LMFDB - Embedded newform 294.3.h.b.275.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,3,Mod(263,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("294.263");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	294.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.01091977219$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.1
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	294.275
Dual form			294.3.h.b.263.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +(1.94949 - 2.28024i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-7.34847 - 4.24264i) q^{5} +(-4.00000 + 1.41421i) q^{6} -2.82843i q^{8} +(-1.39898 - 8.89060i) q^{9} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +(1.94949 - 2.28024i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-7.34847 - 4.24264i) q^{5} +(-4.00000 + 1.41421i) q^{6} -2.82843i q^{8} +(-1.39898 - 8.89060i) q^{9} +(6.00000 + 10.3923i) q^{10} +(5.89898 + 1.09638i) q^{12} +1.00000 q^{13} +(-24.0000 + 8.48528i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-7.34847 + 4.24264i) q^{17} +(-4.57321 + 11.8780i) q^{18} +(-15.5000 + 26.8468i) q^{19} -16.9706i q^{20} +(-7.34847 - 4.24264i) q^{23} +(-6.44949 - 5.51399i) q^{24} +(23.5000 + 40.7032i) q^{25} +(-1.22474 - 0.707107i) q^{26} +(-23.0000 - 14.1421i) q^{27} -16.9706i q^{29} +(35.3939 + 6.57826i) q^{30} +(-3.50000 - 6.06218i) q^{31} +(4.89898 - 2.82843i) q^{32} +12.0000 q^{34} +(14.0000 - 11.3137i) q^{36} +(0.500000 - 0.866025i) q^{37} +(37.9671 - 21.9203i) q^{38} +(1.94949 - 2.28024i) q^{39} +(-12.0000 + 20.7846i) q^{40} +33.9411i q^{41} -31.0000 q^{43} +(-27.4393 + 71.2677i) q^{45} +(6.00000 + 10.3923i) q^{46} +(-36.7423 - 21.2132i) q^{47} +(4.00000 + 11.3137i) q^{48} -66.4680i q^{50} +(-4.65153 + 25.0273i) q^{51} +(1.00000 + 1.73205i) q^{52} +(-22.0454 + 12.7279i) q^{53} +(18.1691 + 33.5840i) q^{54} +(31.0000 + 87.6812i) q^{57} +(-12.0000 + 20.7846i) q^{58} +(-7.34847 + 4.24264i) q^{59} +(-38.6969 - 33.0839i) q^{60} +(25.0000 - 43.3013i) q^{61} +9.89949i q^{62} -8.00000 q^{64} +(-7.34847 - 4.24264i) q^{65} +(-32.5000 - 56.2917i) q^{67} +(-14.6969 - 8.48528i) q^{68} +(-24.0000 + 8.48528i) q^{69} +59.3970i q^{71} +(-25.1464 + 3.95691i) q^{72} +(-48.5000 - 84.0045i) q^{73} +(-1.22474 + 0.707107i) q^{74} +(138.626 + 25.7648i) q^{75} -62.0000 q^{76} +(-4.00000 + 1.41421i) q^{78} +(51.5000 - 89.2006i) q^{79} +(29.3939 - 16.9706i) q^{80} +(-77.0857 + 24.8755i) q^{81} +(24.0000 - 41.5692i) q^{82} +42.4264i q^{83} +72.0000 q^{85} +(37.9671 + 21.9203i) q^{86} +(-38.6969 - 33.0839i) q^{87} +(-102.879 - 59.3970i) q^{89} +(84.0000 - 67.8823i) q^{90} -16.9706i q^{92} +(-20.6464 - 3.83732i) q^{93} +(30.0000 + 51.9615i) q^{94} +(227.803 - 131.522i) q^{95} +(3.10102 - 16.6848i) q^{96} +166.000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 4 q^{4} - 16 q^{6} + 14 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 4 * q^4 - 16 * q^6 + 14 * q^9	$ 4 q - 2 q^{3} + 4 q^{4} - 16 q^{6} + 14 q^{9} + 24 q^{10} + 4 q^{12} + 4 q^{13} - 96 q^{15} - 8 q^{16} + 16 q^{18} - 62 q^{19} - 16 q^{24} + 94 q^{25} - 92 q^{27} + 24 q^{30} - 14 q^{31} + 48 q^{34} + 56 q^{36} + 2 q^{37} - 2 q^{39} - 48 q^{40} - 124 q^{43} + 96 q^{45} + 24 q^{46} + 16 q^{48} - 48 q^{51} + 4 q^{52} - 40 q^{54} + 124 q^{57} - 48 q^{58} - 96 q^{60} + 100 q^{61} - 32 q^{64} - 130 q^{67} - 96 q^{69} - 32 q^{72} - 194 q^{73} + 94 q^{75} - 248 q^{76} - 16 q^{78} + 206 q^{79} - 34 q^{81} + 96 q^{82} + 288 q^{85} - 96 q^{87} + 336 q^{90} - 14 q^{93} + 120 q^{94} + 32 q^{96} + 664 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 4 * q^4 - 16 * q^6 + 14 * q^9 + 24 * q^10 + 4 * q^12 + 4 * q^13 - 96 * q^15 - 8 * q^16 + 16 * q^18 - 62 * q^19 - 16 * q^24 + 94 * q^25 - 92 * q^27 + 24 * q^30 - 14 * q^31 + 48 * q^34 + 56 * q^36 + 2 * q^37 - 2 * q^39 - 48 * q^40 - 124 * q^43 + 96 * q^45 + 24 * q^46 + 16 * q^48 - 48 * q^51 + 4 * q^52 - 40 * q^54 + 124 * q^57 - 48 * q^58 - 96 * q^60 + 100 * q^61 - 32 * q^64 - 130 * q^67 - 96 * q^69 - 32 * q^72 - 194 * q^73 + 94 * q^75 - 248 * q^76 - 16 * q^78 + 206 * q^79 - 34 * q^81 + 96 * q^82 + 288 * q^85 - 96 * q^87 + 336 * q^90 - 14 * q^93 + 120 * q^94 + 32 * q^96 + 664 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$	1.94949	−	2.28024i	0.649830	−	0.760080i
$3$	1.94949	−	2.28024i	0.649830	−	0.760080i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	−7.34847	−	4.24264i	−1.46969	−	0.848528i	−0.470272	−	0.882522i	$-0.655844\pi$
$5$	−7.34847	−	4.24264i	−1.46969	−	0.848528i	−0.999422	+	0.0339935i	$0.989177\pi$
$6$	−4.00000	+	1.41421i	−0.666667	+	0.235702i
$7$		0			0
$7$		0			0
$8$		−	2.82843i		−	0.353553i
$9$	−1.39898	−	8.89060i	−0.155442	−	0.987845i
$10$	6.00000	+	10.3923i	0.600000	+	1.03923i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$	5.89898	+	1.09638i	0.491582	+	0.0913647i
$13$	1.00000			0.0769231			0.0384615	−	0.999260i	$-0.487754\pi$
$13$	1.00000			0.0769231			0.0384615	+	0.999260i	$0.487754\pi$
$14$		0			0
$15$	−24.0000	+	8.48528i	−1.60000	+	0.565685i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−7.34847	+	4.24264i	−0.432263	+	0.249567i	−0.700310	−	0.713839i	$-0.746955\pi$
$17$	−7.34847	+	4.24264i	−0.432263	+	0.249567i	0.268047	+	0.963406i	$0.413622\pi$
$18$	−4.57321	+	11.8780i	−0.254067	+	0.659886i
$19$	−15.5000	+	26.8468i	−0.815789	+	1.41299i	0.0929702	+	0.995669i	$0.470364\pi$
$19$	−15.5000	+	26.8468i	−0.815789	+	1.41299i	−0.908760	+	0.417320i	$0.862969\pi$
$20$		−	16.9706i		−	0.848528i
$21$		0			0
$22$		0			0
$23$	−7.34847	−	4.24264i	−0.319499	−	0.184463i	0.331670	−	0.943395i	$-0.392388\pi$
$23$	−7.34847	−	4.24264i	−0.319499	−	0.184463i	−0.651169	+	0.758933i	$0.725721\pi$
$24$	−6.44949	−	5.51399i	−0.268729	−	0.229750i
$25$	23.5000	+	40.7032i	0.940000	+	1.62813i
$26$	−1.22474	−	0.707107i	−0.0471056	−	0.0271964i
$27$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$28$		0			0
$29$		−	16.9706i		−	0.585192i	−0.956236	−	0.292596i	$-0.905481\pi$
$29$		−	16.9706i		−	0.585192i	0.956236	−	0.292596i	$-0.0945191\pi$
$30$	35.3939	+	6.57826i	1.17980	+	0.219275i
$31$	−3.50000	−	6.06218i	−0.112903	−	0.195554i	0.804036	−	0.594580i	$-0.202682\pi$
$31$	−3.50000	−	6.06218i	−0.112903	−	0.195554i	−0.916940	+	0.399026i	$0.869348\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$		0			0
$34$	12.0000			0.352941
$35$		0			0
$36$	14.0000	−	11.3137i	0.388889	−	0.314270i
$37$	0.500000	−	0.866025i	0.0135135	−	0.0234061i	−0.859190	−	0.511657i	$-0.829032\pi$
$37$	0.500000	−	0.866025i	0.0135135	−	0.0234061i	0.872703	+	0.488251i	$0.162365\pi$
$38$	37.9671	−	21.9203i	0.999134	−	0.576850i
$39$	1.94949	−	2.28024i	0.0499869	−	0.0584677i
$40$	−12.0000	+	20.7846i	−0.300000	+	0.519615i
$41$			33.9411i			0.827832i	0.910315	+	0.413916i	$0.135839\pi$
$41$			33.9411i			0.827832i	−0.910315	+	0.413916i	$0.864161\pi$
$42$		0			0
$43$	−31.0000			−0.720930			−0.360465	−	0.932773i	$-0.617382\pi$
$43$	−31.0000			−0.720930			−0.360465	+	0.932773i	$0.617382\pi$
$44$		0			0
$45$	−27.4393	+	71.2677i	−0.609762	+	1.58373i
$46$	6.00000	+	10.3923i	0.130435	+	0.225920i
$47$	−36.7423	−	21.2132i	−0.781752	−	0.451345i	0.0552988	−	0.998470i	$-0.482389\pi$
$47$	−36.7423	−	21.2132i	−0.781752	−	0.451345i	−0.837051	+	0.547125i	$0.815722\pi$
$48$	4.00000	+	11.3137i	0.0833333	+	0.235702i
$49$		0			0
$50$		−	66.4680i		−	1.32936i
$51$	−4.65153	+	25.0273i	−0.0912065	+	0.490730i
$52$	1.00000	+	1.73205i	0.0192308	+	0.0333087i
$53$	−22.0454	+	12.7279i	−0.415951	+	0.240149i	−0.693344	−	0.720607i	$-0.743863\pi$
$53$	−22.0454	+	12.7279i	−0.415951	+	0.240149i	0.277392	+	0.960757i	$0.410530\pi$
$54$	18.1691	+	33.5840i	0.336465	+	0.621925i
$55$		0			0
$56$		0			0
$57$	31.0000	+	87.6812i	0.543860	+	1.53827i
$58$	−12.0000	+	20.7846i	−0.206897	+	0.358355i
$59$	−7.34847	+	4.24264i	−0.124550	+	0.0719092i	−0.560981	−	0.827829i	$-0.689576\pi$
$59$	−7.34847	+	4.24264i	−0.124550	+	0.0719092i	0.436430	+	0.899738i	$0.356243\pi$
$60$	−38.6969	−	33.0839i	−0.644949	−	0.551399i
$61$	25.0000	−	43.3013i	0.409836	−	0.709857i	−0.585035	−	0.811008i	$-0.698919\pi$
$61$	25.0000	−	43.3013i	0.409836	−	0.709857i	0.994871	+	0.101151i	$0.0322526\pi$
