LMFDB - Embedded newform 216.3.u.a.41.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(41,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 17]))

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

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

chi := DirichletCharacter("216.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.u (of order $18$, degree $6$, 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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.9
Character	$\chi$	$=$	216.41
Dual form			216.3.u.a.137.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.111253 + 2.99794i) q^{3} +(-2.18378 + 2.60253i) q^{5} +(-6.99436 - 2.54574i) q^{7} +(-8.97525 + 0.667061i) q^{9} +O(q^{10})$	\(q+(0.111253 + 2.99794i) q^{3} +(-2.18378 + 2.60253i) q^{5} +(-6.99436 - 2.54574i) q^{7} +(-8.97525 + 0.667061i) q^{9} +(-4.16991 - 4.96950i) q^{11} +(-0.380081 + 2.15555i) q^{13} +(-8.04518 - 6.25731i) q^{15} +(5.93670 + 3.42755i) q^{17} +(-15.2207 - 26.3631i) q^{19} +(6.85381 - 21.2519i) q^{21} +(6.13455 + 16.8545i) q^{23} +(2.33694 + 13.2534i) q^{25} +(-2.99833 - 26.8330i) q^{27} +(-19.8076 + 3.49261i) q^{29} +(-54.7865 + 19.9407i) q^{31} +(14.4343 - 13.0540i) q^{33} +(21.8995 - 12.6437i) q^{35} +(-4.23715 + 7.33896i) q^{37} +(-6.50447 - 0.899646i) q^{39} +(57.5289 + 10.1439i) q^{41} +(-44.8479 + 37.6319i) q^{43} +(17.8640 - 24.8151i) q^{45} +(-11.0508 + 30.3618i) q^{47} +(4.90408 + 4.11501i) q^{49} +(-9.61511 + 18.1792i) q^{51} +36.5011i q^{53} +22.0395 q^{55} +(77.3415 - 48.5638i) q^{57} +(-11.8435 + 14.1145i) q^{59} +(4.97280 + 1.80995i) q^{61} +(64.4742 + 18.1830i) q^{63} +(-4.77986 - 5.69642i) q^{65} +(11.3273 - 64.2402i) q^{67} +(-49.8464 + 20.2661i) q^{69} +(59.6010 + 34.4107i) q^{71} +(19.4734 + 33.7290i) q^{73} +(-39.4730 + 8.48049i) q^{75} +(16.5148 + 45.3740i) q^{77} +(3.14606 + 17.8422i) q^{79} +(80.1101 - 11.9741i) q^{81} +(104.452 - 18.4177i) q^{83} +(-21.8848 + 7.96541i) q^{85} +(-12.6743 - 58.9933i) q^{87} +(38.3336 - 22.1319i) q^{89} +(8.14587 - 14.1091i) q^{91} +(-65.8760 - 162.028i) q^{93} +(101.850 + 17.9588i) q^{95} +(-56.7201 + 47.5938i) q^{97} +(40.7409 + 41.8209i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q+O(q^{10}) $ 108 * q	$ 108 q - 18 q^{11} - 24 q^{15} + 48 q^{21} + 72 q^{23} + 174 q^{27} + 108 q^{29} + 18 q^{33} - 144 q^{39} + 90 q^{41} - 90 q^{43} + 108 q^{45} - 72 q^{49} + 84 q^{51} - 18 q^{57} - 252 q^{59} + 144 q^{61} - 360 q^{63} - 216 q^{65} + 126 q^{67} - 120 q^{69} - 252 q^{75} - 504 q^{77} - 552 q^{81} - 180 q^{83} - 60 q^{87} - 486 q^{89} - 360 q^{93} - 1116 q^{95} + 270 q^{97} - 564 q^{99}+O(q^{100}) $ 108 * q - 18 * q^11 - 24 * q^15 + 48 * q^21 + 72 * q^23 + 174 * q^27 + 108 * q^29 + 18 * q^33 - 144 * q^39 + 90 * q^41 - 90 * q^43 + 108 * q^45 - 72 * q^49 + 84 * q^51 - 18 * q^57 - 252 * q^59 + 144 * q^61 - 360 * q^63 - 216 * q^65 + 126 * q^67 - 120 * q^69 - 252 * q^75 - 504 * q^77 - 552 * q^81 - 180 * q^83 - 60 * q^87 - 486 * q^89 - 360 * q^93 - 1116 * q^95 + 270 * q^97 - 564 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{17}{18}\right)$

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
$3$	0.111253	+	2.99794i	0.0370845	+	0.999312i
$3$	0.111253	+	2.99794i	0.0370845	+	0.999312i
$4$		0			0
$5$	−2.18378	+	2.60253i	−0.436757	+	0.520507i	−0.938859	−	0.344302i	$-0.888116\pi$
$5$	−2.18378	+	2.60253i	−0.436757	+	0.520507i	0.502102	+	0.864808i	$0.332560\pi$
$6$		0			0
$7$	−6.99436	−	2.54574i	−0.999194	−	0.363677i	−0.209920	−	0.977718i	$-0.567320\pi$
$7$	−6.99436	−	2.54574i	−0.999194	−	0.363677i	−0.789274	+	0.614042i	$0.789543\pi$
$8$		0			0
$9$	−8.97525	+	0.667061i	−0.997249	+	0.0741179i
$10$		0			0
$11$	−4.16991	−	4.96950i	−0.379083	−	0.451773i	0.542442	−	0.840093i	$-0.317500\pi$
$11$	−4.16991	−	4.96950i	−0.379083	−	0.451773i	−0.921524	+	0.388320i	$0.873055\pi$
$12$		0			0
$13$	−0.380081	+	2.15555i	−0.0292370	+	0.165811i	−0.995930	−	0.0901262i	$-0.971273\pi$
$13$	−0.380081	+	2.15555i	−0.0292370	+	0.165811i	0.966693	+	0.255937i	$0.0823841\pi$
$14$		0			0
$15$	−8.04518	−	6.25731i	−0.536346	−	0.417154i
$16$		0			0
$17$	5.93670	+	3.42755i	0.349218	+	0.201621i	0.664341	−	0.747430i	$-0.268712\pi$
$17$	5.93670	+	3.42755i	0.349218	+	0.201621i	−0.315123	+	0.949051i	$0.602046\pi$
$18$		0			0
$19$	−15.2207	−	26.3631i	−0.801091	−	1.38753i	−0.918899	−	0.394494i	$-0.870920\pi$
$19$	−15.2207	−	26.3631i	−0.801091	−	1.38753i	0.117807	−	0.993036i	$-0.462413\pi$
$20$		0			0
$21$	6.85381	−	21.2519i	0.326372	−	1.01199i
$22$		0			0
$23$	6.13455	+	16.8545i	0.266720	+	0.732806i	0.998675	+	0.0514539i	$0.0163855\pi$
$23$	6.13455	+	16.8545i	0.266720	+	0.732806i	−0.731956	+	0.681352i	$0.761392\pi$
$24$		0			0
$25$	2.33694	+	13.2534i	0.0934776	+	0.530138i
$26$		0			0
$27$	−2.99833	−	26.8330i	−0.111049	−	0.993815i
$28$		0			0
$29$	−19.8076	+	3.49261i	−0.683020	+	0.120435i	−0.504383	−	0.863480i	$-0.668280\pi$
$29$	−19.8076	+	3.49261i	−0.683020	+	0.120435i	−0.178637	+	0.983915i	$0.557169\pi$
$30$		0			0
$31$	−54.7865	+	19.9407i	−1.76731	+	0.643247i	−0.767309	+	0.641278i	$0.778405\pi$
$31$	−54.7865	+	19.9407i	−1.76731	+	0.643247i	−0.999998	+	0.00196904i	$0.999373\pi$
$32$		0			0
$33$	14.4343	−	13.0540i	0.437404	−	0.395576i
$34$		0			0
$35$	21.8995	−	12.6437i	0.625701	−	0.361249i
$36$		0			0
$37$	−4.23715	+	7.33896i	−0.114518	+	0.198350i	−0.917587	−	0.397535i	$-0.869866\pi$
$37$	−4.23715	+	7.33896i	−0.114518	+	0.198350i	0.803069	+	0.595886i	$0.203199\pi$
$38$		0			0
$39$	−6.50447	−	0.899646i	−0.166781	−	0.0230679i
$40$		0			0
$41$	57.5289	+	10.1439i	1.40314	+	0.247412i	0.823434	−	0.567412i	$-0.192055\pi$
$41$	57.5289	+	10.1439i	1.40314	+	0.247412i	0.579709	+	0.814824i	$0.303166\pi$
$42$		0			0
$43$	−44.8479	+	37.6319i	−1.04297	+	0.875160i	−0.992337	−	0.123557i	$-0.960570\pi$
$43$	−44.8479	+	37.6319i	−1.04297	+	0.875160i	−0.0506373	+	0.998717i	$0.516125\pi$
$44$		0			0
$45$	17.8640	−	24.8151i	0.396977	−	0.551447i
$46$		0			0
$47$	−11.0508	+	30.3618i	−0.235123	+	0.645995i	0.764875	+	0.644178i	$0.222801\pi$
$47$	−11.0508	+	30.3618i	−0.235123	+	0.645995i	−0.999998	+	0.00181691i	$0.999422\pi$
$48$		0			0
$49$	4.90408	+	4.11501i	0.100083	+	0.0839798i
$50$		0			0
$51$	−9.61511	+	18.1792i	−0.188532	+	0.356454i
$52$		0			0
$53$			36.5011i			0.688700i	0.938841	+	0.344350i	$0.111901\pi$
$53$			36.5011i			0.688700i	−0.938841	+	0.344350i	$0.888099\pi$
$54$		0			0
$55$	22.0395			0.400718
$56$		0			0
$57$	77.3415	−	48.5638i	1.35687	−	0.851996i
$58$		0			0
$59$	−11.8435	+	14.1145i	−0.200737	+	0.239229i	−0.857017	−	0.515289i	$-0.827685\pi$
$59$	−11.8435	+	14.1145i	−0.200737	+	0.239229i	0.656280	+	0.754518i	$0.272129\pi$
$60$		0			0
$61$	4.97280	+	1.80995i	0.0815213	+	0.0296713i	0.382459	−	0.923973i	$-0.375077\pi$
$61$	4.97280	+	1.80995i	0.0815213	+	0.0296713i	−0.300938	+	0.953644i	$0.597300\pi$
$62$		0			0
$63$	64.4742	+	18.1830i	1.02340	+	0.288618i
$64$		0			0
$65$	−4.77986	−	5.69642i	−0.0735364	−	0.0876372i
