LMFDB - Embedded newform 294.3.b.b.197.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,3,Mod(197,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("294.197");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	294.b (of order $2$, degree $1$, 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:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.2
Root			$1.41421i$ of defining polynomial
Character	$\chi$	$=$	294.197
Dual form			294.3.b.b.197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(-1.00000 - 2.82843i) q^{3} -2.00000 q^{4} -8.48528i q^{5} +(4.00000 - 1.41421i) q^{6} -2.82843i q^{8} +(-7.00000 + 5.65685i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(-1.00000 - 2.82843i) q^{3} -2.00000 q^{4} -8.48528i q^{5} +(4.00000 - 1.41421i) q^{6} -2.82843i q^{8} +(-7.00000 + 5.65685i) q^{9} +12.0000 q^{10} +(2.00000 + 5.65685i) q^{12} -1.00000 q^{13} +(-24.0000 + 8.48528i) q^{15} +4.00000 q^{16} +8.48528i q^{17} +(-8.00000 - 9.89949i) q^{18} -31.0000 q^{19} +16.9706i q^{20} +8.48528i q^{23} +(-8.00000 + 2.82843i) q^{24} -47.0000 q^{25} -1.41421i q^{26} +(23.0000 + 14.1421i) q^{27} -16.9706i q^{29} +(-12.0000 - 33.9411i) q^{30} -7.00000 q^{31} +5.65685i q^{32} -12.0000 q^{34} +(14.0000 - 11.3137i) q^{36} -1.00000 q^{37} -43.8406i q^{38} +(1.00000 + 2.82843i) q^{39} -24.0000 q^{40} -33.9411i q^{41} -31.0000 q^{43} +(48.0000 + 59.3970i) q^{45} -12.0000 q^{46} -42.4264i q^{47} +(-4.00000 - 11.3137i) q^{48} -66.4680i q^{50} +(24.0000 - 8.48528i) q^{51} +2.00000 q^{52} -25.4558i q^{53} +(-20.0000 + 32.5269i) q^{54} +(31.0000 + 87.6812i) q^{57} +24.0000 q^{58} +8.48528i q^{59} +(48.0000 - 16.9706i) q^{60} +50.0000 q^{61} -9.89949i q^{62} -8.00000 q^{64} +8.48528i q^{65} +65.0000 q^{67} -16.9706i q^{68} +(24.0000 - 8.48528i) q^{69} +59.3970i q^{71} +(16.0000 + 19.7990i) q^{72} -97.0000 q^{73} -1.41421i q^{74} +(47.0000 + 132.936i) q^{75} +62.0000 q^{76} +(-4.00000 + 1.41421i) q^{78} -103.000 q^{79} -33.9411i q^{80} +(17.0000 - 79.1960i) q^{81} +48.0000 q^{82} -42.4264i q^{83} +72.0000 q^{85} -43.8406i q^{86} +(-48.0000 + 16.9706i) q^{87} -118.794i q^{89} +(-84.0000 + 67.8823i) q^{90} -16.9706i q^{92} +(7.00000 + 19.7990i) q^{93} +60.0000 q^{94} +263.044i q^{95} +(16.0000 - 5.65685i) q^{96} -166.000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 4 q^{4} + 8 q^{6} - 14 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 - 4 * q^4 + 8 * q^6 - 14 * q^9	$ 2 q - 2 q^{3} - 4 q^{4} + 8 q^{6} - 14 q^{9} + 24 q^{10} + 4 q^{12} - 2 q^{13} - 48 q^{15} + 8 q^{16} - 16 q^{18} - 62 q^{19} - 16 q^{24} - 94 q^{25} + 46 q^{27} - 24 q^{30} - 14 q^{31} - 24 q^{34} + 28 q^{36} - 2 q^{37} + 2 q^{39} - 48 q^{40} - 62 q^{43} + 96 q^{45} - 24 q^{46} - 8 q^{48} + 48 q^{51} + 4 q^{52} - 40 q^{54} + 62 q^{57} + 48 q^{58} + 96 q^{60} + 100 q^{61} - 16 q^{64} + 130 q^{67} + 48 q^{69} + 32 q^{72} - 194 q^{73} + 94 q^{75} + 124 q^{76} - 8 q^{78} - 206 q^{79} + 34 q^{81} + 96 q^{82} + 144 q^{85} - 96 q^{87} - 168 q^{90} + 14 q^{93} + 120 q^{94} + 32 q^{96} - 332 q^{97}+O(q^{100}) $ 2 * q - 2 * q^3 - 4 * q^4 + 8 * q^6 - 14 * q^9 + 24 * q^10 + 4 * q^12 - 2 * q^13 - 48 * q^15 + 8 * q^16 - 16 * q^18 - 62 * q^19 - 16 * q^24 - 94 * q^25 + 46 * q^27 - 24 * q^30 - 14 * q^31 - 24 * q^34 + 28 * q^36 - 2 * q^37 + 2 * q^39 - 48 * q^40 - 62 * q^43 + 96 * q^45 - 24 * q^46 - 8 * q^48 + 48 * q^51 + 4 * q^52 - 40 * q^54 + 62 * q^57 + 48 * q^58 + 96 * q^60 + 100 * q^61 - 16 * q^64 + 130 * q^67 + 48 * q^69 + 32 * q^72 - 194 * q^73 + 94 * q^75 + 124 * q^76 - 8 * q^78 - 206 * q^79 + 34 * q^81 + 96 * q^82 + 144 * q^85 - 96 * q^87 - 168 * q^90 + 14 * q^93 + 120 * q^94 + 32 * q^96 - 332 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$199$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$3$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$4$	−2.00000			−0.500000
$5$		−	8.48528i		−	1.69706i	−0.529150	−	0.848528i	$-0.677489\pi$
$5$		−	8.48528i		−	1.69706i	0.529150	−	0.848528i	$-0.322511\pi$
$6$	4.00000	−	1.41421i	0.666667	−	0.235702i
$7$		0			0
$7$		0			0
$8$		−	2.82843i		−	0.353553i
$9$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$10$	12.0000			1.20000
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$	2.00000	+	5.65685i	0.166667	+	0.471405i
$13$	−1.00000			−0.0769231			−0.0384615	−	0.999260i	$-0.512246\pi$
$13$	−1.00000			−0.0769231			−0.0384615	+	0.999260i	$0.512246\pi$
$14$		0			0
$15$	−24.0000	+	8.48528i	−1.60000	+	0.565685i
$16$	4.00000			0.250000
$17$			8.48528i			0.499134i	0.968358	+	0.249567i	$0.0802883\pi$
$17$			8.48528i			0.499134i	−0.968358	+	0.249567i	$0.919712\pi$
$18$	−8.00000	−	9.89949i	−0.444444	−	0.549972i
$19$	−31.0000			−1.63158			−0.815789	−	0.578349i	$-0.803697\pi$
$19$	−31.0000			−1.63158			−0.815789	+	0.578349i	$0.803697\pi$
$20$			16.9706i			0.848528i
$21$		0			0
$22$		0			0
$23$			8.48528i			0.368925i	0.982840	+	0.184463i	$0.0590545\pi$
$23$			8.48528i			0.368925i	−0.982840	+	0.184463i	$0.940946\pi$
$24$	−8.00000	+	2.82843i	−0.333333	+	0.117851i
$25$	−47.0000			−1.88000
$26$		−	1.41421i		−	0.0543928i
$27$	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	$-0.0945191\pi$
$30$	−12.0000	−	33.9411i	−0.400000	−	1.13137i
$31$	−7.00000			−0.225806			−0.112903	−	0.993606i	$-0.536015\pi$
$31$	−7.00000			−0.225806			−0.112903	+	0.993606i	$0.536015\pi$
$32$			5.65685i			0.176777i
$33$		0			0
$34$	−12.0000			−0.352941
$35$		0			0
$36$	14.0000	−	11.3137i	0.388889	−	0.314270i
$37$	−1.00000			−0.0270270			−0.0135135	−	0.999909i	$-0.504302\pi$
$37$	−1.00000			−0.0270270			−0.0135135	+	0.999909i	$0.504302\pi$
$38$		−	43.8406i		−	1.15370i
$39$	1.00000	+	2.82843i	0.0256410	+	0.0725238i
$40$	−24.0000			−0.600000
$41$		−	33.9411i		−	0.827832i	−0.910315	−	0.413916i	$-0.864161\pi$
$41$		−	33.9411i		−	0.827832i	0.910315	−	0.413916i	$-0.135839\pi$
$42$		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
$45$	48.0000	+	59.3970i	1.06667	+	1.31993i
$46$	−12.0000			−0.260870
$47$		−	42.4264i		−	0.902690i	−0.892350	−	0.451345i	$-0.850944\pi$
$47$		−	42.4264i		−	0.902690i	0.892350	−	0.451345i	$-0.149056\pi$
$48$	−4.00000	−	11.3137i	−0.0833333	−	0.235702i
$49$		0			0
$50$		−	66.4680i		−	1.32936i
$51$	24.0000	−	8.48528i	0.470588	−	0.166378i
$52$	2.00000			0.0384615
$53$		−	25.4558i		−	0.480299i	−0.970736	−	0.240149i	$-0.922804\pi$
$53$		−	25.4558i		−	0.480299i	0.970736	−	0.240149i	$-0.0771965\pi$
$54$	−20.0000	+	32.5269i	−0.370370	+	0.602350i
$55$		0			0
$56$		0			0
$57$	31.0000	+	87.6812i	0.543860	+	1.53827i
