+	0.854475i	$0.673879\pi$
$558$		0			0
$559$			387.979i			0.694060i
$560$	−560.000			−1.00000
$561$		0			0
$562$	−556.000			−0.989324
$563$	604.500	−	349.008i	1.07371	−	0.619908i	0.144519	−	0.989502i	$-0.453837\pi$
$563$	604.500	−	349.008i	1.07371	−	0.619908i	0.929193	+	0.369594i	$0.120503\pi$
$564$		0			0
$565$	40.0000	−	69.2820i	0.0707965	−	0.122623i
$566$	−30.0000	+	17.3205i	−0.0530035	+	0.0306016i
$567$		0			0
$568$		−	581.969i		−	1.02459i
$569$	356.000	−	616.610i	0.625659	−	1.08367i	−0.362754	−	0.931885i	$-0.618163\pi$
$569$	356.000	−	616.610i	0.625659	−	1.08367i	0.988413	−	0.151788i	$-0.0485032\pi$
$570$		0			0
$571$	−57.0000	+	32.9090i	−0.0998249	+	0.0576339i	−0.549081	−	0.835769i	$-0.685022\pi$
$571$	−57.0000	+	32.9090i	−0.0998249	+	0.0576339i	0.449256	+	0.893403i	$0.351689\pi$
$572$	−288.000	+	166.277i	−0.503497	+	0.290694i
$573$		0			0
$574$	280.000	+	484.974i	0.487805	+	0.844903i
$575$		0			0
$576$		0			0
$577$	78.5000	+	135.966i	0.136049	+	0.235643i	0.925998	−	0.377530i	$-0.123226\pi$
$577$	78.5000	+	135.966i	0.136049	+	0.235643i	−0.789949	+	0.613173i	$0.789893\pi$
$578$	−273.000	+	472.850i	−0.472318	+	0.818079i
$579$		0			0
$580$	370.000	−	640.859i	0.637931	−	1.10493i
$581$	808.500	−	466.788i	1.39157	−	0.803421i
$582$		0			0
$583$	328.500	+	189.660i	0.563465	+	0.325317i
$584$	−376.000	−	651.251i	−0.643836	−	1.11516i
$585$		0			0
$586$	122.000			0.208191
$587$		−	788.083i		−	1.34256i	−0.741204	−	0.671280i	$-0.765745\pi$
$587$		−	788.083i		−	1.34256i	0.741204	−	0.671280i	$-0.234255\pi$
$588$		0			0
$589$	528.000			0.896435
$590$			294.449i			0.499065i
$591$		0			0
$592$	−544.000	+	942.236i	−0.918919	+	1.59161i
$593$	−34.0000	+	58.8897i	−0.0573356	+	0.0993081i	−0.893269	−	0.449523i	$-0.851594\pi$
$593$	−34.0000	+	58.8897i	−0.0573356	+	0.0993081i	0.835933	+	0.548832i	$0.184927\pi$
$594$		0			0
$595$	−70.0000	−	121.244i	−0.117647	−	0.203771i
$596$	332.000	−	575.041i	0.557047	−	0.964834i
$597$		0			0
$598$	576.000	+	332.554i	0.963211	+	0.556110i
$599$	−237.000	+	136.832i	−0.395659	+	0.228434i	−0.684609	−	0.728910i	$-0.740027\pi$
$599$	−237.000	+	136.832i	−0.395659	+	0.228434i	0.288950	+	0.957344i	$0.406694\pi$
$600$		0			0
$601$	971.000			1.61564			0.807820	−	0.589429i	$-0.200647\pi$
$601$	971.000			1.61564			0.807820	+	0.589429i	$0.200647\pi$
$602$	−294.000	+	169.741i	−0.488372	+	0.281962i
$603$		0			0
$604$	486.000	−	280.592i	0.804636	−	0.464557i
$605$	−235.000	−	407.032i	−0.388430	−	0.672780i
$606$		0			0
$607$	−76.5000	−	44.1673i	−0.126030	−	0.0727633i	0.435660	−	0.900111i	$-0.356515\pi$
$607$	−76.5000	−	44.1673i	−0.126030	−	0.0727633i	−0.561689	+	0.827348i	$0.689848\pi$
$608$	768.000	+	443.405i	1.26316	+	0.729285i
$609$		0			0
$610$	−410.000	−	710.141i	−0.672131	−	1.16417i
$611$	624.000	+	360.267i	1.02128	+	0.589634i
$612$		0			0
$613$	−418.000	−	723.997i	−0.681892	−	1.18107i	−0.974403	−	0.224810i	$-0.927824\pi$
$613$	−418.000	−	723.997i	−0.681892	−	1.18107i	0.292510	−	0.956262i	$-0.405509\pi$
$614$		−	872.954i		−	1.42175i
$615$		0			0
$616$	−252.000	−	145.492i	−0.409091	−	0.236189i
$617$	−394.000			−0.638574			−0.319287	−	0.947658i	$-0.603443\pi$
