LMFDB - Embedded newform 216.2.q.a.169.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(25,216)]

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, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("216.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.q (of order $9$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.4
Character	$\chi$	$=$	216.169
Dual form			216.2.q.a.193.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56067 - 0.751197i) q^{3} +(-0.0770674 - 0.437071i) q^{5} +(0.935232 + 0.784753i) q^{7} +(1.87141 - 2.34475i) q^{9} +O(q^{10})$	\(q+(1.56067 - 0.751197i) q^{3} +(-0.0770674 - 0.437071i) q^{5} +(0.935232 + 0.784753i) q^{7} +(1.87141 - 2.34475i) q^{9} +(0.00921771 - 0.0522762i) q^{11} +(1.58518 + 0.576957i) q^{13} +(-0.448603 - 0.624232i) q^{15} +(-2.44650 - 4.23746i) q^{17} +(-1.83033 + 3.17022i) q^{19} +(2.04910 + 0.522200i) q^{21} +(-5.10868 + 4.28669i) q^{23} +(4.51337 - 1.64273i) q^{25} +(1.15929 - 5.06518i) q^{27} +(0.444832 - 0.161906i) q^{29} +(-6.09742 + 5.11634i) q^{31} +(-0.0248839 - 0.0885104i) q^{33} +(0.270917 - 0.469242i) q^{35} +(4.58110 + 7.93469i) q^{37} +(2.90735 - 0.290338i) q^{39} +(-5.04020 - 1.83448i) q^{41} +(-0.366331 + 2.07757i) q^{43} +(-1.16905 - 0.637234i) q^{45} +(0.992456 + 0.832769i) q^{47} +(-0.956715 - 5.42580i) q^{49} +(-7.00135 - 4.77549i) q^{51} -11.9018 q^{53} -0.0235588 q^{55} +(-0.475085 + 6.32261i) q^{57} +(1.65278 + 9.37338i) q^{59} +(-0.214574 - 0.180049i) q^{61} +(3.59025 - 0.724291i) q^{63} +(0.130006 - 0.737299i) q^{65} +(-7.43634 - 2.70660i) q^{67} +(-4.75284 + 10.5278i) q^{69} +(-2.96200 - 5.13033i) q^{71} +(-4.57777 + 7.92893i) q^{73} +(5.80989 - 5.95420i) q^{75} +(0.0496446 - 0.0416568i) q^{77} +(9.33162 - 3.39643i) q^{79} +(-1.99567 - 8.77595i) q^{81} +(10.6764 - 3.88590i) q^{83} +(-1.66353 + 1.39586i) q^{85} +(0.572615 - 0.586838i) q^{87} +(3.10545 - 5.37880i) q^{89} +(1.02974 + 1.78356i) q^{91} +(-5.67270 + 12.5653i) q^{93} +(1.52667 + 0.555662i) q^{95} +(2.80539 - 15.9101i) q^{97} +(-0.105324 - 0.119443i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{7} + 6 q^{9}+O(q^{10}) $ 24 * q - 3 * q^7 + 6 * q^9	$ 24 q - 3 q^{7} + 6 q^{9} + 6 q^{11} + 12 q^{13} - 3 q^{15} + 6 q^{17} + 9 q^{19} - 18 q^{21} + 24 q^{23} - 24 q^{25} - 9 q^{29} - 27 q^{31} + 21 q^{33} - 18 q^{35} + 15 q^{37} - 15 q^{39} - 6 q^{41} + 39 q^{43} - 69 q^{45} - 36 q^{47} + 3 q^{49} - 36 q^{51} - 18 q^{53} - 54 q^{55} + 27 q^{57} - 30 q^{59} + 12 q^{61} + 18 q^{63} - 18 q^{65} + 54 q^{67} - 57 q^{69} + 36 q^{73} - 51 q^{75} - 24 q^{77} - 45 q^{79} + 18 q^{81} + 33 q^{83} - 57 q^{85} + 90 q^{87} + 9 q^{89} + 39 q^{91} + 42 q^{93} + 87 q^{95} + 57 q^{97} - 24 q^{99}+O(q^{100}) $ 24 * q - 3 * q^7 + 6 * q^9 + 6 * q^11 + 12 * q^13 - 3 * q^15 + 6 * q^17 + 9 * q^19 - 18 * q^21 + 24 * q^23 - 24 * q^25 - 9 * q^29 - 27 * q^31 + 21 * q^33 - 18 * q^35 + 15 * q^37 - 15 * q^39 - 6 * q^41 + 39 * q^43 - 69 * q^45 - 36 * q^47 + 3 * q^49 - 36 * q^51 - 18 * q^53 - 54 * q^55 + 27 * q^57 - 30 * q^59 + 12 * q^61 + 18 * q^63 - 18 * q^65 + 54 * q^67 - 57 * q^69 + 36 * q^73 - 51 * q^75 - 24 * q^77 - 45 * q^79 + 18 * q^81 + 33 * q^83 - 57 * q^85 + 90 * q^87 + 9 * q^89 + 39 * q^91 + 42 * q^93 + 87 * q^95 + 57 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{9}\right)$

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
$3$	1.56067	−	0.751197i	0.901056	−	0.433704i
$3$	1.56067	−	0.751197i	0.901056	−	0.433704i
$4$		0			0
$5$	−0.0770674	−	0.437071i	−0.0344656	−	0.195464i	0.962714	−	0.270523i	$-0.0871966\pi$
$5$	−0.0770674	−	0.437071i	−0.0344656	−	0.195464i	−0.997179	+	0.0750589i	$0.976086\pi$
$6$		0			0
$7$	0.935232	+	0.784753i	0.353485	+	0.296609i	0.802188	−	0.597072i	$-0.203669\pi$
$7$	0.935232	+	0.784753i	0.353485	+	0.296609i	−0.448703	+	0.893681i	$0.648114\pi$
$8$		0			0
$9$	1.87141	−	2.34475i	0.623802	−	0.781582i
$10$		0			0
$11$	0.00921771	−	0.0522762i	0.00277924	−	0.0157619i	−0.983387	−	0.181524i	$-0.941897\pi$
$11$	0.00921771	−	0.0522762i	0.00277924	−	0.0157619i	0.986166	+	0.165762i	$0.0530082\pi$
$12$		0			0
$13$	1.58518	+	0.576957i	0.439649	+	0.160019i	0.552355	−	0.833609i	$-0.313729\pi$
$13$	1.58518	+	0.576957i	0.439649	+	0.160019i	−0.112706	+	0.993628i	$0.535952\pi$
$14$		0			0
$15$	−0.448603	−	0.624232i	−0.115829	−	0.161176i
$16$		0			0
$17$	−2.44650	−	4.23746i	−0.593363	−	1.02773i	−0.993776	−	0.111400i	$-0.964467\pi$
$17$	−2.44650	−	4.23746i	−0.593363	−	1.02773i	0.400413	−	0.916335i	$-0.368867\pi$
$18$		0			0
$19$	−1.83033	+	3.17022i	−0.419905	+	0.727297i	−0.995930	−	0.0901352i	$-0.971270\pi$
$19$	−1.83033	+	3.17022i	−0.419905	+	0.727297i	0.576024	+	0.817433i	$0.304603\pi$
$20$		0			0
$21$	2.04910	+	0.522200i	0.447150	+	0.113953i
$22$		0			0
$23$	−5.10868	+	4.28669i	−1.06523	+	0.893837i	−0.994612	−	0.103666i	$-0.966943\pi$
$23$	−5.10868	+	4.28669i	−1.06523	+	0.893837i	−0.0706216	+	0.997503i	$0.522498\pi$
$24$		0			0
$25$	4.51337	−	1.64273i	0.902674	−	0.328547i
$26$		0			0
$27$	1.15929	−	5.06518i	0.223105	−	0.974794i
$28$		0			0
$29$	0.444832	−	0.161906i	0.0826032	−	0.0300651i	−0.300388	−	0.953817i	$-0.597116\pi$
$29$	0.444832	−	0.161906i	0.0826032	−	0.0300651i	0.382991	+	0.923752i	$0.374894\pi$
$30$		0			0
$31$	−6.09742	+	5.11634i	−1.09513	+	0.918922i	−0.997088	−	0.0762601i	$-0.975702\pi$
$31$	−6.09742	+	5.11634i	−1.09513	+	0.918922i	−0.0980410	+	0.995182i	$0.531258\pi$
$32$		0			0
$33$	−0.0248839	−	0.0885104i	−0.00433173	−	0.0154077i
$34$		0			0
$35$	0.270917	−	0.469242i	0.0457933	−	0.0793163i
$36$		0			0
$37$	4.58110	+	7.93469i	0.753128	+	1.30446i	0.946300	+	0.323291i	$0.104789\pi$
$37$	4.58110	+	7.93469i	0.753128	+	1.30446i	−0.193172	+	0.981165i	$0.561878\pi$
$38$		0			0
$39$	2.90735	−	0.290338i	0.465549	−	0.0464912i
$40$		0			0
$41$	−5.04020	−	1.83448i	−0.787146	−	0.286498i	−0.0829971	−	0.996550i	$-0.526449\pi$
$41$	−5.04020	−	1.83448i	−0.787146	−	0.286498i	−0.704149	+	0.710052i	$0.748671\pi$
$42$		0			0
$43$	−0.366331	+	2.07757i	−0.0558649	+	0.316826i	−0.999916	−	0.0129740i	$-0.995870\pi$
$43$	−0.366331	+	2.07757i	−0.0558649	+	0.316826i	0.944051	+	0.329800i	$0.106981\pi$
$44$		0			0
$45$	−1.16905	−	0.637234i	−0.174271	−	0.0949932i
$46$		0			0
$47$	0.992456	+	0.832769i	0.144765	+	0.121472i	0.712294	−	0.701881i	$-0.247656\pi$
$47$	0.992456	+	0.832769i	0.144765	+	0.121472i	−0.567529	+	0.823353i	$0.692101\pi$
$48$		0			0
$49$	−0.956715	−	5.42580i	−0.136674	−	0.775114i
$50$		0			0
$51$	−7.00135	−	4.77549i	−0.980385	−	0.668703i
$52$		0			0
$53$	−11.9018			−1.63484			−0.817420	−	0.576043i	$-0.804596\pi$
$53$	−11.9018			−1.63484			−0.817420	+	0.576043i	$0.804596\pi$
$54$		0			0
$55$	−0.0235588			−0.00317667
$56$		0			0
$57$	−0.475085	+	6.32261i	−0.0629265	+	0.837450i
$58$		0			0
$59$	1.65278	+	9.37338i	0.215174	+	1.22031i	0.880605	+	0.473851i	$0.157137\pi$
$59$	1.65278	+	9.37338i	0.215174	+	1.22031i	−0.665431	+	0.746459i	$0.731752\pi$
$60$		0			0
$61$	−0.214574	−	0.180049i	−0.0274734	−	0.0230529i	0.628948	−	0.777448i	$-0.283486\pi$
$61$	−0.214574	−	0.180049i	−0.0274734	−	0.0230529i	−0.656421	+	0.754395i	$0.727930\pi$
