LMFDB - Embedded newform 432.2.be.a.239.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([9, 0, 7]))

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

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

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			239.2
Character	$\chi$	$=$	432.239
Dual form			432.2.be.a.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.991247 - 1.42036i) q^{3} +(-3.85028 - 0.678908i) q^{5} +(1.90230 + 2.26708i) q^{7} +(-1.03486 + 2.81586i) q^{9} +O(q^{10})$	\(q+(-0.991247 - 1.42036i) q^{3} +(-3.85028 - 0.678908i) q^{5} +(1.90230 + 2.26708i) q^{7} +(-1.03486 + 2.81586i) q^{9} +(0.560068 + 3.17630i) q^{11} +(1.43878 - 0.523674i) q^{13} +(2.85228 + 6.14175i) q^{15} +(-2.60029 - 1.50128i) q^{17} +(4.90409 - 2.83138i) q^{19} +(1.33442 - 4.94920i) q^{21} +(6.11794 + 5.13356i) q^{23} +(9.66525 + 3.51786i) q^{25} +(5.02534 - 1.32134i) q^{27} +(-1.57709 + 4.33301i) q^{29} +(-6.11407 + 7.28646i) q^{31} +(3.95634 - 3.94400i) q^{33} +(-5.78526 - 10.0204i) q^{35} +(-2.24428 + 3.88720i) q^{37} +(-2.17000 - 1.52450i) q^{39} +(0.210120 + 0.577300i) q^{41} +(-3.35455 + 0.591498i) q^{43} +(5.89620 - 10.1393i) q^{45} +(-0.982922 + 0.824769i) q^{47} +(-0.305345 + 1.73170i) q^{49} +(0.445172 + 5.18150i) q^{51} +5.01133i q^{53} -12.6099i q^{55} +(-8.88275 - 4.15899i) q^{57} +(-0.0386715 + 0.219317i) q^{59} +(-10.2571 + 8.60675i) q^{61} +(-8.35239 + 3.01052i) q^{63} +(-5.89524 + 1.03949i) q^{65} +(1.16511 + 3.20112i) q^{67} +(1.22713 - 13.7783i) q^{69} +(4.12205 - 7.13960i) q^{71} +(3.87009 + 6.70320i) q^{73} +(-4.58401 - 17.2152i) q^{75} +(-6.13551 + 7.31202i) q^{77} +(-1.28358 + 3.52662i) q^{79} +(-6.85814 - 5.82803i) q^{81} +(11.3755 + 4.14034i) q^{83} +(8.99262 + 7.54571i) q^{85} +(7.71773 - 2.05505i) q^{87} +(0.527753 - 0.304698i) q^{89} +(3.92421 + 2.26565i) q^{91} +(16.4100 + 1.46151i) q^{93} +(-20.8044 + 7.57217i) q^{95} +(-3.21509 - 18.2337i) q^{97} +(-9.52362 - 1.70995i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^5 - 12 * q^9	$ 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97}+O(q^{100}) $ 36 * q - 6 * q^5 - 12 * q^9 - 36 * q^21 + 18 * q^25 - 24 * q^29 - 36 * q^33 - 18 * q^41 - 18 * q^45 + 42 * q^65 + 54 * q^69 - 18 * q^73 + 90 * q^77 + 36 * q^81 + 72 * q^85 + 72 * q^89 + 54 * q^93 + 54 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{18}\right)$

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
$3$	−0.991247	−	1.42036i	−0.572297	−	0.820047i
$3$	−0.991247	−	1.42036i	−0.572297	−	0.820047i
$4$		0			0
$5$	−3.85028	−	0.678908i	−1.72190	−	0.303617i	−0.776640	−	0.629945i	$-0.783077\pi$
$5$	−3.85028	−	0.678908i	−1.72190	−	0.303617i	−0.945256	+	0.326328i	$0.894188\pi$
$6$		0			0
$7$	1.90230	+	2.26708i	0.719004	+	0.856875i	0.994534	−	0.104417i	$-0.0332978\pi$
$7$	1.90230	+	2.26708i	0.719004	+	0.856875i	−0.275530	+	0.961293i	$0.588853\pi$
$8$		0			0
$9$	−1.03486	+	2.81586i	−0.344953	+	0.938620i
$10$		0			0
$11$	0.560068	+	3.17630i	0.168867	+	0.957692i	0.944987	+	0.327107i	$0.106074\pi$
$11$	0.560068	+	3.17630i	0.168867	+	0.957692i	−0.776120	+	0.630585i	$0.782815\pi$
$12$		0			0
$13$	1.43878	−	0.523674i	0.399046	−	0.145241i	−0.134698	−	0.990887i	$-0.543007\pi$
$13$	1.43878	−	0.523674i	0.399046	−	0.145241i	0.533745	+	0.845646i	$0.320784\pi$
$14$		0			0
$15$	2.85228	+	6.14175i	0.736456	+	1.58579i
$16$		0			0
$17$	−2.60029	−	1.50128i	−0.630664	−	0.364114i	0.150345	−	0.988634i	$-0.451962\pi$
$17$	−2.60029	−	1.50128i	−0.630664	−	0.364114i	−0.781009	+	0.624520i	$0.785295\pi$
$18$		0			0
$19$	4.90409	−	2.83138i	1.12508	−	0.649563i	0.182384	−	0.983227i	$-0.441619\pi$
$19$	4.90409	−	2.83138i	1.12508	−	0.649563i	0.942692	+	0.333665i	$0.108285\pi$
$20$		0			0
$21$	1.33442	−	4.94920i	0.291194	−	1.08000i
$22$		0			0
$23$	6.11794	+	5.13356i	1.27568	+	1.07042i	0.993824	+	0.110965i	$0.0353941\pi$
$23$	6.11794	+	5.13356i	1.27568	+	1.07042i	0.281855	+	0.959457i	$0.409050\pi$
$24$		0			0
$25$	9.66525	+	3.51786i	1.93305	+	0.703573i
$26$		0			0
$27$	5.02534	−	1.32134i	0.967127	−	0.254292i
$28$		0			0
$29$	−1.57709	+	4.33301i	−0.292858	+	0.804621i	0.702788	+	0.711400i	$0.251938\pi$
$29$	−1.57709	+	4.33301i	−0.292858	+	0.804621i	−0.995645	+	0.0932208i	$0.970284\pi$
$30$		0			0
$31$	−6.11407	+	7.28646i	−1.09812	+	1.30869i	−0.150740	+	0.988573i	$0.548166\pi$
$31$	−6.11407	+	7.28646i	−1.09812	+	1.30869i	−0.947379	+	0.320114i	$0.896279\pi$
$32$		0			0
$33$	3.95634	−	3.94400i	0.688710	−	0.686563i
$34$		0			0
$35$	−5.78526	−	10.0204i	−0.977888	−	1.69375i
$36$		0			0
$37$	−2.24428	+	3.88720i	−0.368957	+	0.639052i	−0.989403	−	0.145197i	$-0.953618\pi$
$37$	−2.24428	+	3.88720i	−0.368957	+	0.639052i	0.620446	+	0.784249i	$0.286952\pi$
$38$		0			0
$39$	−2.17000	−	1.52450i	−0.347477	−	0.244116i
$40$		0			0
$41$	0.210120	+	0.577300i	0.0328152	+	0.0901591i	0.955018	−	0.296547i	$-0.0958351\pi$
$41$	0.210120	+	0.577300i	0.0328152	+	0.0901591i	−0.922203	+	0.386706i	$0.873613\pi$
$42$		0			0
$43$	−3.35455	+	0.591498i	−0.511565	+	0.0902026i	−0.423471	−	0.905910i	$-0.639189\pi$
$43$	−3.35455	+	0.591498i	−0.511565	+	0.0902026i	−0.0880934	+	0.996112i	$0.528077\pi$
$44$		0			0
$45$	5.89620	−	10.1393i	0.878953	−	1.51147i
$46$		0			0
$47$	−0.982922	+	0.824769i	−0.143374	+	0.120305i	−0.711654	−	0.702530i	$-0.752054\pi$
$47$	−0.982922	+	0.824769i	−0.143374	+	0.120305i	0.568280	+	0.822835i	$0.307609\pi$
$48$		0			0
$49$	−0.305345	+	1.73170i	−0.0436207	+	0.247385i
$50$		0			0
$51$	0.445172	+	5.18150i	0.0623366	+	0.725555i
$52$		0			0
$53$			5.01133i			0.688359i	0.938904	+	0.344179i	$0.111843\pi$
$53$			5.01133i			0.688359i	−0.938904	+	0.344179i	$0.888157\pi$
$54$		0			0
$55$		−	12.6099i		−	1.70032i
$56$		0			0
$57$	−8.88275	−	4.15899i	−1.17655	−	0.550872i
$58$		0			0
$59$	−0.0386715	+	0.219317i	−0.00503460	+	0.0285526i	−0.987222	−	0.159354i	$-0.949059\pi$
$59$	−0.0386715	+	0.219317i	−0.00503460	+	0.0285526i	0.982187	+	0.187906i	$0.0601701\pi$
$60$		0			0
$61$	−10.2571	+	8.60675i	−1.31329	+	1.10198i	−0.325609	+	0.945504i	$0.605569\pi$
$61$	−10.2571	+	8.60675i	−1.31329	+	1.10198i	−0.987682	+	0.156477i	$0.949986\pi$
$62$		0			0
$63$	−8.35239	+	3.01052i	−1.05230	+	0.379290i
$64$		0			0
$65$	−5.89524	+	1.03949i	−0.731214	+	0.128933i
$66$		0			0
$67$	1.16511	+	3.20112i	0.142341	+	0.391079i	0.990293	−	0.138994i	$-0.0443868\pi$
$67$	1.16511	+	3.20112i	0.142341	+	0.391079i	−0.847952	+	0.530073i	$0.822165\pi$
$68$		0			0
$69$	1.22713	−	13.7783i	0.147729	−	1.65872i
$70$		0			0
$71$	4.12205	−	7.13960i	0.489197	−	0.847315i	−0.510725	−	0.859744i	$-0.670623\pi$
$71$	4.12205	−	7.13960i	0.489197	−	0.847315i	0.999923	+	0.0124293i	$0.00395647\pi$
$72$		0			0
$73$	3.87009	+	6.70320i	0.452960	+	0.784550i	0.998568	−	0.0534906i	$-0.0170347\pi$
$73$	3.87009	+	6.70320i	0.452960	+	0.784550i	−0.545608	+	0.838040i	$0.683701\pi$
