LMFDB - Embedded newform 720.2.bm.h.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(109,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("720.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bm (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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.3
Character	$\chi$	$=$	720.109
Dual form			720.2.bm.h.469.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36038 + 0.386472i) q^{2} +(1.70128 - 1.05150i) q^{4} +(1.03097 - 1.98421i) q^{5} +3.91927 q^{7} +(-1.90801 + 2.08794i) q^{8} +O(q^{10})$	\(q+(-1.36038 + 0.386472i) q^{2} +(1.70128 - 1.05150i) q^{4} +(1.03097 - 1.98421i) q^{5} +3.91927 q^{7} +(-1.90801 + 2.08794i) q^{8} +(-0.635669 + 3.09773i) q^{10} +(2.93423 - 2.93423i) q^{11} +(0.732828 - 0.732828i) q^{13} +(-5.33170 + 1.51469i) q^{14} +(1.78869 - 3.57779i) q^{16} +2.89302i q^{17} +(1.67534 + 1.67534i) q^{19} +(-0.332434 - 4.45976i) q^{20} +(-2.85767 + 5.12567i) q^{22} -1.73133 q^{23} +(-2.87420 - 4.09133i) q^{25} +(-0.713708 + 1.28014i) q^{26} +(6.66776 - 4.12111i) q^{28} +(4.99003 + 4.99003i) q^{29} -10.8149 q^{31} +(-1.05059 + 5.55844i) q^{32} +(-1.11807 - 3.93561i) q^{34} +(4.04065 - 7.77666i) q^{35} +(-6.41524 - 6.41524i) q^{37} +(-2.92658 - 1.63163i) q^{38} +(2.17581 + 5.93850i) q^{40} -0.00577512i q^{41} +(2.23930 + 2.23930i) q^{43} +(1.90660 - 8.07728i) q^{44} +(2.35527 - 0.669110i) q^{46} -11.6451i q^{47} +8.36066 q^{49} +(5.49120 + 4.45497i) q^{50} +(0.476175 - 2.01731i) q^{52} +(5.55765 + 5.55765i) q^{53} +(-2.79703 - 8.84724i) q^{55} +(-7.47801 + 8.18319i) q^{56} +(-8.71685 - 4.85983i) q^{58} +(-3.83290 + 3.83290i) q^{59} +(9.30595 + 9.30595i) q^{61} +(14.7123 - 4.17964i) q^{62} +(-0.718981 - 7.96763i) q^{64} +(-0.698563 - 2.20961i) q^{65} +(3.85243 - 3.85243i) q^{67} +(3.04201 + 4.92182i) q^{68} +(-2.49136 + 12.1408i) q^{70} -1.15355i q^{71} +7.98713 q^{73} +(11.2065 + 6.24786i) q^{74} +(4.61185 + 1.08860i) q^{76} +(11.5000 - 11.5000i) q^{77} +0.843960 q^{79} +(-5.25501 - 7.23774i) q^{80} +(0.00223193 + 0.00785637i) q^{82} +(-5.20069 + 5.20069i) q^{83} +(5.74036 + 2.98261i) q^{85} +(-3.91173 - 2.18088i) q^{86} +(0.527948 + 11.7250i) q^{88} +5.40896i q^{89} +(2.87215 - 2.87215i) q^{91} +(-2.94547 + 1.82049i) q^{92} +(4.50051 + 15.8418i) q^{94} +(5.05147 - 1.59701i) q^{95} +2.24154i q^{97} +(-11.3737 + 3.23117i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{10} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 48 q^{31} - 28 q^{34} - 24 q^{35} - 16 q^{40} + 40 q^{44} - 4 q^{46} + 48 q^{49} + 32 q^{50} - 48 q^{56} + 32 q^{59} + 16 q^{61} + 48 q^{64} - 16 q^{65} - 40 q^{74} + 60 q^{76} - 96 q^{79} - 72 q^{80} - 16 q^{86} - 32 q^{91} + 44 q^{94} + 48 q^{95}+O(q^{100}) $ 48 * q + 12 * q^10 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 40 * q^26 - 48 * q^31 - 28 * q^34 - 24 * q^35 - 16 * q^40 + 40 * q^44 - 4 * q^46 + 48 * q^49 + 32 * q^50 - 48 * q^56 + 32 * q^59 + 16 * q^61 + 48 * q^64 - 16 * q^65 - 40 * q^74 + 60 * q^76 - 96 * q^79 - 72 * q^80 - 16 * q^86 - 32 * q^91 + 44 * q^94 + 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.36038	+	0.386472i	−0.961935	+	0.273277i
$2$	−1.36038	+	0.386472i	−0.961935	+	0.273277i
$3$		0			0
$3$		0			0
$4$	1.70128	−	1.05150i	0.850639	−	0.525750i
$5$	1.03097	−	1.98421i	0.461064	−	0.887367i
$5$	1.03097	−	1.98421i	0.461064	−	0.887367i
$6$		0			0
$7$	3.91927			1.48134			0.740672	−	0.671867i	$-0.234507\pi$
$7$	3.91927			1.48134			0.740672	+	0.671867i	$0.234507\pi$
$8$	−1.90801	+	2.08794i	−0.674584	+	0.738198i
$9$		0			0
$10$	−0.635669	+	3.09773i	−0.201016	+	0.979588i
$11$	2.93423	−	2.93423i	0.884703	−	0.884703i	−0.109305	−	0.994008i	$-0.534862\pi$
$11$	2.93423	−	2.93423i	0.884703	−	0.884703i	0.994008	+	0.109305i	$0.0348625\pi$
$12$		0			0
$13$	0.732828	−	0.732828i	0.203250	−	0.203250i	−0.598141	−	0.801391i	$-0.704094\pi$
$13$	0.732828	−	0.732828i	0.203250	−	0.203250i	0.801391	+	0.598141i	$0.204094\pi$
$14$	−5.33170	+	1.51469i	−1.42496	+	0.404818i
$15$		0			0
$16$	1.78869	−	3.57779i	0.447173	−	0.894447i
$17$			2.89302i			0.701659i	0.936439	+	0.350830i	$0.114100\pi$
$17$			2.89302i			0.701659i	−0.936439	+	0.350830i	$0.885900\pi$
$18$		0			0
$19$	1.67534	+	1.67534i	0.384350	+	0.384350i	0.872667	−	0.488316i	$-0.162389\pi$
$19$	1.67534	+	1.67534i	0.384350	+	0.384350i	−0.488316	+	0.872667i	$0.662389\pi$
$20$	−0.332434	−	4.45976i	−0.0743346	−	0.997233i
$21$		0			0
$22$	−2.85767	+	5.12567i	−0.609258	+	1.09280i
$23$	−1.73133			−0.361006			−0.180503	−	0.983574i	$-0.557773\pi$
$23$	−1.73133			−0.361006			−0.180503	+	0.983574i	$0.557773\pi$
$24$		0			0
$25$	−2.87420	−	4.09133i	−0.574841	−	0.818265i
$26$	−0.713708	+	1.28014i	−0.139970	+	0.251057i
$27$		0			0
$28$	6.66776	−	4.12111i	1.26009	−	0.778817i
$29$	4.99003	+	4.99003i	0.926625	+	0.926625i	0.997486	−	0.0708617i	$-0.0225749\pi$
$29$	4.99003	+	4.99003i	0.926625	+	0.926625i	−0.0708617	+	0.997486i	$0.522575\pi$
$30$		0			0
$31$	−10.8149			−1.94241			−0.971203	−	0.238254i	$-0.923425\pi$
$31$	−10.8149			−1.94241			−0.971203	+	0.238254i	$0.923425\pi$
$32$	−1.05059	+	5.55844i	−0.185720	+	0.982603i
$33$		0			0
$34$	−1.11807	−	3.93561i	−0.191748	−	0.674951i
$35$	4.04065	−	7.77666i	0.682994	−	1.31450i
$36$		0			0
$37$	−6.41524	−	6.41524i	−1.05466	−	1.05466i	−0.998417	−	0.0562413i	$-0.982088\pi$
$37$	−6.41524	−	6.41524i	−1.05466	−	1.05466i	−0.0562413	−	0.998417i	$-0.517912\pi$
$38$	−2.92658	−	1.63163i	−0.474754	−	0.264686i
$39$		0			0
$40$	2.17581	+	5.93850i	0.344026	+	0.938960i
$41$		−	0.00577512i		−	0.000901923i	−1.00000		0.000450961i	$-0.999856\pi$
$41$		−	0.00577512i		−	0.000901923i	1.00000		0.000450961i	$-0.000143545\pi$
$42$		0			0
$43$	2.23930	+	2.23930i	0.341490	+	0.341490i	0.856927	−	0.515437i	$-0.172370\pi$
$43$	2.23930	+	2.23930i	0.341490	+	0.341490i	−0.515437	+	0.856927i	$0.672370\pi$
$44$	1.90660	−	8.07728i	0.287430	−	1.21770i
$45$		0			0
$46$	2.35527	−	0.669110i	0.347265	−	0.0986549i
$47$		−	11.6451i		−	1.69861i	−0.527900	−	0.849307i	$-0.677020\pi$
$47$		−	11.6451i		−	1.69861i	0.527900	−	0.849307i	$-0.322980\pi$
$48$		0			0
$49$	8.36066			1.19438
$50$	5.49120	+	4.45497i	0.776573	+	0.630028i
$51$		0			0
$52$	0.476175	−	2.01731i	0.0660336	−	0.279751i
$53$	5.55765	+	5.55765i	0.763402	+	0.763402i	0.976936	−	0.213533i	$-0.0684972\pi$
$53$	5.55765	+	5.55765i	0.763402	+	0.763402i	−0.213533	+	0.976936i	$0.568497\pi$
$54$		0			0
$55$	−2.79703	−	8.84724i	−0.377152	−	1.19296i
$56$	−7.47801	+	8.18319i	−0.999291	+	1.09353i
$57$		0			0
$58$	−8.71685	−	4.85983i	−1.14458	−	0.638127i
$59$	−3.83290	+	3.83290i	−0.499001	+	0.499001i	−0.911127	−	0.412126i	$-0.864786\pi$
$59$	−3.83290	+	3.83290i	−0.499001	+	0.499001i	0.412126	+	0.911127i	$0.364786\pi$
$60$		0			0
$61$	9.30595	+	9.30595i	1.19150	+	1.19150i	0.976645	+	0.214859i	$0.0689293\pi$
$61$	9.30595	+	9.30595i	1.19150	+	1.19150i	0.214859	+	0.976645i	$0.431071\pi$
$62$	14.7123	−	4.17964i	1.86847	−	0.530815i
$63$		0			0
$64$	−0.718981	−	7.96763i	−0.0898726	−	0.995953i
$65$	−0.698563	−	2.20961i	−0.0866461	−	0.274068i
$66$		0			0
$67$	3.85243	−	3.85243i	0.470649	−	0.470649i	−0.431476	−	0.902124i	$-0.642007\pi$
