LMFDB - Embedded newform 864.2.w.b.107.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(107,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 4]))

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

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

chi := DirichletCharacter("864.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.w (of order $8$, degree $4$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			107.16
Character	$\chi$	$=$	864.107
Dual form			864.2.w.b.323.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0136252 - 1.41415i) q^{2} +(-1.99963 + 0.0385360i) q^{4} +(-0.327253 - 0.135553i) q^{5} +(1.35777 - 1.35777i) q^{7} +(0.0817409 + 2.82725i) q^{8} +O(q^{10})$	\(q+(-0.0136252 - 1.41415i) q^{2} +(-1.99963 + 0.0385360i) q^{4} +(-0.327253 - 0.135553i) q^{5} +(1.35777 - 1.35777i) q^{7} +(0.0817409 + 2.82725i) q^{8} +(-0.187232 + 0.464631i) q^{10} +(3.85851 + 1.59825i) q^{11} +(-0.231385 - 0.558613i) q^{13} +(-1.93859 - 1.90159i) q^{14} +(3.99703 - 0.154115i) q^{16} +5.94707 q^{17} +(-5.21566 + 2.16040i) q^{19} +(0.659608 + 0.258444i) q^{20} +(2.20758 - 5.47828i) q^{22} +(5.60841 - 5.60841i) q^{23} +(-3.44681 - 3.44681i) q^{25} +(-0.786809 + 0.334824i) q^{26} +(-2.66271 + 2.76736i) q^{28} +(2.17035 + 5.23968i) q^{29} -1.38880i q^{31} +(-0.272402 - 5.65029i) q^{32} +(-0.0810299 - 8.41004i) q^{34} +(-0.628383 + 0.260285i) q^{35} +(2.77178 - 6.69167i) q^{37} +(3.12619 + 7.34629i) q^{38} +(0.356490 - 0.936304i) q^{40} +(-4.65385 - 4.65385i) q^{41} +(0.655749 - 1.58312i) q^{43} +(-7.77717 - 3.04721i) q^{44} +(-8.00753 - 7.85470i) q^{46} -2.50386i q^{47} +3.31292i q^{49} +(-4.82734 + 4.92127i) q^{50} +(0.484211 + 1.10810i) q^{52} +(2.06467 - 4.98454i) q^{53} +(-1.04606 - 1.04606i) q^{55} +(3.94973 + 3.72776i) q^{56} +(7.38011 - 3.14058i) q^{58} +(-1.31191 + 3.16723i) q^{59} +(9.16929 - 3.79804i) q^{61} +(-1.96397 + 0.0189226i) q^{62} +(-7.98664 + 0.462203i) q^{64} +0.214173i q^{65} +(-3.66131 - 8.83919i) q^{67} +(-11.8919 + 0.229176i) q^{68} +(0.376643 + 0.885080i) q^{70} +(1.84855 + 1.84855i) q^{71} +(3.57147 - 3.57147i) q^{73} +(-9.50077 - 3.82853i) q^{74} +(10.3461 - 4.52099i) q^{76} +(7.40902 - 3.06892i) q^{77} -8.73451 q^{79} +(-1.32893 - 0.491373i) q^{80} +(-6.51783 + 6.64464i) q^{82} +(3.89900 + 9.41302i) q^{83} +(-1.94620 - 0.806141i) q^{85} +(-2.24770 - 0.905756i) q^{86} +(-4.20324 + 11.0396i) q^{88} +(1.90777 - 1.90777i) q^{89} +(-1.07264 - 0.444301i) q^{91} +(-10.9986 + 11.4309i) q^{92} +(-3.54082 + 0.0341155i) q^{94} +1.99969 q^{95} +18.0271 q^{97} +(4.68496 - 0.0451392i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) $ 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

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 $

$2$	−0.0136252	−	1.41415i	−0.00963445	−	0.999954i
$2$	−0.0136252	−	1.41415i	−0.00963445	−	0.999954i
$3$		0			0
$3$		0			0
$4$	−1.99963	+	0.0385360i	−0.999814	+	0.0192680i
$5$	−0.327253	−	0.135553i	−0.146352	−	0.0606209i	0.308305	−	0.951287i	$-0.400238\pi$
$5$	−0.327253	−	0.135553i	−0.146352	−	0.0606209i	−0.454657	+	0.890667i	$0.650238\pi$
$6$		0			0
$7$	1.35777	−	1.35777i	0.513189	−	0.513189i	−0.402313	−	0.915502i	$-0.631794\pi$
$7$	1.35777	−	1.35777i	0.513189	−	0.513189i	0.915502	+	0.402313i	$0.131794\pi$
$8$	0.0817409	+	2.82725i	0.0288998	+	0.999582i
$9$		0			0
$10$	−0.187232	+	0.464631i	−0.0592081	+	0.146929i
$11$	3.85851	+	1.59825i	1.16338	+	0.481889i	0.879000	−	0.476821i	$-0.158211\pi$
$11$	3.85851	+	1.59825i	1.16338	+	0.481889i	0.284384	+	0.958711i	$0.408211\pi$
$12$		0			0
$13$	−0.231385	−	0.558613i	−0.0641747	−	0.154932i	0.888539	−	0.458802i	$-0.151721\pi$
$13$	−0.231385	−	0.558613i	−0.0641747	−	0.154932i	−0.952713	+	0.303870i	$0.901721\pi$
$14$	−1.93859	−	1.90159i	−0.518109	−	0.508221i
$15$		0			0
$16$	3.99703	−	0.154115i	0.999257	−	0.0385289i
$17$	5.94707			1.44238			0.721188	−	0.692739i	$-0.243596\pi$
$17$	5.94707			1.44238			0.721188	+	0.692739i	$0.243596\pi$
$18$		0			0
$19$	−5.21566	+	2.16040i	−1.19656	+	0.495630i	−0.889884	−	0.456186i	$-0.849215\pi$
$19$	−5.21566	+	2.16040i	−1.19656	+	0.495630i	−0.306671	+	0.951816i	$0.599215\pi$
$20$	0.659608	+	0.258444i	0.147493	+	0.0577898i
$21$		0			0
$22$	2.20758	−	5.47828i	0.470659	−	1.16797i
$23$	5.60841	−	5.60841i	1.16943	−	1.16943i	0.187091	−	0.982343i	$-0.440094\pi$
$23$	5.60841	−	5.60841i	1.16943	−	1.16943i	0.982343	−	0.187091i	$-0.0599061\pi$
$24$		0			0
$25$	−3.44681	−	3.44681i	−0.689363	−	0.689363i
$26$	−0.786809	+	0.334824i	−0.154306	+	0.0656644i
$27$		0			0
$28$	−2.66271	+	2.76736i	−0.503205	+	0.522982i
$29$	2.17035	+	5.23968i	0.403023	+	0.972984i	0.986928	+	0.161162i	$0.0515242\pi$
$29$	2.17035	+	5.23968i	0.403023	+	0.972984i	−0.583905	+	0.811822i	$0.698476\pi$
$30$		0			0
$31$		−	1.38880i		−	0.249436i	−0.992192	−	0.124718i	$-0.960197\pi$
$31$		−	1.38880i		−	0.249436i	0.992192	−	0.124718i	$-0.0398025\pi$
$32$	−0.272402	−	5.65029i	−0.0481544	−	0.998840i
$33$		0			0
$34$	−0.0810299	−	8.41004i	−0.0138965	−	1.44231i
$35$	−0.628383	+	0.260285i	−0.106216	+	0.0439962i
$36$		0			0
$37$	2.77178	−	6.69167i	0.455678	−	1.10010i	−0.514453	−	0.857519i	$-0.672005\pi$
$37$	2.77178	−	6.69167i	0.455678	−	1.10010i	0.970130	−	0.242584i	$-0.0779951\pi$
$38$	3.12619	+	7.34629i	0.507135	+	1.19172i
$39$		0			0
$40$	0.356490	−	0.936304i	0.0563661	−	0.148043i
$41$	−4.65385	−	4.65385i	−0.726810	−	0.726810i	0.243173	−	0.969983i	$-0.421812\pi$
$41$	−4.65385	−	4.65385i	−0.726810	−	0.726810i	−0.969983	+	0.243173i	$0.921812\pi$
$42$		0			0
$43$	0.655749	−	1.58312i	0.100001	−	0.241423i	−0.865959	−	0.500115i	$-0.833291\pi$
$43$	0.655749	−	1.58312i	0.100001	−	0.241423i	0.965960	+	0.258691i	$0.0832912\pi$
$44$	−7.77717	−	3.04721i	−1.17245	−	0.459384i
$45$		0			0
$46$	−8.00753	−	7.85470i	−1.18065	−	1.15811i
$47$		−	2.50386i		−	0.365225i	−0.983185	−	0.182613i	$-0.941545\pi$
$47$		−	2.50386i		−	0.365225i	0.983185	−	0.182613i	$-0.0584554\pi$
$48$		0			0
$49$			3.31292i			0.473275i
$50$	−4.82734	+	4.92127i	−0.682689	+	0.695972i
$51$		0			0
$52$	0.484211	+	1.10810i	0.0671480	+	0.153666i
$53$	2.06467	−	4.98454i	0.283604	−	0.684680i	−0.716310	−	0.697782i	$-0.754171\pi$
$53$	2.06467	−	4.98454i	0.283604	−	0.684680i	0.999914	+	0.0131018i	$0.00417056\pi$
$54$		0			0
$55$	−1.04606	−	1.04606i	−0.141051	−	0.141051i
$56$	3.94973	+	3.72776i	0.527805	+	0.498143i
$57$		0			0
$58$	7.38011	−	3.14058i	0.969056	−	0.412379i
$59$	−1.31191	+	3.16723i	−0.170796	+	0.412338i	−0.985980	−	0.166864i	$-0.946636\pi$
$59$	−1.31191	+	3.16723i	−0.170796	+	0.412338i	0.815184	+	0.579202i	$0.196636\pi$
$60$		0			0
$61$	9.16929	−	3.79804i	1.17401	−	0.486290i	0.291492	−	0.956573i	$-0.405848\pi$
$61$	9.16929	−	3.79804i	1.17401	−	0.486290i	0.882515	+	0.470284i	$0.155848\pi$
$62$	−1.96397	+	0.0189226i	−0.249424	+	0.00240318i
$63$		0			0
$64$	−7.98664	+	0.462203i	−0.998330	+	0.0577754i
$65$			0.214173i			0.0265649i
$66$		0			0
$67$	−3.66131	−	8.83919i	−0.447300	−	1.07988i	−0.973329	−	0.229412i	$-0.926320\pi$
$67$	−3.66131	−	8.83919i	−0.447300	−	1.07988i	0.526029	−	0.850467i	$-0.323680\pi$
$68$	−11.8919	+	0.229176i	−1.44211	+	0.0277917i
$69$		0			0
$70$	0.376643	+	0.885080i	0.0450174	+	0.105787i
$71$	1.84855	+	1.84855i	0.219383	+	0.219383i	0.808238	−	0.588856i	$-0.200421\pi$
$71$	1.84855	+	1.84855i	0.219383	+	0.219383i	−0.588856	+	0.808238i	$0.700421\pi$
$72$		0			0
$73$	3.57147	−	3.57147i	0.418009	−	0.418009i	−0.466508	−	0.884517i	$-0.654488\pi$
