LMFDB - Embedded newform 72.3.m.b.41.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,3,Mod(41,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("72.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	72.m (of order $6$, degree $2$, 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:	$1.96185790339$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.19269881856.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144 $ x^8 - 2x^7 + 15x^6 - 2x^5 + 133x^4 - 84x^3 + 276x^2 + 144*x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.4
Root			$-1.41950 + 2.45865i$ of defining polynomial
Character	$\chi$	$=$	72.41
Dual form			72.3.m.b.65.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.91950 + 0.690286i) q^{3} +(1.80902 + 1.04444i) q^{5} +(-0.781452 - 1.35351i) q^{7} +(8.04701 + 4.03058i) q^{9} +O(q^{10})$	\(q+(2.91950 + 0.690286i) q^{3} +(1.80902 + 1.04444i) q^{5} +(-0.781452 - 1.35351i) q^{7} +(8.04701 + 4.03058i) q^{9} +(-10.8302 + 6.25280i) q^{11} +(11.0441 - 19.1289i) q^{13} +(4.56049 + 4.29799i) q^{15} +12.6991i q^{17} -21.7686 q^{19} +(-1.34714 - 4.49102i) q^{21} +(-28.7989 - 16.6271i) q^{23} +(-10.3183 - 17.8718i) q^{25} +(20.7110 + 17.3220i) q^{27} +(-25.7787 + 14.8833i) q^{29} +(6.91549 - 11.9780i) q^{31} +(-35.9349 + 10.7792i) q^{33} -3.26472i q^{35} -8.26807 q^{37} +(45.4476 - 48.2234i) q^{39} +(43.8453 + 25.3141i) q^{41} +(35.5364 + 61.5508i) q^{43} +(10.3475 + 15.6960i) q^{45} +(57.2470 - 33.0516i) q^{47} +(23.2787 - 40.3198i) q^{49} +(-8.76600 + 37.0750i) q^{51} -6.04384i q^{53} -26.1227 q^{55} +(-63.5536 - 15.0266i) q^{57} +(-8.01575 - 4.62789i) q^{59} +(51.9009 + 89.8950i) q^{61} +(-0.832899 - 14.0415i) q^{63} +(39.9580 - 23.0698i) q^{65} +(-19.8853 + 34.4424i) q^{67} +(-72.6012 - 68.4223i) q^{69} -18.3599i q^{71} -68.5777 q^{73} +(-17.7876 - 59.2994i) q^{75} +(16.9265 + 9.77252i) q^{77} +(13.3130 + 23.0587i) q^{79} +(48.5088 + 64.8683i) q^{81} +(21.0376 - 12.1461i) q^{83} +(-13.2634 + 22.9729i) q^{85} +(-85.5347 + 25.6573i) q^{87} -111.730i q^{89} -34.5217 q^{91} +(28.4580 - 30.1961i) q^{93} +(-39.3800 - 22.7360i) q^{95} +(-2.51182 - 4.35061i) q^{97} +(-112.353 + 6.66446i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{3} - 6 q^{5} + 6 q^{7} - 22 q^{9}+O(q^{10}) $ 8 * q + 10 * q^3 - 6 * q^5 + 6 * q^7 - 22 * q^9	$ 8 q + 10 q^{3} - 6 q^{5} + 6 q^{7} - 22 q^{9} + 36 q^{11} + 14 q^{13} + 10 q^{15} + 4 q^{19} - 54 q^{21} - 102 q^{23} + 10 q^{25} - 20 q^{27} - 114 q^{29} - 50 q^{31} - 104 q^{33} + 120 q^{37} + 82 q^{39} + 264 q^{41} - 28 q^{43} + 206 q^{45} + 150 q^{47} + 94 q^{49} + 170 q^{51} - 244 q^{55} - 178 q^{57} - 108 q^{59} + 14 q^{61} - 210 q^{63} - 198 q^{65} - 20 q^{67} - 14 q^{69} - 76 q^{73} + 326 q^{75} + 66 q^{77} + 26 q^{79} + 194 q^{81} + 246 q^{83} - 224 q^{85} - 18 q^{87} + 108 q^{91} - 130 q^{93} - 456 q^{95} - 236 q^{97} - 634 q^{99}+O(q^{100}) $ 8 * q + 10 * q^3 - 6 * q^5 + 6 * q^7 - 22 * q^9 + 36 * q^11 + 14 * q^13 + 10 * q^15 + 4 * q^19 - 54 * q^21 - 102 * q^23 + 10 * q^25 - 20 * q^27 - 114 * q^29 - 50 * q^31 - 104 * q^33 + 120 * q^37 + 82 * q^39 + 264 * q^41 - 28 * q^43 + 206 * q^45 + 150 * q^47 + 94 * q^49 + 170 * q^51 - 244 * q^55 - 178 * q^57 - 108 * q^59 + 14 * q^61 - 210 * q^63 - 198 * q^65 - 20 * q^67 - 14 * q^69 - 76 * q^73 + 326 * q^75 + 66 * q^77 + 26 * q^79 + 194 * q^81 + 246 * q^83 - 224 * q^85 - 18 * q^87 + 108 * q^91 - 130 * q^93 - 456 * q^95 - 236 * q^97 - 634 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	2.91950	+	0.690286i	0.973168	+	0.230095i
$3$	2.91950	+	0.690286i	0.973168	+	0.230095i
$4$		0			0
$5$	1.80902	+	1.04444i	0.361805	+	0.208888i	0.669872	−	0.742476i	$-0.266349\pi$
$5$	1.80902	+	1.04444i	0.361805	+	0.208888i	−0.308067	+	0.951365i	$0.599682\pi$
$6$		0			0
$7$	−0.781452	−	1.35351i	−0.111636	−	0.193359i	0.804794	−	0.593554i	$-0.202276\pi$
$7$	−0.781452	−	1.35351i	−0.111636	−	0.193359i	−0.916430	+	0.400195i	$0.868942\pi$
$8$		0			0
$9$	8.04701	+	4.03058i	0.894112	+	0.447843i
$10$		0			0
$11$	−10.8302	+	6.25280i	−0.984560	+	0.568436i	−0.903644	−	0.428285i	$-0.859118\pi$
$11$	−10.8302	+	6.25280i	−0.984560	+	0.568436i	−0.0809165	+	0.996721i	$0.525785\pi$
$12$		0			0
$13$	11.0441	−	19.1289i	0.849545	−	1.47145i	−0.0320708	−	0.999486i	$-0.510210\pi$
$13$	11.0441	−	19.1289i	0.849545	−	1.47145i	0.881615	−	0.471969i	$-0.156456\pi$
$14$		0			0
$15$	4.56049	+	4.29799i	0.304033	+	0.286533i
$16$		0			0
$17$			12.6991i			0.747005i	0.927629	+	0.373503i	$0.121843\pi$
$17$			12.6991i			0.747005i	−0.927629	+	0.373503i	$0.878157\pi$
$18$		0			0
$19$	−21.7686			−1.14572			−0.572859	−	0.819654i	$-0.694166\pi$
$19$	−21.7686			−1.14572			−0.572859	+	0.819654i	$0.694166\pi$
$20$		0			0
$21$	−1.34714	−	4.49102i	−0.0641495	−	0.213858i
$22$		0			0
$23$	−28.7989	−	16.6271i	−1.25213	−	0.722916i	−0.280596	−	0.959826i	$-0.590532\pi$
$23$	−28.7989	−	16.6271i	−1.25213	−	0.722916i	−0.971532	+	0.236909i	$0.923866\pi$
$24$		0			0
$25$	−10.3183	−	17.8718i	−0.412732	−	0.714872i
$26$		0			0
$27$	20.7110	+	17.3220i	0.767075	+	0.641557i
$28$		0			0
$29$	−25.7787	+	14.8833i	−0.888920	+	0.513218i	−0.873589	−	0.486665i	$-0.838213\pi$
$29$	−25.7787	+	14.8833i	−0.888920	+	0.513218i	−0.0153306	+	0.999882i	$0.504880\pi$
$30$		0			0
$31$	6.91549	−	11.9780i	0.223080	−	0.386386i	−0.732662	−	0.680593i	$-0.761722\pi$
$31$	6.91549	−	11.9780i	0.223080	−	0.386386i	0.955742	+	0.294207i	$0.0950555\pi$
$32$		0			0
$33$	−35.9349	+	10.7792i	−1.08894	+	0.326641i
$34$		0			0
$35$		−	3.26472i		−	0.0932777i
$36$		0			0
$37$	−8.26807			−0.223461			−0.111731	−	0.993739i	$-0.535639\pi$
$37$	−8.26807			−0.223461			−0.111731	+	0.993739i	$0.535639\pi$
$38$		0			0
$39$	45.4476	−	48.2234i	1.16532	−	1.23650i
$40$		0			0
$41$	43.8453	+	25.3141i	1.06940	+	0.617418i	0.928017	−	0.372538i	$-0.121512\pi$
$41$	43.8453	+	25.3141i	1.06940	+	0.617418i	0.141382	+	0.989955i	$0.454846\pi$
$42$		0			0
$43$	35.5364	+	61.5508i	0.826427	+	1.43141i	0.900824	+	0.434185i	$0.142964\pi$
$43$	35.5364	+	61.5508i	0.826427	+	1.43141i	−0.0743965	+	0.997229i	$0.523703\pi$
$44$		0			0
$45$	10.3475	+	15.6960i	0.229945	+	0.348801i
$46$		0			0
$47$	57.2470	−	33.0516i	1.21802	−	0.703225i	0.253527	−	0.967328i	$-0.418409\pi$
$47$	57.2470	−	33.0516i	1.21802	−	0.703225i	0.964495	+	0.264103i	$0.0850759\pi$
$48$		0			0
$49$	23.2787	−	40.3198i	0.475075	−	0.822854i
$50$		0			0
$51$	−8.76600	+	37.0750i	−0.171882	+	0.726962i
$52$		0			0
$53$		−	6.04384i		−	0.114035i	−0.998373	−	0.0570174i	$-0.981841\pi$
$53$		−	6.04384i		−	0.114035i	0.998373	−	0.0570174i	$-0.0181590\pi$
$54$		0			0
$55$	−26.1227			−0.474958
$56$		0			0
$57$	−63.5536	−	15.0266i	−1.11498	−	0.263624i
$58$		0			0
$59$	−8.01575	−	4.62789i	−0.135860	−	0.0784389i	0.430529	−	0.902577i	$-0.358327\pi$
$59$	−8.01575	−	4.62789i	−0.135860	−	0.0784389i	−0.566390	+	0.824138i	$0.691660\pi$
$60$		0			0
$61$	51.9009	+	89.8950i	0.850834	+	1.47369i	0.880457	+	0.474127i	$0.157236\pi$
