LMFDB - Embedded newform 405.2.f.a.323.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(242,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("405.242");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.f (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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.6
Root			$-1.29724 + 0.347596i$ of defining polynomial
Character	$\chi$	$=$	405.323
Dual form			405.2.f.a.242.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.949649 + 0.949649i) q^{2} -0.196335i q^{4} +(2.15519 + 0.595953i) q^{5} +(-1.44851 + 1.44851i) q^{7} +(2.08575 - 2.08575i) q^{8} +O(q^{10})$	\(q+(0.949649 + 0.949649i) q^{2} -0.196335i q^{4} +(2.15519 + 0.595953i) q^{5} +(-1.44851 + 1.44851i) q^{7} +(2.08575 - 2.08575i) q^{8} +(1.48073 + 2.61262i) q^{10} -0.880206i q^{11} +(3.92923 + 3.92923i) q^{13} -2.75114 q^{14} +3.56878 q^{16} +(-1.13610 - 1.13610i) q^{17} -1.52456i q^{19} +(0.117006 - 0.423138i) q^{20} +(0.835887 - 0.835887i) q^{22} +(1.12246 - 1.12246i) q^{23} +(4.28968 + 2.56878i) q^{25} +7.46278i q^{26} +(0.284392 + 0.284392i) q^{28} -1.59317 q^{29} -6.99036 q^{31} +(-0.782402 - 0.782402i) q^{32} -2.15779i q^{34} +(-3.98504 + 2.25856i) q^{35} +(-4.25746 + 4.25746i) q^{37} +(1.44780 - 1.44780i) q^{38} +(5.73818 - 3.25217i) q^{40} -3.59742i q^{41} +(1.36045 + 1.36045i) q^{43} -0.172815 q^{44} +2.13189 q^{46} +(-5.85598 - 5.85598i) q^{47} +2.80367i q^{49} +(1.63425 + 6.51313i) q^{50} +(0.771444 - 0.771444i) q^{52} +(4.65601 - 4.65601i) q^{53} +(0.524562 - 1.89701i) q^{55} +6.04243i q^{56} +(-1.51295 - 1.51295i) q^{58} -7.63559 q^{59} -13.2800 q^{61} +(-6.63838 - 6.63838i) q^{62} -8.62358i q^{64} +(6.12660 + 10.8099i) q^{65} +(-2.34883 + 2.34883i) q^{67} +(-0.223055 + 0.223055i) q^{68} +(-5.92923 - 1.63955i) q^{70} -5.89798i q^{71} +(1.58900 + 1.58900i) q^{73} -8.08618 q^{74} -0.299324 q^{76} +(1.27498 + 1.27498i) q^{77} -7.72958i q^{79} +(7.69140 + 2.12683i) q^{80} +(3.41628 - 3.41628i) q^{82} +(7.02601 - 7.02601i) q^{83} +(-1.77144 - 3.12557i) q^{85} +2.58390i q^{86} +(-1.83589 - 1.83589i) q^{88} -4.62765 q^{89} -11.3830 q^{91} +(-0.220378 - 0.220378i) q^{92} -11.1222i q^{94} +(0.908567 - 3.28572i) q^{95} +(-2.80367 + 2.80367i) q^{97} +(-2.66250 + 2.66250i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{7}+O(q^{10}) $ 16 * q + 4 * q^7	$ 16 q + 4 q^{7} - 8 q^{10} + 4 q^{13} + 16 q^{16} + 20 q^{22} - 8 q^{25} - 16 q^{28} + 8 q^{31} + 4 q^{37} - 12 q^{40} + 4 q^{43} + 32 q^{46} + 28 q^{52} - 16 q^{55} + 12 q^{58} - 16 q^{61} - 8 q^{67} - 36 q^{70} - 8 q^{73} - 48 q^{76} + 32 q^{82} - 44 q^{85} - 36 q^{88} - 40 q^{91} - 56 q^{97}+O(q^{100}) $ 16 * q + 4 * q^7 - 8 * q^10 + 4 * q^13 + 16 * q^16 + 20 * q^22 - 8 * q^25 - 16 * q^28 + 8 * q^31 + 4 * q^37 - 12 * q^40 + 4 * q^43 + 32 * q^46 + 28 * q^52 - 16 * q^55 + 12 * q^58 - 16 * q^61 - 8 * q^67 - 36 * q^70 - 8 * q^73 - 48 * q^76 + 32 * q^82 - 44 * q^85 - 36 * q^88 - 40 * q^91 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.949649	+	0.949649i	0.671503	+	0.671503i	0.958062	−	0.286559i	$-0.0925116\pi$
$2$	0.949649	+	0.949649i	0.671503	+	0.671503i	−0.286559	+	0.958062i	$0.592512\pi$
$3$		0			0
$3$		0			0
$4$		−	0.196335i		−	0.0981673i
$5$	2.15519	+	0.595953i	0.963830	+	0.266518i
$5$	2.15519	+	0.595953i	0.963830	+	0.266518i
$6$		0			0
$7$	−1.44851	+	1.44851i	−0.547484	+	0.547484i	−0.925712	−	0.378229i	$-0.876533\pi$
$7$	−1.44851	+	1.44851i	−0.547484	+	0.547484i	0.378229	+	0.925712i	$0.376533\pi$
$8$	2.08575	−	2.08575i	0.737423	−	0.737423i
$9$		0			0
$10$	1.48073	+	2.61262i	0.468247	+	0.826183i
$11$		−	0.880206i		−	0.265392i	−0.991157	−	0.132696i	$-0.957637\pi$
$11$		−	0.880206i		−	0.265392i	0.991157	−	0.132696i	$-0.0423634\pi$
$12$		0			0
$13$	3.92923	+	3.92923i	1.08977	+	1.08977i	0.995551	+	0.0942215i	$0.0300362\pi$
$13$	3.92923	+	3.92923i	1.08977	+	1.08977i	0.0942215	+	0.995551i	$0.469964\pi$
$14$	−2.75114			−0.735274
$15$		0			0
$16$	3.56878			0.892196
$17$	−1.13610	−	1.13610i	−0.275544	−	0.275544i	0.555783	−	0.831327i	$-0.312418\pi$
$17$	−1.13610	−	1.13610i	−0.275544	−	0.275544i	−0.831327	+	0.555783i	$0.812418\pi$
$18$		0			0
$19$		−	1.52456i		−	0.349758i	−0.984590	−	0.174879i	$-0.944047\pi$
$19$		−	1.52456i		−	0.349758i	0.984590	−	0.174879i	$-0.0559535\pi$
$20$	0.117006	−	0.423138i	0.0261634	−	0.0946166i
$21$		0			0
$22$	0.835887	−	0.835887i	0.178212	−	0.178212i
$23$	1.12246	−	1.12246i	0.234050	−	0.234050i	−0.580331	−	0.814381i	$-0.697077\pi$
$23$	1.12246	−	1.12246i	0.234050	−	0.234050i	0.814381	+	0.580331i	$0.197077\pi$
$24$		0			0
$25$	4.28968	+	2.56878i	0.857936	+	0.513757i
$26$			7.46278i			1.46357i
$27$		0			0
$28$	0.284392	+	0.284392i	0.0537450	+	0.0537450i
$29$	−1.59317			−0.295843			−0.147922	−	0.988999i	$-0.547258\pi$
$29$	−1.59317			−0.295843			−0.147922	+	0.988999i	$0.547258\pi$
$30$		0			0
$31$	−6.99036			−1.25550			−0.627752	−	0.778413i	$-0.716025\pi$
$31$	−6.99036			−1.25550			−0.627752	+	0.778413i	$0.716025\pi$
$32$	−0.782402	−	0.782402i	−0.138310	−	0.138310i
$33$		0			0
$34$		−	2.15779i		−	0.370057i
$35$	−3.98504	+	2.25856i	−0.673595	+	0.381767i
$36$		0			0
$37$	−4.25746	+	4.25746i	−0.699922	+	0.699922i	−0.964393	−	0.264472i	$-0.914802\pi$
$37$	−4.25746	+	4.25746i	−0.699922	+	0.699922i	0.264472	+	0.964393i	$0.414802\pi$
$38$	1.44780	−	1.44780i	0.234864	−	0.234864i
$39$		0			0
$40$	5.73818	−	3.25217i	0.907287	−	0.514213i
$41$		−	3.59742i		−	0.561822i	−0.959734	−	0.280911i	$-0.909363\pi$
$41$		−	3.59742i		−	0.561822i	0.959734	−	0.280911i	$-0.0906366\pi$
$42$		0			0
$43$	1.36045	+	1.36045i	0.207466	+	0.207466i	0.803190	−	0.595723i	$-0.203135\pi$
$43$	1.36045	+	1.36045i	0.207466	+	0.207466i	−0.595723	+	0.803190i	$0.703135\pi$
$44$	−0.172815			−0.0260528
$45$		0			0
$46$	2.13189			0.314330
$47$	−5.85598	−	5.85598i	−0.854182	−	0.854182i	0.136463	−	0.990645i	$-0.456427\pi$
$47$	−5.85598	−	5.85598i	−0.854182	−	0.854182i	−0.990645	+	0.136463i	$0.956427\pi$
$48$		0			0
$49$			2.80367i			0.400524i
$50$	1.63425	+	6.51313i	0.231117	+	0.921096i
$51$		0			0
$52$	0.771444	−	0.771444i	0.106980	−	0.106980i
$53$	4.65601	−	4.65601i	0.639552	−	0.639552i	−0.310893	−	0.950445i	$-0.600628\pi$
$53$	4.65601	−	4.65601i	0.639552	−	0.639552i	0.950445	+	0.310893i	$0.100628\pi$
$54$		0			0
$55$	0.524562	−	1.89701i	0.0707319	−	0.255793i
$56$			6.04243i			0.807454i
$57$		0			0
$58$	−1.51295	−	1.51295i	−0.198660	−	0.198660i
$59$	−7.63559			−0.994070			−0.497035	−	0.867731i	$-0.665578\pi$
$59$	−7.63559			−0.994070			−0.497035	+	0.867731i	$0.665578\pi$
$60$		0			0
$61$	−13.2800			−1.70033			−0.850167	−	0.526513i	$-0.823499\pi$
$61$	−13.2800			−1.70033			−0.850167	+	0.526513i	$0.823499\pi$
$62$	−6.63838	−	6.63838i	−0.843075	−	0.843075i
$63$		0			0
$64$		−	8.62358i		−	1.07795i
$65$	6.12660	+	10.8099i	0.759911	+	1.34080i
$66$		0			0
$67$	−2.34883	+	2.34883i	−0.286956	+	0.286956i	−0.835875	−	0.548919i	$-0.815039\pi$
$67$	−2.34883	+	2.34883i	−0.286956	+	0.286956i	0.548919	+	0.835875i	$0.315039\pi$
$68$	−0.223055	+	0.223055i	−0.0270494	+	0.0270494i
$69$		0			0
$70$	−5.92923	−	1.63955i	−0.708679	−	0.195964i
$71$		−	5.89798i		−	0.699961i	−0.936757	−	0.349980i	$-0.886188\pi$
