LMFDB - Embedded newform 432.3.bc.c.353.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(65,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

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

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

chi := DirichletCharacter("432.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.bc (of order $18$, degree $6$, not 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:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			353.6
Character	$\chi$	$=$	432.353
Dual form			432.3.bc.c.257.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.97067 + 0.418457i) q^{3} +(5.54906 + 6.61311i) q^{5} +(-7.83131 + 2.85036i) q^{7} +(8.64979 + 2.48620i) q^{9} +(10.8191 - 12.8937i) q^{11} +(0.524960 + 2.97720i) q^{13} +(13.7171 + 21.9674i) q^{15} +(8.43596 - 4.87051i) q^{17} +(-3.84677 + 6.66281i) q^{19} +(-24.4570 + 5.19043i) q^{21} +(-10.1434 + 27.8689i) q^{23} +(-8.59998 + 48.7729i) q^{25} +(24.6553 + 11.0052i) q^{27} +(-10.5809 - 1.86569i) q^{29} +(10.8017 + 3.93149i) q^{31} +(37.5353 - 33.7755i) q^{33} +(-62.3062 - 35.9725i) q^{35} +(-11.5925 - 20.0787i) q^{37} +(0.313655 + 9.06395i) q^{39} +(-16.7264 + 2.94931i) q^{41} +(-18.0881 - 15.1778i) q^{43} +(31.5567 + 70.9981i) q^{45} +(5.67901 + 15.6029i) q^{47} +(15.6687 - 13.1476i) q^{49} +(27.0986 - 10.9386i) q^{51} -75.3383i q^{53} +145.303 q^{55} +(-14.2156 + 18.1833i) q^{57} +(38.6968 + 46.1170i) q^{59} +(32.1023 - 11.6843i) q^{61} +(-74.8257 + 5.18485i) q^{63} +(-16.7755 + 19.9923i) q^{65} +(-6.53483 - 37.0609i) q^{67} +(-41.7948 + 78.5447i) q^{69} +(-44.0325 + 25.4222i) q^{71} +(49.2453 - 85.2954i) q^{73} +(-45.9571 + 141.290i) q^{75} +(-47.9758 + 131.813i) q^{77} +(14.0913 - 79.9158i) q^{79} +(68.6376 + 43.0102i) q^{81} +(15.8868 + 2.80127i) q^{83} +(79.0209 + 28.7612i) q^{85} +(-30.6516 - 9.97000i) q^{87} +(14.0161 + 8.09222i) q^{89} +(-12.5972 - 21.8190i) q^{91} +(30.4431 + 16.1992i) q^{93} +(-65.4078 + 11.5332i) q^{95} +(-101.648 - 85.2929i) q^{97} +(125.639 - 84.6291i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{5} - 12 q^{9} + 18 q^{11} + 18 q^{15} - 228 q^{21} + 180 q^{23} + 18 q^{25} - 54 q^{27} + 144 q^{29} + 90 q^{31} + 324 q^{33} - 486 q^{35} - 102 q^{39} - 90 q^{41} - 90 q^{43} - 378 q^{45}+ \cdots - 126 q^{99}+O(q^{100}) $ 36 * q + 18 * q^5 - 12 * q^9 + 18 * q^11 + 18 * q^15 - 228 * q^21 + 180 * q^23 + 18 * q^25 - 54 * q^27 + 144 * q^29 + 90 * q^31 + 324 * q^33 - 486 * q^35 - 102 * q^39 - 90 * q^41 - 90 * q^43 - 378 * q^45 + 378 * q^47 + 72 * q^49 + 54 * q^51 + 72 * q^57 - 252 * q^59 - 144 * q^61 - 318 * q^63 + 18 * q^65 + 594 * q^67 - 522 * q^69 + 648 * q^71 + 126 * q^73 + 438 * q^75 - 342 * q^77 + 72 * q^79 + 324 * q^81 - 594 * q^83 + 360 * q^85 - 1062 * q^87 + 648 * q^89 + 198 * q^91 + 462 * q^93 - 252 * q^95 + 702 * q^97 - 126 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{18}\right)$

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
$3$	2.97067	+	0.418457i	0.990224	+	0.139486i
$3$	2.97067	+	0.418457i	0.990224	+	0.139486i
$4$		0			0
$5$	5.54906	+	6.61311i	1.10981	+	1.32262i	0.941547	+	0.336880i	$0.109372\pi$
$5$	5.54906	+	6.61311i	1.10981	+	1.32262i	0.168264	+	0.985742i	$0.446184\pi$
$6$		0			0
$7$	−7.83131	+	2.85036i	−1.11876	+	0.407195i	−0.834199	−	0.551463i	$-0.814070\pi$
$7$	−7.83131	+	2.85036i	−1.11876	+	0.407195i	−0.284560	+	0.958658i	$0.591847\pi$
$8$		0			0
$9$	8.64979	+	2.48620i	0.961087	+	0.276244i
$10$		0			0
$11$	10.8191	−	12.8937i	0.983551	−	1.17215i	−0.00151930	−	0.999999i	$-0.500484\pi$
$11$	10.8191	−	12.8937i	0.983551	−	1.17215i	0.985070	−	0.172152i	$-0.0550719\pi$
$12$		0			0
$13$	0.524960	+	2.97720i	0.0403815	+	0.229015i	0.998319	−	0.0579628i	$-0.0184605\pi$
$13$	0.524960	+	2.97720i	0.0403815	+	0.229015i	−0.957937	+	0.286978i	$0.907349\pi$
$14$		0			0
$15$	13.7171	+	21.9674i	0.914475	+	1.46450i
$16$		0			0
$17$	8.43596	−	4.87051i	0.496233	−	0.286500i	−0.230924	−	0.972972i	$-0.574175\pi$
$17$	8.43596	−	4.87051i	0.496233	−	0.286500i	0.727157	+	0.686472i	$0.240841\pi$
$18$		0			0
$19$	−3.84677	+	6.66281i	−0.202462	+	0.350674i	−0.949321	−	0.314308i	$-0.898228\pi$
$19$	−3.84677	+	6.66281i	−0.202462	+	0.350674i	0.746859	+	0.664982i	$0.231561\pi$
$20$		0			0
$21$	−24.4570	+	5.19043i	−1.16462	+	0.247163i
$22$		0			0
$23$	−10.1434	+	27.8689i	−0.441019	+	1.21169i	0.497804	+	0.867290i	$0.334140\pi$
$23$	−10.1434	+	27.8689i	−0.441019	+	1.21169i	−0.938823	+	0.344400i	$0.888082\pi$
$24$		0			0
$25$	−8.59998	+	48.7729i	−0.343999	+	1.95092i
$26$		0			0
$27$	24.6553	+	11.0052i	0.913160	+	0.407602i
$28$		0			0
$29$	−10.5809	−	1.86569i	−0.364858	−	0.0643342i	−0.0117860	−	0.999931i	$-0.503752\pi$
$29$	−10.5809	−	1.86569i	−0.364858	−	0.0643342i	−0.353072	+	0.935596i	$0.614863\pi$
$30$		0			0
$31$	10.8017	+	3.93149i	0.348441	+	0.126822i	0.510311	−	0.859990i	$-0.329530\pi$
$31$	10.8017	+	3.93149i	0.348441	+	0.126822i	−0.161870	+	0.986812i	$0.551752\pi$
$32$		0			0
$33$	37.5353	−	33.7755i	1.13743	−	1.02350i
$34$		0			0
$35$	−62.3062	−	35.9725i	−1.78018	−	1.02779i
$36$		0			0
$37$	−11.5925	−	20.0787i	−0.313309	−	0.542668i	0.665767	−	0.746160i	$-0.268104\pi$
$37$	−11.5925	−	20.0787i	−0.313309	−	0.542668i	−0.979077	+	0.203492i	$0.934771\pi$
$38$		0			0
$39$	0.313655	+	9.06395i	0.00804244	+	0.232409i
$40$		0			0
$41$	−16.7264	+	2.94931i	−0.407960	+	0.0719344i	−0.373863	−	0.927484i	$-0.621967\pi$
$41$	−16.7264	+	2.94931i	−0.407960	+	0.0719344i	−0.0340976	+	0.999419i	$0.510856\pi$
$42$		0			0
$43$	−18.0881	−	15.1778i	−0.420655	−	0.352971i	0.407757	−	0.913090i	$-0.366311\pi$
$43$	−18.0881	−	15.1778i	−0.420655	−	0.352971i	−0.828412	+	0.560119i	$0.810755\pi$
$44$		0			0
$45$	31.5567	+	70.9981i	0.701259	+	1.57773i
$46$		0			0
$47$	5.67901	+	15.6029i	0.120830	+	0.331977i	0.985331	−	0.170653i	$-0.0545878\pi$
$47$	5.67901	+	15.6029i	0.120830	+	0.331977i	−0.864501	+	0.502631i	$0.832366\pi$
$48$		0			0
$49$	15.6687	−	13.1476i	0.319769	−	0.268318i
$50$		0			0
$51$	27.0986	−	10.9386i	0.531345	−	0.214482i
$52$		0			0
$53$		−	75.3383i		−	1.42148i	−0.703456	−	0.710739i	$-0.748361\pi$
$53$		−	75.3383i		−	1.42148i	0.703456	−	0.710739i	$-0.251639\pi$
$54$		0			0
$55$	145.303			2.64187
$56$		0			0
$57$	−14.2156	+	18.1833i	−0.249397	+	0.319005i
$58$		0			0
$59$	38.6968	+	46.1170i	0.655878	+	0.781645i	0.986788	−	0.162017i	$-0.0518001\pi$
$59$	38.6968	+	46.1170i	0.655878	+	0.781645i	−0.330910	+	0.943662i	$0.607356\pi$
$60$		0			0
$61$	32.1023	−	11.6843i	0.526267	−	0.191546i	−0.0652037	−	0.997872i	$-0.520770\pi$
$61$	32.1023	−	11.6843i	0.526267	−	0.191546i	0.591471	+	0.806326i	$0.298547\pi$
$62$		0			0
$63$	−74.8257	+	5.18485i	−1.18771	+	0.0822992i
$64$		0			0
$65$	−16.7755	+	19.9923i	−0.258085	+	0.307573i
$66$		0			0
$67$	−6.53483	−	37.0609i	−0.0975348	−	0.553147i	−0.993941	−	0.109914i	$-0.964942\pi$
$67$	−6.53483	−	37.0609i	−0.0975348	−	0.553147i	0.896406	−	0.443233i	$-0.146169\pi$