$617$	−394.000			−0.638574			−0.319287	+	0.947658i	$0.603443\pi$
$618$		0			0
$619$	603.000	−	348.142i	0.974152	−	0.562427i	0.0736524	−	0.997284i	$-0.476534\pi$
$619$	603.000	−	348.142i	0.974152	−	0.562427i	0.900499	+	0.434857i	$0.143201\pi$
$620$		−	381.051i		−	0.614599i
$621$		0			0
$622$	−264.000	+	152.420i	−0.424437	+	0.245049i
$623$	406.000			0.651685
$624$		0			0
$625$	312.500	−	541.266i	0.500000	−	0.866025i
$626$	233.000	−	403.568i	0.372204	−	0.644677i
$627$		0			0
$628$	104.000	+	180.133i	0.165605	+	0.286836i
$629$	−272.000			−0.432432
$630$		0			0
$631$			254.611i			0.403505i	0.979437	+	0.201752i	$0.0646636\pi$
$631$			254.611i			0.403505i	−0.979437	+	0.201752i	$0.935336\pi$
$632$	60.0000	+	34.6410i	0.0949367	+	0.0548117i
$633$		0			0
$634$	107.000	−	185.329i	0.168770	−	0.292318i
$635$	−472.500	−	272.798i	−0.744094	−	0.429603i
$636$		0			0
$637$	392.000	−	678.964i	0.615385	−	1.06588i
$638$	333.000	−	192.258i	0.521944	−	0.301344i
$639$		0			0
$640$	320.000	−	554.256i	0.500000	−	0.866025i
$641$	89.0000	+	154.153i	0.138846	+	0.240488i	0.927060	−	0.374913i	$-0.122328\pi$
$641$	89.0000	+	154.153i	0.138846	+	0.240488i	−0.788214	+	0.615401i	$0.788994\pi$
$642$		0			0
$643$		−	266.736i		−	0.414830i	−0.978253	−	0.207415i	$-0.933495\pi$
$643$		−	266.736i		−	0.414830i	0.978253	−	0.207415i	$-0.0665051\pi$
$644$			581.969i			0.903679i
$645$		0			0
$646$			221.703i			0.343193i
$647$	−15.0000	+	8.66025i	−0.0231839	+	0.0133852i	−0.511547	−	0.859255i	$-0.670927\pi$
$647$	−15.0000	+	8.66025i	−0.0231839	+	0.0133852i	0.488363	+	0.872640i	$0.337594\pi$
$648$		0			0
$649$	−76.5000	+	132.502i	−0.117874	+	0.204163i
$650$		0			0
$651$		0			0
$652$	264.000	+	152.420i	0.404908	+	0.233774i
$653$	−368.500	+	638.261i	−0.564319	+	0.977428i	0.432794	+	0.901493i	$0.357528\pi$
$653$	−368.500	+	638.261i	−0.564319	+	0.977428i	−0.997113	+	0.0759356i	$0.975806\pi$
$654$		0			0
$655$	−67.5000	+	38.9711i	−0.103053	+	0.0594979i
$656$	−640.000			−0.975610
$657$		0			0
$658$			630.466i			0.958156i
$659$		−	678.964i		−	1.03029i	−0.857102	−	0.515147i	$-0.827737\pi$
$659$		−	678.964i		−	1.03029i	0.857102	−	0.515147i	$-0.172263\pi$
$660$		0			0
$661$	341.000	+	590.629i	0.515885	+	0.893539i	0.999830	+	0.0184406i	$0.00587016\pi$
$661$	341.000	+	590.629i	0.515885	+	0.893539i	−0.483945	+	0.875098i	$0.660797\pi$
$662$	708.000	+	408.764i	1.06949	+	0.617468i
$663$		0			0
$664$			1066.94i			1.60684i
$665$	840.000	+	484.974i	1.26316	+	0.729285i
$666$		0			0
$667$	−666.000	−	384.515i	−0.998501	−	0.576485i
$668$			678.964i			1.01641i
$669$		0			0
$670$		−	796.743i		−	1.18917i
$671$		−	426.084i		−	0.634999i
$672$		0			0
$673$	−1027.00			−1.52600			−0.763001	−	0.646397i	$-0.776275\pi$
$673$	−1027.00			−1.52600			−0.763001	+	0.646397i	$0.776275\pi$
$674$	−298.000			−0.442136
$675$		0			0
$676$	348.000			0.514793
$677$	165.500	−	286.654i	0.244461	−	0.423419i	−0.717519	−	0.696539i	$-0.754722\pi$
$677$	165.500	−	286.654i	0.244461	−	0.423419i	0.961980	+	0.273120i	$0.0880557\pi$
$678$		0			0
$679$	164.500	+	284.922i	0.242268	+	0.419621i
$680$	160.000			0.235294
$681$		0			0
