LMFDB - Embedded newform 180.4.i.c.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,4,Mod(61,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("180.61");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	180.i (of order $3$, 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:	$10.6203438010$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 7 x^{13} + 180 x^{12} - 989 x^{11} + 11627 x^{10} - 49236 x^{9} + 328637 x^{8} - 1029725 x^{7} + \cdots + 1484973 $ x^14 - 7x^13 + 180x^12 - 989x^11 + 11627x^10 - 49236x^9 + 328637x^8 - 1029725x^7 + 3973395x^6 - 8512360x^5 + 18130585x^4 - 23182065x^3 + 18357462x^2 - 8027505*x + 1484973
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			61.1
Root			$0.500000 + 7.22388i$ of defining polynomial
Character	$\chi$	$=$	180.61
Dual form			180.4.i.c.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.91025 + 1.69983i) q^{3} +(-2.50000 - 4.33013i) q^{5} +(6.86720 - 11.8943i) q^{7} +(21.2211 - 16.6932i) q^{9} +O(q^{10})$	\(q+(-4.91025 + 1.69983i) q^{3} +(-2.50000 - 4.33013i) q^{5} +(6.86720 - 11.8943i) q^{7} +(21.2211 - 16.6932i) q^{9} +(-10.8215 + 18.7434i) q^{11} +(39.8133 + 68.9586i) q^{13} +(19.6361 + 17.0124i) q^{15} -64.3628 q^{17} -144.503 q^{19} +(-13.5013 + 70.0773i) q^{21} +(13.4725 + 23.3351i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(-75.8256 + 118.040i) q^{27} +(-148.503 + 257.215i) q^{29} +(48.3254 + 83.7020i) q^{31} +(21.2757 - 110.429i) q^{33} -68.6720 q^{35} +401.580 q^{37} +(-312.711 - 270.928i) q^{39} +(5.84448 + 10.1229i) q^{41} +(-146.136 + 253.114i) q^{43} +(-125.337 - 50.1573i) q^{45} +(-87.6812 + 151.868i) q^{47} +(77.1832 + 133.685i) q^{49} +(316.037 - 109.406i) q^{51} +155.406 q^{53} +108.215 q^{55} +(709.544 - 245.630i) q^{57} +(-297.582 - 515.427i) q^{59} +(31.0535 - 53.7862i) q^{61} +(-52.8247 - 367.047i) q^{63} +(199.066 - 344.793i) q^{65} +(80.3318 + 139.139i) q^{67} +(-105.819 - 91.6802i) q^{69} -959.723 q^{71} +763.424 q^{73} +(24.5757 - 127.558i) q^{75} +(148.627 + 257.429i) q^{77} +(-31.9825 + 55.3952i) q^{79} +(171.674 - 708.498i) q^{81} +(-458.663 + 794.427i) q^{83} +(160.907 + 278.699i) q^{85} +(291.966 - 1515.42i) q^{87} -1318.88 q^{89} +1093.62 q^{91} +(-379.569 - 328.853i) q^{93} +(361.256 + 625.714i) q^{95} +(64.0845 - 110.998i) q^{97} +(83.2424 + 578.402i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 5 q^{3} - 35 q^{5} - 8 q^{7} + 5 q^{9}+O(q^{10}) $ 14 * q + 5 * q^3 - 35 * q^5 - 8 * q^7 + 5 * q^9	$ 14 q + 5 q^{3} - 35 q^{5} - 8 q^{7} + 5 q^{9} - 27 q^{11} - 32 q^{13} - 20 q^{15} + 246 q^{17} - 134 q^{19} + 28 q^{21} - 42 q^{23} - 175 q^{25} - 484 q^{27} - 324 q^{29} - 98 q^{31} + 657 q^{33} + 80 q^{35} + 712 q^{37} - 848 q^{39} - 339 q^{41} - 119 q^{43} - 125 q^{45} + 96 q^{47} - 813 q^{49} + 1383 q^{51} + 1716 q^{53} + 270 q^{55} - 599 q^{57} - 549 q^{59} - 260 q^{61} - 632 q^{63} - 160 q^{65} - 881 q^{67} + 666 q^{69} + 684 q^{71} + 1474 q^{73} - 25 q^{75} + 456 q^{77} - 1886 q^{79} + 353 q^{81} + 132 q^{83} - 615 q^{85} + 4302 q^{87} + 792 q^{89} + 2528 q^{91} - 4904 q^{93} + 335 q^{95} - 1991 q^{97} + 270 q^{99}+O(q^{100}) $ 14 * q + 5 * q^3 - 35 * q^5 - 8 * q^7 + 5 * q^9 - 27 * q^11 - 32 * q^13 - 20 * q^15 + 246 * q^17 - 134 * q^19 + 28 * q^21 - 42 * q^23 - 175 * q^25 - 484 * q^27 - 324 * q^29 - 98 * q^31 + 657 * q^33 + 80 * q^35 + 712 * q^37 - 848 * q^39 - 339 * q^41 - 119 * q^43 - 125 * q^45 + 96 * q^47 - 813 * q^49 + 1383 * q^51 + 1716 * q^53 + 270 * q^55 - 599 * q^57 - 549 * q^59 - 260 * q^61 - 632 * q^63 - 160 * q^65 - 881 * q^67 + 666 * q^69 + 684 * q^71 + 1474 * q^73 - 25 * q^75 + 456 * q^77 - 1886 * q^79 + 353 * q^81 + 132 * q^83 - 615 * q^85 + 4302 * q^87 + 792 * q^89 + 2528 * q^91 - 4904 * q^93 + 335 * q^95 - 1991 * q^97 + 270 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.91025	+	1.69983i	−0.944978	+	0.327133i
$3$	−4.91025	+	1.69983i	−0.944978	+	0.327133i
$4$		0			0
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$		0			0
$7$	6.86720	−	11.8943i	0.370794	−	0.642234i	−0.618894	−	0.785475i	$-0.712419\pi$
$7$	6.86720	−	11.8943i	0.370794	−	0.642234i	0.989688	+	0.143241i	$0.0457523\pi$
$8$		0			0
$9$	21.2211	−	16.6932i	0.785968	−	0.618267i
$10$		0			0
$11$	−10.8215	+	18.7434i	−0.296619	+	0.513759i	−0.975360	−	0.220619i	$-0.929192\pi$
$11$	−10.8215	+	18.7434i	−0.296619	+	0.513759i	0.678741	+	0.734377i	$0.262526\pi$
$12$		0			0
$13$	39.8133	+	68.9586i	0.849401	+	1.47121i	0.881743	+	0.471730i	$0.156370\pi$
$13$	39.8133	+	68.9586i	0.849401	+	1.47121i	−0.0323418	+	0.999477i	$0.510297\pi$
$14$		0			0
$15$	19.6361	+	17.0124i	0.338002	+	0.292839i
$16$		0			0
$17$	−64.3628			−0.918251			−0.459125	−	0.888371i	$-0.651837\pi$
$17$	−64.3628			−0.918251			−0.459125	+	0.888371i	$0.651837\pi$
$18$		0			0
$19$	−144.503			−1.74480			−0.872399	−	0.488795i	$-0.837437\pi$
$19$	−144.503			−1.74480			−0.872399	+	0.488795i	$0.837437\pi$
$20$		0			0
$21$	−13.5013	+	70.0773i	−0.140297	+	0.728196i
$22$		0			0
$23$	13.4725	+	23.3351i	0.122140	+	0.211552i	0.920611	−	0.390480i	$-0.127691\pi$
$23$	13.4725	+	23.3351i	0.122140	+	0.211552i	−0.798471	+	0.602033i	$0.794358\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$		0			0
$27$	−75.8256	+	118.040i	−0.540468	+	0.841365i
$28$		0			0
$29$	−148.503	+	257.215i	−0.950908	+	1.64702i	−0.207443	+	0.978247i	$0.566514\pi$
$29$	−148.503	+	257.215i	−0.950908	+	1.64702i	−0.743465	+	0.668775i	$0.766819\pi$
$30$		0			0
$31$	48.3254	+	83.7020i	0.279984	+	0.484946i	0.971380	−	0.237529i	$-0.0763376\pi$
$31$	48.3254	+	83.7020i	0.279984	+	0.484946i	−0.691397	+	0.722475i	$0.743004\pi$
$32$		0			0
$33$	21.2757	−	110.429i	0.112231	−	0.582524i
$34$		0			0
$35$	−68.6720			−0.331648
$36$		0			0
$37$	401.580			1.78431			0.892153	−	0.451734i	$-0.149194\pi$
$37$	401.580			1.78431			0.892153	+	0.451734i	$0.149194\pi$
$38$		0			0
$39$	−312.711	−	270.928i	−1.28395	−	1.11239i
$40$		0			0
$41$	5.84448	+	10.1229i	0.0222623	+	0.0385595i	0.876942	−	0.480596i	$-0.159580\pi$
$41$	5.84448	+	10.1229i	0.0222623	+	0.0385595i	−0.854680	+	0.519156i	$0.826246\pi$
$42$		0			0
$43$	−146.136	+	253.114i	−0.518267	+	0.897665i	0.481508	+	0.876442i	$0.340089\pi$
$43$	−146.136	+	253.114i	−0.518267	+	0.897665i	−0.999775	+	0.0212231i	$0.993244\pi$
$44$		0			0
$45$	−125.337	−	50.1573i	−0.415202	−	0.166156i
$46$		0			0
$47$	−87.6812	+	151.868i	−0.272119	+	0.471325i	−0.969404	−	0.245469i	$-0.921058\pi$
$47$	−87.6812	+	151.868i	−0.272119	+	0.471325i	0.697285	+	0.716794i	$0.254391\pi$
$48$		0			0
$49$	77.1832	+	133.685i	0.225024	+	0.389753i
$50$		0			0
$51$	316.037	−	109.406i	0.867727	−	0.300390i
$52$		0			0
$53$	155.406			0.402767			0.201383	−	0.979513i	$-0.435456\pi$
$53$	155.406			0.402767			0.201383	+	0.979513i	$0.435456\pi$
$54$		0			0
$55$	108.215			0.265304
