LMFDB - Embedded newform 864.2.bn.a.35.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(35,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("864.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, not 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:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			35.9
Character	$\chi$	$=$	864.35
Dual form			864.2.bn.a.395.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12313 + 0.859413i) q^{2} +(0.522820 - 1.93046i) q^{4} +(-3.20104 - 2.45624i) q^{5} +(2.32357 - 0.622598i) q^{7} +(1.07187 + 2.61746i) q^{8} +O(q^{10})$	\(q+(-1.12313 + 0.859413i) q^{2} +(0.522820 - 1.93046i) q^{4} +(-3.20104 - 2.45624i) q^{5} +(2.32357 - 0.622598i) q^{7} +(1.07187 + 2.61746i) q^{8} +(5.70609 + 0.00765608i) q^{10} +(-0.00383159 + 0.0291038i) q^{11} +(0.663576 - 0.0873614i) q^{13} +(-2.07459 + 2.69616i) q^{14} +(-3.45332 - 2.01856i) q^{16} +7.10921 q^{17} +(-4.43809 - 1.83832i) q^{19} +(-6.41524 + 4.89529i) q^{20} +(-0.0207088 - 0.0359801i) q^{22} +(0.732071 - 2.73212i) q^{23} +(2.91942 + 10.8954i) q^{25} +(-0.670199 + 0.668403i) q^{26} +(0.0129104 - 4.81105i) q^{28} +(-1.37882 - 1.79691i) q^{29} +(0.933304 - 0.538843i) q^{31} +(5.61329 - 0.700726i) q^{32} +(-7.98453 + 6.10974i) q^{34} +(-8.96708 - 3.71429i) q^{35} +(-2.70652 - 6.53412i) q^{37} +(6.56441 - 1.74949i) q^{38} +(2.99804 - 11.0114i) q^{40} +(-10.4042 - 2.78780i) q^{41} +(-9.14997 - 1.20462i) q^{43} +(0.0541803 + 0.0226128i) q^{44} +(1.52582 + 3.69767i) q^{46} +(-8.79455 - 5.07754i) q^{47} +(-1.05084 + 0.606706i) q^{49} +(-12.6425 - 9.72794i) q^{50} +(0.178284 - 1.32668i) q^{52} +(-0.361368 - 0.872419i) q^{53} +(0.0837510 - 0.0837510i) q^{55} +(4.12018 + 5.41451i) q^{56} +(3.09287 + 0.833182i) q^{58} +(0.669653 - 0.872709i) q^{59} +(2.75521 - 2.11415i) q^{61} +(-0.585129 + 1.40728i) q^{62} +(-5.70221 + 5.61113i) q^{64} +(-2.33871 - 1.35026i) q^{65} +(1.27632 - 0.168031i) q^{67} +(3.71684 - 13.7240i) q^{68} +(13.2633 - 3.53481i) q^{70} +(5.54582 - 5.54582i) q^{71} +(-1.91778 - 1.91778i) q^{73} +(8.65526 + 5.01261i) q^{74} +(-5.86912 + 7.60643i) q^{76} +(0.00921701 + 0.0700101i) q^{77} +(-4.14646 + 7.18188i) q^{79} +(6.09612 + 14.9437i) q^{80} +(14.0811 - 5.81047i) q^{82} +(8.96833 + 11.6878i) q^{83} +(-22.7568 - 17.4619i) q^{85} +(11.3118 - 6.51067i) q^{86} +(-0.0802850 + 0.0211663i) q^{88} +(-4.61864 - 4.61864i) q^{89} +(1.48747 - 0.616131i) q^{91} +(-4.89150 - 2.84164i) q^{92} +(14.2411 - 1.85544i) q^{94} +(9.69115 + 16.7856i) q^{95} +(6.69755 - 11.6005i) q^{97} +(0.658820 - 1.58452i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.12313	+	0.859413i	−0.794169	+	0.607696i
$2$	−1.12313	+	0.859413i	−0.794169	+	0.607696i
$3$		0			0
$3$		0			0
$4$	0.522820	−	1.93046i	0.261410	−	0.965228i
$5$	−3.20104	−	2.45624i	−1.43155	−	1.09847i	−0.978327	−	0.207067i	$-0.933608\pi$
$5$	−3.20104	−	2.45624i	−1.43155	−	1.09847i	−0.453221	−	0.891398i	$-0.649725\pi$
$6$		0			0
$7$	2.32357	−	0.622598i	0.878226	−	0.235320i	0.208584	−	0.978004i	$-0.433114\pi$
$7$	2.32357	−	0.622598i	0.878226	−	0.235320i	0.669641	+	0.742685i	$0.266448\pi$
$8$	1.07187	+	2.61746i	0.378962	+	0.925412i
$9$		0			0
$10$	5.70609	+	0.00765608i	1.80443	+	0.00242107i
$11$	−0.00383159	+	0.0291038i	−0.00115527	+	0.00877512i	−0.992013	−	0.126137i	$-0.959742\pi$
$11$	−0.00383159	+	0.0291038i	−0.00115527	+	0.00877512i	0.990858	+	0.134912i	$0.0430753\pi$
$12$		0			0
$13$	0.663576	−	0.0873614i	0.184043	−	0.0242297i	−0.0379414	−	0.999280i	$-0.512080\pi$
$13$	0.663576	−	0.0873614i	0.184043	−	0.0242297i	0.221984	+	0.975050i	$0.428747\pi$
$14$	−2.07459	+	2.69616i	−0.554457	+	0.720578i
$15$		0			0
$16$	−3.45332	−	2.01856i	−0.863329	−	0.504641i
$17$	7.10921			1.72424			0.862118	−	0.506708i	$-0.169138\pi$
$17$	7.10921			1.72424			0.862118	+	0.506708i	$0.169138\pi$
$18$		0			0
$19$	−4.43809	−	1.83832i	−1.01817	−	0.421739i	−0.189740	−	0.981834i	$-0.560765\pi$
$19$	−4.43809	−	1.83832i	−1.01817	−	0.421739i	−0.828428	+	0.560095i	$0.810765\pi$
$20$	−6.41524	+	4.89529i	−1.43449	+	1.09462i
$21$		0			0
$22$	−0.0207088	−	0.0359801i	−0.00441513	−	0.00767098i
$23$	0.732071	−	2.73212i	0.152647	−	0.569687i	−0.846648	−	0.532153i	$-0.821383\pi$
$23$	0.732071	−	2.73212i	0.152647	−	0.569687i	0.999295	−	0.0375341i	$-0.0119503\pi$
$24$		0			0
$25$	2.91942	+	10.8954i	0.583884	+	2.17909i
$26$	−0.670199	+	0.668403i	−0.131437	+	0.131085i
$27$		0			0
$28$	0.0129104	−	4.81105i	0.00243983	−	0.909203i
$29$	−1.37882	−	1.79691i	−0.256040	−	0.333678i	0.647592	−	0.761987i	$-0.275776\pi$
$29$	−1.37882	−	1.79691i	−0.256040	−	0.333678i	−0.903632	+	0.428309i	$0.859109\pi$
$30$		0			0
$31$	0.933304	−	0.538843i	0.167626	−	0.0967791i	−0.413840	−	0.910350i	$-0.635813\pi$
$31$	0.933304	−	0.538843i	0.167626	−	0.0967791i	0.581466	+	0.813571i	$0.302479\pi$
$32$	5.61329	−	0.700726i	0.992298	−	0.123872i
$33$		0			0
$34$	−7.98453	+	6.10974i	−1.36934	+	1.04781i
$35$	−8.96708	−	3.71429i	−1.51571	−	0.627829i
$36$		0			0
$37$	−2.70652	−	6.53412i	−0.444949	−	1.07420i	−0.974190	−	0.225730i	$-0.927523\pi$
$37$	−2.70652	−	6.53412i	−0.444949	−	1.07420i	0.529241	−	0.848472i	$-0.322477\pi$
$38$	6.56441	−	1.74949i	1.06489	−	0.283805i
$39$		0			0
$40$	2.99804	−	11.0114i	0.474032	−	1.74105i
$41$	−10.4042	−	2.78780i	−1.62487	−	0.435382i	−0.672441	−	0.740151i	$-0.734754\pi$
$41$	−10.4042	−	2.78780i	−1.62487	−	0.435382i	−0.952426	+	0.304769i	$0.901421\pi$
$42$		0			0
$43$	−9.14997	−	1.20462i	−1.39536	−	0.183702i	−0.604940	−	0.796271i	$-0.706803\pi$
$43$	−9.14997	−	1.20462i	−1.39536	−	0.183702i	−0.790418	+	0.612568i	$0.790136\pi$
$44$	0.0541803	+	0.0226128i	0.00816799	+	0.00340900i
$45$		0			0
$46$	1.52582	+	3.69767i	0.224969	+	0.545191i
$47$	−8.79455	−	5.07754i	−1.28282	−	0.740635i	−0.305454	−	0.952207i	$-0.598808\pi$
$47$	−8.79455	−	5.07754i	−1.28282	−	0.740635i	−0.977362	+	0.211572i	$0.932142\pi$
$48$		0			0
$49$	−1.05084	+	0.606706i	−0.150121	+	0.0866722i
$50$	−12.6425	−	9.72794i	−1.78793	−	1.37574i
$51$		0			0
$52$	0.178284	−	1.32668i	0.0247235	−	0.183977i
$53$	−0.361368	−	0.872419i	−0.0496377	−	0.119836i	0.897116	−	0.441796i	$-0.145658\pi$
$53$	−0.361368	−	0.872419i	−0.0496377	−	0.119836i	−0.946753	+	0.321960i	$0.895658\pi$
$54$		0			0
$55$	0.0837510	−	0.0837510i	0.0112930	−	0.0112930i
$56$	4.12018	+	5.41451i	0.550582	+	0.723544i
$57$		0			0
$58$	3.09287	+	0.833182i	0.406114	+	0.109402i
$59$	0.669653	−	0.872709i	0.0871814	−	0.113617i	−0.747726	−	0.664007i	$-0.768854\pi$
$59$	0.669653	−	0.872709i	0.0871814	−	0.113617i	0.834908	+	0.550390i	$0.185521\pi$
$60$		0			0
$61$	2.75521	−	2.11415i	0.352768	−	0.270689i	−0.417141	−	0.908842i	$-0.636968\pi$
$61$	2.75521	−	2.11415i	0.352768	−	0.270689i	0.769910	+	0.638153i	$0.220301\pi$
$62$	−0.585129	+	1.40728i	−0.0743114	+	0.178725i
$63$		0			0
$64$	−5.70221	+	5.61113i	−0.712776	+	0.701391i
$65$	−2.33871	−	1.35026i	−0.290082	−	0.167479i
$66$		0			0
$67$	1.27632	−	0.168031i	0.155927	−	0.0205282i	−0.0521584	−	0.998639i	$-0.516610\pi$
$67$	1.27632	−	0.168031i	0.155927	−	0.0205282i	0.208086	+	0.978111i	$0.433277\pi$
$68$	3.71684	−	13.7240i	0.450733	−	1.66428i
$69$		0			0
$70$	13.2633	−	3.53481i	1.58526	−	0.422491i
$71$	5.54582	−	5.54582i	0.658167	−	0.658167i	−0.296779	−	0.954946i	$-0.595912\pi$
$71$	5.54582	−	5.54582i	0.658167	−	0.658167i	0.954946	+	0.296779i	$0.0959124\pi$
$72$		0			0
$73$	−1.91778	−	1.91778i	−0.224459	−	0.224459i	0.585914	−	0.810373i	$-0.300736\pi$
$73$	−1.91778	−	1.91778i	−0.224459	−	0.224459i	−0.810373	+	0.585914i	$0.800736\pi$
$74$	8.65526	+	5.01261i	1.00615	+	0.582705i
$75$		0			0
$76$	−5.86912	+	7.60643i	−0.673234	+	0.872518i
$77$	0.00921701	+	0.0700101i	0.00105038	+	0.00797839i
$78$		0			0
