LMFDB - Embedded newform 324.3.o.a.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(5,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([0, 23]))

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

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

chi := DirichletCharacter("324.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.o (of order $54$, degree $18$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$18$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			29.2
Character	$\chi$	$=$	324.29
Dual form			324.3.o.a.257.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.97121 + 0.414613i) q^{3} +(-0.778741 + 0.734705i) q^{5} +(1.20130 - 0.140411i) q^{7} +(8.65619 - 2.46381i) q^{9} +O(q^{10})$	\(q+(-2.97121 + 0.414613i) q^{3} +(-0.778741 + 0.734705i) q^{5} +(1.20130 - 0.140411i) q^{7} +(8.65619 - 2.46381i) q^{9} +(5.77404 - 1.72863i) q^{11} +(-0.360819 - 6.19502i) q^{13} +(2.00919 - 2.50584i) q^{15} +(-8.28376 + 22.7594i) q^{17} +(-34.1830 + 12.4416i) q^{19} +(-3.51109 + 0.915264i) q^{21} +(-0.0387925 + 0.331891i) q^{23} +(-1.38697 + 23.8134i) q^{25} +(-24.6978 + 10.9095i) q^{27} +(8.38751 + 16.7009i) q^{29} +(-12.6693 + 17.0178i) q^{31} +(-16.4392 + 7.53013i) q^{33} +(-0.832338 + 0.991941i) q^{35} +(27.8439 - 23.3638i) q^{37} +(3.64061 + 18.2571i) q^{39} +(23.2739 + 35.3863i) q^{41} +(-39.9262 - 9.46267i) q^{43} +(-4.93076 + 8.27841i) q^{45} +(-73.5059 + 54.7231i) q^{47} +(-46.2558 + 10.9628i) q^{49} +(15.1764 - 71.0576i) q^{51} +(37.1563 - 21.4522i) q^{53} +(-3.22645 + 5.58837i) q^{55} +(96.4064 - 51.1393i) q^{57} +(38.6036 + 11.5572i) q^{59} +(-24.0027 + 55.6445i) q^{61} +(10.0527 - 4.17519i) q^{63} +(4.83249 + 4.55922i) q^{65} +(-32.8598 - 16.5028i) q^{67} +(-0.0223457 - 1.00220i) q^{69} +(28.4416 - 5.01502i) q^{71} +(4.09057 - 23.1988i) q^{73} +(-5.75236 - 71.3297i) q^{75} +(6.69361 - 2.88734i) q^{77} +(-24.3817 - 16.0361i) q^{79} +(68.8593 - 42.6544i) q^{81} +(18.8759 - 28.6995i) q^{83} +(-10.2706 - 23.8098i) q^{85} +(-31.8455 - 46.1443i) q^{87} +(41.3193 + 7.28571i) q^{89} +(-1.30330 - 7.39139i) q^{91} +(30.5874 - 55.8164i) q^{93} +(17.4788 - 34.8032i) q^{95} +(44.3589 - 47.0177i) q^{97} +(45.7222 - 29.1895i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q+O(q^{10}) $ 324 * q	$ 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) $ 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{37}{54}\right)$

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
$3$	−2.97121	+	0.414613i	−0.990404	+	0.138204i
$3$	−2.97121	+	0.414613i	−0.990404	+	0.138204i
$4$		0			0
$5$	−0.778741	+	0.734705i	−0.155748	+	0.146941i	−0.760171	−	0.649722i	$-0.774885\pi$
$5$	−0.778741	+	0.734705i	−0.155748	+	0.146941i	0.604423	+	0.796663i	$0.293404\pi$
$6$		0			0
$7$	1.20130	−	0.140411i	0.171614	−	0.0200588i	−0.0298521	−	0.999554i	$-0.509504\pi$
$7$	1.20130	−	0.140411i	0.171614	−	0.0200588i	0.201466	+	0.979496i	$0.435430\pi$
$8$		0			0
$9$	8.65619	−	2.46381i	0.961799	−	0.273756i
$10$		0			0
$11$	5.77404	−	1.72863i	0.524913	−	0.157149i	−0.0133736	−	0.999911i	$-0.504257\pi$
$11$	5.77404	−	1.72863i	0.524913	−	0.157149i	0.538286	+	0.842762i	$0.319072\pi$
$12$		0			0
$13$	−0.360819	−	6.19502i	−0.0277553	−	0.476540i	−0.983334	−	0.181806i	$-0.941806\pi$
$13$	−0.360819	−	6.19502i	−0.0277553	−	0.476540i	0.955579	−	0.294734i	$-0.0952312\pi$
$14$		0			0
$15$	2.00919	−	2.50584i	0.133946	−	0.167056i
$16$		0			0
$17$	−8.28376	+	22.7594i	−0.487280	+	1.33879i	0.415854	+	0.909431i	$0.363483\pi$
$17$	−8.28376	+	22.7594i	−0.487280	+	1.33879i	−0.903134	+	0.429359i	$0.858740\pi$
$18$		0			0
$19$	−34.1830	+	12.4416i	−1.79910	+	0.654820i	−0.800656	+	0.599125i	$0.795515\pi$
$19$	−34.1830	+	12.4416i	−1.79910	+	0.654820i	−0.998448	+	0.0556954i	$0.982262\pi$
$20$		0			0
$21$	−3.51109	+	0.915264i	−0.167195	+	0.0435840i
$22$		0			0
$23$	−0.0387925	+	0.331891i	−0.00168663	+	0.0144300i	−0.994055	−	0.108875i	$-0.965275\pi$
$23$	−0.0387925	+	0.331891i	−0.00168663	+	0.0144300i	0.992369	+	0.123305i	$0.0393493\pi$
$24$		0			0
$25$	−1.38697	+	23.8134i	−0.0554789	+	0.952537i
$26$		0			0
$27$	−24.6978	+	10.9095i	−0.914735	+	0.404054i
$28$		0			0
$29$	8.38751	+	16.7009i	0.289224	+	0.575893i	0.990583	−	0.136916i	$-0.0437190\pi$
$29$	8.38751	+	16.7009i	0.289224	+	0.575893i	−0.701358	+	0.712809i	$0.747423\pi$
$30$		0			0
$31$	−12.6693	+	17.0178i	−0.408687	+	0.548962i	−0.958042	−	0.286627i	$-0.907466\pi$
$31$	−12.6693	+	17.0178i	−0.408687	+	0.548962i	0.549355	+	0.835589i	$0.314873\pi$
$32$		0			0
$33$	−16.4392	+	7.53013i	−0.498157	+	0.228186i
$34$		0			0
$35$	−0.832338	+	0.991941i	−0.0237811	+	0.0283412i
$36$		0			0
$37$	27.8439	−	23.3638i	0.752539	−	0.631455i	−0.183634	−	0.982995i	$-0.558786\pi$
$37$	27.8439	−	23.3638i	0.752539	−	0.631455i	0.936173	+	0.351539i	$0.114342\pi$
$38$		0			0
$39$	3.64061	+	18.2571i	0.0933489	+	0.468131i
$40$		0			0
$41$	23.2739	+	35.3863i	0.567657	+	0.863081i	0.999239	−	0.0389929i	$-0.0124150\pi$
$41$	23.2739	+	35.3863i	0.567657	+	0.863081i	−0.431582	+	0.902074i	$0.642045\pi$
$42$		0			0
$43$	−39.9262	−	9.46267i	−0.928515	−	0.220062i	−0.261583	−	0.965181i	$-0.584245\pi$
$43$	−39.9262	−	9.46267i	−0.928515	−	0.220062i	−0.666932	+	0.745119i	$0.732393\pi$
$44$		0			0
$45$	−4.93076	+	8.27841i	−0.109573	+	0.183965i
$46$		0			0
$47$	−73.5059	+	54.7231i	−1.56396	+	1.16432i	−0.648985	+	0.760801i	$0.724806\pi$
$47$	−73.5059	+	54.7231i	−1.56396	+	1.16432i	−0.914970	+	0.403521i	$0.867786\pi$
$48$		0			0
$49$	−46.2558	+	10.9628i	−0.943996	+	0.223731i
$50$		0			0
$51$	15.1764	−	71.0576i	0.297577	−	1.39329i
$52$		0			0
$53$	37.1563	−	21.4522i	0.701062	−	0.404758i	−0.106681	−	0.994293i	$-0.534022\pi$
$53$	37.1563	−	21.4522i	0.701062	−	0.404758i	0.807743	+	0.589535i	$0.200689\pi$
$54$		0			0
$55$	−3.22645	+	5.58837i	−0.0586627	+	0.101607i
$56$		0			0
$57$	96.4064	−	51.1393i	1.69134	−	0.897180i
$58$		0			0
$59$	38.6036	+	11.5572i	0.654298	+	0.195884i	0.596711	−	0.802456i	$-0.296474\pi$
$59$	38.6036	+	11.5572i	0.654298	+	0.195884i	0.0575876	+	0.998340i	$0.481659\pi$
$60$		0			0
$61$	−24.0027	+	55.6445i	−0.393486	+	0.912204i	0.600183	+	0.799863i	$0.295094\pi$
$61$	−24.0027	+	55.6445i	−0.393486	+	0.912204i	−0.993670	+	0.112342i	$0.964165\pi$
$62$		0			0
$63$	10.0527	−	4.17519i	0.159567	−	0.0662728i
$64$		0			0
$65$	4.83249	+	4.55922i	0.0743461	+	0.0701419i
$66$		0			0
$67$	−32.8598	−	16.5028i	−0.490445	−	0.246311i	0.186348	−	0.982484i	$-0.440335\pi$
$67$	−32.8598	−	16.5028i	−0.490445	−	0.246311i	−0.676794	+	0.736173i	$0.736631\pi$
$68$		0			0
$69$	−0.0223457	−	1.00220i	−0.000323850	−	0.0145247i
$70$		0			0
$71$	28.4416	−	5.01502i	0.400586	−	0.0706340i	0.0302740	−	0.999542i	$-0.490362\pi$
$71$	28.4416	−	5.01502i	0.400586	−	0.0706340i	0.370312	+	0.928908i	$0.379251\pi$
$72$		0			0
$73$	4.09057	−	23.1988i	0.0560352	−	0.317792i	−0.943887	−	0.330269i	$-0.892861\pi$
