LMFDB - Embedded newform 432.2.k.d.109.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(109,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("432.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.9
Character	$\chi$	$=$	432.109
Dual form			432.2.k.d.325.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.305792 + 1.38076i) q^{2} +(-1.81298 + 0.844450i) q^{4} +(1.45562 - 1.45562i) q^{5} -2.37837i q^{7} +(-1.72038 - 2.24506i) q^{8} +O(q^{10})$	\(q+(0.305792 + 1.38076i) q^{2} +(-1.81298 + 0.844450i) q^{4} +(1.45562 - 1.45562i) q^{5} -2.37837i q^{7} +(-1.72038 - 2.24506i) q^{8} +(2.45498 + 1.56474i) q^{10} +(3.09636 - 3.09636i) q^{11} +(3.80115 + 3.80115i) q^{13} +(3.28396 - 0.727288i) q^{14} +(2.57381 - 3.06195i) q^{16} -0.668761 q^{17} +(2.02630 + 2.02630i) q^{19} +(-1.40982 + 3.86821i) q^{20} +(5.22217 + 3.32848i) q^{22} -4.17054i q^{23} +0.762337i q^{25} +(-4.08611 + 6.41083i) q^{26} +(2.00842 + 4.31195i) q^{28} +(-5.21991 - 5.21991i) q^{29} +0.437128 q^{31} +(5.01486 + 2.61749i) q^{32} +(-0.204502 - 0.923396i) q^{34} +(-3.46201 - 3.46201i) q^{35} +(-7.02157 + 7.02157i) q^{37} +(-2.17820 + 3.41745i) q^{38} +(-5.77217 - 0.763743i) q^{40} +5.69876i q^{41} +(4.50786 - 4.50786i) q^{43} +(-2.99893 + 8.22838i) q^{44} +(5.75851 - 1.27532i) q^{46} +9.31583 q^{47} +1.34334 q^{49} +(-1.05260 + 0.233117i) q^{50} +(-10.1013 - 3.68154i) q^{52} +(5.33520 - 5.33520i) q^{53} -9.01427i q^{55} +(-5.33959 + 4.09170i) q^{56} +(5.61122 - 8.80364i) q^{58} +(-10.0544 + 10.0544i) q^{59} +(-3.47595 - 3.47595i) q^{61} +(0.133671 + 0.603568i) q^{62} +(-2.08061 + 7.72471i) q^{64} +11.0661 q^{65} +(-7.26146 - 7.26146i) q^{67} +(1.21245 - 0.564735i) q^{68} +(3.72154 - 5.83885i) q^{70} -3.51581i q^{71} +15.2332i q^{73} +(-11.8422 - 7.54794i) q^{74} +(-5.38474 - 1.96253i) q^{76} +(-7.36431 - 7.36431i) q^{77} -9.00441 q^{79} +(-0.710543 - 8.20352i) q^{80} +(-7.86860 + 1.74264i) q^{82} +(-3.40620 - 3.40620i) q^{83} +(-0.973462 + 0.973462i) q^{85} +(7.60272 + 4.84579i) q^{86} +(-12.2784 - 1.62462i) q^{88} -2.38381i q^{89} +(9.04056 - 9.04056i) q^{91} +(3.52181 + 7.56112i) q^{92} +(2.84871 + 12.8629i) q^{94} +5.89904 q^{95} -1.45526 q^{97} +(0.410784 + 1.85483i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} + 24 q^{16} + 16 q^{19} + 32 q^{22} + 24 q^{28} - 8 q^{34} + 56 q^{40} - 16 q^{43} - 32 q^{49} - 16 q^{52} - 32 q^{61} + 24 q^{64} + 32 q^{67} - 96 q^{70} - 48 q^{76} - 32 q^{79} + 32 q^{85} - 88 q^{88} - 48 q^{91} - 96 q^{94}+O(q^{100}) $ 32 * q - 8 * q^10 + 24 * q^16 + 16 * q^19 + 32 * q^22 + 24 * q^28 - 8 * q^34 + 56 * q^40 - 16 * q^43 - 32 * q^49 - 16 * q^52 - 32 * q^61 + 24 * q^64 + 32 * q^67 - 96 * q^70 - 48 * q^76 - 32 * q^79 + 32 * q^85 - 88 * q^88 - 48 * q^91 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.305792	+	1.38076i	0.216228	+	0.976343i
$2$	0.305792	+	1.38076i	0.216228	+	0.976343i
$3$		0			0
$3$		0			0
$4$	−1.81298	+	0.844450i	−0.906491	+	0.422225i
$5$	1.45562	−	1.45562i	0.650973	−	0.650973i	−0.302254	−	0.953227i	$-0.597739\pi$
$5$	1.45562	−	1.45562i	0.650973	−	0.650973i	0.953227	+	0.302254i	$0.0977391\pi$
$6$		0			0
$7$		−	2.37837i		−	0.898940i	−0.893295	−	0.449470i	$-0.851613\pi$
$7$		−	2.37837i		−	0.898940i	0.893295	−	0.449470i	$-0.148387\pi$
$8$	−1.72038	−	2.24506i	−0.608245	−	0.793749i
$9$		0			0
$10$	2.45498	+	1.56474i	0.776332	+	0.494815i
$11$	3.09636	−	3.09636i	0.933589	−	0.933589i	−0.0643389	−	0.997928i	$-0.520494\pi$
$11$	3.09636	−	3.09636i	0.933589	−	0.933589i	0.997928	+	0.0643389i	$0.0204939\pi$
$12$		0			0
$13$	3.80115	+	3.80115i	1.05425	+	1.05425i	0.998441	+	0.0558089i	$0.0177738\pi$
$13$	3.80115	+	3.80115i	1.05425	+	1.05425i	0.0558089	+	0.998441i	$0.482226\pi$
$14$	3.28396	−	0.727288i	0.877674	−	0.194376i
$15$		0			0
$16$	2.57381	−	3.06195i	0.643452	−	0.765486i
$17$	−0.668761			−0.162198			−0.0810991	−	0.996706i	$-0.525843\pi$
$17$	−0.668761			−0.162198			−0.0810991	+	0.996706i	$0.525843\pi$
$18$		0			0
$19$	2.02630	+	2.02630i	0.464864	+	0.464864i	0.900246	−	0.435382i	$-0.143387\pi$
$19$	2.02630	+	2.02630i	0.464864	+	0.464864i	−0.435382	+	0.900246i	$0.643387\pi$
$20$	−1.40982	+	3.86821i	−0.315244	+	0.864959i
$21$		0			0
$22$	5.22217	+	3.32848i	1.11337	+	0.709635i
$23$		−	4.17054i		−	0.869618i	−0.900523	−	0.434809i	$-0.856816\pi$
$23$		−	4.17054i		−	0.869618i	0.900523	−	0.434809i	$-0.143184\pi$
$24$		0			0
$25$			0.762337i			0.152467i
$26$	−4.08611	+	6.41083i	−0.801352	+	1.25727i
$27$		0			0
$28$	2.00842	+	4.31195i	0.379555	+	0.814881i
$29$	−5.21991	−	5.21991i	−0.969313	−	0.969313i	0.0302295	−	0.999543i	$-0.490376\pi$
$29$	−5.21991	−	5.21991i	−0.969313	−	0.969313i	−0.999543	+	0.0302295i	$0.990376\pi$
$30$		0			0
$31$	0.437128			0.0785106			0.0392553	−	0.999229i	$-0.487501\pi$
$31$	0.437128			0.0785106			0.0392553	+	0.999229i	$0.487501\pi$
$32$	5.01486	+	2.61749i	0.886510	+	0.462710i
$33$		0			0
$34$	−0.204502	−	0.923396i	−0.0350718	−	0.158361i
$35$	−3.46201	−	3.46201i	−0.585186	−	0.585186i
$36$		0			0
$37$	−7.02157	+	7.02157i	−1.15434	+	1.15434i	−0.168665	+	0.985673i	$0.553946\pi$
$37$	−7.02157	+	7.02157i	−1.15434	+	1.15434i	−0.985673	+	0.168665i	$0.946054\pi$
$38$	−2.17820	+	3.41745i	−0.353350	+	0.554383i
$39$		0			0
$40$	−5.77217	−	0.763743i	−0.912661	−	0.120758i
$41$			5.69876i			0.889997i	0.895531	+	0.444998i	$0.146796\pi$
$41$			5.69876i			0.889997i	−0.895531	+	0.444998i	$0.853204\pi$
$42$		0			0
$43$	4.50786	−	4.50786i	0.687442	−	0.687442i	−0.274224	−	0.961666i	$-0.588421\pi$
$43$	4.50786	−	4.50786i	0.687442	−	0.687442i	0.961666	+	0.274224i	$0.0884210\pi$
$44$	−2.99893	+	8.22838i	−0.452105	+	1.24047i
$45$		0			0
$46$	5.75851	−	1.27532i	0.849046	−	0.188036i
$47$	9.31583			1.35885			0.679427	−	0.733743i	$-0.262228\pi$
$47$	9.31583			1.35885			0.679427	+	0.733743i	$0.262228\pi$
$48$		0			0
$49$	1.34334			0.191906
$50$	−1.05260	+	0.233117i	−0.148860	+	0.0329677i
$51$		0			0
$52$	−10.1013	−	3.68154i	−1.40080	−	0.510538i
$53$	5.33520	−	5.33520i	0.732847	−	0.732847i	−0.238336	−	0.971183i	$-0.576602\pi$
$53$	5.33520	−	5.33520i	0.732847	−	0.732847i	0.971183	+	0.238336i	$0.0766020\pi$
$54$		0			0
$55$		−	9.01427i		−	1.21548i
$56$	−5.33959	+	4.09170i	−0.713533	+	0.546776i
$57$		0			0
$58$	5.61122	−	8.80364i	0.736790	−	1.15597i
$59$	−10.0544	+	10.0544i	−1.30897	+	1.30897i	−0.386819	+	0.922156i	$0.626426\pi$
$59$	−10.0544	+	10.0544i	−1.30897	+	1.30897i	−0.922156	+	0.386819i	$0.873574\pi$
$60$		0			0
$61$	−3.47595	−	3.47595i	−0.445049	−	0.445049i	0.448656	−	0.893705i	$-0.351903\pi$
$61$	−3.47595	−	3.47595i	−0.445049	−	0.445049i	−0.893705	+	0.448656i	$0.851903\pi$
$62$	0.133671	+	0.603568i	0.0169762	+	0.0766533i
$63$		0			0
$64$	−2.08061	+	7.72471i	−0.260076	+	0.965588i
$65$	11.0661			1.37258
$66$		0			0
$67$	−7.26146	−	7.26146i	−0.887128	−	0.887128i	0.107118	−	0.994246i	$-0.465838\pi$
$67$	−7.26146	−	7.26146i	−0.887128	−	0.887128i	−0.994246	+	0.107118i	$0.965838\pi$
$68$	1.21245	−	0.564735i	0.147031	−	0.0684842i
$69$		0			0
$70$	3.72154	−	5.83885i	0.444809	−	0.697876i
$71$		−	3.51581i		−	0.417250i	−0.977996	−	0.208625i	$-0.933101\pi$
$71$		−	3.51581i		−	0.417250i	0.977996	−	0.208625i	$-0.0668988\pi$
$72$		0			0
$73$			15.2332i			1.78291i	0.453110	+	0.891455i	$0.350314\pi$