$68$		0			0
$69$	−41.7948	+	78.5447i	−0.605721	+	1.13833i
$70$		0			0
$71$	−44.0325	+	25.4222i	−0.620175	+	0.358058i	−0.776937	−	0.629578i	$-0.783228\pi$
$71$	−44.0325	+	25.4222i	−0.620175	+	0.358058i	0.156762	+	0.987636i	$0.449894\pi$
$72$		0			0
$73$	49.2453	−	85.2954i	0.674593	−	1.16843i	−0.301994	−	0.953310i	$-0.597652\pi$
$73$	49.2453	−	85.2954i	0.674593	−	1.16843i	0.976588	−	0.215120i	$-0.0690144\pi$
$74$		0			0
$75$	−45.9571	+	141.290i	−0.612761	+	1.88386i
$76$		0			0
$77$	−47.9758	+	131.813i	−0.623063	+	1.71185i
$78$		0			0
$79$	14.0913	−	79.9158i	0.178371	−	1.01159i	−0.755809	−	0.654792i	$-0.772756\pi$
$79$	14.0913	−	79.9158i	0.178371	−	1.01159i	0.934180	−	0.356801i	$-0.116133\pi$
$80$		0			0
$81$	68.6376	+	43.0102i	0.847378	+	0.530990i
$82$		0			0
$83$	15.8868	+	2.80127i	0.191407	+	0.0337503i	0.268530	−	0.963271i	$-0.413462\pi$
$83$	15.8868	+	2.80127i	0.191407	+	0.0337503i	−0.0771226	+	0.997022i	$0.524573\pi$
$84$		0			0
$85$	79.0209	+	28.7612i	0.929657	+	0.338368i
$86$		0			0
$87$	−30.6516	−	9.97000i	−0.352317	−	0.114598i
$88$		0			0
$89$	14.0161	+	8.09222i	0.157485	+	0.0909238i	0.576671	−	0.816976i	$-0.304351\pi$
$89$	14.0161	+	8.09222i	0.157485	+	0.0909238i	−0.419187	+	0.907900i	$0.637685\pi$
$90$		0			0
$91$	−12.5972	−	21.8190i	−0.138431	−	0.239769i
$92$		0			0
$93$	30.4431	+	16.1992i	0.327345	+	0.174185i
$94$		0			0
$95$	−65.4078	+	11.5332i	−0.688504	+	0.121402i
$96$		0			0
$97$	−101.648	−	85.2929i	−1.04792	−	0.879308i	−0.0550452	−	0.998484i	$-0.517530\pi$
$97$	−101.648	−	85.2929i	−1.04792	−	0.879308i	−0.992873	+	0.119176i	$0.961975\pi$
$98$		0			0
$99$	125.639	−	84.6291i	1.26908	−	0.854839i
$100$		0			0
$101$	−5.20626	−	14.3041i	−0.0515471	−	0.141625i	0.911247	−	0.411860i	$-0.135121\pi$
$101$	−5.20626	−	14.3041i	−0.0515471	−	0.141625i	−0.962794	+	0.270235i	$0.912898\pi$
$102$		0			0
$103$	28.9968	−	24.3312i	0.281522	−	0.236225i	−0.491082	−	0.871113i	$-0.663398\pi$
$103$	28.9968	−	24.3312i	0.281522	−	0.236225i	0.772604	+	0.634889i	$0.218954\pi$
$104$		0			0
$105$	−170.038	−	132.935i	−1.61941	−	1.26605i
$106$		0			0
$107$		−	118.659i		−	1.10897i	−0.832195	−	0.554483i	$-0.812916\pi$
$107$		−	118.659i		−	1.10897i	0.832195	−	0.554483i	$-0.187084\pi$
$108$		0			0
$109$	206.055			1.89042			0.945208	−	0.326468i	$-0.105859\pi$
$109$	206.055			1.89042			0.945208	+	0.326468i	$0.105859\pi$
$110$		0			0
$111$	−26.0353	−	64.4982i	−0.234552	−	0.581065i
$112$		0			0
$113$	−45.6567	−	54.4116i	−0.404042	−	0.481519i	0.525206	−	0.850975i	$-0.323988\pi$
$113$	−45.6567	−	54.4116i	−0.404042	−	0.481519i	−0.929248	+	0.369457i	$0.879544\pi$
$114$		0			0
$115$	−240.586	+	87.5663i	−2.09206	+	0.761446i
$116$		0			0
$117$	−2.86111	+	27.0573i	−0.0244539	+	0.231259i
$118$		0			0
$119$	−52.1819	+	62.1880i	−0.438504	+	0.522588i
$120$		0			0
$121$	−28.1828	−	159.833i	−0.232916	−	1.32093i
$122$		0			0
$123$	−50.9227	+	1.76216i	−0.414006	+	0.0143265i
$124$		0			0
$125$	−183.357	+	105.861i	−1.46685	+	0.846888i
$126$		0			0
$127$	19.1347	−	33.1422i	0.150667	−	0.260963i	−0.780806	−	0.624774i	$-0.785191\pi$
$127$	19.1347	−	33.1422i	0.150667	−	0.260963i	0.931473	+	0.363811i	$0.118525\pi$
$128$		0			0
$129$	−47.3827	−	52.6573i	−0.367308	−	0.408196i
$130$		0			0
$131$	74.5355	−	204.785i	0.568973	−	1.56324i	−0.237137	−	0.971476i	$-0.576209\pi$
$131$	74.5355	−	204.785i	0.568973	−	1.56324i	0.806110	−	0.591765i	$-0.201569\pi$
$132$		0			0
$133$	11.1339	−	63.1432i	0.0837132	−	0.474761i
$134$		0			0
$135$	64.0349	+	224.117i	0.474333	+	1.66013i
$136$		0			0
$137$	−181.295	−	31.9672i	−1.32332	−	0.233337i	−0.533045	−	0.846087i	$-0.678952\pi$
$137$	−181.295	−	31.9672i	−1.32332	−	0.233337i	−0.790277	+	0.612749i	$0.790064\pi$
$138$		0			0
$139$	228.486	+	83.1623i	1.64379	+	0.598290i	0.987695	−	0.156391i	$-0.0499860\pi$
$139$	228.486	+	83.1623i	1.64379	+	0.598290i	0.656092	+	0.754681i	$0.272208\pi$
$140$		0			0
$141$	10.3413	+	48.7276i	0.0733426	+	0.345586i
$142$		0			0
$143$	44.0665	+	25.4418i	0.308157	+	0.177915i
$144$		0			0
$145$	−46.3758	−	80.3253i	−0.319833	−	0.553968i
$146$		0			0
$147$	52.0482	−	32.5005i	0.354069	−	0.221092i
$148$		0			0
$149$	141.886	−	25.0183i	0.952255	−	0.167908i	0.324123	−	0.946015i	$-0.394931\pi$
$149$	141.886	−	25.0183i	0.952255	−	0.167908i	0.628132	+	0.778107i	$0.283820\pi$
$150$		0			0
$151$	77.8368	+	65.3129i	0.515476	+	0.432535i	0.863051	−	0.505117i	$-0.168551\pi$
$151$	77.8368	+	65.3129i	0.515476	+	0.432535i	−0.347575	+	0.937652i	$0.612995\pi$
$152$		0			0
$153$	85.0783	−	21.1554i	0.556068	−	0.138270i
$154$		0			0
$155$	33.9398	+	93.2488i	0.218966	+	0.601605i
$156$		0			0
$157$	−237.118	+	198.965i	−1.51030	+	1.26730i	−0.647143	+	0.762369i	$0.724036\pi$
$157$	−237.118	+	198.965i	−1.51030	+	1.26730i	−0.863162	+	0.504927i	$0.831519\pi$
$158$		0			0
$159$	31.5259	−	223.805i	0.198276	−	1.40758i
$160$		0			0
$161$		−	247.162i		−	1.53517i
$162$		0			0
$163$	−160.056			−0.981937			−0.490969	−	0.871177i	$-0.663357\pi$
$163$	−160.056			−0.981937			−0.490969	+	0.871177i	$0.663357\pi$
$164$		0			0
$165$	431.647	+	60.8030i	2.61604	+	0.368503i
$166$		0			0
$167$	−160.019	−	190.703i	−0.958197	−	1.14193i	−0.989804	−	0.142434i	$-0.954507\pi$
$167$	−160.019	−	190.703i	−0.958197	−	1.14193i	0.0316076	−	0.999500i	$-0.489937\pi$
$168$		0			0
$169$	150.220	−	54.6756i	0.888875	−	0.323524i
$170$		0			0
$171$	−49.8388	+	48.0680i	−0.291455	+	0.281100i
$172$		0			0
$173$	43.4383	−	51.7678i	0.251088	−	0.299236i	−0.625747	−	0.780026i	$-0.715206\pi$
$173$	43.4383	−	51.7678i	0.251088	−	0.299236i	0.876836	+	0.480790i	$0.159650\pi$
$174$		0			0
$175$	−71.6714	−	406.469i	−0.409551	−	2.32268i
$176$		0			0
$177$	95.6575	+	153.192i	0.540438	+	0.865489i
$178$		0			0
$179$	−203.717	+	117.616i	−1.13808	+	0.657073i	−0.945955	−	0.324297i	$-0.894872\pi$
$179$	−203.717	+	117.616i	−1.13808	+	0.657073i	−0.192128	+	0.981370i	$0.561539\pi$
$180$		0			0
$181$	−108.916	+	188.647i	−0.601744	+	1.04225i	0.390813	+	0.920470i	$0.372194\pi$
$181$	−108.916	+	188.647i	−0.601744	+	1.04225i	−0.992557	+	0.121781i	$0.961140\pi$
$182$		0			0
$183$	100.255	−	21.2767i	0.547840	−	0.116266i
$184$		0			0
$185$	68.4556	−	188.080i	0.370030	−	1.01665i
$186$		0			0
$187$	28.4706	−	161.465i	0.152249	−	0.863448i
$188$		0			0
$189$	−224.452	−	15.9089i	−1.18758	−	0.0841739i
$190$		0			0
$191$	−253.418	−	44.6844i	−1.32679	−	0.233950i	−0.535060	−	0.844814i	$-0.679711\pi$
$191$	−253.418	−	44.6844i	−1.32679	−	0.233950i	−0.791735	+	0.610864i	$0.790822\pi$
$192$		0			0
$193$	72.0472	+	26.2230i	0.373302	+	0.135871i	0.521856	−	0.853034i	$-0.325240\pi$
$193$	72.0472	+	26.2230i	0.373302	+	0.135871i	−0.148554	+	0.988904i	$0.547462\pi$
$194$		0			0
$195$	−58.2004	+	52.3706i	−0.298464	+	0.268567i
$196$		0			0
$197$	−211.300	−	121.994i	−1.07259	−	0.619260i	−0.143702	−	0.989621i	$-0.545901\pi$
$197$	−211.300	−	121.994i	−1.07259	−	0.619260i	−0.928888	+	0.370361i	$0.879234\pi$