$62$		0			0
$63$	3.59025	−	0.724291i	0.452329	−	0.0912521i
$64$		0			0
$65$	0.130006	−	0.737299i	0.0161252	−	0.0914507i
$66$		0			0
$67$	−7.43634	−	2.70660i	−0.908493	−	0.330664i	−0.154842	−	0.987939i	$-0.549487\pi$
$67$	−7.43634	−	2.70660i	−0.908493	−	0.330664i	−0.753651	+	0.657275i	$0.771709\pi$
$68$		0			0
$69$	−4.75284	+	10.5278i	−0.572174	+	1.26739i
$70$		0			0
$71$	−2.96200	−	5.13033i	−0.351525	−	0.608858i	0.634992	−	0.772519i	$-0.281003\pi$
$71$	−2.96200	−	5.13033i	−0.351525	−	0.608858i	−0.986517	+	0.163660i	$0.947670\pi$
$72$		0			0
$73$	−4.57777	+	7.92893i	−0.535788	+	0.928012i	0.463337	+	0.886182i	$0.346652\pi$
$73$	−4.57777	+	7.92893i	−0.535788	+	0.928012i	−0.999125	+	0.0418294i	$0.986681\pi$
$74$		0			0
$75$	5.80989	−	5.95420i	0.670868	−	0.687532i
$76$		0			0
$77$	0.0496446	−	0.0416568i	0.00565753	−	0.00474723i
$78$		0			0
$79$	9.33162	−	3.39643i	1.04989	−	0.382128i	0.241268	−	0.970459i	$-0.422437\pi$
$79$	9.33162	−	3.39643i	1.04989	−	0.382128i	0.808621	+	0.588330i	$0.200214\pi$
$80$		0			0
$81$	−1.99567	−	8.77595i	−0.221742	−	0.975105i
$82$		0			0
$83$	10.6764	−	3.88590i	1.17189	−	0.426533i	0.318560	−	0.947903i	$-0.396801\pi$
$83$	10.6764	−	3.88590i	1.17189	−	0.426533i	0.853331	+	0.521369i	$0.174579\pi$
$84$		0			0
$85$	−1.66353	+	1.39586i	−0.180435	+	0.151403i
$86$		0			0
$87$	0.572615	−	0.586838i	0.0613907	−	0.0629156i
$88$		0			0
$89$	3.10545	−	5.37880i	0.329177	−	0.570152i	−0.653172	−	0.757210i	$-0.726562\pi$
$89$	3.10545	−	5.37880i	0.329177	−	0.570152i	0.982349	+	0.187058i	$0.0598953\pi$
$90$		0			0
$91$	1.02974	+	1.78356i	0.107946	+	0.186968i
$92$		0			0
$93$	−5.67270	+	12.5653i	−0.588232	+	1.30296i
$94$		0			0
$95$	1.52667	+	0.555662i	0.156633	+	0.0570097i
$96$		0			0
$97$	2.80539	−	15.9101i	0.284844	−	1.61543i	−0.420998	−	0.907062i	$-0.638320\pi$
$97$	2.80539	−	15.9101i	0.284844	−	1.61543i	0.705842	−	0.708369i	$-0.250569\pi$
$98$		0			0
$99$	−0.105324	−	0.119443i	−0.0105855	−	0.0120045i
$100$		0			0
$101$	10.9928	+	9.22402i	1.09382	+	0.917824i	0.996994	−	0.0774773i	$-0.0246865\pi$
$101$	10.9928	+	9.22402i	1.09382	+	0.917824i	0.0968259	+	0.995301i	$0.469131\pi$
$102$		0			0
$103$	−3.03225	−	17.1967i	−0.298776	−	1.69444i	−0.651445	−	0.758696i	$-0.725837\pi$
$103$	−3.03225	−	17.1967i	−0.298776	−	1.69444i	0.352669	−	0.935748i	$-0.385274\pi$
$104$		0			0
$105$	0.0703200	−	0.935845i	0.00686253	−	0.0913292i
$106$		0			0
$107$	18.5879			1.79696			0.898482	−	0.439010i	$-0.144671\pi$
$107$	18.5879			1.79696			0.898482	+	0.439010i	$0.144671\pi$
$108$		0			0
$109$	1.45278			0.139151			0.0695753	−	0.997577i	$-0.477836\pi$
$109$	1.45278			0.139151			0.0695753	+	0.997577i	$0.477836\pi$
$110$		0			0
$111$	13.1101	+	8.94216i	1.24436	+	0.848753i
$112$		0			0
$113$	0.276022	+	1.56540i	0.0259659	+	0.147260i	0.995034	−	0.0995321i	$-0.0317346\pi$
$113$	0.276022	+	1.56540i	0.0259659	+	0.147260i	−0.969068	+	0.246792i	$0.920623\pi$
$114$		0			0
$115$	2.26730	+	1.90249i	0.211427	+	0.177408i
$116$		0			0
$117$	4.31933	−	2.63712i	0.399322	−	0.243801i
$118$		0			0
$119$	1.03732	−	5.88291i	0.0950905	−	0.539285i
$120$		0			0
$121$	10.3340	+	3.76126i	0.939452	+	0.341933i
$122$		0			0
$123$	−9.24416	+	0.923152i	−0.833518	+	0.0832378i
$124$		0			0
$125$	−2.17536	−	3.76783i	−0.194570	−	0.337005i
$126$		0			0
$127$	5.87831	−	10.1815i	0.521616	−	0.903465i	−0.478068	−	0.878323i	$-0.658663\pi$
$127$	5.87831	−	10.1815i	0.521616	−	0.903465i	0.999684	−	0.0251425i	$-0.00800395\pi$
$128$		0			0
$129$	0.988938	+	3.51759i	0.0870711	+	0.309706i
$130$		0			0
$131$	−5.11753	+	4.29412i	−0.447121	+	0.375179i	−0.838366	−	0.545107i	$-0.816489\pi$
$131$	−5.11753	+	4.29412i	−0.447121	+	0.375179i	0.391245	+	0.920286i	$0.372044\pi$
$132$		0			0
$133$	−4.19962	+	1.52854i	−0.364153	+	0.132541i
$134$		0			0
$135$	−2.30319	−	0.116332i	−0.198227	−	0.0100122i
$136$		0			0
$137$	12.2681	−	4.46524i	1.04814	−	0.381491i	0.240178	−	0.970729i	$-0.422794\pi$
$137$	12.2681	−	4.46524i	1.04814	−	0.381491i	0.807960	+	0.589238i	$0.200572\pi$
$138$		0			0
$139$	−16.5772	+	13.9099i	−1.40606	+	1.17983i	−0.447729	+	0.894169i	$0.647767\pi$
$139$	−16.5772	+	13.9099i	−1.40606	+	1.17983i	−0.958332	+	0.285656i	$0.907788\pi$
$140$		0			0
$141$	2.17447	+	0.554152i	0.183124	+	0.0466680i
$142$		0			0
$143$	0.0447728	−	0.0775488i	0.00374409	−	0.00648496i
$144$		0			0
$145$	−0.105046	−	0.181945i	−0.00872362	−	0.0151097i
$146$		0			0
$147$	−5.56896	−	7.74923i	−0.459320	−	0.639145i
$148$		0			0
$149$	8.48430	+	3.08803i	0.695061	+	0.252981i	0.665301	−	0.746576i	$-0.268303\pi$
$149$	8.48430	+	3.08803i	0.695061	+	0.252981i	0.0297602	+	0.999557i	$0.490526\pi$
$150$		0			0
$151$	1.09988	−	6.23773i	0.0895069	−	0.507619i	−0.906786	−	0.421592i	$-0.861472\pi$
$151$	1.09988	−	6.23773i	0.0895069	−	0.507619i	0.996293	−	0.0860275i	$-0.0274173\pi$
$152$		0			0
$153$	−14.5142	−	2.19359i	−1.17340	−	0.177341i
$154$		0			0
$155$	2.70612	+	2.27070i	0.217361	+	0.182387i
$156$		0			0
$157$	−3.93460	−	22.3142i	−0.314015	−	1.78087i	−0.577688	−	0.816257i	$-0.696045\pi$
$157$	−3.93460	−	22.3142i	−0.314015	−	1.78087i	0.263673	−	0.964612i	$-0.415066\pi$
$158$		0			0
$159$	−18.5748	+	8.94060i	−1.47308	+	0.709036i
$160$		0			0
$161$	−8.14180			−0.641664
$162$		0			0
$163$	−2.49680			−0.195565			−0.0977823	−	0.995208i	$-0.531175\pi$
$163$	−2.49680			−0.195565			−0.0977823	+	0.995208i	$0.531175\pi$
$164$		0			0
$165$	−0.0367676	+	0.0176973i	−0.00286235	+	0.00137773i
$166$		0			0
$167$	0.435926	+	2.47226i	0.0337329	+	0.191309i	0.997018	−	0.0771726i	$-0.0245893\pi$
$167$	0.435926	+	2.47226i	0.0337329	+	0.191309i	−0.963285	+	0.268482i	$0.913478\pi$
$168$		0			0
$169$	−7.77867	−	6.52708i	−0.598359	−	0.502083i
$170$		0			0
$171$	4.00807	+	10.2244i	0.306505	+	0.781880i
$172$		0			0
$173$	−2.38044	+	13.5001i	−0.180982	+	1.02640i	0.750029	+	0.661405i	$0.230039\pi$
$173$	−2.38044	+	13.5001i	−0.180982	+	1.02640i	−0.931011	+	0.364992i	$0.881072\pi$
$174$		0			0
$175$	5.51019	+	2.00555i	0.416531	+	0.151605i
$176$		0			0
$177$	9.62071	+	13.3872i	0.723137	+	1.00625i
$178$		0			0
$179$	−1.96977	−	3.41174i	−0.147227	−	0.255005i	0.782974	−	0.622054i	$-0.213702\pi$
$179$	−1.96977	−	3.41174i	−0.147227	−	0.255005i	−0.930202	+	0.367049i	$0.880368\pi$
$180$		0			0
$181$	−3.98124	+	6.89571i	−0.295923	+	0.512554i	−0.975199	−	0.221329i	$-0.928961\pi$
$181$	−3.98124	+	6.89571i	−0.295923	+	0.512554i	0.679276	+	0.733883i	$0.262294\pi$
$182$		0			0
$183$	−0.470133	−	0.119811i	−0.0347532	−	0.00885665i
$184$		0			0
$185$	3.11497	−	2.61377i	0.229017	−	0.192168i
$186$		0			0
$187$	−0.244069	+	0.0888340i	−0.0178481	+	0.00649619i
$188$		0			0
$189$	5.05912	−	3.82736i	0.367997	−	0.278400i
$190$		0			0
$191$	−11.2633	+	4.09951i	−0.814985	+	0.296630i	−0.715682	−	0.698427i	$-0.753884\pi$
$191$	−11.2633	+	4.09951i	−0.814985	+	0.296630i	−0.0993039	+	0.995057i	$0.531662\pi$
$192$		0			0
$193$	−6.55375	+	5.49925i	−0.471749	+	0.395845i	−0.847432	−	0.530904i	$-0.821853\pi$
$193$	−6.55375	+	5.49925i	−0.471749	+	0.395845i	0.375683	+	0.926748i	$0.377408\pi$
$194$		0			0
$195$	−0.350960	−	1.24834i	−0.0251328	−	0.0893957i
