LMFDB - Embedded newform 294.3.h.b.263.2

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			263.2
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	294.263
Dual form			294.3.h.b.275.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(-2.94949 - 0.548188i) q^{3} +(1.00000 - 1.73205i) q^{4} +(7.34847 - 4.24264i) q^{5} +(-4.00000 + 1.41421i) q^{6} -2.82843i q^{8} +(8.39898 + 3.23375i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(-2.94949 - 0.548188i) q^{3} +(1.00000 - 1.73205i) q^{4} +(7.34847 - 4.24264i) q^{5} +(-4.00000 + 1.41421i) q^{6} -2.82843i q^{8} +(8.39898 + 3.23375i) q^{9} +(6.00000 - 10.3923i) q^{10} +(-3.89898 + 4.56048i) q^{12} +1.00000 q^{13} +(-24.0000 + 8.48528i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(7.34847 + 4.24264i) q^{17} +(12.5732 - 1.97846i) q^{18} +(-15.5000 - 26.8468i) q^{19} -16.9706i q^{20} +(7.34847 - 4.24264i) q^{23} +(-1.55051 + 8.34242i) q^{24} +(23.5000 - 40.7032i) q^{25} +(1.22474 - 0.707107i) q^{26} +(-23.0000 - 14.1421i) q^{27} -16.9706i q^{29} +(-23.3939 + 27.3629i) 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} +(-2.94949 - 0.548188i) q^{39} +(-12.0000 - 20.7846i) q^{40} +33.9411i q^{41} -31.0000 q^{43} +(75.4393 - 11.8707i) q^{45} +(6.00000 - 10.3923i) q^{46} +(36.7423 - 21.2132i) q^{47} +(4.00000 + 11.3137i) q^{48} -66.4680i q^{50} +(-19.3485 - 16.5420i) q^{51} +(1.00000 - 1.73205i) q^{52} +(22.0454 + 12.7279i) q^{53} +(-38.1691 - 1.05705i) q^{54} +(31.0000 + 87.6812i) q^{57} +(-12.0000 - 20.7846i) q^{58} +(7.34847 + 4.24264i) q^{59} +(-9.30306 + 50.0545i) 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} +(9.14643 - 23.7559i) q^{72} +(-48.5000 + 84.0045i) q^{73} +(1.22474 + 0.707107i) q^{74} +(-91.6260 + 107.171i) q^{75} -62.0000 q^{76} +(-4.00000 + 1.41421i) q^{78} +(51.5000 + 89.2006i) q^{79} +(-29.3939 - 16.9706i) q^{80} +(60.0857 + 54.3204i) q^{81} +(24.0000 + 41.5692i) q^{82} +42.4264i q^{83} +72.0000 q^{85} +(-37.9671 + 21.9203i) q^{86} +(-9.30306 + 50.0545i) q^{87} +(102.879 - 59.3970i) q^{89} +(84.0000 - 67.8823i) q^{90} -16.9706i q^{92} +(13.6464 - 15.9617i) q^{93} +(30.0000 - 51.9615i) q^{94} +(-227.803 - 131.522i) q^{95} +(12.8990 + 11.0280i) 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 $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	−2.94949	−	0.548188i	−0.983163	−	0.182729i
$3$	−2.94949	−	0.548188i	−0.983163	−	0.182729i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	7.34847	−	4.24264i	1.46969	−	0.848528i	0.470272	−	0.882522i	$-0.344156\pi$
$5$	7.34847	−	4.24264i	1.46969	−	0.848528i	0.999422	+	0.0339935i	$0.0108226\pi$
$6$	−4.00000	+	1.41421i	−0.666667	+	0.235702i
$7$		0			0
$7$		0			0
$8$		−	2.82843i		−	0.353553i
$9$	8.39898	+	3.23375i	0.933220	+	0.359306i
$10$	6.00000	−	10.3923i	0.600000	−	1.03923i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	−3.89898	+	4.56048i	−0.324915	+	0.380040i
$13$	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	$-0.253045\pi$
$17$	7.34847	+	4.24264i	0.432263	+	0.249567i	−0.268047	+	0.963406i	$0.586378\pi$
$18$	12.5732	−	1.97846i	0.698512	−	0.109914i
$19$	−15.5000	−	26.8468i	−0.815789	−	1.41299i	−0.908760	−	0.417320i	$-0.862969\pi$
$19$	−15.5000	−	26.8468i	−0.815789	−	1.41299i	0.0929702	−	0.995669i	$-0.470364\pi$
$20$		−	16.9706i		−	0.848528i
$21$		0			0
$22$		0			0
$23$	7.34847	−	4.24264i	0.319499	−	0.184463i	−0.331670	−	0.943395i	$-0.607612\pi$
$23$	7.34847	−	4.24264i	0.319499	−	0.184463i	0.651169	+	0.758933i	$0.274279\pi$
$24$	−1.55051	+	8.34242i	−0.0646046	+	0.347601i
$25$	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	$-0.0945191\pi$
$30$	−23.3939	+	27.3629i	−0.779796	+	0.912096i
$31$	−3.50000	+	6.06218i	−0.112903	+	0.195554i	−0.916940	−	0.399026i	$-0.869348\pi$
$31$	−3.50000	+	6.06218i	−0.112903	+	0.195554i	0.804036	+	0.594580i	$0.202682\pi$
$32$	−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	0.872703	−	0.488251i	$-0.162365\pi$
$37$	0.500000	+	0.866025i	0.0135135	+	0.0234061i	−0.859190	+	0.511657i	$0.829032\pi$
$38$	−37.9671	−	21.9203i	−0.999134	−	0.576850i
$39$	−2.94949	−	0.548188i	−0.0756279	−	0.0140561i
$40$	−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
$45$	75.4393	−	11.8707i	1.67643	−	0.263794i
$46$	6.00000	−	10.3923i	0.130435	−	0.225920i
$47$	36.7423	−	21.2132i	0.781752	−	0.451345i	−0.0552988	−	0.998470i	$-0.517611\pi$
$47$	36.7423	−	21.2132i	0.781752	−	0.451345i	0.837051	+	0.547125i	$0.184278\pi$
$48$	4.00000	+	11.3137i	0.0833333	+	0.235702i
$49$		0			0
$50$		−	66.4680i		−	1.32936i
$51$	−19.3485	−	16.5420i	−0.379382	−	0.324352i
$52$	1.00000	−	1.73205i	0.0192308	−	0.0333087i
$53$	22.0454	+	12.7279i	0.415951	+	0.240149i	0.693344	−	0.720607i	$-0.256137\pi$
$53$	22.0454	+	12.7279i	0.415951	+	0.240149i	−0.277392	+	0.960757i	$0.589470\pi$
$54$	−38.1691	−	1.05705i	−0.706836	−	0.0195750i
$55$		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	$-0.310424\pi$
$59$	7.34847	+	4.24264i	0.124550	+	0.0719092i	−0.436430	+	0.899738i	$0.643757\pi$
$60$	−9.30306	+	50.0545i	−0.155051	+	0.834242i
$61$	25.0000	+	43.3013i	0.409836	+	0.709857i	0.994871	−	0.101151i	$-0.0322526\pi$
$61$	25.0000	+	43.3013i	0.409836	+	0.709857i	−0.585035	+	0.811008i	$0.698919\pi$
$62$			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	−0.999853	−	0.0171494i	$-0.994541\pi$