$79$	−4.14646	+	7.18188i	−0.466513	+	0.808024i	−0.999268	−	0.0382451i	$-0.987823\pi$
$79$	−4.14646	+	7.18188i	−0.466513	+	0.808024i	0.532755	+	0.846269i	$0.321157\pi$
$80$	6.09612	+	14.9437i	0.681567	+	1.67075i
$81$		0			0
$82$	14.0811	−	5.81047i	1.55500	−	0.641659i
$83$	8.96833	+	11.6878i	0.984402	+	1.28290i	0.959055	+	0.283219i	$0.0914023\pi$
$83$	8.96833	+	11.6878i	0.984402	+	1.28290i	0.0253466	+	0.999679i	$0.491931\pi$
$84$		0			0
$85$	−22.7568	−	17.4619i	−2.46833	−	1.89401i
$86$	11.3118	−	6.51067i	1.21979	−	0.702063i
$87$		0			0
$88$	−0.0802850	+	0.0211663i	−0.00855841	+	0.00225634i
$89$	−4.61864	−	4.61864i	−0.489574	−	0.489574i	0.418597	−	0.908172i	$-0.362522\pi$
$89$	−4.61864	−	4.61864i	−0.489574	−	0.489574i	−0.908172	+	0.418597i	$0.862522\pi$
$90$		0			0
$91$	1.48747	−	0.616131i	0.155929	−	0.0645880i
$92$	−4.89150	−	2.84164i	−0.509975	−	0.296261i
$93$		0			0
$94$	14.2411	−	1.85544i	1.46885	−	0.191374i
$95$	9.69115	+	16.7856i	0.994291	+	1.72216i
$96$		0			0
$97$	6.69755	−	11.6005i	0.680034	−	1.17785i	−0.294937	−	0.955517i	$-0.595299\pi$
$97$	6.69755	−	11.6005i	0.680034	−	1.17785i	0.974970	−	0.222336i	$-0.0713682\pi$
$98$	0.658820	−	1.58452i	0.0665509	−	0.160060i
$99$		0			0
$100$	22.5595	+	0.0605379i	2.25595	+	0.00605379i
$101$	0.808369	−	6.14017i	0.0804358	−	0.610970i	−0.902990	−	0.429661i	$-0.858633\pi$
$101$	0.808369	−	6.14017i	0.0804358	−	0.610970i	0.983426	−	0.181309i	$-0.0580335\pi$
$102$		0			0
$103$	−1.07721	+	4.02021i	−0.106141	+	0.396123i	−0.998472	−	0.0552582i	$-0.982402\pi$
$103$	−1.07721	+	4.02021i	−0.106141	+	0.396123i	0.892331	+	0.451381i	$0.149068\pi$
$104$	0.939929	+	1.64324i	0.0921676	+	0.161133i
$105$		0			0
$106$	1.15563	+	0.669272i	0.112245	+	0.0650055i
$107$	−15.3286	+	6.34933i	−1.48188	+	0.613813i	−0.969531	−	0.244967i	$-0.921223\pi$
$107$	−15.3286	+	6.34933i	−1.48188	+	0.613813i	−0.512344	+	0.858780i	$0.671223\pi$
$108$		0			0
$109$	−0.274825	+	0.663485i	−0.0263234	+	0.0635503i	−0.936495	−	0.350682i	$-0.885950\pi$
$109$	−0.274825	+	0.663485i	−0.0263234	+	0.0635503i	0.910171	+	0.414232i	$0.135950\pi$
$110$	−0.0220862	+	0.166040i	−0.00210584	+	0.0158313i
$111$		0			0
$112$	−9.28077	−	2.54024i	−0.876950	−	0.240030i
$113$	0.165657	+	0.286926i	0.0155837	+	0.0269917i	0.873712	−	0.486443i	$-0.161706\pi$
$113$	0.165657	+	0.286926i	0.0155837	+	0.0269917i	−0.858128	+	0.513435i	$0.828373\pi$
$114$		0			0
$115$	−9.05415	+	6.94749i	−0.844304	+	0.647857i
$116$	−4.18973	+	1.72229i	−0.389007	+	0.159910i
$117$		0			0
$118$	−0.00208730	+	1.55567i	−0.000192152	+	0.143211i
$119$	16.5187	−	4.42618i	1.51427	−	0.405747i
$120$		0			0
$121$	10.6244	+	2.84679i	0.965850	+	0.258799i
$122$	−1.27752	+	4.74231i	−0.115661	+	0.429349i
$123$		0			0
$124$	−0.552263	−	2.08342i	−0.0495947	−	0.187097i
$125$	9.69635	−	23.4091i	0.867268	−	2.09377i
$126$		0			0
$127$		−	4.17344i		−	0.370333i	−0.982707	−	0.185167i	$-0.940718\pi$
$127$		−	4.17344i		−	0.370333i	0.982707	−	0.185167i	$-0.0592824\pi$
$128$	1.58202	−	11.2026i	0.139832	−	0.990175i
$129$		0			0
$130$	3.78709	−	0.493412i	0.332150	−	0.0432751i
$131$	2.26618	+	17.2134i	0.197997	+	1.50394i	0.745145	+	0.666902i	$0.232380\pi$
$131$	2.26618	+	17.2134i	0.197997	+	1.50394i	−0.547148	+	0.837036i	$0.684286\pi$
$132$		0			0
$133$	−11.4567	−	1.50831i	−0.993425	−	0.130787i
$134$	−1.28906	+	1.28560i	−0.111358	+	0.111059i
$135$		0			0
$136$	7.62011	+	18.6081i	0.653419	+	1.59563i
$137$	−2.83464	−	10.5790i	−0.242180	−	0.903826i	−0.974780	−	0.223168i	$-0.928360\pi$
$137$	−2.83464	−	10.5790i	−0.242180	−	0.903826i	0.732601	−	0.680659i	$-0.238306\pi$
$138$		0			0
$139$	4.18985	−	5.46031i	0.355378	−	0.463138i	−0.581116	−	0.813821i	$-0.697384\pi$
$139$	4.18985	−	5.46031i	0.355378	−	0.463138i	0.936494	+	0.350683i	$0.114050\pi$
$140$	−11.8584	+	15.3686i	−1.00222	+	1.29889i
$141$		0			0
$142$	−1.46250	+	10.9948i	−0.122730	+	0.922662i
$143$			0.0196473i			0.00164299i
$144$		0			0
$145$			9.13870i			0.758927i
$146$	3.80207	+	0.505743i	0.314662	+	0.0418556i
$147$		0			0
$148$	−14.0288	+	1.80865i	−1.15316	+	0.148670i
$149$	4.88901	−	6.37148i	0.400523	−	0.521972i	−0.548935	−	0.835865i	$-0.684967\pi$
$149$	4.88901	−	6.37148i	0.400523	−	0.521972i	0.949458	+	0.313893i	$0.101633\pi$
$150$		0			0
$151$	−2.44112	−	9.11039i	−0.198656	−	0.741393i	−0.991290	−	0.131696i	$-0.957958\pi$
$151$	−2.44112	−	9.11039i	−0.198656	−	0.741393i	0.792635	−	0.609697i	$-0.208709\pi$
$152$	0.0546908	−	13.5870i	0.00443601	−	1.10205i
$153$		0			0
$154$	−0.0705194	−	0.0707089i	−0.00568262	−	0.00569789i
$155$	−4.31107	−	0.567564i	−0.346274	−	0.0455878i
$156$		0			0
$157$	−2.21454	−	16.8211i	−0.176740	−	1.34247i	−0.818031	−	0.575174i	$-0.804934\pi$
$157$	−2.21454	−	16.8211i	−0.176740	−	1.34247i	0.641291	−	0.767297i	$-0.278399\pi$
$158$	−1.51520	−	11.6297i	−0.120543	−	0.925206i
$159$		0			0
$160$	−19.6895	−	11.5445i	−1.55659	−	0.912677i
$161$		−	6.80406i		−	0.536235i
$162$		0			0
$163$	−4.20303	+	10.1470i	−0.329207	+	0.794776i	0.669445	+	0.742862i	$0.266532\pi$
$163$	−4.20303	+	10.1470i	−0.329207	+	0.794776i	−0.998652	+	0.0519141i	$0.983468\pi$
$164$	−10.8213	+	18.6274i	−0.844999	+	1.45455i
$165$		0			0
$166$	−20.1172	−	5.41932i	−1.56139	−	0.420620i
$167$	1.07478	+	0.287986i	0.0831689	+	0.0222850i	0.300164	−	0.953888i	$-0.402959\pi$
$167$	1.07478	+	0.287986i	0.0831689	+	0.0222850i	−0.216995	+	0.976173i	$0.569625\pi$
$168$		0			0
$169$	−12.1243	+	3.24871i	−0.932641	+	0.249900i
$170$	40.5658	+	0.0544287i	3.11125	+	0.00417449i
$171$		0			0
$172$	−7.10925	+	17.0338i	−0.542075	+	1.29882i
$173$	−6.92993	+	5.31752i	−0.526873	+	0.404284i	−0.837657	−	0.546197i	$-0.816075\pi$
$173$	−6.92993	+	5.31752i	−0.526873	+	0.404284i	0.310784	+	0.950481i	$0.399408\pi$
$174$		0			0
$175$	13.5669	+	23.4986i	1.02556	+	1.77633i
$176$	0.0719795	−	0.0927703i	0.00542566	−	0.00699283i
$177$		0			0
$178$	9.15662	+	1.21799i	0.686318	+	0.0912924i
$179$	1.03794	−	2.50582i	0.0775795	−	0.187293i	−0.880331	−	0.474359i	$-0.842680\pi$
$179$	1.03794	−	2.50582i	0.0775795	−	0.187293i	0.957911	+	0.287066i	$0.0926798\pi$
$180$		0			0
$181$	8.80197	−	3.64590i	0.654245	−	0.270997i	−0.0307694	−	0.999527i	$-0.509796\pi$
$181$	8.80197	−	3.64590i	0.654245	−	0.270997i	0.685015	+	0.728529i	$0.259796\pi$
$182$	−1.14111	+	1.97034i	−0.0845844	+	0.146052i
$183$		0			0
$184$	7.93591	−	1.01230i	0.585043	−	0.0746279i
$185$	−7.38571	+	27.5638i	−0.543008	+	2.02653i
$186$		0			0
$187$	−0.0272395	+	0.206905i	−0.00199195	+	0.0151304i
$188$	−14.3999	+	14.3228i	−1.05022	+	1.04460i
$189$		0			0
$190$	−25.3101	−	10.5236i	−1.83619	−	0.763462i
$191$	0.999615	−	1.73138i	0.0723296	−	0.125279i	−0.827592	−	0.561330i	$-0.810290\pi$
$191$	0.999615	−	1.73138i	0.0723296	−	0.125279i	0.899922	+	0.436051i	$0.143623\pi$
$192$		0			0
$193$	0.229439	+	0.397400i	0.0165154	+	0.0286055i	0.874165	−	0.485629i	$-0.161409\pi$
$193$	0.229439	+	0.397400i	0.0165154	+	0.0286055i	−0.857650	+	0.514235i	$0.828076\pi$
$194$	2.44743	+	18.7848i	0.175715	+	1.34867i
$195$		0			0
$196$	0.621815	+	2.34581i	0.0444154	+	0.167558i
$197$	−18.5148	+	7.66907i	−1.31912	+	0.546399i	−0.927533	−	0.373741i	$-0.878075\pi$
$197$	−18.5148	+	7.66907i	−1.31912	+	0.546399i	−0.391590	+	0.920140i	$0.628075\pi$
$198$		0			0
$199$	−2.98114	−	2.98114i	−0.211327	−	0.211327i	0.593504	−	0.804831i	$-0.297744\pi$
$199$	−2.98114	−	2.98114i	−0.211327	−	0.211327i	−0.804831	+	0.593504i	$0.797744\pi$
$200$	−25.3891	+	19.3199i	−1.79528	+	1.36612i
$201$		0			0
$202$	4.36904	+	7.59091i	0.307405	+	0.534094i
$203$	−4.32253	−	3.31679i	−0.303382	−	0.232793i
$204$		0			0
$205$	26.4568	+	34.4792i	1.84782	+	2.40813i
$206$	−2.24517	−	5.44097i	−0.156429	−	0.379090i
$207$		0			0
$208$	−2.46788	−	1.03778i	−0.171117	−	0.0719573i