$196$		0			0
$197$	4.14032	−	7.17125i	0.294986	−	0.510930i	−0.679996	−	0.733216i	$-0.738018\pi$
$197$	4.14032	−	7.17125i	0.294986	−	0.510930i	0.974982	+	0.222286i	$0.0713518\pi$
$198$		0			0
$199$	−3.75733	−	6.50789i	−0.266350	−	0.461332i	0.701566	−	0.712604i	$-0.252484\pi$
$199$	−3.75733	−	6.50789i	−0.266350	−	0.461332i	−0.967916	+	0.251272i	$0.919151\pi$
$200$		0			0
$201$	−13.6389	+	1.36202i	−0.962013	+	0.0960698i
$202$		0			0
$203$	0.543077	+	0.197664i	0.0381165	+	0.0138733i
$204$		0			0
$205$	−0.413364	+	2.34430i	−0.0288706	+	0.163733i
$206$		0			0
$207$	0.490788	+	20.0007i	0.0341121	+	1.39015i
$208$		0			0
$209$	0.148855	+	0.124905i	0.0102965	+	0.00863983i
$210$		0			0
$211$	−0.539398	−	3.05908i	−0.0371337	−	0.210596i	0.960595	−	0.277951i	$-0.0896551\pi$
$211$	−0.539398	−	3.05908i	−0.0371337	−	0.210596i	−0.997729	+	0.0673549i	$0.978544\pi$
$212$		0			0
$213$	−8.47660	−	5.78173i	−0.580807	−	0.396158i
$214$		0			0
$215$	0.936276			0.0638535
$216$		0			0
$217$	−9.71757			−0.659672
$218$		0			0
$219$	−1.18822	+	15.8133i	−0.0802925	+	1.06856i
$220$		0			0
$221$	−1.43330	−	8.12865i	−0.0964142	−	0.546792i
$222$		0			0
$223$	10.2343	+	8.58764i	0.685343	+	0.575071i	0.917562	−	0.397593i	$-0.130154\pi$
$223$	10.2343	+	8.58764i	0.685343	+	0.575071i	−0.232219	+	0.972663i	$0.574599\pi$
$224$		0			0
$225$	4.59456	−	13.6569i	0.306304	−	0.910462i
$226$		0			0
$227$	2.28119	−	12.9372i	0.151408	−	0.858675i	−0.810589	−	0.585615i	$-0.800853\pi$
$227$	2.28119	−	12.9372i	0.151408	−	0.858675i	0.961997	−	0.273060i	$-0.0880358\pi$
$228$		0			0
$229$	9.24176	+	3.36373i	0.610713	+	0.222281i	0.628815	−	0.777555i	$-0.283540\pi$
$229$	9.24176	+	3.36373i	0.610713	+	0.222281i	−0.0181024	+	0.999836i	$0.505762\pi$
$230$		0			0
$231$	0.0461866	−	0.102306i	0.00303886	−	0.00673121i
$232$		0			0
$233$	13.1999	+	22.8629i	0.864756	+	1.49780i	0.867289	+	0.497805i	$0.165860\pi$
$233$	13.1999	+	22.8629i	0.864756	+	1.49780i	−0.00253310	+	0.999997i	$0.500806\pi$
$234$		0			0
$235$	0.287493	−	0.497953i	0.0187540	−	0.0324829i
$236$		0			0
$237$	12.0122	−	12.3106i	0.780278	−	0.799659i
$238$		0			0
$239$	−11.8363	+	9.93187i	−0.765630	+	0.642440i	−0.939586	−	0.342314i	$-0.888789\pi$
$239$	−11.8363	+	9.93187i	−0.765630	+	0.642440i	0.173956	+	0.984753i	$0.444345\pi$
$240$		0			0
$241$	−4.24187	+	1.54391i	−0.273243	+	0.0994522i	−0.475007	−	0.879982i	$-0.657555\pi$
$241$	−4.24187	+	1.54391i	−0.273243	+	0.0994522i	0.201765	+	0.979434i	$0.435332\pi$
$242$		0			0
$243$	−9.70706	−	12.1973i	−0.622708	−	0.782454i
$244$		0			0
$245$	−2.29773	+	0.836305i	−0.146796	+	0.0534295i
$246$		0			0
$247$	−4.73047	+	3.96933i	−0.300992	+	0.252563i
$248$		0			0
$249$	13.7434	−	14.0847i	0.870950	−	0.892584i
$250$		0			0
$251$	−4.29663	+	7.44198i	−0.271201	+	0.469733i	−0.969170	−	0.246395i	$-0.920754\pi$
$251$	−4.29663	+	7.44198i	−0.271201	+	0.469733i	0.697969	+	0.716128i	$0.254087\pi$
$252$		0			0
$253$	0.177002	+	0.306576i	0.0111280	+	0.0192743i
$254$		0			0
$255$	−1.54765	+	3.42812i	−0.0969178	+	0.214677i
$256$		0			0
$257$	1.48529	+	0.540602i	0.0926499	+	0.0337218i	0.387929	−	0.921689i	$-0.373190\pi$
$257$	1.48529	+	0.540602i	0.0926499	+	0.0337218i	−0.295279	+	0.955411i	$0.595413\pi$
$258$		0			0
$259$	−1.94239	+	11.0158i	−0.120694	+	0.684489i
$260$		0			0
$261$	0.452834	−	1.34601i	0.0280297	−	0.0833159i
$262$		0			0
$263$	−21.8949	−	18.3720i	−1.35010	−	1.13286i	−0.978907	−	0.204308i	$-0.934506\pi$
$263$	−21.8949	−	18.3720i	−1.35010	−	1.13286i	−0.371189	−	0.928557i	$-0.621050\pi$
$264$		0			0
$265$	0.917242	+	5.20194i	0.0563457	+	0.319552i
$266$		0			0
$267$	0.806060	−	10.7274i	0.0493301	−	0.656504i
$268$		0			0
$269$	−19.7693			−1.20536			−0.602678	−	0.797984i	$-0.705900\pi$
$269$	−19.7693			−1.20536			−0.602678	+	0.797984i	$0.705900\pi$
$270$		0			0
$271$	15.6042			0.947890			0.473945	−	0.880555i	$-0.342830\pi$
$271$	15.6042			0.947890			0.473945	+	0.880555i	$0.342830\pi$
$272$		0			0
$273$	2.94689	+	2.01002i	0.178354	+	0.121652i
$274$		0			0
$275$	−0.0442729	−	0.251084i	−0.00266976	−	0.0151409i
$276$		0			0
$277$	−6.09930	−	5.11792i	−0.366471	−	0.307506i	0.440892	−	0.897560i	$-0.354662\pi$
$277$	−6.09930	−	5.11792i	−0.366471	−	0.307506i	−0.807364	+	0.590054i	$0.799106\pi$
$278$		0			0
$279$	0.585775	+	23.8717i	0.0350694	+	1.42916i
$280$		0			0
$281$	−0.539642	+	3.06046i	−0.0321923	+	0.182572i	−0.996664	−	0.0816146i	$-0.973992\pi$
$281$	−0.539642	+	3.06046i	−0.0321923	+	0.182572i	0.964472	+	0.264186i	$0.0851034\pi$
$282$		0			0
$283$	19.8942	+	7.24091i	1.18259	+	0.430428i	0.857116	−	0.515123i	$-0.172254\pi$
$283$	19.8942	+	7.24091i	1.18259	+	0.430428i	0.325474	+	0.945551i	$0.394476\pi$
$284$		0			0
$285$	2.80004	−	0.279621i	0.165860	−	0.0165633i
$286$		0			0
$287$	−3.27414	−	5.67098i	−0.193266	−	0.334747i
$288$		0			0
$289$	−3.47071	+	6.01145i	−0.204159	+	0.353614i
$290$		0			0
$291$	−7.57336	−	26.9380i	−0.443958	−	1.57913i
$292$		0			0
$293$	20.9909	−	17.6135i	1.22630	−	1.02899i	0.227831	−	0.973701i	$-0.426837\pi$
$293$	20.9909	−	17.6135i	1.22630	−	1.02899i	0.998470	−	0.0552880i	$-0.0176077\pi$
$294$		0			0
$295$	3.96946	−	1.44476i	0.231111	−	0.0841174i
$296$		0			0
$297$	−0.254102	−	0.107293i	−0.0147445	−	0.00622575i
$298$		0			0
$299$	−10.5714	+	3.84768i	−0.611360	+	0.222517i
$300$		0			0
$301$	−1.97298	+	1.65553i	−0.113721	+	0.0954230i
$302$		0			0
$303$	24.0852	+	6.13796i	1.38366	+	0.352617i
$304$		0			0
$305$	−0.0621575	+	0.107660i	−0.00355913	+	0.00616460i
$306$		0			0
$307$	−3.06815	−	5.31419i	−0.175108	−	0.303297i	0.765090	−	0.643923i	$-0.222694\pi$
$307$	−3.06815	−	5.31419i	−0.175108	−	0.303297i	−0.940199	+	0.340626i	$0.889361\pi$
$308$		0			0
$309$	−17.6505	−	24.5607i	−1.00410	−	1.39721i
$310$		0			0
$311$	−20.7023	−	7.53500i	−1.17392	−	0.427271i	−0.319867	−	0.947462i	$-0.603638\pi$
$311$	−20.7023	−	7.53500i	−1.17392	−	0.427271i	−0.854050	+	0.520191i	$0.825861\pi$
$312$		0			0
$313$	−2.01293	+	11.4159i	−0.113778	+	0.645264i	0.873571	+	0.486697i	$0.161799\pi$
$313$	−2.01293	+	11.4159i	−0.113778	+	0.645264i	−0.987348	+	0.158567i	$0.949313\pi$
$314$		0			0
$315$	−0.593258	−	1.51337i	−0.0334263	−	0.0852690i
$316$		0			0
$317$	6.93161	+	5.81631i	0.389318	+	0.326677i	0.816347	−	0.577561i	$-0.195995\pi$
$317$	6.93161	+	5.81631i	0.389318	+	0.326677i	−0.427029	+	0.904238i	$0.640440\pi$
$318$		0			0
$319$	−0.00436348	−	0.0247465i	−0.000244308	−	0.00138554i
$320$		0			0
$321$	29.0097	−	13.9632i	1.61916	−	0.779350i
$322$		0			0
$323$	17.9116			0.996625
$324$		0			0
$325$	8.10228			0.449433
$326$		0			0
$327$	2.26731	−	1.09132i	0.125382	−	0.0603502i
$328$		0			0
$329$	0.274658	+	1.55767i	0.0151424	+	0.0858769i
$330$		0			0
$331$	11.3760	+	9.54559i	0.625281	+	0.524673i	0.899458	−	0.437006i	$-0.143961\pi$
$331$	11.3760	+	9.54559i	0.625281	+	0.524673i	−0.274178	+	0.961679i	$0.588406\pi$
$332$		0			0
$333$	27.1779	+	4.10753i	1.48934	+	0.225091i
$334$		0			0
$335$	−0.609879	+	3.45880i	−0.0333213	+	0.188974i
$336$		0			0
$337$	29.8302	+	10.8573i	1.62496	+	0.591436i	0.984317	−	0.176406i	$-0.0564472\pi$