$67$	−32.5000	+	56.2917i	−0.485075	+	0.840174i	0.514778	+	0.857323i	$0.327874\pi$
$68$	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	$0.862630\pi$
$72$	9.14643	−	23.7559i	0.127034	−	0.329943i
$73$	−48.5000	+	84.0045i	−0.664384	+	1.15075i	0.315068	+	0.949069i	$0.397973\pi$
$73$	−48.5000	+	84.0045i	−0.664384	+	1.15075i	−0.979452	+	0.201677i	$0.935361\pi$
$74$	1.22474	+	0.707107i	0.0165506	+	0.00955550i
$75$	−91.6260	+	107.171i	−1.22168	+	1.42895i
$76$	−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	0.982662	+	0.185408i	$0.0593606\pi$
$79$	51.5000	+	89.2006i	0.651899	+	1.12912i	−0.330763	+	0.943714i	$0.607306\pi$
$80$	−29.3939	−	16.9706i	−0.367423	−	0.212132i
$81$	60.0857	+	54.3204i	0.741799	+	0.670622i
$82$	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
$87$	−9.30306	+	50.0545i	−0.106932	+	0.575339i
$88$		0			0
$89$	102.879	−	59.3970i	1.15594	−	0.667382i	0.205612	−	0.978634i	$-0.434082\pi$
$89$	102.879	−	59.3970i	1.15594	−	0.667382i	0.950327	+	0.311252i	$0.100748\pi$
$90$	84.0000	−	67.8823i	0.933333	−	0.754247i
$91$		0			0
$92$		−	16.9706i		−	0.184463i
$93$	13.6464	−	15.9617i	0.146736	−	0.171631i
$94$	30.0000	−	51.9615i	0.319149	−	0.552782i
$95$	−227.803	−	131.522i	−2.39792	−	1.38444i
$96$	12.8990	+	11.0280i	0.134364	+	0.114875i
$97$	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	$-0.567941\pi$
$101$	−117.576	−	67.8823i	−1.16411	−	0.672101i	−0.952286	+	0.305206i	$0.901275\pi$
$102$	−35.3939	−	6.57826i	−0.346999	−	0.0644927i
$103$	32.5000	+	56.2917i	0.315534	+	0.546521i	0.979551	−	0.201197i	$-0.0644830\pi$
$103$	32.5000	+	56.2917i	0.315534	+	0.546521i	−0.664017	+	0.747718i	$0.731150\pi$
$104$		−	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	$-0.395096\pi$
$107$	139.621	−	80.6102i	1.30487	−	0.753366i	0.981235	+	0.192816i	$0.0617622\pi$
$108$	−47.4949	+	25.6950i	−0.439768	+	0.237917i
$109$	−83.5000	+	144.626i	−0.766055	+	1.32685i	0.173632	+	0.984811i	$0.444450\pi$
$109$	−83.5000	+	144.626i	−0.766055	+	1.32685i	−0.939687	+	0.342036i	$0.888884\pi$
$110$		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	$-0.252830\pi$
$114$	99.9671	+	85.4668i	0.876904	+	0.749709i
$115$	36.0000	−	62.3538i	0.313043	−	0.542207i
$116$	−29.3939	−	16.9706i	−0.253395	−	0.146298i
$117$	8.39898	+	3.23375i	0.0717861	+	0.0276389i
$118$	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
$123$	18.6061	−	100.109i	0.151269	−	0.813894i
$124$	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
$129$	91.4342	+	16.9938i	0.708792	+	0.131735i
$130$	6.00000	−	10.3923i	0.0461538	−	0.0799408i
$131$	−73.4847	+	42.4264i	−0.560952	+	0.323866i	−0.753527	−	0.657416i	$-0.771649\pi$
$131$	−73.4847	+	42.4264i	−0.560952	+	0.323866i	0.192576	+	0.981282i	$0.438316\pi$
$132$		0			0
$133$		0			0
$134$			91.9239i			0.685999i
$135$	−229.015	−	6.34231i	−1.69641	−	0.0469801i
$136$	12.0000	−	20.7846i	0.0882353	−	0.152828i
$137$	161.666	+	93.3381i	1.18005	+	0.681300i	0.956025	−	0.293284i	$-0.0947483\pi$
$137$	161.666	+	93.3381i	1.18005	+	0.681300i	0.224021	+	0.974584i	$0.428082\pi$
$138$	−23.3939	+	27.3629i	−0.169521	+	0.198282i
$139$	−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
$144$	−5.59592	−	35.5624i	−0.0388605	−	0.246961i
$145$	−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	$-0.739818\pi$
$149$	−58.7878	+	33.9411i	−0.394549	+	0.227793i	0.289580	+	0.957154i	$0.406484\pi$
$150$	−36.4370	+	196.047i	−0.242913	+	1.30698i
$151$	29.0000	−	50.2295i	0.192053	−	0.332646i	−0.753877	−	0.657015i	$-0.771819\pi$
$151$	29.0000	−	50.2295i	0.192053	−	0.332646i	0.945930	+	0.324370i	$0.105152\pi$
$152$	−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
$156$	−3.89898	+	4.56048i	−0.0249935	+	0.0292338i
$157$	−59.0000	+	102.191i	−0.375796	+	0.650898i	−0.990446	−	0.137902i	$-0.955964\pi$
$157$	−59.0000	+	102.191i	−0.375796	+	0.650898i	0.614650	+	0.788800i	$0.289297\pi$
$158$	126.149	+	72.8320i	0.798410	+	0.460962i
$159$	−58.0454	−	49.6259i	−0.365065	−	0.312113i
$160$	−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	0.981543	−	0.191240i	$-0.0612507\pi$
$163$	53.0000	+	91.7987i	0.325153	+	0.563182i	−0.656390	+	0.754422i	$0.727917\pi$
$164$	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
$171$	−43.3684	−	275.609i	−0.253616	−	1.61175i
$172$	−31.0000	+	53.6936i	−0.180233	+	0.312172i
$173$	66.1362	−	38.1838i	0.382290	−	0.220715i	−0.296524	−	0.955025i	$-0.595827\pi$
$173$	66.1362	−	38.1838i	0.382290	−	0.220715i	0.678814	+	0.734310i	$0.262494\pi$
$174$	24.0000	+	67.8823i	0.137931	+	0.390128i
$175$		0			0
$176$		0			0
$177$	−19.3485	−	16.5420i	−0.109313	−	0.0934575i
$178$	84.0000	−	145.492i	0.471910	−	0.817372i
$179$	139.621	+	80.6102i	0.780005	+	0.450336i	0.836432	−	0.548071i	$-0.184637\pi$
$179$	139.621	+	80.6102i	0.780005	+	0.450336i	−0.0564270	+	0.998407i	$0.517971\pi$
$180$	54.8786	−	142.535i	0.304881	−	0.791863i
$181$	−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
$186$	5.42679	−	29.1985i	0.0291763	−	0.156981i
$187$		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	$-0.821141\pi$
$191$	−154.318	+	89.0955i	−0.807947	+	0.466468i	0.0382955	+	0.999266i	$0.487807\pi$
$192$	23.5959	+	4.38551i	0.122895	+	0.0228412i
$193$	48.5000	−	84.0045i	0.251295	−	0.435256i	−0.712587	−	0.701583i	$-0.752477\pi$