$61$	51.9009	+	89.8950i	0.850834	+	1.47369i	−0.0296226	+	0.999561i	$0.509431\pi$
$62$		0			0
$63$	−0.832899	−	14.0415i	−0.0132206	−	0.222880i
$64$		0			0
$65$	39.9580	−	23.0698i	0.614738	−	0.354919i
$66$		0			0
$67$	−19.8853	+	34.4424i	−0.296796	+	0.514065i	−0.975401	−	0.220438i	$-0.929251\pi$
$67$	−19.8853	+	34.4424i	−0.296796	+	0.514065i	0.678605	+	0.734503i	$0.262585\pi$
$68$		0			0
$69$	−72.6012	−	68.4223i	−1.05219	−	0.991628i
$70$		0			0
$71$		−	18.3599i		−	0.258590i	−0.991606	−	0.129295i	$-0.958729\pi$
$71$		−	18.3599i		−	0.258590i	0.991606	−	0.129295i	$-0.0412714\pi$
$72$		0			0
$73$	−68.5777			−0.939421			−0.469711	−	0.882820i	$-0.655642\pi$
$73$	−68.5777			−0.939421			−0.469711	+	0.882820i	$0.655642\pi$
$74$		0			0
$75$	−17.7876	−	59.2994i	−0.237169	−	0.790658i
$76$		0			0
$77$	16.9265	+	9.77252i	0.219825	+	0.126916i
$78$		0			0
$79$	13.3130	+	23.0587i	0.168518	+	0.291883i	0.937899	−	0.346908i	$-0.112768\pi$
$79$	13.3130	+	23.0587i	0.168518	+	0.291883i	−0.769381	+	0.638791i	$0.779435\pi$
$80$		0			0
$81$	48.5088	+	64.8683i	0.598874	+	0.800843i
$82$		0			0
$83$	21.0376	−	12.1461i	0.253465	−	0.146338i	−0.367885	−	0.929871i	$-0.619918\pi$
$83$	21.0376	−	12.1461i	0.253465	−	0.146338i	0.621350	+	0.783533i	$0.286585\pi$
$84$		0			0
$85$	−13.2634	+	22.9729i	−0.156040	+	0.270270i
$86$		0			0
$87$	−85.5347	+	25.6573i	−0.983157	+	0.294911i
$88$		0			0
$89$		−	111.730i		−	1.25539i	−0.778459	−	0.627695i	$-0.783999\pi$
$89$		−	111.730i		−	1.25539i	0.778459	−	0.627695i	$-0.216001\pi$
$90$		0			0
$91$	−34.5217			−0.379359
$92$		0			0
$93$	28.4580	−	30.1961i	0.306000	−	0.324689i
$94$		0			0
$95$	−39.3800	−	22.7360i	−0.414526	−	0.239327i
$96$		0			0
$97$	−2.51182	−	4.35061i	−0.0258951	−	0.0448516i	0.852787	−	0.522258i	$-0.174910\pi$
$97$	−2.51182	−	4.35061i	−0.0258951	−	0.0448516i	−0.878683	+	0.477407i	$0.841577\pi$
$98$		0			0
$99$	−112.353	+	6.66446i	−1.13488	+	0.0673178i
$100$		0			0
$101$	−86.1052	+	49.7129i	−0.852527	+	0.492207i	−0.861503	−	0.507753i	$-0.830476\pi$
$101$	−86.1052	+	49.7129i	−0.852527	+	0.492207i	0.00897555	+	0.999960i	$0.497143\pi$
$102$		0			0
$103$	13.6160	−	23.5836i	0.132194	−	0.228967i	−0.792328	−	0.610096i	$-0.791131\pi$
$103$	13.6160	−	23.5836i	0.132194	−	0.228967i	0.924522	+	0.381128i	$0.124464\pi$
$104$		0			0
$105$	2.25359	−	9.53136i	0.0214627	−	0.0907748i
$106$		0			0
$107$			127.242i			1.18918i	0.804030	+	0.594588i	$0.202685\pi$
$107$			127.242i			1.18918i	−0.804030	+	0.594588i	$0.797315\pi$
$108$		0			0
$109$	55.3100			0.507431			0.253716	−	0.967279i	$-0.418347\pi$
$109$	55.3100			0.507431			0.253716	+	0.967279i	$0.418347\pi$
$110$		0			0
$111$	−24.1387	−	5.70733i	−0.217465	−	0.0514174i
$112$		0			0
$113$	102.845	+	59.3775i	0.910131	+	0.525464i	0.880473	−	0.474096i	$-0.157225\pi$
$113$	102.845	+	59.3775i	0.910131	+	0.525464i	0.0296577	+	0.999560i	$0.490558\pi$
$114$		0			0
$115$	−34.7320	−	60.1576i	−0.302017	−	0.523109i
$116$		0			0
$117$	165.972	−	109.416i	1.41857	−	0.935183i
$118$		0			0
$119$	17.1884	−	9.92372i	0.144440	−	0.0833926i
$120$		0			0
$121$	17.6950	−	30.6486i	0.146239	−	0.253294i
$122$		0			0
$123$	110.533	+	104.170i	0.898640	+	0.846915i
$124$		0			0
$125$		−	95.3294i		−	0.762635i
$126$		0			0
$127$	74.4516			0.586233			0.293116	−	0.956077i	$-0.405308\pi$
$127$	74.4516			0.586233			0.293116	+	0.956077i	$0.405308\pi$
$128$		0			0
$129$	61.2610	+	204.228i	0.474891	+	1.58316i
$130$		0			0
$131$	−7.08499	−	4.09052i	−0.0540839	−	0.0312254i	0.472714	−	0.881216i	$-0.343274\pi$
$131$	−7.08499	−	4.09052i	−0.0540839	−	0.0312254i	−0.526798	+	0.849990i	$0.676608\pi$
$132$		0			0
$133$	17.0111	+	29.4642i	0.127903	+	0.221535i
$134$		0			0
$135$	19.3749	+	52.9674i	0.143518	+	0.392351i
$136$		0			0
$137$	−41.7273	+	24.0913i	−0.304579	+	0.175849i	−0.644498	−	0.764606i	$-0.722934\pi$
$137$	−41.7273	+	24.0913i	−0.304579	+	0.175849i	0.339919	+	0.940455i	$0.389600\pi$
$138$		0			0
$139$	119.023	−	206.155i	0.856284	−	1.48313i	−0.0191645	−	0.999816i	$-0.506101\pi$
$139$	119.023	−	206.155i	0.856284	−	1.48313i	0.875449	−	0.483311i	$-0.160566\pi$
$140$		0			0
$141$	189.948	−	56.9775i	1.34715	−	0.404095i
$142$		0			0
$143$			276.226i			1.93165i
$144$		0			0
$145$	−62.1789			−0.428820
$146$		0			0
$147$	95.7944	−	101.645i	0.651662	−	0.691463i
$148$		0			0
$149$	−246.854	−	142.521i	−1.65674	−	0.956517i	−0.974207	−	0.225658i	$-0.927547\pi$
$149$	−246.854	−	142.521i	−1.65674	−	0.956517i	−0.682529	−	0.730859i	$-0.739120\pi$
$150$		0			0
$151$	−77.2434	−	133.790i	−0.511546	−	0.886024i	−0.999910	−	0.0133838i	$-0.995740\pi$
$151$	−77.2434	−	133.790i	−0.511546	−	0.886024i	0.488365	−	0.872640i	$-0.337594\pi$
$152$		0			0
$153$	−51.1847	+	102.190i	−0.334541	+	0.667907i
$154$		0			0
$155$	25.0206	−	14.4456i	0.161423	−	0.0931976i
$156$		0			0
$157$	−119.947	+	207.754i	−0.763993	+	1.32328i	0.176784	+	0.984250i	$0.443431\pi$
$157$	−119.947	+	207.754i	−0.763993	+	1.32328i	−0.940777	+	0.339026i	$0.889903\pi$
$158$		0			0
$159$	4.17198	−	17.6450i	0.0262388	−	0.110975i
$160$		0			0
$161$			51.9730i			0.322814i
$162$		0			0
$163$	111.245			0.682483			0.341241	−	0.939976i	$-0.389153\pi$
$163$	111.245			0.682483			0.341241	+	0.939976i	$0.389153\pi$
$164$		0			0
$165$	−76.2653	−	18.0321i	−0.462214	−	0.109286i
$166$		0			0
$167$	37.9116	+	21.8883i	0.227016	+	0.131068i	0.609195	−	0.793021i	$-0.291493\pi$
$167$	37.9116	+	21.8883i	0.227016	+	0.131068i	−0.382179	+	0.924088i	$0.624826\pi$
$168$		0			0
$169$	−159.443	−	276.164i	−0.943452	−	1.63411i
$170$		0			0
$171$	−175.172	−	87.7403i	−1.02440	−	0.513101i
$172$		0			0
$173$	−253.383	+	146.291i	−1.46464	+	0.845611i	−0.999220	−	0.0394795i	$-0.987430\pi$
$173$	−253.383	+	146.291i	−1.46464	+	0.845611i	−0.465420	+	0.885090i	$0.654097\pi$
$174$		0			0
$175$	−16.1265	+	27.9319i	−0.0921514	+	0.159611i
$176$		0			0
$177$	−20.2074	−	19.0443i	−0.114166	−	0.107595i
$178$		0			0
$179$		−	194.612i		−	1.08722i	−0.839338	−	0.543610i	$-0.817057\pi$
$179$		−	194.612i		−	1.08722i	0.839338	−	0.543610i	$-0.182943\pi$
$180$		0			0
$181$	89.3906			0.493871			0.246935	−	0.969032i	$-0.420576\pi$
$181$	89.3906			0.493871			0.246935	+	0.969032i	$0.420576\pi$
$182$		0			0
$183$	89.4716	+	298.275i	0.488916	+	1.62992i
$184$		0			0
$185$	−14.9571	−	8.63550i	−0.0808494	−	0.0466784i
$186$		0			0
$187$	−79.4048	−	137.533i	−0.424625	−	0.735472i
$188$		0			0
$189$	7.26096	−	41.5690i	0.0384178	−	0.219942i
$190$		0			0
$191$	−44.9085	+	25.9279i	−0.235123	+	0.135748i	−0.612933	−	0.790135i	$-0.710011\pi$
$191$	−44.9085	+	25.9279i	−0.235123	+	0.135748i	0.377810	+	0.925883i	$0.376677\pi$
$192$		0			0
$193$	−29.7763	+	51.5741i	−0.154281	+	0.267223i	−0.932797	−	0.360402i	$-0.882640\pi$
$193$	−29.7763	+	51.5741i	−0.154281	+	0.267223i	0.778516	+	0.627625i	$0.215973\pi$
$194$		0			0
$195$	132.582	−	39.7698i	0.679909	−	0.203948i
$196$		0			0