$198$		0			0
$199$	41.0539	+	71.1075i	0.206301	+	0.357324i	0.950547	−	0.310582i	$-0.100524\pi$
$199$	41.0539	+	71.1075i	0.206301	+	0.357324i	−0.744245	+	0.667906i	$0.767191\pi$
$200$		0			0
$201$	−3.90445	−	112.830i	−0.0194251	−	0.561344i
$202$		0			0
$203$	88.1800	−	15.5485i	0.434384	−	0.0765936i
$204$		0			0
$205$	−112.320	−	94.2474i	−0.547901	−	0.459743i
$206$		0			0
$207$	−157.026	+	215.841i	−0.758580	+	1.04271i
$208$		0			0
$209$	44.2895	+	121.684i	0.211911	+	0.582221i
$210$		0			0
$211$	−44.0427	+	36.9562i	−0.208733	+	0.175148i	−0.741161	−	0.671328i	$-0.765724\pi$
$211$	−44.0427	+	36.9562i	−0.208733	+	0.175148i	0.532427	+	0.846476i	$0.321280\pi$
$212$		0			0
$213$	−141.444	+	57.0952i	−0.664057	+	0.268052i
$214$		0			0
$215$		−	203.841i		−	0.948098i
$216$		0			0
$217$	−95.7975			−0.441463
$218$		0			0
$219$	181.984	−	232.778i	0.830978	−	1.06291i
$220$		0			0
$221$	18.9290	+	22.5587i	0.0856516	+	0.102076i
$222$		0			0
$223$	217.997	−	79.3444i	0.977565	−	0.355805i	0.196672	−	0.980469i	$-0.436987\pi$
$223$	217.997	−	79.3444i	0.977565	−	0.355805i	0.780893	+	0.624665i	$0.214764\pi$
$224$		0			0
$225$	−195.647	+	400.494i	−0.869542	+	1.77997i
$226$		0			0
$227$	−137.899	+	164.342i	−0.607485	+	0.723973i	−0.978865	−	0.204508i	$-0.934440\pi$
$227$	−137.899	+	164.342i	−0.607485	+	0.723973i	0.371379	+	0.928481i	$0.378885\pi$
$228$		0			0
$229$	−68.6623	−	389.403i	−0.299835	−	1.70045i	−0.646871	−	0.762599i	$-0.723923\pi$
$229$	−68.6623	−	389.403i	−0.299835	−	1.70045i	0.347036	−	0.937852i	$-0.387188\pi$
$230$		0			0
$231$	−197.678	+	371.496i	−0.855750	+	1.60821i
$232$		0			0
$233$	82.9298	−	47.8796i	0.355922	−	0.205492i	−0.311368	−	0.950289i	$-0.600787\pi$
$233$	82.9298	−	47.8796i	0.355922	−	0.205492i	0.667290	+	0.744798i	$0.267454\pi$
$234$		0			0
$235$	−71.6708	+	124.138i	−0.304982	+	0.528245i
$236$		0			0
$237$	75.3020	−	231.507i	0.317730	−	0.976823i
$238$		0			0
$239$	30.1617	−	82.8687i	0.126200	−	0.346731i	−0.860462	−	0.509514i	$-0.829825\pi$
$239$	30.1617	−	82.8687i	0.126200	−	0.346731i	0.986662	+	0.162784i	$0.0520473\pi$
$240$		0			0
$241$	−66.8780	+	379.284i	−0.277502	+	1.57379i	0.453399	+	0.891308i	$0.350211\pi$
$241$	−66.8780	+	379.284i	−0.277502	+	1.57379i	−0.730901	+	0.682484i	$0.760900\pi$
$242$		0			0
$243$	185.902	+	156.491i	0.765029	+	0.643996i
$244$		0			0
$245$	173.893	+	30.6620i	0.709767	+	0.125151i
$246$		0			0
$247$	−21.8559	−	7.95489i	−0.0884854	−	0.0322060i
$248$		0			0
$249$	46.0223	+	14.9696i	0.184828	+	0.0601189i
$250$		0			0
$251$	126.850	+	73.2368i	0.505378	+	0.291780i	0.730932	−	0.682451i	$-0.239086\pi$
$251$	126.850	+	73.2368i	0.505378	+	0.291780i	−0.225554	+	0.974231i	$0.572419\pi$
$252$		0			0
$253$	249.589	+	432.301i	0.986518	+	1.70870i
$254$		0			0
$255$	222.710	+	118.507i	0.873371	+	0.464734i
$256$		0			0
$257$	204.456	−	36.0511i	0.795548	−	0.140277i	0.238921	−	0.971039i	$-0.423206\pi$
$257$	204.456	−	36.0511i	0.795548	−	0.140277i	0.556627	+	0.830762i	$0.312095\pi$
$258$		0			0
$259$	148.016	+	124.200i	0.571489	+	0.479536i
$260$		0			0
$261$	−86.8838	−	42.4440i	−0.332888	−	0.162621i
$262$		0			0
$263$	11.3833	+	31.2753i	0.0432825	+	0.118918i	0.959451	−	0.281876i	$-0.0909567\pi$
$263$	11.3833	+	31.2753i	0.0432825	+	0.118918i	−0.916168	+	0.400794i	$0.868734\pi$
$264$		0			0
$265$	498.221	−	418.057i	1.88008	−	1.57757i
$266$		0			0
$267$	38.2511	+	29.9045i	0.143263	+	0.112002i
$268$		0			0
$269$			399.099i			1.48364i	0.670599	+	0.741820i	$0.266037\pi$
$269$			399.099i			1.48364i	−0.670599	+	0.741820i	$0.733963\pi$
$270$		0			0
$271$	83.9974			0.309954			0.154977	−	0.987918i	$-0.450470\pi$
$271$	83.9974			0.309954			0.154977	+	0.987918i	$0.450470\pi$
$272$		0			0
$273$	−28.2919	−	70.0886i	−0.103633	−	0.256735i
$274$		0			0
$275$	535.817	+	638.562i	1.94843	+	2.32204i
$276$		0			0
$277$	−168.403	+	61.2936i	−0.607953	+	0.221277i	−0.627607	−	0.778530i	$-0.715966\pi$
$277$	−168.403	+	61.2936i	−0.607953	+	0.221277i	0.0196546	+	0.999807i	$0.493743\pi$
$278$		0			0
$279$	83.6578	+	60.8617i	0.299849	+	0.218142i
$280$		0			0
$281$	−298.873	+	356.183i	−1.06361	+	1.26756i	−0.101513	+	0.994834i	$0.532368\pi$
$281$	−298.873	+	356.183i	−1.06361	+	1.26756i	−0.962093	+	0.272722i	$0.912076\pi$
$282$		0			0
$283$	−45.4847	−	257.956i	−0.160723	−	0.911507i	−0.953365	−	0.301819i	$-0.902406\pi$
$283$	−45.4847	−	257.956i	−0.160723	−	0.911507i	0.792642	−	0.609687i	$-0.208705\pi$
$284$		0			0
$285$	−199.131	+	6.89088i	−0.698707	+	0.0241785i
$286$		0			0
$287$	122.583	−	70.7732i	0.427118	−	0.246596i
$288$		0			0
$289$	−97.0563	+	168.107i	−0.335835	+	0.581683i
$290$		0			0
$291$	−266.272	−	295.913i	−0.915023	−	1.01688i
$292$		0			0
$293$	−33.5970	+	92.3071i	−0.114666	+	0.315041i	−0.983729	−	0.179660i	$-0.942500\pi$
$293$	−33.5970	+	92.3071i	−0.114666	+	0.315041i	0.869063	+	0.494701i	$0.164722\pi$
$294$		0			0
$295$	−90.2463	+	511.812i	−0.305920	+	1.73496i
$296$		0			0
$297$	408.645	−	198.831i	1.37591	−	0.669464i
$298$		0			0
$299$	−88.2960	−	15.5690i	−0.295304	−	0.0520701i
$300$		0			0
$301$	184.916	+	67.3039i	0.614339	+	0.223601i
$302$		0			0
$303$	−9.48045	−	44.6713i	−0.0312886	−	0.147430i
$304$		0			0
$305$	255.407	+	147.459i	0.837400	+	0.483473i
$306$		0			0
$307$	246.426	+	426.822i	0.802690	+	1.39030i	0.917840	+	0.396952i	$0.129932\pi$
$307$	246.426	+	426.822i	0.802690	+	1.39030i	−0.115150	+	0.993348i	$0.536735\pi$
$308$		0			0
$309$	96.3214	−	60.1460i	0.311720	−	0.194647i
$310$		0			0
$311$	16.6486	−	2.93559i	0.0535324	−	0.00943921i	−0.146818	−	0.989164i	$-0.546903\pi$
$311$	16.6486	−	2.93559i	0.0535324	−	0.00943921i	0.200350	+	0.979724i	$0.435792\pi$
$312$		0			0
$313$	319.525	+	268.113i	1.02085	+	0.856591i	0.989734	−	0.142925i	$-0.0456507\pi$
$313$	319.525	+	268.113i	1.02085	+	0.856591i	0.0311120	+	0.999516i	$0.490095\pi$
$314$		0			0
$315$	−449.500	−	466.060i	−1.42699	−	1.47956i
$316$		0			0
$317$	155.193	+	426.388i	0.489567	+	1.34507i	0.901074	+	0.433666i	$0.142780\pi$
$317$	155.193	+	426.388i	0.489567	+	1.34507i	−0.411507	+	0.911407i	$0.634997\pi$
$318$		0			0
$319$	−138.531	+	116.241i	−0.434265	+	0.364392i
$320$		0			0
$321$	49.6539	−	352.498i	0.154685	−	1.09813i
$322$		0			0
$323$			74.9429i			0.232021i
$324$		0			0
$325$	−149.721			−0.460680
$326$		0			0
$327$	612.123	+	86.2254i	1.87194	+	0.263686i
$328$		0			0
$329$	−88.9481	−	106.004i	−0.270359	−	0.322201i
$330$		0			0
$331$	−220.616	+	80.2978i	−0.666515	+	0.242591i	−0.653046	−	0.757318i	$-0.726509\pi$
$331$	−220.616	+	80.2978i	−0.666515	+	0.242591i	−0.0134681	+	0.999909i	$0.504287\pi$
$332$		0			0
$333$	−50.3526	−	202.498i	−0.151209	−	0.608101i
$334$		0			0
$335$	208.825	−	248.868i	0.623360	−	0.742891i
$336$		0			0
$337$	−55.0894	−	312.428i	−0.163470	−	0.927085i	−0.950628	−	0.310333i	$-0.899559\pi$
$337$	−55.0894	−	312.428i	−0.163470	−	0.927085i	0.787158	−	0.616752i	$-0.211552\pi$
$338$		0			0