$73$			15.2332i			1.78291i	−0.453110	+	0.891455i	$0.649686\pi$
$74$	−11.8422	−	7.54794i	−1.37663	−	0.877430i
$75$		0			0
$76$	−5.38474	−	1.96253i	−0.617672	−	0.225118i
$77$	−7.36431	−	7.36431i	−0.839241	−	0.839241i
$78$		0			0
$79$	−9.00441			−1.01307			−0.506537	−	0.862218i	$-0.669075\pi$
$79$	−9.00441			−1.01307			−0.506537	+	0.862218i	$0.669075\pi$
$80$	−0.710543	−	8.20352i	−0.0794412	−	0.917181i
$81$		0			0
$82$	−7.86860	+	1.74264i	−0.868942	+	0.192442i
$83$	−3.40620	−	3.40620i	−0.373879	−	0.373879i	0.495009	−	0.868888i	$-0.335165\pi$
$83$	−3.40620	−	3.40620i	−0.373879	−	0.373879i	−0.868888	+	0.495009i	$0.835165\pi$
$84$		0			0
$85$	−0.973462	+	0.973462i	−0.105587	+	0.105587i
$86$	7.60272	+	4.84579i	0.819823	+	0.522535i
$87$		0			0
$88$	−12.2784	−	1.62462i	−1.30889	−	0.173185i
$89$		−	2.38381i		−	0.252684i	−0.991987	−	0.126342i	$-0.959676\pi$
$89$		−	2.38381i		−	0.252684i	0.991987	−	0.126342i	$-0.0403236\pi$
$90$		0			0
$91$	9.04056	−	9.04056i	0.947708	−	0.947708i
$92$	3.52181	+	7.56112i	0.367175	+	0.788301i
$93$		0			0
$94$	2.84871	+	12.8629i	0.293822	+	1.32671i
$95$	5.89904			0.605228
$96$		0			0
$97$	−1.45526			−0.147759			−0.0738797	−	0.997267i	$-0.523538\pi$
$97$	−1.45526			−0.147759			−0.0738797	+	0.997267i	$0.523538\pi$
$98$	0.410784	+	1.85483i	0.0414954	+	0.187366i
$99$		0			0
$100$	−0.643756	−	1.38210i	−0.0643756	−	0.138210i
$101$	8.26039	−	8.26039i	0.821940	−	0.821940i	−0.164446	−	0.986386i	$-0.552584\pi$
$101$	8.26039	−	8.26039i	0.821940	−	0.821940i	0.986386	+	0.164446i	$0.0525838\pi$
$102$		0			0
$103$		−	0.710619i		−	0.0700193i	−0.999387	−	0.0350097i	$-0.988854\pi$
$103$		−	0.710619i		−	0.0700193i	0.999387	−	0.0350097i	$-0.0111462\pi$
$104$	1.99441	−	15.0732i	0.195568	−	1.47805i
$105$		0			0
$106$	8.99809	+	5.73516i	0.873972	+	0.557048i
$107$	−6.97782	+	6.97782i	−0.674571	+	0.674571i	−0.958766	−	0.284195i	$-0.908274\pi$
$107$	−6.97782	+	6.97782i	−0.674571	+	0.674571i	0.284195	+	0.958766i	$0.408274\pi$
$108$		0			0
$109$	5.41046	+	5.41046i	0.518228	+	0.518228i	0.917035	−	0.398807i	$-0.130576\pi$
$109$	5.41046	+	5.41046i	0.518228	+	0.518228i	−0.398807	+	0.917035i	$0.630576\pi$
$110$	12.4465	−	2.75649i	1.18673	−	0.262821i
$111$		0			0
$112$	−7.28245	−	6.12148i	−0.688127	−	0.578425i
$113$	−8.31315			−0.782036			−0.391018	−	0.920383i	$-0.627877\pi$
$113$	−8.31315			−0.782036			−0.391018	+	0.920383i	$0.627877\pi$
$114$		0			0
$115$	−6.07073	−	6.07073i	−0.566098	−	0.566098i
$116$	13.8716	+	5.05565i	1.28794	+	0.469406i
$117$		0			0
$118$	−16.9573	−	10.8082i	−1.56104	−	0.994971i
$119$			1.59056i			0.145807i
$120$		0			0
$121$		−	8.17495i		−	0.743177i
$122$	3.73652	−	5.86235i	0.338289	−	0.530753i
$123$		0			0
$124$	−0.792506	+	0.369133i	−0.0711691	+	0.0331491i
$125$	8.38778	+	8.38778i	0.750226	+	0.750226i
$126$		0			0
$127$	12.6823			1.12537			0.562687	−	0.826670i	$-0.309768\pi$
$127$	12.6823			1.12537			0.562687	+	0.826670i	$0.309768\pi$
$128$	−11.3022	−	0.510659i	−0.998981	−	0.0451363i
$129$		0			0
$130$	3.38392	+	15.2796i	0.296790	+	1.34011i
$131$	−8.89909	−	8.89909i	−0.777517	−	0.777517i	0.201891	−	0.979408i	$-0.435291\pi$
$131$	−8.89909	−	8.89909i	−0.777517	−	0.777517i	−0.979408	+	0.201891i	$0.935291\pi$
$132$		0			0
$133$	4.81929	−	4.81929i	0.417885	−	0.417885i
$134$	7.80581	−	12.2468i	0.674320	−	1.05796i
$135$		0			0
$136$	1.15052	+	1.50141i	0.0986563	+	0.128745i
$137$			20.0662i			1.71437i	0.515009	+	0.857185i	$0.327789\pi$
$137$			20.0662i			1.71437i	−0.515009	+	0.857185i	$0.672211\pi$
$138$		0			0
$139$	−14.5022	+	14.5022i	−1.23006	+	1.23006i	−0.266116	+	0.963941i	$0.585740\pi$
$139$	−14.5022	+	14.5022i	−1.23006	+	1.23006i	−0.963941	+	0.266116i	$0.914260\pi$
$140$	9.20005	+	3.35307i	0.777546	+	0.283386i
$141$		0			0
$142$	4.85448	−	1.07511i	0.407379	−	0.0902210i
$143$	23.5395			1.96847
$144$		0			0
$145$	−15.1964			−1.26199
$146$	−21.0333	+	4.65819i	−1.74073	+	0.385515i
$147$		0			0
$148$	6.80061	−	18.6593i	0.559007	−	1.53379i
$149$	−12.9589	+	12.9589i	−1.06164	+	1.06164i	−0.0636670	+	0.997971i	$0.520280\pi$
$149$	−12.9589	+	12.9589i	−1.06164	+	1.06164i	−0.997971	+	0.0636670i	$0.979720\pi$
$150$		0			0
$151$		−	5.00441i		−	0.407253i	−0.979049	−	0.203626i	$-0.934727\pi$
$151$		−	5.00441i		−	0.407253i	0.979049	−	0.203626i	$-0.0652728\pi$
$152$	1.06317	−	8.03515i	0.0862343	−	0.651737i
$153$		0			0
$154$	7.91638	−	12.4203i	0.637920	−	1.00085i
$155$	0.636293	−	0.636293i	0.0511083	−	0.0511083i
$156$		0			0
$157$	1.10862	+	1.10862i	0.0884776	+	0.0884776i	0.749960	−	0.661483i	$-0.230073\pi$
$157$	1.10862	+	1.10862i	0.0884776	+	0.0884776i	−0.661483	+	0.749960i	$0.730073\pi$
$158$	−2.75348	−	12.4329i	−0.219055	−	0.989108i
$159$		0			0
$160$	11.1098	−	3.48966i	0.878306	−	0.275882i
$161$	−9.91910			−0.781735
$162$		0			0
$163$	−7.90042	−	7.90042i	−0.618809	−	0.618809i	0.326417	−	0.945226i	$-0.394159\pi$
$163$	−7.90042	−	7.90042i	−0.618809	−	0.618809i	−0.945226	+	0.326417i	$0.894159\pi$
$164$	−4.81232	−	10.3317i	−0.375779	−	0.806774i
$165$		0			0
$166$	3.66155	−	5.74473i	0.284191	−	0.445878i
$167$			14.7687i			1.14284i	0.820659	+	0.571418i	$0.193606\pi$
$167$			14.7687i			1.14284i	−0.820659	+	0.571418i	$0.806394\pi$
$168$		0			0
$169$			15.8975i			1.22289i
$170$	−1.64179	−	1.04644i	−0.125920	−	0.0802581i
$171$		0			0
$172$	−4.36600	+	11.9793i	−0.332905	+	0.913415i
$173$	−11.4096	−	11.4096i	−0.867457	−	0.867457i	0.124733	−	0.992190i	$-0.460192\pi$
$173$	−11.4096	−	11.4096i	−0.867457	−	0.867457i	−0.992190	+	0.124733i	$0.960192\pi$
$174$		0			0
$175$	1.81312			0.137059
$176$	−1.51145	−	17.4504i	−0.113930	−	1.31537i
$177$		0			0
$178$	3.29147	−	0.728951i	0.246706	−	0.0546372i
$179$	5.55916	+	5.55916i	0.415511	+	0.415511i	0.883653	−	0.468142i	$-0.155076\pi$
$179$	5.55916	+	5.55916i	0.415511	+	0.415511i	−0.468142	+	0.883653i	$0.655076\pi$
$180$		0			0
$181$	−2.26188	+	2.26188i	−0.168124	+	0.168124i	−0.786154	−	0.618030i	$-0.787931\pi$
$181$	−2.26188	+	2.26188i	−0.168124	+	0.168124i	0.618030	+	0.786154i	$0.287931\pi$
$182$	15.2474	+	9.71829i	1.13021	+	0.720367i
$183$		0			0
$184$	−9.36313	+	7.17490i	−0.690259	+	0.528941i
$185$			20.4415i			1.50289i
$186$		0			0
$187$	−2.07073	+	2.07073i	−0.151427	+	0.151427i
$188$	−16.8894	+	7.86676i	−1.23179	+	0.573742i
$189$		0			0
$190$	1.80388	+	8.14514i	0.130867	+	0.590910i
$191$	−3.80820			−0.275551			−0.137776	−	0.990463i	$-0.543995\pi$
$191$	−3.80820			−0.275551			−0.137776	+	0.990463i	$0.543995\pi$
$192$		0			0
$193$	6.44527			0.463941			0.231970	−	0.972723i	$-0.425483\pi$
$193$	6.44527			0.463941			0.231970	+	0.972723i	$0.425483\pi$
$194$	−0.445008	−	2.00936i	−0.0319497	−	0.144264i
$195$		0			0
$196$	−2.43546	+	1.13439i	−0.173961	+	0.0810275i
$197$	0.710359	−	0.710359i	0.0506110	−	0.0506110i	−0.681348	−	0.731959i	$-0.738606\pi$
$197$	0.710359	−	0.710359i	0.0506110	−	0.0506110i	0.731959	+	0.681348i	$0.238606\pi$
$198$		0			0
$199$			3.32476i			0.235686i	0.993032	+	0.117843i	$0.0375980\pi$
$199$			3.32476i			0.235686i	−0.993032	+	0.117843i	$0.962402\pi$
$200$	1.71149	−	1.31151i	0.121021	−	0.0927375i
$201$		0			0
$202$	13.9316	+	8.87963i	0.980221	+	0.624769i
$203$	−12.4149	+	12.4149i	−0.871355	+	0.871355i