$197$		−	47.4968i		−	0.241100i	−0.992707	−	0.120550i	$-0.961534\pi$
$197$		−	47.4968i		−	0.241100i	0.992707	−	0.120550i	$-0.0384659\pi$
$198$		0			0
$199$	29.5239			0.148361			0.0741805	−	0.997245i	$-0.476366\pi$
$199$	29.5239			0.148361			0.0741805	+	0.997245i	$0.476366\pi$
$200$		0			0
$201$	−81.8303	+	86.8281i	−0.407116	+	0.431981i
$202$		0			0
$203$	40.2896	+	23.2612i	0.198471	+	0.114587i
$204$		0			0
$205$	52.8782	+	91.5877i	0.257942	+	0.446769i
$206$		0			0
$207$	−164.729	−	249.875i	−0.795790	−	1.20712i
$208$		0			0
$209$	235.758	−	136.115i	1.12803	−	0.651268i
$210$		0			0
$211$	−81.0561	+	140.393i	−0.384152	+	0.665371i	−0.991651	−	0.128949i	$-0.958840\pi$
$211$	−81.0561	+	140.393i	−0.384152	+	0.665371i	0.607499	+	0.794320i	$0.292173\pi$
$212$		0			0
$213$	12.6736	−	53.6017i	0.0595003	−	0.251651i
$214$		0			0
$215$			148.462i			0.690523i
$216$		0			0
$217$	−21.6165			−0.0996151
$218$		0			0
$219$	−200.213	−	47.3382i	−0.914215	−	0.216156i
$220$		0			0
$221$	242.920	+	140.250i	1.09918	+	0.634614i
$222$		0			0
$223$	102.706	+	177.891i	0.460564	+	0.797719i	0.998989	−	0.0449536i	$-0.0143140\pi$
$223$	102.706	+	177.891i	0.460564	+	0.797719i	−0.538426	+	0.842673i	$0.680981\pi$
$224$		0			0
$225$	−10.9976	−	185.403i	−0.0488782	−	0.824015i
$226$		0			0
$227$	54.0416	−	31.2009i	0.238069	−	0.137449i	−0.376220	−	0.926530i	$-0.622776\pi$
$227$	54.0416	−	31.2009i	0.238069	−	0.137449i	0.614289	+	0.789081i	$0.289443\pi$
$228$		0			0
$229$	−5.73790	+	9.93834i	−0.0250563	+	0.0433989i	−0.878282	−	0.478144i	$-0.841310\pi$
$229$	−5.73790	+	9.93834i	−0.0250563	+	0.0433989i	0.853225	+	0.521542i	$0.174643\pi$
$230$		0			0
$231$	42.6712	+	40.2150i	0.184724	+	0.174091i
$232$		0			0
$233$		−	177.096i		−	0.760069i	−0.924972	−	0.380035i	$-0.875912\pi$
$233$		−	177.096i		−	0.760069i	0.924972	−	0.380035i	$-0.124088\pi$
$234$		0			0
$235$	138.082			0.587581
$236$		0			0
$237$	22.9501	+	76.5098i	0.0968360	+	0.322826i
$238$		0			0
$239$	−231.234	−	133.503i	−0.967505	−	0.558589i	−0.0690305	−	0.997615i	$-0.521991\pi$
$239$	−231.234	−	133.503i	−0.967505	−	0.558589i	−0.898475	+	0.439025i	$0.855324\pi$
$240$		0			0
$241$	40.7178	+	70.5252i	0.168953	+	0.292636i	0.938052	−	0.346494i	$-0.112628\pi$
$241$	40.7178	+	70.5252i	0.168953	+	0.292636i	−0.769099	+	0.639130i	$0.779295\pi$
$242$		0			0
$243$	96.8440	+	222.868i	0.398535	+	0.917153i
$244$		0			0
$245$	84.2233	−	48.6263i	0.343769	−	0.198475i
$246$		0			0
$247$	−240.415	+	416.410i	−0.973338	+	1.68587i
$248$		0			0
$249$	69.8036	−	20.9385i	0.280336	−	0.0840905i
$250$		0			0
$251$		−	311.819i		−	1.24231i	−0.783689	−	0.621153i	$-0.786664\pi$
$251$		−	311.819i		−	1.24231i	0.783689	−	0.621153i	$-0.213336\pi$
$252$		0			0
$253$	415.863			1.64373
$254$		0			0
$255$	−54.5806	+	57.9141i	−0.214041	+	0.227114i
$256$		0			0
$257$	335.121	+	193.482i	1.30397	+	0.752849i	0.981083	−	0.193588i	$-0.0620125\pi$
$257$	335.121	+	193.482i	1.30397	+	0.752849i	0.322889	+	0.946437i	$0.395346\pi$
$258$		0			0
$259$	6.46110	+	11.1909i	0.0249463	+	0.0432083i
$260$		0			0
$261$	−267.430	+	15.8632i	−1.02463	+	0.0607785i
$262$		0			0
$263$	417.095	−	240.810i	1.58591	−	0.915627i	0.591942	−	0.805981i	$-0.298362\pi$
$263$	417.095	−	240.810i	1.58591	−	0.915627i	0.993971	−	0.109646i	$-0.0349718\pi$
$264$		0			0
$265$	6.31243	−	10.9334i	0.0238205	−	0.0412583i
$266$		0			0
$267$	77.1254	−	326.195i	0.288859	−	1.22171i
$268$		0			0
$269$			225.818i			0.839474i	0.907646	+	0.419737i	$0.137878\pi$
$269$			225.818i			0.839474i	−0.907646	+	0.419737i	$0.862122\pi$
$270$		0			0
$271$	−23.6619			−0.0873135			−0.0436567	−	0.999047i	$-0.513901\pi$
$271$	−23.6619			−0.0873135			−0.0436567	+	0.999047i	$0.513901\pi$
$272$		0			0
$273$	−100.786	−	23.8298i	−0.369180	−	0.0872887i
$274$		0			0
$275$	223.498	+	129.036i	0.812718	+	0.469223i
$276$		0			0
$277$	−27.9969	−	48.4920i	−0.101072	−	0.175061i	0.811055	−	0.584970i	$-0.198894\pi$
$277$	−27.9969	−	48.4920i	−0.101072	−	0.175061i	−0.912126	+	0.409909i	$0.865560\pi$
$278$		0			0
$279$	103.927	−	68.5135i	0.372499	−	0.245568i
$280$		0			0
$281$	122.023	−	70.4498i	0.434244	−	0.250711i	−0.266909	−	0.963722i	$-0.586002\pi$
$281$	122.023	−	70.4498i	0.434244	−	0.250711i	0.701153	+	0.713011i	$0.252669\pi$
$282$		0			0
$283$	−155.690	+	269.663i	−0.550141	+	0.952872i	0.448123	+	0.893972i	$0.352093\pi$
$283$	−155.690	+	269.663i	−0.550141	+	0.952872i	−0.998264	+	0.0589002i	$0.981241\pi$
$284$		0			0
$285$	−99.2757	−	93.5614i	−0.348336	−	0.328286i
$286$		0			0
$287$		−	79.1271i		−	0.275704i
$288$		0			0
$289$	127.733			0.441983
$290$		0			0
$291$	−4.33012	−	14.4355i	−0.0148801	−	0.0496065i
$292$		0			0
$293$	−273.621	−	157.975i	−0.933859	−	0.539164i	−0.0458290	−	0.998949i	$-0.514593\pi$
$293$	−273.621	−	157.975i	−0.933859	−	0.539164i	−0.888030	+	0.459786i	$0.847926\pi$
$294$		0			0
$295$	−9.66712	−	16.7439i	−0.0327699	−	0.0567591i
$296$		0			0
$297$	−332.615	−	58.0987i	−1.11992	−	0.195618i
$298$		0			0
$299$	−636.116	+	367.262i	−2.12748	+	1.22830i
$300$		0			0
$301$	55.5399	−	96.1980i	0.184518	−	0.319595i
$302$		0			0
$303$	−285.701	+	85.6998i	−0.942907	+	0.282838i
$304$		0			0
$305$			216.829i			0.710916i
$306$		0			0
$307$	−379.819			−1.23720			−0.618598	−	0.785707i	$-0.712299\pi$
$307$	−379.819			−1.23720			−0.618598	+	0.785707i	$0.712299\pi$
$308$		0			0
$309$	56.0315	−	59.4536i	0.181332	−	0.192406i
$310$		0			0
$311$	−335.497	−	193.699i	−1.07877	−	0.622827i	−0.148204	−	0.988957i	$-0.547349\pi$
$311$	−335.497	−	193.699i	−1.07877	−	0.622827i	−0.930564	+	0.366130i	$0.880683\pi$
$312$		0			0
$313$	−100.742	−	174.491i	−0.321860	−	0.557479i	0.659011	−	0.752133i	$-0.270975\pi$
$313$	−100.742	−	174.491i	−0.321860	−	0.557479i	−0.980872	+	0.194654i	$0.937642\pi$
$314$		0			0
$315$	13.1587	−	26.2712i	0.0417737	−	0.0834007i
$316$		0			0
$317$	319.046	−	184.201i	1.00645	−	0.581077i	0.0963027	−	0.995352i	$-0.469298\pi$
$317$	319.046	−	184.201i	1.00645	−	0.581077i	0.910152	+	0.414275i	$0.135965\pi$
$318$		0			0
$319$	186.125	−	322.378i	0.583463	−	1.01059i
$320$		0			0
$321$	−87.8332	+	371.483i	−0.273624	+	1.15727i
$322$		0			0
$323$		−	276.442i		−	0.855857i
$324$		0			0
$325$	−455.824			−1.40254
$326$		0			0
$327$	161.478	+	38.1797i	0.493816	+	0.116758i
$328$		0			0
$329$	−89.4716	−	51.6564i	−0.271950	−	0.157010i
$330$		0			0
$331$	150.832	+	261.248i	0.455684	+	0.789268i	0.998727	−	0.0504365i	$-0.0160613\pi$
$331$	150.832	+	261.248i	0.455684	+	0.789268i	−0.543043	+	0.839705i	$0.682728\pi$
$332$		0			0
$333$	−66.5333	−	33.3251i	−0.199800	−	0.100076i
$334$		0			0
$335$	−71.9460	+	41.5380i	−0.214764	+	0.123994i
$336$		0			0
$337$	85.5075	−	148.103i	0.253732	−	0.439476i	−0.710819	−	0.703375i	$-0.751675\pi$
$337$	85.5075	−	148.103i	0.253732	−	0.439476i	0.964550	+	0.263899i	$0.0850087\pi$
$338$		0			0
$339$	259.268	+	244.345i	0.764804	+	0.720782i
$340$		0			0
$341$			172.965i			0.507227i