$209$	0.0705070	−	0.122122i	0.00487707	−	0.00844733i
$210$		0			0
$211$	1.29409	+	9.82957i	0.0890886	+	0.676695i	0.976469	+	0.215657i	$0.0691894\pi$
$211$	1.29409	+	9.82957i	0.0890886	+	0.676695i	−0.887380	+	0.461038i	$0.847477\pi$
$212$	−1.87310	+	0.241486i	−0.128645	+	0.0165853i
$213$		0			0
$214$	11.7593	−	20.3047i	0.803848	−	1.38800i
$215$	26.3306	+	26.3306i	1.79573	+	1.79573i
$216$		0			0
$217$	1.83311	−	1.83311i	0.124440	−	0.124440i
$218$	−0.261545	−	0.981364i	−0.0177141	−	0.0664664i
$219$		0			0
$220$	−0.117891	−	0.205464i	−0.00794820	−	0.0138524i
$221$	4.71750	−	0.621070i	0.317333	−	0.0417777i
$222$		0			0
$223$	6.73338	+	3.88752i	0.450900	+	0.260327i	0.708210	−	0.706001i	$-0.249503\pi$
$223$	6.73338	+	3.88752i	0.450900	+	0.260327i	−0.257310	+	0.966329i	$0.582836\pi$
$224$	12.6066	−	5.12300i	0.842312	−	0.342295i
$225$		0			0
$226$	−0.432641	−	0.179886i	−0.0287789	−	0.0119659i
$227$	16.9215	−	12.9843i	1.12312	−	0.861799i	0.131540	−	0.991311i	$-0.458008\pi$
$227$	16.9215	−	12.9843i	1.12312	−	0.861799i	0.991578	+	0.129512i	$0.0413411\pi$
$228$		0			0
$229$	14.8124	−	19.3039i	0.978832	−	1.27564i	0.0176153	−	0.999845i	$-0.494393\pi$
$229$	14.8124	−	19.3039i	0.978832	−	1.27564i	0.961217	−	0.275794i	$-0.0889407\pi$
$230$	4.19818	−	15.5842i	0.276820	−	1.02759i
$231$		0			0
$232$	3.22544	−	5.53505i	0.211760	−	0.363394i
$233$	−14.1779	+	14.1779i	−0.928826	+	0.928826i	−0.997630	−	0.0688041i	$-0.978082\pi$
$233$	−14.1779	+	14.1779i	−0.928826	+	0.928826i	0.0688041	+	0.997630i	$0.478082\pi$
$234$		0			0
$235$	15.6800	+	37.8549i	1.02285	+	2.46938i
$236$	−1.33462	−	1.74901i	−0.0868762	−	0.113851i
$237$		0			0
$238$	−14.7487	+	19.1675i	−0.956015	+	1.24245i
$239$	13.7410	−	7.93337i	0.888831	−	0.513167i	0.0152710	−	0.999883i	$-0.495139\pi$
$239$	13.7410	−	7.93337i	0.888831	−	0.513167i	0.873560	+	0.486717i	$0.161806\pi$
$240$		0			0
$241$	−12.1765	−	7.03013i	−0.784360	−	0.452850i	0.0536132	−	0.998562i	$-0.482926\pi$
$241$	−12.1765	−	7.03013i	−0.784360	−	0.452850i	−0.837973	+	0.545711i	$0.816260\pi$
$242$	−14.3790	+	5.93340i	−0.924320	+	0.381414i
$243$		0			0
$244$	−2.64079	−	6.42413i	−0.169059	−	0.411263i
$245$	4.85401	+	0.639043i	0.310111	+	0.0408269i
$246$		0			0
$247$	−3.10561	−	0.832146i	−0.197605	−	0.0529482i
$248$	2.41078	+	1.86532i	0.153085	+	0.118448i
$249$		0			0
$250$	9.22782	+	34.6245i	0.583619	+	2.18984i
$251$	−6.65731	−	16.0722i	−0.420205	−	1.01447i	−0.982287	−	0.187384i	$-0.939999\pi$
$251$	−6.65731	−	16.0722i	−0.420205	−	1.01447i	0.562081	−	0.827082i	$-0.310001\pi$
$252$		0			0
$253$	0.0767102	+	0.0317744i	0.00482273	+	0.00199764i
$254$	3.58671	+	4.68730i	0.225050	+	0.294107i
$255$		0			0
$256$	7.85081	+	13.9415i	0.490676	+	0.871342i
$257$	−0.923715	+	0.533307i	−0.0576198	+	0.0332668i	−0.528533	−	0.848913i	$-0.677258\pi$
$257$	−0.923715	+	0.533307i	−0.0576198	+	0.0332668i	0.470913	+	0.882179i	$0.343924\pi$
$258$		0			0
$259$	−10.3569	−	13.4974i	−0.643547	−	0.838686i
$260$	−3.82934	+	3.80884i	−0.237485	+	0.236214i
$261$		0			0
$262$	−17.3386	−	17.3852i	−1.07118	−	1.07406i
$263$	5.24775	+	19.5849i	0.323590	+	1.20765i	0.915722	+	0.401813i	$0.131620\pi$
$263$	5.24775	+	19.5849i	0.323590	+	1.20765i	−0.592132	+	0.805841i	$0.701713\pi$
$264$		0			0
$265$	−0.986122	+	3.68026i	−0.0605770	+	0.226076i
$266$	14.1636	−	8.15205i	0.868427	−	0.499834i
$267$		0			0
$268$	0.342910	−	2.55173i	0.0209466	−	0.155872i
$269$	23.0590	+	9.55137i	1.40593	+	0.582357i	0.951285	−	0.308313i	$-0.0997644\pi$
$269$	23.0590	+	9.55137i	1.40593	+	0.582357i	0.454650	+	0.890670i	$0.349764\pi$
$270$		0			0
$271$	−7.36251			−0.447241			−0.223620	−	0.974676i	$-0.571788\pi$
$271$	−7.36251			−0.447241			−0.223620	+	0.974676i	$0.571788\pi$
$272$	−24.5504	−	14.3504i	−1.48858	−	0.870120i
$273$		0			0
$274$	12.2754	+	9.44544i	0.741584	+	0.570620i
$275$	−0.328284	+	0.0432194i	−0.0197963	+	0.00260623i
$276$		0			0
$277$	0.000335069	−	0.00254510i	2.01323e−5	−	0.000152920i	−0.991435	−	0.130603i	$-0.958309\pi$
$277$	0.000335069	−	0.00254510i	2.01323e−5	−	0.000152920i	0.991455	+	0.130450i	$0.0416421\pi$
$278$	−0.0130597	+	9.73342i	−0.000783269	+	0.583772i
$279$		0			0
$280$	0.110502	−	27.4522i	0.00660373	−	1.64058i
$281$	18.1188	−	4.85492i	1.08088	−	0.289620i	0.325922	−	0.945397i	$-0.394325\pi$
$281$	18.1188	−	4.85492i	1.08088	−	0.289620i	0.754955	+	0.655777i	$0.227659\pi$
$282$		0			0
$283$	−3.93854	−	3.02215i	−0.234122	−	0.179648i	0.485037	−	0.874494i	$-0.338806\pi$
$283$	−3.93854	−	3.02215i	−0.234122	−	0.179648i	−0.719159	+	0.694845i	$0.755473\pi$
$284$	−7.80649	−	13.6054i	−0.463230	−	0.807333i
$285$		0			0
$286$	−0.0168851	−	0.0220664i	−0.000998439	−	0.00130481i
$287$	−25.9106			−1.52945
$288$		0			0
$289$	33.5408			1.97299
$290$	−7.85391	−	10.2639i	−0.461198	−	0.602717i
$291$		0			0
$292$	−4.70484	+	2.69953i	−0.275330	+	0.157978i
$293$	18.2017	+	13.9666i	1.06335	+	0.815939i	0.983507	−	0.180869i	$-0.0578909\pi$
$293$	18.2017	+	13.9666i	1.06335	+	0.815939i	0.0798448	+	0.996807i	$0.474558\pi$
$294$		0			0
$295$	−4.28717	+	1.14874i	−0.249609	+	0.0668825i
$296$	14.2018	−	14.0879i	0.825461	−	0.818843i
$297$		0			0
$298$	−0.0152390	+	11.3576i	−0.000882771	+	0.657931i
$299$	0.247102	−	1.87693i	0.0142903	−	0.108545i
$300$		0			0
$301$	−22.0106	+	2.89775i	−1.26867	+	0.167023i
$302$	10.5713	+	8.13417i	0.608308	+	0.468069i
$303$		0			0
$304$	11.6154	+	15.3069i	0.666188	+	0.877909i
$305$	−14.0124			−0.802347
$306$		0			0
$307$	12.7843	+	5.29544i	0.729640	+	0.302227i	0.716404	−	0.697686i	$-0.245787\pi$
$307$	12.7843	+	5.29544i	0.729640	+	0.302227i	0.0132358	+	0.999912i	$0.495787\pi$
$308$	0.139970	+	0.0188097i	0.00797555	+	0.00107178i
$309$		0			0
$310$	5.32965	−	3.06755i	0.302704	−	0.174225i
$311$	−3.77980	+	14.1064i	−0.214333	+	0.799900i	0.772068	+	0.635540i	$0.219223\pi$
$311$	−3.77980	+	14.1064i	−0.214333	+	0.799900i	−0.986400	+	0.164360i	$0.947444\pi$
$312$		0			0
$313$	−1.09566	−	4.08906i	−0.0619305	−	0.231128i	0.928023	−	0.372524i	$-0.121508\pi$
$313$	−1.09566	−	4.08906i	−0.0619305	−	0.231128i	−0.989953	+	0.141396i	$0.954841\pi$
$314$	16.9435	+	16.9890i	0.956176	+	0.958746i
$315$		0			0
$316$	11.6964	+	11.7594i	0.657976	+	0.661517i
$317$	−5.45490	−	7.10897i	−0.306378	−	0.399279i	0.614635	−	0.788812i	$-0.289303\pi$
$317$	−5.45490	−	7.10897i	−0.306378	−	0.399279i	−0.921013	+	0.389532i	$0.872637\pi$
$318$		0			0
$319$	0.0575800	−	0.0332438i	0.00322386	−	0.00186130i
$320$	32.0353	−	3.95543i	1.79083	−	0.221115i
$321$		0			0
$322$	5.84749	+	7.64181i	0.325868	+	0.425861i
$323$	−31.5513	−	13.0690i	−1.75556	−	0.727178i
$324$		0			0
$325$	2.88910	+	6.97490i	0.160258	+	0.386898i
$326$	−3.99994	−	15.0085i	−0.221536	−	0.831245i
$327$		0			0
$328$	−3.85496	−	30.2208i	−0.212854	−	1.66867i
$329$	−23.5960	−	6.32252i	−1.30089	−	0.348572i
$330$		0			0
$331$	5.30380	+	0.698259i	0.291523	+	0.0383798i	0.274869	−	0.961482i	$-0.411365\pi$
$331$	5.30380	+	0.698259i	0.291523	+	0.0383798i	0.0166538	+	0.999861i	$0.494699\pi$
$332$	27.2515	−	11.2024i	1.49562	−	0.614810i
$333$		0			0
$334$	−1.45461	+	0.600234i	−0.0795928	+	0.0328434i
$335$	−4.49827	−	2.59708i	−0.245767	−	0.141894i
$336$		0			0
$337$	−0.951714	+	0.549472i	−0.0518432	+	0.0299317i	−0.525698	−	0.850672i	$-0.676196\pi$
$337$	−0.951714	+	0.549472i	−0.0518432	+	0.0299317i	0.473854	+	0.880603i	$0.342862\pi$
$338$	10.8252	−	14.0685i	0.588811	−	0.765226i
$339$		0			0
$340$	−45.6072	+	34.8016i	−2.47340	+	1.88738i
$341$	0.0121063	+	0.0292273i	0.000655596	+	0.00158275i
$342$		0			0
$343$	−13.9708	+	13.9708i	−0.754350	+	0.754350i
$344$	−6.65450	−	25.2409i	−0.358787	−	1.36090i
$345$		0			0
$346$	3.21323	−	11.9279i	0.172744	−	0.641248i
$347$	10.4846	−	13.6638i	0.562844	−	0.733512i	−0.422069	−	0.906564i	$-0.638696\pi$