$66$		0			0
$67$	11.3273	−	64.2402i	0.169064	−	0.958809i	−0.775711	−	0.631088i	$-0.782608\pi$
$67$	11.3273	−	64.2402i	0.169064	−	0.958809i	0.944775	−	0.327720i	$-0.106280\pi$
$68$		0			0
$69$	−49.8464	+	20.2661i	−0.722411	+	0.293712i
$70$		0			0
$71$	59.6010	+	34.4107i	0.839451	+	0.484657i	0.857078	−	0.515187i	$-0.172278\pi$
$71$	59.6010	+	34.4107i	0.839451	+	0.484657i	−0.0176267	+	0.999845i	$0.505611\pi$
$72$		0			0
$73$	19.4734	+	33.7290i	0.266759	+	0.462041i	0.968023	−	0.250861i	$-0.0807138\pi$
$73$	19.4734	+	33.7290i	0.266759	+	0.462041i	−0.701264	+	0.712902i	$0.747380\pi$
$74$		0			0
$75$	−39.4730	+	8.48049i	−0.526307	+	0.113073i
$76$		0			0
$77$	16.5148	+	45.3740i	0.214478	+	0.589272i
$78$		0			0
$79$	3.14606	+	17.8422i	0.0398235	+	0.225851i	0.998224	−	0.0595775i	$-0.0189754\pi$
$79$	3.14606	+	17.8422i	0.0398235	+	0.225851i	−0.958400	+	0.285428i	$0.907864\pi$
$80$		0			0
$81$	80.1101	−	11.9741i	0.989013	−	0.147828i
$82$		0			0
$83$	104.452	−	18.4177i	1.25846	−	0.221900i	0.495648	−	0.868524i	$-0.334931\pi$
$83$	104.452	−	18.4177i	1.25846	−	0.221900i	0.762809	+	0.646624i	$0.223820\pi$
$84$		0			0
$85$	−21.8848	+	7.96541i	−0.257468	+	0.0937108i
$86$		0			0
$87$	−12.6743	−	58.9933i	−0.145681	−	0.678084i
$88$		0			0
$89$	38.3336	−	22.1319i	0.430714	−	0.248673i	−0.268937	−	0.963158i	$-0.586672\pi$
$89$	38.3336	−	22.1319i	0.430714	−	0.248673i	0.699651	+	0.714485i	$0.253339\pi$
$90$		0			0
$91$	8.14587	−	14.1091i	0.0895151	−	0.155045i
$92$		0			0
$93$	−65.8760	−	162.028i	−0.708344	−	1.74224i
$94$		0			0
$95$	101.850	+	17.9588i	1.07210	+	0.189040i
$96$		0			0
$97$	−56.7201	+	47.5938i	−0.584744	+	0.490658i	−0.886501	−	0.462727i	$-0.846871\pi$
$97$	−56.7201	+	47.5938i	−0.584744	+	0.490658i	0.301757	+	0.953385i	$0.402427\pi$
$98$		0			0
$99$	40.7409	+	41.8209i	0.411524	+	0.422434i
$100$		0			0
$101$	−65.3202	+	179.466i	−0.646735	+	1.77689i	−0.0172813	+	0.999851i	$0.505501\pi$
$101$	−65.3202	+	179.466i	−0.646735	+	1.77689i	−0.629453	+	0.777038i	$0.716721\pi$
$102$		0			0
$103$	−89.6800	−	75.2504i	−0.870679	−	0.730587i	0.0935617	−	0.995613i	$-0.470175\pi$
$103$	−89.6800	−	75.2504i	−0.870679	−	0.730587i	−0.964241	+	0.265027i	$0.914619\pi$
$104$		0			0
$105$	40.3414	+	64.2468i	0.384204	+	0.611874i
$106$		0			0
$107$		−	181.297i		−	1.69436i	−0.531305	−	0.847181i	$-0.678298\pi$
$107$		−	181.297i		−	1.69436i	0.531305	−	0.847181i	$-0.321702\pi$
$108$		0			0
$109$	48.8624			0.448279			0.224139	−	0.974557i	$-0.428043\pi$
$109$	48.8624			0.448279			0.224139	+	0.974557i	$0.428043\pi$
$110$		0			0
$111$	−22.4731	−	11.8862i	−0.202461	−	0.107083i
$112$		0			0
$113$	−10.8538	+	12.9351i	−0.0960516	+	0.114470i	−0.811929	−	0.583756i	$-0.801582\pi$
$113$	−10.8538	+	12.9351i	−0.0960516	+	0.114470i	0.715877	+	0.698226i	$0.246027\pi$
$114$		0			0
$115$	−57.2610	−	20.8413i	−0.497922	−	0.181229i
$116$		0			0
$117$	1.97344	−	19.6001i	0.0168670	−	0.167522i
$118$		0			0
$119$	−32.7977	−	39.0868i	−0.275611	−	0.328461i
$120$		0			0
$121$	13.7036	−	77.7170i	0.113253	−	0.642289i
$122$		0			0
$123$	−24.0105	+	173.596i	−0.195207	+	1.41135i
$124$		0			0
$125$	−113.151	−	65.3278i	−0.905208	−	0.522622i
$126$		0			0
$127$	9.68727	+	16.7788i	0.0762777	+	0.132117i	0.901641	−	0.432485i	$-0.142363\pi$
$127$	9.68727	+	16.7788i	0.0762777	+	0.132117i	−0.825363	+	0.564602i	$0.809030\pi$
$128$		0			0
$129$	−117.807	−	130.265i	−0.913236	−	1.00980i
$130$		0			0
$131$	61.6846	+	169.477i	0.470875	+	1.29372i	0.917050	+	0.398773i	$0.130564\pi$
$131$	61.6846	+	169.477i	0.470875	+	1.29372i	−0.446175	+	0.894946i	$0.647214\pi$
$132$		0			0
$133$	39.3457	+	223.141i	0.295833	+	1.67775i
$134$		0			0
$135$	76.3815	+	50.7942i	0.565789	+	0.376254i
$136$		0			0
$137$	−188.206	+	33.1857i	−1.37376	+	0.242232i	−0.811319	−	0.584604i	$-0.801250\pi$
$137$	−188.206	+	33.1857i	−1.37376	+	0.242232i	−0.562444	+	0.826835i	$0.690139\pi$
$138$		0			0
$139$	−221.713	+	80.6969i	−1.59506	+	0.580553i	−0.978408	−	0.206684i	$-0.933733\pi$
$139$	−221.713	+	80.6969i	−1.59506	+	0.580553i	−0.616650	+	0.787238i	$0.711511\pi$
$140$		0			0
$141$	−92.2521	−	29.7517i	−0.654270	−	0.211005i
$142$		0			0
$143$	12.2969	−	7.09961i	0.0859922	−	0.0496476i
$144$		0			0
$145$	34.1659	−	59.1770i	0.235627	−	0.408117i
$146$		0			0
$147$	−11.7910	+	15.1599i	−0.0802105	+	0.103129i
$148$		0			0
$149$	−212.088	−	37.3969i	−1.42341	−	0.250986i	−0.591683	−	0.806170i	$-0.701536\pi$
$149$	−212.088	−	37.3969i	−1.42341	−	0.250986i	−0.831727	+	0.555185i	$0.812648\pi$
$150$		0			0
$151$	91.6248	−	76.8823i	0.606786	−	0.509154i	−0.286832	−	0.957981i	$-0.592602\pi$
$151$	91.6248	−	76.8823i	0.606786	−	0.509154i	0.893619	+	0.448826i	$0.148158\pi$
$152$		0			0
$153$	−55.5697	−	26.8030i	−0.363201	−	0.175183i
$154$		0			0
$155$	67.7457	−	186.130i	0.437069	−	1.20084i
$156$		0			0
$157$	−41.0206	−	34.4204i	−0.261278	−	0.219238i	0.502733	−	0.864442i	$-0.332328\pi$
$157$	−41.0206	−	34.4204i	−0.261278	−	0.219238i	−0.764011	+	0.645204i	$0.776772\pi$
$158$		0			0
$159$	−109.428	+	4.06087i	−0.688226	+	0.0255401i
$160$		0			0
$161$		−	133.504i		−	0.829215i
$162$		0			0
$163$	309.914			1.90131			0.950657	−	0.310243i	$-0.100410\pi$
$163$	309.914			1.90131			0.950657	+	0.310243i	$0.100410\pi$
$164$		0			0
$165$	2.45197	+	66.0730i	0.0148604	+	0.400442i
$166$		0			0
$167$	−25.6872	+	30.6128i	−0.153816	+	0.183310i	−0.837449	−	0.546515i	$-0.815954\pi$
$167$	−25.6872	+	30.6128i	−0.153816	+	0.183310i	0.683634	+	0.729825i	$0.260399\pi$
$168$		0			0
$169$	154.306	+	56.1628i	0.913054	+	0.332325i
$170$		0			0
$171$	154.196	+	226.462i	0.901729	+	1.32434i
$172$		0			0
$173$	−204.150	−	243.297i	−1.18006	−	1.40634i	−0.893963	−	0.448141i	$-0.852086\pi$
$173$	−204.150	−	243.297i	−1.18006	−	1.40634i	−0.286097	−	0.958201i	$-0.592358\pi$
$174$		0			0
$175$	17.3944	−	98.6486i	0.0993966	−	0.563706i
$176$		0			0
$177$	−43.6320	−	33.9357i	−0.246508	−	0.191727i
$178$		0			0
$179$	−76.1643	−	43.9735i	−0.425499	−	0.245662i	0.271928	−	0.962317i	$-0.412339\pi$
$179$	−76.1643	−	43.9735i	−0.425499	−	0.245662i	−0.697427	+	0.716656i	$0.745672\pi$
$180$		0			0
$181$	−151.692	−	262.738i	−0.838077	−	1.45159i	−0.891500	−	0.453020i	$-0.850346\pi$
$181$	−151.692	−	262.738i	−0.838077	−	1.45159i	0.0534230	−	0.998572i	$-0.482987\pi$
$182$		0			0
$183$	−4.87288	+	15.1095i	−0.0266277	+	0.0825656i
$184$		0			0
$185$	−9.84687	−	27.0540i	−0.0532263	−	0.146238i
$186$		0			0
$187$	−7.72225	−	43.7950i	−0.0412954	−	0.234198i
$188$		0			0
$189$	−47.3384	+	195.313i	−0.250468	+	1.03340i
$190$		0			0
$191$	−295.788	+	52.1553i	−1.54863	+	0.273065i	−0.881610	−	0.471979i	$-0.843540\pi$
$191$	−295.788	+	52.1553i	−1.54863	+	0.273065i	−0.667016	+	0.745043i	$0.732429\pi$
$192$		0			0
$193$	231.020	−	84.0842i	1.19699	−	0.435670i	0.334819	−	0.942283i	$-0.391325\pi$
$193$	231.020	−	84.0842i	1.19699	−	0.435670i	0.862174	+	0.506613i	$0.169103\pi$
$194$		0			0
$195$	16.5457	−	14.9635i	0.0848499	−	0.0767358i
$196$		0			0