$193$	48.5000	−	84.0045i	0.251295	−	0.435256i	0.963883	+	0.266327i	$0.0858101\pi$
$194$	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	−0.967912	−	0.251291i	$-0.919145\pi$
$199$	−53.0000	+	91.7987i	−0.266332	+	0.461300i	0.701580	+	0.712591i	$0.252478\pi$
$200$	−115.126	−	66.4680i	−0.575630	−	0.332340i
$201$	126.717	−	148.216i	0.630432	−	0.737391i
$202$	−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
$207$	75.4393	−	11.8707i	0.364441	−	0.0573465i
$208$	−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
$213$	32.5607	−	175.191i	0.152867	−	0.822492i
$214$	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
$219$	189.101	−	221.183i	0.863473	−	1.00997i
$220$		0			0
$221$	7.34847	+	4.24264i	0.0332510	+	0.0191975i
$222$	−3.22474	−	2.75699i	−0.0145259	−	0.0124189i
$223$	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	$-0.321432\pi$
$227$	14.6969	+	8.48528i	0.0647442	+	0.0373801i	−0.467278	+	0.884110i	$0.654765\pi$
$228$	182.868	+	33.9877i	0.802054	+	0.149069i
$229$	−0.500000	−	0.866025i	−0.00218341	−	0.00378177i	0.864932	−	0.501890i	$-0.167362\pi$
$229$	−0.500000	−	0.866025i	−0.00218341	−	0.00378177i	−0.867115	+	0.498108i	$0.834028\pi$
$230$		−	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	$-0.918036\pi$
$233$	−286.590	+	165.463i	−1.23000	+	0.710142i	−0.262971	+	0.964804i	$0.584702\pi$
$234$	12.5732	−	1.97846i	0.0537317	−	0.00845494i
$235$	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	$0.591926\pi$
$240$	77.3939	+	66.1679i	0.322474	+	0.275699i
$241$	−11.0000	+	19.0526i	−0.0456432	+	0.0790563i	−0.887944	−	0.459951i	$-0.847867\pi$
$241$	−11.0000	+	19.0526i	−0.0456432	+	0.0790563i	0.842301	+	0.539007i	$0.181200\pi$
$242$	−148.194	−	85.5599i	−0.612372	−	0.353553i
$243$	−147.444	−	193.156i	−0.606767	−	0.794880i
$244$	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
$249$	23.2577	−	125.136i	0.0934042	−	0.502555i
$250$	−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
$255$	−212.363	−	39.4695i	−0.832797	−	0.154783i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−242.499	+	140.007i	−0.943578	+	0.544775i	−0.891080	−	0.453846i	$-0.850052\pi$
$257$	−242.499	+	140.007i	−0.943578	+	0.544775i	−0.0524977	+	0.998621i	$0.516718\pi$
$258$	124.000	−	43.8406i	0.480620	−	0.169925i
$259$		0			0
$260$		−	16.9706i		−	0.0652714i
$261$	54.8786	−	142.535i	0.210263	−	0.546113i
$262$	−60.0000	+	103.923i	−0.229008	+	0.396653i
$263$	−88.1816	−	50.9117i	−0.335291	−	0.193581i	0.322897	−	0.946434i	$-0.395343\pi$
$263$	−88.1816	−	50.9117i	−0.335291	−	0.193581i	−0.658188	+	0.752854i	$0.728677\pi$
$264$		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	$-0.0441422\pi$
$269$	367.423	+	212.132i	1.36589	+	0.788595i	0.375487	+	0.926828i	$0.377476\pi$
$270$	−284.969	+	154.170i	−1.05544	+	0.571001i
$271$	−125.000	−	216.506i	−0.461255	−	0.798916i	0.537769	−	0.843092i	$-0.319267\pi$
$271$	−125.000	−	216.506i	−0.461255	−	0.798916i	−0.999024	+	0.0441757i	$0.985934\pi$
$272$		−	33.9411i		−	0.124784i
$273$		0			0
$274$	264.000			0.963504
$275$		0			0
$276$	−9.30306	+	50.0545i	−0.0337067	+	0.181357i
$277$	−191.500	+	331.688i	−0.691336	+	1.19743i	0.280065	+	0.959981i	$0.409644\pi$
$277$	−191.500	+	331.688i	−0.691336	+	1.19743i	−0.971400	+	0.237447i	$0.923689\pi$
$278$	−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	$0.897302\pi$
$282$	−116.969	+	136.814i	−0.414785	+	0.485157i
$283$	152.500	−	264.138i	0.538869	−	0.933349i	−0.460096	−	0.887869i	$-0.652185\pi$
$283$	152.500	−	264.138i	0.538869	−	0.933349i	0.998965	−	0.0454798i	$-0.0144817\pi$
$284$	102.879	+	59.3970i	0.362248	+	0.209144i
$285$	599.803	+	512.801i	2.10457	+	1.79930i
$286$		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
$291$	−489.615	−	90.9992i	−1.68253	−	0.312712i
$292$	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
$303$	309.576	+	264.672i	1.02170	+	0.873503i
$304$	−62.0000	+	107.387i	−0.203947	+	0.353247i
$305$	367.423	+	212.132i	1.20467	+	0.695515i
$306$	100.788	+	38.8050i	0.329372	+	0.126814i
$307$	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	$-0.584358\pi$
$311$	−382.120	−	220.617i	−1.22868	−	0.709380i	−0.966754	+	0.255707i	$0.917692\pi$
$312$	−1.55051	+	8.34242i	−0.00496958	+	0.0267385i
$313$	59.5000	+	103.057i	0.190096	+	0.329256i	0.945282	−	0.326255i	$-0.105787\pi$
$313$	59.5000	+	103.057i	0.190096	+	0.329256i	−0.755186	+	0.655511i	$0.772453\pi$
$314$			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	$-0.562577\pi$
$317$	176.363	−	101.823i	0.556351	−	0.321209i	0.751680	+	0.659528i	$0.229244\pi$
$318$	−106.182	−	19.7348i	−0.333904	−	0.0620590i
$319$		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
$324$	154.171	−	49.7511i	0.475838	−	0.153553i
$325$	23.5000	−	40.7032i	0.0723077	−	0.125241i
$326$	129.823	+	74.9533i	0.398230	+	0.229918i
$327$	325.565	−	380.800i	0.995611	−	1.16453i
$328$	96.0000			0.292683
$329$		0			0
$330$		0			0
$331$	−260.500	−	451.199i	−0.787009	−	1.36314i	−0.927791	−	0.373099i	$-0.878295\pi$
$331$	−260.500	−	451.199i	−0.787009	−	1.36314i	0.140782	−	0.990041i	$-0.455038\pi$
$332$	73.4847	+	42.4264i	0.221339	+	0.127790i
$333$	1.39898	+	8.89060i	0.00420114	+	0.0266985i
$334$	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
$339$	−88.3791	+	475.518i	−0.260705	+	1.40271i
