LMFDB - Embedded newform 336.3.bn.g.305.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,3,Mod(65,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.65"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.bn (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,2,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.4857532416.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 7x^{6} - 2x^{5} + 98x^{4} - 98x^{3} + 67x^{2} - 30x + 9 $ x^8 - 2x^7 - 7x^6 - 2x^5 + 98x^4 - 98x^3 + 67x^2 - 30*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			305.1
Root			$0.461396 + 0.310963i$ of defining polynomial
Character	$\chi$	$=$	336.305
Dual form			336.3.bn.g.65.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.97112 + 0.415287i) q^{3} +(0.422792 - 0.244099i) q^{5} +(-4.69042 - 5.19615i) q^{7} +(8.65507 - 2.46773i) q^{9} +(13.1367 + 7.58446i) q^{11} -17.3808 q^{13} +(-1.15479 + 0.900826i) q^{15} +(0.422792 + 0.244099i) q^{17} +(6.53562 + 11.3200i) q^{19} +(16.0937 + 13.4905i) q^{21} +(-5.78819 + 3.34181i) q^{23} +(-12.3808 + 21.4442i) q^{25} +(-24.6904 + 10.9263i) q^{27} +47.3084i q^{29} +(-14.2260 + 24.6402i) q^{31} +(-42.1803 - 17.0788i) q^{33} +(-3.25144 - 1.05196i) q^{35} +(0.500000 + 0.866025i) q^{37} +(51.6405 - 7.21804i) q^{39} -28.3850i q^{41} +2.14249 q^{43} +(3.05692 - 3.15603i) q^{45} +(-63.7304 + 36.7947i) q^{47} +(-5.00000 + 48.7442i) q^{49} +(-1.35753 - 0.549666i) q^{51} +(52.7077 + 30.4308i) q^{53} +7.40543 q^{55} +(-24.1192 - 30.9190i) q^{57} +(87.4669 + 50.4991i) q^{59} +(17.1192 + 29.6513i) q^{61} +(-53.4186 - 33.3984i) q^{63} +(-7.34847 + 4.24264i) q^{65} +(-49.9877 + 86.5812i) q^{67} +(15.8096 - 12.3327i) q^{69} -82.9000i q^{71} +(25.8808 - 44.8269i) q^{73} +(27.8794 - 68.8549i) q^{75} +(-22.2064 - 103.834i) q^{77} +(-33.3685 - 57.7960i) q^{79} +(68.8206 - 42.7168i) q^{81} -88.7584i q^{83} +0.238337 q^{85} +(-19.6466 - 140.559i) q^{87} +(-50.6945 + 29.2685i) q^{89} +(81.5233 + 90.3134i) q^{91} +(32.0345 - 79.1169i) q^{93} +(5.52641 + 3.19068i) q^{95} +25.0958 q^{97} +(132.415 + 33.2262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 10 q^{9} - 64 q^{13} - 28 q^{15} - 4 q^{19} + 26 q^{21} - 24 q^{25} - 160 q^{27} - 20 q^{31} - 106 q^{33} + 4 q^{37} + 72 q^{39} - 208 q^{43} - 58 q^{45} - 40 q^{49} - 14 q^{51} + 472 q^{55}+ \cdots + 140 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 - 10 * q^9 - 64 * q^13 - 28 * q^15 - 4 * q^19 + 26 * q^21 - 24 * q^25 - 160 * q^27 - 20 * q^31 - 106 * q^33 + 4 * q^37 + 72 * q^39 - 208 * q^43 - 58 * q^45 - 40 * q^49 - 14 * q^51 + 472 * q^55 - 268 * q^57 + 212 * q^61 - 178 * q^63 - 156 * q^67 + 164 * q^69 + 132 * q^73 - 164 * q^75 + 52 * q^79 + 98 * q^81 + 152 * q^85 + 260 * q^87 + 352 * q^91 - 210 * q^93 + 576 * q^97 + 140 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−2.97112	+	0.415287i	−0.990372	+	0.138429i
$3$	−2.97112	+	0.415287i	−0.990372	+	0.138429i
$4$		0			0
$5$	0.422792	−	0.244099i	0.0845583	−	0.0488198i	−0.457125	−	0.889403i	$-0.651121\pi$
$5$	0.422792	−	0.244099i	0.0845583	−	0.0488198i	0.541683	+	0.840583i	$0.317787\pi$
$6$		0			0
$7$	−4.69042	−	5.19615i	−0.670059	−	0.742307i
$7$	−4.69042	−	5.19615i	−0.670059	−	0.742307i
$8$		0			0
$9$	8.65507	−	2.46773i	0.961675	−	0.274193i
$10$		0			0
$11$	13.1367	+	7.58446i	1.19424	+	0.689496i	0.959266	−	0.282505i	$-0.0911654\pi$
$11$	13.1367	+	7.58446i	1.19424	+	0.689496i	0.234976	+	0.972001i	$0.424499\pi$
$12$		0			0
$13$	−17.3808			−1.33699			−0.668494	−	0.743718i	$-0.733061\pi$
$13$	−17.3808			−1.33699			−0.668494	+	0.743718i	$0.733061\pi$
$14$		0			0
$15$	−1.15479	+	0.900826i	−0.0769861	+	0.0600551i
$16$		0			0
$17$	0.422792	+	0.244099i	0.0248701	+	0.0143588i	0.512384	−	0.858757i	$-0.328763\pi$
$17$	0.422792	+	0.244099i	0.0248701	+	0.0143588i	−0.487513	+	0.873116i	$0.662096\pi$
$18$		0			0
$19$	6.53562	+	11.3200i	0.343980	+	0.595791i	0.985168	−	0.171593i	$-0.0548914\pi$
$19$	6.53562	+	11.3200i	0.343980	+	0.595791i	−0.641188	+	0.767384i	$0.721558\pi$
$20$		0			0
$21$	16.0937	+	13.4905i	0.766365	+	0.642405i
$22$		0			0
$23$	−5.78819	+	3.34181i	−0.251661	+	0.145296i	−0.620524	−	0.784187i	$-0.713080\pi$
$23$	−5.78819	+	3.34181i	−0.251661	+	0.145296i	0.368864	+	0.929483i	$0.379747\pi$
$24$		0			0
$25$	−12.3808	+	21.4442i	−0.495233	+	0.857769i
$26$		0			0
$27$	−24.6904	+	10.9263i	−0.914460	+	0.404677i
$28$		0			0
$29$			47.3084i			1.63132i	0.578529	+	0.815662i	$0.303627\pi$
$29$			47.3084i			1.63132i	−0.578529	+	0.815662i	$0.696373\pi$
$30$		0			0
$31$	−14.2260	+	24.6402i	−0.458904	+	0.794846i	−0.998903	−	0.0468198i	$-0.985091\pi$
$31$	−14.2260	+	24.6402i	−0.458904	+	0.794846i	0.539999	+	0.841666i	$0.318425\pi$
$32$		0			0
$33$	−42.1803	−	17.0788i	−1.27819	−	0.517540i
$34$		0			0
$35$	−3.25144	−	1.05196i	−0.0928984	−	0.0300561i
$36$		0			0
$37$	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	$0.829032\pi$
$38$		0			0
$39$	51.6405	−	7.21804i	1.32411	−	0.185078i
$40$		0			0
$41$		−	28.3850i		−	0.692318i	−0.938176	−	0.346159i	$-0.887486\pi$
$41$		−	28.3850i		−	0.692318i	0.938176	−	0.346159i	$-0.112514\pi$
$42$		0			0
$43$	2.14249			0.0498255			0.0249127	−	0.999690i	$-0.492069\pi$
$43$	2.14249			0.0498255			0.0249127	+	0.999690i	$0.492069\pi$
$44$		0			0
$45$	3.05692	−	3.15603i	0.0679316	−	0.0701340i
$46$		0			0
$47$	−63.7304	+	36.7947i	−1.35597	+	0.782867i	−0.989077	−	0.147398i	$-0.952910\pi$
$47$	−63.7304	+	36.7947i	−1.35597	+	0.782867i	−0.366888	+	0.930265i	$0.619577\pi$
$48$		0			0
$49$	−5.00000	+	48.7442i	−0.102041	+	0.994780i
$50$		0			0
$51$	−1.35753	−	0.549666i	−0.0266183	−	0.0107778i
$52$		0			0
$53$	52.7077	+	30.4308i	0.994484	+	0.574166i	0.906612	−	0.421966i	$-0.138660\pi$
$53$	52.7077	+	30.4308i	0.994484	+	0.574166i	0.0878725	+	0.996132i	$0.471993\pi$
$54$		0			0
$55$	7.40543			0.134644
$56$		0			0
$57$	−24.1192	−	30.9190i	−0.423143	−	0.542438i
$58$		0			0
$59$	87.4669	+	50.4991i	1.48249	+	0.855916i	0.999802	−	0.0198761i	$-0.00632718\pi$
$59$	87.4669	+	50.4991i	1.48249	+	0.855916i	0.482688	+	0.875792i	$0.339661\pi$
$60$		0			0
$61$	17.1192	+	29.6513i	0.280642	+	0.486086i	0.971543	−	0.236863i	$-0.0761193\pi$
$61$	17.1192	+	29.6513i	0.280642	+	0.486086i	−0.690901	+	0.722949i	$0.742786\pi$
$62$		0			0
$63$	−53.4186	−	33.3984i	−0.847915	−	0.530133i
$64$		0			0
$65$	−7.34847	+	4.24264i	−0.113053	+	0.0652714i
$66$		0			0
$67$	−49.9877	+	86.5812i	−0.746085	+	1.29226i	0.203601	+	0.979054i	$0.434735\pi$
$67$	−49.9877	+	86.5812i	−0.746085	+	1.29226i	−0.949686	+	0.313203i	$0.898598\pi$
$68$		0			0
$69$	15.8096	−	12.3327i	0.229124	−	0.178735i
$70$		0			0
$71$		−	82.9000i		−	1.16761i	−0.811895	−	0.583803i	$-0.801564\pi$
$71$		−	82.9000i		−	1.16761i	0.811895	−	0.583803i	$-0.198436\pi$