$73$	3.57147	−	3.57147i	0.418009	−	0.418009i	0.884517	+	0.466508i	$0.154488\pi$
$74$	−9.50077	−	3.82853i	−1.10444	−	0.445058i
$75$		0			0
$76$	10.3461	−	4.52099i	1.18678	−	0.518593i
$77$	7.40902	−	3.06892i	0.844336	−	0.349735i
$78$		0			0
$79$	−8.73451			−0.982709			−0.491355	−	0.870960i	$-0.663498\pi$
$79$	−8.73451			−0.982709			−0.491355	+	0.870960i	$0.663498\pi$
$80$	−1.32893	−	0.491373i	−0.148579	−	0.0549372i
$81$		0			0
$82$	−6.51783	+	6.64464i	−0.719773	+	0.733778i
$83$	3.89900	+	9.41302i	0.427971	+	1.03321i	0.979930	+	0.199342i	$0.0638805\pi$
$83$	3.89900	+	9.41302i	0.427971	+	1.03321i	−0.551959	+	0.833871i	$0.686119\pi$
$84$		0			0
$85$	−1.94620	−	0.806141i	−0.211095	−	0.0874382i
$86$	−2.24770	−	0.905756i	−0.242376	−	0.0976702i
$87$		0			0
$88$	−4.20324	+	11.0396i	−0.448067	+	1.17682i
$89$	1.90777	−	1.90777i	0.202223	−	0.202223i	−0.598729	−	0.800952i	$-0.704327\pi$
$89$	1.90777	−	1.90777i	0.202223	−	0.202223i	0.800952	+	0.598729i	$0.204327\pi$
$90$		0			0
$91$	−1.07264	−	0.444301i	−0.112443	−	0.0465753i
$92$	−10.9986	+	11.4309i	−1.14668	+	1.19175i
$93$		0			0
$94$	−3.54082	+	0.0341155i	−0.365208	+	0.00351874i
$95$	1.99969			0.205164
$96$		0			0
$97$	18.0271			1.83037			0.915185	−	0.403033i	$-0.132044\pi$
$97$	18.0271			1.83037			0.915185	+	0.403033i	$0.132044\pi$
$98$	4.68496	−	0.0451392i	0.473253	−	0.00455974i
$99$		0			0
$100$	7.02517	+	6.75952i	0.702517	+	0.675952i
$101$	11.5009	+	4.76383i	1.14438	+	0.474019i	0.872646	−	0.488353i	$-0.162402\pi$
$101$	11.5009	+	4.76383i	1.14438	+	0.474019i	0.271737	+	0.962372i	$0.412402\pi$
$102$		0			0
$103$	−11.2259	+	11.2259i	−1.10612	+	1.10612i	−0.112463	+	0.993656i	$0.535874\pi$
$103$	−11.2259	+	11.2259i	−1.10612	+	1.10612i	−0.993656	+	0.112463i	$0.964126\pi$
$104$	1.56042	−	0.699845i	0.153012	−	0.0686254i
$105$		0			0
$106$	−7.07702	−	2.85183i	−0.687380	−	0.276994i
$107$	−12.5991	−	5.21873i	−1.21800	−	0.504514i	−0.321230	−	0.947001i	$-0.604096\pi$
$107$	−12.5991	−	5.21873i	−1.21800	−	0.504514i	−0.896775	+	0.442487i	$0.854096\pi$
$108$		0			0
$109$	5.25693	+	12.6913i	0.503522	+	1.21561i	0.947553	+	0.319599i	$0.103548\pi$
$109$	5.25693	+	12.6913i	0.503522	+	1.21561i	−0.444031	+	0.896011i	$0.646452\pi$
$110$	−1.46503	+	1.49354i	−0.139685	+	0.142403i
$111$		0			0
$112$	5.21779	−	5.63630i	0.493035	−	0.532580i
$113$	−5.64986			−0.531495			−0.265747	−	0.964043i	$-0.585619\pi$
$113$	−5.64986			−0.531495			−0.265747	+	0.964043i	$0.585619\pi$
$114$		0			0
$115$	−2.59560	+	1.07513i	−0.242041	+	0.100257i
$116$	−4.54180	−	10.3938i	−0.421696	−	0.965038i
$117$		0			0
$118$	4.49681	+	1.81208i	0.413965	+	0.166816i
$119$	8.07475	−	8.07475i	0.740211	−	0.740211i
$120$		0			0
$121$	4.55552	+	4.55552i	0.414138	+	0.414138i
$122$	−5.49593	−	12.9150i	−0.497578	−	1.16927i
$123$		0			0
$124$	0.0535188	+	2.77708i	0.00480613	+	0.249389i
$125$	1.33852	+	3.23147i	0.119721	+	0.289031i
$126$		0			0
$127$			2.88665i			0.256149i	0.991765	+	0.128075i	$0.0408797\pi$
$127$			2.88665i			0.256149i	−0.991765	+	0.128075i	$0.959120\pi$
$128$	0.762443	+	11.2880i	0.0673911	+	0.997727i
$129$		0			0
$130$	0.302872	−	0.00291814i	0.0265636	−	0.000255938i
$131$	1.75340	−	0.726281i	0.153195	−	0.0634555i	−0.304768	−	0.952426i	$-0.598579\pi$
$131$	1.75340	−	0.726281i	0.153195	−	0.0634555i	0.457963	+	0.888971i	$0.348579\pi$
$132$		0			0
$133$	−4.14835	+	10.0150i	−0.359707	+	0.868410i
$134$	−12.4500	+	5.29807i	−1.07552	+	0.457684i
$135$		0			0
$136$	0.486119	+	16.8138i	0.0416844	+	1.44177i
$137$	2.05864	+	2.05864i	0.175881	+	0.175881i	0.789558	−	0.613676i	$-0.210310\pi$
$137$	2.05864	+	2.05864i	0.175881	+	0.175881i	−0.613676	+	0.789558i	$0.710310\pi$
$138$		0			0
$139$	−7.92275	+	19.1272i	−0.671999	+	1.62235i	0.106209	+	0.994344i	$0.466129\pi$
$139$	−7.92275	+	19.1272i	−0.671999	+	1.62235i	−0.778209	+	0.628006i	$0.783871\pi$
$140$	1.24650	−	0.544688i	0.105349	−	0.0460346i
$141$		0			0
$142$	2.58894	−	2.63931i	0.217259	−	0.221486i
$143$		−	2.52523i		−	0.211170i
$144$		0			0
$145$		−	2.00890i		−	0.166830i
$146$	−5.09925	−	5.00192i	−0.422017	−	0.413962i
$147$		0			0
$148$	−5.28466	+	13.4877i	−0.434396	+	1.10868i
$149$	−4.28040	+	10.3338i	−0.350664	+	0.846579i	0.645874	+	0.763444i	$0.276493\pi$
$149$	−4.28040	+	10.3338i	−0.350664	+	0.846579i	−0.996538	+	0.0831346i	$0.973507\pi$
$150$		0			0
$151$	−10.0998	−	10.0998i	−0.821911	−	0.821911i	0.164471	−	0.986382i	$-0.447408\pi$
$151$	−10.0998	−	10.0998i	−0.821911	−	0.821911i	−0.986382	+	0.164471i	$0.947408\pi$
$152$	−6.53431	−	14.5694i	−0.530003	−	1.18173i
$153$		0			0
$154$	−4.44085	−	10.4356i	−0.357854	−	0.840927i
$155$	−0.188255	+	0.454488i	−0.0151210	+	0.0365054i
$156$		0			0
$157$	6.33086	−	2.62233i	0.505257	−	0.209284i	−0.115470	−	0.993311i	$-0.536837\pi$
$157$	6.33086	−	2.62233i	0.505257	−	0.209284i	0.620727	+	0.784027i	$0.286837\pi$
$158$	0.119009	+	12.3519i	0.00946786	+	0.982663i
$159$		0			0
$160$	−0.676767	+	1.88600i	−0.0535031	+	0.149101i
$161$		−	15.2299i		−	1.20028i
$162$		0			0
$163$	−1.44372	−	3.48545i	−0.113081	−	0.273001i	0.857200	−	0.514984i	$-0.172202\pi$
$163$	−1.44372	−	3.48545i	−0.113081	−	0.273001i	−0.970281	+	0.241983i	$0.922202\pi$
$164$	9.48532	+	9.12664i	0.740679	+	0.712670i
$165$		0			0
$166$	13.2583	−	5.64202i	1.02904	−	0.437906i
$167$	−0.816766	−	0.816766i	−0.0632032	−	0.0632032i	0.674799	−	0.738002i	$-0.264230\pi$
$167$	−0.816766	−	0.816766i	−0.0632032	−	0.0632032i	−0.738002	+	0.674799i	$0.764230\pi$
$168$		0			0
$169$	8.93388	−	8.93388i	0.687221	−	0.687221i
$170$	−1.11348	+	2.76319i	−0.0854004	+	0.211927i
$171$		0			0
$172$	−1.25025	+	3.19092i	−0.0953305	+	0.243305i
$173$	−3.56357	+	1.47608i	−0.270933	+	0.112224i	−0.514014	−	0.857782i	$-0.671842\pi$
$173$	−3.56357	+	1.47608i	−0.270933	+	0.112224i	0.243081	+	0.970006i	$0.421842\pi$
$174$		0			0
$175$	−9.35996			−0.707546
$176$	15.6689	+	5.79358i	1.18109	+	0.436708i
$177$		0			0
$178$	−2.72386	−	2.67187i	−0.204162	−	0.200265i
$179$	2.38269	+	5.75233i	0.178091	+	0.429949i	0.987566	−	0.157205i	$-0.0502483\pi$
$179$	2.38269	+	5.75233i	0.178091	+	0.429949i	−0.809475	+	0.587154i	$0.800248\pi$
$180$		0			0
$181$	2.45291	+	1.01603i	0.182323	+	0.0755207i	0.471977	−	0.881611i	$-0.343540\pi$
$181$	2.45291	+	1.01603i	0.182323	+	0.0755207i	−0.289654	+	0.957131i	$0.593540\pi$
$182$	−0.613692	+	1.52292i	−0.0454899	+	0.112886i
$183$		0			0
$184$	16.3148	+	15.3979i	1.20274	+	1.13515i
$185$	−1.81414	+	1.81414i	−0.133379	+	0.133379i
$186$		0			0
$187$	22.9468	+	9.50488i	1.67804	+	0.695066i
$188$	0.0964887	+	5.00678i	0.00703716	+	0.365157i
$189$		0			0
$190$	−0.0272461	−	2.82786i	−0.00197664	−	0.205154i
$191$	20.9183			1.51360			0.756798	−	0.653649i	$-0.226763\pi$
$191$	20.9183			1.51360			0.756798	+	0.653649i	$0.226763\pi$
$192$		0			0
$193$	−10.2191			−0.735590			−0.367795	−	0.929907i	$-0.619887\pi$
$193$	−10.2191			−0.735590			−0.367795	+	0.929907i	$0.619887\pi$
$194$	−0.245622	−	25.4929i	−0.0176346	−	1.83029i
$195$		0			0
$196$	−0.127667	−	6.62462i	−0.00911906	−	0.473187i
$197$	18.0834	+	7.49038i	1.28839	+	0.533667i	0.918504	−	0.395411i	$-0.129398\pi$
$197$	18.0834	+	7.49038i	1.28839	+	0.533667i	0.369883	+	0.929079i	$0.379398\pi$
$198$		0			0
$199$	14.7199	−	14.7199i	1.04347	−	1.04347i	0.0444566	−	0.999011i	$-0.485844\pi$
$199$	14.7199	−	14.7199i	1.04347	−	1.04347i	0.999011	−	0.0444566i	$-0.0141556\pi$
$200$	9.46324	−	10.0267i	0.669152	−	0.708997i
$201$		0			0
$202$	6.58006	−	16.3289i	0.462972	−	1.14890i