$339$	−112.862	−	180.744i	−0.332927	−	0.533169i
$340$		0			0
$341$	167.555	−	96.7381i	0.491365	−	0.283689i
$342$		0			0
$343$	118.950	−	206.027i	0.346793	−	0.600662i
$344$		0			0
$345$	−751.346	+	159.456i	−2.17782	+	0.462190i
$346$		0			0
$347$	15.0965	−	41.4774i	0.0435059	−	0.119531i	−0.916037	−	0.401093i	$-0.868630\pi$
$347$	15.0965	−	41.4774i	0.0435059	−	0.119531i	0.959543	+	0.281562i	$0.0908525\pi$
$348$		0			0
$349$	57.3986	−	325.523i	0.164466	−	0.932732i	−0.785148	−	0.619309i	$-0.787413\pi$
$349$	57.3986	−	325.523i	0.164466	−	0.932732i	0.949614	−	0.313423i	$-0.101476\pi$
$350$		0			0
$351$	−19.8217	+	79.1810i	−0.0564721	+	0.225587i
$352$		0			0
$353$	−466.298	−	82.2209i	−1.32096	−	0.232920i	−0.531673	−	0.846949i	$-0.678437\pi$
$353$	−466.298	−	82.2209i	−1.32096	−	0.232920i	−0.789283	+	0.614029i	$0.789548\pi$
$354$		0			0
$355$	−412.458	−	150.123i	−1.16185	−	0.422880i
$356$		0			0
$357$	−181.038	+	162.904i	−0.507111	+	0.456315i
$358$		0			0
$359$	−378.055	−	218.270i	−1.05308	−	0.607994i	−0.129568	−	0.991571i	$-0.541359\pi$
$359$	−378.055	−	218.270i	−1.05308	−	0.607994i	−0.923509	+	0.383576i	$0.874692\pi$
$360$		0			0
$361$	150.905	+	261.375i	0.418018	+	0.724029i
$362$		0			0
$363$	−16.8388	−	486.604i	−0.0463878	−	1.34051i
$364$		0			0
$365$	837.333	−	147.644i	2.29406	−	0.404505i
$366$		0			0
$367$	−365.154	−	306.401i	−0.994970	−	0.834879i	−0.00869048	−	0.999962i	$-0.502766\pi$
$367$	−365.154	−	306.401i	−0.994970	−	0.834879i	−0.986280	+	0.165083i	$0.947211\pi$
$368$		0			0
$369$	−152.012	−	16.0742i	−0.411957	−	0.0435614i
$370$		0			0
$371$	214.742	+	589.998i	0.578818	+	1.59029i
$372$		0			0
$373$	−282.763	+	237.266i	−0.758077	+	0.636102i	−0.937625	−	0.347647i	$-0.886981\pi$
$373$	−282.763	+	237.266i	−0.758077	+	0.636102i	0.179549	+	0.983749i	$0.442536\pi$
$374$		0			0
$375$	−588.991	+	237.752i	−1.57064	+	0.634004i
$376$		0			0
$377$		−	32.4807i		−	0.0861558i
$378$		0			0
$379$	216.903			0.572304			0.286152	−	0.958184i	$-0.407624\pi$
$379$	216.903			0.572304			0.286152	+	0.958184i	$0.407624\pi$
$380$		0			0
$381$	70.7115	−	90.4477i	0.185594	−	0.237396i
$382$		0			0
$383$	346.686	+	413.164i	0.905185	+	1.07876i	0.996555	+	0.0829400i	$0.0264310\pi$
$383$	346.686	+	413.164i	0.905185	+	1.07876i	−0.0913699	+	0.995817i	$0.529125\pi$
$384$		0			0
$385$	−1137.91	+	414.166i	−2.95561	+	1.07576i
$386$		0			0
$387$	−118.724	−	176.255i	−0.306780	−	0.455439i
$388$		0			0
$389$	94.9161	−	113.117i	0.244000	−	0.290788i	−0.630120	−	0.776498i	$-0.716994\pi$
$389$	94.9161	−	113.117i	0.244000	−	0.290788i	0.874120	+	0.485710i	$0.161439\pi$
$390$		0			0
$391$	50.1658	+	284.504i	0.128301	+	0.727633i
$392$		0			0
$393$	307.114	−	577.158i	0.781461	−	1.46860i
$394$		0			0
$395$	606.686	−	350.270i	1.53591	−	0.886760i
$396$		0			0
$397$	251.308	−	435.278i	0.633017	−	1.09642i	−0.353915	−	0.935278i	$-0.615150\pi$
$397$	251.308	−	435.278i	0.633017	−	1.09642i	0.986932	−	0.161139i	$-0.0515169\pi$
$398$		0			0
$399$	59.4978	−	182.919i	0.149117	−	0.458443i
$400$		0			0
$401$	79.1589	−	217.487i	0.197404	−	0.542362i	−0.801011	−	0.598650i	$-0.795704\pi$
$401$	79.1589	−	217.487i	0.197404	−	0.542362i	0.998415	+	0.0562876i	$0.0179264\pi$
$402$		0			0
$403$	−6.03437	+	34.2226i	−0.0149736	+	0.0849196i
$404$		0			0
$405$	96.4433	+	692.574i	0.238132	+	1.71006i
$406$		0			0
$407$	−384.307	−	67.7638i	−0.944244	−	0.166496i
$408$		0			0
$409$	−423.279	−	154.061i	−1.03491	−	0.376677i	−0.231963	−	0.972725i	$-0.574515\pi$
$409$	−423.279	−	154.061i	−1.03491	−	0.376677i	−0.802949	+	0.596048i	$0.796737\pi$
$410$		0			0
$411$	−525.192	−	170.828i	−1.27784	−	0.415641i
$412$		0			0
$413$	−434.497	−	250.857i	−1.05205	−	0.607402i
$414$		0			0
$415$	69.6317	+	120.606i	0.167787	+	0.290616i
$416$		0			0
$417$	643.959	+	342.660i	1.54427	+	0.821726i
$418$		0			0
$419$	324.142	−	57.1549i	0.773608	−	0.136408i	0.227111	−	0.973869i	$-0.427072\pi$
$419$	324.142	−	57.1549i	0.773608	−	0.136408i	0.546497	+	0.837461i	$0.315961\pi$
$420$		0			0
$421$	−156.740	−	131.520i	−0.372303	−	0.312399i	0.437369	−	0.899282i	$-0.355910\pi$
$421$	−156.740	−	131.520i	−0.372303	−	0.312399i	−0.809672	+	0.586883i	$0.800355\pi$
$422$		0			0
$423$	10.3302	+	149.081i	0.0244213	+	0.352438i
$424$		0			0
$425$	165.000	+	453.333i	0.388234	+	1.06666i
$426$		0			0
$427$	−218.099	+	183.006i	−0.510770	+	0.428587i
$428$		0			0
$429$	120.261	+	94.0192i	0.280328	+	0.219159i
$430$		0			0
$431$			5.85402i			0.0135824i	0.999977	+	0.00679120i	$0.00216172\pi$
$431$			5.85402i			0.0135824i	−0.999977	+	0.00679120i	$0.997838\pi$
$432$		0			0
$433$	233.310			0.538821			0.269411	−	0.963025i	$-0.413171\pi$
$433$	233.310			0.538821			0.269411	+	0.963025i	$0.413171\pi$
$434$		0			0
$435$	−104.155	−	258.026i	−0.239436	−	0.593164i
$436$		0			0
$437$	−146.665	−	174.789i	−0.335619	−	0.399975i
$438$		0			0
$439$	−126.662	+	46.1012i	−0.288524	+	0.105014i	−0.482227	−	0.876046i	$-0.660172\pi$
$439$	−126.662	+	46.1012i	−0.288524	+	0.105014i	0.193704	+	0.981060i	$0.437950\pi$
$440$		0			0
$441$	168.218	−	74.7683i	0.381447	−	0.169543i
$442$		0			0
$443$	−18.4121	+	21.9426i	−0.0415622	+	0.0495319i	−0.786425	−	0.617686i	$-0.788070\pi$
$443$	−18.4121	+	21.9426i	−0.0415622	+	0.0495319i	0.744863	+	0.667218i	$0.232515\pi$
$444$		0			0
$445$	24.2616	+	137.594i	0.0545205	+	0.309201i
$446$		0			0
$447$	431.966	−	14.9480i	0.966367	−	0.0334408i
$448$		0			0
$449$	430.226	−	248.391i	0.958188	−	0.553210i	0.0625728	−	0.998040i	$-0.480069\pi$
$449$	430.226	−	248.391i	0.958188	−	0.553210i	0.895615	+	0.444831i	$0.146736\pi$
$450$		0			0
$451$	−142.936	+	247.573i	−0.316932	+	0.548942i
$452$		0			0
$453$	203.897	+	226.594i	0.450104	+	0.500209i
$454$		0			0
$455$	74.3889	−	204.382i	0.163492	−	0.449191i
$456$		0			0
$457$	−80.5387	+	456.758i	−0.176234	+	0.999470i	0.760477	+	0.649365i	$0.224965\pi$
$457$	−80.5387	+	456.758i	−0.176234	+	0.999470i	−0.936710	+	0.350105i	$0.886146\pi$
$458$		0			0
$459$	261.592	−	27.2440i	0.569918	−	0.0593551i
$460$		0			0
$461$	−262.335	−	46.2568i	−0.569057	−	0.100340i	−0.118286	−	0.992980i	$-0.537740\pi$
$461$	−262.335	−	46.2568i	−0.569057	−	0.100340i	−0.450771	+	0.892640i	$0.648851\pi$
$462$		0			0
$463$	224.935	+	81.8697i	0.485821	+	0.176824i	0.573306	−	0.819341i	$-0.305661\pi$
$463$	224.935	+	81.8697i	0.485821	+	0.176824i	−0.0874848	+	0.996166i	$0.527883\pi$
$464$		0			0
$465$	61.8033	+	291.214i	0.132910	+	0.626266i
$466$		0			0
$467$	184.565	+	106.559i	0.395215	+	0.228177i	0.684417	−	0.729091i	$-0.260057\pi$
$467$	184.565	+	106.559i	0.395215	+	0.228177i	−0.289202	+	0.957268i	$0.593390\pi$
$468$		0			0
$469$	156.813	+	271.609i	0.334357	+	0.579123i
$470$		0			0
$471$	−787.658	+	491.838i	−1.67231	+	1.04424i
$472$		0			0
$473$	−391.394	+	69.0132i	−0.827470	+	0.145905i
$474$		0			0
$475$	−291.882	−	244.918i	−0.614489	−	0.515617i
$476$		0			0
$477$	187.306	−	651.660i	0.392675	−	1.36616i
$478$		0			0