$342$		0			0
$343$	−149.347			−0.435414
$344$		0			0
$345$	−59.8743	−	199.605i	−0.173549	−	0.578566i
$346$		0			0
$347$	264.744	+	152.850i	0.762950	+	0.440489i	0.830354	−	0.557237i	$-0.188138\pi$
$347$	264.744	+	152.850i	0.762950	+	0.440489i	−0.0674041	+	0.997726i	$0.521472\pi$
$348$		0			0
$349$	−11.1944	−	19.3893i	−0.0320756	−	0.0555566i	0.849542	−	0.527521i	$-0.176878\pi$
$349$	−11.1944	−	19.3893i	−0.0320756	−	0.0555566i	−0.881618	+	0.471964i	$0.843545\pi$
$350$		0			0
$351$	560.086	−	204.873i	1.59569	−	0.583685i
$352$		0			0
$353$	−462.657	+	267.115i	−1.31064	+	0.756700i	−0.982203	−	0.187825i	$-0.939856\pi$
$353$	−462.657	+	267.115i	−1.31064	+	0.756700i	−0.328440	+	0.944525i	$0.606523\pi$
$354$		0			0
$355$	19.1758	−	33.2134i	0.0540163	−	0.0935590i
$356$		0			0
$357$	57.0318	−	17.1075i	0.159753	−	0.0479200i
$358$		0			0
$359$		−	217.172i		−	0.604936i	−0.953159	−	0.302468i	$-0.902189\pi$
$359$		−	217.172i		−	0.604936i	0.953159	−	0.302468i	$-0.0978106\pi$
$360$		0			0
$361$	112.874			0.312669
$362$		0			0
$363$	72.8168	−	77.2641i	0.200597	−	0.212849i
$364$		0			0
$365$	−124.059	−	71.6253i	−0.339887	−	0.196234i
$366$		0			0
$367$	−51.1847	−	88.6546i	−0.139468	−	0.241566i	0.787827	−	0.615896i	$-0.211206\pi$
$367$	−51.1847	−	88.6546i	−0.139468	−	0.241566i	−0.927295	+	0.374330i	$0.877873\pi$
$368$		0			0
$369$	250.793	+	380.425i	0.679657	+	1.03096i
$370$		0			0
$371$	−8.18042	+	4.72297i	−0.0220497	+	0.0127304i
$372$		0			0
$373$	243.458	−	421.682i	0.652702	−	1.13051i	−0.329762	−	0.944064i	$-0.606969\pi$
$373$	243.458	−	421.682i	0.652702	−	1.13051i	0.982464	−	0.186450i	$-0.0596982\pi$
$374$		0			0
$375$	65.8045	−	278.314i	0.175479	−	0.742172i
$376$		0			0
$377$			657.490i			1.74401i
$378$		0			0
$379$	553.727			1.46102			0.730510	−	0.682901i	$-0.239282\pi$
$379$	553.727			1.46102			0.730510	+	0.682901i	$0.239282\pi$
$380$		0			0
$381$	217.362	+	51.3929i	0.570503	+	0.134889i
$382$		0			0
$383$	184.612	+	106.586i	0.482016	+	0.278292i	0.721256	−	0.692668i	$-0.243565\pi$
$383$	184.612	+	106.586i	0.482016	+	0.278292i	−0.239240	+	0.970960i	$0.576898\pi$
$384$		0			0
$385$	20.4136	+	35.3574i	0.0530224	+	0.0918375i
$386$		0			0
$387$	37.8759	+	638.532i	0.0978707	+	1.64995i
$388$		0			0
$389$	−82.4958	+	47.6290i	−0.212071	+	0.122439i	−0.602274	−	0.798290i	$-0.705738\pi$
$389$	−82.4958	+	47.6290i	−0.212071	+	0.122439i	0.390202	+	0.920729i	$0.372405\pi$
$390$		0			0
$391$	211.149	−	365.720i	0.540022	−	0.935346i
$392$		0			0
$393$	−17.8610	−	16.8330i	−0.0454479	−	0.0428320i
$394$		0			0
$395$			55.6184i			0.140806i
$396$		0			0
$397$	−481.407			−1.21261			−0.606306	−	0.795231i	$-0.707349\pi$
$397$	−481.407			−1.21261			−0.606306	+	0.795231i	$0.707349\pi$
$398$		0			0
$399$	29.3254	+	97.7633i	0.0734973	+	0.245021i
$400$		0			0
$401$	−517.354	−	298.694i	−1.29016	−	0.744874i	−0.311477	−	0.950254i	$-0.600824\pi$
$401$	−517.354	−	298.694i	−1.29016	−	0.744874i	−0.978682	+	0.205380i	$0.934157\pi$
$402$		0			0
$403$	−152.750	−	264.571i	−0.379033	−	0.656505i
$404$		0			0
$405$	20.0025	+	168.013i	0.0493888	+	0.414846i
$406$		0			0
$407$	89.5446	−	51.6986i	0.220011	−	0.127024i
$408$		0			0
$409$	−53.7260	+	93.0562i	−0.131359	+	0.227521i	−0.924201	−	0.381907i	$-0.875268\pi$
$409$	−53.7260	+	93.0562i	−0.131359	+	0.227521i	0.792841	+	0.609428i	$0.208601\pi$
$410$		0			0
$411$	−138.453	+	41.5308i	−0.336868	+	0.101048i
$412$		0			0
$413$			14.4659i			0.0350264i
$414$		0			0
$415$	50.7433			0.122273
$416$		0			0
$417$	489.795	−	519.709i	1.17457	−	1.24631i
$418$		0			0
$419$	39.6993	+	22.9204i	0.0947477	+	0.0547026i	0.546625	−	0.837377i	$-0.315912\pi$
$419$	39.6993	+	22.9204i	0.0947477	+	0.0547026i	−0.451878	+	0.892080i	$0.649246\pi$
$420$		0			0
$421$	−5.53062	−	9.57932i	−0.0131369	−	0.0227537i	0.859382	−	0.511334i	$-0.170848\pi$
$421$	−5.53062	−	9.57932i	−0.0131369	−	0.0227537i	−0.872519	+	0.488580i	$0.837515\pi$
$422$		0			0
$423$	593.885	−	35.2276i	1.40398	−	0.0832803i
$424$		0			0
$425$	226.956	−	131.033i	0.534013	−	0.308313i
$426$		0			0
$427$	81.1161	−	140.497i	0.189967	−	0.329033i
$428$		0			0
$429$	−190.675	+	806.442i	−0.444463	+	1.87982i
$430$		0			0
$431$			590.788i			1.37074i	0.728196	+	0.685369i	$0.240359\pi$
$431$			590.788i			1.37074i	−0.728196	+	0.685369i	$0.759641\pi$
$432$		0			0
$433$	−13.9683			−0.0322594			−0.0161297	−	0.999870i	$-0.505134\pi$
$433$	−13.9683			−0.0322594			−0.0161297	+	0.999870i	$0.505134\pi$
$434$		0			0
$435$	−181.532	−	42.9212i	−0.417314	−	0.0986695i
$436$		0			0
$437$	626.914	+	361.949i	1.43459	+	0.828258i
$438$		0			0
$439$	35.9051	+	62.1894i	0.0817883	+	0.141662i	0.904018	−	0.427494i	$-0.140604\pi$
$439$	35.9051	+	62.1894i	0.0817883	+	0.141662i	−0.822230	+	0.569156i	$0.807270\pi$
$440$		0			0
$441$	349.836	−	230.628i	0.793279	−	0.522965i
$442$		0			0
$443$	−581.028	+	335.457i	−1.31158	+	0.757239i	−0.982357	−	0.187015i	$-0.940119\pi$
$443$	−581.028	+	335.457i	−1.31158	+	0.757239i	−0.329219	+	0.944254i	$0.606786\pi$
$444$		0			0
$445$	116.695	−	202.122i	0.262236	−	0.454206i
$446$		0			0
$447$	−622.310	−	586.490i	−1.39219	−	1.31206i
$448$		0			0
$449$		−	830.401i		−	1.84945i	−0.380642	−	0.924723i	$-0.624297\pi$
$449$		−	830.401i		−	1.84945i	0.380642	−	0.924723i	$-0.375703\pi$
$450$		0			0
$451$	−633.136			−1.40385
$452$		0			0
$453$	−133.160	−	443.919i	−0.293950	−	0.979954i
$454$		0			0
$455$	−62.4505	−	36.0558i	−0.137254	−	0.0792435i
$456$		0			0
$457$	423.113	+	732.854i	0.925850	+	1.60362i	0.790188	+	0.612864i	$0.209983\pi$
$457$	423.113	+	732.854i	0.925850	+	1.60362i	0.135661	+	0.990755i	$0.456684\pi$
$458$		0			0
$459$	−219.974	+	263.011i	−0.479247	+	0.573009i
$460$		0			0
$461$	109.019	−	62.9423i	0.236484	−	0.136534i	−0.377076	−	0.926182i	$-0.623070\pi$
$461$	109.019	−	62.9423i	0.236484	−	0.136534i	0.613560	+	0.789648i	$0.289737\pi$
$462$		0			0
$463$	307.121	−	531.950i	0.663329	−	1.14892i	−0.316407	−	0.948624i	$-0.602476\pi$
$463$	307.121	−	531.950i	0.663329	−	1.14892i	0.979735	−	0.200296i	$-0.0641903\pi$
$464$		0			0
$465$	83.0192	−	24.9027i	0.178536	−	0.0535543i
$466$		0			0
$467$		−	172.270i		−	0.368887i	−0.982843	−	0.184444i	$-0.940952\pi$
$467$		−	172.270i		−	0.368887i	0.982843	−	0.184444i	$-0.0590484\pi$
$468$		0			0
$469$	62.1576			0.132532
$470$		0			0
$471$	−493.595	+	523.742i	−1.04797	+	1.11198i
$472$		0			0
$473$	−769.729	−	444.403i	−1.62733	−	0.939542i
$474$		0			0
$475$	224.615	+	389.045i	0.472874	+	0.819042i
$476$		0			0
$477$	24.3602	−	48.6349i	0.0510696	−	0.101960i
$478$		0			0
$479$	−174.532	+	100.766i	−0.364367	+	0.210367i	−0.670995	−	0.741462i	$-0.734133\pi$
$479$	−174.532	+	100.766i	−0.364367	+	0.210367i	0.306628	+	0.951829i	$0.400799\pi$
$480$		0			0
$481$	−91.3132	+	158.159i	−0.189840	+	0.328813i
$482$		0			0
$483$	−35.8762	+	151.736i	−0.0742779	+	0.314152i
$484$		0			0
$485$		−	10.4938i		−	0.0216367i
$486$		0			0