$203$	10.0611	+	4.16745i	0.706152	+	0.292498i
$204$		0			0
$205$	0.892145	+	2.15383i	0.0623101	+	0.150430i
$206$	16.0280	+	15.7221i	1.11672	+	1.09541i
$207$		0			0
$208$	−1.01094	−	2.19713i	−0.0700964	−	0.152344i
$209$	−23.5775			−1.63089
$210$		0			0
$211$	−23.9151	+	9.90595i	−1.64638	+	0.681954i	−0.996919	−	0.0784400i	$-0.975006\pi$
$211$	−23.9151	+	9.90595i	−1.64638	+	0.681954i	−0.649463	+	0.760394i	$0.725006\pi$
$212$	−3.93648	+	10.0468i	−0.270359	+	0.690017i
$213$		0			0
$214$	−7.20840	+	17.8882i	−0.492756	+	1.22281i
$215$	−0.429192	+	0.429192i	−0.0292706	+	0.0292706i
$216$		0			0
$217$	−1.88567	−	1.88567i	−0.128008	−	0.128008i
$218$	17.8758	−	7.60699i	1.21070	−	0.515211i
$219$		0			0
$220$	2.13205	+	2.05142i	0.143742	+	0.138307i
$221$	−1.37606	−	3.32211i	−0.0925641	−	0.223470i
$222$		0			0
$223$			22.0919i			1.47938i	0.672946	+	0.739692i	$0.265029\pi$
$223$			22.0919i			1.47938i	−0.672946	+	0.739692i	$0.734971\pi$
$224$	−8.04165	−	7.30193i	−0.537306	−	0.487881i
$225$		0			0
$226$	0.0769804	+	7.98974i	0.00512066	+	0.531470i
$227$	−9.36227	+	3.87798i	−0.621395	+	0.257390i	−0.671092	−	0.741374i	$-0.734175\pi$
$227$	−9.36227	+	3.87798i	−0.621395	+	0.257390i	0.0496967	+	0.998764i	$0.484175\pi$
$228$		0			0
$229$	−0.814906	+	1.96736i	−0.0538505	+	0.130007i	−0.948515	−	0.316732i	$-0.897415\pi$
$229$	−0.814906	+	1.96736i	−0.0538505	+	0.130007i	0.894665	+	0.446738i	$0.147415\pi$
$230$	1.55576	+	3.65592i	0.102584	+	0.241064i
$231$		0			0
$232$	−14.6365	+	6.56440i	−0.960931	+	0.430974i
$233$	−10.5516	−	10.5516i	−0.691257	−	0.691257i	0.271252	−	0.962508i	$-0.412562\pi$
$233$	−10.5516	−	10.5516i	−0.691257	−	0.691257i	−0.962508	+	0.271252i	$0.912562\pi$
$234$		0			0
$235$	−0.339404	+	0.819394i	−0.0221403	+	0.0534514i
$236$	2.50128	−	6.38384i	0.162820	−	0.415553i
$237$		0			0
$238$	−11.5289	−	11.3089i	−0.747308	−	0.733045i
$239$		−	27.5958i		−	1.78503i	−0.451021	−	0.892513i	$-0.648940\pi$
$239$		−	27.5958i		−	1.78503i	0.451021	−	0.892513i	$-0.351060\pi$
$240$		0			0
$241$			13.8237i			0.890461i	0.895416	+	0.445231i	$0.146878\pi$
$241$			13.8237i			0.890461i	−0.895416	+	0.445231i	$0.853122\pi$
$242$	6.38011	−	6.50425i	0.410129	−	0.418109i
$243$		0			0
$244$	−18.1888	+	7.94802i	−1.16442	+	0.508820i
$245$	0.449075	−	1.08416i	0.0286904	−	0.0692647i
$246$		0			0
$247$	2.41366	+	2.41366i	0.153577	+	0.153577i
$248$	3.92647	−	0.113522i	0.249331	−	0.00720863i
$249$		0			0
$250$	4.55154	−	1.93689i	0.287864	−	0.122500i
$251$	−10.0290	+	24.2121i	−0.633025	+	1.52826i	0.202777	+	0.979225i	$0.435003\pi$
$251$	−10.0290	+	24.2121i	−0.633025	+	1.52826i	−0.835801	+	0.549032i	$0.814997\pi$
$252$		0			0
$253$	30.6037	−	12.6765i	1.92404	−	0.796963i
$254$	4.08216	−	0.0393312i	0.256137	−	0.00246786i
$255$		0			0
$256$	15.9525	−	1.23201i	0.997031	−	0.0770005i
$257$		−	8.55207i		−	0.533464i	−0.963771	−	0.266732i	$-0.914056\pi$
$257$		−	8.55207i		−	0.533464i	0.963771	−	0.266732i	$-0.0859438\pi$
$258$		0			0
$259$	−5.32230	−	12.8492i	−0.330712	−	0.798409i
$260$	−0.00825336	−	0.428266i	−0.000511852	−	0.0265599i
$261$		0			0
$262$	−1.05096	−	2.46967i	−0.0649285	−	0.152577i
$263$	0.462903	+	0.462903i	0.0285438	+	0.0285438i	0.721235	−	0.692691i	$-0.243575\pi$
$263$	0.462903	+	0.462903i	0.0285438	+	0.0285438i	−0.692691	+	0.721235i	$0.743575\pi$
$264$		0			0
$265$	−1.35134	+	1.35134i	−0.0830119	+	0.0830119i
$266$	14.2192	+	5.72992i	0.871835	+	0.351324i
$267$		0			0
$268$	7.66189	+	17.5340i	0.468025	+	1.07106i
$269$	17.9979	−	7.45497i	1.09735	−	0.454537i	0.240786	−	0.970578i	$-0.422595\pi$
$269$	17.9979	−	7.45497i	1.09735	−	0.454537i	0.856564	+	0.516041i	$0.172595\pi$
$270$		0			0
$271$	−4.14941			−0.252058			−0.126029	−	0.992027i	$-0.540223\pi$
$271$	−4.14941			−0.252058			−0.126029	+	0.992027i	$0.540223\pi$
$272$	23.7706	−	0.916536i	1.44131	−	0.0555731i
$273$		0			0
$274$	2.88317	−	2.93927i	0.174179	−	0.177568i
$275$	−7.79070	−	18.8084i	−0.469797	−	1.13419i
$276$		0			0
$277$	−6.66289	−	2.75986i	−0.400334	−	0.165824i	0.173427	−	0.984847i	$-0.444516\pi$
$277$	−6.66289	−	2.75986i	−0.400334	−	0.165824i	−0.573761	+	0.819023i	$0.694516\pi$
$278$	27.1567	+	10.9433i	1.62875	+	0.656338i
$279$		0			0
$280$	−0.787254	−	1.75532i	−0.0470474	−	0.104900i
$281$	−13.3600	+	13.3600i	−0.796991	+	0.796991i	−0.982620	−	0.185629i	$-0.940568\pi$
$281$	−13.3600	+	13.3600i	−0.796991	+	0.796991i	0.185629	+	0.982620i	$0.440568\pi$
$282$		0			0
$283$	−13.8635	−	5.74244i	−0.824099	−	0.341353i	−0.0695349	−	0.997580i	$-0.522152\pi$
$283$	−13.8635	−	5.74244i	−0.824099	−	0.341353i	−0.754564	+	0.656227i	$0.772152\pi$
$284$	−3.76765	−	3.62518i	−0.223569	−	0.215115i
$285$		0			0
$286$	−3.57104	+	0.0344066i	−0.211160	+	0.00203451i
$287$	−12.6377			−0.745981
$288$		0			0
$289$	18.3676			1.08045
$290$	−2.84088	+	0.0273716i	−0.166822	+	0.00160731i
$291$		0			0
$292$	−7.00398	+	7.27924i	−0.409877	+	0.425985i
$293$	12.9706	+	5.37260i	0.757750	+	0.313870i	0.727899	−	0.685684i	$-0.240497\pi$
$293$	12.9706	+	5.37260i	0.757750	+	0.313870i	0.0298509	+	0.999554i	$0.490497\pi$
$294$		0			0
$295$	0.858653	−	0.858653i	0.0499927	−	0.0499927i
$296$	19.1456	+	7.28952i	1.11281	+	0.423695i
$297$		0			0
$298$	14.6719	+	5.91232i	0.849918	+	0.342492i
$299$	−4.43064	−	1.83523i	−0.256230	−	0.106134i
$300$		0			0
$301$	−1.25915	−	3.03987i	−0.0725764	−	0.175215i
$302$	−14.1450	+	14.4202i	−0.813954	+	0.829792i
$303$		0			0
$304$	−20.5142	+	9.43899i	−1.17657	+	0.541363i
$305$	−3.51551			−0.201297
$306$		0			0
$307$	1.31576	−	0.545004i	0.0750942	−	0.0311050i	−0.344820	−	0.938669i	$-0.612060\pi$
$307$	1.31576	−	0.545004i	0.0750942	−	0.0311050i	0.419914	+	0.907564i	$0.362060\pi$
$308$	−14.6970	+	6.42220i	−0.837440	+	0.365939i
$309$		0			0
$310$	0.645279	+	0.260028i	0.0366494	+	0.0147686i
$311$	−16.3578	+	16.3578i	−0.927567	+	0.927567i	−0.997548	−	0.0699809i	$-0.977706\pi$
$311$	−16.3578	+	16.3578i	−0.927567	+	0.927567i	0.0699809	+	0.997548i	$0.477706\pi$
$312$		0			0
$313$	−16.0035	−	16.0035i	−0.904570	−	0.904570i	0.0912571	−	0.995827i	$-0.470911\pi$
$313$	−16.0035	−	16.0035i	−0.904570	−	0.904570i	−0.995827	+	0.0912571i	$0.970911\pi$
$314$	−3.79462	−	8.91704i	−0.214143	−	0.503218i
$315$		0			0
$316$	17.4658	−	0.336593i	0.982527	−	0.0189348i
$317$	7.88890	+	19.0455i	0.443085	+	1.06970i	0.974860	+	0.222816i	$0.0715249\pi$
$317$	7.88890	+	19.0455i	0.443085	+	1.06970i	−0.531776	+	0.846885i	$0.678475\pi$
$318$		0			0
$319$			23.6861i			1.32617i
$320$	2.67630	+	0.931352i	0.149610	+	0.0520641i
$321$		0			0
$322$	−21.5373	+	0.207509i	−1.20022	+	0.0115640i
$323$	−31.0179	+	12.8480i	−1.72588	+	0.714884i
$324$		0			0
$325$	−1.12789	+	2.72298i	−0.0625643	+	0.151044i
$326$	−4.90927	+	2.08912i	−0.271899	+	0.115706i
$327$		0			0
$328$	12.7772	−	13.5380i	0.705501	−	0.747511i
$329$	−3.39966	−	3.39966i	−0.187429	−	0.187429i
$330$		0			0
$331$	3.28947	−	7.94148i	0.180805	−	0.436503i	−0.807328	−	0.590104i	$-0.799087\pi$
$331$	3.28947	−	7.94148i	0.180805	−	0.436503i	0.988133	+	0.153601i	$0.0490869\pi$
$332$	−8.15930	−	18.6723i	−0.447800	−	1.02478i
$333$		0			0
$334$	−1.14390	+	1.16616i	−0.0625914	+	0.0638092i
$335$			3.38895i			0.185158i
$336$		0			0
$337$			32.3798i			1.76384i	0.471399	+	0.881920i	$0.343749\pi$
$337$			32.3798i			1.76384i	−0.471399	+	0.881920i	$0.656251\pi$
$338$	−12.7556	−	12.5121i	−0.693811	−	0.680569i
$339$		0			0
$340$	3.92273	+	1.53698i	0.212740	+	0.0833546i
$341$	2.21964	−	5.35869i	0.120200	−	0.290189i
$342$		0			0