$337$	29.8302	+	10.8573i	1.62496	+	0.591436i	0.640639	+	0.767842i	$0.278669\pi$
$338$		0			0
$339$	1.60670	+	2.23573i	0.0872640	+	0.121428i
$340$		0			0
$341$	0.211259	+	0.365911i	0.0114403	+	0.0198152i
$342$		0			0
$343$	7.63617	−	13.2262i	0.412314	−	0.714150i
$344$		0			0
$345$	4.96766	+	1.26598i	0.267450	+	0.0681581i
$346$		0			0
$347$	24.5612	−	20.6093i	1.31851	−	1.10637i	0.331897	−	0.943316i	$-0.392311\pi$
$347$	24.5612	−	20.6093i	1.31851	−	1.10637i	0.986618	−	0.163050i	$-0.0521331\pi$
$348$		0			0
$349$	−23.0107	+	8.37522i	−1.23174	+	0.448315i	−0.874192	−	0.485581i	$-0.838608\pi$
$349$	−23.0107	+	8.37522i	−1.23174	+	0.448315i	−0.357545	+	0.933896i	$0.616386\pi$
$350$		0			0
$351$	4.76007	−	7.36034i	0.254074	−	0.392866i
$352$		0			0
$353$	−19.0675	+	6.94001i	−1.01486	+	0.369379i	−0.795298	−	0.606219i	$-0.792686\pi$
$353$	−19.0675	+	6.94001i	−1.01486	+	0.369379i	−0.219563	+	0.975598i	$0.570463\pi$
$354$		0			0
$355$	−2.01405	+	1.68998i	−0.106894	+	0.0896951i
$356$		0			0
$357$	−2.80031	−	9.96053i	−0.148208	−	0.527167i
$358$		0			0
$359$	−8.61062	+	14.9140i	−0.454451	+	0.787133i	−0.998656	−	0.0518195i	$-0.983498\pi$
$359$	−8.61062	+	14.9140i	−0.454451	+	0.787133i	0.544205	+	0.838952i	$0.316831\pi$
$360$		0			0
$361$	2.79982	+	4.84943i	0.147359	+	0.255233i
$362$		0			0
$363$	18.9534	−	1.89275i	0.994796	−	0.0993435i
$364$		0			0
$365$	3.81830	+	1.38975i	0.199859	+	0.0727428i
$366$		0			0
$367$	−0.632469	+	3.58691i	−0.0330146	+	0.187235i	−0.996855	−	0.0792442i	$-0.974749\pi$
$367$	−0.632469	+	3.58691i	−0.0330146	+	0.187235i	0.963841	+	0.266479i	$0.0858604\pi$
$368$		0			0
$369$	−13.7337	+	8.38492i	−0.714945	+	0.436502i
$370$		0			0
$371$	−11.1310	−	9.33998i	−0.577891	−	0.484908i
$372$		0			0
$373$	−1.18473	−	6.71895i	−0.0613431	−	0.347894i	−0.999995	−	0.00302919i	$-0.999036\pi$
$373$	−1.18473	−	6.71895i	−0.0613431	−	0.347894i	0.938652	−	0.344865i	$-0.112075\pi$
$374$		0			0
$375$	−6.22541	−	4.24623i	−0.321479	−	0.219275i
$376$		0			0
$377$	0.798550			0.0411274
$378$		0			0
$379$	2.12744			0.109279			0.0546396	−	0.998506i	$-0.482599\pi$
$379$	2.12744			0.109279			0.0546396	+	0.998506i	$0.482599\pi$
$380$		0			0
$381$	1.52579	−	20.3058i	0.0781687	−	1.04030i
$382$		0			0
$383$	−3.68105	−	20.8763i	−0.188093	−	1.06673i	−0.921917	−	0.387388i	$-0.873377\pi$
$383$	−3.68105	−	20.8763i	−0.188093	−	1.06673i	0.733824	−	0.679340i	$-0.237734\pi$
$384$		0			0
$385$	−0.0220330	−	0.0184878i	−0.00112290	−	0.000942228i
$386$		0			0
$387$	4.18581	+	4.74692i	0.212777	+	0.241300i
$388$		0			0
$389$	−0.229463	+	1.30135i	−0.0116342	+	0.0659811i	−0.990072	−	0.140560i	$-0.955110\pi$
$389$	−0.229463	+	1.30135i	−0.0116342	+	0.0659811i	0.978438	+	0.206541i	$0.0662208\pi$
$390$		0			0
$391$	30.6631	+	11.1604i	1.55070	+	0.564408i
$392$		0			0
$393$	−4.76107	+	10.5460i	−0.240164	+	0.531975i
$394$		0			0
$395$	−2.20364	−	3.81682i	−0.110877	−	0.192045i
$396$		0			0
$397$	11.7027	−	20.2696i	0.587340	−	1.01730i	−0.407239	−	0.913322i	$-0.633508\pi$
$397$	11.7027	−	20.2696i	0.587340	−	1.01730i	0.994579	−	0.103981i	$-0.0331582\pi$
$398$		0			0
$399$	−5.40600	+	5.54028i	−0.270639	+	0.277361i
$400$		0			0
$401$	−24.3865	+	20.4627i	−1.21780	+	1.02186i	−0.218866	+	0.975755i	$0.570236\pi$
$401$	−24.3865	+	20.4627i	−1.21780	+	1.02186i	−0.998937	+	0.0461030i	$0.985320\pi$
$402$		0			0
$403$	−12.6174	+	4.59236i	−0.628517	+	0.228762i
$404$		0			0
$405$	−3.68191	+	1.54859i	−0.182956	+	0.0769501i
$406$		0			0
$407$	0.457023	−	0.166343i	0.0226538	−	0.00824530i
$408$		0			0
$409$	−13.5058	+	11.3327i	−0.667820	+	0.560368i	−0.912419	−	0.409257i	$-0.865788\pi$
$409$	−13.5058	+	11.3327i	−0.667820	+	0.560368i	0.244599	+	0.969624i	$0.421344\pi$
$410$		0			0
$411$	15.7923	−	16.1846i	0.778976	−	0.798326i
$412$		0			0
$413$	−5.81006	+	10.0633i	−0.285894	+	0.495183i
$414$		0			0
$415$	−2.52122	−	4.36688i	−0.123762	−	0.214362i
$416$		0			0
$417$	−15.4225	+	34.1616i	−0.755245	+	1.67290i
$418$		0			0
$419$	−4.78294	−	1.74085i	−0.233662	−	0.0850459i	0.222536	−	0.974925i	$-0.428567\pi$
$419$	−4.78294	−	1.74085i	−0.233662	−	0.0850459i	−0.456197	+	0.889879i	$0.650789\pi$
$420$		0			0
$421$	−5.06322	+	28.7150i	−0.246766	+	1.39948i	0.569588	+	0.821930i	$0.307103\pi$
$421$	−5.06322	+	28.7150i	−0.246766	+	1.39948i	−0.816355	+	0.577551i	$0.804008\pi$
$422$		0			0
$423$	3.80992	−	0.768607i	0.185245	−	0.0373710i
$424$		0			0
$425$	−18.0030	−	15.1063i	−0.873272	−	0.732763i
$426$		0			0
$427$	−0.0593826	−	0.336775i	−0.00287373	−	0.0162977i
$428$		0			0
$429$	0.0116214	−	0.154662i	0.000561085	−	0.00746713i
$430$		0			0
$431$	11.9171			0.574024			0.287012	−	0.957927i	$-0.407338\pi$
$431$	11.9171			0.574024			0.287012	+	0.957927i	$0.407338\pi$
$432$		0			0
$433$	−35.2817			−1.69553			−0.847765	−	0.530373i	$-0.822052\pi$
$433$	−35.2817			−1.69553			−0.847765	+	0.530373i	$0.822052\pi$
$434$		0			0
$435$	−0.300620	−	0.205047i	−0.0144136	−	0.00983126i
$436$		0			0
$437$	−4.23919	−	24.0417i	−0.202788	−	1.15007i
$438$		0			0
$439$	−16.5157	−	13.8583i	−0.788253	−	0.661423i	0.157060	−	0.987589i	$-0.449799\pi$
$439$	−16.5157	−	13.8583i	−0.788253	−	0.661423i	−0.945312	+	0.326167i	$0.894243\pi$
$440$		0			0
$441$	−14.5125	−	7.91063i	−0.691073	−	0.376696i
$442$		0			0
$443$	−1.74502	+	9.89647i	−0.0829082	+	0.470196i	0.914880	+	0.403725i	$0.132285\pi$
$443$	−1.74502	+	9.89647i	−0.0829082	+	0.470196i	−0.997788	+	0.0664703i	$0.978826\pi$
$444$		0			0
$445$	−2.59025	−	0.942772i	−0.122789	−	0.0446917i
$446$		0			0
$447$	15.5609	−	1.55397i	0.736007	−	0.0735001i
$448$		0			0
$449$	21.1303	+	36.5987i	0.997200	+	1.72720i	0.563358	+	0.826213i	$0.309509\pi$
$449$	21.1303	+	36.5987i	0.997200	+	1.72720i	0.433843	+	0.900989i	$0.357157\pi$
$450$		0			0
$451$	−0.142359	+	0.246573i	−0.00670341	+	0.0116107i
$452$		0			0
$453$	−2.96921	−	10.5613i	−0.139506	−	0.496212i
$454$		0			0
$455$	0.700184	−	0.587524i	0.0328251	−	0.0275435i
$456$		0			0
$457$	7.45512	−	2.71344i	0.348736	−	0.126929i	−0.161713	−	0.986838i	$-0.551702\pi$
$457$	7.45512	−	2.71344i	0.348736	−	0.126929i	0.510448	+	0.859908i	$0.329479\pi$
$458$		0			0
$459$	−24.2997	+	7.47951i	−1.13421	+	0.349114i
$460$		0			0
$461$	−23.3655	+	8.50436i	−1.08824	+	0.396087i	−0.822969	−	0.568086i	$-0.807684\pi$
$461$	−23.3655	+	8.50436i	−1.08824	+	0.396087i	−0.265272	+	0.964174i	$0.585462\pi$
$462$		0			0
$463$	9.41524	−	7.90032i	0.437563	−	0.367159i	−0.397233	−	0.917718i	$-0.630030\pi$
$463$	9.41524	−	7.90032i	0.437563	−	0.367159i	0.834797	+	0.550559i	$0.185585\pi$
$464$		0			0
$465$	5.92911	+	1.51100i	0.274956	+	0.0700709i
$466$		0			0
$467$	−4.30296	+	7.45295i	−0.199117	+	0.344881i	−0.948242	−	0.317547i	$-0.897141\pi$
$467$	−4.30296	+	7.45295i	−0.199117	+	0.344881i	0.749125	+	0.662429i	$0.230474\pi$
$468$		0			0
$469$	−4.83069	−	8.36699i	−0.223060	−	0.386352i
$470$		0			0
$471$	−22.9030	−	31.8696i	−1.05532	−	1.46847i
$472$		0			0
$473$	0.105231	+	0.0383008i	0.00483851	+	0.00176107i
$474$		0			0
$475$	−3.05312	+	17.3151i	−0.140087	+	0.794471i
$476$		0			0
$477$	−22.2731	+	27.9067i	−1.01982	+	1.27776i
$478$		0			0