$204$		0			0
$205$	8.29523	+	8.29523i	0.579364	+	0.579364i
$206$	0.981192	−	0.217302i	0.0683629	−	0.0151401i
$207$		0			0
$208$	21.4224	−	1.85549i	1.48537	−	0.128655i
$209$	12.5483			0.867984
$210$		0			0
$211$	12.8867	+	12.8867i	0.887157	+	0.887157i	0.994249	−	0.107092i	$-0.0341541\pi$
$211$	12.8867	+	12.8867i	0.887157	+	0.887157i	−0.107092	+	0.994249i	$0.534154\pi$
$212$	−5.16732	+	14.1779i	−0.354893	+	0.973745i
$213$		0			0
$214$	−11.7684	−	7.50091i	−0.804474	−	0.512752i
$215$		−	13.1235i		−	0.895012i
$216$		0			0
$217$		−	1.03965i		−	0.0705763i
$218$	−5.81606	+	9.12501i	−0.393913	+	0.618024i
$219$		0			0
$220$	7.61210	+	16.3427i	0.513207	+	1.10182i
$221$	−2.54206	−	2.54206i	−0.170998	−	0.170998i
$222$		0			0
$223$	10.6260			0.711572			0.355786	−	0.934567i	$-0.384213\pi$
$223$	10.6260			0.711572			0.355786	+	0.934567i	$0.384213\pi$
$224$	6.22536	−	11.9272i	0.415949	−	0.796919i
$225$		0			0
$226$	−2.54210	−	11.4784i	−0.169098	−	0.763535i
$227$	−0.358234	−	0.358234i	−0.0237768	−	0.0237768i	0.695118	−	0.718895i	$-0.255352\pi$
$227$	−0.358234	−	0.358234i	−0.0237768	−	0.0237768i	−0.718895	+	0.695118i	$0.755352\pi$
$228$		0			0
$229$	15.2513	−	15.2513i	1.00784	−	1.00784i	0.00786620	−	0.999969i	$-0.497496\pi$
$229$	15.2513	−	15.2513i	1.00784	−	1.00784i	0.999969	−	0.00786620i	$-0.00250391\pi$
$230$	6.52582	−	10.2386i	0.430300	−	0.675112i
$231$		0			0
$232$	−2.73881	+	20.6992i	−0.179812	+	1.35897i
$233$			22.1491i			1.45104i	0.688202	+	0.725519i	$0.258400\pi$
$233$			22.1491i			1.45104i	−0.688202	+	0.725519i	$0.741600\pi$
$234$		0			0
$235$	13.5603	−	13.5603i	0.884578	−	0.884578i
$236$	9.73803	−	26.7190i	0.633892	−	1.73926i
$237$		0			0
$238$	−2.19618	+	0.486382i	−0.142357	+	0.0315274i
$239$	−5.09119			−0.329322			−0.164661	−	0.986350i	$-0.552653\pi$
$239$	−5.09119			−0.329322			−0.164661	+	0.986350i	$0.552653\pi$
$240$		0			0
$241$	17.3528			1.11779			0.558896	−	0.829238i	$-0.311225\pi$
$241$	17.3528			1.11779			0.558896	+	0.829238i	$0.311225\pi$
$242$	11.2876	−	2.49984i	0.725596	−	0.160696i
$243$		0			0
$244$	9.23709	+	3.36656i	0.591344	+	0.215522i
$245$	1.95540	−	1.95540i	0.124926	−	0.124926i
$246$		0			0
$247$			15.4045i			0.980166i
$248$	−0.752026	−	0.981381i	−0.0477537	−	0.0623177i
$249$		0			0
$250$	−9.01657	+	14.1464i	−0.570258	+	0.894697i
$251$	−21.7579	+	21.7579i	−1.37335	+	1.37335i	−0.517917	+	0.855431i	$0.673292\pi$
$251$	−21.7579	+	21.7579i	−1.37335	+	1.37335i	−0.855431	+	0.517917i	$0.826708\pi$
$252$		0			0
$253$	−12.9135	−	12.9135i	−0.811866	−	0.811866i
$254$	3.87816	+	17.5112i	0.243337	+	1.09875i
$255$		0			0
$256$	−2.75102	−	15.7617i	−0.171939	−	0.985108i
$257$	7.41381			0.462461			0.231230	−	0.972899i	$-0.425725\pi$
$257$	7.41381			0.462461			0.231230	+	0.972899i	$0.425725\pi$
$258$		0			0
$259$	16.6999	+	16.6999i	1.03768	+	1.03768i
$260$	−20.0626	+	9.34475i	−1.24423	+	0.579537i
$261$		0			0
$262$	9.56621	−	15.0088i	0.591003	−	0.927244i
$263$			15.1627i			0.934972i	0.884000	+	0.467486i	$0.154840\pi$
$263$			15.1627i			0.934972i	−0.884000	+	0.467486i	$0.845160\pi$
$264$		0			0
$265$		−	15.5321i		−	0.954127i
$266$	8.12797	+	5.18057i	0.498358	+	0.317641i
$267$		0			0
$268$	19.2968	+	7.03295i	1.17874	+	0.429606i
$269$	−14.4025	−	14.4025i	−0.878134	−	0.878134i	0.115207	−	0.993341i	$-0.463247\pi$
$269$	−14.4025	−	14.4025i	−0.878134	−	0.878134i	−0.993341	+	0.115207i	$0.963247\pi$
$270$		0			0
$271$	4.83874			0.293933			0.146966	−	0.989142i	$-0.453049\pi$
$271$	4.83874			0.293933			0.146966	+	0.989142i	$0.453049\pi$
$272$	−1.72126	+	2.04771i	−0.104367	+	0.124161i
$273$		0			0
$274$	−27.7065	+	6.13609i	−1.67381	+	0.370694i
$275$	2.36047	+	2.36047i	0.142342	+	0.142342i
$276$		0			0
$277$	−8.06923	+	8.06923i	−0.484833	+	0.484833i	−0.906671	−	0.421838i	$-0.861385\pi$
$277$	−8.06923	+	8.06923i	−0.484833	+	0.484833i	0.421838	+	0.906671i	$0.361385\pi$
$278$	−24.4586	−	15.5893i	−1.46693	−	0.934985i
$279$		0			0
$280$	−1.81647	+	13.7284i	−0.108555	+	0.820428i
$281$			12.1974i			0.727635i	0.931470	+	0.363818i	$0.118527\pi$
$281$			12.1974i			0.727635i	−0.931470	+	0.363818i	$0.881473\pi$
$282$		0			0
$283$	2.11962	−	2.11962i	0.125998	−	0.125998i	−0.641296	−	0.767294i	$-0.721603\pi$
$283$	2.11962	−	2.11962i	0.125998	−	0.125998i	0.767294	+	0.641296i	$0.221603\pi$
$284$	2.96892	+	6.37410i	0.176173	+	0.378233i
$285$		0			0
$286$	7.19820	+	32.5024i	0.425639	+	1.92191i
$287$	13.5538			0.800054
$288$		0			0
$289$	−16.5528			−0.973692
$290$	−4.64695	−	20.9826i	−0.272878	−	1.23214i
$291$		0			0
$292$	−12.8637	−	27.6175i	−0.752789	−	1.61619i
$293$	21.0873	−	21.0873i	1.23193	−	1.23193i	0.268712	−	0.963221i	$-0.413402\pi$
$293$	21.0873	−	21.0873i	1.23193	−	1.23193i	0.963221	−	0.268712i	$-0.0865981\pi$
$294$		0			0
$295$			29.2709i			1.70422i
$296$	27.8436	+	3.68411i	1.61838	+	0.214135i
$297$		0			0
$298$	−21.8559	−	13.9304i	−1.26608	−	0.806967i
$299$	15.8529	−	15.8529i	0.916795	−	0.916795i
$300$		0			0
$301$	−10.7214	−	10.7214i	−0.617969	−	0.617969i
$302$	6.90987	−	1.53031i	0.397618	−	0.0880594i
$303$		0			0
$304$	11.4197	−	0.989111i	0.654965	−	0.0567294i
$305$	−10.1193			−0.579430
$306$		0			0
$307$	2.19515	+	2.19515i	0.125284	+	0.125284i	0.766969	−	0.641685i	$-0.221764\pi$
$307$	2.19515	+	2.19515i	0.125284	+	0.125284i	−0.641685	+	0.766969i	$0.721764\pi$
$308$	19.5702	+	7.13257i	1.11511	+	0.406416i
$309$		0			0
$310$	1.07314	+	0.683993i	0.0609503	+	0.0388482i
$311$		−	10.9902i		−	0.623199i	−0.950214	−	0.311599i	$-0.899135\pi$
$311$		−	10.9902i		−	0.623199i	0.950214	−	0.311599i	$-0.100865\pi$
$312$		0			0
$313$		−	26.9405i		−	1.52277i	−0.648301	−	0.761384i	$-0.724520\pi$
$313$		−	26.9405i		−	1.52277i	0.648301	−	0.761384i	$-0.275480\pi$
$314$	−1.19173	+	1.86975i	−0.0672532	+	0.105516i
$315$		0			0
$316$	16.3248	−	7.60377i	0.918343	−	0.427746i
$317$	−10.5672	−	10.5672i	−0.593514	−	0.593514i	0.345065	−	0.938579i	$-0.387857\pi$
$317$	−10.5672	−	10.5672i	−0.593514	−	0.593514i	−0.938579	+	0.345065i	$0.887857\pi$
$318$		0			0
$319$	−32.3255			−1.80988
$320$	8.21567	+	14.2728i	0.459270	+	0.797875i
$321$		0			0
$322$	−3.03319	−	13.6959i	−0.169033	−	0.763241i
$323$	−1.35511	−	1.35511i	−0.0754002	−	0.0754002i
$324$		0			0
$325$	−2.89776	+	2.89776i	−0.160739	+	0.160739i
$326$	8.49268	−	13.3245i	0.470366	−	0.737973i
$327$		0			0
$328$	12.7941	−	9.80401i	0.706434	−	0.541336i
$329$		−	22.1565i		−	1.22153i
$330$		0			0
$331$	−19.5071	+	19.5071i	−1.07221	+	1.07221i	−0.0750273	+	0.997181i	$0.523904\pi$
$331$	−19.5071	+	19.5071i	−1.07221	+	1.07221i	−0.997181	+	0.0750273i	$0.976096\pi$
$332$	9.05175	+	3.29902i	0.496780	+	0.181057i
$333$		0			0
$334$	−20.3920	+	4.51615i	−1.11580	+	0.247113i
$335$	−21.1399			−1.15499
$336$		0			0
$337$	35.5385			1.93591			0.967954	−	0.251129i	$-0.0808018\pi$
$337$	35.5385			1.93591			0.967954	+	0.251129i	$0.0808018\pi$
$338$	−21.9506	+	4.86135i	−1.19396	+	0.264422i
$339$		0			0
$340$	0.942829	−	2.58691i	0.0511321	−	0.140295i
$341$	1.35351	−	1.35351i	0.0732966	−	0.0732966i
$342$		0			0
$343$		−	19.8436i		−	1.07145i
$344$	−17.8756	−	2.36521i	−0.963789	−	0.127523i
$345$		0			0
$346$	12.2649	−	19.2429i	0.659367	−	1.03450i
$347$	21.3140	−	21.3140i	1.14419	−	1.14419i	0.156520	−	0.987675i	$-0.449972\pi$