$72$		0			0
$73$	25.8808	−	44.8269i	0.354532	−	0.614067i	−0.632506	−	0.774556i	$-0.717974\pi$
$73$	25.8808	−	44.8269i	0.354532	−	0.614067i	0.987038	+	0.160488i	$0.0513069\pi$
$74$		0			0
$75$	27.8794	−	68.8549i	0.371725	−	0.918066i
$76$		0			0
$77$	−22.2064	−	103.834i	−0.288395	−	1.34850i
$78$		0			0
$79$	−33.3685	−	57.7960i	−0.422387	−	0.731595i	0.573786	−	0.819005i	$-0.305474\pi$
$79$	−33.3685	−	57.7960i	−0.422387	−	0.731595i	−0.996172	+	0.0874105i	$0.972141\pi$
$80$		0			0
$81$	68.8206	−	42.7168i	0.849637	−	0.527368i
$82$		0			0
$83$		−	88.7584i		−	1.06938i	−0.845049	−	0.534689i	$-0.820429\pi$
$83$		−	88.7584i		−	1.06938i	0.845049	−	0.534689i	$-0.179571\pi$
$84$		0			0
$85$	0.238337			0.00280396
$86$		0			0
$87$	−19.6466	−	140.559i	−0.225823	−	1.61562i
$88$		0			0
$89$	−50.6945	+	29.2685i	−0.569601	+	0.328859i	−0.756990	−	0.653427i	$-0.773331\pi$
$89$	−50.6945	+	29.2685i	−0.569601	+	0.328859i	0.187389	+	0.982286i	$0.439997\pi$
$90$		0			0
$91$	81.5233	+	90.3134i	0.895861	+	0.992455i
$92$		0			0
$93$	32.0345	−	79.1169i	0.344457	−	0.850719i
$94$		0			0
$95$	5.52641	+	3.19068i	0.0581728	+	0.0335861i
$96$		0			0
$97$	25.0958			0.258720			0.129360	−	0.991598i	$-0.458708\pi$
$97$	25.0958			0.258720			0.129360	+	0.991598i	$0.458708\pi$
$98$		0			0
$99$	132.415	+	33.2262i	1.33753	+	0.335618i
$100$		0			0
$101$	−81.5177	−	47.0643i	−0.807106	−	0.465983i	0.0388437	−	0.999245i	$-0.487633\pi$
$101$	−81.5177	−	47.0643i	−0.807106	−	0.465983i	−0.845950	+	0.533262i	$0.820966\pi$
$102$		0			0
$103$	−4.74937	−	8.22614i	−0.0461103	−	0.0798655i	0.842049	−	0.539401i	$-0.181349\pi$
$103$	−4.74937	−	8.22614i	−0.0461103	−	0.0798655i	−0.888159	+	0.459535i	$0.848016\pi$
$104$		0			0
$105$	10.0973	+	1.77523i	0.0961646	+	0.0169069i
$106$		0			0
$107$	29.5248	−	17.0461i	0.275932	−	0.159310i	−0.355648	−	0.934620i	$-0.615740\pi$
$107$	29.5248	−	17.0461i	0.275932	−	0.159310i	0.631581	+	0.775310i	$0.282407\pi$
$108$		0			0
$109$	−33.1904	+	57.4875i	−0.304499	+	0.527408i	−0.977150	−	0.212552i	$-0.931822\pi$
$109$	−33.1904	+	57.4875i	−0.304499	+	0.527408i	0.672650	+	0.739960i	$0.265156\pi$
$110$		0			0
$111$	−1.84521	−	2.36542i	−0.0166235	−	0.0213101i
$112$		0			0
$113$		−	72.0901i		−	0.637966i	−0.947761	−	0.318983i	$-0.896659\pi$
$113$		−	72.0901i		−	0.637966i	0.947761	−	0.318983i	$-0.103341\pi$
$114$		0			0
$115$	−1.63147	+	2.82578i	−0.0141867	+	0.0245720i
$116$		0			0
$117$	−150.432	+	42.8913i	−1.28575	+	0.366592i
$118$		0			0
$119$	−0.714694	−	3.34181i	−0.00600583	−	0.0280825i
$120$		0			0
$121$	54.5479	+	94.4798i	0.450809	+	0.780825i
$122$		0			0
$123$	11.7879	+	84.3352i	0.0958369	+	0.685652i
$124$		0			0
$125$			24.2935i			0.194348i
$126$		0			0
$127$	59.3808			0.467566			0.233783	−	0.972289i	$-0.424890\pi$
$127$	59.3808			0.467566			0.233783	+	0.972289i	$0.424890\pi$
$128$		0			0
$129$	−6.36560	+	0.889751i	−0.0493458	+	0.00689729i
$130$		0			0
$131$	−87.7287	+	50.6502i	−0.669685	+	0.386643i	−0.795957	−	0.605353i	$-0.793032\pi$
$131$	−87.7287	+	50.6502i	−0.669685	+	0.386643i	0.126272	+	0.991996i	$0.459699\pi$
$132$		0			0
$133$	28.1658	−	87.0558i	0.211773	−	0.654555i
$134$		0			0
$135$	−7.77181	+	10.6464i	−0.0575690	+	0.0788625i
$136$		0			0
$137$	115.140	+	66.4758i	0.840434	+	0.485225i	0.857412	−	0.514631i	$-0.172071\pi$
$137$	115.140	+	66.4758i	0.840434	+	0.485225i	−0.0169774	+	0.999856i	$0.505404\pi$
$138$		0			0
$139$	−71.6658			−0.515581			−0.257791	−	0.966201i	$-0.582995\pi$
$139$	−71.6658			−0.515581			−0.257791	+	0.966201i	$0.582995\pi$
$140$		0			0
$141$	174.070	−	135.788i	1.23454	−	0.963035i
$142$		0			0
$143$	−228.326	−	131.824i	−1.59669	−	0.921847i
$144$		0			0
$145$	11.5479	+	20.0016i	0.0796408	+	0.137942i
$146$		0			0
$147$	−5.38728	−	146.901i	−0.0366481	−	0.999328i
$148$		0			0
$149$	−15.9653	+	9.21758i	−0.107150	+	0.0618629i	−0.552617	−	0.833435i	$-0.686371\pi$
$149$	−15.9653	+	9.21758i	−0.107150	+	0.0618629i	0.445467	+	0.895298i	$0.353038\pi$
$150$		0			0
$151$	25.0123	−	43.3226i	0.165644	−	0.286904i	−0.771240	−	0.636545i	$-0.780363\pi$
$151$	25.0123	−	43.3226i	0.165644	−	0.286904i	0.936884	+	0.349641i	$0.113696\pi$
$152$		0			0
$153$	4.26166	+	1.06936i	0.0278540	+	0.00698925i
$154$		0			0
$155$			13.8902i			0.0896144i
$156$		0			0
$157$	0.500000	−	0.866025i	0.00318471	−	0.00551609i	−0.864429	−	0.502756i	$-0.832320\pi$
$157$	0.500000	−	0.866025i	0.00318471	−	0.00551609i	0.867613	+	0.497239i	$0.165653\pi$
$158$		0			0
$159$	−169.238	−	68.5246i	−1.06439	−	0.430972i
$160$		0			0
$161$	44.5136	+	14.4018i	0.276482	+	0.0894524i
$162$		0			0
$163$	57.9631	+	100.395i	0.355602	+	0.615921i	0.987221	−	0.159358i	$-0.0509426\pi$
$163$	57.9631	+	100.395i	0.355602	+	0.615921i	−0.631619	+	0.775279i	$0.717609\pi$
$164$		0			0
$165$	−22.0024	+	3.07538i	−0.133348	+	0.0186387i
$166$		0			0
$167$			199.369i			1.19383i	0.802305	+	0.596914i	$0.203607\pi$
$167$			199.369i			1.19383i	−0.802305	+	0.596914i	$0.796393\pi$
$168$		0			0
$169$	133.093			0.787534
$170$		0			0
$171$	84.5011	+	81.8475i	0.494159	+	0.478640i
$172$		0			0
$173$	30.0784	−	17.3658i	0.173864	−	0.100380i	−0.410543	−	0.911841i	$-0.634661\pi$
$173$	30.0784	−	17.3658i	0.173864	−	0.100380i	0.584406	+	0.811461i	$0.301327\pi$
$174$		0			0
$175$	169.499	−	36.2497i	0.968564	−	0.207141i
$176$		0			0
$177$	−280.846	−	113.715i	−1.58670	−	0.642456i
$178$		0			0
$179$	187.165	+	108.060i	1.04561	+	0.603685i	0.921418	−	0.388573i	$-0.127032\pi$
$179$	187.165	+	108.060i	1.04561	+	0.603685i	0.124195	+	0.992258i	$0.460365\pi$
$180$		0			0
$181$	−320.093			−1.76847			−0.884236	−	0.467041i	$-0.845320\pi$
$181$	−320.093			−1.76847			−0.884236	+	0.467041i	$0.845320\pi$
$182$		0			0
$183$	−63.1768	−	80.9880i	−0.345229	−	0.442557i
$184$		0			0
$185$	0.422792	+	0.244099i	0.00228536	+	0.00131945i
$186$		0			0
$187$	3.70271	+	6.41329i	0.0198006	+	0.0342957i
$188$		0			0
$189$	172.583	+	77.0464i	0.913137	+	0.407653i
$190$		0			0
$191$	34.5983	−	19.9753i	0.181143	−	0.104583i	−0.406687	−	0.913568i	$-0.633316\pi$
$191$	34.5983	−	19.9753i	0.181143	−	0.104583i	0.587829	+	0.808985i	$0.299983\pi$
$192$		0			0
$193$	−173.426	+	300.383i	−0.898581	+	1.55639i	−0.0692729	+	0.997598i	$0.522068\pi$
$193$	−173.426	+	300.383i	−0.898581	+	1.55639i	−0.829309	+	0.558791i	$0.811265\pi$
$194$		0			0
$195$	20.0712	−	15.6571i	0.102929	−	0.0802929i
$196$		0			0
$197$		−	92.3617i		−	0.468841i	−0.972135	−	0.234421i	$-0.924681\pi$
$197$		−	92.3617i		−	0.468841i	0.972135	−	0.234421i	$-0.0753193\pi$
$198$		0			0
$199$	−21.6069	+	37.4242i	−0.108577	+	0.188061i	−0.915194	−	0.403013i	$-0.867963\pi$
$199$	−21.6069	+	37.4242i	−0.108577	+	0.188061i	0.806617	+	0.591075i	$0.201296\pi$
$200$		0			0
$201$	112.563	−	278.002i	0.560016	−	1.38310i