$58$	24.0000			0.413793
$59$			8.48528i			0.143818i	0.997411	+	0.0719092i	$0.0229092\pi$
$59$			8.48528i			0.143818i	−0.997411	+	0.0719092i	$0.977091\pi$
$60$	48.0000	−	16.9706i	0.800000	−	0.282843i
$61$	50.0000			0.819672			0.409836	−	0.912159i	$-0.365586\pi$
$61$	50.0000			0.819672			0.409836	+	0.912159i	$0.365586\pi$
$62$		−	9.89949i		−	0.159669i
$63$		0			0
$64$	−8.00000			−0.125000
$65$			8.48528i			0.130543i
$66$		0			0
$67$	65.0000			0.970149			0.485075	−	0.874473i	$-0.338792\pi$
$67$	65.0000			0.970149			0.485075	+	0.874473i	$0.338792\pi$
$68$		−	16.9706i		−	0.249567i
$69$	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	$0.862630\pi$
$72$	16.0000	+	19.7990i	0.222222	+	0.274986i
$73$	−97.0000			−1.32877			−0.664384	−	0.747392i	$-0.731306\pi$
$73$	−97.0000			−1.32877			−0.664384	+	0.747392i	$0.731306\pi$
$74$		−	1.41421i		−	0.0191110i
$75$	47.0000	+	132.936i	0.626667	+	1.77248i
$76$	62.0000			0.815789
$77$		0			0
$78$	−4.00000	+	1.41421i	−0.0512821	+	0.0181309i
$79$	−103.000			−1.30380			−0.651899	−	0.758306i	$-0.726027\pi$
$79$	−103.000			−1.30380			−0.651899	+	0.758306i	$0.726027\pi$
$80$		−	33.9411i		−	0.424264i
$81$	17.0000	−	79.1960i	0.209877	−	0.977728i
$82$	48.0000			0.585366
$83$		−	42.4264i		−	0.511162i	−0.966788	−	0.255581i	$-0.917733\pi$
$83$		−	42.4264i		−	0.511162i	0.966788	−	0.255581i	$-0.0822667\pi$
$84$		0			0
$85$	72.0000			0.847059
$86$		−	43.8406i		−	0.509775i
$87$	−48.0000	+	16.9706i	−0.551724	+	0.195064i
$88$		0			0
$89$		−	118.794i		−	1.33476i	−0.744716	−	0.667382i	$-0.767415\pi$
$89$		−	118.794i		−	1.33476i	0.744716	−	0.667382i	$-0.232585\pi$
$90$	−84.0000	+	67.8823i	−0.933333	+	0.754247i
$91$		0			0
$92$		−	16.9706i		−	0.184463i
$93$	7.00000	+	19.7990i	0.0752688	+	0.212892i
$94$	60.0000			0.638298
$95$			263.044i			2.76888i
$96$	16.0000	−	5.65685i	0.166667	−	0.0589256i
$97$	−166.000			−1.71134			−0.855670	−	0.517522i	$-0.826855\pi$
$97$	−166.000			−1.71134			−0.855670	+	0.517522i	$0.826855\pi$
$98$		0			0
$99$		0			0
$100$	94.0000			0.940000
$101$		−	135.765i		−	1.34420i	−0.740459	−	0.672101i	$-0.765392\pi$
$101$		−	135.765i		−	1.34420i	0.740459	−	0.672101i	$-0.234608\pi$
$102$	12.0000	+	33.9411i	0.117647	+	0.332756i
$103$	65.0000			0.631068			0.315534	−	0.948914i	$-0.397816\pi$
$103$	65.0000			0.631068			0.315534	+	0.948914i	$0.397816\pi$
$104$			2.82843i			0.0271964i
$105$		0			0
$106$	36.0000			0.339623
$107$			161.220i			1.50673i	0.657601	+	0.753366i	$0.271571\pi$
$107$			161.220i			1.50673i	−0.657601	+	0.753366i	$0.728429\pi$
$108$	−46.0000	−	28.2843i	−0.425926	−	0.261891i
$109$	167.000			1.53211			0.766055	−	0.642775i	$-0.222217\pi$
$109$	167.000			1.53211			0.766055	+	0.642775i	$0.222217\pi$
$110$		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	$-0.252830\pi$
$114$	−124.000	+	43.8406i	−1.08772	+	0.384567i
$115$	72.0000			0.626087
$116$			33.9411i			0.292596i
$117$	7.00000	−	5.65685i	0.0598291	−	0.0483492i
$118$	−12.0000			−0.101695
$119$		0			0
$120$	24.0000	+	67.8823i	0.200000	+	0.565685i
$121$	121.000			1.00000
$122$			70.7107i			0.579596i
$123$	−96.0000	+	33.9411i	−0.780488	+	0.275944i
$124$	14.0000			0.112903
$125$			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	$0.353246\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	31.0000	+	87.6812i	0.240310	+	0.679700i
$130$	−12.0000			−0.0923077
$131$			84.8528i			0.647731i	0.946103	+	0.323866i	$0.104983\pi$
$131$			84.8528i			0.647731i	−0.946103	+	0.323866i	$0.895017\pi$
$132$		0			0
$133$		0			0
$134$			91.9239i			0.685999i
$135$	120.000	−	195.161i	0.888889	−	1.44564i
$136$	24.0000			0.176471
$137$		−	186.676i		−	1.36260i	−0.732004	−	0.681300i	$-0.761415\pi$
$137$		−	186.676i		−	1.36260i	0.732004	−	0.681300i	$-0.238585\pi$
$138$	12.0000	+	33.9411i	0.0869565	+	0.245950i
$139$	113.000			0.812950			0.406475	−	0.913662i	$-0.366758\pi$
$139$	113.000			0.812950			0.406475	+	0.913662i	$0.366758\pi$
$140$		0			0
$141$	−120.000	+	42.4264i	−0.851064	+	0.300897i
$142$	−84.0000			−0.591549
$143$		0			0
$144$	−28.0000	+	22.6274i	−0.194444	+	0.157135i
$145$	−144.000			−0.993103
$146$		−	137.179i		−	0.939580i
$147$		0			0
$148$	2.00000			0.0135135
$149$		−	67.8823i		−	0.455586i	−0.973710	−	0.227793i	$-0.926849\pi$
$149$		−	67.8823i		−	0.455586i	0.973710	−	0.227793i	$-0.0731509\pi$
$150$	−188.000	+	66.4680i	−1.25333	+	0.443120i
$151$	−58.0000			−0.384106			−0.192053	−	0.981385i	$-0.561515\pi$
$151$	−58.0000			−0.384106			−0.192053	+	0.981385i	$0.561515\pi$
$152$			87.6812i			0.576850i
$153$	−48.0000	−	59.3970i	−0.313725	−	0.388215i
$154$		0			0
$155$			59.3970i			0.383206i
$156$	−2.00000	−	5.65685i	−0.0128205	−	0.0362619i
$157$	−118.000			−0.751592			−0.375796	−	0.926702i	$-0.622631\pi$
$157$	−118.000			−0.751592			−0.375796	+	0.926702i	$0.622631\pi$
$158$		−	145.664i		−	0.921924i
$159$	−72.0000	+	25.4558i	−0.452830	+	0.160100i
$160$	48.0000			0.300000
$161$		0			0
$162$	112.000	+	24.0416i	0.691358	+	0.148405i
$163$	−106.000			−0.650307			−0.325153	−	0.945661i	$-0.605416\pi$
$163$	−106.000			−0.650307			−0.325153	+	0.945661i	$0.605416\pi$
$164$			67.8823i			0.413916i
$165$		0			0
$166$	60.0000			0.361446
$167$		−	144.250i		−	0.863771i	−0.901928	−	0.431886i	$-0.857848\pi$
$167$		−	144.250i		−	0.863771i	0.901928	−	0.431886i	$-0.142152\pi$
$168$		0			0
$169$	−168.000			−0.994083
$170$			101.823i			0.598961i
$171$	217.000	−	175.362i	1.26901	−	1.02551i
$172$	62.0000			0.360465
$173$		−	76.3675i		−	0.441431i	−0.975338	−	0.220715i	$-0.929161\pi$
$173$		−	76.3675i		−	0.441431i	0.975338	−	0.220715i	$-0.0708392\pi$
$174$	−24.0000	−	67.8823i	−0.137931	−	0.390128i
$175$		0			0
$176$		0			0
$177$	24.0000	−	8.48528i	0.135593	−	0.0479394i
$178$	168.000			0.943820
$179$		−	161.220i		−	0.900672i	−0.892859	−	0.450336i	$-0.851304\pi$
$179$		−	161.220i		−	0.900672i	0.892859	−	0.450336i	$-0.148696\pi$
$180$	−96.0000	−	118.794i	−0.533333	−	0.659966i
$181$	215.000			1.18785			0.593923	−	0.804522i	$-0.297579\pi$
$181$	215.000			1.18785			0.593923	+	0.804522i	$0.297579\pi$
$182$		0			0
$183$	−50.0000	−	141.421i	−0.273224	−	0.772794i
$184$	24.0000			0.130435
$185$			8.48528i			0.0458664i
$186$	−28.0000	+	9.89949i	−0.150538	+	0.0532231i
$187$		0			0
$188$			84.8528i			0.451345i
$189$		0			0
$190$	−372.000			−1.95789
$191$		−	178.191i		−	0.932937i	−0.884538	−	0.466468i	$-0.845526\pi$
$191$		−	178.191i		−	0.932937i	0.884538	−	0.466468i	$-0.154474\pi$
$192$	8.00000	+	22.6274i	0.0416667	+	0.117851i