$340$	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
$345$	−140.363	+	164.177i	−0.406850	+	0.475876i
$346$	54.0000	−	93.5307i	0.156069	−	0.270320i
$347$	−95.5301	−	55.1543i	−0.275303	−	0.158946i	0.355992	−	0.934489i	$-0.384143\pi$
$347$	−95.5301	−	55.1543i	−0.275303	−	0.158946i	−0.631295	+	0.775543i	$0.717476\pi$
$348$	77.3939	+	66.1679i	0.222396	+	0.190138i
$349$	−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	$-0.259998\pi$
$353$	139.621	+	80.6102i	0.395527	+	0.228357i	−0.289025	+	0.957321i	$0.593331\pi$
$354$	−35.3939	−	6.57826i	−0.0999827	−	0.0185826i
$355$	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	$-0.474670\pi$
$359$	352.727	−	203.647i	0.982525	−	0.567261i	0.903032	+	0.429574i	$0.141336\pi$
$360$	−33.5755	−	213.375i	−0.0932653	−	0.592707i
$361$	−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
$366$	−161.237	−	137.850i	−0.440539	−	0.376639i
$367$	−267.500	+	463.324i	−0.728883	+	1.26246i	0.228473	+	0.973550i	$0.426627\pi$
$367$	−267.500	+	463.324i	−0.728883	+	1.26246i	−0.957356	+	0.288912i	$0.906707\pi$
$368$	−29.3939	−	16.9706i	−0.0798747	−	0.0461157i
$369$	−109.757	+	285.071i	−0.297445	+	0.772550i
$370$	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	0.999826	+	0.0186750i	$0.00594477\pi$
$373$	192.500	+	333.420i	0.516086	+	0.893887i	−0.483740	+	0.875212i	$0.660722\pi$
$374$		0			0
$375$	−102.334	+	550.600i	−0.272890	+	1.46827i
$376$	−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
$381$	−333.292	−	61.9453i	−0.874783	−	0.162586i
$382$	−126.000	+	218.238i	−0.329843	+	0.571305i
$383$	−360.075	+	207.889i	−0.940144	+	0.542792i	−0.890005	−	0.455950i	$-0.849300\pi$
$383$	−360.075	+	207.889i	−0.940144	+	0.542792i	−0.0501383	+	0.998742i	$0.515966\pi$
$384$	32.0000	−	11.3137i	0.0833333	−	0.0294628i
$385$		0			0
$386$		−	137.179i		−	0.355385i
$387$	−260.368	−	100.246i	−0.672786	−	0.259034i
$388$	166.000	−	287.520i	0.427835	−	0.741032i
$389$	−330.681	−	190.919i	−0.850080	−	0.490794i	0.0105979	−	0.999944i	$-0.496627\pi$
$389$	−330.681	−	190.919i	−0.850080	−	0.490794i	−0.860678	+	0.509150i	$0.829960\pi$
$390$	−23.3939	+	27.3629i	−0.0599843	+	0.0701612i
$391$	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	−0.991926	−	0.126822i	$-0.959522\pi$
$397$	−240.500	−	416.558i	−0.605793	−	1.04927i	0.386132	−	0.922443i	$-0.373811\pi$
$398$			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	$-0.697023\pi$
$401$	−66.1362	+	38.1838i	−0.164928	+	0.0952214i	0.415264	+	0.909701i	$0.363689\pi$
$402$	50.3916	−	271.129i	0.125352	−	0.674449i
$403$	−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
$408$	−46.7878	+	54.7257i	−0.114676	+	0.134132i
$409$	−24.5000	+	42.4352i	−0.0599022	+	0.103754i	−0.894421	−	0.447225i	$-0.852412\pi$
$409$	−24.5000	+	42.4352i	−0.0599022	+	0.103754i	0.834519	+	0.550979i	$0.185746\pi$
$410$	352.727	+	203.647i	0.860309	+	0.496699i
$411$	−425.666	−	363.923i	−1.03568	−	0.885458i
$412$	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
$417$	333.292	+	61.9453i	0.799262	+	0.148550i
$418$		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
$423$	377.196	−	59.3537i	0.891717	−	0.140316i
$424$	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	$-0.465572\pi$
$431$	−301.287	−	173.948i	−0.699042	−	0.403592i	−0.806991	+	0.590564i	$0.798905\pi$
$432$	−2.98979	+	107.959i	−0.00692082	+	0.249904i
$433$	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
$438$	75.1997	−	404.607i	0.171689	−	0.923761i
$439$	187.000	+	323.894i	0.425968	+	0.737798i	0.996510	−	0.0834699i	$-0.0266002\pi$
$439$	187.000	+	323.894i	0.425968	+	0.737798i	−0.570542	+	0.821268i	$0.693267\pi$
$440$		0			0
$441$		0			0
$442$	12.0000			0.0271493
$443$	−521.741	+	301.227i	−1.17775	+	0.679972i	−0.955492	−	0.295017i	$-0.904675\pi$
$443$	−521.741	+	301.227i	−1.17775	+	0.679972i	−0.222254	+	0.974989i	$0.571341\pi$
$444$	−5.89898	−	1.09638i	−0.0132860	−	0.00246932i
$445$	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	$-0.0150443\pi$
$450$	214.941	−	558.264i	0.477647	−	1.24059i
$451$		0			0
$452$	−279.242	−	161.220i	−0.617792	−	0.356682i
$453$	−113.070	+	132.254i	−0.249604	+	0.291951i
$454$	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	0.502185	−	0.864760i	$-0.332530\pi$
$457$	−227.500	−	394.042i	−0.497812	−	0.862235i	−0.999997	+	0.00252486i	$0.999196\pi$
$458$	−1.22474	−	0.707107i	−0.00267412	−	0.00154390i
$459$	−109.015	−	201.504i	−0.237505	−	0.439006i
$460$	−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
$465$	32.5607	−	175.191i	0.0700230	−	0.376754i
$466$	−234.000	+	405.300i	−0.502146	+	0.869742i
$467$	536.438	−	309.713i	1.14869	−	0.663197i	0.200122	−	0.979771i	$-0.435866\pi$
$467$	536.438	−	309.713i	1.14869	−	0.663197i	0.948568	+	0.316574i	$0.102533\pi$
$468$	14.0000	−	11.3137i	0.0299145	−	0.0241746i
$469$		0			0
$470$		−	509.117i		−	1.08323i
$471$	230.040	−	269.068i	0.488407	−	0.571270i
$472$	12.0000	−	20.7846i	0.0254237	−	0.0440352i
$473$		0			0
$474$	−332.149	−	283.970i	−0.700736	−	0.599094i
$475$	−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	$-0.580028\pi$
$479$	−580.529	−	335.169i	−1.21196	−	0.699726i	−0.963186	+	0.268836i	$0.913361\pi$
$480$	141.576	+	26.3130i	0.294949	+	0.0548188i
$481$	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
$486$	−317.164	−	132.308i	−0.652600	−	0.272238i