$56$		0			0
$57$	709.544	−	245.630i	1.64880	−	0.570780i
$58$		0			0
$59$	−297.582	−	515.427i	−0.656641	−	1.13734i	−0.981480	−	0.191567i	$-0.938643\pi$
$59$	−297.582	−	515.427i	−0.656641	−	1.13734i	0.324838	−	0.945770i	$-0.394690\pi$
$60$		0			0
$61$	31.0535	−	53.7862i	0.0651802	−	0.112895i	−0.831594	−	0.555384i	$-0.812571\pi$
$61$	31.0535	−	53.7862i	0.0651802	−	0.112895i	0.896774	+	0.442489i	$0.145904\pi$
$62$		0			0
$63$	−52.8247	−	367.047i	−0.105639	−	0.734025i
$64$		0			0
$65$	199.066	−	344.793i	0.379864	−	0.657944i
$66$		0			0
$67$	80.3318	+	139.139i	0.146479	+	0.253709i	0.929924	−	0.367752i	$-0.119873\pi$
$67$	80.3318	+	139.139i	0.146479	+	0.253709i	−0.783445	+	0.621461i	$0.786539\pi$
$68$		0			0
$69$	−105.819	−	91.6802i	−0.184625	−	0.159957i
$70$		0			0
$71$	−959.723			−1.60420			−0.802100	−	0.597190i	$-0.796284\pi$
$71$	−959.723			−1.60420			−0.802100	+	0.597190i	$0.796284\pi$
$72$		0			0
$73$	763.424			1.22400			0.612000	−	0.790858i	$-0.290365\pi$
$73$	763.424			1.22400			0.612000	+	0.790858i	$0.290365\pi$
$74$		0			0
$75$	24.5757	−	127.558i	0.0378368	−	0.196388i
$76$		0			0
$77$	148.627	+	257.429i	0.219969	+	0.380997i
$78$		0			0
$79$	−31.9825	+	55.3952i	−0.0455482	+	0.0788918i	−0.887901	−	0.460035i	$-0.847837\pi$
$79$	−31.9825	+	55.3952i	−0.0455482	+	0.0788918i	0.842352	+	0.538927i	$0.181170\pi$
$80$		0			0
$81$	171.674	−	708.498i	0.235493	−	0.971876i
$82$		0			0
$83$	−458.663	+	794.427i	−0.606564	+	1.05060i	0.385239	+	0.922817i	$0.374119\pi$
$83$	−458.663	+	794.427i	−0.606564	+	1.05060i	−0.991802	+	0.127782i	$0.959214\pi$
$84$		0			0
$85$	160.907	+	278.699i	0.205327	+	0.355637i
$86$		0			0
$87$	291.966	−	1515.42i	0.359793	−	1.86747i
$88$		0			0
$89$	−1318.88			−1.57080			−0.785399	−	0.618990i	$-0.787542\pi$
$89$	−1318.88			−1.57080			−0.785399	+	0.618990i	$0.787542\pi$
$90$		0			0
$91$	1093.62			1.25981
$92$		0			0
$93$	−379.569	−	328.853i	−0.423220	−	0.366672i
$94$		0			0
$95$	361.256	+	625.714i	0.390149	+	0.675757i
$96$		0			0
$97$	64.0845	−	110.998i	0.0670804	−	0.116187i	−0.830535	−	0.556967i	$-0.811965\pi$
$97$	64.0845	−	110.998i	0.0670804	−	0.116187i	0.897615	+	0.440780i	$0.145298\pi$
$98$		0			0
$99$	83.2424	+	578.402i	0.0845069	+	0.587187i
$100$		0			0
$101$	230.204	−	398.725i	0.226793	−	0.392818i	−0.730063	−	0.683380i	$-0.760509\pi$
$101$	230.204	−	398.725i	0.226793	−	0.392818i	0.956856	+	0.290563i	$0.0938424\pi$
$102$		0			0
$103$	−358.731	−	621.340i	−0.343173	−	0.594393i	0.641847	−	0.766832i	$-0.278168\pi$
$103$	−358.731	−	621.340i	−0.343173	−	0.594393i	−0.985020	+	0.172440i	$0.944835\pi$
$104$		0			0
$105$	337.197	−	116.731i	0.313400	−	0.108493i
$106$		0			0
$107$	1361.76			1.23034			0.615171	−	0.788393i	$-0.289087\pi$
$107$	1361.76			1.23034			0.615171	+	0.788393i	$0.289087\pi$
$108$		0			0
$109$	225.862			0.198474			0.0992369	−	0.995064i	$-0.468360\pi$
$109$	225.862			0.198474			0.0992369	+	0.995064i	$0.468360\pi$
$110$		0			0
$111$	−1971.86	+	682.618i	−1.68613	+	0.583705i
$112$		0			0
$113$	−984.234	−	1704.74i	−0.819371	−	1.41919i	−0.906146	−	0.422965i	$-0.860989\pi$
$113$	−984.234	−	1704.74i	−0.819371	−	1.41919i	0.0867746	−	0.996228i	$-0.472344\pi$
$114$		0			0
$115$	67.3627	−	116.676i	0.0546226	−	0.0946091i
$116$		0			0
$117$	1996.02	+	798.770i	1.57720	+	0.631165i
$118$		0			0
$119$	−441.992	+	765.552i	−0.340482	+	0.589732i
$120$		0			0
$121$	431.290	+	747.017i	0.324035	+	0.561245i
$122$		0			0
$123$	−45.9052	−	39.7716i	−0.0336515	−	0.0291551i
$124$		0			0
$125$	125.000			0.0894427
$126$		0			0
$127$	751.204			0.524871			0.262435	−	0.964950i	$-0.415474\pi$
$127$	751.204			0.524871			0.262435	+	0.964950i	$0.415474\pi$
$128$		0			0
$129$	287.311	−	1491.26i	0.196096	−	1.01782i
$130$		0			0
$131$	39.7899	+	68.9181i	0.0265378	+	0.0459649i	0.878989	−	0.476841i	$-0.158218\pi$
$131$	39.7899	+	68.9181i	0.0265378	+	0.0459649i	−0.852451	+	0.522806i	$0.824885\pi$
$132$		0			0
$133$	−992.328	+	1718.76i	−0.646960	+	1.12057i
$134$		0			0
$135$	700.693	+	33.2339i	0.446711	+	0.0211876i
$136$		0			0
$137$	−401.792	+	695.924i	−0.250565	+	0.433991i	−0.963682	−	0.267054i	$-0.913950\pi$
$137$	−401.792	+	695.924i	−0.250565	+	0.433991i	0.713116	+	0.701046i	$0.247283\pi$
$138$		0			0
$139$	−880.833	−	1525.65i	−0.537491	−	0.930962i	−0.999038	−	0.0438460i	$-0.986039\pi$
$139$	−880.833	−	1525.65i	−0.537491	−	0.930962i	0.461547	−	0.887116i	$-0.347294\pi$
$140$		0			0
$141$	172.386	−	894.755i	0.102961	−	0.534411i
$142$		0			0
$143$	−1723.36			−1.00779
$144$		0			0
$145$	1485.03			0.850518
$146$		0			0
$147$	−606.231	−	525.230i	−0.340143	−	0.294695i
$148$		0			0
$149$	1204.96	+	2087.04i	0.662509	+	1.14750i	0.979954	+	0.199222i	$0.0638416\pi$
$149$	1204.96	+	2087.04i	0.662509	+	1.14750i	−0.317446	+	0.948276i	$0.602825\pi$
$150$		0			0
$151$	−923.839	+	1600.14i	−0.497887	+	0.862366i	−0.999997	−	0.00243799i	$-0.999224\pi$
$151$	−923.839	+	1600.14i	−0.497887	+	0.862366i	0.502110	+	0.864804i	$0.332557\pi$
$152$		0			0
$153$	−1365.85	+	1074.42i	−0.721716	+	0.567724i
$154$		0			0
$155$	241.627	−	418.510i	0.125212	−	0.216874i
$156$		0			0
$157$	43.0700	+	74.5995i	0.0218940	+	0.0379216i	0.876765	−	0.480919i	$-0.159697\pi$
$157$	43.0700	+	74.5995i	0.0218940	+	0.0379216i	−0.854871	+	0.518841i	$0.826364\pi$
$158$		0			0
$159$	−763.082	+	264.164i	−0.380606	+	0.131758i
$160$		0			0
$161$	370.074			0.181155
$162$		0			0
$163$	−1127.15			−0.541625			−0.270812	−	0.962632i	$-0.587292\pi$
$163$	−1127.15			−0.541625			−0.270812	+	0.962632i	$0.587292\pi$
$164$		0			0
$165$	−531.363	+	183.947i	−0.250706	+	0.0867895i
$166$		0			0
$167$	484.322	+	838.871i	0.224419	+	0.388705i	0.956145	−	0.292894i	$-0.0946182\pi$
$167$	484.322	+	838.871i	0.224419	+	0.388705i	−0.731726	+	0.681599i	$0.761285\pi$
$168$		0			0
$169$	−2071.70	+	3588.28i	−0.942966	+	1.63326i
$170$		0			0
$171$	−3066.51	+	2412.21i	−1.37136	+	1.07875i
$172$		0			0
$173$	−876.037	+	1517.34i	−0.384993	+	0.666828i	−0.991768	−	0.128046i	$-0.959130\pi$
$173$	−876.037	+	1517.34i	−0.384993	+	0.666828i	0.606775	+	0.794874i	$0.292463\pi$
$174$		0			0
$175$	171.680	+	297.358i	0.0741588	+	0.128447i
$176$		0			0
$177$	2337.34	+	2025.04i	0.992572	+	0.859949i
$178$		0			0
$179$	−880.297			−0.367578			−0.183789	−	0.982966i	$-0.558836\pi$
$179$	−880.297			−0.367578			−0.183789	+	0.982966i	$0.558836\pi$
$180$		0			0
$181$	335.846			0.137919			0.0689593	−	0.997619i	$-0.478032\pi$
$181$	335.846			0.137919			0.0689593	+	0.997619i	$0.478032\pi$
$182$		0			0
$183$	−61.0530	+	316.890i	−0.0246621	+	0.128006i
$184$		0			0
$185$	−1003.95	−	1738.89i	−0.398983	−	0.691059i
$186$		0			0
$187$	696.502	−	1206.38i	0.272370	−	0.471759i
$188$		0			0
$189$	883.300	+	1712.50i	0.339951	+	0.659080i
$190$		0			0
$191$	1988.65	−	3444.43i	0.753368	−	1.30487i	−0.192813	−	0.981235i	$-0.561761\pi$