$347$	21.3140	−	21.3140i	1.14419	−	1.14419i	0.987675	−	0.156520i	$-0.0500276\pi$
$348$		0			0
$349$	−6.57868	−	6.57868i	−0.352149	−	0.352149i	0.508760	−	0.860909i	$-0.330104\pi$
$349$	−6.57868	−	6.57868i	−0.352149	−	0.352149i	−0.860909	+	0.508760i	$0.830104\pi$
$350$	0.554439	+	2.50348i	0.0296360	+	0.133817i
$351$		0			0
$352$	23.6325	−	7.42313i	1.25962	−	0.395654i
$353$	27.9146			1.48574			0.742872	−	0.669433i	$-0.233463\pi$
$353$	27.9146			1.48574			0.742872	+	0.669433i	$0.233463\pi$
$354$		0			0
$355$	−5.11768	−	5.11768i	−0.271618	−	0.271618i
$356$	2.01301	+	4.32181i	0.106689	+	0.229055i
$357$		0			0
$358$	−5.97590	+	9.37580i	−0.315836	+	0.495527i
$359$		−	25.8870i		−	1.36626i	−0.730295	−	0.683132i	$-0.760617\pi$
$359$		−	25.8870i		−	1.36626i	0.730295	−	0.683132i	$-0.239383\pi$
$360$		0			0
$361$		−	10.7883i		−	0.567803i
$362$	−3.81477	−	2.43144i	−0.200500	−	0.127794i
$363$		0			0
$364$	−8.75607	+	24.0247i	−0.458943	+	1.25924i
$365$	22.1737	+	22.1737i	1.16063	+	1.16063i
$366$		0			0
$367$	−11.6416			−0.607689			−0.303845	−	0.952722i	$-0.598270\pi$
$367$	−11.6416			−0.607689			−0.303845	+	0.952722i	$0.598270\pi$
$368$	−12.7700	−	10.7342i	−0.665681	−	0.559558i
$369$		0			0
$370$	−28.2247	+	6.25085i	−1.46733	+	0.324966i
$371$	−12.6891	−	12.6891i	−0.658786	−	0.658786i
$372$		0			0
$373$	1.36178	−	1.36178i	0.0705104	−	0.0705104i	−0.670972	−	0.741483i	$-0.734123\pi$
$373$	1.36178	−	1.36178i	0.0705104	−	0.0705104i	0.741483	+	0.670972i	$0.234123\pi$
$374$	−3.49238	−	2.22596i	−0.180587	−	0.115102i
$375$		0			0
$376$	−16.0267	−	20.9146i	−0.826516	−	1.07859i
$377$		−	39.6834i		−	2.04380i
$378$		0			0
$379$	−8.91869	+	8.91869i	−0.458122	+	0.458122i	−0.898039	−	0.439916i	$-0.855008\pi$
$379$	−8.91869	+	8.91869i	−0.458122	+	0.458122i	0.439916	+	0.898039i	$0.355008\pi$
$380$	−10.6948	+	4.98144i	−0.548634	+	0.255543i
$381$		0			0
$382$	−1.16452	−	5.25820i	−0.0595819	−	0.269033i
$383$	22.3019			1.13958			0.569788	−	0.821792i	$-0.307025\pi$
$383$	22.3019			1.13958			0.569788	+	0.821792i	$0.307025\pi$
$384$		0			0
$385$	−21.4393			−1.09265
$386$	1.97091	+	8.89936i	0.100317	+	0.452965i
$387$		0			0
$388$	2.63836	−	1.22890i	0.133943	−	0.0623877i
$389$	−12.3519	+	12.3519i	−0.626267	+	0.626267i	−0.947127	−	0.320860i	$-0.896028\pi$
$389$	−12.3519	+	12.3519i	−0.626267	+	0.626267i	0.320860	+	0.947127i	$0.396028\pi$
$390$		0			0
$391$			2.78909i			0.141051i
$392$	−2.31105	−	3.01589i	−0.116726	−	0.152325i
$393$		0			0
$394$	1.19806	+	0.763611i	0.0603572	+	0.0384702i
$395$	−13.1070	+	13.1070i	−0.659485	+	0.659485i
$396$		0			0
$397$	1.83271	+	1.83271i	0.0919811	+	0.0919811i	0.751600	−	0.659619i	$-0.229282\pi$
$397$	1.83271	+	1.83271i	0.0919811	+	0.0919811i	−0.659619	+	0.751600i	$0.729282\pi$
$398$	−4.59069	+	1.01669i	−0.230111	+	0.0509619i
$399$		0			0
$400$	2.33423	+	1.96211i	0.116712	+	0.0981055i
$401$	−23.9322			−1.19512			−0.597559	−	0.801825i	$-0.703863\pi$
$401$	−23.9322			−1.19512			−0.597559	+	0.801825i	$0.703863\pi$
$402$		0			0
$403$	1.66159	+	1.66159i	0.0827698	+	0.0827698i
$404$	−8.00045	+	21.9514i	−0.398037	+	1.09212i
$405$		0			0
$406$	−20.9383	−	13.3456i	−1.03915	−	0.662330i
$407$			43.4827i			2.15536i
$408$		0			0
$409$			4.59984i			0.227447i	0.993512	+	0.113724i	$0.0362779\pi$
$409$			4.59984i			0.227447i	−0.993512	+	0.113724i	$0.963722\pi$
$410$	−8.91709	+	13.9903i	−0.440383	+	0.690933i
$411$		0			0
$412$	0.600082	+	1.28834i	0.0295639	+	0.0634719i
$413$	23.9132	+	23.9132i	1.17669	+	1.17669i
$414$		0			0
$415$	−9.91628			−0.486771
$416$	9.11277	+	29.0117i	0.446790	+	1.42242i
$417$		0			0
$418$	3.83717	+	17.3262i	0.187682	+	0.847450i
$419$	9.28363	+	9.28363i	0.453535	+	0.453535i	0.896526	−	0.442991i	$-0.146083\pi$
$419$	9.28363	+	9.28363i	0.453535	+	0.453535i	−0.442991	+	0.896526i	$0.646083\pi$
$420$		0			0
$421$	14.1635	−	14.1635i	0.690287	−	0.690287i	−0.272008	−	0.962295i	$-0.587688\pi$
$421$	14.1635	−	14.1635i	0.690287	−	0.690287i	0.962295	+	0.272008i	$0.0876877\pi$
$422$	−13.8527	+	21.7341i	−0.674341	+	1.05800i
$423$		0			0
$424$	−21.1564	−	2.79930i	−1.02745	−	0.135946i
$425$		−	0.509821i		−	0.0247300i
$426$		0			0
$427$	−8.26709	+	8.26709i	−0.400073	+	0.400073i
$428$	6.75824	−	18.5431i	0.326672	−	0.896313i
$429$		0			0
$430$	18.1203	−	4.01305i	0.873839	−	0.193527i
$431$	−7.36480			−0.354750			−0.177375	−	0.984143i	$-0.556760\pi$
$431$	−7.36480			−0.354750			−0.177375	+	0.984143i	$0.556760\pi$
$432$		0			0
$433$	14.5876			0.701034			0.350517	−	0.936556i	$-0.386006\pi$
$433$	14.5876			0.701034			0.350517	+	0.936556i	$0.386006\pi$
$434$	1.43551	−	0.317918i	0.0689067	−	0.0152606i
$435$		0			0
$436$	−14.3779	−	5.24021i	−0.688578	−	0.250960i
$437$	8.45075	−	8.45075i	0.404254	−	0.404254i
$438$		0			0
$439$			4.36821i			0.208483i	0.994552	+	0.104242i	$0.0332415\pi$
$439$			4.36821i			0.208483i	−0.994552	+	0.104242i	$0.966758\pi$
$440$	−20.2376	+	15.5079i	−0.964789	+	0.739312i
$441$		0			0
$442$	2.73263	−	4.28731i	0.129978	−	0.203927i
$443$	18.1179	−	18.1179i	0.860807	−	0.860807i	−0.130624	−	0.991432i	$-0.541698\pi$
$443$	18.1179	−	18.1179i	0.860807	−	0.860807i	0.991432	+	0.130624i	$0.0416982\pi$
$444$		0			0
$445$	−3.46993	−	3.46993i	−0.164490	−	0.164490i
$446$	3.24936	+	14.6720i	0.153862	+	0.694738i
$447$		0			0
$448$	18.3722	+	4.94846i	0.868006	+	0.233793i
$449$	−9.90212			−0.467310			−0.233655	−	0.972320i	$-0.575069\pi$
$449$	−9.90212			−0.467310			−0.233655	+	0.972320i	$0.575069\pi$
$450$		0			0
$451$	17.6454	+	17.6454i	0.830891	+	0.830891i
$452$	15.0716	−	7.02004i	0.708908	−	0.330195i
$453$		0			0
$454$	0.385089	−	0.604180i	0.0180731	−	0.0283556i
$455$		−	26.3193i		−	1.23387i
$456$		0			0
$457$		−	30.1271i		−	1.40929i	−0.709562	−	0.704643i	$-0.751107\pi$
$457$		−	30.1271i		−	1.40929i	0.709562	−	0.704643i	$-0.248893\pi$
$458$	25.7221	+	16.3946i	1.20191	+	0.766071i
$459$		0			0
$460$	16.1325	+	5.87969i	0.752184	+	0.274142i
$461$	−23.0548	−	23.0548i	−1.07377	−	1.07377i	−0.997053	−	0.0767153i	$-0.975557\pi$
$461$	−23.0548	−	23.0548i	−1.07377	−	1.07377i	−0.0767153	−	0.997053i	$-0.524443\pi$
$462$		0			0
$463$	−7.30078			−0.339296			−0.169648	−	0.985505i	$-0.554263\pi$
$463$	−7.30078			−0.339296			−0.169648	+	0.985505i	$0.554263\pi$
$464$	−29.4181	+	2.54804i	−1.36570	+	0.118290i
$465$		0			0
$466$	−30.5826	+	6.77304i	−1.41671	+	0.313755i
$467$	−12.9119	−	12.9119i	−0.597492	−	0.597492i	0.342152	−	0.939644i	$-0.388844\pi$
$467$	−12.9119	−	12.9119i	−0.597492	−	0.597492i	−0.939644	+	0.342152i	$0.888844\pi$
$468$		0			0
$469$	−17.2705	+	17.2705i	−0.797476	+	0.797476i
$470$	22.8702	+	14.5769i	1.05492	+	0.672381i
$471$		0			0
$472$	39.8702	+	5.27541i	1.83518	+	0.242820i
$473$		−	27.9159i		−	1.28358i
$474$		0			0
$475$	−1.54472	+	1.54472i	−0.0708766	+	0.0708766i
$476$	−1.34315	−	2.88366i	−0.0615632	−	0.132172i
$477$		0			0
$478$	−1.55685	−	7.02971i	−0.0712086	−	0.321531i
$479$	−17.2756			−0.789344			−0.394672	−	0.918822i	$-0.629142\pi$
$479$	−17.2756			−0.789344			−0.394672	+	0.918822i	$0.629142\pi$
$480$		0			0
$481$	−53.3801			−2.43392
$482$	5.30635	+	23.9600i	0.241698	+	1.09135i
$483$		0			0
$484$	6.90334	+	14.8210i	0.313788	+	0.673684i
$485$	−2.11831	+	2.11831i	−0.0961875	+	0.0961875i