$193$	−97.0000			−0.502591			−0.251295	−	0.967910i	$-0.580857\pi$
$193$	−97.0000			−0.502591			−0.251295	+	0.967910i	$0.580857\pi$
$194$		−	234.759i		−	1.21010i
$195$	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
$199$	−106.000			−0.532663			−0.266332	−	0.963881i	$-0.585812\pi$
$199$	−106.000			−0.532663			−0.266332	+	0.963881i	$0.585812\pi$
$200$			132.936i			0.664680i
$201$	−65.0000	−	183.848i	−0.323383	−	0.914665i
$202$	192.000			0.950495
$203$		0			0
$204$	−48.0000	+	16.9706i	−0.235294	+	0.0831890i
$205$	−288.000			−1.40488
$206$			91.9239i			0.446232i
$207$	−48.0000	−	59.3970i	−0.231884	−	0.286942i
$208$	−4.00000			−0.0192308
$209$		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	$0.453064\pi$
$212$			50.9117i			0.240149i
$213$	168.000	−	59.3970i	0.788732	−	0.278859i
$214$	−228.000			−1.06542
$215$			263.044i			1.22346i
$216$	40.0000	−	65.0538i	0.185185	−	0.301175i
$217$		0			0
$218$			236.174i			1.08337i
$219$	97.0000	+	274.357i	0.442922	+	1.25277i
$220$		0			0
$221$		−	8.48528i		−	0.0383949i
$222$	−4.00000	+	1.41421i	−0.0180180	+	0.00637033i
$223$	−202.000			−0.905830			−0.452915	−	0.891554i	$-0.649616\pi$
$223$	−202.000			−0.905830			−0.452915	+	0.891554i	$0.649616\pi$
$224$		0			0
$225$	329.000	−	265.872i	1.46222	−	1.18165i
$226$	228.000			1.00885
$227$			16.9706i			0.0747602i	0.999301	+	0.0373801i	$0.0119012\pi$
$227$			16.9706i			0.0747602i	−0.999301	+	0.0373801i	$0.988099\pi$
$228$	−62.0000	−	175.362i	−0.271930	−	0.769134i
$229$	−1.00000			−0.00436681			−0.00218341	−	0.999998i	$-0.500695\pi$
$229$	−1.00000			−0.00436681			−0.00218341	+	0.999998i	$0.500695\pi$
$230$			101.823i			0.442710i
$231$		0			0
$232$	−48.0000			−0.206897
$233$		−	330.926i		−	1.42028i	−0.704059	−	0.710142i	$-0.748631\pi$
$233$		−	330.926i		−	1.42028i	0.704059	−	0.710142i	$-0.251369\pi$
$234$	8.00000	+	9.89949i	0.0341880	+	0.0423055i
$235$	−360.000			−1.53191
$236$		−	16.9706i		−	0.0719092i
$237$	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	$0.591926\pi$
$240$	−96.0000	+	33.9411i	−0.400000	+	0.141421i
$241$	−22.0000			−0.0912863			−0.0456432	−	0.998958i	$-0.514534\pi$
$241$	−22.0000			−0.0912863			−0.0456432	+	0.998958i	$0.514534\pi$
$242$			171.120i			0.707107i
$243$	−241.000	+	31.1127i	−0.991770	+	0.128036i
$244$	−100.000			−0.409836
$245$		0			0
$246$	−48.0000	−	135.765i	−0.195122	−	0.551888i
$247$	31.0000			0.125506
$248$			19.7990i			0.0798346i
$249$	−120.000	+	42.4264i	−0.481928	+	0.170387i
$250$	−264.000			−1.05600
$251$			178.191i			0.709924i	0.934881	+	0.354962i	$0.115506\pi$
$251$			178.191i			0.709924i	−0.934881	+	0.354962i	$0.884494\pi$
$252$		0			0
$253$		0			0
$254$			159.806i			0.629158i
$255$	−72.0000	−	203.647i	−0.282353	−	0.798615i
$256$	16.0000			0.0625000
$257$			280.014i			1.08955i	0.838582	+	0.544775i	$0.183385\pi$
$257$			280.014i			1.08955i	−0.838582	+	0.544775i	$0.816615\pi$
$258$	−124.000	+	43.8406i	−0.480620	+	0.169925i
$259$		0			0
$260$		−	16.9706i		−	0.0652714i
$261$	96.0000	+	118.794i	0.367816	+	0.455149i
$262$	−120.000			−0.458015
$263$			101.823i			0.387161i	0.981084	+	0.193581i	$0.0620101\pi$
$263$			101.823i			0.387161i	−0.981084	+	0.193581i	$0.937990\pi$
$264$		0			0
$265$	−216.000			−0.815094
$266$		0			0
$267$	−336.000	+	118.794i	−1.25843	+	0.444921i
$268$	−130.000			−0.485075
$269$			424.264i			1.57719i	0.614913	+	0.788595i	$0.289191\pi$
$269$			424.264i			1.57719i	−0.614913	+	0.788595i	$0.710809\pi$
$270$	276.000	+	169.706i	1.02222	+	0.628539i
$271$	−250.000			−0.922509			−0.461255	−	0.887268i	$-0.652601\pi$
$271$	−250.000			−0.922509			−0.461255	+	0.887268i	$0.652601\pi$
$272$			33.9411i			0.124784i
$273$		0			0
$274$	264.000			0.963504
$275$		0			0
$276$	−48.0000	+	16.9706i	−0.173913	+	0.0614875i
$277$	383.000			1.38267			0.691336	−	0.722534i	$-0.257023\pi$
$277$	383.000			1.38267			0.691336	+	0.722534i	$0.257023\pi$
$278$			159.806i			0.574842i
$279$	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	$0.897302\pi$
$282$	−60.0000	−	169.706i	−0.212766	−	0.601793i
$283$	305.000			1.07774			0.538869	−	0.842389i	$-0.318852\pi$
$283$	305.000			1.07774			0.538869	+	0.842389i	$0.318852\pi$
$284$		−	118.794i		−	0.418289i
$285$	744.000	−	263.044i	2.61053	−	0.922960i
$286$		0			0
$287$		0			0
$288$	−32.0000	−	39.5980i	−0.111111	−	0.137493i
$289$	217.000			0.750865
$290$		−	203.647i		−	0.702230i
$291$	166.000	+	469.519i	0.570447	+	1.61347i
$292$	194.000			0.664384
$293$			135.765i			0.463360i	0.972792	+	0.231680i	$0.0744222\pi$
$293$			135.765i			0.463360i	−0.972792	+	0.231680i	$0.925578\pi$
$294$		0			0
$295$	72.0000			0.244068
$296$			2.82843i			0.00955550i
$297$		0			0
$298$	96.0000			0.322148
$299$		−	8.48528i		−	0.0283789i
$300$	−94.0000	−	265.872i	−0.313333	−	0.886240i
$301$		0			0
$302$		−	82.0244i		−	0.271604i
$303$	−384.000	+	135.765i	−1.26733	+	0.448068i
$304$	−124.000			−0.407895
$305$		−	424.264i		−	1.39103i
$306$	84.0000	−	67.8823i	0.274510	−	0.221837i
$307$	−199.000			−0.648208			−0.324104	−	0.946021i	$-0.605063\pi$
$307$	−199.000			−0.648208			−0.324104	+	0.946021i	$0.605063\pi$
$308$		0			0
$309$	−65.0000	−	183.848i	−0.210356	−	0.594977i
$310$	−84.0000			−0.270968
$311$		−	441.235i		−	1.41876i	−0.704826	−	0.709380i	$-0.748975\pi$
$311$		−	441.235i		−	1.41876i	0.704826	−	0.709380i	$-0.251025\pi$
$312$	8.00000	−	2.82843i	0.0256410	−	0.00906547i
$313$	119.000			0.380192			0.190096	−	0.981766i	$-0.439120\pi$
$313$	119.000			0.380192			0.190096	+	0.981766i	$0.439120\pi$
$314$		−	166.877i		−	0.531456i
$315$		0			0
$316$	206.000			0.651899
$317$			203.647i			0.642419i	0.947008	+	0.321209i	$0.104089\pi$
$317$			203.647i			0.642419i	−0.947008	+	0.321209i	$0.895911\pi$
$318$	−36.0000	−	101.823i	−0.113208	−	0.320199i
$319$		0			0
$320$			67.8823i			0.212132i
$321$	456.000	−	161.220i	1.42056	−	0.502244i
$322$		0			0
$323$		−	263.044i		−	0.814377i
$324$	−34.0000	+	158.392i	−0.104938	+	0.488864i
$325$	47.0000			0.144615
$326$		−	149.907i		−	0.459836i
$327$	−167.000	−	472.347i	−0.510703	−	1.44449i
$328$	−96.0000			−0.292683
$329$		0			0
$330$		0			0
$331$	521.000			1.57402			0.787009	−	0.616941i	$-0.211628\pi$
$331$	521.000			1.57402			0.787009	+	0.616941i	$0.211628\pi$
$332$			84.8528i			0.255581i
$333$	7.00000	−	5.65685i	0.0210210	−	0.0169876i
$334$	204.000			0.610778
$335$		−	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	$0.347339\pi$
$338$		−	237.588i		−	0.702923i
$339$	−456.000	+	161.220i	−1.34513	+	0.475576i
$340$	−144.000			−0.423529
$341$		0			0
