LMFDB - Embedded newform 72.3.m.b.65.4

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			65.4
Root			$-1.41950 - 2.45865i$ of defining polynomial
Character	$\chi$	$=$	72.65
Dual form			72.3.m.b.41.4

$q$-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 $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

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

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	−0.308067	−	0.951365i	$-0.599682\pi$
$5$	1.80902	−	1.04444i	0.361805	−	0.208888i	0.669872	+	0.742476i	$0.266349\pi$
$6$		0			0
$7$	−0.781452	+	1.35351i	−0.111636	+	0.193359i	−0.916430	−	0.400195i	$-0.868942\pi$
$7$	−0.781452	+	1.35351i	−0.111636	+	0.193359i	0.804794	+	0.593554i	$0.202276\pi$
$8$		0			0
$9$	8.04701	−	4.03058i	0.894112	−	0.447843i
$10$		0			0
$11$	−10.8302	−	6.25280i	−0.984560	−	0.568436i	−0.0809165	−	0.996721i	$-0.525785\pi$
$11$	−10.8302	−	6.25280i	−0.984560	−	0.568436i	−0.903644	+	0.428285i	$0.859118\pi$
$12$		0			0
$13$	11.0441	+	19.1289i	0.849545	+	1.47145i	0.881615	+	0.471969i	$0.156456\pi$
$13$	11.0441	+	19.1289i	0.849545	+	1.47145i	−0.0320708	+	0.999486i	$0.510210\pi$
$14$		0			0
$15$	4.56049	−	4.29799i	0.304033	−	0.286533i
$16$		0			0
$17$		−	12.6991i		−	0.747005i	−0.927629	−	0.373503i	$-0.878157\pi$
$17$		−	12.6991i		−	0.747005i	0.927629	−	0.373503i	$-0.121843\pi$
$18$		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	−0.971532	−	0.236909i	$-0.923866\pi$
$23$	−28.7989	+	16.6271i	−1.25213	+	0.722916i	−0.280596	+	0.959826i	$0.590532\pi$
$24$		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	−0.0153306	−	0.999882i	$-0.504880\pi$
$29$	−25.7787	−	14.8833i	−0.888920	−	0.513218i	−0.873589	+	0.486665i	$0.838213\pi$
$30$		0			0
$31$	6.91549	+	11.9780i	0.223080	+	0.386386i	0.955742	−	0.294207i	$-0.0950555\pi$
$31$	6.91549	+	11.9780i	0.223080	+	0.386386i	−0.732662	+	0.680593i	$0.761722\pi$
$32$		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	0.141382	−	0.989955i	$-0.454846\pi$
$41$	43.8453	−	25.3141i	1.06940	−	0.617418i	0.928017	+	0.372538i	$0.121512\pi$
$42$		0			0
$43$	35.5364	−	61.5508i	0.826427	−	1.43141i	−0.0743965	−	0.997229i	$-0.523703\pi$
$43$	35.5364	−	61.5508i	0.826427	−	1.43141i	0.900824	−	0.434185i	$-0.142964\pi$
$44$		0			0
$45$	10.3475	−	15.6960i	0.229945	−	0.348801i
$46$		0			0
$47$	57.2470	+	33.0516i	1.21802	+	0.703225i	0.964495	−	0.264103i	$-0.0850759\pi$
$47$	57.2470	+	33.0516i	1.21802	+	0.703225i	0.253527	+	0.967328i	$0.418409\pi$
$48$		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	$0.0181590\pi$
$53$			6.04384i			0.114035i	−0.998373	+	0.0570174i	$0.981841\pi$
$54$		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	−0.566390	−	0.824138i	$-0.691660\pi$
$59$	−8.01575	+	4.62789i	−0.135860	+	0.0784389i	0.430529	+	0.902577i	$0.358327\pi$
$60$		0			0
$61$	51.9009	−	89.8950i	0.850834	−	1.47369i	−0.0296226	−	0.999561i	$-0.509431\pi$
$61$	51.9009	−	89.8950i	0.850834	−	1.47369i	0.880457	−	0.474127i	$-0.157236\pi$
$62$		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	0.678605	−	0.734503i	$-0.262585\pi$
$67$	−19.8853	−	34.4424i	−0.296796	−	0.514065i	−0.975401	+	0.220438i	$0.929251\pi$
$68$		0			0
$69$	−72.6012	+	68.4223i	−1.05219	+	0.991628i
$70$		0			0
$71$			18.3599i			0.258590i	0.991606	+	0.129295i	$0.0412714\pi$
$71$			18.3599i			0.258590i	−0.991606	+	0.129295i	$0.958729\pi$
$72$		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	−0.769381	−	0.638791i	$-0.779435\pi$