$486$		0			0
$487$			1.74421i			0.0790375i	0.999219	+	0.0395187i	$0.0125825\pi$
$487$			1.74421i			0.0790375i	−0.999219	+	0.0395187i	$0.987418\pi$
$488$	−1.82378	+	13.7836i	−0.0825585	+	0.623956i
$489$		0			0
$490$	3.29787	+	2.10198i	0.148983	+	0.0949579i
$491$	0.384534	−	0.384534i	0.0173538	−	0.0173538i	−0.698377	−	0.715730i	$-0.746094\pi$
$491$	0.384534	−	0.384534i	0.0173538	−	0.0173538i	0.715730	+	0.698377i	$0.246094\pi$
$492$		0			0
$493$	3.49087	+	3.49087i	0.157221	+	0.157221i
$494$	−21.2699	+	4.71059i	−0.956979	+	0.211939i
$495$		0			0
$496$	1.12508	−	1.33846i	0.0505178	−	0.0600988i
$497$	−8.36190			−0.375083
$498$		0			0
$499$	3.07267	+	3.07267i	0.137551	+	0.137551i	0.772530	−	0.634978i	$-0.218991\pi$
$499$	3.07267	+	3.07267i	0.137551	+	0.137551i	−0.634978	+	0.772530i	$0.718991\pi$
$500$	−22.2899	−	8.12383i	−0.996837	−	0.363309i
$501$		0			0
$502$	−36.6958	−	23.3890i	−1.63781	−	1.04390i
$503$		−	8.98384i		−	0.400570i	−0.979738	−	0.200285i	$-0.935813\pi$
$503$		−	8.98384i		−	0.400570i	0.979738	−	0.200285i	$-0.0641867\pi$
$504$		0			0
$505$		−	24.0480i		−	1.07012i
$506$	13.8816	−	21.7793i	0.617112	−	0.968208i
$507$		0			0
$508$	−22.9928	+	10.7096i	−1.02014	+	0.475161i
$509$	0.691585	+	0.691585i	0.0306540	+	0.0306540i	0.722268	−	0.691614i	$-0.243100\pi$
$509$	0.691585	+	0.691585i	0.0306540	+	0.0306540i	−0.691614	+	0.722268i	$0.743100\pi$
$510$		0			0
$511$	36.2302			1.60273
$512$	20.9219	−	8.61831i	0.924625	−	0.380879i
$513$		0			0
$514$	2.26709	+	10.2367i	0.0999969	+	0.451520i
$515$	−1.03439	−	1.03439i	−0.0455807	−	0.0455807i
$516$		0			0
$517$	28.8452	−	28.8452i	1.26861	−	1.26861i
$518$	−17.9518	+	28.1652i	−0.788757	+	1.23751i
$519$		0			0
$520$	−19.0378	−	24.8440i	−0.834864	−	1.08948i
$521$		−	12.0831i		−	0.529372i	−0.964335	−	0.264686i	$-0.914732\pi$
$521$		−	12.0831i		−	0.529372i	0.964335	−	0.264686i	$-0.0852683\pi$
$522$		0			0
$523$	−1.02761	+	1.02761i	−0.0449344	+	0.0449344i	−0.729217	−	0.684283i	$-0.760115\pi$
$523$	−1.02761	+	1.02761i	−0.0449344	+	0.0449344i	0.684283	+	0.729217i	$0.260115\pi$
$524$	23.6487	+	8.61905i	1.03310	+	0.376525i
$525$		0			0
$526$	−20.9360	+	4.63664i	−0.912853	+	0.202167i
$527$	−0.292334			−0.0127343
$528$		0			0
$529$	5.60658			0.243764
$530$	21.4460	−	4.74959i	0.931555	−	0.206309i
$531$		0			0
$532$	−4.66763	+	12.8069i	−0.202368	+	0.555251i
$533$	−21.6619	+	21.6619i	−0.938279	+	0.938279i
$534$		0			0
$535$			20.3141i			0.878255i
$536$	−3.80998	+	28.7949i	−0.164566	+	1.24375i
$537$		0			0
$538$	15.4822	−	24.2905i	0.667483	−	1.04724i
$539$	4.15948	−	4.15948i	0.179161	−	0.179161i
$540$		0			0
$541$	−9.95907	−	9.95907i	−0.428174	−	0.428174i	0.459832	−	0.888006i	$-0.347910\pi$
$541$	−9.95907	−	9.95907i	−0.428174	−	0.428174i	−0.888006	+	0.459832i	$0.847910\pi$
$542$	1.47965	+	6.68113i	0.0635564	+	0.286979i
$543$		0			0
$544$	−3.35374	−	1.75047i	−0.143790	−	0.0750508i
$545$	15.7512			0.674706
$546$		0			0
$547$	−15.5372	−	15.5372i	−0.664324	−	0.664324i	0.292072	−	0.956396i	$-0.405655\pi$
$547$	−15.5372	−	15.5372i	−0.664324	−	0.664324i	−0.956396	+	0.292072i	$0.905655\pi$
$548$	−16.9449	−	36.3796i	−0.723850	−	1.55406i
$549$		0			0
$550$	−2.53743	+	3.98106i	−0.108196	+	0.169753i
$551$		−	21.1542i		−	0.901198i
$552$		0			0
$553$			21.4158i			0.910694i
$554$	−13.6092	−	8.67414i	−0.578198	−	0.368529i
$555$		0			0
$556$	14.0458	−	38.5385i	0.595675	−	1.63440i
$557$	28.3732	+	28.3732i	1.20221	+	1.20221i	0.973493	+	0.228718i	$0.0734535\pi$
$557$	28.3732	+	28.3732i	1.20221	+	1.20221i	0.228718	+	0.973493i	$0.426547\pi$
$558$		0			0
$559$	34.2701			1.44947
$560$	−19.5110	+	1.68994i	−0.824491	+	0.0714129i
$561$		0			0
$562$	−16.8416	+	3.72987i	−0.710421	+	0.157335i
$563$	10.6117	+	10.6117i	0.447230	+	0.447230i	0.894433	−	0.447203i	$-0.147580\pi$
$563$	10.6117	+	10.6117i	0.447230	+	0.447230i	−0.447203	+	0.894433i	$0.647580\pi$
$564$		0			0
$565$	−12.1008	+	12.1008i	−0.509084	+	0.509084i
$566$	3.57485	+	2.27852i	0.150262	+	0.0957733i
$567$		0			0
$568$	−7.89321	+	6.04851i	−0.331192	+	0.253790i
$569$			1.68459i			0.0706217i	0.999376	+	0.0353108i	$0.0112421\pi$
$569$			1.68459i			0.0706217i	−0.999376	+	0.0353108i	$0.988758\pi$
$570$		0			0
$571$	7.71672	−	7.71672i	0.322935	−	0.322935i	−0.526957	−	0.849892i	$-0.676667\pi$
$571$	7.71672	−	7.71672i	0.322935	−	0.322935i	0.849892	+	0.526957i	$0.176667\pi$
$572$	−42.6767	+	19.8779i	−1.78440	+	0.831139i
$573$		0			0
$574$	4.14464	+	18.7145i	0.172994	+	0.781127i
$575$	3.17936			0.132588
$576$		0			0
$577$	20.2172			0.841653			0.420827	−	0.907141i	$-0.361740\pi$
$577$	20.2172			0.841653			0.420827	+	0.907141i	$0.361740\pi$
$578$	−5.06171	−	22.8553i	−0.210539	−	0.950657i
$579$		0			0
$580$	27.5508	−	12.8326i	1.14399	−	0.532846i
$581$	−8.10122	+	8.10122i	−0.336095	+	0.336095i
$582$		0			0
$583$		−	33.0395i		−	1.36836i
$584$	34.1994	−	26.2068i	1.41518	−	1.08445i
$585$		0			0
$586$	35.5648	+	22.6681i	1.46917	+	0.936411i
$587$	13.1299	−	13.1299i	0.541929	−	0.541929i	−0.382165	−	0.924094i	$-0.624821\pi$
$587$	13.1299	−	13.1299i	0.541929	−	0.541929i	0.924094	+	0.382165i	$0.124821\pi$
$588$		0			0
$589$	0.885752	+	0.885752i	0.0364968	+	0.0364968i
$590$	−40.4160	+	8.95080i	−1.66390	+	0.368499i
$591$		0			0
$592$	3.42749	+	39.5718i	0.140869	+	1.62639i
$593$	5.03339			0.206697			0.103348	−	0.994645i	$-0.467044\pi$
$593$	5.03339			0.206697			0.103348	+	0.994645i	$0.467044\pi$
$594$		0			0
$595$	2.31526	+	2.31526i	0.0949162	+	0.0949162i
$596$	12.5512	−	34.4375i	0.514115	−	1.41062i
$597$		0			0
$598$	26.7367	+	17.0413i	1.09334	+	0.696870i
$599$		−	11.1242i		−	0.454523i	−0.973834	−	0.227262i	$-0.927023\pi$
$599$		−	11.1242i		−	0.454523i	0.973834	−	0.227262i	$-0.0729772\pi$
$600$		0			0
$601$			17.7786i			0.725205i	0.931944	+	0.362603i	$0.118112\pi$
$601$			17.7786i			0.725205i	−0.931944	+	0.362603i	$0.881888\pi$
$602$	11.5251	−	18.0821i	0.469728	−	0.736972i
$603$		0			0
$604$	4.22597	+	9.07290i	0.171952	+	0.369171i
$605$	−11.8996	−	11.8996i	−0.483789	−	0.483789i
$606$		0			0
$607$	6.52320			0.264769			0.132384	−	0.991198i	$-0.457737\pi$
$607$	6.52320			0.264769			0.132384	+	0.991198i	$0.457737\pi$
$608$	4.85778	+	15.4654i	0.197009	+	0.627204i
$609$		0			0
$610$	−3.09441	−	13.9723i	−0.125289	−	0.565723i
$611$	35.4109	+	35.4109i	1.43257	+	1.43257i
$612$		0			0
$613$	18.6138	−	18.6138i	0.751804	−	0.751804i	−0.223012	−	0.974816i	$-0.571589\pi$
$613$	18.6138	−	18.6138i	0.751804	−	0.751804i	0.974816	+	0.223012i	$0.0715888\pi$
$614$	−2.35971	+	3.70224i	−0.0952303	+	0.149410i
$615$		0			0
$616$	−3.86395	+	29.2027i	−0.155683	+	1.17661i
$617$		−	2.15336i		−	0.0866908i	−0.999060	−	0.0433454i	$-0.986198\pi$
$617$		−	2.15336i		−	0.0866908i	0.999060	−	0.0433454i	$-0.0138016\pi$
$618$		0			0
$619$	11.9987	−	11.9987i	0.482267	−	0.482267i	−0.423588	−	0.905855i	$-0.639230\pi$
$619$	11.9987	−	11.9987i	0.482267	−	0.482267i	0.905855	+	0.423588i	$0.139230\pi$
$620$	−0.616270	+	1.69091i	−0.0247500	+	0.0679084i
$621$		0			0
$622$	15.1748	−	3.36073i	0.608456	−	0.134753i
$623$	−5.66959			−0.227147
$624$		0			0
$625$	20.6072			0.824286
$626$	37.1983	−	8.23820i	1.48674	−	0.329265i
$627$		0			0
$628$	−2.94609	−	1.07374i	−0.117562	−	0.0428467i