$71$		−	5.89798i		−	0.699961i	0.936757	−	0.349980i	$-0.113812\pi$
$72$		0			0
$73$	1.58900	+	1.58900i	0.185979	+	0.185979i	0.793955	−	0.607976i	$-0.208018\pi$
$73$	1.58900	+	1.58900i	0.185979	+	0.185979i	−0.607976	+	0.793955i	$0.708018\pi$
$74$	−8.08618			−0.939999
$75$		0			0
$76$	−0.299324			−0.0343348
$77$	1.27498	+	1.27498i	0.145298	+	0.145298i
$78$		0			0
$79$		−	7.72958i		−	0.869646i	−0.900516	−	0.434823i	$-0.856811\pi$
$79$		−	7.72958i		−	0.869646i	0.900516	−	0.434823i	$-0.143189\pi$
$80$	7.69140	+	2.12683i	0.859925	+	0.237787i
$81$		0			0
$82$	3.41628	−	3.41628i	0.377265	−	0.377265i
$83$	7.02601	−	7.02601i	0.771204	−	0.771204i	−0.207113	−	0.978317i	$-0.566407\pi$
$83$	7.02601	−	7.02601i	0.771204	−	0.771204i	0.978317	+	0.207113i	$0.0664067\pi$
$84$		0			0
$85$	−1.77144	−	3.12557i	−0.192140	−	0.339015i
$86$			2.58390i			0.278629i
$87$		0			0
$88$	−1.83589	−	1.83589i	−0.195706	−	0.195706i
$89$	−4.62765			−0.490530			−0.245265	−	0.969456i	$-0.578875\pi$
$89$	−4.62765			−0.490530			−0.245265	+	0.969456i	$0.578875\pi$
$90$		0			0
$91$	−11.3830			−1.19327
$92$	−0.220378	−	0.220378i	−0.0229760	−	0.0229760i
$93$		0			0
$94$		−	11.1222i		−	1.14717i
$95$	0.908567	−	3.28572i	0.0932170	−	0.337108i
$96$		0			0
$97$	−2.80367	+	2.80367i	−0.284669	+	0.284669i	−0.834968	−	0.550299i	$-0.814514\pi$
$97$	−2.80367	+	2.80367i	−0.284669	+	0.284669i	0.550299	+	0.834968i	$0.314514\pi$
$98$	−2.66250	+	2.66250i	−0.268953	+	0.268953i
$99$		0			0
$100$	0.504341	−	0.842213i	0.0504341	−	0.0842213i
$101$		−	2.57723i		−	0.256444i	−0.991745	−	0.128222i	$-0.959073\pi$
$101$		−	2.57723i		−	0.256444i	0.991745	−	0.128222i	$-0.0409271\pi$
$102$		0			0
$103$	−9.23724	−	9.23724i	−0.910172	−	0.910172i	0.0861132	−	0.996285i	$-0.472555\pi$
$103$	−9.23724	−	9.23724i	−0.910172	−	0.910172i	−0.996285	+	0.0861132i	$0.972555\pi$
$104$	16.3908			1.60725
$105$		0			0
$106$	8.84314			0.858922
$107$	9.23034	+	9.23034i	0.892331	+	0.892331i	0.994742	−	0.102411i	$-0.0326557\pi$
$107$	9.23034	+	9.23034i	0.892331	+	0.892331i	−0.102411	+	0.994742i	$0.532656\pi$
$108$		0			0
$109$			8.05480i			0.771510i	0.922601	+	0.385755i	$0.126059\pi$
$109$			8.05480i			0.771510i	−0.922601	+	0.385755i	$0.873941\pi$
$110$	2.29964	−	1.30334i	0.219262	−	0.124269i
$111$		0			0
$112$	−5.16940	+	5.16940i	−0.488463	+	0.488463i
$113$	8.48744	−	8.48744i	0.798431	−	0.798431i	−0.184417	−	0.982848i	$-0.559040\pi$
$113$	8.48744	−	8.48744i	0.798431	−	0.798431i	0.982848	+	0.184417i	$0.0590397\pi$
$114$		0			0
$115$	3.08806	−	1.75019i	0.287963	−	0.163206i
$116$			0.312794i			0.0290422i
$117$		0			0
$118$	−7.25113	−	7.25113i	−0.667521	−	0.667521i
$119$	3.29129			0.301712
$120$		0			0
$121$	10.2252			0.929567
$122$	−12.6114	−	12.6114i	−1.14178	−	1.14178i
$123$		0			0
$124$			1.37245i			0.123250i
$125$	7.71420	+	8.09266i	0.689979	+	0.723830i
$126$		0			0
$127$	1.90230	−	1.90230i	0.168802	−	0.168802i	−0.617651	−	0.786452i	$-0.711915\pi$
$127$	1.90230	−	1.90230i	0.168802	−	0.168802i	0.786452	+	0.617651i	$0.211915\pi$
$128$	6.62457	−	6.62457i	0.585535	−	0.585535i
$129$		0			0
$130$	−4.44747	+	16.0837i	−0.390069	+	1.41063i
$131$			21.3746i			1.86751i	0.357916	+	0.933754i	$0.383487\pi$
$131$			21.3746i			1.86751i	−0.357916	+	0.933754i	$0.616513\pi$
$132$		0			0
$133$	2.20834	+	2.20834i	0.191487	+	0.191487i
$134$	−4.46113			−0.385383
$135$		0			0
$136$	−4.73922			−0.406385
$137$	4.85052	+	4.85052i	0.414408	+	0.414408i	0.883271	−	0.468863i	$-0.155336\pi$
$137$	4.85052	+	4.85052i	0.414408	+	0.414408i	−0.468863	+	0.883271i	$0.655336\pi$
$138$		0			0
$139$			1.44179i			0.122291i	0.998129	+	0.0611456i	$0.0194754\pi$
$139$			1.44179i			0.122291i	−0.998129	+	0.0611456i	$0.980525\pi$
$140$	0.443434	+	0.782402i	0.0374770	+	0.0661250i
$141$		0			0
$142$	5.60100	−	5.60100i	0.470026	−	0.470026i
$143$	3.45853	−	3.45853i	0.289217	−	0.289217i
$144$		0			0
$145$	−3.43357	−	0.949452i	−0.285143	−	0.0788477i
$146$			3.01799i			0.249771i
$147$		0			0
$148$	0.835887	+	0.835887i	0.0687094	+	0.0687094i
$149$	−16.5691			−1.35740			−0.678699	−	0.734417i	$-0.737456\pi$
$149$	−16.5691			−1.35740			−0.678699	+	0.734417i	$0.737456\pi$
$150$		0			0
$151$	−0.00567460			−0.000461793			−0.000230896	−	1.00000i	$-0.500073\pi$
$151$	−0.00567460			−0.000461793			−0.000230896		1.00000i	$0.500073\pi$
$152$	−3.17985	−	3.17985i	−0.257920	−	0.257920i
$153$		0			0
$154$			2.42157i			0.195136i
$155$	−15.0655	−	4.16592i	−1.21009	−	0.334615i
$156$		0			0
$157$	5.98167	−	5.98167i	0.477389	−	0.477389i	−0.426906	−	0.904296i	$-0.640397\pi$
$157$	5.98167	−	5.98167i	0.477389	−	0.477389i	0.904296	+	0.426906i	$0.140397\pi$
$158$	7.34038	−	7.34038i	0.583970	−	0.583970i
$159$		0			0
$160$	−1.21995	−	2.15250i	−0.0964455	−	0.170170i
$161$			3.25179i			0.256277i
$162$		0			0
$163$	4.19302	+	4.19302i	0.328422	+	0.328422i	0.851986	−	0.523564i	$-0.175398\pi$
$163$	4.19302	+	4.19302i	0.328422	+	0.328422i	−0.523564	+	0.851986i	$0.675398\pi$
$164$	−0.706298			−0.0551526
$165$		0			0
$166$	13.3445			1.03573
$167$	4.21906	+	4.21906i	0.326480	+	0.326480i	0.851246	−	0.524766i	$-0.175847\pi$
$167$	4.21906	+	4.21906i	0.326480	+	0.326480i	−0.524766	+	0.851246i	$0.675847\pi$
$168$		0			0
$169$			17.8777i			1.37521i
$170$	1.28594	−	4.65044i	0.0986271	−	0.356672i
$171$		0			0
$172$	0.267103	−	0.267103i	0.0203664	−	0.0203664i
$173$	−9.66264	+	9.66264i	−0.734637	+	0.734637i	−0.971535	−	0.236898i	$-0.923869\pi$
$173$	−9.66264	+	9.66264i	−0.734637	+	0.734637i	0.236898	+	0.971535i	$0.423869\pi$
$174$		0			0
$175$	−9.93452	+	2.49273i	−0.750979	+	0.188432i
$176$		−	3.14126i		−	0.236782i
$177$		0			0
$178$	−4.39464	−	4.39464i	−0.329392	−	0.329392i
$179$	−17.2370			−1.28836			−0.644178	−	0.764875i	$-0.722801\pi$
$179$	−17.2370			−1.28836			−0.644178	+	0.764875i	$0.722801\pi$
$180$		0			0
$181$	14.7708			1.09790			0.548952	−	0.835854i	$-0.315027\pi$
$181$	14.7708			1.09790			0.548952	+	0.835854i	$0.315027\pi$
$182$	−10.8099	−	10.8099i	−0.801281	−	0.801281i
$183$		0			0
$184$		−	4.68235i		−	0.345187i
$185$	−11.7129	+	6.63838i	−0.861148	+	0.488064i
$186$		0			0
$187$	−1.00000	+	1.00000i	−0.0731272	+	0.0731272i
$188$	−1.14973	+	1.14973i	−0.0838528	+	0.0838528i
$189$		0			0
$190$	3.98310	−	2.25746i	0.288964	−	0.163773i
$191$			5.27457i			0.381655i	0.981624	+	0.190827i	$0.0611171\pi$
$191$			5.27457i			0.381655i	−0.981624	+	0.190827i	$0.938883\pi$
$192$		0			0
$193$	6.58078	+	6.58078i	0.473695	+	0.473695i	0.903108	−	0.429413i	$-0.141280\pi$
$193$	6.58078	+	6.58078i	0.473695	+	0.473695i	−0.429413	+	0.903108i	$0.641280\pi$
$194$	−5.32499			−0.382312
$195$		0			0
$196$	0.550457			0.0393183
$197$	−9.49539	−	9.49539i	−0.676519	−	0.676519i	0.282692	−	0.959211i	$-0.408773\pi$
$197$	−9.49539	−	9.49539i	−0.676519	−	0.676519i	−0.959211	+	0.282692i	$0.908773\pi$
$198$		0			0
$199$			17.6342i			1.25005i	0.780604	+	0.625026i	$0.214912\pi$
$199$			17.6342i			1.25005i	−0.780604	+	0.625026i	$0.785088\pi$
$200$	14.3050	−	3.58935i	1.01152	−	0.253806i
$201$		0			0
$202$	2.44747	−	2.44747i	0.172203	−	0.172203i
$203$	2.30771	−	2.30771i	0.161969	−	0.161969i
$204$		0			0
$205$	2.14389	−	7.75312i	0.149736	−	0.541501i