$191$	1988.65	−	3444.43i	0.753368	−	1.30487i	0.946181	−	0.323637i	$-0.104906\pi$
$192$		0			0
$193$	−2079.55	−	3601.89i	−0.775593	−	1.34337i	−0.934460	−	0.356067i	$-0.884118\pi$
$193$	−2079.55	−	3601.89i	−0.775593	−	1.34337i	0.158867	−	0.987300i	$-0.449216\pi$
$194$		0			0
$195$	−391.376	+	2031.40i	−0.143728	+	0.746008i
$196$		0			0
$197$	1581.17			0.571846			0.285923	−	0.958253i	$-0.407700\pi$
$197$	1581.17			0.571846			0.285923	+	0.958253i	$0.407700\pi$
$198$		0			0
$199$	−2139.37			−0.762090			−0.381045	−	0.924557i	$-0.624436\pi$
$199$	−2139.37			−0.762090			−0.381045	+	0.924557i	$0.624436\pi$
$200$		0			0
$201$	−630.962	−	546.656i	−0.221416	−	0.191832i
$202$		0			0
$203$	2039.60	+	3532.69i	0.705182	+	1.22141i
$204$		0			0
$205$	29.2224	−	50.6147i	0.00995601	−	0.0172443i
$206$		0			0
$207$	675.440	+	270.298i	0.226794	+	0.0907586i
$208$		0			0
$209$	1563.73	−	2708.47i	0.517539	−	0.896405i
$210$		0			0
$211$	88.1421	+	152.667i	0.0287581	+	0.0498105i	0.880046	−	0.474888i	$-0.157511\pi$
$211$	88.1421	+	152.667i	0.0287581	+	0.0498105i	−0.851288	+	0.524698i	$0.824178\pi$
$212$		0			0
$213$	4712.48	−	1631.37i	1.51593	−	0.524786i
$214$		0			0
$215$	1461.36			0.463552
$216$		0			0
$217$	1327.44			0.415265
$218$		0			0
$219$	−3748.60	+	1297.69i	−1.15665	+	0.400410i
$220$		0			0
$221$	−2562.49	−	4438.37i	−0.779964	−	1.35094i
$222$		0			0
$223$	1811.18	−	3137.06i	0.543883	−	0.942033i	−0.454793	−	0.890597i	$-0.650287\pi$
$223$	1811.18	−	3137.06i	0.543883	−	0.942033i	0.998676	−	0.0514358i	$-0.0163798\pi$
$224$		0			0
$225$	96.1540	+	668.116i	0.0284901	+	0.197960i
$226$		0			0
$227$	−388.172	+	672.333i	−0.113497	+	0.196583i	−0.917178	−	0.398478i	$-0.869539\pi$
$227$	−388.172	+	672.333i	−0.113497	+	0.196583i	0.803681	+	0.595061i	$0.202872\pi$
$228$		0			0
$229$	−2543.04	−	4404.68i	−0.733838	−	1.27105i	−0.955231	−	0.295861i	$-0.904394\pi$
$229$	−2543.04	−	4404.68i	−0.733838	−	1.27105i	0.221393	−	0.975185i	$-0.428940\pi$
$230$		0			0
$231$	−1167.38	−	1011.40i	−0.332502	−	0.288075i
$232$		0			0
$233$	3896.93			1.09569			0.547846	−	0.836579i	$-0.315448\pi$
$233$	3896.93			1.09569			0.547846	+	0.836579i	$0.315448\pi$
$234$		0			0
$235$	876.812			0.243391
$236$		0			0
$237$	62.8794	−	326.369i	0.0172340	−	0.0894514i
$238$		0			0
$239$	617.365	+	1069.31i	0.167088	+	0.289405i	0.937395	−	0.348268i	$-0.113230\pi$
$239$	617.365	+	1069.31i	0.167088	+	0.289405i	−0.770307	+	0.637673i	$0.779897\pi$
$240$		0			0
$241$	−959.223	+	1661.42i	−0.256386	+	0.444073i	−0.965271	−	0.261251i	$-0.915865\pi$
$241$	−959.223	+	1661.42i	−0.256386	+	0.444073i	0.708885	+	0.705324i	$0.249198\pi$
$242$		0			0
$243$	361.362	+	3770.72i	0.0953967	+	0.995439i
$244$		0			0
$245$	385.916	−	668.426i	0.100634	−	0.174303i
$246$		0			0
$247$	−5753.12	−	9964.70i	−1.48203	−	2.56696i
$248$		0			0
$249$	901.758	−	4680.49i	0.229504	−	1.19122i
$250$		0			0
$251$	7109.99			1.78796			0.893981	−	0.448105i	$-0.147901\pi$
$251$	7109.99			1.78796			0.893981	+	0.448105i	$0.147901\pi$
$252$		0			0
$253$	−583.172			−0.144916
$254$		0			0
$255$	−1263.83	−	1094.97i	−0.310370	−	0.268900i
$256$		0			0
$257$	2091.14	+	3621.96i	0.507555	+	0.879111i	0.999962	+	0.00874607i	$0.00278399\pi$
$257$	2091.14	+	3621.96i	0.507555	+	0.879111i	−0.492407	+	0.870365i	$0.663883\pi$
$258$		0			0
$259$	2757.73	−	4776.52i	0.661610	−	1.14594i
$260$		0			0
$261$	1142.33	+	7937.39i	0.270914	+	1.88242i
$262$		0			0
$263$	2108.30	−	3651.69i	0.494310	−	0.856170i	−0.505668	−	0.862728i	$-0.668754\pi$
$263$	2108.30	−	3651.69i	0.494310	−	0.856170i	0.999978	+	0.00655782i	$0.00208743\pi$
$264$		0			0
$265$	−388.515	−	672.927i	−0.0900614	−	0.155991i
$266$		0			0
$267$	6476.03	−	2241.87i	1.48437	−	0.513859i
$268$		0			0
$269$	−3271.14			−0.741431			−0.370715	−	0.928747i	$-0.620887\pi$
$269$	−3271.14			−0.741431			−0.370715	+	0.928747i	$0.620887\pi$
$270$		0			0
$271$	6407.18			1.43619			0.718096	−	0.695944i	$-0.245014\pi$
$271$	6407.18			1.43619			0.718096	+	0.695944i	$0.245014\pi$
$272$		0			0
$273$	−5369.96	+	1858.97i	−1.19049	+	0.412125i
$274$		0			0
$275$	−270.538	−	468.585i	−0.0593237	−	0.102752i
$276$		0			0
$277$	−3163.13	+	5478.70i	−0.686116	+	1.18839i	0.286969	+	0.957940i	$0.407352\pi$
$277$	−3163.13	+	5478.70i	−0.686116	+	1.18839i	−0.973085	+	0.230448i	$0.925981\pi$
$278$		0			0
$279$	2422.77	+	969.547i	0.519884	+	0.208048i
$280$		0			0
$281$	1991.29	−	3449.01i	0.422741	−	0.732208i	−0.573466	−	0.819230i	$-0.694401\pi$
$281$	1991.29	−	3449.01i	0.422741	−	0.732208i	0.996206	+	0.0870212i	$0.0277348\pi$
$282$		0			0
$283$	1839.84	+	3186.70i	0.386456	+	0.669362i	0.991970	−	0.126473i	$-0.0403657\pi$
$283$	1839.84	+	3186.70i	0.386456	+	0.669362i	−0.605514	+	0.795835i	$0.707032\pi$
$284$		0			0
$285$	−2837.47	−	2458.34i	−0.589744	−	0.510946i
$286$		0			0
$287$	160.541			0.0330189
$288$		0			0
$289$	−770.434			−0.156815
$290$		0			0
$291$	−125.994	+	653.959i	−0.0253811	+	0.131738i
$292$		0			0
$293$	−4473.14	−	7747.71i	−0.891890	−	1.54480i	−0.837607	−	0.546273i	$-0.816046\pi$
$293$	−4473.14	−	7747.71i	−0.891890	−	1.54480i	−0.0542823	−	0.998526i	$-0.517287\pi$
$294$		0			0
$295$	−1487.91	+	2577.13i	−0.293659	+	0.508632i
$296$		0			0
$297$	−1391.93	−	2698.60i	−0.271945	−	0.527235i
$298$		0			0
$299$	−1072.77	+	1858.09i	−0.207492	+	0.359386i
$300$		0			0
$301$	2007.09	+	3476.37i	0.384341	+	0.665697i
$302$		0			0
$303$	−452.594	+	2349.15i	−0.0858114	+	0.445396i
$304$		0			0
$305$	−310.535			−0.0582989
$306$		0			0
$307$	−9746.88			−1.81200			−0.906000	−	0.423278i	$-0.860879\pi$
$307$	−9746.88			−1.81200			−0.906000	+	0.423278i	$0.860879\pi$
$308$		0			0
$309$	2817.63	+	2441.15i	0.518736	+	0.449425i
$310$		0			0
$311$	−2639.51	−	4571.77i	−0.481264	−	0.833573i	0.518505	−	0.855074i	$-0.326489\pi$
$311$	−2639.51	−	4571.77i	−0.481264	−	0.833573i	−0.999769	+	0.0215015i	$0.993155\pi$
$312$		0			0
$313$	−2267.20	+	3926.90i	−0.409424	+	0.709142i	−0.994825	−	0.101601i	$-0.967603\pi$
$313$	−2267.20	+	3926.90i	−0.409424	+	0.709142i	0.585402	+	0.810743i	$0.300937\pi$
$314$		0			0
$315$	−1457.30	+	1146.36i	−0.260665	+	0.205047i
$316$		0			0
$317$	−1117.38	+	1935.37i	−0.197977	+	0.342905i	−0.947872	−	0.318651i	$-0.896770\pi$
$317$	−1117.38	+	1935.37i	−0.197977	+	0.342905i	0.749896	+	0.661556i	$0.230104\pi$
$318$		0			0
$319$	−3214.05	−	5566.91i	−0.564114	−	0.977075i
$320$		0			0
$321$	−6686.60	+	2314.77i	−1.16265	+	0.402485i
$322$		0			0
$323$	9300.58			1.60216
$324$		0			0
$325$	−1990.66			−0.339761
$326$		0			0
$327$	−1109.04	+	383.927i	−0.187553	+	0.0649272i
$328$		0			0
$329$	1204.25	+	2085.82i	0.201800	+	0.349529i
$330$		0			0
$331$	920.763	−	1594.81i	0.152899	−	0.264829i	−0.779393	−	0.626536i	$-0.784472\pi$
$331$	920.763	−	1594.81i	0.152899	−	0.264829i	0.932292	+	0.361706i	$0.117806\pi$