$629$	4.69575	−	4.69575i	0.187232	−	0.187232i
$630$		0			0
$631$			33.5397i			1.33519i	0.744523	+	0.667597i	$0.232677\pi$
$631$			33.5397i			1.33519i	−0.744523	+	0.667597i	$0.767323\pi$
$632$	15.4910	+	20.2154i	0.616198	+	0.804127i
$633$		0			0
$634$	11.3594	−	17.8221i	0.451139	−	0.707807i
$635$	18.4606	−	18.4606i	0.732588	−	0.732588i
$636$		0			0
$637$	5.10625	+	5.10625i	0.202317	+	0.202317i
$638$	−9.88489	−	44.6337i	−0.391347	−	1.76706i
$639$		0			0
$640$	−17.1950	+	15.7084i	−0.679692	+	0.620927i
$641$	−18.2237			−0.719791			−0.359896	−	0.932993i	$-0.617188\pi$
$641$	−18.2237			−0.719791			−0.359896	+	0.932993i	$0.617188\pi$
$642$		0			0
$643$	10.6873	+	10.6873i	0.421464	+	0.421464i	0.885708	−	0.464243i	$-0.153674\pi$
$643$	10.6873	+	10.6873i	0.421464	+	0.421464i	−0.464243	+	0.885708i	$0.653674\pi$
$644$	17.9832	−	8.37619i	0.708636	−	0.330068i
$645$		0			0
$646$	1.45669	−	2.28546i	0.0573128	−	0.0899200i
$647$			4.45231i			0.175039i	0.996163	+	0.0875193i	$0.0278939\pi$
$647$			4.45231i			0.175039i	−0.996163	+	0.0875193i	$0.972106\pi$
$648$		0			0
$649$			62.2643i			2.44409i
$650$	−4.88722	−	3.11499i	−0.191692	−	0.122180i
$651$		0			0
$652$	20.9948	+	7.65181i	0.822221	+	0.299668i
$653$	3.35549	+	3.35549i	0.131311	+	0.131311i	0.769707	−	0.638397i	$-0.220402\pi$
$653$	3.35549	+	3.35549i	0.131311	+	0.131311i	−0.638397	+	0.769707i	$0.720402\pi$
$654$		0			0
$655$	−25.9074			−1.01229
$656$	17.4493	+	14.6675i	0.681280	+	0.572670i
$657$		0			0
$658$	30.5928	−	6.77530i	1.19263	−	0.264129i
$659$	8.39660	+	8.39660i	0.327085	+	0.327085i	0.851477	−	0.524392i	$-0.175707\pi$
$659$	8.39660	+	8.39660i	0.327085	+	0.327085i	−0.524392	+	0.851477i	$0.675707\pi$
$660$		0			0
$661$	−23.9534	+	23.9534i	−0.931681	+	0.931681i	−0.997811	−	0.0661299i	$-0.978935\pi$
$661$	−23.9534	+	23.9534i	−0.931681	+	0.931681i	0.0661299	+	0.997811i	$0.478935\pi$
$662$	−32.8997	−	20.9695i	−1.27868	−	0.815002i
$663$		0			0
$664$	−1.78718	+	13.5071i	−0.0693562	+	0.524177i
$665$		−	14.0301i		−	0.544064i
$666$		0			0
$667$	−21.7699	+	21.7699i	−0.842933	+	0.842933i
$668$	−12.4714	−	26.7754i	−0.482534	−	1.03597i
$669$		0			0
$670$	−6.46441	−	29.1890i	−0.249742	−	1.12767i
$671$	−21.5256			−0.830986
$672$		0			0
$673$	−4.09820			−0.157974			−0.0789870	−	0.996876i	$-0.525169\pi$
$673$	−4.09820			−0.157974			−0.0789870	+	0.996876i	$0.525169\pi$
$674$	10.8674	+	49.0701i	0.418597	+	1.89011i
$675$		0			0
$676$	−13.4247	−	28.8220i	−0.516334	−	1.10854i
$677$	−9.61109	+	9.61109i	−0.369384	+	0.369384i	−0.867253	−	0.497868i	$-0.834116\pi$
$677$	−9.61109	+	9.61109i	−0.369384	+	0.369384i	0.497868	+	0.867253i	$0.334116\pi$
$678$		0			0
$679$			3.46116i			0.132827i
$680$	3.86020	+	0.510761i	0.148032	+	0.0195868i
$681$		0			0
$682$	2.28276	+	1.45498i	0.0874114	+	0.0557139i
$683$	11.5025	−	11.5025i	0.440132	−	0.440132i	−0.451924	−	0.892056i	$-0.649262\pi$
$683$	11.5025	−	11.5025i	0.440132	−	0.440132i	0.892056	+	0.451924i	$0.149262\pi$
$684$		0			0
$685$	29.2088	+	29.2088i	1.11601	+	1.11601i
$686$	27.3992	−	6.06801i	1.04611	−	0.231678i
$687$		0			0
$688$	−2.20045	−	25.4052i	−0.0838915	−	0.968563i
$689$	40.5599			1.54521
$690$		0			0
$691$	−26.6841	−	26.6841i	−1.01511	−	1.01511i	−0.999884	−	0.0152281i	$-0.995153\pi$
$691$	−26.6841	−	26.6841i	−1.01511	−	1.01511i	−0.0152281	−	0.999884i	$-0.504847\pi$
$692$	30.3203	+	11.0506i	1.15260	+	0.420080i
$693$		0			0
$694$	35.9471	+	22.9118i	1.36453	+	0.869720i
$695$			42.2193i			1.60147i
$696$		0			0
$697$		−	3.81111i		−	0.144356i
$698$	7.07185	−	11.0953i	0.267674	−	0.419962i
$699$		0			0
$700$	−3.28716	+	1.53109i	−0.124243	+	0.0578698i
$701$	17.4387	+	17.4387i	0.658651	+	0.658651i	0.955061	−	0.296410i	$-0.0957895\pi$
$701$	17.4387	+	17.4387i	0.658651	+	0.658651i	−0.296410	+	0.955061i	$0.595790\pi$
$702$		0			0
$703$	−28.4555			−1.07322
$704$	17.4762	+	30.3608i	0.658659	+	1.14427i
$705$		0			0
$706$	8.53607	+	38.5433i	0.321259	+	1.45060i
$707$	−19.6463	−	19.6463i	−0.738875	−	0.738875i
$708$		0			0
$709$	8.85045	−	8.85045i	0.332386	−	0.332386i	−0.521106	−	0.853492i	$-0.674480\pi$
$709$	8.85045	−	8.85045i	0.332386	−	0.332386i	0.853492	+	0.521106i	$0.174480\pi$
$710$	5.50133	−	8.63123i	0.206461	−	0.323924i
$711$		0			0
$712$	−5.35181	+	4.10105i	−0.200567	+	0.153694i
$713$		−	1.82306i		−	0.0682742i
$714$		0			0
$715$	34.2646	−	34.2646i	1.28142	−	1.28142i
$716$	−14.7731	−	5.38423i	−0.552096	−	0.201218i
$717$		0			0
$718$	35.7437	−	7.91605i	1.33394	−	0.295424i
$719$	−41.8247			−1.55980			−0.779899	−	0.625905i	$-0.784730\pi$
$719$	−41.8247			−1.55980			−0.779899	+	0.625905i	$0.784730\pi$
$720$		0			0
$721$	−1.69012			−0.0629432
$722$	14.8960	−	3.29896i	0.554370	−	0.122775i
$723$		0			0
$724$	2.19070	−	6.01079i	0.0814168	−	0.223389i
$725$	3.97933	−	3.97933i	0.147789	−	0.147789i
$726$		0			0
$727$			8.75490i			0.324701i	0.986733	+	0.162351i	$0.0519075\pi$
$727$			8.75490i			0.324701i	−0.986733	+	0.162351i	$0.948092\pi$
$728$	−35.8498	−	4.74345i	−1.32868	−	0.175804i
$729$		0			0
$730$	−23.8360	+	37.3971i	−0.882210	+	1.38413i
$731$	−3.01468	+	3.01468i	−0.111502	+	0.111502i
$732$		0			0
$733$	−4.85097	−	4.85097i	−0.179175	−	0.179175i	0.611821	−	0.790996i	$-0.290437\pi$
$733$	−4.85097	−	4.85097i	−0.179175	−	0.179175i	−0.790996	+	0.611821i	$0.790437\pi$
$734$	−3.55993	−	16.0743i	−0.131399	−	0.593313i
$735$		0			0
$736$	10.9163	−	20.9147i	0.402381	−	0.770925i
$737$	−44.9682			−1.65643
$738$		0			0
$739$	−20.7370	−	20.7370i	−0.762822	−	0.762822i	0.214009	−	0.976832i	$-0.431348\pi$
$739$	−20.7370	−	20.7370i	−0.762822	−	0.762822i	−0.976832	+	0.214009i	$0.931348\pi$
$740$	−17.2618	−	37.0600i	−0.634557	−	1.36235i
$741$		0			0
$742$	13.6403	−	21.4008i	0.500753	−	0.785648i
$743$			43.1123i			1.58164i	0.612051	+	0.790819i	$0.290345\pi$
$743$			43.1123i			1.58164i	−0.612051	+	0.790819i	$0.709655\pi$
$744$		0			0
$745$			37.7266i			1.38220i
$746$	2.29671	+	1.46387i	0.0840887	+	0.0535960i
$747$		0			0
$748$	2.00557	−	5.50282i	0.0733307	−	0.201203i
$749$	16.5959	+	16.5959i	0.606399	+	0.606399i
$750$		0			0
$751$	40.5687			1.48037			0.740187	−	0.672401i	$-0.234737\pi$
$751$	40.5687			1.48037			0.740187	+	0.672401i	$0.234737\pi$
$752$	23.9772	−	28.5246i	0.874357	−	1.04018i
$753$		0			0
$754$	54.7931	−	12.1349i	1.99545	−	0.441926i
$755$	−7.28452	−	7.28452i	−0.265111	−	0.265111i
$756$		0			0
$757$	10.5426	−	10.5426i	0.383178	−	0.383178i	−0.489068	−	0.872246i	$-0.662663\pi$
$757$	10.5426	−	10.5426i	0.383178	−	0.383178i	0.872246	+	0.489068i	$0.162663\pi$
$758$	−15.0418	−	9.58728i	−0.546343	−	0.348226i
$759$		0			0
$760$	−10.1486	−	13.2437i	−0.368127	−	0.480400i
$761$		−	15.7830i		−	0.572132i	−0.958210	−	0.286066i	$-0.907652\pi$
$761$		−	15.7830i		−	0.572132i	0.958210	−	0.286066i	$-0.0923476\pi$
$762$		0			0
$763$	12.8681	−	12.8681i	0.465856	−	0.465856i
$764$	6.90419	−	3.21583i	0.249785	−	0.116345i
$765$		0			0
$766$	6.81976	+	30.7936i	0.246408	+	1.11262i
$767$	−76.4368			−2.75997
$768$		0			0
$769$	3.02976			0.109256			0.0546279	−	0.998507i	$-0.482603\pi$
$769$	3.02976			0.109256			0.0546279	+	0.998507i	$0.482603\pi$
$770$	−6.55597	−	29.6025i	−0.236261	−	1.06680i
$771$		0			0
$772$	−11.6852	+	5.44271i	−0.420558	+	0.195887i