$67$	3.85243	−	3.85243i	0.470649	−	0.470649i	0.902124	+	0.431476i	$0.142007\pi$
$68$	3.04201	+	4.92182i	0.368898	+	0.596859i
$69$		0			0
$70$	−2.49136	+	12.1408i	−0.297774	+	1.45111i
$71$		−	1.15355i		−	0.136901i	−0.997655	−	0.0684504i	$-0.978195\pi$
$71$		−	1.15355i		−	0.136901i	0.997655	−	0.0684504i	$-0.0218055\pi$
$72$		0			0
$73$	7.98713			0.934823			0.467411	−	0.884040i	$-0.345187\pi$
$73$	7.98713			0.934823			0.467411	+	0.884040i	$0.345187\pi$
$74$	11.2065	+	6.24786i	1.30273	+	0.726299i
$75$		0			0
$76$	4.61185	+	1.08860i	0.529016	+	0.124871i
$77$	11.5000	−	11.5000i	1.31055	−	1.31055i
$78$		0			0
$79$	0.843960			0.0949529			0.0474765	−	0.998872i	$-0.484882\pi$
$79$	0.843960			0.0949529			0.0474765	+	0.998872i	$0.484882\pi$
$80$	−5.25501	−	7.23774i	−0.587528	−	0.809204i
$81$		0			0
$82$	0.00223193	+	0.00785637i	0.000246475	+	0.000867591i
$83$	−5.20069	+	5.20069i	−0.570850	+	0.570850i	−0.932366	−	0.361516i	$-0.882259\pi$
$83$	−5.20069	+	5.20069i	−0.570850	+	0.570850i	0.361516	+	0.932366i	$0.382259\pi$
$84$		0			0
$85$	5.74036	+	2.98261i	0.622629	+	0.323510i
$86$	−3.91173	−	2.18088i	−0.421813	−	0.235170i
$87$		0			0
$88$	0.527948	+	11.7250i	0.0562794	+	1.24989i
$89$			5.40896i			0.573349i	0.958028	+	0.286674i	$0.0925498\pi$
$89$			5.40896i			0.573349i	−0.958028	+	0.286674i	$0.907450\pi$
$90$		0			0
$91$	2.87215	−	2.87215i	0.301083	−	0.301083i
$92$	−2.94547	+	1.82049i	−0.307086	+	0.189799i
$93$		0			0
$94$	4.50051	+	15.8418i	0.464193	+	1.63396i
$95$	5.05147	−	1.59701i	0.518270	−	0.163850i
$96$		0			0
$97$			2.24154i			0.227594i	0.993504	+	0.113797i	$0.0363013\pi$
$97$			2.24154i			0.227594i	−0.993504	+	0.113797i	$0.963699\pi$
$98$	−11.3737	+	3.23117i	−1.14892	+	0.326397i
$99$		0			0
$100$	−9.19185	−	3.93826i	−0.919185	−	0.393826i
$101$	7.50655	−	7.50655i	0.746930	−	0.746930i	−0.226972	−	0.973901i	$-0.572882\pi$
$101$	7.50655	−	7.50655i	0.746930	−	0.746930i	0.973901	+	0.226972i	$0.0728824\pi$
$102$		0			0
$103$	−3.91110			−0.385372			−0.192686	−	0.981260i	$-0.561720\pi$
$103$	−3.91110			−0.385372			−0.192686	+	0.981260i	$0.561720\pi$
$104$	0.131856	+	2.92834i	0.0129295	+	0.287148i
$105$		0			0
$106$	−9.70841	−	5.41265i	−0.942964	−	0.525723i
$107$	−2.60233	−	2.60233i	−0.251577	−	0.251577i	0.570040	−	0.821617i	$-0.306928\pi$
$107$	−2.60233	−	2.60233i	−0.251577	−	0.251577i	−0.821617	+	0.570040i	$0.806928\pi$
$108$		0			0
$109$	−2.06635	−	2.06635i	−0.197920	−	0.197920i	0.601188	−	0.799108i	$-0.294694\pi$
$109$	−2.06635	−	2.06635i	−0.197920	−	0.197920i	−0.799108	+	0.601188i	$0.794694\pi$
$110$	7.22425	+	10.9546i	0.688805	+	1.04448i
$111$		0			0
$112$	7.01037	−	14.0223i	0.662418	−	1.32498i
$113$		−	8.13610i		−	0.765380i	−0.923877	−	0.382690i	$-0.874998\pi$
$113$		−	8.13610i		−	0.765380i	0.923877	−	0.382690i	$-0.125002\pi$
$114$		0			0
$115$	−1.78495	+	3.43532i	−0.166447	+	0.320345i
$116$	13.7364	+	3.24241i	1.27540	+	0.301050i
$117$		0			0
$118$	3.73290	−	6.69551i	0.343641	−	0.616372i
$119$			11.3385i			1.03940i
$120$		0			0
$121$		−	6.21941i		−	0.565401i
$122$	−16.2561	−	9.06315i	−1.47176	−	0.820539i
$123$		0			0
$124$	−18.3991	+	11.3718i	−1.65229	+	1.02122i
$125$	−11.0813	+	1.48500i	−0.991140	+	0.132822i
$126$		0			0
$127$		−	16.0862i		−	1.42742i	−0.700442	−	0.713709i	$-0.747014\pi$
$127$		−	16.0862i		−	1.42742i	0.700442	−	0.713709i	$-0.252986\pi$
$128$	4.05736	+	10.5611i	0.358623	+	0.933482i
$129$		0			0
$130$	1.80427	+	2.73594i	0.158245	+	0.239958i
$131$	−13.0407	−	13.0407i	−1.13937	−	1.13937i	−0.988563	−	0.150808i	$-0.951813\pi$
$131$	−13.0407	−	13.0407i	−1.13937	−	1.13937i	−0.150808	−	0.988563i	$-0.548187\pi$
$132$		0			0
$133$	6.56612	+	6.56612i	0.569355	+	0.569355i
$134$	−3.75191	+	6.72963i	−0.324116	+	0.581351i
$135$		0			0
$136$	−6.04044	−	5.51991i	−0.517964	−	0.473328i
$137$	−6.51614			−0.556711			−0.278356	−	0.960478i	$-0.589789\pi$
$137$	−6.51614			−0.556711			−0.278356	+	0.960478i	$0.589789\pi$
$138$		0			0
$139$	−15.0953	+	15.0953i	−1.28036	+	1.28036i	−0.339902	+	0.940461i	$0.610394\pi$
$139$	−15.0953	+	15.0953i	−1.28036	+	1.28036i	−0.940461	+	0.339902i	$0.889606\pi$
$140$	−1.30290	−	17.4790i	−0.110115	−	1.47725i
$141$		0			0
$142$	0.445814	+	1.56926i	0.0374119	+	0.131690i
$143$		−	4.30057i		−	0.359632i
$144$		0			0
$145$	15.0458	−	4.75671i	1.24949	−	0.395023i
$146$	−10.8655	+	3.08681i	−0.899239	+	0.255466i
$147$		0			0
$148$	−17.6597	−	4.16848i	−1.45162	−	0.342647i
$149$	−4.27402	+	4.27402i	−0.350141	+	0.350141i	−0.860162	−	0.510021i	$-0.829638\pi$
$149$	−4.27402	+	4.27402i	−0.350141	+	0.350141i	0.510021	+	0.860162i	$0.329638\pi$
$150$		0			0
$151$			8.39998i			0.683581i	0.939776	+	0.341790i	$0.111033\pi$
$151$			8.39998i			0.683581i	−0.939776	+	0.341790i	$0.888967\pi$
$152$	−6.69459	+	0.301440i	−0.543003	+	0.0244500i
$153$		0			0
$154$	−11.2000	+	20.0889i	−0.902521	+	1.61881i
$155$	−11.1498	+	21.4590i	−0.895573	+	1.72363i
$156$		0			0
$157$	5.68893	−	5.68893i	0.454026	−	0.454026i	−0.442662	−	0.896689i	$-0.645966\pi$
$157$	5.68893	−	5.68893i	0.454026	−	0.454026i	0.896689	+	0.442662i	$0.145966\pi$
$158$	−1.14811	+	0.326167i	−0.0913386	+	0.0259485i
$159$		0			0
$160$	9.94600	+	7.81518i	0.786301	+	0.617844i
$161$	−6.78553			−0.534775
$162$		0			0
$163$	−5.63869	+	5.63869i	−0.441656	+	0.441656i	−0.892568	−	0.450912i	$-0.851099\pi$
$163$	−5.63869	+	5.63869i	−0.441656	+	0.441656i	0.450912	+	0.892568i	$0.351099\pi$
$164$	−0.00607254	−	0.00982509i	−0.000474186	−	0.000767211i
$165$		0			0
$166$	5.06500	−	9.08485i	0.393120	−	0.705121i
$167$	−6.45583			−0.499567			−0.249783	−	0.968302i	$-0.580359\pi$
$167$	−6.45583			−0.499567			−0.249783	+	0.968302i	$0.580359\pi$
$168$		0			0
$169$			11.9259i			0.917379i
$170$	−8.96178	−	1.83900i	−0.687337	−	0.141045i
$171$		0			0
$172$	6.16430	+	1.45505i	0.470023	+	0.110946i
$173$	7.33664	−	7.33664i	0.557795	−	0.557795i	−0.370884	−	0.928679i	$-0.620945\pi$
$173$	7.33664	−	7.33664i	0.557795	−	0.557795i	0.928679	+	0.370884i	$0.120945\pi$
$174$		0			0
$175$	−11.2648	−	16.0350i	−0.851537	−	1.21213i
$176$	−5.24962	−	15.7465i	−0.395705	−	1.18694i
$177$		0			0
$178$	−2.09042	−	7.35826i	−0.156683	−	0.551525i
$179$	1.04377	+	1.04377i	0.0780153	+	0.0780153i	0.745038	−	0.667022i	$-0.232431\pi$
$179$	1.04377	+	1.04377i	0.0780153	+	0.0780153i	−0.667022	+	0.745038i	$0.732431\pi$
$180$		0			0
$181$	−12.1024	+	12.1024i	−0.899567	+	0.899567i	−0.995398	−	0.0958310i	$-0.969449\pi$
$181$	−12.1024	+	12.1024i	−0.899567	+	0.899567i	0.0958310	+	0.995398i	$0.469449\pi$
$182$	−2.79721	+	5.01723i	−0.207343	+	0.371901i
$183$		0			0
$184$	3.30339	−	3.61490i	0.243529	−	0.266494i
$185$	−19.3431	+	6.11528i	−1.42213	+	0.449604i
$186$		0			0
$187$	8.48877	+	8.48877i	0.620761	+	0.620761i
$188$	−12.2448	−	19.8116i	−0.893046	−	1.44491i
$189$		0			0
$190$	−6.25473	+	4.12480i	−0.453766	+	0.299244i
$191$	21.2273			1.53596			0.767978	−	0.640477i	$-0.221263\pi$
$191$	21.2273			1.53596			0.767978	+	0.640477i	$0.221263\pi$
$192$		0			0
$193$			19.2782i			1.38767i	0.720132	+	0.693837i	$0.244081\pi$
$193$			19.2782i			1.38767i	−0.720132	+	0.693837i	$0.755919\pi$