$62$			9.89949i			0.159669i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−7.34847	−	4.24264i	−0.113053	−	0.0652714i
$66$		0			0
$67$	−32.5000	−	56.2917i	−0.485075	−	0.840174i	0.514778	−	0.857323i	$-0.327874\pi$
$67$	−32.5000	−	56.2917i	−0.485075	−	0.840174i	−0.999853	+	0.0171494i	$0.994541\pi$
$68$	−14.6969	−	8.48528i	−0.216131	−	0.124784i
$69$	−24.0000	+	8.48528i	−0.347826	+	0.122975i
$70$		0			0
$71$			59.3970i			0.836577i	0.908314	+	0.418289i	$0.137370\pi$
$71$			59.3970i			0.836577i	−0.908314	+	0.418289i	$0.862630\pi$
$72$	−25.1464	+	3.95691i	−0.349256	+	0.0549571i
$73$	−48.5000	−	84.0045i	−0.664384	−	1.15075i	−0.979452	−	0.201677i	$-0.935361\pi$
$73$	−48.5000	−	84.0045i	−0.664384	−	1.15075i	0.315068	−	0.949069i	$-0.397973\pi$
$74$	−1.22474	+	0.707107i	−0.0165506	+	0.00955550i
$75$	138.626	+	25.7648i	1.84835	+	0.343531i
$76$	−62.0000			−0.815789
$77$		0			0
$78$	−4.00000	+	1.41421i	−0.0512821	+	0.0181309i
$79$	51.5000	−	89.2006i	0.651899	−	1.12912i	−0.330763	−	0.943714i	$-0.607306\pi$
$79$	51.5000	−	89.2006i	0.651899	−	1.12912i	0.982662	−	0.185408i	$-0.0593606\pi$
$80$	29.3939	−	16.9706i	0.367423	−	0.212132i
$81$	−77.0857	+	24.8755i	−0.951675	+	0.307106i
$82$	24.0000	−	41.5692i	0.292683	−	0.506942i
$83$			42.4264i			0.511162i	0.966788	+	0.255581i	$0.0822667\pi$
$83$			42.4264i			0.511162i	−0.966788	+	0.255581i	$0.917733\pi$
$84$		0			0
$85$	72.0000			0.847059
$86$	37.9671	+	21.9203i	0.441478	+	0.254887i
$87$	−38.6969	−	33.0839i	−0.444792	−	0.380275i
$88$		0			0
$89$	−102.879	−	59.3970i	−1.15594	−	0.667382i	−0.205612	−	0.978634i	$-0.565918\pi$
$89$	−102.879	−	59.3970i	−1.15594	−	0.667382i	−0.950327	+	0.311252i	$0.899252\pi$
$90$	84.0000	−	67.8823i	0.933333	−	0.754247i
$91$		0			0
$92$		−	16.9706i		−	0.184463i
$93$	−20.6464	−	3.83732i	−0.222005	−	0.0412615i
$94$	30.0000	+	51.9615i	0.319149	+	0.552782i
$95$	227.803	−	131.522i	2.39792	−	1.38444i
$96$	3.10102	−	16.6848i	0.0323023	−	0.173800i
$97$	166.000			1.71134			0.855670	−	0.517522i	$-0.173145\pi$
$97$	166.000			1.71134			0.855670	+	0.517522i	$0.173145\pi$
$98$		0			0
$99$		0			0
$100$	−47.0000	+	81.4064i	−0.470000	+	0.814064i
$101$	117.576	−	67.8823i	1.16411	−	0.672101i	0.211827	−	0.977307i	$-0.432059\pi$
$101$	117.576	−	67.8823i	1.16411	−	0.672101i	0.952286	+	0.305206i	$0.0987252\pi$
$102$	23.3939	−	27.3629i	0.229352	−	0.268263i
$103$	32.5000	−	56.2917i	0.315534	−	0.546521i	−0.664017	−	0.747718i	$-0.731150\pi$
$103$	32.5000	−	56.2917i	0.315534	−	0.546521i	0.979551	+	0.201197i	$0.0644830\pi$
$104$		−	2.82843i		−	0.0271964i
$105$		0			0
$106$	36.0000			0.339623
$107$	−139.621	−	80.6102i	−1.30487	−	0.753366i	−0.323634	−	0.946183i	$-0.604904\pi$
$107$	−139.621	−	80.6102i	−1.30487	−	0.753366i	−0.981235	+	0.192816i	$0.938238\pi$
$108$	1.49490	−	53.9793i	0.0138416	−	0.499808i
$109$	−83.5000	−	144.626i	−0.766055	−	1.32685i	−0.939687	−	0.342036i	$-0.888884\pi$
$109$	−83.5000	−	144.626i	−0.766055	−	1.32685i	0.173632	−	0.984811i	$-0.444450\pi$
$110$		0			0
$111$	−1.00000	−	2.82843i	−0.00900901	−	0.0254813i
$112$		0			0
$113$		−	161.220i		−	1.42673i	−0.700793	−	0.713364i	$-0.747170\pi$
$113$		−	161.220i		−	1.42673i	0.700793	−	0.713364i	$-0.252830\pi$
$114$	24.0329	−	129.307i	0.210815	−	1.13428i
$115$	36.0000	+	62.3538i	0.313043	+	0.542207i
$116$	29.3939	−	16.9706i	0.253395	−	0.146298i
$117$	−1.39898	−	8.89060i	−0.0119571	−	0.0759881i
$118$	12.0000			0.101695
$119$		0			0
$120$	24.0000	+	67.8823i	0.200000	+	0.565685i
$121$	−60.5000	+	104.789i	−0.500000	+	0.866025i
$122$	−61.2372	+	35.3553i	−0.501945	+	0.289798i
$123$	77.3939	+	66.1679i	0.629219	+	0.537950i
$124$	7.00000	−	12.1244i	0.0564516	−	0.0977771i
$125$		−	186.676i		−	1.49341i
$126$		0			0
$127$	113.000			0.889764			0.444882	−	0.895589i	$-0.353246\pi$
$127$	113.000			0.889764			0.444882	+	0.895589i	$0.353246\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$	−60.4342	+	70.6874i	−0.468482	+	0.547964i
$130$	6.00000	+	10.3923i	0.0461538	+	0.0799408i
$131$	73.4847	+	42.4264i	0.560952	+	0.323866i	0.753527	−	0.657416i	$-0.228351\pi$
$131$	73.4847	+	42.4264i	0.560952	+	0.323866i	−0.192576	+	0.981282i	$0.561684\pi$
$132$		0			0
$133$		0			0
$134$			91.9239i			0.685999i
$135$	109.015	+	201.504i	0.807517	+	1.49262i
$136$	12.0000	+	20.7846i	0.0882353	+	0.152828i
$137$	−161.666	+	93.3381i	−1.18005	+	0.681300i	−0.956025	−	0.293284i	$-0.905252\pi$
$137$	−161.666	+	93.3381i	−1.18005	+	0.681300i	−0.224021	+	0.974584i	$0.571918\pi$
$138$	35.3939	+	6.57826i	0.256477	+	0.0476685i
$139$	−113.000			−0.812950			−0.406475	−	0.913662i	$-0.633242\pi$
$139$	−113.000			−0.812950			−0.406475	+	0.913662i	$0.633242\pi$
$140$		0			0
$141$	−120.000	+	42.4264i	−0.851064	+	0.300897i
$142$	42.0000	−	72.7461i	0.295775	−	0.512297i
$143$		0			0
$144$	33.5959	+	12.9350i	0.233305	+	0.0898264i
$145$	−72.0000	+	124.708i	−0.496552	+	0.860053i
$146$			137.179i			0.939580i
$147$		0			0
$148$	2.00000			0.0135135
$149$	58.7878	+	33.9411i	0.394549	+	0.227793i	0.684129	−	0.729361i	$-0.260182\pi$
$149$	58.7878	+	33.9411i	0.394549	+	0.227793i	−0.289580	+	0.957154i	$0.593516\pi$
$150$	−151.563	−	129.579i	−1.01042	−	0.863858i
$151$	29.0000	+	50.2295i	0.192053	+	0.332646i	0.945930	−	0.324370i	$-0.105152\pi$
$151$	29.0000	+	50.2295i	0.192053	+	0.332646i	−0.753877	+	0.657015i	$0.771819\pi$
$152$	75.9342	+	43.8406i	0.499567	+	0.288425i
$153$	48.0000	+	59.3970i	0.313725	+	0.388215i
$154$		0			0
$155$			59.3970i			0.383206i
$156$	5.89898	+	1.09638i	0.0378140	+	0.00702805i
$157$	−59.0000	−	102.191i	−0.375796	−	0.650898i	0.614650	−	0.788800i	$-0.289297\pi$
$157$	−59.0000	−	102.191i	−0.375796	−	0.650898i	−0.990446	+	0.137902i	$0.955964\pi$
$158$	−126.149	+	72.8320i	−0.798410	+	0.460962i
$159$	−13.9546	+	75.0818i	−0.0877647	+	0.472212i
$160$	−48.0000			−0.300000
$161$		0			0
$162$	112.000	+	24.0416i	0.691358	+	0.148405i
$163$	53.0000	−	91.7987i	0.325153	−	0.563182i	−0.656390	−	0.754422i	$-0.727917\pi$
$163$	53.0000	−	91.7987i	0.325153	−	0.563182i	0.981543	+	0.191240i	$0.0612507\pi$
$164$	−58.7878	+	33.9411i	−0.358462	+	0.206958i
$165$		0			0
$166$	30.0000	−	51.9615i	0.180723	−	0.313021i
$167$			144.250i			0.863771i	0.901928	+	0.431886i	$0.142152\pi$
$167$			144.250i			0.863771i	−0.901928	+	0.431886i	$0.857848\pi$
$168$		0			0
$169$	−168.000			−0.994083
$170$	−88.1816	−	50.9117i	−0.518715	−	0.299481i
$171$	260.368	+	100.246i	1.52262	+	0.586236i
$172$	−31.0000	−	53.6936i	−0.180233	−	0.312172i
$173$	−66.1362	−	38.1838i	−0.382290	−	0.220715i	0.296524	−	0.955025i	$-0.404173\pi$
$173$	−66.1362	−	38.1838i	−0.382290	−	0.220715i	−0.678814	+	0.734310i	$0.737506\pi$
$174$	24.0000	+	67.8823i	0.137931	+	0.390128i
$175$		0			0
$176$		0			0
$177$	−4.65153	+	25.0273i	−0.0262798	+	0.141397i
$178$	84.0000	+	145.492i	0.471910	+	0.817372i
$179$	−139.621	+	80.6102i	−0.780005	+	0.450336i	−0.836432	−	0.548071i	$-0.815363\pi$
$179$	−139.621	+	80.6102i	−0.780005	+	0.450336i	0.0564270	+	0.998407i	$0.482029\pi$
$180$	−150.879	+	23.7415i	−0.838214	+	0.131897i
$181$	−215.000			−1.18785			−0.593923	−	0.804522i	$-0.702421\pi$
$181$	−215.000			−1.18785			−0.593923	+	0.804522i	$0.702421\pi$
$182$		0			0
$183$	−50.0000	−	141.421i	−0.273224	−	0.772794i
$184$	−12.0000	+	20.7846i	−0.0652174	+	0.112960i
$185$	−7.34847	+	4.24264i	−0.0397215	+	0.0229332i
$186$	22.5732	+	19.2990i	0.121361	+	0.103758i
$187$		0			0
$188$		−	84.8528i		−	0.451345i
$189$		0			0
$190$	−372.000			−1.95789
$191$	154.318	+	89.0955i	0.807947	+	0.466468i	0.846242	−	0.532798i	$-0.178859\pi$
$191$	154.318	+	89.0955i	0.807947	+	0.466468i	−0.0382955	+	0.999266i	$0.512193\pi$
$192$	−15.5959	+	18.2419i	−0.0812287	+	0.0950100i
$193$	48.5000	+	84.0045i	0.251295	+	0.435256i	0.963883	−	0.266327i	$-0.0858101\pi$
$193$	48.5000	+	84.0045i	0.251295	+	0.435256i	−0.712587	+	0.701583i	$0.752477\pi$
$194$	−203.308	−	117.380i	−1.04798	−	0.605050i
$195$	−24.0000	+	8.48528i	−0.123077	+	0.0435143i
$196$		0			0
$197$		−	364.867i		−	1.85212i	−0.377380	−	0.926059i	$-0.623175\pi$
$197$		−	364.867i		−	1.85212i	0.377380	−	0.926059i	$-0.376825\pi$
$198$		0			0
$199$	−53.0000	−	91.7987i	−0.266332	−	0.461300i	0.701580	−	0.712591i	$-0.252478\pi$