$79$	13.3130	−	23.0587i	0.168518	−	0.291883i	0.937899	+	0.346908i	$0.112768\pi$
$80$		0			0
$81$	48.5088	−	64.8683i	0.598874	−	0.800843i
$82$		0			0
$83$	21.0376	+	12.1461i	0.253465	+	0.146338i	0.621350	−	0.783533i	$-0.286585\pi$
$83$	21.0376	+	12.1461i	0.253465	+	0.146338i	−0.367885	+	0.929871i	$0.619918\pi$
$84$		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	$0.216001\pi$
$89$			111.730i			1.25539i	−0.778459	+	0.627695i	$0.783999\pi$
$90$		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	−0.878683	−	0.477407i	$-0.841577\pi$
$97$	−2.51182	+	4.35061i	−0.0258951	+	0.0448516i	0.852787	+	0.522258i	$0.174910\pi$
$98$		0			0
$99$	−112.353	−	6.66446i	−1.13488	−	0.0673178i
$100$		0			0
$101$	−86.1052	−	49.7129i	−0.852527	−	0.492207i	0.00897555	−	0.999960i	$-0.497143\pi$
$101$	−86.1052	−	49.7129i	−0.852527	−	0.492207i	−0.861503	+	0.507753i	$0.830476\pi$
$102$		0			0
$103$	13.6160	+	23.5836i	0.132194	+	0.228967i	0.924522	−	0.381128i	$-0.124464\pi$
$103$	13.6160	+	23.5836i	0.132194	+	0.228967i	−0.792328	+	0.610096i	$0.791131\pi$
$104$		0			0
$105$	2.25359	+	9.53136i	0.0214627	+	0.0907748i
$106$		0			0
$107$		−	127.242i		−	1.18918i	−0.804030	−	0.594588i	$-0.797315\pi$
$107$		−	127.242i		−	1.18918i	0.804030	−	0.594588i	$-0.202685\pi$
$108$		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	0.0296577	−	0.999560i	$-0.490558\pi$
$113$	102.845	−	59.3775i	0.910131	−	0.525464i	0.880473	+	0.474096i	$0.157225\pi$
$114$		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	−0.526798	−	0.849990i	$-0.676608\pi$
$131$	−7.08499	+	4.09052i	−0.0540839	+	0.0312254i	0.472714	+	0.881216i	$0.343274\pi$
$132$		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	0.339919	−	0.940455i	$-0.389600\pi$
$137$	−41.7273	−	24.0913i	−0.304579	−	0.175849i	−0.644498	+	0.764606i	$0.722934\pi$
$138$		0			0
$139$	119.023	+	206.155i	0.856284	+	1.48313i	0.875449	+	0.483311i	$0.160566\pi$
$139$	119.023	+	206.155i	0.856284	+	1.48313i	−0.0191645	+	0.999816i	$0.506101\pi$
$140$		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	−0.682529	+	0.730859i	$0.739120\pi$
$149$	−246.854	+	142.521i	−1.65674	+	0.956517i	−0.974207	+	0.225658i	$0.927547\pi$
$150$		0			0
$151$	−77.2434	+	133.790i	−0.511546	+	0.886024i	0.488365	+	0.872640i	$0.337594\pi$
$151$	−77.2434	+	133.790i	−0.511546	+	0.886024i	−0.999910	+	0.0133838i	$0.995740\pi$
$152$		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	−0.940777	−	0.339026i	$-0.889903\pi$
$157$	−119.947	−	207.754i	−0.763993	−	1.32328i	0.176784	−	0.984250i	$-0.443431\pi$
$158$		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	−0.382179	−	0.924088i	$-0.624826\pi$
$167$	37.9116	−	21.8883i	0.227016	−	0.131068i	0.609195	+	0.793021i	$0.291493\pi$
$168$		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	−0.465420	−	0.885090i	$-0.654097\pi$
$173$	−253.383	−	146.291i	−1.46464	−	0.845611i	−0.999220	+	0.0394795i	$0.987430\pi$
$174$		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	$0.182943\pi$
$179$			194.612i			1.08722i	−0.839338	+	0.543610i	$0.817057\pi$
$180$		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	0.377810	−	0.925883i	$-0.376677\pi$
$191$	−44.9085	−	25.9279i	−0.235123	−	0.135748i	−0.612933	+	0.790135i	$0.710011\pi$
$192$		0			0
$193$	−29.7763	−	51.5741i	−0.154281	−	0.267223i	0.778516	−	0.627625i	$-0.215973\pi$
$193$	−29.7763	−	51.5741i	−0.154281	−	0.267223i	−0.932797	+	0.360402i	$0.882640\pi$
$194$		0			0