$73$	4.09057	−	23.1988i	0.0560352	−	0.317792i	0.999922	+	0.0124771i	$0.00397170\pi$
$74$		0			0
$75$	−5.75236	−	71.3297i	−0.0766982	−	0.951063i
$76$		0			0
$77$	6.69361	−	2.88734i	0.0869300	−	0.0374979i
$78$		0			0
$79$	−24.3817	−	16.0361i	−0.308630	−	0.202989i	0.385740	−	0.922608i	$-0.373946\pi$
$79$	−24.3817	−	16.0361i	−0.308630	−	0.202989i	−0.694369	+	0.719619i	$0.744317\pi$
$80$		0			0
$81$	68.8593	−	42.6544i	0.850115	−	0.526597i
$82$		0			0
$83$	18.8759	−	28.6995i	0.227421	−	0.345777i	−0.703694	−	0.710504i	$-0.748467\pi$
$83$	18.8759	−	28.6995i	0.227421	−	0.345777i	0.931115	+	0.364727i	$0.118838\pi$
$84$		0			0
$85$	−10.2706	−	23.8098i	−0.120830	−	0.280116i
$86$		0			0
$87$	−31.8455	−	46.1443i	−0.366040	−	0.530395i
$88$		0			0
$89$	41.3193	+	7.28571i	0.464262	+	0.0818619i	0.400886	−	0.916128i	$-0.368702\pi$
$89$	41.3193	+	7.28571i	0.464262	+	0.0818619i	0.0633757	+	0.997990i	$0.479813\pi$
$90$		0			0
$91$	−1.30330	−	7.39139i	−0.0143220	−	0.0812240i
$92$		0			0
$93$	30.5874	−	55.8164i	0.328896	−	0.600177i
$94$		0			0
$95$	17.4788	−	34.8032i	0.183987	−	0.366349i
$96$		0			0
$97$	44.3589	−	47.0177i	0.457308	−	0.484718i	−0.457155	−	0.889387i	$-0.651132\pi$
$97$	44.3589	−	47.0177i	0.457308	−	0.484718i	0.914463	+	0.404669i	$0.132613\pi$
$98$		0			0
$99$	45.7222	−	29.1895i	0.461840	−	0.294844i
$100$		0			0
$101$	150.506	+	64.9217i	1.49015	+	0.642789i	0.976560	−	0.215244i	$-0.0690548\pi$
$101$	150.506	+	64.9217i	1.49015	+	0.642789i	0.513593	+	0.858034i	$0.328314\pi$
$102$		0			0
$103$	2.83290	−	9.46253i	0.0275038	−	0.0918692i	−0.943136	−	0.332408i	$-0.892139\pi$
$103$	2.83290	−	9.46253i	0.0275038	−	0.0918692i	0.970640	+	0.240539i	$0.0773241\pi$
$104$		0			0
$105$	2.06178	−	3.29237i	0.0196360	−	0.0313559i
$106$		0			0
$107$	−34.7426	−	20.0586i	−0.324697	−	0.187464i	0.328787	−	0.944404i	$-0.393360\pi$
$107$	−34.7426	−	20.0586i	−0.324697	−	0.187464i	−0.653484	+	0.756940i	$0.726693\pi$
$108$		0			0
$109$	−44.3700	−	76.8512i	−0.407065	−	0.705057i	0.587495	−	0.809228i	$-0.300114\pi$
$109$	−44.3700	−	76.8512i	−0.407065	−	0.705057i	−0.994559	+	0.104171i	$0.966781\pi$
$110$		0			0
$111$	−73.0433	+	80.9634i	−0.658048	+	0.729400i
$112$		0			0
$113$	34.3857	+	145.085i	0.304298	+	1.28394i	0.883376	+	0.468664i	$0.155265\pi$
$113$	34.3857	+	145.085i	0.304298	+	1.28394i	−0.579078	+	0.815272i	$0.696587\pi$
$114$		0			0
$115$	−0.213633	−	0.286958i	−0.00185767	−	0.00249529i
$116$		0			0
$117$	−18.3866	−	52.7363i	−0.157151	−	0.450738i
$118$		0			0
$119$	−6.75556	+	28.5039i	−0.0567694	+	0.239529i
$120$		0			0
$121$	−70.7427	+	46.5282i	−0.584650	+	0.384530i
$122$		0			0
$123$	−83.8234	−	95.4905i	−0.681491	−	0.776346i
$124$		0			0
$125$	−33.6203	−	40.0671i	−0.268962	−	0.320537i
$126$		0			0
$127$	−54.3795	−	45.6298i	−0.428185	−	0.359290i	0.403081	−	0.915164i	$-0.367939\pi$
$127$	−54.3795	−	45.6298i	−0.428185	−	0.359290i	−0.831266	+	0.555874i	$0.812384\pi$
$128$		0			0
$129$	122.552	+	11.5617i	0.950019	+	0.0896255i
$130$		0			0
$131$	114.940	+	85.5695i	0.877403	+	0.653202i	0.938631	−	0.344922i	$-0.112095\pi$
$131$	114.940	+	85.5695i	0.877403	+	0.653202i	−0.0612287	+	0.998124i	$0.519502\pi$
$132$		0			0
$133$	−39.3169	+	19.7457i	−0.295616	+	0.148464i
$134$		0			0
$135$	11.2180	−	26.6413i	0.0830963	−	0.197343i
$136$		0			0
$137$	−150.380	−	8.75864i	−1.09766	−	0.0639317i	−0.500262	−	0.865874i	$-0.666763\pi$
$137$	−150.380	−	8.75864i	−1.09766	−	0.0639317i	−0.597402	+	0.801942i	$0.703800\pi$
$138$		0			0
$139$	−91.9529	−	10.7477i	−0.661531	−	0.0773219i	−0.221299	−	0.975206i	$-0.571030\pi$
$139$	−91.9529	−	10.7477i	−0.661531	−	0.0773219i	−0.440232	+	0.897884i	$0.645104\pi$
$140$		0			0
$141$	195.713	−	193.070i	1.38803	−	1.36929i
$142$		0			0
$143$	−12.7923	−	35.1466i	−0.0894567	−	0.245780i
$144$		0			0
$145$	−18.8019	−	6.84334i	−0.129668	−	0.0471955i
$146$		0			0
$147$	132.890	−	51.7511i	0.904017	−	0.352049i
$148$		0			0
$149$	59.2658	−	3.45184i	0.397757	−	0.0231667i	0.141899	−	0.989881i	$-0.454679\pi$
$149$	59.2658	−	3.45184i	0.397757	−	0.0231667i	0.255858	+	0.966714i	$0.417642\pi$
$150$		0			0
$151$	77.5199	+	258.934i	0.513377	+	1.71480i	0.684019	+	0.729464i	$0.260230\pi$
$151$	77.5199	+	258.934i	0.513377	+	1.71480i	−0.170643	+	0.985333i	$0.554584\pi$
$152$		0			0
$153$	−15.6309	+	217.420i	−0.102163	+	1.42104i
$154$		0			0
$155$	−2.63697	−	22.5607i	−0.0170127	−	0.145553i
$156$		0			0
$157$	−148.884	−	157.808i	−0.948305	−	1.00514i	−0.999979	−	0.00648054i	$-0.997937\pi$
$157$	−148.884	−	157.808i	−0.948305	−	1.00514i	0.0516740	−	0.998664i	$-0.483544\pi$
$158$		0			0
$159$	−101.505	+	79.1444i	−0.638395	+	0.497764i
$160$		0			0
$161$			0.404146i			0.00251022i
$162$		0			0
$163$	89.0345			0.546224			0.273112	−	0.961982i	$-0.411947\pi$
$163$	89.0345			0.546224			0.273112	+	0.961982i	$0.411947\pi$
$164$		0			0
$165$	7.26945	−	17.9420i	0.0440573	−	0.108739i
$166$		0			0
$167$	69.4702	−	65.5418i	0.415989	−	0.392466i	−0.449592	−	0.893234i	$-0.648431\pi$
$167$	69.4702	−	65.5418i	0.415989	−	0.392466i	0.865581	+	0.500768i	$0.166949\pi$
$168$		0			0
$169$	129.609	−	15.1491i	0.766918	−	0.0896399i
$170$		0			0
$171$	−265.241	+	191.917i	−1.55112	+	1.12232i
$172$		0			0
$173$	−261.821	+	78.3839i	−1.51341	+	0.453086i	−0.932588	−	0.360942i	$-0.882455\pi$
$173$	−261.821	+	78.3839i	−1.51341	+	0.453086i	−0.580825	+	0.814028i	$0.697270\pi$
$174$		0			0
$175$	1.67751	+	28.8017i	0.00958576	+	0.164581i
$176$		0			0
$177$	−119.491	−	18.3332i	−0.675092	−	0.103577i
$178$		0			0
$179$	94.6285	−	259.990i	0.528651	−	1.45246i	−0.332009	−	0.943276i	$-0.607726\pi$
$179$	94.6285	−	259.990i	0.528651	−	1.45246i	0.860660	−	0.509180i	$-0.170051\pi$
$180$		0			0
$181$	228.647	−	83.2208i	1.26324	−	0.459783i	0.378388	−	0.925647i	$-0.376479\pi$
$181$	228.647	−	83.2208i	1.26324	−	0.459783i	0.884856	+	0.465864i	$0.154256\pi$
$182$		0			0
$183$	48.2461	−	175.283i	0.263640	−	0.957832i
$184$		0			0
$185$	−4.51771	+	38.6515i	−0.0244200	+	0.208927i
$186$		0			0
$187$	−8.48801	+	145.733i	−0.0453904	+	0.779323i
$188$		0			0
$189$	−28.1376	+	16.5733i	−0.148876	+	0.0876896i
$190$		0			0
$191$	72.9716	+	145.298i	0.382050	+	0.760725i	0.999668	−	0.0257533i	$-0.00819845\pi$
$191$	72.9716	+	145.298i	0.382050	+	0.760725i	−0.617618	+	0.786478i	$0.711902\pi$
$192$		0			0
$193$	−30.1128	+	40.4485i	−0.156025	+	0.209578i	−0.873261	−	0.487252i	$-0.837999\pi$
$193$	−30.1128	+	40.4485i	−0.156025	+	0.209578i	0.717237	+	0.696830i	$0.245407\pi$
$194$		0			0
$195$	−16.2487	−	11.5428i	−0.0833265	−	0.0591938i
$196$		0			0
$197$	−21.5514	+	25.6840i	−0.109398	+	0.130376i	−0.817965	−	0.575268i	$-0.804898\pi$
$197$	−21.5514	+	25.6840i	−0.109398	+	0.130376i	0.708567	+	0.705644i	$0.249342\pi$
$198$		0			0
$199$	125.777	−	105.539i	0.632045	−	0.530349i	−0.269519	−	0.962995i	$-0.586865\pi$
$199$	125.777	−	105.539i	0.632045	−	0.530349i	0.901564	+	0.432647i	$0.142420\pi$