$74$		0			0
$75$	−4.58401	−	17.2152i	−0.529316	−	1.98784i
$76$		0			0
$77$	−6.13551	+	7.31202i	−0.699206	+	0.833282i
$78$		0			0
$79$	−1.28358	+	3.52662i	−0.144414	+	0.396775i	−0.990719	−	0.135923i	$-0.956600\pi$
$79$	−1.28358	+	3.52662i	−0.144414	+	0.396775i	0.846305	+	0.532699i	$0.178822\pi$
$80$		0			0
$81$	−6.85814	−	5.82803i	−0.762015	−	0.647559i
$82$		0			0
$83$	11.3755	+	4.14034i	1.24862	+	0.454462i	0.879936	−	0.475092i	$-0.157585\pi$
$83$	11.3755	+	4.14034i	1.24862	+	0.454462i	0.368687	+	0.929553i	$0.379807\pi$
$84$		0			0
$85$	8.99262	+	7.54571i	0.975387	+	0.818447i
$86$		0			0
$87$	7.71773	−	2.05505i	0.827428	−	0.220325i
$88$		0			0
$89$	0.527753	−	0.304698i	0.0559417	−	0.0322980i	−0.471768	−	0.881723i	$-0.656384\pi$
$89$	0.527753	−	0.304698i	0.0559417	−	0.0322980i	0.527710	+	0.849425i	$0.323051\pi$
$90$		0			0
$91$	3.92421	+	2.26565i	0.411369	+	0.237504i
$92$		0			0
$93$	16.4100	+	1.46151i	1.70163	+	0.151551i
$94$		0			0
$95$	−20.8044	+	7.57217i	−2.13448	+	0.776888i
$96$		0			0
$97$	−3.21509	−	18.2337i	−0.326443	−	1.85135i	−0.499336	−	0.866409i	$-0.666422\pi$
$97$	−3.21509	−	18.2337i	−0.326443	−	1.85135i	0.172893	−	0.984941i	$-0.444689\pi$
$98$		0			0
$99$	−9.52362	−	1.70995i	−0.957160	−	0.171856i
$100$		0			0
$101$	−5.45656	−	6.50288i	−0.542948	−	0.647061i	0.422898	−	0.906177i	$-0.361013\pi$
$101$	−5.45656	−	6.50288i	−0.542948	−	0.647061i	−0.965846	+	0.259117i	$0.916569\pi$
$102$		0			0
$103$	8.08845	+	1.42621i	0.796978	+	0.140529i	0.557287	−	0.830320i	$-0.311843\pi$
$103$	8.08845	+	1.42621i	0.796978	+	0.140529i	0.239692	+	0.970849i	$0.422954\pi$
$104$		0			0
$105$	−8.49793	+	18.1498i	−0.829313	+	1.77124i
$106$		0			0
$107$	−15.6604			−1.51395			−0.756974	−	0.653445i	$-0.773323\pi$
$107$	−15.6604			−1.51395			−0.756974	+	0.653445i	$0.773323\pi$
$108$		0			0
$109$	9.01637			0.863611			0.431806	−	0.901967i	$-0.357877\pi$
$109$	9.01637			0.863611			0.431806	+	0.901967i	$0.357877\pi$
$110$		0			0
$111$	7.74587	−	0.665492i	0.735205	−	0.0631657i
$112$		0			0
$113$	6.84827	+	1.20753i	0.644231	+	0.113595i	0.486212	−	0.873841i	$-0.338378\pi$
$113$	6.84827	+	1.20753i	0.644231	+	0.113595i	0.158019	+	0.987436i	$0.449489\pi$
$114$		0			0
$115$	−20.0706	−	23.9192i	−1.87159	−	2.23047i
$116$		0			0
$117$	−0.0143422	+	4.59334i	−0.00132593	+	0.424654i
$118$		0			0
$119$	−1.54303	−	8.75097i	−0.141449	−	0.802200i
$120$		0			0
$121$	0.561386	−	0.204328i	0.0510351	−	0.0185753i
$122$		0			0
$123$	0.611694	−	0.870694i	0.0551546	−	0.0785078i
$124$		0			0
$125$	−17.8962	−	10.3324i	−1.60069	−	0.924156i
$126$		0			0
$127$	8.87022	−	5.12122i	0.787105	−	0.454435i	−0.0518375	−	0.998656i	$-0.516508\pi$
$127$	8.87022	−	5.12122i	0.787105	−	0.454435i	0.838942	+	0.544220i	$0.183174\pi$
$128$		0			0
$129$	4.16533	+	4.17836i	0.366737	+	0.367884i
$130$		0			0
$131$	−0.436664	−	0.366404i	−0.0381515	−	0.0320129i	0.623513	−	0.781813i	$-0.285705\pi$
$131$	−0.436664	−	0.366404i	−0.0381515	−	0.0320129i	−0.661664	+	0.749800i	$0.730149\pi$
$132$		0			0
$133$	15.7480	+	5.73182i	1.36553	+	0.497011i
$134$		0			0
$135$	−20.2460	+	1.67579i	−1.74250	+	0.144229i
$136$		0			0
$137$	2.42588	−	6.66504i	0.207257	−	0.569433i	−0.791893	−	0.610659i	$-0.790904\pi$
$137$	2.42588	−	6.66504i	0.207257	−	0.569433i	0.999150	+	0.0412269i	$0.0131267\pi$
$138$		0			0
$139$	1.82538	−	2.17540i	0.154827	−	0.184515i	−0.683055	−	0.730367i	$-0.739349\pi$
$139$	1.82538	−	2.17540i	0.154827	−	0.184515i	0.837882	+	0.545851i	$0.183794\pi$
$140$		0			0
$141$	2.14579	+	0.578555i	0.180708	+	0.0487231i
$142$		0			0
$143$	2.46916	+	4.27672i	0.206482	+	0.357637i
$144$		0			0
$145$	9.01394	−	15.6126i	0.748567	−	1.29656i
$146$		0			0
$147$	2.76231	−	1.28284i	0.227831	−	0.105807i
$148$		0			0
$149$	−2.77050	−	7.61188i	−0.226968	−	0.623590i	0.772973	−	0.634439i	$-0.218769\pi$
$149$	−2.77050	−	7.61188i	−0.226968	−	0.623590i	−0.999941	+	0.0108491i	$0.996547\pi$
$150$		0			0
$151$	−18.5383	+	3.26880i	−1.50862	+	0.266011i	−0.865950	−	0.500130i	$-0.833285\pi$
$151$	−18.5383	+	3.26880i	−1.50862	+	0.266011i	−0.642672	+	0.766141i	$0.722174\pi$
$152$		0			0
$153$	6.91833	−	5.76845i	0.559314	−	0.466352i
$154$		0			0
$155$	28.4877	−	23.9040i	2.28819	−	1.92002i
$156$		0			0
$157$	−1.04493	+	5.92610i	−0.0833945	+	0.472954i	0.914297	+	0.405045i	$0.132744\pi$
$157$	−1.04493	+	5.92610i	−0.0833945	+	0.472954i	−0.997691	+	0.0679094i	$0.978367\pi$
$158$		0			0
$159$	7.11790	−	4.96746i	0.564486	−	0.393945i
$160$		0			0
$161$			23.6355i			1.86273i
$162$		0			0
$163$			16.4440i			1.28800i	0.765028	+	0.643998i	$0.222725\pi$
$163$			16.4440i			1.28800i	−0.765028	+	0.643998i	$0.777275\pi$
$164$		0			0
$165$	−17.9106	+	12.4995i	−1.39434	+	0.973086i
$166$		0			0
$167$	−2.56815	+	14.5647i	−0.198729	+	1.12705i	0.708278	+	0.705934i	$0.249472\pi$
$167$	−2.56815	+	14.5647i	−0.198729	+	1.12705i	−0.907007	+	0.421115i	$0.861639\pi$
$168$		0			0
$169$	−8.16272	+	6.84933i	−0.627901	+	0.526872i
$170$		0			0
$171$	2.89773	+	16.7393i	0.221595	+	1.28009i
$172$		0			0
$173$	2.00249	−	0.353093i	0.152246	−	0.0268451i	−0.0970054	−	0.995284i	$-0.530926\pi$
$173$	2.00249	−	0.353093i	0.152246	−	0.0268451i	0.249252	+	0.968439i	$0.419815\pi$
$174$		0			0
$175$	10.4110	+	28.6039i	0.786996	+	2.16225i
$176$		0			0
$177$	0.349843	−	0.162470i	0.0262958	−	0.0122120i
$178$		0			0
$179$	−0.253380	+	0.438867i	−0.0189385	+	0.0328024i	−0.875339	−	0.483509i	$-0.839362\pi$
$179$	−0.253380	+	0.438867i	−0.0189385	+	0.0328024i	0.856401	+	0.516312i	$0.172695\pi$
$180$		0			0
$181$	−4.56085	−	7.89962i	−0.339005	−	0.587174i	0.645241	−	0.763979i	$-0.276757\pi$
$181$	−4.56085	−	7.89962i	−0.339005	−	0.587174i	−0.984246	+	0.176805i	$0.943424\pi$
$182$		0			0
$183$	22.3921	+	6.03742i	1.65527	+	0.446299i
$184$		0			0
$185$	11.2801	−	13.4431i	0.829332	−	0.988359i
$186$		0			0
$187$	3.31218	−	9.10015i	0.242211	−	0.665469i
$188$		0			0
$189$	12.5553	+	8.87925i	0.913265	+	0.645870i
$190$		0			0
$191$	12.4556	+	4.53348i	0.901259	+	0.328031i	0.750757	−	0.660578i	$-0.229689\pi$
$191$	12.4556	+	4.53348i	0.901259	+	0.328031i	0.150502	+	0.988610i	$0.451911\pi$
$192$		0			0
$193$	−15.8300	−	13.2829i	−1.13947	−	0.956126i	−0.140045	−	0.990145i	$-0.544725\pi$
$193$	−15.8300	−	13.2829i	−1.13947	−	0.956126i	−0.999421	+	0.0340192i	$0.989169\pi$
$194$		0			0
$195$	7.32009	+	7.34298i	0.524202	+	0.525842i
$196$		0			0
$197$	21.7739	−	12.5711i	1.55132	−	0.895657i	0.553289	−	0.832989i	$-0.313373\pi$
$197$	21.7739	−	12.5711i	1.55132	−	0.895657i	0.998034	−	0.0626676i	$-0.0199608\pi$
$198$		0			0
$199$	0.870852	+	0.502786i	0.0617330	+	0.0356416i	0.530549	−	0.847654i	$-0.321986\pi$
$199$	0.870852	+	0.502786i	0.0617330	+	0.0356416i	−0.468816	+	0.883296i	$0.655319\pi$
$200$		0			0
$201$	3.39184	−	4.82798i	0.239242	−	0.340540i