$773$	−6.99199	+	6.99199i	−0.251484	+	0.251484i	−0.821579	−	0.570095i	$-0.806906\pi$
$773$	−6.99199	+	6.99199i	−0.251484	+	0.251484i	0.570095	+	0.821579i	$0.306906\pi$
$774$		0			0
$775$			0.333239i			0.0119703i
$776$	2.50360	+	3.26715i	0.0898740	+	0.117284i
$777$		0			0
$778$	−20.8321	−	13.2779i	−0.746868	−	0.476035i
$779$	−11.5474	+	11.5474i	−0.413728	+	0.413728i
$780$		0			0
$781$	−10.8862	−	10.8862i	−0.389540	−	0.389540i
$782$	−3.85106	+	0.852884i	−0.137714	+	0.0304991i
$783$		0			0
$784$	3.45750	−	4.11324i	0.123482	−	0.146901i
$785$	3.22746			0.115193
$786$		0			0
$787$	−17.5120	−	17.5120i	−0.624236	−	0.624236i	0.322375	−	0.946612i	$-0.395519\pi$
$787$	−17.5120	−	17.5120i	−0.624236	−	0.624236i	−0.946612	+	0.322375i	$0.895519\pi$
$788$	−0.688005	+	1.88773i	−0.0245092	+	0.0672476i
$789$		0			0
$790$	−22.1056	−	14.0896i	−0.786482	−	0.501284i
$791$			19.7718i			0.703004i
$792$		0			0
$793$		−	26.4252i		−	0.938387i
$794$	−1.97010	+	3.09096i	−0.0699162	+	0.109694i
$795$		0			0
$796$	−2.80760	−	6.02774i	−0.0995127	−	0.213648i
$797$	9.32258	+	9.32258i	0.330223	+	0.330223i	0.852671	−	0.522448i	$-0.174981\pi$
$797$	9.32258	+	9.32258i	0.330223	+	0.330223i	−0.522448	+	0.852671i	$0.674981\pi$
$798$		0			0
$799$	−6.23006			−0.220404
$800$	−1.99541	+	3.82301i	−0.0705483	+	0.135164i
$801$		0			0
$802$	−7.31829	−	33.0446i	−0.258418	−	1.16685i
$803$	47.1675	+	47.1675i	1.66450	+	1.66450i
$804$		0			0
$805$	−14.4385	+	14.4385i	−0.508889	+	0.508889i
$806$	−1.78615	+	2.80236i	−0.0629146	+	0.0987089i
$807$		0			0
$808$	−32.7561	−	4.33411i	−1.15235	−	0.152473i
$809$		−	41.3890i		−	1.45516i	−0.686023	−	0.727580i	$-0.740645\pi$
$809$		−	41.3890i		−	1.45516i	0.686023	−	0.727580i	$-0.259355\pi$
$810$		0			0
$811$	14.1584	−	14.1584i	0.497169	−	0.497169i	−0.413387	−	0.910556i	$-0.635654\pi$
$811$	14.1584	−	14.1584i	0.497169	−	0.497169i	0.910556	+	0.413387i	$0.135654\pi$
$812$	12.0242	−	32.9918i	0.421968	−	1.15778i
$813$		0			0
$814$	−60.0390	+	13.2967i	−2.10437	+	0.466048i
$815$	−23.0000			−0.805656
$816$		0			0
$817$	18.2685			0.639134
$818$	−6.35126	+	1.40660i	−0.222067	+	0.0491805i
$819$		0			0
$820$	−22.0440	−	8.03420i	−0.769810	−	0.280566i
$821$	−4.27171	+	4.27171i	−0.149084	+	0.149084i	−0.777709	−	0.628625i	$-0.783618\pi$
$821$	−4.27171	+	4.27171i	−0.149084	+	0.149084i	0.628625	+	0.777709i	$0.283618\pi$
$822$		0			0
$823$		−	45.0044i		−	1.56875i	−0.620285	−	0.784377i	$-0.712983\pi$
$823$		−	45.0044i		−	1.56875i	0.620285	−	0.784377i	$-0.287017\pi$
$824$	−1.59538	+	1.22253i	−0.0555778	+	0.0425889i
$825$		0			0
$826$	−25.7058	+	40.3308i	−0.894420	+	1.40329i
$827$	−4.42312	+	4.42312i	−0.153807	+	0.153807i	−0.779816	−	0.626009i	$-0.784687\pi$
$827$	−4.42312	+	4.42312i	−0.153807	+	0.153807i	0.626009	+	0.779816i	$0.284687\pi$
$828$		0			0
$829$	−7.71485	−	7.71485i	−0.267948	−	0.267948i	0.560325	−	0.828273i	$-0.310676\pi$
$829$	−7.71485	−	7.71485i	−0.267948	−	0.267948i	−0.828273	+	0.560325i	$0.810676\pi$
$830$	−3.03232	−	13.6920i	−0.105253	−	0.475255i
$831$		0			0
$832$	−37.2715	+	21.4541i	−1.29216	+	0.743787i
$833$	−0.898374			−0.0311268
$834$		0			0
$835$	21.4976	+	21.4976i	0.743955	+	0.743955i
$836$	−22.7498	+	10.5964i	−0.786820	+	0.366485i
$837$		0			0
$838$	−9.97957	+	15.6573i	−0.344739	+	0.540872i
$839$			23.8478i			0.823318i	0.911338	+	0.411659i	$0.135051\pi$
$839$			23.8478i			0.823318i	−0.911338	+	0.411659i	$0.864949\pi$
$840$		0			0
$841$			25.4950i			0.879137i
$842$	23.8875	+	15.2253i	0.823216	+	0.524698i
$843$		0			0
$844$	−34.2455	−	12.4812i	−1.17878	−	0.429620i
$845$	23.1408	+	23.1408i	0.796067	+	0.796067i
$846$		0			0
$847$	−19.4431			−0.668072
$848$	−2.60431	−	30.0679i	−0.0894325	−	1.03254i
$849$		0			0
$850$	0.703939	−	0.155899i	0.0241449	−	0.00534730i
$851$	29.2837	+	29.2837i	1.00383	+	1.00383i
$852$		0			0
$853$	−5.12113	+	5.12113i	−0.175344	+	0.175344i	−0.789323	−	0.613979i	$-0.789568\pi$
$853$	−5.12113	+	5.12113i	−0.175344	+	0.175344i	0.613979	+	0.789323i	$0.289568\pi$
$854$	−13.9429	−	8.88684i	−0.477115	−	0.304101i
$855$		0			0
$856$	27.6701	+	3.66116i	0.945745	+	0.125136i
$857$			37.1683i			1.26965i	0.772658	+	0.634823i	$0.218927\pi$
$857$			37.1683i			1.26965i	−0.772658	+	0.634823i	$0.781073\pi$
$858$		0			0
$859$	−19.8972	+	19.8972i	−0.678884	+	0.678884i	−0.959748	−	0.280864i	$-0.909379\pi$
$859$	−19.8972	+	19.8972i	−0.678884	+	0.678884i	0.280864	+	0.959748i	$0.409379\pi$
$860$	11.0821	+	23.7926i	0.377897	+	0.811321i
$861$		0			0
$862$	−2.25210	−	10.1690i	−0.0767068	−	0.346357i
$863$	−4.81937			−0.164053			−0.0820266	−	0.996630i	$-0.526139\pi$
$863$	−4.81937			−0.164053			−0.0820266	+	0.996630i	$0.526139\pi$
$864$		0			0
$865$	−33.2161			−1.12938
$866$	4.46077	+	20.1419i	0.151583	+	0.684449i
$867$		0			0
$868$	0.877936	+	1.88488i	0.0297991	+	0.0639768i
$869$	−27.8809	+	27.8809i	−0.945796	+	0.945796i
$870$		0			0
$871$		−	55.2038i		−	1.87051i
$872$	2.83879	−	21.4549i	0.0961336	−	0.726553i
$873$		0			0
$874$	14.2526	+	9.08426i	0.482102	+	0.307280i
$875$	19.9493	−	19.9493i	0.674408	−	0.674408i
$876$		0			0
$877$	28.8904	+	28.8904i	0.975559	+	0.975559i	0.999708	−	0.0241498i	$-0.00768786\pi$
$877$	28.8904	+	28.8904i	0.975559	+	0.975559i	−0.0241498	+	0.999708i	$0.507688\pi$
$878$	−6.03144	+	1.33577i	−0.203551	+	0.0450799i
$879$		0			0
$880$	−27.6012	−	23.2010i	−0.930436	−	0.782105i
$881$	−28.5651			−0.962383			−0.481191	−	0.876616i	$-0.659796\pi$
$881$	−28.5651			−0.962383			−0.481191	+	0.876616i	$0.659796\pi$
$882$		0			0
$883$	0.201285	+	0.201285i	0.00677378	+	0.00677378i	0.710486	−	0.703712i	$-0.248475\pi$
$883$	0.201285	+	0.201285i	0.00677378	+	0.00677378i	−0.703712	+	0.710486i	$0.748475\pi$
$884$	6.75536	+	2.46207i	0.227207	+	0.0828083i
$885$		0			0
$886$	30.5567	+	19.4761i	1.02657	+	0.654313i
$887$		−	5.29975i		−	0.177948i	−0.996034	−	0.0889741i	$-0.971641\pi$
$887$		−	5.29975i		−	0.177948i	0.996034	−	0.0889741i	$-0.0283588\pi$
$888$		0			0
$889$		−	30.1633i		−	1.01164i
$890$	3.73005	−	5.85220i	0.125032	−	0.196166i
$891$		0			0
$892$	−19.2648	+	8.97315i	−0.645033	+	0.300443i
$893$	18.8766	+	18.8766i	0.631682	+	0.631682i
$894$		0			0
$895$	16.1841			0.540973
$896$	−1.21454	+	26.8808i	−0.0405748	+	0.898024i
$897$		0			0
$898$	−3.02799	−	13.6724i	−0.101045	−	0.456255i
$899$	−2.28177	−	2.28177i	−0.0761014	−	0.0761014i
$900$		0			0
$901$	−3.56798	+	3.56798i	−0.118866	+	0.118866i
$902$	−18.9682	+	29.7599i	−0.631573	+	0.990897i
$903$		0			0
$904$	14.3018	+	18.6635i	0.475669	+	0.620740i
$905$			6.58487i			0.218889i
$906$		0			0
$907$	−8.40401	+	8.40401i	−0.279051	+	0.279051i	−0.832730	−	0.553679i	$-0.813223\pi$
$907$	−8.40401	+	8.40401i	−0.279051	+	0.279051i	0.553679	+	0.832730i	$0.313223\pi$
$908$	0.951983	+	0.346961i	0.0315927	+	0.0115143i
$909$		0			0
$910$	36.3405	−	8.04823i	1.20468	−	0.266796i
$911$	−7.70528			−0.255287			−0.127644	−	0.991820i	$-0.540741\pi$
$911$	−7.70528			−0.255287			−0.127644	+	0.991820i	$0.540741\pi$
$912$		0			0
$913$	−21.0937			−0.698099
$914$	41.5982	−	9.21264i	1.37595	−	0.304727i
$915$		0			0
$916$	−14.7714	+	40.5293i	−0.488060	+	1.33913i
$917$	−21.1654	+	21.1654i	−0.698942	+	0.698942i
$918$		0			0
$919$		−	25.9186i		−	0.854975i	−0.904021	−	0.427487i	$-0.859399\pi$