$343$	14.0026	+	14.0026i	0.756068	+	0.756068i
$344$	4.52947	+	1.72456i	0.244213	+	0.0929820i
$345$		0			0
$346$	2.13595	+	5.01930i	0.114829	+	0.269839i
$347$	−9.16367	+	22.1230i	−0.491931	+	1.18763i	0.461805	+	0.886982i	$0.347202\pi$
$347$	−9.16367	+	22.1230i	−0.491931	+	1.18763i	−0.953736	+	0.300646i	$0.902798\pi$
$348$		0			0
$349$	0.254938	−	0.105599i	0.0136465	−	0.00565257i	−0.375850	−	0.926681i	$-0.622649\pi$
$349$	0.254938	−	0.105599i	0.0136465	−	0.00565257i	0.389496	+	0.921028i	$0.372649\pi$
$350$	0.127531	+	13.2364i	0.00681682	+	0.707514i
$351$		0			0
$352$	7.97949	−	22.2371i	0.425308	−	1.18524i
$353$		−	0.199829i		−	0.0106358i	−0.999986	−	0.00531791i	$-0.998307\pi$
$353$		−	0.199829i		−	0.0106358i	0.999986	−	0.00531791i	$-0.00169275\pi$
$354$		0			0
$355$	−0.354368	−	0.855519i	−0.0188079	−	0.0454062i
$356$	−3.74131	+	3.88834i	−0.198289	+	0.206082i
$357$		0			0
$358$	8.10218	−	3.44785i	0.428213	−	0.182225i
$359$	−10.2625	−	10.2625i	−0.541633	−	0.541633i	0.382374	−	0.924008i	$-0.375106\pi$
$359$	−10.2625	−	10.2625i	−0.541633	−	0.541633i	−0.924008	+	0.382374i	$0.875106\pi$
$360$		0			0
$361$	9.10080	−	9.10080i	0.478990	−	0.478990i
$362$	1.40339	−	3.48261i	0.0737606	−	0.183042i
$363$		0			0
$364$	2.16200	+	0.847101i	0.113319	+	0.0444002i
$365$	−1.65289	+	0.684651i	−0.0865165	+	0.0358363i
$366$		0			0
$367$	−20.6773			−1.07934			−0.539672	−	0.841875i	$-0.681452\pi$
$367$	−20.6773			−1.07934			−0.539672	+	0.841875i	$0.681452\pi$
$368$	21.5526	−	23.2813i	1.12351	−	1.21362i
$369$		0			0
$370$	2.59019	+	2.54075i	0.134657	+	0.132087i
$371$	−3.96452	−	9.57120i	−0.205828	−	0.496912i
$372$		0			0
$373$	−18.7074	−	7.74887i	−0.968634	−	0.401221i	−0.158431	−	0.987370i	$-0.550643\pi$
$373$	−18.7074	−	7.74887i	−0.968634	−	0.401221i	−0.810204	+	0.586149i	$0.800643\pi$
$374$	13.1287	−	32.5797i	0.678867	−	1.68466i
$375$		0			0
$376$	7.07902	−	0.204668i	0.365073	−	0.0105549i
$377$	2.42477	−	2.42477i	0.124882	−	0.124882i
$378$		0			0
$379$	4.51122	+	1.86861i	0.231726	+	0.0959839i	0.495525	−	0.868594i	$-0.334976\pi$
$379$	4.51122	+	1.86861i	0.231726	+	0.0959839i	−0.263799	+	0.964578i	$0.584976\pi$
$380$	−3.99863	+	0.0770600i	−0.205126	+	0.00395310i
$381$		0			0
$382$	−0.285016	−	29.5816i	−0.0145827	−	1.51353i
$383$	21.7757			1.11269			0.556344	−	0.830952i	$-0.312204\pi$
$383$	21.7757			1.11269			0.556344	+	0.830952i	$0.312204\pi$
$384$		0			0
$385$	−2.84062			−0.144771
$386$	0.139238	+	14.4514i	0.00708701	+	0.735556i
$387$		0			0
$388$	−36.0474	+	0.694691i	−1.83003	+	0.0352676i
$389$	−33.8004	−	14.0006i	−1.71375	−	0.709858i	−0.999955	−	0.00950254i	$-0.996975\pi$
$389$	−33.8004	−	14.0006i	−1.71375	−	0.709858i	−0.713794	−	0.700356i	$-0.753025\pi$
$390$		0			0
$391$	33.3536	−	33.3536i	1.68676	−	1.68676i
$392$	−9.36645	+	0.270801i	−0.473077	+	0.0136775i
$393$		0			0
$394$	10.3461	−	25.6746i	0.521230	−	1.29347i
$395$	2.85839	+	1.18398i	0.143821	+	0.0595727i
$396$		0			0
$397$	−14.6043	−	35.2580i	−0.732971	−	1.76955i	−0.632433	−	0.774615i	$-0.717944\pi$
$397$	−14.6043	−	35.2580i	−0.732971	−	1.76955i	−0.100538	−	0.994933i	$-0.532056\pi$
$398$	−21.0167	−	20.6156i	−1.05347	−	1.03337i
$399$		0			0
$400$	−14.3082	−	13.2458i	−0.715411	−	0.662291i
$401$	−35.3074			−1.76317			−0.881585	−	0.472026i	$-0.843523\pi$
$401$	−35.3074			−1.76317			−0.881585	+	0.472026i	$0.843523\pi$
$402$		0			0
$403$	−0.775802	+	0.321348i	−0.0386454	+	0.0160075i
$404$	−23.1811	−	9.08270i	−1.15330	−	0.451881i
$405$		0			0
$406$	5.75630	−	14.2847i	0.285681	−	0.708937i
$407$	21.3899	−	21.3899i	1.06026	−	1.06026i
$408$		0			0
$409$	−8.37059	−	8.37059i	−0.413899	−	0.413899i	0.469195	−	0.883094i	$-0.344544\pi$
$409$	−8.37059	−	8.37059i	−0.413899	−	0.413899i	−0.883094	+	0.469195i	$0.844544\pi$
$410$	3.03368	−	1.29097i	0.149823	−	0.0637565i
$411$		0			0
$412$	22.0150	−	22.8802i	1.08460	−	1.12723i
$413$	2.51910	+	6.08164i	0.123957	+	0.299258i
$414$		0			0
$415$		−	3.60896i		−	0.177157i
$416$	−3.09330	+	1.45956i	−0.151661	+	0.0715609i
$417$		0			0
$418$	0.321248	+	33.3421i	0.0157128	+	1.63082i
$419$	−13.3316	+	5.52213i	−0.651292	+	0.269774i	−0.683769	−	0.729699i	$-0.739660\pi$
$419$	−13.3316	+	5.52213i	−0.651292	+	0.269774i	0.0324771	+	0.999472i	$0.489660\pi$
$420$		0			0
$421$	−6.05805	+	14.6254i	−0.295251	+	0.712800i	0.704743	+	0.709463i	$0.251062\pi$
$421$	−6.05805	+	14.6254i	−0.295251	+	0.712800i	−0.999994	+	0.00333741i	$0.998938\pi$
$422$	14.3343	+	33.6845i	0.697784	+	1.63973i
$423$		0			0
$424$	14.2613	+	5.42988i	0.692590	+	0.263698i
$425$	−20.4984	−	20.4984i	−0.994321	−	0.994321i
$426$		0			0
$427$	7.29291	−	17.6066i	0.352929	−	0.852045i
$428$	25.3947	+	9.95001i	1.22750	+	0.480952i
$429$		0			0
$430$	0.612788	+	0.601093i	0.0295513	+	0.0289873i
$431$			3.14531i			0.151504i	0.997127	+	0.0757521i	$0.0241358\pi$
$431$			3.14531i			0.151504i	−0.997127	+	0.0757521i	$0.975864\pi$
$432$		0			0
$433$			28.7874i			1.38343i	0.722169	+	0.691716i	$0.243145\pi$
$433$			28.7874i			1.38343i	−0.722169	+	0.691716i	$0.756855\pi$
$434$	−2.64092	+	2.69231i	−0.126768	+	0.129235i
$435$		0			0
$436$	−11.0010	−	25.1754i	−0.526851	−	1.20568i
$437$	−17.1352	+	41.3680i	−0.819687	+	1.97890i
$438$		0			0
$439$	−23.1922	−	23.1922i	−1.10690	−	1.10690i	−0.993555	−	0.113348i	$-0.963843\pi$
$439$	−23.1922	−	23.1922i	−1.10690	−	1.10690i	−0.113348	−	0.993555i	$-0.536157\pi$
$440$	2.87197	−	3.04298i	0.136916	−	0.145068i
$441$		0			0
$442$	−4.67921	+	1.99122i	−0.222567	+	0.0947128i
$443$	5.82238	−	14.0565i	0.276630	−	0.667843i	−0.723108	−	0.690735i	$-0.757287\pi$
$443$	5.82238	−	14.0565i	0.276630	−	0.667843i	0.999738	+	0.0228916i	$0.00728725\pi$
$444$		0			0
$445$	−0.882924	+	0.365719i	−0.0418546	+	0.0173368i
$446$	31.2412	−	0.301006i	1.47932	−	0.0142531i
$447$		0			0
$448$	−10.2164	+	11.4716i	−0.482682	+	0.541981i
$449$			21.5258i			1.01587i	0.861396	+	0.507933i	$0.169590\pi$
$449$			21.5258i			1.01587i	−0.861396	+	0.507933i	$0.830410\pi$
$450$		0			0
$451$	−10.5189	−	25.3949i	−0.495317	−	1.19580i
$452$	11.2976	−	0.217723i	0.531396	−	0.0102408i
$453$		0			0
$454$	5.61160	+	13.1868i	0.263365	+	0.618887i
$455$	0.290797	+	0.290797i	0.0136328	+	0.0136328i
$456$		0			0
$457$	29.3952	−	29.3952i	1.37505	−	1.37505i	0.522271	−	0.852779i	$-0.325085\pi$
$457$	29.3952	−	29.3952i	1.37505	−	1.37505i	0.852779	−	0.522271i	$-0.174915\pi$
$458$	2.79324	+	1.12559i	0.130519	+	0.0525955i
$459$		0			0
$460$	5.14881	−	2.24989i	0.240064	−	0.104902i
$461$	−16.1597	+	6.69355i	−0.752630	+	0.311750i	−0.725814	−	0.687891i	$-0.758537\pi$
$461$	−16.1597	+	6.69355i	−0.752630	+	0.311750i	−0.0268161	+	0.999640i	$0.508537\pi$
$462$		0			0
$463$	−9.62772			−0.447438			−0.223719	−	0.974654i	$-0.571820\pi$
$463$	−9.62772			−0.447438			−0.223719	+	0.974654i	$0.571820\pi$
$464$	9.48246	+	20.6087i	0.440212	+	0.956734i
$465$		0			0
$466$	−14.7777	+	15.0653i	−0.684565	+	0.697884i
$467$	11.0306	+	26.6303i	0.510436	+	1.23230i	0.943630	+	0.331001i	$0.107386\pi$
$467$	11.0306	+	26.6303i	0.510436	+	1.23230i	−0.433195	+	0.901300i	$0.642614\pi$
$468$		0			0
$469$	−16.9728	−	7.03036i	−0.783731	−	0.324632i
$470$	1.16337	+	0.468803i	0.0536622	+	0.0216243i
$471$		0			0
$472$	−9.06178	−	3.45020i	−0.417102	−	0.158808i
$473$	5.06043	−	5.06043i	0.232679	−	0.232679i
$474$		0			0
$475$	25.4239	+	10.5309i	1.16653	+	0.483192i
$476$	−15.8353	+	16.4577i	−0.725811	+	0.754336i
$477$		0			0
$478$	−39.0246	+	0.375998i	−1.78494	+	0.0171978i