$347$	10.4846	−	13.6638i	0.562844	−	0.733512i	0.984913	+	0.173052i	$0.0553627\pi$
$348$		0			0
$349$	8.59962	−	6.59872i	0.460327	−	0.353222i	−0.352416	−	0.935843i	$-0.614640\pi$
$349$	8.59962	−	6.59872i	0.460327	−	0.353222i	0.812743	+	0.582622i	$0.197973\pi$
$350$	−35.4324	−	14.7323i	−1.89394	−	0.787475i
$351$		0			0
$352$	−0.00111401	+	0.166053i	−5.93771e−5	+	0.00885064i
$353$	−9.62174	−	5.55512i	−0.512114	−	0.295669i	0.221588	−	0.975140i	$-0.428876\pi$
$353$	−9.62174	−	5.55512i	−0.512114	−	0.295669i	−0.733702	+	0.679471i	$0.762209\pi$
$354$		0			0
$355$	−31.3742	+	4.13050i	−1.66517	+	0.219224i
$356$	−11.3308	+	6.50136i	−0.600531	+	0.344571i
$357$		0			0
$358$	0.987789	+	3.70637i	0.0522063	+	0.195887i
$359$	4.94376	−	4.94376i	0.260922	−	0.260922i	−0.564507	−	0.825429i	$-0.690934\pi$
$359$	4.94376	−	4.94376i	0.260922	−	0.260922i	0.825429	+	0.564507i	$0.190934\pi$
$360$		0			0
$361$	2.88224	+	2.88224i	0.151697	+	0.151697i
$362$	−6.75239	+	11.6593i	−0.354898	+	0.612800i
$363$		0			0
$364$	−0.411733	−	3.19362i	−0.0215807	−	0.167391i
$365$	1.42835	+	10.8494i	0.0747634	+	0.567884i
$366$		0			0
$367$	17.2455	−	29.8701i	0.900210	−	1.55921i	0.0729879	−	0.997333i	$-0.476747\pi$
$367$	17.2455	−	29.8701i	0.900210	−	1.55921i	0.827222	−	0.561876i	$-0.189920\pi$
$368$	−8.04304	+	7.95716i	−0.419272	+	0.414796i
$369$		0			0
$370$	−15.3936	−	37.3050i	−0.800277	−	1.93939i
$371$	−1.38283	−	1.80214i	−0.0717929	−	0.0935623i
$372$		0			0
$373$	−1.77020	−	1.35832i	−0.0916573	−	0.0703311i	0.561916	−	0.827194i	$-0.310064\pi$
$373$	−1.77020	−	1.35832i	−0.0916573	−	0.0703311i	−0.653574	+	0.756863i	$0.726731\pi$
$374$	−0.147223	−	0.255790i	−0.00761273	−	0.0132266i
$375$		0			0
$376$	3.86368	−	28.4618i	0.199254	−	1.46781i
$377$	−1.07193	−	1.07193i	−0.0552073	−	0.0552073i
$378$		0			0
$379$	−9.65470	+	3.99911i	−0.495928	+	0.205420i	−0.616607	−	0.787271i	$-0.711493\pi$
$379$	−9.65470	+	3.99911i	−0.495928	+	0.205420i	0.120678	+	0.992692i	$0.461493\pi$
$380$	37.4705	−	9.93251i	1.92220	−	0.509527i
$381$		0			0
$382$	0.365280	+	2.80364i	0.0186894	+	0.143447i
$383$	−16.3573	−	28.3316i	−0.835817	−	1.44768i	−0.893364	−	0.449334i	$-0.851661\pi$
$383$	−16.3573	−	28.3316i	−0.835817	−	1.44768i	0.0575467	−	0.998343i	$-0.481672\pi$
$384$		0			0
$385$	0.142458	−	0.246744i	0.00726033	−	0.0125753i
$386$	−0.599219	−	0.249147i	−0.0304995	−	0.0126813i
$387$		0			0
$388$	−18.8926	−	18.9943i	−0.959129	−	0.964290i
$389$	2.88575	−	21.9195i	0.146314	−	1.11136i	−0.747929	−	0.663779i	$-0.768952\pi$
$389$	2.88575	−	21.9195i	0.146314	−	1.11136i	0.894242	−	0.447583i	$-0.147715\pi$
$390$		0			0
$391$	5.20444	−	19.4232i	0.263200	−	0.982275i
$392$	−2.71439	−	2.10024i	−0.137098	−	0.106078i
$393$		0			0
$394$	14.2035	−	24.5252i	0.715563	−	1.23556i
$395$	30.9134	−	12.8048i	1.55542	−	0.644277i
$396$		0			0
$397$	9.34212	−	22.5539i	0.468867	−	1.13195i	−0.495791	−	0.868442i	$-0.665122\pi$
$397$	9.34212	−	22.5539i	0.468867	−	1.13195i	0.964658	−	0.263504i	$-0.0848783\pi$
$398$	5.91021	+	0.786163i	0.296252	+	0.0394068i
$399$		0			0
$400$	11.9114	−	43.5184i	0.595571	−	2.17592i
$401$	−5.01523	−	8.68663i	−0.250448	−	0.433789i	0.713201	−	0.700960i	$-0.247245\pi$
$401$	−5.01523	−	8.68663i	−0.250448	−	0.433789i	−0.963649	+	0.267170i	$0.913911\pi$
$402$		0			0
$403$	0.572244	−	0.439098i	0.0285055	−	0.0218730i
$404$	−11.4307	−	4.77073i	−0.568699	−	0.237353i
$405$		0			0
$406$	7.70524	+	0.0103384i	0.382404	+	0.000513087i
$407$	0.200538	−	0.0537339i	0.00994029	−	0.00266349i
$408$		0			0
$409$	20.9411	+	5.61115i	1.03547	+	0.277454i	0.736235	−	0.676725i	$-0.236602\pi$
$409$	20.9411	+	5.61115i	1.03547	+	0.277454i	0.299236	+	0.954179i	$0.403268\pi$
$410$	−59.3461	−	15.9871i	−2.93090	−	0.789548i
$411$		0			0
$412$	7.19764	+	4.18136i	0.354603	+	0.206001i
$413$	1.01264	−	2.44472i	0.0498286	−	0.120297i
$414$		0			0
$415$		−	59.4413i		−	2.91786i
$416$	3.66362	−	0.955369i	0.179624	−	0.0468408i
$417$		0			0
$418$	0.0257647	+	0.197753i	0.00126019	+	0.00967239i
$419$	0.00739172	+	0.0561457i	0.000361109	+	0.00274289i	0.991624	−	0.129155i	$-0.0412264\pi$
$419$	0.00739172	+	0.0561457i	0.000361109	+	0.00274289i	−0.991263	+	0.131898i	$0.957893\pi$
$420$		0			0
$421$	−3.16906	−	0.417214i	−0.154450	−	0.0203338i	0.0529044	−	0.998600i	$-0.483152\pi$
$421$	−3.16906	−	0.417214i	−0.154450	−	0.0203338i	−0.207355	+	0.978266i	$0.566485\pi$
$422$	−9.90107	−	9.92768i	−0.481977	−	0.483272i
$423$		0			0
$424$	1.89619	−	1.88098i	0.0920870	−	0.0913486i
$425$	20.7548	+	77.4579i	1.00675	+	3.75726i
$426$		0			0
$427$	5.08565	−	6.62775i	0.246112	−	0.320739i
$428$	4.24298	+	32.9108i	0.205092	+	1.59080i
$429$		0			0
$430$	−52.2014	−	6.94371i	−2.51737	−	0.334855i
$431$			12.7755i			0.615376i	0.951487	+	0.307688i	$0.0995552\pi$
$431$			12.7755i			0.615376i	−0.951487	+	0.307688i	$0.900445\pi$
$432$		0			0
$433$		−	33.4527i		−	1.60763i	−0.594877	−	0.803817i	$-0.702799\pi$
$433$		−	33.4527i		−	1.60763i	0.594877	−	0.803817i	$-0.297201\pi$
$434$	−0.483415	+	3.63421i	−0.0232047	+	0.174448i
$435$		0			0
$436$	1.13714	+	0.877420i	0.0544594	+	0.0420208i
$437$	−8.27151	+	10.7796i	−0.395680	+	0.515661i
$438$		0			0
$439$	8.91720	+	33.2794i	0.425595	+	1.58834i	0.762621	+	0.646846i	$0.223912\pi$
$439$	8.91720	+	33.2794i	0.425595	+	1.58834i	−0.337026	+	0.941495i	$0.609421\pi$
$440$	0.308985	+	0.129445i	0.0147303	+	0.00617106i
$441$		0			0
$442$	−4.76458	+	4.75182i	−0.226628	+	0.226021i
$443$	16.1746	+	2.12943i	0.768479	+	0.101172i	0.504565	−	0.863374i	$-0.331653\pi$
$443$	16.1746	+	2.12943i	0.768479	+	0.101172i	0.263915	+	0.964546i	$0.414986\pi$
$444$		0			0
$445$	3.43994	+	26.1289i	0.163069	+	1.23863i
$446$	−10.9034	+	1.42058i	−0.516291	+	0.0672664i
$447$		0			0
$448$	−9.75599	+	16.5880i	−0.460927	+	0.783710i
$449$			18.4415i			0.870309i	0.900356	+	0.435154i	$0.143306\pi$
$449$			18.4415i			0.870309i	−0.900356	+	0.435154i	$0.856694\pi$
$450$		0			0
$451$	0.121000	−	0.292121i	0.00569768	−	0.0137554i
$452$	0.640507	−	0.169782i	0.0301269	−	0.00798589i
$453$		0			0
$454$	−7.84606	+	29.1255i	−0.368234	+	1.36693i
$455$	−6.27482	−	1.68133i	−0.294168	−	0.0788221i
$456$		0			0
$457$	21.2108	−	5.68341i	0.992198	−	0.265859i	0.274025	−	0.961723i	$-0.411645\pi$
$457$	21.2108	−	5.68341i	0.992198	−	0.265859i	0.718174	+	0.695864i	$0.244978\pi$
$458$	−0.0461701	+	34.4107i	−0.00215739	+	1.60791i
$459$		0			0
$460$	8.67813	+	21.1109i	0.404620	+	0.984302i
$461$	32.5741	−	24.9950i	1.51713	−	1.16413i	0.580270	−	0.814424i	$-0.302947\pi$
$461$	32.5741	−	24.9950i	1.51713	−	1.16413i	0.936858	−	0.349709i	$-0.113720\pi$
$462$		0			0
$463$	2.55376	+	4.42324i	0.118683	+	0.205566i	0.919246	−	0.393683i	$-0.128799\pi$
$463$	2.55376	+	4.42324i	0.118683	+	0.205566i	−0.800563	+	0.599249i	$0.795466\pi$
$464$	1.13432	+	8.98854i	0.0526595	+	0.417282i
$465$		0			0
$466$	3.73890	−	28.1082i	0.173201	−	1.30209i
$467$	−8.45429	+	20.4105i	−0.391218	+	0.944484i	0.598457	+	0.801155i	$0.295781\pi$
$467$	−8.45429	+	20.4105i	−0.391218	+	0.944484i	−0.989675	+	0.143329i	$0.954219\pi$
$468$		0			0
$469$	2.86100	−	1.18506i	0.132109	−	0.0547212i
$470$	−50.1436	−	29.0402i	−2.31295	−	1.33953i
$471$		0			0
$472$	3.00206	+	0.817365i	0.138181	+	0.0376223i
$473$	0.0701178	−	0.261683i	0.00322402	−	0.0120322i
$474$		0			0
$475$	7.07261	−	53.7218i	0.324513	−	2.46492i
$476$	0.0917824	−	34.2027i	0.00420684	−	1.56768i
$477$		0			0
$478$	−8.61482	+	20.7193i	−0.394033	+	0.947681i
$479$	−17.2770	+	29.9247i	−0.789407	+	1.36729i	0.136924	+	0.990582i	$0.456278\pi$
$479$	−17.2770	+	29.9247i	−0.789407	+	1.36729i	−0.926331	+	0.376711i	$0.877055\pi$
$480$		0			0
$481$	−2.36681	−	4.09944i	−0.107917	−	0.186918i