$682$	99.0000	−	171.473i	0.145161	−	0.251427i
$683$	−226.500	+	130.770i	−0.331625	+	0.191464i	−0.656562	−	0.754272i	$-0.727990\pi$
$683$	−226.500	+	130.770i	−0.331625	+	0.191464i	0.324937	+	0.945736i	$0.394657\pi$
$684$		0			0
$685$	370.000			0.540146
$686$	686.000			1.00000
$687$		0			0
$688$		−	387.979i		−	0.563924i
$689$	−584.000	−	1011.52i	−0.847605	−	1.46810i
$690$		0			0
$691$	1068.00	+	616.610i	1.54559	+	0.892345i	0.998470	+	0.0552875i	$0.0176075\pi$
$691$	1068.00	+	616.610i	1.54559	+	0.892345i	0.547116	+	0.837057i	$0.315726\pi$
$692$	−52.0000	+	90.0666i	−0.0751445	+	0.130154i
$693$		0			0
$694$	−660.000	+	381.051i	−0.951009	+	0.549065i
$695$	−735.000	−	424.352i	−1.05755	−	0.610579i
$696$		0			0
$697$	−80.0000	−	138.564i	−0.114778	−	0.198801i
$698$	788.000			1.12894
$699$		0			0
$700$		0			0
$701$	467.000			0.666191			0.333096	−	0.942893i	$-0.391907\pi$
$701$	467.000			0.666191			0.333096	+	0.942893i	$0.391907\pi$
$702$		0			0
$703$	1632.00	−	942.236i	2.32148	−	1.34031i
$704$	288.000	−	166.277i	0.409091	−	0.236189i
$705$		0			0
$706$	−256.000	−	443.405i	−0.362606	−	0.628052i
$707$	−455.000	+	788.083i	−0.643564	+	1.11469i
$708$		0			0
$709$	−265.000	+	458.993i	−0.373766	+	0.647381i	−0.990141	−	0.140071i	$-0.955267\pi$
$709$	−265.000	+	458.993i	−0.373766	+	0.647381i	0.616376	+	0.787452i	$0.288600\pi$
$710$	630.000	+	363.731i	0.887324	+	0.512297i
$711$		0			0
$712$	−232.000	+	401.836i	−0.325843	+	0.564376i
$713$	−396.000			−0.555400
$714$		0			0
$715$		−	415.692i		−	0.581388i
$716$	−1032.00	+	595.825i	−1.44134	+	0.832158i
$717$		0			0
$718$	678.000	+	391.443i	0.944290	+	0.545186i
$719$	−627.000	−	361.999i	−0.872045	−	0.503475i	−0.00401739	−	0.999992i	$-0.501279\pi$
$719$	−627.000	−	361.999i	−0.872045	−	0.503475i	−0.868027	+	0.496517i	$0.834612\pi$
$720$		0			0
$721$			145.492i			0.201792i
$722$	−407.000	−	704.945i	−0.563712	−	0.976378i
$723$		0			0
$724$	−64.0000			−0.0883978
$725$		0			0
$726$		0			0
$727$		−	60.6218i		−	0.0833862i	−0.999130	−	0.0416931i	$-0.986725\pi$
$727$		−	60.6218i		−	0.0833862i	0.999130	−	0.0416931i	$-0.0132752\pi$
$728$	448.000	+	775.959i	0.615385	+	1.06588i
$729$		0			0
$730$	940.000			1.28767
$731$	84.0000	−	48.4974i	0.114911	−	0.0663439i
$732$		0			0
$733$	293.000	−	507.491i	0.399727	−	0.692348i	−0.593965	−	0.804491i	$-0.702438\pi$
$733$	293.000	−	507.491i	0.399727	−	0.692348i	0.993692	+	0.112143i	$0.0357715\pi$
$734$	−513.000	+	296.181i	−0.698910	+	0.403516i
$735$		0			0
$736$	−576.000	−	332.554i	−0.782609	−	0.451839i
$737$	207.000	−	358.535i	0.280868	−	0.486478i
$738$		0			0
$739$	111.000	−	64.0859i	0.150203	−	0.0867197i	−0.423015	−	0.906123i	$-0.639028\pi$
$739$	111.000	−	64.0859i	0.150203	−	0.0867197i	0.573218	+	0.819403i	$0.305695\pi$
$740$	−680.000	−	1177.79i	−0.918919	−	1.59161i
$741$		0			0
$742$	511.000	−	885.078i	0.688679	−	1.19283i
$743$			24.2487i			0.0326362i	0.999867	+	0.0163181i	$0.00519445\pi$
$743$			24.2487i			0.0326362i	−0.999867	+	0.0163181i	$0.994806\pi$
$744$		0			0
$745$	415.000	+	718.801i	0.557047	+	0.964834i
$746$	656.000	−	1136.23i	0.879357	−	1.52309i
$747$		0			0