$199$	−53.0000	−	91.7987i	−0.266332	−	0.461300i	−0.967912	+	0.251291i	$0.919145\pi$
$200$	115.126	−	66.4680i	0.575630	−	0.332340i
$201$	−191.717	−	35.6322i	−0.953815	−	0.177275i
$202$	−192.000			−0.950495
$203$		0			0
$204$	−48.0000	+	16.9706i	−0.235294	+	0.0831890i
$205$	144.000	−	249.415i	0.702439	−	1.21666i
$206$	−79.6084	+	45.9619i	−0.386449	+	0.223116i
$207$	−27.4393	+	71.2677i	−0.132557	+	0.344288i
$208$	−2.00000	+	3.46410i	−0.00961538	+	0.0166543i
$209$		0			0
$210$		0			0
$211$	62.0000			0.293839			0.146919	−	0.989148i	$-0.453064\pi$
$211$	62.0000			0.293839			0.146919	+	0.989148i	$0.453064\pi$
$212$	−44.0908	−	25.4558i	−0.207976	−	0.120075i
$213$	135.439	+	115.794i	0.635865	+	0.543633i
$214$	114.000	+	197.454i	0.532710	+	0.922681i
$215$	227.803	+	131.522i	1.05955	+	0.611730i
$216$	−40.0000	+	65.0538i	−0.185185	+	0.301175i
$217$		0			0
$218$			236.174i			1.08337i
$219$	−286.101	−	53.1743i	−1.30640	−	0.242805i
$220$		0			0
$221$	−7.34847	+	4.24264i	−0.0332510	+	0.0191975i
$222$	−0.775255	+	4.17121i	−0.00349214	+	0.0187892i
$223$	202.000			0.905830			0.452915	−	0.891554i	$-0.350384\pi$
$223$	202.000			0.905830			0.452915	+	0.891554i	$0.350384\pi$
$224$		0			0
$225$	329.000	−	265.872i	1.46222	−	1.18165i
$226$	−114.000	+	197.454i	−0.504425	+	0.873689i
$227$	−14.6969	+	8.48528i	−0.0647442	+	0.0373801i	−0.532023	−	0.846730i	$-0.678568\pi$
$227$	−14.6969	+	8.48528i	−0.0647442	+	0.0373801i	0.467278	+	0.884110i	$0.345235\pi$
$228$	−120.868	+	141.375i	−0.530124	+	0.620065i
$229$	−0.500000	+	0.866025i	−0.00218341	+	0.00378177i	−0.867115	−	0.498108i	$-0.834028\pi$
$229$	−0.500000	+	0.866025i	−0.00218341	+	0.00378177i	0.864932	+	0.501890i	$0.167362\pi$
$230$		−	101.823i		−	0.442710i
$231$		0			0
$232$	−48.0000			−0.206897
$233$	286.590	+	165.463i	1.23000	+	0.710142i	0.967030	−	0.254662i	$-0.0819642\pi$
$233$	286.590	+	165.463i	1.23000	+	0.710142i	0.262971	+	0.964804i	$0.415298\pi$
$234$	−4.57321	+	11.8780i	−0.0195436	+	0.0507605i
$235$	180.000	+	311.769i	0.765957	+	1.32668i
$236$	−14.6969	−	8.48528i	−0.0622752	−	0.0359546i
$237$	−103.000	−	291.328i	−0.434599	−	1.22923i
$238$		0			0
$239$			458.205i			1.91718i	0.284796	+	0.958588i	$0.408074\pi$
$239$			458.205i			1.91718i	−0.284796	+	0.958588i	$0.591926\pi$
$240$	18.6061	−	100.109i	0.0775255	−	0.417121i
$241$	−11.0000	−	19.0526i	−0.0456432	−	0.0790563i	0.842301	−	0.539007i	$-0.181200\pi$
$241$	−11.0000	−	19.0526i	−0.0456432	−	0.0790563i	−0.887944	+	0.459951i	$0.847867\pi$
$242$	148.194	−	85.5599i	0.612372	−	0.353553i
$243$	−93.5556	+	224.268i	−0.385003	+	0.922916i
$244$	100.000			0.409836
$245$		0			0
$246$	−48.0000	−	135.765i	−0.195122	−	0.551888i
$247$	−15.5000	+	26.8468i	−0.0627530	+	0.108691i
$248$	−17.1464	+	9.89949i	−0.0691388	+	0.0399173i
$249$	96.7423	+	82.7098i	0.388523	+	0.332168i
$250$	−132.000	+	228.631i	−0.528000	+	0.914523i
$251$		−	178.191i		−	0.709924i	−0.934881	−	0.354962i	$-0.884494\pi$
$251$		−	178.191i		−	0.709924i	0.934881	−	0.354962i	$-0.115506\pi$
$252$		0			0
$253$		0			0
$254$	−138.396	−	79.9031i	−0.544867	−	0.314579i
$255$	140.363	−	164.177i	0.550444	−	0.643832i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	242.499	+	140.007i	0.943578	+	0.544775i	0.891080	−	0.453846i	$-0.149948\pi$
$257$	242.499	+	140.007i	0.943578	+	0.544775i	0.0524977	+	0.998621i	$0.483282\pi$
$258$	124.000	−	43.8406i	0.480620	−	0.169925i
$259$		0			0
$260$		−	16.9706i		−	0.0652714i
$261$	−150.879	+	23.7415i	−0.578079	+	0.0909635i
$262$	−60.0000	−	103.923i	−0.229008	−	0.396653i
$263$	88.1816	−	50.9117i	0.335291	−	0.193581i	−0.322897	−	0.946434i	$-0.604657\pi$
$263$	88.1816	−	50.9117i	0.335291	−	0.193581i	0.658188	+	0.752854i	$0.271323\pi$
$264$		0			0
$265$	216.000			0.815094
$266$		0			0
$267$	−336.000	+	118.794i	−1.25843	+	0.444921i
$268$	65.0000	−	112.583i	0.242537	−	0.420087i
$269$	−367.423	+	212.132i	−1.36589	+	0.788595i	−0.990400	−	0.138233i	$-0.955858\pi$
$269$	−367.423	+	212.132i	−1.36589	+	0.788595i	−0.375487	+	0.926828i	$0.622524\pi$
$270$	8.96938	−	323.876i	0.0332199	−	1.19954i
$271$	−125.000	+	216.506i	−0.461255	+	0.798916i	−0.999024	−	0.0441757i	$-0.985934\pi$
$271$	−125.000	+	216.506i	−0.461255	+	0.798916i	0.537769	+	0.843092i	$0.319267\pi$
$272$		−	33.9411i		−	0.124784i
$273$		0			0
$274$	264.000			0.963504
$275$		0			0
$276$	−38.6969	−	33.0839i	−0.140206	−	0.119869i
$277$	−191.500	−	331.688i	−0.691336	−	1.19743i	−0.971400	−	0.237447i	$-0.923689\pi$
$277$	−191.500	−	331.688i	−0.691336	−	1.19743i	0.280065	−	0.959981i	$-0.409644\pi$
$278$	138.396	+	79.9031i	0.497828	+	0.287421i
$279$	−49.0000	+	39.5980i	−0.175627	+	0.141928i
$280$		0			0
$281$			178.191i			0.634131i	0.948404	+	0.317066i	$0.102698\pi$
$281$			178.191i			0.634131i	−0.948404	+	0.317066i	$0.897302\pi$
$282$	176.969	+	32.8913i	0.627551	+	0.116636i
$283$	152.500	+	264.138i	0.538869	+	0.933349i	0.998965	+	0.0454798i	$0.0144817\pi$
$283$	152.500	+	264.138i	0.538869	+	0.933349i	−0.460096	+	0.887869i	$0.652185\pi$
$284$	−102.879	+	59.3970i	−0.362248	+	0.209144i
$285$	144.197	−	775.845i	0.505956	−	2.72226i
$286$		0			0
$287$		0			0
$288$	−32.0000	−	39.5980i	−0.111111	−	0.137493i
$289$	−108.500	+	187.928i	−0.375433	+	0.650268i
$290$	176.363	−	101.823i	0.608149	−	0.351115i
$291$	323.615	−	378.520i	1.11208	−	1.30075i
$292$	97.0000	−	168.009i	0.332192	−	0.575373i
$293$		−	135.765i		−	0.463360i	−0.972792	−	0.231680i	$-0.925578\pi$
$293$		−	135.765i		−	0.463360i	0.972792	−	0.231680i	$-0.0744222\pi$
$294$		0			0
$295$	72.0000			0.244068
$296$	−2.44949	−	1.41421i	−0.00827530	−	0.00477775i
$297$		0			0
$298$	−48.0000	−	83.1384i	−0.161074	−	0.278988i
$299$	−7.34847	−	4.24264i	−0.0245768	−	0.0141894i
$300$	94.0000	+	265.872i	0.313333	+	0.886240i
$301$		0			0
$302$		−	82.0244i		−	0.271604i
$303$	74.4245	−	400.436i	0.245625	−	1.32157i
$304$	−62.0000	−	107.387i	−0.203947	−	0.353247i
$305$	−367.423	+	212.132i	−1.20467	+	0.695515i
$306$	−16.7878	−	106.687i	−0.0548619	−	0.348651i
$307$	199.000			0.648208			0.324104	−	0.946021i	$-0.394937\pi$
$307$	199.000			0.648208			0.324104	+	0.946021i	$0.394937\pi$
$308$		0			0
$309$	−65.0000	−	183.848i	−0.210356	−	0.594977i
$310$	42.0000	−	72.7461i	0.135484	−	0.234665i
$311$	382.120	−	220.617i	1.22868	−	0.709380i	0.261929	−	0.965087i	$-0.415642\pi$
$311$	382.120	−	220.617i	1.22868	−	0.709380i	0.966754	+	0.255707i	$0.0823082\pi$
$312$	−6.44949	−	5.51399i	−0.0206714	−	0.0176730i
$313$	59.5000	−	103.057i	0.190096	−	0.329256i	−0.755186	−	0.655511i	$-0.772453\pi$
$313$	59.5000	−	103.057i	0.190096	−	0.329256i	0.945282	+	0.326255i	$0.105787\pi$
$314$			166.877i			0.531456i
$315$		0			0
$316$	206.000			0.651899
$317$	−176.363	−	101.823i	−0.556351	−	0.321209i	0.195329	−	0.980738i	$-0.437423\pi$
$317$	−176.363	−	101.823i	−0.556351	−	0.321209i	−0.751680	+	0.659528i	$0.770756\pi$
$318$	70.1816	−	82.0886i	0.220697	−	0.258140i
$319$		0			0
$320$	58.7878	+	33.9411i	0.183712	+	0.106066i
$321$	−456.000	+	161.220i	−1.42056	+	0.502244i
$322$		0			0
$323$		−	263.044i		−	0.814377i
$324$	−120.171	−	108.641i	−0.370899	−	0.335311i
$325$	23.5000	+	40.7032i	0.0723077	+	0.125241i
$326$	−129.823	+	74.9533i	−0.398230	+	0.229918i
$327$	−492.565	−	91.5474i	−1.50631	−	0.279962i
$328$	96.0000			0.292683
$329$		0			0
$330$		0			0
$331$	−260.500	+	451.199i	−0.787009	+	1.36314i	0.140782	+	0.990041i	$0.455038\pi$
$331$	−260.500	+	451.199i	−0.787009	+	1.36314i	−0.927791	+	0.373099i	$0.878295\pi$
$332$	−73.4847	+	42.4264i	−0.221339	+	0.127790i
$333$	−8.39898	−	3.23375i	−0.0252222	−	0.00971096i
$334$	102.000	−	176.669i	0.305389	−	0.528950i
$335$			551.543i			1.64640i
$336$		0			0
$337$	311.000			0.922849			0.461424	−	0.887180i	$-0.347339\pi$
$337$	311.000			0.922849			0.461424	+	0.887180i	$0.347339\pi$
$338$	205.757	+	118.794i	0.608749	+	0.351461i
$339$	−367.621	−	314.297i	−1.08443	−	0.927131i
$340$	72.0000	+	124.708i	0.211765	+	0.366787i
$341$		0			0
$342$	−248.000	−	306.884i	−0.725146	−	0.897323i
$343$		0			0
$344$			87.6812i			0.254887i
$345$	212.363	+	39.4695i	0.615546	+	0.114404i
$346$	54.0000	+	93.5307i	0.156069	+	0.270320i
$347$	95.5301	−	55.1543i	0.275303	−	0.158946i	−0.355992	−	0.934489i	$-0.615857\pi$