$487$	−801.178			−1.64513			−0.822565	−	0.568671i	$-0.807458\pi$
$487$	−801.178			−1.64513			−0.822565	+	0.568671i	$0.807458\pi$
$488$		0			0
$489$	324.779	+	76.7906i	0.664170	+	0.157036i
$490$		0			0
$491$	625.711	+	361.255i	1.27436	+	0.735753i	0.975806	−	0.218640i	$-0.0701619\pi$
$491$	625.711	+	361.255i	1.27436	+	0.735753i	0.298555	+	0.954392i	$0.403495\pi$
$492$		0			0
$493$	−189.005	−	327.366i	−0.383376	−	0.664028i
$494$		0			0
$495$	−210.210	−	105.290i	−0.424666	−	0.212706i
$496$		0			0
$497$	−24.8503	+	14.3474i	−0.0500007	+	0.0288679i
$498$		0			0
$499$	−69.4409	+	120.275i	−0.139160	+	0.241032i	−0.927179	−	0.374619i	$-0.877774\pi$
$499$	−69.4409	+	120.275i	−0.139160	+	0.241032i	0.788019	+	0.615651i	$0.211107\pi$
$500$		0			0
$501$	95.5740	+	90.0728i	0.190766	+	0.179786i
$502$		0			0
$503$		−	794.533i		−	1.57959i	−0.613372	−	0.789794i	$-0.710187\pi$
$503$		−	794.533i		−	1.57959i	0.613372	−	0.789794i	$-0.289813\pi$
$504$		0			0
$505$	−207.689			−0.411264
$506$		0			0
$507$	−274.864	−	916.323i	−0.542137	−	1.80734i
$508$		0			0
$509$	−179.929	−	103.882i	−0.353495	−	0.204090i	0.312729	−	0.949843i	$-0.398757\pi$
$509$	−179.929	−	103.882i	−0.353495	−	0.204090i	−0.666224	+	0.745752i	$0.732090\pi$
$510$		0			0
$511$	53.5902	+	92.8209i	0.104873	+	0.181646i
$512$		0			0
$513$	−450.851	−	377.077i	−0.878852	−	0.735043i
$514$		0			0
$515$	49.2634	−	28.4422i	0.0956571	−	0.0552276i
$516$		0			0
$517$	−413.330	+	715.908i	−0.799477	+	1.38474i
$518$		0			0
$519$	−840.734	+	252.190i	−1.61991	+	0.485914i
$520$		0			0
$521$			248.275i			0.476535i	0.971200	+	0.238267i	$0.0765795\pi$
$521$			248.275i			0.476535i	−0.971200	+	0.238267i	$0.923421\pi$
$522$		0			0
$523$	−108.678			−0.207797			−0.103898	−	0.994588i	$-0.533132\pi$
$523$	−108.678			−0.207797			−0.103898	+	0.994588i	$0.533132\pi$
$524$		0			0
$525$	−66.3623	+	70.4154i	−0.126404	+	0.134125i
$526$		0			0
$527$	152.109	+	87.8204i	0.288633	+	0.166642i
$528$		0			0
$529$	288.420	+	499.557i	0.545216	+	0.944343i
$530$		0			0
$531$	−45.8497	−	69.5489i	−0.0863460	−	0.130977i
$532$		0			0
$533$	968.463	−	559.142i	1.81700	−	1.04905i
$534$		0			0
$535$	−132.896	+	230.183i	−0.248405	+	0.430249i
$536$		0			0
$537$	134.338	−	568.171i	0.250164	−	1.05805i
$538$		0			0
$539$			582.227i			1.08020i
$540$		0			0
$541$	−20.0646			−0.0370880			−0.0185440	−	0.999828i	$-0.505903\pi$
$541$	−20.0646			−0.0370880			−0.0185440	+	0.999828i	$0.505903\pi$
$542$		0			0
$543$	260.976	+	61.7051i	0.480619	+	0.113637i
$544$		0			0
$545$	100.057	+	57.7680i	0.183591	+	0.105996i
$546$		0			0
$547$	86.6937	+	150.158i	0.158489	+	0.274512i	0.934324	−	0.356424i	$-0.116004\pi$
$547$	86.6937	+	150.158i	0.158489	+	0.274512i	−0.775835	+	0.630936i	$0.782671\pi$
$548$		0			0
$549$	55.3178	+	932.577i	0.100761	+	1.69868i
$550$		0			0
$551$	561.167	−	323.990i	1.01845	−	0.588003i
$552$		0			0
$553$	20.8069	−	36.0386i	0.0376254	−	0.0651692i
$554$		0			0
$555$	−37.7064	−	35.5361i	−0.0679395	−	0.0640290i
$556$		0			0
$557$		−	434.666i		−	0.780370i	−0.920737	−	0.390185i	$-0.872411\pi$
$557$		−	434.666i		−	0.780370i	0.920737	−	0.390185i	$-0.127589\pi$
$558$		0			0
$559$	1569.87			2.80835
$560$		0			0
$561$	−136.886	−	456.341i	−0.244003	−	0.813442i
$562$		0			0
$563$	86.8277	+	50.1300i	0.154223	+	0.0890409i	0.575126	−	0.818065i	$-0.304953\pi$
$563$	86.8277	+	50.1300i	0.154223	+	0.0890409i	−0.420902	+	0.907106i	$0.638286\pi$
$564$		0			0
$565$	124.032	+	214.830i	0.219526	+	0.380231i
$566$		0			0
$567$	49.8929	−	116.349i	0.0879945	−	0.205201i
$568$		0			0
$569$	44.1556	−	25.4932i	0.0776020	−	0.0448036i	−0.460697	−	0.887558i	$-0.652400\pi$
$569$	44.1556	−	25.4932i	0.0776020	−	0.0448036i	0.538299	+	0.842754i	$0.319067\pi$
$570$		0			0
$571$	430.481	−	745.615i	0.753907	−	1.30581i	−0.192009	−	0.981393i	$-0.561500\pi$
$571$	430.481	−	745.615i	0.753907	−	1.30581i	0.945916	−	0.324412i	$-0.105166\pi$
$572$		0			0
$573$	−149.008	+	44.6970i	−0.260049	+	0.0780053i
$574$		0			0
$575$			686.252i			1.19348i
$576$		0			0
$577$	59.3431			0.102848			0.0514239	−	0.998677i	$-0.483624\pi$
$577$	59.3431			0.102848			0.0514239	+	0.998677i	$0.483624\pi$
$578$		0			0
$579$	−122.533	+	130.017i	−0.211628	+	0.224554i
$580$		0			0
$581$	−32.8797	−	18.9831i	−0.0565916	−	0.0326732i
$582$		0			0
$583$	37.7909	+	65.4558i	0.0648215	+	0.112274i
$584$		0			0
$585$	414.527	−	24.5886i	0.708593	−	0.0420318i
$586$		0			0
$587$	534.777	−	308.754i	0.911034	−	0.525986i	0.0302706	−	0.999542i	$-0.490363\pi$
$587$	534.777	−	308.754i	0.911034	−	0.525986i	0.880764	+	0.473556i	$0.157030\pi$
$588$		0			0
$589$	−150.541	+	260.744i	−0.255587	+	0.442690i
$590$		0			0
$591$	32.7863	−	138.667i	0.0554760	−	0.234631i
$592$		0			0
$593$			342.310i			0.577251i	0.957442	+	0.288626i	$0.0931983\pi$
$593$			342.310i			0.577251i	−0.957442	+	0.288626i	$0.906802\pi$
$594$		0			0
$595$	41.4589			0.0696789
$596$		0			0
$597$	86.1950	+	20.3799i	0.144380	+	0.0341372i
$598$		0			0
$599$	379.292	+	218.984i	0.633209	+	0.365583i	0.781994	−	0.623286i	$-0.214203\pi$
$599$	379.292	+	218.984i	0.633209	+	0.365583i	−0.148785	+	0.988870i	$0.547536\pi$
$600$		0			0
$601$	304.452	+	527.327i	0.506576	+	0.877416i	0.999971	+	0.00761053i	$0.00242253\pi$
$601$	304.452	+	527.327i	0.506576	+	0.877416i	−0.493395	+	0.869806i	$0.664244\pi$
$602$		0			0
$603$	−298.840	+	197.009i	−0.495589	+	0.326714i
$604$		0			0
$605$	64.0212	−	36.9627i	0.105820	−	0.0610953i
$606$		0			0
$607$	−540.751	+	936.608i	−0.890858	+	1.54301i	−0.0520102	+	0.998647i	$0.516563\pi$
$607$	−540.751	+	936.608i	−0.890858	+	1.54301i	−0.838848	+	0.544365i	$0.816770\pi$
$608$		0			0
$609$	101.569	+	95.7225i	0.166779	+	0.157180i
$610$		0			0
$611$		−	1460.10i		−	2.38968i
$612$		0			0
$613$	−222.279			−0.362609			−0.181304	−	0.983427i	$-0.558032\pi$
$613$	−222.279			−0.362609			−0.181304	+	0.983427i	$0.558032\pi$
$614$		0			0
$615$	91.1564	+	303.892i	0.148222	+	0.494133i
$616$		0			0
$617$	−31.0310	−	17.9158i	−0.0502934	−	0.0290369i	0.474642	−	0.880179i	$-0.342577\pi$
$617$	−31.0310	−	17.9158i	−0.0502934	−	0.0290369i	−0.524936	+	0.851142i	$0.675911\pi$
$618$		0			0
$619$	−161.494	−	279.717i	−0.260896	−	0.451885i	0.705584	−	0.708626i	$-0.250685\pi$
$619$	−161.494	−	279.717i	−0.260896	−	0.451885i	−0.966480	+	0.256741i	$0.917351\pi$
$620$		0			0
$621$	−308.441	−	843.221i	−0.496684	−	1.35784i
$622$		0			0
$623$	−151.228	+	87.3114i	−0.242741	+	0.140147i
$624$		0			0
$625$	−158.391	+	274.342i	−0.253426	+	0.438947i
$626$		0			0
$627$	782.254	−	234.648i	1.24761	−	0.374239i
$628$		0			0
$629$		−	104.997i		−	0.166927i
$630$		0			0
$631$	−794.037			−1.25838			−0.629189	−	0.777252i	$-0.716613\pi$
$631$	−794.037			−1.25838			−0.629189	+	0.777252i	$0.716613\pi$
$632$		0			0
$633$	−333.555	+	353.927i	−0.526943	+	0.559126i
$634$		0			0
$635$	134.685	+	77.7602i	0.212102	+	0.122457i
$636$		0			0
$637$	−514.183	−	890.591i	−0.807194	−	1.39810i
$638$		0			0