$332$		0			0
$333$	8521.98	−	6703.65i	1.40241	−	1.10318i
$334$		0			0
$335$	401.659	−	695.694i	0.0655074	−	0.113462i
$336$		0			0
$337$	−3517.09	−	6091.78i	−0.568511	−	0.984690i	−0.996714	−	0.0810072i	$-0.974186\pi$
$337$	−3517.09	−	6091.78i	−0.568511	−	0.984690i	0.428203	−	0.903683i	$-0.359147\pi$
$338$		0			0
$339$	7730.61	+	6697.69i	1.23855	+	1.07306i
$340$		0			0
$341$	−2091.81			−0.332193
$342$		0			0
$343$	6831.03			1.07534
$344$		0			0
$345$	−132.439	+	687.411i	−0.0206675	+	0.107272i
$346$		0			0
$347$	5887.57	+	10197.6i	0.910839	+	1.57762i	0.812881	+	0.582429i	$0.197898\pi$
$347$	5887.57	+	10197.6i	0.910839	+	1.57762i	0.0979579	+	0.995191i	$0.468769\pi$
$348$		0			0
$349$	−3949.29	+	6840.37i	−0.605733	+	1.04916i	0.386202	+	0.922414i	$0.373787\pi$
$349$	−3949.29	+	6840.37i	−0.605733	+	1.04916i	−0.991935	+	0.126746i	$0.959547\pi$
$350$		0			0
$351$	−11158.8	−	529.261i	−1.69690	−	0.0804839i
$352$		0			0
$353$	−4483.96	+	7766.44i	−0.676082	+	1.17101i	0.300070	+	0.953917i	$0.402990\pi$
$353$	−4483.96	+	7766.44i	−0.676082	+	1.17101i	−0.976151	+	0.217091i	$0.930343\pi$
$354$		0			0
$355$	2399.31	+	4155.72i	0.358710	+	0.621304i
$356$		0			0
$357$	868.982	−	4510.37i	0.128827	−	0.668667i
$358$		0			0
$359$	8351.48			1.22778			0.613892	−	0.789390i	$-0.289603\pi$
$359$	8351.48			1.22778			0.613892	+	0.789390i	$0.289603\pi$
$360$		0			0
$361$	14022.0			2.04432
$362$		0			0
$363$	−3387.55	−	2934.92i	−0.489807	−	0.424362i
$364$		0			0
$365$	−1908.56	−	3305.72i	−0.273695	−	0.474053i
$366$		0			0
$367$	−55.2588	+	95.7111i	−0.00785964	+	0.0136133i	−0.869928	−	0.493178i	$-0.835835\pi$
$367$	−55.2588	+	95.7111i	−0.00785964	+	0.0136133i	0.862069	+	0.506791i	$0.169168\pi$
$368$		0			0
$369$	293.011	+	117.257i	0.0413375	+	0.0165425i
$370$		0			0
$371$	1067.20	−	1848.45i	0.149343	−	0.258670i
$372$		0			0
$373$	−2447.97	−	4240.01i	−0.339816	−	0.588578i	0.644582	−	0.764535i	$-0.277031\pi$
$373$	−2447.97	−	4240.01i	−0.339816	−	0.588578i	−0.984398	+	0.175957i	$0.943698\pi$
$374$		0			0
$375$	−613.781	+	212.479i	−0.0845214	+	0.0292596i
$376$		0			0
$377$	−23649.6			−3.23081
$378$		0			0
$379$	10326.8			1.39962			0.699808	−	0.714331i	$-0.253269\pi$
$379$	10326.8			1.39962			0.699808	+	0.714331i	$0.253269\pi$
$380$		0			0
$381$	−3688.60	+	1276.92i	−0.495992	+	0.171702i
$382$		0			0
$383$	4166.26	+	7216.17i	0.555838	+	0.962739i	0.997838	+	0.0657244i	$0.0209358\pi$
$383$	4166.26	+	7216.17i	0.555838	+	0.962739i	−0.442000	+	0.897015i	$0.645731\pi$
$384$		0			0
$385$	743.134	−	1287.15i	0.0983730	−	0.170387i
$386$		0			0
$387$	1124.12	+	7810.85i	0.147655	+	1.02596i
$388$		0			0
$389$	−1035.75	+	1793.97i	−0.134999	+	0.233825i	−0.925597	−	0.378510i	$-0.876436\pi$
$389$	−1035.75	+	1793.97i	−0.134999	+	0.233825i	0.790598	+	0.612335i	$0.209770\pi$
$390$		0			0
$391$	−867.129	−	1501.91i	−0.112155	−	0.194258i
$392$		0			0
$393$	−312.527	−	270.769i	−0.0401143	−	0.0347544i
$394$		0			0
$395$	319.825			0.0407396
$396$		0			0
$397$	−7891.46			−0.997635			−0.498818	−	0.866707i	$-0.666232\pi$
$397$	−7891.46			−0.997635			−0.498818	+	0.866707i	$0.666232\pi$
$398$		0			0
$399$	1950.97	−	10126.3i	0.244789	−	1.27055i
$400$		0			0
$401$	−866.818	−	1501.37i	−0.107947	−	0.186970i	0.806991	−	0.590563i	$-0.201094\pi$
$401$	−866.818	−	1501.37i	−0.107947	−	0.186970i	−0.914939	+	0.403593i	$0.867761\pi$
$402$		0			0
$403$	−3847.98	+	6664.90i	−0.475637	+	0.823827i
$404$		0			0
$405$	−3497.07	+	1027.87i	−0.429064	+	0.126112i
$406$		0			0
$407$	−4345.70	+	7526.97i	−0.529258	+	0.916702i
$408$		0			0
$409$	4706.30	+	8151.55i	0.568977	+	0.985497i	0.996667	+	0.0815720i	$0.0259941\pi$
$409$	4706.30	+	8151.55i	0.568977	+	0.985497i	−0.427690	+	0.903925i	$0.640673\pi$
$410$		0			0
$411$	789.946	−	4100.14i	0.0948058	−	0.492080i
$412$		0			0
$413$	−8174.21			−0.973914
$414$		0			0
$415$	4586.63			0.542527
$416$		0			0
$417$	6918.45	+	5994.04i	0.812465	+	0.703908i
$418$		0			0
$419$	1934.35	+	3350.40i	0.225535	+	0.390639i	0.956480	−	0.291798i	$-0.0942535\pi$
$419$	1934.35	+	3350.40i	0.225535	+	0.390639i	−0.730945	+	0.682437i	$0.760920\pi$
$420$		0			0
$421$	−6462.48	+	11193.4i	−0.748129	+	1.29580i	0.200590	+	0.979675i	$0.435714\pi$
$421$	−6462.48	+	11193.4i	−0.748129	+	1.29580i	−0.948719	+	0.316122i	$0.897619\pi$
$422$		0			0
$423$	674.471	+	4686.50i	0.0775270	+	0.538689i
$424$		0			0
$425$	804.535	−	1393.49i	0.0918251	−	0.159046i
$426$		0			0
$427$	−426.501	−	738.721i	−0.0483368	−	0.0837219i
$428$		0			0
$429$	8462.12	−	2929.42i	0.952343	−	0.329682i
$430$		0			0
$431$	−13183.6			−1.47339			−0.736697	−	0.676223i	$-0.763616\pi$
$431$	−13183.6			−1.47339			−0.736697	+	0.676223i	$0.763616\pi$
$432$		0			0
$433$	−7584.46			−0.841769			−0.420884	−	0.907114i	$-0.638280\pi$
$433$	−7584.46			−0.841769			−0.420884	+	0.907114i	$0.638280\pi$
$434$		0			0
$435$	−7291.88	+	2524.30i	−0.803722	+	0.278232i
$436$		0			0
$437$	−1946.81	−	3371.98i	−0.213109	−	0.369116i
$438$		0			0
$439$	3773.23	−	6535.43i	0.410220	−	0.710521i	−0.584694	−	0.811254i	$-0.698785\pi$
$439$	3773.23	−	6535.43i	0.410220	−	0.710521i	0.994914	+	0.100733i	$0.0321187\pi$
$440$		0			0
$441$	3869.55	+	1548.52i	0.417833	+	0.167209i
$442$		0			0
$443$	−1022.52	+	1771.06i	−0.109665	+	0.189945i	−0.915634	−	0.402012i	$-0.868311\pi$
$443$	−1022.52	+	1771.06i	−0.109665	+	0.189945i	0.805970	+	0.591957i	$0.201644\pi$
$444$		0			0
$445$	3297.20	+	5710.92i	0.351241	+	0.608367i
$446$		0			0
$447$	−9464.26	−	8199.69i	−1.00144	−	0.867633i
$448$		0			0
$449$	10723.2			1.12708			0.563541	−	0.826088i	$-0.309439\pi$
$449$	10723.2			1.12708			0.563541	+	0.826088i	$0.309439\pi$
$450$		0			0
$451$	−252.984			−0.0264137
$452$		0			0
$453$	1816.32	−	9427.44i	0.188385	−	0.977792i
$454$		0			0
$455$	−2734.06	−	4735.53i	−0.281702	−	0.487923i
$456$		0			0
$457$	2330.29	−	4036.18i	0.238526	−	0.413139i	−0.721766	−	0.692138i	$-0.756669\pi$
$457$	2330.29	−	4036.18i	0.238526	−	0.413139i	0.960292	+	0.278998i	$0.0900024\pi$
$458$		0			0
$459$	4880.34	−	7597.39i	0.496285	−	0.772584i
$460$		0			0
$461$	8320.18	−	14411.0i	0.840584	−	1.45593i	−0.0488170	−	0.998808i	$-0.515545\pi$
$461$	8320.18	−	14411.0i	0.840584	−	1.45593i	0.889401	−	0.457127i	$-0.151122\pi$
$462$		0			0
$463$	1734.35	+	3003.97i	0.174086	+	0.301526i	0.939845	−	0.341602i	$-0.110970\pi$
$463$	1734.35	+	3003.97i	0.174086	+	0.301526i	−0.765759	+	0.643128i	$0.777636\pi$
$464$		0			0
$465$	−475.052	+	2465.71i	−0.0473764	+	0.245903i
$466$		0			0
$467$	−9920.55			−0.983016			−0.491508	−	0.870873i	$-0.663554\pi$
$467$	−9920.55			−0.983016			−0.491508	+	0.870873i	$0.663554\pi$
$468$		0			0
$469$	2206.62			0.217254
$470$		0			0
$471$	−338.291	−	293.090i	−0.0330948	−	0.0286728i
$472$		0			0
$473$	−3162.82	−	5478.16i	−0.307455	−	0.532528i
$474$		0			0