$482$	19.7176	−	2.56896i	0.898110	−	0.117013i
$483$		0			0
$484$	11.0502	−	19.0215i	0.502283	−	0.864613i
$485$	−49.9328	+	20.6828i	−2.26733	+	0.939159i
$486$		0			0
$487$	9.54616	+	9.54616i	0.432578	+	0.432578i	0.889504	−	0.456927i	$-0.151050\pi$
$487$	9.54616	+	9.54616i	0.432578	+	0.432578i	−0.456927	+	0.889504i	$0.651050\pi$
$488$	8.48691	+	4.94557i	0.384184	+	0.223876i
$489$		0			0
$490$	−6.00086	+	3.45387i	−0.271091	+	0.156030i
$491$	−11.9332	−	9.15666i	−0.538537	−	0.413234i	0.303357	−	0.952877i	$-0.401893\pi$
$491$	−11.9332	−	9.15666i	−0.538537	−	0.413234i	−0.841894	+	0.539643i	$0.818559\pi$
$492$		0			0
$493$	−9.80231	−	12.7746i	−0.441474	−	0.575340i
$494$	4.20315	−	1.73440i	0.189108	−	0.0780342i
$495$		0			0
$496$	−4.31069	−	0.0231355i	−0.193555	−	0.00103881i
$497$	9.43326	−	16.3389i	0.423140	−	0.732899i
$498$		0			0
$499$	4.50032	+	34.1833i	0.201462	+	1.53025i	0.731241	+	0.682119i	$0.238941\pi$
$499$	4.50032	+	34.1833i	0.201462	+	1.53025i	−0.529779	+	0.848135i	$0.677725\pi$
$500$	−40.1207	−	30.9571i	−1.79425	−	1.38444i
$501$		0			0
$502$	21.2896	+	12.3297i	0.950201	+	0.550300i
$503$	8.40559	+	8.40559i	0.374787	+	0.374787i	0.869217	−	0.494431i	$-0.164623\pi$
$503$	8.40559	+	8.40559i	0.374787	+	0.374787i	−0.494431	+	0.869217i	$0.664623\pi$
$504$		0			0
$505$	−17.6694	+	17.6694i	−0.786277	+	0.786277i
$506$	−0.113462	+	0.0302391i	−0.00504402	+	0.00134429i
$507$		0			0
$508$	−8.05664	−	2.18196i	−0.357456	−	0.0968088i
$509$	33.6763	−	4.43357i	1.49267	−	0.196514i	0.660415	−	0.750901i	$-0.270380\pi$
$509$	33.6763	−	4.43357i	1.49267	−	0.196514i	0.832259	+	0.554386i	$0.187047\pi$
$510$		0			0
$511$	−5.65009	−	3.26208i	−0.249945	−	0.144306i
$512$	−20.7989	−	8.91094i	−0.919191	−	0.393812i
$513$		0			0
$514$	0.579117	−	1.39282i	0.0255437	−	0.0614348i
$515$	13.3228	−	10.2229i	0.587073	−	0.450477i
$516$		0			0
$517$	0.181473	−	0.236500i	0.00798115	−	0.0104012i
$518$	23.2319	+	6.25839i	1.02075	+	0.274978i
$519$		0			0
$520$	1.02746	−	7.56878i	0.0450571	−	0.331913i
$521$	17.2744	−	17.2744i	0.756804	−	0.756804i	−0.218935	−	0.975739i	$-0.570258\pi$
$521$	17.2744	−	17.2744i	0.756804	−	0.756804i	0.975739	+	0.218935i	$0.0702584\pi$
$522$		0			0
$523$	−6.07147	−	14.6578i	−0.265487	−	0.640942i	0.733773	−	0.679394i	$-0.237757\pi$
$523$	−6.07147	−	14.6578i	−0.265487	−	0.640942i	−0.999260	+	0.0384519i	$0.987757\pi$
$524$	34.4144	+	4.62473i	1.50340	+	0.202032i
$525$		0			0
$526$	−22.7254	−	17.4863i	−0.990872	−	0.762438i
$527$	6.63505	−	3.83075i	0.289027	−	0.166870i
$528$		0			0
$529$	12.9900	+	7.49978i	0.564783	+	0.326078i
$530$	−2.05532	−	4.98087i	−0.0892774	−	0.216355i
$531$		0			0
$532$	−8.90154	+	21.3282i	−0.385931	+	0.924693i
$533$	−7.14754	−	0.940991i	−0.309594	−	0.0407589i
$534$		0			0
$535$	64.6631	+	17.3264i	2.79563	+	0.749086i
$536$	1.80786	+	3.16061i	0.0780875	+	0.136518i
$537$		0			0
$538$	−34.1068	+	9.08985i	−1.47045	+	0.391891i
$539$	−0.0136310	−	0.0329082i	−0.000587130	−	0.00141746i
$540$		0			0
$541$	−9.21880	−	3.81855i	−0.396347	−	0.164172i	0.175602	−	0.984461i	$-0.443813\pi$
$541$	−9.21880	−	3.81855i	−0.396347	−	0.164172i	−0.571949	+	0.820289i	$0.693813\pi$
$542$	8.26902	−	6.32744i	0.355185	−	0.271787i
$543$		0			0
$544$	39.9060	−	4.98161i	1.71096	−	0.213585i
$545$	2.50940	−	1.44881i	0.107491	−	0.0620600i
$546$		0			0
$547$	2.13562	+	2.78319i	0.0913124	+	0.119001i	0.836775	−	0.547547i	$-0.184438\pi$
$547$	2.13562	+	2.78319i	0.0913124	+	0.119001i	−0.745463	+	0.666547i	$0.767771\pi$
$548$	−21.9043	−	0.0587799i	−0.935707	−	0.00251095i
$549$		0			0
$550$	0.331561	−	0.330672i	0.0141378	−	0.0140999i
$551$	2.81603	+	10.5096i	0.119967	+	0.447723i
$552$		0			0
$553$	−5.16315	+	19.2691i	−0.219559	+	0.819407i
$554$	0.00181097	+	0.00314643i	7.69406e−5	+	0.000133679i
$555$		0			0
$556$	−8.35036	−	10.9431i	−0.354134	−	0.464090i
$557$	−17.9461	−	7.43352i	−0.760401	−	0.314969i	−0.0314237	−	0.999506i	$-0.510004\pi$
$557$	−17.9461	−	7.43352i	−0.760401	−	0.314969i	−0.728978	+	0.684538i	$0.760004\pi$
$558$		0			0
$559$	−6.17694			−0.261257
$560$	23.4687	+	30.9272i	0.991732	+	1.30691i
$561$		0			0
$562$	−16.1773	+	21.0242i	−0.682398	+	0.886853i
$563$	−27.3603	+	3.60206i	−1.15310	+	0.151809i	−0.682737	−	0.730664i	$-0.739211\pi$
$563$	−27.3603	+	3.60206i	−1.15310	+	0.151809i	−0.470363	+	0.882473i	$0.655877\pi$
$564$		0			0
$565$	0.174486	−	1.32536i	0.00734069	−	0.0557581i
$566$	7.02075	+	0.00942001i	0.295104	+	0.000395953i
$567$		0			0
$568$	20.4603	+	8.57160i	0.858496	+	0.359656i
$569$	34.2938	−	9.18899i	1.43767	−	0.385223i	0.545953	−	0.837816i	$-0.316168\pi$
$569$	34.2938	−	9.18899i	1.43767	−	0.385223i	0.891717	+	0.452593i	$0.149501\pi$
$570$		0			0
$571$	8.12418	+	6.23391i	0.339987	+	0.260881i	0.764616	−	0.644487i	$-0.222929\pi$
$571$	8.12418	+	6.23391i	0.339987	+	0.260881i	−0.424629	+	0.905367i	$0.639595\pi$
$572$	0.0379282	+	0.0102720i	0.00158586	+	0.000429494i
$573$		0			0
$574$	29.1008	−	22.2679i	1.21465	−	0.929444i
$575$	31.9049			1.33053
$576$		0			0
$577$	−0.100738			−0.00419377			−0.00209688	−	0.999998i	$-0.500667\pi$
$577$	−0.100738			−0.00419377			−0.00209688	+	0.999998i	$0.500667\pi$
$578$	−37.6705	+	28.8254i	−1.56689	+	1.19898i
$579$		0			0
$580$	17.6418	+	4.77790i	0.732538	+	0.198391i
$581$	28.1153	+	21.5736i	1.16642	+	0.895024i
$582$		0			0
$583$	0.0267753	−	0.00717443i	0.00110892	−	0.000297134i
$584$	2.96411	−	7.07531i	0.122656	−	0.292779i
$585$		0			0
$586$	−32.4458	−	0.0435338i	−1.34032	−	0.00179837i
$587$	−1.51894	+	11.5375i	−0.0626934	+	0.476204i	0.931083	+	0.364808i	$0.118865\pi$
$587$	−1.51894	+	11.5375i	−0.0626934	+	0.476204i	−0.993776	+	0.111396i	$0.964468\pi$
$588$		0			0
$589$	−5.13266	+	0.675727i	−0.211488	+	0.0278429i
$590$	3.82779	−	4.97463i	0.157587	−	0.204802i
$591$		0			0
$592$	−3.84305	+	28.0277i	−0.157948	+	1.15193i
$593$	4.85470			0.199359			0.0996793	−	0.995020i	$-0.468218\pi$
$593$	4.85470			0.199359			0.0996793	+	0.995020i	$0.468218\pi$
$594$		0			0
$595$	−63.7488	−	26.4056i	−2.61345	−	1.08252i
$596$	−9.74379	−	12.7692i	−0.399121	−	0.523045i
$597$		0			0
$598$	1.33553	+	2.32039i	0.0546138	+	0.0948876i
$599$	−11.3882	+	42.5012i	−0.465307	+	1.73655i	0.190561	+	0.981675i	$0.438969\pi$
$599$	−11.3882	+	42.5012i	−0.465307	+	1.73655i	−0.655868	+	0.754876i	$0.727697\pi$
$600$		0			0
$601$	8.05246	+	30.0522i	0.328467	+	1.22586i	0.910781	+	0.412891i	$0.135481\pi$
$601$	8.05246	+	30.0522i	0.328467	+	1.22586i	−0.582314	+	0.812964i	$0.697852\pi$
$602$	22.2303	−	22.1707i	0.906038	−	0.903610i
$603$		0			0
$604$	−18.8635	−	0.0506198i	−0.767543	−	0.00205969i
$605$	−27.0166	−	35.2087i	−1.09838	−	1.43144i
$606$		0			0
$607$	21.9441	−	12.6694i	0.890683	−	0.514236i	0.0165172	−	0.999864i	$-0.494742\pi$
$607$	21.9441	−	12.6694i	0.890683	−	0.514236i	0.874166	+	0.485628i	$0.161409\pi$
$608$	−26.2005	−	7.20912i	−1.06257	−	0.292369i
$609$		0			0
$610$	15.7377	−	12.0424i	0.637200	−	0.487583i
$611$	−6.27943	−	2.60102i	−0.254039	−	0.105226i
$612$		0			0
$613$	−5.22440	−	12.6128i	−0.211012	−	0.509427i	0.782568	−	0.622566i	$-0.213910\pi$
$613$	−5.22440	−	12.6128i	−0.211012	−	0.509427i	−0.993579	+	0.113138i	$0.963910\pi$
$614$	−18.9094	+	5.03956i	−0.763120	+	0.203380i
$615$		0			0
$616$	−0.173369	+	0.0991666i	−0.00698525	+	0.00399553i
$617$	11.6933	+	3.13322i	0.470756	+	0.126139i	0.486395	−	0.873739i	$-0.338312\pi$
$617$	11.6933	+	3.13322i	0.470756	+	0.126139i	−0.0156389	+	0.999878i	$0.504978\pi$
$618$		0			0
$619$	28.5910	+	3.76408i	1.14917	+	0.151291i	0.680957	−	0.732324i	$-0.261564\pi$
$619$	28.5910	+	3.76408i	1.14917	+	0.151291i	0.468214	+	0.883615i	$0.344898\pi$
$620$	−3.34957	+	8.02560i	−0.134522	+	0.322316i
$621$		0			0
$622$	−7.87803	−	19.0917i	−0.315880	−	0.765506i