$202$		0			0
$203$	−12.8234	+	4.66733i	−0.900025	+	0.327582i
$204$		0			0
$205$	−0.417087	−	2.36542i	−0.0291306	−	0.165208i
$206$		0			0
$207$	−20.7866	+	11.9148i	−1.44477	+	0.828133i
$208$		0			0
$209$	11.7399	+	13.9911i	0.812069	+	0.967786i
$210$		0			0
$211$	11.1122	+	1.95939i	0.764998	+	0.134890i	0.542514	−	0.840046i	$-0.317472\pi$
$211$	11.1122	+	1.95939i	0.764998	+	0.134890i	0.222484	+	0.974936i	$0.428583\pi$
$212$		0			0
$213$	−14.2268	+	1.22231i	−0.974803	+	0.0837510i
$214$		0			0
$215$	13.3175			0.908248
$216$		0			0
$217$	−28.1498			−1.91093
$218$		0			0
$219$	5.68475	−	12.1415i	0.384140	−	0.820444i
$220$		0			0
$221$	−4.52744	−	0.798310i	−0.304549	−	0.0537001i
$222$		0			0
$223$	2.04837	+	2.44115i	0.137169	+	0.163471i	0.830256	−	0.557383i	$-0.188194\pi$
$223$	2.04837	+	2.44115i	0.137169	+	0.163471i	−0.693087	+	0.720854i	$0.743750\pi$
$224$		0			0
$225$	−19.9080	+	23.5755i	−1.32720	+	1.57170i
$226$		0			0
$227$	2.84631	+	16.1423i	0.188917	+	1.07140i	0.920819	+	0.389990i	$0.127521\pi$
$227$	2.84631	+	16.1423i	0.188917	+	1.07140i	−0.731903	+	0.681409i	$0.761367\pi$
$228$		0			0
$229$	−7.62322	+	2.77463i	−0.503757	+	0.183352i	−0.581383	−	0.813630i	$-0.697488\pi$
$229$	−7.62322	+	2.77463i	−0.503757	+	0.183352i	0.0776261	+	0.996983i	$0.475266\pi$
$230$		0			0
$231$	16.4675	+	1.46663i	1.08348	+	0.0964972i
$232$		0			0
$233$	5.45161	+	3.14749i	0.357147	+	0.206199i	0.667829	−	0.744315i	$-0.267224\pi$
$233$	5.45161	+	3.14749i	0.357147	+	0.206199i	−0.310682	+	0.950514i	$0.600557\pi$
$234$		0			0
$235$	4.34446	−	2.50828i	0.283402	−	0.163622i
$236$		0			0
$237$	6.28142	−	1.67260i	0.408022	−	0.108647i
$238$		0			0
$239$	−8.17874	−	6.86278i	−0.529039	−	0.443916i	0.338730	−	0.940883i	$-0.390003\pi$
$239$	−8.17874	−	6.86278i	−0.529039	−	0.443916i	−0.867769	+	0.496967i	$0.834447\pi$
$240$		0			0
$241$	−17.5678	−	6.39416i	−1.13164	−	0.411884i	−0.292754	−	0.956188i	$-0.594572\pi$
$241$	−17.5678	−	6.39416i	−1.13164	−	0.411884i	−0.838888	+	0.544304i	$0.816794\pi$
$242$		0			0
$243$	−1.47980	+	15.5181i	−0.0949292	+	0.995484i
$244$		0			0
$245$	2.35132	−	6.46021i	0.150220	−	0.412727i
$246$		0			0
$247$	5.57320	−	6.64188i	0.354614	−	0.422613i
$248$		0			0
$249$	−5.39515	−	20.2614i	−0.341904	−	1.28402i
$250$		0			0
$251$	−6.86771	−	11.8952i	−0.433486	−	0.750820i	0.563685	−	0.825990i	$-0.309383\pi$
$251$	−6.86771	−	11.8952i	−0.433486	−	0.750820i	−0.997171	+	0.0751704i	$0.976050\pi$
$252$		0			0
$253$	−12.8793	+	22.3076i	−0.809714	+	1.40247i
$254$		0			0
$255$	1.80372	−	20.2524i	0.112954	−	1.26826i
$256$		0			0
$257$	9.34803	+	25.6835i	0.583114	+	1.60209i	0.782827	+	0.622239i	$0.213777\pi$
$257$	9.34803	+	25.6835i	0.583114	+	1.60209i	−0.199713	+	0.979854i	$0.564001\pi$
$258$		0			0
$259$	−13.0819	+	2.30669i	−0.812869	+	0.143331i
$260$		0			0
$261$	−10.5691	−	8.92491i	−0.654211	−	0.552438i
$262$		0			0
$263$	−6.99737	+	5.87149i	−0.431476	+	0.362051i	−0.832508	−	0.554012i	$-0.813096\pi$
$263$	−6.99737	+	5.87149i	−0.431476	+	0.362051i	0.401032	+	0.916064i	$0.368652\pi$
$264$		0			0
$265$	3.40223	−	19.2950i	0.208997	−	1.18528i
$266$		0			0
$267$	−0.955916	−	0.447569i	−0.0585011	−	0.0273908i
$268$		0			0
$269$			1.49499i			0.0911509i	0.998961	+	0.0455754i	$0.0145121\pi$
$269$			1.49499i			0.0911509i	−0.998961	+	0.0455754i	$0.985488\pi$
$270$		0			0
$271$		−	24.4160i		−	1.48317i	−0.670861	−	0.741583i	$-0.734075\pi$
$271$		−	24.4160i		−	1.48317i	0.670861	−	0.741583i	$-0.265925\pi$
$272$		0			0
$273$	−0.671828	−	7.81962i	−0.0406609	−	0.473265i
$274$		0			0
$275$	−5.76061	+	32.6700i	−0.347378	+	1.97008i
$276$		0			0
$277$	5.49016	−	4.60679i	0.329872	−	0.276795i	−0.462776	−	0.886475i	$-0.653147\pi$
$277$	5.49016	−	4.60679i	0.329872	−	0.276795i	0.792648	+	0.609680i	$0.208702\pi$
$278$		0			0
$279$	−14.1905	−	24.7568i	−0.849561	−	1.48215i
$280$		0			0
$281$	25.8279	−	4.55416i	1.54076	−	0.271678i	0.662209	−	0.749319i	$-0.269619\pi$
$281$	25.8279	−	4.55416i	1.54076	−	0.271678i	0.878555	+	0.477641i	$0.158508\pi$
$282$		0			0
$283$	4.65241	+	12.7824i	0.276557	+	0.759834i	0.997747	+	0.0670962i	$0.0213734\pi$
$283$	4.65241	+	12.7824i	0.276557	+	0.759834i	−0.721190	+	0.692738i	$0.756404\pi$
$284$		0			0
$285$	31.3775	+	22.0438i	1.85864	+	1.30576i
$286$		0			0
$287$	−0.909072	+	1.57456i	−0.0536608	+	0.0929433i
$288$		0			0
$289$	−3.99231	−	6.91489i	−0.234842	−	0.406758i
$290$		0			0
$291$	−22.7115	+	22.6407i	−1.33137	+	1.32722i
$292$		0			0
$293$	5.19618	−	6.19256i	0.303564	−	0.361773i	−0.592600	−	0.805497i	$-0.701898\pi$
$293$	5.19618	−	6.19256i	0.303564	−	0.361773i	0.896164	+	0.443724i	$0.146343\pi$
$294$		0			0
$295$	0.297792	−	0.818177i	0.0173381	−	0.0476361i
$296$		0			0
$297$	7.01152	+	15.2220i	0.406849	+	0.883268i
$298$		0			0
$299$	11.4907	+	4.18227i	0.664524	+	0.241867i
$300$		0			0
$301$	−7.72236	−	6.47983i	−0.445109	−	0.373491i
$302$		0			0
$303$	−3.82764	+	14.1963i	−0.219892	+	0.815554i
$304$		0			0
$305$	45.3360	−	26.1747i	2.59593	−	1.49876i
$306$		0			0
$307$	21.6044	+	12.4733i	1.23303	+	0.711890i	0.967660	−	0.252257i	$-0.0811730\pi$
$307$	21.6044	+	12.4733i	1.23303	+	0.711890i	0.265369	+	0.964147i	$0.414506\pi$
$308$		0			0
$309$	−5.99191	−	12.9023i	−0.340868	−	0.733983i
$310$		0			0
$311$	27.1209	−	9.87120i	1.53788	−	0.559744i	0.572348	−	0.820011i	$-0.306033\pi$
$311$	27.1209	−	9.87120i	1.53788	−	0.559744i	0.965537	+	0.260267i	$0.0838106\pi$
$312$		0			0
$313$	0.406391	+	2.30476i	0.0229706	+	0.130273i	0.994137	−	0.108132i	$-0.0344868\pi$
$313$	0.406391	+	2.30476i	0.0229706	+	0.130273i	−0.971166	+	0.238404i	$0.923376\pi$
$314$		0			0
$315$	34.2029	−	5.92084i	1.92711	−	0.333601i
$316$		0			0
$317$	5.49865	+	6.55303i	0.308835	+	0.368055i	0.898029	−	0.439937i	$-0.144999\pi$
$317$	5.49865	+	6.55303i	0.308835	+	0.368055i	−0.589194	+	0.807992i	$0.700555\pi$
$318$		0			0
$319$	−14.6462	−	2.58253i	−0.820033	−	0.144594i
$320$		0			0
$321$	15.5233	+	22.2434i	0.866427	+	1.24151i
$322$		0			0
$323$	−17.0028			−0.946060
$324$		0			0
$325$	15.7484			0.873564
$326$		0			0
$327$	−8.93745	−	12.8065i	−0.494242	−	0.708202i
$328$		0			0
$329$	−3.73963	−	0.659398i	−0.206173	−	0.0363538i
$330$		0			0
$331$	6.63073	+	7.90220i	0.364458	+	0.434344i	0.916845	−	0.399244i	$-0.130727\pi$
$331$	6.63073	+	7.90220i	0.364458	+	0.434344i	−0.552387	+	0.833588i	$0.686283\pi$
$332$		0			0
$333$	−8.62331	−	10.3423i	−0.472554	−	0.566753i
$334$		0			0
$335$	−2.31274	−	13.1162i	−0.126359	−	0.716615i
$336$		0			0
$337$	5.42698	−	1.97526i	0.295626	−	0.107599i	−0.189949	−	0.981794i	$-0.560832\pi$
$337$	5.42698	−	1.97526i	0.295626	−	0.107599i	0.485576	+	0.874195i	$0.338610\pi$
$338$		0			0
$339$	−5.07319	−	10.9240i	−0.275538	−	0.593309i
$340$		0			0
$341$	−26.5683	−	15.3392i	−1.43876	−	0.830666i
$342$		0			0