$342$	248.000	+	306.884i	0.725146	+	0.897323i
$343$		0			0
$344$			87.6812i			0.254887i
$345$	−72.0000	−	203.647i	−0.208696	−	0.590280i
$346$	108.000			0.312139
$347$			110.309i			0.317892i	0.987287	+	0.158946i	$0.0508096\pi$
$347$			110.309i			0.317892i	−0.987287	+	0.158946i	$0.949190\pi$
$348$	96.0000	−	33.9411i	0.275862	−	0.0975320i
$349$	50.0000			0.143266			0.0716332	−	0.997431i	$-0.477179\pi$
$349$	50.0000			0.143266			0.0716332	+	0.997431i	$0.477179\pi$
$350$		0			0
$351$	−23.0000	−	14.1421i	−0.0655271	−	0.0402910i
$352$		0			0
$353$			161.220i			0.456715i	0.973577	+	0.228357i	$0.0733355\pi$
$353$			161.220i			0.456715i	−0.973577	+	0.228357i	$0.926665\pi$
$354$	12.0000	+	33.9411i	0.0338983	+	0.0958789i
$355$	504.000			1.41972
$356$			237.588i			0.667382i
$357$		0			0
$358$	228.000			0.636872
$359$			407.294i			1.13452i	0.823538	+	0.567261i	$0.191997\pi$
$359$			407.294i			1.13452i	−0.823538	+	0.567261i	$0.808003\pi$
$360$	168.000	−	135.765i	0.466667	−	0.377124i
$361$	600.000			1.66205
$362$			304.056i			0.839933i
$363$	−121.000	−	342.240i	−0.333333	−	0.942809i
$364$		0			0
$365$			823.072i			2.25499i
$366$	200.000	−	70.7107i	0.546448	−	0.193199i
$367$	−535.000			−1.45777			−0.728883	−	0.684638i	$-0.759960\pi$
$367$	−535.000			−1.45777			−0.728883	+	0.684638i	$0.759960\pi$
$368$			33.9411i			0.0922313i
$369$	192.000	+	237.588i	0.520325	+	0.643870i
$370$	−12.0000			−0.0324324
$371$		0			0
$372$	−14.0000	−	39.5980i	−0.0376344	−	0.106446i
$373$	−385.000			−1.03217			−0.516086	−	0.856537i	$-0.672611\pi$
$373$	−385.000			−1.03217			−0.516086	+	0.856537i	$0.672611\pi$
$374$		0			0
$375$	528.000	−	186.676i	1.40800	−	0.497803i
$376$	−120.000			−0.319149
$377$			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	$0.523117\pi$
$380$		−	526.087i		−	1.38444i
$381$	−113.000	−	319.612i	−0.296588	−	0.838877i
$382$	252.000			0.659686
$383$			415.779i			1.08558i	0.839867	+	0.542792i	$0.182633\pi$
$383$			415.779i			1.08558i	−0.839867	+	0.542792i	$0.817367\pi$
$384$	−32.0000	+	11.3137i	−0.0833333	+	0.0294628i
$385$		0			0
$386$		−	137.179i		−	0.355385i
$387$	217.000	−	175.362i	0.560724	−	0.453133i
$388$	332.000			0.855670
$389$			381.838i			0.981588i	0.871276	+	0.490794i	$0.163293\pi$
$389$			381.838i			0.981588i	−0.871276	+	0.490794i	$0.836707\pi$
$390$	12.0000	+	33.9411i	0.0307692	+	0.0870285i
$391$	−72.0000			−0.184143
$392$		0			0
$393$	240.000	−	84.8528i	0.610687	−	0.215910i
$394$	516.000			1.30964
$395$			873.984i			2.21262i
$396$		0			0
$397$	−481.000			−1.21159			−0.605793	−	0.795622i	$-0.707144\pi$
$397$	−481.000			−1.21159			−0.605793	+	0.795622i	$0.707144\pi$
$398$		−	149.907i		−	0.376650i
$399$		0			0
$400$	−188.000			−0.470000
$401$		−	76.3675i		−	0.190443i	−0.995456	−	0.0952214i	$-0.969644\pi$
$401$		−	76.3675i		−	0.190443i	0.995456	−	0.0952214i	$-0.0303559\pi$
$402$	260.000	−	91.9239i	0.646766	−	0.228666i
$403$	7.00000			0.0173697
$404$			271.529i			0.672101i
$405$	−672.000	−	144.250i	−1.65926	−	0.356172i
$406$		0			0
$407$		0			0
$408$	−24.0000	−	67.8823i	−0.0588235	−	0.166378i
$409$	−49.0000			−0.119804			−0.0599022	−	0.998204i	$-0.519079\pi$
$409$	−49.0000			−0.119804			−0.0599022	+	0.998204i	$0.519079\pi$
$410$		−	407.294i		−	0.993399i
$411$	−528.000	+	186.676i	−1.28467	+	0.454200i
$412$	−130.000			−0.315534
$413$		0			0
$414$	84.0000	−	67.8823i	0.202899	−	0.163967i
$415$	−360.000			−0.867470
$416$		−	5.65685i		−	0.0135982i
$417$	−113.000	−	319.612i	−0.270983	−	0.766456i
$418$		0			0
$419$			322.441i			0.769548i	0.923011	+	0.384774i	$0.125721\pi$
$419$			322.441i			0.769548i	−0.923011	+	0.384774i	$0.874279\pi$
$420$		0			0
$421$	−313.000			−0.743468			−0.371734	−	0.928339i	$-0.621237\pi$
$421$	−313.000			−0.743468			−0.371734	+	0.928339i	$0.621237\pi$
$422$			87.6812i			0.207775i
$423$	240.000	+	296.985i	0.567376	+	0.702092i
$424$	−72.0000			−0.169811
$425$		−	398.808i		−	0.938372i
$426$	84.0000	+	237.588i	0.197183	+	0.557718i
$427$		0			0
$428$		−	322.441i		−	0.753366i
$429$		0			0
$430$	−372.000			−0.865116
$431$			347.897i			0.807185i	0.914939	+	0.403592i	$0.132239\pi$
$431$			347.897i			0.807185i	−0.914939	+	0.403592i	$0.867761\pi$
$432$	92.0000	+	56.5685i	0.212963	+	0.130946i
$433$	−97.0000			−0.224018			−0.112009	−	0.993707i	$-0.535729\pi$
$433$	−97.0000			−0.224018			−0.112009	+	0.993707i	$0.535729\pi$
$434$		0			0
$435$	144.000	+	407.294i	0.331034	+	0.936307i
$436$	−334.000			−0.766055
$437$		−	263.044i		−	0.601931i
$438$	−388.000	+	137.179i	−0.885845	+	0.313193i
$439$	374.000			0.851936			0.425968	−	0.904738i	$-0.359934\pi$
$439$	374.000			0.851936			0.425968	+	0.904738i	$0.359934\pi$
$440$		0			0
$441$		0			0
$442$	12.0000			0.0271493
$443$		−	602.455i		−	1.35994i	−0.733238	−	0.679972i	$-0.761992\pi$
$443$		−	602.455i		−	1.35994i	0.733238	−	0.679972i	$-0.238008\pi$
$444$	−2.00000	−	5.65685i	−0.00450450	−	0.0127407i
$445$	−1008.00			−2.26517
$446$		−	285.671i		−	0.640518i
$447$	−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	$-0.0150443\pi$
$450$	376.000	+	465.276i	0.835556	+	1.03395i
$451$		0			0
$452$			322.441i			0.713364i
$453$	58.0000	+	164.049i	0.128035	+	0.362139i
$454$	−24.0000			−0.0528634
$455$		0			0
$456$	248.000	−	87.6812i	0.543860	−	0.192283i
$457$	455.000			0.995624			0.497812	−	0.867285i	$-0.334137\pi$
$457$	455.000			0.995624			0.497812	+	0.867285i	$0.334137\pi$
$458$		−	1.41421i		−	0.00308780i
$459$	−120.000	+	195.161i	−0.261438	+	0.425188i
$460$	−144.000			−0.313043
$461$			220.617i			0.478563i	0.970950	+	0.239281i	$0.0769118\pi$
$461$			220.617i			0.478563i	−0.970950	+	0.239281i	$0.923088\pi$
$462$		0			0
$463$	−7.00000			−0.0151188			−0.00755940	−	0.999971i	$-0.502406\pi$
$463$	−7.00000			−0.0151188			−0.00755940	+	0.999971i	$0.502406\pi$
$464$		−	67.8823i		−	0.146298i
$465$	168.000	−	59.3970i	0.361290	−	0.127735i
$466$	468.000			1.00429
$467$		−	619.426i		−	1.32639i	−0.748445	−	0.663197i	$-0.769199\pi$
$467$		−	619.426i		−	1.32639i	0.748445	−	0.663197i	$-0.230801\pi$
$468$	−14.0000	+	11.3137i	−0.0299145	+	0.0241746i
$469$		0			0
$470$		−	509.117i		−	1.08323i
$471$	118.000	+	333.754i	0.250531	+	0.708608i
$472$	24.0000			0.0508475
$473$		0			0
$474$	−412.000	+	145.664i	−0.869198	+	0.307308i
$475$	1457.00			3.06737
$476$		0			0
$477$	144.000	+	178.191i	0.301887	+	0.373566i
$478$	−648.000			−1.35565
$479$		−	670.337i		−	1.39945i	−0.714412	−	0.699726i	$-0.753306\pi$
$479$		−	670.337i		−	1.39945i	0.714412	−	0.699726i	$-0.246694\pi$
$480$	−48.0000	−	135.765i	−0.100000	−	0.282843i