$479$	−136.882	−	376.079i	−0.285765	−	0.785134i	−0.996647	−	0.0818220i	$-0.973926\pi$
$479$	−136.882	−	376.079i	−0.285765	−	0.785134i	0.710882	−	0.703312i	$-0.248296\pi$
$480$		0			0
$481$	53.6927	−	45.0535i	0.111627	−	0.0936664i
$482$		0			0
$483$	103.427	−	734.238i	0.214134	−	1.52016i
$484$		0			0
$485$		−	1145.51i		−	2.36187i
$486$		0			0
$487$	323.676			0.664632			0.332316	−	0.943168i	$-0.392170\pi$
$487$	323.676			0.664632			0.332316	+	0.943168i	$0.392170\pi$
$488$		0			0
$489$	−475.473	−	66.9765i	−0.972338	−	0.136966i
$490$		0			0
$491$	−589.862	−	702.970i	−1.20135	−	1.43171i	−0.873392	−	0.487018i	$-0.838085\pi$
$491$	−589.862	−	702.970i	−1.20135	−	1.43171i	−0.327956	−	0.944693i	$-0.606360\pi$
$492$		0			0
$493$	−98.3467	+	35.7953i	−0.199486	+	0.0726070i
$494$		0			0
$495$	1256.84	+	361.252i	2.53907	+	0.729801i
$496$		0			0
$497$	272.369	−	324.597i	0.548027	−	0.653113i
$498$		0			0
$499$	37.5201	+	212.787i	0.0751906	+	0.426427i	0.999045	+	0.0436840i	$0.0139095\pi$
$499$	37.5201	+	212.787i	0.0751906	+	0.426427i	−0.923855	+	0.382743i	$0.874979\pi$
$500$		0			0
$501$	−395.562	−	633.477i	−0.789546	−	1.26443i
$502$		0			0
$503$	−31.3557	+	18.1032i	−0.0623373	+	0.0359905i	−0.530845	−	0.847469i	$-0.678125\pi$
$503$	−31.3557	+	18.1032i	−0.0623373	+	0.0359905i	0.468507	+	0.883460i	$0.344792\pi$
$504$		0			0
$505$	65.7046	−	113.804i	0.130108	−	0.225354i
$506$		0			0
$507$	469.134	−	99.5626i	0.925313	−	0.196376i
$508$		0			0
$509$	−79.8138	+	219.287i	−0.156805	+	0.430818i	−0.993072	−	0.117503i	$-0.962511\pi$
$509$	−79.8138	+	219.287i	−0.156805	+	0.430818i	0.836267	+	0.548322i	$0.184733\pi$
$510$		0			0
$511$	−142.532	+	808.342i	−0.278929	+	1.58188i
$512$		0			0
$513$	−168.169	+	121.939i	−0.327815	+	0.237698i
$514$		0			0
$515$	321.809	+	56.7437i	0.624873	+	0.110182i
$516$		0			0
$517$	262.620	+	95.5860i	0.507970	+	0.184886i
$518$		0			0
$519$	150.704	−	135.608i	0.290373	−	0.261287i
$520$		0			0
$521$	−119.806	−	69.1700i	−0.229954	−	0.132764i	0.380597	−	0.924741i	$-0.375719\pi$
$521$	−119.806	−	69.1700i	−0.229954	−	0.132764i	−0.610551	+	0.791977i	$0.709052\pi$
$522$		0			0
$523$	−98.4346	−	170.494i	−0.188212	−	0.325992i	0.756442	−	0.654060i	$-0.226936\pi$
$523$	−98.4346	−	170.494i	−0.188212	−	0.325992i	−0.944654	+	0.328068i	$0.893602\pi$
$524$		0			0
$525$	−42.8225	−	1237.48i	−0.0815667	−	2.35710i
$526$		0			0
$527$	110.271	−	19.4437i	0.209243	−	0.0368951i
$528$		0			0
$529$	−268.547	−	225.338i	−0.507651	−	0.425969i
$530$		0			0
$531$	220.063	+	495.111i	0.414431	+	0.932412i
$532$		0			0
$533$	−17.5613	−	48.2494i	−0.0329481	−	0.0905242i
$534$		0			0
$535$	784.708	−	658.448i	1.46674	−	1.23074i
$536$		0			0
$537$	−654.394	+	264.152i	−1.21861	+	0.491903i
$538$		0			0
$539$		−	344.271i		−	0.638722i
$540$		0			0
$541$	−136.735			−0.252745			−0.126373	−	0.991983i	$-0.540334\pi$
$541$	−136.735			−0.252745			−0.126373	+	0.991983i	$0.540334\pi$
$542$		0			0
$543$	−402.493	+	514.833i	−0.741240	+	0.948127i
$544$		0			0
$545$	1143.41	+	1362.67i	2.09801	+	2.50031i
$546$		0			0
$547$	−625.697	+	227.735i	−1.14387	+	0.416335i	−0.843310	−	0.537428i	$-0.819396\pi$
$547$	−625.697	+	227.735i	−1.14387	+	0.416335i	−0.300561	+	0.953763i	$0.597174\pi$
$548$		0			0
$549$	306.727	−	21.2539i	0.558702	−	0.0387138i
$550$		0			0
$551$	53.1330	−	63.3214i	0.0964300	−	0.114921i
$552$		0			0
$553$	117.436	+	666.011i	0.212361	+	1.20436i
$554$		0			0
$555$	282.063	−	530.079i	0.508221	−	0.955097i
$556$		0			0
$557$	−943.861	+	544.939i	−1.69454	+	0.978346i	−0.743784	+	0.668420i	$0.766971\pi$
$557$	−943.861	+	544.939i	−1.69454	+	0.978346i	−0.950761	+	0.309926i	$0.899696\pi$
$558$		0			0
$559$	35.6916	−	61.8197i	0.0638490	−	0.110590i
$560$		0			0
$561$	152.143	−	467.745i	0.271199	−	0.833770i
$562$		0			0
$563$	−209.400	+	575.323i	−0.371937	+	1.02189i	0.602675	+	0.797987i	$0.294102\pi$
$563$	−209.400	+	575.323i	−0.371937	+	1.02189i	−0.974612	+	0.223901i	$0.928121\pi$
$564$		0			0
$565$	106.478	−	603.866i	0.188457	−	1.06879i
$566$		0			0
$567$	−660.117	−	141.184i	−1.16423	−	0.249001i
$568$		0			0
$569$	491.784	+	86.7148i	0.864295	+	0.152399i	0.588184	−	0.808727i	$-0.299843\pi$
$569$	491.784	+	86.7148i	0.864295	+	0.152399i	0.276111	+	0.961126i	$0.410954\pi$
$570$		0			0
$571$	−284.552	−	103.569i	−0.498341	−	0.181381i	0.0806069	−	0.996746i	$-0.474314\pi$
$571$	−284.552	−	103.569i	−0.498341	−	0.181381i	−0.578947	+	0.815365i	$0.696536\pi$
$572$		0			0
$573$	−734.123	−	238.787i	−1.28119	−	0.416732i
$574$		0			0
$575$	−1272.01	−	734.397i	−2.21220	−	1.27721i
$576$		0			0
$577$	−18.5614	−	32.1493i	−0.0321688	−	0.0557181i	0.849493	−	0.527600i	$-0.176908\pi$
$577$	−18.5614	−	32.1493i	−0.0321688	−	0.0557181i	−0.881662	+	0.471882i	$0.843575\pi$
$578$		0			0
$579$	203.055	+	108.049i	0.350700	+	0.186613i
$580$		0			0
$581$	−132.399	+	23.3455i	−0.227881	+	0.0401817i
$582$		0			0
$583$	−971.386	−	815.090i	−1.66619	−	1.39810i
$584$		0			0
$585$	−194.809	+	131.222i	−0.333007	+	0.224310i
$586$		0			0
$587$	299.988	+	824.210i	0.511053	+	1.40411i	0.880141	+	0.474712i	$0.157448\pi$
$587$	299.988	+	824.210i	0.511053	+	1.40411i	−0.369088	+	0.929394i	$0.620330\pi$
$588$		0			0
$589$	−67.7464	+	56.8459i	−0.115019	+	0.0965126i
$590$		0			0
$591$	−576.654	−	450.825i	−0.975726	−	0.762817i
$592$		0			0
$593$			284.591i			0.479917i	0.970783	+	0.239958i	$0.0771338\pi$
$593$			284.591i			0.479917i	−0.970783	+	0.239958i	$0.922866\pi$
$594$		0			0
$595$	−700.817			−1.17784
$596$		0			0
$597$	92.2024	+	228.416i	0.154443	+	0.382607i
$598$		0			0
$599$	211.516	+	252.075i	0.353115	+	0.420827i	0.913138	−	0.407651i	$-0.133652\pi$
$599$	211.516	+	252.075i	0.353115	+	0.420827i	−0.560022	+	0.828477i	$0.689207\pi$
$600$		0			0
$601$	−6.64685	+	2.41926i	−0.0110597	+	0.00402538i	−0.347544	−	0.937664i	$-0.612984\pi$
$601$	−6.64685	+	2.41926i	−0.0110597	+	0.00402538i	0.336484	+	0.941689i	$0.390762\pi$
$602$		0			0
$603$	35.6158	−	336.815i	0.0590643	−	0.558566i
$604$		0			0
$605$	900.604	−	1073.30i	1.48860	−	1.77405i
$606$		0			0
$607$	−83.8924	−	475.778i	−0.138208	−	0.783818i	−0.972572	−	0.232603i	$-0.925276\pi$
$607$	−83.8924	−	475.778i	−0.138208	−	0.783818i	0.834363	−	0.551215i	$-0.185835\pi$
$608$		0			0
$609$	268.460	−	9.28998i	0.440821	−	0.0152545i
$610$		0			0
$611$	−43.4718	+	25.0984i	−0.0711485	+	0.0410776i
$612$		0			0
$613$	−287.932	+	498.713i	−0.469710	+	0.813562i	−0.999400	−	0.0346296i	$-0.988975\pi$
$613$	−287.932	+	498.713i	−0.469710	+	0.813562i	0.529690	+	0.848191i	$0.322308\pi$
$614$		0			0
$615$	−294.226	−	326.979i	−0.478417	−	0.531673i
$616$		0			0
$617$	−239.991	+	659.369i	−0.388964	+	1.06867i	0.578505	+	0.815679i	$0.303636\pi$
$617$	−239.991	+	659.369i	−0.388964	+	1.06867i	−0.967469	+	0.252991i	$0.918586\pi$
$618$		0			0
$619$	−78.3389	+	444.282i	−0.126557	+	0.717741i	0.853814	+	0.520579i	$0.174284\pi$
$619$	−78.3389	+	444.282i	−0.126557	+	0.717741i	−0.980371	+	0.197162i	$0.936827\pi$