$748$	72.0000	+	41.5692i	0.0962567	+	0.0555738i
$749$			569.845i			0.760807i
$750$		0			0
$751$	−490.500	−	283.190i	−0.653129	−	0.377084i	0.136525	−	0.990637i	$-0.456407\pi$
$751$	−490.500	−	283.190i	−0.653129	−	0.377084i	−0.789654	+	0.613552i	$0.789740\pi$
$752$	−624.000	−	360.267i	−0.829787	−	0.479078i
$753$		0			0
$754$	−1184.00			−1.57029
$755$			701.481i			0.929113i
$756$		0			0
$757$	−250.000			−0.330251			−0.165125	−	0.986273i	$-0.552803\pi$
$757$	−250.000			−0.330251			−0.165125	+	0.986273i	$0.552803\pi$
$758$			581.969i			0.767769i
$759$		0			0
$760$	−960.000	+	554.256i	−1.26316	+	0.729285i
$761$	−160.000	+	277.128i	−0.210250	+	0.364163i	−0.951793	−	0.306742i	$-0.900761\pi$
$761$	−160.000	+	277.128i	−0.210250	+	0.364163i	0.741543	+	0.670905i	$0.234094\pi$
$762$		0			0
$763$	427.000	−	739.586i	0.559633	−	0.969313i
$764$	1248.00	+	720.533i	1.63351	+	0.943106i
$765$		0			0
$766$	−342.000	−	197.454i	−0.446475	−	0.257773i
$767$	408.000	−	235.559i	0.531943	−	0.307117i
$768$		0			0
$769$	425.000			0.552666			0.276333	−	0.961062i	$-0.410881\pi$
$769$	425.000			0.552666			0.276333	+	0.961062i	$0.410881\pi$
$770$	315.000	−	181.865i	0.409091	−	0.236189i
$771$		0			0
$772$	302.000	+	523.079i	0.391192	+	0.677564i
$773$	65.0000	+	112.583i	0.0840880	+	0.145645i	0.905002	−	0.425407i	$-0.139869\pi$
$773$	65.0000	+	112.583i	0.0840880	+	0.145645i	−0.820914	+	0.571051i	$0.806536\pi$
$774$		0			0
$775$		0			0
$776$	−376.000			−0.484536
$777$		0			0
$778$	410.000	+	710.141i	0.526992	+	0.912777i
$779$	960.000	+	554.256i	1.23235	+	0.711497i
$780$		0			0
$781$	189.000	+	327.358i	0.241997	+	0.419152i
$782$		−	166.277i		−	0.212630i
$783$		0			0
$784$	−392.000	+	678.964i	−0.500000	+	0.866025i
$785$	−260.000			−0.331210
$786$		0			0
$787$	−867.000	+	500.563i	−1.10165	+	0.636039i	−0.936654	−	0.350255i	$-0.886095\pi$
$787$	−867.000	+	500.563i	−1.10165	+	0.636039i	−0.164997	+	0.986294i	$0.552762\pi$
$788$	1112.00			1.41117
$789$		0			0
$790$	−75.0000	+	43.3013i	−0.0949367	+	0.0548117i
$791$	−56.0000	−	96.9948i	−0.0707965	−	0.122623i
$792$		0			0
$793$	−656.000	+	1136.23i	−0.827238	+	1.43282i
$794$	212.000	−	367.195i	0.267003	−	0.462462i
$795$		0			0
$796$	480.000	−	277.128i	0.603015	−	0.348151i
$797$	−439.000			−0.550816			−0.275408	−	0.961327i	$-0.588813\pi$
$797$	−439.000			−0.550816			−0.275408	+	0.961327i	$0.588813\pi$
$798$		0			0
$799$		−	180.133i		−	0.225448i
$800$		0			0
$801$		0			0
$802$	464.000	−	803.672i	0.578554	−	1.00208i
$803$	423.000	+	244.219i	0.526775	+	0.304133i
$804$		0			0
$805$	−630.000	−	363.731i	−0.782609	−	0.451839i
$806$	−528.000	+	304.841i	−0.655087	+	0.378215i
$807$		0			0
$808$	−520.000	−	900.666i	−0.643564	−	1.11469i
$809$	−520.000	−	900.666i	−0.642769	−	1.11331i	−0.984812	−	0.173624i	$-0.944452\pi$
$809$	−520.000	−	900.666i	−0.642769	−	1.11331i	0.342043	−	0.939684i	$-0.388881\pi$
$810$		0			0
$811$			1236.68i			1.52489i	0.647054	+	0.762444i	$0.276001\pi$
$811$			1236.68i			1.52489i	−0.647054	+	0.762444i	$0.723999\pi$
$812$	−518.000	−	897.202i	−0.637931	−	1.10493i
$813$		0			0
$814$		−	706.677i		−	0.868153i
$815$	−330.000	+	190.526i	−0.404908	+	0.233774i