$202$		0			0
$203$	245.822	−	221.896i	1.21094	−	1.09308i
$204$		0			0
$205$	−6.92875	−	12.0010i	−0.0337988	−	0.0585412i
$206$		0			0
$207$	−41.8505	+	43.2074i	−0.202176	+	0.208731i
$208$		0			0
$209$			198.277i			0.948692i
$210$		0			0
$211$	−306.142			−1.45091			−0.725456	−	0.688268i	$-0.758371\pi$
$211$	−306.142			−1.45091			−0.725456	+	0.688268i	$0.758371\pi$
$212$		0			0
$213$	34.4273	+	246.306i	0.161631	+	1.15636i
$214$		0			0
$215$	0.905829	−	0.522980i	0.00421316	−	0.00243247i
$216$		0			0
$217$	194.760	−	41.6522i	0.897513	−	0.191946i
$218$		0			0
$219$	−58.2789	+	143.934i	−0.266114	+	0.657233i
$220$		0			0
$221$	−7.34847	−	4.24264i	−0.0332510	−	0.0191975i
$222$		0			0
$223$	−1.57252			−0.00705164			−0.00352582	−	0.999994i	$-0.501122\pi$
$223$	−1.57252			−0.00705164			−0.00352582	+	0.999994i	$0.501122\pi$
$224$		0			0
$225$	−54.2383	+	216.154i	−0.241059	+	0.960684i
$226$		0			0
$227$	4.15727	+	2.40020i	0.0183140	+	0.0105736i	0.509129	−	0.860690i	$-0.329968\pi$
$227$	4.15727	+	2.40020i	0.0183140	+	0.0105736i	−0.490815	+	0.871264i	$0.663301\pi$
$228$		0			0
$229$	−155.903	−	270.032i	−0.680799	−	1.17918i	−0.974737	−	0.223354i	$-0.928300\pi$
$229$	−155.903	−	270.032i	−0.680799	−	1.17918i	0.293939	−	0.955824i	$-0.405034\pi$
$230$		0			0
$231$	109.099	+	299.282i	0.472290	+	1.29559i
$232$		0			0
$233$	−105.315	+	60.8034i	−0.451994	+	0.260959i	−0.708672	−	0.705538i	$-0.750705\pi$
$233$	−105.315	+	60.8034i	−0.451994	+	0.260959i	0.256678	+	0.966497i	$0.417372\pi$
$234$		0			0
$235$	−17.9631	+	31.1130i	−0.0764388	+	0.132396i
$236$		0			0
$237$	123.144	+	157.861i	0.519594	+	0.666081i
$238$		0			0
$239$		−	59.6992i		−	0.249788i	−0.992170	−	0.124894i	$-0.960141\pi$
$239$		−	59.6992i		−	0.249788i	0.992170	−	0.124894i	$-0.0398590\pi$
$240$		0			0
$241$	98.3575	−	170.360i	0.408122	−	0.706889i	−0.586557	−	0.809908i	$-0.699517\pi$
$241$	98.3575	−	170.360i	0.408122	−	0.706889i	0.994679	+	0.103019i	$0.0328503\pi$
$242$		0			0
$243$	−186.734	+	155.497i	−0.768454	+	0.639906i
$244$		0			0
$245$	9.78445	+	21.8291i	0.0399365	+	0.0890985i
$246$		0			0
$247$	−113.595	−	196.752i	−0.459897	−	0.796565i
$248$		0			0
$249$	36.8602	+	263.712i	0.148033	+	1.05908i
$250$		0			0
$251$			269.204i			1.07253i	0.844051	+	0.536264i	$0.180165\pi$
$251$			269.204i			1.07253i	−0.844051	+	0.536264i	$0.819835\pi$
$252$		0			0
$253$	−101.383			−0.400725
$254$		0			0
$255$	−0.708127	+	0.0989783i	−0.00277697	+	0.000388150i
$256$		0			0
$257$	−163.458	+	94.3727i	−0.636024	+	0.367209i	−0.783081	−	0.621919i	$-0.786353\pi$
$257$	−163.458	+	94.3727i	−0.636024	+	0.367209i	0.147057	+	0.989128i	$0.453020\pi$
$258$		0			0
$259$	2.15479	−	6.66010i	0.00831966	−	0.0257147i
$260$		0			0
$261$	116.745	+	409.458i	0.447297	+	1.56880i
$262$		0			0
$263$	179.554	+	103.666i	0.682717	+	0.394167i	0.800878	−	0.598828i	$-0.204367\pi$
$263$	179.554	+	103.666i	0.682717	+	0.394167i	−0.118161	+	0.992994i	$0.537700\pi$
$264$		0			0
$265$	29.7125			0.112123
$266$		0			0
$267$	138.464	−	108.013i	0.518593	−	0.404542i
$268$		0			0
$269$	158.445	+	91.4783i	0.589015	+	0.340068i	0.764708	−	0.644377i	$-0.222883\pi$
$269$	158.445	+	91.4783i	0.589015	+	0.340068i	−0.175693	+	0.984445i	$0.556217\pi$
$270$		0			0
$271$	−97.5110	−	168.894i	−0.359819	−	0.623225i	0.628111	−	0.778124i	$-0.283828\pi$
$271$	−97.5110	−	168.894i	−0.359819	−	0.623225i	−0.987930	+	0.154898i	$0.950495\pi$
$272$		0			0
$273$	−279.721	−	234.476i	−1.02462	−	0.858887i
$274$		0			0
$275$	−325.286	+	187.804i	−1.18286	+	0.682923i
$276$		0			0
$277$	52.6425	−	91.1795i	0.190045	−	0.329168i	−0.755220	−	0.655472i	$-0.772470\pi$
$277$	52.6425	−	91.1795i	0.190045	−	0.329168i	0.945265	+	0.326304i	$0.105803\pi$
$278$		0			0
$279$	−62.3219	+	248.369i	−0.223376	+	0.890212i
$280$		0			0
$281$		−	472.177i		−	1.68035i	−0.542319	−	0.840173i	$-0.682454\pi$
$281$		−	472.177i		−	1.68035i	0.542319	−	0.840173i	$-0.317546\pi$
$282$		0			0
$283$	159.725	−	276.651i	0.564398	−	0.977567i	−0.432707	−	0.901535i	$-0.642441\pi$
$283$	159.725	−	276.651i	0.564398	−	0.977567i	0.997105	−	0.0760322i	$-0.0242252\pi$
$284$		0			0
$285$	−17.7447	−	7.18482i	−0.0622620	−	0.0252099i
$286$		0			0
$287$	−147.493	+	133.138i	−0.513913	+	0.463894i
$288$		0			0
$289$	−144.381	−	250.075i	−0.499588	−	0.865311i
$290$		0			0
$291$	−74.5627	+	10.4220i	−0.256229	+	0.0358144i
$292$		0			0
$293$			477.594i			1.63001i	0.579451	+	0.815007i	$0.303267\pi$
$293$			477.594i			1.63001i	−0.579451	+	0.815007i	$0.696733\pi$
$294$		0			0
$295$	49.3070			0.167143
$296$		0			0
$297$	−407.219	−	43.7286i	−1.37111	−	0.147234i
$298$		0			0
$299$	100.604	−	58.0835i	0.336467	−	0.194259i
$300$		0			0
$301$	−10.0492	−	11.1327i	−0.0333860	−	0.0369858i
$302$		0			0
$303$	261.744	+	105.980i	0.863841	+	0.349770i
$304$		0			0
$305$	14.4757	+	8.35754i	0.0474612	+	0.0274018i
$306$		0			0
$307$	104.619			0.340779			0.170390	−	0.985377i	$-0.445497\pi$
$307$	104.619			0.340779			0.170390	+	0.985377i	$0.445497\pi$
$308$		0			0
$309$	17.5271	+	22.4685i	0.0567221	+	0.0727135i
$310$		0			0
$311$	−166.931	−	96.3776i	−0.536755	−	0.309896i	0.207007	−	0.978339i	$-0.433628\pi$
$311$	−166.931	−	96.3776i	−0.536755	−	0.309896i	−0.743763	+	0.668443i	$0.766961\pi$
$312$		0			0
$313$	270.451	+	468.435i	0.864060	+	1.49660i	0.867977	+	0.496604i	$0.165420\pi$
$313$	270.451	+	468.435i	0.864060	+	1.49660i	−0.00391733	+	0.999992i	$0.501247\pi$
$314$		0			0
$315$	−30.7374	−	1.08113i	−0.0975792	−	0.00343216i
$316$		0			0
$317$	268.088	−	154.781i	0.845704	−	0.488268i	−0.0134949	−	0.999909i	$-0.504296\pi$
$317$	268.088	−	154.781i	0.845704	−	0.488268i	0.859199	+	0.511641i	$0.170962\pi$
$318$		0			0
$319$	−358.808	+	621.474i	−1.12479	+	1.94820i
$320$		0			0
$321$	−80.6425	+	62.9073i	−0.251223	+	0.195973i
$322$		0			0
$323$			6.38135i			0.0197565i
$324$		0			0
$325$	215.189	−	372.719i	0.662120	−	1.14683i
$326$		0			0
$327$	74.7388	−	184.586i	0.228559	−	0.564482i
$328$		0			0
$329$	490.113	+	158.570i	1.48971	+	0.481976i
$330$		0			0
$331$	−166.749	−	288.818i	−0.503775	−	0.872563i	−0.999990	−	0.00436394i	$-0.998611\pi$
$331$	−166.749	−	288.818i	−0.503775	−	0.872563i	0.496216	−	0.868199i	$-0.334722\pi$
$332$		0			0
$333$	6.46466	+	6.26165i	0.0194134	+	0.0188037i
$334$		0			0
$335$			48.8078i			0.145695i
$336$		0			0
$337$	138.619			0.411333			0.205666	−	0.978622i	$-0.434064\pi$
$337$	138.619			0.411333			0.205666	+	0.978622i	$0.434064\pi$
$338$		0			0
$339$	29.9381	+	214.188i	0.0883130	+	0.631823i
$340$		0			0
$341$	−373.765	+	215.794i	−1.09609	+	0.632826i
$342$		0			0
$343$	276.735	−	202.650i	0.806806	−	0.590816i
$344$		0			0
$345$	3.67377	−	9.07326i	0.0106486	−	0.0262993i
$346$		0			0
$347$	−371.400	−	214.428i	−1.07032	−	0.617948i	−0.142049	−	0.989860i	$-0.545369\pi$