$206$		−	17.5443i		−	1.22237i
$207$		0			0
$208$	14.0226	+	14.0226i	0.972291	+	0.972291i
$209$	−1.34193			−0.0928231
$210$		0			0
$211$	−0.123210			−0.00848213			−0.00424106	−	0.999991i	$-0.501350\pi$
$211$	−0.123210			−0.00848213			−0.00424106	+	0.999991i	$0.501350\pi$
$212$	−0.914136	−	0.914136i	−0.0627831	−	0.0627831i
$213$		0			0
$214$			17.5312i			1.19841i
$215$	2.12126	+	3.74279i	0.144669	+	0.255256i
$216$		0			0
$217$	10.1256	−	10.1256i	0.687368	−	0.687368i
$218$	−7.64923	+	7.64923i	−0.518071	+	0.518071i
$219$		0			0
$220$	−0.372449	−	0.102990i	−0.0251105	−	0.00694356i
$221$		−	8.92798i		−	0.600561i
$222$		0			0
$223$	1.77041	+	1.77041i	0.118555	+	0.118555i	0.763895	−	0.645340i	$-0.223284\pi$
$223$	1.77041	+	1.77041i	0.118555	+	0.118555i	−0.645340	+	0.763895i	$0.723284\pi$
$224$	2.26663			0.151445
$225$		0			0
$226$	16.1202			1.07230
$227$	10.7826	+	10.7826i	0.715667	+	0.715667i	0.967715	−	0.252048i	$-0.0811041\pi$
$227$	10.7826	+	10.7826i	0.715667	+	0.715667i	−0.252048	+	0.967715i	$0.581104\pi$
$228$		0			0
$229$			22.0644i			1.45806i	0.684483	+	0.729029i	$0.260028\pi$
$229$			22.0644i			1.45806i	−0.684483	+	0.729029i	$0.739972\pi$
$230$	4.59463	+	1.27051i	0.302961	+	0.0837748i
$231$		0			0
$232$	−3.32294	+	3.32294i	−0.218162	+	0.218162i
$233$	−4.22173	+	4.22173i	−0.276575	+	0.276575i	−0.831740	−	0.555165i	$-0.812655\pi$
$233$	−4.22173	+	4.22173i	−0.276575	+	0.276575i	0.555165	+	0.831740i	$0.312655\pi$
$234$		0			0
$235$	−9.13085	−	16.1106i	−0.595631	−	1.05094i
$236$			1.49913i			0.0975852i
$237$		0			0
$238$	3.12557	+	3.12557i	0.202600	+	0.202600i
$239$	13.5840			0.878675			0.439338	−	0.898322i	$-0.355213\pi$
$239$	13.5840			0.878675			0.439338	+	0.898322i	$0.355213\pi$
$240$		0			0
$241$	5.13456			0.330746			0.165373	−	0.986231i	$-0.447117\pi$
$241$	5.13456			0.330746			0.165373	+	0.986231i	$0.447117\pi$
$242$	9.71038	+	9.71038i	0.624207	+	0.624207i
$243$		0			0
$244$			2.60733i			0.166917i
$245$	−1.67085	+	6.04243i	−0.106747	+	0.386037i
$246$		0			0
$247$	5.99036	−	5.99036i	0.381157	−	0.381157i
$248$	−14.5801	+	14.5801i	−0.925838	+	0.925838i
$249$		0			0
$250$	−0.359410	+	15.0110i	−0.0227311	+	0.949377i
$251$			2.60221i			0.164250i	0.996622	+	0.0821251i	$0.0261707\pi$
$251$			2.60221i			0.164250i	−0.996622	+	0.0821251i	$0.973829\pi$
$252$		0			0
$253$	−0.987999	−	0.987999i	−0.0621150	−	0.0621150i
$254$	3.61303			0.226702
$255$		0			0
$256$	−4.66514			−0.291571
$257$	7.46387	+	7.46387i	0.465584	+	0.465584i	0.900480	−	0.434897i	$-0.143215\pi$
$257$	7.46387	+	7.46387i	0.465584	+	0.465584i	−0.434897	+	0.900480i	$0.643215\pi$
$258$		0			0
$259$		−	12.3339i		−	0.766391i
$260$	2.12235	−	1.20286i	0.131623	−	0.0745984i
$261$		0			0
$262$	−20.2984	+	20.2984i	−1.25404	+	1.25404i
$263$	5.94822	−	5.94822i	0.366783	−	0.366783i	−0.499520	−	0.866302i	$-0.666490\pi$
$263$	5.94822	−	5.94822i	0.366783	−	0.366783i	0.866302	+	0.499520i	$0.166490\pi$
$264$		0			0
$265$	12.8093	−	7.25981i	0.786871	−	0.445967i
$266$			4.19429i			0.257168i
$267$		0			0
$268$	0.461157	+	0.461157i	0.0281697	+	0.0281697i
$269$	26.7708			1.63225			0.816123	−	0.577878i	$-0.196119\pi$
$269$	26.7708			1.63225			0.816123	+	0.577878i	$0.196119\pi$
$270$		0			0
$271$	−18.5850			−1.12896			−0.564480	−	0.825447i	$-0.690923\pi$
$271$	−18.5850			−1.12896			−0.564480	+	0.825447i	$0.690923\pi$
$272$	−4.05449	−	4.05449i	−0.245839	−	0.245839i
$273$		0			0
$274$			9.21259i			0.556553i
$275$	2.26106	−	3.77580i	0.136347	−	0.227689i
$276$		0			0
$277$	19.2680	−	19.2680i	1.15770	−	1.15770i	0.172736	−	0.984968i	$-0.444739\pi$
$277$	19.2680	−	19.2680i	1.15770	−	1.15770i	0.984968	−	0.172736i	$-0.0552607\pi$
$278$	−1.36920	+	1.36920i	−0.0821189	+	0.0821189i
$279$		0			0
$280$	−3.60100	+	13.0226i	−0.215201	+	0.778248i
$281$		−	26.2175i		−	1.56400i	−0.623276	−	0.782002i	$-0.714199\pi$
$281$		−	26.2175i		−	1.56400i	0.623276	−	0.782002i	$-0.285801\pi$
$282$		0			0
$283$	−2.51862	−	2.51862i	−0.149717	−	0.149717i	0.628275	−	0.777991i	$-0.283761\pi$
$283$	−2.51862	−	2.51862i	−0.149717	−	0.149717i	−0.777991	+	0.628275i	$0.783761\pi$
$284$	−1.15798			−0.0687133
$285$		0			0
$286$	6.56878			0.388420
$287$	5.21088	+	5.21088i	0.307589	+	0.307589i
$288$		0			0
$289$		−	14.4186i		−	0.848151i
$290$	−2.35904	−	4.16233i	−0.138528	−	0.244421i
$291$		0			0
$292$	0.311976	−	0.311976i	0.0182570	−	0.0182570i
$293$	2.10696	−	2.10696i	0.123090	−	0.123090i	−0.642878	−	0.765968i	$-0.722260\pi$
$293$	2.10696	−	2.10696i	0.123090	−	0.123090i	0.765968	+	0.642878i	$0.222260\pi$
$294$		0			0
$295$	−16.4561	−	4.55046i	−0.958114	−	0.264938i
$296$			17.7600i			1.03228i
$297$		0			0
$298$	−15.7349	−	15.7349i	−0.911496	−	0.911496i
$299$	8.82084			0.510122
$300$		0			0
$301$	−3.94123			−0.227169
$302$	−0.00538888	−	0.00538888i	−0.000310095	−	0.000310095i
$303$		0			0
$304$		−	5.44083i		−	0.312053i
$305$	−28.6210	−	7.91428i	−1.63883	−	0.453170i
$306$		0			0
$307$	21.8017	−	21.8017i	1.24429	−	1.24429i	0.286081	−	0.958205i	$-0.407647\pi$
$307$	21.8017	−	21.8017i	1.24429	−	1.24429i	0.958205	−	0.286081i	$-0.0923528\pi$
$308$	0.250323	−	0.250323i	0.0142635	−	0.0142635i
$309$		0			0
$310$	−10.3508	−	18.2631i	−0.587886	−	1.03728i
$311$		−	33.9341i		−	1.92423i	−0.272646	−	0.962114i	$-0.587899\pi$
$311$		−	33.9341i		−	1.92423i	0.272646	−	0.962114i	$-0.412101\pi$
$312$		0			0
$313$	16.3999	+	16.3999i	0.926979	+	0.926979i	0.997510	−	0.0705309i	$-0.0224693\pi$
$313$	16.3999	+	16.3999i	0.926979	+	0.926979i	−0.0705309	+	0.997510i	$0.522469\pi$
$314$	11.3610			0.641137
$315$		0			0
$316$	−1.51758			−0.0853708
$317$	−2.82865	−	2.82865i	−0.158873	−	0.158873i	0.623194	−	0.782067i	$-0.285835\pi$
$317$	−2.82865	−	2.82865i	−0.158873	−	0.158873i	−0.782067	+	0.623194i	$0.785835\pi$
$318$		0			0
$319$			1.40231i			0.0785145i
$320$	5.13925	−	18.5854i	0.287293	−	1.03896i
$321$		0			0
$322$	−3.08806	+	3.08806i	−0.172091	+	0.172091i
$323$	−1.73205	+	1.73205i	−0.0963739	+	0.0963739i
$324$		0			0
$325$	6.76180	+	26.9485i	0.375077	+	1.49483i
$326$			7.96378i			0.441073i
$327$		0			0
$328$	−7.50330	−	7.50330i	−0.414301	−	0.414301i
$329$	16.9648			0.935302
$330$		0			0
$331$	5.96350			0.327784			0.163892	−	0.986478i	$-0.447595\pi$
$331$	5.96350			0.327784			0.163892	+	0.986478i	$0.447595\pi$
$332$	−1.37945	−	1.37945i	−0.0757071	−	0.0757071i
$333$		0			0
$334$			8.01324i			0.438465i
$335$	−6.46198	+	3.66239i	−0.353055	+	0.200098i
$336$		0			0
$337$	−7.00490	+	7.00490i	−0.381581	+	0.381581i	−0.871672	−	0.490090i	$-0.836964\pi$
$337$	−7.00490	+	7.00490i	−0.381581	+	0.381581i	0.490090	+	0.871672i	$0.336964\pi$
$338$	−16.9776	+	16.9776i	−0.923457	+	0.923457i
$339$		0			0
$340$	−0.613657	+	0.347796i	−0.0332802	+	0.0188619i
$341$			6.15295i			0.333201i
$342$		0			0
$343$	−14.2007	−	14.2007i	−0.766764	−	0.766764i
$344$	5.67510			0.305981
$345$		0			0
$346$	−18.3522			−0.986622
$347$	7.50136	+	7.50136i	0.402694	+	0.402694i	0.879181	−	0.476487i	$-0.158090\pi$
$347$	7.50136	+	7.50136i	0.402694	+	0.402694i	−0.476487	+	0.879181i	$0.658090\pi$
$348$		0			0
$349$		−	9.33958i		−	0.499936i	−0.968254	−	0.249968i	$-0.919580\pi$