$347$	95.5301	−	55.1543i	0.275303	−	0.158946i	0.631295	+	0.775543i	$0.282524\pi$
$348$	18.6061	−	100.109i	0.0534659	−	0.287670i
$349$	−50.0000			−0.143266			−0.0716332	−	0.997431i	$-0.522821\pi$
$349$	−50.0000			−0.143266			−0.0716332	+	0.997431i	$0.522821\pi$
$350$		0			0
$351$	−23.0000	−	14.1421i	−0.0655271	−	0.0402910i
$352$		0			0
$353$	−139.621	+	80.6102i	−0.395527	+	0.228357i	−0.684552	−	0.728964i	$-0.740002\pi$
$353$	−139.621	+	80.6102i	−0.395527	+	0.228357i	0.289025	+	0.957321i	$0.406669\pi$
$354$	23.3939	−	27.3629i	0.0660844	−	0.0772962i
$355$	252.000	−	436.477i	0.709859	−	1.22951i
$356$		−	237.588i		−	0.667382i
$357$		0			0
$358$	228.000			0.636872
$359$	−352.727	−	203.647i	−0.982525	−	0.567261i	−0.0794936	−	0.996835i	$-0.525330\pi$
$359$	−352.727	−	203.647i	−0.982525	−	0.567261i	−0.903032	+	0.429574i	$0.858664\pi$
$360$	201.576	+	77.6100i	0.559932	+	0.215583i
$361$	−300.000	−	519.615i	−0.831025	−	1.43938i
$362$	263.320	+	152.028i	0.727404	+	0.419967i
$363$	121.000	+	342.240i	0.333333	+	0.942809i
$364$		0			0
$365$			823.072i			2.25499i
$366$	−38.7628	+	208.560i	−0.105909	+	0.569837i
$367$	−267.500	−	463.324i	−0.728883	−	1.26246i	−0.957356	−	0.288912i	$-0.906707\pi$
$367$	−267.500	−	463.324i	−0.728883	−	1.26246i	0.228473	−	0.973550i	$-0.426627\pi$
$368$	29.3939	−	16.9706i	0.0798747	−	0.0461157i
$369$	301.757	−	47.4829i	0.817770	−	0.128680i
$370$	12.0000			0.0324324
$371$		0			0
$372$	−14.0000	−	39.5980i	−0.0376344	−	0.106446i
$373$	192.500	−	333.420i	0.516086	−	0.893887i	−0.483740	−	0.875212i	$-0.660722\pi$
$373$	192.500	−	333.420i	0.516086	−	0.893887i	0.999826	−	0.0186750i	$-0.00594477\pi$
$374$		0			0
$375$	−425.666	−	363.923i	−1.13511	−	0.970462i
$376$	−60.0000	+	103.923i	−0.159574	+	0.276391i
$377$		−	16.9706i		−	0.0450148i
$378$		0			0
$379$	−55.0000			−0.145119			−0.0725594	−	0.997364i	$-0.523117\pi$
$379$	−55.0000			−0.145119			−0.0725594	+	0.997364i	$0.523117\pi$
$380$	455.605	+	263.044i	1.19896	+	0.692220i
$381$	220.292	−	257.667i	0.578195	−	0.676291i
$382$	−126.000	−	218.238i	−0.329843	−	0.571305i
$383$	360.075	+	207.889i	0.940144	+	0.542792i	0.890005	−	0.455950i	$-0.150700\pi$
$383$	360.075	+	207.889i	0.940144	+	0.542792i	0.0501383	+	0.998742i	$0.484034\pi$
$384$	32.0000	−	11.3137i	0.0833333	−	0.0294628i
$385$		0			0
$386$		−	137.179i		−	0.355385i
$387$	43.3684	+	275.609i	0.112063	+	0.712167i
$388$	166.000	+	287.520i	0.427835	+	0.741032i
$389$	330.681	−	190.919i	0.850080	−	0.490794i	−0.0105979	−	0.999944i	$-0.503373\pi$
$389$	330.681	−	190.919i	0.850080	−	0.490794i	0.860678	+	0.509150i	$0.170040\pi$
$390$	35.3939	+	6.57826i	0.0907535	+	0.0168673i
$391$	72.0000			0.184143
$392$		0			0
$393$	240.000	−	84.8528i	0.610687	−	0.215910i
$394$	−258.000	+	446.869i	−0.654822	+	1.13419i
$395$	−756.892	+	436.992i	−1.91618	+	1.10631i
$396$		0			0
$397$	−240.500	+	416.558i	−0.605793	+	1.04927i	0.386132	+	0.922443i	$0.373811\pi$
$397$	−240.500	+	416.558i	−0.605793	+	1.04927i	−0.991926	+	0.126822i	$0.959522\pi$
$398$			149.907i			0.376650i
$399$		0			0
$400$	−188.000			−0.470000
$401$	66.1362	+	38.1838i	0.164928	+	0.0952214i	0.580192	−	0.814480i	$-0.302977\pi$
$401$	66.1362	+	38.1838i	0.164928	+	0.0952214i	−0.415264	+	0.909701i	$0.636311\pi$
$402$	209.608	+	179.205i	0.521414	+	0.445783i
$403$	−3.50000	−	6.06218i	−0.00868486	−	0.0150426i
$404$	235.151	+	135.765i	0.582057	+	0.336051i
$405$	672.000	+	144.250i	1.65926	+	0.356172i
$406$		0			0
$407$		0			0
$408$	70.7878	+	13.1565i	0.173499	+	0.0322464i
$409$	−24.5000	−	42.4352i	−0.0599022	−	0.103754i	0.834519	−	0.550979i	$-0.185746\pi$
$409$	−24.5000	−	42.4352i	−0.0599022	−	0.103754i	−0.894421	+	0.447225i	$0.852412\pi$
$410$	−352.727	+	203.647i	−0.860309	+	0.496699i
$411$	−102.334	+	550.600i	−0.248987	+	1.33966i
$412$	130.000			0.315534
$413$		0			0
$414$	84.0000	−	67.8823i	0.202899	−	0.163967i
$415$	180.000	−	311.769i	0.433735	−	0.751251i
$416$	4.89898	−	2.82843i	0.0117764	−	0.00679910i
$417$	−220.292	+	257.667i	−0.528279	+	0.617906i
$418$		0			0
$419$		−	322.441i		−	0.769548i	−0.923011	−	0.384774i	$-0.874279\pi$
$419$		−	322.441i		−	0.769548i	0.923011	−	0.384774i	$-0.125721\pi$
$420$		0			0
$421$	−313.000			−0.743468			−0.371734	−	0.928339i	$-0.621237\pi$
$421$	−313.000			−0.743468			−0.371734	+	0.928339i	$0.621237\pi$
$422$	−75.9342	−	43.8406i	−0.179939	−	0.103888i
$423$	−137.196	+	356.339i	−0.324341	+	0.842408i
$424$	36.0000	+	62.3538i	0.0849057	+	0.147061i
$425$	−345.378	−	199.404i	−0.812654	−	0.469186i
$426$	−84.0000	−	237.588i	−0.197183	−	0.557718i
$427$		0			0
$428$		−	322.441i		−	0.753366i
$429$		0			0
$430$	−186.000	−	322.161i	−0.432558	−	0.749213i
$431$	301.287	−	173.948i	0.699042	−	0.403592i	−0.107948	−	0.994157i	$-0.534428\pi$
$431$	301.287	−	173.948i	0.699042	−	0.403592i	0.806991	+	0.590564i	$0.201095\pi$
$432$	94.9898	−	51.3901i	0.219884	−	0.118958i
$433$	97.0000			0.224018			0.112009	−	0.993707i	$-0.464271\pi$
$433$	97.0000			0.224018			0.112009	+	0.993707i	$0.464271\pi$
$434$		0			0
$435$	144.000	+	407.294i	0.331034	+	0.936307i
$436$	167.000	−	289.252i	0.383028	−	0.663423i
$437$	227.803	−	131.522i	0.521287	−	0.300965i
$438$	312.800	+	267.428i	0.714156	+	0.610567i
$439$	187.000	−	323.894i	0.425968	−	0.737798i	−0.570542	−	0.821268i	$-0.693267\pi$
$439$	187.000	−	323.894i	0.425968	−	0.737798i	0.996510	+	0.0834699i	$0.0266002\pi$
$440$		0			0
$441$		0			0
$442$	12.0000			0.0271493
$443$	521.741	+	301.227i	1.17775	+	0.679972i	0.955492	−	0.295017i	$-0.0953254\pi$
$443$	521.741	+	301.227i	1.17775	+	0.679972i	0.222254	+	0.974989i	$0.428659\pi$
$444$	3.89898	−	4.56048i	0.00878149	−	0.0102713i
$445$	504.000	+	872.954i	1.13258	+	1.96169i
$446$	−247.398	−	142.836i	−0.554705	−	0.320259i
$447$	192.000	−	67.8823i	0.429530	−	0.151862i
$448$		0			0
$449$		−	42.4264i		−	0.0944909i	−0.998883	−	0.0472454i	$-0.984956\pi$
$449$		−	42.4264i		−	0.0944909i	0.998883	−	0.0472454i	$-0.0150443\pi$
$450$	−590.941	+	92.9874i	−1.31320	+	0.206639i
$451$		0			0
$452$	279.242	−	161.220i	0.617792	−	0.356682i
$453$	171.070	+	31.7949i	0.377639	+	0.0701874i
$454$	24.0000			0.0528634
$455$		0			0
$456$	248.000	−	87.6812i	0.543860	−	0.192283i
$457$	−227.500	+	394.042i	−0.497812	+	0.862235i	−0.999997	−	0.00252486i	$-0.999196\pi$
$457$	−227.500	+	394.042i	−0.497812	+	0.862235i	0.502185	+	0.864760i	$0.332530\pi$
$458$	1.22474	−	0.707107i	0.00267412	−	0.00154390i
$459$	229.015	+	6.34231i	0.498943	+	0.0138177i
$460$	−72.0000	+	124.708i	−0.156522	+	0.271104i
$461$		−	220.617i		−	0.478563i	−0.970950	−	0.239281i	$-0.923088\pi$
$461$		−	220.617i		−	0.478563i	0.970950	−	0.239281i	$-0.0769118\pi$
$462$		0			0
$463$	−7.00000			−0.0151188			−0.00755940	−	0.999971i	$-0.502406\pi$
$463$	−7.00000			−0.0151188			−0.00755940	+	0.999971i	$0.502406\pi$
$464$	58.7878	+	33.9411i	0.126698	+	0.0731490i
$465$	135.439	+	115.794i	0.291267	+	0.249019i
$466$	−234.000	−	405.300i	−0.502146	−	0.869742i
$467$	−536.438	−	309.713i	−1.14869	−	0.663197i	−0.200122	−	0.979771i	$-0.564134\pi$
$467$	−536.438	−	309.713i	−1.14869	−	0.663197i	−0.948568	+	0.316574i	$0.897467\pi$
$468$	14.0000	−	11.3137i	0.0299145	−	0.0241746i
$469$		0			0
$470$		−	509.117i		−	1.08323i
$471$	−348.040	−	64.6862i	−0.738938	−	0.137338i
$472$	12.0000	+	20.7846i	0.0254237	+	0.0440352i
$473$		0			0
$474$	−79.8513	+	429.634i	−0.168463	+	0.906402i
$475$	−1457.00			−3.06737
$476$		0			0
$477$	144.000	+	178.191i	0.301887	+	0.373566i
$478$	324.000	−	561.184i	0.677824	−	1.17403i
$479$	580.529	−	335.169i	1.21196	−	0.699726i	0.248774	−	0.968561i	$-0.419972\pi$
$479$	580.529	−	335.169i	1.21196	−	0.699726i	0.963186	+	0.268836i	$0.0866389\pi$
$480$	−93.5755	+	109.451i	−0.194949	+	0.228024i
$481$	0.500000	−	0.866025i	0.00103950	−	0.00180047i
$482$			31.1127i			0.0645492i
$483$		0			0
$484$	−242.000			−0.500000
$485$	−1219.85	−	704.278i	−2.51515	−	1.45212i
$486$	273.164	−	208.518i	0.562065	−	0.429049i
$487$	231.500	+	400.970i	0.475359	+	0.823347i	0.999602	−	0.0282226i	$-0.00898473\pi$
$487$	231.500	+	400.970i	0.475359	+	0.823347i	−0.524242	+	0.851569i	$0.675651\pi$
$488$	−122.474	−	70.7107i	−0.250972	−	0.144899i
$489$	−106.000	−	299.813i	−0.216769	−	0.613115i