$620$		0			0
$621$	−556.793	+	575.485i	−0.896608	+	0.926707i
$622$		0			0
$623$	−132.830	−	23.4216i	−0.213211	−	0.0375949i
$624$		0			0
$625$	−554.064	−	201.663i	−0.886502	−	0.322660i
$626$		0			0
$627$	80.6498	+	380.017i	0.128628	+	0.606088i
$628$		0			0
$629$	−195.587	−	112.922i	−0.310949	−	0.179527i
$630$		0			0
$631$	−283.716	−	491.411i	−0.449630	−	0.778782i	0.548732	−	0.835998i	$-0.315111\pi$
$631$	−283.716	−	491.411i	−0.449630	−	0.778782i	−0.998362	+	0.0572166i	$0.981777\pi$
$632$		0			0
$633$	−146.301	+	91.3548i	−0.231123	+	0.144320i
$634$		0			0
$635$	325.353	−	57.3685i	0.512367	−	0.0903441i
$636$		0			0
$637$	47.3684	+	39.7468i	0.0743616	+	0.0623968i
$638$		0			0
$639$	−444.076	+	110.423i	−0.694954	+	0.172806i
$640$		0			0
$641$	50.9735	+	140.049i	0.0795219	+	0.218485i	0.973082	−	0.230459i	$-0.0740227\pi$
$641$	50.9735	+	140.049i	0.0795219	+	0.218485i	−0.893560	+	0.448943i	$0.851800\pi$
$642$		0			0
$643$	20.8996	−	17.5368i	0.0325032	−	0.0272734i	−0.626391	−	0.779509i	$-0.715469\pi$
$643$	20.8996	−	17.5368i	0.0325032	−	0.0272734i	0.658895	+	0.752235i	$0.271024\pi$
$644$		0			0
$645$	85.2988	−	605.545i	0.132246	−	0.938830i
$646$		0			0
$647$			263.970i			0.407991i	0.978972	+	0.203996i	$0.0653929\pi$
$647$			263.970i			0.407991i	−0.978972	+	0.203996i	$0.934607\pi$
$648$		0			0
$649$	1013.28			1.56129
$650$		0			0
$651$	−284.583	−	40.0871i	−0.437147	−	0.0615778i
$652$		0			0
$653$	−538.345	−	641.575i	−0.824418	−	0.982503i	0.175580	−	0.984465i	$-0.443820\pi$
$653$	−538.345	−	641.575i	−0.824418	−	0.982503i	−0.999998	+	0.00196193i	$0.999375\pi$
$654$		0			0
$655$	1767.87	−	643.450i	2.69903	−	0.982367i
$656$		0			0
$657$	638.023	−	615.353i	0.971115	−	0.936611i
$658$		0			0
$659$	477.726	−	569.332i	0.724926	−	0.863933i	−0.270173	−	0.962812i	$-0.587081\pi$
$659$	477.726	−	569.332i	0.724926	−	0.863933i	0.995100	+	0.0988784i	$0.0315255\pi$
$660$		0			0
$661$	46.6386	+	264.501i	0.0705577	+	0.400152i	0.999548	+	0.0300495i	$0.00956649\pi$
$661$	46.6386	+	264.501i	0.0705577	+	0.400152i	−0.928991	+	0.370103i	$0.879322\pi$
$662$		0			0
$663$	46.7920	+	74.9355i	0.0705762	+	0.113025i
$664$		0			0
$665$	479.355	−	276.756i	0.720835	−	0.416174i
$666$		0			0
$667$	159.321	−	275.952i	0.238862	−	0.413722i
$668$		0			0
$669$	680.800	−	144.484i	1.01764	−	0.215970i
$670$		0			0
$671$	196.664	−	540.329i	0.293090	−	0.805259i
$672$		0			0
$673$	114.573	−	649.776i	0.170242	−	0.965492i	−0.773251	−	0.634100i	$-0.781371\pi$
$673$	114.573	−	649.776i	0.170242	−	0.965492i	0.943493	−	0.331392i	$-0.107518\pi$
$674$		0			0
$675$	−748.793	+	1107.87i	−1.10932	+	1.64128i
$676$		0			0
$677$	251.116	+	44.2786i	0.370925	+	0.0654041i	0.356004	−	0.934485i	$-0.384139\pi$
$677$	251.116	+	44.2786i	0.370925	+	0.0654041i	0.0149216	+	0.999889i	$0.495250\pi$
$678$		0			0
$679$	1039.15	+	378.221i	1.53042	+	0.557026i
$680$		0			0
$681$	−478.423	+	430.501i	−0.702531	+	0.632160i
$682$		0			0
$683$	376.413	+	217.322i	0.551117	+	0.318187i	0.749572	−	0.661923i	$-0.230259\pi$
$683$	376.413	+	217.322i	0.551117	+	0.318187i	−0.198456	+	0.980110i	$0.563593\pi$
$684$		0			0
$685$	−794.615	−	1376.31i	−1.16002	−	2.00922i
$686$		0			0
$687$	−41.0246	−	1185.52i	−0.0597156	−	1.72565i
$688$		0			0
$689$	224.297	−	39.5496i	0.325540	−	0.0574015i
$690$		0			0
$691$	1022.63	+	858.086i	1.47992	+	1.24180i	0.906266	+	0.422707i	$0.138920\pi$
$691$	1022.63	+	858.086i	1.47992	+	1.24180i	0.573657	+	0.819096i	$0.305524\pi$
$692$		0			0
$693$	−742.693	+	1020.87i	−1.07171	+	1.47312i
$694$		0			0
$695$	717.924	+	1972.48i	1.03298	+	2.83810i
$696$		0			0
$697$	−126.738	+	106.346i	−0.181834	+	0.152577i
$698$		0			0
$699$	266.393	−	107.532i	0.381106	−	0.153837i
$700$		0			0
$701$			1001.61i			1.42883i	0.699722	+	0.714415i	$0.253307\pi$
$701$			1001.61i			1.42883i	−0.699722	+	0.714415i	$0.746693\pi$
$702$		0			0
$703$	178.374			0.253733
$704$		0			0
$705$	−264.857	+	338.781i	−0.375683	+	0.480540i
$706$		0			0
$707$	81.5437	+	97.1800i	0.115338	+	0.137454i
$708$		0			0
$709$	720.055	−	262.078i	1.01559	−	0.369645i	0.220014	−	0.975497i	$-0.429390\pi$
$709$	720.055	−	262.078i	1.01559	−	0.369645i	0.795578	+	0.605852i	$0.207167\pi$
$710$		0			0
$711$	320.574	−	656.221i	0.450877	−	0.922955i
$712$		0			0
$713$	−219.132	+	261.152i	−0.307339	+	0.366272i
$714$		0			0
$715$	76.2782	+	432.595i	0.106683	+	0.605028i
$716$		0			0
$717$	124.278	−	233.554i	0.173330	−	0.325738i
$718$		0			0
$719$	−544.595	+	314.422i	−0.757434	+	0.437305i	−0.828374	−	0.560176i	$-0.810733\pi$
$719$	−544.595	+	314.422i	−0.757434	+	0.437305i	0.0709399	+	0.997481i	$0.477400\pi$
$720$		0			0
$721$	−157.730	+	273.196i	−0.218765	+	0.378913i
$722$		0			0
$723$	−357.387	+	1098.74i	−0.494311	+	1.51970i
$724$		0			0
$725$	181.990	−	500.015i	0.251021	−	0.689675i
$726$		0			0
$727$	116.145	−	658.690i	0.159759	−	0.906039i	−0.794546	−	0.607204i	$-0.792291\pi$
$727$	116.145	−	658.690i	0.159759	−	0.906039i	0.954305	−	0.298835i	$-0.0965979\pi$
$728$		0			0
$729$	486.769	+	542.676i	0.667722	+	0.744411i
$730$		0			0
$731$	−226.514	−	39.9406i	−0.309869	−	0.0546383i
$732$		0			0
$733$	−104.288	−	37.9578i	−0.142276	−	0.0517842i	0.269901	−	0.962888i	$-0.413009\pi$
$733$	−104.288	−	37.9578i	−0.142276	−	0.0517842i	−0.412177	+	0.911104i	$0.635231\pi$
$734$		0			0
$735$	503.748	+	163.853i	0.685371	+	0.222930i
$736$		0			0
$737$	−548.551	−	316.706i	−0.744302	−	0.429723i
$738$		0			0
$739$	231.298	+	400.619i	0.312987	+	0.542110i	0.979008	−	0.203824i	$-0.0653369\pi$
$739$	231.298	+	400.619i	0.312987	+	0.542110i	−0.666020	+	0.745934i	$0.732004\pi$
$740$		0			0
$741$	−61.5979	−	32.7771i	−0.0831280	−	0.0442336i
$742$		0			0
$743$	−952.218	+	167.902i	−1.28159	+	0.225978i	−0.772653	−	0.634829i	$-0.781071\pi$
$743$	−952.218	+	167.902i	−1.28159	+	0.225978i	−0.508932	+	0.860807i	$0.669960\pi$
$744$		0			0
$745$	952.783	+	799.480i	1.27890	+	1.07313i
$746$		0			0
$747$	130.453	+	63.7282i	0.174636	+	0.0853121i
$748$		0			0
$749$	338.223	+	929.259i	0.451566	+	1.24067i
$750$		0			0
$751$	805.112	−	675.569i	1.07205	−	0.899560i	0.0768166	−	0.997045i	$-0.475524\pi$
$751$	805.112	−	675.569i	1.07205	−	0.899560i	0.995237	+	0.0974855i	$0.0310800\pi$
$752$		0			0
$753$	346.183	+	270.644i	0.459739	+	0.359421i
$754$		0			0
$755$			877.168i			1.16181i
$756$		0			0
$757$	−266.724			−0.352343			−0.176172	−	0.984359i	$-0.556371\pi$
$757$	−266.724			−0.352343			−0.176172	+	0.984359i	$0.556371\pi$
$758$		0			0
$759$	560.548	+	1388.67i	0.738535	+	1.82960i
$760$		0			0
$761$	−0.229396	−	0.273383i	−0.000301440	−	0.000359242i	0.765894	−	0.642967i	$-0.222297\pi$
$761$	−0.229396	−	0.273383i	−0.000301440	−	0.000359242i	−0.766195	+	0.642608i	$0.777852\pi$
$762$		0			0
$763$	−1613.68	+	587.333i	−2.11492	+	0.769768i
$764$		0			0
$765$	612.007	+	445.240i	0.800010	+	0.582013i
$766$		0			0
$767$	−116.985	+	139.418i	−0.152523	+	0.181770i
$768$		0			0