$197$	293.891	−	169.678i	1.49183	−	0.861309i	0.491875	−	0.870666i	$-0.336312\pi$
$197$	293.891	−	169.678i	1.49183	−	0.861309i	0.999956	+	0.00935613i	$0.00297819\pi$
$198$		0			0
$199$	−51.5586	+	89.3022i	−0.259089	+	0.448755i	−0.965998	−	0.258549i	$-0.916755\pi$
$199$	−51.5586	+	89.3022i	−0.259089	+	0.448755i	0.706909	+	0.707304i	$0.250089\pi$
$200$		0			0
$201$	193.848	+	26.8115i	0.964419	+	0.133391i
$202$		0			0
$203$	147.433	+	25.9963i	0.726269	+	0.128061i
$204$		0			0
$205$	−152.031	+	127.569i	−0.741612	+	0.622287i
$206$		0			0
$207$	−66.3021	−	147.182i	−0.320300	−	0.711022i
$208$		0			0
$209$	−67.5424	+	185.571i	−0.323169	+	0.887900i
$210$		0			0
$211$	−149.423	−	125.381i	−0.708166	−	0.594222i	0.215918	−	0.976411i	$-0.430726\pi$
$211$	−149.423	−	125.381i	−0.708166	−	0.594222i	−0.924084	+	0.382190i	$0.875170\pi$
$212$		0			0
$213$	−96.5302	+	182.508i	−0.453193	+	0.856847i
$214$		0			0
$215$		−	198.898i		−	0.925107i
$216$		0			0
$217$	433.960			1.99982
$218$		0			0
$219$	−98.9508	+	62.1326i	−0.451830	+	0.283710i
$220$		0			0
$221$	−9.64467	+	11.4941i	−0.0436411	+	0.0520094i
$222$		0			0
$223$	291.677	+	106.162i	1.30797	+	0.476062i	0.899584	−	0.436747i	$-0.143869\pi$
$223$	291.677	+	106.162i	1.30797	+	0.476062i	0.408386	+	0.912809i	$0.366092\pi$
$224$		0			0
$225$	−29.8155	−	117.394i	−0.132513	−	0.521751i
$226$		0			0
$227$	11.3951	+	13.5801i	0.0501987	+	0.0598244i	0.790560	−	0.612385i	$-0.209790\pi$
$227$	11.3951	+	13.5801i	0.0501987	+	0.0598244i	−0.740361	+	0.672210i	$0.765345\pi$
$228$		0			0
$229$	−33.3954	+	189.395i	−0.145831	+	0.827051i	0.820864	+	0.571123i	$0.193492\pi$
$229$	−33.3954	+	189.395i	−0.145831	+	0.827051i	−0.966696	+	0.255928i	$0.917619\pi$
$230$		0			0
$231$	−134.191	+	54.5583i	−0.580913	+	0.236183i
$232$		0			0
$233$	175.680	+	101.429i	0.753993	+	0.435318i	0.827135	−	0.562003i	$-0.189969\pi$
$233$	175.680	+	101.429i	0.753993	+	0.435318i	−0.0731417	+	0.997322i	$0.523303\pi$
$234$		0			0
$235$	−54.8850	−	95.0636i	−0.233553	−	0.404526i
$236$		0			0
$237$	−53.1397	+	11.4167i	−0.224218	+	0.0481717i
$238$		0			0
$239$	69.0968	+	189.842i	0.289108	+	0.794317i	0.996192	+	0.0871877i	$0.0277880\pi$
$239$	69.0968	+	189.842i	0.289108	+	0.794317i	−0.707084	+	0.707129i	$0.749990\pi$
$240$		0			0
$241$	38.5050	+	218.373i	0.159772	+	0.906110i	0.954293	+	0.298873i	$0.0966109\pi$
$241$	38.5050	+	218.373i	0.159772	+	0.906110i	−0.794521	+	0.607237i	$0.792278\pi$
$242$		0			0
$243$	44.8100	+	238.833i	0.184403	+	0.982851i
$244$		0			0
$245$	−21.4189	+	3.77673i	−0.0874241	+	0.0154152i
$246$		0			0
$247$	62.6119	−	22.7889i	0.253490	−	0.0922626i
$248$		0			0
$249$	66.8357	+	311.091i	0.268417	+	1.24936i
$250$		0			0
$251$	−64.5660	+	37.2772i	−0.257235	+	0.148515i	−0.623073	−	0.782164i	$-0.714116\pi$
$251$	−64.5660	+	37.2772i	−0.257235	+	0.148515i	0.365838	+	0.930679i	$0.380783\pi$
$252$		0			0
$253$	58.1782	−	100.768i	0.229953	−	0.398291i
$254$		0			0
$255$	−26.3146	−	64.7231i	−0.103194	−	0.253816i
$256$		0			0
$257$	307.492	+	54.2191i	1.19647	+	0.210969i	0.736171	−	0.676796i	$-0.236632\pi$
$257$	307.492	+	54.2191i	1.19647	+	0.210969i	0.460296	+	0.887765i	$0.347743\pi$
$258$		0			0
$259$	48.3192	−	40.5446i	0.186561	−	0.156543i
$260$		0			0
$261$	175.448	−	44.5599i	0.672215	−	0.170728i
$262$		0			0
$263$	28.1752	−	77.4108i	0.107130	−	0.294337i	−0.874532	−	0.484968i	$-0.838831\pi$
$263$	28.1752	−	77.4108i	0.107130	−	0.294337i	0.981662	+	0.190631i	$0.0610533\pi$
$264$		0			0
$265$	−94.9953	−	79.7105i	−0.358473	−	0.300795i
$266$		0			0
$267$	70.6147	+	112.459i	0.264475	+	0.421196i
$268$		0			0
$269$			232.151i			0.863013i	0.902110	+	0.431507i	$0.142018\pi$
$269$			232.151i			0.863013i	−0.902110	+	0.431507i	$0.857982\pi$
$270$		0			0
$271$	452.189			1.66859			0.834296	−	0.551316i	$-0.185874\pi$
$271$	452.189			1.66859			0.834296	+	0.551316i	$0.185874\pi$
$272$		0			0
$273$	43.2043	+	22.8511i	0.158258	+	0.0837038i
$274$		0			0
$275$	56.1182	−	66.8791i	0.204066	−	0.243197i
$276$		0			0
$277$	−25.5129	−	9.28593i	−0.0921043	−	0.0335232i	0.295557	−	0.955325i	$-0.404495\pi$
$277$	−25.5129	−	9.28593i	−0.0921043	−	0.0335232i	−0.387661	+	0.921802i	$0.626717\pi$
$278$		0			0
$279$	478.421	−	215.518i	1.71477	−	0.772467i
$280$		0			0
$281$	−130.043	−	154.980i	−0.462788	−	0.551529i	0.483293	−	0.875459i	$-0.339441\pi$
$281$	−130.043	−	154.980i	−0.462788	−	0.551529i	−0.946081	+	0.323929i	$0.894996\pi$
$282$		0			0
$283$	−38.3285	+	217.372i	−0.135436	+	0.768098i	0.839118	+	0.543949i	$0.183071\pi$
$283$	−38.3285	+	217.372i	−0.135436	+	0.768098i	−0.974555	+	0.224149i	$0.928040\pi$
$284$		0			0
$285$	−42.5083	+	307.337i	−0.149152	+	1.07837i
$286$		0			0
$287$	−376.554	−	217.403i	−1.31203	−	0.757503i
$288$		0			0
$289$	−121.004	−	209.585i	−0.418698	−	0.725206i
$290$		0			0
$291$	−148.994	−	164.748i	−0.512006	−	0.566146i
$292$		0			0
$293$	−76.1408	−	209.195i	−0.259866	−	0.713976i	−0.999175	−	0.0406100i	$-0.987070\pi$
$293$	−76.1408	−	209.195i	−0.259866	−	0.713976i	0.739309	−	0.673366i	$-0.235152\pi$
$294$		0			0
$295$	−10.8699	−	61.6460i	−0.0368470	−	0.208970i
$296$		0			0
$297$	−120.844	+	126.791i	−0.406882	+	0.426907i
$298$		0			0
$299$	−38.6623	+	6.81721i	−0.129306	+	0.0228000i
$300$		0			0
$301$	409.483	−	149.040i	1.36041	−	0.495149i
$302$		0			0
$303$	−545.294	−	175.860i	−1.79965	−	0.580395i
$304$		0			0
$305$	−15.5700	+	8.98933i	−0.0510491	+	0.0294732i
$306$		0			0
$307$	−66.4225	+	115.047i	−0.216360	+	0.374746i	−0.953692	−	0.300784i	$-0.902752\pi$
$307$	−66.4225	+	115.047i	−0.216360	+	0.374746i	0.737332	+	0.675530i	$0.236085\pi$
$308$		0			0
$309$	215.619	−	277.227i	0.697795	−	0.897174i
$310$		0			0
$311$	−159.322	−	28.0927i	−0.512288	−	0.0903302i	−0.0884723	−	0.996079i	$-0.528198\pi$
$311$	−159.322	−	28.0927i	−0.512288	−	0.0903302i	−0.423816	+	0.905748i	$0.639310\pi$
$312$		0			0
$313$	−106.117	+	89.0424i	−0.339031	+	0.284481i	−0.796368	−	0.604813i	$-0.793248\pi$
$313$	−106.117	+	89.0424i	−0.339031	+	0.284481i	0.457337	+	0.889294i	$0.348803\pi$
$314$		0			0
$315$	−188.120	+	128.089i	−0.597205	+	0.406631i
$316$		0			0
$317$	3.91556	−	10.7579i	0.0123519	−	0.0339367i	−0.933363	−	0.358933i	$-0.883141\pi$
$317$	3.91556	−	10.7579i	0.0123519	−	0.0339367i	0.945715	+	0.324996i	$0.105363\pi$
$318$		0			0
$319$	99.9524	+	83.8700i	0.313330	+	0.262915i
$320$		0			0
$321$	543.516	−	20.1699i	1.69320	−	0.0628345i
$322$		0			0
$323$		−	208.680i		−	0.646067i
$324$		0			0
$325$	−29.4566			−0.0906358
$326$		0			0
$327$	5.43610	+	146.486i	0.0166242	+	0.447970i
$328$		0			0
$329$	154.586	−	184.229i	0.469867	−	0.559966i
$330$		0			0
$331$	−596.921	−	217.262i	−1.80339	−	0.656380i	−0.997971	−	0.0636711i	$-0.979719\pi$
$331$	−596.921	−	217.262i	−1.80339	−	0.656380i	−0.805417	−	0.592708i	$-0.798059\pi$
$332$		0			0
$333$	33.1339	−	68.6954i	0.0995013	−	0.206293i
$334$		0			0
$335$	142.451	+	169.766i	0.425227	+	0.506765i
$336$		0			0
$337$	53.3463	−	302.542i	0.158298	−	0.897751i	−0.797411	−	0.603437i	$-0.793798\pi$