$487$	231.500	−	400.970i	0.475359	−	0.823347i	−0.524242	−	0.851569i	$-0.675651\pi$
$487$	231.500	−	400.970i	0.475359	−	0.823347i	0.999602	+	0.0282226i	$0.00898473\pi$
$488$	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	$-0.118218\pi$
$492$	−154.788	−	132.336i	−0.314609	−	0.268975i
$493$	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	0.999111	+	0.0421660i	$0.0134258\pi$
$499$	267.500	+	463.324i	0.536072	+	0.928504i	−0.463038	+	0.886338i	$0.653241\pi$
$500$	−323.333	−	186.676i	−0.646665	−	0.373352i
$501$	79.0760	−	425.463i	0.157836	−	0.849228i
$502$	−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
$507$	495.514	+	92.0956i	0.977346	+	0.181648i
$508$	113.000	−	195.722i	0.222441	−	0.385279i
$509$	551.135	−	318.198i	1.08278	−	0.625144i	0.151135	−	0.988513i	$-0.451707\pi$
$509$	551.135	−	318.198i	1.08278	−	0.625144i	0.931645	+	0.363370i	$0.118374\pi$
$510$	−288.000	+	101.823i	−0.564706	+	0.199654i
$511$		0			0
$512$			22.6274i			0.0441942i
$513$	−23.1709	+	836.679i	−0.0451675	+	1.63095i
$514$	−198.000	+	342.946i	−0.385214	+	0.667210i
$515$	477.650	+	275.772i	0.927477	+	0.535479i
$516$	120.868	−	141.375i	0.234241	−	0.273982i
$517$		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	$-0.120917\pi$
$521$	558.484	+	322.441i	1.07195	+	0.618888i	0.143233	+	0.989689i	$0.454250\pi$
$522$	−33.5755	−	213.375i	−0.0643209	−	0.408763i
$523$	344.500	+	596.692i	0.658700	+	1.14090i	0.980952	+	0.194248i	$0.0622266\pi$
$523$	344.500	+	596.692i	0.658700	+	1.14090i	−0.322253	+	0.946654i	$0.604440\pi$
$524$			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
$534$	−327.514	+	383.080i	−0.613323	+	0.717379i
$535$	684.000	−	1184.72i	1.27850	−	2.21444i
$536$	159.217	+	91.9239i	0.297046	+	0.171500i
$537$	−367.621	−	314.297i	−0.684583	−	0.585284i
$538$	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	−0.999327	−	0.0366729i	$-0.988324\pi$
$541$	−287.500	−	497.965i	−0.531423	−	0.920452i	0.467904	−	0.883779i	$-0.345009\pi$
$542$	−306.186	−	176.777i	−0.564919	−	0.326156i
$543$	634.140	+	117.860i	1.16785	+	0.217054i
$544$	−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
$549$	69.9490	+	444.530i	0.127412	+	0.809709i
$550$		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
$555$	−19.3485	−	16.5420i	−0.0348621	−	0.0298053i
$556$	−113.000	+	195.722i	−0.203237	+	0.352018i
$557$	117.576	+	67.8823i	0.211087	+	0.121871i	0.601817	−	0.798634i	$-0.294444\pi$
$557$	117.576	+	67.8823i	0.211087	+	0.121871i	−0.390729	+	0.920506i	$0.627777\pi$
$558$	−32.0125	+	83.1457i	−0.0573701	+	0.149007i
$559$	−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	$-0.513037\pi$
$563$	−521.741	−	301.227i	−0.926716	−	0.535040i	−0.885772	+	0.464121i	$0.846370\pi$
$564$	−46.5153	+	250.273i	−0.0824739	+	0.443746i
$565$	−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	$-0.864237\pi$
$569$	−573.181	+	330.926i	−1.00735	+	0.581592i	−0.0969334	+	0.995291i	$0.530903\pi$
$570$	1097.21	+	203.926i	1.92493	+	0.357765i
$571$	−56.5000	+	97.8609i	−0.0989492	+	0.171385i	−0.911250	−	0.411854i	$-0.864881\pi$
$571$	−56.5000	+	97.8609i	−0.0989492	+	0.171385i	0.812301	+	0.583239i	$0.198215\pi$
$572$		0			0
$573$	504.000	−	178.191i	0.879581	−	0.310979i
$574$		0			0
$575$		−	398.808i		−	0.693580i
$576$	−67.1918	−	25.8700i	−0.116652	−	0.0449132i
$577$	−60.5000	+	104.789i	−0.104853	+	0.181610i	−0.913678	−	0.406439i	$-0.866770\pi$
$577$	−60.5000	+	104.789i	−0.104853	+	0.181610i	0.808825	+	0.588049i	$0.200104\pi$
$578$	−265.770	−	153.442i	−0.459809	−	0.265471i
$579$	−189.101	+	221.183i	−0.326598	+	0.382009i
$580$	−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
$585$	75.4393	−	11.8707i	0.128956	−	0.0202919i
$586$	−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
$591$	−200.016	+	1076.17i	−0.338436	+	1.82093i
$592$	2.00000	−	3.46410i	0.00337838	−	0.00585152i
$593$	−426.211	+	246.073i	−0.718737	+	0.414963i	−0.814288	−	0.580461i	$-0.802872\pi$
$593$	−426.211	+	246.073i	−0.718737	+	0.414963i	0.0955505	+	0.995425i	$0.469539\pi$
$594$		0			0
$595$		0			0
$596$			135.765i			0.227793i
$597$	206.646	−	241.705i	0.346141	−	0.404867i
$598$	6.00000	−	10.3923i	0.0100334	−	0.0173784i
$599$	88.1816	+	50.9117i	0.147215	+	0.0849945i	0.571798	−	0.820394i	$-0.306246\pi$
$599$	88.1816	+	50.9117i	0.147215	+	0.0849945i	−0.424583	+	0.905389i	$0.639579\pi$
$600$	303.126	+	259.158i	0.505210	+	0.431929i
$601$	−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
$606$	566.302	+	105.252i	0.934492	+	0.173683i
$607$	56.5000	+	97.8609i	0.0930807	+	0.161221i	0.908806	−	0.417219i	$-0.136995\pi$
$607$	56.5000	+	97.8609i	0.0930807	+	0.161221i	−0.815725	+	0.578440i	$0.803662\pi$
$608$			175.362i			0.288425i
$609$		0			0
$610$	600.000			0.983607
$611$	36.7423	−	21.2132i	0.0601348	−	0.0347188i
$612$	150.879	−	23.7415i	0.246534	−	0.0387933i
$613$	287.000	−	497.099i	0.468189	−	0.810928i	−0.531150	−	0.847278i	$-0.678240\pi$
$613$	287.000	−	497.099i	0.468189	−	0.810928i	0.999339	+	0.0363503i	$0.0115732\pi$
$614$	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	$-0.180196\pi$
$618$	−209.608	−	179.205i	−0.339172	−	0.289975i
$619$	476.500	−	825.322i	0.769790	−	1.33332i	−0.167887	−	0.985806i	$-0.553694\pi$
$619$	476.500	−	825.322i	0.769790	−	1.33332i	0.937677	−	0.347509i	$-0.112972\pi$