$194$	−0.866292	−	3.04935i	−0.0621961	−	0.218930i
$195$		0			0
$196$	14.2238	−	8.79124i	1.01599	−	0.627946i
$197$	9.48350	+	9.48350i	0.675672	+	0.675672i	0.959018	−	0.283346i	$-0.0914445\pi$
$197$	9.48350	+	9.48350i	0.675672	+	0.675672i	−0.283346	+	0.959018i	$0.591444\pi$
$198$		0			0
$199$		−	8.65421i		−	0.613481i	−0.951793	−	0.306740i	$-0.900762\pi$
$199$		−	8.65421i		−	0.613481i	0.951793	−	0.306740i	$-0.0992383\pi$
$200$	14.0265	+	1.80514i	0.991820	+	0.127643i
$201$		0			0
$202$	−7.31070	+	13.1129i	−0.514379	+	0.922617i
$203$	19.5572	+	19.5572i	1.37265	+	1.37265i
$204$		0			0
$205$	−0.0114591	−	0.00595398i	−0.000800336	−	0.000415844i
$206$	5.32059	−	1.51153i	0.370703	−	0.105313i
$207$		0			0
$208$	−1.31110	−	3.93271i	−0.0909083	−	0.272684i
$209$	9.83169			0.680072
$210$		0			0
$211$	−0.875946	−	0.875946i	−0.0603026	−	0.0603026i	0.676312	−	0.736615i	$-0.263577\pi$
$211$	−0.875946	−	0.875946i	−0.0603026	−	0.0603026i	−0.736615	+	0.676312i	$0.763577\pi$
$212$	15.2990	+	3.61124i	1.05074	+	0.248021i
$213$		0			0
$214$	4.54589	+	2.53443i	0.310751	+	0.173250i
$215$	6.75190	−	2.13460i	0.460476	−	0.145578i
$216$		0			0
$217$	−42.3863			−2.87737
$218$	3.60961	+	2.01243i	0.244473	+	0.136299i
$219$		0			0
$220$	−14.0614	−	12.1105i	−0.948020	−	0.816492i
$221$	2.12008	+	2.12008i	0.142612	+	0.142612i
$222$		0			0
$223$			10.4375i			0.698946i	0.936946	+	0.349473i	$0.113639\pi$
$223$			10.4375i			0.698946i	−0.936946	+	0.349473i	$0.886361\pi$
$224$	−4.11754	+	21.7850i	−0.275115	+	1.45557i
$225$		0			0
$226$	3.14438	+	11.0682i	0.209161	+	0.736246i
$227$	−13.7218	+	13.7218i	−0.910747	+	0.910747i	−0.996331	−	0.0855842i	$-0.972724\pi$
$227$	−13.7218	+	13.7218i	−0.910747	+	0.910747i	0.0855842	+	0.996331i	$0.472724\pi$
$228$		0			0
$229$	8.43878	−	8.43878i	0.557651	−	0.557651i	−0.370987	−	0.928638i	$-0.620981\pi$
$229$	8.43878	−	8.43878i	0.557651	−	0.557651i	0.928638	+	0.370987i	$0.120981\pi$
$230$	1.10055	−	5.36318i	0.0725681	−	0.353638i
$231$		0			0
$232$	−19.9399	+	0.897842i	−1.30912	+	0.0589462i
$233$	−28.6100			−1.87431			−0.937153	−	0.348919i	$-0.886549\pi$
$233$	−28.6100			−1.87431			−0.937153	+	0.348919i	$0.886549\pi$
$234$		0			0
$235$	−23.1064	−	12.0058i	−1.50729	−	0.783169i
$236$	−2.49053	+	10.5511i	−0.162120	+	0.686819i
$237$		0			0
$238$	−4.38202	−	15.4247i	−0.284044	−	0.999835i
$239$	−21.4924			−1.39023			−0.695115	−	0.718899i	$-0.744646\pi$
$239$	−21.4924			−1.39023			−0.695115	+	0.718899i	$0.744646\pi$
$240$		0			0
$241$	−19.5943			−1.26218			−0.631091	−	0.775709i	$-0.717393\pi$
$241$	−19.5943			−1.26218			−0.631091	+	0.775709i	$0.717393\pi$
$242$	2.40363	+	8.46077i	0.154511	+	0.543879i
$243$		0			0
$244$	25.6172	+	6.04680i	1.63997	+	0.387106i
$245$	8.61959	−	16.5893i	0.550685	−	1.05985i
$246$		0			0
$247$	2.45548			0.156238
$248$	20.6349	−	22.5808i	1.31032	−	1.43388i
$249$		0			0
$250$	14.5009	−	6.30277i	0.917115	−	0.398622i
$251$	9.58072	−	9.58072i	0.604730	−	0.604730i	−0.336834	−	0.941564i	$-0.609356\pi$
$251$	9.58072	−	9.58072i	0.604730	−	0.604730i	0.941564	+	0.336834i	$0.109356\pi$
$252$		0			0
$253$	−5.08011	+	5.08011i	−0.319384	+	0.319384i
$254$	6.21687	+	21.8834i	0.390081	+	1.37308i
$255$		0			0
$256$	−9.60115	−	12.7991i	−0.600072	−	0.799946i
$257$			13.2730i			0.827946i	0.910289	+	0.413973i	$0.135859\pi$
$257$			13.2730i			0.827946i	−0.910289	+	0.413973i	$0.864141\pi$
$258$		0			0
$259$	−25.1430	−	25.1430i	−1.56231	−	1.56231i
$260$	−3.51186	−	3.02462i	−0.217796	−	0.187579i
$261$		0			0
$262$	22.7802	+	12.7005i	1.40737	+	0.784637i
$263$	13.0606			0.805349			0.402675	−	0.915343i	$-0.368081\pi$
$263$	13.0606			0.805349			0.402675	+	0.915343i	$0.368081\pi$
$264$		0			0
$265$	16.7573	−	5.29780i	1.02940	−	0.325441i
$266$	−11.4701	−	6.39481i	−0.703274	−	0.392091i
$267$		0			0
$268$	2.50322	−	10.6049i	0.152908	−	0.647796i
$269$	12.4067	+	12.4067i	0.756451	+	0.756451i	0.975675	−	0.219224i	$-0.0703525\pi$
$269$	12.4067	+	12.4067i	0.756451	+	0.756451i	−0.219224	+	0.975675i	$0.570353\pi$
$270$		0			0
$271$	2.11193			0.128291			0.0641453	−	0.997941i	$-0.479568\pi$
$271$	2.11193			0.128291			0.0641453	+	0.997941i	$0.479568\pi$
$272$	10.3506	+	5.17472i	0.627597	+	0.313763i
$273$		0			0
$274$	8.86444	−	2.51831i	0.535520	−	0.152137i
$275$	−20.4385	−	3.57132i	−1.23249	−	0.215359i
$276$		0			0
$277$	13.2116	+	13.2116i	0.793808	+	0.793808i	0.982111	−	0.188303i	$-0.0602988\pi$
$277$	13.2116	+	13.2116i	0.793808	+	0.793808i	−0.188303	+	0.982111i	$0.560299\pi$
$278$	14.7014	−	26.3692i	0.881732	−	1.58152i
$279$		0			0
$280$	8.52760	+	23.2746i	0.509621	+	1.39092i
$281$		−	3.78786i		−	0.225965i	−0.993597	−	0.112982i	$-0.963960\pi$
$281$		−	3.78786i		−	0.225965i	0.993597	−	0.112982i	$-0.0360404\pi$
$282$		0			0
$283$	3.16274	+	3.16274i	0.188005	+	0.188005i	0.794833	−	0.606828i	$-0.207558\pi$
$283$	3.16274	+	3.16274i	0.188005	+	0.188005i	−0.606828	+	0.794833i	$0.707558\pi$
$284$	−1.21295	−	1.96250i	−0.0719756	−	0.116453i
$285$		0			0
$286$	1.66205	+	5.85042i	0.0982792	+	0.345942i
$287$		−	0.0226343i		−	0.00133606i
$288$		0			0
$289$	8.63046			0.507674
$290$	−18.6298	+	12.2857i	−1.09398	+	0.721444i
$291$		0			0
$292$	13.5883	−	8.39847i	0.795197	−	0.491483i
$293$	8.51339	+	8.51339i	0.497357	+	0.497357i	0.910614	−	0.413257i	$-0.135609\pi$
$293$	8.51339	+	8.51339i	0.497357	+	0.497357i	−0.413257	+	0.910614i	$0.635609\pi$
$294$		0			0
$295$	3.65368	+	11.5569i	0.212726	+	0.672868i
$296$	25.6350	−	1.15428i	1.49000	−	0.0670909i
$297$		0			0
$298$	4.16251	−	7.46609i	0.241128	−	0.432499i
$299$	−1.26876	+	1.26876i	−0.0733745	+	0.0733745i
$300$		0			0
$301$	8.77642	+	8.77642i	0.505864	+	0.505864i
$302$	−3.24636	−	11.4272i	−0.186807	−	0.657560i
$303$		0			0
$304$	8.99071	−	2.99735i	0.515652	−	0.171910i
$305$	28.0591	−	8.87083i	1.60666	−	0.507942i
$306$		0			0
$307$	−7.12093	+	7.12093i	−0.406413	+	0.406413i	−0.880486	−	0.474073i	$-0.842783\pi$
$307$	−7.12093	+	7.12093i	−0.406413	+	0.406413i	0.474073	+	0.880486i	$0.342783\pi$
$308$	7.47246	−	31.6570i	0.425783	−	1.80383i
$309$		0			0
$310$	6.87467	−	33.5015i	0.390455	−	1.90276i
$311$		−	21.2980i		−	1.20770i	−0.797099	−	0.603849i	$-0.793633\pi$
$311$		−	21.2980i		−	1.20770i	0.797099	−	0.603849i	$-0.206367\pi$
$312$		0			0
$313$	−7.49789			−0.423806			−0.211903	−	0.977291i	$-0.567966\pi$
$313$	−7.49789			−0.423806			−0.211903	+	0.977291i	$0.567966\pi$
$314$	−5.54051	+	9.93774i	−0.312669	+	0.560819i
$315$		0			0
$316$	1.43581	−	0.887425i	0.0807707	−	0.0499215i
$317$	2.35354	−	2.35354i	0.132188	−	0.132188i	−0.637917	−	0.770105i	$-0.720204\pi$
$317$	2.35354	−	2.35354i	0.132188	−	0.132188i	0.770105	+	0.637917i	$0.220204\pi$
$318$		0			0
$319$	29.2838			1.63958
$320$	−16.5507	−	6.78777i	−0.925213	−	0.379448i
$321$		0			0
$322$	9.23091	−	2.62242i	0.514419	−	0.146142i
$323$	−4.84680	+	4.84680i	−0.269683	+	0.269683i
$324$		0			0
$325$	−5.10453	−	0.891943i	−0.283149	−	0.0494761i
$326$	5.49157	−	9.84997i	0.304150	−	0.545539i
$327$		0			0
$328$	0.0120581	+	0.0110190i	0.000665797	+	0.000608423i
$329$		−	45.6403i		−	2.51623i
$330$		0			0
$331$	22.6845	−	22.6845i	1.24685	−	1.24685i	0.289753	−	0.957102i	$-0.406427\pi$