$769$	77.8630	+	441.583i	0.101252	+	0.574230i	0.992651	+	0.121011i	$0.0386136\pi$
$769$	77.8630	+	441.583i	0.101252	+	0.574230i	−0.891399	+	0.453220i	$0.850275\pi$
$770$		0			0
$771$	622.457	−	21.5399i	0.807338	−	0.0279377i
$772$		0			0
$773$	580.814	−	335.333i	0.751376	−	0.433807i	−0.0748149	−	0.997197i	$-0.523837\pi$
$773$	580.814	−	335.333i	0.751376	−	0.433807i	0.826191	+	0.563390i	$0.190503\pi$
$774$		0			0
$775$	−284.644	+	493.018i	−0.367283	+	0.636153i
$776$		0			0
$777$	387.734	+	430.896i	0.499014	+	0.554563i
$778$		0			0
$779$	44.6918	−	122.790i	0.0573708	−	0.157625i
$780$		0			0
$781$	−148.605	+	842.783i	−0.190276	+	1.07911i
$782$		0			0
$783$	−240.342	−	162.444i	−0.306951	−	0.207464i
$784$		0			0
$785$	−2631.56	−	464.015i	−3.35231	−	0.591102i
$786$		0			0
$787$	−1152.23	−	419.377i	−1.46408	−	0.532881i	−0.517592	−	0.855627i	$-0.673172\pi$
$787$	−1152.23	−	419.377i	−1.46408	−	0.532881i	−0.946485	+	0.322747i	$0.895394\pi$
$788$		0			0
$789$	20.7286	+	97.6722i	0.0262720	+	0.123792i
$790$		0			0
$791$	512.645	+	295.976i	0.648097	+	0.374179i
$792$		0			0
$793$	51.6388	+	89.4411i	0.0651183	+	0.112788i
$794$		0			0
$795$	1654.99	−	1033.43i	2.08175	−	1.29991i
$796$		0			0
$797$	−391.758	+	69.0776i	−0.491541	+	0.0866720i	−0.413924	−	0.910311i	$-0.635842\pi$
$797$	−391.758	+	69.0776i	−0.491541	+	0.0866720i	−0.0776168	+	0.996983i	$0.524731\pi$
$798$		0			0
$799$	123.902	+	103.966i	0.155071	+	0.130120i
$800$		0			0
$801$	101.118	+	104.843i	0.126239	+	0.130890i
$802$		0			0
$803$	−566.981	−	1557.77i	−0.706079	−	1.93994i
$804$		0			0
$805$	1634.51	−	1371.52i	2.03045	−	1.70375i
$806$		0			0
$807$	−167.006	+	1185.59i	−0.206947	+	1.46914i
$808$		0			0
$809$		−	438.654i		−	0.542218i	−0.962549	−	0.271109i	$-0.912610\pi$
$809$		−	438.654i		−	0.542218i	0.962549	−	0.271109i	$-0.0873903\pi$
$810$		0			0
$811$	1037.62			1.27943			0.639716	−	0.768611i	$-0.279052\pi$
$811$	1037.62			1.27943			0.639716	+	0.768611i	$0.279052\pi$
$812$		0			0
$813$	249.529	+	35.1493i	0.306924	+	0.0432341i
$814$		0			0
$815$	−888.159	−	1058.47i	−1.08977	−	1.29873i
$816$		0			0
$817$	170.707	−	62.1324i	0.208944	−	0.0760495i
$818$		0			0
$819$	−54.7168	−	220.049i	−0.0668093	−	0.268680i
$820$		0			0
$821$	−919.156	+	1095.41i	−1.11956	+	1.33424i	−0.183245	+	0.983067i	$0.558660\pi$
$821$	−919.156	+	1095.41i	−1.11956	+	1.33424i	−0.936312	+	0.351168i	$0.885784\pi$
$822$		0			0
$823$	245.722	+	1393.56i	0.298568	+	1.69327i	0.652334	+	0.757932i	$0.273790\pi$
$823$	245.722	+	1393.56i	0.298568	+	1.69327i	−0.353765	+	0.935334i	$0.615099\pi$
$824$		0			0
$825$	1324.53	+	2121.18i	1.60549	+	2.57112i
$826$		0			0
$827$	−609.863	+	352.105i	−0.737440	+	0.425761i	−0.821138	−	0.570730i	$-0.806660\pi$
$827$	−609.863	+	352.105i	−0.737440	+	0.425761i	0.0836977	+	0.996491i	$0.473327\pi$
$828$		0			0
$829$	−145.579	+	252.151i	−0.175608	+	0.304162i	−0.940372	−	0.340149i	$-0.889523\pi$
$829$	−145.579	+	252.151i	−0.175608	+	0.304162i	0.764763	+	0.644311i	$0.222856\pi$
$830$		0			0
$831$	−525.918	+	111.614i	−0.632874	+	0.134313i
$832$		0			0
$833$	68.1450	−	187.227i	0.0818067	−	0.224762i
$834$		0			0
$835$	373.186	−	2116.44i	0.446930	−	2.53466i
$836$		0			0
$837$	223.052	+	215.807i	0.266490	+	0.257834i
$838$		0			0
$839$	−852.208	−	150.267i	−1.01574	−	0.179103i	−0.359096	−	0.933301i	$-0.616915\pi$
$839$	−852.208	−	150.267i	−1.01574	−	0.179103i	−0.656647	+	0.754198i	$0.728026\pi$
$840$		0			0
$841$	−681.808	−	248.158i	−0.810710	−	0.295074i
$842$		0			0
$843$	−1036.90	+	933.038i	−1.23001	+	1.10681i
$844$		0			0
$845$	1195.16	+	690.023i	1.41438	+	0.816595i
$846$		0			0
$847$	676.290	+	1171.37i	0.798454	+	1.38296i
$848$		0			0
$849$	−27.1764	−	785.337i	−0.0320098	−	0.925014i
$850$		0			0
$851$	677.158	−	119.401i	0.795721	−	0.140307i
$852$		0			0
$853$	−83.2215	−	69.8311i	−0.0975633	−	0.0818653i	0.592701	−	0.805422i	$-0.298061\pi$
$853$	−83.2215	−	69.8311i	−0.0975633	−	0.0818653i	−0.690265	+	0.723557i	$0.742506\pi$
$854$		0			0
$855$	−594.438	−	62.8574i	−0.695249	−	0.0735175i
$856$		0			0
$857$	−364.690	−	1001.98i	−0.425543	−	1.16917i	−0.948491	−	0.316804i	$-0.897390\pi$
$857$	−364.690	−	1001.98i	−0.425543	−	1.16917i	0.522948	−	0.852364i	$-0.324832\pi$
$858$		0			0
$859$	42.4891	−	35.6526i	0.0494635	−	0.0415048i	−0.617721	−	0.786398i	$-0.711944\pi$
$859$	42.4891	−	35.6526i	0.0494635	−	0.0415048i	0.667184	+	0.744893i	$0.267499\pi$
$860$		0			0
$861$	393.769	−	158.948i	0.457339	−	0.184609i
$862$		0			0
$863$		−	75.8244i		−	0.0878614i	−0.999035	−	0.0439307i	$-0.986012\pi$
$863$		−	75.8244i		−	0.0878614i	0.999035	−	0.0439307i	$-0.0139881\pi$
$864$		0			0
$865$	583.388			0.674437
$866$		0			0
$867$	−358.668	+	458.775i	−0.413689	+	0.529153i
$868$		0			0
$869$	−877.953	−	1046.30i	−1.01030	−	1.20403i
$870$		0			0
$871$	106.907	−	38.9109i	0.122740	−	0.0446739i
$872$		0			0
$873$	−667.179	−	990.482i	−0.764237	−	1.13457i
$874$		0			0
$875$	1134.18	−	1351.66i	1.29621	−	1.54476i
$876$		0			0
$877$	100.329	+	568.994i	0.114400	+	0.648796i	0.987045	+	0.160441i	$0.0512918\pi$
$877$	100.329	+	568.994i	0.114400	+	0.648796i	−0.872645	+	0.488355i	$0.837597\pi$
$878$		0			0
$879$	−138.432	+	260.155i	−0.157488	+	0.295967i
$880$		0			0
$881$	118.578	−	68.4609i	0.134594	−	0.0777082i	−0.431191	−	0.902261i	$-0.641906\pi$
$881$	118.578	−	68.4609i	0.134594	−	0.0777082i	0.565785	+	0.824553i	$0.308573\pi$
$882$		0			0
$883$	−634.745	+	1099.41i	−0.718851	+	1.24509i	0.242605	+	0.970125i	$0.421998\pi$
$883$	−634.745	+	1099.41i	−0.718851	+	1.24509i	−0.961455	+	0.274961i	$0.911335\pi$
$884$		0			0
$885$	−482.264	+	1482.66i	−0.544931	+	1.67533i
$886$		0			0
$887$	−220.369	+	605.458i	−0.248443	+	0.682591i	0.751301	+	0.659960i	$0.229427\pi$
$887$	−220.369	+	605.458i	−0.248443	+	0.682591i	−0.999744	+	0.0226314i	$0.992796\pi$
$888$		0			0
$889$	−55.3822	+	314.088i	−0.0622972	+	0.353305i
$890$		0			0
$891$	1297.15	−	419.660i	1.45584	−	0.470999i
$892$		0			0
$893$	−125.805	−	22.1829i	−0.140879	−	0.0248408i
$894$		0			0
$895$	−1908.25	−	694.545i	−2.13212	−	0.776027i
$896$		0			0
$897$	−255.784	−	83.1984i	−0.285154	−	0.0927518i
$898$		0			0
$899$	−106.956	−	61.7512i	−0.118972	−	0.0686888i
$900$		0			0
$901$	−366.936	−	635.551i	−0.407254	−	0.705384i
$902$		0			0
$903$	521.161	+	277.317i	0.577144	+	0.307107i
$904$		0			0
$905$	−1851.93	+	326.544i	−2.04633	+	0.360823i
$906$		0			0
$907$	468.430	+	393.059i	0.516461	+	0.433362i	0.863396	−	0.504527i	$-0.168333\pi$
$907$	468.430	+	393.059i	0.516461	+	0.433362i	−0.346935	+	0.937889i	$0.612778\pi$
$908$		0			0
$909$	−9.47026	−	136.671i	−0.0104183	−	0.150353i
$910$		0			0
$911$	−359.212	−	986.926i	−0.394305	−	1.08334i	−0.965016	−	0.262193i	$-0.915554\pi$
$911$	−359.212	−	986.926i	−0.394305	−	1.08334i	0.570711	−	0.821151i	$-0.306668\pi$
$912$		0			0
$913$	207.999	−	174.532i	0.227819	−	0.191163i
$914$		0			0
$915$	697.025	+	544.930i	0.761776	+	0.595552i
$916$		0			0