$479$	5.21251	+	4.37381i	0.238166	+	0.199845i	0.754056	−	0.656810i	$-0.228095\pi$
$479$	5.21251	+	4.37381i	0.238166	+	0.199845i	−0.515891	+	0.856654i	$0.672539\pi$
$480$		0			0
$481$	2.68387	+	15.2210i	0.122374	+	0.694017i
$482$		0			0
$483$	−12.7067	+	6.11609i	−0.578175	+	0.278292i
$484$		0			0
$485$	−7.17007			−0.325576
$486$		0			0
$487$	−13.6682			−0.619364			−0.309682	−	0.950840i	$-0.600223\pi$
$487$	−13.6682			−0.619364			−0.309682	+	0.950840i	$0.600223\pi$
$488$		0			0
$489$	−3.89669	+	1.87559i	−0.176215	+	0.0848171i
$490$		0			0
$491$	2.78778	+	15.8103i	0.125811	+	0.713508i	0.980823	+	0.194900i	$0.0624383\pi$
$491$	2.78778	+	15.8103i	0.125811	+	0.713508i	−0.855012	+	0.518608i	$0.826451\pi$
$492$		0			0
$493$	−1.77435	−	1.48886i	−0.0799127	−	0.0670547i
$494$		0			0
$495$	−0.0440881	+	0.0552394i	−0.00198161	+	0.00248283i
$496$		0			0
$497$	1.25589	−	7.12249i	0.0563342	−	0.319487i
$498$		0			0
$499$	5.99466	+	2.18188i	0.268358	+	0.0976743i	0.472694	−	0.881226i	$-0.343281\pi$
$499$	5.99466	+	2.18188i	0.268358	+	0.0976743i	−0.204336	+	0.978901i	$0.565504\pi$
$500$		0			0
$501$	2.53749	+	3.53092i	0.113367	+	0.157750i
$502$		0			0
$503$	−3.62821	−	6.28424i	−0.161774	−	0.280200i	0.773731	−	0.633514i	$-0.218388\pi$
$503$	−3.62821	−	6.28424i	−0.161774	−	0.280200i	−0.935505	+	0.353314i	$0.885055\pi$
$504$		0			0
$505$	3.18437	−	5.51549i	0.141702	−	0.245436i
$506$		0			0
$507$	−17.0431	−	4.34333i	−0.756910	−	0.192894i
$508$		0			0
$509$	18.6070	−	15.6131i	0.824741	−	0.692040i	−0.129336	−	0.991601i	$-0.541285\pi$
$509$	18.6070	−	15.6131i	0.824741	−	0.692040i	0.954077	+	0.299561i	$0.0968401\pi$
$510$		0			0
$511$	−10.5035	+	3.82298i	−0.464649	+	0.169118i
$512$		0			0
$513$	13.9358	+	12.9461i	0.615282	+	0.571585i
$514$		0			0
$515$	−7.28250	+	2.65061i	−0.320905	+	0.116800i
$516$		0			0
$517$	0.0526822	−	0.0442056i	0.00231696	−	0.00194416i
$518$		0			0
$519$	6.42618	+	22.8575i	0.282078	+	1.00333i
$520$		0			0
$521$	13.2398	−	22.9320i	0.580046	−	1.00467i	−0.415428	−	0.909626i	$-0.636368\pi$
$521$	13.2398	−	22.9320i	0.580046	−	1.00467i	0.995473	−	0.0950422i	$-0.0302986\pi$
$522$		0			0
$523$	−8.95994	−	15.5191i	−0.391791	−	0.678601i	0.600895	−	0.799328i	$-0.294811\pi$
$523$	−8.95994	−	15.5191i	−0.391791	−	0.678601i	−0.992686	+	0.120726i	$0.961478\pi$
$524$		0			0
$525$	10.1062	−	1.00924i	0.441070	−	0.0440466i
$526$		0			0
$527$	36.5976	+	13.3204i	1.59422	+	0.580248i
$528$		0			0
$529$	3.72898	−	21.1481i	0.162130	−	0.919483i
$530$		0			0
$531$	25.0712	+	13.6661i	1.08800	+	0.593057i
$532$		0			0
$533$	−6.93118	−	5.81595i	−0.300223	−	0.251917i
$534$		0			0
$535$	−1.43252	−	8.12425i	−0.0619334	−	0.351242i
$536$		0			0
$537$	−5.63706	−	3.84493i	−0.243257	−	0.165921i
$538$		0			0
$539$	−0.292459			−0.0125971
$540$		0			0
$541$	41.1015			1.76709			0.883547	−	0.468343i	$-0.155149\pi$
$541$	41.1015			1.76709			0.883547	+	0.468343i	$0.155149\pi$
$542$		0			0
$543$	−1.03338	+	13.7527i	−0.0443467	+	0.590183i
$544$		0			0
$545$	−0.111962	−	0.634966i	−0.00479591	−	0.0271990i
$546$		0			0
$547$	−21.7775	−	18.2735i	−0.931139	−	0.781319i	0.0448824	−	0.998992i	$-0.485709\pi$
$547$	−21.7775	−	18.2735i	−0.931139	−	0.781319i	−0.976022	+	0.217674i	$0.930153\pi$
$548$		0			0
$549$	−0.823725	+	0.166177i	−0.0351557	+	0.00709226i
$550$		0			0
$551$	−0.300911	+	1.70655i	−0.0128193	+	0.0727016i
$552$		0			0
$553$	11.3926	+	4.14656i	0.484462	+	0.176330i
$554$		0			0
$555$	2.89800	−	6.41920i	0.123013	−	0.272480i
$556$		0			0
$557$	5.94115	+	10.2904i	0.251735	+	0.436017i	0.964003	−	0.265890i	$-0.0856657\pi$
$557$	5.94115	+	10.2904i	0.251735	+	0.436017i	−0.712269	+	0.701907i	$0.752332\pi$
$558$		0			0
$559$	−1.77937	+	3.08195i	−0.0752591	+	0.130353i
$560$		0			0
$561$	−0.314181	+	0.321985i	−0.0132647	+	0.0135942i
$562$		0			0
$563$	14.2029	−	11.9177i	0.598582	−	0.502270i	−0.292408	−	0.956294i	$-0.594456\pi$
$563$	14.2029	−	11.9177i	0.598582	−	0.502270i	0.890989	+	0.454024i	$0.150012\pi$
$564$		0			0
$565$	0.662917	−	0.241282i	0.0278891	−	0.0101508i
$566$		0			0
$567$	5.02054	−	9.77366i	0.210843	−	0.410455i
$568$		0			0
$569$	25.8144	−	9.39569i	1.08220	−	0.393888i	0.261472	−	0.965211i	$-0.415792\pi$
$569$	25.8144	−	9.39569i	1.08220	−	0.393888i	0.820725	+	0.571323i	$0.193570\pi$
$570$		0			0
$571$	−9.74026	+	8.17305i	−0.407617	+	0.342032i	−0.823429	−	0.567419i	$-0.807942\pi$
$571$	−9.74026	+	8.17305i	−0.407617	+	0.342032i	0.415812	+	0.909451i	$0.363497\pi$
$572$		0			0
$573$	−14.4988	+	14.8590i	−0.605697	+	0.620743i
$574$		0			0
$575$	−16.0155	+	27.7396i	−0.667892	+	1.15682i
$576$		0			0
$577$	−18.9550	−	32.8311i	−0.789109	−	1.36678i	−0.926514	−	0.376261i	$-0.877209\pi$
$577$	−18.9550	−	32.8311i	−0.789109	−	1.36678i	0.137405	−	0.990515i	$-0.456124\pi$
$578$		0			0
$579$	−6.09725	+	13.5057i	−0.253393	+	0.561277i
$580$		0			0
$581$	13.0344	+	4.74414i	0.540759	+	0.196820i
$582$		0			0
$583$	−0.109707	+	0.622182i	−0.00454362	+	0.0257681i
$584$		0			0
$585$	−1.48549	−	1.68462i	−0.0614173	−	0.0696504i
$586$		0			0
$587$	27.3606	+	22.9583i	1.12929	+	0.947590i	0.999036	−	0.0438900i	$-0.0139751\pi$
$587$	27.3606	+	22.9583i	1.12929	+	0.947590i	0.130258	+	0.991480i	$0.458420\pi$
$588$		0			0
$589$	−5.05965	−	28.6947i	−0.208479	−	1.18234i
$590$		0			0
$591$	1.07467	−	14.3022i	0.0442062	−	0.588313i
$592$		0			0
$593$	19.5452			0.802624			0.401312	−	0.915941i	$-0.368554\pi$
$593$	19.5452			0.802624			0.401312	+	0.915941i	$0.368554\pi$
$594$		0			0
$595$	−2.65119			−0.108688
$596$		0			0
$597$	−10.7527	−	7.33420i	−0.440078	−	0.300169i
$598$		0			0
$599$	−4.43167	−	25.1332i	−0.181073	−	1.02692i	−0.930898	−	0.365280i	$-0.880973\pi$
$599$	−4.43167	−	25.1332i	−0.181073	−	1.02692i	0.749825	−	0.661637i	$-0.230138\pi$
$600$		0			0
$601$	11.5383	+	9.68176i	0.470656	+	0.394927i	0.847034	−	0.531539i	$-0.178386\pi$
$601$	11.5383	+	9.68176i	0.470656	+	0.394927i	−0.376378	+	0.926466i	$0.622831\pi$
$602$		0			0
$603$	−20.2627	+	12.3712i	−0.825161	+	0.503793i
$604$		0			0
$605$	0.847524	−	4.80655i	0.0344568	−	0.195414i
$606$		0			0
$607$	−25.5353	−	9.29408i	−1.03645	−	0.377235i	−0.232914	−	0.972497i	$-0.574826\pi$
$607$	−25.5353	−	9.29408i	−1.03645	−	0.377235i	−0.803532	+	0.595262i	$0.797048\pi$
$608$		0			0
$609$	0.996051	−	0.0994689i	0.0403620	−	0.00403068i
$610$		0			0
$611$	1.09275	+	1.89269i	0.0442078	+	0.0765701i
$612$		0			0
$613$	3.98720	−	6.90604i	0.161042	−	0.278932i	−0.774201	−	0.632940i	$-0.781848\pi$
$613$	3.98720	−	6.90604i	0.161042	−	0.278932i	0.935243	+	0.354008i	$0.115181\pi$
$614$		0			0
$615$	1.11591	+	3.96921i	0.0449977	+	0.160054i
$616$		0			0
$617$	−6.33313	+	5.31412i	−0.254962	+	0.213939i	−0.761306	−	0.648393i	$-0.775441\pi$
$617$	−6.33313	+	5.31412i	−0.254962	+	0.213939i	0.506343	+	0.862332i	$0.330997\pi$
$618$		0			0
$619$	−2.23620	+	0.813909i	−0.0898803	+	0.0327137i	−0.386569	−	0.922261i	$-0.626340\pi$
$619$	−2.23620	+	0.813909i	−0.0898803	+	0.0327137i	0.296689	+	0.954974i	$0.404118\pi$
$620$		0			0
$621$	15.7904	+	30.8459i	0.633648	+	1.23780i
$622$		0			0
$623$	7.12535	−	2.59342i	0.285471	−	0.103903i
$624$		0			0