$200$		0			0
$201$	104.476	+	35.4093i	0.519780	+	0.176166i
$202$		0			0
$203$	12.4209	+	18.8850i	0.0611866	+	0.0930296i
$204$		0			0
$205$	−44.1229	−	10.4573i	−0.215233	−	0.0510113i
$206$		0			0
$207$	0.481920	+	2.96849i	0.00232812	+	0.0143405i
$208$		0			0
$209$	−175.867	+	130.928i	−0.841468	+	0.626450i
$210$		0			0
$211$	−243.815	+	57.7853i	−1.15552	+	0.273864i	−0.763323	−	0.646017i	$-0.776434\pi$
$211$	−243.815	+	57.7853i	−1.15552	+	0.273864i	−0.392199	+	0.919880i	$0.628286\pi$
$212$		0			0
$213$	−82.4266	+	26.6929i	−0.386980	+	0.125319i
$214$		0			0
$215$	38.0444	−	21.9650i	0.176951	−	0.102163i
$216$		0			0
$217$	−12.8301	+	22.2224i	−0.0591248	+	0.102407i
$218$		0			0
$219$	−2.53543	+	70.6245i	−0.0115773	+	0.322486i
$220$		0			0
$221$	143.984	+	43.1060i	0.651512	+	0.195050i
$222$		0			0
$223$	−33.7256	+	78.1847i	−0.151236	+	0.350604i	−0.976945	−	0.213492i	$-0.931516\pi$
$223$	−33.7256	+	78.1847i	−0.151236	+	0.350604i	0.825709	+	0.564096i	$0.190775\pi$
$224$		0			0
$225$	46.6657	+	209.551i	0.207403	+	0.931337i
$226$		0			0
$227$	−76.3324	−	72.0159i	−0.336266	−	0.317251i	0.499524	−	0.866300i	$-0.333508\pi$
$227$	−76.3324	−	72.0159i	−0.336266	−	0.317251i	−0.835790	+	0.549049i	$0.814990\pi$
$228$		0			0
$229$	−96.3716	−	48.3996i	−0.420837	−	0.211352i	0.225762	−	0.974182i	$-0.427513\pi$
$229$	−96.3716	−	48.3996i	−0.420837	−	0.211352i	−0.646599	+	0.762830i	$0.723809\pi$
$230$		0			0
$231$	−18.6910	+	11.3542i	−0.0809134	+	0.0491522i
$232$		0			0
$233$	181.840	−	32.0634i	0.780431	−	0.137611i	0.230781	−	0.973006i	$-0.425872\pi$
$233$	181.840	−	32.0634i	0.780431	−	0.137611i	0.549650	+	0.835395i	$0.314761\pi$
$234$		0			0
$235$	17.0368	−	96.6203i	0.0724969	−	0.411150i
$236$		0			0
$237$	79.0921	+	37.5377i	0.333722	+	0.158387i
$238$		0			0
$239$	−128.718	+	55.5236i	−0.538569	+	0.232316i	−0.647949	−	0.761684i	$-0.724373\pi$
$239$	−128.718	+	55.5236i	−0.538569	+	0.232316i	0.109379	+	0.994000i	$0.465114\pi$
$240$		0			0
$241$	78.3341	+	51.5212i	0.325038	+	0.213781i	0.701532	−	0.712638i	$-0.252500\pi$
$241$	78.3341	+	51.5212i	0.325038	+	0.213781i	−0.376494	+	0.926419i	$0.622870\pi$
$242$		0			0
$243$	−186.911	+	155.285i	−0.769179	+	0.639033i
$244$		0			0
$245$	27.9669	−	42.5216i	0.114150	−	0.173557i
$246$		0			0
$247$	89.4097	+	207.275i	0.361983	+	0.839170i
$248$		0			0
$249$	−44.1852	+	93.0984i	−0.177451	+	0.373889i
$250$		0			0
$251$	−438.833	−	77.3781i	−1.74834	−	0.308279i	−0.794203	−	0.607652i	$-0.792111\pi$
$251$	−438.833	−	77.3781i	−1.74834	−	0.308279i	−0.954136	+	0.299373i	$0.903223\pi$
$252$		0			0
$253$	0.349729	+	1.98341i	0.00138233	+	0.00783957i
$254$		0			0
$255$	40.3879	+	66.4857i	0.158384	+	0.260728i
$256$		0			0
$257$	10.1176	−	20.1458i	0.0393682	−	0.0783885i	−0.873089	−	0.487562i	$-0.837886\pi$
$257$	10.1176	−	20.1458i	0.0393682	−	0.0783885i	0.912457	+	0.409173i	$0.134183\pi$
$258$		0			0
$259$	30.1683	−	31.9765i	0.116480	−	0.123461i
$260$		0			0
$261$	113.752	+	123.901i	0.435830	+	0.474717i
$262$		0			0
$263$	−298.996	−	128.974i	−1.13687	−	0.490397i	−0.257376	−	0.966311i	$-0.582858\pi$
$263$	−298.996	−	128.974i	−1.13687	−	0.490397i	−0.879492	+	0.475914i	$0.842117\pi$
$264$		0			0
$265$	−13.1741	+	44.0046i	−0.0497136	+	0.166055i
$266$		0			0
$267$	−125.789	−	4.51585i	−0.471121	−	0.0169133i
$268$		0			0
$269$	−262.094	−	151.320i	−0.974327	−	0.562528i	−0.0737745	−	0.997275i	$-0.523505\pi$
$269$	−262.094	−	151.320i	−0.974327	−	0.562528i	−0.900553	+	0.434747i	$0.856838\pi$
$270$		0			0
$271$	110.665	+	191.678i	0.408360	+	0.707300i	0.994706	−	0.102761i	$-0.0327676\pi$
$271$	110.665	+	191.678i	0.408360	+	0.707300i	−0.586346	+	0.810060i	$0.699434\pi$
$272$		0			0
$273$	6.93695	+	21.4210i	0.0254101	+	0.0784652i
$274$		0			0
$275$	33.1562	+	139.897i	0.120568	+	0.508717i
$276$		0			0
$277$	234.429	+	314.893i	0.846315	+	1.13680i	0.989129	+	0.147049i	$0.0469776\pi$
$277$	234.429	+	314.893i	0.846315	+	1.13680i	−0.142814	+	0.989750i	$0.545615\pi$
$278$		0			0
$279$	−67.7393	+	178.524i	−0.242793	+	0.639872i
$280$		0			0
$281$	17.3731	−	73.3029i	0.0618260	−	0.260864i	−0.933350	−	0.358967i	$-0.883129\pi$
$281$	17.3731	−	73.3029i	0.0618260	−	0.260864i	0.995176	+	0.0981024i	$0.0312773\pi$
$282$		0			0
$283$	327.917	−	215.674i	1.15872	−	0.762100i	0.183428	−	0.983033i	$-0.441281\pi$
$283$	327.917	−	215.674i	1.15872	−	0.762100i	0.975289	+	0.220933i	$0.0709103\pi$
$284$		0			0
$285$	−37.5034	+	110.654i	−0.131591	+	0.388261i
$286$		0			0
$287$	32.9275	+	39.2415i	0.114730	+	0.136730i
$288$		0			0
$289$	−227.984	−	191.301i	−0.788873	−	0.661943i
$290$		0			0
$291$	−112.306	+	158.091i	−0.385930	+	0.543269i
$292$		0			0
$293$	−170.905	−	127.234i	−0.583294	−	0.434246i	0.264641	−	0.964347i	$-0.414747\pi$
$293$	−170.905	−	127.234i	−0.583294	−	0.434246i	−0.847935	+	0.530101i	$0.822154\pi$
$294$		0			0
$295$	−38.5533	+	19.3622i	−0.130689	+	0.0656346i
$296$		0			0
$297$	−123.748	+	105.685i	−0.416660	+	0.355843i
$298$		0			0
$299$	2.07007	+	0.120568i	0.00692331	+	0.000403237i
$300$		0			0
$301$	−49.2918	−	5.76138i	−0.163760	−	0.0191408i
$302$		0			0
$303$	−474.101	−	130.495i	−1.56469	−	0.430675i
$304$		0			0
$305$	−22.1904	−	60.9675i	−0.0727553	−	0.199893i
$306$		0			0
$307$	309.152	+	112.522i	1.00701	+	0.366522i	0.792284	−	0.610152i	$-0.208892\pi$
$307$	309.152	+	112.522i	1.00701	+	0.366522i	0.214726	+	0.976674i	$0.431114\pi$
$308$		0			0
$309$	−4.49384	+	29.2897i	−0.0145432	+	0.0947888i
$310$		0			0
$311$	396.037	−	23.0665i	1.27343	−	0.0741688i	0.591931	−	0.805988i	$-0.298366\pi$
$311$	396.037	−	23.0665i	1.27343	−	0.0741688i	0.681498	+	0.731820i	$0.261329\pi$
$312$		0			0
$313$	−86.6535	−	289.443i	−0.276848	−	0.924738i	−0.977447	−	0.211182i	$-0.932269\pi$
$313$	−86.6535	−	289.443i	−0.276848	−	0.924738i	0.700599	−	0.713556i	$-0.252916\pi$
$314$		0			0
$315$	−4.76092	+	10.6372i	−0.0151140	+	0.0337687i
$316$		0			0
$317$	48.3177	+	413.385i	0.152422	+	1.30405i	0.825467	+	0.564451i	$0.190912\pi$
$317$	48.3177	+	413.385i	0.152422	+	1.30405i	−0.673045	+	0.739602i	$0.735014\pi$
$318$		0			0
$319$	77.2996	+	81.9328i	0.242318	+	0.256843i
$320$		0			0
$321$	111.544	+	45.1937i	0.347490	+	0.140790i
$322$		0			0
$323$		−	881.048i		−	2.72770i
$324$		0			0
$325$	148.025			0.455462
$326$		0			0
$327$	163.696	+	209.945i	0.500600	+	0.642033i
$328$		0			0
$329$	−80.6186	+	76.0597i	−0.245041	+	0.231184i
$330$		0			0
$331$	481.426	−	56.2707i	1.45446	−	0.170002i	0.648158	−	0.761506i	$-0.275540\pi$
$331$	481.426	−	56.2707i	1.45446	−	0.170002i	0.806302	+	0.591504i	$0.201465\pi$
$332$		0			0
$333$	183.459	−	270.844i	0.550926	−	0.813345i
$334$		0			0
$335$	37.7140	−	11.2908i	0.112579	−	0.0337040i
$336$		0			0
$337$	−27.0241	−	463.986i	−0.0801902	−	1.37681i	−0.763086	−	0.646297i	$-0.776317\pi$
$337$	−27.0241	−	463.986i	−0.0801902	−	1.37681i	0.682896	−	0.730516i	$-0.260720\pi$
$338$		0			0