$481$	1.00000			0.00207900
$482$		−	31.1127i		−	0.0645492i
$483$		0			0
$484$	−242.000			−0.500000
$485$			1408.56i			2.90424i
$486$	−44.0000	−	340.825i	−0.0905350	−	0.701287i
$487$	−463.000			−0.950719			−0.475359	−	0.879792i	$-0.657682\pi$
$487$	−463.000			−0.950719			−0.475359	+	0.879792i	$0.657682\pi$
$488$		−	141.421i		−	0.289798i
$489$	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	$-0.118218\pi$
$492$	192.000	−	67.8823i	0.390244	−	0.137972i
$493$	144.000			0.292089
$494$			43.8406i			0.0887462i
$495$		0			0
$496$	−28.0000			−0.0564516
$497$		0			0
$498$	−60.0000	−	169.706i	−0.120482	−	0.340774i
$499$	−535.000			−1.07214			−0.536072	−	0.844172i	$-0.680093\pi$
$499$	−535.000			−1.07214			−0.536072	+	0.844172i	$0.680093\pi$
$500$		−	373.352i		−	0.746705i
$501$	−408.000	+	144.250i	−0.814371	+	0.287924i
$502$	−252.000			−0.501992
$503$			627.911i			1.24833i	0.781292	+	0.624166i	$0.214561\pi$
$503$			627.911i			1.24833i	−0.781292	+	0.624166i	$0.785439\pi$
$504$		0			0
$505$	−1152.00			−2.28119
$506$		0			0
$507$	168.000	+	475.176i	0.331361	+	0.937230i
$508$	−226.000			−0.444882
$509$		−	636.396i		−	1.25029i	−0.780510	−	0.625144i	$-0.785040\pi$
$509$		−	636.396i		−	1.25029i	0.780510	−	0.625144i	$-0.214960\pi$
$510$	288.000	−	101.823i	0.564706	−	0.199654i
$511$		0			0
$512$			22.6274i			0.0441942i
$513$	−713.000	−	438.406i	−1.38986	−	0.854593i
$514$	−396.000			−0.770428
$515$		−	551.543i		−	1.07096i
$516$	−62.0000	−	175.362i	−0.120155	−	0.339850i
$517$		0			0
$518$		0			0
$519$	−216.000	+	76.3675i	−0.416185	+	0.147144i
$520$	24.0000			0.0461538
$521$			644.881i			1.23778i	0.785479	+	0.618888i	$0.212417\pi$
$521$			644.881i			1.23778i	−0.785479	+	0.618888i	$0.787583\pi$
$522$	−168.000	+	135.765i	−0.321839	+	0.260085i
$523$	689.000			1.31740			0.658700	−	0.752406i	$-0.271107\pi$
$523$	689.000			1.31740			0.658700	+	0.752406i	$0.271107\pi$
$524$		−	169.706i		−	0.323866i
$525$		0			0
$526$	−144.000			−0.273764
$527$		−	59.3970i		−	0.112708i
$528$		0			0
$529$	457.000			0.863894
$530$		−	305.470i		−	0.576359i
$531$	−48.0000	−	59.3970i	−0.0903955	−	0.111859i
$532$		0			0
$533$			33.9411i			0.0636794i
$534$	−168.000	−	475.176i	−0.314607	−	0.889842i
$535$	1368.00			2.55701
$536$		−	183.848i		−	0.343000i
$537$	−456.000	+	161.220i	−0.849162	+	0.300224i
$538$	−600.000			−1.11524
$539$		0			0
$540$	−240.000	+	390.323i	−0.444444	+	0.722820i
$541$	575.000			1.06285			0.531423	−	0.847106i	$-0.321657\pi$
$541$	575.000			1.06285			0.531423	+	0.847106i	$0.321657\pi$
$542$		−	353.553i		−	0.652313i
$543$	−215.000	−	608.112i	−0.395948	−	1.11991i
$544$	−48.0000			−0.0882353
$545$		−	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	$0.410974\pi$
$548$			373.352i			0.681300i
$549$	−350.000	+	282.843i	−0.637523	+	0.515196i
$550$		0			0
$551$			526.087i			0.954787i
$552$	−24.0000	−	67.8823i	−0.0434783	−	0.122975i
$553$		0			0
$554$			541.644i			0.977696i
$555$	24.0000	−	8.48528i	0.0432432	−	0.0152888i
$556$	−226.000			−0.406475
$557$		−	135.765i		−	0.243742i	−0.992546	−	0.121871i	$-0.961111\pi$
$557$		−	135.765i		−	0.243742i	0.992546	−	0.121871i	$-0.0388895\pi$
$558$	56.0000	+	69.2965i	0.100358	+	0.124187i
$559$	31.0000			0.0554562
$560$		0			0
$561$		0			0
$562$	−252.000			−0.448399
$563$		−	602.455i		−	1.07008i	−0.844827	−	0.535040i	$-0.820297\pi$
$563$		−	602.455i		−	1.07008i	0.844827	−	0.535040i	$-0.179703\pi$
$564$	240.000	−	84.8528i	0.425532	−	0.150448i
$565$	−1368.00			−2.42124
$566$			431.335i			0.762076i
$567$		0			0
$568$	168.000			0.295775
$569$		−	661.852i		−	1.16318i	−0.813480	−	0.581592i	$-0.802430\pi$
$569$		−	661.852i		−	1.16318i	0.813480	−	0.581592i	$-0.197570\pi$
$570$	372.000	+	1052.17i	0.652632	+	1.84592i
$571$	113.000			0.197898			0.0989492	−	0.995092i	$-0.468452\pi$
$571$	113.000			0.197898			0.0989492	+	0.995092i	$0.468452\pi$
$572$		0			0
$573$	−504.000	+	178.191i	−0.879581	+	0.310979i
$574$		0			0
$575$		−	398.808i		−	0.693580i
$576$	56.0000	−	45.2548i	0.0972222	−	0.0785674i
$577$	−121.000			−0.209705			−0.104853	−	0.994488i	$-0.533437\pi$
$577$	−121.000			−0.209705			−0.104853	+	0.994488i	$0.533437\pi$
$578$			306.884i			0.530942i
$579$	97.0000	+	274.357i	0.167530	+	0.473847i
$580$	288.000			0.496552
$581$		0			0
$582$	−664.000	+	234.759i	−1.14089	+	0.403367i
$583$		0			0
$584$			274.357i			0.469790i
$585$	−48.0000	−	59.3970i	−0.0820513	−	0.101533i
$586$	−192.000			−0.327645
$587$			67.8823i			0.115643i	0.998327	+	0.0578213i	$0.0184154\pi$
$587$			67.8823i			0.115643i	−0.998327	+	0.0578213i	$0.981585\pi$
$588$		0			0
$589$	217.000			0.368421
$590$			101.823i			0.172582i
$591$	−1032.00	+	364.867i	−1.74619	+	0.617372i
$592$	−4.00000			−0.00675676
$593$			492.146i			0.829926i	0.909838	+	0.414963i	$0.136206\pi$
$593$			492.146i			0.829926i	−0.909838	+	0.414963i	$0.863794\pi$
$594$		0			0
$595$		0			0
$596$			135.765i			0.227793i
$597$	106.000	+	299.813i	0.177554	+	0.502200i
$598$	12.0000			0.0200669
$599$		−	101.823i		−	0.169989i	−0.996381	−	0.0849945i	$-0.972913\pi$
$599$		−	101.823i		−	0.169989i	0.996381	−	0.0849945i	$-0.0270873\pi$
$600$	376.000	−	132.936i	0.626667	−	0.221560i
$601$	791.000			1.31614			0.658070	−	0.752957i	$-0.271373\pi$
$601$	791.000			1.31614			0.658070	+	0.752957i	$0.271373\pi$
$602$		0			0
$603$	−455.000	+	367.696i	−0.754561	+	0.609777i
$604$	116.000			0.192053
$605$		−	1026.72i		−	1.69706i
$606$	−192.000	−	543.058i	−0.316832	−	0.896135i
$607$	113.000			0.186161			0.0930807	−	0.995659i	$-0.470329\pi$
$607$	113.000			0.186161			0.0930807	+	0.995659i	$0.470329\pi$
$608$		−	175.362i		−	0.288425i
$609$		0			0
$610$	600.000			0.983607
$611$			42.4264i			0.0694377i
$612$	96.0000	+	118.794i	0.156863	+	0.194108i
$613$	−574.000			−0.936378			−0.468189	−	0.883628i	$-0.655093\pi$
$613$	−574.000			−0.936378			−0.468189	+	0.883628i	$0.655093\pi$
$614$		−	281.428i		−	0.458353i
$615$	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	$-0.180196\pi$
$618$	260.000	−	91.9239i	0.420712	−	0.148744i
$619$	953.000			1.53958			0.769790	−	0.638297i	$-0.220361\pi$
$619$	953.000			1.53958			0.769790	+	0.638297i	$0.220361\pi$
$620$		−	118.794i		−	0.191603i
$621$	−120.000	+	195.161i	−0.193237	+	0.314270i
$622$	624.000			1.00322
$623$		0			0
$624$	4.00000	+	11.3137i	0.00641026	+	0.0181309i
$625$	409.000			0.654400
$626$			168.291i			0.268836i
$627$		0			0
$628$	236.000			0.375796
$629$		−	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	$0.294915\pi$
$632$			291.328i			0.460962i