$639$	74.0010	−	147.742i	0.115808	−	0.231208i
$640$		0			0
$641$	−753.063	+	434.781i	−1.17483	+	0.678286i	−0.954812	−	0.297211i	$-0.903943\pi$
$641$	−753.063	+	434.781i	−1.17483	+	0.678286i	−0.220013	+	0.975497i	$0.570610\pi$
$642$		0			0
$643$	31.2519	−	54.1299i	0.0486033	−	0.0841834i	−0.840700	−	0.541501i	$-0.817856\pi$
$643$	31.2519	−	54.1299i	0.0486033	−	0.0841834i	0.889304	+	0.457317i	$0.151190\pi$
$644$		0			0
$645$	−102.481	+	433.437i	−0.158886	+	0.671995i
$646$		0			0
$647$			761.439i			1.17688i	0.808542	+	0.588438i	$0.200257\pi$
$647$			761.439i			1.17688i	−0.808542	+	0.588438i	$0.799743\pi$
$648$		0			0
$649$	115.749			0.178350
$650$		0			0
$651$	−63.1094	−	14.9215i	−0.0969422	−	0.0229210i
$652$		0			0
$653$	129.622	+	74.8371i	0.198502	+	0.114605i	0.595956	−	0.803017i	$-0.296773\pi$
$653$	129.622	+	74.8371i	0.198502	+	0.114605i	−0.397455	+	0.917622i	$0.630106\pi$
$654$		0			0
$655$	−8.54461	−	14.7997i	−0.0130452	−	0.0225950i
$656$		0			0
$657$	−551.846	−	276.408i	−0.839948	−	0.420713i
$658$		0			0
$659$	−564.273	+	325.783i	−0.856256	+	0.494360i	−0.862757	−	0.505619i	$-0.831264\pi$
$659$	−564.273	+	325.783i	−0.856256	+	0.494360i	0.00650063	+	0.999979i	$0.497931\pi$
$660$		0			0
$661$	596.672	−	1033.47i	0.902681	−	1.56349i	0.0786818	−	0.996900i	$-0.474929\pi$
$661$	596.672	−	1033.47i	0.902681	−	1.56349i	0.824000	−	0.566590i	$-0.191738\pi$
$662$		0			0
$663$	612.393	+	577.144i	0.923669	+	0.870503i
$664$		0			0
$665$			71.0685i			0.106870i
$666$		0			0
$667$	989.865			1.48405
$668$		0			0
$669$	177.054	+	590.251i	0.264654	+	0.882289i
$670$		0			0
$671$	−1124.19	−	649.051i	−1.67539	−	0.967290i
$672$		0			0
$673$	−74.7771	−	129.518i	−0.111110	−	0.192448i	0.805108	−	0.593128i	$-0.202107\pi$
$673$	−74.7771	−	129.518i	−0.111110	−	0.192448i	−0.916218	+	0.400680i	$0.868774\pi$
$674$		0			0
$675$	95.8737	−	548.877i	0.142035	−	0.813152i
$676$		0			0
$677$	−607.487	+	350.733i	−0.897322	+	0.518069i	−0.876331	−	0.481710i	$-0.840016\pi$
$677$	−607.487	+	350.733i	−0.897322	+	0.518069i	−0.0209919	+	0.999780i	$0.506682\pi$
$678$		0			0
$679$	−3.92574	+	6.79958i	−0.00578165	+	0.0100141i
$680$		0			0
$681$	179.312	−	53.7871i	0.263307	−	0.0789826i
$682$		0			0
$683$		−	503.096i		−	0.736597i	−0.929708	−	0.368299i	$-0.879940\pi$
$683$		−	503.096i		−	0.736597i	0.929708	−	0.368299i	$-0.120060\pi$
$684$		0			0
$685$	−100.648			−0.146931
$686$		0			0
$687$	−23.6121	+	25.0542i	−0.0343699	+	0.0364690i
$688$		0			0
$689$	−115.612	−	66.7487i	−0.167797	−	0.0968776i
$690$		0			0
$691$	−329.413	−	570.561i	−0.476720	−	0.825703i	0.522924	−	0.852379i	$-0.324841\pi$
$691$	−329.413	−	570.561i	−0.476720	−	0.825703i	−0.999644	+	0.0266761i	$0.991508\pi$
$692$		0			0
$693$	96.8188	+	146.863i	0.139710	+	0.211924i
$694$		0			0
$695$	430.633	−	248.626i	0.619615	−	0.357735i
$696$		0			0
$697$	−321.466	+	556.796i	−0.461214	+	0.798846i
$698$		0			0
$699$	122.247	−	517.033i	0.174888	−	0.739675i
$700$		0			0
$701$			172.963i			0.246738i	0.992361	+	0.123369i	$0.0393698\pi$
$701$			172.963i			0.246738i	−0.992361	+	0.123369i	$0.960630\pi$
$702$		0			0
$703$	179.985			0.256024
$704$		0			0
$705$	403.130	+	95.3158i	0.571815	+	0.135200i
$706$		0			0
$707$	134.574	+	77.6964i	0.190345	+	0.109896i
$708$		0			0
$709$	−527.267	−	913.254i	−0.743677	−	1.28809i	−0.950810	−	0.309774i	$-0.899747\pi$
$709$	−527.267	−	913.254i	−0.743677	−	1.28809i	0.207133	−	0.978313i	$-0.433587\pi$
$710$		0			0
$711$	14.1894	+	239.213i	0.0199570	+	0.336446i
$712$		0			0
$713$	−398.317	+	229.969i	−0.558650	+	0.322537i
$714$		0			0
$715$	−288.501	+	499.699i	−0.403498	+	0.698879i
$716$		0			0
$717$	−582.933	−	549.380i	−0.813017	−	0.766220i
$718$		0			0
$719$			1164.78i			1.62000i	0.586432	+	0.809998i	$0.300532\pi$
$719$			1164.78i			1.62000i	−0.586432	+	0.809998i	$0.699468\pi$
$720$		0			0
$721$	−42.5611			−0.0590306
$722$		0			0
$723$	70.1931	+	234.006i	0.0970859	+	0.323659i
$724$		0			0
$725$	531.983	+	307.141i	0.733770	+	0.423642i
$726$		0			0
$727$	−492.209	−	852.530i	−0.677041	−	1.17267i	−0.975868	−	0.218362i	$-0.929929\pi$
$727$	−492.209	−	852.530i	−0.677041	−	1.17267i	0.298827	−	0.954307i	$-0.403405\pi$
$728$		0			0
$729$	128.894	+	717.515i	0.176809	+	0.984245i
$730$		0			0
$731$	−781.639	+	451.280i	−1.06927	+	0.617345i
$732$		0			0
$733$	246.459	−	426.879i	0.336233	−	0.582372i	−0.647488	−	0.762076i	$-0.724180\pi$
$733$	246.459	−	426.879i	0.336233	−	0.582372i	0.983721	+	0.179703i	$0.0575138\pi$
$734$		0			0
$735$	279.456	−	83.8267i	0.380213	−	0.114050i
$736$		0			0
$737$		−	497.355i		−	0.674837i
$738$		0			0
$739$	−571.150			−0.772869			−0.386435	−	0.922317i	$-0.626293\pi$
$739$	−571.150			−0.772869			−0.386435	+	0.922317i	$0.626293\pi$
$740$		0			0
$741$	−989.333	+	1049.76i	−1.33513	+	1.41668i
$742$		0			0
$743$	−910.255	−	525.536i	−1.22511	−	0.707316i	−0.259105	−	0.965849i	$-0.583427\pi$
$743$	−910.255	−	525.536i	−1.22511	−	0.707316i	−0.966002	+	0.258533i	$0.916761\pi$
$744$		0			0
$745$	−297.709	−	515.648i	−0.399610	−	0.692144i
$746$		0			0
$747$	218.246	−	12.9457i	0.292163	−	0.0173303i
$748$		0			0
$749$	172.224	−	99.4334i	0.229938	−	0.132755i
$750$		0			0
$751$	−42.3053	+	73.2749i	−0.0563319	+	0.0975698i	−0.892816	−	0.450421i	$-0.851274\pi$
$751$	−42.3053	+	73.2749i	−0.0563319	+	0.0975698i	0.836484	+	0.547991i	$0.184607\pi$
$752$		0			0
$753$	215.244	−	910.357i	0.285849	−	1.20897i
$754$		0			0
$755$		−	322.705i		−	0.427423i
$756$		0			0
$757$	1007.63			1.33109			0.665543	−	0.746360i	$-0.268200\pi$
$757$	1007.63			1.33109			0.665543	+	0.746360i	$0.268200\pi$
$758$		0			0
$759$	1214.11	+	287.064i	1.59962	+	0.378214i
$760$		0			0
$761$	393.981	+	227.465i	0.517715	+	0.298903i	0.735999	−	0.676983i	$-0.236713\pi$
$761$	393.981	+	227.465i	0.517715	+	0.298903i	−0.218285	+	0.975885i	$0.570046\pi$
$762$		0			0
$763$	−43.2221	−	74.8629i	−0.0566476	−	0.0981165i
$764$		0			0
$765$	−199.325	+	131.404i	−0.260556	+	0.171770i
$766$		0			0
$767$	−177.053	+	102.222i	−0.230838	+	0.133275i
$768$		0			0
$769$	352.232	−	610.084i	0.458039	−	0.793347i	−0.540818	−	0.841139i	$-0.681885\pi$
$769$	352.232	−	610.084i	0.458039	−	0.793347i	0.998857	+	0.0477927i	$0.0152187\pi$
$770$		0			0
$771$	844.829	+	796.201i	1.09576	+	1.03269i
$772$		0			0
$773$			1021.43i			1.32138i	0.750658	+	0.660691i	$0.229737\pi$
$773$			1021.43i			1.32138i	−0.750658	+	0.660691i	$0.770263\pi$
$774$		0			0
$775$	−285.424			−0.368289
$776$		0			0
$777$	11.1383	+	37.1320i	0.0143349	+	0.0477890i
$778$		0			0
$779$	−954.453	−	551.054i	−1.22523	−	0.707386i
$780$		0			0
$781$	114.801	+	198.840i	0.146992	+	0.254597i
$782$		0			0
$783$	−791.712	−	138.290i	−1.01113	−	0.176616i
$784$		0			0
$785$	−433.974	+	250.555i	−0.552833	+	0.319178i
$786$		0			0
$787$	−202.007	+	349.886i	−0.256680	+	0.444582i	−0.965350	−	0.260957i	$-0.915962\pi$
$787$	−202.007	+	349.886i	−0.256680	+	0.444582i	0.708671	+	0.705539i	$0.249295\pi$