$339$	−162.321	−	416.821i	−0.478824	−	1.22956i
$340$		0			0
$341$	−43.7355	+	120.162i	−0.128257	+	0.352382i
$342$		0			0
$343$	−109.718	+	39.9340i	−0.319877	+	0.116426i
$344$		0			0
$345$	0.753724	+	0.764039i	0.00218471	+	0.00221461i
$346$		0			0
$347$	37.1225	−	317.603i	0.106981	−	0.915284i	−0.828034	−	0.560677i	$-0.810541\pi$
$347$	37.1225	−	317.603i	0.106981	−	0.915284i	0.935016	−	0.354606i	$-0.115385\pi$
$348$		0			0
$349$	−17.5818	+	301.868i	−0.0503776	+	0.864951i	0.874580	+	0.484881i	$0.161137\pi$
$349$	−17.5818	+	301.868i	−0.0503776	+	0.864951i	−0.924958	+	0.380070i	$0.875900\pi$
$350$		0			0
$351$	76.4958	+	149.067i	0.217937	+	0.424693i
$352$		0			0
$353$	−80.0934	−	159.479i	−0.226894	−	0.451782i	0.751164	−	0.660115i	$-0.229493\pi$
$353$	−80.0934	−	159.479i	−0.226894	−	0.451782i	−0.978058	+	0.208333i	$0.933196\pi$
$354$		0			0
$355$	−18.4641	+	24.8016i	−0.0520115	+	0.0698635i
$356$		0			0
$357$	8.25408	−	87.4921i	0.0231207	−	0.245076i
$358$		0			0
$359$	189.196	−	225.475i	0.527009	−	0.628065i	−0.435214	−	0.900327i	$-0.643327\pi$
$359$	189.196	−	225.475i	0.527009	−	0.628065i	0.962223	+	0.272262i	$0.0877716\pi$
$360$		0			0
$361$	737.140	−	618.534i	2.04194	−	1.71339i
$362$		0			0
$363$	190.900	−	167.576i	0.525896	−	0.461641i
$364$		0			0
$365$	13.8588	+	21.0712i	0.0379692	+	0.0577294i
$366$		0			0
$367$	194.178	+	46.0211i	0.529096	+	0.125398i	0.486477	−	0.873693i	$-0.338282\pi$
$367$	194.178	+	46.0211i	0.529096	+	0.125398i	0.0426191	+	0.999091i	$0.486430\pi$
$368$		0			0
$369$	288.649	+	248.968i	0.782246	+	0.674710i
$370$		0			0
$371$	41.6235	−	30.9876i	0.112193	−	0.0835244i
$372$		0			0
$373$	−390.052	+	92.4440i	−1.04572	+	0.247839i	−0.717351	−	0.696712i	$-0.754646\pi$
$373$	−390.052	+	92.4440i	−1.04572	+	0.247839i	−0.328365	+	0.944551i	$0.606497\pi$
$374$		0			0
$375$	116.505	+	105.108i	0.310681	+	0.280289i
$376$		0			0
$377$	100.436	−	57.9868i	0.266409	−	0.153811i
$378$		0			0
$379$	106.140	−	183.841i	0.280054	−	0.485068i	−0.691344	−	0.722526i	$-0.742981\pi$
$379$	106.140	−	183.841i	0.280054	−	0.485068i	0.971398	+	0.237458i	$0.0763143\pi$
$380$		0			0
$381$	180.492	+	113.029i	0.473731	+	0.296665i
$382$		0			0
$383$	415.047	+	124.257i	1.08367	+	0.324430i	0.778358	−	0.627821i	$-0.216053\pi$
$383$	415.047	+	124.257i	1.08367	+	0.324430i	0.305315	+	0.952251i	$0.401238\pi$
$384$		0			0
$385$	−3.09125	+	7.16632i	−0.00802921	+	0.0186138i
$386$		0			0
$387$	−368.923	+	16.4596i	−0.953289	+	0.0425313i
$388$		0			0
$389$	−506.880	−	478.217i	−1.30303	−	1.22935i	−0.956645	−	0.291258i	$-0.905926\pi$
$389$	−506.880	−	478.217i	−1.30303	−	1.22935i	−0.346389	−	0.938091i	$-0.612592\pi$
$390$		0			0
$391$	−7.23230	−	3.63220i	−0.0184969	−	0.00928951i
$392$		0			0
$393$	−376.989	−	206.589i	−0.959258	−	0.525673i
$394$		0			0
$395$	30.7689	−	5.42539i	0.0778959	−	0.0137352i
$396$		0			0
$397$	102.876	−	583.438i	0.259133	−	1.46962i	−0.526103	−	0.850421i	$-0.676347\pi$
$397$	102.876	−	583.438i	0.259133	−	1.46962i	0.785236	−	0.619196i	$-0.212541\pi$
$398$		0			0
$399$	108.632	−	74.9699i	0.272261	−	0.187895i
$400$		0			0
$401$	−265.409	+	114.486i	−0.661868	+	0.285502i	−0.700395	−	0.713756i	$-0.746993\pi$
$401$	−265.409	+	114.486i	−0.661868	+	0.285502i	0.0385269	+	0.999258i	$0.487733\pi$
$402$		0			0
$403$	109.997	+	72.3463i	0.272946	+	0.179519i
$404$		0			0
$405$	−22.2852	+	83.8080i	−0.0550253	+	0.206933i
$406$		0			0
$407$	120.385	−	183.036i	0.295785	−	0.449719i
$408$		0			0
$409$	−42.3672	−	98.2183i	−0.103587	−	0.240143i	0.858538	−	0.512750i	$-0.171373\pi$
$409$	−42.3672	−	98.2183i	−0.103587	−	0.240143i	−0.962125	+	0.272607i	$0.912114\pi$
$410$		0			0
$411$	450.442	−	36.3258i	1.09597	−	0.0883838i
$412$		0			0
$413$	47.9971	+	8.46318i	0.116216	+	0.0204920i
$414$		0			0
$415$	6.38616	+	36.2177i	0.0153883	+	0.0872716i
$416$		0			0
$417$	277.668	−	6.19104i	0.665869	−	0.0148466i
$418$		0			0
$419$	258.406	−	514.528i	0.616720	−	1.22799i	−0.340939	−	0.940085i	$-0.610745\pi$
$419$	258.406	−	514.528i	0.616720	−	1.22799i	0.957659	−	0.287905i	$-0.0929586\pi$
$420$		0			0
$421$	−45.7837	+	48.5279i	−0.108750	+	0.115268i	−0.779462	−	0.626450i	$-0.784507\pi$
$421$	−45.7837	+	48.5279i	−0.108750	+	0.115268i	0.670712	+	0.741718i	$0.265989\pi$
$422$		0			0
$423$	−501.454	+	654.798i	−1.18547	+	1.54799i
$424$		0			0
$425$	−530.490	−	228.831i	−1.24821	−	0.538426i
$426$		0			0
$427$	−21.0212	+	70.2157i	−0.0492300	+	0.164440i
$428$		0			0
$429$	52.5809	+	99.1241i	0.122566	+	0.231058i
$430$		0			0
$431$	108.057	+	62.3866i	0.250712	+	0.144749i	0.620090	−	0.784531i	$-0.287096\pi$
$431$	108.057	+	62.3866i	0.250712	+	0.144749i	−0.369378	+	0.929279i	$0.620429\pi$
$432$		0			0
$433$	46.4896	+	80.5223i	0.107366	+	0.185964i	0.914702	−	0.404128i	$-0.132425\pi$
$433$	46.4896	+	80.5223i	0.107366	+	0.185964i	−0.807336	+	0.590092i	$0.799092\pi$
$434$		0			0
$435$	58.7018	+	12.5375i	0.134947	+	0.0288218i
$436$		0			0
$437$	−2.80321	−	11.8277i	−0.00641466	−	0.0270656i
$438$		0			0
$439$	409.665	+	550.276i	0.933178	+	1.25348i	0.967190	+	0.254054i	$0.0817642\pi$
$439$	409.665	+	550.276i	0.933178	+	1.25348i	−0.0340117	+	0.999421i	$0.510828\pi$
$440$		0			0
$441$	−373.389	+	208.862i	−0.846687	+	0.473609i
$442$		0			0
$443$	−129.689	+	547.203i	−0.292753	+	1.23522i	0.605537	+	0.795817i	$0.292958\pi$
$443$	−129.689	+	547.203i	−0.292753	+	1.23522i	−0.898290	+	0.439403i	$0.855190\pi$
$444$		0			0
$445$	−37.5299	+	24.6838i	−0.0843369	+	0.0554692i
$446$		0			0
$447$	−174.660	+	34.8285i	−0.390738	+	0.0779161i
$448$		0			0
$449$	8.81629	+	10.5068i	0.0196354	+	0.0234006i	0.775773	−	0.631012i	$-0.217360\pi$
$449$	8.81629	+	10.5068i	0.0196354	+	0.0234006i	−0.756137	+	0.654413i	$0.772916\pi$
$450$		0			0
$451$	195.555	+	164.090i	0.433602	+	0.363836i
$452$		0			0
$453$	−337.685	−	737.208i	−0.745443	−	1.62739i
$454$		0			0
$455$	6.44542	+	4.79844i	0.0141658	+	0.0105460i
$456$		0			0
$457$	−426.168	+	214.030i	−0.932534	+	0.468336i	−0.849133	−	0.528180i	$-0.822875\pi$
$457$	−426.168	+	214.030i	−0.932534	+	0.468336i	−0.0834016	+	0.996516i	$0.526578\pi$
$458$		0			0
$459$	−43.7022	−	652.480i	−0.0952117	−	1.42153i
$460$		0			0
$461$	319.978	+	18.6366i	0.694096	+	0.0404265i	0.401566	−	0.915830i	$-0.368466\pi$
$461$	319.978	+	18.6366i	0.694096	+	0.0404265i	0.292530	+	0.956256i	$0.405503\pi$
$462$		0			0
$463$	431.949	+	50.4875i	0.932934	+	0.109044i	0.568961	−	0.822365i	$-0.307346\pi$
$463$	431.949	+	50.4875i	0.932934	+	0.109044i	0.363974	+	0.931409i	$0.381420\pi$
$464$		0			0
$465$	17.1889	+	65.9392i	0.0369655	+	0.141805i
$466$		0			0
$467$	18.2564	+	50.1589i	0.0390929	+	0.107407i	0.957703	−	0.287758i	$-0.0929098\pi$
$467$	18.2564	+	50.1589i	0.0390929	+	0.107407i	−0.918610	+	0.395165i	$0.870688\pi$
$468$		0			0
$469$	−41.7916	−	15.2109i	−0.0891078	−	0.0324326i
$470$		0			0
$471$	507.795	+	407.151i	1.07812	+	0.864439i
$472$		0			0