$633$	−62.0000	−	175.362i	−0.0979463	−	0.277034i
$634$	−288.000			−0.454259
$635$		−	958.837i		−	1.50998i
$636$	144.000	−	50.9117i	0.226415	−	0.0800498i
$637$		0			0
$638$		0			0
$639$	−336.000	−	415.779i	−0.525822	−	0.650671i
$640$	−96.0000			−0.150000
$641$			1077.63i			1.68117i	0.541679	+	0.840586i	$0.317789\pi$
$641$			1077.63i			1.68117i	−0.541679	+	0.840586i	$0.682211\pi$
$642$	228.000	+	644.881i	0.355140	+	1.00449i
$643$	−1111.00			−1.72784			−0.863919	−	0.503631i	$-0.831997\pi$
$643$	−1111.00			−1.72784			−0.863919	+	0.503631i	$0.831997\pi$
$644$		0			0
$645$	744.000	−	263.044i	1.15349	−	0.407820i
$646$	372.000			0.575851
$647$			339.411i			0.524592i	0.964987	+	0.262296i	$0.0844797\pi$
$647$			339.411i			0.524592i	−0.964987	+	0.262296i	$0.915520\pi$
$648$	−224.000	−	48.0833i	−0.345679	−	0.0742026i
$649$		0			0
$650$			66.4680i			0.102259i
$651$		0			0
$652$	212.000			0.325153
$653$		−	644.881i		−	0.987567i	−0.869585	−	0.493784i	$-0.835613\pi$
$653$		−	644.881i		−	0.987567i	0.869585	−	0.493784i	$-0.164387\pi$
$654$	668.000	−	236.174i	1.02141	−	0.361122i
$655$	720.000			1.09924
$656$		−	135.765i		−	0.206958i
$657$	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
$661$	−865.000			−1.30862			−0.654312	−	0.756225i	$-0.727042\pi$
$661$	−865.000			−1.30862			−0.654312	+	0.756225i	$0.727042\pi$
$662$			736.805i			1.11300i
$663$	−24.0000	+	8.48528i	−0.0361991	+	0.0127983i
$664$	−120.000			−0.180723
$665$		0			0
$666$	8.00000	+	9.89949i	0.0120120	+	0.0148641i
$667$	144.000			0.215892
$668$			288.500i			0.431886i
$669$	202.000	+	571.342i	0.301943	+	0.854024i
$670$	780.000			1.16418
$671$		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	$0.622421\pi$
$674$			439.820i			0.652553i
$675$	−1081.00	−	664.680i	−1.60148	−	0.984712i
$676$	336.000			0.497041
$677$		−	322.441i		−	0.476279i	−0.971231	−	0.238139i	$-0.923463\pi$
$677$		−	322.441i		−	0.476279i	0.971231	−	0.238139i	$-0.0765375\pi$
$678$	−228.000	−	644.881i	−0.336283	−	0.951152i
$679$		0			0
$680$		−	203.647i		−	0.299481i
$681$	48.0000	−	16.9706i	0.0704846	−	0.0249201i
$682$		0			0
$683$		−	789.131i		−	1.15539i	−0.816253	−	0.577695i	$-0.803952\pi$
$683$		−	789.131i		−	1.15539i	0.816253	−	0.577695i	$-0.196048\pi$
$684$	−434.000	+	350.725i	−0.634503	+	0.512756i
$685$	−1584.00			−2.31241
$686$		0			0
$687$	1.00000	+	2.82843i	0.00145560	+	0.00411707i
$688$	−124.000			−0.180233
$689$			25.4558i			0.0369461i
$690$	288.000	−	101.823i	0.417391	−	0.147570i
$691$	185.000			0.267728			0.133864	−	0.991000i	$-0.457261\pi$
$691$	185.000			0.267728			0.133864	+	0.991000i	$0.457261\pi$
$692$			152.735i			0.220715i
$693$		0			0
$694$	−156.000			−0.224784
$695$		−	958.837i		−	1.37962i
$696$	48.0000	+	135.765i	0.0689655	+	0.195064i
$697$	288.000			0.413199
$698$			70.7107i			0.101305i
$699$	−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	$-0.0212072\pi$
$702$	20.0000	−	32.5269i	0.0284900	−	0.0463346i
$703$	31.0000			0.0440967
$704$		0			0
$705$	360.000	+	1018.23i	0.510638	+	1.44430i
$706$	−228.000			−0.322946
$707$		0			0
$708$	−48.0000	+	16.9706i	−0.0677966	+	0.0239697i
$709$	194.000			0.273625			0.136812	−	0.990597i	$-0.456314\pi$
$709$	194.000			0.273625			0.136812	+	0.990597i	$0.456314\pi$
$710$			712.764i			1.00389i
$711$	721.000	−	582.656i	1.01406	−	0.819488i
$712$	−336.000			−0.471910
$713$		−	59.3970i		−	0.0833057i
$714$		0			0
$715$		0			0
$716$			322.441i			0.450336i
$717$	1296.00	−	458.205i	1.80753	−	0.639059i
$718$	−576.000			−0.802228
$719$		−	390.323i		−	0.542869i	−0.962457	−	0.271435i	$-0.912502\pi$
$719$		−	390.323i		−	0.542869i	0.962457	−	0.271435i	$-0.0874981\pi$
$720$	192.000	+	237.588i	0.266667	+	0.329983i
$721$		0			0
$722$			848.528i			1.17525i
$723$	22.0000	+	62.2254i	0.0304288	+	0.0860656i
$724$	−430.000			−0.593923
$725$			797.616i			1.10016i
$726$	484.000	−	171.120i	0.666667	−	0.235702i
$727$	425.000			0.584594			0.292297	−	0.956328i	$-0.405580\pi$
$727$	425.000			0.584594			0.292297	+	0.956328i	$0.405580\pi$
$728$		0			0
$729$	329.000	+	650.538i	0.451303	+	0.892371i
$730$	−1164.00			−1.59452
$731$		−	263.044i		−	0.359841i
$732$	100.000	+	282.843i	0.136612	+	0.386397i
$733$	407.000			0.555252			0.277626	−	0.960689i	$-0.410452\pi$
$733$	407.000			0.555252			0.277626	+	0.960689i	$0.410452\pi$
$734$		−	756.604i		−	1.03080i
$735$		0			0
$736$	−48.0000			−0.0652174
$737$		0			0
$738$	−336.000	+	271.529i	−0.455285	+	0.367925i
$739$	761.000			1.02977			0.514885	−	0.857259i	$-0.327835\pi$
$739$	761.000			1.02977			0.514885	+	0.857259i	$0.327835\pi$
$740$		−	16.9706i		−	0.0229332i
$741$	−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	$-0.126934\pi$
$744$	56.0000	−	19.7990i	0.0752688	−	0.0266115i
$745$	−576.000			−0.773154
$746$		−	544.472i		−	0.729856i
$747$	240.000	+	296.985i	0.321285	+	0.397570i
$748$		0			0
$749$		0			0
$750$	264.000	+	746.705i	0.352000	+	0.995606i
$751$	689.000			0.917443			0.458722	−	0.888580i	$-0.348307\pi$
$751$	689.000			0.917443			0.458722	+	0.888580i	$0.348307\pi$
$752$		−	169.706i		−	0.225672i
$753$	504.000	−	178.191i	0.669323	−	0.236641i
$754$	−24.0000			−0.0318302
$755$			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	$0.529899\pi$
$758$		−	77.7817i		−	0.102614i
$759$		0			0
$760$	744.000			0.978947
$761$			1111.57i			1.46067i	0.683088	+	0.730336i	$0.260637\pi$
$761$			1111.57i			1.46067i	−0.683088	+	0.730336i	$0.739363\pi$
$762$	452.000	−	159.806i	0.593176	−	0.209719i
$763$		0			0
$764$			356.382i			0.466468i
$765$	−504.000	+	407.294i	−0.658824	+	0.532410i
$766$	−588.000			−0.767624
$767$		−	8.48528i		−	0.0110629i
$768$	−16.0000	−	45.2548i	−0.0208333	−	0.0589256i
$769$	1127.00			1.46554			0.732770	−	0.680477i	$-0.238227\pi$
$769$	1127.00			1.46554			0.732770	+	0.680477i	$0.238227\pi$
$770$		0			0
$771$	792.000	−	280.014i	1.02724	−	0.363183i
$772$	194.000			0.251295
$773$		−	458.205i		−	0.592762i	−0.955070	−	0.296381i	$-0.904220\pi$
$773$		−	458.205i		−	0.592762i	0.955070	−	0.296381i	$-0.0957799\pi$
$774$	248.000	+	306.884i	0.320413	+	0.396491i
$775$	329.000			0.424516
$776$			469.519i			0.605050i
$777$		0			0
$778$	−540.000			−0.694087
$779$			1052.17i			1.35067i
$780$	−48.0000	+	16.9706i	−0.0615385	+	0.0217571i
$781$		0			0
$782$		−	101.823i		−	0.130209i
$783$	240.000	−	390.323i	0.306513	−	0.498497i
$784$		0			0
$785$			1001.26i			1.27549i
$786$	120.000	+	339.411i	0.152672	+	0.431821i
$787$	−586.000			−0.744600			−0.372300	−	0.928112i	$-0.621431\pi$