$479$	−16.5668			−0.756957			−0.378478	−	0.925610i	$-0.623553\pi$
$479$	−16.5668			−0.756957			−0.378478	+	0.925610i	$0.623553\pi$
$480$		0			0
$481$	−4.37940			−0.199684
$482$	19.5487	−	0.188350i	0.890420	−	0.00857911i
$483$		0			0
$484$	−9.28490	−	8.93380i	−0.422041	−	0.406082i
$485$	−5.89941	−	2.44361i	−0.267878	−	0.110959i
$486$		0			0
$487$	5.75529	−	5.75529i	0.260797	−	0.260797i	−0.564581	−	0.825378i	$-0.690962\pi$
$487$	5.75529	−	5.75529i	0.260797	−	0.260797i	0.825378	+	0.564581i	$0.190962\pi$
$488$	11.4875	+	25.6134i	0.520015	+	1.15946i
$489$		0			0
$490$	−1.53929	−	0.620287i	−0.0695379	−	0.0280217i
$491$	−9.54737	−	3.95465i	−0.430867	−	0.178471i	0.156701	−	0.987646i	$-0.449914\pi$
$491$	−9.54737	−	3.95465i	−0.430867	−	0.178471i	−0.587567	+	0.809175i	$0.699914\pi$
$492$		0			0
$493$	12.9072	+	31.1608i	0.581311	+	1.40341i
$494$	3.38038	−	3.44615i	0.152090	−	0.155050i
$495$		0			0
$496$	−0.214035	−	5.55107i	−0.00961047	−	0.249250i
$497$	5.01981			0.225169
$498$		0			0
$499$	1.29860	−	0.537896i	0.0581331	−	0.0240795i	−0.353427	−	0.935462i	$-0.614984\pi$
$499$	1.29860	−	0.537896i	0.0581331	−	0.0240795i	0.411561	+	0.911382i	$0.364984\pi$
$500$	−2.80107	−	6.41016i	−0.125268	−	0.286671i
$501$		0			0
$502$	34.3762	+	13.8526i	1.53428	+	0.618271i
$503$	13.5669	−	13.5669i	0.604918	−	0.604918i	−0.336696	−	0.941613i	$-0.609309\pi$
$503$	13.5669	−	13.5669i	0.604918	−	0.604918i	0.941613	+	0.336696i	$0.109309\pi$
$504$		0			0
$505$	−3.11796	−	3.11796i	−0.138747	−	0.138747i
$506$	−18.3434	−	43.1055i	−0.815463	−	1.91627i
$507$		0			0
$508$	−0.111240	−	5.77224i	−0.00493549	−	0.256102i
$509$	−1.72657	−	4.16831i	−0.0765290	−	0.184757i	0.880985	−	0.473144i	$-0.156881\pi$
$509$	−1.72657	−	4.16831i	−0.0765290	−	0.184757i	−0.957514	+	0.288387i	$0.906881\pi$
$510$		0			0
$511$		−	9.69846i		−	0.429035i
$512$	−1.95960	−	22.5424i	−0.0866028	−	0.996243i
$513$		0			0
$514$	−12.0939	+	0.116523i	−0.533439	+	0.00513963i
$515$	5.19540	−	2.15200i	0.228937	−	0.0948286i
$516$		0			0
$517$	4.00178	−	9.66115i	0.175998	−	0.424897i
$518$	−18.0981	+	7.70160i	−0.795186	+	0.338389i
$519$		0			0
$520$	−0.605519	+	0.0175067i	−0.0265538	+	0.000767718i
$521$	−18.6965	−	18.6965i	−0.819106	−	0.819106i	0.166872	−	0.985979i	$-0.446633\pi$
$521$	−18.6965	−	18.6965i	−0.819106	−	0.819106i	−0.985979	+	0.166872i	$0.946633\pi$
$522$		0			0
$523$	−1.08876	+	2.62850i	−0.0476081	+	0.114936i	−0.945895	−	0.324474i	$-0.894813\pi$
$523$	−1.08876	+	2.62850i	−0.0476081	+	0.114936i	0.898286	+	0.439410i	$0.144813\pi$
$524$	−3.47816	+	1.51986i	−0.151944	+	0.0663954i
$525$		0			0
$526$	0.648307	−	0.660921i	0.0282675	−	0.0288175i
$527$		−	8.25928i		−	0.359780i
$528$		0			0
$529$		−	39.9085i		−	1.73515i
$530$	1.92940	+	1.89258i	0.0838078	+	0.0822083i
$531$		0			0
$532$	7.90921	−	20.1861i	0.342908	−	0.875180i
$533$	−1.52287	+	3.67654i	−0.0659629	+	0.159249i
$534$		0			0
$535$	3.41569	+	3.41569i	0.147673	+	0.147673i
$536$	24.6913	−	11.0740i	1.06650	−	0.478322i
$537$		0			0
$538$	−10.7876	−	25.3501i	−0.465089	−	1.09292i
$539$	−5.29487	+	12.7829i	−0.228066	+	0.550600i
$540$		0			0
$541$	10.5960	−	4.38900i	0.455557	−	0.188698i	−0.143092	−	0.989709i	$-0.545704\pi$
$541$	10.5960	−	4.38900i	0.455557	−	0.188698i	0.598649	+	0.801011i	$0.295704\pi$
$542$	0.0565364	+	5.86787i	0.00242844	+	0.252047i
$543$		0			0
$544$	−1.62000	−	33.6027i	−0.0694567	−	1.44070i
$545$		−	4.86587i		−	0.208431i
$546$		0			0
$547$	7.81077	+	18.8569i	0.333964	+	0.806261i	0.998270	+	0.0588002i	$0.0187275\pi$
$547$	7.81077	+	18.8569i	0.333964	+	0.806261i	−0.664305	+	0.747461i	$0.731273\pi$
$548$	−4.19585	−	4.03718i	−0.179238	−	0.172460i
$549$		0			0
$550$	−26.4917	+	11.2735i	−1.12961	+	0.480703i
$551$	−22.6396	−	22.6396i	−0.964480	−	0.964480i
$552$		0			0
$553$	−11.8595	+	11.8595i	−0.504315	+	0.504315i
$554$	−3.81207	+	9.45991i	−0.161959	+	0.401913i
$555$		0			0
$556$	15.1055	−	38.5527i	0.640615	−	1.63500i
$557$	13.8043	−	5.71791i	0.584905	−	0.242276i	−0.0705520	−	0.997508i	$-0.522476\pi$
$557$	13.8043	−	5.71791i	0.584905	−	0.242276i	0.655457	+	0.755233i	$0.272476\pi$
$558$		0			0
$559$	−1.03608			−0.0438216
$560$	−2.47155	+	1.13721i	−0.104442	+	0.0480559i
$561$		0			0
$562$	19.0751	+	18.7110i	0.804633	+	0.789276i
$563$	10.8599	+	26.2182i	0.457692	+	1.10497i	0.969330	+	0.245764i	$0.0790388\pi$
$563$	10.8599	+	26.2182i	0.457692	+	1.10497i	−0.511638	+	0.859201i	$0.670961\pi$
$564$		0			0
$565$	1.84893	+	0.765854i	0.0777852	+	0.0322197i
$566$	−7.93177	+	19.6833i	−0.333397	+	0.827349i
$567$		0			0
$568$	−5.07521	+	5.37741i	−0.212951	+	0.225631i
$569$	10.1878	−	10.1878i	0.427095	−	0.427095i	−0.460542	−	0.887638i	$-0.652345\pi$
$569$	10.1878	−	10.1878i	0.427095	−	0.427095i	0.887638	+	0.460542i	$0.152345\pi$
$570$		0			0
$571$	7.64321	+	3.16592i	0.319859	+	0.132490i	0.536835	−	0.843687i	$-0.319620\pi$
$571$	7.64321	+	3.16592i	0.319859	+	0.132490i	−0.216977	+	0.976177i	$0.569620\pi$
$572$	0.0973122	+	5.04951i	0.00406883	+	0.211131i
$573$		0			0
$574$	0.172191	+	17.8716i	0.00718712	+	0.745946i
$575$	−38.6623			−1.61233
$576$		0			0
$577$	−32.8749			−1.36860			−0.684299	−	0.729201i	$-0.739892\pi$
$577$	−32.8749			−1.36860			−0.684299	+	0.729201i	$0.739892\pi$
$578$	−0.250262	−	25.9746i	−0.0104095	−	1.08040i
$579$		0			0
$580$	0.0774149	+	4.01705i	0.00321448	+	0.166799i
$581$	18.0747	+	7.48677i	0.749863	+	0.310604i
$582$		0			0
$583$	15.9331	−	15.9331i	0.659880	−	0.659880i
$584$	10.3894	+	9.80548i	0.429915	+	0.405754i
$585$		0			0
$586$	7.42092	−	18.4155i	0.306555	−	0.760739i
$587$	−3.31499	−	1.37311i	−0.136824	−	0.0566744i	0.313221	−	0.949680i	$-0.398592\pi$
$587$	−3.31499	−	1.37311i	−0.136824	−	0.0566744i	−0.450045	+	0.893006i	$0.648592\pi$
$588$		0			0
$589$	3.00036	+	7.24351i	0.123628	+	0.298464i
$590$	−1.22596	−	1.20256i	−0.0504720	−	0.0495087i
$591$		0			0
$592$	10.0476	−	27.1740i	0.412954	−	1.11684i
$593$	35.4165			1.45438			0.727191	−	0.686436i	$-0.240826\pi$
$593$	35.4165			1.45438			0.727191	+	0.686436i	$0.240826\pi$
$594$		0			0
$595$	−3.73704	+	1.54793i	−0.153204	+	0.0634590i
$596$	8.16099	−	20.8287i	0.334287	−	0.853178i
$597$		0			0
$598$	−2.53492	+	6.29058i	−0.103660	+	0.257241i
$599$	12.0624	−	12.0624i	0.492855	−	0.492855i	−0.416350	−	0.909205i	$-0.636691\pi$
$599$	12.0624	−	12.0624i	0.492855	−	0.492855i	0.909205	+	0.416350i	$0.136691\pi$
$600$		0			0
$601$	−12.0566	−	12.0566i	−0.491799	−	0.491799i	0.417074	−	0.908873i	$-0.363056\pi$
$601$	−12.0566	−	12.0566i	−0.491799	−	0.491799i	−0.908873	+	0.417074i	$0.863056\pi$
$602$	−4.28167	+	1.82205i	−0.174508	+	0.0742612i
$603$		0			0
$604$	20.5851	+	19.8067i	0.837595	+	0.805922i
$605$	−0.873295	−	2.10832i	−0.0355045	−	0.0857154i
$606$		0			0
$607$			25.3896i			1.03053i	0.857030	+	0.515266i	$0.172307\pi$
$607$			25.3896i			1.03053i	−0.857030	+	0.515266i	$0.827693\pi$
$608$	13.6276	+	28.8815i	0.552674	+	1.17130i
$609$		0			0
$610$	0.0478994	+	4.97145i	0.00193939	+	0.201288i
$611$	−1.39869	+	0.579356i	−0.0565849	+	0.0234382i
$612$		0			0
$613$	−15.2639	+	36.8504i	−0.616504	+	1.48837i	0.239233	+	0.970962i	$0.423104\pi$
$613$	−15.2639	+	36.8504i	−0.616504	+	1.48837i	−0.855737	+	0.517411i	$0.826896\pi$
$614$	−0.788644	−	1.85325i	−0.0318271	−	0.0747911i
$615$		0			0
$616$	9.28220	+	20.6963i	0.373990	+	0.833876i
$617$	33.0964	+	33.0964i	1.33241	+	1.33241i	0.903210	+	0.429199i	$0.141204\pi$
$617$	33.0964	+	33.0964i	1.33241	+	1.33241i	0.429199	+	0.903210i	$0.358796\pi$
$618$		0			0