$331$	22.6845	−	22.6845i	1.24685	−	1.24685i	0.957102	−	0.289753i	$-0.0935730\pi$
$332$	−3.37929	+	14.3163i	−0.185463	+	0.785712i
$333$		0			0
$334$	8.78239	−	2.49500i	0.480551	−	0.136520i
$335$	−3.67230	−	11.6158i	−0.200639	−	0.634637i
$336$		0			0
$337$			8.90357i			0.485008i	0.970150	+	0.242504i	$0.0779688\pi$
$337$			8.90357i			0.485008i	−0.970150	+	0.242504i	$0.922031\pi$
$338$	−4.60904	−	16.2238i	−0.250699	−	0.882459i
$339$		0			0
$340$	12.9022	−	0.961738i	0.699718	−	0.0521576i
$341$	−31.7333	+	31.7333i	−1.71845	+	1.71845i
$342$		0			0
$343$	5.33279			0.287944
$344$	−8.94814	+	0.402911i	−0.482451	+	0.0217235i
$345$		0			0
$346$	−7.14523	+	12.8160i	−0.384130	+	0.688995i
$347$	8.87783	+	8.87783i	0.476587	+	0.476587i	0.904038	−	0.427451i	$-0.140588\pi$
$347$	8.87783	+	8.87783i	0.476587	+	0.476587i	−0.427451	+	0.904038i	$0.640588\pi$
$348$		0			0
$349$	−8.23040	−	8.23040i	−0.440563	−	0.440563i	0.451638	−	0.892201i	$-0.350840\pi$
$349$	−8.23040	−	8.23040i	−0.440563	−	0.440563i	−0.892201	+	0.451638i	$0.850840\pi$
$350$	21.5215	+	17.4602i	1.15037	+	0.933288i
$351$		0			0
$352$	13.2271	+	19.3924i	0.705005	+	1.03362i
$353$			34.7125i			1.84756i	0.382922	+	0.923781i	$0.374918\pi$
$353$			34.7125i			1.84756i	−0.382922	+	0.923781i	$0.625082\pi$
$354$		0			0
$355$	−2.28888	−	1.18927i	−0.121481	−	0.0631200i
$356$	5.68753	+	9.20215i	0.301438	+	0.487713i
$357$		0			0
$358$	−1.82332	−	1.01654i	−0.0963655	−	0.0537259i
$359$		−	2.81082i		−	0.148350i	−0.997245	−	0.0741748i	$-0.976368\pi$
$359$		−	2.81082i		−	0.148350i	0.997245	−	0.0741748i	$-0.0236323\pi$
$360$		0			0
$361$		−	13.3864i		−	0.704550i
$362$	11.7867	−	21.1412i	0.619494	−	1.11116i
$363$		0			0
$364$	1.86626	−	7.90639i	0.0978185	−	0.414407i
$365$	8.23449	−	15.8482i	0.431013	−	0.829531i
$366$		0			0
$367$		−	18.2835i		−	0.954392i	−0.878797	−	0.477196i	$-0.841653\pi$
$367$		−	18.2835i		−	0.954392i	0.878797	−	0.477196i	$-0.158347\pi$
$368$	−3.09681	+	6.19432i	−0.161433	+	0.322901i
$369$		0			0
$370$	23.9506	−	15.7947i	1.24513	−	0.821127i
$371$	21.7819	+	21.7819i	1.13086	+	1.13086i
$372$		0			0
$373$	23.4176	+	23.4176i	1.21252	+	1.21252i	0.970195	+	0.242324i	$0.0779098\pi$
$373$	23.4176	+	23.4176i	1.21252	+	1.21252i	0.242324	+	0.970195i	$0.422090\pi$
$374$	−14.8287	−	8.26730i	−0.766771	−	0.427492i
$375$		0			0
$376$	24.3143	+	22.2190i	1.25391	+	1.14586i
$377$	7.31366			0.376673
$378$		0			0
$379$	−6.20944	+	6.20944i	−0.318957	+	0.318957i	−0.848367	−	0.529409i	$-0.822414\pi$
$379$	−6.20944	+	6.20944i	−0.318957	+	0.318957i	0.529409	+	0.848367i	$0.322414\pi$
$380$	6.91470	−	8.02858i	0.354716	−	0.411857i
$381$		0			0
$382$	−28.8773	+	8.20378i	−1.47749	+	0.419742i
$383$		−	14.4005i		−	0.735832i	−0.929859	−	0.367916i	$-0.880071\pi$
$383$		−	14.4005i		−	0.735832i	0.929859	−	0.367916i	$-0.119929\pi$
$384$		0			0
$385$	−10.9623	−	34.6747i	−0.558692	−	1.76719i
$386$	−7.45049	−	26.2257i	−0.379220	−	1.33485i
$387$		0			0
$388$	2.35698	+	3.81348i	0.119657	+	0.193600i
$389$	−15.4753	+	15.4753i	−0.784630	+	0.784630i	−0.980608	−	0.195978i	$-0.937212\pi$
$389$	−15.4753	+	15.4753i	−0.784630	+	0.784630i	0.195978	+	0.980608i	$0.437212\pi$
$390$		0			0
$391$		−	5.00875i		−	0.253304i
$392$	−15.9522	+	17.4566i	−0.805710	+	0.881689i
$393$		0			0
$394$	−16.5663	−	9.23607i	−0.834598	−	0.465307i
$395$	0.870098	−	1.67460i	0.0437794	−	0.0842581i
$396$		0			0
$397$	15.0440	−	15.0440i	0.755036	−	0.755036i	−0.220378	−	0.975414i	$-0.570729\pi$
$397$	15.0440	−	15.0440i	0.755036	−	0.755036i	0.975414	+	0.220378i	$0.0707292\pi$
$398$	3.34461	+	11.7730i	0.167650	+	0.590129i
$399$		0			0
$400$	−19.7790	+	2.96516i	−0.988949	+	0.148258i
$401$	−28.7953			−1.43797			−0.718985	−	0.695026i	$-0.755393\pi$
$401$	−28.7953			−1.43797			−0.718985	+	0.695026i	$0.755393\pi$
$402$		0			0
$403$	−7.92543	+	7.92543i	−0.394794	+	0.394794i
$404$	4.87759	−	20.6639i	0.242669	−	1.02807i
$405$		0			0
$406$	−34.1637	−	19.0470i	−1.69551	−	0.945286i
$407$	−37.6476			−1.86612
$408$		0			0
$409$			23.3562i			1.15489i	0.816430	+	0.577444i	$0.195950\pi$
$409$			23.3562i			1.15489i	−0.816430	+	0.577444i	$0.804050\pi$
$410$	0.0178898	+	0.00367107i	0.000883512	+	0.000181301i
$411$		0			0
$412$	−6.65387	+	4.11252i	−0.327813	+	0.202610i
$413$	−15.0222	+	15.0222i	−0.739192	+	0.739192i
$414$		0			0
$415$	4.95752	+	15.6810i	0.243355	+	0.769751i
$416$	3.30348	+	4.84328i	0.161966	+	0.237461i
$417$		0			0
$418$	−13.3749	+	3.79968i	−0.654185	+	0.185848i
$419$	22.4332	+	22.4332i	1.09594	+	1.09594i	0.994881	+	0.101055i	$0.0322217\pi$
$419$	22.4332	+	22.4332i	1.09594	+	1.09594i	0.101055	+	0.994881i	$0.467778\pi$
$420$		0			0
$421$	14.7632	−	14.7632i	0.719513	−	0.719513i	−0.248993	−	0.968505i	$-0.580100\pi$
$421$	14.7632	−	14.7632i	0.719513	−	0.719513i	0.968505	+	0.248993i	$0.0800995\pi$
$422$	1.53015	+	0.853092i	0.0744865	+	0.0415279i
$423$		0			0
$424$	−22.2081	+	0.999973i	−1.07852	+	0.0485630i
$425$	11.8363	−	8.31511i	0.574144	−	0.403342i
$426$		0			0
$427$	36.4725	+	36.4725i	1.76503	+	1.76503i
$428$	−7.16364	−	1.69094i	−0.346268	−	0.0817345i
$429$		0			0
$430$	−8.36020	+	5.51329i	−0.403165	+	0.265875i
$431$	−5.92220			−0.285262			−0.142631	−	0.989776i	$-0.545556\pi$
$431$	−5.92220			−0.285262			−0.142631	+	0.989776i	$0.545556\pi$
$432$		0			0
$433$		−	5.27026i		−	0.253272i	−0.991949	−	0.126636i	$-0.959582\pi$
$433$		−	5.27026i		−	0.253272i	0.991949	−	0.126636i	$-0.0404181\pi$
$434$	57.6616	−	16.3811i	2.76784	−	0.786320i
$435$		0			0
$436$	−5.68819	−	1.34267i	−0.272415	−	0.0643020i
$437$	−2.90057	−	2.90057i	−0.138753	−	0.138753i
$438$		0			0
$439$			17.8427i			0.851587i	0.904820	+	0.425793i	$0.140005\pi$
$439$			17.8427i			0.851587i	−0.904820	+	0.425793i	$0.859995\pi$
$440$	23.8093	+	11.0406i	1.13506	+	0.526340i
$441$		0			0
$442$	−3.70348	−	2.06477i	−0.176156	−	0.0982110i
$443$	−5.89855	−	5.89855i	−0.280248	−	0.280248i	0.552960	−	0.833208i	$-0.313498\pi$
$443$	−5.89855	−	5.89855i	−0.280248	−	0.280248i	−0.833208	+	0.552960i	$0.813498\pi$
$444$		0			0
$445$	10.7325	+	5.57648i	0.508771	+	0.264350i
$446$	−4.03380	−	14.1990i	−0.191006	−	0.672341i
$447$		0			0
$448$	−2.81788	−	31.2273i	−0.133132	−	1.47535i
$449$	−8.12803			−0.383586			−0.191793	−	0.981435i	$-0.561430\pi$
$449$	−8.12803			−0.383586			−0.191793	+	0.981435i	$0.561430\pi$
$450$		0			0
$451$	−0.0169455	−	0.0169455i	−0.000797934	−	0.000797934i
$452$	−8.55511	−	13.8418i	−0.402399	−	0.651062i
$453$		0			0
$454$	13.3638	−	23.9700i	0.627193	−	1.12497i
$455$	−2.73786	−	8.66005i	−0.128353	−	0.405990i
$456$		0			0
$457$	6.35488			0.297269			0.148634	−	0.988892i	$-0.452512\pi$
$457$	6.35488			0.297269			0.148634	+	0.988892i	$0.452512\pi$
$458$	−8.21861	+	14.7413i	−0.384030	+	0.688817i
$459$		0			0
$460$	0.575553	+	7.72131i	0.0268353	+	0.360008i
$461$	−2.13085	−	2.13085i	−0.0992438	−	0.0992438i	0.655742	−	0.754985i	$-0.272356\pi$
$461$	−2.13085	−	2.13085i	−0.0992438	−	0.0992438i	−0.754985	+	0.655742i	$0.772356\pi$
$462$		0			0
$463$			18.4540i			0.857630i	0.903392	+	0.428815i	$0.141069\pi$
$463$			18.4540i			0.857630i	−0.903392	+	0.428815i	$0.858931\pi$