$347$	−371.400	−	214.428i	−1.07032	−	0.617948i	−0.928268	+	0.371912i	$0.878702\pi$
$348$		0			0
$349$	166.236			0.476320			0.238160	−	0.971226i	$-0.423456\pi$
$349$	166.236			0.476320			0.238160	+	0.971226i	$0.423456\pi$
$350$		0			0
$351$	429.140	−	189.908i	1.22262	−	0.541047i
$352$		0			0
$353$	−246.566	−	142.355i	−0.698488	−	0.403272i	0.108296	−	0.994119i	$-0.465461\pi$
$353$	−246.566	−	142.355i	−0.698488	−	0.403272i	−0.806784	+	0.590846i	$0.798794\pi$
$354$		0			0
$355$	−20.2358	−	35.0494i	−0.0570023	−	0.0987308i
$356$		0			0
$357$	3.51125	+	9.63212i	0.00983544	+	0.0269807i
$358$		0			0
$359$	365.863	−	211.231i	1.01912	−	0.588388i	0.105269	−	0.994444i	$-0.466430\pi$
$359$	365.863	−	211.231i	1.01912	−	0.588388i	0.913848	+	0.406056i	$0.133096\pi$
$360$		0			0
$361$	95.0712	−	164.668i	0.263355	−	0.456145i
$362$		0			0
$363$	−201.305	−	258.057i	−0.554558	−	0.710902i
$364$		0			0
$365$		−	25.2699i		−	0.0692327i
$366$		0			0
$367$	85.2506	−	147.658i	0.232291	−	0.402339i	−0.726191	−	0.687493i	$-0.758711\pi$
$367$	85.2506	−	147.658i	0.232291	−	0.402339i	0.958482	+	0.285154i	$0.0920446\pi$
$368$		0			0
$369$	−70.0467	−	245.675i	−0.189828	−	0.665785i
$370$		0			0
$371$	−89.0979	−	416.610i	−0.240156	−	1.12294i
$372$		0			0
$373$	−152.262	−	263.725i	−0.408208	−	0.707037i	0.586481	−	0.809963i	$-0.300513\pi$
$373$	−152.262	−	263.725i	−0.408208	−	0.707037i	−0.994689	+	0.102926i	$0.967180\pi$
$374$		0			0
$375$	−10.0888	−	72.1789i	−0.0269035	−	0.192477i
$376$		0			0
$377$		−	822.259i		−	2.18106i
$378$		0			0
$379$	512.899			1.35330			0.676648	−	0.736307i	$-0.263432\pi$
$379$	512.899			1.35330			0.676648	+	0.736307i	$0.263432\pi$
$380$		0			0
$381$	−176.427	+	24.6601i	−0.463064	+	0.0647247i
$382$		0			0
$383$	371.340	−	214.393i	0.969555	−	0.559773i	0.0704548	−	0.997515i	$-0.477555\pi$
$383$	371.340	−	214.393i	0.969555	−	0.559773i	0.899101	+	0.437742i	$0.144222\pi$
$384$		0			0
$385$	−34.7345	−	38.4797i	−0.0902196	−	0.0999473i
$386$		0			0
$387$	18.5434	−	5.28711i	0.0479159	−	0.0136618i
$388$		0			0
$389$	−61.2237	−	35.3475i	−0.157387	−	0.0908677i	0.419238	−	0.907876i	$-0.362297\pi$
$389$	−61.2237	−	35.3475i	−0.157387	−	0.0908677i	−0.576625	+	0.817009i	$0.695631\pi$
$390$		0			0
$391$	−3.26293			−0.00834509
$392$		0			0
$393$	239.618	−	186.920i	0.609715	−	0.475624i
$394$		0			0
$395$	−28.2159	−	16.2904i	−0.0714326	−	0.0412416i
$396$		0			0
$397$	−26.6646	−	46.1844i	−0.0671651	−	0.116333i	0.830487	−	0.557038i	$-0.188062\pi$
$397$	−26.6646	−	46.1844i	−0.0671651	−	0.116333i	−0.897652	+	0.440704i	$0.854729\pi$
$398$		0			0
$399$	−47.5308	+	270.350i	−0.119125	+	0.677568i
$400$		0			0
$401$	−253.211	+	146.191i	−0.631448	+	0.364567i	−0.781313	−	0.624140i	$-0.785449\pi$
$401$	−253.211	+	146.191i	−0.631448	+	0.364567i	0.149865	+	0.988707i	$0.452116\pi$
$402$		0			0
$403$	247.260	−	428.268i	0.613549	−	1.06270i
$404$		0			0
$405$	18.6696	−	34.8593i	0.0460978	−	0.0860725i
$406$		0			0
$407$			15.1689i			0.0372701i
$408$		0			0
$409$	2.28372	−	3.95552i	0.00558367	−	0.00967120i	−0.863220	−	0.504828i	$-0.831556\pi$
$409$	2.28372	−	3.95552i	0.00558367	−	0.00967120i	0.868804	+	0.495157i	$0.164889\pi$
$410$		0			0
$411$	−369.700	−	149.692i	−0.899512	−	0.364213i
$412$		0			0
$413$	−147.855	−	691.353i	−0.358004	−	1.67398i
$414$		0			0
$415$	−21.6658	−	37.5263i	−0.0522068	−	0.0904248i
$416$		0			0
$417$	212.928	−	29.7619i	0.510618	−	0.0713715i
$418$		0			0
$419$		−	378.002i		−	0.902152i	−0.892486	−	0.451076i	$-0.851040\pi$
$419$		−	378.002i		−	0.902152i	0.892486	−	0.451076i	$-0.148960\pi$
$420$		0			0
$421$	−742.806			−1.76438			−0.882192	−	0.470890i	$-0.843933\pi$
$421$	−742.806			−1.76438			−0.882192	+	0.470890i	$0.843933\pi$
$422$		0			0
$423$	−460.791	+	475.731i	−1.08934	+	1.12466i
$424$		0			0
$425$	−10.4690	+	6.04429i	−0.0246330	+	0.0142219i
$426$		0			0
$427$	73.7765	−	228.031i	0.172779	−	0.534029i
$428$		0			0
$429$	733.128	+	296.844i	1.70892	+	0.691944i
$430$		0			0
$431$	328.013	+	189.379i	0.761052	+	0.439394i	0.829673	−	0.558249i	$-0.188527\pi$
$431$	328.013	+	189.379i	0.761052	+	0.439394i	−0.0686212	+	0.997643i	$0.521860\pi$
$432$		0			0
$433$	521.567			1.20454			0.602272	−	0.798291i	$-0.294262\pi$
$433$	521.567			1.20454			0.602272	+	0.798291i	$0.294262\pi$
$434$		0			0
$435$	−42.6166	−	54.6313i	−0.0979693	−	0.125589i
$436$		0			0
$437$	−75.6589	−	43.6817i	−0.173132	−	0.0999581i
$438$		0			0
$439$	365.056	+	632.296i	0.831564	+	1.44031i	0.896798	+	0.442440i	$0.145887\pi$
$439$	365.056	+	632.296i	0.831564	+	1.44031i	−0.0652343	+	0.997870i	$0.520779\pi$
$440$		0			0
$441$	77.0125	+	434.224i	0.174631	+	0.984634i
$442$		0			0
$443$	−559.279	+	322.900i	−1.26248	+	0.728894i	−0.973554	−	0.228457i	$-0.926632\pi$
$443$	−559.279	+	322.900i	−1.26248	+	0.728894i	−0.288928	+	0.957351i	$0.593299\pi$
$444$		0			0
$445$	−14.2888	+	24.7489i	−0.0321097	+	0.0556156i
$446$		0			0
$447$	43.6069	−	34.0167i	0.0975545	−	0.0761000i
$448$		0			0
$449$			681.682i			1.51822i	0.650961	+	0.759112i	$0.274366\pi$
$449$			681.682i			1.51822i	−0.650961	+	0.759112i	$0.725634\pi$
$450$		0			0
$451$	215.285	−	372.885i	0.477350	−	0.826795i
$452$		0			0
$453$	−56.3231	+	139.104i	−0.124334	+	0.307072i
$454$		0			0
$455$	56.5128	+	18.2840i	0.124204	+	0.0401847i
$456$		0			0
$457$	31.4533	+	54.4788i	0.0688257	+	0.119210i	0.898385	−	0.439210i	$-0.144741\pi$
$457$	31.4533	+	54.4788i	0.0688257	+	0.119210i	−0.829559	+	0.558419i	$0.811408\pi$
$458$		0			0
$459$	−13.1060	−	1.40737i	−0.0285534	−	0.00306616i
$460$		0			0
$461$		−	113.099i		−	0.245333i	−0.992448	−	0.122667i	$-0.960855\pi$
$461$		−	113.099i		−	0.245333i	0.992448	−	0.122667i	$-0.0391446\pi$
$462$		0			0
$463$	−595.951			−1.28715			−0.643575	−	0.765383i	$-0.722550\pi$
$463$	−595.951			−1.28715			−0.643575	+	0.765383i	$0.722550\pi$
$464$		0			0
$465$	−5.76844	−	41.2695i	−0.0124052	−	0.0887517i
$466$		0			0
$467$	−452.173	+	261.062i	−0.968250	+	0.559020i	−0.898702	−	0.438559i	$-0.855489\pi$
$467$	−452.173	+	261.062i	−0.968250	+	0.559020i	−0.0695480	+	0.997579i	$0.522156\pi$
$468$		0			0
$469$	684.352	−	146.358i	1.45917	−	0.312065i
$470$		0			0
$471$	−1.12591	+	2.78071i	−0.00239047	+	0.00590384i
$472$		0			0
$473$	28.1452	+	16.2497i	0.0595036	+	0.0343544i
$474$		0			0
$475$	−323.666			−0.681402
$476$		0			0
$477$	531.284	+	133.312i	1.11380	+	0.279480i
$478$		0			0
$479$	614.222	+	354.621i	1.28230	+	0.740336i	0.977268	−	0.212006i	$-0.0679997\pi$
$479$	614.222	+	354.621i	1.28230	+	0.740336i	0.305031	+	0.952342i	$0.401333\pi$
$480$		0			0
$481$	−8.69042	−	15.0522i	−0.0180674	−	0.0312936i
$482$		0			0
$483$	−138.236	−	24.3036i	−0.286203	−	0.0503180i
$484$		0			0
$485$	10.6103	−	6.12587i	0.0218769	−	0.0126307i