$337$	53.3463	−	302.542i	0.158298	−	0.897751i	0.955709	−	0.294314i	$-0.0950913\pi$
$338$		0			0
$339$	−39.9861	−	31.1000i	−0.117953	−	0.0917405i
$340$		0			0
$341$	327.550	+	189.111i	0.960557	+	0.554578i
$342$		0			0
$343$	158.534	+	274.589i	0.462199	+	0.800552i
$344$		0			0
$345$	56.1105	−	173.984i	0.162639	−	0.504300i
$346$		0			0
$347$	3.90527	+	10.7296i	0.0112544	+	0.0309211i	0.945193	−	0.326513i	$-0.105874\pi$
$347$	3.90527	+	10.7296i	0.0112544	+	0.0309211i	−0.933938	+	0.357434i	$0.883652\pi$
$348$		0			0
$349$	10.4419	+	59.2190i	0.0299195	+	0.169682i	0.996106	−	0.0881616i	$-0.0280992\pi$
$349$	10.4419	+	59.2190i	0.0299195	+	0.169682i	−0.966187	+	0.257844i	$0.916988\pi$
$350$		0			0
$351$	58.9794	+	3.73567i	0.168032	+	0.0106429i
$352$		0			0
$353$	−67.7610	+	11.9481i	−0.191958	+	0.0338473i	−0.268800	−	0.963196i	$-0.586627\pi$
$353$	−67.7610	+	11.9481i	−0.191958	+	0.0338473i	0.0768427	+	0.997043i	$0.475516\pi$
$354$		0			0
$355$	−219.711	+	79.9681i	−0.618903	+	0.225262i
$356$		0			0
$357$	113.531	−	102.674i	0.318014	−	0.287602i
$358$		0			0
$359$	−341.857	+	197.371i	−0.952248	+	0.549780i	−0.893778	−	0.448509i	$-0.851955\pi$
$359$	−341.857	+	197.371i	−0.952248	+	0.549780i	−0.0584693	+	0.998289i	$0.518622\pi$
$360$		0			0
$361$	−282.841	+	489.895i	−0.783494	+	1.35705i
$362$		0			0
$363$	234.515	+	32.4363i	0.646047	+	0.0893561i
$364$		0			0
$365$	−130.307	−	22.9766i	−0.357004	−	0.0629495i
$366$		0			0
$367$	−54.4331	+	45.6748i	−0.148319	+	0.124455i	−0.713928	−	0.700219i	$-0.753086\pi$
$367$	−54.4331	+	45.6748i	−0.148319	+	0.124455i	0.565609	+	0.824674i	$0.308641\pi$
$368$		0			0
$369$	−523.102	−	52.6687i	−1.41762	−	0.142733i
$370$		0			0
$371$	92.9222	−	255.302i	0.250464	−	0.688145i
$372$		0			0
$373$	−176.007	−	147.688i	−0.471870	−	0.395946i	0.375606	−	0.926779i	$-0.377435\pi$
$373$	−176.007	−	147.688i	−0.471870	−	0.395946i	−0.847476	+	0.530833i	$0.821879\pi$
$374$		0			0
$375$	183.260	−	346.488i	0.488694	−	0.923967i
$376$		0			0
$377$		−	44.0236i		−	0.116774i
$378$		0			0
$379$	−150.157			−0.396192			−0.198096	−	0.980183i	$-0.563476\pi$
$379$	−150.157			−0.396192			−0.198096	+	0.980183i	$0.563476\pi$
$380$		0			0
$381$	−49.2242	+	30.9085i	−0.129197	+	0.0811247i
$382$		0			0
$383$	−471.111	+	561.448i	−1.23006	+	1.46592i	−0.392336	+	0.919822i	$0.628333\pi$
$383$	−471.111	+	561.448i	−1.23006	+	1.46592i	−0.837720	+	0.546101i	$0.816112\pi$
$384$		0			0
$385$	−154.152	−	56.1067i	−0.400395	−	0.145732i
$386$		0			0
$387$	377.418	−	367.672i	0.975241	−	0.950056i
$388$		0			0
$389$	438.382	+	522.443i	1.12694	+	1.34304i	0.932098	+	0.362207i	$0.117977\pi$
$389$	438.382	+	522.443i	1.12694	+	1.34304i	0.194847	+	0.980834i	$0.437579\pi$
$390$		0			0
$391$	−21.3509	+	121.087i	−0.0546058	+	0.309685i
$392$		0			0
$393$	−501.219	+	203.781i	−1.27537	+	0.518528i
$394$		0			0
$395$	−53.3052	−	30.7758i	−0.134950	−	0.0779134i
$396$		0			0
$397$	−341.008	−	590.643i	−0.858962	−	1.48777i	−0.872920	−	0.487864i	$-0.837776\pi$
$397$	−341.008	−	590.643i	−0.858962	−	1.48777i	0.0139574	−	0.999903i	$-0.495557\pi$
$398$		0			0
$399$	−664.585	+	142.781i	−1.66563	+	0.357848i
$400$		0			0
$401$	−26.3758	−	72.4668i	−0.0657750	−	0.180715i	0.902451	−	0.430793i	$-0.141766\pi$
$401$	−26.3758	−	72.4668i	−0.0657750	−	0.180715i	−0.968226	+	0.250078i	$0.919544\pi$
$402$		0			0
$403$	−22.1597	−	125.674i	−0.0549868	−	0.311846i
$404$		0			0
$405$	−143.780	+	234.638i	−0.355013	+	0.579353i
$406$		0			0
$407$	54.1395	−	9.54626i	0.133021	−	0.0234552i
$408$		0			0
$409$	−504.537	+	183.636i	−1.23359	+	0.448989i	−0.874824	−	0.484441i	$-0.839023\pi$
$409$	−504.537	+	183.636i	−1.23359	+	0.448989i	−0.358762	+	0.933429i	$0.616801\pi$
$410$		0			0
$411$	−120.427	−	560.536i	−0.293010	−	1.36384i
$412$		0			0
$413$	118.769	−	68.5714i	0.287577	−	0.166033i
$414$		0			0
$415$	−180.168	+	312.060i	−0.434140	+	0.751952i
$416$		0			0
$417$	−266.591	−	655.704i	−0.639306	−	1.57243i
$418$		0			0
$419$	130.177	+	22.9537i	0.310685	+	0.0547822i	0.326817	−	0.945088i	$-0.394024\pi$
$419$	130.177	+	22.9537i	0.310685	+	0.0547822i	−0.0161316	+	0.999870i	$0.505135\pi$
$420$		0			0
$421$	−88.4764	+	74.2405i	−0.210158	+	0.176343i	−0.741791	−	0.670632i	$-0.766023\pi$
$421$	−88.4764	+	74.2405i	−0.210158	+	0.176343i	0.531633	+	0.846975i	$0.321579\pi$
$422$		0			0
$423$	78.9303	−	279.876i	0.186597	−	0.661645i
$424$		0			0
$425$	−31.5532	+	86.6917i	−0.0742428	+	0.203980i
$426$		0			0
$427$	−30.1739	−	25.3189i	−0.0706648	−	0.0592948i
$428$		0			0
$429$	22.6523	+	36.0754i	0.0528025	+	0.0840919i
$430$		0			0
$431$			780.590i			1.81111i	0.424224	+	0.905557i	$0.360547\pi$
$431$			780.590i			1.81111i	−0.424224	+	0.905557i	$0.639453\pi$
$432$		0			0
$433$	−506.835			−1.17052			−0.585259	−	0.810846i	$-0.699007\pi$
$433$	−506.835			−1.17052			−0.585259	+	0.810846i	$0.699007\pi$
$434$		0			0
$435$	181.210	+	95.8435i	0.416575	+	0.220330i
$436$		0			0
$437$	350.965	−	418.264i	0.803124	−	0.957126i
$438$		0			0
$439$	561.549	+	204.387i	1.27916	+	0.465574i	0.890153	−	0.455662i	$-0.150598\pi$
$439$	561.549	+	204.387i	1.27916	+	0.465574i	0.389002	+	0.921237i	$0.372820\pi$
$440$		0			0
$441$	−46.7603	−	33.6619i	−0.106032	−	0.0763309i
$442$		0			0
$443$	311.050	+	370.695i	0.702144	+	0.836782i	0.992767	−	0.120055i	$-0.0383071\pi$
$443$	311.050	+	370.695i	0.702144	+	0.836782i	−0.290623	+	0.956838i	$0.593863\pi$
$444$		0			0
$445$	−26.1133	+	148.096i	−0.0586815	+	0.332799i
$446$		0			0
$447$	88.5179	−	639.987i	0.198027	−	1.43174i
$448$		0			0
$449$	232.287	+	134.111i	0.517343	+	0.298688i	0.735847	−	0.677148i	$-0.236784\pi$
$449$	232.287	+	134.111i	0.517343	+	0.298688i	−0.218504	+	0.975836i	$0.570118\pi$
$450$		0			0
$451$	−189.480	−	328.189i	−0.420133	−	0.727692i
$452$		0			0
$453$	240.682	+	266.132i	0.531306	+	0.587487i
$454$		0			0
$455$	18.9305	+	52.0111i	0.0416055	+	0.114310i
$456$		0			0
$457$	−62.0589	−	351.953i	−0.135796	−	0.770139i	−0.974302	−	0.225246i	$-0.927681\pi$
$457$	−62.0589	−	351.953i	−0.135796	−	0.770139i	0.838506	−	0.544893i	$-0.183430\pi$
$458$		0			0
$459$	74.1714	−	169.576i	0.161593	−	0.369447i
$460$		0			0
$461$	83.5773	−	14.7369i	0.181296	−	0.0319673i	−0.0822632	−	0.996611i	$-0.526215\pi$
$461$	83.5773	−	14.7369i	0.181296	−	0.0319673i	0.263559	+	0.964643i	$0.415104\pi$
$462$		0			0
$463$	−204.556	+	74.4524i	−0.441806	+	0.160804i	−0.553339	−	0.832956i	$-0.686646\pi$
$463$	−204.556	+	74.4524i	−0.441806	+	0.160804i	0.111532	+	0.993761i	$0.464424\pi$
$464$		0			0
$465$	565.542	+	182.390i	1.21622	+	0.392236i
$466$		0			0
$467$	374.773	−	216.375i	0.802512	−	0.463330i	−0.0418370	−	0.999124i	$-0.513321\pi$
$467$	374.773	−	216.375i	0.802512	−	0.463330i	0.844349	+	0.535794i	$0.179988\pi$
$468$		0			0
$469$	−242.766	+	420.483i	−0.517624	+	0.896552i
$470$		0			0
$471$	98.6265	−	126.807i	0.209398	−	0.269229i
$472$		0			0
$473$	374.023	+	65.9504i	0.790747	+	0.139430i
$474$		0			0
$475$	313.832	−	263.336i	0.660698	−	0.554392i