$623$	−13.6073	−	7.85616i	−0.545163	−	0.314750i
$624$		0			0
$625$	−39.6939	+	22.9173i	−1.58775	+	0.916690i
$626$	4.74476	+	3.65091i	0.189639	+	0.145920i
$627$		0			0
$628$	−33.6302	−	4.51935i	−1.34199	−	0.180342i
$629$	−19.2412	−	46.4524i	−0.767197	−	1.85218i
$630$		0			0
$631$	−5.44377	+	5.44377i	−0.216713	+	0.216713i	−0.807112	−	0.590399i	$-0.798971\pi$
$631$	−5.44377	+	5.44377i	−0.216713	+	0.216713i	0.590399	+	0.807112i	$0.298971\pi$
$632$	−23.2427	−	3.15519i	−0.924546	−	0.125507i
$633$		0			0
$634$	12.2361	+	3.29625i	0.485957	+	0.130911i
$635$	−10.2510	+	13.3593i	−0.406798	+	0.530149i
$636$		0			0
$637$	−0.644312	+	0.494398i	−0.0255286	+	0.0195888i
$638$	−0.0360994	+	0.0868219i	−0.00142919	+	0.00343731i
$639$		0			0
$640$	−32.5803	+	31.9740i	−1.28785	+	1.26388i
$641$	−13.4648	−	7.77393i	−0.531829	−	0.307052i	0.209932	−	0.977716i	$-0.432676\pi$
$641$	−13.4648	−	7.77393i	−0.531829	−	0.307052i	−0.741761	+	0.670664i	$0.766009\pi$
$642$		0			0
$643$	8.08377	−	1.06425i	0.318793	−	0.0419699i	0.0305681	−	0.999533i	$-0.490268\pi$
$643$	8.08377	−	1.06425i	0.318793	−	0.0419699i	0.288225	+	0.957563i	$0.406935\pi$
$644$	−13.1349	−	3.55730i	−0.517589	−	0.140177i
$645$		0			0
$646$	46.6678	−	12.4375i	1.83612	−	0.489347i
$647$	27.9651	−	27.9651i	1.09942	−	1.09942i	0.104944	−	0.994478i	$-0.466534\pi$
$647$	27.9651	−	27.9651i	1.09942	−	1.09942i	0.994478	−	0.104944i	$-0.0334663\pi$
$648$		0			0
$649$	0.0228333	+	0.0228333i	0.000896285	+	0.000896285i
$650$	−9.23913	−	5.35076i	−0.362389	−	0.209874i
$651$		0			0
$652$	17.3909	+	13.4188i	0.681082	+	0.525522i
$653$	−6.21118	−	47.1786i	−0.243062	−	1.84624i	−0.483211	−	0.875504i	$-0.660529\pi$
$653$	−6.21118	−	47.1786i	−0.243062	−	1.84624i	0.240149	−	0.970736i	$-0.422804\pi$
$654$		0			0
$655$	35.0261	−	60.6669i	1.36858	−	2.37045i
$656$	30.3017	+	30.6288i	1.18308	+	1.19585i
$657$		0			0
$658$	31.9349	−	13.1777i	1.24495	−	0.513720i
$659$	−0.195012	−	0.254145i	−0.00759661	−	0.00990009i	0.789540	−	0.613700i	$-0.210319\pi$
$659$	−0.195012	−	0.254145i	−0.00759661	−	0.00990009i	−0.797136	+	0.603800i	$0.793653\pi$
$660$		0			0
$661$	28.0330	+	21.5105i	1.09036	+	0.836661i	0.987435	−	0.158028i	$-0.0505136\pi$
$661$	28.0330	+	21.5105i	1.09036	+	0.836661i	0.102924	+	0.994689i	$0.467180\pi$
$662$	−6.55692	+	3.77392i	−0.254842	+	0.146678i
$663$		0			0
$664$	−20.9794	+	36.0019i	−0.814159	+	1.39715i
$665$	32.9687	+	32.9687i	1.27847	+	1.27847i
$666$		0			0
$667$	−5.91878	+	2.45164i	−0.229176	+	0.0949278i
$668$	1.11786	−	1.92425i	0.0432513	−	0.0744514i
$669$		0			0
$670$	7.28408	−	0.949027i	0.281409	−	0.0366641i
$671$	0.0509728	+	0.0882875i	0.00196778	+	0.00340830i
$672$		0			0
$673$	−16.1528	+	27.9774i	−0.622643	+	1.07845i	0.366349	+	0.930478i	$0.380608\pi$
$673$	−16.1528	+	27.9774i	−0.622643	+	1.07845i	−0.988992	+	0.147972i	$0.952726\pi$
$674$	0.596671	−	1.43504i	0.0229829	−	0.0552757i
$675$		0			0
$676$	−0.0673661	+	25.1040i	−0.00259100	+	0.965538i
$677$	−4.71702	+	35.8293i	−0.181290	+	1.37703i	0.622733	+	0.782435i	$0.286022\pi$
$677$	−4.71702	+	35.8293i	−0.181290	+	1.37703i	−0.804023	+	0.594599i	$0.797311\pi$
$678$		0			0
$679$	8.33976	−	31.1244i	0.320051	−	1.19445i
$680$	21.3137	−	78.2820i	0.817343	−	3.00198i
$681$		0			0
$682$	−0.0387153	−	0.0224216i	−0.00148248	−	0.000858567i
$683$	8.61033	−	3.56652i	0.329465	−	0.136469i	−0.211818	−	0.977309i	$-0.567939\pi$
$683$	8.61033	−	3.56652i	0.329465	−	0.136469i	0.541284	+	0.840840i	$0.317939\pi$
$684$		0			0
$685$	−16.9109	+	40.8264i	−0.646130	+	1.55990i
$686$	3.68427	−	27.6975i	0.140666	−	1.05750i
$687$		0			0
$688$	29.1662	+	22.6297i	1.11195	+	0.862750i
$689$	−0.316011	−	0.547347i	−0.0120391	−	0.0208522i
$690$		0			0
$691$	−12.1349	+	9.31143i	−0.461633	+	0.354224i	−0.813244	−	0.581923i	$-0.802301\pi$
$691$	−12.1349	+	9.31143i	−0.461633	+	0.354224i	0.351611	+	0.936146i	$0.385634\pi$
$692$	6.64213	+	16.1580i	0.252496	+	0.614236i
$693$		0			0
$694$	−0.0326804	+	24.3568i	−0.00124053	+	0.924571i
$695$	−26.8237	+	7.18739i	−1.01748	+	0.272633i
$696$		0			0
$697$	−73.9658	−	19.8191i	−2.80165	−	0.750701i
$698$	−3.98743	+	14.8018i	−0.150926	+	0.560257i
$699$		0			0
$700$	52.4561	−	13.9048i	1.98266	−	0.525553i
$701$	−4.97726	+	12.0162i	−0.187989	+	0.453845i	−0.989572	−	0.144038i	$-0.953991\pi$
$701$	−4.97726	+	12.0162i	−0.187989	+	0.453845i	0.801584	+	0.597883i	$0.203991\pi$
$702$		0			0
$703$			33.9745i			1.28137i
$704$	−0.141457	−	0.187455i	−0.00533135	−	0.00706499i
$705$		0			0
$706$	15.5806	−	2.02996i	0.586382	−	0.0763984i
$707$	−1.94456	−	14.7704i	−0.0731327	−	0.555498i
$708$		0			0
$709$	−35.4191	−	4.66302i	−1.33019	−	0.175123i	−0.568298	−	0.822823i	$-0.692398\pi$
$709$	−35.4191	−	4.66302i	−1.33019	−	0.175123i	−0.761896	+	0.647700i	$0.775731\pi$
$710$	31.6874	−	31.6025i	1.18921	−	1.18602i
$711$		0			0
$712$	7.13855	−	17.0397i	0.267528	−	0.638588i
$713$	−0.788943	−	2.94437i	−0.0295461	−	0.110268i
$714$		0			0
$715$	0.0482585	−	0.0628918i	0.00180477	−	0.00235202i
$716$	−4.29471	−	3.31379i	−0.160501	−	0.123842i
$717$		0			0
$718$	−1.30373	+	9.80120i	−0.0486549	+	0.365778i
$719$		−	25.6407i		−	0.956237i	−0.878295	−	0.478119i	$-0.841319\pi$
$719$		−	25.6407i		−	0.956237i	0.878295	−	0.478119i	$-0.158681\pi$
$720$		0			0
$721$			10.0119i			0.372862i
$722$	−5.71415	−	0.760083i	−0.212659	−	0.0282874i
$723$		0			0
$724$	−2.43639	−	18.8980i	−0.0905477	−	0.702337i
$725$	15.5528	−	20.2688i	0.577615	−	0.752763i
$726$		0			0
$727$	6.85449	+	25.5813i	0.254219	+	0.948758i	0.968523	+	0.248923i	$0.0800765\pi$
$727$	6.85449	+	25.5813i	0.254219	+	0.948758i	−0.714304	+	0.699835i	$0.753257\pi$
$728$	3.20707	+	3.23299i	0.118862	+	0.119823i
$729$		0			0
$730$	−10.9283	−	10.9577i	−0.404476	−	0.405563i
$731$	−65.0491	−	8.56387i	−2.40593	−	0.316746i
$732$		0			0
$733$	−0.335350	−	2.54724i	−0.0123864	−	0.0940844i	0.984135	−	0.177421i	$-0.0567755\pi$
$733$	−0.335350	−	2.54724i	−0.0123864	−	0.0940844i	−0.996521	+	0.0833370i	$0.973442\pi$
$734$	6.30188	+	48.3689i	0.232607	+	1.78533i
$735$		0			0
$736$	2.19485	−	15.8492i	0.0809033	−	0.584208i
$737$			0.0377896i			0.00139200i
$738$		0			0
$739$	10.2651	−	24.7822i	0.377609	−	0.911630i	−0.614804	−	0.788680i	$-0.710765\pi$
$739$	10.2651	−	24.7822i	0.377609	−	0.911630i	0.992413	−	0.122949i	$-0.0392353\pi$
$740$	49.3494	+	28.6687i	1.81412	+	1.05388i
$741$		0			0
$742$	3.10187	+	0.835606i	0.113873	+	0.0306761i
$743$	−38.6460	−	10.3552i	−1.41779	−	0.379895i	−0.533088	−	0.846060i	$-0.678969\pi$
$743$	−38.6460	−	10.3552i	−1.41779	−	0.379895i	−0.884698	+	0.466165i	$0.845635\pi$
$744$		0			0
$745$	−31.2998	+	8.38676i	−1.14674	+	0.307267i
$746$	3.15551	+	0.00423387i	0.115531	+	0.000155013i
$747$		0			0
$748$	0.385179	+	0.160759i	0.0140835	+	0.00587792i
$749$	−31.6640	+	24.2967i	−1.15698	+	0.887781i
$750$		0			0
$751$	−11.9982	−	20.7815i	−0.437822	−	0.758329i	0.559700	−	0.828696i	$-0.310917\pi$
$751$	−11.9982	−	20.7815i	−0.437822	−	0.758329i	−0.997521	+	0.0703662i	$0.977583\pi$
$752$	20.1211	+	35.2867i	0.733739	+	1.28677i
$753$		0			0
$754$	2.12514	+	0.282682i	0.0773932	+	0.0102947i
$755$	−14.5632	+	35.1587i	−0.530009	+	1.27956i
$756$		0			0
$757$	0.259402	−	0.107448i	0.00942812	−	0.00390525i	−0.377964	−	0.925820i	$-0.623376\pi$
$757$	0.259402	−	0.107448i	0.00942812	−	0.00390525i	0.387393	+	0.921915i	$0.373376\pi$
$758$	7.40655	−	12.7889i	0.269018	−	0.464512i
$759$		0			0
$760$	−33.5480	+	43.3581i	−1.21691	+	1.57276i
$761$	−0.0632458	+	0.236036i	−0.00229266	+	0.00855632i	−0.967063	−	0.254538i	$-0.918076\pi$
$761$	−0.0632458	+	0.236036i	−0.00229266	+	0.00855632i	0.964770	+	0.263095i	$0.0847432\pi$
$762$		0			0
$763$	−0.225489	+	1.71276i	−0.00816324	+	0.0620060i
$764$	−2.81974	−	2.83491i	−0.102015	−	0.102564i