$486$		0			0
$487$	202.391	−	350.551i	0.415586	−	0.719817i	−0.579903	−	0.814685i	$-0.696910\pi$
$487$	202.391	−	350.551i	0.415586	−	0.719817i	0.995490	+	0.0948684i	$0.0302430\pi$
$488$		0			0
$489$	−213.908	−	274.214i	−0.437440	−	0.560765i
$490$		0			0
$491$		−	202.531i		−	0.412487i	−0.978501	−	0.206244i	$-0.933876\pi$
$491$		−	202.531i		−	0.412487i	0.978501	−	0.206244i	$-0.0661239\pi$
$492$		0			0
$493$	−11.5479	+	20.0016i	−0.0234238	+	0.0405712i
$494$		0			0
$495$	64.0945	−	18.2746i	0.129484	−	0.0369184i
$496$		0			0
$497$	−430.761	+	388.836i	−0.866723	+	0.782365i
$498$		0			0
$499$	9.58481	+	16.6014i	0.0192080	+	0.0332693i	0.875470	−	0.483273i	$-0.160552\pi$
$499$	9.58481	+	16.6014i	0.0192080	+	0.0332693i	−0.856262	+	0.516542i	$0.827219\pi$
$500$		0			0
$501$	−82.7956	−	592.350i	−0.165261	−	1.18233i
$502$		0			0
$503$		−	234.752i		−	0.466704i	−0.972392	−	0.233352i	$-0.925031\pi$
$503$		−	234.752i		−	0.466704i	0.972392	−	0.233352i	$-0.0749695\pi$
$504$		0			0
$505$	−45.9533			−0.0909967
$506$		0			0
$507$	−395.436	+	55.2720i	−0.779952	+	0.109018i
$508$		0			0
$509$	621.600	−	358.881i	1.22122	−	0.705071i	0.256041	−	0.966666i	$-0.417582\pi$
$509$	621.600	−	358.881i	1.22122	−	0.705071i	0.965178	+	0.261595i	$0.0842486\pi$
$510$		0			0
$511$	−354.319	+	75.7761i	−0.693384	+	0.148290i
$512$		0			0
$513$	−285.053	−	208.086i	−0.555659	−	0.405626i
$514$		0			0
$515$	−4.01598	−	2.31863i	−0.00779803	−	0.00450219i
$516$		0			0
$517$	−1116.27			−2.15913
$518$		0			0
$519$	−82.1548	+	64.0870i	−0.158294	+	0.123482i
$520$		0			0
$521$	529.130	+	305.494i	1.01561	+	0.586360i	0.912828	−	0.408344i	$-0.133894\pi$
$521$	529.130	+	305.494i	1.01561	+	0.586360i	0.102777	+	0.994704i	$0.467227\pi$
$522$		0			0
$523$	213.676	+	370.097i	0.408558	+	0.707642i	0.994728	−	0.102545i	$-0.0326986\pi$
$523$	213.676	+	370.097i	0.408558	+	0.707642i	−0.586171	+	0.810187i	$0.699365\pi$
$524$		0			0
$525$	−488.547	+	178.093i	−0.930565	+	0.339224i
$526$		0			0
$527$	−12.0293	+	6.94512i	−0.0228260	+	0.0131786i
$528$		0			0
$529$	−242.165	+	419.441i	−0.457778	+	0.792895i
$530$		0			0
$531$	881.651	+	221.228i	1.66036	+	0.416625i
$532$		0			0
$533$			493.355i			0.925620i
$534$		0			0
$535$	8.32188	−	14.4139i	0.0155549	−	0.0269419i
$536$		0			0
$537$	−600.964	−	243.331i	−1.11911	−	0.453130i
$538$		0			0
$539$	−435.382	+	602.414i	−0.807758	+	1.11765i
$540$		0			0
$541$	163.758	+	283.637i	0.302695	+	0.524283i	0.976745	−	0.214402i	$-0.0687804\pi$
$541$	163.758	+	283.637i	0.302695	+	0.524283i	−0.674051	+	0.738685i	$0.735447\pi$
$542$		0			0
$543$	951.035	−	132.931i	1.75145	−	0.244808i
$544$		0			0
$545$			32.4070i			0.0594623i
$546$		0			0
$547$	−313.754			−0.573591			−0.286795	−	0.957992i	$-0.592590\pi$
$547$	−313.754			−0.573591			−0.286795	+	0.957992i	$0.592590\pi$
$548$		0			0
$549$	221.339	+	214.388i	0.403168	+	0.390507i
$550$		0			0
$551$	−535.532	+	309.190i	−0.971928	+	0.561143i
$552$		0			0
$553$	−143.805	+	444.475i	−0.260044	+	0.803753i
$554$		0			0
$555$	−1.35753	−	0.549666i	−0.00244601	−	0.000990390i
$556$		0			0
$557$	−156.050	−	90.0952i	−0.280161	−	0.161751i	0.353335	−	0.935497i	$-0.385047\pi$
$557$	−156.050	−	90.0952i	−0.280161	−	0.161751i	−0.633496	+	0.773746i	$0.718381\pi$
$558$		0			0
$559$	−37.2383			−0.0666160
$560$		0			0
$561$	−13.6646	−	17.5169i	−0.0243575	−	0.0312245i
$562$		0			0
$563$	348.106	+	200.979i	0.618305	+	0.356979i	0.776209	−	0.630476i	$-0.217140\pi$
$563$	348.106	+	200.979i	0.618305	+	0.356979i	−0.157904	+	0.987455i	$0.550474\pi$
$564$		0			0
$565$	−17.5971	−	30.4791i	−0.0311453	−	0.0539453i
$566$		0			0
$567$	−544.760	−	157.242i	−0.960777	−	0.277324i
$568$		0			0
$569$	−37.0446	+	21.3877i	−0.0651048	+	0.0375883i	−0.532199	−	0.846619i	$-0.678634\pi$
$569$	−37.0446	+	21.3877i	−0.0651048	+	0.0375883i	0.467094	+	0.884208i	$0.345301\pi$
$570$		0			0
$571$	−256.084	+	443.550i	−0.448483	+	0.776795i	−0.998287	−	0.0584985i	$-0.981369\pi$
$571$	−256.084	+	443.550i	−0.448483	+	0.776795i	0.549805	+	0.835293i	$0.314702\pi$
$572$		0			0
$573$	−94.5000	+	73.7172i	−0.164921	+	0.128651i
$574$		0			0
$575$		−	165.498i		−	0.287822i
$576$		0			0
$577$	34.7409	−	60.1730i	0.0602095	−	0.104286i	−0.834349	−	0.551236i	$-0.814156\pi$
$577$	34.7409	−	60.1730i	0.0602095	−	0.104286i	0.894559	+	0.446950i	$0.147490\pi$
$578$		0			0
$579$	390.524	−	964.495i	0.674481	−	1.66579i
$580$		0			0
$581$	−461.202	+	416.314i	−0.793807	+	0.716547i
$582$		0			0
$583$	461.602	+	799.518i	0.791770	+	1.37139i
$584$		0			0
$585$	−53.1318	+	54.8544i	−0.0908236	+	0.0937683i
$586$		0			0
$587$		−	462.715i		−	0.788271i	−0.919052	−	0.394136i	$-0.871044\pi$
$587$		−	462.715i		−	0.788271i	0.919052	−	0.394136i	$-0.128956\pi$
$588$		0			0
$589$	−371.904			−0.631416
$590$		0			0
$591$	38.3566	+	274.417i	0.0649013	+	0.464327i
$592$		0			0
$593$	470.604	−	271.704i	0.793599	−	0.458185i	−0.0476289	−	0.998865i	$-0.515166\pi$
$593$	470.604	−	271.704i	0.793599	−	0.458185i	0.841228	+	0.540680i	$0.181833\pi$
$594$		0			0
$595$	−1.11790	−	1.23844i	−0.00187882	−	0.00208140i
$596$		0			0
$597$	48.6547	−	120.165i	0.0814987	−	0.201281i
$598$		0			0
$599$	−117.002	−	67.5512i	−0.195329	−	0.112773i	0.399146	−	0.916887i	$-0.369307\pi$
$599$	−117.002	−	67.5512i	−0.195329	−	0.112773i	−0.594475	+	0.804114i	$0.702640\pi$
$600$		0			0
$601$	846.422			1.40836			0.704178	−	0.710023i	$-0.251316\pi$
$601$	846.422			1.40836			0.704178	+	0.710023i	$0.251316\pi$
$602$		0			0
$603$	−218.988	+	872.723i	−0.363164	+	1.44730i
$604$		0			0
$605$	46.1248	+	26.6302i	0.0762393	+	0.0440168i
$606$		0			0
$607$	211.916	+	367.050i	0.349121	+	0.604695i	0.986094	−	0.166191i	$-0.0531469\pi$
$607$	211.916	+	367.050i	0.349121	+	0.604695i	−0.636973	+	0.770886i	$0.719814\pi$
$608$		0			0
$609$	−638.214	+	761.366i	−1.04797	+	1.25019i
$610$		0			0
$611$	1107.69	−	639.523i	1.81291	−	1.04668i
$612$		0			0
$613$	42.4754	−	73.5696i	0.0692910	−	0.120016i	−0.829298	−	0.558806i	$-0.811260\pi$
$613$	42.4754	−	73.5696i	0.0692910	−	0.120016i	0.898589	+	0.438790i	$0.144593\pi$
$614$		0			0
$615$	25.5700	+	32.7788i	0.0415772	+	0.0532989i
$616$		0			0
$617$		−	241.052i		−	0.390684i	−0.980735	−	0.195342i	$-0.937418\pi$
$617$		−	241.052i		−	0.390684i	0.980735	−	0.195342i	$-0.0625817\pi$
$618$		0			0
$619$	0.872341	−	1.51094i	0.00140927	−	0.00244094i	−0.865320	−	0.501220i	$-0.832885\pi$
$619$	0.872341	−	1.51094i	0.00140927	−	0.00244094i	0.866729	+	0.498779i	$0.166218\pi$
$620$		0			0
$621$	106.399	−	145.754i	0.171335	−	0.234709i
$622$		0			0
$623$	389.862	+	126.135i	0.625781	+	0.202464i
$624$		0			0
$625$	−303.591	−	525.835i	−0.485745	−	0.841335i
$626$		0			0
$627$	−82.3417	−	589.103i	−0.131327	−	0.939558i
$628$		0			0