$464$	26.7789	−	8.92763i	1.24318	−	0.414455i
$465$		0			0
$466$	38.9206	−	11.0570i	1.80296	−	0.512205i
$467$	−5.63243	+	5.63243i	−0.260638	+	0.260638i	−0.825313	−	0.564675i	$-0.809001\pi$
$467$	−5.63243	+	5.63243i	−0.260638	+	0.260638i	0.564675	+	0.825313i	$0.309001\pi$
$468$		0			0
$469$	15.0987	−	15.0987i	0.697193	−	0.697193i
$470$	36.0734	+	7.40243i	1.66394	+	0.341449i
$471$		0			0
$472$	−0.689643	−	15.3161i	−0.0317434	−	0.704979i
$473$	13.1412			0.604235
$474$		0			0
$475$	2.03910	−	11.6697i	0.0935604	−	0.535441i
$476$	11.9224	+	19.2899i	0.546464	+	0.884153i
$477$		0			0
$478$	29.2379	−	8.30623i	1.33731	−	0.379918i
$479$	−21.4860			−0.981720			−0.490860	−	0.871239i	$-0.663317\pi$
$479$	−21.4860			−0.981720			−0.490860	+	0.871239i	$0.663317\pi$
$480$		0			0
$481$	−9.40253			−0.428718
$482$	26.6558	−	7.57267i	1.21414	−	0.344926i
$483$		0			0
$484$	−6.53971	−	10.5809i	−0.297259	−	0.480952i
$485$	4.44769	+	2.31096i	0.201959	+	0.104935i
$486$		0			0
$487$	−36.3297			−1.64626			−0.823128	−	0.567856i	$-0.807773\pi$
$487$	−36.3297			−1.64626			−0.823128	+	0.567856i	$0.807773\pi$
$488$	−37.1861	+	1.67439i	−1.68334	+	0.0757962i
$489$		0			0
$490$	−5.31461	+	25.8991i	−0.240090	+	1.17000i
$491$	−1.63599	+	1.63599i	−0.0738313	+	0.0738313i	−0.743058	−	0.669227i	$-0.766625\pi$
$491$	−1.63599	+	1.63599i	−0.0738313	+	0.0738313i	0.669227	+	0.743058i	$0.266625\pi$
$492$		0			0
$493$	−14.4362	+	14.4362i	−0.650175	+	0.650175i
$494$	−3.34039	+	0.948974i	−0.150291	+	0.0426964i
$495$		0			0
$496$	−19.3445	+	38.6933i	−0.868592	+	1.73738i
$497$		−	4.52106i		−	0.202797i
$498$		0			0
$499$	18.7955	+	18.7955i	0.841402	+	0.841402i	0.989041	−	0.147639i	$-0.0471674\pi$
$499$	18.7955	+	18.7955i	0.841402	+	0.841402i	−0.147639	+	0.989041i	$0.547167\pi$
$500$	−17.2909	+	14.1784i	−0.773271	+	0.634076i
$501$		0			0
$502$	−9.33076	+	16.7361i	−0.416452	+	0.746970i
$503$	13.8118			0.615838			0.307919	−	0.951413i	$-0.400367\pi$
$503$	13.8118			0.615838			0.307919	+	0.951413i	$0.400367\pi$
$504$		0			0
$505$	−7.15557	−	22.6336i	−0.318419	−	1.00718i
$506$	4.94757	−	8.87421i	0.219946	−	0.394507i
$507$		0			0
$508$	−16.9146	−	27.3671i	−0.750465	−	1.21422i
$509$	5.40184	+	5.40184i	0.239432	+	0.239432i	0.816615	−	0.577183i	$-0.195848\pi$
$509$	5.40184	+	5.40184i	0.239432	+	0.239432i	−0.577183	+	0.816615i	$0.695848\pi$
$510$		0			0
$511$	31.3037			1.38479
$512$	18.0077	+	13.7011i	0.795837	+	0.605510i
$513$		0			0
$514$	−5.12964	−	18.0563i	−0.226259	−	0.796431i
$515$	−4.03223	+	7.76046i	−0.177681	+	0.341967i
$516$		0			0
$517$	−34.1694	−	34.1694i	−1.50277	−	1.50277i
$518$	43.9212	+	24.4870i	1.92979	+	1.07590i
$519$		0			0
$520$	5.94640	+	2.75740i	0.260767	+	0.120920i
$521$			33.6969i			1.47629i	0.674642	+	0.738145i	$0.264298\pi$
$521$			33.6969i			1.47629i	−0.674642	+	0.738145i	$0.735702\pi$
$522$		0			0
$523$	4.31481	+	4.31481i	0.188673	+	0.188673i	0.795122	−	0.606449i	$-0.207407\pi$
$523$	4.31481	+	4.31481i	0.188673	+	0.188673i	−0.606449	+	0.795122i	$0.707407\pi$
$524$	−35.8981	−	8.47355i	−1.56822	−	0.370169i
$525$		0			0
$526$	−17.7674	+	5.04755i	−0.774694	+	0.220084i
$527$		−	31.2876i		−	1.36291i
$528$		0			0
$529$	−20.0025			−0.869674
$530$	−20.7489	+	13.6833i	−0.901276	+	0.594364i
$531$		0			0
$532$	18.0751	+	4.26652i	0.783654	+	0.184977i
$533$	−0.00423217	−	0.00423217i	−0.000183316	−	0.000183316i
$534$		0			0
$535$	−7.84650	+	2.48065i	−0.339234	+	0.107248i
$536$	0.693156	+	15.3941i	0.0299398	+	0.664924i
$537$		0			0
$538$	−21.6727	−	12.0830i	−0.934377	−	0.520936i
$539$	24.5321	−	24.5321i	1.05667	−	1.05667i
$540$		0			0
$541$	−22.8010	−	22.8010i	−0.980290	−	0.980290i	0.0195198	−	0.999809i	$-0.493786\pi$
$541$	−22.8010	−	22.8010i	−0.980290	−	0.980290i	−0.999809	+	0.0195198i	$0.993786\pi$
$542$	−2.87303	+	0.816203i	−0.123407	+	0.0350589i
$543$		0			0
$544$	−16.0807	−	3.03937i	−0.689452	−	0.130312i
$545$	−6.23041	+	1.96973i	−0.266882	+	0.0843740i
$546$		0			0
$547$	5.56014	−	5.56014i	0.237735	−	0.237735i	−0.578177	−	0.815911i	$-0.696236\pi$
$547$	5.56014	−	5.56014i	0.237735	−	0.237735i	0.815911	+	0.578177i	$0.196236\pi$
$548$	−11.0858	+	6.85172i	−0.473560	+	0.292691i
$549$		0			0
$550$	29.1843	−	3.04054i	1.24442	−	0.129649i
$551$			16.7200i			0.712297i
$552$		0			0
$553$	3.30771			0.140658
$554$	−23.0787	−	12.8669i	−0.980521	−	0.546662i
$555$		0			0
$556$	−9.80856	+	41.5539i	−0.415976	+	1.76228i
$557$	12.2628	−	12.2628i	0.519591	−	0.519591i	−0.397857	−	0.917447i	$-0.630246\pi$
$557$	12.2628	−	12.2628i	0.519591	−	0.519591i	0.917447	+	0.397857i	$0.130246\pi$
$558$		0			0
$559$	3.28204			0.138816
$560$	−20.5958	−	28.3667i	−0.870330	−	1.19871i
$561$		0			0
$562$	1.46390	+	5.15294i	0.0617510	+	0.217363i
$563$	0.327630	−	0.327630i	0.0138079	−	0.0138079i	−0.700169	−	0.713977i	$-0.746892\pi$
$563$	0.327630	−	0.327630i	0.0138079	−	0.0138079i	0.713977	+	0.700169i	$0.246892\pi$
$564$		0			0
$565$	−16.1438	−	8.38807i	−0.679173	−	0.352889i
$566$	−5.52484	−	3.08022i	−0.232226	−	0.129471i
$567$		0			0
$568$	2.40853	+	2.20098i	0.101060	+	0.0923511i
$569$		−	35.6010i		−	1.49247i	−0.665681	−	0.746237i	$-0.731859\pi$
$569$		−	35.6010i		−	1.49247i	0.665681	−	0.746237i	$-0.268141\pi$
$570$		0			0
$571$	3.57427	−	3.57427i	0.149579	−	0.149579i	−0.628351	−	0.777930i	$-0.716270\pi$
$571$	3.57427	−	3.57427i	0.149579	−	0.149579i	0.777930	+	0.628351i	$0.216270\pi$
$572$	−4.52205	−	7.31646i	−0.189076	−	0.305917i
$573$		0			0
$574$	0.00874752	+	0.0307912i	0.000365114	+	0.00128520i
$575$	4.97618	+	7.08342i	0.207521	+	0.295399i
$576$		0			0
$577$			8.80260i			0.366457i	0.983070	+	0.183229i	$0.0586548\pi$
$577$			8.80260i			0.366457i	−0.983070	+	0.183229i	$0.941345\pi$
$578$	−11.7407	+	3.33543i	−0.488350	+	0.138736i
$579$		0			0
$580$	20.5955	−	23.9132i	0.855181	−	0.992941i
$581$	−20.3829	+	20.3829i	−0.845625	+	0.845625i
$582$		0			0
$583$	32.6149			1.35077
$584$	−15.2395	+	16.6766i	−0.630616	+	0.690084i
$585$		0			0
$586$	−14.8716	−	8.29127i	−0.614342	−	0.342509i
$587$	17.9887	+	17.9887i	0.742475	+	0.742475i	0.973054	−	0.230579i	$-0.0740619\pi$
$587$	17.9887	+	17.9887i	0.742475	+	0.742475i	−0.230579	+	0.973054i	$0.574062\pi$
$588$		0			0
$589$	−18.1186	−	18.1186i	−0.746564	−	0.746564i
$590$	−9.43682	−	14.3097i	−0.388508	−	0.589122i
$591$		0			0
$592$	−34.4273	+	11.4775i	−1.41495	+	0.471721i
$593$		−	25.4791i		−	1.04630i	−0.852240	−	0.523150i	$-0.824757\pi$
$593$		−	25.4791i		−	1.04630i	0.852240	−	0.523150i	$-0.175243\pi$
$594$		0			0
$595$	22.4980	+	11.6897i	0.922328	+	0.479229i
$596$	−2.77716	+	11.7654i	−0.113757	+	0.481931i
$597$		0			0
$598$	1.23566	−	2.21635i	0.0505299	−	0.0906331i
$599$		−	14.6977i		−	0.600532i	−0.953856	−	0.300266i	$-0.902925\pi$
$599$		−	14.6977i		−	0.600532i	0.953856	−	0.300266i	$-0.0970754\pi$
$600$		0			0
$601$			12.2790i			0.500869i	0.968134	+	0.250434i	$0.0805735\pi$
$601$			12.2790i			0.500869i	−0.968134	+	0.250434i	$0.919427\pi$
$602$	−15.3311	−	8.54744i	−0.624850	−	0.348368i
$603$		0			0
$604$	8.83258	+	14.2907i	0.359393	+	0.581480i
$605$	−12.3406	−	6.41202i	−0.501718	−	0.260686i
$606$		0			0