$476$		0			0
$477$	−24.3485	−	327.606i	−0.0510450	−	0.686806i
$478$		0			0
$479$	50.2428	−	138.041i	0.104891	−	0.288186i	−0.876134	−	0.482068i	$-0.839886\pi$
$479$	50.2428	−	138.041i	0.104891	−	0.288186i	0.981025	+	0.193882i	$0.0621080\pi$
$480$		0			0
$481$	−14.2090	−	11.9228i	−0.0295405	−	0.0247875i
$482$		0			0
$483$	400.235	−	14.8527i	0.828645	−	0.0307510i
$484$		0			0
$485$		−	251.551i		−	0.518661i
$486$		0			0
$487$	733.027			1.50519			0.752595	−	0.658484i	$-0.228802\pi$
$487$	733.027			1.50519			0.752595	+	0.658484i	$0.228802\pi$
$488$		0			0
$489$	34.4790	+	929.103i	0.0705092	+	1.90001i
$490$		0			0
$491$	−262.913	+	313.328i	−0.535465	+	0.638142i	−0.964164	−	0.265305i	$-0.914527\pi$
$491$	−262.913	+	313.328i	−0.535465	+	0.638142i	0.428700	+	0.903447i	$0.358972\pi$
$492$		0			0
$493$	−129.563	−	47.1570i	−0.262805	−	0.0956531i
$494$		0			0
$495$	−197.810	+	14.7017i	−0.399616	+	0.0297004i
$496$		0			0
$497$	−329.270	−	392.409i	−0.662516	−	0.789555i
$498$		0			0
$499$	7.46907	−	42.3592i	0.0149681	−	0.0848881i	−0.976409	−	0.215931i	$-0.930721\pi$
$499$	7.46907	−	42.3592i	0.0149681	−	0.0848881i	0.991377	+	0.131043i	$0.0418325\pi$
$500$		0			0
$501$	−94.6331	−	73.6028i	−0.188888	−	0.146912i
$502$		0			0
$503$	−6.60922	−	3.81583i	−0.0131396	−	0.00758615i	0.493416	−	0.869794i	$-0.335748\pi$
$503$	−6.60922	−	3.81583i	−0.0131396	−	0.00758615i	−0.506555	+	0.862207i	$0.669081\pi$
$504$		0			0
$505$	−324.420	−	561.913i	−0.642417	−	1.11270i
$506$		0			0
$507$	−151.206	+	468.848i	−0.298236	+	0.924750i
$508$		0			0
$509$	38.3888	+	105.472i	0.0754200	+	0.207215i	0.971673	−	0.236327i	$-0.0759438\pi$
$509$	38.3888	+	105.472i	0.0754200	+	0.207215i	−0.896253	+	0.443542i	$0.853722\pi$
$510$		0			0
$511$	−50.3390	−	285.487i	−0.0985108	−	0.558682i
$512$		0			0
$513$	−661.764	+	487.463i	−1.28999	+	0.950221i
$514$		0			0
$515$	391.684	−	69.0644i	0.760551	−	0.134106i
$516$		0			0
$517$	196.964	−	71.6889i	0.380974	−	0.138663i
$518$		0			0
$519$	706.677	−	639.098i	1.36161	−	1.23140i
$520$		0			0
$521$	−419.995	+	242.484i	−0.806132	+	0.465420i	−0.845611	−	0.533800i	$-0.820764\pi$
$521$	−419.995	+	242.484i	−0.806132	+	0.465420i	0.0394789	+	0.999220i	$0.487430\pi$
$522$		0			0
$523$	−516.637	+	894.842i	−0.987835	+	1.71098i	−0.359243	+	0.933244i	$0.616965\pi$
$523$	−516.637	+	894.842i	−0.987835	+	1.71098i	−0.628591	+	0.777736i	$0.716368\pi$
$524$		0			0
$525$	297.677	+	41.1723i	0.567005	+	0.0784235i
$526$		0			0
$527$	−393.599	−	69.4021i	−0.746867	−	0.131693i
$528$		0			0
$529$	158.795	−	133.245i	0.300179	−	0.251880i
$530$		0			0
$531$	96.8827	−	134.581i	0.182453	−	0.253449i
$532$		0			0
$533$	−43.7312	+	120.151i	−0.0820473	+	0.225423i
$534$		0			0
$535$	471.831	+	395.913i	0.881927	+	0.740024i
$536$		0			0
$537$	123.356	−	233.228i	0.229713	−	0.434316i
$538$		0			0
$539$		−	41.5301i		−	0.0770502i
$540$		0			0
$541$	266.600			0.492790			0.246395	−	0.969169i	$-0.420754\pi$
$541$	266.600			0.492790			0.246395	+	0.969169i	$0.420754\pi$
$542$		0			0
$543$	770.796	−	483.993i	1.41951	−	0.891332i
$544$		0			0
$545$	−106.705	+	127.166i	−0.195789	+	0.233332i
$546$		0			0
$547$	291.778	+	106.199i	0.533415	+	0.194147i	0.594663	−	0.803975i	$-0.297286\pi$
$547$	291.778	+	106.199i	0.533415	+	0.194147i	−0.0612474	+	0.998123i	$0.519508\pi$
$548$		0			0
$549$	−45.8394	−	12.9276i	−0.0834963	−	0.0235475i
$550$		0			0
$551$	393.562	+	469.029i	0.714268	+	0.851232i
$552$		0			0
$553$	23.4169	−	132.804i	0.0423452	−	0.240151i
$554$		0			0
$555$	80.0108	−	32.5301i	0.144164	−	0.0586128i
$556$		0			0
$557$	511.510	+	295.320i	0.918330	+	0.530198i	0.883102	−	0.469181i	$-0.155451\pi$
$557$	511.510	+	295.320i	0.918330	+	0.530198i	0.0352283	+	0.999379i	$0.488784\pi$
$558$		0			0
$559$	−64.0714	−	110.975i	−0.114618	−	0.198524i
$560$		0			0
$561$	130.436	−	28.0231i	0.232506	−	0.0499521i
$562$		0			0
$563$	60.5467	+	166.351i	0.107543	+	0.295472i	0.981778	−	0.190031i	$-0.0608588\pi$
$563$	60.5467	+	166.351i	0.107543	+	0.295472i	−0.874235	+	0.485503i	$0.838637\pi$
$564$		0			0
$565$	−9.96158	−	56.4949i	−0.0176311	−	0.0999910i
$566$		0			0
$567$	−590.801	−	120.188i	−1.04198	−	0.211972i
$568$		0			0
$569$	838.648	−	147.876i	1.47390	−	0.259888i	0.621761	−	0.783207i	$-0.286417\pi$
$569$	838.648	−	147.876i	1.47390	−	0.259888i	0.852137	+	0.523319i	$0.175306\pi$
$570$		0			0
$571$	−112.566	+	40.9706i	−0.197138	+	0.0717523i	−0.438702	−	0.898632i	$-0.644562\pi$
$571$	−112.566	+	40.9706i	−0.197138	+	0.0717523i	0.241564	+	0.970385i	$0.422339\pi$
$572$		0			0
$573$	−189.266	−	880.950i	−0.330307	−	1.53743i
$574$		0			0
$575$	−209.045	+	120.692i	−0.363556	+	0.209899i
$576$		0			0
$577$	−544.186	+	942.558i	−0.943130	+	1.63355i	−0.183677	+	0.982987i	$0.558800\pi$
$577$	−544.186	+	942.558i	−0.943130	+	1.63355i	−0.759453	+	0.650562i	$0.774533\pi$
$578$		0			0
$579$	277.781	+	683.227i	0.479760	+	1.18001i
$580$		0			0
$581$	−777.461	−	137.087i	−1.33814	−	0.235951i
$582$		0			0
$583$	181.392	−	152.206i	0.311136	−	0.261074i
$584$		0			0
$585$	46.7003	+	47.9383i	0.0798296	+	0.0819458i
$586$		0			0
$587$	289.985	−	796.728i	0.494012	−	1.35729i	−0.402967	−	0.915215i	$-0.632021\pi$
$587$	289.985	−	796.728i	0.494012	−	1.35729i	0.896979	−	0.442073i	$-0.145757\pi$
$588$		0			0
$589$	1359.59	+	1140.83i	2.30830	+	1.93689i
$590$		0			0
$591$	541.380	+	862.189i	0.916041	+	1.45886i
$592$		0			0
$593$			847.621i			1.42938i	0.699443	+	0.714689i	$0.253432\pi$
$593$			847.621i			1.42938i	−0.699443	+	0.714689i	$0.746568\pi$
$594$		0			0
$595$	173.348			0.291341
$596$		0			0
$597$	−273.458	−	144.634i	−0.458054	−	0.242269i
$598$		0			0
$599$	424.502	−	505.902i	0.708684	−	0.844577i	−0.284795	−	0.958588i	$-0.591926\pi$
$599$	424.502	−	505.902i	0.708684	−	0.844577i	0.993479	+	0.114011i	$0.0363700\pi$
$600$		0			0
$601$	−654.635	−	238.268i	−1.08924	−	0.396452i	−0.265903	−	0.964000i	$-0.585670\pi$
$601$	−654.635	−	238.268i	−1.08924	−	0.396452i	−0.823341	+	0.567548i	$0.807892\pi$
$602$		0			0
$603$	−58.8130	+	584.128i	−0.0975340	+	0.968702i
$604$		0			0
$605$	172.335	+	205.381i	0.284852	+	0.339473i
$606$		0			0
$607$	−80.2584	+	455.168i	−0.132221	+	0.749865i	0.844533	+	0.535503i	$0.179878\pi$
$607$	−80.2584	+	455.168i	−0.132221	+	0.749865i	−0.976754	+	0.214361i	$0.931233\pi$
$608$		0			0
$609$	−61.5330	+	444.886i	−0.101039	+	0.730519i
$610$		0			0
$611$	−61.2460	−	35.3604i	−0.100239	−	0.0578730i
$612$		0			0
$613$	−387.969	−	671.982i	−0.632902	−	1.09622i	−0.986955	−	0.160994i	$-0.948530\pi$
$613$	−387.969	−	671.982i	−0.632902	−	1.09622i	0.354053	−	0.935225i	$-0.384803\pi$
$614$		0			0
$615$	−399.357	−	441.585i	−0.649361	−	0.718025i
$616$		0			0
$617$	−403.568	−	1108.79i	−0.654081	−	1.79707i	−0.602094	−	0.798425i	$-0.705667\pi$
$617$	−403.568	−	1108.79i	−0.654081	−	1.79707i	−0.0519865	−	0.998648i	$-0.516555\pi$
$618$		0			0
$619$	7.02797	+	39.8576i	0.0113537	+	0.0643903i	0.989958	−	0.141360i	$-0.0451476\pi$