$629$			0.488198i			0.000776149i
$630$		0			0
$631$	−655.852			−1.03939			−0.519693	−	0.854353i	$-0.673954\pi$
$631$	−655.852			−1.03939			−0.519693	+	0.854353i	$0.673954\pi$
$632$		0			0
$633$	909.585	−	127.137i	1.43694	−	0.200848i
$634$		0			0
$635$	25.1057	−	14.4948i	0.0395366	−	0.0228264i
$636$		0			0
$637$	86.9042	−	847.215i	0.136427	−	1.33001i
$638$		0			0
$639$	−204.575	−	717.506i	−0.320149	−	1.12286i
$640$		0			0
$641$	830.357	+	479.407i	1.29541	+	0.747905i	0.979608	−	0.200920i	$-0.0643933\pi$
$641$	830.357	+	479.407i	1.29541	+	0.747905i	0.315802	+	0.948825i	$0.397727\pi$
$642$		0			0
$643$	−1189.28			−1.84958			−0.924788	−	0.380483i	$-0.875758\pi$
$643$	−1189.28			−1.84958			−0.924788	+	0.380483i	$0.875758\pi$
$644$		0			0
$645$	−2.47414	+	1.93002i	−0.00383587	+	0.00299227i
$646$		0			0
$647$	−383.479	−	221.402i	−0.592703	−	0.342198i	0.173462	−	0.984841i	$-0.444505\pi$
$647$	−383.479	−	221.402i	−0.592703	−	0.342198i	−0.766166	+	0.642643i	$0.777838\pi$
$648$		0			0
$649$	766.016	+	1326.78i	1.18030	+	2.04434i
$650$		0			0
$651$	−561.358	+	204.635i	−0.862302	+	0.314340i
$652$		0			0
$653$	752.726	−	434.586i	1.15272	−	0.665523i	0.203171	−	0.979143i	$-0.434875\pi$
$653$	752.726	−	434.586i	1.15272	−	0.665523i	0.949548	+	0.313620i	$0.101542\pi$
$654$		0			0
$655$	−24.7273	+	42.8290i	−0.0377516	+	0.0653877i
$656$		0			0
$657$	113.380	−	451.847i	0.172572	−	0.687743i
$658$		0			0
$659$			892.094i			1.35371i	0.736117	+	0.676854i	$0.236657\pi$
$659$			892.094i			1.35371i	−0.736117	+	0.676854i	$0.763343\pi$
$660$		0			0
$661$	−610.399	+	1057.24i	−0.923448	+	1.59946i	−0.129409	+	0.991591i	$0.541308\pi$
$661$	−610.399	+	1057.24i	−0.923448	+	1.59946i	−0.794038	+	0.607867i	$0.792025\pi$
$662$		0			0
$663$	23.5951	+	9.55366i	0.0355884	+	0.0144097i
$664$		0			0
$665$	−9.34194	−	43.6817i	−0.0140480	−	0.0656867i
$666$		0			0
$667$	−158.096	−	273.830i	−0.237025	−	0.410540i
$668$		0			0
$669$	4.67213	−	0.653046i	0.00698375	−	0.000976153i
$670$		0			0
$671$			519.358i			0.774006i
$672$		0			0
$673$	−476.142			−0.707493			−0.353746	−	0.935341i	$-0.615092\pi$
$673$	−476.142			−0.707493			−0.353746	+	0.935341i	$0.615092\pi$
$674$		0			0
$675$	71.3824	−	664.743i	0.105752	−	0.984805i
$676$		0			0
$677$	−592.287	+	341.957i	−0.874870	+	0.505107i	−0.868964	−	0.494876i	$-0.835214\pi$
$677$	−592.287	+	341.957i	−0.874870	+	0.505107i	−0.00590674	+	0.999983i	$0.501880\pi$
$678$		0			0
$679$	−117.710	−	130.402i	−0.173358	−	0.192050i
$680$		0			0
$681$	−13.3485	−	5.40482i	−0.0196013	−	0.00793659i
$682$		0			0
$683$	−182.353	−	105.282i	−0.266988	−	0.154146i	0.360530	−	0.932748i	$-0.382596\pi$
$683$	−182.353	−	105.282i	−0.266988	−	0.154146i	−0.627518	+	0.778602i	$0.715929\pi$
$684$		0			0
$685$	64.9067			0.0947543
$686$		0			0
$687$	575.346	+	737.551i	0.837477	+	1.07358i
$688$		0			0
$689$	−916.103	−	528.912i	−1.32961	−	0.767652i
$690$		0			0
$691$	465.536	+	806.331i	0.673713	+	1.16690i	0.976843	+	0.213956i	$0.0686349\pi$
$691$	465.536	+	806.331i	0.673713	+	1.16690i	−0.303130	+	0.952949i	$0.598032\pi$
$692$		0			0
$693$	−448.434	−	843.894i	−0.647091	−	1.21774i
$694$		0			0
$695$	−30.2997	+	17.4935i	−0.0435967	+	0.0251706i
$696$		0			0
$697$	6.92875	−	12.0010i	0.00994082	−	0.0172180i
$698$		0			0
$699$	287.651	−	224.390i	0.411518	−	0.321015i
$700$		0			0
$701$			459.553i			0.655568i	0.944753	+	0.327784i	$0.106302\pi$
$701$			459.553i			0.655568i	−0.944753	+	0.327784i	$0.893698\pi$
$702$		0			0
$703$	−6.53562	+	11.3200i	−0.00929676	+	0.0161025i
$704$		0			0
$705$	40.4497	−	99.9003i	0.0573754	−	0.141702i
$706$		0			0
$707$	137.799	+	644.330i	0.194906	+	0.911357i
$708$		0			0
$709$	81.6400	+	141.405i	0.115148	+	0.199442i	0.917839	−	0.396953i	$-0.129932\pi$
$709$	81.6400	+	141.405i	0.115148	+	0.199442i	−0.802691	+	0.596395i	$0.796599\pi$
$710$		0			0
$711$	−431.432	−	417.884i	−0.606796	−	0.587741i
$712$		0			0
$713$		−	190.163i		−	0.266708i
$714$		0			0
$715$	−128.712			−0.180017
$716$		0			0
$717$	24.7923	+	177.373i	0.0345779	+	0.247383i
$718$		0			0
$719$	535.422	−	309.126i	0.744676	−	0.429939i	−0.0790907	−	0.996867i	$-0.525202\pi$
$719$	535.422	−	309.126i	0.744676	−	0.429939i	0.823767	+	0.566928i	$0.191868\pi$
$720$		0			0
$721$	−20.4678	+	63.2625i	−0.0283881	+	0.0877427i
$722$		0			0
$723$	−221.483	+	547.007i	−0.306339	+	0.756579i
$724$		0			0
$725$	−1014.49	−	585.717i	−1.39930	−	0.807886i
$726$		0			0
$727$	870.614			1.19754			0.598772	−	0.800920i	$-0.295656\pi$
$727$	870.614			1.19754			0.598772	+	0.800920i	$0.295656\pi$
$728$		0			0
$729$	490.233	−	539.548i	0.672474	−	0.740121i
$730$		0			0
$731$	0.905829	+	0.522980i	0.00123916	+	0.000715431i
$732$		0			0
$733$	578.834	+	1002.57i	0.789678	+	1.36776i	0.926164	+	0.377121i	$0.123086\pi$
$733$	578.834	+	1002.57i	0.789678	+	1.36776i	−0.136486	+	0.990642i	$0.543581\pi$
$734$		0			0
$735$	−38.1361	−	60.7936i	−0.0518859	−	0.0827124i
$736$		0			0
$737$	−1313.34	+	758.259i	−1.78201	+	1.02885i
$738$		0			0
$739$	−233.941	+	405.198i	−0.316564	+	0.548306i	−0.979769	−	0.200133i	$-0.935863\pi$
$739$	−233.941	+	405.198i	−0.316564	+	0.548306i	0.663204	+	0.748438i	$0.269196\pi$
$740$		0			0
$741$	419.211	+	537.398i	0.565737	+	0.725233i
$742$		0			0
$743$			659.621i			0.887780i	0.896081	+	0.443890i	$0.146402\pi$
$743$			659.621i			0.887780i	−0.896081	+	0.443890i	$0.853598\pi$
$744$		0			0
$745$	−4.50000	+	7.79423i	−0.00604027	+	0.0104621i
$746$		0			0
$747$	−219.032	−	768.210i	−0.293216	−	1.02839i
$748$		0			0
$749$	−227.058	−	73.4617i	−0.303148	−	0.0980798i
$750$		0			0
$751$	76.3490	+	132.240i	0.101663	+	0.176086i	0.912370	−	0.409367i	$-0.134250\pi$
$751$	76.3490	+	132.240i	0.101663	+	0.176086i	−0.810707	+	0.585452i	$0.800917\pi$
$752$		0			0
$753$	−111.797	−	799.838i	−0.148469	−	1.06220i
$754$		0			0
$755$		−	24.4219i		−	0.0323469i
$756$		0			0
$757$	304.909			0.402786			0.201393	−	0.979510i	$-0.435453\pi$
$757$	304.909			0.402786			0.201393	+	0.979510i	$0.435453\pi$
$758$		0			0
$759$	301.222	−	42.1032i	0.396867	−	0.0554720i
$760$		0			0
$761$	1011.81	−	584.172i	1.32959	−	0.767637i	0.344350	−	0.938841i	$-0.388099\pi$
$761$	1011.81	−	584.172i	1.32959	−	0.767637i	0.985236	+	0.171204i	$0.0547659\pi$
$762$		0			0
$763$	454.391	−	97.1778i	0.595532	−	0.127363i
$764$		0			0
$765$	2.06282	−	0.588152i	0.00269650	−	0.000768827i
$766$		0			0
$767$	−1520.25	−	877.716i	−1.98207	−	1.14435i
$768$		0			0
$769$	−684.909			−0.890649			−0.445325	−	0.895369i	$-0.646912\pi$
$769$	−684.909			−0.890649			−0.445325	+	0.895369i	$0.646912\pi$
$770$		0			0
$771$	446.462	−	348.274i	0.579069	−	0.451718i
$772$		0			0
$773$	1300.52	+	750.854i	1.68243	+	0.971351i	0.960039	+	0.279866i	$0.0902899\pi$