$625$	16.9175	−	14.1955i	0.676700	−	0.567819i
$626$		0			0
$627$	0.326143	+	0.0831156i	0.0130249	+	0.00331932i
$628$		0			0
$629$	22.4153	−	38.8244i	0.893756	−	1.54803i
$630$		0			0
$631$	8.96183	+	15.5224i	0.356765	+	0.617935i	0.987418	−	0.158130i	$-0.0505464\pi$
$631$	8.96183	+	15.5224i	0.356765	+	0.617935i	−0.630653	+	0.776065i	$0.717213\pi$
$632$		0			0
$633$	−3.13979	−	4.36903i	−0.124796	−	0.173653i
$634$		0			0
$635$	−4.90308	−	1.78458i	−0.194573	−	0.0708187i
$636$		0			0
$637$	1.61389	−	9.15284i	0.0639447	−	0.362649i
$638$		0			0
$639$	−17.5724	−	2.65580i	−0.695155	−	0.105062i
$640$		0			0
$641$	−16.6588	−	13.9784i	−0.657985	−	0.552115i	0.251497	−	0.967858i	$-0.419077\pi$
$641$	−16.6588	−	13.9784i	−0.657985	−	0.552115i	−0.909482	+	0.415743i	$0.863521\pi$
$642$		0			0
$643$	−1.96011	−	11.1163i	−0.0772991	−	0.438385i	−0.998754	−	0.0499002i	$-0.984110\pi$
$643$	−1.96011	−	11.1163i	−0.0772991	−	0.438385i	0.921455	−	0.388485i	$-0.127001\pi$
$644$		0			0
$645$	1.46122	−	0.703327i	0.0575355	−	0.0276935i
$646$		0			0
$647$	42.1713			1.65792			0.828962	−	0.559306i	$-0.188932\pi$
$647$	42.1713			1.65792			0.828962	+	0.559306i	$0.188932\pi$
$648$		0			0
$649$	0.505240			0.0198324
$650$		0			0
$651$	−15.1660	+	7.29981i	−0.594401	+	0.286102i
$652$		0			0
$653$	4.45235	+	25.2505i	0.174234	+	0.988130i	0.939024	+	0.343851i	$0.111731\pi$
$653$	4.45235	+	25.2505i	0.174234	+	0.988130i	−0.764790	+	0.644279i	$0.777158\pi$
$654$		0			0
$655$	2.27123	+	1.90579i	0.0887443	+	0.0744653i
$656$		0			0
$657$	10.0245	+	25.5720i	0.391092	+	0.997658i
$658$		0			0
$659$	−3.39623	+	19.2610i	−0.132298	+	0.750302i	0.844405	+	0.535706i	$0.179954\pi$
$659$	−3.39623	+	19.2610i	−0.132298	+	0.750302i	−0.976703	+	0.214596i	$0.931157\pi$
$660$		0			0
$661$	−17.0405	−	6.20222i	−0.662797	−	0.241238i	−0.0113536	−	0.999936i	$-0.503614\pi$
$661$	−17.0405	−	6.20222i	−0.662797	−	0.241238i	−0.651444	+	0.758697i	$0.725836\pi$
$662$		0			0
$663$	−8.34313	−	11.6095i	−0.324020	−	0.450875i
$664$		0			0
$665$	0.991732	+	1.71773i	0.0384577	+	0.0666107i
$666$		0			0
$667$	−1.57847	+	2.73398i	−0.0611184	+	0.105860i
$668$		0			0
$669$	22.4235	+	5.71449i	0.866942	+	0.220935i
$670$		0			0
$671$	−0.0113902	+	0.00955748i	−0.000439712	+	0.000368963i
$672$		0			0
$673$	33.9708	−	12.3643i	1.30948	−	0.476610i	0.409405	−	0.912353i	$-0.365736\pi$
$673$	33.9708	−	12.3643i	1.30948	−	0.476610i	0.900071	+	0.435742i	$0.143514\pi$
$674$		0			0
$675$	−3.08843	−	24.7654i	−0.118874	−	0.953222i
$676$		0			0
$677$	8.70097	−	3.16689i	0.334405	−	0.121714i	−0.169360	−	0.985554i	$-0.554170\pi$
$677$	8.70097	−	3.16689i	0.334405	−	0.121714i	0.503765	+	0.863841i	$0.331948\pi$
$678$		0			0
$679$	15.1092	−	12.6782i	0.579839	−	0.486543i
$680$		0			0
$681$	−6.15823	−	21.9044i	−0.235984	−	0.839380i
$682$		0			0
$683$	−10.3685	+	17.9588i	−0.396741	+	0.687175i	−0.993322	−	0.115378i	$-0.963192\pi$
$683$	−10.3685	+	17.9588i	−0.396741	+	0.687175i	0.596581	+	0.802553i	$0.296526\pi$
$684$		0			0
$685$	−2.89710	−	5.01792i	−0.110692	−	0.191725i
$686$		0			0
$687$	16.9502	−	1.69270i	0.646690	−	0.0645806i
$688$		0			0
$689$	−18.8665	−	6.86683i	−0.718755	−	0.261606i
$690$		0			0
$691$	7.63048	−	43.2746i	0.290277	−	1.64624i	−0.395525	−	0.918455i	$-0.629437\pi$
$691$	7.63048	−	43.2746i	0.290277	−	1.64624i	0.685802	−	0.727788i	$-0.259452\pi$
$692$		0			0
$693$	−0.00476932	−	0.194361i	−0.000181172	−	0.00738316i
$694$		0			0
$695$	7.35719	+	6.17342i	0.279074	+	0.234171i
$696$		0			0
$697$	4.55729	+	25.8457i	0.172620	+	0.978975i
$698$		0			0
$699$	37.7754	+	25.7659i	1.42880	+	0.974554i
$700$		0			0
$701$	−35.3552			−1.33535			−0.667673	−	0.744455i	$-0.732709\pi$
$701$	−35.3552			−1.33535			−0.667673	+	0.744455i	$0.732709\pi$
$702$		0			0
$703$	−33.5396			−1.26497
$704$		0			0
$705$	0.0746226	−	0.993106i	0.00281045	−	0.0374025i
$706$		0			0
$707$	3.04220	+	17.2532i	0.114414	+	0.648873i
$708$		0			0
$709$	15.0176	+	12.6013i	0.563999	+	0.473251i	0.879648	−	0.475625i	$-0.157778\pi$
$709$	15.0176	+	12.6013i	0.563999	+	0.473251i	−0.315650	+	0.948876i	$0.602222\pi$
$710$		0			0
$711$	9.49948	−	28.2364i	0.356258	−	1.05895i
$712$		0			0
$713$	9.21759	−	52.2755i	0.345201	−	1.95773i
$714$		0			0
$715$	−0.0373449	−	0.0135924i	−0.00139662	−	0.000508328i
$716$		0			0
$717$	−11.0119	+	24.3918i	−0.411246	+	0.910930i
$718$		0			0
$719$	−7.20116	−	12.4728i	−0.268558	−	0.465156i	0.699932	−	0.714210i	$-0.253214\pi$
$719$	−7.20116	−	12.4728i	−0.268558	−	0.465156i	−0.968490	+	0.249054i	$0.919880\pi$
$720$		0			0
$721$	10.6593	−	18.4625i	0.396974	−	0.687580i
$722$		0			0
$723$	−5.46039	+	5.59602i	−0.203074	+	0.208118i
$724$		0			0
$725$	1.74172	−	1.46148i	0.0646860	−	0.0542780i
$726$		0			0
$727$	−34.7163	+	12.6357i	−1.28755	+	0.468632i	−0.892924	−	0.450208i	$-0.851350\pi$
$727$	−34.7163	+	12.6357i	−1.28755	+	0.468632i	−0.394631	+	0.918840i	$0.629128\pi$
$728$		0			0
$729$	−24.3121	−	11.7440i	−0.900448	−	0.434964i
$730$		0			0
$731$	9.69983	−	3.53045i	0.358761	−	0.130578i
$732$		0			0
$733$	6.41038	−	5.37895i	0.236773	−	0.198676i	−0.516679	−	0.856179i	$-0.672832\pi$
$733$	6.41038	−	5.37895i	0.236773	−	0.198676i	0.753452	+	0.657503i	$0.228387\pi$
$734$		0			0
$735$	−2.95778	+	3.03125i	−0.109099	+	0.111809i
$736$		0			0
$737$	−0.210037	+	0.363795i	−0.00773681	+	0.0134006i
$738$		0			0
$739$	11.4109	+	19.7642i	0.419755	+	0.727037i	0.995915	−	0.0903001i	$-0.0287826\pi$
$739$	11.4109	+	19.7642i	0.419755	+	0.727037i	−0.576159	+	0.817337i	$0.695449\pi$
$740$		0			0
$741$	−4.40097	+	9.74835i	−0.161674	+	0.358115i
$742$		0			0
$743$	40.4756	+	14.7319i	1.48491	+	0.540461i	0.952103	−	0.305778i	$-0.0989166\pi$
$743$	40.4756	+	14.7319i	1.48491	+	0.540461i	0.532803	+	0.846240i	$0.321139\pi$
$744$		0			0
$745$	0.695826	−	3.94623i	0.0254931	−	0.144579i
$746$		0			0
$747$	10.8685	−	32.3056i	0.397657	−	1.18200i
$748$		0			0
$749$	17.3840	+	14.5869i	0.635199	+	0.532995i
$750$		0			0
$751$	5.58064	+	31.6494i	0.203640	+	1.15490i	0.899565	+	0.436787i	$0.143884\pi$
$751$	5.58064	+	31.6494i	0.203640	+	1.15490i	−0.695925	+	0.718115i	$0.745005\pi$
$752$		0			0
$753$	−1.11525	+	14.8421i	−0.0406418	+	0.540877i
$754$		0			0
$755$	−2.81109			−0.102306
$756$		0			0
$757$	17.7136			0.643812			0.321906	−	0.946772i	$-0.395677\pi$
$757$	17.7136			0.643812			0.321906	+	0.946772i	$0.395677\pi$
$758$		0			0
$759$	0.506541	+	0.345502i	0.0183863	+	0.0125409i
$760$		0			0
$761$	2.69487	+	15.2834i	0.0976891	+	0.554022i	0.993890	+	0.110374i	$0.0352049\pi$
$761$	2.69487	+	15.2834i	0.0976891	+	0.554022i	−0.896201	+	0.443648i	$0.853684\pi$
$762$		0			0
$763$	1.35868	+	1.14007i	0.0491876	+	0.0412733i
$764$		0			0
$765$	0.159814	+	6.51277i	0.00577808	+	0.235470i
$766$		0			0
$767$	−2.78809	+	15.8121i	−0.100672	+	0.570940i
$768$		0			0
$769$	−20.4690	−	7.45012i	−0.738132	−	0.268658i	−0.0545293	−	0.998512i	$-0.517366\pi$
$769$	−20.4690	−	7.45012i	−0.738132	−	0.268658i	−0.683603	+	0.729854i	$0.739588\pi$
$770$		0			0
$771$	2.72415	−	0.272043i	0.0981080	−	0.00979738i
$772$		0			0
$773$	−0.242952	−	0.420805i	−0.00873837	−	0.0151353i	0.861623	−	0.507549i	$-0.169448\pi$