$195$	132.582	+	39.7698i	0.679909	+	0.203948i
$196$		0			0
$197$			47.4968i			0.241100i	0.992707	+	0.120550i	$0.0384659\pi$
$197$			47.4968i			0.241100i	−0.992707	+	0.120550i	$0.961534\pi$
$198$		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	0.607499	−	0.794320i	$-0.292173\pi$
$211$	−81.0561	−	140.393i	−0.384152	−	0.665371i	−0.991651	+	0.128949i	$0.958840\pi$
$212$		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	−0.538426	−	0.842673i	$-0.680981\pi$
$223$	102.706	−	177.891i	0.460564	−	0.797719i	0.998989	+	0.0449536i	$0.0143140\pi$
$224$		0			0
$225$	−10.9976	+	185.403i	−0.0488782	+	0.824015i
$226$		0			0
$227$	54.0416	+	31.2009i	0.238069	+	0.137449i	0.614289	−	0.789081i	$-0.289443\pi$
$227$	54.0416	+	31.2009i	0.238069	+	0.137449i	−0.376220	+	0.926530i	$0.622776\pi$
$228$		0			0
$229$	−5.73790	−	9.93834i	−0.0250563	−	0.0433989i	0.853225	−	0.521542i	$-0.174643\pi$
$229$	−5.73790	−	9.93834i	−0.0250563	−	0.0433989i	−0.878282	+	0.478144i	$0.841310\pi$
$230$		0			0
$231$	42.6712	−	40.2150i	0.184724	−	0.174091i
$232$		0			0
$233$			177.096i			0.760069i	0.924972	+	0.380035i	$0.124088\pi$
$233$			177.096i			0.760069i	−0.924972	+	0.380035i	$0.875912\pi$
$234$		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	−0.898475	−	0.439025i	$-0.855324\pi$
$239$	−231.234	+	133.503i	−0.967505	+	0.558589i	−0.0690305	+	0.997615i	$0.521991\pi$
$240$		0			0
$241$	40.7178	−	70.5252i	0.168953	−	0.292636i	−0.769099	−	0.639130i	$-0.779295\pi$
$241$	40.7178	−	70.5252i	0.168953	−	0.292636i	0.938052	+	0.346494i	$0.112628\pi$
$242$		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	$0.213336\pi$
$251$			311.819i			1.24231i	−0.783689	+	0.621153i	$0.786664\pi$
$252$		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	0.322889	−	0.946437i	$-0.395346\pi$
$257$	335.121	−	193.482i	1.30397	−	0.752849i	0.981083	+	0.193588i	$0.0620125\pi$
$258$		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	0.993971	+	0.109646i	$0.0349718\pi$
$263$	417.095	+	240.810i	1.58591	+	0.915627i	0.591942	+	0.805981i	$0.298362\pi$
$264$		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	$-0.862122\pi$
$269$		−	225.818i		−	0.839474i	0.907646	−	0.419737i	$-0.137878\pi$
$270$		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	−0.912126	−	0.409909i	$-0.865560\pi$
$277$	−27.9969	+	48.4920i	−0.101072	+	0.175061i	0.811055	+	0.584970i	$0.198894\pi$
$278$		0			0
$279$	103.927	+	68.5135i	0.372499	+	0.245568i
$280$		0			0
$281$	122.023	+	70.4498i	0.434244	+	0.250711i	0.701153	−	0.713011i	$-0.252669\pi$
$281$	122.023	+	70.4498i	0.434244	+	0.250711i	−0.266909	+	0.963722i	$0.586002\pi$
$282$		0			0
$283$	−155.690	−	269.663i	−0.550141	−	0.952872i	−0.998264	−	0.0589002i	$-0.981241\pi$
$283$	−155.690	−	269.663i	−0.550141	−	0.952872i	0.448123	−	0.893972i	$-0.352093\pi$
$284$		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	−0.888030	−	0.459786i	$-0.847926\pi$
$293$	−273.621	+	157.975i	−0.933859	+	0.539164i	−0.0458290	+	0.998949i	$0.514593\pi$
$294$		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	−0.930564	−	0.366130i	$-0.880683\pi$
$311$	−335.497	+	193.699i	−1.07877	+	0.622827i	−0.148204	+	0.988957i	$0.547349\pi$
$312$		0			0
$313$	−100.742	+	174.491i	−0.321860	+	0.557479i	−0.980872	−	0.194654i	$-0.937642\pi$
$313$	−100.742	+	174.491i	−0.321860	+	0.557479i	0.659011	+	0.752133i	$0.270975\pi$
$314$		0			0
$315$	13.1587	+	26.2712i	0.0417737	+	0.0834007i
$316$		0			0