$788$		0			0
$789$	1383.94	−	415.131i	1.75404	−	0.526148i
$790$		0			0
$791$		−	185.603i		−	0.234643i
$792$		0			0
$793$	2292.79			2.89129
$794$		0			0
$795$	25.9764	−	27.5629i	0.0326747	−	0.0346703i
$796$		0			0
$797$	765.042	+	441.697i	0.959902	+	0.554200i	0.896143	−	0.443766i	$-0.146358\pi$
$797$	765.042	+	441.697i	0.959902	+	0.554200i	0.0637592	+	0.997965i	$0.479691\pi$
$798$		0			0
$799$	419.725	+	726.985i	0.525313	+	0.909869i
$800$		0			0
$801$	450.336	−	899.090i	0.562217	−	1.12246i
$802$		0			0
$803$	742.708	−	428.803i	0.924917	−	0.534001i
$804$		0			0
$805$	−54.2827	+	94.0204i	−0.0674320	+	0.116796i
$806$		0			0
$807$	−155.879	+	659.278i	−0.193159	+	0.816949i
$808$		0			0
$809$			372.575i			0.460537i	0.973127	+	0.230269i	$0.0739605\pi$
$809$			372.575i			0.460537i	−0.973127	+	0.230269i	$0.926040\pi$
$810$		0			0
$811$	267.519			0.329863			0.164932	−	0.986305i	$-0.447260\pi$
$811$	267.519			0.329863			0.164932	+	0.986305i	$0.447260\pi$
$812$		0			0
$813$	−69.0812	−	16.3335i	−0.0849707	−	0.0200904i
$814$		0			0
$815$	201.244	+	116.188i	0.246925	+	0.142562i
$816$		0			0
$817$	−773.578	−	1339.88i	−0.946852	−	1.64000i
$818$		0			0
$819$	−277.796	−	139.142i	−0.339189	−	0.169893i
$820$		0			0
$821$	574.911	−	331.925i	0.700257	−	0.404293i	−0.107186	−	0.994239i	$-0.534184\pi$
$821$	574.911	−	331.925i	0.700257	−	0.404293i	0.807443	+	0.589946i	$0.200851\pi$
$822$		0			0
$823$	−468.171	+	810.896i	−0.568859	+	0.985292i	0.427820	+	0.903864i	$0.359282\pi$
$823$	−468.171	+	810.896i	−0.568859	+	0.985292i	−0.996679	+	0.0814286i	$0.974052\pi$
$824$		0			0
$825$	563.430	+	530.999i	0.682946	+	0.643636i
$826$		0			0
$827$			499.832i			0.604392i	0.953246	+	0.302196i	$0.0977196\pi$
$827$			499.832i			0.604392i	−0.953246	+	0.302196i	$0.902280\pi$
$828$		0			0
$829$	−667.578			−0.805280			−0.402640	−	0.915358i	$-0.631907\pi$
$829$	−667.578			−0.805280			−0.402640	+	0.915358i	$0.631907\pi$
$830$		0			0
$831$	−48.2636	−	160.898i	−0.0580790	−	0.193620i
$832$		0			0
$833$	512.025	+	295.618i	0.614676	+	0.354883i
$834$		0			0
$835$	45.7220	+	79.1929i	0.0547569	+	0.0948418i
$836$		0			0
$837$	350.710	−	128.286i	0.419008	−	0.153269i
$838$		0			0
$839$	64.1295	−	37.0252i	0.0764356	−	0.0441301i	−0.461295	−	0.887247i	$-0.652615\pi$
$839$	64.1295	−	37.0252i	0.0764356	−	0.0441301i	0.537731	+	0.843117i	$0.319282\pi$
$840$		0			0
$841$	22.5264	−	39.0169i	0.0267853	−	0.0463935i
$842$		0			0
$843$	404.876	−	121.448i	0.480280	−	0.144066i
$844$		0			0
$845$		−	666.116i		−	0.788303i
$846$		0			0
$847$	−55.3110			−0.0653023
$848$		0			0
$849$	−640.682	+	679.811i	−0.754631	+	0.800720i
$850$		0			0
$851$	238.112	+	137.474i	0.279802	+	0.161544i
$852$		0			0
$853$	553.775	+	959.167i	0.649209	+	1.12446i	0.983312	+	0.181927i	$0.0582333\pi$
$853$	553.775	+	959.167i	0.649209	+	1.12446i	−0.334103	+	0.942537i	$0.608433\pi$
$854$		0			0
$855$	−225.252	−	341.681i	−0.263452	−	0.399627i
$856$		0			0
$857$	687.370	−	396.854i	0.802066	−	0.463073i	−0.0421271	−	0.999112i	$-0.513413\pi$
$857$	687.370	−	396.854i	0.802066	−	0.463073i	0.844193	+	0.536039i	$0.180080\pi$
$858$		0			0
$859$	121.830	−	211.016i	0.141828	−	0.245653i	−0.786357	−	0.617772i	$-0.788035\pi$
$859$	121.830	−	211.016i	0.141828	−	0.245653i	0.928185	+	0.372119i	$0.121369\pi$
$860$		0			0
$861$	54.6203	−	231.012i	0.0634382	−	0.268306i
$862$		0			0
$863$		−	841.279i		−	0.974830i	−0.873170	−	0.487415i	$-0.837940\pi$
$863$		−	841.279i		−	0.974830i	0.873170	−	0.487415i	$-0.162060\pi$
$864$		0			0
$865$	−611.167			−0.706552
$866$		0			0
$867$	372.917	+	88.1723i	0.430124	+	0.101698i
$868$		0			0
$869$	−288.363	−	166.486i	−0.331833	−	0.191584i
$870$		0			0
$871$	439.230	+	760.768i	0.504282	+	0.873442i
$872$		0			0
$873$	−2.67719	−	45.1335i	−0.00306666	−	0.0516993i
$874$		0			0
$875$	−129.030	+	74.4953i	−0.147462	+	0.0851375i
$876$		0			0
$877$	−302.656	+	524.216i	−0.345104	+	0.597738i	−0.985373	−	0.170413i	$-0.945490\pi$
$877$	−302.656	+	524.216i	−0.345104	+	0.597738i	0.640269	+	0.768151i	$0.278823\pi$
$878$		0			0
$879$	−689.789	−	650.085i	−0.784743	−	0.739573i
$880$		0			0
$881$		−	820.188i		−	0.930974i	−0.885055	−	0.465487i	$-0.845879\pi$
$881$		−	820.188i		−	0.930974i	0.885055	−	0.465487i	$-0.154121\pi$
$882$		0			0
$883$	−623.820			−0.706478			−0.353239	−	0.935533i	$-0.614920\pi$
$883$	−623.820			−0.706478			−0.353239	+	0.935533i	$0.614920\pi$
$884$		0			0
$885$	−16.6651	−	55.5571i	−0.0188306	−	0.0627764i
$886$		0			0
$887$	−212.242	−	122.538i	−0.239281	−	0.138149i	0.375565	−	0.926796i	$-0.377449\pi$
$887$	−212.242	−	122.538i	−0.239281	−	0.138149i	−0.614846	+	0.788647i	$0.710782\pi$
$888$		0			0
$889$	−58.1803	−	100.771i	−0.0654447	−	0.113353i
$890$		0			0
$891$	−930.967	−	399.219i	−1.04486	−	0.448057i
$892$		0			0
$893$	−1246.19	+	719.488i	−1.39551	+	0.805698i
$894$		0			0
$895$	203.261	−	352.058i	0.227107	−	0.393361i
$896$		0			0
$897$	−2110.66	+	633.120i	−2.35302	+	0.705820i
$898$		0			0
$899$			411.702i			0.457955i
$900$		0			0
$901$	76.7513			0.0851845
$902$		0			0
$903$	228.553	−	242.512i	0.253104	−	0.268562i
$904$		0			0
$905$	161.710	+	93.3632i	0.178685	+	0.103164i
$906$		0			0
$907$	−109.071	−	188.917i	−0.120255	−	0.208287i	0.799613	−	0.600515i	$-0.205038\pi$
$907$	−109.071	−	188.917i	−0.120255	−	0.208287i	−0.919868	+	0.392228i	$0.871704\pi$
$908$		0			0
$909$	−893.262	+	52.9858i	−0.982686	+	0.0582902i
$910$		0			0
$911$	558.980	−	322.727i	0.613589	−	0.354256i	−0.160780	−	0.986990i	$-0.551401\pi$
$911$	558.980	−	322.727i	0.613589	−	0.354256i	0.774369	+	0.632735i	$0.218068\pi$
$912$		0			0
$913$	−151.894	+	263.088i	−0.166368	+	0.288157i
$914$		0			0
$915$	−149.674	+	633.034i	−0.163578	+	0.691841i
$916$		0			0
$917$			12.7862i			0.0139435i
$918$		0			0
$919$	1567.66			1.70583			0.852917	−	0.522047i	$-0.174831\pi$
$919$	1567.66			1.70583			0.852917	+	0.522047i	$0.174831\pi$
$920$		0			0
$921$	−1108.88	−	262.184i	−1.20400	−	0.284673i
$922$		0			0
$923$	−351.204	−	202.768i	−0.380503	−	0.219684i
$924$		0			0
$925$	85.3123	+	147.765i	0.0922296	+	0.159746i
$926$		0			0
$927$	204.624	−	134.897i	0.220738	−	0.145520i
$928$		0			0
$929$	78.1550	−	45.1228i	0.0841281	−	0.0485714i	−0.457346	−	0.889289i	$-0.651200\pi$
$929$	78.1550	−	45.1228i	0.0841281	−	0.0485714i	0.541474	+	0.840718i	$0.317867\pi$
$930$		0			0
$931$	−506.745	+	877.708i	−0.544302	+	0.942758i
$932$		0			0
$933$	−845.777	−	797.094i	−0.906513	−	0.854335i
$934$		0			0
$935$		−	331.734i		−	0.354796i
$936$		0			0
$937$	−593.849			−0.633777			−0.316889	−	0.948463i	$-0.602638\pi$
$937$	−593.849			−0.633777			−0.316889	+	0.948463i	$0.602638\pi$
$938$		0			0
$939$	−173.669	−	578.968i	−0.184951	−	0.616579i
$940$		0			0
$941$	40.2459	+	23.2360i	0.0427693	+	0.0246928i	0.521232	−	0.853415i	$-0.325473\pi$
$941$	40.2459	+	23.2360i	0.0427693	+	0.0246928i	−0.478463	+	0.878108i	$0.658806\pi$
$942$		0			0