$787$	−586.000			−0.744600			−0.372300	+	0.928112i	$0.621431\pi$
$788$			729.734i			0.926059i
$789$	288.000	−	101.823i	0.365019	−	0.129054i
$790$	−1236.00			−1.56456
$791$		0			0
$792$		0			0
$793$	−50.0000			−0.0630517
$794$		−	680.237i		−	0.856721i
$795$	216.000	+	610.940i	0.271698	+	0.768478i
$796$	212.000			0.266332
$797$			483.661i			0.606852i	0.952855	+	0.303426i	$0.0981305\pi$
$797$			483.661i			0.606852i	−0.952855	+	0.303426i	$0.901869\pi$
$798$		0			0
$799$	360.000			0.450563
$800$		−	265.872i		−	0.332340i
$801$	672.000	+	831.558i	0.838951	+	1.03815i
$802$	108.000			0.134663
$803$		0			0
$804$	130.000	+	367.696i	0.161692	+	0.457333i
$805$		0			0
$806$			9.89949i			0.0122823i
$807$	1200.00	−	424.264i	1.48699	−	0.525730i
$808$	−384.000			−0.475248
$809$		−	806.102i		−	0.996417i	−0.867057	−	0.498209i	$-0.833991\pi$
$809$		−	806.102i		−	0.996417i	0.867057	−	0.498209i	$-0.166009\pi$
$810$	204.000	−	950.352i	0.251852	−	1.17327i
$811$	398.000			0.490752			0.245376	−	0.969428i	$-0.421089\pi$
$811$	398.000			0.490752			0.245376	+	0.969428i	$0.421089\pi$
$812$		0			0
$813$	250.000	+	707.107i	0.307503	+	0.869750i
$814$		0			0
$815$			899.440i			1.10361i
$816$	96.0000	−	33.9411i	0.117647	−	0.0415945i
$817$	961.000			1.17625
$818$		−	69.2965i		−	0.0847145i
$819$		0			0
$820$	576.000			0.702439
$821$			1620.69i			1.97404i	0.160590	+	0.987021i	$0.448660\pi$
$821$			1620.69i			1.97404i	−0.160590	+	0.987021i	$0.551340\pi$
$822$	−264.000	−	746.705i	−0.321168	−	0.908400i
$823$	−1162.00			−1.41191			−0.705954	−	0.708258i	$-0.749481\pi$
$823$	−1162.00			−1.41191			−0.705954	+	0.708258i	$0.749481\pi$
$824$		−	183.848i		−	0.223116i
$825$		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	$0.972204\pi$
$828$	96.0000	+	118.794i	0.115942	+	0.143471i
$829$	1247.00			1.50422			0.752111	−	0.659036i	$-0.229036\pi$
$829$	1247.00			1.50422			0.752111	+	0.659036i	$0.229036\pi$
$830$		−	509.117i		−	0.613394i
$831$	−383.000	−	1083.29i	−0.460890	−	1.30360i
$832$	8.00000			0.00961538
$833$		0			0
$834$	452.000	−	159.806i	0.541966	−	0.191614i
$835$	−1224.00			−1.46587
$836$		0			0
$837$	−161.000	−	98.9949i	−0.192354	−	0.118274i
$838$	−456.000			−0.544153
$839$		−	1001.26i		−	1.19340i	−0.802464	−	0.596700i	$-0.796478\pi$
$839$		−	1001.26i		−	1.19340i	0.802464	−	0.596700i	$-0.203522\pi$
$840$		0			0
$841$	553.000			0.657551
$842$		−	442.649i		−	0.525711i
$843$	504.000	−	178.191i	0.597865	−	0.211377i
$844$	−124.000			−0.146919
$845$			1425.53i			1.68701i
$846$	−420.000	+	339.411i	−0.496454	+	0.401195i
$847$		0			0
$848$		−	101.823i		−	0.120075i
$849$	−305.000	−	862.670i	−0.359246	−	1.01610i
$850$	564.000			0.663529
$851$		−	8.48528i		−	0.00997095i
$852$	−336.000	+	118.794i	−0.394366	+	0.139430i
$853$	−337.000			−0.395076			−0.197538	−	0.980295i	$-0.563295\pi$
$853$	−337.000			−0.395076			−0.197538	+	0.980295i	$0.563295\pi$
$854$		0			0
$855$	−1488.00	−	1841.31i	−1.74035	−	2.15357i
$856$	456.000			0.532710
$857$		−	1120.06i		−	1.30695i	−0.756948	−	0.653476i	$-0.773310\pi$
$857$		−	1120.06i		−	1.30695i	0.756948	−	0.653476i	$-0.226690\pi$
$858$		0			0
$859$	−1090.00			−1.26892			−0.634459	−	0.772957i	$-0.718777\pi$
$859$	−1090.00			−1.26892			−0.634459	+	0.772957i	$0.718777\pi$
$860$		−	526.087i		−	0.611730i
$861$		0			0
$862$	−492.000			−0.570766
$863$			1154.00i			1.33719i	0.743625	+	0.668597i	$0.233105\pi$
$863$			1154.00i			1.33719i	−0.743625	+	0.668597i	$0.766895\pi$
$864$	−80.0000	+	130.108i	−0.0925926	+	0.150588i
$865$	−648.000			−0.749133
$866$		−	137.179i		−	0.158405i
$867$	−217.000	−	613.769i	−0.250288	−	0.707922i
$868$		0			0
$869$		0			0
$870$	−576.000	+	203.647i	−0.662069	+	0.234077i
$871$	−65.0000			−0.0746269
$872$		−	472.347i		−	0.541683i
$873$	1162.00	−	939.038i	1.33104	−	1.07564i
$874$	372.000			0.425629
$875$		0			0
$876$	−194.000	−	548.715i	−0.221461	−	0.626387i
$877$	−46.0000			−0.0524515			−0.0262258	−	0.999656i	$-0.508349\pi$
$877$	−46.0000			−0.0524515			−0.0262258	+	0.999656i	$0.508349\pi$
$878$			528.916i			0.602410i
$879$	384.000	−	135.765i	0.436860	−	0.154453i
$880$		0			0
$881$			924.896i			1.04982i	0.851156	+	0.524912i	$0.175902\pi$
$881$			924.896i			1.04982i	−0.851156	+	0.524912i	$0.824098\pi$
$882$		0			0
$883$	329.000			0.372593			0.186297	−	0.982494i	$-0.440351\pi$
$883$	329.000			0.372593			0.186297	+	0.982494i	$0.440351\pi$
$884$			16.9706i			0.0191975i
$885$	−72.0000	−	203.647i	−0.0813559	−	0.230109i
$886$	852.000			0.961625
$887$		−	1408.56i		−	1.58800i	−0.607917	−	0.794000i	$-0.707995\pi$
$887$		−	1408.56i		−	1.58800i	0.607917	−	0.794000i	$-0.292005\pi$
$888$	8.00000	−	2.82843i	0.00900901	−	0.00318517i
$889$		0			0
$890$		−	1425.53i		−	1.60172i
$891$		0			0
$892$	404.000			0.452915
$893$			1315.22i			1.47281i
$894$	−96.0000	−	271.529i	−0.107383	−	0.303724i
$895$	−1368.00			−1.52849
$896$		0			0
$897$	−24.0000	+	8.48528i	−0.0267559	+	0.00945962i
$898$	60.0000			0.0668151
$899$			118.794i			0.132140i
$900$	−658.000	+	531.744i	−0.731111	+	0.590827i
$901$	216.000			0.239734
$902$		0			0
$903$		0			0
$904$	−456.000			−0.504425
$905$		−	1824.34i		−	2.01584i
$906$	−232.000	+	82.0244i	−0.256071	+	0.0905346i
$907$	−175.000			−0.192944			−0.0964719	−	0.995336i	$-0.530756\pi$
$907$	−175.000			−0.192944			−0.0964719	+	0.995336i	$0.530756\pi$
$908$		−	33.9411i		−	0.0373801i
$909$	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	$0.706752\pi$
$912$	124.000	+	350.725i	0.135965	+	0.384567i
$913$		0			0
$914$			643.467i			0.704012i
$915$	−1200.00	+	424.264i	−1.31148	+	0.463677i
$916$	2.00000			0.00218341
$917$		0			0
$918$	−276.000	−	169.706i	−0.300654	−	0.184865i
$919$	1097.00			1.19369			0.596844	−	0.802357i	$-0.296421\pi$
$919$	1097.00			1.19369			0.596844	+	0.802357i	$0.296421\pi$
$920$		−	203.647i		−	0.221355i
$921$	199.000	+	562.857i	0.216069	+	0.611137i
$922$	−312.000			−0.338395
$923$		−	59.3970i		−	0.0643521i
$924$		0			0
$925$	47.0000			0.0508108
$926$		−	9.89949i		−	0.0106906i
$927$	−455.000	+	367.696i	−0.490831	+	0.396651i
$928$	96.0000			0.103448
$929$			568.514i			0.611963i	0.952037	+	0.305982i	$0.0989846\pi$
$929$			568.514i			0.611963i	−0.952037	+	0.305982i	$0.901015\pi$
$930$	84.0000	+	237.588i	0.0903226	+	0.255471i
$931$		0			0
$932$			661.852i			0.710142i
$933$	−1248.00	+	441.235i	−1.33762	+	0.472920i
$934$	876.000			0.937901
$935$		0			0
$936$	−16.0000	−	19.7990i	−0.0170940	−	0.0211528i
$937$	−1.00000			−0.00106724			−0.000533618	−	1.00000i	$-0.500170\pi$
$937$	−1.00000			−0.00106724			−0.000533618		1.00000i	$0.500170\pi$