$349$		−	9.33958i		−	0.499936i	0.968254	−	0.249968i	$-0.0804201\pi$
$350$	−11.8015	−	7.06709i	−0.630818	−	0.377752i
$351$		0			0
$352$	−0.688675	+	0.688675i	−0.0367065	+	0.0367065i
$353$	13.5773	−	13.5773i	0.722648	−	0.722648i	−0.246496	−	0.969144i	$-0.579279\pi$
$353$	13.5773	−	13.5773i	0.722648	−	0.722648i	0.969144	+	0.246496i	$0.0792791\pi$
$354$		0			0
$355$	3.51492	−	12.7113i	0.186552	−	0.674643i
$356$			0.908567i			0.0481540i
$357$		0			0
$358$	−16.3691	−	16.3691i	−0.865135	−	0.865135i
$359$	12.5944			0.664705			0.332352	−	0.943155i	$-0.392158\pi$
$359$	12.5944			0.664705			0.332352	+	0.943155i	$0.392158\pi$
$360$		0			0
$361$	16.6757			0.877669
$362$	14.0271	+	14.0271i	0.737246	+	0.737246i
$363$		0			0
$364$			2.23488i			0.117140i
$365$	2.47763	+	4.37158i	0.129685	+	0.228819i
$366$		0			0
$367$	−20.0042	+	20.0042i	−1.04421	+	1.04421i	−0.0452371	+	0.998976i	$0.514404\pi$
$367$	−20.0042	+	20.0042i	−1.04421	+	1.04421i	−0.998976	+	0.0452371i	$0.985596\pi$
$368$	4.00583	−	4.00583i	0.208818	−	0.208818i
$369$		0			0
$370$	−17.4272	−	4.81898i	−0.905999	−	0.250527i
$371$			13.4885i			0.700288i
$372$		0			0
$373$	1.65248	+	1.65248i	0.0855624	+	0.0855624i	0.748593	−	0.663030i	$-0.230730\pi$
$373$	1.65248	+	1.65248i	0.0855624	+	0.0855624i	−0.663030	+	0.748593i	$0.730730\pi$
$374$	−1.89930			−0.0982103
$375$		0			0
$376$	−24.4282			−1.25979
$377$	−6.25992	−	6.25992i	−0.322402	−	0.322402i
$378$		0			0
$379$		−	18.4618i		−	0.948320i	−0.880439	−	0.474160i	$-0.842752\pi$
$379$		−	18.4618i		−	0.948320i	0.880439	−	0.474160i	$-0.157248\pi$
$380$	−0.645100	−	0.178383i	−0.0330929	−	0.00915087i
$381$		0			0
$382$	−5.00899	+	5.00899i	−0.256282	+	0.256282i
$383$	−17.1158	+	17.1158i	−0.874575	+	0.874575i	−0.992967	−	0.118392i	$-0.962226\pi$
$383$	−17.1158	+	17.1158i	−0.874575	+	0.874575i	0.118392	+	0.992967i	$0.462226\pi$
$384$		0			0
$385$	1.98800	+	3.50766i	0.101318	+	0.178767i
$386$			12.4989i			0.636176i
$387$		0			0
$388$	0.550457	+	0.550457i	0.0279452	+	0.0279452i
$389$	−27.0888			−1.37346			−0.686729	−	0.726913i	$-0.740954\pi$
$389$	−27.0888			−1.37346			−0.686729	+	0.726913i	$0.740954\pi$
$390$		0			0
$391$	−2.55046			−0.128982
$392$	5.84773	+	5.84773i	0.295355	+	0.295355i
$393$		0			0
$394$		−	18.0346i		−	0.908569i
$395$	4.60647	−	16.6587i	0.231776	−	0.838190i
$396$		0			0
$397$	−18.2252	+	18.2252i	−0.914698	+	0.914698i	−0.996637	−	0.0819389i	$-0.973889\pi$
$397$	−18.2252	+	18.2252i	−0.914698	+	0.914698i	0.0819389	+	0.996637i	$0.473889\pi$
$398$	−16.7463	+	16.7463i	−0.839414	+	0.839414i
$399$		0			0
$400$	15.3089	+	9.16743i	0.765447	+	0.458372i
$401$			12.8512i			0.641756i	0.947121	+	0.320878i	$0.103978\pi$
$401$			12.8512i			0.641756i	−0.947121	+	0.320878i	$0.896022\pi$
$402$		0			0
$403$	−27.4667	−	27.4667i	−1.36822	−	1.36822i
$404$	−0.506000			−0.0251745
$405$		0			0
$406$	4.38302			0.217526
$407$	3.74744	+	3.74744i	0.185754	+	0.185754i
$408$		0			0
$409$		−	25.6863i		−	1.27011i	−0.772469	−	0.635053i	$-0.780978\pi$
$409$		−	25.6863i		−	1.27011i	0.772469	−	0.635053i	$-0.219022\pi$
$410$	9.39868	−	5.32679i	0.464168	−	0.263072i
$411$		0			0
$412$	−1.81359	+	1.81359i	−0.0893492	+	0.0893492i
$413$	11.0602	−	11.0602i	0.544237	−	0.544237i
$414$		0			0
$415$	19.3295	−	10.9552i	0.948850	−	0.537770i
$416$		−	6.14848i		−	0.301454i
$417$		0			0
$418$	−1.27436	−	1.27436i	−0.0623310	−	0.0623310i
$419$	−12.2649			−0.599177			−0.299589	−	0.954068i	$-0.596849\pi$
$419$	−12.2649			−0.599177			−0.299589	+	0.954068i	$0.596849\pi$
$420$		0			0
$421$	14.4811			0.705766			0.352883	−	0.935667i	$-0.385201\pi$
$421$	14.4811			0.705766			0.352883	+	0.935667i	$0.385201\pi$
$422$	−0.117006	−	0.117006i	−0.00569577	−	0.00569577i
$423$		0			0
$424$		−	19.4225i		−	0.943240i
$425$	−1.95511	−	7.79188i	−0.0948366	−	0.377962i
$426$		0			0
$427$	19.2362	−	19.2362i	0.930905	−	0.930905i
$428$	1.81224	−	1.81224i	0.0875977	−	0.0875977i
$429$		0			0
$430$	−1.53988	+	5.56878i	−0.0742596	+	0.268551i
$431$		−	35.9660i		−	1.73242i	−0.499678	−	0.866211i	$-0.666548\pi$
$431$		−	35.9660i		−	1.73242i	0.499678	−	0.866211i	$-0.333452\pi$
$432$		0			0
$433$	−0.331545	−	0.331545i	−0.0159331	−	0.0159331i	0.699095	−	0.715028i	$-0.253586\pi$
$433$	−0.331545	−	0.331545i	−0.0159331	−	0.0159331i	−0.715028	+	0.699095i	$0.753586\pi$
$434$	19.2315			0.923140
$435$		0			0
$436$	1.58144			0.0757370
$437$	−1.71126	−	1.71126i	−0.0818609	−	0.0818609i
$438$		0			0
$439$		−	1.48902i		−	0.0710671i	−0.999368	−	0.0355336i	$-0.988687\pi$
$439$		−	1.48902i		−	0.0710671i	0.999368	−	0.0355336i	$-0.0113131\pi$
$440$	−2.86258	−	5.05078i	−0.136468	−	0.240787i
$441$		0			0
$442$	8.47845	−	8.47845i	0.403279	−	0.403279i
$443$	−22.6547	+	22.6547i	−1.07636	+	1.07636i	−0.0795224	+	0.996833i	$0.525340\pi$
$443$	−22.6547	+	22.6547i	−1.07636	+	1.07636i	−0.996833	+	0.0795224i	$0.974660\pi$
$444$		0			0
$445$	−9.97345	−	2.75786i	−0.472787	−	0.130735i
$446$			3.36253i			0.159220i
$447$		0			0
$448$	12.4913	+	12.4913i	0.590159	+	0.590159i
$449$	−21.8283			−1.03014			−0.515071	−	0.857147i	$-0.672234\pi$
$449$	−21.8283			−1.03014			−0.515071	+	0.857147i	$0.672234\pi$
$450$		0			0
$451$	−3.16647			−0.149103
$452$	−1.66638	−	1.66638i	−0.0783798	−	0.0783798i
$453$		0			0
$454$			20.4794i			0.961145i
$455$	−24.5326	−	6.78375i	−1.15010	−	0.318027i
$456$		0			0
$457$	−0.644453	+	0.644453i	−0.0301462	+	0.0301462i	−0.722019	−	0.691873i	$-0.756786\pi$
$457$	−0.644453	+	0.644453i	−0.0301462	+	0.0301462i	0.691873	+	0.722019i	$0.256786\pi$
$458$	−20.9534	+	20.9534i	−0.979090	+	0.979090i
$459$		0			0
$460$	−0.343622	−	0.606293i	−0.0160215	−	0.0282685i
$461$		−	21.6298i		−	1.00740i	−0.863879	−	0.503700i	$-0.831972\pi$
$461$		−	21.6298i		−	1.00740i	0.863879	−	0.503700i	$-0.168028\pi$
$462$		0			0
$463$	13.2680	+	13.2680i	0.616618	+	0.616618i	0.944662	−	0.328044i	$-0.106390\pi$
$463$	13.2680	+	13.2680i	0.616618	+	0.616618i	−0.328044	+	0.944662i	$0.606390\pi$
$464$	−5.68566			−0.263950
$465$		0			0
$466$	−8.01833			−0.371442
$467$	16.8295	+	16.8295i	0.778777	+	0.778777i	0.979623	−	0.200846i	$-0.0643691\pi$
$467$	16.8295	+	16.8295i	0.778777	+	0.778777i	−0.200846	+	0.979623i	$0.564369\pi$
$468$		0			0
$469$		−	6.80460i		−	0.314207i
$470$	6.62834	−	23.9705i	0.305742	−	1.10568i
$471$		0			0
$472$	−15.9259	+	15.9259i	−0.733050	+	0.733050i
$473$	1.19747	−	1.19747i	0.0550599	−	0.0550599i
$474$		0			0
$475$	3.91627	−	6.53988i	0.179691	−	0.300070i
$476$		−	0.646194i		−	0.0296182i
$477$		0			0
$478$	12.9000	+	12.9000i	0.590033	+	0.590033i
$479$	17.8345			0.814878			0.407439	−	0.913232i	$-0.366422\pi$
$479$	17.8345			0.814878			0.407439	+	0.913232i	$0.366422\pi$
$480$		0			0
$481$	−33.4571			−1.52551
$482$	4.87603	+	4.87603i	0.222097	+	0.222097i
$483$		0			0
$484$		−	2.00757i		−	0.0912531i
$485$	−7.71328	+	4.37158i	−0.350242	+	0.198503i
$486$		0			0
$487$	−21.8232	+	21.8232i	−0.988904	+	0.988904i	−0.999939	−	0.0110354i	$-0.996487\pi$
$487$	−21.8232	+	21.8232i	−0.988904	+	0.988904i	0.0110354	+	0.999939i	$0.496487\pi$
$488$	−27.6988	+	27.6988i	−1.25387	+	1.25387i
$489$		0			0
$490$	−7.32491	+	4.15146i	−0.330906	+	0.187544i
$491$		−	40.6074i		−	1.83258i	−0.400510	−	0.916292i	$-0.631167\pi$