$816$		0			0
$817$	−336.000	+	581.969i	−0.411261	+	0.712324i
$818$	515.000	+	892.006i	0.629584	+	1.09047i
$819$		0			0
$820$	400.000	−	692.820i	0.487805	−	0.844903i
$821$	72.5000	−	125.574i	0.0883069	−	0.152952i	−0.818489	−	0.574523i	$-0.805188\pi$
$821$	72.5000	−	125.574i	0.0883069	−	0.152952i	0.906796	+	0.421571i	$0.138521\pi$
$822$		0			0
$823$	−1254.00	+	723.997i	−1.52369	+	0.879705i	−0.524087	+	0.851665i	$0.675593\pi$
$823$	−1254.00	+	723.997i	−1.52369	+	0.879705i	−0.999607	+	0.0280403i	$0.991073\pi$
$824$	−144.000	−	83.1384i	−0.174757	−	0.100896i
$825$		0			0
$826$	357.000	+	206.114i	0.432203	+	0.249533i
$827$			545.596i			0.659729i	0.944028	+	0.329865i	$0.107003\pi$
$827$			545.596i			0.659729i	−0.944028	+	0.329865i	$0.892997\pi$
$828$		0			0
$829$	−184.000	−	318.697i	−0.221954	−	0.384436i	0.733447	−	0.679746i	$-0.237910\pi$
$829$	−184.000	−	318.697i	−0.221954	−	0.384436i	−0.955401	+	0.295311i	$0.904577\pi$
$830$	−1155.00	−	666.840i	−1.39157	−	0.803421i
$831$		0			0
$832$	−1024.00			−1.23077
$833$	−196.000			−0.235294
$834$		0			0
$835$	−735.000	−	424.352i	−0.880240	−	0.508207i
$836$	−576.000			−0.688995
$837$		0			0
$838$		−	193.990i		−	0.231491i
$839$			921.451i			1.09827i	0.835733	+	0.549136i	$0.185043\pi$
$839$			921.451i			1.09827i	−0.835733	+	0.549136i	$0.814957\pi$
$840$		0			0
$841$	528.000			0.627824
$842$	−340.000			−0.403800
$843$		0			0
$844$		−	484.974i		−	0.574614i
$845$	−217.500	+	376.721i	−0.257396	+	0.445824i
$846$		0			0
$847$	−658.000			−0.776860
$848$	584.000	+	1011.52i	0.688679	+	1.19283i
$849$		0			0
$850$		0			0
$851$	−1224.00	+	706.677i	−1.43831	+	0.830407i
$852$		0			0
$853$	−1150.00			−1.34818			−0.674091	−	0.738648i	$-0.735465\pi$
$853$	−1150.00			−1.34818			−0.674091	+	0.738648i	$0.735465\pi$
$854$	−1148.00			−1.34426
$855$		0			0
$856$	−564.000	−	325.626i	−0.658879	−	0.380404i
$857$	107.000	+	185.329i	0.124854	+	0.216254i	0.921676	−	0.387961i	$-0.126820\pi$
$857$	107.000	+	185.329i	0.124854	+	0.216254i	−0.796822	+	0.604214i	$0.793487\pi$
$858$		0			0
$859$	711.000	+	410.496i	0.827707	+	0.477877i	0.853067	−	0.521802i	$-0.174740\pi$
$859$	711.000	+	410.496i	0.827707	+	0.477877i	−0.0253602	+	0.999678i	$0.508073\pi$
$860$	420.000	+	242.487i	0.488372	+	0.281962i
$861$		0			0
$862$	12.0000	−	6.92820i	0.0139211	−	0.00803736i
$863$	−339.000	−	195.722i	−0.392816	−	0.226792i	0.290564	−	0.956856i	$-0.406157\pi$
$863$	−339.000	−	195.722i	−0.392816	−	0.226792i	−0.683379	+	0.730063i	$0.739491\pi$
$864$		0			0
$865$	−65.0000	−	112.583i	−0.0751445	−	0.130154i
$866$	452.000			0.521940
$867$		0			0
$868$	−462.000	−	266.736i	−0.532258	−	0.307299i
$869$	−45.0000			−0.0517837
$870$		0			0
$871$	−1104.00	+	637.395i	−1.26751	+	0.731796i
$872$	488.000	+	845.241i	0.559633	+	0.969313i
$873$		0			0
$874$	576.000	+	997.661i	0.659039	+	1.14149i
$875$	−437.500	−	757.772i	−0.500000	−	0.866025i
$876$		0			0
$877$	−160.000	+	277.128i	−0.182440	+	0.315996i	−0.942711	−	0.333611i	$-0.891733\pi$
$877$	−160.000	+	277.128i	−0.182440	+	0.315996i	0.760271	+	0.649606i	$0.225066\pi$
$878$	−309.000	−	178.401i	−0.351936	−	0.203190i
$879$		0			0