$620$	102.879	+	59.3970i	0.165933	+	0.0958016i
$621$	−229.015	−	6.34231i	−0.368784	−	0.0102131i
$622$	−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
$633$	−182.868	−	33.9877i	−0.288892	−	0.0536930i
$634$	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
$639$	−192.075	+	498.874i	−0.300587	+	0.780710i
$640$	−48.0000	+	83.1384i	−0.0750000	+	0.129904i
$641$	−933.256	−	538.815i	−1.45594	−	0.840586i	−0.457129	−	0.889400i	$-0.651122\pi$
$641$	−933.256	−	538.815i	−1.45594	−	0.840586i	−0.998808	+	0.0488147i	$0.984456\pi$
$642$	−444.484	+	519.894i	−0.692342	+	0.809804i
$643$	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	$-0.248854\pi$
$647$	293.939	+	169.706i	0.454310	+	0.262296i	−0.255339	+	0.966852i	$0.582187\pi$
$648$	153.641	−	169.948i	0.237101	−	0.262266i
$649$		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	$-0.831053\pi$
$653$	−558.484	+	322.441i	−0.855258	+	0.493784i	0.00716327	+	0.999974i	$0.497720\pi$
$654$	129.468	−	696.592i	0.197963	−	1.06513i
$655$	−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	0.327754	+	0.944763i	$0.393708\pi$
$661$	−432.500	+	749.112i	−0.654312	+	1.13330i	−0.982066	+	0.188538i	$0.939625\pi$
$662$	−638.092	−	368.403i	−0.963885	−	0.556499i
$663$	−19.3485	−	16.5420i	−0.0291832	−	0.0249502i
$664$	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
$669$	−595.797	−	110.734i	−0.890578	−	0.165522i
$670$	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
$675$	−1116.13	+	603.833i	−1.65353	+	0.894568i
$676$	−168.000	+	290.985i	−0.248521	+	0.430450i
$677$	279.242	−	161.220i	0.412469	−	0.238139i	−0.279381	−	0.960180i	$-0.590129\pi$
$677$	279.242	−	161.220i	0.412469	−	0.238139i	0.691850	+	0.722041i	$0.256796\pi$
$678$	228.000	+	644.881i	0.336283	+	0.951152i
$679$		0			0
$680$		−	203.647i		−	0.299481i
$681$	−38.6969	−	33.0839i	−0.0568237	−	0.0485814i
$682$		0			0
$683$	683.408	+	394.566i	1.00060	+	0.577695i	0.908425	−	0.418048i	$-0.137286\pi$
$683$	683.408	+	394.566i	1.00060	+	0.577695i	0.0921720	+	0.995743i	$0.470619\pi$
$684$	−520.737	−	200.493i	−0.761311	−	0.293118i
$685$	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
$690$	−55.8184	+	300.327i	−0.0808962	+	0.435257i
$691$	92.5000	+	160.215i	0.133864	+	0.231859i	0.925163	−	0.379570i	$-0.123928\pi$
$691$	92.5000	+	160.215i	0.133864	+	0.231859i	−0.791299	+	0.611429i	$0.790595\pi$
$692$		−	152.735i		−	0.220715i
$693$		0			0
$694$	−156.000			−0.224784
$695$	−830.377	+	479.418i	−1.19479	+	0.689811i
$696$	141.576	+	26.3130i	0.203413	+	0.0378061i
$697$	−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	$-0.0212072\pi$
$702$	−38.1691	−	1.05705i	−0.0543720	−	0.00150577i
$703$	15.5000	−	26.8468i	0.0220484	−	0.0381889i
$704$		0			0
$705$	−701.816	+	820.886i	−0.995484	+	1.16438i
$706$	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	0.789476	−	0.613782i	$-0.210352\pi$
$709$	−97.0000	−	168.009i	−0.136812	−	0.236966i	−0.926288	+	0.376815i	$0.877019\pi$
$710$	617.271	+	356.382i	0.869396	+	0.501946i
$711$	144.095	+	915.732i	0.202665	+	1.28795i
$712$	−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
$717$	251.183	−	1351.47i	0.350324	−	1.88490i
$718$	288.000	−	498.831i	0.401114	−	0.694750i
$719$	338.030	−	195.161i	0.470139	−	0.271435i	−0.246159	−	0.969229i	$-0.579169\pi$
$719$	338.030	−	195.161i	0.470139	−	0.271435i	0.716298	+	0.697795i	$0.245835\pi$
$720$	−192.000	−	237.588i	−0.266667	−	0.329983i
$721$		0			0
$722$			848.528i			1.17525i
$723$	42.8888	−	50.1653i	0.0593206	−	0.0693849i
$724$	−215.000	+	372.391i	−0.296961	+	0.514352i
$725$	−690.756	−	398.808i	−0.952767	−	0.550080i
$726$	390.194	+	333.596i	0.537457	+	0.459499i
$727$	−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
$732$	−294.949	−	54.8188i	−0.402936	−	0.0748891i
$733$	203.500	+	352.472i	0.277626	+	0.480863i	0.970794	−	0.239913i	$-0.0771190\pi$
$733$	203.500	+	352.472i	0.277626	+	0.480863i	−0.693168	+	0.720776i	$0.743786\pi$
$734$			756.604i			1.03080i
$735$		0			0
$736$	−48.0000			−0.0652174
$737$		0			0
$738$	67.1510	+	426.749i	0.0909905	+	0.578251i
$739$	−380.500	+	659.045i	−0.514885	+	0.891807i	0.484966	+	0.874533i	$0.338832\pi$
$739$	−380.500	+	659.045i	−0.514885	+	0.891807i	−0.999851	+	0.0172738i	$0.994501\pi$
$740$	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	$-0.126934\pi$
$744$	−45.1464	−	38.5979i	−0.0606807	−	0.0518789i
$745$	−288.000	+	498.831i	−0.386577	+	0.669571i
$746$	471.527	+	272.236i	0.632073	+	0.364928i
$747$	−137.196	+	356.339i	−0.183663	+	0.477026i
$748$		0			0
$749$		0			0
$750$	264.000	+	746.705i	0.352000	+	0.995606i
$751$	−344.500	−	596.692i	−0.458722	−	0.794529i	0.540172	−	0.841555i	$-0.318359\pi$
$751$	−344.500	−	596.692i	−0.458722	−	0.794529i	−0.998894	+	0.0470253i	$0.985026\pi$
$752$	−146.969	−	84.8528i	−0.195438	−	0.112836i
$753$	−97.6821	+	525.572i	−0.129724	+	0.697971i
$754$	−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	$-0.927303\pi$
$761$	−962.649	+	555.786i	−1.26498	+	0.730336i	−0.290946	+	0.956740i	$0.593970\pi$
$762$	−452.000	+	159.806i	−0.593176	+	0.209719i
$763$		0			0
$764$			356.382i			0.466468i
$765$	604.727	+	232.830i	0.790492	+	0.304353i
$766$	−294.000	+	509.223i	−0.383812	+	0.664782i
$767$	7.34847	+	4.24264i	0.00958079	+	0.00553147i
$768$	31.1918	−	36.4838i	0.0406144	−	0.0475050i