$943$	−841.800	−	1458.04i	−0.892683	−	1.54617i
$944$		0			0
$945$	56.5516	−	67.6157i	0.0598429	−	0.0715510i
$946$		0			0
$947$	1614.20	−	931.957i	1.70454	−	0.984115i	0.763502	−	0.645806i	$-0.223478\pi$
$947$	1614.20	−	931.957i	1.70454	−	0.984115i	0.941035	−	0.338309i	$-0.109855\pi$
$948$		0			0
$949$	−757.378	+	1311.82i	−0.798080	+	1.38232i
$950$		0			0
$951$	1058.61	−	317.544i	1.11315	−	0.333905i
$952$		0			0
$953$			293.678i			0.308162i	0.988058	+	0.154081i	$0.0492416\pi$
$953$			293.678i			0.308162i	−0.988058	+	0.154081i	$0.950758\pi$
$954$		0			0
$955$	−108.321			−0.113425
$956$		0			0
$957$	765.925	−	812.704i	0.800339	−	0.849220i
$958$		0			0
$959$	65.2158	+	37.6523i	0.0680039	+	0.0392621i
$960$		0			0
$961$	384.852	+	666.583i	0.400470	+	0.693635i
$962$		0			0
$963$	−512.859	+	1023.92i	−0.532564	+	1.06326i
$964$		0			0
$965$	−107.732	+	62.1991i	−0.111639	+	0.0644550i
$966$		0			0
$967$	−56.1241	+	97.2098i	−0.0580394	+	0.100527i	−0.893585	−	0.448894i	$-0.851818\pi$
$967$	−56.1241	+	97.2098i	−0.0580394	+	0.100527i	0.835546	+	0.549421i	$0.185152\pi$
$968$		0			0
$969$	190.824	−	807.073i	0.196929	−	0.832893i
$970$		0			0
$971$			1539.13i			1.58510i	0.609807	+	0.792550i	$0.291247\pi$
$971$			1539.13i			1.58510i	−0.609807	+	0.792550i	$0.708753\pi$
$972$		0			0
$973$	−372.044			−0.382368
$974$		0			0
$975$	−1330.78	−	314.649i	−1.36490	−	0.322717i
$976$		0			0
$977$	294.065	+	169.778i	0.300987	+	0.173775i	0.642886	−	0.765962i	$-0.277737\pi$
$977$	294.065	+	169.778i	0.300987	+	0.173775i	−0.341899	+	0.939737i	$0.611070\pi$
$978$		0			0
$979$	698.623	+	1210.05i	0.713609	+	1.23601i
$980$		0			0
$981$	445.080	+	222.932i	0.453701	+	0.227249i
$982$		0			0
$983$	892.130	−	515.072i	0.907559	−	0.523979i	0.0279139	−	0.999610i	$-0.491114\pi$
$983$	892.130	−	515.072i	0.907559	−	0.523979i	0.879645	+	0.475631i	$0.157780\pi$
$984$		0			0
$985$	49.6075	−	85.9228i	0.0503630	−	0.0872312i
$986$		0			0
$987$	−225.555	−	212.572i	−0.228526	−	0.215372i
$988$		0			0
$989$		−	2363.46i		−	2.38975i
$990$		0			0
$991$	−439.103			−0.443091			−0.221546	−	0.975150i	$-0.571110\pi$
$991$	−439.103			−0.443091			−0.221546	+	0.975150i	$0.571110\pi$
$992$		0			0
$993$	260.018	+	866.831i	0.261851	+	0.872942i
$994$		0			0
$995$	53.4094	+	30.8359i	0.0536777	+	0.0309909i
$996$		0			0
$997$	381.047	+	659.993i	0.382194	+	0.661979i	0.991376	−	0.131051i	$-0.0418353\pi$
$997$	381.047	+	659.993i	0.382194	+	0.661979i	−0.609182	+	0.793031i	$0.708502\pi$
$998$		0			0
$999$	−171.240	−	143.220i	−0.171412	−	0.143363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.m.b.41.4	✓	8
3.2	odd	2		216.3.m.b.17.2		8
4.3	odd	2		144.3.q.e.113.1		8
8.3	odd	2		576.3.q.j.257.4		8
8.5	even	2		576.3.q.i.257.1		8
9.2	odd	6	inner	72.3.m.b.65.4	yes	8
9.4	even	3		648.3.e.c.161.3		8
9.5	odd	6		648.3.e.c.161.6		8
9.7	even	3		216.3.m.b.89.2		8
12.11	even	2		432.3.q.e.17.2		8
24.5	odd	2		1728.3.q.j.449.3		8
24.11	even	2		1728.3.q.i.449.3		8
36.7	odd	6		432.3.q.e.305.2		8
36.11	even	6		144.3.q.e.65.1		8
36.23	even	6		1296.3.e.i.161.6		8
36.31	odd	6		1296.3.e.i.161.3		8
72.11	even	6		576.3.q.j.65.4		8
72.29	odd	6		576.3.q.i.65.1		8
72.43	odd	6		1728.3.q.i.1601.3		8
72.61	even	6		1728.3.q.j.1601.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.m.b.41.4	✓	8	1.1	even	1	trivial
72.3.m.b.65.4	yes	8	9.2	odd	6	inner
144.3.q.e.65.1		8	36.11	even	6
144.3.q.e.113.1		8	4.3	odd	2
216.3.m.b.17.2		8	3.2	odd	2
216.3.m.b.89.2		8	9.7	even	3
432.3.q.e.17.2		8	12.11	even	2
432.3.q.e.305.2		8	36.7	odd	6
576.3.q.i.65.1		8	72.29	odd	6
576.3.q.i.257.1		8	8.5	even	2
576.3.q.j.65.4		8	72.11	even	6
576.3.q.j.257.4		8	8.3	odd	2
648.3.e.c.161.3		8	9.4	even	3
648.3.e.c.161.6		8	9.5	odd	6
1296.3.e.i.161.3		8	36.31	odd	6
1296.3.e.i.161.6		8	36.23	even	6
1728.3.q.i.449.3		8	24.11	even	2
1728.3.q.i.1601.3		8	72.43	odd	6
1728.3.q.j.449.3		8	24.5	odd	2
1728.3.q.j.1601.3		8	72.61	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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	72.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.91950 + 0.690286i) q^{3} +(1.80902 + 1.04444i) q^{5} +(-0.781452 - 1.35351i) q^{7} +(8.04701 + 4.03058i) q^{9} +O(q^{10})\)	\(q+(2.91950 + 0.690286i) q^{3} +(1.80902 + 1.04444i) q^{5} +(-0.781452 - 1.35351i) q^{7} +(8.04701 + 4.03058i) q^{9} +(-10.8302 + 6.25280i) q^{11} +(11.0441 - 19.1289i) q^{13} +(4.56049 + 4.29799i) q^{15} +12.6991i q^{17} -21.7686 q^{19} +(-1.34714 - 4.49102i) q^{21} +(-28.7989 - 16.6271i) q^{23} +(-10.3183 - 17.8718i) q^{25} +(20.7110 + 17.3220i) q^{27} +(-25.7787 + 14.8833i) q^{29} +(6.91549 - 11.9780i) q^{31} +(-35.9349 + 10.7792i) q^{33} -3.26472i q^{35} -8.26807 q^{37} +(45.4476 - 48.2234i) q^{39} +(43.8453 + 25.3141i) q^{41} +(35.5364 + 61.5508i) q^{43} +(10.3475 + 15.6960i) q^{45} +(57.2470 - 33.0516i) q^{47} +(23.2787 - 40.3198i) q^{49} +(-8.76600 + 37.0750i) q^{51} -6.04384i q^{53} -26.1227 q^{55} +(-63.5536 - 15.0266i) q^{57} +(-8.01575 - 4.62789i) q^{59} +(51.9009 + 89.8950i) q^{61} +(-0.832899 - 14.0415i) q^{63} +(39.9580 - 23.0698i) q^{65} +(-19.8853 + 34.4424i) q^{67} +(-72.6012 - 68.4223i) q^{69} -18.3599i q^{71} -68.5777 q^{73} +(-17.7876 - 59.2994i) q^{75} +(16.9265 + 9.77252i) q^{77} +(13.3130 + 23.0587i) q^{79} +(48.5088 + 64.8683i) q^{81} +(21.0376 - 12.1461i) q^{83} +(-13.2634 + 22.9729i) q^{85} +(-85.5347 + 25.6573i) q^{87} -111.730i q^{89} -34.5217 q^{91} +(28.4580 - 30.1961i) q^{93} +(-39.3800 - 22.7360i) q^{95} +(-2.51182 - 4.35061i) q^{97} +(-112.353 + 6.66446i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{3} - 6 q^{5} + 6 q^{7} - 22 q^{9}+O(q^{10}) \) 8 * q + 10 * q^3 - 6 * q^5 + 6 * q^7 - 22 * q^9	\( 8 q + 10 q^{3} - 6 q^{5} + 6 q^{7} - 22 q^{9} + 36 q^{11} + 14 q^{13} + 10 q^{15} + 4 q^{19} - 54 q^{21} - 102 q^{23} + 10 q^{25} - 20 q^{27} - 114 q^{29} - 50 q^{31} - 104 q^{33} + 120 q^{37} + 82 q^{39} + 264 q^{41} - 28 q^{43} + 206 q^{45} + 150 q^{47} + 94 q^{49} + 170 q^{51} - 244 q^{55} - 178 q^{57} - 108 q^{59} + 14 q^{61} - 210 q^{63} - 198 q^{65} - 20 q^{67} - 14 q^{69} - 76 q^{73} + 326 q^{75} + 66 q^{77} + 26 q^{79} + 194 q^{81} + 246 q^{83} - 224 q^{85} - 18 q^{87} + 108 q^{91} - 130 q^{93} - 456 q^{95} - 236 q^{97} - 634 q^{99}+O(q^{100}) \) 8 * q + 10 * q^3 - 6 * q^5 + 6 * q^7 - 22 * q^9 + 36 * q^11 + 14 * q^13 + 10 * q^15 + 4 * q^19 - 54 * q^21 - 102 * q^23 + 10 * q^25 - 20 * q^27 - 114 * q^29 - 50 * q^31 - 104 * q^33 + 120 * q^37 + 82 * q^39 + 264 * q^41 - 28 * q^43 + 206 * q^45 + 150 * q^47 + 94 * q^49 + 170 * q^51 - 244 * q^55 - 178 * q^57 - 108 * q^59 + 14 * q^61 - 210 * q^63 - 198 * q^65 - 20 * q^67 - 14 * q^69 - 76 * q^73 + 326 * q^75 + 66 * q^77 + 26 * q^79 + 194 * q^81 + 246 * q^83 - 224 * q^85 - 18 * q^87 + 108 * q^91 - 130 * q^93 - 456 * q^95 - 236 * q^97 - 634 * q^99

Introduction

L-functions

Modular forms

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