$880$			415.692i			0.472377i
$881$	−502.000			−0.569807			−0.284904	−	0.958556i	$-0.591962\pi$
$881$	−502.000			−0.569807			−0.284904	+	0.958556i	$0.591962\pi$
$882$		0			0
$883$			290.985i			0.329541i	0.986332	+	0.164770i	$0.0526883\pi$
$883$			290.985i			0.329541i	−0.986332	+	0.164770i	$0.947312\pi$
$884$	−128.000	−	221.703i	−0.144796	−	0.250795i
$885$		0			0
$886$	1077.00	+	621.806i	1.21558	+	0.701813i
$887$	234.000	+	135.100i	0.263811	+	0.152311i	0.626072	−	0.779766i	$-0.284662\pi$
$887$	234.000	+	135.100i	0.263811	+	0.152311i	−0.362261	+	0.932077i	$0.617995\pi$
$888$		0			0
$889$	−661.500	+	381.917i	−0.744094	+	0.429603i
$890$	−290.000	−	502.295i	−0.325843	−	0.564376i
$891$		0			0
$892$			48.4974i			0.0543693i
$893$	624.000	+	1080.80i	0.698768	+	1.21030i
$894$		0			0
$895$		−	1489.56i		−	1.66432i
$896$	−448.000	−	775.959i	−0.500000	−	0.866025i
$897$		0			0
$898$	1040.00			1.15813
$899$	610.500	−	352.472i	0.679088	−	0.392072i
$900$		0			0
$901$	−146.000	+	252.879i	−0.162042	+	0.280665i
$902$	360.000	−	207.846i	0.399113	−	0.230428i
$903$		0			0
$904$	128.000			0.141593
$905$	40.0000	−	69.2820i	0.0441989	−	0.0765547i
$906$		0			0
$907$	−162.000	+	93.5307i	−0.178611	+	0.103121i	−0.586640	−	0.809848i	$-0.699550\pi$
$907$	−162.000	+	93.5307i	−0.178611	+	0.103121i	0.408029	+	0.912969i	$0.366216\pi$
$908$	−522.000	+	301.377i	−0.574890	+	0.331913i
$909$		0			0
$910$	−1120.00			−1.23077
$911$		−	1624.66i		−	1.78338i	−0.452642	−	0.891692i	$-0.649518\pi$
$911$		−	1624.66i		−	1.78338i	0.452642	−	0.891692i	$-0.350482\pi$
$912$		0			0
$913$	−346.500	−	600.156i	−0.379518	−	0.657345i
$914$	−37.0000	+	64.0859i	−0.0404814	+	0.0701158i
$915$		0			0
$916$	−424.000	+	734.390i	−0.462882	+	0.801735i
$917$			109.119i			0.118996i
$918$		0			0
$919$	66.0000	+	38.1051i	0.0718172	+	0.0414637i	0.535479	−	0.844549i	$-0.320131\pi$
$919$	66.0000	+	38.1051i	0.0718172	+	0.0414637i	−0.463661	+	0.886012i	$0.653465\pi$
$920$	720.000	−	415.692i	0.782609	−	0.451839i
$921$		0			0
$922$	500.000			0.542299
$923$		−	1163.94i		−	1.26104i
$924$		0			0
$925$		0			0
$926$			678.964i			0.733222i
$927$		0			0
$928$	1184.00			1.27586
$929$	−643.000	+	1113.71i	−0.692142	+	1.19883i	0.278993	+	0.960293i	$0.410000\pi$
$929$	−643.000	+	1113.71i	−0.692142	+	1.19883i	−0.971135	+	0.238532i	$0.923334\pi$
$930$		0			0
$931$	1176.00	−	678.964i	1.26316	−	0.729285i
$932$	−424.000	+	734.390i	−0.454936	+	0.787972i
$933$		0			0
$934$	1380.00	+	796.743i	1.47752	+	0.853044i
$935$	−90.0000	+	51.9615i	−0.0962567	+	0.0555738i
$936$		0			0
$937$	1727.00			1.84312			0.921558	−	0.388240i	$-0.126917\pi$
$937$	1727.00			1.84312			0.921558	+	0.388240i	$0.126917\pi$
$938$	−966.000	−	557.720i	−1.02985	−	0.594585i
$939$		0			0
$940$	780.000	−	450.333i	0.829787	−	0.479078i
$941$	201.500	+	349.008i	0.214134	+	0.370891i	0.953004	−	0.302957i	$-0.0979738\pi$
$941$	201.500	+	349.008i	0.214134	+	0.370891i	−0.738870	+	0.673848i	$0.764640\pi$
$942$		0			0
$943$	−720.000	−	415.692i	−0.763521	−	0.440819i
$944$	−408.000	+	235.559i	−0.432203	+	0.249533i
$945$		0			0
$946$	126.000	+	218.238i	0.133192	+	0.230696i