$490$		0			0
$491$		−	356.382i		−	0.725829i	−0.931823	−	0.362914i	$-0.881782\pi$
$491$		−	356.382i		−	0.725829i	0.931823	−	0.362914i	$-0.118218\pi$
$492$	−37.2122	+	200.218i	−0.0756346	+	0.406947i
$493$	72.0000	+	124.708i	0.146045	+	0.252957i
$494$	37.9671	−	21.9203i	0.0768565	−	0.0443731i
$495$		0			0
$496$	28.0000			0.0564516
$497$		0			0
$498$	−60.0000	−	169.706i	−0.120482	−	0.340774i
$499$	267.500	−	463.324i	0.536072	−	0.928504i	−0.463038	−	0.886338i	$-0.653241\pi$
$499$	267.500	−	463.324i	0.536072	−	0.928504i	0.999111	−	0.0421660i	$-0.0134258\pi$
$500$	323.333	−	186.676i	0.646665	−	0.373352i
$501$	328.924	+	281.213i	0.656535	+	0.561304i
$502$	−126.000	+	218.238i	−0.250996	+	0.434738i
$503$		−	627.911i		−	1.24833i	−0.781292	−	0.624166i	$-0.785439\pi$
$503$		−	627.911i		−	1.24833i	0.781292	−	0.624166i	$-0.214561\pi$
$504$		0			0
$505$	−1152.00			−2.28119
$506$		0			0
$507$	−327.514	+	383.080i	−0.645985	+	0.755582i
$508$	113.000	+	195.722i	0.222441	+	0.385279i
$509$	−551.135	−	318.198i	−1.08278	−	0.625144i	−0.151135	−	0.988513i	$-0.548293\pi$
$509$	−551.135	−	318.198i	−1.08278	−	0.625144i	−0.931645	+	0.363370i	$0.881626\pi$
$510$	−288.000	+	101.823i	−0.564706	+	0.199654i
$511$		0			0
$512$			22.6274i			0.0441942i
$513$	736.171	−	398.273i	1.43503	−	0.776361i
$514$	−198.000	−	342.946i	−0.385214	−	0.667210i
$515$	−477.650	+	275.772i	−0.927477	+	0.535479i
$516$	−182.868	−	33.9877i	−0.354396	−	0.0658676i
$517$		0			0
$518$		0			0
$519$	−216.000	+	76.3675i	−0.416185	+	0.147144i
$520$	−12.0000	+	20.7846i	−0.0230769	+	0.0399704i
$521$	−558.484	+	322.441i	−1.07195	+	0.618888i	−0.928712	−	0.370801i	$-0.879083\pi$
$521$	−558.484	+	322.441i	−1.07195	+	0.618888i	−0.143233	+	0.989689i	$0.545750\pi$
$522$	201.576	+	77.6100i	0.386160	+	0.148678i
$523$	344.500	−	596.692i	0.658700	−	1.14090i	−0.322253	−	0.946654i	$-0.604440\pi$
$523$	344.500	−	596.692i	0.658700	−	1.14090i	0.980952	−	0.194248i	$-0.0622266\pi$
$524$			169.706i			0.323866i
$525$		0			0
$526$	−144.000			−0.273764
$527$	51.4393	+	29.6985i	0.0976078	+	0.0563539i
$528$		0			0
$529$	−228.500	−	395.774i	−0.431947	−	0.748154i
$530$	−264.545	−	152.735i	−0.499141	−	0.288179i
$531$	48.0000	+	59.3970i	0.0903955	+	0.111859i
$532$		0			0
$533$			33.9411i			0.0636794i
$534$	495.514	+	92.0956i	0.927929	+	0.172464i
$535$	684.000	+	1184.72i	1.27850	+	2.21444i
$536$	−159.217	+	91.9239i	−0.297046	+	0.171500i
$537$	−88.3791	+	475.518i	−0.164579	+	0.885508i
$538$	600.000			1.11524
$539$		0			0
$540$	−240.000	+	390.323i	−0.444444	+	0.722820i
$541$	−287.500	+	497.965i	−0.531423	+	0.920452i	0.467904	+	0.883779i	$0.345009\pi$
$541$	−287.500	+	497.965i	−0.531423	+	0.920452i	−0.999327	+	0.0366729i	$0.988324\pi$
$542$	306.186	−	176.777i	0.564919	−	0.326156i
$543$	−419.140	+	490.251i	−0.771897	+	0.902857i
$544$	−24.0000	+	41.5692i	−0.0441176	+	0.0764140i
$545$			1417.04i			2.60008i
$546$		0			0
$547$	302.000			0.552102			0.276051	−	0.961143i	$-0.410974\pi$
$547$	302.000			0.552102			0.276051	+	0.961143i	$0.410974\pi$
$548$	−323.333	−	186.676i	−0.590023	−	0.340650i
$549$	−419.949	−	161.688i	−0.764934	−	0.294513i
$550$		0			0
$551$	455.605	+	263.044i	0.826869	+	0.477393i
$552$	24.0000	+	67.8823i	0.0434783	+	0.122975i
$553$		0			0
$554$			541.644i			0.977696i
$555$	−4.65153	+	25.0273i	−0.00838114	+	0.0450941i
$556$	−113.000	−	195.722i	−0.203237	−	0.352018i
$557$	−117.576	+	67.8823i	−0.211087	+	0.121871i	−0.601817	−	0.798634i	$-0.705556\pi$
$557$	−117.576	+	67.8823i	−0.211087	+	0.121871i	0.390729	+	0.920506i	$0.372223\pi$
$558$	88.0125	−	13.8492i	0.157728	−	0.0248193i
$559$	−31.0000			−0.0554562
$560$		0			0
$561$		0			0
$562$	126.000	−	218.238i	0.224199	−	0.388325i
$563$	521.741	−	301.227i	0.926716	−	0.535040i	0.0409448	−	0.999161i	$-0.486963\pi$
$563$	521.741	−	301.227i	0.926716	−	0.535040i	0.885772	+	0.464121i	$0.153630\pi$
$564$	−193.485	−	165.420i	−0.343058	−	0.293297i
$565$	−684.000	+	1184.72i	−1.21062	+	2.09685i
$566$		−	431.335i		−	0.762076i
$567$		0			0
$568$	168.000			0.295775
$569$	573.181	+	330.926i	1.00735	+	0.581592i	0.910414	−	0.413699i	$-0.135763\pi$
$569$	573.181	+	330.926i	1.00735	+	0.581592i	0.0969334	+	0.995291i	$0.469097\pi$
$570$	−725.210	+	848.249i	−1.27230	+	1.48816i
$571$	−56.5000	−	97.8609i	−0.0989492	−	0.171385i	0.812301	−	0.583239i	$-0.198215\pi$
$571$	−56.5000	−	97.8609i	−0.0989492	−	0.171385i	−0.911250	+	0.411854i	$0.864881\pi$
$572$		0			0
$573$	504.000	−	178.191i	0.879581	−	0.310979i
$574$		0			0
$575$		−	398.808i		−	0.693580i
$576$	11.1918	+	71.1248i	0.0194303	+	0.123481i
$577$	−60.5000	−	104.789i	−0.104853	−	0.181610i	0.808825	−	0.588049i	$-0.200104\pi$
$577$	−60.5000	−	104.789i	−0.104853	−	0.181610i	−0.913678	+	0.406439i	$0.866770\pi$
$578$	265.770	−	153.442i	0.459809	−	0.265471i
$579$	286.101	+	53.1743i	0.494129	+	0.0918381i
$580$	−288.000			−0.496552
$581$		0			0
$582$	−664.000	+	234.759i	−1.14089	+	0.403367i
$583$		0			0
$584$	−237.601	+	137.179i	−0.406850	+	0.234895i
$585$	−27.4393	+	71.2677i	−0.0469048	+	0.121825i
$586$	−96.0000	+	166.277i	−0.163823	+	0.283749i
$587$		−	67.8823i		−	0.115643i	−0.998327	−	0.0578213i	$-0.981585\pi$
$587$		−	67.8823i		−	0.115643i	0.998327	−	0.0578213i	$-0.0184154\pi$
$588$		0			0
$589$	217.000			0.368421
$590$	−88.1816	−	50.9117i	−0.149460	−	0.0862910i
$591$	−831.984	−	711.305i	−1.40776	−	1.20356i
$592$	2.00000	+	3.46410i	0.00337838	+	0.00585152i
$593$	426.211	+	246.073i	0.718737	+	0.414963i	0.814288	−	0.580461i	$-0.197128\pi$
$593$	426.211	+	246.073i	0.718737	+	0.414963i	−0.0955505	+	0.995425i	$0.530461\pi$
$594$		0			0
$595$		0			0
$596$			135.765i			0.227793i
$597$	−312.646	−	58.1079i	−0.523695	−	0.0973332i
$598$	6.00000	+	10.3923i	0.0100334	+	0.0173784i
$599$	−88.1816	+	50.9117i	−0.147215	+	0.0849945i	−0.571798	−	0.820394i	$-0.693754\pi$
$599$	−88.1816	+	50.9117i	−0.147215	+	0.0849945i	0.424583	+	0.905389i	$0.360421\pi$
$600$	72.8740	−	392.094i	0.121457	−	0.653489i
$601$	−791.000			−1.31614			−0.658070	−	0.752957i	$-0.728627\pi$
$601$	−791.000			−1.31614			−0.658070	+	0.752957i	$0.728627\pi$
$602$		0			0
$603$	−455.000	+	367.696i	−0.754561	+	0.609777i
$604$	−58.0000	+	100.459i	−0.0960265	+	0.166323i
$605$	889.165	−	513.360i	1.46969	−	0.848528i
$606$	−374.302	+	437.806i	−0.617660	+	0.722452i
$607$	56.5000	−	97.8609i	0.0930807	−	0.161221i	−0.815725	−	0.578440i	$-0.803662\pi$
$607$	56.5000	−	97.8609i	0.0930807	−	0.161221i	0.908806	+	0.417219i	$0.136995\pi$
$608$			175.362i			0.288425i
$609$		0			0
$610$	600.000			0.983607
$611$	−36.7423	−	21.2132i	−0.0601348	−	0.0347188i
$612$	−54.8786	+	142.535i	−0.0896709	+	0.232901i
$613$	287.000	+	497.099i	0.468189	+	0.810928i	0.999339	−	0.0363503i	$-0.0115732\pi$
$613$	287.000	+	497.099i	0.468189	+	0.810928i	−0.531150	+	0.847278i	$0.678240\pi$
$614$	−243.724	−	140.714i	−0.396945	−	0.229176i
$615$	−288.000	−	814.587i	−0.468293	−	1.32453i
$616$		0			0
$617$		−	661.852i		−	1.07269i	−0.843998	−	0.536347i	$-0.819804\pi$
$617$		−	661.852i		−	1.07269i	0.843998	−	0.536347i	$-0.180196\pi$
$618$	−50.3916	+	271.129i	−0.0815398	+	0.438719i
$619$	476.500	+	825.322i	0.769790	+	1.33332i	0.937677	+	0.347509i	$0.112972\pi$
$619$	476.500	+	825.322i	0.769790	+	1.33332i	−0.167887	+	0.985806i	$0.553694\pi$
$620$	−102.879	+	59.3970i	−0.165933	+	0.0958016i
$621$	109.015	+	201.504i	0.175547	+	0.324483i
$622$	−624.000			−1.00322
$623$		0			0
$624$	4.00000	+	11.3137i	0.00641026	+	0.0181309i
$625$	−204.500	+	354.204i	−0.327200	+	0.566727i
$626$	−145.745	+	84.1457i	−0.232819	+	0.134418i
$627$		0			0
$628$	118.000	−	204.382i	0.187898	−	0.325449i
$629$			8.48528i			0.0134901i
$630$		0			0
$631$	758.000			1.20127			0.600634	−	0.799524i	$-0.294915\pi$
$631$	758.000			1.20127			0.600634	+	0.799524i	$0.294915\pi$
$632$	−252.297	−	145.664i	−0.399205	−	0.230481i
$633$	120.868	−	141.375i	0.190945	−	0.223341i
$634$	144.000	+	249.415i	0.227129	+	0.393400i
$635$	−830.377	−	479.418i	−1.30768	−	0.754990i
$636$	−144.000	+	50.9117i	−0.226415	+	0.0800498i
$637$		0			0
$638$		0			0
$639$	528.075	−	83.0951i	0.826408	−	0.130039i
$640$	−48.0000	−	83.1384i	−0.0750000	−	0.129904i