$475$	1806.28	−	3128.57i	0.174480	−	0.302208i
$476$		0			0
$477$	3297.89	−	2594.22i	0.316562	−	0.249017i
$478$		0			0
$479$	−9132.33	+	15817.7i	−0.871120	+	1.50882i	−0.0102812	+	0.999947i	$0.503273\pi$
$479$	−9132.33	+	15817.7i	−0.871120	+	1.50882i	−0.860839	+	0.508877i	$0.830061\pi$
$480$		0			0
$481$	15988.2	+	27692.4i	1.51559	+	2.62508i
$482$		0			0
$483$	−1817.16	+	629.064i	−0.171187	+	0.0592617i
$484$		0			0
$485$	−640.845			−0.0599985
$486$		0			0
$487$	−3244.55			−0.301899			−0.150949	−	0.988542i	$-0.548233\pi$
$487$	−3244.55			−0.301899			−0.150949	+	0.988542i	$0.548233\pi$
$488$		0			0
$489$	5534.57	−	1915.96i	0.511824	−	0.177183i
$490$		0			0
$491$	295.547	+	511.902i	0.0271646	+	0.0470505i	0.879288	−	0.476290i	$-0.158019\pi$
$491$	295.547	+	511.902i	0.0271646	+	0.0470505i	−0.852124	+	0.523341i	$0.824685\pi$
$492$		0			0
$493$	9558.08	−	16555.1i	0.873173	−	1.51238i
$494$		0			0
$495$	2296.45	−	1806.45i	0.208520	−	0.164028i
$496$		0			0
$497$	−6590.61	+	11415.3i	−0.594827	+	1.03027i
$498$		0			0
$499$	4822.49	+	8352.79i	0.432634	+	0.749343i	0.997099	−	0.0761132i	$-0.0242510\pi$
$499$	4822.49	+	8352.79i	0.432634	+	0.749343i	−0.564466	+	0.825457i	$0.690918\pi$
$500$		0			0
$501$	−3804.08	−	3295.80i	−0.339229	−	0.293903i
$502$		0			0
$503$	723.099			0.0640982			0.0320491	−	0.999486i	$-0.489797\pi$
$503$	723.099			0.0640982			0.0320491	+	0.999486i	$0.489797\pi$
$504$		0			0
$505$	−2302.04			−0.202850
$506$		0			0
$507$	4073.07	−	21140.9i	0.356788	−	1.85187i
$508$		0			0
$509$	1342.27	+	2324.88i	0.116886	+	0.202453i	0.918532	−	0.395346i	$-0.129375\pi$
$509$	1342.27	+	2324.88i	0.116886	+	0.202453i	−0.801646	+	0.597799i	$0.796042\pi$
$510$		0			0
$511$	5242.58	−	9080.42i	0.453852	−	0.786094i
$512$		0			0
$513$	10957.0	−	17057.1i	0.943007	−	1.46801i
$514$		0			0
$515$	−1793.65	+	3106.70i	−0.153472	+	0.265820i
$516$		0			0
$517$	−1897.68	−	3286.88i	−0.161431	−	0.279607i
$518$		0			0
$519$	1722.34	−	8939.64i	0.145669	−	0.756082i
$520$		0			0
$521$	−4203.80			−0.353497			−0.176748	−	0.984256i	$-0.556558\pi$
$521$	−4203.80			−0.353497			−0.176748	+	0.984256i	$0.556558\pi$
$522$		0			0
$523$	10571.8			0.883883			0.441942	−	0.897044i	$-0.354290\pi$
$523$	10571.8			0.883883			0.441942	+	0.897044i	$0.354290\pi$
$524$		0			0
$525$	−1348.45	−	1168.28i	−0.112098	−	0.0971197i
$526$		0			0
$527$	−3110.35	−	5387.29i	−0.257095	−	0.445302i
$528$		0			0
$529$	5720.48	−	9908.17i	0.470164	−	0.814347i
$530$		0			0
$531$	−14919.1	−	5970.35i	−1.21928	−	0.487931i
$532$		0			0
$533$	−465.376	+	806.055i	−0.0378193	+	0.0655049i
$534$		0			0
$535$	−3404.41	−	5896.61i	−0.275113	−	0.476510i
$536$		0			0
$537$	4322.48	−	1496.36i	0.347354	−	0.120247i
$538$		0			0
$539$	−3340.95			−0.266985
$540$		0			0
$541$	15310.3			1.21671			0.608356	−	0.793664i	$-0.291829\pi$
$541$	15310.3			1.21671			0.608356	+	0.793664i	$0.291829\pi$
$542$		0			0
$543$	−1649.09	+	570.882i	−0.130330	+	0.0451177i
$544$		0			0
$545$	−564.654	−	978.010i	−0.0443801	−	0.0768685i
$546$		0			0
$547$	447.172	−	774.525i	0.0349538	−	0.0605417i	−0.848019	−	0.529965i	$-0.822205\pi$
$547$	447.172	−	774.525i	0.0349538	−	0.0605417i	0.882973	+	0.469424i	$0.155538\pi$
$548$		0			0
$549$	−238.873	−	1659.79i	−0.0185699	−	0.129031i
$550$		0			0
$551$	21459.1	−	37168.2i	1.65914	−	2.87372i
$552$		0			0
$553$	439.260	+	760.820i	0.0337780	+	0.0585052i
$554$		0			0
$555$	7885.47	+	6831.85i	0.603098	+	0.522515i
$556$		0			0
$557$	25371.2			1.93000			0.965001	−	0.262245i	$-0.0844627\pi$
$557$	25371.2			1.93000			0.965001	+	0.262245i	$0.0844627\pi$
$558$		0			0
$559$	−23272.6			−1.76087
$560$		0			0
$561$	−1369.36	+	7107.55i	−0.103056	+	0.534904i
$562$		0			0
$563$	−424.449	−	735.167i	−0.0317733	−	0.0550330i	0.849701	−	0.527264i	$-0.176782\pi$
$563$	−424.449	−	735.167i	−0.0317733	−	0.0550330i	−0.881475	+	0.472231i	$0.843449\pi$
$564$		0			0
$565$	−4921.17	+	8523.72i	−0.366434	+	0.634682i
$566$		0			0
$567$	−7248.19	−	6907.35i	−0.536852	−	0.511607i
$568$		0			0
$569$	4318.33	−	7479.57i	0.318161	−	0.551072i	−0.661943	−	0.749554i	$-0.730268\pi$
$569$	4318.33	−	7479.57i	0.318161	−	0.551072i	0.980104	+	0.198482i	$0.0636013\pi$
$570$		0			0
$571$	3615.99	+	6263.08i	0.265017	+	0.459022i	0.967568	−	0.252611i	$-0.0812892\pi$
$571$	3615.99	+	6263.08i	0.265017	+	0.459022i	−0.702551	+	0.711633i	$0.747956\pi$
$572$		0			0
$573$	−3909.79	+	20293.4i	−0.285050	+	1.47953i
$574$		0			0
$575$	−673.627			−0.0488559
$576$		0			0
$577$	−5882.23			−0.424403			−0.212201	−	0.977226i	$-0.568063\pi$
$577$	−5882.23			−0.424403			−0.212201	+	0.977226i	$0.568063\pi$
$578$		0			0
$579$	16333.7	+	14151.3i	1.17238	+	1.01573i
$580$		0			0
$581$	6299.46	+	10911.0i	0.449820	+	0.779111i
$582$		0			0
$583$	−1681.72	+	2912.83i	−0.119468	+	0.206925i
$584$		0			0
$585$	−1531.28	−	10640.0i	−0.108223	−	0.751980i
$586$		0			0
$587$	−9666.38	+	16742.7i	−0.679684	+	1.17725i	0.295392	+	0.955376i	$0.404550\pi$
$587$	−9666.38	+	16742.7i	−0.679684	+	1.17725i	−0.975076	+	0.221871i	$0.928784\pi$
$588$		0			0
$589$	−6983.14	−	12095.1i	−0.488515	−	0.846132i
$590$		0			0
$591$	−7763.95	+	2687.72i	−0.540383	+	0.187070i
$592$		0			0
$593$	−4318.26			−0.299039			−0.149519	−	0.988759i	$-0.547773\pi$
$593$	−4318.26			−0.299039			−0.149519	+	0.988759i	$0.547773\pi$
$594$		0			0
$595$	4419.92			0.304536
$596$		0			0
$597$	10504.8	−	3636.57i	0.720158	−	0.249304i
$598$		0			0
$599$	−7690.82	−	13320.9i	−0.524605	−	0.908643i	−0.999590	−	0.0286487i	$-0.990880\pi$
$599$	−7690.82	−	13320.9i	−0.524605	−	0.908643i	0.474984	−	0.879994i	$-0.342454\pi$
$600$		0			0
$601$	−2086.27	+	3613.53i	−0.141599	+	0.245256i	−0.928099	−	0.372334i	$-0.878558\pi$
$601$	−2086.27	+	3613.53i	−0.141599	+	0.245256i	0.786500	+	0.617590i	$0.211891\pi$
$602$		0			0
$603$	4027.40	+	1611.69i	0.271988	+	0.108844i
$604$		0			0
$605$	2156.45	−	3735.08i	0.144913	−	0.250996i
$606$		0			0
$607$	−346.410	−	600.000i	−0.0231637	−	0.0401207i	0.854211	−	0.519926i	$-0.174041\pi$
$607$	−346.410	−	600.000i	−0.0231637	−	0.0401207i	−0.877375	+	0.479806i	$0.840707\pi$
$608$		0			0
$609$	−16019.9	−	13879.4i	−1.06595	−	0.923519i
$610$		0			0
$611$	−13963.5			−0.924555
$612$		0			0
$613$	11649.8			0.767584			0.383792	−	0.923419i	$-0.374618\pi$
$613$	11649.8			0.767584			0.383792	+	0.923419i	$0.374618\pi$
$614$		0			0
$615$	−57.4530	+	298.204i	−0.00376704	+	0.0195524i
$616$		0			0
$617$	10893.6	+	18868.2i	0.710793	+	1.23113i	0.964560	+	0.263864i	$0.0849969\pi$
$617$	10893.6	+	18868.2i	0.710793	+	1.23113i	−0.253767	+	0.967265i	$0.581670\pi$
$618$		0			0
$619$	2485.00	−	4304.15i	0.161358	−	0.279480i	−0.773998	−	0.633188i	$-0.781746\pi$
$619$	2485.00	−	4304.15i	0.161358	−	0.279480i	0.935356	+	0.353708i	$0.115079\pi$
$620$		0			0
$621$	−3776.04	−	179.098i	−0.244005	−	0.0115732i