$343$	13.4340	−	7.75614i	0.725369	−	0.418792i
$344$		0			0
$345$	−14.0790	+	52.2173i	−0.757987	+	2.81128i
$346$		0			0
$347$	4.31009	+	3.61659i	0.231378	+	0.194149i	0.751104	−	0.660184i	$-0.229522\pi$
$347$	4.31009	+	3.61659i	0.231378	+	0.194149i	−0.519726	+	0.854333i	$0.673966\pi$
$348$		0			0
$349$	−16.8949	−	6.14924i	−0.904363	−	0.329161i	−0.152363	−	0.988325i	$-0.548688\pi$
$349$	−16.8949	−	6.14924i	−0.904363	−	0.329161i	−0.752000	+	0.659163i	$0.770911\pi$
$350$		0			0
$351$	6.53842	−	4.53276i	0.348995	−	0.241941i
$352$		0			0
$353$	−5.25148	+	14.4283i	−0.279508	+	0.767942i	0.717911	+	0.696135i	$0.245099\pi$
$353$	−5.25148	+	14.4283i	−0.279508	+	0.767942i	−0.997419	+	0.0718066i	$0.977124\pi$
$354$		0			0
$355$	−20.7182	+	24.6909i	−1.09961	+	1.31046i
$356$		0			0
$357$	−10.9000	+	10.8660i	−0.576890	+	0.575092i
$358$		0			0
$359$	−16.4899	−	28.5614i	−0.870305	−	1.50741i	−0.861682	−	0.507449i	$-0.830589\pi$
$359$	−16.4899	−	28.5614i	−0.870305	−	1.50741i	−0.00862297	−	0.999963i	$-0.502745\pi$
$360$		0			0
$361$	6.53341	−	11.3162i	0.343864	−	0.595589i
$362$		0			0
$363$	−0.846692	−	0.594832i	−0.0444398	−	0.0312206i
$364$		0			0
$365$	−10.3501	−	28.4366i	−0.541748	−	1.48844i
$366$		0			0
$367$	−1.19429	+	0.210586i	−0.0623416	+	0.0109925i	−0.204732	−	0.978818i	$-0.565632\pi$
$367$	−1.19429	+	0.210586i	−0.0623416	+	0.0109925i	0.142390	+	0.989811i	$0.454521\pi$
$368$		0			0
$369$	−1.84304	−	0.00575468i	−0.0959449	−	0.000299577i
$370$		0			0
$371$	−11.3611	+	9.53307i	−0.589837	+	0.494932i
$372$		0			0
$373$	1.14523	−	6.49494i	0.0592979	−	0.336295i	−0.940698	−	0.339246i	$-0.889828\pi$
$373$	1.14523	−	6.49494i	0.0592979	−	0.336295i	0.999996	+	0.00295067i	$0.000939230\pi$
$374$		0			0
$375$	3.06384	+	35.6610i	0.158216	+	1.84153i
$376$		0			0
$377$			7.06014i			0.363616i
$378$		0			0
$379$		−	23.0138i		−	1.18214i	−0.806620	−	0.591070i	$-0.798706\pi$
$379$		−	23.0138i		−	1.18214i	0.806620	−	0.591070i	$-0.201294\pi$
$380$		0			0
$381$	−16.0666	−	7.52253i	−0.823116	−	0.385391i
$382$		0			0
$383$	3.25873	−	18.4812i	0.166513	−	0.944344i	−0.780977	−	0.624560i	$-0.785278\pi$
$383$	3.25873	−	18.4812i	0.166513	−	0.944344i	0.947490	−	0.319784i	$-0.103610\pi$
$384$		0			0
$385$	28.5876	−	23.9878i	1.45696	−	1.22253i
$386$		0			0
$387$	1.80591	−	10.0581i	0.0917995	−	0.511280i
$388$		0			0
$389$	−26.3690	+	4.64957i	−1.33696	+	0.235743i	−0.795996	−	0.605301i	$-0.793053\pi$
$389$	−26.3690	+	4.64957i	−1.33696	+	0.235743i	−0.540967	+	0.841044i	$0.681942\pi$
$390$		0			0
$391$	−8.20153	−	22.5335i	−0.414769	−	1.13957i
$392$		0			0
$393$	−0.0875852	+	0.983418i	−0.00441809	+	0.0496069i
$394$		0			0
$395$	7.33640	−	12.7070i	0.369134	−	0.639359i
$396$		0			0
$397$	−9.33339	−	16.1659i	−0.468429	−	0.811343i	0.530920	−	0.847422i	$-0.321847\pi$
$397$	−9.33339	−	16.1659i	−0.468429	−	0.811343i	−0.999349	+	0.0360788i	$0.988513\pi$
$398$		0			0
$399$	−7.46894	−	28.0496i	−0.373915	−	1.40423i
$400$		0			0
$401$	−10.2927	+	12.2664i	−0.513994	+	0.612554i	−0.959150	−	0.282899i	$-0.908704\pi$
$401$	−10.2927	+	12.2664i	−0.513994	+	0.612554i	0.445156	+	0.895453i	$0.353148\pi$
$402$		0			0
$403$	−4.98108	+	13.6854i	−0.248125	+	0.681719i
$404$		0			0
$405$	22.4490	+	27.0956i	1.11550	+	1.34639i
$406$		0			0
$407$	−13.6039	−	4.95141i	−0.674319	−	0.245432i
$408$		0			0
$409$	12.0693	+	10.1274i	0.596791	+	0.500767i	0.890412	−	0.455155i	$-0.150416\pi$
$409$	12.0693	+	10.1274i	0.596791	+	0.500767i	−0.293622	+	0.955922i	$0.594861\pi$
$410$		0			0
$411$	−11.8714	+	3.16108i	−0.585573	+	0.155925i
$412$		0			0
$413$	−0.570774	+	0.329537i	−0.0280860	+	0.0162154i
$414$		0			0
$415$	−40.9879	−	23.6644i	−2.01202	−	1.16164i
$416$		0			0
$417$	−4.89926	−	0.436338i	−0.239918	−	0.0213676i
$418$		0			0
$419$	15.8780	−	5.77912i	0.775691	−	0.282329i	0.0763166	−	0.997084i	$-0.475684\pi$
$419$	15.8780	−	5.77912i	0.775691	−	0.282329i	0.699375	+	0.714755i	$0.253462\pi$
$420$		0			0
$421$	4.75431	+	26.9630i	0.231711	+	1.31410i	0.849431	+	0.527700i	$0.176945\pi$
$421$	4.75431	+	26.9630i	0.231711	+	1.31410i	−0.617720	+	0.786398i	$0.711944\pi$
$422$		0			0
$423$	−1.30525	−	3.62129i	−0.0634635	−	0.176073i
$424$		0			0
$425$	−19.8512	−	23.6577i	−0.962925	−	1.14757i
$426$		0			0
$427$	−39.0244	−	6.88105i	−1.88852	−	0.332997i
$428$		0			0
$429$	3.62694	−	7.74639i	0.175110	−	0.373999i
$430$		0			0
$431$	6.64210			0.319939			0.159969	−	0.987122i	$-0.448860\pi$
$431$	6.64210			0.319939			0.159969	+	0.987122i	$0.448860\pi$
$432$		0			0
$433$	−7.60807			−0.365621			−0.182810	−	0.983148i	$-0.558519\pi$
$433$	−7.60807			−0.365621			−0.182810	+	0.983148i	$0.558519\pi$
$434$		0			0
$435$	−31.1106	+	2.67289i	−1.49164	+	0.128155i
$436$		0			0
$437$	44.5380	+	7.85325i	2.13054	+	0.375672i
$438$		0			0
$439$	−1.70790	−	2.03539i	−0.0815135	−	0.0971440i	0.723746	−	0.690066i	$-0.242419\pi$
$439$	−1.70790	−	2.03539i	−0.0815135	−	0.0971440i	−0.805260	+	0.592922i	$0.797974\pi$
$440$		0			0
$441$	−4.56022	−	2.65187i	−0.217154	−	0.126279i
$442$		0			0
$443$	1.28130	+	7.26659i	0.0608762	+	0.345246i	0.999999	+	0.00166347i	$0.000529499\pi$
$443$	1.28130	+	7.26659i	0.0608762	+	0.345246i	−0.939122	+	0.343583i	$0.888359\pi$
$444$		0			0
$445$	−2.23886	+	0.814878i	−0.106132	+	0.0386289i
$446$		0			0
$447$	−8.06538	+	11.4804i	−0.381479	+	0.543003i
$448$		0			0
$449$	−28.2078	−	16.2858i	−1.33121	−	0.768573i	−0.345723	−	0.938337i	$-0.612366\pi$
$449$	−28.2078	−	16.2858i	−1.33121	−	0.768573i	−0.985485	+	0.169764i	$0.945700\pi$
$450$		0			0
$451$	−1.71600	+	0.990733i	−0.0808032	+	0.0466518i
$452$		0			0
$453$	23.0189	+	23.0909i	1.08152	+	1.08490i
$454$		0			0
$455$	−13.5711	−	11.3875i	−0.636225	−	0.533856i
$456$		0			0
$457$	−24.9862	−	9.09423i	−1.16880	−	0.425410i	−0.316570	−	0.948569i	$-0.602531\pi$
$457$	−24.9862	−	9.09423i	−1.16880	−	0.425410i	−0.852235	+	0.523159i	$0.824753\pi$
$458$		0			0
$459$	−15.0511	−	4.10857i	−0.702524	−	0.191772i
$460$		0			0
$461$	6.89899	−	18.9548i	0.321318	−	0.882814i	−0.668909	−	0.743345i	$-0.733238\pi$
$461$	6.89899	−	18.9548i	0.321318	−	0.882814i	0.990226	−	0.139469i	$-0.0445395\pi$
$462$		0			0
$463$	5.25098	−	6.25787i	0.244034	−	0.290828i	−0.630099	−	0.776514i	$-0.716986\pi$
$463$	5.25098	−	6.25787i	0.244034	−	0.290828i	0.874133	+	0.485686i	$0.161430\pi$
$464$		0			0
$465$	−62.1907	−	16.7681i	−2.88403	−	0.777600i
$466$		0			0
$467$	−6.73312	−	11.6621i	−0.311571	−	0.539658i	0.667131	−	0.744940i	$-0.267522\pi$
$467$	−6.73312	−	11.6621i	−0.311571	−	0.539658i	−0.978703	+	0.205283i	$0.934189\pi$
$468$		0			0
$469$	−5.04079	+	8.73091i	−0.232762	+	0.403156i
$470$		0			0
$471$	9.45299	−	4.39005i	0.435571	−	0.202283i
$472$		0			0
$473$	−3.75756	−	10.3238i	−0.172773	−	0.474689i
$474$		0			0
$475$	57.3597	−	10.1141i	2.63184	−	0.464065i
$476$		0			0