$491$		−	40.6074i		−	1.83258i	0.400510	−	0.916292i	$-0.368833\pi$
$492$		0			0
$493$	1.80999	+	1.80999i	0.0815179	+	0.0815179i
$494$	11.3775			0.511896
$495$		0			0
$496$	−24.9471			−1.12016
$497$	8.54325	+	8.54325i	0.383217	+	0.383217i
$498$		0			0
$499$		−	43.1162i		−	1.93015i	−0.261981	−	0.965073i	$-0.584376\pi$
$499$		−	43.1162i		−	1.93015i	0.261981	−	0.965073i	$-0.415624\pi$
$500$	1.58887	−	1.51456i	0.0710564	−	0.0677334i
$501$		0			0
$502$	−2.47119	+	2.47119i	−0.110295	+	0.110295i
$503$	−28.0936	+	28.0936i	−1.25263	+	1.25263i	−0.298093	+	0.954537i	$0.596351\pi$
$503$	−28.0936	+	28.0936i	−1.25263	+	1.25263i	−0.954537	+	0.298093i	$0.903649\pi$
$504$		0			0
$505$	1.53591	−	5.55443i	0.0683471	−	0.247169i
$506$		−	1.87650i		−	0.0834208i
$507$		0			0
$508$	−0.373487	−	0.373487i	−0.0165708	−	0.0165708i
$509$	−14.7838			−0.655278			−0.327639	−	0.944803i	$-0.606253\pi$
$509$	−14.7838			−0.655278			−0.327639	+	0.944803i	$0.606253\pi$
$510$		0			0
$511$	−4.60336			−0.203641
$512$	−17.6794	−	17.6794i	−0.781325	−	0.781325i
$513$		0			0
$514$			14.1761i			0.625282i
$515$	−14.4030	−	25.4130i	−0.634673	−	1.11983i
$516$		0			0
$517$	−5.15447	+	5.15447i	−0.226693	+	0.226693i
$518$	11.7129	−	11.7129i	0.514634	−	0.514634i
$519$		0			0
$520$	35.3252	+	9.76813i	1.54911	+	0.428361i
$521$			28.4812i			1.24778i	0.781511	+	0.623892i	$0.214449\pi$
$521$			28.4812i			1.24778i	−0.781511	+	0.623892i	$0.785551\pi$
$522$		0			0
$523$	15.4076	+	15.4076i	0.673726	+	0.673726i	0.958573	−	0.284847i	$-0.0919428\pi$
$523$	15.4076	+	15.4076i	0.673726	+	0.673726i	−0.284847	+	0.958573i	$0.591943\pi$
$524$	4.19657			0.183328
$525$		0			0
$526$	11.2974			0.492591
$527$	7.94173	+	7.94173i	0.345947	+	0.345947i
$528$		0			0
$529$			20.4802i			0.890441i
$530$	19.0586	+	5.27010i	0.827855	+	0.228918i
$531$		0			0
$532$	0.433573	−	0.433573i	0.0187978	−	0.0187978i
$533$	14.1351	−	14.1351i	0.612259	−	0.612259i
$534$		0			0
$535$	14.3923	+	25.3940i	0.622233	+	1.09788i
$536$			9.79814i			0.423215i
$537$		0			0
$538$	25.4229	+	25.4229i	1.09606	+	1.09606i
$539$	2.46780			0.106296
$540$		0			0
$541$	−1.11754			−0.0480466			−0.0240233	−	0.999711i	$-0.507648\pi$
$541$	−1.11754			−0.0480466			−0.0240233	+	0.999711i	$0.507648\pi$
$542$	−17.6493	−	17.6493i	−0.758100	−	0.758100i
$543$		0			0
$544$			1.77777i			0.0762213i
$545$	−4.80028	+	17.3596i	−0.205621	+	0.743604i
$546$		0			0
$547$	22.7824	−	22.7824i	0.974105	−	0.974105i	−0.0255677	−	0.999673i	$-0.508139\pi$
$547$	22.7824	−	22.7824i	0.974105	−	0.974105i	0.999673	+	0.0255677i	$0.00813935\pi$
$548$	0.952326	−	0.952326i	0.0406813	−	0.0406813i
$549$		0			0
$550$	5.73290	−	1.43847i	0.244452	−	0.0613367i
$551$			2.42888i			0.103474i
$552$		0			0
$553$	11.1963	+	11.1963i	0.476117	+	0.476117i
$554$	36.5957			1.55480
$555$		0			0
$556$	0.283074			0.0120050
$557$	30.4033	+	30.4033i	1.28823	+	1.28823i	0.935862	+	0.352366i	$0.114623\pi$
$557$	30.4033	+	30.4033i	1.28823	+	1.28823i	0.352366	+	0.935862i	$0.385377\pi$
$558$		0			0
$559$			10.6910i			0.452182i
$560$	−14.2218	+	8.06032i	−0.600979	+	0.340611i
$561$		0			0
$562$	24.8974	−	24.8974i	1.05023	−	1.05023i
$563$	0.821506	−	0.821506i	0.0346223	−	0.0346223i	−0.689584	−	0.724206i	$-0.742206\pi$
$563$	0.821506	−	0.821506i	0.0346223	−	0.0346223i	0.724206	+	0.689584i	$0.242206\pi$
$564$		0			0
$565$	23.3502	−	13.2339i	0.982348	−	0.556755i
$566$		−	4.78361i		−	0.201070i
$567$		0			0
$568$	−12.3017	−	12.3017i	−0.516167	−	0.516167i
$569$	0.290735			0.0121882			0.00609412	−	0.999981i	$-0.498060\pi$
$569$	0.290735			0.0121882			0.00609412	+	0.999981i	$0.498060\pi$
$570$		0			0
$571$	26.0565			1.09043			0.545215	−	0.838296i	$-0.316448\pi$
$571$	26.0565			1.09043			0.545215	+	0.838296i	$0.316448\pi$
$572$	−0.679030	−	0.679030i	−0.0283917	−	0.0283917i
$573$		0			0
$574$			9.89701i			0.413093i
$575$	7.69838	−	1.93164i	0.321044	−	0.0805551i
$576$		0			0
$577$	−2.52834	+	2.52834i	−0.105256	+	0.105256i	−0.757774	−	0.652517i	$-0.773713\pi$
$577$	−2.52834	+	2.52834i	−0.105256	+	0.105256i	0.652517	+	0.757774i	$0.273713\pi$
$578$	13.6926	−	13.6926i	0.569536	−	0.569536i
$579$		0			0
$580$	−0.186410	+	0.674129i	−0.00774027	+	0.0279917i
$581$			20.3544i			0.844443i
$582$		0			0
$583$	−4.09825	−	4.09825i	−0.169732	−	0.169732i
$584$	6.62852			0.274290
$585$		0			0
$586$	4.00174			0.165310
$587$	29.2909	+	29.2909i	1.20896	+	1.20896i	0.971363	+	0.237600i	$0.0763607\pi$
$587$	29.2909	+	29.2909i	1.20896	+	1.20896i	0.237600	+	0.971363i	$0.423639\pi$
$588$		0			0
$589$			10.6572i			0.439123i
$590$	−11.3062	−	19.9489i	−0.465470	−	0.821283i
$591$		0			0
$592$	−15.1939	+	15.1939i	−0.624467	+	0.624467i
$593$	26.6583	−	26.6583i	1.09473	−	1.09473i	0.0997087	−	0.995017i	$-0.468209\pi$
$593$	26.6583	−	26.6583i	1.09473	−	1.09473i	0.995017	−	0.0997087i	$-0.0317911\pi$
$594$		0			0
$595$	7.09335	+	1.96145i	0.290799	+	0.0804117i
$596$			3.25310i			0.133252i
$597$		0			0
$598$	8.37670	+	8.37670i	0.342549	+	0.342549i
$599$	26.4853			1.08216			0.541080	−	0.840971i	$-0.318016\pi$
$599$	26.4853			1.08216			0.541080	+	0.840971i	$0.318016\pi$
$600$		0			0
$601$	−8.53421			−0.348118			−0.174059	−	0.984735i	$-0.555688\pi$
$601$	−8.53421			−0.348118			−0.174059	+	0.984735i	$0.555688\pi$
$602$	−3.74279	−	3.74279i	−0.152545	−	0.152545i
$603$		0			0
$604$			0.00111412i			4.53329e-5i
$605$	22.0373	+	6.09376i	0.895944	+	0.247747i
$606$		0			0
$607$	−32.5113	+	32.5113i	−1.31959	+	1.31959i	−0.405499	+	0.914096i	$0.632902\pi$
$607$	−32.5113	+	32.5113i	−1.31959	+	1.31959i	−0.914096	+	0.405499i	$0.867098\pi$
$608$	−1.19282	+	1.19282i	−0.0483752	+	0.0483752i
$609$		0			0
$610$	−19.6641	−	34.6957i	−0.796176	−	1.40479i
$611$		−	46.0190i		−	1.86173i
$612$		0			0
$613$	17.3219	+	17.3219i	0.699625	+	0.699625i	0.964330	−	0.264705i	$-0.0852744\pi$
$613$	17.3219	+	17.3219i	0.699625	+	0.699625i	−0.264705	+	0.964330i	$0.585274\pi$
$614$	41.4078			1.67108
$615$		0			0
$616$	5.31858			0.214292
$617$	−26.6253	−	26.6253i	−1.07189	−	1.07189i	−0.997207	−	0.0746867i	$-0.976204\pi$
$617$	−26.6253	−	26.6253i	−1.07189	−	1.07189i	−0.0746867	−	0.997207i	$-0.523796\pi$
$618$		0			0
$619$			9.90079i			0.397946i	0.980005	+	0.198973i	$0.0637607\pi$
$619$			9.90079i			0.397946i	−0.980005	+	0.198973i	$0.936239\pi$
$620$	−0.817915	+	2.95789i	−0.0328483	+	0.118792i
$621$		0			0
$622$	32.2255	−	32.2255i	1.29213	−	1.29213i
$623$	6.70317	−	6.70317i	0.268557	−	0.268557i
$624$		0			0
$625$	11.8027	+	22.0385i	0.472108	+	0.881541i
$626$			31.1483i			1.24494i
$627$		0			0
$628$	−1.17441	−	1.17441i	−0.0468640	−	0.0468640i
$629$	9.67378			0.385719
$630$		0			0
$631$	−22.0279			−0.876918			−0.438459	−	0.898751i	$-0.644476\pi$
$631$	−22.0279			−0.876918			−0.438459	+	0.898751i	$0.644476\pi$
$632$	−16.1219	−	16.1219i	−0.641296	−	0.641296i
$633$		0			0
$634$		−	5.37245i		−	0.213367i
$635$	5.23349	−	2.96613i	0.207685	−	0.117707i
$636$		0			0
$637$	−11.0163	+	11.0163i	−0.436480	+	0.436480i
$638$	−1.33171	+	1.33171i	−0.0527227	+	0.0527227i
$639$		0			0
$640$	18.2251	−	10.3293i	0.720412	−	0.408300i
$641$			25.1788i			0.994501i	0.867607	+	0.497251i	$0.165657\pi$