$622$		0			0
$623$	−9057.01	+	15687.2i	−0.582442	+	1.00882i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−3074.39	+	15957.3i	−0.195820	+	1.01639i
$628$		0			0
$629$	−25846.8			−1.63844
$630$		0			0
$631$	−16907.2			−1.06666			−0.533331	−	0.845906i	$-0.679060\pi$
$631$	−16907.2			−1.06666			−0.533331	+	0.845906i	$0.679060\pi$
$632$		0			0
$633$	−692.308	−	599.805i	−0.0434704	−	0.0376621i
$634$		0			0
$635$	−1878.01	−	3252.81i	−0.117365	−	0.203282i
$636$		0			0
$637$	−6145.83	+	10644.9i	−0.382271	+	0.662113i
$638$		0			0
$639$	−20366.4	+	16020.8i	−1.26085	+	0.991823i
$640$		0			0
$641$	−10734.9	+	18593.5i	−0.661474	+	1.14571i	0.318755	+	0.947837i	$0.396735\pi$
$641$	−10734.9	+	18593.5i	−0.661474	+	1.14571i	−0.980229	+	0.197869i	$0.936598\pi$
$642$		0			0
$643$	8856.22	+	15339.4i	0.543165	+	0.940790i	0.998720	+	0.0505819i	$0.0161076\pi$
$643$	8856.22	+	15339.4i	0.543165	+	0.940790i	−0.455555	+	0.890208i	$0.650559\pi$
$644$		0			0
$645$	−7175.63	+	2484.06i	−0.438047	+	0.151643i
$646$		0			0
$647$	12632.9			0.767619			0.383809	−	0.923412i	$-0.374612\pi$
$647$	12632.9			0.767619			0.383809	+	0.923412i	$0.374612\pi$
$648$		0			0
$649$	12881.1			0.779088
$650$		0			0
$651$	−6518.06	+	2256.42i	−0.392416	+	0.135847i
$652$		0			0
$653$	−8085.08	−	14003.8i	−0.484523	−	0.839219i	0.515319	−	0.856999i	$-0.327674\pi$
$653$	−8085.08	−	14003.8i	−0.484523	−	0.839219i	−0.999842	+	0.0177796i	$0.994340\pi$
$654$		0			0
$655$	198.949	−	344.590i	0.0118681	−	0.0205561i
$656$		0			0
$657$	16200.7	−	12744.0i	0.962026	−	0.756758i
$658$		0			0
$659$	−3876.38	+	6714.09i	−0.229139	+	0.396880i	−0.957553	−	0.288257i	$-0.906924\pi$
$659$	−3876.38	+	6714.09i	−0.229139	+	0.396880i	0.728414	+	0.685137i	$0.240258\pi$
$660$		0			0
$661$	−5846.77	−	10126.9i	−0.344044	−	0.595901i	0.641136	−	0.767427i	$-0.278464\pi$
$661$	−5846.77	−	10126.9i	−0.344044	−	0.595901i	−0.985180	+	0.171526i	$0.945130\pi$
$662$		0			0
$663$	20127.0	+	17437.7i	1.17898	+	1.02145i
$664$		0			0
$665$	9923.28			0.578659
$666$		0			0
$667$	−8002.85			−0.464575
$668$		0			0
$669$	−3560.89	+	18482.5i	−0.205788	+	1.06812i
$670$		0			0
$671$	672.091	+	1164.10i	0.0386673	+	0.0669738i
$672$		0			0
$673$	2059.46	−	3567.08i	0.117959	−	0.204310i	−0.801000	−	0.598664i	$-0.795698\pi$
$673$	2059.46	−	3567.08i	0.117959	−	0.204310i	0.918959	+	0.394354i	$0.129032\pi$
$674$		0			0
$675$	−1607.83	−	3117.17i	−0.0916818	−	0.177748i
$676$		0			0
$677$	6801.97	−	11781.4i	0.386146	−	0.668825i	−0.605781	−	0.795631i	$-0.707139\pi$
$677$	6801.97	−	11781.4i	0.386146	−	0.668825i	0.991928	+	0.126806i	$0.0404726\pi$
$678$		0			0
$679$	−880.162	−	1524.49i	−0.0497460	−	0.0861626i
$680$		0			0
$681$	763.168	−	3961.15i	0.0429437	−	0.222895i
$682$		0			0
$683$	28073.3			1.57276			0.786381	−	0.617742i	$-0.211952\pi$
$683$	28073.3			1.57276			0.786381	+	0.617742i	$0.211952\pi$
$684$		0			0
$685$	4017.92			0.224112
$686$		0			0
$687$	19974.2	+	17305.3i	1.10926	+	0.961048i
$688$		0			0
$689$	6187.22	+	10716.6i	0.342111	+	0.592553i
$690$		0			0
$691$	7958.75	−	13785.0i	0.438155	−	0.758907i	−0.559392	−	0.828903i	$-0.688965\pi$
$691$	7958.75	−	13785.0i	0.438155	−	0.758907i	0.997547	+	0.0699960i	$0.0222987\pi$
$692$		0			0
$693$	7451.35	+	2981.89i	0.408446	+	0.163452i
$694$		0			0
$695$	−4404.16	+	7628.23i	−0.240373	+	0.416339i
$696$		0			0
$697$	−376.167	−	651.541i	−0.0204424	−	0.0354073i
$698$		0			0
$699$	−19134.9	+	6624.12i	−1.03540	+	0.358437i
$700$		0			0
$701$	17451.6			0.940280			0.470140	−	0.882592i	$-0.344203\pi$
$701$	17451.6			0.940280			0.470140	+	0.882592i	$0.344203\pi$
$702$		0			0
$703$	−58029.3			−3.11325
$704$		0			0
$705$	−4305.37	+	1490.43i	−0.229999	+	0.0796212i
$706$		0			0
$707$	−3161.71	−	5476.24i	−0.168187	−	0.291309i
$708$		0			0
$709$	−15089.1	+	26135.1i	−0.799273	+	1.38438i	0.120818	+	0.992675i	$0.461448\pi$
$709$	−15089.1	+	26135.1i	−0.799273	+	1.38438i	−0.920090	+	0.391706i	$0.871885\pi$
$710$		0			0
$711$	246.019	+	1709.44i	0.0129767	+	0.0901674i
$712$		0			0
$713$	−1302.13	+	2255.36i	−0.0683943	+	0.118462i
$714$		0			0
$715$	4308.40	+	7462.36i	0.225349	+	0.390317i
$716$		0			0
$717$	−4849.06	−	4201.16i	−0.252568	−	0.218822i
$718$		0			0
$719$	−7009.26			−0.363562			−0.181781	−	0.983339i	$-0.558186\pi$
$719$	−7009.26			−0.363562			−0.181781	+	0.983339i	$0.558186\pi$
$720$		0			0
$721$	−9853.90			−0.508985
$722$		0			0
$723$	1885.89	−	9788.53i	0.0970082	−	0.503512i
$724$		0			0
$725$	−3712.58	−	6430.38i	−0.190182	−	0.329404i
$726$		0			0
$727$	15583.0	−	26990.6i	0.794968	−	1.37693i	−0.127891	−	0.991788i	$-0.540821\pi$
$727$	15583.0	−	26990.6i	0.794968	−	1.37693i	0.922859	−	0.385137i	$-0.125846\pi$
$728$		0			0
$729$	−8183.97	−	17900.9i	−0.415789	−	0.909461i
$730$		0			0
$731$	9405.70	−	16291.1i	0.475899	−	0.824282i
$732$		0			0
$733$	−16038.1	−	27778.7i	−0.808158	−	1.39977i	−0.914139	−	0.405402i	$-0.867132\pi$
$733$	−16038.1	−	27778.7i	−0.808158	−	1.39977i	0.105981	−	0.994368i	$-0.466202\pi$
$734$		0			0
$735$	−758.733	+	3938.13i	−0.0380766	+	0.197633i
$736$		0			0
$737$	−3477.24			−0.173794
$738$		0			0
$739$	−35798.6			−1.78197			−0.890984	−	0.454035i	$-0.849984\pi$
$739$	−35798.6			−1.78197			−0.890984	+	0.454035i	$0.849984\pi$
$740$		0			0
$741$	45187.6	+	39149.8i	2.24023	+	1.94090i
$742$		0			0
$743$	521.962	+	904.064i	0.0257724	+	0.0446392i	0.878624	−	0.477514i	$-0.158462\pi$
$743$	521.962	+	904.064i	0.0257724	+	0.0446392i	−0.852852	+	0.522153i	$0.825129\pi$
$744$		0			0
$745$	6024.78	−	10435.2i	0.296283	−	0.513177i
$746$		0			0
$747$	3528.18	+	24515.2i	0.172810	+	1.20076i
$748$		0			0
$749$	9351.50	−	16197.3i	0.456204	−	0.790168i
$750$		0			0
$751$	20122.4	+	34853.0i	0.977731	+	1.69348i	0.670613	+	0.741808i	$0.266031\pi$
$751$	20122.4	+	34853.0i	0.977731	+	1.69348i	0.307118	+	0.951672i	$0.400635\pi$
$752$		0			0
$753$	−34911.8	+	12085.8i	−1.68959	+	0.584901i
$754$		0			0
$755$	9238.39			0.445324
$756$		0			0
$757$	1971.31			0.0946480			0.0473240	−	0.998880i	$-0.484931\pi$
$757$	1971.31			0.0946480			0.0473240	+	0.998880i	$0.484931\pi$
$758$		0			0
$759$	2863.52	−	991.294i	0.136942	−	0.0474067i
$760$		0			0
$761$	7438.23	+	12883.4i	0.354317	+	0.613696i	0.987001	−	0.160715i	$-0.0513799\pi$
$761$	7438.23	+	12883.4i	0.354317	+	0.613696i	−0.632683	+	0.774410i	$0.718047\pi$
$762$		0			0
$763$	1551.04	−	2686.48i	0.0735928	−	0.127467i
$764$		0			0
$765$	8067.01	+	3228.26i	0.381259	+	0.152573i
$766$		0			0
$767$	23695.4	−	41041.7i	1.11550	−	1.93211i
$768$		0			0
$769$	−1142.37	−	1978.64i	−0.0535695	−	0.0927851i	0.837997	−	0.545675i	$-0.183727\pi$
$769$	−1142.37	−	1978.64i	−0.0535695	−	0.0927851i	−0.891567	+	0.452890i	$0.850393\pi$
$770$		0			0
$771$	−16424.7	−	14230.2i	−0.767215	−	0.664703i
$772$		0			0
$773$	15649.7			0.728177			0.364089	−	0.931364i	$-0.381380\pi$