$947$	816.000	+	471.118i	0.861668	+	0.497484i	0.864571	−	0.502511i	$-0.167590\pi$
$947$	816.000	+	471.118i	0.861668	+	0.497484i	−0.00290222	+	0.999996i	$0.500924\pi$
$948$		0			0
$949$	−752.000	−	1302.50i	−0.792413	−	1.37250i
$950$		0			0
$951$		0			0
$952$	112.000	−	193.990i	0.117647	−	0.203771i
$953$	−730.000			−0.766002			−0.383001	−	0.923748i	$-0.625109\pi$
$953$	−730.000			−0.766002			−0.383001	+	0.923748i	$0.625109\pi$
$954$		0			0
$955$	−1560.00	+	900.666i	−1.63351	+	0.943106i
$956$		−	193.990i		−	0.202918i
$957$		0			0
$958$	−306.000	+	176.669i	−0.319415	+	0.184415i
$959$	259.000	−	448.601i	0.270073	−	0.467780i
$960$		0			0
$961$	−299.000	+	517.883i	−0.311134	+	0.538900i
$962$	−1088.00	+	1884.47i	−1.13098	+	1.95891i
$963$		0			0
$964$	−22.0000	−	38.1051i	−0.0228216	−	0.0395281i
$965$	−755.000			−0.782383
$966$		0			0
$967$		−	157.617i		−	0.162995i	−0.996674	−	0.0814977i	$-0.974030\pi$
$967$		−	157.617i		−	0.162995i	0.996674	−	0.0814977i	$-0.0259703\pi$
$968$	376.000	−	651.251i	0.388430	−	0.672780i
$969$		0			0
$970$	235.000	−	407.032i	0.242268	−	0.419621i
$971$	790.500	+	456.395i	0.814109	+	0.470026i	0.848381	−	0.529386i	$-0.177578\pi$
$971$	790.500	+	456.395i	0.814109	+	0.470026i	−0.0342717	+	0.999413i	$0.510911\pi$
$972$		0			0
$973$	−1029.00	+	594.093i	−1.05755	+	0.610579i
$974$	−537.000	+	310.037i	−0.551335	+	0.318313i
$975$		0			0
$976$	656.000	−	1136.23i	0.672131	−	1.16417i
$977$	173.000	+	299.645i	0.177073	+	0.306699i	0.940877	−	0.338749i	$-0.110004\pi$
$977$	173.000	+	299.645i	0.177073	+	0.306699i	−0.763804	+	0.645448i	$0.776671\pi$
$978$		0			0
$979$		−	301.377i		−	0.307842i
$980$	−490.000	−	848.705i	−0.500000	−	0.866025i
$981$		0			0
$982$			460.726i			0.469171i
$983$	−666.000	+	384.515i	−0.677518	+	0.391165i	−0.798919	−	0.601438i	$-0.794595\pi$
$983$	−666.000	+	384.515i	−0.677518	+	0.391165i	0.121401	+	0.992604i	$0.461261\pi$
$984$		0			0
$985$	−695.000	+	1203.78i	−0.705584	+	1.22211i
$986$	148.000	+	256.344i	0.150101	+	0.259983i
$987$		0			0
$988$	1536.00	+	886.810i	1.55466	+	0.897581i
$989$	252.000	−	436.477i	0.254803	−	0.441331i
$990$		0			0
$991$	961.500	−	555.122i	0.970232	−	0.560164i	0.0709251	−	0.997482i	$-0.477405\pi$
$991$	961.500	−	555.122i	0.970232	−	0.560164i	0.899307	+	0.437318i	$0.144072\pi$
$992$	528.000	−	304.841i	0.532258	−	0.307299i
$993$		0			0
$994$	882.000	−	509.223i	0.887324	−	0.512297i
$995$			692.820i			0.696302i
$996$		0			0
$997$	215.000	+	372.391i	0.215647	+	0.373511i	0.953473	−	0.301480i	$-0.0974806\pi$
$997$	215.000	+	372.391i	0.215647	+	0.373511i	−0.737826	+	0.674991i	$0.764147\pi$
$998$	414.000	+	239.023i	0.414830	+	0.239502i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.3.y.a.163.1		2
3.2	odd	2		84.3.l.b.79.1	yes	2
4.3	odd	2		252.3.y.b.163.1		2
7.4	even	3		252.3.y.b.235.1		2
12.11	even	2		84.3.l.a.79.1	yes	2
21.2	odd	6		588.3.g.a.295.1		2
21.5	even	6		588.3.g.c.295.1		2
21.11	odd	6		84.3.l.a.67.1	✓	2
28.11	odd	6	inner	252.3.y.a.235.1		2
84.11	even	6		84.3.l.b.67.1	yes	2
84.23	even	6		588.3.g.a.295.2		2
84.47	odd	6		588.3.g.c.295.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.l.a.67.1	✓	2	21.11	odd	6