$473$	−246.893	+	14.3799i	−0.521972	+	0.0304014i
$474$		0			0
$475$	−248.866	−	831.269i	−0.523928	−	1.75004i
$476$		0			0
$477$	268.778	−	277.240i	0.563475	−	0.581216i
$478$		0			0
$479$	99.2174	+	848.859i	0.207134	+	1.77215i	0.552337	+	0.833621i	$0.313736\pi$
$479$	99.2174	+	848.859i	0.207134	+	1.77215i	−0.345203	+	0.938528i	$0.612190\pi$
$480$		0			0
$481$	−154.786	−	164.064i	−0.321801	−	0.341089i
$482$		0			0
$483$	−0.167564	−	1.20080i	−0.000346924	−	0.00248614i
$484$		0			0
$485$			69.2053i			0.142691i
$486$		0			0
$487$	−465.553			−0.955962			−0.477981	−	0.878370i	$-0.658631\pi$
$487$	−465.553			−0.955962			−0.477981	+	0.878370i	$0.658631\pi$
$488$		0			0
$489$	−264.540	+	36.9149i	−0.540982	+	0.0754905i
$490$		0			0
$491$	229.030	−	216.079i	0.466456	−	0.440078i	−0.416780	−	0.909007i	$-0.636841\pi$
$491$	229.030	−	216.079i	0.466456	−	0.440078i	0.883236	+	0.468929i	$0.155360\pi$
$492$		0			0
$493$	−449.583	+	52.5487i	−0.911933	+	0.106590i
$494$		0			0
$495$	−14.1601	+	56.3234i	−0.0286062	+	0.113785i
$496$		0			0
$497$	33.4626	−	10.0180i	0.0673291	−	0.0201570i
$498$		0			0
$499$	8.24337	+	141.533i	0.0165198	+	0.283634i	0.996444	+	0.0842616i	$0.0268532\pi$
$499$	8.24337	+	141.533i	0.0165198	+	0.283634i	−0.979924	+	0.199372i	$0.936110\pi$
$500$		0			0
$501$	−179.236	+	223.542i	−0.357757	+	0.446191i
$502$		0			0
$503$	35.0652	−	96.3409i	0.0697122	−	0.191533i	−0.899944	−	0.436006i	$-0.856393\pi$
$503$	35.0652	−	96.3409i	0.0697122	−	0.191533i	0.969656	+	0.244473i	$0.0786150\pi$
$504$		0			0
$505$	−164.903	+	60.0198i	−0.326541	+	0.118851i
$506$		0			0
$507$	−378.815	+	98.7490i	−0.747170	+	0.194771i
$508$		0			0
$509$	−113.919	+	974.639i	−0.223809	+	1.91481i	0.152476	+	0.988307i	$0.451275\pi$
$509$	−113.919	+	974.639i	−0.223809	+	1.91481i	−0.376285	+	0.926504i	$0.622799\pi$
$510$		0			0
$511$	1.65661	−	28.4430i	0.00324191	−	0.0556614i
$512$		0			0
$513$	708.515	−	680.198i	1.38112	−	1.32592i
$514$		0			0
$515$	4.74607	+	9.45021i	0.00921567	+	0.0183499i
$516$		0			0
$517$	−329.830	+	443.038i	−0.637969	+	0.856941i
$518$		0			0
$519$	745.425	−	341.450i	1.43627	−	0.657899i
$520$		0			0
$521$	−576.849	+	687.462i	−1.10720	+	1.31950i	−0.164302	+	0.986410i	$0.552537\pi$
$521$	−576.849	+	687.462i	−1.10720	+	1.31950i	−0.942894	+	0.333094i	$0.891907\pi$
$522$		0			0
$523$	−572.084	+	480.036i	−1.09385	+	0.917850i	−0.996996	−	0.0774481i	$-0.975323\pi$
$523$	−572.084	+	480.036i	−1.09385	+	0.917850i	−0.0968552	+	0.995298i	$0.530878\pi$
$524$		0			0
$525$	−16.9258	−	84.8804i	−0.0322396	−	0.161677i
$526$		0			0
$527$	−282.367	−	429.318i	−0.535800	−	0.814645i
$528$		0			0
$529$	514.632	+	121.970i	0.972839	+	0.230567i
$530$		0			0
$531$	362.635	+	4.92919i	0.682928	+	0.00928284i
$532$		0			0
$533$	210.821	−	156.951i	0.395537	−	0.294466i
$534$		0			0
$535$	41.7927	−	9.90504i	0.0781171	−	0.0185141i
$536$		0			0
$537$	−173.366	+	811.718i	−0.322842	+	1.51158i
$538$		0			0
$539$	−248.132	+	143.259i	−0.460357	+	0.265787i
$540$		0			0
$541$	−401.428	+	695.295i	−0.742012	+	1.28520i	0.209566	+	0.977795i	$0.432795\pi$
$541$	−401.428	+	695.295i	−0.742012	+	1.28520i	−0.951578	+	0.307408i	$0.900538\pi$
$542$		0			0
$543$	−644.855	+	342.067i	−1.18758	+	0.629957i
$544$		0			0
$545$	91.0157	+	27.2483i	0.167001	+	0.0499969i
$546$		0			0
$547$	30.5581	−	70.8416i	0.0558649	−	0.129509i	−0.887998	−	0.459848i	$-0.847904\pi$
$547$	30.5581	−	70.8416i	0.0558649	−	0.129509i	0.943862	+	0.330339i	$0.107163\pi$
$548$		0			0
$549$	−70.6746	+	540.807i	−0.128733	+	0.985077i
$550$		0			0
$551$	−494.496	−	466.533i	−0.897451	−	0.846702i
$552$		0			0
$553$	−31.5413	−	15.8407i	−0.0570368	−	0.0286449i
$554$		0			0
$555$	−2.60234	−	116.715i	−0.00468890	−	0.210297i
$556$		0			0
$557$	771.582	−	136.051i	1.38525	−	0.244256i	0.569179	−	0.822214i	$-0.307261\pi$
$557$	771.582	−	136.051i	1.38525	−	0.244256i	0.816067	+	0.577958i	$0.196150\pi$
$558$		0			0
$559$	−44.2154	+	250.758i	−0.0790972	+	0.448583i
$560$		0			0
$561$	−35.2033	−	436.524i	−0.0627511	−	0.778118i
$562$		0			0
$563$	148.337	−	63.9865i	0.263477	−	0.113653i	−0.260244	−	0.965543i	$-0.583803\pi$
$563$	148.337	−	63.9865i	0.263477	−	0.113653i	0.523720	+	0.851890i	$0.324544\pi$
$564$		0			0
$565$	−133.372	−	87.7202i	−0.236057	−	0.155257i
$566$		0			0
$567$	76.7312	−	60.9091i	0.135328	−	0.107423i
$568$		0			0
$569$	201.744	−	306.737i	0.354559	−	0.539081i	−0.613535	−	0.789668i	$-0.710253\pi$
$569$	201.744	−	306.737i	0.354559	−	0.539081i	0.968094	+	0.250586i	$0.0806234\pi$
$570$		0			0
$571$	242.246	+	561.588i	0.424248	+	0.983517i	0.987556	+	0.157270i	$0.0502693\pi$
$571$	242.246	+	561.588i	0.424248	+	0.983517i	−0.563308	+	0.826247i	$0.690471\pi$
$572$		0			0
$573$	−277.057	−	401.457i	−0.483520	−	0.700624i
$574$		0			0
$575$	−7.84965	−	1.38411i	−0.0136516	−	0.00240714i
$576$		0			0
$577$	−44.5737	−	252.790i	−0.0772508	−	0.438111i	−0.998761	−	0.0497578i	$-0.984155\pi$
$577$	−44.5737	−	252.790i	−0.0772508	−	0.438111i	0.921510	−	0.388354i	$-0.126956\pi$
$578$		0			0
$579$	72.7010	−	132.666i	0.125563	−	0.229130i
$580$		0			0
$581$	18.6459	−	37.1269i	0.0320927	−	0.0639018i
$582$		0			0
$583$	177.459	−	188.095i	0.304389	−	0.322634i
$584$		0			0
$585$	53.0640	+	27.5592i	0.0907078	+	0.0471097i
$586$		0			0
$587$	771.561	+	332.819i	1.31441	+	0.566983i	0.933815	−	0.357757i	$-0.116458\pi$
$587$	771.561	+	332.819i	1.31441	+	0.566983i	0.380599	+	0.924740i	$0.375718\pi$
$588$		0			0
$589$	221.346	−	739.346i	0.375799	−	1.25526i
$590$		0			0
$591$	53.3849	−	85.2481i	0.0903299	−	0.144244i
$592$		0			0
$593$	−599.640	−	346.203i	−1.01120	−	0.583815i	−0.0996558	−	0.995022i	$-0.531774\pi$
$593$	−599.640	−	346.203i	−1.01120	−	0.583815i	−0.911542	+	0.411207i	$0.865108\pi$
$594$		0			0
$595$	−15.6811	−	27.1605i	−0.0263549	−	0.0456479i
$596$		0			0
$597$	−329.952	+	365.729i	−0.552683	+	0.612611i
$598$		0			0
$599$	244.171	+	1030.24i	0.407631	+	1.71993i	0.659090	+	0.752064i	$0.270942\pi$
$599$	244.171	+	1030.24i	0.407631	+	1.71993i	−0.251459	+	0.967868i	$0.580910\pi$
$600$		0			0
$601$	−158.278	−	212.604i	−0.263357	−	0.353750i	0.650700	−	0.759335i	$-0.274475\pi$
$601$	−158.278	−	212.604i	−0.263357	−	0.353750i	−0.914058	+	0.405585i	$0.867068\pi$
$602$		0			0
$603$	−325.101	−	61.8914i	−0.539139	−	0.102639i
$604$		0			0
$605$	20.9058	−	88.2084i	0.0345550	−	0.145799i
$606$		0			0
$607$	58.2652	−	38.3216i	0.0959887	−	0.0631328i	−0.500607	−	0.865675i	$-0.666890\pi$
$607$	58.2652	−	38.3216i	0.0959887	−	0.0631328i	0.596596	+	0.802542i	$0.296520\pi$
$608$		0			0
$609$	−44.7350	−	50.9615i	−0.0734565	−	0.0836806i
$610$		0			0
$611$	365.533	+	435.626i	0.598254	+	0.712971i
$612$		0			0
$613$	−797.070	−	668.821i	−1.30028	−	1.09106i	−0.990097	−	0.140384i	$-0.955166\pi$
$613$	−797.070	−	668.821i	−1.30028	−	1.09106i	−0.310180	−	0.950678i	$-0.600389\pi$
$614$		0			0
$615$	135.434	+	12.7770i	0.220218	+	0.0207755i