$773$	−0.242952	−	0.420805i	−0.00873837	−	0.0151353i	−0.870362	+	0.492413i	$0.836115\pi$
$774$		0			0
$775$	−19.1151	+	33.1084i	−0.686636	+	1.18929i
$776$		0			0
$777$	5.24361	+	18.6512i	0.188114	+	0.669108i
$778$		0			0
$779$	15.0409	−	12.6208i	0.538896	−	0.452188i
$780$		0			0
$781$	−0.295497	+	0.107552i	−0.0105737	+	0.00384852i
$782$		0			0
$783$	−0.304392	−	2.44085i	−0.0108781	−	0.0872288i
$784$		0			0
$785$	−9.44967	+	3.43940i	−0.337273	+	0.122757i
$786$		0			0
$787$	11.1001	−	9.31412i	0.395677	−	0.332012i	−0.423143	−	0.906063i	$-0.639073\pi$
$787$	11.1001	−	9.31412i	0.395677	−	0.332012i	0.818820	+	0.574051i	$0.194629\pi$
$788$		0			0
$789$	−47.9717	−	12.2253i	−1.70784	−	0.435233i
$790$		0			0
$791$	−0.970306	+	1.68062i	−0.0345001	+	0.0597559i
$792$		0			0
$793$	−0.236257	−	0.409210i	−0.00838974	−	0.0145315i
$794$		0			0
$795$	5.33919	+	7.42950i	0.189362	+	0.263497i
$796$		0			0
$797$	−41.8020	−	15.2147i	−1.48070	−	0.538931i	−0.529718	−	0.848174i	$-0.677702\pi$
$797$	−41.8020	−	15.2147i	−1.48070	−	0.538931i	−0.950983	+	0.309242i	$0.899925\pi$
$798$		0			0
$799$	1.10078	−	6.24286i	0.0389430	−	0.220857i
$800$		0			0
$801$	−6.80036	−	17.3474i	−0.240279	−	0.612941i
$802$		0			0
$803$	0.372298	+	0.312395i	0.0131381	+	0.0110242i
$804$		0			0
$805$	0.627467	+	3.55854i	0.0221153	+	0.125422i
$806$		0			0
$807$	−30.8534	+	14.8506i	−1.08609	+	0.522767i
$808$		0			0
$809$	23.9692			0.842713			0.421357	−	0.906895i	$-0.361554\pi$
$809$	23.9692			0.842713			0.421357	+	0.906895i	$0.361554\pi$
$810$		0			0
$811$	−0.274670			−0.00964497			−0.00482249	−	0.999988i	$-0.501535\pi$
$811$	−0.274670			−0.00964497			−0.00482249	+	0.999988i	$0.501535\pi$
$812$		0			0
$813$	24.3531	−	11.7218i	0.854101	−	0.411103i
$814$		0			0
$815$	0.192422	+	1.09128i	0.00674025	+	0.0382259i
$816$		0			0
$817$	−5.91583	−	4.96397i	−0.206969	−	0.173667i
$818$		0			0
$819$	6.10906	+	0.923290i	0.213468	+	0.0322624i
$820$		0			0
$821$	−8.00229	+	45.3833i	−0.279282	+	1.58389i	0.445741	+	0.895162i	$0.352940\pi$
$821$	−8.00229	+	45.3833i	−0.279282	+	1.58389i	−0.725023	+	0.688725i	$0.758171\pi$
$822$		0			0
$823$	−23.2491	−	8.46198i	−0.810413	−	0.294966i	−0.0966186	−	0.995321i	$-0.530803\pi$
$823$	−23.2491	−	8.46198i	−0.810413	−	0.294966i	−0.713794	+	0.700355i	$0.753025\pi$
$824$		0			0
$825$	−0.257709	−	0.358603i	−0.00897228	−	0.0124849i
$826$		0			0
$827$	−24.3668	−	42.2045i	−0.847316	−	1.46759i	−0.883594	−	0.468253i	$-0.844884\pi$
$827$	−24.3668	−	42.2045i	−0.847316	−	1.46759i	0.0362782	−	0.999342i	$-0.488450\pi$
$828$		0			0
$829$	0.832320	−	1.44162i	0.0289077	−	0.0500695i	−0.851210	−	0.524826i	$-0.824130\pi$
$829$	0.832320	−	1.44162i	0.0289077	−	0.0500695i	0.880117	+	0.474756i	$0.157464\pi$
$830$		0			0
$831$	−13.3636	−	3.40563i	−0.463578	−	0.118140i
$832$		0			0
$833$	−20.6510	+	17.3283i	−0.715515	+	0.600388i
$834$		0			0
$835$	1.04696	−	0.381061i	0.0362314	−	0.0131872i
$836$		0			0
$837$	18.8465	+	36.8159i	0.651431	+	1.27254i
$838$		0			0
$839$	9.81480	−	3.57230i	0.338845	−	0.123329i	−0.166993	−	0.985958i	$-0.553406\pi$
$839$	9.81480	−	3.57230i	0.338845	−	0.123329i	0.505838	+	0.862629i	$0.331184\pi$
$840$		0			0
$841$	−22.0436	+	18.4968i	−0.760125	+	0.637821i
$842$		0			0
$843$	1.45680	+	5.18176i	0.0501750	+	0.178469i
$844$		0			0
$845$	−2.25332	+	3.90286i	−0.0775164	+	0.134262i
$846$		0			0
$847$	6.71301	+	11.6273i	0.230662	+	0.399518i
$848$		0			0
$849$	36.4878	−	3.64379i	1.25226	−	0.125055i
$850$		0			0
$851$	−57.4170	−	20.8981i	−1.96823	−	0.716376i
$852$		0			0
$853$	−9.70797	+	55.0566i	−0.332395	+	1.88510i	0.119184	+	0.992872i	$0.461972\pi$
$853$	−9.70797	+	55.0566i	−0.332395	+	1.88510i	−0.451579	+	0.892231i	$0.649139\pi$
$854$		0			0
$855$	4.15990	−	2.53978i	0.142266	−	0.0868587i
$856$		0			0
$857$	−21.5858	−	18.1126i	−0.737356	−	0.618715i	0.194770	−	0.980849i	$-0.437604\pi$
$857$	−21.5858	−	18.1126i	−0.737356	−	0.618715i	−0.932126	+	0.362134i	$0.882048\pi$
$858$		0			0
$859$	−2.12084	−	12.0279i	−0.0723622	−	0.410386i	−0.999375	−	0.0353561i	$-0.988743\pi$
$859$	−2.12084	−	12.0279i	−0.0723622	−	0.410386i	0.927013	−	0.375030i	$-0.122368\pi$
$860$		0			0
$861$	−9.36989	−	6.39102i	−0.319325	−	0.217805i
$862$		0			0
$863$	−46.3682			−1.57839			−0.789196	−	0.614141i	$-0.789502\pi$
$863$	−46.3682			−1.57839			−0.789196	+	0.614141i	$0.789502\pi$
$864$		0			0
$865$	6.08398			0.206861
$866$		0			0
$867$	−0.900868	+	11.9891i	−0.0305951	+	0.407171i
$868$		0			0
$869$	−0.0915364	−	0.519129i	−0.00310516	−	0.0176102i
$870$		0			0
$871$	−10.2263	−	8.58089i	−0.346505	−	0.290752i
$872$		0			0
$873$	−32.0552	−	36.3523i	−1.08491	−	1.23034i
$874$		0			0
$875$	0.922352	−	5.23092i	0.0311812	−	0.176837i
$876$		0			0
$877$	−50.3989	−	18.3437i	−1.70185	−	0.619423i	−0.705817	−	0.708394i	$-0.749420\pi$
$877$	−50.3989	−	18.3437i	−1.70185	−	0.619423i	−0.996034	+	0.0889709i	$0.971642\pi$
$878$		0			0
$879$	19.5288	−	43.2571i	0.658689	−	1.45903i
$880$		0			0
$881$	−9.75309	−	16.8929i	−0.328590	−	0.569135i	0.653642	−	0.756804i	$-0.273240\pi$
$881$	−9.75309	−	16.8929i	−0.328590	−	0.569135i	−0.982232	+	0.187669i	$0.939907\pi$
$882$		0			0
$883$	−13.0023	+	22.5206i	−0.437561	+	0.757879i	−0.997501	−	0.0706549i	$-0.977491\pi$
$883$	−13.0023	+	22.5206i	−0.437561	+	0.757879i	0.559939	+	0.828534i	$0.310824\pi$
$884$		0			0
$885$	5.10973	−	5.23665i	0.171762	−	0.176028i
$886$		0			0
$887$	−37.4775	+	31.4474i	−1.25837	+	1.05590i	−0.262519	+	0.964927i	$0.584553\pi$
$887$	−37.4775	+	31.4474i	−1.25837	+	1.05590i	−0.995853	+	0.0909726i	$0.971002\pi$
$888$		0			0
$889$	13.4876	−	4.90908i	0.452359	−	0.164645i
$890$		0			0
$891$	−0.477169	+	0.0234321i	−0.0159858	+	0.000785006i
$892$		0			0
$893$	−4.45658	+	1.62206i	−0.149134	+	0.0542802i
$894$		0			0
$895$	−1.33937	+	1.12386i	−0.0447701	+	0.0375666i
$896$		0			0
$897$	−13.6081	+	13.9462i	−0.454363	+	0.465649i
$898$		0			0
$899$	−1.88396	+	3.26312i	−0.0628337	+	0.108831i
$900$		0			0
$901$	29.1178	+	50.4334i	0.970053	+	1.68018i
$902$		0			0
$903$	−1.83555	+	4.06584i	−0.0610834	+	0.135303i
$904$		0			0
$905$	3.32074	+	1.20865i	0.110385	+	0.0401769i
$906$		0			0
$907$	2.30165	−	13.0533i	0.0764251	−	0.433428i	−0.922455	−	0.386106i	$-0.873820\pi$
$907$	2.30165	−	13.0533i	0.0764251	−	0.433428i	0.998880	−	0.0473225i	$-0.0150688\pi$
$908$		0			0
$909$	42.1999	−	8.51334i	1.39968	−	0.282370i
$910$		0			0
$911$	43.1404	+	36.1991i	1.42930	+	1.19933i	0.946123	+	0.323808i	$0.104963\pi$
$911$	43.1404	+	36.1991i	1.42930	+	1.19933i	0.483181	+	0.875520i	$0.339481\pi$
$912$		0			0
$913$	−0.104728	−	0.593943i	−0.00346599	−	0.0196566i
$914$		0			0
$915$	−0.0161338	+	0.214715i	−0.000533367	+	0.00709825i
$916$		0			0
$917$	−8.15591			−0.269332
$918$		0			0
$919$	34.0776			1.12412			0.562059	−	0.827097i	$-0.310010\pi$
$919$	34.0776			1.12412			0.562059	+	0.827097i	$0.310010\pi$
$920$		0			0
$921$	−8.78037	−	5.98893i	−0.289323	−	0.197342i
$922$		0			0
$923$	−1.73531	−	9.84143i	−0.0571184	−	0.323935i
$924$		0			0
$925$	33.7108	+	28.2867i	1.10840	+	0.930061i
$926$		0			0