84.3.l.a.79.1	yes	2	12.11	even	2
84.3.l.b.67.1	yes	2	84.11	even	6
84.3.l.b.79.1	yes	2	3.2	odd	2
252.3.y.a.163.1		2	1.1	even	1	trivial
252.3.y.a.235.1		2	28.11	odd	6	inner
252.3.y.b.163.1		2	4.3	odd	2
252.3.y.b.235.1		2	7.4	even	3
588.3.g.a.295.1		2	21.2	odd	6
588.3.g.a.295.2		2	84.23	even	6
588.3.g.c.295.1		2	21.5	even	6
588.3.g.c.295.2		2	84.47	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	252.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +4.00000 q^{4} +(-2.50000 + 4.33013i) q^{5} +(3.50000 + 6.06218i) q^{7} -8.00000 q^{8} +(5.00000 - 8.66025i) q^{10} +(4.50000 - 2.59808i) q^{11} -16.0000 q^{13} +(-7.00000 - 12.1244i) q^{14} +16.0000 q^{16} +(2.00000 + 3.46410i) q^{17} +(-24.0000 - 13.8564i) q^{19} +(-10.0000 + 17.3205i) q^{20} +(-9.00000 + 5.19615i) q^{22} +(18.0000 + 10.3923i) q^{23} +32.0000 q^{26} +(14.0000 + 24.2487i) q^{28} -37.0000 q^{29} +(-16.5000 + 9.52628i) q^{31} -32.0000 q^{32} +(-4.00000 - 6.92820i) q^{34} -35.0000 q^{35} +(-34.0000 + 58.8897i) q^{37} +(48.0000 + 27.7128i) q^{38} +(20.0000 - 34.6410i) q^{40} -40.0000 q^{41} -24.2487i q^{43} +(18.0000 - 10.3923i) q^{44} +(-36.0000 - 20.7846i) q^{46} +(-39.0000 - 22.5167i) q^{47} +(-24.5000 + 42.4352i) q^{49} -64.0000 q^{52} +(36.5000 + 63.2199i) q^{53} +25.9808i q^{55} +(-28.0000 - 48.4974i) q^{56} +74.0000 q^{58} +(-25.5000 + 14.7224i) q^{59} +(41.0000 - 71.0141i) q^{61} +(33.0000 - 19.0526i) q^{62} +64.0000 q^{64} +(40.0000 - 69.2820i) q^{65} +(69.0000 - 39.8372i) q^{67} +(8.00000 + 13.8564i) q^{68} +70.0000 q^{70} +72.7461i q^{71} +(47.0000 + 81.4064i) q^{73} +(68.0000 - 117.779i) q^{74} +(-96.0000 - 55.4256i) q^{76} +(31.5000 + 18.1865i) q^{77} +(-7.50000 - 4.33013i) q^{79} +(-40.0000 + 69.2820i) q^{80} +80.0000 q^{82} -133.368i q^{83} -20.0000 q^{85} +48.4974i q^{86} +(-36.0000 + 20.7846i) q^{88} +(29.0000 - 50.2295i) q^{89} +(-56.0000 - 96.9948i) q^{91} +(72.0000 + 41.5692i) q^{92} +(78.0000 + 45.0333i) q^{94} +(120.000 - 69.2820i) q^{95} +47.0000 q^{97} +(49.0000 - 84.8705i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} + 8 q^{4} - 5 q^{5} + 7 q^{7} - 16 q^{8} + 10 q^{10} + 9 q^{11} - 32 q^{13} - 14 q^{14} + 32 q^{16} + 4 q^{17} - 48 q^{19} - 20 q^{20} - 18 q^{22} + 36 q^{23} + 64 q^{26} + 28 q^{28} - 74 q^{29}+ \cdots + 98 q^{98}+O(q^{100}) \) 2 * q - 4 * q^2 + 8 * q^4 - 5 * q^5 + 7 * q^7 - 16 * q^8 + 10 * q^10 + 9 * q^11 - 32 * q^13 - 14 * q^14 + 32 * q^16 + 4 * q^17 - 48 * q^19 - 20 * q^20 - 18 * q^22 + 36 * q^23 + 64 * q^26 + 28 * q^28 - 74 * q^29 - 33 * q^31 - 64 * q^32 - 8 * q^34 - 70 * q^35 - 68 * q^37 + 96 * q^38 + 40 * q^40 - 80 * q^41 + 36 * q^44 - 72 * q^46 - 78 * q^47 - 49 * q^49 - 128 * q^52 + 73 * q^53 - 56 * q^56 + 148 * q^58 - 51 * q^59 + 82 * q^61 + 66 * q^62 + 128 * q^64 + 80 * q^65 + 138 * q^67 + 16 * q^68 + 140 * q^70 + 94 * q^73 + 136 * q^74 - 192 * q^76 + 63 * q^77 - 15 * q^79 - 80 * q^80 + 160 * q^82 - 40 * q^85 - 72 * q^88 + 58 * q^89 - 112 * q^91 + 144 * q^92 + 156 * q^94 + 240 * q^95 + 94 * q^97 + 98 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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