$477$	−14.1112	−	5.18601i	−0.646107	−	0.237451i
$478$		0			0
$479$	−25.8908	+	21.7250i	−1.18298	+	0.992641i	−0.183028	+	0.983108i	$0.558590\pi$
$479$	−25.8908	+	21.7250i	−1.18298	+	0.992641i	−0.999955	+	0.00953287i	$0.996966\pi$
$480$		0			0
$481$	−1.19340	+	6.76810i	−0.0544143	+	0.308599i
$482$		0			0
$483$	33.5709	−	23.4286i	1.52753	−	1.06604i
$484$		0			0
$485$			72.3874i			3.28694i
$486$		0			0
$487$			15.6103i			0.707368i	0.935365	+	0.353684i	$0.115071\pi$
$487$			15.6103i			0.707368i	−0.935365	+	0.353684i	$0.884929\pi$
$488$		0			0
$489$	23.3565	−	16.3001i	1.05622	−	0.737116i
$490$		0			0
$491$	−3.17929	+	18.0307i	−0.143479	+	0.813712i	0.825096	+	0.564992i	$0.191121\pi$
$491$	−3.17929	+	18.0307i	−0.143479	+	0.813712i	−0.968575	+	0.248720i	$0.919990\pi$
$492$		0			0
$493$	10.6060	−	8.89946i	0.477669	−	0.400812i
$494$		0			0
$495$	35.5077	+	13.0494i	1.59595	+	0.586529i
$496$		0			0
$497$	24.0274	−	4.23668i	1.07778	−	0.190041i
$498$		0			0
$499$	−9.65791	−	26.5349i	−0.432348	−	1.18787i	−0.944368	−	0.328892i	$-0.893325\pi$
$499$	−9.65791	−	26.5349i	−0.432348	−	1.18787i	0.512020	−	0.858973i	$-0.328897\pi$
$500$		0			0
$501$	23.2328	−	10.7895i	1.03796	−	0.482039i
$502$		0			0
$503$	−0.320624	+	0.555338i	−0.0142959	+	0.0247613i	−0.873085	−	0.487568i	$-0.837884\pi$
$503$	−0.320624	+	0.555338i	−0.0142959	+	0.0247613i	0.858789	+	0.512330i	$0.171217\pi$
$504$		0			0
$505$	16.5944	+	28.7424i	0.738442	+	1.27902i
$506$		0			0
$507$	17.8198	+	4.80463i	0.791405	+	0.213381i
$508$		0			0
$509$	−8.99662	+	10.7218i	−0.398768	+	0.475233i	−0.927644	−	0.373466i	$-0.878169\pi$
$509$	−8.99662	+	10.7218i	−0.398768	+	0.475233i	0.528876	+	0.848699i	$0.322614\pi$
$510$		0			0
$511$	−7.83458	+	21.5253i	−0.346581	+	0.952224i
$512$		0			0
$513$	20.9035	−	20.7086i	0.922913	−	0.914308i
$514$		0			0
$515$	−30.1745	−	10.9826i	−1.32965	−	0.483952i
$516$		0			0
$517$	−3.17022	−	2.66013i	−0.139426	−	0.116992i
$518$		0			0
$519$	−2.48648	−	2.49426i	−0.109144	−	0.109486i
$520$		0			0
$521$	4.55944	−	2.63240i	0.199753	−	0.115327i	−0.396787	−	0.917911i	$-0.629875\pi$
$521$	4.55944	−	2.63240i	0.199753	−	0.115327i	0.596540	+	0.802583i	$0.296542\pi$
$522$		0			0
$523$	8.39941	+	4.84940i	0.367280	+	0.212049i	0.672270	−	0.740306i	$-0.265320\pi$
$523$	8.39941	+	4.84940i	0.367280	+	0.212049i	−0.304989	+	0.952356i	$0.598653\pi$
$524$		0			0
$525$	30.3081	−	43.1409i	1.32275	−	1.88283i
$526$		0			0
$527$	26.8374	−	9.76802i	1.16906	−	0.425502i
$528$		0			0
$529$	7.08184	+	40.1631i	0.307906	+	1.74622i
$530$		0			0
$531$	−0.577547	−	0.335856i	−0.0250634	−	0.0145749i
$532$		0			0
$533$	0.604634	+	0.720575i	0.0261896	+	0.0312116i
$534$		0			0
$535$	60.2969	+	10.6320i	2.60686	+	0.459660i
$536$		0			0
$537$	0.874512	−	0.0751343i	0.0377380	−	0.00324229i
$538$		0			0
$539$	−5.67141			−0.244285
$540$		0			0
$541$	23.0789			0.992241			0.496121	−	0.868254i	$-0.334757\pi$
$541$	23.0789			0.992241			0.496121	+	0.868254i	$0.334757\pi$
$542$		0			0
$543$	−6.69940	+	14.3085i	−0.287499	+	0.614038i
$544$		0			0
$545$	−34.7155	−	6.12128i	−1.48705	−	0.262207i
$546$		0			0
$547$	10.3472	+	12.3313i	0.442414	+	0.527249i	0.940461	−	0.339901i	$-0.110394\pi$
$547$	10.3472	+	12.3313i	0.442414	+	0.527249i	−0.498047	+	0.867150i	$0.665949\pi$
$548$		0			0
$549$	−13.6207	−	37.7894i	−0.581319	−	1.61281i
$550$		0			0
$551$	4.53422	+	25.7148i	0.193164	+	1.09549i
$552$		0			0
$553$	−10.4369	+	3.79871i	−0.443821	+	0.161538i
$554$		0			0
$555$	−30.2755	−	2.69640i	−1.28512	−	0.114456i
$556$		0			0
$557$	0.287981	+	0.166266i	0.0122022	+	0.00704492i	0.506089	−	0.862481i	$-0.331091\pi$
$557$	0.287981	+	0.166266i	0.0122022	+	0.00704492i	−0.493887	+	0.869526i	$0.664424\pi$
$558$		0			0
$559$	−4.51672	+	2.60773i	−0.191037	+	0.110295i
$560$		0			0
$561$	−16.2087	+	4.31600i	−0.684332	+	0.182222i
$562$		0			0
$563$	23.2634	+	19.5203i	0.980435	+	0.822682i	0.984155	−	0.177311i	$-0.0567398\pi$
$563$	23.2634	+	19.5203i	0.980435	+	0.822682i	−0.00372038	+	0.999993i	$0.501184\pi$
$564$		0			0
$565$	−25.5479	−	9.29868i	−1.07481	−	0.391199i
$566$		0			0
$567$	0.166329	−	26.6346i	0.00698515	−	1.11855i
$568$		0			0
$569$	−3.31656	+	9.11217i	−0.139037	+	0.382002i	−0.989595	−	0.143880i	$-0.954042\pi$
$569$	−3.31656	+	9.11217i	−0.139037	+	0.382002i	0.850558	+	0.525881i	$0.176264\pi$
$570$		0			0
$571$	−13.1651	+	15.6896i	−0.550944	+	0.656590i	−0.967604	−	0.252473i	$-0.918756\pi$
$571$	−13.1651	+	15.6896i	−0.550944	+	0.656590i	0.416660	+	0.909063i	$0.363201\pi$
$572$		0			0
$573$	−5.90744	−	22.1853i	−0.246787	−	0.926806i
$574$		0			0
$575$	41.0723	+	71.1393i	1.71283	+	2.96671i
$576$		0			0
$577$	19.3818	−	33.5702i	0.806873	−	1.39755i	−0.108146	−	0.994135i	$-0.534491\pi$
$577$	19.3818	−	33.5702i	0.806873	−	1.39755i	0.915019	−	0.403410i	$-0.132175\pi$
$578$		0			0
$579$	−3.17515	+	35.6510i	−0.131955	+	1.48160i
$580$		0			0
$581$	12.2532	+	33.6654i	0.508348	+	1.39667i
$582$		0			0
$583$	−15.9175	+	2.80668i	−0.659235	+	0.116241i
$584$		0			0
$585$	3.17367	−	17.6759i	0.131215	−	0.730808i
$586$		0			0
$587$	32.0219	−	26.8696i	1.32169	−	1.10903i	0.335742	−	0.941954i	$-0.391013\pi$
$587$	32.0219	−	26.8696i	1.32169	−	1.10903i	0.985945	−	0.167073i	$-0.0534315\pi$
$588$		0			0
$589$	−9.35322	+	53.0447i	−0.385393	+	2.18567i
$590$		0			0
$591$	−39.4389	−	18.4657i	−1.62230	−	0.759576i
$592$		0			0
$593$			16.1880i			0.664760i	0.943146	+	0.332380i	$0.107852\pi$
$593$			16.1880i			0.664760i	−0.943146	+	0.332380i	$0.892148\pi$
$594$		0			0
$595$			34.7412i			1.42425i
$596$		0			0
$597$	−0.149090	−	1.73531i	−0.00610187	−	0.0710215i
$598$		0			0
$599$	6.02017	−	34.1421i	0.245977	−	1.39501i	−0.572234	−	0.820090i	$-0.693923\pi$
$599$	6.02017	−	34.1421i	0.245977	−	1.39501i	0.818212	−	0.574917i	$-0.194966\pi$
$600$		0			0
$601$	−2.59895	+	2.18078i	−0.106013	+	0.0889558i	−0.694254	−	0.719730i	$-0.744265\pi$
$601$	−2.59895	+	2.18078i	−0.106013	+	0.0889558i	0.588240	+	0.808686i	$0.299821\pi$
$602$		0			0
$603$	−10.2196	−	0.0319096i	−0.416176	−	0.00129946i
$604$		0			0
$605$	−2.30021	+	0.405589i	−0.0935169	+	0.0164896i
$606$		0			0
$607$	−0.0868318	−	0.238568i	−0.00352439	−	0.00968319i	0.937918	−	0.346857i	$-0.112751\pi$
$607$	−0.0868318	−	0.238568i	−0.00352439	−	0.00968319i	−0.941442	+	0.337174i	$0.890529\pi$
$608$		0			0
$609$	19.3404	+	13.5874i	0.783715	+	0.550588i
$610$		0			0
$611$	−0.982300	+	1.70139i	−0.0397396	+	0.0688310i
$612$		0			0
$613$	−0.676216	−	1.17124i	−0.0273121	−	0.0473059i	0.852046	−	0.523466i	$-0.175361\pi$
$613$	−0.676216	−	1.17124i	−0.0273121	−	0.0473059i	−0.879358	+	0.476161i	$0.842028\pi$
$614$		0			0
$615$	−2.94631	+	2.93713i	−0.118807	+	0.118436i
$616$		0			0
$617$	23.9230	−	28.5104i	0.963105	−	1.14778i	−0.0258648	−	0.999665i	$-0.508234\pi$