$641$			25.1788i			0.994501i	−0.867607	+	0.497251i	$0.834343\pi$
$642$		0			0
$643$	−21.9975	−	21.9975i	−0.867498	−	0.867498i	0.124697	−	0.992195i	$-0.460204\pi$
$643$	−21.9975	−	21.9975i	−0.867498	−	0.867498i	−0.992195	+	0.124697i	$0.960204\pi$
$644$	0.638439			0.0251580
$645$		0			0
$646$	−3.28968			−0.129431
$647$	−7.86580	−	7.86580i	−0.309237	−	0.309237i	0.535377	−	0.844613i	$-0.320170\pi$
$647$	−7.86580	−	7.86580i	−0.309237	−	0.309237i	−0.844613	+	0.535377i	$0.820170\pi$
$648$		0			0
$649$			6.72090i			0.263818i
$650$	−19.1703	+	32.0129i	−0.751920	+	1.25565i
$651$		0			0
$652$	0.823234	−	0.823234i	0.0322403	−	0.0322403i
$653$	0.204737	−	0.204737i	0.00801199	−	0.00801199i	−0.703089	−	0.711101i	$-0.748197\pi$
$653$	0.204737	−	0.204737i	0.00801199	−	0.00801199i	0.711101	+	0.703089i	$0.248197\pi$
$654$		0			0
$655$	−12.7383	+	46.0663i	−0.497725	+	1.79996i
$656$		−	12.8384i		−	0.501256i
$657$		0			0
$658$	16.1106	+	16.1106i	0.628058	+	0.628058i
$659$	−26.8018			−1.04405			−0.522026	−	0.852930i	$-0.674824\pi$
$659$	−26.8018			−1.04405			−0.522026	+	0.852930i	$0.674824\pi$
$660$		0			0
$661$	25.2876			0.983574			0.491787	−	0.870716i	$-0.336344\pi$
$661$	25.2876			0.983574			0.491787	+	0.870716i	$0.336344\pi$
$662$	5.66323	+	5.66323i	0.220108	+	0.220108i
$663$		0			0
$664$		−	29.3089i		−	1.13741i
$665$	3.44332	+	6.07544i	0.133526	+	0.235596i
$666$		0			0
$667$	−1.78827	+	1.78827i	−0.0692421	+	0.0692421i
$668$	0.828347	−	0.828347i	0.0320497	−	0.0320497i
$669$		0			0
$670$	−9.61459	−	2.65863i	−0.371444	−	0.102712i
$671$			11.6892i			0.451255i
$672$		0			0
$673$	17.2198	+	17.2198i	0.663776	+	0.663776i	0.956268	−	0.292492i	$-0.0944844\pi$
$673$	17.2198	+	17.2198i	0.663776	+	0.663776i	−0.292492	+	0.956268i	$0.594484\pi$
$674$	−13.3044			−0.512466
$675$		0			0
$676$	3.51002			0.135001
$677$	−0.656416	−	0.656416i	−0.0252281	−	0.0252281i	0.694380	−	0.719608i	$-0.255679\pi$
$677$	−0.656416	−	0.656416i	−0.0252281	−	0.0252281i	−0.719608	+	0.694380i	$0.755679\pi$
$678$		0			0
$679$		−	8.12225i		−	0.311703i
$680$	−10.2139	−	2.82435i	−0.391686	−	0.108309i
$681$		0			0
$682$	−5.84314	+	5.84314i	−0.223746	+	0.223746i
$683$	−22.2024	+	22.2024i	−0.849550	+	0.849550i	−0.990077	−	0.140526i	$-0.955120\pi$
$683$	−22.2024	+	22.2024i	−0.849550	+	0.849550i	0.140526	+	0.990077i	$0.455120\pi$
$684$		0			0
$685$	7.56311	+	13.3445i	0.288972	+	0.509866i
$686$		−	26.9713i		−	1.02977i
$687$		0			0
$688$	4.85514	+	4.85514i	0.185101	+	0.185101i
$689$	36.5891			1.39393
$690$		0			0
$691$	8.11754			0.308806			0.154403	−	0.988008i	$-0.450655\pi$
$691$	8.11754			0.308806			0.154403	+	0.988008i	$0.450655\pi$
$692$	1.89711	+	1.89711i	0.0721173	+	0.0721173i
$693$		0			0
$694$			14.2473i			0.540821i
$695$	−0.859241	+	3.10734i	−0.0325929	+	0.117868i
$696$		0			0
$697$	−4.08702	+	4.08702i	−0.154807	+	0.154807i
$698$	8.86932	−	8.86932i	0.335709	−	0.335709i
$699$		0			0
$700$	0.489409	+	1.95049i	0.0184979	+	0.0737216i
$701$		−	19.6359i		−	0.741637i	−0.928705	−	0.370819i	$-0.879077\pi$
$701$		−	19.6359i		−	0.741637i	0.928705	−	0.370819i	$-0.120923\pi$
$702$		0			0
$703$	6.49076	+	6.49076i	0.244804	+	0.244804i
$704$	−7.59053			−0.286079
$705$		0			0
$706$	25.7874			0.970521
$707$	3.73314	+	3.73314i	0.140399	+	0.140399i
$708$		0			0
$709$		−	3.09902i		−	0.116386i	−0.998305	−	0.0581931i	$-0.981466\pi$
$709$		−	3.09902i		−	0.116386i	0.998305	−	0.0581931i	$-0.0185339\pi$
$710$	15.4092	−	8.73329i	0.578295	−	0.327754i
$711$		0			0
$712$	−9.65210	+	9.65210i	−0.361728	+	0.361728i
$713$	−7.84642	+	7.84642i	−0.293851	+	0.293851i
$714$		0			0
$715$	9.51492	−	5.39267i	0.355838	−	0.201674i
$716$			3.38423i			0.126475i
$717$		0			0
$718$	11.9602	+	11.9602i	0.446351	+	0.446351i
$719$	−20.3126			−0.757533			−0.378767	−	0.925492i	$-0.623652\pi$
$719$	−20.3126			−0.757533			−0.378767	+	0.925492i	$0.623652\pi$
$720$		0			0
$721$	26.7604			0.996608
$722$	15.8361	+	15.8361i	0.589357	+	0.589357i
$723$		0			0
$724$		−	2.90002i		−	0.107778i
$725$	−6.83417	−	4.09250i	−0.253815	−	0.151992i
$726$		0			0
$727$	12.4922	−	12.4922i	0.463311	−	0.463311i	−0.436428	−	0.899739i	$-0.643757\pi$
$727$	12.4922	−	12.4922i	0.463311	−	0.463311i	0.899739	+	0.436428i	$0.143757\pi$
$728$	−23.7421	+	23.7421i	−0.879941	+	0.879941i
$729$		0			0
$730$	−1.79858	+	6.50434i	−0.0665685	+	0.240736i
$731$		−	3.09120i		−	0.114332i
$732$		0			0
$733$	−18.6515	−	18.6515i	−0.688910	−	0.688910i	0.273081	−	0.961991i	$-0.411957\pi$
$733$	−18.6515	−	18.6515i	−0.688910	−	0.688910i	−0.961991	+	0.273081i	$0.911957\pi$
$734$	−37.9940			−1.40238
$735$		0			0
$736$	−1.75644			−0.0647431
$737$	2.06746	+	2.06746i	0.0761558	+	0.0761558i
$738$		0			0
$739$		−	6.41459i		−	0.235965i	−0.993016	−	0.117982i	$-0.962357\pi$
$739$		−	6.41459i		−	0.235965i	0.993016	−	0.117982i	$-0.0376426\pi$
$740$	1.30334	+	2.29964i	0.0479119	+	0.0845365i
$741$		0			0
$742$	−12.8093	+	12.8093i	−0.470246	+	0.470246i
$743$	−13.5407	+	13.5407i	−0.496761	+	0.496761i	−0.910428	−	0.413667i	$-0.864248\pi$
$743$	−13.5407	+	13.5407i	−0.496761	+	0.496761i	0.413667	+	0.910428i	$0.364248\pi$
$744$		0			0
$745$	−35.7096	−	9.87443i	−1.30830	−	0.361771i
$746$			3.13856i			0.114911i
$747$		0			0
$748$	0.196335	+	0.196335i	0.00717870	+	0.00717870i
$749$	−26.7404			−0.977073
$750$		0			0
$751$	3.93916			0.143742			0.0718709	−	0.997414i	$-0.477103\pi$
$751$	3.93916			0.143742			0.0718709	+	0.997414i	$0.477103\pi$
$752$	−20.8987	−	20.8987i	−0.762098	−	0.762098i
$753$		0			0
$754$		−	11.8894i		−	0.432988i
$755$	−0.0122298	−	0.00338180i	−0.000445090	−	0.000123076i
$756$		0			0
$757$	17.3710	−	17.3710i	0.631361	−	0.631361i	−0.317049	−	0.948409i	$-0.602692\pi$
$757$	17.3710	−	17.3710i	0.631361	−	0.631361i	0.948409	+	0.317049i	$0.102692\pi$
$758$	17.5322	−	17.5322i	0.636800	−	0.636800i
$759$		0			0
$760$	−4.95813	−	8.74822i	−0.179850	−	0.317331i
$761$		−	8.21986i		−	0.297970i	−0.988839	−	0.148985i	$-0.952399\pi$
$761$		−	8.21986i		−	0.297970i	0.988839	−	0.148985i	$-0.0476005\pi$
$762$		0			0
$763$	−11.6674	−	11.6674i	−0.422389	−	0.422389i
$764$	1.03558			0.0374660
$765$		0			0
$766$	−32.5079			−1.17456
$767$	−30.0020	−	30.0020i	−1.08331	−	1.08331i
$768$		0			0
$769$			2.21259i			0.0797879i	0.999204	+	0.0398939i	$0.0127020\pi$
$769$			2.21259i			0.0797879i	−0.999204	+	0.0398939i	$0.987298\pi$
$770$	−1.44314	+	5.21895i	−0.0520073	+	0.188078i
$771$		0			0
$772$	1.29204	−	1.29204i	0.0465014	−	0.0465014i
$773$	8.23173	−	8.23173i	0.296075	−	0.296075i	−0.543400	−	0.839474i	$-0.682863\pi$
$773$	8.23173	−	8.23173i	0.296075	−	0.296075i	0.839474	+	0.543400i	$0.182863\pi$
$774$		0			0
$775$	−29.9864	−	17.9567i	−1.07714	−	0.645024i
$776$			11.6955i			0.419843i
$777$		0			0
$778$	−25.7249	−	25.7249i	−0.922282	−	0.922282i
$779$	−5.48449			−0.196502
$780$		0			0
$781$	−5.19143			−0.185764
$782$	−2.42204	−	2.42204i	−0.0866119	−	0.0866119i
$783$		0			0
$784$			10.0057i			0.357346i
$785$	16.4564	−	9.32684i	0.587355	−	0.332889i
$786$		0			0
$787$	−24.7830	+	24.7830i	−0.883417	+	0.883417i	−0.993880	−	0.110463i	$-0.964767\pi$
$787$	−24.7830	+	24.7830i	−0.883417	+	0.883417i	0.110463	+	0.993880i	$0.464767\pi$