$317$	319.046	+	184.201i	1.00645	+	0.581077i	0.910152	−	0.414275i	$-0.135965\pi$
$317$	319.046	+	184.201i	1.00645	+	0.581077i	0.0963027	+	0.995352i	$0.469298\pi$
$318$		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	−0.543043	−	0.839705i	$-0.682728\pi$
$331$	150.832	−	261.248i	0.455684	−	0.789268i	0.998727	+	0.0504365i	$0.0160613\pi$
$332$		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	0.964550	−	0.263899i	$-0.0850087\pi$
$337$	85.5075	+	148.103i	0.253732	+	0.439476i	−0.710819	+	0.703375i	$0.751675\pi$
$338$		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	−0.0674041	−	0.997726i	$-0.521472\pi$
$347$	264.744	−	152.850i	0.762950	−	0.440489i	0.830354	+	0.557237i	$0.188138\pi$
$348$		0			0
$349$	−11.1944	+	19.3893i	−0.0320756	+	0.0555566i	−0.881618	−	0.471964i	$-0.843545\pi$
$349$	−11.1944	+	19.3893i	−0.0320756	+	0.0555566i	0.849542	+	0.527521i	$0.176878\pi$
$350$		0			0
$351$	560.086	+	204.873i	1.59569	+	0.583685i
$352$		0			0
$353$	−462.657	−	267.115i	−1.31064	−	0.756700i	−0.328440	−	0.944525i	$-0.606523\pi$
$353$	−462.657	−	267.115i	−1.31064	−	0.756700i	−0.982203	+	0.187825i	$0.939856\pi$
$354$		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	$0.0978106\pi$
$359$			217.172i			0.604936i	−0.953159	+	0.302468i	$0.902189\pi$
$360$		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	−0.927295	−	0.374330i	$-0.877873\pi$
$367$	−51.1847	+	88.6546i	−0.139468	+	0.241566i	0.787827	+	0.615896i	$0.211206\pi$
$368$		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	0.982464	+	0.186450i	$0.0596982\pi$
$373$	243.458	+	421.682i	0.652702	+	1.13051i	−0.329762	+	0.944064i	$0.606969\pi$
$374$		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	−0.239240	−	0.970960i	$-0.576898\pi$
$383$	184.612	−	106.586i	0.482016	−	0.278292i	0.721256	+	0.692668i	$0.243565\pi$
$384$		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	0.390202	−	0.920729i	$-0.372405\pi$
$389$	−82.4958	−	47.6290i	−0.212071	−	0.122439i	−0.602274	+	0.798290i	$0.705738\pi$
$390$		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	−0.978682	−	0.205380i	$-0.934157\pi$
$401$	−517.354	+	298.694i	−1.29016	+	0.744874i	−0.311477	+	0.950254i	$0.600824\pi$
$402$		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	0.792841	−	0.609428i	$-0.208601\pi$
$409$	−53.7260	−	93.0562i	−0.131359	−	0.227521i	−0.924201	+	0.381907i	$0.875268\pi$
$410$		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	−0.451878	−	0.892080i	$-0.649246\pi$
$419$	39.6993	−	22.9204i	0.0947477	−	0.0547026i	0.546625	+	0.837377i	$0.315912\pi$
$420$		0			0
$421$	−5.53062	+	9.57932i	−0.0131369	+	0.0227537i	−0.872519	−	0.488580i	$-0.837515\pi$
$421$	−5.53062	+	9.57932i	−0.0131369	+	0.0227537i	0.859382	+	0.511334i	$0.170848\pi$
$422$		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	$-0.759641\pi$
$431$		−	590.788i		−	1.37074i	0.728196	−	0.685369i	$-0.240359\pi$
$432$		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	−0.822230	−	0.569156i	$-0.807270\pi$
$439$	35.9051	−	62.1894i	0.0817883	−	0.141662i	0.904018	+	0.427494i	$0.140604\pi$
$440$		0			0
$441$	349.836	+	230.628i	0.793279	+	0.522965i
$442$		0			0
$443$	−581.028	−	335.457i	−1.31158	−	0.757239i	−0.329219	−	0.944254i	$-0.606786\pi$
$443$	−581.028	−	335.457i	−1.31158	−	0.757239i	−0.982357	+	0.187015i	$0.940119\pi$
$444$		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	$0.375703\pi$
$449$			830.401i			1.84945i	−0.380642	+	0.924723i	$0.624297\pi$