$773$	15649.7			0.728177			0.364089	+	0.931364i	$0.381380\pi$
$774$		0			0
$775$	−2416.27			−0.111993
$776$		0			0
$777$	−5421.85	+	28141.6i	−0.250332	+	1.29932i
$778$		0			0
$779$	−844.543	−	1462.79i	−0.0388432	−	0.0672785i
$780$		0			0
$781$	10385.6	−	17988.5i	0.475836	−	0.824171i
$782$		0			0
$783$	−19101.4	−	37032.8i	−0.871810	−	1.69022i
$784$		0			0
$785$	215.350	−	372.997i	0.00979131	−	0.0169590i
$786$		0			0
$787$	15210.3	+	26345.1i	0.688932	+	1.19327i	0.972184	+	0.234220i	$0.0752536\pi$
$787$	15210.3	+	26345.1i	0.688932	+	1.19327i	−0.283251	+	0.959046i	$0.591413\pi$
$788$		0			0
$789$	−4145.05	+	21514.5i	−0.187031	+	0.970767i
$790$		0			0
$791$	−27035.7			−1.21527
$792$		0			0
$793$	4945.37			0.221457
$794$		0			0
$795$	3051.57	+	2643.83i	0.136136	+	0.117946i
$796$		0			0
$797$	9307.98	+	16121.9i	0.413683	+	0.716521i	0.995289	−	0.0969501i	$-0.0309087\pi$
$797$	9307.98	+	16121.9i	0.413683	+	0.716521i	−0.581606	+	0.813471i	$0.697575\pi$
$798$		0			0
$799$	5643.40	−	9774.66i	0.249874	−	0.432794i
$800$		0			0
$801$	−27988.1	+	22016.3i	−1.23460	+	0.971172i
$802$		0			0
$803$	−8261.39	+	14309.2i	−0.363061	+	0.628841i
$804$		0			0
$805$	−925.185	−	1602.47i	−0.0405075	−	0.0701610i
$806$		0			0
$807$	16062.1	−	5560.38i	0.700636	−	0.242546i
$808$		0			0
$809$	42989.2			1.86826			0.934129	−	0.356935i	$-0.116178\pi$
$809$	42989.2			1.86826			0.934129	+	0.356935i	$0.116178\pi$
$810$		0			0
$811$	−28303.4			−1.22548			−0.612741	−	0.790284i	$-0.709933\pi$
$811$	−28303.4			−1.22548			−0.612741	+	0.790284i	$0.709933\pi$
$812$		0			0
$813$	−31460.9	+	10891.1i	−1.35717	+	0.469826i
$814$		0			0
$815$	2817.86	+	4880.68i	0.121111	+	0.209770i
$816$		0			0
$817$	21117.0	−	36575.7i	0.904271	−	1.56624i
$818$		0			0
$819$	23207.9	−	18256.1i	0.990172	−	0.778899i
$820$		0			0
$821$	−5297.09	+	9174.83i	−0.225176	+	0.390017i	−0.956372	−	0.292151i	$-0.905629\pi$
$821$	−5297.09	+	9174.83i	−0.225176	+	0.390017i	0.731196	+	0.682167i	$0.238962\pi$
$822$		0			0
$823$	12299.2	+	21302.8i	0.520925	+	0.902269i	0.999704	+	0.0243334i	$0.00774633\pi$
$823$	12299.2	+	21302.8i	0.520925	+	0.902269i	−0.478779	+	0.877936i	$0.658920\pi$
$824$		0			0
$825$	2124.92	+	1841.00i	0.0896731	+	0.0776914i
$826$		0			0
$827$	−15104.9			−0.635126			−0.317563	−	0.948237i	$-0.602865\pi$
$827$	−15104.9			−0.635126			−0.317563	+	0.948237i	$0.602865\pi$
$828$		0			0
$829$	−33824.6			−1.41710			−0.708551	−	0.705660i	$-0.750651\pi$
$829$	−33824.6			−1.41710			−0.708551	+	0.705660i	$0.750651\pi$
$830$		0			0
$831$	6218.90	−	32278.6i	0.259604	−	1.34745i
$832$		0			0
$833$	−4967.72	−	8604.35i	−0.206628	−	0.357891i
$834$		0			0
$835$	2421.61	−	4194.36i	0.100363	−	0.173834i
$836$		0			0
$837$	−13544.5	−	642.416i	−0.559338	−	0.0265295i
$838$		0			0
$839$	−2683.31	+	4647.63i	−0.110415	+	0.191244i	−0.915938	−	0.401321i	$-0.868551\pi$
$839$	−2683.31	+	4647.63i	−0.110415	+	0.191244i	0.805523	+	0.592565i	$0.201885\pi$
$840$		0			0
$841$	−31911.9	−	55273.0i	−1.30845	−	2.26631i
$842$		0			0
$843$	−3914.98	+	20320.3i	−0.159952	+	0.830213i
$844$		0			0
$845$	20717.0			0.843414
$846$		0			0
$847$	11847.0			0.480600
$848$		0			0
$849$	−14450.9	−	12520.1i	−0.584163	−	0.506110i
$850$		0			0
$851$	5410.30	+	9370.91i	0.217935	+	0.377474i
$852$		0			0
$853$	−8191.63	+	14188.3i	−0.328812	+	0.569518i	−0.982276	−	0.187439i	$-0.939981\pi$
$853$	−8191.63	+	14188.3i	−0.328812	+	0.569518i	0.653465	+	0.756957i	$0.273315\pi$
$854$		0			0
$855$	18111.4	+	7247.85i	0.724443	+	0.289908i
$856$		0			0
$857$	14059.2	−	24351.2i	0.560389	−	0.970622i	−0.437074	−	0.899426i	$-0.643985\pi$
$857$	14059.2	−	24351.2i	0.560389	−	0.970622i	0.997462	−	0.0711960i	$-0.0226816\pi$
$858$		0			0
$859$	−16111.5	−	27905.9i	−0.639949	−	1.10842i	−0.985443	−	0.170003i	$-0.945622\pi$
$859$	−16111.5	−	27905.9i	−0.639949	−	1.10842i	0.345494	−	0.938421i	$-0.387711\pi$
$860$		0			0
$861$	−788.296	+	272.892i	−0.0312022	+	0.0108016i
$862$		0			0
$863$	37447.4			1.47709			0.738543	−	0.674206i	$-0.235514\pi$
$863$	37447.4			1.47709			0.738543	+	0.674206i	$0.235514\pi$
$864$		0			0
$865$	8760.37			0.344349
$866$		0			0
$867$	3783.02	−	1309.61i	0.148187	−	0.0512994i
$868$		0			0
$869$	−692.196	−	1198.92i	−0.0270209	−	0.0468016i
$870$		0			0
$871$	−6396.55	+	11079.1i	−0.248839	+	0.431002i
$872$		0			0
$873$	−492.959	−	3425.27i	−0.0191112	−	0.132793i
$874$		0			0
$875$	858.400	−	1486.79i	0.0331648	−	0.0574431i
$876$		0			0
$877$	3916.87	+	6784.21i	0.150813	+	0.261216i	0.931527	−	0.363673i	$-0.118477\pi$
$877$	3916.87	+	6784.21i	0.150813	+	0.261216i	−0.780713	+	0.624889i	$0.785144\pi$
$878$		0			0
$879$	35134.0	+	30439.6i	1.34817	+	1.16803i
$880$		0			0
$881$	−3195.87			−0.122215			−0.0611076	−	0.998131i	$-0.519463\pi$
$881$	−3195.87			−0.122215			−0.0611076	+	0.998131i	$0.519463\pi$
$882$		0			0
$883$	6033.49			0.229947			0.114973	−	0.993369i	$-0.463322\pi$
$883$	6033.49			0.229947			0.114973	+	0.993369i	$0.463322\pi$
$884$		0			0
$885$	2925.31	−	15183.6i	0.111111	−	0.576712i
$886$		0			0
$887$	1739.61	+	3013.09i	0.0658515	+	0.114058i	0.897071	−	0.441886i	$-0.145690\pi$
$887$	1739.61	+	3013.09i	0.0658515	+	0.114058i	−0.831220	+	0.555944i	$0.812357\pi$
$888$		0			0
$889$	5158.67	−	8935.08i	0.194619	−	0.337090i
$890$		0			0
$891$	11421.9	+	10884.8i	0.429458	+	0.409263i
$892$		0			0
$893$	12670.2	−	21945.3i	0.474793	−	0.822366i
$894$		0			0
$895$	2200.74	+	3811.80i	0.0821930	+	0.142362i
$896$		0			0
$897$	2109.13	−	10947.2i	0.0785082	−	0.407489i
$898$		0			0
$899$	−28705.9			−1.06496
$900$		0			0
$901$	−10002.3			−0.369841
$902$		0			0
$903$	−15764.5	−	13658.2i	−0.580965	−	0.503339i
$904$		0			0
$905$	−839.616	−	1454.26i	−0.0308395	−	0.0534156i
$906$		0			0
$907$	−2191.65	+	3796.06i	−0.0802345	+	0.138970i	−0.903351	−	0.428903i	$-0.858900\pi$
$907$	−2191.65	+	3796.06i	−0.0802345	+	0.138970i	0.823116	+	0.567873i	$0.192234\pi$
$908$		0			0
$909$	−1770.80	−	12304.2i	−0.0646136	−	0.448961i
$910$		0			0
$911$	2342.68	−	4057.64i	0.0851992	−	0.147569i	−0.820277	−	0.571967i	$-0.806181\pi$
$911$	2342.68	−	4057.64i	0.0851992	−	0.147569i	0.905476	+	0.424397i	$0.139514\pi$
$912$		0			0
$913$	−9926.84	−	17193.8i	−0.359836	−	0.623255i
$914$		0			0
$915$	1524.80	−	527.857i	0.0550912	−	0.0190715i
$916$		0			0
$917$	1092.98			0.0393603
$918$		0			0
$919$	36353.0			1.30487			0.652434	−	0.757846i	$-0.273748\pi$
$919$	36353.0			1.30487			0.652434	+	0.757846i	$0.273748\pi$
$920$		0			0
$921$	47859.7	−	16568.1i	1.71230	−	0.592764i
$922$		0			0
$923$	−38209.7	−	66181.2i	−1.36261	−	2.36011i
$924$		0			0
$925$	−5019.75	+	8694.46i	−0.178431	+	0.309051i
$926$		0			0
$927$	−17984.8	−	7197.18i	−0.637216	−	0.255002i
$928$		0			0
$929$	−4271.06	+	7397.69i	−0.150838	+	0.261260i	−0.931536	−	0.363649i	$-0.881531\pi$