$616$		0			0
$617$	−82.5136	−	61.4291i	−0.133733	−	0.0995609i	0.528213	−	0.849112i	$-0.322862\pi$
$617$	−82.5136	−	61.4291i	−0.133733	−	0.0995609i	−0.661947	+	0.749551i	$0.730270\pi$
$618$		0			0
$619$	−902.223	+	453.114i	−1.45755	+	0.732009i	−0.988508	−	0.151167i	$-0.951697\pi$
$619$	−902.223	+	453.114i	−1.45755	+	0.732009i	−0.469042	+	0.883176i	$0.655401\pi$
$620$		0			0
$621$	−2.66266	−	8.62020i	−0.00428770	−	0.0138812i
$622$		0			0
$623$	50.6597	+	2.95059i	0.0813157	+	0.00473610i
$624$		0			0
$625$	−536.693	−	62.7304i	−0.858709	−	0.100369i
$626$		0			0
$627$	468.253	−	461.932i	0.746815	−	0.736733i
$628$		0			0
$629$	301.095	+	827.253i	0.478689	+	1.31519i
$630$		0			0
$631$	721.784	+	262.708i	1.14387	+	0.416336i	0.843311	−	0.537426i	$-0.180603\pi$
$631$	721.784	+	262.708i	1.14387	+	0.416336i	0.300562	+	0.953762i	$0.402826\pi$
$632$		0			0
$633$	700.468	−	272.781i	1.10658	−	0.430934i
$634$		0			0
$635$	75.8720	−	4.41904i	0.119483	−	0.00695912i
$636$		0			0
$637$	84.6049	+	282.600i	0.132818	+	0.443642i
$638$		0			0
$639$	233.840	−	113.485i	0.365946	−	0.177599i
$640$		0			0
$641$	60.7427	+	519.687i	0.0947625	+	0.810745i	0.954131	+	0.299388i	$0.0967826\pi$
$641$	60.7427	+	519.687i	0.0947625	+	0.810745i	−0.859369	+	0.511356i	$0.829143\pi$
$642$		0			0
$643$	−438.664	−	464.957i	−0.682215	−	0.723106i	0.290044	−	0.957013i	$-0.406330\pi$
$643$	−438.664	−	464.957i	−0.682215	−	0.723106i	−0.972259	+	0.233908i	$0.924849\pi$
$644$		0			0
$645$	−103.931	+	81.0362i	−0.161133	+	0.125638i
$646$		0			0
$647$		−	60.2187i		−	0.0930738i	−0.998917	−	0.0465369i	$-0.985181\pi$
$647$		−	60.2187i		−	0.0930738i	0.998917	−	0.0465369i	$-0.0148185\pi$
$648$		0			0
$649$	242.877			0.374233
$650$		0			0
$651$	28.9072	−	71.3468i	0.0444043	−	0.109596i
$652$		0			0
$653$	−578.261	+	545.561i	−0.885546	+	0.835469i	−0.987222	−	0.159348i	$-0.949061\pi$
$653$	−578.261	+	545.561i	−0.885546	+	0.835469i	0.101677	+	0.994817i	$0.467579\pi$
$654$		0			0
$655$	−152.377	+	17.8103i	−0.232636	+	0.0271913i
$656$		0			0
$657$	−21.7486	−	210.892i	−0.0331028	−	0.320992i
$658$		0			0
$659$	−45.9575	+	13.7588i	−0.0697382	+	0.0208782i	−0.321482	−	0.946916i	$-0.604181\pi$
$659$	−45.9575	+	13.7588i	−0.0697382	+	0.0208782i	0.251744	+	0.967794i	$0.418996\pi$
$660$		0			0
$661$	−0.623298	−	10.7016i	−0.000942962	−	0.0161900i	0.997804	−	0.0662379i	$-0.0210996\pi$
$661$	−0.623298	−	10.7016i	−0.000942962	−	0.0161900i	−0.998747	+	0.0500479i	$0.984063\pi$
$662$		0			0
$663$	−445.679	−	68.3793i	−0.672216	−	0.103136i
$664$		0			0
$665$	16.1104	−	44.2631i	0.0242262	−	0.0665610i
$666$		0			0
$667$	−5.86825	+	2.13587i	−0.00879798	+	0.00320220i
$668$		0			0
$669$	67.7894	−	246.286i	0.101330	−	0.368141i
$670$		0			0
$671$	−42.4035	+	362.785i	−0.0631945	+	0.540664i
$672$		0			0
$673$	−4.39869	+	75.5226i	−0.00653594	+	0.112218i	−0.999998	−	0.00194400i	$-0.999381\pi$
$673$	−4.39869	+	75.5226i	−0.00653594	+	0.112218i	0.993462	+	0.114162i	$0.0364182\pi$
$674$		0			0
$675$	−225.536	−	603.271i	−0.334128	−	0.893735i
$676$		0			0
$677$	487.570	+	970.833i	0.720193	+	1.43402i	0.893458	+	0.449146i	$0.148272\pi$
$677$	487.570	+	970.833i	0.720193	+	1.43402i	−0.173266	+	0.984875i	$0.555432\pi$
$678$		0			0
$679$	46.6863	−	62.7106i	0.0687575	−	0.0923573i
$680$		0			0
$681$	256.658	+	182.326i	0.376885	+	0.267733i
$682$		0			0
$683$	−398.492	+	474.905i	−0.583444	+	0.695321i	−0.974332	−	0.225117i	$-0.927724\pi$
$683$	−398.492	+	474.905i	−0.583444	+	0.695321i	0.390888	+	0.920438i	$0.372168\pi$
$684$		0			0
$685$	123.542	−	103.664i	0.180353	−	0.151335i
$686$		0			0
$687$	306.407	+	103.849i	0.446008	+	0.151162i
$688$		0			0
$689$	−146.303	−	222.443i	−0.212342	−	0.322850i
$690$		0			0
$691$	−630.545	−	149.442i	−0.912511	−	0.216269i	−0.252563	−	0.967580i	$-0.581274\pi$
$691$	−630.545	−	149.442i	−0.912511	−	0.216269i	−0.659948	+	0.751311i	$0.729422\pi$
$692$		0			0
$693$	50.8273	−	41.4851i	0.0733439	−	0.0598631i
$694$		0			0
$695$	79.5039	−	59.1885i	0.114394	−	0.0851633i
$696$		0			0
$697$	−998.168	+	236.570i	−1.43209	+	0.339412i
$698$		0			0
$699$	−526.993	+	170.661i	−0.753924	+	0.244150i
$700$		0			0
$701$	921.497	−	532.027i	1.31455	−	0.758954i	0.331701	−	0.943385i	$-0.392377\pi$
$701$	921.497	−	532.027i	1.31455	−	0.758954i	0.982846	+	0.184431i	$0.0590442\pi$
$702$		0			0
$703$	−661.105	+	1145.07i	−0.940406	+	1.62883i
$704$		0			0
$705$	−10.5598	+	294.143i	−0.0149784	+	0.417224i
$706$		0			0
$707$	189.917	+	56.8575i	0.268624	+	0.0804208i
$708$		0			0
$709$	160.548	−	372.193i	0.226444	−	0.524955i	−0.766680	−	0.642030i	$-0.778092\pi$
$709$	160.548	−	372.193i	0.226444	−	0.524955i	0.993123	+	0.117075i	$0.0373517\pi$
$710$		0			0
$711$	−250.563	−	78.7399i	−0.352409	−	0.110745i
$712$		0			0
$713$	−5.15659	−	4.86499i	−0.00723225	−	0.00682327i
$714$		0			0
$715$	35.7843	+	17.9715i	0.0500479	+	0.0251350i
$716$		0			0
$717$	359.428	−	218.340i	0.501294	−	0.304519i
$718$		0			0
$719$	−160.541	+	28.3078i	−0.223284	+	0.0393710i	−0.284171	−	0.958774i	$-0.591718\pi$
$719$	−160.541	+	28.3078i	−0.223284	+	0.0393710i	0.0608866	+	0.998145i	$0.480607\pi$
$720$		0			0
$721$	2.07450	−	11.7651i	0.00287725	−	0.0163177i
$722$		0			0
$723$	−254.109	−	120.602i	−0.351464	−	0.166808i
$724$		0			0
$725$	−409.339	+	176.572i	−0.564605	+	0.243547i
$726$		0			0
$727$	−604.538	−	397.611i	−0.831552	−	0.546920i	0.0608578	−	0.998146i	$-0.480616\pi$
$727$	−604.538	−	397.611i	−0.831552	−	0.546920i	−0.892410	+	0.451226i	$0.850987\pi$
$728$		0			0
$729$	490.967	−	538.880i	0.673481	−	0.739205i
$730$		0			0
$731$	546.104	−	830.310i	0.747064	−	1.13586i
$732$		0			0
$733$	442.571	+	1025.99i	0.603780	+	1.39972i	0.896295	+	0.443459i	$0.146249\pi$
$733$	442.571	+	1025.99i	0.603780	+	1.39972i	−0.292515	+	0.956261i	$0.594492\pi$
$734$		0			0
$735$	−65.4655	+	137.936i	−0.0890687	+	0.187668i
$736$		0			0
$737$	−218.261	−	38.4854i	−0.296149	−	0.0522190i
$738$		0			0
$739$	−121.724	−	690.330i	−0.164714	−	0.934140i	−0.949359	−	0.314194i	$-0.898266\pi$
$739$	−121.724	−	690.330i	−0.164714	−	0.934140i	0.784645	−	0.619946i	$-0.212845\pi$
$740$		0			0
$741$	−351.594	−	578.787i	−0.474486	−	0.781090i
$742$		0			0
$743$	410.024	−	816.424i	0.551849	−	1.09882i	−0.428864	−	0.903369i	$-0.641086\pi$
$743$	410.024	−	816.424i	0.551849	−	1.09882i	0.980713	−	0.195452i	$-0.0626175\pi$
$744$		0			0
$745$	−43.6166	+	46.2309i	−0.0585458	+	0.0620549i
$746$		0			0
$747$	92.6838	−	294.935i	0.124075	−	0.394826i
$748$		0			0
$749$	−44.5526	−	19.2181i	−0.0594827	−	0.0256583i
$750$		0			0
$751$	−364.595	+	1217.83i	−0.485480	+	1.62162i	0.267490	+	0.963561i	$0.413806\pi$
$751$	−364.595	+	1217.83i	−0.485480	+	1.62162i	−0.752970	+	0.658055i	$0.771379\pi$
$752$		0			0
$753$	1335.95	+	47.9608i	1.77417	+	0.0636929i
$754$		0			0
$755$	−250.608	−	144.689i	−0.331931	−	0.191641i
$756$		0			0