$773$	1300.52	+	750.854i	1.68243	+	0.971351i	0.722390	+	0.691485i	$0.243043\pi$
$774$		0			0
$775$	−352.260	−	610.133i	−0.454530	−	0.787268i
$776$		0			0
$777$	−3.63629	+	20.6828i	−0.00467991	+	0.0266188i
$778$		0			0
$779$	321.319	−	185.514i	0.412477	−	0.238144i
$780$		0			0
$781$	628.752	−	1089.03i	0.805060	−	1.39440i
$782$		0			0
$783$	−516.904	−	1168.06i	−0.660159	−	1.49178i
$784$		0			0
$785$		−	0.488198i		−	0.000621908i
$786$		0			0
$787$	−394.224	+	682.815i	−0.500919	+	0.867618i	0.499080	+	0.866556i	$0.333671\pi$
$787$	−394.224	+	682.815i	−0.500919	+	0.867618i	−0.999999	+	0.00106186i	$0.999662\pi$
$788$		0			0
$789$	−576.528	−	233.437i	−0.730708	−	0.295864i
$790$		0			0
$791$	−374.591	+	338.133i	−0.473567	+	0.427475i
$792$		0			0
$793$	−297.545	−	515.364i	−0.375215	−	0.649891i
$794$		0			0
$795$	−88.2792	+	12.3392i	−0.111043	+	0.0155210i
$796$		0			0
$797$			1050.25i			1.31775i	0.752253	+	0.658875i	$0.228967\pi$
$797$			1050.25i			1.31775i	−0.752253	+	0.658875i	$0.771033\pi$
$798$		0			0
$799$	−35.9262			−0.0449640
$800$		0			0
$801$	−366.538	+	378.421i	−0.457600	+	0.472436i
$802$		0			0
$803$	679.975	−	392.584i	0.846794	−	0.488897i
$804$		0			0
$805$	22.3354	−	4.77675i	0.0277459	−	0.00593385i
$806$		0			0
$807$	−508.748	−	205.992i	−0.630419	−	0.255257i
$808$		0			0
$809$	−255.525	−	147.527i	−0.315853	−	0.182358i	0.333690	−	0.942683i	$-0.391706\pi$
$809$	−255.525	−	147.527i	−0.315853	−	0.182358i	−0.649543	+	0.760325i	$0.725040\pi$
$810$		0			0
$811$	1122.32			1.38387			0.691935	−	0.721960i	$-0.256758\pi$
$811$	1122.32			1.38387			0.691935	+	0.721960i	$0.256758\pi$
$812$		0			0
$813$	359.856	+	461.309i	0.442628	+	0.567416i
$814$		0			0
$815$	49.0126	+	28.2975i	0.0601382	+	0.0347208i
$816$		0			0
$817$	14.0025	+	24.2531i	0.0171390	+	0.0296856i
$818$		0			0
$819$	928.460	+	580.492i	1.13365	+	0.708781i
$820$		0			0
$821$	1020.75	−	589.332i	1.24330	−	0.717822i	0.273539	−	0.961861i	$-0.411806\pi$
$821$	1020.75	−	589.332i	1.24330	−	0.717822i	0.969765	+	0.244039i	$0.0784725\pi$
$822$		0			0
$823$	−182.990	+	316.948i	−0.222345	+	0.385113i	−0.955520	−	0.294927i	$-0.904705\pi$
$823$	−182.990	+	316.948i	−0.222345	+	0.385113i	0.733174	+	0.680041i	$0.238038\pi$
$824$		0			0
$825$	888.469	−	693.074i	1.07693	−	0.840089i
$826$		0			0
$827$		−	791.154i		−	0.956655i	−0.878182	−	0.478327i	$-0.841243\pi$
$827$		−	791.154i		−	0.956655i	0.878182	−	0.478327i	$-0.158757\pi$
$828$		0			0
$829$	−206.615	+	357.868i	−0.249234	+	0.431687i	−0.963314	−	0.268378i	$-0.913512\pi$
$829$	−206.615	+	357.868i	−0.249234	+	0.431687i	0.714079	+	0.700065i	$0.246846\pi$
$830$		0			0
$831$	−118.541	+	292.767i	−0.142649	+	0.352306i
$832$		0			0
$833$	−14.0124	+	19.3882i	−0.0168216	+	0.0232751i
$834$		0			0
$835$	48.6658	+	84.2917i	0.0582824	+	0.100948i
$836$		0			0
$837$	82.0211	−	763.815i	0.0979942	−	0.912563i
$838$		0			0
$839$		−	1406.19i		−	1.67603i	−0.545650	−	0.838013i	$-0.683717\pi$
$839$		−	1406.19i		−	1.67603i	0.545650	−	0.838013i	$-0.316283\pi$
$840$		0			0
$841$	−1397.08			−1.66122
$842$		0			0
$843$	196.089	+	1402.89i	0.232609	+	1.66417i
$844$		0			0
$845$	56.2707	−	32.4879i	0.0665926	−	0.0384472i
$846$		0			0
$847$	235.079	−	726.589i	0.277543	−	0.857838i
$848$		0			0
$849$	−359.671	+	888.295i	−0.423641	+	1.04628i
$850$		0			0
$851$	−5.78819	−	3.34181i	−0.00680164	−	0.00392693i
$852$		0			0
$853$	451.573			0.529393			0.264697	−	0.964332i	$-0.414728\pi$
$853$	451.573			0.529393			0.264697	+	0.964332i	$0.414728\pi$
$854$		0			0
$855$	55.7053	+	13.9778i	0.0651523	+	0.0163483i
$856$		0			0
$857$	−981.314	−	566.562i	−1.14506	−	0.661099i	−0.197379	−	0.980327i	$-0.563243\pi$
$857$	−981.314	−	566.562i	−1.14506	−	0.661099i	−0.947678	+	0.319228i	$0.896576\pi$
$858$		0			0
$859$	544.103	+	942.414i	0.633415	+	1.09711i	0.986849	+	0.161647i	$0.0516805\pi$
$859$	544.103	+	942.414i	0.633415	+	1.09711i	−0.353434	+	0.935459i	$0.614986\pi$
$860$		0			0
$861$	382.928	−	456.819i	0.444748	−	0.530568i
$862$		0			0
$863$	−789.679	+	455.921i	−0.915039	+	0.528298i	−0.882049	−	0.471157i	$-0.843836\pi$
$863$	−789.679	+	455.921i	−0.915039	+	0.528298i	−0.0329902	+	0.999456i	$0.510503\pi$
$864$		0			0
$865$	8.47794	−	14.6842i	0.00980109	−	0.0169760i
$866$		0			0
$867$	532.825	+	683.042i	0.614562	+	0.787823i
$868$		0			0
$869$		−	1012.33i		−	1.16494i
$870$		0			0
$871$	868.828	−	1504.85i	0.997506	−	1.72773i
$872$		0			0
$873$	217.206	−	61.9299i	0.248805	−	0.0709391i
$874$		0			0
$875$	126.233	−	113.947i	0.144266	−	0.130225i
$876$		0			0
$877$	496.092	+	859.257i	0.565669	+	0.979768i	0.996987	+	0.0775680i	$0.0247155\pi$
$877$	496.092	+	859.257i	0.565669	+	0.979768i	−0.431318	+	0.902200i	$0.641951\pi$
$878$		0			0
$879$	−198.339	−	1418.99i	−0.225641	−	1.61432i
$880$		0			0
$881$		−	1072.77i		−	1.21768i	−0.793294	−	0.608838i	$-0.791636\pi$
$881$		−	1072.77i		−	1.21768i	0.793294	−	0.608838i	$-0.208364\pi$
$882$		0			0
$883$	−615.282			−0.696809			−0.348405	−	0.937344i	$-0.613276\pi$
$883$	−615.282			−0.696809			−0.348405	+	0.937344i	$0.613276\pi$
$884$		0			0
$885$	−146.497	+	20.4766i	−0.165533	+	0.0231374i
$886$		0			0
$887$	145.006	−	83.7193i	0.163479	−	0.0943848i	−0.416028	−	0.909352i	$-0.636578\pi$
$887$	145.006	−	83.7193i	0.163479	−	0.0943848i	0.579507	+	0.814967i	$0.303245\pi$
$888$		0			0
$889$	−278.521	−	308.552i	−0.313297	−	0.347077i
$890$		0			0
$891$	1228.06	−	39.1902i	1.37829	−	0.0439845i
$892$		0			0
$893$	−833.035	−	480.953i	−0.932850	−	0.538581i
$894$		0			0
$895$	105.509			0.117887
$896$		0			0
$897$	−274.784	+	214.352i	−0.306336	+	0.238966i
$898$		0			0
$899$	−1165.69	−	673.011i	−1.29665	−	0.748622i
$900$		0			0
$901$	14.8562	+	25.7318i	0.0164886	+	0.0285591i
$902$		0			0
$903$	34.4806	+	28.9033i	0.0381845	+	0.0320081i
$904$		0			0
$905$	−135.333	+	78.1344i	−0.149539	+	0.0863364i
$906$		0			0
$907$	791.771	−	1371.39i	0.872956	−	1.51200i	0.0140325	−	0.999902i	$-0.495533\pi$
$907$	791.771	−	1371.39i	0.872956	−	1.51200i	0.858924	−	0.512103i	$-0.171133\pi$
$908$		0			0
$909$	−821.684	−	206.181i	−0.903943	−	0.226821i
$910$		0			0
$911$		−	375.771i		−	0.412481i	−0.978501	−	0.206241i	$-0.933877\pi$
$911$		−	375.771i		−	0.412481i	0.978501	−	0.206241i	$-0.0661230\pi$
$912$		0			0
$913$	673.184	−	1165.99i	0.737332	−	1.27710i
$914$		0			0
$915$	−46.4797	−	18.8197i	−0.0507975	−	0.0205679i
$916$		0			0
$917$	674.670	+	218.281i	0.735736	+	0.238038i
$918$		0			0
$919$	90.8647	+	157.382i	0.0988735	+	0.171254i	0.911219	−	0.411923i	$-0.135143\pi$
$919$	90.8647	+	157.382i	0.0988735	+	0.171254i	−0.812345	+	0.583177i	$0.801809\pi$
$920$		0			0
$921$	−310.836	+	43.4470i	−0.337498	+	0.0471737i
$922$		0			0
$923$			1440.87i			1.56107i
$924$		0			0
$925$	−24.7617			−0.0267694
$926$		0			0
$927$	−61.4060	−	59.4777i	−0.0662417	−	0.0641615i