$929$	−4271.06	+	7397.69i	−0.150838	+	0.261260i	0.780698	+	0.624909i	$0.214864\pi$
$930$		0			0
$931$	−11153.2	−	19317.8i	−0.392621	−	0.680040i
$932$		0			0
$933$	20731.9	+	17961.8i	0.727473	+	0.630271i
$934$		0			0
$935$	−6965.02			−0.243615
$936$		0			0
$937$	33521.5			1.16873			0.584364	−	0.811491i	$-0.301344\pi$
$937$	33521.5			1.16873			0.584364	+	0.811491i	$0.301344\pi$
$938$		0			0
$939$	4457.44	−	23135.9i	0.154913	−	0.804060i
$940$		0			0
$941$	−12037.0	−	20848.7i	−0.416997	−	0.722260i	0.578639	−	0.815584i	$-0.303584\pi$
$941$	−12037.0	−	20848.7i	−0.416997	−	0.722260i	−0.995636	+	0.0933239i	$0.970251\pi$
$942$		0			0
$943$	−157.480	+	272.763i	−0.00543823	+	0.00941930i
$944$		0			0
$945$	5207.09	−	8106.05i	0.179245	−	0.279037i
$946$		0			0
$947$	20540.1	−	35576.6i	0.704820	−	1.22078i	−0.261936	−	0.965085i	$-0.584361\pi$
$947$	20540.1	−	35576.6i	0.704820	−	1.22078i	0.966756	−	0.255699i	$-0.0823056\pi$
$948$		0			0
$949$	30394.4	+	52644.7i	1.03967	+	1.80076i
$950$		0			0
$951$	2196.84	−	11402.5i	0.0749080	−	0.388803i
$952$		0			0
$953$	−28047.0			−0.953337			−0.476668	−	0.879083i	$-0.658156\pi$
$953$	−28047.0			−0.953337			−0.476668	+	0.879083i	$0.658156\pi$
$954$		0			0
$955$	−19886.5			−0.673833
$956$		0			0
$957$	25244.6	+	21871.6i	0.852709	+	0.738774i
$958$		0			0
$959$	5518.37	+	9558.10i	0.185816	+	0.321843i
$960$		0			0
$961$	10224.8	−	17709.9i	0.343218	−	0.594472i
$962$		0			0
$963$	28898.2	−	22732.2i	0.967011	−	0.760680i
$964$		0			0
$965$	−10397.8	+	18009.5i	−0.346856	+	0.600772i
$966$		0			0
$967$	2656.52	+	4601.22i	0.0883432	+	0.153015i	0.906811	−	0.421538i	$-0.138509\pi$
$967$	2656.52	+	4601.22i	0.0883432	+	0.153015i	−0.818468	+	0.574552i	$0.805176\pi$
$968$		0			0
$969$	−45668.2	+	15809.4i	−1.51401	+	0.524119i
$970$		0			0
$971$	17611.7			0.582065			0.291032	−	0.956713i	$-0.406001\pi$
$971$	17611.7			0.582065			0.291032	+	0.956713i	$0.406001\pi$
$972$		0			0
$973$	−24195.4			−0.797193
$974$		0			0
$975$	9774.66	−	3383.79i	0.321066	−	0.111147i
$976$		0			0
$977$	21636.6	+	37475.6i	0.708511	+	1.22718i	0.965409	+	0.260738i	$0.0839660\pi$
$977$	21636.6	+	37475.6i	0.708511	+	1.22718i	−0.256899	+	0.966438i	$0.582701\pi$
$978$		0			0
$979$	14272.3	−	24720.3i	0.465928	−	0.807011i
$980$		0			0
$981$	4793.05	−	3770.36i	0.155994	−	0.122710i
$982$		0			0
$983$	−23359.8	+	40460.4i	−0.757948	+	1.31280i	0.185947	+	0.982560i	$0.440465\pi$
$983$	−23359.8	+	40460.4i	−0.757948	+	1.31280i	−0.943895	+	0.330245i	$0.892869\pi$
$984$		0			0
$985$	−3952.93	−	6846.67i	−0.127869	−	0.221475i
$986$		0			0
$987$	−9458.70	−	8194.88i	−0.305039	−	0.264281i
$988$		0			0
$989$	−7875.27			−0.253204
$990$		0			0
$991$	−4961.78			−0.159047			−0.0795237	−	0.996833i	$-0.525340\pi$
$991$	−4961.78			−0.159047			−0.0795237	+	0.996833i	$0.525340\pi$
$992$		0			0
$993$	−1810.27	+	9396.05i	−0.0578522	+	0.300276i
$994$		0			0
$995$	5348.42	+	9263.74i	0.170408	+	0.295156i
$996$		0			0
$997$	−14670.1	+	25409.3i	−0.466004	+	0.807142i	−0.999246	−	0.0388205i	$-0.987640\pi$
$997$	−14670.1	+	25409.3i	−0.466004	+	0.807142i	0.533243	+	0.845962i	$0.320973\pi$
$998$		0			0
$999$	−30450.0	+	47402.5i	−0.964360	+	1.50125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.4.i.c.61.1	✓	14
3.2	odd	2		540.4.i.c.181.5		14
9.2	odd	6		1620.4.a.k.1.3		7
9.4	even	3	inner	180.4.i.c.121.1	yes	14
9.5	odd	6		540.4.i.c.361.5		14
9.7	even	3		1620.4.a.l.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.4.i.c.61.1	✓	14	1.1	even	1	trivial
180.4.i.c.121.1	yes	14	9.4	even	3	inner
540.4.i.c.181.5		14	3.2	odd	2
540.4.i.c.361.5		14	9.5	odd	6
1620.4.a.k.1.3		7	9.2	odd	6
1620.4.a.l.1.3		7	9.7	even	3

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	180.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.91025 + 1.69983i) q^{3} +(-2.50000 - 4.33013i) q^{5} +(6.86720 - 11.8943i) q^{7} +(21.2211 - 16.6932i) q^{9} +O(q^{10})\)	\(q+(-4.91025 + 1.69983i) q^{3} +(-2.50000 - 4.33013i) q^{5} +(6.86720 - 11.8943i) q^{7} +(21.2211 - 16.6932i) q^{9} +(-10.8215 + 18.7434i) q^{11} +(39.8133 + 68.9586i) q^{13} +(19.6361 + 17.0124i) q^{15} -64.3628 q^{17} -144.503 q^{19} +(-13.5013 + 70.0773i) q^{21} +(13.4725 + 23.3351i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(-75.8256 + 118.040i) q^{27} +(-148.503 + 257.215i) q^{29} +(48.3254 + 83.7020i) q^{31} +(21.2757 - 110.429i) q^{33} -68.6720 q^{35} +401.580 q^{37} +(-312.711 - 270.928i) q^{39} +(5.84448 + 10.1229i) q^{41} +(-146.136 + 253.114i) q^{43} +(-125.337 - 50.1573i) q^{45} +(-87.6812 + 151.868i) q^{47} +(77.1832 + 133.685i) q^{49} +(316.037 - 109.406i) q^{51} +155.406 q^{53} +108.215 q^{55} +(709.544 - 245.630i) q^{57} +(-297.582 - 515.427i) q^{59} +(31.0535 - 53.7862i) q^{61} +(-52.8247 - 367.047i) q^{63} +(199.066 - 344.793i) q^{65} +(80.3318 + 139.139i) q^{67} +(-105.819 - 91.6802i) q^{69} -959.723 q^{71} +763.424 q^{73} +(24.5757 - 127.558i) q^{75} +(148.627 + 257.429i) q^{77} +(-31.9825 + 55.3952i) q^{79} +(171.674 - 708.498i) q^{81} +(-458.663 + 794.427i) q^{83} +(160.907 + 278.699i) q^{85} +(291.966 - 1515.42i) q^{87} -1318.88 q^{89} +1093.62 q^{91} +(-379.569 - 328.853i) q^{93} +(361.256 + 625.714i) q^{95} +(64.0845 - 110.998i) q^{97} +(83.2424 + 578.402i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 5 q^{3} - 35 q^{5} - 8 q^{7} + 5 q^{9}+O(q^{10}) \) 14 * q + 5 * q^3 - 35 * q^5 - 8 * q^7 + 5 * q^9	\( 14 q + 5 q^{3} - 35 q^{5} - 8 q^{7} + 5 q^{9} - 27 q^{11} - 32 q^{13} - 20 q^{15} + 246 q^{17} - 134 q^{19} + 28 q^{21} - 42 q^{23} - 175 q^{25} - 484 q^{27} - 324 q^{29} - 98 q^{31} + 657 q^{33} + 80 q^{35} + 712 q^{37} - 848 q^{39} - 339 q^{41} - 119 q^{43} - 125 q^{45} + 96 q^{47} - 813 q^{49} + 1383 q^{51} + 1716 q^{53} + 270 q^{55} - 599 q^{57} - 549 q^{59} - 260 q^{61} - 632 q^{63} - 160 q^{65} - 881 q^{67} + 666 q^{69} + 684 q^{71} + 1474 q^{73} - 25 q^{75} + 456 q^{77} - 1886 q^{79} + 353 q^{81} + 132 q^{83} - 615 q^{85} + 4302 q^{87} + 792 q^{89} + 2528 q^{91} - 4904 q^{93} + 335 q^{95} - 1991 q^{97} + 270 q^{99}+O(q^{100}) \) 14 * q + 5 * q^3 - 35 * q^5 - 8 * q^7 + 5 * q^9 - 27 * q^11 - 32 * q^13 - 20 * q^15 + 246 * q^17 - 134 * q^19 + 28 * q^21 - 42 * q^23 - 175 * q^25 - 484 * q^27 - 324 * q^29 - 98 * q^31 + 657 * q^33 + 80 * q^35 + 712 * q^37 - 848 * q^39 - 339 * q^41 - 119 * q^43 - 125 * q^45 + 96 * q^47 - 813 * q^49 + 1383 * q^51 + 1716 * q^53 + 270 * q^55 - 599 * q^57 - 549 * q^59 - 260 * q^61 - 632 * q^63 - 160 * q^65 - 881 * q^67 + 666 * q^69 + 684 * q^71 + 1474 * q^73 - 25 * q^75 + 456 * q^77 - 1886 * q^79 + 353 * q^81 + 132 * q^83 - 615 * q^85 + 4302 * q^87 + 792 * q^89 + 2528 * q^91 - 4904 * q^93 + 335 * q^95 - 1991 * q^97 + 270 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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