$641$	933.256	−	538.815i	1.45594	−	0.840586i	0.457129	−	0.889400i	$-0.348878\pi$
$641$	933.256	−	538.815i	1.45594	−	0.840586i	0.998808	+	0.0488147i	$0.0155444\pi$
$642$	672.484	+	124.987i	1.04748	+	0.194684i
$643$	1111.00			1.72784			0.863919	−	0.503631i	$-0.168003\pi$
$643$	1111.00			1.72784			0.863919	+	0.503631i	$0.168003\pi$
$644$		0			0
$645$	744.000	−	263.044i	1.15349	−	0.407820i
$646$	−186.000	+	322.161i	−0.287926	+	0.498702i
$647$	−293.939	+	169.706i	−0.454310	+	0.262296i	−0.709649	−	0.704556i	$-0.751146\pi$
$647$	−293.939	+	169.706i	−0.454310	+	0.262296i	0.255339	+	0.966852i	$0.417813\pi$
$648$	70.3587	+	218.031i	0.108578	+	0.336468i
$649$		0			0
$650$		−	66.4680i		−	0.102259i
$651$		0			0
$652$	212.000			0.325153
$653$	558.484	+	322.441i	0.855258	+	0.493784i	0.862422	−	0.506191i	$-0.168947\pi$
$653$	558.484	+	322.441i	0.855258	+	0.493784i	−0.00716327	+	0.999974i	$0.502280\pi$
$654$	538.532	+	460.418i	0.823444	+	0.704003i
$655$	−360.000	−	623.538i	−0.549618	−	0.951967i
$656$	−117.576	−	67.8823i	−0.179231	−	0.103479i
$657$	−679.000	+	548.715i	−1.03349	+	0.835182i
$658$		0			0
$659$		−	873.984i		−	1.32623i	−0.748519	−	0.663114i	$-0.769235\pi$
$659$		−	873.984i		−	1.32623i	0.748519	−	0.663114i	$-0.230765\pi$
$660$		0			0
$661$	−432.500	−	749.112i	−0.654312	−	1.13330i	−0.982066	−	0.188538i	$-0.939625\pi$
$661$	−432.500	−	749.112i	−0.654312	−	1.13330i	0.327754	−	0.944763i	$-0.393708\pi$
$662$	638.092	−	368.403i	0.963885	−	0.556499i
$663$	−4.65153	+	25.0273i	−0.00701588	+	0.0377485i
$664$	120.000			0.180723
$665$		0			0
$666$	8.00000	+	9.89949i	0.0120120	+	0.0148641i
$667$	−72.0000	+	124.708i	−0.107946	+	0.186968i
$668$	−249.848	+	144.250i	−0.374024	+	0.215943i
$669$	393.797	−	460.608i	0.588635	−	0.688503i
$670$	390.000	−	675.500i	0.582090	−	1.00821i
$671$		0			0
$672$		0			0
$673$	−505.000			−0.750371			−0.375186	−	0.926950i	$-0.622421\pi$
$673$	−505.000			−0.750371			−0.375186	+	0.926950i	$0.622421\pi$
$674$	−380.896	−	219.910i	−0.565127	−	0.326276i
$675$	35.1301	−	1268.51i	0.0520446	−	1.87928i
$676$	−168.000	−	290.985i	−0.248521	−	0.430450i
$677$	−279.242	−	161.220i	−0.412469	−	0.238139i	0.279381	−	0.960180i	$-0.409871\pi$
$677$	−279.242	−	161.220i	−0.412469	−	0.238139i	−0.691850	+	0.722041i	$0.743204\pi$
$678$	228.000	+	644.881i	0.336283	+	0.951152i
$679$		0			0
$680$		−	203.647i		−	0.299481i
$681$	−9.30306	+	50.0545i	−0.0136609	+	0.0735015i
$682$		0			0
$683$	−683.408	+	394.566i	−1.00060	+	0.577695i	−0.908425	−	0.418048i	$-0.862714\pi$
$683$	−683.408	+	394.566i	−1.00060	+	0.577695i	−0.0921720	+	0.995743i	$0.529381\pi$
$684$	86.7367	+	551.218i	0.126808	+	0.805874i
$685$	1584.00			2.31241
$686$		0			0
$687$	1.00000	+	2.82843i	0.00145560	+	0.00411707i
$688$	62.0000	−	107.387i	0.0901163	−	0.156086i
$689$	−22.0454	+	12.7279i	−0.0319962	+	0.0184730i
$690$	−232.182	−	198.504i	−0.336495	−	0.287686i
$691$	92.5000	−	160.215i	0.133864	−	0.231859i	−0.791299	−	0.611429i	$-0.790595\pi$
$691$	92.5000	−	160.215i	0.133864	−	0.231859i	0.925163	+	0.379570i	$0.123928\pi$
$692$		−	152.735i		−	0.220715i
$693$		0			0
$694$	−156.000			−0.224784
$695$	830.377	+	479.418i	1.19479	+	0.689811i
$696$	−93.5755	+	109.451i	−0.134448	+	0.157258i
$697$	−144.000	−	249.415i	−0.206600	−	0.357841i
$698$	61.2372	+	35.3553i	0.0877324	+	0.0506523i
$699$	936.000	−	330.926i	1.33906	−	0.473428i
$700$		0			0
$701$		−	93.3381i		−	0.133150i	−0.997781	−	0.0665750i	$-0.978793\pi$
$701$		−	93.3381i		−	0.133150i	0.997781	−	0.0665750i	$-0.0212072\pi$
$702$	18.1691	+	33.5840i	0.0258820	+	0.0478404i
$703$	15.5000	+	26.8468i	0.0220484	+	0.0381889i
$704$		0			0
$705$	1061.82	+	197.348i	1.50612	+	0.279926i
$706$	228.000			0.322946
$707$		0			0
$708$	−48.0000	+	16.9706i	−0.0677966	+	0.0239697i
$709$	−97.0000	+	168.009i	−0.136812	+	0.236966i	−0.926288	−	0.376815i	$-0.877019\pi$
$709$	−97.0000	+	168.009i	−0.136812	+	0.236966i	0.789476	+	0.613782i	$0.210352\pi$
$710$	−617.271	+	356.382i	−0.869396	+	0.501946i
$711$	−865.095	−	333.076i	−1.21673	−	0.468462i
$712$	−168.000	+	290.985i	−0.235955	+	0.408686i
$713$			59.3970i			0.0833057i
$714$		0			0
$715$		0			0
$716$	−279.242	−	161.220i	−0.390003	−	0.225168i
$717$	1044.82	+	893.266i	1.45721	+	1.24584i
$718$	288.000	+	498.831i	0.401114	+	0.694750i
$719$	−338.030	−	195.161i	−0.470139	−	0.271435i	0.246159	−	0.969229i	$-0.420831\pi$
$719$	−338.030	−	195.161i	−0.470139	−	0.271435i	−0.716298	+	0.697795i	$0.754165\pi$
$720$	−192.000	−	237.588i	−0.266667	−	0.329983i
$721$		0			0
$722$			848.528i			1.17525i
$723$	−64.8888	−	12.0601i	−0.0897493	−	0.0166807i
$724$	−215.000	−	372.391i	−0.296961	−	0.514352i
$725$	690.756	−	398.808i	0.952767	−	0.550080i
$726$	93.8059	−	504.716i	0.129209	−	0.695201i
$727$	−425.000			−0.584594			−0.292297	−	0.956328i	$-0.594420\pi$
$727$	−425.000			−0.584594			−0.292297	+	0.956328i	$0.594420\pi$
$728$		0			0
$729$	329.000	+	650.538i	0.451303	+	0.892371i
$730$	582.000	−	1008.05i	0.797260	−	1.38090i
$731$	227.803	−	131.522i	0.311631	−	0.179920i
$732$	194.949	−	228.024i	0.266324	−	0.311508i
$733$	203.500	−	352.472i	0.277626	−	0.480863i	−0.693168	−	0.720776i	$-0.743786\pi$
$733$	203.500	−	352.472i	0.277626	−	0.480863i	0.970794	+	0.239913i	$0.0771190\pi$
$734$			756.604i			1.03080i
$735$		0			0
$736$	−48.0000			−0.0652174
$737$		0			0
$738$	−403.151	−	155.220i	−0.546275	−	0.210325i
$739$	−380.500	−	659.045i	−0.514885	−	0.891807i	−0.999851	−	0.0172738i	$-0.994501\pi$
$739$	−380.500	−	659.045i	−0.514885	−	0.891807i	0.484966	−	0.874533i	$-0.338832\pi$
$740$	−14.6969	−	8.48528i	−0.0198607	−	0.0114666i
$741$	31.0000	+	87.6812i	0.0418354	+	0.118328i
$742$		0			0
$743$		−	576.999i		−	0.776580i	−0.921537	−	0.388290i	$-0.873066\pi$
$743$		−	576.999i		−	0.776580i	0.921537	−	0.388290i	$-0.126934\pi$
$744$	−10.8536	+	58.3969i	−0.0145881	+	0.0784905i
$745$	−288.000	−	498.831i	−0.386577	−	0.669571i
$746$	−471.527	+	272.236i	−0.632073	+	0.364928i
$747$	377.196	−	59.3537i	0.504948	−	0.0794561i
$748$		0			0
$749$		0			0
$750$	264.000	+	746.705i	0.352000	+	0.995606i
$751$	−344.500	+	596.692i	−0.458722	+	0.794529i	−0.998894	−	0.0470253i	$-0.985026\pi$
$751$	−344.500	+	596.692i	−0.458722	+	0.794529i	0.540172	+	0.841555i	$0.318359\pi$
$752$	146.969	−	84.8528i	0.195438	−	0.112836i
$753$	−406.318	−	347.381i	−0.539599	−	0.461330i
$754$	−12.0000	+	20.7846i	−0.0159151	+	0.0275658i
$755$		−	492.146i		−	0.651849i
$756$		0			0
$757$	−142.000			−0.187583			−0.0937913	−	0.995592i	$-0.529899\pi$
$757$	−142.000			−0.187583			−0.0937913	+	0.995592i	$0.529899\pi$
$758$	67.3610	+	38.8909i	0.0888667	+	0.0513072i
$759$		0			0
$760$	−372.000	−	644.323i	−0.489474	−	0.847793i
$761$	962.649	+	555.786i	1.26498	+	0.730336i	0.974034	−	0.226403i	$-0.0726967\pi$
$761$	962.649	+	555.786i	1.26498	+	0.730336i	0.290946	+	0.956740i	$0.406030\pi$
$762$	−452.000	+	159.806i	−0.593176	+	0.209719i
$763$		0			0
$764$			356.382i			0.466468i
$765$	−100.727	−	640.124i	−0.131669	−	0.836763i
$766$	−294.000	−	509.223i	−0.383812	−	0.664782i
$767$	−7.34847	+	4.24264i	−0.00958079	+	0.00553147i
$768$	−47.1918	−	8.77101i	−0.0614477	−	0.0114206i
$769$	−1127.00			−1.46554			−0.732770	−	0.680477i	$-0.761773\pi$
$769$	−1127.00			−1.46554			−0.732770	+	0.680477i	$0.761773\pi$
$770$		0			0
$771$	792.000	−	280.014i	1.02724	−	0.363183i
$772$	−97.0000	+	168.009i	−0.125648	+	0.217628i
$773$	396.817	−	229.103i	0.513347	−	0.296381i	−0.220861	−	0.975305i	$-0.570887\pi$
$773$	396.817	−	229.103i	0.513347	−	0.296381i	0.734208	+	0.678924i	$0.237553\pi$
$774$	141.770	−	368.216i	0.183165	−	0.475732i
$775$	164.500	−	284.922i	0.212258	−	0.367642i
$776$		−	469.519i		−	0.605050i
$777$		0			0
$778$	−540.000			−0.694087
$779$	−911.210	−	526.087i	−1.16972	−	0.675337i
$780$	−38.6969	−	33.0839i	−0.0496115	−	0.0424153i
$781$		0			0
$782$	−88.1816	−	50.9117i	−0.112764	−	0.0651045i
$783$	−240.000	+	390.323i	−0.306513	+	0.498497i
$784$		0			0
$785$			1001.26i			1.27549i
$786$	−353.939	−	65.7826i	−0.450304	−	0.0836928i
$787$	−293.000	−	507.491i	−0.372300	−	0.644842i	0.617619	−	0.786477i	$-0.288097\pi$
$787$	−293.000	−	507.491i	−0.372300	−	0.644842i	−0.989919	+	0.141635i	$0.954764\pi$