$450$		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	0.135661	−	0.990755i	$-0.456684\pi$
$457$	423.113	−	732.854i	0.925850	−	1.60362i	0.790188	−	0.612864i	$-0.209983\pi$
$458$		0			0
$459$	−219.974	−	263.011i	−0.479247	−	0.573009i
$460$		0			0
$461$	109.019	+	62.9423i	0.236484	+	0.136534i	0.613560	−	0.789648i	$-0.289737\pi$
$461$	109.019	+	62.9423i	0.236484	+	0.136534i	−0.377076	+	0.926182i	$0.623070\pi$
$462$		0			0
$463$	307.121	+	531.950i	0.663329	+	1.14892i	0.979735	+	0.200296i	$0.0641903\pi$
$463$	307.121	+	531.950i	0.663329	+	1.14892i	−0.316407	+	0.948624i	$0.602476\pi$
$464$		0			0
$465$	83.0192	+	24.9027i	0.178536	+	0.0535543i
$466$		0			0
$467$			172.270i			0.368887i	0.982843	+	0.184444i	$0.0590484\pi$
$467$			172.270i			0.368887i	−0.982843	+	0.184444i	$0.940952\pi$
$468$		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	0.306628	−	0.951829i	$-0.400799\pi$
$479$	−174.532	−	100.766i	−0.364367	−	0.210367i	−0.670995	+	0.741462i	$0.734133\pi$
$480$		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	0.298555	−	0.954392i	$-0.403495\pi$
$491$	625.711	−	361.255i	1.27436	−	0.735753i	0.975806	+	0.218640i	$0.0701619\pi$
$492$		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	0.788019	−	0.615651i	$-0.211107\pi$
$499$	−69.4409	−	120.275i	−0.139160	−	0.241032i	−0.927179	+	0.374619i	$0.877774\pi$
$500$		0			0
$501$	95.5740	−	90.0728i	0.190766	−	0.179786i
$502$		0			0
$503$			794.533i			1.57959i	0.613372	+	0.789794i	$0.289813\pi$
$503$			794.533i			1.57959i	−0.613372	+	0.789794i	$0.710187\pi$
$504$		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	−0.666224	−	0.745752i	$-0.732090\pi$
$509$	−179.929	+	103.882i	−0.353495	+	0.204090i	0.312729	+	0.949843i	$0.398757\pi$
$510$		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	$-0.923421\pi$
$521$		−	248.275i		−	0.476535i	0.971200	−	0.238267i	$-0.0765795\pi$
$522$		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	−0.775835	−	0.630936i	$-0.782671\pi$
$547$	86.6937	−	150.158i	0.158489	−	0.274512i	0.934324	+	0.356424i	$0.116004\pi$
$548$		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	$0.127589\pi$
$557$			434.666i			0.780370i	−0.920737	+	0.390185i	$0.872411\pi$
$558$		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	−0.420902	−	0.907106i	$-0.638286\pi$
$563$	86.8277	−	50.1300i	0.154223	−	0.0890409i	0.575126	+	0.818065i	$0.304953\pi$
$564$		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	0.538299	−	0.842754i	$-0.319067\pi$
$569$	44.1556	+	25.4932i	0.0776020	+	0.0448036i	−0.460697	+	0.887558i	$0.652400\pi$
$570$		0			0
$571$	430.481	+	745.615i	0.753907	+	1.30581i	0.945916	+	0.324412i	$0.105166\pi$
$571$	430.481	+	745.615i	0.753907	+	1.30581i	−0.192009	+	0.981393i	$0.561500\pi$
$572$		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	0.880764	−	0.473556i	$-0.157030\pi$
$587$	534.777	+	308.754i	0.911034	+	0.525986i	0.0302706	+	0.999542i	$0.490363\pi$
$588$		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	$-0.906802\pi$
$593$		−	342.310i		−	0.577251i	0.957442	−	0.288626i	$-0.0931983\pi$
$594$		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	−0.148785	−	0.988870i	$-0.547536\pi$
$599$	379.292	−	218.984i	0.633209	−	0.365583i	0.781994	+	0.623286i	$0.214203\pi$
$600$		0			0
$601$	304.452	−	527.327i	0.506576	−	0.877416i	−0.493395	−	0.869806i	$-0.664244\pi$
$601$	304.452	−	527.327i	0.506576	−	0.877416i	0.999971	−	0.00761053i	$-0.00242253\pi$
$602$		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	−0.838848	−	0.544365i	$-0.816770\pi$