$607$			26.2195i			1.06421i	0.846677	+	0.532107i	$0.178600\pi$
$607$			26.2195i			1.06421i	−0.846677	+	0.532107i	$0.821400\pi$
$608$	−11.0724	+	7.55220i	−0.449045	+	0.306282i
$609$		0			0
$610$	−34.7428	+	22.9118i	−1.40669	+	0.927672i
$611$	−8.53386	−	8.53386i	−0.345243	−	0.345243i
$612$		0			0
$613$	−23.4055	−	23.4055i	−0.945340	−	0.945340i	0.0532416	−	0.998582i	$-0.483045\pi$
$613$	−23.4055	−	23.4055i	−0.945340	−	0.945340i	−0.998582	+	0.0532416i	$0.983045\pi$
$614$	6.93514	−	12.4392i	0.279880	−	0.502007i
$615$		0			0
$616$	2.06917	+	45.9536i	0.0833692	+	1.85152i
$617$	−27.5735			−1.11007			−0.555033	−	0.831828i	$-0.687294\pi$
$617$	−27.5735			−1.11007			−0.555033	+	0.831828i	$0.687294\pi$
$618$		0			0
$619$	−12.2452	+	12.2452i	−0.492176	+	0.492176i	−0.908991	−	0.416815i	$-0.863146\pi$
$619$	−12.2452	+	12.2452i	−0.492176	+	0.492176i	0.416815	+	0.908991i	$0.363146\pi$
$620$	3.59523	+	48.2317i	0.144388	+	1.93703i
$621$		0			0
$622$	8.23108	+	28.9734i	0.330036	+	1.16173i
$623$			21.1992i			0.849327i
$624$		0			0
$625$	−8.47792	+	23.5186i	−0.339117	+	0.940744i
$626$	10.2000	−	2.89773i	0.407673	−	0.115816i
$627$		0			0
$628$	3.69654	−	15.6604i	0.147508	−	0.624917i
$629$	18.5594	−	18.5594i	0.740011	−	0.740011i
$630$		0			0
$631$		−	25.5846i		−	1.01851i	−0.860617	−	0.509253i	$-0.829922\pi$
$631$		−	25.5846i		−	1.01851i	0.860617	−	0.509253i	$-0.170078\pi$
$632$	−1.61029	+	1.76214i	−0.0640537	+	0.0700941i
$633$		0			0
$634$	−2.29214	+	4.11130i	−0.0910324	+	0.163281i
$635$	−31.9184	−	16.5844i	−1.26664	−	0.658131i
$636$		0			0
$637$	6.12692	−	6.12692i	0.242758	−	0.242758i
$638$	−39.8371	+	11.3174i	−1.57717	+	0.448059i
$639$		0			0
$640$	25.1386	+	2.83757i	0.993690	+	0.112165i
$641$	3.52020			0.139040			0.0695198	−	0.997581i	$-0.477853\pi$
$641$	3.52020			0.139040			0.0695198	+	0.997581i	$0.477853\pi$
$642$		0			0
$643$	19.0869	−	19.0869i	0.752715	−	0.752715i	−0.222270	−	0.974985i	$-0.571347\pi$
$643$	19.0869	−	19.0869i	0.752715	−	0.752715i	0.974985	+	0.222270i	$0.0713466\pi$
$644$	−11.5441	+	7.13499i	−0.454900	+	0.281158i
$645$		0			0
$646$	4.72034	−	8.46665i	0.185719	−	0.333116i
$647$	5.02456			0.197536			0.0987678	−	0.995111i	$-0.468510\pi$
$647$	5.02456			0.197536			0.0987678	+	0.995111i	$0.468510\pi$
$648$		0			0
$649$			22.4932i			0.882935i
$650$	7.28883	−	0.759379i	0.285891	−	0.0297853i
$651$		0			0
$652$	−3.66389	+	15.5221i	−0.143489	+	0.607891i
$653$	−6.07220	+	6.07220i	−0.237623	+	0.237623i	−0.815865	−	0.578242i	$-0.803739\pi$
$653$	−6.07220	+	6.07220i	−0.237623	+	0.237623i	0.578242	+	0.815865i	$0.303739\pi$
$654$		0			0
$655$	−39.3201	+	12.4310i	−1.53636	+	0.485718i
$656$	−0.0206622	−	0.0103299i	−0.000806722	−	0.000403316i
$657$		0			0
$658$	17.6387	+	62.0882i	0.687629	+	2.42045i
$659$	5.88182	+	5.88182i	0.229123	+	0.229123i	0.812326	−	0.583203i	$-0.198201\pi$
$659$	5.88182	+	5.88182i	0.229123	+	0.229123i	−0.583203	+	0.812326i	$0.698201\pi$
$660$		0			0
$661$	−24.0275	+	24.0275i	−0.934562	+	0.934562i	−0.997987	−	0.0634242i	$-0.979798\pi$
$661$	−24.0275	+	24.0275i	−0.934562	+	0.934562i	0.0634242	+	0.997987i	$0.479798\pi$
$662$	−22.0927	+	39.6266i	−0.858656	+	1.54013i
$663$		0			0
$664$	−0.935746	−	20.7817i	−0.0363140	−	0.806486i
$665$	19.7981	−	6.25911i	0.767736	−	0.242718i
$666$		0			0
$667$	−8.63936	−	8.63936i	−0.334517	−	0.334517i
$668$	−10.9832	+	6.78831i	−0.424951	+	0.262647i
$669$		0			0
$670$	9.48490	+	14.3826i	0.366434	+	0.555650i
$671$	54.6116			2.10826
$672$		0			0
$673$		−	36.5327i		−	1.40823i	−0.710084	−	0.704117i	$-0.751343\pi$
$673$		−	36.5327i		−	1.40823i	0.710084	−	0.704117i	$-0.248657\pi$
$674$	−3.44098	−	12.1123i	−0.132542	−	0.466546i
$675$		0			0
$676$	12.5401	+	20.2893i	0.482312	+	0.780358i
$677$	20.5460	+	20.5460i	0.789645	+	0.789645i	0.981436	−	0.191791i	$-0.0614294\pi$
$677$	20.5460	+	20.5460i	0.789645	+	0.789645i	−0.191791	+	0.981436i	$0.561429\pi$
$678$		0			0
$679$			8.78518i			0.337144i
$680$	−17.1802	+	6.29466i	−0.658830	+	0.241389i
$681$		0			0
$682$	30.9053	−	55.4334i	1.18343	−	2.12265i
$683$	−18.2074	−	18.2074i	−0.696688	−	0.696688i	0.267007	−	0.963695i	$-0.413965\pi$
$683$	−18.2074	−	18.2074i	−0.696688	−	0.696688i	−0.963695	+	0.267007i	$0.913965\pi$
$684$		0			0
$685$	−6.71794	+	12.9294i	−0.256679	+	0.494007i
$686$	−7.25464	+	2.06098i	−0.276983	+	0.0786885i
$687$		0			0
$688$	12.0172	−	4.00632i	0.458150	−	0.152740i
$689$	8.14561			0.310323
$690$		0			0
$691$	11.5350	+	11.5350i	0.438811	+	0.438811i	0.891612	−	0.452801i	$-0.149575\pi$
$691$	11.5350	+	11.5350i	0.438811	+	0.438811i	−0.452801	+	0.891612i	$0.649575\pi$
$692$	4.76719	−	20.1962i	0.181221	−	0.767743i
$693$		0			0
$694$	−15.5083	−	8.64620i	−0.588686	−	0.328205i
$695$	14.3894	+	45.5149i	0.545823	+	1.72648i
$696$		0			0
$697$	0.0167075			0.000632842
$698$	14.3773	+	8.01567i	0.544189	+	0.303397i
$699$		0			0
$700$	−36.0253	−	15.4351i	−1.36163	−	0.583392i
$701$	−16.5440	−	16.5440i	−0.624859	−	0.624859i	0.321911	−	0.946770i	$-0.395675\pi$
$701$	−16.5440	−	16.5440i	−0.624859	−	0.624859i	−0.946770	+	0.321911i	$0.895675\pi$
$702$		0			0
$703$		−	21.4955i		−	0.810717i
$704$	−25.4885	−	21.2692i	−0.960634	−	0.801613i
$705$		0			0
$706$	−13.4154	−	47.2223i	−0.504897	−	1.77723i
$707$	29.4202	−	29.4202i	1.10646	−	1.10646i
$708$		0			0
$709$	−8.47518	+	8.47518i	−0.318292	+	0.318292i	−0.848111	−	0.529819i	$-0.822260\pi$
$709$	−8.47518	+	8.47518i	−0.318292	+	0.318292i	0.529819	+	0.848111i	$0.322260\pi$
$710$	3.57337	+	0.733274i	0.134106	+	0.0275193i
$711$		0			0
$712$	−11.2936	−	10.3204i	−0.423245	−	0.386772i
$713$	18.7240			0.701221
$714$		0			0
$715$	−8.53325	−	4.43376i	−0.319125	−	0.165813i
$716$	2.87328	+	0.678221i	0.107379	+	0.0253463i
$717$		0			0
$718$	1.08631	+	3.82380i	0.0405406	+	0.142703i
$719$	11.5303			0.430008			0.215004	−	0.976613i	$-0.431024\pi$
$719$	11.5303			0.430008			0.215004	+	0.976613i	$0.431024\pi$
$720$		0			0
$721$	−15.3287			−0.570869
$722$	5.17349	+	18.2107i	0.192537	+	0.677731i
$723$		0			0
$724$	−7.86389	+	33.3153i	−0.292259	+	1.23815i
$725$	6.07348	−	34.7582i	0.225564	−	1.29089i
$726$		0			0
$727$	−32.2855			−1.19740			−0.598702	−	0.800972i	$-0.704316\pi$
$727$	−32.2855			−1.19740			−0.598702	+	0.800972i	$0.704316\pi$
$728$	0.516778	+	11.4770i	0.0191531	+	0.425365i
$729$		0			0
$730$	−5.07717	+	24.7420i	−0.187914	+	0.915741i
$731$	−6.47833	+	6.47833i	−0.239610	+	0.239610i
$732$		0			0
$733$	33.6309	−	33.6309i	1.24219	−	1.24219i	0.283094	−	0.959092i	$-0.408639\pi$
$733$	33.6309	−	33.6309i	1.24219	−	1.24219i	0.959092	−	0.283094i	$-0.0913609\pi$
$734$	7.06607	+	24.8726i	0.260814	+	0.918063i
$735$		0			0
$736$	1.81891	−	9.62347i	0.0670461	−	0.354726i
$737$		−	22.6078i		−	0.832769i
$738$		0			0
$739$	−11.6806	−	11.6806i	−0.429676	−	0.429676i	0.458842	−	0.888518i	$-0.348264\pi$
$739$	−11.6806	−	11.6806i	−0.429676	−	0.429676i	−0.888518	+	0.458842i	$0.848264\pi$
$740$	−26.4778	+	30.7431i	−0.973343	+	1.13014i
$741$		0			0
$742$	−38.0499	−	21.2136i	−1.39685	−	0.778777i
$743$	−11.7641			−0.431582			−0.215791	−	0.976440i	$-0.569233\pi$
$743$	−11.7641			−0.431582			−0.215791	+	0.976440i	$0.569233\pi$
$744$		0			0