$919$		−	25.9186i		−	0.854975i	0.904021	−	0.427487i	$-0.140601\pi$
$920$	−3.18522	+	24.0731i	−0.105014	+	0.793667i
$921$		0			0
$922$	24.7831	−	38.8830i	0.816188	−	1.28054i
$923$	13.3641	−	13.3641i	0.439886	−	0.439886i
$924$		0			0
$925$	−5.35280	−	5.35280i	−0.175999	−	0.175999i
$926$	−2.23252	−	10.0806i	−0.0733653	−	0.331269i
$927$		0			0
$928$	−12.5141	−	39.8402i	−0.410794	−	1.30782i
$929$	8.82298			0.289472			0.144736	−	0.989470i	$-0.453767\pi$
$929$	8.82298			0.289472			0.144736	+	0.989470i	$0.453767\pi$
$930$		0			0
$931$	2.72201	+	2.72201i	0.0892102	+	0.0892102i
$932$	−18.7038	−	40.1560i	−0.612665	−	1.31535i
$933$		0			0
$934$	13.8799	−	21.7766i	0.454163	−	0.712551i
$935$			6.02839i			0.197149i
$936$		0			0
$937$			4.48109i			0.146391i	0.997318	+	0.0731955i	$0.0233197\pi$
$937$			4.48109i			0.146391i	−0.997318	+	0.0731955i	$0.976680\pi$
$938$	−29.1275	−	18.5651i	−0.951046	−	0.606173i
$939$		0			0
$940$	−13.1336	+	36.0356i	−0.428371	+	1.17535i
$941$	−3.12592	−	3.12592i	−0.101902	−	0.101902i	0.654318	−	0.756220i	$-0.272956\pi$
$941$	−3.12592	−	3.12592i	−0.101902	−	0.101902i	−0.756220	+	0.654318i	$0.772956\pi$
$942$		0			0
$943$	23.7669			0.773957
$944$	4.90794	+	56.6643i	0.159740	+	1.84426i
$945$		0			0
$946$	38.5451	−	8.53648i	1.25321	−	0.277545i
$947$	−32.2488	−	32.2488i	−1.04795	−	1.04795i	−0.998791	−	0.0491547i	$-0.984347\pi$
$947$	−32.2488	−	32.2488i	−1.04795	−	1.04795i	−0.0491547	−	0.998791i	$-0.515653\pi$
$948$		0			0
$949$	−57.9037	+	57.9037i	−1.87963	+	1.87963i
$950$	−2.60525	−	1.66052i	−0.0845254	−	0.0538744i
$951$		0			0
$952$	3.57091	−	2.73637i	0.115734	−	0.0886861i
$953$			40.7465i			1.31991i	0.751306	+	0.659954i	$0.229424\pi$
$953$			40.7465i			1.31991i	−0.751306	+	0.659954i	$0.770576\pi$
$954$		0			0
$955$	−5.54329	+	5.54329i	−0.179377	+	0.179377i
$956$	9.23025	−	4.29926i	0.298527	−	0.139048i
$957$		0			0
$958$	−5.28276	−	23.8535i	−0.170678	−	0.770670i
$959$	47.7249			1.54112
$960$		0			0
$961$	−30.8089			−0.993836
$962$	−16.3232	−	73.7050i	−0.526282	−	2.37634i
$963$		0			0
$964$	−31.4603	+	14.6536i	−1.01327	+	0.471960i
$965$	9.38187	−	9.38187i	0.302013	−	0.302013i
$966$		0			0
$967$		−	57.6088i		−	1.85258i	−0.376818	−	0.926288i	$-0.622982\pi$
$967$		−	57.6088i		−	1.85258i	0.376818	−	0.926288i	$-0.377018\pi$
$968$	−18.3533	+	14.0640i	−0.589897	+	0.452034i
$969$		0			0
$970$	−3.57263	−	2.27711i	−0.114710	−	0.0731135i
$971$	−0.210240	+	0.210240i	−0.00674694	+	0.00674694i	−0.710472	−	0.703725i	$-0.751519\pi$
$971$	−0.210240	+	0.210240i	−0.00674694	+	0.00674694i	0.703725	+	0.710472i	$0.251519\pi$
$972$		0			0
$973$	34.4915	+	34.4915i	1.10575	+	1.10575i
$974$	−2.40832	+	0.533365i	−0.0771677	+	0.0170901i
$975$		0			0
$976$	−19.5896	+	1.69674i	−0.627047	+	0.0543113i
$977$	−21.2950			−0.681287			−0.340643	−	0.940193i	$-0.610645\pi$
$977$	−21.2950			−0.681287			−0.340643	+	0.940193i	$0.610645\pi$
$978$		0			0
$979$	−7.38115	−	7.38115i	−0.235903	−	0.235903i
$980$	−1.89386	+	5.19633i	−0.0604973	+	0.165991i
$981$		0			0
$982$	0.648536	+	0.413361i	0.0206956	+	0.0131909i
$983$		−	42.2064i		−	1.34618i	−0.739563	−	0.673088i	$-0.764968\pi$
$983$		−	42.2064i		−	1.34618i	0.739563	−	0.673088i	$-0.235032\pi$
$984$		0			0
$985$		−	2.06803i		−	0.0658928i
$986$	−3.75257	+	5.88753i	−0.119506	+	0.187497i
$987$		0			0
$988$	−13.0084	−	27.9281i	−0.413851	−	0.888512i
$989$	−18.8002	−	18.8002i	−0.597812	−	0.597812i
$990$		0			0
$991$	−26.8992			−0.854480			−0.427240	−	0.904138i	$-0.640514\pi$
$991$	−26.8992			−0.854480			−0.427240	+	0.904138i	$0.640514\pi$
$992$	2.19214	+	1.14418i	0.0696004	+	0.0363277i
$993$		0			0
$994$	−2.55701	−	11.5458i	−0.0811033	−	0.366209i
$995$	4.83960	+	4.83960i	0.153426	+	0.153426i
$996$		0			0
$997$	−14.1692	+	14.1692i	−0.448743	+	0.448743i	−0.894937	−	0.446193i	$-0.852779\pi$
$997$	−14.1692	+	14.1692i	−0.448743	+	0.448743i	0.446193	+	0.894937i	$0.352779\pi$
$998$	−3.30301	+	5.18221i	−0.104555	+	0.164040i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.k.d.109.9	yes	32
3.2	odd	2	inner	432.2.k.d.109.8	✓	32
4.3	odd	2		1728.2.k.d.1297.13		32
12.11	even	2		1728.2.k.d.1297.4		32
16.5	even	4	inner	432.2.k.d.325.9	yes	32
16.11	odd	4		1728.2.k.d.433.13		32
48.5	odd	4	inner	432.2.k.d.325.8	yes	32
48.11	even	4		1728.2.k.d.433.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.k.d.109.8	✓	32	3.2	odd	2	inner
432.2.k.d.109.9	yes	32	1.1	even	1	trivial
432.2.k.d.325.8	yes	32	48.5	odd	4	inner
432.2.k.d.325.9	yes	32	16.5	even	4	inner
1728.2.k.d.433.4		32	48.11	even	4
1728.2.k.d.433.13		32	16.11	odd	4
1728.2.k.d.1297.4		32	12.11	even	2
1728.2.k.d.1297.13		32	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.305792 + 1.38076i) q^{2} +(-1.81298 + 0.844450i) q^{4} +(1.45562 - 1.45562i) q^{5} -2.37837i q^{7} +(-1.72038 - 2.24506i) q^{8} +O(q^{10})\)	\(q+(0.305792 + 1.38076i) q^{2} +(-1.81298 + 0.844450i) q^{4} +(1.45562 - 1.45562i) q^{5} -2.37837i q^{7} +(-1.72038 - 2.24506i) q^{8} +(2.45498 + 1.56474i) q^{10} +(3.09636 - 3.09636i) q^{11} +(3.80115 + 3.80115i) q^{13} +(3.28396 - 0.727288i) q^{14} +(2.57381 - 3.06195i) q^{16} -0.668761 q^{17} +(2.02630 + 2.02630i) q^{19} +(-1.40982 + 3.86821i) q^{20} +(5.22217 + 3.32848i) q^{22} -4.17054i q^{23} +0.762337i q^{25} +(-4.08611 + 6.41083i) q^{26} +(2.00842 + 4.31195i) q^{28} +(-5.21991 - 5.21991i) q^{29} +0.437128 q^{31} +(5.01486 + 2.61749i) q^{32} +(-0.204502 - 0.923396i) q^{34} +(-3.46201 - 3.46201i) q^{35} +(-7.02157 + 7.02157i) q^{37} +(-2.17820 + 3.41745i) q^{38} +(-5.77217 - 0.763743i) q^{40} +5.69876i q^{41} +(4.50786 - 4.50786i) q^{43} +(-2.99893 + 8.22838i) q^{44} +(5.75851 - 1.27532i) q^{46} +9.31583 q^{47} +1.34334 q^{49} +(-1.05260 + 0.233117i) q^{50} +(-10.1013 - 3.68154i) q^{52} +(5.33520 - 5.33520i) q^{53} -9.01427i q^{55} +(-5.33959 + 4.09170i) q^{56} +(5.61122 - 8.80364i) q^{58} +(-10.0544 + 10.0544i) q^{59} +(-3.47595 - 3.47595i) q^{61} +(0.133671 + 0.603568i) q^{62} +(-2.08061 + 7.72471i) q^{64} +11.0661 q^{65} +(-7.26146 - 7.26146i) q^{67} +(1.21245 - 0.564735i) q^{68} +(3.72154 - 5.83885i) q^{70} -3.51581i q^{71} +15.2332i q^{73} +(-11.8422 - 7.54794i) q^{74} +(-5.38474 - 1.96253i) q^{76} +(-7.36431 - 7.36431i) q^{77} -9.00441 q^{79} +(-0.710543 - 8.20352i) q^{80} +(-7.86860 + 1.74264i) q^{82} +(-3.40620 - 3.40620i) q^{83} +(-0.973462 + 0.973462i) q^{85} +(7.60272 + 4.84579i) q^{86} +(-12.2784 - 1.62462i) q^{88} -2.38381i q^{89} +(9.04056 - 9.04056i) q^{91} +(3.52181 + 7.56112i) q^{92} +(2.84871 + 12.8629i) q^{94} +5.89904 q^{95} -1.45526 q^{97} +(0.410784 + 1.85483i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} + 24 q^{16} + 16 q^{19} + 32 q^{22} + 24 q^{28} - 8 q^{34} + 56 q^{40} - 16 q^{43} - 32 q^{49} - 16 q^{52} - 32 q^{61} + 24 q^{64} + 32 q^{67} - 96 q^{70} - 48 q^{76} - 32 q^{79} + 32 q^{85} - 88 q^{88} - 48 q^{91} - 96 q^{94}+O(q^{100}) \) 32 * q - 8 * q^10 + 24 * q^16 + 16 * q^19 + 32 * q^22 + 24 * q^28 - 8 * q^34 + 56 * q^40 - 16 * q^43 - 32 * q^49 - 16 * q^52 - 32 * q^61 + 24 * q^64 + 32 * q^67 - 96 * q^70 - 48 * q^76 - 32 * q^79 + 32 * q^85 - 88 * q^88 - 48 * q^91 - 96 * q^94

Introduction

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