$788$	631.968	−	364.867i	0.801990	−	0.463029i
$789$	55.8184	−	300.327i	0.0707457	−	0.380643i
$790$	1236.00			1.56456
$791$		0			0
$792$		0			0
$793$	25.0000	−	43.3013i	0.0315259	−	0.0546044i
$794$	589.102	−	340.118i	0.741942	−	0.428361i
$795$	421.090	−	492.532i	0.529673	−	0.619537i
$796$	106.000	−	183.597i	0.133166	−	0.230650i
$797$		−	483.661i		−	0.606852i	−0.952855	−	0.303426i	$-0.901869\pi$
$797$		−	483.661i		−	0.606852i	0.952855	−	0.303426i	$-0.0981305\pi$
$798$		0			0
$799$	360.000			0.450563
$800$	230.252	+	132.936i	0.287815	+	0.166170i
$801$	−384.150	+	997.748i	−0.479588	+	1.24563i
$802$	−54.0000	−	93.5307i	−0.0673317	−	0.116622i
$803$		0			0
$804$	−130.000	−	367.696i	−0.161692	−	0.457333i
$805$		0			0
$806$			9.89949i			0.0122823i
$807$	−232.577	+	1251.36i	−0.288199	+	1.55064i
$808$	−192.000	−	332.554i	−0.237624	−	0.411576i
$809$	−698.105	+	403.051i	−0.862923	+	0.498209i	−0.864990	−	0.501789i	$-0.832675\pi$
$809$	−698.105	+	403.051i	−0.862923	+	0.498209i	0.00206714	+	0.999998i	$0.499342\pi$
$810$	−721.029	−	651.845i	−0.890159	−	0.804747i
$811$	−398.000			−0.490752			−0.245376	−	0.969428i	$-0.578911\pi$
$811$	−398.000			−0.490752			−0.245376	+	0.969428i	$0.578911\pi$
$812$		0			0
$813$	250.000	+	707.107i	0.307503	+	0.869750i
$814$		0			0
$815$	−778.938	+	449.720i	−0.955752	+	0.551804i
$816$	−77.3939	−	66.1679i	−0.0948454	−	0.0810881i
$817$	480.500	−	832.250i	0.588127	−	1.01867i
$818$			69.2965i			0.0847145i
$819$		0			0
$820$	576.000			0.702439
$821$	−1403.56	−	810.344i	−1.70957	−	0.987021i	−0.935081	−	0.354435i	$-0.884673\pi$
$821$	−1403.56	−	810.344i	−1.70957	−	0.987021i	−0.774490	−	0.632586i	$-0.781994\pi$
$822$	514.665	−	601.983i	0.626113	−	0.732340i
$823$	581.000	+	1006.32i	0.705954	+	1.22275i	0.966346	+	0.257245i	$0.0828147\pi$
$823$	581.000	+	1006.32i	0.705954	+	1.22275i	−0.260392	+	0.965503i	$0.583852\pi$
$824$	−159.217	−	91.9239i	−0.193224	−	0.111558i
$825$		0			0
$826$		0			0
$827$			144.250i			0.174425i	0.996190	+	0.0872127i	$0.0277960\pi$
$827$			144.250i			0.174425i	−0.996190	+	0.0872127i	$0.972204\pi$
$828$	−150.879	+	23.7415i	−0.182220	+	0.0286733i
$829$	623.500	+	1079.93i	0.752111	+	1.30269i	0.946798	+	0.321829i	$0.104298\pi$
$829$	623.500	+	1079.93i	0.752111	+	1.30269i	−0.194687	+	0.980865i	$0.562369\pi$
$830$	−440.908	+	254.558i	−0.531215	+	0.306697i
$831$	−1129.65	−	209.956i	−1.35939	−	0.252655i
$832$	−8.00000			−0.00961538
$833$		0			0
$834$	452.000	−	159.806i	0.541966	−	0.191614i
$835$	612.000	−	1060.02i	0.732934	−	1.26948i
$836$		0			0
$837$	−5.23214	+	188.928i	−0.00625106	+	0.225720i
$838$	−228.000	+	394.908i	−0.272076	+	0.471250i
$839$			1001.26i			1.19340i	0.802464	+	0.596700i	$0.203522\pi$
$839$			1001.26i			1.19340i	−0.802464	+	0.596700i	$0.796478\pi$
$840$		0			0
$841$	553.000			0.657551
$842$	383.345	+	221.324i	0.455279	+	0.262856i
$843$	406.318	+	347.381i	0.481990	+	0.412078i
$844$	62.0000	+	107.387i	0.0734597	+	0.127236i
$845$	1234.54	+	712.764i	1.46100	+	0.843507i
$846$	420.000	−	339.411i	0.496454	−	0.401195i
$847$		0			0
$848$		−	101.823i		−	0.120075i
$849$	899.594	+	167.197i	1.05959	+	0.196934i
$850$	282.000	+	488.438i	0.331765	+	0.574633i
$851$	−7.34847	+	4.24264i	−0.00863510	+	0.00498548i
$852$	−65.1214	+	350.382i	−0.0764336	+	0.411246i
$853$	337.000			0.395076			0.197538	−	0.980295i	$-0.436705\pi$
$853$	337.000			0.395076			0.197538	+	0.980295i	$0.436705\pi$
$854$		0			0
$855$	−1488.00	−	1841.31i	−1.74035	−	2.15357i
$856$	−228.000	+	394.908i	−0.266355	+	0.461341i
$857$	969.998	−	560.029i	1.13185	−	0.653476i	0.187453	−	0.982274i	$-0.439977\pi$
$857$	969.998	−	560.029i	1.13185	−	0.653476i	0.944400	+	0.328798i	$0.106644\pi$
$858$		0			0
$859$	−545.000	+	943.968i	−0.634459	+	1.09891i	0.352171	+	0.935936i	$0.385444\pi$
$859$	−545.000	+	943.968i	−0.634459	+	1.09891i	−0.986630	+	0.162979i	$0.947890\pi$
$860$			526.087i			0.611730i
$861$		0			0
$862$	−492.000			−0.570766
$863$	−999.392	−	576.999i	−1.15804	−	0.668597i	−0.207209	−	0.978297i	$-0.566438\pi$
$863$	−999.392	−	576.999i	−1.15804	−	0.668597i	−0.950834	+	0.309700i	$0.899771\pi$
$864$	−152.677	−	4.22821i	−0.176709	−	0.00489376i
$865$	324.000	+	561.184i	0.374566	+	0.648768i
$866$	−118.800	−	68.5894i	−0.137183	−	0.0792025i
$867$	217.000	+	613.769i	0.250288	+	0.707922i
$868$		0			0
$869$		0			0
$870$	111.637	−	600.654i	0.128318	−	0.690407i
$871$	−32.5000	−	56.2917i	−0.0373134	−	0.0646288i
$872$	−409.065	+	236.174i	−0.469111	+	0.270841i
$873$	−232.231	−	1475.84i	−0.266014	−	1.69054i
$874$	−372.000			−0.425629
$875$		0			0
$876$	−194.000	−	548.715i	−0.221461	−	0.626387i
$877$	23.0000	−	39.8372i	0.0262258	−	0.0454244i	−0.852615	−	0.522540i	$-0.824984\pi$
$877$	23.0000	−	39.8372i	0.0262258	−	0.0454244i	0.878840	+	0.477116i	$0.158318\pi$
$878$	−458.055	+	264.458i	−0.521702	+	0.301205i
$879$	−309.576	−	264.672i	−0.352191	−	0.301105i
$880$		0			0
$881$		−	924.896i		−	1.04982i	−0.851156	−	0.524912i	$-0.824098\pi$
$881$		−	924.896i		−	1.04982i	0.851156	−	0.524912i	$-0.175902\pi$
$882$		0			0
$883$	329.000			0.372593			0.186297	−	0.982494i	$-0.440351\pi$
$883$	329.000			0.372593			0.186297	+	0.982494i	$0.440351\pi$
$884$	−14.6969	−	8.48528i	−0.0166255	−	0.00959873i
$885$	140.363	−	164.177i	0.158603	−	0.185511i
$886$	−426.000	−	737.854i	−0.480813	−	0.832792i
$887$	−1219.85	−	704.278i	−1.37525	−	0.794000i	−0.383666	−	0.923472i	$-0.625339\pi$
$887$	−1219.85	−	704.278i	−1.37525	−	0.794000i	−0.991583	+	0.129472i	$0.958672\pi$
$888$	−8.00000	+	2.82843i	−0.00900901	+	0.00318517i
$889$		0			0
$890$		−	1425.53i		−	1.60172i
$891$		0			0
$892$	202.000	+	349.874i	0.226457	+	0.392236i
$893$	1139.01	−	657.609i	1.27549	−	0.736405i
$894$	−283.151	−	52.6261i	−0.316724	−	0.0588658i
$895$	1368.00			1.52849
$896$		0			0
$897$	−24.0000	+	8.48528i	−0.0267559	+	0.00945962i
$898$	−30.0000	+	51.9615i	−0.0334076	+	0.0578636i
$899$	−102.879	+	59.3970i	−0.114437	+	0.0660700i
$900$	789.504	+	303.973i	0.877227	+	0.337747i
$901$	108.000	−	187.061i	0.119867	−	0.207615i
$902$		0			0
$903$		0			0
$904$	−456.000			−0.504425
$905$	1579.92	+	912.168i	1.74577	+	1.00792i
$906$	−187.035	−	159.906i	−0.206441	−	0.176496i
$907$	87.5000	+	151.554i	0.0964719	+	0.167094i	0.910222	−	0.414121i	$-0.135911\pi$
$907$	87.5000	+	151.554i	0.0964719	+	0.167094i	−0.813750	+	0.581215i	$0.802578\pi$
$908$	−29.3939	−	16.9706i	−0.0323721	−	0.0186900i
$909$	−768.000	−	950.352i	−0.844884	−	1.04549i
$910$		0			0
$911$			1450.98i			1.59274i	0.604812	+	0.796368i	$0.293248\pi$
$911$			1450.98i			1.59274i	−0.604812	+	0.796368i	$0.706752\pi$
$912$	−365.737	−	67.9753i	−0.401027	−	0.0745344i
$913$		0			0
$914$	557.259	−	321.734i	0.609692	−	0.352006i
$915$	−232.577	+	1251.36i	−0.254182	+	1.36761i
$916$	−2.00000			−0.00218341
$917$		0			0
$918$	−276.000	−	169.706i	−0.300654	−	0.184865i
$919$	−548.500	+	950.030i	−0.596844	+	1.03376i	0.396439	+	0.918061i	$0.370246\pi$
$919$	−548.500	+	950.030i	−0.596844	+	1.03376i	−0.993284	+	0.115704i	$0.963088\pi$
$920$	176.363	−	101.823i	0.191699	−	0.110678i
$921$	387.948	−	453.768i	0.421225	−	0.492690i
$922$	−156.000	+	270.200i	−0.169197	+	0.293058i
$923$			59.3970i			0.0643521i
$924$		0			0
$925$	47.0000			0.0508108
$926$	8.57321	+	4.94975i	0.00925833	+	0.00534530i
$927$	−545.934	−	210.194i	−0.588925	−	0.226746i
$928$	−48.0000	−	83.1384i	−0.0517241	−	0.0895888i
$929$	492.347	+	284.257i	0.529976	+	0.305982i	0.741007	−	0.671498i	$-0.234349\pi$
$929$	492.347	+	284.257i	0.529976	+	0.305982i	−0.211031	+	0.977479i	$0.567682\pi$
$930$	−84.0000	−	237.588i	−0.0903226	−	0.255471i
$931$		0			0
$932$			661.852i			0.710142i
$933$	241.880	−	1301.42i	0.259249	−	1.39487i
$934$	438.000	+	758.638i	0.468951	+	0.812247i
$935$		0			0
$936$	−25.1464	+	3.95691i	−0.0268658	+	0.00422747i
$937$	1.00000			0.00106724			0.000533618	−	1.00000i	$-0.499830\pi$
$937$	1.00000			0.00106724			0.000533618		1.00000i	$0.499830\pi$
$938$		0			0
$939$	−119.000	−	336.583i	−0.126731	−	0.358448i
$940$	−360.000	+	623.538i	−0.382979	+	0.663339i
$941$	−330.681	+	190.919i	−0.351415	+	0.202889i	−0.665308	−	0.746569i	$-0.731700\pi$
$941$	−330.681	+	190.919i	−0.351415	+	0.202889i	0.313894	+	0.949458i	$0.398366\pi$