$745$	4.07418	+	12.8870i	0.149266	+	0.472142i
$746$	−40.9072	−	22.8067i	−1.49772	−	0.835011i
$747$		0			0
$748$	23.3677	+	5.51582i	0.854408	+	0.201678i
$749$	−10.1992	−	10.1992i	−0.372672	−	0.372672i
$750$		0			0
$751$	9.89062			0.360914			0.180457	−	0.983583i	$-0.442242\pi$
$751$	9.89062			0.360914			0.180457	+	0.983583i	$0.442242\pi$
$752$	−41.6637	−	20.8295i	−1.51932	−	0.759575i
$753$		0			0
$754$	−9.94937	+	2.82653i	−0.362335	+	0.102936i
$755$	16.6673	+	8.66012i	0.606587	+	0.315174i
$756$		0			0
$757$	19.7078	+	19.7078i	0.716291	+	0.716291i	0.967844	−	0.251553i	$-0.0809413\pi$
$757$	19.7078	+	19.7078i	0.716291	+	0.716291i	−0.251553	+	0.967844i	$0.580941\pi$
$758$	6.04743	−	10.8470i	0.219653	−	0.393980i
$759$		0			0
$760$	−6.30380	+	13.5943i	−0.228663	+	0.493116i
$761$			48.2102i			1.74762i	0.486270	+	0.873808i	$0.338357\pi$
$761$			48.2102i			1.74762i	−0.486270	+	0.873808i	$0.661643\pi$
$762$		0			0
$763$	−8.09857	−	8.09857i	−0.293188	−	0.293188i
$764$	36.1136	−	22.3205i	1.30654	−	0.807529i
$765$		0			0
$766$	5.56540	+	19.5902i	0.201086	+	0.707823i
$767$			5.61771i			0.202844i
$768$		0			0
$769$	−30.7814			−1.11000			−0.555002	−	0.831849i	$-0.687283\pi$
$769$	−30.7814			−1.11000			−0.555002	+	0.831849i	$0.687283\pi$
$770$	28.3138	+	42.9342i	1.02036	+	1.54724i
$771$		0			0
$772$	20.2710	+	32.7975i	0.729570	+	1.18041i
$773$	−31.7802	−	31.7802i	−1.14306	−	1.14306i	−0.987888	−	0.155167i	$-0.950408\pi$
$773$	−31.7802	−	31.7802i	−1.14306	−	1.14306i	−0.155167	−	0.987888i	$-0.549592\pi$
$774$		0			0
$775$	31.0841	+	44.2471i	1.11657	+	1.58940i
$776$	−4.68019	−	4.27688i	−0.168009	−	0.153531i
$777$		0			0
$778$	15.0716	−	27.0331i	0.540342	−	0.969185i
$779$	0.00967532	−	0.00967532i	0.000346654	−	0.000346654i
$780$		0			0
$781$	−3.38477	−	3.38477i	−0.121117	−	0.121117i
$782$	1.93575	+	6.81382i	0.0692221	+	0.243662i
$783$		0			0
$784$	14.9547	−	29.9127i	0.534095	−	1.06831i
$785$	−5.42294	−	17.1532i	−0.193553	−	0.612223i
$786$		0			0
$787$	21.8749	−	21.8749i	0.779754	−	0.779754i	−0.200035	−	0.979789i	$-0.564105\pi$
$787$	21.8749	−	21.8749i	0.779754	−	0.779754i	0.979789	+	0.200035i	$0.0641054\pi$
$788$	26.1060	+	6.16217i	0.929987	+	0.219518i
$789$		0			0
$790$	−0.536479	+	2.61436i	−0.0190871	+	0.0930148i
$791$		−	31.8876i		−	1.13379i
$792$		0			0
$793$	13.6393			0.484346
$794$	−14.6515	+	26.2797i	−0.519962	+	0.932630i
$795$		0			0
$796$	−9.09990	−	14.7232i	−0.322538	−	0.521850i
$797$	16.0370	−	16.0370i	0.568058	−	0.568058i	−0.363526	−	0.931584i	$-0.618427\pi$
$797$	16.0370	−	16.0370i	0.568058	−	0.568058i	0.931584	+	0.363526i	$0.118427\pi$
$798$		0			0
$799$	33.6895			1.19185
$800$	25.7610	−	11.6778i	0.910789	−	0.412872i
$801$		0			0
$802$	39.1726	−	11.1286i	1.38323	−	0.392964i
$803$	23.4361	−	23.4361i	0.827041	−	0.827041i
$804$		0			0
$805$	−6.99568	+	13.4639i	−0.246565	+	0.474542i
$806$	7.71865	−	13.8446i	0.271878	−	0.487654i
$807$		0			0
$808$	1.35063	+	29.9958i	0.0475151	+	1.05525i
$809$			37.0836i			1.30379i	0.758309	+	0.651895i	$0.226026\pi$
$809$			37.0836i			1.30379i	−0.758309	+	0.651895i	$0.773974\pi$
$810$		0			0
$811$	−11.8858	+	11.8858i	−0.417369	+	0.417369i	−0.884296	−	0.466927i	$-0.845361\pi$
$811$	−11.8858	+	11.8858i	−0.417369	+	0.417369i	0.466927	+	0.884296i	$0.345361\pi$
$812$	53.8368	+	12.7079i	1.88930	+	0.445959i
$813$		0			0
$814$	51.2151	−	14.5497i	1.79509	−	0.509968i
$815$	5.37504	+	17.0017i	0.188279	+	0.595543i
$816$		0			0
$817$			7.50320i			0.262504i
$818$	−9.02651	−	31.7733i	−0.315605	−	1.11093i
$819$		0			0
$820$	−0.0257557	+	0.00191985i	−0.000899427	+	6.70441e-5i
$821$	18.0568	−	18.0568i	0.630186	−	0.630186i	−0.317928	−	0.948115i	$-0.602987\pi$
$821$	18.0568	−	18.0568i	0.630186	−	0.630186i	0.948115	+	0.317928i	$0.102987\pi$
$822$		0			0
$823$	9.66750			0.336988			0.168494	−	0.985703i	$-0.446110\pi$
$823$	9.66750			0.336988			0.168494	+	0.985703i	$0.446110\pi$
$824$	7.46243	−	8.16614i	0.259966	−	0.284481i
$825$		0			0
$826$	14.6302	−	26.2415i	0.509050	−	0.913059i
$827$	15.9204	+	15.9204i	0.553607	+	0.553607i	0.927480	−	0.373873i	$-0.121970\pi$
$827$	15.9204	+	15.9204i	0.553607	+	0.553607i	−0.373873	+	0.927480i	$0.621970\pi$
$828$		0			0
$829$	6.21199	+	6.21199i	0.215751	+	0.215751i	0.806705	−	0.590954i	$-0.201249\pi$
$829$	6.21199	+	6.21199i	0.215751	+	0.215751i	−0.590954	+	0.806705i	$0.701249\pi$
$830$	−12.8044	−	19.4162i	−0.444448	−	0.673948i
$831$		0			0
$832$	−6.36579	−	5.31201i	−0.220694	−	0.184161i
$833$			24.1875i			0.838048i
$834$		0			0
$835$	−6.65576	+	12.8097i	−0.230332	+	0.443299i
$836$	16.7264	−	10.3380i	0.578496	−	0.357548i
$837$		0			0
$838$	−39.1876	−	21.8479i	−1.35371	−	0.754725i
$839$			11.4138i			0.394047i	0.980399	+	0.197023i	$0.0631275\pi$
$839$			11.4138i			0.394047i	−0.980399	+	0.197023i	$0.936873\pi$
$840$		0			0
$841$			20.8007i			0.717266i
$842$	−14.3780	+	25.7891i	−0.495498	+	0.888751i
$843$		0			0
$844$	−2.41128	−	0.569170i	−0.0829998	−	0.0195916i
$845$	23.6636	+	12.2953i	0.814052	+	0.422970i
$846$		0			0
$847$		−	24.3755i		−	0.837553i
$848$	29.8251	−	9.94317i	1.02420	−	0.341450i
$849$		0			0
$850$	−12.8883	+	15.8861i	−0.442065	+	0.544890i
$851$	11.1069	+	11.1069i	0.380739	+	0.380739i
$852$		0			0
$853$	12.1530	+	12.1530i	0.416110	+	0.416110i	0.883861	−	0.467751i	$-0.154935\pi$
$853$	12.1530	+	12.1530i	0.416110	+	0.416110i	−0.467751	+	0.883861i	$0.654935\pi$
$854$	−63.7121	−	35.5209i	−2.18018	−	1.21550i
$855$		0			0
$856$	10.3988	−	0.468230i	0.355423	−	0.0160038i
$857$	−23.6445			−0.807681			−0.403840	−	0.914829i	$-0.632325\pi$
$857$	−23.6445			−0.807681			−0.403840	+	0.914829i	$0.632325\pi$
$858$		0			0
$859$	18.9186	−	18.9186i	0.645494	−	0.645494i	−0.306407	−	0.951901i	$-0.599127\pi$
$859$	18.9186	−	18.9186i	0.645494	−	0.645494i	0.951901	+	0.306407i	$0.0991268\pi$
$860$	9.24233	−	10.7312i	0.315161	−	0.365930i
$861$		0			0
$862$	8.05645	−	2.28877i	0.274404	−	0.0779557i
$863$			32.1371i			1.09396i	0.837146	+	0.546980i	$0.184223\pi$
$863$			32.1371i			1.09396i	−0.837146	+	0.546980i	$0.815777\pi$
$864$		0			0
$865$	−6.99361	−	22.1213i	−0.237790	−	0.752148i
$866$	2.03681	+	7.16956i	0.0692136	+	0.243632i
$867$		0			0
$868$	−72.1109	+	44.5692i	−2.44760	+	1.51278i
$869$	2.47637	−	2.47637i	0.0840052	−	0.0840052i
$870$		0			0
$871$		−	5.64633i		−	0.191319i
$872$	8.25702	−	0.371792i	0.279618	−	0.0125905i
$873$		0			0
$874$	5.06687	+	2.82489i	0.171389	+	0.0955533i
$875$	−43.4305	+	5.82010i	−1.46822	+	0.196755i
$876$		0			0
$877$	33.5598	−	33.5598i	1.13323	−	1.13323i	0.143597	−	0.989636i	$-0.454133\pi$
$877$	33.5598	−	33.5598i	1.13323	−	1.13323i	0.989636	−	0.143597i	$-0.0458670\pi$
$878$	−6.89572	−	24.2729i	−0.232719	−	0.819171i
$879$		0			0
$880$	−36.6566	−	5.81780i	−1.23569	−	0.196118i
$881$	−3.11390			−0.104910			−0.0524550	−	0.998623i	$-0.516705\pi$
$881$	−3.11390			−0.104910			−0.0524550	+	0.998623i	$0.516705\pi$
$882$		0			0
$883$	−36.1043	+	36.1043i	−1.21501	+	1.21501i	−0.245647	+	0.969359i	$0.579000\pi$
$883$	−36.1043	+	36.1043i	−1.21501	+	1.21501i	−0.969359	+	0.245647i	$0.921000\pi$
$884$	5.83612	+	1.37758i	0.196290	+	0.0463331i
$885$		0			0