$619$	7.02797	+	39.8576i	0.0113537	+	0.0643903i	−0.978604	+	0.205751i	$0.934036\pi$
$620$		0			0
$621$	433.864	−	215.144i	0.698655	−	0.346448i
$622$		0			0
$623$	−324.461	+	57.2112i	−0.520804	+	0.0918317i
$624$		0			0
$625$	100.958	−	36.7457i	0.161533	−	0.0587931i
$626$		0			0
$627$	−563.845	−	181.842i	−0.899274	−	0.290020i
$628$		0			0
$629$	−50.3094	+	29.0461i	−0.0799831	+	0.0461783i
$630$		0			0
$631$	−11.4649	+	19.8578i	−0.0181694	+	0.0314703i	−0.874967	−	0.484182i	$-0.839117\pi$
$631$	−11.4649	+	19.8578i	−0.0181694	+	0.0314703i	0.856798	+	0.515653i	$0.172450\pi$
$632$		0			0
$633$	359.260	−	461.910i	0.567551	−	0.729715i
$634$		0			0
$635$	−64.8224	−	11.4299i	−0.102083	−	0.0179999i
$636$		0			0
$637$	−10.7340	+	9.00693i	−0.0168509	+	0.0141396i
$638$		0			0
$639$	−557.888	−	269.087i	−0.873064	−	0.421106i
$640$		0			0
$641$	−269.893	+	741.525i	−0.421050	+	1.15683i	0.530056	+	0.847963i	$0.322171\pi$
$641$	−269.893	+	741.525i	−0.421050	+	1.15683i	−0.951106	+	0.308863i	$0.900051\pi$
$642$		0			0
$643$	−282.533	−	237.074i	−0.439399	−	0.368699i	0.396086	−	0.918214i	$-0.370368\pi$
$643$	−282.533	−	237.074i	−0.439399	−	0.368699i	−0.835484	+	0.549514i	$0.814813\pi$
$644$		0			0
$645$	596.284	−	22.1281i	0.924471	−	0.0343071i
$646$		0			0
$647$			670.419i			1.03620i	0.855321	+	0.518098i	$0.173360\pi$
$647$			670.419i			1.03620i	−0.855321	+	0.518098i	$0.826640\pi$
$648$		0			0
$649$	119.528			0.184173
$650$		0			0
$651$	48.2795	+	1300.98i	0.0741621	+	1.99844i
$652$		0			0
$653$	77.2311	−	92.0404i	0.118271	−	0.140950i	−0.703660	−	0.710537i	$-0.748452\pi$
$653$	77.2311	−	92.0404i	0.118271	−	0.140950i	0.821931	+	0.569587i	$0.192897\pi$
$654$		0			0
$655$	−575.776	−	209.565i	−0.879047	−	0.319947i
$656$		0			0
$657$	−197.278	−	289.736i	−0.300271	−	0.440998i
$658$		0			0
$659$	−113.103	−	134.790i	−0.171628	−	0.204538i	0.673373	−	0.739303i	$-0.264845\pi$
$659$	−113.103	−	134.790i	−0.171628	−	0.204538i	−0.845001	+	0.534765i	$0.820400\pi$
$660$		0			0
$661$	108.446	−	615.027i	0.164063	−	0.930449i	−0.785962	−	0.618275i	$-0.787832\pi$
$661$	108.446	−	615.027i	0.164063	−	0.930449i	0.950025	−	0.312174i	$-0.101057\pi$
$662$		0			0
$663$	−35.5315	−	27.6354i	−0.0535920	−	0.0416823i
$664$		0			0
$665$	−666.654	−	384.893i	−1.00249	−	0.578786i
$666$		0			0
$667$	−180.377	−	312.422i	−0.270430	−	0.468399i
$668$		0			0
$669$	−285.817	+	886.241i	−0.427229	+	1.32473i
$670$		0			0
$671$	−11.7416	−	32.2597i	−0.0174986	−	0.0480770i
$672$		0			0
$673$	−20.2310	−	114.735i	−0.0300609	−	0.170484i	0.966081	−	0.258238i	$-0.0831420\pi$
$673$	−20.2310	−	114.735i	−0.0300609	−	0.170484i	−0.996142	+	0.0877547i	$0.972031\pi$
$674$		0			0
$675$	348.623	−	102.445i	0.516478	−	0.151771i
$676$		0			0
$677$	1010.59	−	178.193i	1.49274	−	0.263210i	0.633084	−	0.774083i	$-0.281789\pi$
$677$	1010.59	−	178.193i	1.49274	−	0.263210i	0.859656	+	0.510873i	$0.170678\pi$
$678$		0			0
$679$	517.882	−	188.494i	0.762713	−	0.277605i
$680$		0			0
$681$	−39.4447	+	35.6726i	−0.0579217	+	0.0523827i
$682$		0			0
$683$	−843.558	+	487.028i	−1.23508	+	0.713072i	−0.968084	−	0.250626i	$-0.919363\pi$
$683$	−843.558	+	487.028i	−1.23508	+	0.713072i	−0.266993	+	0.963698i	$0.586030\pi$
$684$		0			0
$685$	324.634	−	562.282i	0.473918	−	0.820849i
$686$		0			0
$687$	−571.509	−	79.0465i	−0.831890	−	0.115060i
$688$		0			0
$689$	−78.6798	−	13.8734i	−0.114194	−	0.0201355i
$690$		0			0
$691$	358.834	−	301.097i	0.519297	−	0.435742i	−0.345090	−	0.938570i	$-0.612152\pi$
$691$	358.834	−	301.097i	0.519297	−	0.435742i	0.864386	+	0.502828i	$0.167707\pi$
$692$		0			0
$693$	−178.491	−	396.226i	−0.257563	−	0.571755i
$694$		0			0
$695$	274.157	−	753.240i	0.394471	−	1.08380i
$696$		0			0
$697$	306.763	+	257.405i	0.440119	+	0.369304i
$698$		0			0
$699$	−284.533	+	537.963i	−0.407057	+	0.769618i
$700$		0			0
$701$		−	727.947i		−	1.03844i	−0.854641	−	0.519220i	$-0.826222\pi$
$701$		−	727.947i		−	1.03844i	0.854641	−	0.519220i	$-0.173778\pi$
$702$		0			0
$703$	257.970			0.366956
$704$		0			0
$705$	278.889	−	175.118i	0.395587	−	0.248394i
$706$		0			0
$707$	913.746	−	1088.96i	1.29243	−	1.54025i
$708$		0			0
$709$	136.865	+	49.8146i	0.193039	+	0.0702604i	0.436731	−	0.899592i	$-0.356136\pi$
$709$	136.865	+	49.8146i	0.193039	+	0.0702604i	−0.243692	+	0.969853i	$0.578359\pi$
$710$		0			0
$711$	−40.1385	−	158.039i	−0.0564536	−	0.222278i
$712$		0			0
$713$	−672.181	−	801.074i	−0.942751	−	1.12353i
$714$		0			0
$715$	−8.37678	+	47.5071i	−0.0117158	+	0.0664435i
$716$		0			0
$717$	−561.446	+	228.268i	−0.783049	+	0.318366i
$718$		0			0
$719$	−820.131	−	473.503i	−1.14066	−	0.658558i	−0.194063	−	0.980989i	$-0.562167\pi$
$719$	−820.131	−	473.503i	−1.14066	−	0.658558i	−0.946593	+	0.322431i	$0.895500\pi$
$720$		0			0
$721$	435.686	+	754.630i	0.604280	+	1.04664i
$722$		0			0
$723$	−650.383	+	139.730i	−0.899562	+	0.193264i
$724$		0			0
$725$	−92.5783	−	254.357i	−0.127694	−	0.350837i
$726$		0			0
$727$	−175.940	−	997.804i	−0.242008	−	1.37249i	−0.827340	−	0.561701i	$-0.810147\pi$
$727$	−175.940	−	997.804i	−0.242008	−	1.37249i	0.585332	−	0.810793i	$-0.300964\pi$
$728$		0			0
$729$	−711.020	+	160.909i	−0.975336	+	0.220725i
$730$		0			0
$731$	−395.234	+	69.6904i	−0.540676	+	0.0953357i
$732$		0			0
$733$	636.102	−	231.522i	0.867806	−	0.315856i	0.130528	−	0.991445i	$-0.458333\pi$
$733$	636.102	−	231.522i	0.867806	−	0.315856i	0.737279	+	0.675589i	$0.236111\pi$
$734$		0			0
$735$	−13.7053	−	63.7924i	−0.0186467	−	0.0867923i
$736$		0			0
$737$	−366.476	+	211.585i	−0.497253	+	0.287089i
$738$		0			0
$739$	−312.974	+	542.086i	−0.423510	+	0.733540i	−0.996280	−	0.0861757i	$-0.972535\pi$
$739$	−312.974	+	542.086i	−0.423510	+	0.733540i	0.572770	+	0.819716i	$0.305869\pi$
$740$		0			0
$741$	75.2854	+	185.171i	0.101600	+	0.249894i
$742$		0			0
$743$	−536.211	−	94.5485i	−0.721684	−	0.127252i	−0.199270	−	0.979945i	$-0.563857\pi$
$743$	−536.211	−	94.5485i	−0.721684	−	0.127252i	−0.522414	+	0.852692i	$0.674968\pi$
$744$		0			0
$745$	560.482	−	470.300i	0.752324	−	0.631275i
$746$		0			0
$747$	−925.196	+	234.979i	−1.23855	+	0.314564i
$748$		0			0
$749$	−461.534	+	1268.05i	−0.616200	+	1.69300i
$750$		0			0
$751$	97.6730	+	81.9574i	0.130057	+	0.109131i	0.705496	−	0.708714i	$-0.250724\pi$
$751$	97.6730	+	81.9574i	0.130057	+	0.109131i	−0.575439	+	0.817845i	$0.695169\pi$
$752$		0			0
$753$	−118.938	−	189.418i	−0.157952	−	0.251551i
$754$		0			0
$755$			406.351i			0.538213i
$756$		0			0
$757$	−247.528			−0.326985			−0.163493	−	0.986545i	$-0.552276\pi$
$757$	−247.528			−0.326985			−0.163493	+	0.986545i	$0.552276\pi$
$758$		0			0
$759$	308.567	+	163.204i	0.406544	+	0.215025i
$760$		0			0
$761$	−142.479	+	169.800i	−0.187226	+	0.223128i	−0.851490	−	0.524371i	$-0.824301\pi$
$761$	−142.479	+	169.800i	−0.187226	+	0.223128i	0.664264	+	0.747498i	$0.268745\pi$
$762$		0			0
$763$	−341.761	−	124.391i	−0.447917	−	0.163029i
$764$		0			0
$765$	191.108	−	86.0900i	0.249814	−	0.112536i
$766$		0			0
$767$	−25.9229	−	30.8938i	−0.0337978	−	0.0402787i