$928$		0			0
$929$	1400.44	−	808.543i	1.50747	−	0.870337i	0.507506	−	0.861648i	$-0.330567\pi$
$929$	1400.44	−	808.543i	1.50747	−	0.870337i	0.999962	−	0.00868915i	$-0.00276588\pi$
$930$		0			0
$931$	−584.464	+	261.974i	−0.627781	+	0.281390i
$932$		0			0
$933$	535.996	+	217.025i	0.574486	+	0.232610i
$934$		0			0
$935$	3.13095	+	1.80766i	0.00334861	+	0.00193332i
$936$		0			0
$937$	911.700			0.972999			0.486499	−	0.873681i	$-0.338274\pi$
$937$	911.700			0.972999			0.486499	+	0.873681i	$0.338274\pi$
$938$		0			0
$939$	−998.076	−	1279.46i	−1.06291	−	1.36258i
$940$		0			0
$941$	−306.260	−	176.819i	−0.325462	−	0.187906i	0.328362	−	0.944552i	$-0.393503\pi$
$941$	−306.260	−	176.819i	−0.325462	−	0.187906i	−0.653825	+	0.756646i	$0.726837\pi$
$942$		0			0
$943$	94.8575	+	164.298i	0.100591	+	0.174229i
$944$		0			0
$945$	91.7735	−	9.55270i	0.0971148	−	0.0101087i
$946$		0			0
$947$	61.3349	−	35.4117i	0.0647676	−	0.0373936i	−0.467267	−	0.884117i	$-0.654761\pi$
$947$	61.3349	−	35.4117i	0.0647676	−	0.0373936i	0.532034	+	0.846723i	$0.321428\pi$
$948$		0			0
$949$	−449.830	+	779.129i	−0.474005	+	0.821000i
$950$		0			0
$951$	−732.243	+	571.206i	−0.769972	+	0.600637i
$952$		0			0
$953$			302.798i			0.317731i	0.987300	+	0.158866i	$0.0507836\pi$
$953$			302.798i			0.317731i	−0.987300	+	0.158866i	$0.949216\pi$
$954$		0			0
$955$	9.75190	−	16.8908i	0.0102114	−	0.0176867i
$956$		0			0
$957$	807.971	−	1995.48i	0.844275	−	2.08514i
$958$		0			0
$959$	−194.634	−	910.082i	−0.202955	−	0.948990i
$960$		0			0
$961$	75.7396	+	131.185i	0.0788133	+	0.136509i
$962$		0			0
$963$	213.474	−	220.395i	0.221676	−	0.228863i
$964$		0			0
$965$			169.333i			0.175474i
$966$		0			0
$967$	−693.562			−0.717231			−0.358615	−	0.933485i	$-0.616751\pi$
$967$	−693.562			−0.717231			−0.358615	+	0.933485i	$0.616751\pi$
$968$		0			0
$969$	−2.65009	−	18.9597i	−0.00273488	−	0.0195663i
$970$		0			0
$971$	1154.63	−	666.624i	1.18911	−	0.686533i	0.231006	−	0.972952i	$-0.425798\pi$
$971$	1154.63	−	666.624i	1.18911	−	0.686533i	0.958104	+	0.286419i	$0.0924651\pi$
$972$		0			0
$973$	336.142	+	372.387i	0.345470	+	0.382720i
$974$		0			0
$975$	−484.567	+	1196.76i	−0.496992	+	1.22744i
$976$		0			0
$977$	−149.808	−	86.4919i	−0.153335	−	0.0885281i	0.421369	−	0.906889i	$-0.361550\pi$
$977$	−149.808	−	86.4919i	−0.153335	−	0.0885281i	−0.574704	+	0.818361i	$0.694883\pi$
$978$		0			0
$979$	−887.941			−0.906988
$980$		0			0
$981$	−145.402	+	579.464i	−0.148218	+	0.590687i
$982$		0			0
$983$	931.635	+	537.880i	0.947747	+	0.547182i	0.892380	−	0.451284i	$-0.149034\pi$
$983$	931.635	+	537.880i	0.947747	+	0.547182i	0.0553665	+	0.998466i	$0.482367\pi$
$984$		0			0
$985$	−22.5454	−	39.0497i	−0.0228887	−	0.0396444i
$986$		0			0
$987$	−1522.04	−	267.592i	−1.54208	−	0.271117i
$988$		0			0
$989$	−12.4012	+	7.15982i	−0.0125391	+	0.00723945i
$990$		0			0
$991$	−84.6069	+	146.543i	−0.0853752	+	0.147874i	−0.905551	−	0.424237i	$-0.860542\pi$
$991$	−84.6069	+	146.543i	−0.0853752	+	0.147874i	0.820176	+	0.572112i	$0.193876\pi$
$992$		0			0
$993$	615.374	+	788.864i	0.619712	+	0.794425i
$994$		0			0
$995$			21.0968i			0.0212029i
$996$		0			0
$997$	793.355	−	1374.13i	0.795742	−	1.37827i	−0.126625	−	0.991951i	$-0.540414\pi$
$997$	793.355	−	1374.13i	0.795742	−	1.37827i	0.922367	−	0.386315i	$-0.126252\pi$
$998$		0			0
$999$	−21.8076	−	15.9194i	−0.0218295	−	0.0159353i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.bn.g.305.1		8
3.2	odd	2	inner	336.3.bn.g.305.3		8
4.3	odd	2		42.3.h.b.11.2	✓	8
7.2	even	3	inner	336.3.bn.g.65.3		8
12.11	even	2		42.3.h.b.11.3	yes	8
21.2	odd	6	inner	336.3.bn.g.65.1		8
28.3	even	6		294.3.b.e.197.2		4
28.11	odd	6		294.3.b.i.197.1		4
28.19	even	6		294.3.h.h.275.4		8
28.23	odd	6		42.3.h.b.23.3	yes	8
28.27	even	2		294.3.h.h.263.1		8
84.11	even	6		294.3.b.i.197.3		4
84.23	even	6		42.3.h.b.23.2	yes	8
84.47	odd	6		294.3.h.h.275.1		8
84.59	odd	6		294.3.b.e.197.4		4
84.83	odd	2		294.3.h.h.263.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.h.b.11.2	✓	8	4.3	odd	2
42.3.h.b.11.3	yes	8	12.11	even	2
42.3.h.b.23.2	yes	8	84.23	even	6
42.3.h.b.23.3	yes	8	28.23	odd	6
294.3.b.e.197.2		4	28.3	even	6
294.3.b.e.197.4		4	84.59	odd	6
294.3.b.i.197.1		4	28.11	odd	6
294.3.b.i.197.3		4	84.11	even	6
294.3.h.h.263.1		8	28.27	even	2
294.3.h.h.263.4		8	84.83	odd	2
294.3.h.h.275.1		8	84.47	odd	6
294.3.h.h.275.4		8	28.19	even	6
336.3.bn.g.65.1		8	21.2	odd	6	inner
336.3.bn.g.65.3		8	7.2	even	3	inner
336.3.bn.g.305.1		8	1.1	even	1	trivial
336.3.bn.g.305.3		8	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.97112 + 0.415287i) q^{3} +(0.422792 - 0.244099i) q^{5} +(-4.69042 - 5.19615i) q^{7} +(8.65507 - 2.46773i) q^{9} +(13.1367 + 7.58446i) q^{11} -17.3808 q^{13} +(-1.15479 + 0.900826i) q^{15} +(0.422792 + 0.244099i) q^{17} +(6.53562 + 11.3200i) q^{19} +(16.0937 + 13.4905i) q^{21} +(-5.78819 + 3.34181i) q^{23} +(-12.3808 + 21.4442i) q^{25} +(-24.6904 + 10.9263i) q^{27} +47.3084i q^{29} +(-14.2260 + 24.6402i) q^{31} +(-42.1803 - 17.0788i) q^{33} +(-3.25144 - 1.05196i) q^{35} +(0.500000 + 0.866025i) q^{37} +(51.6405 - 7.21804i) q^{39} -28.3850i q^{41} +2.14249 q^{43} +(3.05692 - 3.15603i) q^{45} +(-63.7304 + 36.7947i) q^{47} +(-5.00000 + 48.7442i) q^{49} +(-1.35753 - 0.549666i) q^{51} +(52.7077 + 30.4308i) q^{53} +7.40543 q^{55} +(-24.1192 - 30.9190i) q^{57} +(87.4669 + 50.4991i) q^{59} +(17.1192 + 29.6513i) q^{61} +(-53.4186 - 33.3984i) q^{63} +(-7.34847 + 4.24264i) q^{65} +(-49.9877 + 86.5812i) q^{67} +(15.8096 - 12.3327i) q^{69} -82.9000i q^{71} +(25.8808 - 44.8269i) q^{73} +(27.8794 - 68.8549i) q^{75} +(-22.2064 - 103.834i) q^{77} +(-33.3685 - 57.7960i) q^{79} +(68.8206 - 42.7168i) q^{81} -88.7584i q^{83} +0.238337 q^{85} +(-19.6466 - 140.559i) q^{87} +(-50.6945 + 29.2685i) q^{89} +(81.5233 + 90.3134i) q^{91} +(32.0345 - 79.1169i) q^{93} +(5.52641 + 3.19068i) q^{95} +25.0958 q^{97} +(132.415 + 33.2262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 10 q^{9} - 64 q^{13} - 28 q^{15} - 4 q^{19} + 26 q^{21} - 24 q^{25} - 160 q^{27} - 20 q^{31} - 106 q^{33} + 4 q^{37} + 72 q^{39} - 208 q^{43} - 58 q^{45} - 40 q^{49} - 14 q^{51} + 472 q^{55}+ \cdots + 140 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 - 10 * q^9 - 64 * q^13 - 28 * q^15 - 4 * q^19 + 26 * q^21 - 24 * q^25 - 160 * q^27 - 20 * q^31 - 106 * q^33 + 4 * q^37 + 72 * q^39 - 208 * q^43 - 58 * q^45 - 40 * q^49 - 14 * q^51 + 472 * q^55 - 268 * q^57 + 212 * q^61 - 178 * q^63 - 156 * q^67 + 164 * q^69 + 132 * q^73 - 164 * q^75 + 52 * q^79 + 98 * q^81 + 152 * q^85 + 260 * q^87 + 352 * q^91 - 210 * q^93 + 576 * q^97 + 140 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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