$917$			1816.19i			1.98057i
$918$		0			0
$919$	−133.483			−0.145248			−0.0726238	−	0.997359i	$-0.523137\pi$
$919$	−133.483			−0.145248			−0.0726238	+	0.997359i	$0.523137\pi$
$920$		0			0
$921$	553.444	+	1371.07i	0.600916	+	1.48867i
$922$		0			0
$923$	−98.8020	−	117.748i	−0.107044	−	0.127571i
$924$		0			0
$925$	1078.99	−	392.721i	1.16648	−	0.424563i
$926$		0			0
$927$	311.308	−	138.368i	0.335823	−	0.149264i
$928$		0			0
$929$	714.192	−	851.141i	0.768775	−	0.916190i	−0.229594	−	0.973287i	$-0.573740\pi$
$929$	714.192	−	851.141i	0.768775	−	0.916190i	0.998369	+	0.0570965i	$0.0181843\pi$
$930$		0			0
$931$	27.3259	+	154.973i	0.0293512	+	0.166459i
$932$		0			0
$933$	50.6859	−	1.75397i	0.0543257	−	0.00187992i
$934$		0			0
$935$	1225.77	−	707.698i	1.31098	−	0.756896i
$936$		0			0
$937$	862.772	−	1494.36i	0.920781	−	1.59484i	0.122572	−	0.992460i	$-0.460886\pi$
$937$	862.772	−	1494.36i	0.920781	−	1.59484i	0.798209	−	0.602380i	$-0.205781\pi$
$938$		0			0
$939$	837.009	+	930.183i	0.891384	+	0.990611i
$940$		0			0
$941$	465.200	−	1278.13i	0.494368	−	1.35827i	−0.402278	−	0.915517i	$-0.631782\pi$
$941$	465.200	−	1278.13i	0.494368	−	1.35827i	0.896646	−	0.442748i	$-0.145996\pi$
$942$		0			0
$943$	87.4689	−	496.061i	0.0927560	−	0.526046i
$944$		0			0
$945$	−1140.29	−	1572.61i	−1.20666	−	1.66414i
$946$		0			0
$947$	−1590.14	−	280.385i	−1.67914	−	0.296077i	−0.748804	−	0.662792i	$-0.769372\pi$
$947$	−1590.14	−	280.385i	−1.67914	−	0.296077i	−0.930334	+	0.366714i	$0.880483\pi$
$948$		0			0
$949$	279.793	+	101.836i	0.294829	+	0.107309i
$950$		0			0
$951$	282.601	+	1331.60i	0.297162	+	1.40021i
$952$		0			0
$953$	−181.146	−	104.585i	−0.190080	−	0.109743i	0.401940	−	0.915666i	$-0.368336\pi$
$953$	−181.146	−	104.585i	−0.190080	−	0.109743i	−0.592020	+	0.805923i	$0.701669\pi$
$954$		0			0
$955$	−1110.73	−	1923.84i	−1.16307	−	2.01449i
$956$		0			0
$957$	−460.171	+	287.345i	−0.480848	+	0.300256i
$958$		0			0
$959$	1510.90	−	266.412i	1.57549	−	0.277802i
$960$		0			0
$961$	−634.949	−	532.786i	−0.660717	−	0.554407i
$962$		0			0
$963$	295.011	−	1026.38i	0.306346	−	1.06581i
$964$		0			0
$965$	226.378	+	621.969i	0.234589	+	0.644528i
$966$		0			0
$967$	−672.104	+	563.962i	−0.695041	+	0.583208i	−0.920358	−	0.391077i	$-0.872103\pi$
$967$	−672.104	+	563.962i	−0.695041	+	0.583208i	0.225317	+	0.974285i	$0.427658\pi$
$968$		0			0
$969$	−31.3604	+	222.631i	−0.0323637	+	0.229753i
$970$		0			0
$971$		−	686.372i		−	0.706871i	−0.935459	−	0.353435i	$-0.885013\pi$
$971$		−	686.372i		−	0.706871i	0.935459	−	0.353435i	$-0.114987\pi$
$972$		0			0
$973$	−2026.39			−2.08262
$974$		0			0
$975$	−444.772	−	62.6519i	−0.456177	−	0.0642583i
$976$		0			0
$977$	905.640	+	1079.30i	0.926960	+	1.10471i	0.994262	+	0.106975i	$0.0341166\pi$
$977$	905.640	+	1079.30i	0.926960	+	1.10471i	−0.0673015	+	0.997733i	$0.521439\pi$
$978$		0			0
$979$	255.980	−	93.1690i	0.261471	−	0.0951675i
$980$		0			0
$981$	1782.34	+	512.295i	1.81686	+	0.522217i
$982$		0			0
$983$	−606.673	+	723.005i	−0.617165	+	0.735508i	−0.980580	−	0.196119i	$-0.937166\pi$
$983$	−606.673	+	723.005i	−0.617165	+	0.735508i	0.363415	+	0.931627i	$0.381611\pi$
$984$		0			0
$985$	−365.756	−	2074.30i	−0.371326	−	2.10589i
$986$		0			0
$987$	−219.877	−	352.125i	−0.222774	−	0.356763i
$988$		0			0
$989$	606.463	−	350.142i	0.613208	−	0.354036i
$990$		0			0
$991$	424.153	−	734.654i	0.428005	−	0.741326i	−0.568691	−	0.822551i	$-0.692550\pi$
$991$	424.153	−	734.654i	0.428005	−	0.741326i	0.996696	+	0.0812254i	$0.0258834\pi$
$992$		0			0
$993$	−688.980	+	146.220i	−0.693837	+	0.147251i
$994$		0			0
$995$	−242.431	+	666.074i	−0.243649	+	0.669421i
$996$		0			0
$997$	−29.2963	+	166.148i	−0.0293845	+	0.166648i	−0.995969	−	0.0897017i	$-0.971409\pi$
$997$	−29.2963	+	166.148i	−0.0293845	+	0.166648i	0.966584	+	0.256349i	$0.0825198\pi$
$998$		0			0
$999$	−64.8444	−	622.625i	−0.0649093	−	0.623248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.bc.c.353.6		36
4.3	odd	2		54.3.f.a.29.1	✓	36
12.11	even	2		162.3.f.a.89.4		36
27.14	odd	18	inner	432.3.bc.c.257.6		36
108.11	even	18		1458.3.b.c.1457.19		36
108.43	odd	18		1458.3.b.c.1457.18		36
108.67	odd	18		162.3.f.a.71.4		36
108.95	even	18		54.3.f.a.41.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.29.1	✓	36	4.3	odd	2
54.3.f.a.41.1	yes	36	108.95	even	18
162.3.f.a.71.4		36	108.67	odd	18
162.3.f.a.89.4		36	12.11	even	2
432.3.bc.c.257.6		36	27.14	odd	18	inner
432.3.bc.c.353.6		36	1.1	even	1	trivial
1458.3.b.c.1457.18		36	108.43	odd	18
1458.3.b.c.1457.19		36	108.11	even	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.97067 + 0.418457i) q^{3} +(5.54906 + 6.61311i) q^{5} +(-7.83131 + 2.85036i) q^{7} +(8.64979 + 2.48620i) q^{9} +(10.8191 - 12.8937i) q^{11} +(0.524960 + 2.97720i) q^{13} +(13.7171 + 21.9674i) q^{15} +(8.43596 - 4.87051i) q^{17} +(-3.84677 + 6.66281i) q^{19} +(-24.4570 + 5.19043i) q^{21} +(-10.1434 + 27.8689i) q^{23} +(-8.59998 + 48.7729i) q^{25} +(24.6553 + 11.0052i) q^{27} +(-10.5809 - 1.86569i) q^{29} +(10.8017 + 3.93149i) q^{31} +(37.5353 - 33.7755i) q^{33} +(-62.3062 - 35.9725i) q^{35} +(-11.5925 - 20.0787i) q^{37} +(0.313655 + 9.06395i) q^{39} +(-16.7264 + 2.94931i) q^{41} +(-18.0881 - 15.1778i) q^{43} +(31.5567 + 70.9981i) q^{45} +(5.67901 + 15.6029i) q^{47} +(15.6687 - 13.1476i) q^{49} +(27.0986 - 10.9386i) q^{51} -75.3383i q^{53} +145.303 q^{55} +(-14.2156 + 18.1833i) q^{57} +(38.6968 + 46.1170i) q^{59} +(32.1023 - 11.6843i) q^{61} +(-74.8257 + 5.18485i) q^{63} +(-16.7755 + 19.9923i) q^{65} +(-6.53483 - 37.0609i) q^{67} +(-41.7948 + 78.5447i) q^{69} +(-44.0325 + 25.4222i) q^{71} +(49.2453 - 85.2954i) q^{73} +(-45.9571 + 141.290i) q^{75} +(-47.9758 + 131.813i) q^{77} +(14.0913 - 79.9158i) q^{79} +(68.6376 + 43.0102i) q^{81} +(15.8868 + 2.80127i) q^{83} +(79.0209 + 28.7612i) q^{85} +(-30.6516 - 9.97000i) q^{87} +(14.0161 + 8.09222i) q^{89} +(-12.5972 - 21.8190i) q^{91} +(30.4431 + 16.1992i) q^{93} +(-65.4078 + 11.5332i) q^{95} +(-101.648 - 85.2929i) q^{97} +(125.639 - 84.6291i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{5} - 12 q^{9} + 18 q^{11} + 18 q^{15} - 228 q^{21} + 180 q^{23} + 18 q^{25} - 54 q^{27} + 144 q^{29} + 90 q^{31} + 324 q^{33} - 486 q^{35} - 102 q^{39} - 90 q^{41} - 90 q^{43} - 378 q^{45}+ \cdots - 126 q^{99}+O(q^{100}) \) 36 * q + 18 * q^5 - 12 * q^9 + 18 * q^11 + 18 * q^15 - 228 * q^21 + 180 * q^23 + 18 * q^25 - 54 * q^27 + 144 * q^29 + 90 * q^31 + 324 * q^33 - 486 * q^35 - 102 * q^39 - 90 * q^41 - 90 * q^43 - 378 * q^45 + 378 * q^47 + 72 * q^49 + 54 * q^51 + 72 * q^57 - 252 * q^59 - 144 * q^61 - 318 * q^63 + 18 * q^65 + 594 * q^67 - 522 * q^69 + 648 * q^71 + 126 * q^73 + 438 * q^75 - 342 * q^77 + 72 * q^79 + 324 * q^81 - 594 * q^83 + 360 * q^85 - 1062 * q^87 + 648 * q^89 + 198 * q^91 + 462 * q^93 - 252 * q^95 + 702 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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