$788$	−1.86427	+	1.86427i	−0.0664120	+	0.0664120i
$789$		0			0
$790$	20.1944	−	11.4454i	0.718486	−	0.407209i
$791$			24.5882i			0.874256i
$792$		0			0
$793$	−52.1803	−	52.1803i	−1.85298	−	1.85298i
$794$	−34.6151			−1.22845
$795$		0			0
$796$	3.46220			0.122714
$797$	18.5054	+	18.5054i	0.655493	+	0.655493i	0.954310	−	0.298817i	$-0.0965920\pi$
$797$	18.5054	+	18.5054i	0.655493	+	0.655493i	−0.298817	+	0.954310i	$0.596592\pi$
$798$		0			0
$799$			13.3059i			0.470730i
$800$	−1.34643	−	5.36608i	−0.0476036	−	0.189719i
$801$		0			0
$802$	−12.2041	+	12.2041i	−0.430941	+	0.430941i
$803$	1.39865	−	1.39865i	0.0493573	−	0.0493573i
$804$		0			0
$805$	−1.93791	+	7.00822i	−0.0683025	+	0.247007i
$806$		−	52.1675i		−	1.83752i
$807$		0			0
$808$	−5.37546	−	5.37546i	−0.189108	−	0.189108i
$809$	−40.3389			−1.41824			−0.709120	−	0.705088i	$-0.750908\pi$
$809$	−40.3389			−1.41824			−0.709120	+	0.705088i	$0.750908\pi$
$810$		0			0
$811$	−4.50040			−0.158030			−0.0790152	−	0.996873i	$-0.525178\pi$
$811$	−4.50040			−0.158030			−0.0790152	+	0.996873i	$0.525178\pi$
$812$	−0.453083	−	0.453083i	−0.0159001	−	0.0159001i
$813$		0			0
$814$			7.11750i			0.249468i
$815$	6.53790	+	11.5356i	0.229013	+	0.404074i
$816$		0			0
$817$	2.07409	−	2.07409i	0.0725631	−	0.0725631i
$818$	24.3930	−	24.3930i	0.852880	−	0.852880i
$819$		0			0
$820$	−1.52221	−	0.420920i	−0.0531577	−	0.0146992i
$821$			15.3701i			0.536419i	0.963361	+	0.268209i	$0.0864319\pi$
$821$			15.3701i			0.536419i	−0.963361	+	0.268209i	$0.913568\pi$
$822$		0			0
$823$	10.3016	+	10.3016i	0.359091	+	0.359091i	0.863478	−	0.504387i	$-0.168281\pi$
$823$	10.3016	+	10.3016i	0.359091	+	0.359091i	−0.504387	+	0.863478i	$0.668281\pi$
$824$	−38.5331			−1.34236
$825$		0			0
$826$	21.0066			0.730913
$827$	3.31824	+	3.31824i	0.115387	+	0.115387i	0.762443	−	0.647056i	$-0.224000\pi$
$827$	3.31824	+	3.31824i	0.115387	+	0.115387i	−0.647056	+	0.762443i	$0.724000\pi$
$828$		0			0
$829$		−	33.9539i		−	1.17927i	−0.807671	−	0.589633i	$-0.799272\pi$
$829$		−	33.9539i		−	1.17927i	0.807671	−	0.589633i	$-0.200728\pi$
$830$	28.7599	+	7.95268i	0.998270	+	0.276042i
$831$		0			0
$832$	33.8840	−	33.8840i	1.17472	−	1.17472i
$833$	3.18524	−	3.18524i	0.110362	−	0.110362i
$834$		0			0
$835$	6.57850	+	11.6072i	0.227659	+	0.401685i
$836$			0.263467i			0.00911220i
$837$		0			0
$838$	−11.6473	−	11.6473i	−0.402349	−	0.402349i
$839$	11.4365			0.394831			0.197416	−	0.980320i	$-0.436745\pi$
$839$	11.4365			0.394831			0.197416	+	0.980320i	$0.436745\pi$
$840$		0			0
$841$	−26.4618			−0.912477
$842$	13.7520	+	13.7520i	0.473924	+	0.473924i
$843$		0			0
$844$			0.0241904i			0.000832668i
$845$	−10.6543	+	38.5299i	−0.366519	+	1.32547i
$846$		0			0
$847$	−14.8113	+	14.8113i	−0.508923	+	0.508923i
$848$	16.6163	−	16.6163i	0.570606	−	0.570606i
$849$		0			0
$850$	5.54289	−	9.25622i	0.190120	−	0.317486i
$851$			9.55768i			0.327633i
$852$		0			0
$853$	−16.9099	−	16.9099i	−0.578985	−	0.578985i	0.355638	−	0.934624i	$-0.384264\pi$
$853$	−16.9099	−	16.9099i	−0.578985	−	0.578985i	−0.934624	+	0.355638i	$0.884264\pi$
$854$	36.5353			1.25021
$855$		0			0
$856$	38.5043			1.31605
$857$	−10.6055	−	10.6055i	−0.362278	−	0.362278i	0.502373	−	0.864651i	$-0.332460\pi$
$857$	−10.6055	−	10.6055i	−0.362278	−	0.362278i	−0.864651	+	0.502373i	$0.832460\pi$
$858$		0			0
$859$			43.4148i			1.48129i	0.671895	+	0.740646i	$0.265480\pi$
$859$			43.4148i			1.48129i	−0.671895	+	0.740646i	$0.734520\pi$
$860$	0.734839	−	0.416477i	0.0250578	−	0.0142017i
$861$		0			0
$862$	34.1551	−	34.1551i	1.16333	−	1.16333i
$863$	2.78648	−	2.78648i	0.0948527	−	0.0948527i	−0.658088	−	0.752941i	$-0.728635\pi$
$863$	2.78648	−	2.78648i	0.0948527	−	0.0948527i	0.752941	+	0.658088i	$0.228635\pi$
$864$		0			0
$865$	−26.5833	+	15.0663i	−0.903859	+	0.512271i
$866$		−	0.629703i		−	0.0213982i
$867$		0			0
$868$	−1.98800	−	1.98800i	−0.0674771	−	0.0674771i
$869$	−6.80362			−0.230797
$870$		0			0
$871$	−18.4582			−0.625433
$872$	16.8003	+	16.8003i	0.568929	+	0.568929i
$873$		0			0
$874$		−	3.25020i		−	0.109940i
$875$	−22.8963	−	0.548210i	−0.774037	−	0.0185329i
$876$		0			0
$877$	30.4239	−	30.4239i	1.02734	−	1.02734i	0.0277265	−	0.999616i	$-0.491173\pi$
$877$	30.4239	−	30.4239i	1.02734	−	1.02734i	0.999616	−	0.0277265i	$-0.00882674\pi$
$878$	1.41405	−	1.41405i	0.0477218	−	0.0477218i
$879$		0			0
$880$	1.87205	−	6.77002i	0.0631067	−	0.228217i
$881$			47.0487i			1.58511i	0.609801	+	0.792555i	$0.291249\pi$
$881$			47.0487i			1.58511i	−0.609801	+	0.792555i	$0.708751\pi$
$882$		0			0
$883$	21.0669	+	21.0669i	0.708957	+	0.708957i	0.966316	−	0.257359i	$-0.0828523\pi$
$883$	21.0669	+	21.0669i	0.708957	+	0.708957i	−0.257359	+	0.966316i	$0.582852\pi$
$884$	−1.75287			−0.0589555
$885$		0			0
$886$	−43.0279			−1.44555
$887$	−2.56758	−	2.56758i	−0.0862111	−	0.0862111i	0.662686	−	0.748897i	$-0.269416\pi$
$887$	−2.56758	−	2.56758i	−0.0862111	−	0.0862111i	−0.748897	+	0.662686i	$0.769416\pi$
$888$		0			0
$889$			5.51098i			0.184832i
$890$	−6.85228	−	12.0903i	−0.229689	−	0.405267i
$891$		0			0
$892$	0.347592	−	0.347592i	0.0116382	−	0.0116382i
$893$	−8.92780	+	8.92780i	−0.298758	+	0.298758i
$894$		0			0
$895$	−37.1491	−	10.2725i	−1.24176	−	0.343371i
$896$			19.1914i			0.641141i
$897$		0			0
$898$	−20.7292	−	20.7292i	−0.691744	−	0.691744i
$899$	11.1368			0.371433
$900$		0			0
$901$	−10.5794			−0.352450
$902$	−3.00703	−	3.00703i	−0.100123	−	0.100123i
$903$		0			0
$904$		−	35.4053i		−	1.17756i
$905$	31.8339	+	8.80270i	1.05819	+	0.292612i
$906$		0			0
$907$	−7.42025	+	7.42025i	−0.246385	+	0.246385i	−0.819485	−	0.573100i	$-0.805741\pi$
$907$	−7.42025	+	7.42025i	−0.246385	+	0.246385i	0.573100	+	0.819485i	$0.305741\pi$
$908$	2.11700	−	2.11700i	0.0702551	−	0.0702551i
$909$		0			0
$910$	−16.8551	−	29.7395i	−0.558743	−	0.985855i
$911$			7.82323i			0.259195i	0.991567	+	0.129598i	$0.0413686\pi$
$911$			7.82323i			0.259195i	−0.991567	+	0.129598i	$0.958631\pi$
$912$		0			0
$913$	−6.18433	−	6.18433i	−0.204672	−	0.204672i
$914$	−1.22401			−0.0404866
$915$		0			0
$916$	4.33201			0.143134
$917$	−30.9612	−	30.9612i	−1.02243	−	1.02243i
$918$		0			0
$919$			4.61000i			0.152070i	0.997105	+	0.0760349i	$0.0242260\pi$
$919$			4.61000i			0.152070i	−0.997105	+	0.0760349i	$0.975774\pi$
$920$	2.79046	−	10.0913i	0.0919988	−	0.332702i
$921$		0			0
$922$	20.5407	−	20.5407i	0.676472	−	0.676472i
$923$	23.1745	−	23.1745i	0.762798	−	0.762798i
$924$		0			0
$925$	−29.1996	+	7.32664i	−0.960078	+	0.240899i
$926$			25.1999i			0.828122i
$927$		0			0
$928$	1.24650	+	1.24650i	0.0409182	+	0.0409182i
$929$	31.4123			1.03060			0.515302	−	0.857008i	$-0.327680\pi$
$929$	31.4123			1.03060			0.515302	+	0.857008i	$0.327680\pi$
$930$		0			0
$931$	4.27436			0.140087
$932$	0.828872	+	0.828872i	0.0271506	+	0.0271506i
$933$		0			0
$934$			31.9642i			1.04590i
$935$	−2.75114	+	1.55924i	−0.0899720	+	0.0509925i
$936$		0			0
$937$	−21.3617	+	21.3617i	−0.697856	+	0.697856i	−0.963948	−	0.266092i	$-0.914268\pi$
$937$	−21.3617	+	21.3617i	−0.697856	+	0.697856i	0.266092	+	0.963948i	$0.414268\pi$
$938$	6.46198	−	6.46198i	0.210991	−	0.210991i
$939$		0			0
$940$	−3.16308	+	1.79270i	−0.103168	+	0.0584715i