$757$	480.896	+	832.936i	0.635265	+	1.10031i	0.986459	+	0.164008i	$0.0524424\pi$
$757$	480.896	+	832.936i	0.635265	+	1.10031i	−0.351194	+	0.936303i	$0.614224\pi$
$758$		0			0
$759$	−1.86147	−	5.74813i	−0.00245252	−	0.00757329i
$760$		0			0
$761$	−30.8440	−	130.141i	−0.0405309	−	0.171013i	0.949015	−	0.315230i	$-0.102082\pi$
$761$	−30.8440	−	130.141i	−0.0405309	−	0.171013i	−0.989546	+	0.144217i	$0.953934\pi$
$762$		0			0
$763$	−64.0923	−	86.0909i	−0.0840004	−	0.112832i
$764$		0			0
$765$	−147.567	−	180.798i	−0.192898	−	0.236337i
$766$		0			0
$767$	57.6679	−	243.320i	0.0751864	−	0.317236i
$768$		0			0
$769$	1056.66	−	694.974i	1.37407	−	0.903737i	0.374343	−	0.927290i	$-0.377868\pi$
$769$	1056.66	−	694.974i	1.37407	−	0.903737i	0.999723	+	0.0235536i	$0.00749804\pi$
$770$		0			0
$771$	−21.7089	+	64.0524i	−0.0281568	+	0.0830771i
$772$		0			0
$773$	811.830	+	967.501i	1.05023	+	1.25162i	0.966916	+	0.255095i	$0.0821067\pi$
$773$	811.830	+	967.501i	1.05023	+	1.25162i	0.0833162	+	0.996523i	$0.473449\pi$
$774$		0			0
$775$	−387.681	−	325.303i	−0.500233	−	0.419745i
$776$		0			0
$777$	−76.3784	+	107.517i	−0.0982991	+	0.138375i
$778$		0			0
$779$	−1235.83	−	920.044i	−1.58644	−	1.18106i
$780$		0			0
$781$	155.554	−	78.1220i	0.199172	−	0.100028i
$782$		0			0
$783$	−389.351	−	320.973i	−0.497256	−	0.409927i
$784$		0			0
$785$	231.884	+	13.5057i	0.295394	+	0.0172047i
$786$		0			0
$787$	1286.56	+	150.377i	1.63476	+	0.191076i	0.883336	−	0.468740i	$-0.155292\pi$
$787$	1286.56	+	150.377i	1.63476	+	0.191076i	0.751427	+	0.659817i	$0.229366\pi$
$788$		0			0
$789$	941.855	+	259.242i	1.19373	+	0.328571i
$790$		0			0
$791$	61.6790	+	169.462i	0.0779759	+	0.214237i
$792$		0			0
$793$	353.379	+	128.619i	0.445623	+	0.162194i
$794$		0			0
$795$	20.8982	−	136.209i	0.0262870	−	0.171332i
$796$		0			0
$797$	911.902	−	53.1122i	1.14417	−	0.0666402i	0.524433	−	0.851452i	$-0.324277\pi$
$797$	911.902	−	53.1122i	1.14417	−	0.0666402i	0.619735	+	0.784811i	$0.287240\pi$
$798$		0			0
$799$	−636.562	−	2126.27i	−0.796699	−	2.66116i
$800$		0			0
$801$	375.619	−	38.7363i	0.468937	−	0.0483599i
$802$		0			0
$803$	−16.4831	−	141.022i	−0.0205269	−	0.175619i
$804$		0			0
$805$	−0.296928	−	0.314725i	−0.000368855	−	0.000390963i
$806$		0			0
$807$	841.476	+	340.936i	1.04272	+	0.422474i
$808$		0			0
$809$			613.832i			0.758754i	0.925242	+	0.379377i	$0.123862\pi$
$809$			613.832i			0.758754i	−0.925242	+	0.379377i	$0.876138\pi$
$810$		0			0
$811$	−1169.38			−1.44189			−0.720947	−	0.692991i	$-0.756293\pi$
$811$	−1169.38			−1.44189			−0.720947	+	0.692991i	$0.756293\pi$
$812$		0			0
$813$	−408.283	−	523.633i	−0.502193	−	0.644075i
$814$		0			0
$815$	−69.3348	+	65.4140i	−0.0850734	+	0.0802626i
$816$		0			0
$817$	1482.53	−	173.282i	1.81460	−	0.212096i
$818$		0			0
$819$	−29.4926	−	60.7702i	−0.0360105	−	0.0742005i
$820$		0			0
$821$	525.856	−	157.431i	0.640506	−	0.191755i	0.0499504	−	0.998752i	$-0.484094\pi$
$821$	525.856	−	157.431i	0.640506	−	0.191755i	0.590556	+	0.806997i	$0.298908\pi$
$822$		0			0
$823$	−76.4856	−	1313.21i	−0.0929351	−	1.59563i	−0.646557	−	0.762866i	$-0.723792\pi$
$823$	−76.4856	−	1313.21i	−0.0929351	−	1.59563i	0.553622	−	0.832768i	$-0.313245\pi$
$824$		0			0
$825$	−156.517	−	401.917i	−0.189718	−	0.487172i
$826$		0			0
$827$	−340.563	+	935.690i	−0.411806	+	1.13143i	0.544424	+	0.838810i	$0.316748\pi$
$827$	−340.563	+	935.690i	−0.411806	+	1.13143i	−0.956230	+	0.292617i	$0.905474\pi$
$828$		0			0
$829$	−987.884	+	359.560i	−1.19166	+	0.433728i	−0.860305	−	0.509779i	$-0.829727\pi$
$829$	−987.884	+	359.560i	−1.19166	+	0.433728i	−0.331352	+	0.943507i	$0.607505\pi$
$830$		0			0
$831$	−827.098	−	838.417i	−0.995305	−	1.00893i
$832$		0			0
$833$	133.664	−	1143.57i	0.160461	−	1.37283i
$834$		0			0
$835$	−5.94549	+	102.080i	−0.00712035	+	0.122252i
$836$		0			0
$837$	127.249	−	558.519i	0.152030	−	0.667287i
$838$		0			0
$839$	538.589	+	1072.42i	0.641941	+	1.27821i	0.945570	+	0.325420i	$0.105506\pi$
$839$	538.589	+	1072.42i	0.641941	+	1.27821i	−0.303628	+	0.952791i	$0.598198\pi$
$840$		0			0
$841$	293.641	−	394.428i	0.349156	−	0.468998i
$842$		0			0
$843$	−21.2268	+	225.002i	−0.0251801	+	0.266906i
$844$		0			0
$845$	−89.8019	+	107.022i	−0.106274	+	0.126653i
$846$		0			0
$847$	−78.4497	+	65.8271i	−0.0926207	+	0.0777180i
$848$		0			0
$849$	−884.889	+	776.772i	−1.04227	+	0.914926i
$850$		0			0
$851$	6.67411	+	10.1475i	0.00784267	+	0.0119242i
$852$		0			0
$853$	−1360.51	−	322.447i	−1.59497	−	0.378016i	−0.665352	−	0.746530i	$-0.731718\pi$
$853$	−1360.51	−	322.447i	−1.59497	−	0.378016i	−0.929622	+	0.368514i	$0.879867\pi$
$854$		0			0
$855$	65.5516	−	344.327i	0.0766686	−	0.402722i
$856$		0			0
$857$	−393.489	+	292.941i	−0.459146	+	0.341822i	−0.801751	−	0.597658i	$-0.796098\pi$
$857$	−393.489	+	292.941i	−0.459146	+	0.341822i	0.342605	+	0.939480i	$0.388691\pi$
$858$		0			0
$859$	−31.0884	+	7.36808i	−0.0361914	+	0.00857751i	−0.248672	−	0.968588i	$-0.579994\pi$
$859$	−31.0884	+	7.36808i	−0.0361914	+	0.00857751i	0.212480	+	0.977165i	$0.431846\pi$
$860$		0			0
$861$	−114.105	−	102.943i	−0.132526	−	0.119562i
$862$		0			0
$863$	−300.607	+	173.556i	−0.348328	+	0.201107i	−0.663949	−	0.747778i	$-0.731121\pi$
$863$	−300.607	+	173.556i	−0.348328	+	0.201107i	0.315620	+	0.948886i	$0.397787\pi$
$864$		0			0
$865$	146.301	−	253.402i	0.169135	−	0.292950i
$866$		0			0
$867$	756.705	+	473.872i	0.872786	+	0.546565i
$868$		0			0
$869$	−168.502	−	50.4461i	−0.193903	−	0.0580508i
$870$		0			0
$871$	−90.3789	+	209.522i	−0.103765	+	0.240553i
$872$		0			0
$873$	268.137	−	516.286i	0.307144	−	0.591393i
$874$		0			0
$875$	−46.0138	−	43.4117i	−0.0525871	−	0.0496134i
$876$		0			0
$877$	298.106	+	149.714i	0.339916	+	0.170712i	0.610565	−	0.791966i	$-0.290942\pi$
$877$	298.106	+	149.714i	0.339916	+	0.170712i	−0.270650	+	0.962678i	$0.587239\pi$
$878$		0			0
$879$	560.548	+	307.180i	0.637711	+	0.349465i
$880$		0			0
$881$	865.599	−	152.629i	0.982519	−	0.173245i	0.340760	−	0.940150i	$-0.389316\pi$
$881$	865.599	−	152.629i	0.982519	−	0.173245i	0.641760	+	0.766906i	$0.278205\pi$
$882$		0			0
$883$	80.3735	−	455.821i	0.0910232	−	0.516218i	−0.904870	−	0.425687i	$-0.860032\pi$
$883$	80.3735	−	455.821i	0.0910232	−	0.516218i	0.995894	−	0.0905312i	$-0.0288565\pi$
$884$		0			0
$885$	106.522	−	73.5139i	0.120364	−	0.0830666i
$886$		0			0
$887$	−916.767	+	395.455i	−1.03356	+	0.445834i	−0.844174	−	0.536069i	$-0.819909\pi$
$887$	−916.767	+	395.455i	−1.03356	+	0.445834i	−0.189385	+	0.981903i	$0.560650\pi$
$888$		0			0
$889$	−71.7327	−	47.1794i	−0.0806893	−	0.0530702i
$890$		0			0
$891$	323.863	−	365.321i	0.363482	−	0.410012i
$892$		0			0
$893$	1831.81	−	2785.13i	2.05130	−	3.11885i
$894$		0			0
$895$	117.324	+	271.989i	0.131089	+	0.303898i
$896$		0			0
$897$	−6.20060	+	0.500045i	−0.00691260	+	0.000557464i
$898$		0			0
$899$	−390.477	−	68.8516i	−0.434346	−	0.0765869i
$900$		0			0