$619$	−10.5899	+	25.5662i	−0.425643	+	1.02759i	0.555010	+	0.831843i	$0.312714\pi$
$619$	−10.5899	+	25.5662i	−0.425643	+	1.02759i	−0.980654	+	0.195750i	$0.937286\pi$
$620$	0.358926	−	0.916062i	0.0144148	−	0.0367899i
$621$		0			0
$622$	23.3553	+	22.9095i	0.936461	+	0.918588i
$623$		−	5.18061i		−	0.207557i
$624$		0			0
$625$			23.1337i			0.925348i
$626$	−22.4132	+	22.8493i	−0.895813	+	0.913243i
$627$		0			0
$628$	−12.5583	+	5.48765i	−0.501131	+	0.218981i
$629$	16.4840	−	39.7958i	0.657259	−	1.58676i
$630$		0			0
$631$	−8.36910	−	8.36910i	−0.333168	−	0.333168i	0.520620	−	0.853788i	$-0.325701\pi$
$631$	−8.36910	−	8.36910i	−0.333168	−	0.333168i	−0.853788	+	0.520620i	$0.825701\pi$
$632$	−0.713967	−	24.6946i	−0.0284001	−	0.982299i
$633$		0			0
$634$	26.8257	−	11.4156i	1.06538	−	0.453370i
$635$	0.391293	−	0.944666i	0.0155280	−	0.0374879i
$636$		0			0
$637$	1.85064	−	0.766562i	0.0733252	−	0.0303723i
$638$	33.4957	−	0.322727i	1.32611	−	0.0127769i
$639$		0			0
$640$	1.28060	−	3.79738i	0.0506203	−	0.150105i
$641$		−	7.90128i		−	0.312082i	−0.987751	−	0.156041i	$-0.950127\pi$
$641$		−	7.90128i		−	0.312082i	0.987751	−	0.156041i	$-0.0498732\pi$
$642$		0			0
$643$	−9.17759	−	22.1567i	−0.361929	−	0.873773i	−0.995018	−	0.0996945i	$-0.968213\pi$
$643$	−9.17759	−	22.1567i	−0.361929	−	0.873773i	0.633089	−	0.774079i	$-0.281787\pi$
$644$	0.586898	+	30.4540i	0.0231270	+	1.20006i
$645$		0			0
$646$	18.5917	+	43.6889i	0.731479	+	1.71892i
$647$	13.3802	+	13.3802i	0.526030	+	0.526030i	0.919386	−	0.393356i	$-0.128686\pi$
$647$	13.3802	+	13.3802i	0.526030	+	0.526030i	−0.393356	+	0.919386i	$0.628686\pi$
$648$		0			0
$649$	−10.1240	+	10.1240i	−0.397403	+	0.397403i
$650$	3.86606	+	1.55791i	0.151639	+	0.0611062i
$651$		0			0
$652$	3.02122	+	6.91397i	0.118320	+	0.270772i
$653$	2.18855	−	0.906525i	0.0856444	−	0.0354751i	−0.339450	−	0.940624i	$-0.610241\pi$
$653$	2.18855	−	0.906525i	0.0856444	−	0.0354751i	0.425094	+	0.905149i	$0.360241\pi$
$654$		0			0
$655$	−0.672253			−0.0262671
$656$	−19.3188	−	17.8844i	−0.754273	−	0.698267i
$657$		0			0
$658$	−4.76130	+	4.85394i	−0.185615	+	0.189226i
$659$	7.72085	+	18.6398i	0.300762	+	0.726103i	0.999938	+	0.0111532i	$0.00355026\pi$
$659$	7.72085	+	18.6398i	0.300762	+	0.726103i	−0.699176	+	0.714949i	$0.746450\pi$
$660$		0			0
$661$	−20.1543	−	8.34818i	−0.783911	−	0.324707i	−0.0454184	−	0.998968i	$-0.514462\pi$
$661$	−20.1543	−	8.34818i	−0.783911	−	0.324707i	−0.738493	+	0.674261i	$0.764462\pi$
$662$	−11.2752	−	4.54359i	−0.438225	−	0.176592i
$663$		0			0
$664$	−26.2942	+	11.7929i	−1.02041	+	0.457652i
$665$	2.71512	−	2.71512i	0.105288	−	0.105288i
$666$		0			0
$667$	41.5585	+	17.2141i	1.60915	+	0.666532i
$668$	1.66470	+	1.60175i	0.0644093	+	0.0619737i
$669$		0			0
$670$	4.79248	−	0.0461750i	0.185150	−	0.00178390i
$671$	41.4500			1.60016
$672$		0			0
$673$	−39.5181			−1.52331			−0.761655	−	0.647982i	$-0.775613\pi$
$673$	−39.5181			−1.52331			−0.761655	+	0.647982i	$0.775613\pi$
$674$	45.7898	−	0.441180i	1.76376	−	0.0169936i
$675$		0			0
$676$	−17.5202	+	18.2087i	−0.673852	+	0.700335i
$677$	22.1877	+	9.19045i	0.852743	+	0.353218i	0.765865	−	0.643001i	$-0.222311\pi$
$677$	22.1877	+	9.19045i	0.852743	+	0.353218i	0.0868779	+	0.996219i	$0.472311\pi$
$678$		0			0
$679$	24.4766	−	24.4766i	0.939326	−	0.939326i
$680$	2.12007	−	5.56827i	0.0813011	−	0.213533i
$681$		0			0
$682$	−7.60822	−	3.06589i	−0.291334	−	0.117399i
$683$	−37.2272	−	15.4200i	−1.42446	−	0.590030i	−0.468483	−	0.883473i	$-0.655199\pi$
$683$	−37.2272	−	15.4200i	−1.42446	−	0.590030i	−0.955977	+	0.293442i	$0.905199\pi$
$684$		0			0
$685$	−0.394642	−	0.952750i	−0.0150785	−	0.0364027i
$686$	19.6109	−	19.9925i	0.748749	−	0.763317i
$687$		0			0
$688$	2.37707	−	6.42883i	0.0906248	−	0.245097i
$689$	−3.26217			−0.124279
$690$		0			0
$691$	43.9656	−	18.2111i	1.67253	−	0.692785i	0.673603	−	0.739093i	$-0.264746\pi$
$691$	43.9656	−	18.2111i	1.67253	−	0.692785i	0.998927	+	0.0463087i	$0.0147458\pi$
$692$	7.06893	−	3.08893i	0.268720	−	0.117424i
$693$		0			0
$694$	31.4101	+	12.6573i	1.19231	+	0.480466i
$695$	5.18549	−	5.18549i	0.196697	−	0.196697i
$696$		0			0
$697$	−27.6768	−	27.6768i	−1.04833	−	1.04833i
$698$	−0.152806	−	0.359081i	−0.00578379	−	0.0135914i
$699$		0			0
$700$	18.7164	−	0.360696i	0.707415	−	0.0136330i
$701$	15.4418	+	37.2799i	0.583230	+	1.40804i	0.889870	+	0.456215i	$0.150795\pi$
$701$	15.4418	+	37.2799i	0.583230	+	1.40804i	−0.306640	+	0.951826i	$0.599205\pi$
$702$		0			0
$703$			40.8896i			1.54218i
$704$	−31.5552	−	10.9812i	−1.18928	−	0.413870i
$705$		0			0
$706$	−0.282588	+	0.00272270i	−0.0106353	+	0.000102470i
$707$	22.0838	−	9.14740i	0.830546	−	0.344023i
$708$		0			0
$709$	−18.9126	+	45.6590i	−0.710277	+	1.71476i	−0.0109688	+	0.999940i	$0.503492\pi$
$709$	−18.9126	+	45.6590i	−0.710277	+	1.71476i	−0.699308	+	0.714820i	$0.746508\pi$
$710$	−1.20500	+	0.512785i	−0.0452229	+	0.0192445i
$711$		0			0
$712$	5.54967	+	5.23778i	0.207983	+	0.196294i
$713$	−7.78895	−	7.78895i	−0.291698	−	0.291698i
$714$		0			0
$715$	−0.342301	+	0.826387i	−0.0128013	+	0.0309051i
$716$	−4.98617	−	11.4107i	−0.186342	−	0.426438i
$717$		0			0
$718$	−14.3728	+	14.6525i	−0.536390	+	0.546826i
$719$			26.5306i			0.989424i	0.869057	+	0.494712i	$0.164726\pi$
$719$			26.5306i			0.989424i	−0.869057	+	0.494712i	$0.835274\pi$
$720$		0			0
$721$			30.4843i			1.13530i
$722$	−12.9939	−	12.7459i	−0.483582	−	0.474353i
$723$		0			0
$724$	−4.94405	−	1.93715i	−0.183744	−	0.0719936i
$725$	10.5794	−	25.5410i	0.392910	−	0.948569i
$726$		0			0
$727$	22.2992	+	22.2992i	0.827030	+	0.827030i	0.987105	−	0.160075i	$-0.0511736\pi$
$727$	22.2992	+	22.2992i	0.827030	+	0.827030i	−0.160075	+	0.987105i	$0.551174\pi$
$728$	1.16847	−	3.06892i	0.0433063	−	0.113742i
$729$		0			0
$730$	0.990719	+	2.32811i	0.0366682	+	0.0861672i
$731$	3.89979	−	9.41492i	0.144239	−	0.348223i
$732$		0			0
$733$	40.4380	−	16.7499i	1.49361	−	0.618674i	0.521511	−	0.853245i	$-0.325369\pi$
$733$	40.4380	−	16.7499i	1.49361	−	0.618674i	0.972099	+	0.234571i	$0.0753686\pi$
$734$	0.281731	+	29.2407i	0.0103989	+	1.07929i
$735$		0			0
$736$	−33.2169	−	30.1614i	−1.22439	−	1.11176i
$737$		−	39.9578i		−	1.47186i
$738$		0			0
$739$	−5.11464	−	12.3478i	−0.188145	−	0.454222i	0.801458	−	0.598052i	$-0.204058\pi$
$739$	−5.11464	−	12.3478i	−0.188145	−	0.454222i	−0.989602	+	0.143830i	$0.954058\pi$
$740$	3.55771	−	3.69753i	0.130784	−	0.135924i
$741$		0			0
$742$	−13.4811	+	5.73683i	−0.494906	+	0.210606i
$743$	15.5708	+	15.5708i	0.571235	+	0.571235i	0.932474	−	0.361238i	$-0.117646\pi$
$743$	15.5708	+	15.5708i	0.571235	+	0.571235i	−0.361238	+	0.932474i	$0.617646\pi$
$744$		0			0
$745$	2.80155	−	2.80155i	0.102641	−	0.102641i
$746$	−10.7032	+	26.5607i	−0.391871	+	0.972455i
$747$		0			0
$748$	−46.2514	−	18.1220i	−1.69112	−	0.662605i
$749$	−24.1926	+	10.0209i	−0.883977	+	0.366155i
$750$		0			0
$751$	51.8298			1.89129			0.945647	−	0.325194i	$-0.105430\pi$
$751$	51.8298			1.89129			0.945647	+	0.325194i	$0.105430\pi$
$752$	−0.385883	−	10.0080i	−0.0140717	−	0.364954i
$753$		0			0
$754$	−3.46202	−	3.39595i	−0.126079	−	0.123673i
$755$	1.93614	+	4.67425i	0.0704632	+	0.170113i
$756$		0			0
$757$	−46.8920	−	19.4233i	−1.70432	−	0.705952i	−0.704326	−	0.709876i	$-0.748751\pi$
$757$	−46.8920	−	19.4233i	−1.70432	−	0.705952i	−0.999992	+	0.00392460i	$0.998751\pi$
$758$	2.58102	−	6.40499i	0.0937469	−	0.232640i
$759$		0			0
$760$	0.163456	+	5.65361i	0.00592919	+	0.205078i