$768$		0			0
$769$	−7.21456	+	40.9158i	−0.00938174	+	0.0532065i	−0.989139	−	0.146982i	$-0.953044\pi$
$769$	−7.21456	+	40.9158i	−0.00938174	+	0.0532065i	0.979757	+	0.200188i	$0.0641553\pi$
$770$		0			0
$771$	−128.336	+	927.874i	−0.166454	+	1.20347i
$772$		0			0
$773$	47.0366	+	27.1566i	0.0608494	+	0.0351314i	0.530116	−	0.847925i	$-0.322148\pi$
$773$	47.0366	+	27.1566i	0.0608494	+	0.0351314i	−0.469267	+	0.883057i	$0.655482\pi$
$774$		0			0
$775$	−392.315	−	679.510i	−0.506213	−	0.876787i
$776$		0			0
$777$	126.926	+	140.347i	0.163354	+	0.180627i
$778$		0			0
$779$	−608.207	−	1671.04i	−0.780754	−	2.14510i
$780$		0			0
$781$	−77.5269	−	439.677i	−0.0992662	−	0.562966i
$782$		0			0
$783$	153.107	+	521.025i	0.195539	+	0.665421i
$784$		0			0
$785$	179.160	−	31.5908i	0.228230	−	0.0402431i
$786$		0			0
$787$	738.920	−	268.945i	0.938907	−	0.341734i	0.173173	−	0.984891i	$-0.444598\pi$
$787$	738.920	−	268.945i	0.938907	−	0.341734i	0.765734	+	0.643157i	$0.222376\pi$
$788$		0			0
$789$	235.207	+	75.8553i	0.298108	+	0.0961410i
$790$		0			0
$791$	108.845	−	62.8417i	0.137604	−	0.0794459i
$792$		0			0
$793$	−5.79150	+	10.0312i	−0.00730327	+	0.0126496i
$794$		0			0
$795$	228.399	−	293.658i	0.287294	−	0.369381i
$796$		0			0
$797$	−877.464	−	154.721i	−1.10096	−	0.194129i	−0.406493	−	0.913654i	$-0.633248\pi$
$797$	−877.464	−	154.721i	−1.10096	−	0.194129i	−0.694466	+	0.719525i	$0.744359\pi$
$798$		0			0
$799$	−169.672	+	142.372i	−0.212355	+	0.178187i
$800$		0			0
$801$	−329.290	+	224.210i	−0.411098	+	0.279913i
$802$		0			0
$803$	86.4138	−	237.420i	0.107614	−	0.295666i
$804$		0			0
$805$	347.448	+	291.543i	0.431612	+	0.362166i
$806$		0			0
$807$	−695.973	+	25.8275i	−0.862419	+	0.0320044i
$808$		0			0
$809$			1078.04i			1.33256i	0.745702	+	0.666280i	$0.232114\pi$
$809$			1078.04i			1.33256i	−0.745702	+	0.666280i	$0.767886\pi$
$810$		0			0
$811$	−509.210			−0.627879			−0.313939	−	0.949443i	$-0.601649\pi$
$811$	−509.210			−0.627879			−0.313939	+	0.949443i	$0.601649\pi$
$812$		0			0
$813$	50.3075	+	1355.63i	0.0618789	+	1.66744i
$814$		0			0
$815$	−676.786	+	806.562i	−0.830413	+	0.989647i
$816$		0			0
$817$	1674.71	+	609.545i	2.04983	+	0.746077i
$818$		0			0
$819$	−63.6996	+	132.066i	−0.0777773	+	0.161253i
$820$		0			0
$821$	−682.395	−	813.247i	−0.831176	−	0.990557i	−0.999988	−	0.00490854i	$-0.998438\pi$
$821$	−682.395	−	813.247i	−0.831176	−	0.990557i	0.168812	−	0.985648i	$-0.446007\pi$
$822$		0			0
$823$	34.2168	−	194.053i	0.0415756	−	0.235787i	−0.956938	−	0.290293i	$-0.906247\pi$
$823$	34.2168	−	194.053i	0.0415756	−	0.235787i	0.998513	+	0.0545058i	$0.0173583\pi$
$824$		0			0
$825$	206.743	+	160.798i	0.250597	+	0.194907i
$826$		0			0
$827$	804.366	+	464.401i	0.972632	+	0.561549i	0.900037	−	0.435812i	$-0.143539\pi$
$827$	804.366	+	464.401i	0.972632	+	0.561549i	0.0725941	+	0.997362i	$0.476872\pi$
$828$		0			0
$829$	311.615	+	539.733i	0.375892	+	0.651065i	0.990460	−	0.137799i	$-0.0440029\pi$
$829$	311.615	+	539.733i	0.375892	+	0.651065i	−0.614568	+	0.788864i	$0.710670\pi$
$830$		0			0
$831$	25.0002	−	77.5191i	0.0300845	−	0.0932841i
$832$		0			0
$833$	15.0096	+	41.2386i	0.0180188	+	0.0495061i
$834$		0			0
$835$	−23.5756	−	133.704i	−0.0282342	−	0.160124i
$836$		0			0
$837$	699.336	+	1410.30i	0.835527	+	1.68494i
$838$		0			0
$839$	−81.5443	+	14.3785i	−0.0971923	+	0.0171376i	−0.222033	−	0.975039i	$-0.571269\pi$
$839$	−81.5443	+	14.3785i	−0.0971923	+	0.0171376i	0.124840	+	0.992177i	$0.460158\pi$
$840$		0			0
$841$	−410.139	+	149.279i	−0.487681	+	0.177501i
$842$		0			0
$843$	450.152	−	407.104i	0.533988	−	0.482923i
$844$		0			0
$845$	−483.137	+	278.939i	−0.571760	+	0.330106i
$846$		0			0
$847$	−293.695	+	508.695i	−0.346747	+	0.600584i
$848$		0			0
$849$	−655.931	−	90.7231i	−0.772592	−	0.106859i
$850$		0			0
$851$	−149.688	−	26.3940i	−0.175896	−	0.0310153i
$852$		0			0
$853$	−780.383	+	654.819i	−0.914869	+	0.767666i	−0.973039	−	0.230640i	$-0.925918\pi$
$853$	−780.383	+	654.819i	−0.914869	+	0.767666i	0.0581699	+	0.998307i	$0.481473\pi$
$854$		0			0
$855$	−926.105	−	93.2450i	−1.08316	−	0.109059i
$856$		0			0
$857$	458.961	−	1260.99i	0.535544	−	1.47140i	−0.316840	−	0.948479i	$-0.602622\pi$
$857$	458.961	−	1260.99i	0.535544	−	1.47140i	0.852384	−	0.522916i	$-0.175156\pi$
$858$		0			0
$859$	−55.2770	−	46.3829i	−0.0643504	−	0.0539964i	0.610045	−	0.792367i	$-0.291151\pi$
$859$	−55.2770	−	46.3829i	−0.0643504	−	0.0539964i	−0.674396	+	0.738370i	$0.735596\pi$
$860$		0			0
$861$	609.869	−	1153.07i	0.708326	−	1.33922i
$862$		0			0
$863$		−	1062.67i		−	1.23137i	−0.787993	−	0.615684i	$-0.788880\pi$
$863$		−	1062.67i		−	1.23137i	0.787993	−	0.615684i	$-0.211120\pi$
$864$		0			0
$865$	1079.01			1.24741
$866$		0			0
$867$	614.859	−	386.079i	0.709180	−	0.445304i
$868$		0			0
$869$	75.5480	−	90.0347i	0.0869368	−	0.103607i
$870$		0			0
$871$	134.167	+	48.8329i	0.154038	+	0.0560654i
$872$		0			0
$873$	477.329	−	465.002i	0.546769	−	0.532649i
$874$		0			0
$875$	625.111	+	744.979i	0.714413	+	0.851404i
$876$		0			0
$877$	−155.955	+	884.468i	−0.177828	+	1.00851i	0.757000	+	0.653415i	$0.226664\pi$
$877$	−155.955	+	884.468i	−0.177828	+	1.00851i	−0.934828	+	0.355100i	$0.884447\pi$
$878$		0			0
$879$	618.683	−	251.539i	0.703848	−	0.286165i
$880$		0			0
$881$	66.9620	+	38.6605i	0.0760068	+	0.0438825i	0.537522	−	0.843250i	$-0.319361\pi$
$881$	66.9620	+	38.6605i	0.0760068	+	0.0438825i	−0.461515	+	0.887132i	$0.652694\pi$
$882$		0			0
$883$	−132.104	−	228.810i	−0.149608	−	0.259129i	0.781475	−	0.623937i	$-0.214468\pi$
$883$	−132.104	−	228.810i	−0.149608	−	0.259129i	−0.931083	+	0.364808i	$0.881134\pi$
$884$		0			0
$885$	183.602	−	39.4455i	0.207459	−	0.0445711i
$886$		0			0
$887$	195.973	+	538.431i	0.220939	+	0.607025i	0.999796	−	0.0201763i	$-0.00642274\pi$
$887$	195.973	+	538.431i	0.220939	+	0.607025i	−0.778858	+	0.627201i	$0.784201\pi$
$888$		0			0
$889$	−25.0417	−	142.019i	−0.0281684	−	0.159751i
$890$		0			0
$891$	−393.557	−	348.176i	−0.441702	−	0.390770i
$892$		0			0
$893$	968.631	−	170.796i	1.08469	−	0.191261i
$894$		0			0
$895$	280.769	−	102.191i	0.313708	−	0.114180i
$896$		0			0
$897$	−24.7389	−	115.149i	−0.0275796	−	0.128371i
$898$		0			0
$899$	1015.54	−	586.324i	1.12964	−	0.652196i
$900$		0			0
$901$	−125.110	+	216.696i	−0.138856	+	0.240506i
$902$		0			0
$903$	492.368	+	1211.02i	0.545258	+	1.34111i
$904$		0			0
$905$	1015.05	+	178.980i	1.12160	+	0.197768i
$906$		0			0
$907$	−6.73084	+	5.64785i	−0.00742099	+	0.00622695i	−0.646491	−	0.762922i	$-0.723764\pi$
$907$	−6.73084	+	5.64785i	−0.00742099	+	0.00622695i	0.639070	+	0.769149i	$0.279320\pi$
$908$		0			0
$909$	466.550	−	1654.32i	0.513257	−	1.81994i
$910$		0			0
$911$	−80.6749	+	221.652i	−0.0885564	+	0.243307i	−0.976063	−	0.217489i	$-0.930214\pi$
$911$	−80.6749	+	221.652i	−0.0885564	+	0.243307i	0.887506	+	0.460795i	$0.152436\pi$
$912$		0			0
$913$	−527.082	−	442.274i	−0.577308	−	0.484419i
$914$		0			0
$915$	−28.6817	−	45.6777i	−0.0313461	−	0.0499210i