$607$	−540.751	−	936.608i	−0.890858	−	1.54301i	−0.0520102	−	0.998647i	$-0.516563\pi$
$608$		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	−0.524936	−	0.851142i	$-0.675911\pi$
$617$	−31.0310	+	17.9158i	−0.0502934	+	0.0290369i	0.474642	+	0.880179i	$0.342577\pi$
$618$		0			0
$619$	−161.494	+	279.717i	−0.260896	+	0.451885i	−0.966480	−	0.256741i	$-0.917351\pi$
$619$	−161.494	+	279.717i	−0.260896	+	0.451885i	0.705584	+	0.708626i	$0.250685\pi$
$620$		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	−0.220013	−	0.975497i	$-0.570610\pi$
$641$	−753.063	−	434.781i	−1.17483	−	0.678286i	−0.954812	+	0.297211i	$0.903943\pi$
$642$		0			0
$643$	31.2519	+	54.1299i	0.0486033	+	0.0841834i	0.889304	−	0.457317i	$-0.151190\pi$
$643$	31.2519	+	54.1299i	0.0486033	+	0.0841834i	−0.840700	+	0.541501i	$0.817856\pi$
$644$		0			0
$645$	−102.481	−	433.437i	−0.158886	−	0.671995i
$646$		0			0
$647$		−	761.439i		−	1.17688i	−0.808542	−	0.588438i	$-0.799743\pi$
$647$		−	761.439i		−	1.17688i	0.808542	−	0.588438i	$-0.200257\pi$
$648$		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	−0.397455	−	0.917622i	$-0.630106\pi$
$653$	129.622	−	74.8371i	0.198502	−	0.114605i	0.595956	+	0.803017i	$0.296773\pi$
$654$		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	0.00650063	−	0.999979i	$-0.497931\pi$
$659$	−564.273	−	325.783i	−0.856256	−	0.494360i	−0.862757	+	0.505619i	$0.831264\pi$
$660$		0			0
$661$	596.672	+	1033.47i	0.902681	+	1.56349i	0.824000	+	0.566590i	$0.191738\pi$
$661$	596.672	+	1033.47i	0.902681	+	1.56349i	0.0786818	+	0.996900i	$0.474929\pi$
$662$		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	−0.916218	−	0.400680i	$-0.868774\pi$
$673$	−74.7771	+	129.518i	−0.111110	+	0.192448i	0.805108	+	0.593128i	$0.202107\pi$
$674$		0			0
$675$	95.8737	+	548.877i	0.142035	+	0.813152i
$676$		0			0
$677$	−607.487	−	350.733i	−0.897322	−	0.518069i	−0.0209919	−	0.999780i	$-0.506682\pi$
$677$	−607.487	−	350.733i	−0.897322	−	0.518069i	−0.876331	+	0.481710i	$0.840016\pi$
$678$		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	$0.120060\pi$
$683$			503.096i			0.736597i	−0.929708	+	0.368299i	$0.879940\pi$
$684$		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	−0.999644	−	0.0266761i	$-0.991508\pi$
$691$	−329.413	+	570.561i	−0.476720	+	0.825703i	0.522924	+	0.852379i	$0.324841\pi$
$692$		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	$-0.960630\pi$
$701$		−	172.963i		−	0.246738i	0.992361	−	0.123369i	$-0.0393698\pi$
$702$		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	0.207133	+	0.978313i	$0.433587\pi$
$709$	−527.267	+	913.254i	−0.743677	+	1.28809i	−0.950810	+	0.309774i	$0.899747\pi$
$710$		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	$-0.699468\pi$
$719$		−	1164.78i		−	1.62000i	0.586432	−	0.809998i	$-0.300532\pi$
$720$		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	0.298827	+	0.954307i	$0.403405\pi$
$727$	−492.209	+	852.530i	−0.677041	+	1.17267i	−0.975868	+	0.218362i	$0.929929\pi$
$728$		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	0.983721	−	0.179703i	$-0.0575138\pi$
$733$	246.459	+	426.879i	0.336233	+	0.582372i	−0.647488	+	0.762076i	$0.724180\pi$
$734$		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	−0.966002	−	0.258533i	$-0.916761\pi$
$743$	−910.255	+	525.536i	−1.22511	+	0.707316i	−0.259105	+	0.965849i	$0.583427\pi$
$744$		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	0.836484	−	0.547991i	$-0.184607\pi$