$765$		0			0
$766$	42.7198	+	17.7623i	1.54353	+	0.641778i
$767$	0.368124	−	0.637610i	0.0132922	−	0.0230228i
$768$		0			0
$769$	−1.04493	−	1.80987i	−0.0376811	−	0.0652656i	0.846570	−	0.532278i	$-0.178664\pi$
$769$	−1.04493	−	1.80987i	−0.0376811	−	0.0652656i	−0.884251	+	0.467012i	$0.845330\pi$
$770$	0.0520571	+	0.399555i	0.00187601	+	0.0143990i
$771$		0			0
$772$	0.887118	−	0.235153i	0.0319281	−	0.00846334i
$773$	5.65867	−	2.34390i	0.203528	−	0.0843041i	−0.278591	−	0.960410i	$-0.589867\pi$
$773$	5.65867	−	2.34390i	0.203528	−	0.0843041i	0.482119	+	0.876106i	$0.339867\pi$
$774$		0			0
$775$	8.59564	+	8.59564i	0.308765	+	0.308765i
$776$	37.5427	+	5.09642i	1.34771	+	0.182951i
$777$		0			0
$778$	15.5968	+	27.0984i	0.559173	+	0.971524i
$779$	41.0501	+	31.4988i	1.47077	+	1.12856i
$780$		0			0
$781$	0.140155	+	0.182654i	0.00501514	+	0.00653586i
$782$	10.8473	+	26.2875i	0.387900	+	0.940039i
$783$		0			0
$784$	4.85357	+	0.0260491i	0.173342	+	0.000930327i
$785$	−34.2279	+	59.2845i	−1.22165	+	2.11595i
$786$		0			0
$787$	1.66801	+	12.6698i	0.0594583	+	0.451630i	0.995115	+	0.0987197i	$0.0314747\pi$
$787$	1.66801	+	12.6698i	0.0594583	+	0.451630i	−0.935657	+	0.352911i	$0.885192\pi$
$788$	5.12490	+	39.7515i	0.182567	+	1.41609i
$789$		0			0
$790$	−23.7151	+	40.9487i	−0.843744	+	1.45689i
$791$	0.563554	+	0.563554i	0.0200377	+	0.0200377i
$792$		0			0
$793$	1.64360	−	1.64360i	0.0583658	−	0.0583658i
$794$	8.89071	+	33.3595i	0.315519	+	1.18389i
$795$		0			0
$796$	−7.31355	+	4.19635i	−0.259222	+	0.148736i
$797$	−9.09495	+	1.19737i	−0.322160	+	0.0424131i	−0.289872	−	0.957065i	$-0.593613\pi$
$797$	−9.09495	+	1.19737i	−0.322160	+	0.0424131i	−0.0322879	+	0.999479i	$0.510279\pi$
$798$		0			0
$799$	−62.5223	−	36.0973i	−2.21188	−	1.27703i
$800$	24.0223	+	59.1135i	0.849315	+	2.08998i
$801$		0			0
$802$	13.0981	+	5.44602i	0.462511	+	0.192306i
$803$	0.0631628	−	0.0484665i	0.00222897	−	0.00171035i
$804$		0			0
$805$	−16.7124	+	21.7801i	−0.589035	+	0.767646i
$806$	−0.265335	+	0.984956i	−0.00934603	+	0.0346936i
$807$		0			0
$808$	16.9381	−	4.46556i	0.595881	−	0.157098i
$809$	14.8091	−	14.8091i	0.520660	−	0.520660i	−0.397110	−	0.917771i	$-0.629987\pi$
$809$	14.8091	−	14.8091i	0.520660	−	0.520660i	0.917771	+	0.397110i	$0.129987\pi$
$810$		0			0
$811$	18.9307	+	45.7027i	0.664746	+	1.60484i	0.790277	+	0.612749i	$0.209937\pi$
$811$	18.9307	+	45.7027i	0.664746	+	1.60484i	−0.125531	+	0.992090i	$0.540063\pi$
$812$	−8.66283	+	6.61036i	−0.304006	+	0.231978i
$813$		0			0
$814$	−0.179049	+	0.232695i	−0.00627568	+	0.00815594i
$815$	38.3776	−	22.1573i	1.34431	−	0.776138i
$816$		0			0
$817$	38.3940	+	22.1668i	1.34324	+	0.775517i
$818$	−28.3418	+	11.6950i	−0.990947	+	0.408907i
$819$		0			0
$820$	80.3927	−	33.0473i	2.80743	−	1.15406i
$821$	−28.8353	−	3.79624i	−1.00636	−	0.132490i	−0.390713	−	0.920513i	$-0.627772\pi$
$821$	−28.8353	−	3.79624i	−1.00636	−	0.132490i	−0.615646	+	0.788023i	$0.711105\pi$
$822$		0			0
$823$	−45.7970	−	12.2713i	−1.59638	−	0.427749i	−0.652435	−	0.757845i	$-0.726252\pi$
$823$	−45.7970	−	12.2713i	−1.59638	−	0.427749i	−0.943947	+	0.330096i	$0.892919\pi$
$824$	−11.6774	+	1.48956i	−0.406800	+	0.0518913i
$825$		0			0
$826$	0.963707	+	3.61600i	0.0335316	+	0.125817i
$827$	−4.62464	−	11.1649i	−0.160815	−	0.388241i	0.822848	−	0.568261i	$-0.192384\pi$
$827$	−4.62464	−	11.1649i	−0.160815	−	0.388241i	−0.983663	+	0.180020i	$0.942384\pi$
$828$		0			0
$829$	−2.97227	−	1.23116i	−0.103231	−	0.0427598i	0.330470	−	0.943816i	$-0.392793\pi$
$829$	−2.97227	−	1.23116i	−0.103231	−	0.0427598i	−0.433701	+	0.901057i	$0.642793\pi$
$830$	51.0846	+	66.7601i	1.77317	+	2.31728i
$831$		0			0
$832$	−3.29365	+	4.22156i	−0.114187	+	0.146356i
$833$	−7.47067	+	4.31320i	−0.258844	+	0.149443i
$834$		0			0
$835$	−2.73305	−	3.56177i	−0.0945810	−	0.123260i
$836$	−0.198888	−	0.199958i	−0.00687869	−	0.00691570i
$837$		0			0
$838$	−0.0565541	−	0.0567061i	−0.00195363	−	0.00195888i
$839$	−13.9978	−	52.2403i	−0.483256	−	1.80354i	−0.587788	−	0.809015i	$-0.700001\pi$
$839$	−13.9978	−	52.2403i	−0.483256	−	1.80354i	0.104532	−	0.994522i	$-0.466666\pi$
$840$		0			0
$841$	6.17800	−	23.0566i	0.213035	−	0.795056i
$842$	3.91781	−	2.25494i	0.135017	−	0.0777105i
$843$		0			0
$844$	19.6521	+	2.64092i	0.676454	+	0.0909042i
$845$	46.7901	+	19.3811i	1.60963	+	0.666730i
$846$		0			0
$847$	26.4588			0.909135
$848$	−0.513115	+	3.74219i	−0.0176204	+	0.128507i
$849$		0			0
$850$	−89.8785	−	69.1580i	−3.08281	−	2.37210i
$851$	−19.8334	+	2.61111i	−0.679880	+	0.0895078i
$852$		0			0
$853$	−3.54124	+	26.8984i	−0.121250	+	0.920984i	0.817390	+	0.576085i	$0.195420\pi$
$853$	−3.54124	+	26.8984i	−0.121250	+	0.920984i	−0.938640	+	0.344899i	$0.887913\pi$
$854$	−0.0158519	+	11.8145i	−0.000542441	+	0.404282i
$855$		0			0
$856$	−33.0494	−	33.3165i	−1.12960	−	1.13873i
$857$	33.7482	−	9.04281i	1.15282	−	0.308896i	0.368724	−	0.929539i	$-0.379795\pi$
$857$	33.7482	−	9.04281i	1.15282	−	0.308896i	0.784094	+	0.620643i	$0.213128\pi$
$858$		0			0
$859$	10.4664	+	8.03115i	0.357109	+	0.274019i	0.771698	−	0.635990i	$-0.219408\pi$
$859$	10.4664	+	8.03115i	0.357109	+	0.274019i	−0.414589	+	0.910009i	$0.636075\pi$
$860$	64.5962	−	37.0639i	2.20271	−	1.26387i
$861$		0			0
$862$	−10.9794	−	14.3485i	−0.373962	−	0.488712i
$863$	5.30766			0.180675			0.0903375	−	0.995911i	$-0.471205\pi$
$863$	5.30766			0.180675			0.0903375	+	0.995911i	$0.471205\pi$
$864$		0			0
$865$	35.2441			1.19834
$866$	28.7496	+	37.5715i	0.976953	+	1.27673i
$867$		0			0
$868$	−2.58035	−	4.49713i	−0.0875829	−	0.152642i
$869$	−0.193132	−	0.148196i	−0.00655156	−	0.00502719i
$870$		0			0
$871$	0.832255	−	0.223002i	0.0281999	−	0.00755614i
$872$	−2.03122	−	0.00817614i	−0.0687858	−	0.000276879i
$873$		0			0
$874$	0.0257822	−	19.2155i	0.000872097	−	0.649975i
$875$	7.95569	−	60.4294i	0.268951	−	2.04289i
$876$		0			0
$877$	−16.7720	+	2.20807i	−0.566350	+	0.0745614i	−0.408264	−	0.912864i	$-0.633866\pi$
$877$	−16.7720	+	2.20807i	−0.566350	+	0.0745614i	−0.158086	+	0.987425i	$0.550532\pi$
$878$	−38.6159	−	29.7134i	−1.30322	−	1.00278i
$879$		0			0
$880$	−0.458276	+	0.120162i	−0.0154485	+	0.00405067i
$881$	20.3432			0.685381			0.342691	−	0.939448i	$-0.388662\pi$
$881$	20.3432			0.685381			0.342691	+	0.939448i	$0.388662\pi$
$882$		0			0
$883$	−37.1650	−	15.3943i	−1.25070	−	0.518058i	−0.343659	−	0.939095i	$-0.611666\pi$
$883$	−37.1650	−	15.3943i	−1.25070	−	0.518058i	−0.907044	+	0.421037i	$0.861666\pi$
$884$	1.26745	−	9.43163i	0.0426291	−	0.317220i
$885$		0			0
$886$	−19.9962	+	11.5091i	−0.671785	+	0.386654i
$887$	11.4522	−	42.7401i	0.384527	−	1.43507i	−0.454385	−	0.890806i	$-0.650141\pi$
$887$	11.4522	−	42.7401i	0.384527	−	1.43507i	0.838911	−	0.544268i	$-0.183192\pi$
$888$		0			0
$889$	−2.59838	−	9.69727i	−0.0871467	−	0.325236i
$890$	−26.3190	−	26.3897i	−0.882215	−	0.884586i
$891$		0			0
$892$	11.0250	−	10.9660i	0.369145	−	0.367169i
$893$	29.6969	+	38.7018i	0.993769	+	1.29511i
$894$		0			0
$895$	−9.47739	+	5.47177i	−0.316794	+	0.182901i
$896$	−3.29876	−	27.0148i	−0.110204	−	0.902502i
$897$		0			0
$898$	−15.8489	−	20.7121i	−0.528883	−	0.691172i
$899$	−2.25511	−	0.934098i	−0.0752122	−	0.0311539i
$900$		0			0
$901$	−2.56904	−	6.20221i	−0.0855871	−	0.206626i
$902$	0.115154	+	0.432077i	0.00383420	+	0.0143866i
$903$		0			0
$904$	−0.573456	+	0.741147i	−0.0190729	+	0.0246502i
$905$	−37.1307	−	9.94913i	−1.23426	−	0.330720i
$906$		0			0
$907$	28.5227	+	3.75509i	0.947081	+	0.124686i	0.588216	−	0.808704i	$-0.299831\pi$
$907$	28.5227	+	3.75509i	0.947081	+	0.124686i	0.358865	+	0.933389i	$0.383164\pi$
$908$	−16.2187	−	39.4546i	−0.538238	−	1.30935i
$909$		0			0
$910$	8.49237	−	3.50431i	0.281519	−	0.116167i
$911$	−20.3253	−	11.7348i	−0.673406	−	0.388791i	0.123960	−	0.992287i	$-0.460440\pi$