$941$			6.66302i			0.217208i	0.994085	+	0.108604i	$0.0346381\pi$
$941$			6.66302i			0.217208i	−0.994085	+	0.108604i	$0.965362\pi$
$942$		0			0
$943$	−4.03797	−	4.03797i	−0.131494	−	0.131494i
$944$	−27.2498			−0.886905
$945$		0			0
$946$	2.27436			0.0739458
$947$	2.37091	+	2.37091i	0.0770443	+	0.0770443i	0.744579	−	0.667535i	$-0.232650\pi$
$947$	2.37091	+	2.37091i	0.0770443	+	0.0770443i	−0.667535	+	0.744579i	$0.732650\pi$
$948$		0			0
$949$			12.4871i			0.405349i
$950$	9.92967	−	2.49151i	0.322161	−	0.0808353i
$951$		0			0
$952$	6.86479	−	6.86479i	0.222489	−	0.222489i
$953$	30.7161	−	30.7161i	0.994992	−	0.994992i	−0.00499525	−	0.999988i	$-0.501590\pi$
$953$	30.7161	−	30.7161i	0.994992	−	0.994992i	0.999988	+	0.00499525i	$0.00159004\pi$
$954$		0			0
$955$	−3.14340	+	11.3677i	−0.101718	+	0.367850i
$956$		−	2.66701i		−	0.0862572i
$957$		0			0
$958$	16.9365	+	16.9365i	0.547193	+	0.547193i
$959$	−14.0520			−0.453763
$960$		0			0
$961$	17.8651			0.576293
$962$	−31.7725	−	31.7725i	−1.02439	−	1.02439i
$963$		0			0
$964$		−	1.00809i		−	0.0324684i
$965$	10.2610	+	18.1047i	0.330313	+	0.582810i
$966$		0			0
$967$	−4.05487	+	4.05487i	−0.130396	+	0.130396i	−0.769293	−	0.638897i	$-0.779391\pi$
$967$	−4.05487	+	4.05487i	−0.130396	+	0.130396i	0.638897	+	0.769293i	$0.279391\pi$
$968$	21.3273	−	21.3273i	0.685484	−	0.685484i
$969$		0			0
$970$	−11.4764	−	3.17345i	−0.368484	−	0.101893i
$971$			14.2248i			0.456496i	0.973603	+	0.228248i	$0.0732998\pi$
$971$			14.2248i			0.456496i	−0.973603	+	0.228248i	$0.926700\pi$
$972$		0			0
$973$	−2.08844	−	2.08844i	−0.0669524	−	0.0669524i
$974$	−41.4488			−1.32810
$975$		0			0
$976$	−47.3936			−1.51703
$977$	−22.0734	−	22.0734i	−0.706192	−	0.706192i	0.259540	−	0.965732i	$-0.416429\pi$
$977$	−22.0734	−	22.0734i	−0.706192	−	0.706192i	−0.965732	+	0.259540i	$0.916429\pi$
$978$		0			0
$979$			4.07328i			0.130183i
$980$	1.18634	+	0.328046i	0.0378962	+	0.0104791i
$981$		0			0
$982$	38.5627	−	38.5627i	1.23059	−	1.23059i
$983$	−7.28208	+	7.28208i	−0.232262	+	0.232262i	−0.813636	−	0.581374i	$-0.802515\pi$
$983$	−7.28208	+	7.28208i	−0.232262	+	0.232262i	0.581374	+	0.813636i	$0.302515\pi$
$984$		0			0
$985$	−14.8056	−	26.1232i	−0.471744	−	0.832354i
$986$			3.43771i			0.109479i
$987$		0			0
$988$	−1.17611	−	1.17611i	−0.0374172	−	0.0374172i
$989$	3.05411			0.0971150
$990$		0			0
$991$	37.9180			1.20450			0.602252	−	0.798306i	$-0.294270\pi$
$991$	37.9180			1.20450			0.602252	+	0.798306i	$0.294270\pi$
$992$	5.46927	+	5.46927i	0.173649	+	0.173649i
$993$		0			0
$994$			16.2262i			0.514663i
$995$	−10.5091	+	38.0049i	−0.333162	+	1.20484i
$996$		0			0
$997$	−22.0459	+	22.0459i	−0.698201	+	0.698201i	−0.964022	−	0.265821i	$-0.914357\pi$
$997$	−22.0459	+	22.0459i	−0.698201	+	0.698201i	0.265821	+	0.964022i	$0.414357\pi$
$998$	40.9452	−	40.9452i	1.29610	−	1.29610i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.f.a.323.6		16
3.2	odd	2	inner	405.2.f.a.323.3		16
5.2	odd	4	inner	405.2.f.a.242.3		16
9.2	odd	6		135.2.m.a.98.1		16
9.4	even	3		135.2.m.a.8.1		16
9.5	odd	6		45.2.l.a.38.4	yes	16
9.7	even	3		45.2.l.a.23.4	yes	16
15.2	even	4	inner	405.2.f.a.242.6		16
36.7	odd	6		720.2.cu.c.113.3		16
36.23	even	6		720.2.cu.c.353.4		16
45.2	even	12		135.2.m.a.17.1		16
45.4	even	6		675.2.q.a.143.4		16
45.7	odd	12		45.2.l.a.32.4	yes	16
45.13	odd	12		675.2.q.a.332.4		16
45.14	odd	6		225.2.p.b.218.1		16
45.22	odd	12		135.2.m.a.62.1		16
45.23	even	12		225.2.p.b.182.1		16
45.29	odd	6		675.2.q.a.368.4		16
45.32	even	12		45.2.l.a.2.4	✓	16
45.34	even	6		225.2.p.b.68.1		16
45.38	even	12		675.2.q.a.557.4		16
45.43	odd	12		225.2.p.b.32.1		16
180.7	even	12		720.2.cu.c.257.4		16
180.167	odd	12		720.2.cu.c.497.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.4	✓	16	45.32	even	12
45.2.l.a.23.4	yes	16	9.7	even	3
45.2.l.a.32.4	yes	16	45.7	odd	12
45.2.l.a.38.4	yes	16	9.5	odd	6
135.2.m.a.8.1		16	9.4	even	3
135.2.m.a.17.1		16	45.2	even	12
135.2.m.a.62.1		16	45.22	odd	12
135.2.m.a.98.1		16	9.2	odd	6
225.2.p.b.32.1		16	45.43	odd	12
225.2.p.b.68.1		16	45.34	even	6
225.2.p.b.182.1		16	45.23	even	12
225.2.p.b.218.1		16	45.14	odd	6
405.2.f.a.242.3		16	5.2	odd	4	inner
405.2.f.a.242.6		16	15.2	even	4	inner
405.2.f.a.323.3		16	3.2	odd	2	inner
405.2.f.a.323.6		16	1.1	even	1	trivial
675.2.q.a.143.4		16	45.4	even	6
675.2.q.a.332.4		16	45.13	odd	12
675.2.q.a.368.4		16	45.29	odd	6
675.2.q.a.557.4		16	45.38	even	12
720.2.cu.c.113.3		16	36.7	odd	6
720.2.cu.c.257.4		16	180.7	even	12
720.2.cu.c.353.4		16	36.23	even	6
720.2.cu.c.497.3		16	180.167	odd	12

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.949649 + 0.949649i) q^{2} -0.196335i q^{4} +(2.15519 + 0.595953i) q^{5} +(-1.44851 + 1.44851i) q^{7} +(2.08575 - 2.08575i) q^{8} +O(q^{10})\)	\(q+(0.949649 + 0.949649i) q^{2} -0.196335i q^{4} +(2.15519 + 0.595953i) q^{5} +(-1.44851 + 1.44851i) q^{7} +(2.08575 - 2.08575i) q^{8} +(1.48073 + 2.61262i) q^{10} -0.880206i q^{11} +(3.92923 + 3.92923i) q^{13} -2.75114 q^{14} +3.56878 q^{16} +(-1.13610 - 1.13610i) q^{17} -1.52456i q^{19} +(0.117006 - 0.423138i) q^{20} +(0.835887 - 0.835887i) q^{22} +(1.12246 - 1.12246i) q^{23} +(4.28968 + 2.56878i) q^{25} +7.46278i q^{26} +(0.284392 + 0.284392i) q^{28} -1.59317 q^{29} -6.99036 q^{31} +(-0.782402 - 0.782402i) q^{32} -2.15779i q^{34} +(-3.98504 + 2.25856i) q^{35} +(-4.25746 + 4.25746i) q^{37} +(1.44780 - 1.44780i) q^{38} +(5.73818 - 3.25217i) q^{40} -3.59742i q^{41} +(1.36045 + 1.36045i) q^{43} -0.172815 q^{44} +2.13189 q^{46} +(-5.85598 - 5.85598i) q^{47} +2.80367i q^{49} +(1.63425 + 6.51313i) q^{50} +(0.771444 - 0.771444i) q^{52} +(4.65601 - 4.65601i) q^{53} +(0.524562 - 1.89701i) q^{55} +6.04243i q^{56} +(-1.51295 - 1.51295i) q^{58} -7.63559 q^{59} -13.2800 q^{61} +(-6.63838 - 6.63838i) q^{62} -8.62358i q^{64} +(6.12660 + 10.8099i) q^{65} +(-2.34883 + 2.34883i) q^{67} +(-0.223055 + 0.223055i) q^{68} +(-5.92923 - 1.63955i) q^{70} -5.89798i q^{71} +(1.58900 + 1.58900i) q^{73} -8.08618 q^{74} -0.299324 q^{76} +(1.27498 + 1.27498i) q^{77} -7.72958i q^{79} +(7.69140 + 2.12683i) q^{80} +(3.41628 - 3.41628i) q^{82} +(7.02601 - 7.02601i) q^{83} +(-1.77144 - 3.12557i) q^{85} +2.58390i q^{86} +(-1.83589 - 1.83589i) q^{88} -4.62765 q^{89} -11.3830 q^{91} +(-0.220378 - 0.220378i) q^{92} -11.1222i q^{94} +(0.908567 - 3.28572i) q^{95} +(-2.80367 + 2.80367i) q^{97} +(-2.66250 + 2.66250i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7}+O(q^{10}) \) 16 * q + 4 * q^7	\( 16 q + 4 q^{7} - 8 q^{10} + 4 q^{13} + 16 q^{16} + 20 q^{22} - 8 q^{25} - 16 q^{28} + 8 q^{31} + 4 q^{37} - 12 q^{40} + 4 q^{43} + 32 q^{46} + 28 q^{52} - 16 q^{55} + 12 q^{58} - 16 q^{61} - 8 q^{67} - 36 q^{70} - 8 q^{73} - 48 q^{76} + 32 q^{82} - 44 q^{85} - 36 q^{88} - 40 q^{91} - 56 q^{97}+O(q^{100}) \) 16 * q + 4 * q^7 - 8 * q^10 + 4 * q^13 + 16 * q^16 + 20 * q^22 - 8 * q^25 - 16 * q^28 + 8 * q^31 + 4 * q^37 - 12 * q^40 + 4 * q^43 + 32 * q^46 + 28 * q^52 - 16 * q^55 + 12 * q^58 - 16 * q^61 - 8 * q^67 - 36 * q^70 - 8 * q^73 - 48 * q^76 + 32 * q^82 - 44 * q^85 - 36 * q^88 - 40 * q^91 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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