$751$	−42.3053	−	73.2749i	−0.0563319	−	0.0975698i	−0.892816	+	0.450421i	$0.851274\pi$
$752$		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	−0.218285	−	0.975885i	$-0.570046\pi$
$761$	393.981	−	227.465i	0.517715	−	0.298903i	0.735999	+	0.676983i	$0.236713\pi$
$762$		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	0.998857	−	0.0477927i	$-0.0152187\pi$
$769$	352.232	+	610.084i	0.458039	+	0.793347i	−0.540818	+	0.841139i	$0.681885\pi$
$770$		0			0
$771$	844.829	−	796.201i	1.09576	−	1.03269i
$772$		0			0
$773$		−	1021.43i		−	1.32138i	−0.750658	−	0.660691i	$-0.770263\pi$
$773$		−	1021.43i		−	1.32138i	0.750658	−	0.660691i	$-0.229737\pi$
$774$		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	0.708671	−	0.705539i	$-0.249295\pi$
$787$	−202.007	−	349.886i	−0.256680	−	0.444582i	−0.965350	+	0.260957i	$0.915962\pi$
$788$		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	0.0637592	−	0.997965i	$-0.479691\pi$
$797$	765.042	−	441.697i	0.959902	−	0.554200i	0.896143	+	0.443766i	$0.146358\pi$
$798$		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	$-0.926040\pi$
$809$		−	372.575i		−	0.460537i	0.973127	−	0.230269i	$-0.0739605\pi$
$810$		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	0.807443	−	0.589946i	$-0.200851\pi$
$821$	574.911	+	331.925i	0.700257	+	0.404293i	−0.107186	+	0.994239i	$0.534184\pi$
$822$		0			0
$823$	−468.171	−	810.896i	−0.568859	−	0.985292i	−0.996679	−	0.0814286i	$-0.974052\pi$
$823$	−468.171	−	810.896i	−0.568859	−	0.985292i	0.427820	−	0.903864i	$-0.359282\pi$
$824$		0			0
$825$	563.430	−	530.999i	0.682946	−	0.643636i
$826$		0			0
$827$		−	499.832i		−	0.604392i	−0.953246	−	0.302196i	$-0.902280\pi$
$827$		−	499.832i		−	0.604392i	0.953246	−	0.302196i	$-0.0977196\pi$
$828$		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	0.537731	−	0.843117i	$-0.319282\pi$
$839$	64.1295	+	37.0252i	0.0764356	+	0.0441301i	−0.461295	+	0.887247i	$0.652615\pi$
$840$		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	−0.334103	−	0.942537i	$-0.608433\pi$
$853$	553.775	−	959.167i	0.649209	−	1.12446i	0.983312	−	0.181927i	$-0.0582333\pi$
$854$		0			0
$855$	−225.252	+	341.681i	−0.263452	+	0.399627i
$856$		0			0
$857$	687.370	+	396.854i	0.802066	+	0.463073i	0.844193	−	0.536039i	$-0.180080\pi$
$857$	687.370	+	396.854i	0.802066	+	0.463073i	−0.0421271	+	0.999112i	$0.513413\pi$
$858$		0			0
$859$	121.830	+	211.016i	0.141828	+	0.245653i	0.928185	−	0.372119i	$-0.121369\pi$
$859$	121.830	+	211.016i	0.141828	+	0.245653i	−0.786357	+	0.617772i	$0.788035\pi$
$860$		0			0
$861$	54.6203	+	231.012i	0.0634382	+	0.268306i
$862$		0			0
$863$			841.279i			0.974830i	0.873170	+	0.487415i	$0.162060\pi$
$863$			841.279i			0.974830i	−0.873170	+	0.487415i	$0.837940\pi$
$864$		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	0.640269	−	0.768151i	$-0.278823\pi$
$877$	−302.656	−	524.216i	−0.345104	−	0.597738i	−0.985373	+	0.170413i	$0.945490\pi$
$878$		0			0
$879$	−689.789	+	650.085i	−0.784743	+	0.739573i
$880$		0			0
$881$			820.188i			0.930974i	0.885055	+	0.465487i	$0.154121\pi$
$881$			820.188i			0.930974i	−0.885055	+	0.465487i	$0.845879\pi$
$882$		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	−0.614846	−	0.788647i	$-0.710782\pi$
$887$	−212.242	+	122.538i	−0.239281	+	0.138149i	0.375565	+	0.926796i	$0.377449\pi$
$888$		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	−0.919868	−	0.392228i	$-0.871704\pi$