$942$	380.520	+	325.325i	0.403949	+	0.345356i
$943$	144.000	−	249.415i	0.152704	−	0.264491i
$944$		−	33.9411i		−	0.0359546i
$945$		0			0
$946$		0			0
$947$	1455.00	+	840.043i	1.53643	+	0.887057i	0.999044	+	0.0437190i	$0.0139206\pi$
$947$	1455.00	+	840.043i	1.53643	+	0.887057i	0.537384	+	0.843338i	$0.319413\pi$
$948$	401.595	−	469.729i	0.423623	−	0.495495i
$949$	−48.5000	−	84.0045i	−0.0511064	−	0.0885189i
$950$	1784.45	+	1030.25i	1.87837	+	1.08448i
$951$	−576.000	+	203.647i	−0.605678	+	0.214140i
$952$		0			0
$953$		−	195.161i		−	0.204786i	−0.994744	−	0.102393i	$-0.967350\pi$
$953$		−	195.161i		−	0.204786i	0.994744	−	0.102393i	$-0.0326500\pi$
$954$	−50.3633	−	320.062i	−0.0527917	−	0.335495i
$955$	−756.000	−	1309.43i	−0.791623	−	1.37113i
$956$	−793.635	+	458.205i	−0.830162	+	0.479294i
$957$		0			0
$958$	−948.000			−0.989562
$959$		0			0
$960$	192.000	−	67.8823i	0.200000	−	0.0707107i
$961$	456.000	−	789.815i	0.474506	−	0.821868i
$962$	−1.22474	+	0.707107i	−0.00127312	+	0.000735038i
$963$	−521.346	+	1354.09i	−0.541377	+	1.40611i
$964$	22.0000	−	38.1051i	0.0228216	−	0.0395281i
$965$		−	823.072i		−	0.852925i
$966$		0			0
$967$	−223.000			−0.230610			−0.115305	−	0.993330i	$-0.536785\pi$
$967$	−223.000			−0.230610			−0.115305	+	0.993330i	$0.536785\pi$
$968$	296.388	+	171.120i	0.306186	+	0.176777i
$969$	−599.803	−	512.801i	−0.618991	−	0.529206i
$970$	996.000	+	1725.12i	1.02680	+	1.77848i
$971$	492.347	+	284.257i	0.507052	+	0.292747i	0.731621	−	0.681712i	$-0.238764\pi$
$971$	492.347	+	284.257i	0.507052	+	0.292747i	−0.224569	+	0.974458i	$0.572097\pi$
$972$	−482.000	+	62.2254i	−0.495885	+	0.0640179i
$973$		0			0
$974$		−	654.781i		−	0.672260i
$975$	138.626	+	25.7648i	0.142181	+	0.0264255i
$976$	100.000	+	173.205i	0.102459	+	0.177464i
$977$	−1396.21	+	806.102i	−1.42908	+	0.825079i	−0.997048	−	0.0767807i	$-0.975536\pi$
$977$	−1396.21	+	806.102i	−1.42908	+	0.825079i	−0.432030	+	0.901859i	$0.642203\pi$
$978$	−82.1770	+	442.148i	−0.0840256	+	0.452094i
$979$		0			0
$980$		0			0
$981$	−1169.00	+	944.695i	−1.19164	+	0.962991i
$982$	−252.000	+	436.477i	−0.256619	+	0.444477i
$983$	−1491.74	+	861.256i	−1.51754	+	0.876151i	−0.517750	+	0.855532i	$0.673230\pi$
$983$	−1491.74	+	861.256i	−1.51754	+	0.876151i	−0.999787	+	0.0206186i	$0.993436\pi$
$984$	187.151	−	218.903i	0.190194	−	0.222462i
$985$	−1548.00	+	2681.21i	−1.57157	+	2.72205i
$986$		−	203.647i		−	0.206538i
$987$		0			0
$988$	−62.0000			−0.0627530
$989$	227.803	+	131.522i	0.230336	+	0.132985i
$990$		0			0
$991$	447.500	+	775.093i	0.451564	+	0.782132i	0.998483	−	0.0550534i	$-0.0175329\pi$
$991$	447.500	+	775.093i	0.451564	+	0.782132i	−0.546919	+	0.837185i	$0.684200\pi$
$992$	−34.2929	−	19.7990i	−0.0345694	−	0.0199587i
$993$	521.000	+	1473.61i	0.524673	+	1.48400i
$994$		0			0
$995$			899.440i			0.903960i
$996$	−46.5153	+	250.273i	−0.0467021	+	0.251278i
$997$	203.500	+	352.472i	0.204112	+	0.353533i	0.949850	−	0.312707i	$-0.101236\pi$
$997$	203.500	+	352.472i	0.204112	+	0.353533i	−0.745737	+	0.666240i	$0.767903\pi$
$998$	−655.239	+	378.302i	−0.656552	+	0.379060i
$999$	−23.7474	+	12.8475i	−0.0237712	+	0.0128604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.3.h.b.275.1		4
3.2	odd	2	inner	294.3.h.b.275.2		4
7.2	even	3		294.3.b.c.197.2		2
7.3	odd	6		42.3.h.a.11.2	yes	4
7.4	even	3	inner	294.3.h.b.263.2		4
7.5	odd	6		294.3.b.b.197.2		2
7.6	odd	2		42.3.h.a.23.1	yes	4
21.2	odd	6		294.3.b.c.197.1		2
21.5	even	6		294.3.b.b.197.1		2
21.11	odd	6	inner	294.3.h.b.263.1		4
21.17	even	6		42.3.h.a.11.1	✓	4
21.20	even	2		42.3.h.a.23.2	yes	4
28.3	even	6		336.3.bn.c.305.1		4
28.27	even	2		336.3.bn.c.65.2		4
84.59	odd	6		336.3.bn.c.305.2		4
84.83	odd	2		336.3.bn.c.65.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.h.a.11.1	✓	4	21.17	even	6
42.3.h.a.11.2	yes	4	7.3	odd	6
42.3.h.a.23.1	yes	4	7.6	odd	2
42.3.h.a.23.2	yes	4	21.20	even	2
294.3.b.b.197.1		2	21.5	even	6
294.3.b.b.197.2		2	7.5	odd	6
294.3.b.c.197.1		2	21.2	odd	6
294.3.b.c.197.2		2	7.2	even	3
294.3.h.b.263.1		4	21.11	odd	6	inner
294.3.h.b.263.2		4	7.4	even	3	inner
294.3.h.b.275.1		4	1.1	even	1	trivial
294.3.h.b.275.2		4	3.2	odd	2	inner
336.3.bn.c.65.1		4	84.83	odd	2
336.3.bn.c.65.2		4	28.27	even	2
336.3.bn.c.305.1		4	28.3	even	6
336.3.bn.c.305.2		4	84.59	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	294.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.94949 - 2.28024i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-7.34847 - 4.24264i) q^{5} +(-4.00000 + 1.41421i) q^{6} -2.82843i q^{8} +(-1.39898 - 8.89060i) q^{9} +O(q^{10})\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.94949 - 2.28024i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-7.34847 - 4.24264i) q^{5} +(-4.00000 + 1.41421i) q^{6} -2.82843i q^{8} +(-1.39898 - 8.89060i) q^{9} +(6.00000 + 10.3923i) q^{10} +(5.89898 + 1.09638i) q^{12} +1.00000 q^{13} +(-24.0000 + 8.48528i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-7.34847 + 4.24264i) q^{17} +(-4.57321 + 11.8780i) q^{18} +(-15.5000 + 26.8468i) q^{19} -16.9706i q^{20} +(-7.34847 - 4.24264i) q^{23} +(-6.44949 - 5.51399i) q^{24} +(23.5000 + 40.7032i) q^{25} +(-1.22474 - 0.707107i) q^{26} +(-23.0000 - 14.1421i) q^{27} -16.9706i q^{29} +(35.3939 + 6.57826i) q^{30} +(-3.50000 - 6.06218i) q^{31} +(4.89898 - 2.82843i) q^{32} +12.0000 q^{34} +(14.0000 - 11.3137i) q^{36} +(0.500000 - 0.866025i) q^{37} +(37.9671 - 21.9203i) q^{38} +(1.94949 - 2.28024i) q^{39} +(-12.0000 + 20.7846i) q^{40} +33.9411i q^{41} -31.0000 q^{43} +(-27.4393 + 71.2677i) q^{45} +(6.00000 + 10.3923i) q^{46} +(-36.7423 - 21.2132i) q^{47} +(4.00000 + 11.3137i) q^{48} -66.4680i q^{50} +(-4.65153 + 25.0273i) q^{51} +(1.00000 + 1.73205i) q^{52} +(-22.0454 + 12.7279i) q^{53} +(18.1691 + 33.5840i) q^{54} +(31.0000 + 87.6812i) q^{57} +(-12.0000 + 20.7846i) q^{58} +(-7.34847 + 4.24264i) q^{59} +(-38.6969 - 33.0839i) q^{60} +(25.0000 - 43.3013i) q^{61} +9.89949i q^{62} -8.00000 q^{64} +(-7.34847 - 4.24264i) q^{65} +(-32.5000 - 56.2917i) q^{67} +(-14.6969 - 8.48528i) q^{68} +(-24.0000 + 8.48528i) q^{69} +59.3970i q^{71} +(-25.1464 + 3.95691i) q^{72} +(-48.5000 - 84.0045i) q^{73} +(-1.22474 + 0.707107i) q^{74} +(138.626 + 25.7648i) q^{75} -62.0000 q^{76} +(-4.00000 + 1.41421i) q^{78} +(51.5000 - 89.2006i) q^{79} +(29.3939 - 16.9706i) q^{80} +(-77.0857 + 24.8755i) q^{81} +(24.0000 - 41.5692i) q^{82} +42.4264i q^{83} +72.0000 q^{85} +(37.9671 + 21.9203i) q^{86} +(-38.6969 - 33.0839i) q^{87} +(-102.879 - 59.3970i) q^{89} +(84.0000 - 67.8823i) q^{90} -16.9706i q^{92} +(-20.6464 - 3.83732i) q^{93} +(30.0000 + 51.9615i) q^{94} +(227.803 - 131.522i) q^{95} +(3.10102 - 16.6848i) q^{96} +166.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 4 q^{4} - 16 q^{6} + 14 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 4 * q^4 - 16 * q^6 + 14 * q^9	\( 4 q - 2 q^{3} + 4 q^{4} - 16 q^{6} + 14 q^{9} + 24 q^{10} + 4 q^{12} + 4 q^{13} - 96 q^{15} - 8 q^{16} + 16 q^{18} - 62 q^{19} - 16 q^{24} + 94 q^{25} - 92 q^{27} + 24 q^{30} - 14 q^{31} + 48 q^{34} + 56 q^{36} + 2 q^{37} - 2 q^{39} - 48 q^{40} - 124 q^{43} + 96 q^{45} + 24 q^{46} + 16 q^{48} - 48 q^{51} + 4 q^{52} - 40 q^{54} + 124 q^{57} - 48 q^{58} - 96 q^{60} + 100 q^{61} - 32 q^{64} - 130 q^{67} - 96 q^{69} - 32 q^{72} - 194 q^{73} + 94 q^{75} - 248 q^{76} - 16 q^{78} + 206 q^{79} - 34 q^{81} + 96 q^{82} + 288 q^{85} - 96 q^{87} + 336 q^{90} - 14 q^{93} + 120 q^{94} + 32 q^{96} + 664 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 4 * q^4 - 16 * q^6 + 14 * q^9 + 24 * q^10 + 4 * q^12 + 4 * q^13 - 96 * q^15 - 8 * q^16 + 16 * q^18 - 62 * q^19 - 16 * q^24 + 94 * q^25 - 92 * q^27 + 24 * q^30 - 14 * q^31 + 48 * q^34 + 56 * q^36 + 2 * q^37 - 2 * q^39 - 48 * q^40 - 124 * q^43 + 96 * q^45 + 24 * q^46 + 16 * q^48 - 48 * q^51 + 4 * q^52 - 40 * q^54 + 124 * q^57 - 48 * q^58 - 96 * q^60 + 100 * q^61 - 32 * q^64 - 130 * q^67 - 96 * q^69 - 32 * q^72 - 194 * q^73 + 94 * q^75 - 248 * q^76 - 16 * q^78 + 206 * q^79 - 34 * q^81 + 96 * q^82 + 288 * q^85 - 96 * q^87 + 336 * q^90 - 14 * q^93 + 120 * q^94 + 32 * q^96 + 664 * q^97

Introduction

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