$927$	−45.9965	−	25.0722i	−1.51072	−	0.823480i
$928$		0			0
$929$	4.23618	−	24.0246i	0.138985	−	0.788221i	−0.833017	−	0.553247i	$-0.813388\pi$
$929$	4.23618	−	24.0246i	0.138985	−	0.788221i	0.972002	−	0.234974i	$-0.0755004\pi$
$930$		0			0
$931$	18.9521	+	6.89799i	0.621129	+	0.226072i
$932$		0			0
$933$	−37.9697	+	3.79178i	−1.24307	+	0.124137i
$934$		0			0
$935$	0.0576366	+	0.0998295i	0.00188492	+	0.00326477i
$936$		0			0
$937$	−12.5275	+	21.6983i	−0.409256	+	0.708853i	−0.994807	−	0.101783i	$-0.967545\pi$
$937$	−12.5275	+	21.6983i	−0.409256	+	0.708853i	0.585550	+	0.810636i	$0.300878\pi$
$938$		0			0
$939$	5.43405	+	19.3286i	0.177334	+	0.630765i
$940$		0			0
$941$	−36.7342	+	30.8236i	−1.19750	+	1.00482i	−0.197802	+	0.980242i	$0.563380\pi$
$941$	−36.7342	+	30.8236i	−1.19750	+	1.00482i	−0.999698	+	0.0245796i	$0.992175\pi$
$942$		0			0
$943$	33.6126	−	12.2340i	1.09458	−	0.398394i
$944$		0			0
$945$	−2.06272	−	1.91623i	−0.0671004	−	0.0623350i
$946$		0			0
$947$	18.9322	−	6.89077i	0.615215	−	0.223920i	−0.0155686	−	0.999879i	$-0.504956\pi$
$947$	18.9322	−	6.89077i	0.615215	−	0.223920i	0.630783	+	0.775959i	$0.282734\pi$
$948$		0			0
$949$	−11.8312	+	9.92758i	−0.384058	+	0.322263i
$950$		0			0
$951$	15.1872	+	3.87036i	0.492478	+	0.125505i
$952$		0			0
$953$	12.6941	−	21.9868i	0.411201	−	0.712221i	−0.583820	−	0.811883i	$-0.698443\pi$
$953$	12.6941	−	21.9868i	0.411201	−	0.712221i	0.995021	+	0.0996619i	$0.0317761\pi$
$954$		0			0
$955$	2.65981	+	4.60693i	0.0860696	+	0.149077i
$956$		0			0
$957$	−0.0253995	−	0.0353434i	−0.000821049	−	0.00114249i
$958$		0			0
$959$	14.9777	+	5.45143i	0.483654	+	0.176036i
$960$		0			0
$961$	5.61847	−	31.8639i	0.181241	−	1.02787i
$962$		0			0
$963$	34.7856	−	43.5840i	1.12095	−	1.40448i
$964$		0			0
$965$	2.90864	+	2.44064i	0.0936325	+	0.0785670i
$966$		0			0
$967$	4.52956	+	25.6884i	0.145661	+	0.826084i	0.966834	+	0.255405i	$0.0822088\pi$
$967$	4.52956	+	25.6884i	0.145661	+	0.826084i	−0.821173	+	0.570679i	$0.806680\pi$
$968$		0			0
$969$	27.9541	−	13.4551i	0.898015	−	0.432240i
$970$		0			0
$971$	−48.3981			−1.55317			−0.776584	−	0.630014i	$-0.783049\pi$
$971$	−48.3981			−1.55317			−0.776584	+	0.630014i	$0.783049\pi$
$972$		0			0
$973$	−26.4194			−0.846968
$974$		0			0
$975$	12.6450	−	6.08640i	0.404965	−	0.194921i
$976$		0			0
$977$	6.00721	+	34.0686i	0.192188	+	1.08995i	0.916367	+	0.400339i	$0.131108\pi$
$977$	6.00721	+	34.0686i	0.192188	+	1.08995i	−0.724179	+	0.689612i	$0.757781\pi$
$978$		0			0
$979$	−0.252558	−	0.211921i	−0.00807179	−	0.00677304i
$980$		0			0
$981$	2.71873	−	3.40639i	0.0868025	−	0.108758i
$982$		0			0
$983$	1.67463	−	9.49730i	0.0534124	−	0.302917i	−0.946385	−	0.323041i	$-0.895295\pi$
$983$	1.67463	−	9.49730i	0.0534124	−	0.302917i	0.999797	+	0.0201239i	$0.00640606\pi$
$984$		0			0
$985$	−3.45343	−	1.25694i	−0.110035	−	0.0400496i
$986$		0			0
$987$	1.59877	+	2.22469i	0.0508893	+	0.0708125i
$988$		0			0
$989$	−7.03442	−	12.1840i	−0.223681	−	0.387428i
$990$		0			0
$991$	−11.9282	+	20.6602i	−0.378910	+	0.656292i	−0.990904	−	0.134571i	$-0.957034\pi$
$991$	−11.9282	+	20.6602i	−0.378910	+	0.656292i	0.611994	+	0.790863i	$0.290368\pi$
$992$		0			0
$993$	24.9248	+	6.35194i	0.790965	+	0.201573i
$994$		0			0
$995$	−2.55484	+	2.14377i	−0.0809939	+	0.0679620i
$996$		0			0
$997$	4.20493	−	1.53047i	0.133172	−	0.0484705i	−0.274575	−	0.961566i	$-0.588537\pi$
$997$	4.20493	−	1.53047i	0.133172	−	0.0484705i	0.407746	+	0.913095i	$0.366315\pi$
$998$		0			0
$999$	45.5015	−	14.0055i	1.43960	−	0.443114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.q.a.169.4	✓	24
3.2	odd	2		648.2.q.a.505.3		24
4.3	odd	2		432.2.u.e.385.1		24
27.2	odd	18		5832.2.a.i.1.8		12
27.4	even	9	inner	216.2.q.a.193.4	yes	24
27.23	odd	18		648.2.q.a.145.3		24
27.25	even	9		5832.2.a.h.1.5		12
108.31	odd	18		432.2.u.e.193.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.a.169.4	✓	24	1.1	even	1	trivial
216.2.q.a.193.4	yes	24	27.4	even	9	inner
432.2.u.e.193.1		24	108.31	odd	18
432.2.u.e.385.1		24	4.3	odd	2
648.2.q.a.145.3		24	27.23	odd	18
648.2.q.a.505.3		24	3.2	odd	2
5832.2.a.h.1.5		12	27.25	even	9
5832.2.a.i.1.8		12	27.2	odd	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.56067 - 0.751197i) q^{3} +(-0.0770674 - 0.437071i) q^{5} +(0.935232 + 0.784753i) q^{7} +(1.87141 - 2.34475i) q^{9} +O(q^{10})\)	\(q+(1.56067 - 0.751197i) q^{3} +(-0.0770674 - 0.437071i) q^{5} +(0.935232 + 0.784753i) q^{7} +(1.87141 - 2.34475i) q^{9} +(0.00921771 - 0.0522762i) q^{11} +(1.58518 + 0.576957i) q^{13} +(-0.448603 - 0.624232i) q^{15} +(-2.44650 - 4.23746i) q^{17} +(-1.83033 + 3.17022i) q^{19} +(2.04910 + 0.522200i) q^{21} +(-5.10868 + 4.28669i) q^{23} +(4.51337 - 1.64273i) q^{25} +(1.15929 - 5.06518i) q^{27} +(0.444832 - 0.161906i) q^{29} +(-6.09742 + 5.11634i) q^{31} +(-0.0248839 - 0.0885104i) q^{33} +(0.270917 - 0.469242i) q^{35} +(4.58110 + 7.93469i) q^{37} +(2.90735 - 0.290338i) q^{39} +(-5.04020 - 1.83448i) q^{41} +(-0.366331 + 2.07757i) q^{43} +(-1.16905 - 0.637234i) q^{45} +(0.992456 + 0.832769i) q^{47} +(-0.956715 - 5.42580i) q^{49} +(-7.00135 - 4.77549i) q^{51} -11.9018 q^{53} -0.0235588 q^{55} +(-0.475085 + 6.32261i) q^{57} +(1.65278 + 9.37338i) q^{59} +(-0.214574 - 0.180049i) q^{61} +(3.59025 - 0.724291i) q^{63} +(0.130006 - 0.737299i) q^{65} +(-7.43634 - 2.70660i) q^{67} +(-4.75284 + 10.5278i) q^{69} +(-2.96200 - 5.13033i) q^{71} +(-4.57777 + 7.92893i) q^{73} +(5.80989 - 5.95420i) q^{75} +(0.0496446 - 0.0416568i) q^{77} +(9.33162 - 3.39643i) q^{79} +(-1.99567 - 8.77595i) q^{81} +(10.6764 - 3.88590i) q^{83} +(-1.66353 + 1.39586i) q^{85} +(0.572615 - 0.586838i) q^{87} +(3.10545 - 5.37880i) q^{89} +(1.02974 + 1.78356i) q^{91} +(-5.67270 + 12.5653i) q^{93} +(1.52667 + 0.555662i) q^{95} +(2.80539 - 15.9101i) q^{97} +(-0.105324 - 0.119443i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{7} + 6 q^{9}+O(q^{10}) \) 24 * q - 3 * q^7 + 6 * q^9	\( 24 q - 3 q^{7} + 6 q^{9} + 6 q^{11} + 12 q^{13} - 3 q^{15} + 6 q^{17} + 9 q^{19} - 18 q^{21} + 24 q^{23} - 24 q^{25} - 9 q^{29} - 27 q^{31} + 21 q^{33} - 18 q^{35} + 15 q^{37} - 15 q^{39} - 6 q^{41} + 39 q^{43} - 69 q^{45} - 36 q^{47} + 3 q^{49} - 36 q^{51} - 18 q^{53} - 54 q^{55} + 27 q^{57} - 30 q^{59} + 12 q^{61} + 18 q^{63} - 18 q^{65} + 54 q^{67} - 57 q^{69} + 36 q^{73} - 51 q^{75} - 24 q^{77} - 45 q^{79} + 18 q^{81} + 33 q^{83} - 57 q^{85} + 90 q^{87} + 9 q^{89} + 39 q^{91} + 42 q^{93} + 87 q^{95} + 57 q^{97} - 24 q^{99}+O(q^{100}) \) 24 * q - 3 * q^7 + 6 * q^9 + 6 * q^11 + 12 * q^13 - 3 * q^15 + 6 * q^17 + 9 * q^19 - 18 * q^21 + 24 * q^23 - 24 * q^25 - 9 * q^29 - 27 * q^31 + 21 * q^33 - 18 * q^35 + 15 * q^37 - 15 * q^39 - 6 * q^41 + 39 * q^43 - 69 * q^45 - 36 * q^47 + 3 * q^49 - 36 * q^51 - 18 * q^53 - 54 * q^55 + 27 * q^57 - 30 * q^59 + 12 * q^61 + 18 * q^63 - 18 * q^65 + 54 * q^67 - 57 * q^69 + 36 * q^73 - 51 * q^75 - 24 * q^77 - 45 * q^79 + 18 * q^81 + 33 * q^83 - 57 * q^85 + 90 * q^87 + 9 * q^89 + 39 * q^91 + 42 * q^93 + 87 * q^95 + 57 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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