$938$		0			0
$939$	−119.000	−	336.583i	−0.126731	−	0.358448i
$940$	720.000			0.765957
$941$			381.838i			0.405779i	0.979202	+	0.202889i	$0.0650332\pi$
$941$			381.838i			0.405779i	−0.979202	+	0.202889i	$0.934967\pi$
$942$	−472.000	+	166.877i	−0.501062	+	0.177152i
$943$	288.000			0.305408
$944$			33.9411i			0.0359546i
$945$		0			0
$946$		0			0
$947$		−	1680.09i		−	1.77411i	−0.461660	−	0.887057i	$-0.652746\pi$
$947$		−	1680.09i		−	1.77411i	0.461660	−	0.887057i	$-0.347254\pi$
$948$	−206.000	−	582.656i	−0.217300	−	0.614616i
$949$	97.0000			0.102213
$950$			2060.51i			2.16896i
$951$	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	$-0.0326500\pi$
$954$	−252.000	+	203.647i	−0.264151	+	0.213466i
$955$	−1512.00			−1.58325
$956$		−	916.410i		−	0.958588i
$957$		0			0
$958$	948.000			0.989562
$959$		0			0
$960$	192.000	−	67.8823i	0.200000	−	0.0707107i
$961$	−912.000			−0.949011
$962$			1.41421i			0.00147008i
$963$	−912.000	−	1128.54i	−0.947040	−	1.17190i
$964$	44.0000			0.0456432
$965$			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	$0.536785\pi$
$968$		−	342.240i		−	0.353553i
$969$	−744.000	+	263.044i	−0.767802	+	0.271459i
$970$	−1992.00			−2.05361
$971$			568.514i			0.585493i	0.956190	+	0.292747i	$0.0945692\pi$
$971$			568.514i			0.585493i	−0.956190	+	0.292747i	$0.905431\pi$
$972$	482.000	−	62.2254i	0.495885	−	0.0640179i
$973$		0			0
$974$		−	654.781i		−	0.672260i
$975$	−47.0000	−	132.936i	−0.0482051	−	0.136345i
$976$	200.000			0.204918
$977$		−	1612.20i		−	1.65016i	−0.565018	−	0.825079i	$-0.691131\pi$
$977$		−	1612.20i		−	1.65016i	0.565018	−	0.825079i	$-0.308869\pi$
$978$	−424.000	+	149.907i	−0.433538	+	0.153279i
$979$		0			0
$980$		0			0
$981$	−1169.00	+	944.695i	−1.19164	+	0.962991i
$982$	504.000			0.513238
$983$			1722.51i			1.75230i	0.482037	+	0.876151i	$0.339897\pi$
$983$			1722.51i			1.75230i	−0.482037	+	0.876151i	$0.660103\pi$
$984$	96.0000	+	271.529i	0.0975610	+	0.275944i
$985$	−3096.00			−3.14315
$986$			203.647i			0.206538i
$987$		0			0
$988$	−62.0000			−0.0627530
$989$		−	263.044i		−	0.265969i
$990$		0			0
$991$	−895.000			−0.903128			−0.451564	−	0.892239i	$-0.649134\pi$
$991$	−895.000			−0.903128			−0.451564	+	0.892239i	$0.649134\pi$
$992$		−	39.5980i		−	0.0399173i
$993$	−521.000	−	1473.61i	−0.524673	−	1.48400i
$994$		0			0
$995$			899.440i			0.903960i
$996$	240.000	−	84.8528i	0.240964	−	0.0851936i
$997$	407.000			0.408225			0.204112	−	0.978947i	$-0.434569\pi$
$997$	407.000			0.408225			0.204112	+	0.978947i	$0.434569\pi$
$998$		−	756.604i		−	0.758120i
$999$	−23.0000	−	14.1421i	−0.0230230	−	0.0141563i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.h.a.11.1	✓	4	21.2	odd	6
42.3.h.a.11.2	yes	4	7.2	even	3
42.3.h.a.23.1	yes	4	7.4	even	3
42.3.h.a.23.2	yes	4	21.11	odd	6
294.3.b.b.197.1		2	3.2	odd	2	inner
294.3.b.b.197.2		2	1.1	even	1	trivial
294.3.b.c.197.1		2	21.20	even	2
294.3.b.c.197.2		2	7.6	odd	2
294.3.h.b.263.1		4	21.5	even	6
294.3.h.b.263.2		4	7.5	odd	6
294.3.h.b.275.1		4	7.3	odd	6
294.3.h.b.275.2		4	21.17	even	6
336.3.bn.c.65.1		4	84.11	even	6
336.3.bn.c.65.2		4	28.11	odd	6
336.3.bn.c.305.1		4	28.23	odd	6
336.3.bn.c.305.2		4	84.23	even	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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(-1.00000 - 2.82843i) q^{3} -2.00000 q^{4} -8.48528i q^{5} +(4.00000 - 1.41421i) q^{6} -2.82843i q^{8} +(-7.00000 + 5.65685i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(-1.00000 - 2.82843i) q^{3} -2.00000 q^{4} -8.48528i q^{5} +(4.00000 - 1.41421i) q^{6} -2.82843i q^{8} +(-7.00000 + 5.65685i) q^{9} +12.0000 q^{10} +(2.00000 + 5.65685i) q^{12} -1.00000 q^{13} +(-24.0000 + 8.48528i) q^{15} +4.00000 q^{16} +8.48528i q^{17} +(-8.00000 - 9.89949i) q^{18} -31.0000 q^{19} +16.9706i q^{20} +8.48528i q^{23} +(-8.00000 + 2.82843i) q^{24} -47.0000 q^{25} -1.41421i q^{26} +(23.0000 + 14.1421i) q^{27} -16.9706i q^{29} +(-12.0000 - 33.9411i) q^{30} -7.00000 q^{31} +5.65685i q^{32} -12.0000 q^{34} +(14.0000 - 11.3137i) q^{36} -1.00000 q^{37} -43.8406i q^{38} +(1.00000 + 2.82843i) q^{39} -24.0000 q^{40} -33.9411i q^{41} -31.0000 q^{43} +(48.0000 + 59.3970i) q^{45} -12.0000 q^{46} -42.4264i q^{47} +(-4.00000 - 11.3137i) q^{48} -66.4680i q^{50} +(24.0000 - 8.48528i) q^{51} +2.00000 q^{52} -25.4558i q^{53} +(-20.0000 + 32.5269i) q^{54} +(31.0000 + 87.6812i) q^{57} +24.0000 q^{58} +8.48528i q^{59} +(48.0000 - 16.9706i) q^{60} +50.0000 q^{61} -9.89949i q^{62} -8.00000 q^{64} +8.48528i q^{65} +65.0000 q^{67} -16.9706i q^{68} +(24.0000 - 8.48528i) q^{69} +59.3970i q^{71} +(16.0000 + 19.7990i) q^{72} -97.0000 q^{73} -1.41421i q^{74} +(47.0000 + 132.936i) q^{75} +62.0000 q^{76} +(-4.00000 + 1.41421i) q^{78} -103.000 q^{79} -33.9411i q^{80} +(17.0000 - 79.1960i) q^{81} +48.0000 q^{82} -42.4264i q^{83} +72.0000 q^{85} -43.8406i q^{86} +(-48.0000 + 16.9706i) q^{87} -118.794i q^{89} +(-84.0000 + 67.8823i) q^{90} -16.9706i q^{92} +(7.00000 + 19.7990i) q^{93} +60.0000 q^{94} +263.044i q^{95} +(16.0000 - 5.65685i) q^{96} -166.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 4 q^{4} + 8 q^{6} - 14 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 - 4 * q^4 + 8 * q^6 - 14 * q^9	\( 2 q - 2 q^{3} - 4 q^{4} + 8 q^{6} - 14 q^{9} + 24 q^{10} + 4 q^{12} - 2 q^{13} - 48 q^{15} + 8 q^{16} - 16 q^{18} - 62 q^{19} - 16 q^{24} - 94 q^{25} + 46 q^{27} - 24 q^{30} - 14 q^{31} - 24 q^{34} + 28 q^{36} - 2 q^{37} + 2 q^{39} - 48 q^{40} - 62 q^{43} + 96 q^{45} - 24 q^{46} - 8 q^{48} + 48 q^{51} + 4 q^{52} - 40 q^{54} + 62 q^{57} + 48 q^{58} + 96 q^{60} + 100 q^{61} - 16 q^{64} + 130 q^{67} + 48 q^{69} + 32 q^{72} - 194 q^{73} + 94 q^{75} + 124 q^{76} - 8 q^{78} - 206 q^{79} + 34 q^{81} + 96 q^{82} + 144 q^{85} - 96 q^{87} - 168 q^{90} + 14 q^{93} + 120 q^{94} + 32 q^{96} - 332 q^{97}+O(q^{100}) \) 2 * q - 2 * q^3 - 4 * q^4 + 8 * q^6 - 14 * q^9 + 24 * q^10 + 4 * q^12 - 2 * q^13 - 48 * q^15 + 8 * q^16 - 16 * q^18 - 62 * q^19 - 16 * q^24 - 94 * q^25 + 46 * q^27 - 24 * q^30 - 14 * q^31 - 24 * q^34 + 28 * q^36 - 2 * q^37 + 2 * q^39 - 48 * q^40 - 62 * q^43 + 96 * q^45 - 24 * q^46 - 8 * q^48 + 48 * q^51 + 4 * q^52 - 40 * q^54 + 62 * q^57 + 48 * q^58 + 96 * q^60 + 100 * q^61 - 16 * q^64 + 130 * q^67 + 48 * q^69 + 32 * q^72 - 194 * q^73 + 94 * q^75 + 124 * q^76 - 8 * q^78 - 206 * q^79 + 34 * q^81 + 96 * q^82 + 144 * q^85 - 96 * q^87 - 168 * q^90 + 14 * q^93 + 120 * q^94 + 32 * q^96 - 332 * q^97

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