$769$	−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	$-0.429113\pi$
$773$	−396.817	−	229.103i	−0.513347	−	0.296381i	−0.734208	+	0.678924i	$0.762447\pi$
$774$	−389.770	+	61.3321i	−0.503578	+	0.0792405i
$775$	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
$780$	−9.30306	+	50.0545i	−0.0119270	+	0.0641724i
$781$		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
$786$	233.939	−	273.629i	0.297632	−	0.348128i
$787$	−293.000	+	507.491i	−0.372300	+	0.644842i	−0.989919	−	0.141635i	$-0.954764\pi$
$787$	−293.000	+	507.491i	−0.372300	+	0.644842i	0.617619	+	0.786477i	$0.288097\pi$
$788$	−631.968	−	364.867i	−0.801990	−	0.463029i
$789$	232.182	+	198.504i	0.294273	+	0.251589i
$790$	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
$795$	−637.090	−	118.409i	−0.801371	−	0.148942i
$796$	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
$801$	1056.15	−	166.190i	1.31854	−	0.207479i
$802$	−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
$807$	−967.423	−	827.098i	−1.19879	−	1.02491i
$808$	−192.000	+	332.554i	−0.237624	+	0.411576i
$809$	698.105	+	403.051i	0.862923	+	0.498209i	0.864990	−	0.501789i	$-0.167325\pi$
$809$	698.105	+	403.051i	0.862923	+	0.498209i	−0.00206714	+	0.999998i	$0.500658\pi$
$810$	925.029	−	298.507i	1.14201	−	0.368527i
$811$	−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
$816$	−18.6061	+	100.109i	−0.0228016	+	0.122683i
$817$	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	0.774490	−	0.632586i	$-0.218006\pi$
$821$	1403.56	−	810.344i	1.70957	−	0.987021i	0.935081	−	0.354435i	$-0.115327\pi$
$822$	−778.665	−	144.722i	−0.947281	−	0.176060i
$823$	581.000	−	1006.32i	0.705954	−	1.22275i	−0.260392	−	0.965503i	$-0.583852\pi$
$823$	581.000	−	1006.32i	0.705954	−	1.22275i	0.966346	−	0.257245i	$-0.0828147\pi$
$824$	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	$0.972204\pi$
$828$	54.8786	−	142.535i	0.0662785	−	0.172144i
$829$	623.500	−	1079.93i	0.752111	−	1.30269i	−0.194687	−	0.980865i	$-0.562369\pi$
$829$	623.500	−	1079.93i	0.752111	−	1.30269i	0.946798	−	0.321829i	$-0.104298\pi$
$830$	440.908	+	254.558i	0.531215	+	0.306697i
$831$	746.655	−	873.332i	0.898501	−	1.05094i
$832$	−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
$837$	166.232	−	89.9326i	0.198605	−	0.107446i
$838$	−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
$843$	97.6821	−	525.572i	0.115874	−	0.623455i
$844$	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
$849$	−594.594	+	695.473i	−0.700347	+	0.819167i
$850$	282.000	−	488.438i	0.331765	−	0.574633i
$851$	7.34847	+	4.24264i	0.00863510	+	0.00498548i
$852$	−270.879	−	231.588i	−0.317933	−	0.271816i
$853$	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	$-0.560023\pi$
$857$	−969.998	−	560.029i	−1.13185	−	0.653476i	−0.944400	+	0.328798i	$0.893356\pi$
$858$		0			0
$859$	−545.000	−	943.968i	−0.634459	−	1.09891i	−0.986630	−	0.162979i	$-0.947890\pi$
$859$	−545.000	−	943.968i	−0.634459	−	1.09891i	0.352171	−	0.935936i	$-0.385444\pi$
$860$			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	$-0.433562\pi$
$863$	999.392	−	576.999i	1.15804	−	0.668597i	0.950834	+	0.309700i	$0.100229\pi$
$864$	72.6765	+	134.336i	0.0841164	+	0.155481i
$865$	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
$870$	464.363	+	397.007i	0.533751	+	0.456330i
$871$	−32.5000	+	56.2917i	−0.0373134	+	0.0646288i
$872$	409.065	+	236.174i	0.469111	+	0.270841i
$873$	1394.23	+	536.803i	1.59706	+	0.614894i
$874$	−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	0.878840	−	0.477116i	$-0.158318\pi$
$877$	23.0000	+	39.8372i	0.0262258	+	0.0454244i	−0.852615	+	0.522540i	$0.824984\pi$
$878$	458.055	+	264.458i	0.521702	+	0.301205i
$879$	−74.4245	+	400.436i	−0.0846695	+	0.455559i
$880$		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
$885$	−212.363	−	39.4695i	−0.239958	−	0.0445984i
$886$	−426.000	+	737.854i	−0.480813	+	0.832792i
$887$	1219.85	−	704.278i	1.37525	−	0.794000i	0.383666	−	0.923472i	$-0.374661\pi$
$887$	1219.85	−	704.278i	1.37525	−	0.794000i	0.991583	+	0.129472i	$0.0413281\pi$
$888$	−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
$894$	187.151	−	218.903i	0.209341	−	0.244858i
$895$	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
$900$	−131.504	−	835.717i	−0.146116	−	0.928574i
$901$	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
$906$	−44.9648	+	241.930i	−0.0496300	+	0.267031i
$907$	87.5000	−	151.554i	0.0964719	−	0.167094i	−0.813750	−	0.581215i	$-0.802578\pi$
$907$	87.5000	−	151.554i	0.0964719	−	0.167094i	0.910222	+	0.414121i	$0.135911\pi$
$908$	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	$0.706752\pi$
$912$	241.737	−	282.750i	0.265062	−	0.310032i
$913$		0			0
$914$	−557.259	−	321.734i	−0.609692	−	0.352006i
$915$	−967.423	−	827.098i	−1.05729	−	0.903933i
$916$	−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	−0.993284	−	0.115704i	$-0.963088\pi$
$919$	−548.500	−	950.030i	−0.596844	−	1.03376i	0.396439	−	0.918061i	$-0.370246\pi$
$920$	−176.363	−	101.823i	−0.191699	−	0.110678i
$921$	−586.948	−	109.089i	−0.637295	−	0.118447i
$922$	−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
$927$	90.9337	+	577.889i	0.0980946	+	0.623397i
$928$	−48.0000	+	83.1384i	−0.0517241	+	0.0895888i
$929$	−492.347	+	284.257i	−0.529976	+	0.305982i	−0.741007	−	0.671498i	$-0.765651\pi$