$617$	23.9230	−	28.5104i	0.963105	−	1.14778i	0.988970	−	0.148118i	$-0.0473216\pi$
$618$		0			0
$619$	14.9951	−	41.1988i	0.602705	−	1.65592i	−0.143063	−	0.989714i	$-0.545695\pi$
$619$	14.9951	−	41.1988i	0.602705	−	1.65592i	0.745768	−	0.666206i	$-0.232083\pi$
$620$		0			0
$621$	37.5279	+	17.7140i	1.50594	+	0.710839i
$622$		0			0
$623$	1.69472	+	0.616829i	0.0678976	+	0.0247127i
$624$		0			0
$625$	22.4947	+	18.8753i	0.899788	+	0.755012i
$626$		0			0
$627$	8.23527	−	30.5436i	0.328885	−	1.21980i
$628$		0			0
$629$	11.6716	−	6.73858i	0.465376	−	0.268685i
$630$		0			0
$631$	15.7443	+	9.08996i	0.626770	+	0.361866i	0.779500	−	0.626402i	$-0.215473\pi$
$631$	15.7443	+	9.08996i	0.626770	+	0.361866i	−0.152730	+	0.988268i	$0.548807\pi$
$632$		0			0
$633$	−8.23194	−	17.7256i	−0.327190	−	0.704531i
$634$		0			0
$635$	−37.6296	+	13.6961i	−1.49329	+	0.543512i
$636$		0			0
$637$	0.467519	+	2.65143i	0.0185238	+	0.105054i
$638$		0			0
$639$	15.8384	+	18.9956i	0.626557	+	0.751454i
$640$		0			0
$641$	15.1322	+	18.0338i	0.597685	+	0.712293i	0.977063	−	0.212949i	$-0.0683067\pi$
$641$	15.1322	+	18.0338i	0.597685	+	0.712293i	−0.379379	+	0.925241i	$0.623862\pi$
$642$		0			0
$643$	−18.8082	−	3.31639i	−0.741722	−	0.130786i	−0.209996	−	0.977702i	$-0.567345\pi$
$643$	−18.8082	−	3.31639i	−0.741722	−	0.130786i	−0.531726	+	0.846917i	$0.678456\pi$
$644$		0			0
$645$	−13.2010	−	18.9157i	−0.519788	−	0.744806i
$646$		0			0
$647$	−4.40584			−0.173211			−0.0866057	−	0.996243i	$-0.527602\pi$
$647$	−4.40584			−0.173211			−0.0866057	+	0.996243i	$0.527602\pi$
$648$		0			0
$649$	−0.718276			−0.0281948
$650$		0			0
$651$	27.9034	+	39.9829i	1.09362	+	1.56705i
$652$		0			0
$653$	−17.9597	−	3.16677i	−0.702816	−	0.123925i	−0.189191	−	0.981940i	$-0.560587\pi$
$653$	−17.9597	−	3.16677i	−0.702816	−	0.123925i	−0.513625	+	0.858015i	$0.671698\pi$
$654$		0			0
$655$	1.43252	+	1.70721i	0.0559733	+	0.0667063i
$656$		0			0
$657$	−22.8803	+	3.96078i	−0.892644	+	0.154525i
$658$		0			0
$659$	−6.46263	−	36.6514i	−0.251748	−	1.42773i	−0.804284	−	0.594246i	$-0.797451\pi$
$659$	−6.46263	−	36.6514i	−0.251748	−	1.42773i	0.552536	−	0.833489i	$-0.313660\pi$
$660$		0			0
$661$	8.82083	−	3.21052i	0.343090	−	0.124875i	−0.164727	−	0.986339i	$-0.552674\pi$
$661$	8.82083	−	3.21052i	0.343090	−	0.124875i	0.507818	+	0.861464i	$0.330452\pi$
$662$		0			0
$663$	3.35392	+	7.22193i	0.130256	+	0.280476i
$664$		0			0
$665$	−56.7429	−	32.7605i	−2.20040	−	1.27040i
$666$		0			0
$667$	−31.8923	+	18.4130i	−1.23488	+	0.712956i
$668$		0			0
$669$	1.43688	−	5.32920i	0.0555528	−	0.206039i
$670$		0			0
$671$	−33.0824	−	27.7594i	−1.27713	−	1.07164i
$672$		0			0
$673$	19.1849	+	6.98275i	0.739525	+	0.269165i	0.684191	−	0.729303i	$-0.260155\pi$
$673$	19.1849	+	6.98275i	0.739525	+	0.269165i	0.0553340	+	0.998468i	$0.482378\pi$
$674$		0			0
$675$	53.2195	+	4.90737i	2.04842	+	0.188885i
$676$		0			0
$677$	−11.4047	+	31.3341i	−0.438317	+	1.20427i	0.502269	+	0.864711i	$0.332499\pi$
$677$	−11.4047	+	31.3341i	−0.438317	+	1.20427i	−0.940586	+	0.339555i	$0.889724\pi$
$678$		0			0
$679$	35.2211	−	41.9749i	1.35166	−	1.61085i
$680$		0			0
$681$	20.1064	−	20.0438i	0.770481	−	0.768079i
$682$		0			0
$683$	22.7613	+	39.4237i	0.870937	+	1.50851i	0.861029	+	0.508556i	$0.169821\pi$
$683$	22.7613	+	39.4237i	0.870937	+	1.50851i	0.00990835	+	0.999951i	$0.496846\pi$
$684$		0			0
$685$	−13.8652	+	24.0153i	−0.529763	+	0.917577i
$686$		0			0
$687$	11.4975	+	8.07740i	0.438656	+	0.308172i
$688$		0			0
$689$	2.62430	+	7.21021i	0.0999779	+	0.274687i
$690$		0			0
$691$	−5.27547	+	0.930207i	−0.200688	+	0.0353867i	−0.273089	−	0.961989i	$-0.588045\pi$
$691$	−5.27547	+	0.930207i	−0.200688	+	0.0353867i	0.0724003	+	0.997376i	$0.476934\pi$
$692$		0			0
$693$	−14.2402	−	24.8436i	−0.540942	−	0.943732i
$694$		0			0
$695$	−8.50512	+	7.13664i	−0.322618	+	0.270708i
$696$		0			0
$697$	0.320315	−	1.81660i	0.0121328	−	0.0688086i
$698$		0			0
$699$	−0.933320	−	10.8632i	−0.0353014	−	0.410884i
$700$		0			0
$701$		−	21.2531i		−	0.802717i	−0.915921	−	0.401358i	$-0.868538\pi$
$701$		−	21.2531i		−	0.802717i	0.915921	−	0.401358i	$-0.131462\pi$
$702$		0			0
$703$			25.4176i			0.958642i
$704$		0			0
$705$	−7.86910	−	3.68439i	−0.296367	−	0.138762i
$706$		0			0
$707$	4.36249	−	24.7409i	0.164068	−	0.930478i
$708$		0			0
$709$	36.3373	−	30.4906i	1.36468	−	1.14510i	0.390170	−	0.920743i	$-0.372416\pi$
$709$	36.3373	−	30.4906i	1.36468	−	1.14510i	0.974507	−	0.224358i	$-0.0720284\pi$
$710$		0			0
$711$	−8.60213	−	7.26394i	−0.322605	−	0.272419i
$712$		0			0
$713$	−74.8110	+	13.1912i	−2.80170	+	0.494014i
$714$		0			0
$715$	−6.60347	−	18.1429i	−0.246956	−	0.678505i
$716$		0			0
$717$	−1.64048	+	18.4195i	−0.0612647	+	0.687889i
$718$		0			0
$719$	−18.7915	+	32.5479i	−0.700806	+	1.21383i	0.267378	+	0.963592i	$0.413843\pi$
$719$	−18.7915	+	32.5479i	−0.700806	+	1.21383i	−0.968184	+	0.250240i	$0.919490\pi$
$720$		0			0
$721$	12.1534	+	21.0502i	0.452615	+	0.783952i
$722$		0			0
$723$	8.33202	+	31.2908i	0.309871	+	1.16372i
$724$		0			0
$725$	−30.4859	+	36.3317i	−1.13222	+	1.34933i
$726$		0			0
$727$	−7.85023	+	21.5683i	−0.291149	+	0.799925i	0.704750	+	0.709456i	$0.251059\pi$
$727$	−7.85023	+	21.5683i	−0.291149	+	0.799925i	−0.995899	+	0.0904698i	$0.971163\pi$
$728$		0			0
$729$	23.5081	−	13.2804i	0.870671	−	0.491866i
$730$		0			0
$731$	9.61083	+	3.49806i	0.355469	+	0.129380i
$732$		0			0
$733$	−4.21278	−	3.53494i	−0.155603	−	0.130566i	0.561663	−	0.827366i	$-0.310162\pi$
$733$	−4.21278	−	3.53494i	−0.155603	−	0.130566i	−0.717265	+	0.696800i	$0.754606\pi$
$734$		0			0
$735$	−11.5066	+	3.06393i	−0.424426	+	0.113015i
$736$		0			0
$737$	−9.51519	+	5.49360i	−0.350497	+	0.202359i
$738$		0			0
$739$	−2.63042	−	1.51867i	−0.0967614	−	0.0558652i	0.450838	−	0.892606i	$-0.351125\pi$
$739$	−2.63042	−	1.51867i	−0.0967614	−	0.0558652i	−0.547600	+	0.836740i	$0.684458\pi$
$740$		0			0
$741$	−14.9583	−	1.33222i	−0.549507	−	0.0489402i
$742$		0			0
$743$	7.90477	−	2.87710i	0.289998	−	0.105551i	−0.192925	−	0.981214i	$-0.561797\pi$
$743$	7.90477	−	2.87710i	0.289998	−	0.105551i	0.482923	+	0.875663i	$0.339575\pi$
$744$		0			0
$745$	5.49942	+	31.1888i	0.201483	+	1.14267i
$746$		0			0
$747$	−23.4307	+	27.7472i	−0.857283	+	1.01522i
$748$		0			0
$749$	−29.7908	−	35.5033i	−1.08853	−	1.29726i
$750$		0			0
$751$	36.4856	+	6.43340i	1.33138	+	0.234758i	0.793658	−	0.608364i	$-0.208174\pi$
$751$	36.4856	+	6.43340i	1.33138	+	0.234758i	0.537722	+	0.843122i	$0.319285\pi$
$752$		0			0
$753$	−10.0879	+	21.5457i	−0.367624	+	0.785170i
$754$		0			0
$755$	73.5967			2.67846
$756$		0			0
$757$	−4.63964			−0.168630			−0.0843152	−	0.996439i	$-0.526870\pi$
$757$	−4.63964			−0.168630			−0.0843152	+	0.996439i	$0.526870\pi$
$758$		0			0
$759$	44.4514	−	3.81908i	1.61348	−	0.138624i
$760$		0			0