$911$	−20.3253	−	11.7348i	−0.673406	−	0.388791i	−0.797366	+	0.603496i	$0.793774\pi$
$912$		0			0
$913$	−0.374521	+	0.216230i	−0.0123948	+	0.00715616i
$914$	−18.9380	+	24.6120i	−0.626412	+	0.814092i
$915$		0			0
$916$	−29.5211	−	38.6872i	−0.975405	−	1.27826i
$917$	15.9826	+	38.5855i	0.527793	+	1.27420i
$918$		0			0
$919$	−19.6882	+	19.6882i	−0.649455	+	0.649455i	−0.952861	−	0.303406i	$-0.901876\pi$
$919$	−19.6882	+	19.6882i	−0.649455	+	0.649455i	0.303406	+	0.952861i	$0.401876\pi$
$920$	−27.8896	−	16.2521i	−0.919494	−	0.535816i
$921$		0			0
$922$	−15.1038	+	56.0671i	−0.497417	+	1.84647i
$923$	3.19558	−	4.16456i	0.105184	−	0.137078i
$924$		0			0
$925$	63.2905	−	48.5645i	2.08098	−	1.59679i
$926$	−6.66958	−	2.77312i	−0.219176	−	0.0911304i
$927$		0			0
$928$	−8.99885	−	9.12040i	−0.295402	−	0.299392i
$929$	11.5434	+	6.66461i	0.378728	+	0.218659i	0.677265	−	0.735739i	$-0.263165\pi$
$929$	11.5434	+	6.66461i	0.378728	+	0.218659i	−0.298537	+	0.954398i	$0.596498\pi$
$930$		0			0
$931$	5.77907	−	0.760829i	0.189401	−	0.0249352i
$932$	19.9573	+	34.7823i	0.653724	+	1.13933i
$933$		0			0
$934$	−8.04578	−	30.1892i	−0.263266	−	0.987822i
$935$	0.595403	−	0.595403i	0.0194718	−	0.0194718i
$936$		0			0
$937$	−12.4737	−	12.4737i	−0.407497	−	0.407497i	0.473368	−	0.880865i	$-0.343038\pi$
$937$	−12.4737	−	12.4737i	−0.407497	−	0.407497i	−0.880865	+	0.473368i	$0.843038\pi$
$938$	−2.19480	+	3.78975i	−0.0716628	+	0.123740i
$939$		0			0
$940$	81.2751	−	10.4783i	2.65090	−	0.341763i
$941$	4.02789	+	30.5948i	0.131305	+	0.997363i	0.922554	+	0.385868i	$0.126098\pi$
$941$	4.02789	+	30.5948i	0.131305	+	0.997363i	−0.791249	+	0.611495i	$0.790569\pi$
$942$		0			0
$943$	−15.2333	+	26.3848i	−0.496063	+	0.859206i
$944$	−4.07414	+	1.66200i	−0.132602	+	0.0540936i
$945$		0			0
$946$	0.146143	+	0.354163i	0.00475151	+	0.0115148i
$947$	1.52487	+	1.98724i	0.0495515	+	0.0645767i	0.817472	−	0.575969i	$-0.195375\pi$
$947$	1.52487	+	1.98724i	0.0495515	+	0.0645767i	−0.767920	+	0.640545i	$0.778708\pi$
$948$		0			0
$949$	−1.44013	−	1.10505i	−0.0467486	−	0.0358715i
$950$	38.2257	+	66.4146i	1.24021	+	2.15477i
$951$		0			0
$952$	29.2912	+	38.4928i	0.949333	+	1.24756i
$953$	5.62522	+	5.62522i	0.182219	+	0.182219i	0.792322	−	0.610103i	$-0.208872\pi$
$953$	5.62522	+	5.62522i	0.182219	+	0.182219i	−0.610103	+	0.792322i	$0.708872\pi$
$954$		0			0
$955$	−7.45250	+	3.08693i	−0.241157	+	0.0998907i
$956$	−8.13094	−	30.6741i	−0.262973	−	0.992071i
$957$		0			0
$958$	−6.31338	−	48.4572i	−0.203976	−	1.56558i
$959$	−13.1729	−	22.8162i	−0.425377	−	0.736774i
$960$		0			0
$961$	−14.9193	+	25.8410i	−0.481268	+	0.833580i
$962$	6.18133	+	2.57011i	0.199294	+	0.0828638i
$963$		0			0
$964$	−19.9375	+	19.8308i	−0.642144	+	0.638706i
$965$	0.241668	−	1.83565i	0.00777957	−	0.0590917i
$966$		0			0
$967$	3.28553	−	12.2618i	0.105656	−	0.394312i	−0.892763	−	0.450526i	$-0.851236\pi$
$967$	3.28553	−	12.2618i	0.105656	−	0.394312i	0.998419	+	0.0562141i	$0.0179030\pi$
$968$	3.93652	+	30.8602i	0.126524	+	0.991885i
$969$		0			0
$970$	38.3057	−	66.1423i	1.22992	−	2.12370i
$971$	2.97541	−	1.23245i	0.0954854	−	0.0395513i	−0.334429	−	0.942421i	$-0.608544\pi$
$971$	2.97541	−	1.23245i	0.0954854	−	0.0395513i	0.429915	+	0.902869i	$0.358544\pi$
$972$		0			0
$973$	6.33581	−	15.2960i	0.203117	−	0.490367i
$974$	−18.9256	−	2.51744i	−0.606416	−	0.0806641i
$975$		0			0
$976$	−13.7822	+	1.73926i	−0.441156	+	0.0556723i
$977$	−14.7846	−	25.6076i	−0.473001	−	0.819261i	0.526522	−	0.850162i	$-0.323496\pi$
$977$	−14.7846	−	25.6076i	−0.473001	−	0.819261i	−0.999522	+	0.0309006i	$0.990162\pi$
$978$		0			0
$979$	0.152116	−	0.116723i	0.00486166	−	0.00373049i
$980$	3.77142	−	9.03635i	0.120474	−	0.288656i
$981$		0			0
$982$	21.2718	+	0.0285412i	0.678811	+	0.000910786i
$983$	−1.88794	+	0.505873i	−0.0602160	+	0.0161348i	−0.288801	−	0.957389i	$-0.593257\pi$
$983$	−1.88794	+	0.505873i	−0.0602160	+	0.0161348i	0.228585	+	0.973524i	$0.426590\pi$
$984$		0			0
$985$	78.1036	+	20.9278i	2.48859	+	0.666815i
$986$	21.9879	+	5.92327i	0.700237	+	0.188635i
$987$		0			0
$988$	−3.23010	+	5.56018i	−0.102763	+	0.176893i
$989$	−9.98959	+	24.1170i	−0.317650	+	0.766876i
$990$		0			0
$991$			49.7375i			1.57996i	0.613131	+	0.789982i	$0.289910\pi$
$991$			49.7375i			1.57996i	−0.613131	+	0.789982i	$0.710090\pi$
$992$	4.86132	−	3.67867i	0.154347	−	0.116798i
$993$		0			0
$994$	3.44711	+	26.4577i	0.109336	+	0.839187i
$995$	2.22034	+	16.8651i	0.0703894	+	0.534660i
$996$		0			0
$997$	−55.9121	−	7.36096i	−1.77075	−	0.233124i	−0.826636	−	0.562737i	$-0.809749\pi$
$997$	−55.9121	−	7.36096i	−1.77075	−	0.233124i	−0.944116	+	0.329613i	$0.893082\pi$
$998$	−34.4320	−	34.5245i	−1.08992	−	1.09285i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.35.9		368
3.2	odd	2		288.2.bf.a.227.38	yes	368
9.4	even	3		288.2.bf.a.131.24	yes	368
9.5	odd	6	inner	864.2.bn.a.611.23		368
32.11	odd	8	inner	864.2.bn.a.683.23		368
96.11	even	8		288.2.bf.a.11.24	✓	368
288.139	odd	24		288.2.bf.a.203.38	yes	368
288.203	even	24	inner	864.2.bn.a.395.9		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.24	✓	368	96.11	even	8
288.2.bf.a.131.24	yes	368	9.4	even	3
288.2.bf.a.203.38	yes	368	288.139	odd	24
288.2.bf.a.227.38	yes	368	3.2	odd	2
864.2.bn.a.35.9		368	1.1	even	1	trivial
864.2.bn.a.395.9		368	288.203	even	24	inner
864.2.bn.a.611.23		368	9.5	odd	6	inner
864.2.bn.a.683.23		368	32.11	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.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.12313 + 0.859413i) q^{2} +(0.522820 - 1.93046i) q^{4} +(-3.20104 - 2.45624i) q^{5} +(2.32357 - 0.622598i) q^{7} +(1.07187 + 2.61746i) q^{8} +O(q^{10})\)	\(q+(-1.12313 + 0.859413i) q^{2} +(0.522820 - 1.93046i) q^{4} +(-3.20104 - 2.45624i) q^{5} +(2.32357 - 0.622598i) q^{7} +(1.07187 + 2.61746i) q^{8} +(5.70609 + 0.00765608i) q^{10} +(-0.00383159 + 0.0291038i) q^{11} +(0.663576 - 0.0873614i) q^{13} +(-2.07459 + 2.69616i) q^{14} +(-3.45332 - 2.01856i) q^{16} +7.10921 q^{17} +(-4.43809 - 1.83832i) q^{19} +(-6.41524 + 4.89529i) q^{20} +(-0.0207088 - 0.0359801i) q^{22} +(0.732071 - 2.73212i) q^{23} +(2.91942 + 10.8954i) q^{25} +(-0.670199 + 0.668403i) q^{26} +(0.0129104 - 4.81105i) q^{28} +(-1.37882 - 1.79691i) q^{29} +(0.933304 - 0.538843i) q^{31} +(5.61329 - 0.700726i) q^{32} +(-7.98453 + 6.10974i) q^{34} +(-8.96708 - 3.71429i) q^{35} +(-2.70652 - 6.53412i) q^{37} +(6.56441 - 1.74949i) q^{38} +(2.99804 - 11.0114i) q^{40} +(-10.4042 - 2.78780i) q^{41} +(-9.14997 - 1.20462i) q^{43} +(0.0541803 + 0.0226128i) q^{44} +(1.52582 + 3.69767i) q^{46} +(-8.79455 - 5.07754i) q^{47} +(-1.05084 + 0.606706i) q^{49} +(-12.6425 - 9.72794i) q^{50} +(0.178284 - 1.32668i) q^{52} +(-0.361368 - 0.872419i) q^{53} +(0.0837510 - 0.0837510i) q^{55} +(4.12018 + 5.41451i) q^{56} +(3.09287 + 0.833182i) q^{58} +(0.669653 - 0.872709i) q^{59} +(2.75521 - 2.11415i) q^{61} +(-0.585129 + 1.40728i) q^{62} +(-5.70221 + 5.61113i) q^{64} +(-2.33871 - 1.35026i) q^{65} +(1.27632 - 0.168031i) q^{67} +(3.71684 - 13.7240i) q^{68} +(13.2633 - 3.53481i) q^{70} +(5.54582 - 5.54582i) q^{71} +(-1.91778 - 1.91778i) q^{73} +(8.65526 + 5.01261i) q^{74} +(-5.86912 + 7.60643i) q^{76} +(0.00921701 + 0.0700101i) q^{77} +(-4.14646 + 7.18188i) q^{79} +(6.09612 + 14.9437i) q^{80} +(14.0811 - 5.81047i) q^{82} +(8.96833 + 11.6878i) q^{83} +(-22.7568 - 17.4619i) q^{85} +(11.3118 - 6.51067i) q^{86} +(-0.0802850 + 0.0211663i) q^{88} +(-4.61864 - 4.61864i) q^{89} +(1.48747 - 0.616131i) q^{91} +(-4.89150 - 2.84164i) q^{92} +(14.2411 - 1.85544i) q^{94} +(9.69115 + 16.7856i) q^{95} +(6.69755 - 11.6005i) q^{97} +(0.658820 - 1.58452i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more