$761$	−14.8239	+	14.8239i	−0.537364	+	0.537364i	−0.922754	−	0.385390i	$-0.874067\pi$
$761$	−14.8239	+	14.8239i	−0.537364	+	0.537364i	0.385390	+	0.922754i	$0.374067\pi$
$762$		0			0
$763$	24.3696	+	10.0942i	0.882239	+	0.365435i
$764$	−41.8289	+	0.806109i	−1.51332	+	0.0291640i
$765$		0			0
$766$	−0.296698	−	30.7941i	−0.0107201	−	1.11264i
$767$	2.07282			0.0748450
$768$		0			0
$769$	45.5096			1.64112			0.820559	−	0.571562i	$-0.193662\pi$
$769$	45.5096			1.64112			0.820559	+	0.571562i	$0.193662\pi$
$770$	0.0387039	+	4.01706i	0.00139479	+	0.144765i
$771$		0			0
$772$	20.4345	−	0.393805i	0.735454	−	0.0141734i
$773$	28.1751	+	11.6705i	1.01339	+	0.419758i	0.826689	−	0.562659i	$-0.190222\pi$
$773$	28.1751	+	11.6705i	1.01339	+	0.419758i	0.186697	+	0.982417i	$0.440222\pi$
$774$		0			0
$775$	−4.78693	+	4.78693i	−0.171952	+	0.171952i
$776$	1.47355	+	50.9669i	0.0528973	+	1.82961i
$777$		0			0
$778$	−19.3384	+	47.9895i	−0.693314	+	1.72051i
$779$	34.3271	+	14.2188i	1.22990	+	0.509440i
$780$		0			0
$781$	4.17821	+	10.0871i	0.149508	+	0.360944i
$782$	−47.6214	−	46.7125i	−1.70294	−	1.67043i
$783$		0			0
$784$	0.510573	+	13.2419i	0.0182347	+	0.472923i
$785$	−2.42725			−0.0866324
$786$		0			0
$787$	−20.9121	+	8.66206i	−0.745434	+	0.308769i	−0.722877	−	0.690977i	$-0.757181\pi$
$787$	−20.9121	+	8.66206i	−0.745434	+	0.308769i	−0.0225571	+	0.999746i	$0.507181\pi$
$788$	−36.4487	−	14.2811i	−1.29843	−	0.508744i
$789$		0			0
$790$	1.63538	−	4.05832i	0.0581843	−	0.144389i
$791$	−7.67121	+	7.67121i	−0.272757	+	0.272757i
$792$		0			0
$793$	−4.24328	−	4.24328i	−0.150683	−	0.150683i
$794$	−49.6610	+	21.1331i	−1.76240	+	0.749985i
$795$		0			0
$796$	−28.8671	+	30.0016i	−1.02317	+	1.06338i
$797$	−11.7535	−	28.3754i	−0.416330	−	1.00511i	−0.983402	−	0.181441i	$-0.941924\pi$
$797$	−11.7535	−	28.3754i	−0.416330	−	1.00511i	0.567072	−	0.823668i	$-0.308076\pi$
$798$		0			0
$799$		−	14.8906i		−	0.526792i
$800$	−18.5366	+	20.4144i	−0.655367	+	0.721759i
$801$		0			0
$802$	0.481070	+	49.9299i	0.0169872	+	1.76309i
$803$	19.4886	−	8.07245i	0.687739	−	0.284871i
$804$		0			0
$805$	−2.06445	+	4.98401i	−0.0727621	+	0.175663i
$806$	0.465003	+	1.09272i	0.0163790	+	0.0384894i
$807$		0			0
$808$	−12.5284	+	32.9053i	−0.440749	+	1.15760i
$809$	15.9011	+	15.9011i	0.559052	+	0.559052i	0.929038	−	0.369985i	$-0.120637\pi$
$809$	15.9011	+	15.9011i	0.559052	+	0.559052i	−0.369985	+	0.929038i	$0.620637\pi$
$810$		0			0
$811$	1.69299	−	4.08723i	0.0594488	−	0.143522i	−0.891364	−	0.453288i	$-0.850251\pi$
$811$	1.69299	−	4.08723i	0.0594488	−	0.143522i	0.950813	+	0.309766i	$0.100251\pi$
$812$	−20.2791	−	7.94564i	−0.711656	−	0.278837i
$813$		0			0
$814$	−30.5399	−	29.9570i	−1.07042	−	1.04999i
$815$			1.33632i			0.0468094i
$816$		0			0
$817$			9.67370i			0.338440i
$818$	−11.7232	+	11.9513i	−0.409892	+	0.417867i
$819$		0			0
$820$	−1.86696	−	4.27248i	−0.0651970	−	0.149201i
$821$	7.70821	−	18.6093i	0.269018	−	0.649468i	−0.730419	−	0.682999i	$-0.760675\pi$
$821$	7.70821	−	18.6093i	0.269018	−	0.649468i	0.999438	+	0.0335313i	$0.0106753\pi$
$822$		0			0
$823$	4.79694	+	4.79694i	0.167211	+	0.167211i	0.785752	−	0.618541i	$-0.212276\pi$
$823$	4.79694	+	4.79694i	0.167211	+	0.167211i	−0.618541	+	0.785752i	$0.712276\pi$
$824$	−32.6559	−	30.8207i	−1.13762	−	1.07369i
$825$		0			0
$826$	8.56602	−	3.64524i	0.298050	−	0.126834i
$827$	17.1053	−	41.2957i	0.594808	−	1.43599i	−0.284003	−	0.958823i	$-0.591663\pi$
$827$	17.1053	−	41.2957i	0.594808	−	1.43599i	0.878811	−	0.477170i	$-0.158337\pi$
$828$		0			0
$829$	−13.1310	+	5.43906i	−0.456060	+	0.188906i	−0.598874	−	0.800843i	$-0.704385\pi$
$829$	−13.1310	+	5.43906i	−0.456060	+	0.188906i	0.142814	+	0.989750i	$0.454385\pi$
$830$	−5.10360	+	0.0491727i	−0.177149	+	0.00170681i
$831$		0			0
$832$	2.10618	+	4.35450i	0.0730188	+	0.150965i
$833$			19.7022i			0.682640i
$834$		0			0
$835$	0.156574	+	0.378003i	0.00541847	+	0.0130813i
$836$	47.1463	−	0.908584i	1.63059	−	0.0314241i
$837$		0			0
$838$	7.99076	+	18.7776i	0.276036	+	0.648663i
$839$	28.9775	+	28.9775i	1.00042	+	1.00042i	1.00000		0.000415895i	$0.000132383\pi$
$839$	28.9775	+	28.9775i	1.00042	+	1.00042i	0.000415895		1.00000i	$0.499868\pi$
$840$		0			0
$841$	−2.23776	+	2.23776i	−0.0771641	+	0.0771641i
$842$	20.7651	+	8.36771i	0.715612	+	0.288370i
$843$		0			0
$844$	47.4395	−	20.7298i	1.63294	−	0.713549i
$845$	−4.13465	+	1.71263i	−0.142236	+	0.0589162i
$846$		0			0
$847$	12.3707			0.425062
$848$	7.48434	−	20.2416i	0.257013	−	0.695098i
$849$		0			0
$850$	−28.7085	+	29.2671i	−0.984695	+	1.00385i
$851$	−21.9843	−	53.0749i	−0.753613	−	1.81938i
$852$		0			0
$853$	−20.6002	−	8.53290i	−0.705339	−	0.292161i	0.00103525	−	0.999999i	$-0.499670\pi$
$853$	−20.6002	−	8.53290i	−0.705339	−	0.292161i	−0.706374	+	0.707838i	$0.749670\pi$
$854$	−24.9978	−	10.0734i	−0.855406	−	0.344703i
$855$		0			0
$856$	13.7248	−	36.0474i	0.469103	−	1.23208i
$857$	−20.6434	+	20.6434i	−0.705164	+	0.705164i	−0.965514	−	0.260350i	$-0.916162\pi$
$857$	−20.6434	+	20.6434i	−0.705164	+	0.705164i	0.260350	+	0.965514i	$0.416162\pi$
$858$		0			0
$859$	39.6723	+	16.4328i	1.35360	+	0.560680i	0.937293	−	0.348543i	$-0.113324\pi$
$859$	39.6723	+	16.4328i	1.35360	+	0.560680i	0.416309	+	0.909223i	$0.363324\pi$
$860$	0.841684	−	0.874763i	0.0287012	−	0.0298292i
$861$		0			0
$862$	4.44793	−	0.0428554i	0.151497	−	0.00145966i
$863$	14.0634			0.478724			0.239362	−	0.970930i	$-0.423062\pi$
$863$	14.0634			0.478724			0.239362	+	0.970930i	$0.423062\pi$
$864$		0			0
$865$	1.36627			0.0464547
$866$	40.7096	−	0.392233i	1.38337	−	0.0133286i
$867$		0			0
$868$	3.84330	+	3.69797i	0.130450	+	0.125517i
$869$	−33.7022	−	13.9599i	−1.14327	−	0.473557i
$870$		0			0
$871$	−4.09052	+	4.09052i	−0.138602	+	0.138602i
$872$	−35.4518	+	15.9000i	−1.20055	+	0.538443i
$873$		0			0
$874$	58.7339	+	23.6680i	1.98670	+	0.800583i
$875$	6.20499	+	2.57019i	0.209767	+	0.0868883i
$876$		0			0
$877$	−16.1346	−	38.9524i	−0.544827	−	1.31533i	−0.921283	−	0.388893i	$-0.872858\pi$
$877$	−16.1346	−	38.9524i	−0.544827	−	1.31533i	0.376456	−	0.926434i	$-0.377142\pi$
$878$	−32.4812	+	33.1132i	−1.09619	+	1.11752i
$879$		0			0
$880$	−4.34235	−	4.01992i	−0.146381	−	0.135512i
$881$	43.2670			1.45770			0.728851	−	0.684673i	$-0.240055\pi$
$881$	43.2670			1.45770			0.728851	+	0.684673i	$0.240055\pi$
$882$		0			0
$883$	−41.1697	+	17.0530i	−1.38547	+	0.573880i	−0.945938	−	0.324347i	$-0.894856\pi$
$883$	−41.1697	+	17.0530i	−1.38547	+	0.573880i	−0.439532	+	0.898227i	$0.644856\pi$
$884$	2.87964	+	6.58997i	0.0968527	+	0.221645i
$885$		0			0
$886$	−19.9573	−	8.04219i	−0.670477	−	0.270183i
$887$	−35.4105	+	35.4105i	−1.18897	+	1.18897i	−0.211614	+	0.977353i	$0.567872\pi$
$887$	−35.4105	+	35.4105i	−1.18897	+	1.18897i	−0.977353	+	0.211614i	$0.932128\pi$
$888$		0			0
$889$	3.91941	+	3.91941i	0.131453	+	0.131453i
$890$	0.529211	+	1.24360i	0.0177392	+	0.0416857i
$891$		0			0
$892$	−0.851334	−	44.1756i	−0.0285048	−	1.47911i
$893$	5.40933	+	13.0593i	0.181016	+	0.437012i
$894$		0			0
$895$		−	2.20544i		−	0.0737199i
$896$	16.3617	+	14.2913i	0.546606	+	0.477438i
$897$		0			0
$898$	30.4407	−	0.293293i	1.01582	−	0.00978732i
$899$	7.27686	−	3.01417i	0.242697	−	0.100528i
$900$		0			0
$901$	12.2787	−	29.6434i	0.409063	−	0.987566i
$902$	−35.7689	+	15.2213i	−1.19097	+	0.506815i
$903$		0			0
$904$	−0.461825	−	15.9736i	−0.0153601	−	0.531273i
$905$	−0.664995	−	0.664995i	−0.0221052	−	0.0221052i
$906$		0			0
$907$	6.88932	−	16.6323i	0.228756	−	0.552266i	−0.767270	−	0.641324i	$-0.778386\pi$