$761$	−28.9212	−	5.09959i	−1.04839	−	0.184860i	−0.377191	−	0.926135i	$-0.623110\pi$
$761$	−28.9212	−	5.09959i	−1.04839	−	0.184860i	−0.671201	+	0.741276i	$0.734221\pi$
$762$		0			0
$763$	17.1519	+	20.4408i	0.620940	+	0.740007i
$764$		0			0
$765$	−30.5537	+	17.5132i	−1.10467	+	0.633192i
$766$		0			0
$767$	0.0592107	+	0.335801i	0.00213798	+	0.0121251i
$768$		0			0
$769$	43.0305	−	15.6618i	1.55172	−	0.564780i	0.582900	−	0.812544i	$-0.301918\pi$
$769$	43.0305	−	15.6618i	1.55172	−	0.564780i	0.968821	+	0.247764i	$0.0796956\pi$
$770$		0			0
$771$	27.2137	−	38.7363i	0.980077	−	1.39505i
$772$		0			0
$773$	−7.09568	−	4.09670i	−0.255214	−	0.147348i	0.366935	−	0.930246i	$-0.380407\pi$
$773$	−7.09568	−	4.09670i	−0.255214	−	0.147348i	−0.622149	+	0.782899i	$0.713740\pi$
$774$		0			0
$775$	−84.7268	+	48.9170i	−3.04348	+	1.75715i
$776$		0			0
$777$	16.2437	+	16.2945i	0.582740	+	0.584563i
$778$		0			0
$779$	2.66500	+	2.23620i	0.0954836	+	0.0801203i
$780$		0			0
$781$	24.9862	+	9.09422i	0.894075	+	0.325417i
$782$		0			0
$783$	−2.20002	+	23.8588i	−0.0786222	+	0.852642i
$784$		0			0
$785$	8.04654	−	22.1077i	0.287193	−	0.789058i
$786$		0			0
$787$	25.8770	−	30.8390i	0.922415	−	1.09929i	−0.0723778	−	0.997377i	$-0.523059\pi$
$787$	25.8770	−	30.8390i	0.922415	−	1.09929i	0.994793	−	0.101915i	$-0.0324968\pi$
$788$		0			0
$789$	15.2758	+	4.11870i	0.543832	+	0.146630i
$790$		0			0
$791$	10.2899	+	17.8227i	0.365867	+	0.633701i
$792$		0			0
$793$	−10.2506	+	17.7546i	−0.364011	+	0.630486i
$794$		0			0
$795$	−30.7783	+	14.2937i	−1.09159	+	0.506946i
$796$		0			0
$797$	−12.3722	−	33.9923i	−0.438245	−	1.20407i	−0.940632	−	0.339427i	$-0.889767\pi$
$797$	−12.3722	−	33.9923i	−0.438245	−	1.20407i	0.502387	−	0.864643i	$-0.332455\pi$
$798$		0			0
$799$	3.79410	−	0.669002i	0.134226	−	0.0236676i
$800$		0			0
$801$	0.311839	+	1.80140i	0.0110183	+	0.0636493i
$802$		0			0
$803$	−19.1239	+	16.0468i	−0.674867	+	0.566280i
$804$		0			0
$805$	16.0463	−	91.0030i	0.565558	−	3.20744i
$806$		0			0
$807$	2.12342	−	1.48190i	0.0747479	−	0.0521654i
$808$		0			0
$809$			32.9789i			1.15948i	0.814803	+	0.579738i	$0.196845\pi$
$809$			32.9789i			1.15948i	−0.814803	+	0.579738i	$0.803155\pi$
$810$		0			0
$811$			10.6015i			0.372268i	0.982524	+	0.186134i	$0.0595959\pi$
$811$			10.6015i			0.372268i	−0.982524	+	0.186134i	$0.940404\pi$
$812$		0			0
$813$	−34.6795	+	24.2023i	−1.21626	+	0.848811i
$814$		0			0
$815$	11.1640	−	63.3140i	0.391057	−	2.21779i
$816$		0			0
$817$	−14.7763	+	12.3988i	−0.516957	+	0.433778i
$818$		0			0
$819$	−10.4407	+	8.70541i	−0.364829	+	0.304192i
$820$		0			0
$821$	30.9146	−	5.45109i	1.07893	−	0.190244i	0.394187	−	0.919030i	$-0.371026\pi$
$821$	30.9146	−	5.45109i	1.07893	−	0.190244i	0.684742	+	0.728786i	$0.259915\pi$
$822$		0			0
$823$	−11.8809	−	32.6426i	−0.414143	−	1.13785i	−0.954967	−	0.296712i	$-0.904110\pi$
$823$	−11.8809	−	32.6426i	−0.414143	−	1.13785i	0.540824	−	0.841136i	$-0.318112\pi$
$824$		0			0
$825$	52.1135	−	24.2019i	1.81436	−	0.842603i
$826$		0			0
$827$	−10.6425	+	18.4334i	−0.370077	+	0.640992i	−0.989577	−	0.144004i	$-0.954002\pi$
$827$	−10.6425	+	18.4334i	−0.370077	+	0.640992i	0.619500	+	0.784997i	$0.287335\pi$
$828$		0			0
$829$	15.7208	+	27.2293i	0.546007	+	0.945712i	0.998543	+	0.0539659i	$0.0171862\pi$
$829$	15.7208	+	27.2293i	0.546007	+	0.945712i	−0.452536	+	0.891746i	$0.649480\pi$
$830$		0			0
$831$	−11.9854	−	3.23155i	−0.415770	−	0.112101i
$832$		0			0
$833$	3.39375	−	4.04451i	0.117586	−	0.140134i
$834$		0			0
$835$	19.7761	−	54.3345i	0.684382	−	1.88032i
$836$		0			0
$837$	−21.0974	+	44.6957i	−0.729232	+	1.54491i
$838$		0			0
$839$	−29.2629	−	10.6508i	−1.01027	−	0.367708i	−0.216733	−	0.976231i	$-0.569540\pi$
$839$	−29.2629	−	10.6508i	−1.01027	−	0.367708i	−0.793536	+	0.608523i	$0.791762\pi$
$840$		0			0
$841$	5.92748	+	4.97375i	0.204396	+	0.171509i
$842$		0			0
$843$	−32.0704	−	32.1707i	−1.10456	−	1.10802i
$844$		0			0
$845$	36.0788	−	20.8301i	1.24115	−	0.716577i
$846$		0			0
$847$	1.53115	+	0.884013i	0.0526111	+	0.0303750i
$848$		0			0
$849$	13.5439	−	19.2786i	0.464827	−	0.661640i
$850$		0			0
$851$	−33.6855	+	12.2605i	−1.15473	+	0.420286i
$852$		0			0
$853$	−3.05089	−	17.3024i	−0.104460	−	0.592424i	−0.991434	−	0.130605i	$-0.958308\pi$
$853$	−3.05089	−	17.3024i	−0.104460	−	0.592424i	0.886974	−	0.461819i	$-0.152803\pi$
$854$		0			0
$855$	0.207383	−	66.4183i	0.00709236	−	2.27146i
$856$		0			0
$857$	7.18052	+	8.55740i	0.245282	+	0.292315i	0.874613	−	0.484822i	$-0.161116\pi$
$857$	7.18052	+	8.55740i	0.245282	+	0.292315i	−0.629331	+	0.777137i	$0.716671\pi$
$858$		0			0
$859$	−36.7491	−	6.47986i	−1.25386	−	0.221090i	−0.493016	−	0.870021i	$-0.664105\pi$
$859$	−36.7491	−	6.47986i	−1.25386	−	0.221090i	−0.760848	+	0.648931i	$0.775217\pi$
$860$		0			0
$861$	3.13756	−	0.269566i	0.106928	−	0.00918678i
$862$		0			0
$863$	3.20635			0.109145			0.0545727	−	0.998510i	$-0.482620\pi$
$863$	3.20635			0.109145			0.0545727	+	0.998510i	$0.482620\pi$
$864$		0			0
$865$	−7.94985			−0.270303
$866$		0			0
$867$	−5.86428	+	12.5249i	−0.199161	+	0.425368i
$868$		0			0
$869$	−11.9205	−	2.10191i	−0.404375	−	0.0713023i
$870$		0			0
$871$	3.35269	+	3.99558i	0.113601	+	0.135385i
$872$		0			0
$873$	54.6706	+	9.81602i	1.85032	+	0.332222i
$874$		0			0
$875$	−10.6197	−	60.2274i	−0.359012	−	2.03606i
$876$		0			0
$877$	7.62013	−	2.77350i	0.257314	−	0.0936545i	−0.210143	−	0.977671i	$-0.567393\pi$
$877$	7.62013	−	2.77350i	0.257314	−	0.0936545i	0.467456	+	0.884016i	$0.345171\pi$
$878$		0			0
$879$	−13.9464	−	1.24209i	−0.470400	−	0.0418948i
$880$		0			0
$881$	15.0617	+	8.69590i	0.507443	+	0.292972i	0.731782	−	0.681539i	$-0.238689\pi$
$881$	15.0617	+	8.69590i	0.507443	+	0.292972i	−0.224339	+	0.974511i	$0.572022\pi$
$882$		0			0
$883$	23.9181	−	13.8091i	0.804909	−	0.464714i	−0.0402760	−	0.999189i	$-0.512824\pi$
$883$	23.9181	−	13.8091i	0.804909	−	0.464714i	0.845185	+	0.534474i	$0.179490\pi$
$884$		0			0
$885$	−1.45729	+	0.388043i	−0.0489864	+	0.0130439i
$886$		0			0
$887$	28.8677	+	24.2229i	0.969282	+	0.813324i	0.982438	−	0.186590i	$-0.0597435\pi$
$887$	28.8677	+	24.2229i	0.969282	+	0.813324i	−0.0131564	+	0.999913i	$0.504188\pi$
$888$		0			0
$889$	28.4841	+	10.3674i	0.955325	+	0.347710i
$890$		0			0
$891$	14.6706	−	25.0476i	0.491483	−	0.839127i
$892$		0			0
$893$	−2.48510	+	6.82777i	−0.0831609	+	0.228483i
$894$		0			0
$895$	1.27353	−	1.51774i	0.0425695	−	0.0507323i
$896$		0			0
$897$	−5.44978	−	20.4666i	−0.181963	−	0.683361i
$898$		0			0
$899$	−21.9299	−	37.9837i	−0.731404	−	1.26683i
$900$		0			0
$901$	7.52341	−	13.0309i	0.250641	−	0.434123i
$902$		0			0
$903$	−1.54894	+	17.3917i	−0.0515454	+	0.578758i
$904$		0			0
$905$	12.1974	+	33.5121i	0.405456	+	1.11398i
$906$		0			0
$907$	17.9368	−	3.16274i	0.595582	−	0.105017i	0.132272	−	0.991213i	$-0.457773\pi$