$916$		0			0
$917$		−	1342.42i		−	1.46392i
$918$		0			0
$919$	−585.987			−0.637635			−0.318818	−	0.947816i	$-0.603286\pi$
$919$	−585.987			−0.637635			−0.318818	+	0.947816i	$0.603286\pi$
$920$		0			0
$921$	−352.294	−	186.331i	−0.382512	−	0.202314i
$922$		0			0
$923$	−96.8269	+	115.394i	−0.104905	+	0.125020i
$924$		0			0
$925$	−107.169	−	39.0061i	−0.115858	−	0.0421688i
$926$		0			0
$927$	855.096	+	615.569i	0.922434	+	0.664044i
$928$		0			0
$929$	−356.989	−	425.443i	−0.384273	−	0.457958i	0.538885	−	0.842379i	$-0.318846\pi$
$929$	−356.989	−	425.443i	−0.384273	−	0.457958i	−0.923158	+	0.384421i	$0.874401\pi$
$930$		0			0
$931$	33.8407	−	191.920i	0.0363488	−	0.206144i
$932$		0			0
$933$	66.4950	−	480.761i	0.0712701	−	0.515285i
$934$		0			0
$935$	130.842	+	75.5415i	0.139938	+	0.0807931i
$936$		0			0
$937$	65.2985	+	113.100i	0.0696889	+	0.120705i	0.898764	−	0.438432i	$-0.144466\pi$
$937$	65.2985	+	113.100i	0.0696889	+	0.120705i	−0.829075	+	0.559137i	$0.811133\pi$
$938$		0			0
$939$	−278.749	−	308.225i	−0.296858	−	0.328248i
$940$		0			0
$941$	309.138	+	849.349i	0.328520	+	0.902602i	0.988487	+	0.151307i	$0.0483483\pi$
$941$	309.138	+	849.349i	0.328520	+	0.902602i	−0.659966	+	0.751295i	$0.729429\pi$
$942$		0			0
$943$	181.943	+	1031.85i	0.192941	+	1.09422i
$944$		0			0
$945$	−404.931	−	549.720i	−0.428498	−	0.581715i
$946$		0			0
$947$	−930.941	+	164.150i	−0.983043	+	0.173337i	−0.641995	−	0.766709i	$-0.721893\pi$
$947$	−930.941	+	164.150i	−0.983043	+	0.173337i	−0.341048	+	0.940046i	$0.610782\pi$
$948$		0			0
$949$	−80.1058	+	29.1561i	−0.0844107	+	0.0307230i
$950$		0			0
$951$	32.6872	+	10.5418i	0.0343714	+	0.0110849i
$952$		0			0
$953$	−476.177	+	274.921i	−0.499661	+	0.288480i	−0.728574	−	0.684967i	$-0.759816\pi$
$953$	−476.177	+	274.921i	−0.499661	+	0.288480i	0.228912	+	0.973447i	$0.426483\pi$
$954$		0			0
$955$	510.200	−	883.693i	0.534241	−	0.925333i
$956$		0			0
$957$	−240.317	+	308.982i	−0.251115	+	0.322865i
$958$		0			0
$959$	1400.86	+	247.009i	1.46075	+	0.257570i
$960$		0			0
$961$	1867.76	−	1567.24i	1.94356	−	1.63084i
$962$		0			0
$963$	120.936	+	1627.18i	0.125583	+	1.68970i
$964$		0			0
$965$	−285.665	+	784.858i	−0.296026	+	0.813324i
$966$		0			0
$967$	124.954	+	104.849i	0.129218	+	0.108427i	0.705106	−	0.709102i	$-0.250899\pi$
$967$	124.954	+	104.849i	0.129218	+	0.108427i	−0.575888	+	0.817528i	$0.695344\pi$
$968$		0			0
$969$	625.608	−	23.2163i	0.645622	−	0.0239590i
$970$		0			0
$971$		−	485.860i		−	0.500371i	−0.968198	−	0.250185i	$-0.919508\pi$
$971$		−	485.860i		−	0.500371i	0.968198	−	0.250185i	$-0.0804915\pi$
$972$		0			0
$973$	1756.17			1.80491
$974$		0			0
$975$	−3.27715	−	88.3091i	−0.00336118	−	0.0905734i
$976$		0			0
$977$	−803.489	+	957.561i	−0.822405	+	0.980104i	−0.999992	−	0.00400147i	$-0.998726\pi$
$977$	−803.489	+	957.561i	−0.822405	+	0.980104i	0.177587	+	0.984105i	$0.443171\pi$
$978$		0			0
$979$	−269.832	−	98.2108i	−0.275620	−	0.100317i
$980$		0			0
$981$	−438.552	+	32.5942i	−0.447046	+	0.0332255i
$982$		0			0
$983$	828.432	+	987.287i	0.842759	+	1.00436i	0.999859	+	0.0167783i	$0.00534095\pi$
$983$	828.432	+	987.287i	0.842759	+	1.00436i	−0.157100	+	0.987583i	$0.550215\pi$
$984$		0			0
$985$	−200.202	+	1135.40i	−0.203251	+	1.15269i
$986$		0			0
$987$	569.504	+	442.944i	0.577005	+	0.448778i
$988$		0			0
$989$	−909.390	−	525.036i	−0.919504	−	0.530876i
$990$		0			0
$991$	−647.663	−	1121.78i	−0.653544	−	1.13197i	−0.982257	−	0.187542i	$-0.939948\pi$
$991$	−647.663	−	1121.78i	−0.653544	−	1.13197i	0.328712	−	0.944430i	$-0.393385\pi$
$992$		0			0
$993$	584.927	−	1813.70i	0.589050	−	1.82649i
$994$		0			0
$995$	−119.819	−	329.200i	−0.120421	−	0.330854i
$996$		0			0
$997$	161.592	+	916.436i	0.162079	+	0.919194i	0.952026	+	0.306019i	$0.0989969\pi$
$997$	161.592	+	916.436i	0.162079	+	0.919194i	−0.789947	+	0.613175i	$0.789892\pi$
$998$		0			0
$999$	209.631	+	91.6908i	0.209841	+	0.0917826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.u.a.41.9	✓	108
4.3	odd	2		432.3.bc.d.257.10		108
27.2	odd	18	inner	216.3.u.a.137.9	yes	108
108.83	even	18		432.3.bc.d.353.10		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.u.a.41.9	✓	108	1.1	even	1	trivial
216.3.u.a.137.9	yes	108	27.2	odd	18	inner
432.3.bc.d.257.10		108	4.3	odd	2
432.3.bc.d.353.10		108	108.83	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.u (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.111253 + 2.99794i) q^{3} +(-2.18378 + 2.60253i) q^{5} +(-6.99436 - 2.54574i) q^{7} +(-8.97525 + 0.667061i) q^{9} +O(q^{10})\)	\(q+(0.111253 + 2.99794i) q^{3} +(-2.18378 + 2.60253i) q^{5} +(-6.99436 - 2.54574i) q^{7} +(-8.97525 + 0.667061i) q^{9} +(-4.16991 - 4.96950i) q^{11} +(-0.380081 + 2.15555i) q^{13} +(-8.04518 - 6.25731i) q^{15} +(5.93670 + 3.42755i) q^{17} +(-15.2207 - 26.3631i) q^{19} +(6.85381 - 21.2519i) q^{21} +(6.13455 + 16.8545i) q^{23} +(2.33694 + 13.2534i) q^{25} +(-2.99833 - 26.8330i) q^{27} +(-19.8076 + 3.49261i) q^{29} +(-54.7865 + 19.9407i) q^{31} +(14.4343 - 13.0540i) q^{33} +(21.8995 - 12.6437i) q^{35} +(-4.23715 + 7.33896i) q^{37} +(-6.50447 - 0.899646i) q^{39} +(57.5289 + 10.1439i) q^{41} +(-44.8479 + 37.6319i) q^{43} +(17.8640 - 24.8151i) q^{45} +(-11.0508 + 30.3618i) q^{47} +(4.90408 + 4.11501i) q^{49} +(-9.61511 + 18.1792i) q^{51} +36.5011i q^{53} +22.0395 q^{55} +(77.3415 - 48.5638i) q^{57} +(-11.8435 + 14.1145i) q^{59} +(4.97280 + 1.80995i) q^{61} +(64.4742 + 18.1830i) q^{63} +(-4.77986 - 5.69642i) q^{65} +(11.3273 - 64.2402i) q^{67} +(-49.8464 + 20.2661i) q^{69} +(59.6010 + 34.4107i) q^{71} +(19.4734 + 33.7290i) q^{73} +(-39.4730 + 8.48049i) q^{75} +(16.5148 + 45.3740i) q^{77} +(3.14606 + 17.8422i) q^{79} +(80.1101 - 11.9741i) q^{81} +(104.452 - 18.4177i) q^{83} +(-21.8848 + 7.96541i) q^{85} +(-12.6743 - 58.9933i) q^{87} +(38.3336 - 22.1319i) q^{89} +(8.14587 - 14.1091i) q^{91} +(-65.8760 - 162.028i) q^{93} +(101.850 + 17.9588i) q^{95} +(-56.7201 + 47.5938i) q^{97} +(40.7409 + 41.8209i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q+O(q^{10}) \) 108 * q	\( 108 q - 18 q^{11} - 24 q^{15} + 48 q^{21} + 72 q^{23} + 174 q^{27} + 108 q^{29} + 18 q^{33} - 144 q^{39} + 90 q^{41} - 90 q^{43} + 108 q^{45} - 72 q^{49} + 84 q^{51} - 18 q^{57} - 252 q^{59} + 144 q^{61} - 360 q^{63} - 216 q^{65} + 126 q^{67} - 120 q^{69} - 252 q^{75} - 504 q^{77} - 552 q^{81} - 180 q^{83} - 60 q^{87} - 486 q^{89} - 360 q^{93} - 1116 q^{95} + 270 q^{97} - 564 q^{99}+O(q^{100}) \) 108 * q - 18 * q^11 - 24 * q^15 + 48 * q^21 + 72 * q^23 + 174 * q^27 + 108 * q^29 + 18 * q^33 - 144 * q^39 + 90 * q^41 - 90 * q^43 + 108 * q^45 - 72 * q^49 + 84 * q^51 - 18 * q^57 - 252 * q^59 + 144 * q^61 - 360 * q^63 - 216 * q^65 + 126 * q^67 - 120 * q^69 - 252 * q^75 - 504 * q^77 - 552 * q^81 - 180 * q^83 - 60 * q^87 - 486 * q^89 - 360 * q^93 - 1116 * q^95 + 270 * q^97 - 564 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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