$929$	−492.347	+	284.257i	−0.529976	+	0.305982i	0.211031	+	0.977479i	$0.432318\pi$
$930$	−84.0000	−	237.588i	−0.0903226	−	0.255471i
$931$		0			0
$932$			661.852i			0.710142i
$933$	1006.12	+	860.182i	1.07837	+	0.921953i
$934$	438.000	−	758.638i	0.468951	−	0.812247i
$935$		0			0
$936$	9.14643	−	23.7559i	0.00977182	−	0.0253802i
$937$	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	$-0.268300\pi$
$941$	330.681	+	190.919i	0.351415	+	0.202889i	−0.313894	+	0.949458i	$0.601634\pi$
$942$	91.4801	−	492.203i	0.0971126	−	0.522508i
$943$	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	−0.537384	+	0.843338i	$0.680587\pi$
$947$	−1455.00	+	840.043i	−1.53643	+	0.887057i	−0.999044	+	0.0437190i	$0.986079\pi$
$948$	−607.595	−	112.927i	−0.640923	−	0.119121i
$949$	−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	$-0.0326500\pi$
$954$	302.363	+	116.415i	0.316943	+	0.122028i
$955$	−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
$963$	1433.35	−	225.544i	1.48842	−	0.234210i
$964$	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
$969$	−144.197	+	775.845i	−0.148811	+	0.800665i
$970$	996.000	−	1725.12i	1.02680	−	1.77848i
$971$	−492.347	+	284.257i	−0.507052	+	0.292747i	−0.731621	−	0.681712i	$-0.761236\pi$
$971$	−492.347	+	284.257i	−0.507052	+	0.292747i	0.224569	+	0.974458i	$0.427903\pi$
$972$	−482.000	+	62.2254i	−0.495885	+	0.0640179i
$973$		0			0
$974$		−	654.781i		−	0.672260i
$975$	−91.6260	+	107.171i	−0.0939754	+	0.109919i
$976$	100.000	−	173.205i	0.102459	−	0.177464i
$977$	1396.21	+	806.102i	1.42908	+	0.825079i	0.997048	−	0.0767807i	$-0.0244641\pi$
$977$	1396.21	+	806.102i	1.42908	+	0.825079i	0.432030	+	0.901859i	$0.357797\pi$
$978$	−341.823	−	292.241i	−0.349512	−	0.298815i
$979$		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	0.999787	+	0.0206186i	$0.00656358\pi$
$983$	1491.74	+	861.256i	1.51754	+	0.876151i	0.517750	+	0.855532i	$0.326770\pi$
$984$	−283.151	−	52.6261i	−0.287755	−	0.0534818i
$985$	−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	−0.546919	−	0.837185i	$-0.684200\pi$
$991$	447.500	−	775.093i	0.451564	−	0.782132i	0.998483	+	0.0550534i	$0.0175329\pi$
$992$	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
$996$	−193.485	−	165.420i	−0.194262	−	0.166084i
$997$	203.500	−	352.472i	0.204112	−	0.353533i	−0.745737	−	0.666240i	$-0.767903\pi$
$997$	203.500	−	352.472i	0.204112	−	0.353533i	0.949850	+	0.312707i	$0.101236\pi$
$998$	655.239	+	378.302i	0.656552	+	0.379060i
$999$	0.747449	−	26.9897i	0.000748197	−	0.0270167i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.h.a.11.1	✓	4	21.20	even	2
42.3.h.a.11.2	yes	4	7.6	odd	2
42.3.h.a.23.1	yes	4	7.5	odd	6
42.3.h.a.23.2	yes	4	21.5	even	6
294.3.b.b.197.1		2	21.17	even	6
294.3.b.b.197.2		2	7.3	odd	6
294.3.b.c.197.1		2	21.11	odd	6
294.3.b.c.197.2		2	7.4	even	3
294.3.h.b.263.1		4	3.2	odd	2	inner
294.3.h.b.263.2		4	1.1	even	1	trivial
294.3.h.b.275.1		4	7.2	even	3	inner
294.3.h.b.275.2		4	21.2	odd	6	inner
336.3.bn.c.65.1		4	84.47	odd	6
336.3.bn.c.65.2		4	28.19	even	6
336.3.bn.c.305.1		4	28.27	even	2
336.3.bn.c.305.2		4	84.83	odd	2

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)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(-2.94949 - 0.548188i) q^{3} +(1.00000 - 1.73205i) q^{4} +(7.34847 - 4.24264i) q^{5} +(-4.00000 + 1.41421i) q^{6} -2.82843i q^{8} +(8.39898 + 3.23375i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(-2.94949 - 0.548188i) q^{3} +(1.00000 - 1.73205i) q^{4} +(7.34847 - 4.24264i) q^{5} +(-4.00000 + 1.41421i) q^{6} -2.82843i q^{8} +(8.39898 + 3.23375i) q^{9} +(6.00000 - 10.3923i) q^{10} +(-3.89898 + 4.56048i) q^{12} +1.00000 q^{13} +(-24.0000 + 8.48528i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(7.34847 + 4.24264i) q^{17} +(12.5732 - 1.97846i) q^{18} +(-15.5000 - 26.8468i) q^{19} -16.9706i q^{20} +(7.34847 - 4.24264i) q^{23} +(-1.55051 + 8.34242i) q^{24} +(23.5000 - 40.7032i) q^{25} +(1.22474 - 0.707107i) q^{26} +(-23.0000 - 14.1421i) q^{27} -16.9706i q^{29} +(-23.3939 + 27.3629i) 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} +(-2.94949 - 0.548188i) q^{39} +(-12.0000 - 20.7846i) q^{40} +33.9411i q^{41} -31.0000 q^{43} +(75.4393 - 11.8707i) q^{45} +(6.00000 - 10.3923i) q^{46} +(36.7423 - 21.2132i) q^{47} +(4.00000 + 11.3137i) q^{48} -66.4680i q^{50} +(-19.3485 - 16.5420i) q^{51} +(1.00000 - 1.73205i) q^{52} +(22.0454 + 12.7279i) q^{53} +(-38.1691 - 1.05705i) q^{54} +(31.0000 + 87.6812i) q^{57} +(-12.0000 - 20.7846i) q^{58} +(7.34847 + 4.24264i) q^{59} +(-9.30306 + 50.0545i) 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} +(9.14643 - 23.7559i) q^{72} +(-48.5000 + 84.0045i) q^{73} +(1.22474 + 0.707107i) q^{74} +(-91.6260 + 107.171i) q^{75} -62.0000 q^{76} +(-4.00000 + 1.41421i) q^{78} +(51.5000 + 89.2006i) q^{79} +(-29.3939 - 16.9706i) q^{80} +(60.0857 + 54.3204i) q^{81} +(24.0000 + 41.5692i) q^{82} +42.4264i q^{83} +72.0000 q^{85} +(-37.9671 + 21.9203i) q^{86} +(-9.30306 + 50.0545i) q^{87} +(102.879 - 59.3970i) q^{89} +(84.0000 - 67.8823i) q^{90} -16.9706i q^{92} +(13.6464 - 15.9617i) q^{93} +(30.0000 - 51.9615i) q^{94} +(-227.803 - 131.522i) q^{95} +(12.8990 + 11.0280i) 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

L-functions

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