$901$	180.446	+	1023.36i	0.200273	+	1.13580i
$902$		0			0
$903$	148.845	−	3.31874i	0.164834	−	0.00367523i
$904$		0			0
$905$	−116.914	+	232.796i	−0.129187	+	0.257233i
$906$		0			0
$907$	954.109	−	1011.30i	1.05194	−	1.11499i	0.0587744	−	0.998271i	$-0.481281\pi$
$907$	954.109	−	1011.30i	1.05194	−	1.11499i	0.993165	−	0.116719i	$-0.0372378\pi$
$908$		0			0
$909$	1462.76	+	191.159i	1.60920	+	0.210295i
$910$		0			0
$911$	477.153	+	205.824i	0.523768	+	0.225932i	0.641513	−	0.767112i	$-0.278307\pi$
$911$	477.153	+	205.824i	0.523768	+	0.225932i	−0.117745	+	0.993044i	$0.537566\pi$
$912$		0			0
$913$	59.3796	−	198.342i	0.0650379	−	0.217242i
$914$		0			0
$915$	91.2102	+	171.947i	0.0996833	+	0.187920i
$916$		0			0
$917$	150.092	+	86.6554i	0.163677	+	0.0944988i
$918$		0			0
$919$	373.535	+	646.982i	0.406458	+	0.704006i	0.994490	−	0.104832i	$-0.0334303\pi$
$919$	373.535	+	646.982i	0.406458	+	0.704006i	−0.588032	+	0.808838i	$0.700097\pi$
$920$		0			0
$921$	−965.210	−	206.149i	−1.04800	−	0.223831i
$922$		0			0
$923$	−41.3304	−	174.387i	−0.0447783	−	0.188935i
$924$		0			0
$925$	517.754	+	695.464i	0.559734	+	0.751853i
$926$		0			0
$927$	1.20824	−	88.8892i	0.00130339	−	0.0958891i
$928$		0			0
$929$	282.980	−	1193.99i	0.304607	−	1.28524i	−0.578351	−	0.815788i	$-0.696304\pi$
$929$	282.980	−	1193.99i	0.304607	−	1.28524i	0.882958	−	0.469451i	$-0.155548\pi$
$930$		0			0
$931$	1444.77	−	950.237i	1.55184	−	1.02066i
$932$		0			0
$933$	−1167.14	+	232.737i	−1.25096	+	0.249451i
$934$		0			0
$935$	−100.461	−	119.725i	−0.107445	−	0.128048i
$936$		0			0
$937$	221.211	+	185.618i	0.236084	+	0.198098i	0.753152	−	0.657846i	$-0.228532\pi$
$937$	221.211	+	185.618i	0.236084	+	0.198098i	−0.517068	+	0.855944i	$0.672977\pi$
$938$		0			0
$939$	377.473	+	824.068i	0.401994	+	0.877602i
$940$		0			0
$941$	−777.108	−	578.535i	−0.825832	−	0.614809i	0.0990420	−	0.995083i	$-0.468422\pi$
$941$	−777.108	−	578.535i	−0.825832	−	0.614809i	−0.924874	+	0.380274i	$0.875830\pi$
$942$		0			0
$943$	−12.6473	+	6.35169i	−0.0134117	+	0.00673562i
$944$		0			0
$945$	9.73540	−	33.5792i	0.0103020	−	0.0355335i
$946$		0			0
$947$	−851.867	−	49.6156i	−0.899542	−	0.0523924i	−0.397862	−	0.917445i	$-0.630248\pi$
$947$	−851.867	−	49.6156i	−0.899542	−	0.0523924i	−0.501681	+	0.865053i	$0.667285\pi$
$948$		0			0
$949$	−145.193	−	16.9706i	−0.152996	−	0.0178826i
$950$		0			0
$951$	−314.957	−	1208.22i	−0.331185	−	1.27047i
$952$		0			0
$953$	35.9066	+	98.6525i	0.0376774	+	0.103518i	0.957105	−	0.289742i	$-0.0935695\pi$
$953$	35.9066	+	98.6525i	0.0376774	+	0.103518i	−0.919427	+	0.393260i	$0.871347\pi$
$954$		0			0
$955$	−163.577	−	59.5373i	−0.171285	−	0.0623428i
$956$		0			0
$957$	−263.644	−	211.390i	−0.275490	−	0.220888i
$958$		0			0
$959$	−181.881	+	10.5933i	−0.189657	+	0.0110462i
$960$		0			0
$961$	146.523	+	489.420i	0.152469	+	0.509282i
$962$		0			0
$963$	−350.159	−	88.0325i	−0.363613	−	0.0914148i
$964$		0			0
$965$	−6.26762	−	53.6229i	−0.00649495	−	0.0555678i
$966$		0			0
$967$	573.484	+	607.858i	0.593055	+	0.628602i	0.952490	−	0.304568i	$-0.0985122\pi$
$967$	573.484	+	607.858i	0.593055	+	0.628602i	−0.359435	+	0.933170i	$0.617031\pi$
$968$		0			0
$969$	365.294	+	2617.78i	0.376980	+	2.70153i
$970$		0			0
$971$		−	1189.09i		−	1.22460i	−0.790625	−	0.612301i	$-0.790244\pi$
$971$		−	1189.09i		−	1.22460i	0.790625	−	0.612301i	$-0.209756\pi$
$972$		0			0
$973$	−111.972			−0.115079
$974$		0			0
$975$	−439.814	+	61.3731i	−0.451091	+	0.0629468i
$976$		0			0
$977$	−188.771	+	178.096i	−0.193215	+	0.182289i	−0.776769	−	0.629785i	$-0.783143\pi$
$977$	−188.771	+	178.096i	−0.193215	+	0.182289i	0.583554	+	0.812074i	$0.301661\pi$
$978$		0			0
$979$	251.174	−	29.3580i	0.256562	−	0.0299878i
$980$		0			0
$981$	−573.422	−	555.919i	−0.584528	−	0.566686i
$982$		0			0
$983$	−518.248	+	155.153i	−0.527210	+	0.157836i	−0.539337	−	0.842090i	$-0.681325\pi$
$983$	−518.248	+	155.153i	−0.527210	+	0.157836i	0.0121267	+	0.999926i	$0.496140\pi$
$984$		0			0
$985$	−2.08716	−	35.8351i	−0.00211894	−	0.0363808i
$986$		0			0
$987$	207.999	−	259.415i	0.210739	−	0.262832i
$988$		0			0
$989$	4.68941	−	12.8841i	0.00474157	−	0.0130274i
$990$		0			0
$991$	−1476.16	+	537.277i	−1.48956	+	0.542157i	−0.953335	−	0.301916i	$-0.902374\pi$
$991$	−1476.16	+	537.277i	−1.48956	+	0.542157i	−0.536229	+	0.844073i	$0.680152\pi$
$992$		0			0
$993$	−1407.09	+	366.798i	−1.41701	+	0.369383i
$994$		0			0
$995$	−20.4074	+	174.597i	−0.0205100	+	0.175474i
$996$		0			0
$997$	−49.9914	+	858.318i	−0.0501418	+	0.860901i	0.875669	+	0.482913i	$0.160421\pi$
$997$	−49.9914	+	858.318i	−0.0501418	+	0.860901i	−0.925810	+	0.377988i	$0.876616\pi$
$998$		0			0
$999$	−432.799	+	880.799i	−0.433232	+	0.881681i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.o.a.29.2	✓	324
81.14	odd	54	inner	324.3.o.a.257.2	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.o.a.29.2	✓	324	1.1	even	1	trivial
324.3.o.a.257.2	yes	324	81.14	odd	54	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.o (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.97121 + 0.414613i) q^{3} +(-0.778741 + 0.734705i) q^{5} +(1.20130 - 0.140411i) q^{7} +(8.65619 - 2.46381i) q^{9} +O(q^{10})\)	\(q+(-2.97121 + 0.414613i) q^{3} +(-0.778741 + 0.734705i) q^{5} +(1.20130 - 0.140411i) q^{7} +(8.65619 - 2.46381i) q^{9} +(5.77404 - 1.72863i) q^{11} +(-0.360819 - 6.19502i) q^{13} +(2.00919 - 2.50584i) q^{15} +(-8.28376 + 22.7594i) q^{17} +(-34.1830 + 12.4416i) q^{19} +(-3.51109 + 0.915264i) q^{21} +(-0.0387925 + 0.331891i) q^{23} +(-1.38697 + 23.8134i) q^{25} +(-24.6978 + 10.9095i) q^{27} +(8.38751 + 16.7009i) q^{29} +(-12.6693 + 17.0178i) q^{31} +(-16.4392 + 7.53013i) q^{33} +(-0.832338 + 0.991941i) q^{35} +(27.8439 - 23.3638i) q^{37} +(3.64061 + 18.2571i) q^{39} +(23.2739 + 35.3863i) q^{41} +(-39.9262 - 9.46267i) q^{43} +(-4.93076 + 8.27841i) q^{45} +(-73.5059 + 54.7231i) q^{47} +(-46.2558 + 10.9628i) q^{49} +(15.1764 - 71.0576i) q^{51} +(37.1563 - 21.4522i) q^{53} +(-3.22645 + 5.58837i) q^{55} +(96.4064 - 51.1393i) q^{57} +(38.6036 + 11.5572i) q^{59} +(-24.0027 + 55.6445i) q^{61} +(10.0527 - 4.17519i) q^{63} +(4.83249 + 4.55922i) q^{65} +(-32.8598 - 16.5028i) q^{67} +(-0.0223457 - 1.00220i) q^{69} +(28.4416 - 5.01502i) q^{71} +(4.09057 - 23.1988i) q^{73} +(-5.75236 - 71.3297i) q^{75} +(6.69361 - 2.88734i) q^{77} +(-24.3817 - 16.0361i) q^{79} +(68.8593 - 42.6544i) q^{81} +(18.8759 - 28.6995i) q^{83} +(-10.2706 - 23.8098i) q^{85} +(-31.8455 - 46.1443i) q^{87} +(41.3193 + 7.28571i) q^{89} +(-1.30330 - 7.39139i) q^{91} +(30.5874 - 55.8164i) q^{93} +(17.4788 - 34.8032i) q^{95} +(44.3589 - 47.0177i) q^{97} +(45.7222 - 29.1895i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q+O(q^{10}) \) 324 * q	\( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) \) 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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