$907$	6.88932	−	16.6323i	0.228756	−	0.552266i	0.996026	+	0.0890575i	$0.0283855\pi$
$908$	18.5716	−	8.11530i	0.616321	−	0.269316i
$909$		0			0
$910$	0.407268	−	0.415192i	0.0135008	−	0.0137635i
$911$		−	41.5029i		−	1.37505i	−0.726160	−	0.687526i	$-0.758697\pi$
$911$		−	41.5029i		−	1.37505i	0.726160	−	0.687526i	$-0.241303\pi$
$912$		0			0
$913$			42.5518i			1.40826i
$914$	−41.9697	−	41.1687i	−1.38823	−	1.36174i
$915$		0			0
$916$	1.55370	−	3.96539i	0.0513356	−	0.131020i
$917$	1.39459	−	3.36683i	0.0460533	−	0.111183i
$918$		0			0
$919$	−9.02728	−	9.02728i	−0.297783	−	0.297783i	0.542362	−	0.840145i	$-0.317530\pi$
$919$	−9.02728	−	9.02728i	−0.297783	−	0.297783i	−0.840145	+	0.542362i	$0.817530\pi$
$920$	−3.25183	−	7.25052i	−0.107210	−	0.239043i
$921$		0			0
$922$	9.68585	+	22.7609i	0.318986	+	0.749592i
$923$	0.604898	−	1.46035i	0.0199105	−	0.0480681i
$924$		0			0
$925$	−32.6187	+	13.5111i	−1.07250	+	0.444243i
$926$	0.131179	+	13.6150i	0.00431082	+	0.447417i
$927$		0			0
$928$	29.0145	−	13.6904i	0.952448	−	0.449409i
$929$			14.2313i			0.466914i	0.972367	+	0.233457i	$0.0750039\pi$
$929$			14.2313i			0.466914i	−0.972367	+	0.233457i	$0.924996\pi$
$930$		0			0
$931$	−7.15724	−	17.2791i	−0.234569	−	0.566300i
$932$	21.5058	+	20.6926i	0.704447	+	0.677809i
$933$		0			0
$934$	37.5088	−	15.9618i	1.22733	−	0.522285i
$935$	−6.22100	−	6.22100i	−0.203448	−	0.203448i
$936$		0			0
$937$	−24.8722	+	24.8722i	−0.812540	+	0.812540i	−0.985014	−	0.172474i	$-0.944824\pi$
$937$	−24.8722	+	24.8722i	−0.812540	+	0.812540i	0.172474	+	0.985014i	$0.444824\pi$
$938$	−9.71072	+	24.0978i	−0.317066	+	0.786822i
$939$		0			0
$940$	0.647106	−	1.65156i	0.0211063	−	0.0538681i
$941$	19.1307	−	7.92420i	0.623643	−	0.258322i	−0.0484062	−	0.998828i	$-0.515414\pi$
$941$	19.1307	−	7.92420i	0.623643	−	0.258322i	0.672049	+	0.740506i	$0.265414\pi$
$942$		0			0
$943$	−52.2014			−1.69991
$944$	−4.75563	+	12.8617i	−0.154782	+	0.418613i
$945$		0			0
$946$	−7.22514	−	7.08724i	−0.234910	−	0.230426i
$947$	−1.13594	−	2.74239i	−0.0369130	−	0.0891158i	0.904348	−	0.426796i	$-0.140358\pi$
$947$	−1.13594	−	2.74239i	−0.0369130	−	0.0891158i	−0.941261	+	0.337680i	$0.890358\pi$
$948$		0			0
$949$	−2.82146	−	1.16869i	−0.0915883	−	0.0379371i
$950$	14.5459	−	36.0967i	0.471931	−	1.17113i
$951$		0			0
$952$	23.4893	+	22.1693i	0.761294	+	0.718510i
$953$	−1.58859	+	1.58859i	−0.0514595	+	0.0514595i	−0.732368	−	0.680909i	$-0.761585\pi$
$953$	−1.58859	+	1.58859i	−0.0514595	+	0.0514595i	0.680909	+	0.732368i	$0.261585\pi$
$954$		0			0
$955$	−6.84558	−	2.83553i	−0.221518	−	0.0917556i
$956$	1.06343	+	55.1814i	0.0343939	+	1.78470i
$957$		0			0
$958$	0.225726	+	23.4279i	0.00729287	+	0.756922i
$959$	5.59032			0.180521
$960$		0			0
$961$	29.0712			0.937782
$962$	0.0596701	+	6.19312i	0.00192384	+	0.199674i
$963$		0			0
$964$	−0.532709	−	27.6422i	−0.0171574	−	0.890296i
$965$	3.34424	+	1.38523i	0.107655	+	0.0445922i
$966$		0			0
$967$	13.4305	−	13.4305i	0.431895	−	0.431895i	−0.457378	−	0.889273i	$-0.651211\pi$
$967$	13.4305	−	13.4305i	0.431895	−	0.431895i	0.889273	+	0.457378i	$0.151211\pi$
$968$	−12.5072	+	13.2520i	−0.401997	+	0.425934i
$969$		0			0
$970$	−3.37525	+	8.37593i	−0.108373	+	0.268935i
$971$	−16.6286	−	6.88778i	−0.533636	−	0.221039i	0.0995589	−	0.995032i	$-0.468257\pi$
$971$	−16.6286	−	6.88778i	−0.533636	−	0.221039i	−0.633195	+	0.773992i	$0.718257\pi$
$972$		0			0
$973$	15.2131	+	36.7276i	0.487709	+	1.17743i
$974$	−8.21724	−	8.06041i	−0.263297	−	0.258272i
$975$		0			0
$976$	36.0646	−	16.5940i	1.15440	−	0.531162i
$977$	−35.3863			−1.13211			−0.566054	−	0.824368i	$-0.691531\pi$
$977$	−35.3863			−1.13211			−0.566054	+	0.824368i	$0.691531\pi$
$978$		0			0
$979$	10.4102	−	4.31205i	0.332712	−	0.137814i
$980$	−0.856204	+	2.18523i	−0.0273504	+	0.0698046i
$981$		0			0
$982$	−5.46238	+	13.5553i	−0.174311	+	0.432566i
$983$	−7.82319	+	7.82319i	−0.249521	+	0.249521i	−0.820774	−	0.571253i	$-0.806458\pi$
$983$	−7.82319	+	7.82319i	−0.249521	+	0.249521i	0.571253	+	0.820774i	$0.306458\pi$
$984$		0			0
$985$	−4.90249	−	4.90249i	−0.156206	−	0.156206i
$986$	43.8901	−	18.6773i	1.39774	−	0.594805i
$987$		0			0
$988$	−4.91943	−	4.73340i	−0.156508	−	0.150590i
$989$	−5.20107	−	12.5565i	−0.165384	−	0.399273i
$990$		0			0
$991$			31.7944i			1.00998i	0.863125	+	0.504991i	$0.168504\pi$
$991$			31.7944i			1.00998i	−0.863125	+	0.504991i	$0.831496\pi$
$992$	−7.84712	+	0.378312i	−0.249146	+	0.0120114i
$993$		0			0
$994$	−0.0683958	−	7.09876i	−0.00216938	−	0.225159i
$995$	−6.81246	+	2.82181i	−0.215970	+	0.0894575i
$996$		0			0
$997$	−2.40002	+	5.79415i	−0.0760093	+	0.183503i	−0.957317	−	0.289040i	$-0.906664\pi$
$997$	−2.40002	+	5.79415i	−0.0760093	+	0.183503i	0.881308	+	0.472543i	$0.156664\pi$
$998$	−0.778358	−	1.82908i	−0.0246385	−	0.0578984i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.b.107.16	✓	128
3.2	odd	2	inner	864.2.w.b.107.17	yes	128
32.3	odd	8	inner	864.2.w.b.323.17	yes	128
96.35	even	8	inner	864.2.w.b.323.16	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.b.107.16	✓	128	1.1	even	1	trivial
864.2.w.b.107.17	yes	128	3.2	odd	2	inner
864.2.w.b.323.16	yes	128	96.35	even	8	inner
864.2.w.b.323.17	yes	128	32.3	odd	8	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0136252 - 1.41415i) q^{2} +(-1.99963 + 0.0385360i) q^{4} +(-0.327253 - 0.135553i) q^{5} +(1.35777 - 1.35777i) q^{7} +(0.0817409 + 2.82725i) q^{8} +O(q^{10})\)	\(q+(-0.0136252 - 1.41415i) q^{2} +(-1.99963 + 0.0385360i) q^{4} +(-0.327253 - 0.135553i) q^{5} +(1.35777 - 1.35777i) q^{7} +(0.0817409 + 2.82725i) q^{8} +(-0.187232 + 0.464631i) q^{10} +(3.85851 + 1.59825i) q^{11} +(-0.231385 - 0.558613i) q^{13} +(-1.93859 - 1.90159i) q^{14} +(3.99703 - 0.154115i) q^{16} +5.94707 q^{17} +(-5.21566 + 2.16040i) q^{19} +(0.659608 + 0.258444i) q^{20} +(2.20758 - 5.47828i) q^{22} +(5.60841 - 5.60841i) q^{23} +(-3.44681 - 3.44681i) q^{25} +(-0.786809 + 0.334824i) q^{26} +(-2.66271 + 2.76736i) q^{28} +(2.17035 + 5.23968i) q^{29} -1.38880i q^{31} +(-0.272402 - 5.65029i) q^{32} +(-0.0810299 - 8.41004i) q^{34} +(-0.628383 + 0.260285i) q^{35} +(2.77178 - 6.69167i) q^{37} +(3.12619 + 7.34629i) q^{38} +(0.356490 - 0.936304i) q^{40} +(-4.65385 - 4.65385i) q^{41} +(0.655749 - 1.58312i) q^{43} +(-7.77717 - 3.04721i) q^{44} +(-8.00753 - 7.85470i) q^{46} -2.50386i q^{47} +3.31292i q^{49} +(-4.82734 + 4.92127i) q^{50} +(0.484211 + 1.10810i) q^{52} +(2.06467 - 4.98454i) q^{53} +(-1.04606 - 1.04606i) q^{55} +(3.94973 + 3.72776i) q^{56} +(7.38011 - 3.14058i) q^{58} +(-1.31191 + 3.16723i) q^{59} +(9.16929 - 3.79804i) q^{61} +(-1.96397 + 0.0189226i) q^{62} +(-7.98664 + 0.462203i) q^{64} +0.214173i q^{65} +(-3.66131 - 8.83919i) q^{67} +(-11.8919 + 0.229176i) q^{68} +(0.376643 + 0.885080i) q^{70} +(1.84855 + 1.84855i) q^{71} +(3.57147 - 3.57147i) q^{73} +(-9.50077 - 3.82853i) q^{74} +(10.3461 - 4.52099i) q^{76} +(7.40902 - 3.06892i) q^{77} -8.73451 q^{79} +(-1.32893 - 0.491373i) q^{80} +(-6.51783 + 6.64464i) q^{82} +(3.89900 + 9.41302i) q^{83} +(-1.94620 - 0.806141i) q^{85} +(-2.24770 - 0.905756i) q^{86} +(-4.20324 + 11.0396i) q^{88} +(1.90777 - 1.90777i) q^{89} +(-1.07264 - 0.444301i) q^{91} +(-10.9986 + 11.4309i) q^{92} +(-3.54082 + 0.0341155i) q^{94} +1.99969 q^{95} +18.0271 q^{97} +(4.68496 - 0.0451392i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) \) 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

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