$907$	17.9368	−	3.16274i	0.595582	−	0.105017i	0.463310	+	0.886196i	$0.346662\pi$
$908$		0			0
$909$	23.9580	−	8.63537i	0.794636	−	0.286417i
$910$		0			0
$911$	−23.3643	+	19.6049i	−0.774092	+	0.649540i	−0.941753	−	0.336304i	$-0.890823\pi$
$911$	−23.3643	+	19.6049i	−0.774092	+	0.649540i	0.167661	+	0.985845i	$0.446379\pi$
$912$		0			0
$913$	−6.77994	+	38.4509i	−0.224383	+	1.27254i
$914$		0			0
$915$	−82.1168	−	38.4479i	−2.71470	−	1.27105i
$916$		0			0
$917$		−	1.68696i		−	0.0557085i
$918$		0			0
$919$			24.8471i			0.819631i	0.912168	+	0.409816i	$0.134407\pi$
$919$			24.8471i			0.819631i	−0.912168	+	0.409816i	$0.865593\pi$
$920$		0			0
$921$	−3.69869	−	43.0502i	−0.121876	−	1.41855i
$922$		0			0
$923$	2.19191	−	12.4309i	0.0721476	−	0.409169i
$924$		0			0
$925$	−35.3661	+	29.6757i	−1.16283	+	0.975732i
$926$		0			0
$927$	−12.3864	+	21.3000i	−0.406823	+	0.699584i
$928$		0			0
$929$	−6.94694	+	1.22493i	−0.227922	+	0.0401887i	−0.286442	−	0.958097i	$-0.592473\pi$
$929$	−6.94694	+	1.22493i	−0.227922	+	0.0401887i	0.0585208	+	0.998286i	$0.481362\pi$
$930$		0			0
$931$	3.40565	+	9.35694i	0.111616	+	0.306661i
$932$		0			0
$933$	−40.9042	−	28.7367i	−1.33914	−	0.940797i
$934$		0			0
$935$	−18.9310	+	32.7894i	−0.619109	+	1.07233i
$936$		0			0
$937$	−19.2685	−	33.3739i	−0.629473	−	1.09028i	−0.987658	−	0.156629i	$-0.949937\pi$
$937$	−19.2685	−	33.3739i	−0.629473	−	1.09028i	0.358184	−	0.933651i	$-0.383396\pi$
$938$		0			0
$939$	2.87076	−	2.86181i	0.0936836	−	0.0933915i
$940$		0			0
$941$	3.15039	−	3.75448i	0.102700	−	0.122393i	−0.712246	−	0.701930i	$-0.752322\pi$
$941$	3.15039	−	3.75448i	0.102700	−	0.122393i	0.814946	+	0.579537i	$0.196767\pi$
$942$		0			0
$943$	−1.67810	+	4.61055i	−0.0546466	+	0.150140i
$944$		0			0
$945$	−42.3133	−	42.7115i	−1.37645	−	1.38940i
$946$		0			0
$947$	−26.5745	−	9.67234i	−0.863556	−	0.314309i	−0.128001	−	0.991774i	$-0.540856\pi$
$947$	−26.5745	−	9.67234i	−0.863556	−	0.314309i	−0.735555	+	0.677465i	$0.763078\pi$
$948$		0			0
$949$	9.07851	+	7.61777i	0.294701	+	0.247283i
$950$		0			0
$951$	3.85716	−	14.3057i	0.125077	−	0.463896i
$952$		0			0
$953$	40.9267	−	23.6291i	1.32575	−	0.765420i	0.341108	−	0.940024i	$-0.389198\pi$
$953$	40.9267	−	23.6291i	1.32575	−	0.765420i	0.984639	+	0.174604i	$0.0558644\pi$
$954$		0			0
$955$	−44.8799	−	25.9114i	−1.45228	−	0.838473i
$956$		0			0
$957$	10.8499	+	23.3629i	0.350728	+	0.755215i
$958$		0			0
$959$	19.7249	−	7.17928i	0.636951	−	0.231831i
$960$		0			0
$961$	−10.3276	−	58.5708i	−0.333149	−	1.88938i
$962$		0			0
$963$	16.2063	−	44.0975i	0.522240	−	1.42102i
$964$		0			0
$965$	51.9319	+	61.8900i	1.67175	+	1.99231i
$966$		0			0
$967$	−44.9336	−	7.92300i	−1.44497	−	0.254786i	−0.604480	−	0.796620i	$-0.706619\pi$
$967$	−44.9336	−	7.92300i	−1.44497	−	0.254786i	−0.840486	+	0.541834i	$0.817730\pi$
$968$		0			0
$969$	16.8540	+	24.1501i	0.541427	+	0.775813i
$970$		0			0
$971$	−23.8881			−0.766605			−0.383302	−	0.923623i	$-0.625213\pi$
$971$	−23.8881			−0.766605			−0.383302	+	0.923623i	$0.625213\pi$
$972$		0			0
$973$	8.40424			0.269428
$974$		0			0
$975$	−15.6106	−	22.3684i	−0.499938	−	0.716363i
$976$		0			0
$977$	25.8784	+	4.56305i	0.827922	+	0.145985i	0.571523	−	0.820586i	$-0.306353\pi$
$977$	25.8784	+	4.56305i	0.827922	+	0.145985i	0.256399	+	0.966571i	$0.417464\pi$
$978$		0			0
$979$	1.26339	+	1.50565i	0.0403782	+	0.0481209i
$980$		0			0
$981$	−9.33066	+	25.3888i	−0.297905	+	0.810603i
$982$		0			0
$983$	4.70819	+	26.7015i	0.150168	+	0.851645i	0.963071	+	0.269246i	$0.0867745\pi$
$983$	4.70819	+	26.7015i	0.150168	+	0.851645i	−0.812903	+	0.582398i	$0.802114\pi$
$984$		0			0
$985$	−92.3700	+	33.6199i	−2.94315	+	1.07122i
$986$		0			0
$987$	2.77032	+	5.96526i	0.0881802	+	0.189876i
$988$		0			0
$989$	−23.5595	−	13.6021i	−0.749147	−	0.432520i
$990$		0			0
$991$	35.0489	−	20.2355i	1.11337	−	0.642802i	0.173667	−	0.984804i	$-0.444438\pi$
$991$	35.0489	−	20.2355i	1.11337	−	0.642802i	0.939699	+	0.342002i	$0.111105\pi$
$992$		0			0
$993$	4.65129	−	17.2511i	0.147604	−	0.547446i
$994$		0			0
$995$	−3.01167	−	2.52709i	−0.0954765	−	0.0801143i
$996$		0			0
$997$	−3.05161	−	1.11069i	−0.0966454	−	0.0351760i	0.293245	−	0.956037i	$-0.405265\pi$
$997$	−3.05161	−	1.11069i	−0.0966454	−	0.0351760i	−0.389890	+	0.920861i	$0.627487\pi$
$998$		0			0
$999$	−6.14194	+	22.5000i	−0.194322	+	0.711867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.a.239.2	yes	36
4.3	odd	2	inner	432.2.be.a.239.5	yes	36
27.20	odd	18	inner	432.2.be.a.47.5	yes	36
108.47	even	18	inner	432.2.be.a.47.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.a.47.2	✓	36	108.47	even	18	inner
432.2.be.a.47.5	yes	36	27.20	odd	18	inner
432.2.be.a.239.2	yes	36	1.1	even	1	trivial
432.2.be.a.239.5	yes	36	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.991247 - 1.42036i) q^{3} +(-3.85028 - 0.678908i) q^{5} +(1.90230 + 2.26708i) q^{7} +(-1.03486 + 2.81586i) q^{9} +O(q^{10})\)	\(q+(-0.991247 - 1.42036i) q^{3} +(-3.85028 - 0.678908i) q^{5} +(1.90230 + 2.26708i) q^{7} +(-1.03486 + 2.81586i) q^{9} +(0.560068 + 3.17630i) q^{11} +(1.43878 - 0.523674i) q^{13} +(2.85228 + 6.14175i) q^{15} +(-2.60029 - 1.50128i) q^{17} +(4.90409 - 2.83138i) q^{19} +(1.33442 - 4.94920i) q^{21} +(6.11794 + 5.13356i) q^{23} +(9.66525 + 3.51786i) q^{25} +(5.02534 - 1.32134i) q^{27} +(-1.57709 + 4.33301i) q^{29} +(-6.11407 + 7.28646i) q^{31} +(3.95634 - 3.94400i) q^{33} +(-5.78526 - 10.0204i) q^{35} +(-2.24428 + 3.88720i) q^{37} +(-2.17000 - 1.52450i) q^{39} +(0.210120 + 0.577300i) q^{41} +(-3.35455 + 0.591498i) q^{43} +(5.89620 - 10.1393i) q^{45} +(-0.982922 + 0.824769i) q^{47} +(-0.305345 + 1.73170i) q^{49} +(0.445172 + 5.18150i) q^{51} +5.01133i q^{53} -12.6099i q^{55} +(-8.88275 - 4.15899i) q^{57} +(-0.0386715 + 0.219317i) q^{59} +(-10.2571 + 8.60675i) q^{61} +(-8.35239 + 3.01052i) q^{63} +(-5.89524 + 1.03949i) q^{65} +(1.16511 + 3.20112i) q^{67} +(1.22713 - 13.7783i) q^{69} +(4.12205 - 7.13960i) q^{71} +(3.87009 + 6.70320i) q^{73} +(-4.58401 - 17.2152i) q^{75} +(-6.13551 + 7.31202i) q^{77} +(-1.28358 + 3.52662i) q^{79} +(-6.85814 - 5.82803i) q^{81} +(11.3755 + 4.14034i) q^{83} +(8.99262 + 7.54571i) q^{85} +(7.71773 - 2.05505i) q^{87} +(0.527753 - 0.304698i) q^{89} +(3.92421 + 2.26565i) q^{91} +(16.4100 + 1.46151i) q^{93} +(-20.8044 + 7.57217i) q^{95} +(-3.21509 - 18.2337i) q^{97} +(-9.52362 - 1.70995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^5 - 12 * q^9	\( 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97}+O(q^{100}) \) 36 * q - 6 * q^5 - 12 * q^9 - 36 * q^21 + 18 * q^25 - 24 * q^29 - 36 * q^33 - 18 * q^41 - 18 * q^45 + 42 * q^65 + 54 * q^69 - 18 * q^73 + 90 * q^77 + 36 * q^81 + 72 * q^85 + 72 * q^89 + 54 * q^93 + 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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