$907$	−109.071	+	188.917i	−0.120255	+	0.208287i	0.799613	+	0.600515i	$0.205038\pi$
$908$		0			0
$909$	−893.262	−	52.9858i	−0.982686	−	0.0582902i
$910$		0			0
$911$	558.980	+	322.727i	0.613589	+	0.354256i	0.774369	−	0.632735i	$-0.218068\pi$
$911$	558.980	+	322.727i	0.613589	+	0.354256i	−0.160780	+	0.986990i	$0.551401\pi$
$912$		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	0.541474	−	0.840718i	$-0.317867\pi$
$929$	78.1550	+	45.1228i	0.0841281	+	0.0485714i	−0.457346	+	0.889289i	$0.651200\pi$
$930$		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	−0.478463	−	0.878108i	$-0.658806\pi$
$941$	40.2459	−	23.2360i	0.0427693	−	0.0246928i	0.521232	+	0.853415i	$0.325473\pi$
$942$		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	0.941035	+	0.338309i	$0.109855\pi$
$947$	1614.20	+	931.957i	1.70454	+	0.984115i	0.763502	+	0.645806i	$0.223478\pi$
$948$		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	$-0.950758\pi$
$953$		−	293.678i		−	0.308162i	0.988058	−	0.154081i	$-0.0492416\pi$
$954$		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	0.835546	−	0.549421i	$-0.185152\pi$
$967$	−56.1241	−	97.2098i	−0.0580394	−	0.100527i	−0.893585	+	0.448894i	$0.851818\pi$
$968$		0			0
$969$	190.824	+	807.073i	0.196929	+	0.832893i
$970$		0			0
$971$		−	1539.13i		−	1.58510i	−0.609807	−	0.792550i	$-0.708753\pi$
$971$		−	1539.13i		−	1.58510i	0.609807	−	0.792550i	$-0.291247\pi$
$972$		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	−0.341899	−	0.939737i	$-0.611070\pi$
$977$	294.065	−	169.778i	0.300987	−	0.173775i	0.642886	+	0.765962i	$0.277737\pi$
$978$		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	0.879645	−	0.475631i	$-0.157780\pi$
$983$	892.130	+	515.072i	0.907559	+	0.523979i	0.0279139	+	0.999610i	$0.491114\pi$
$984$		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	−0.609182	−	0.793031i	$-0.708502\pi$
$997$	381.047	−	659.993i	0.382194	−	0.661979i	0.991376	+	0.131051i	$0.0418353\pi$
$998$		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.65.4	yes	8
3.2	odd	2		216.3.m.b.89.2		8
4.3	odd	2		144.3.q.e.65.1		8
8.3	odd	2		576.3.q.j.65.4		8
8.5	even	2		576.3.q.i.65.1		8
9.2	odd	6		648.3.e.c.161.3		8
9.4	even	3		216.3.m.b.17.2		8
9.5	odd	6	inner	72.3.m.b.41.4	✓	8
9.7	even	3		648.3.e.c.161.6		8
12.11	even	2		432.3.q.e.305.2		8
24.5	odd	2		1728.3.q.j.1601.3		8
24.11	even	2		1728.3.q.i.1601.3		8
36.7	odd	6		1296.3.e.i.161.6		8
36.11	even	6		1296.3.e.i.161.3		8
36.23	even	6		144.3.q.e.113.1		8
36.31	odd	6		432.3.q.e.17.2		8
72.5	odd	6		576.3.q.i.257.1		8
72.13	even	6		1728.3.q.j.449.3		8
72.59	even	6		576.3.q.j.257.4		8
72.67	odd	6		1728.3.q.i.449.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.m.b.41.4	✓	8	9.5	odd	6	inner
72.3.m.b.65.4	yes	8	1.1	even	1	trivial
144.3.q.e.65.1		8	4.3	odd	2
144.3.q.e.113.1		8	36.23	even	6
216.3.m.b.17.2		8	9.4	even	3
216.3.m.b.89.2		8	3.2	odd	2
432.3.q.e.17.2		8	36.31	odd	6
432.3.q.e.305.2		8	12.11	even	2
576.3.q.i.65.1		8	8.5	even	2
576.3.q.i.257.1		8	72.5	odd	6
576.3.q.j.65.4		8	8.3	odd	2
576.3.q.j.257.4		8	72.59	even	6
648.3.e.c.161.3		8	9.2	odd	6
648.3.e.c.161.6		8	9.7	even	3
1296.3.e.i.161.3		8	36.11	even	6
1296.3.e.i.161.6		8	36.7	odd	6
1728.3.q.i.449.3		8	72.67	odd	6
1728.3.q.i.1601.3		8	24.11	even	2
1728.3.q.j.449.3		8	72.13	even	6
1728.3.q.j.1601.3		8	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
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

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