$886$	10.3039	+	5.74465i	0.346166	+	0.192995i
$887$	38.4317			1.29041			0.645206	−	0.764009i	$-0.276772\pi$
$887$	38.4317			1.29041			0.645206	+	0.764009i	$0.276772\pi$
$888$		0			0
$889$		−	63.0461i		−	2.11450i
$890$	−16.7555	−	3.43831i	−0.561646	−	0.115252i
$891$		0			0
$892$	10.9750	+	17.7571i	0.367471	+	0.594551i
$893$	19.5096	−	19.5096i	0.652863	−	0.652863i
$894$		0			0
$895$	3.14717	−	0.994971i	0.105198	−	0.0332582i
$896$	15.9019	+	41.3920i	0.531244	+	1.38281i
$897$		0			0
$898$	11.0572	−	3.14126i	0.368985	−	0.104825i
$899$	−53.9664	−	53.9664i	−1.79988	−	1.79988i
$900$		0			0
$901$	−16.0784	+	16.0784i	−0.535649	+	0.535649i
$902$	0.0296014	+	0.0165034i	0.000985618	+	0.000549504i
$903$		0			0
$904$	16.9877	+	15.5238i	0.565002	+	0.516313i
$905$	11.5366	+	36.4910i	0.383488	+	1.21300i
$906$		0			0
$907$	−37.6279	−	37.6279i	−1.24941	−	1.24941i	−0.955979	−	0.293436i	$-0.905201\pi$
$907$	−37.6279	−	37.6279i	−1.24941	−	1.24941i	−0.293436	−	0.955979i	$-0.594799\pi$
$908$	−8.91611	+	37.7730i	−0.295891	+	1.25354i
$909$		0			0
$910$	7.07140	+	10.7229i	0.234415	+	0.355460i
$911$	11.8631			0.393042			0.196521	−	0.980500i	$-0.437036\pi$
$911$	11.8631			0.393042			0.196521	+	0.980500i	$0.437036\pi$
$912$		0			0
$913$			30.5200i			1.01007i
$914$	−8.64506	+	2.45599i	−0.285953	+	0.0812368i
$915$		0			0
$916$	5.48333	−	23.2301i	0.181174	−	0.767544i
$917$	−51.1100	−	51.1100i	−1.68780	−	1.68780i
$918$		0			0
$919$		−	46.4906i		−	1.53358i	−0.641895	−	0.766792i	$-0.721852\pi$
$919$		−	46.4906i		−	1.53358i	0.641895	−	0.766792i	$-0.278148\pi$
$920$	−3.76704	−	10.2815i	−0.124196	−	0.338971i
$921$		0			0
$922$	3.72229	+	2.07526i	0.122587	+	0.0683450i
$923$	−0.845351	−	0.845351i	−0.0278251	−	0.0278251i
$924$		0			0
$925$	−7.80814	+	44.6855i	−0.256730	+	1.46925i
$926$	−7.13196	−	25.1045i	−0.234371	−	0.824985i
$927$		0			0
$928$	−32.9792	+	22.4943i	−1.08260	+	0.738411i
$929$	−3.18351			−0.104448			−0.0522238	−	0.998635i	$-0.516631\pi$
$929$	−3.18351			−0.104448			−0.0522238	+	0.998635i	$0.516631\pi$
$930$		0			0
$931$	14.0070	+	14.0070i	0.459060	+	0.459060i
$932$	−48.6736	+	30.0835i	−1.59436	+	0.985417i
$933$		0			0
$934$	5.48548	−	9.83903i	0.179490	−	0.321943i
$935$	25.5952	−	8.09187i	0.837053	−	0.264632i
$936$		0			0
$937$	27.2455			0.890072			0.445036	−	0.895513i	$-0.353191\pi$
$937$	27.2455			0.890072			0.445036	+	0.895513i	$0.353191\pi$
$938$	−14.7048	+	26.3752i	−0.480127	+	0.861181i
$939$		0			0
$940$	−51.9344	+	3.87124i	−1.69391	+	0.126266i
$941$	−4.15297	−	4.15297i	−0.135383	−	0.135383i	0.636168	−	0.771551i	$-0.280519\pi$
$941$	−4.15297	−	4.15297i	−0.135383	−	0.135383i	−0.771551	+	0.636168i	$0.780519\pi$
$942$		0			0
$943$			0.00999862i			0.000325600i
$944$	6.85742	+	20.5692i	0.223190	+	0.669470i
$945$		0			0
$946$	−17.8771	+	5.07873i	−0.581235	+	0.165124i
$947$	18.3519	−	18.3519i	0.596358	−	0.596358i	−0.342984	−	0.939341i	$-0.611438\pi$
$947$	18.3519	−	18.3519i	0.596358	−	0.596358i	0.939341	+	0.342984i	$0.111438\pi$
$948$		0			0
$949$	5.85319	−	5.85319i	0.190003	−	0.190003i
$950$	1.73604	+	16.6633i	0.0563247	+	0.540627i
$951$		0			0
$952$	−23.6741	−	21.6340i	−0.767282	−	0.701162i
$953$	52.0669			1.68661			0.843307	−	0.537433i	$-0.180606\pi$
$953$	52.0669			1.68661			0.843307	+	0.537433i	$0.180606\pi$
$954$		0			0
$955$	21.8847	−	42.1195i	0.708173	−	1.36296i
$956$	−36.5646	+	22.5993i	−1.18258	+	0.730913i
$957$		0			0
$958$	29.2291	−	8.30374i	0.944351	−	0.268282i
$959$	−25.5385			−0.824681
$960$		0			0
$961$	85.9611			2.77294
$962$	12.7910	−	3.63382i	0.412399	−	0.117159i
$963$		0			0
$964$	−33.3354	+	20.6035i	−1.07366	+	0.663593i
$965$	38.2520	+	19.8752i	1.23138	+	0.639806i
$966$		0			0
$967$	−32.8074			−1.05502			−0.527508	−	0.849550i	$-0.676873\pi$
$967$	−32.8074			−1.05502			−0.527508	+	0.849550i	$0.676873\pi$
$968$	12.9857	+	11.8667i	0.417378	+	0.381410i
$969$		0			0
$970$	−6.94367	−	1.42487i	−0.222948	−	0.0457500i
$971$	25.4682	−	25.4682i	0.817314	−	0.817314i	−0.168404	−	0.985718i	$-0.553861\pi$
$971$	25.4682	−	25.4682i	0.817314	−	0.817314i	0.985718	+	0.168404i	$0.0538613\pi$
$972$		0			0
$973$	−59.1623	+	59.1623i	−1.89666	+	1.89666i
$974$	49.4223	−	14.0404i	1.58359	−	0.449884i
$975$		0			0
$976$	49.9402	−	16.6492i	1.59855	−	0.532929i
$977$			2.69863i			0.0863367i	0.999068	+	0.0431684i	$0.0137452\pi$
$977$			2.69863i			0.0863367i	−0.999068	+	0.0431684i	$0.986255\pi$
$978$		0			0
$979$	15.8711	+	15.8711i	0.507244	+	0.507244i
$980$	−2.77937	−	37.2866i	−0.0887838	−	1.19108i
$981$		0			0
$982$	1.59331	−	2.85784i	0.0508445	−	0.0911973i
$983$	−25.2037			−0.803875			−0.401937	−	0.915667i	$-0.631663\pi$
$983$	−25.2037			−0.803875			−0.401937	+	0.915667i	$0.631663\pi$
$984$		0			0
$985$	28.5945	−	9.04009i	0.911097	−	0.288041i
$986$	14.0596	−	25.2180i	0.447748	−	0.803104i
$987$		0			0
$988$	4.17745	−	2.58194i	0.132902	−	0.0821423i
$989$	−3.87696	−	3.87696i	−0.123280	−	0.123280i
$990$		0			0
$991$	−9.06410			−0.287931			−0.143965	−	0.989583i	$-0.545985\pi$
$991$	−9.06410			−0.287931			−0.143965	+	0.989583i	$0.545985\pi$
$992$	11.3620	−	60.1137i	0.360743	−	1.90861i
$993$		0			0
$994$	1.74726	+	6.15037i	0.0554199	+	0.195078i
$995$	−17.1718	−	8.92223i	−0.544382	−	0.282854i
$996$		0			0
$997$	25.5035	+	25.5035i	0.807703	+	0.807703i	0.984286	−	0.176583i	$-0.0565044\pi$
$997$	25.5035	+	25.5035i	0.807703	+	0.807703i	−0.176583	+	0.984286i	$0.556504\pi$
$998$	−32.8330	−	18.3051i	−1.03931	−	0.579438i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bm.h.109.3		48
3.2	odd	2		240.2.bl.a.109.22	yes	48
5.4	even	2	inner	720.2.bm.h.109.22		48
12.11	even	2		960.2.bl.a.529.17		48
15.14	odd	2		240.2.bl.a.109.3	✓	48
16.5	even	4	inner	720.2.bm.h.469.22		48
24.5	odd	2		1920.2.bl.a.289.23		48
24.11	even	2		1920.2.bl.b.289.2		48
48.5	odd	4		240.2.bl.a.229.3	yes	48
48.11	even	4		960.2.bl.a.49.2		48
48.29	odd	4		1920.2.bl.a.1249.2		48
48.35	even	4		1920.2.bl.b.1249.23		48
60.59	even	2		960.2.bl.a.529.2		48
80.69	even	4	inner	720.2.bm.h.469.3		48
120.29	odd	2		1920.2.bl.a.289.2		48
120.59	even	2		1920.2.bl.b.289.23		48
240.29	odd	4		1920.2.bl.a.1249.23		48
240.59	even	4		960.2.bl.a.49.17		48
240.149	odd	4		240.2.bl.a.229.22	yes	48
240.179	even	4		1920.2.bl.b.1249.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.3	✓	48	15.14	odd	2
240.2.bl.a.109.22	yes	48	3.2	odd	2
240.2.bl.a.229.3	yes	48	48.5	odd	4
240.2.bl.a.229.22	yes	48	240.149	odd	4
720.2.bm.h.109.3		48	1.1	even	1	trivial
720.2.bm.h.109.22		48	5.4	even	2	inner
720.2.bm.h.469.3		48	80.69	even	4	inner
720.2.bm.h.469.22		48	16.5	even	4	inner
960.2.bl.a.49.2		48	48.11	even	4
960.2.bl.a.49.17		48	240.59	even	4
960.2.bl.a.529.2		48	60.59	even	2
960.2.bl.a.529.17		48	12.11	even	2
1920.2.bl.a.289.2		48	120.29	odd	2
1920.2.bl.a.289.23		48	24.5	odd	2
1920.2.bl.a.1249.2		48	48.29	odd	4
1920.2.bl.a.1249.23		48	240.29	odd	4
1920.2.bl.b.289.2		48	24.11	even	2
1920.2.bl.b.289.23		48	120.59	even	2
1920.2.bl.b.1249.2		48	240.179	even	4
1920.2.bl.b.1249.23		48	48.35	even	4

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.bm (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36038 + 0.386472i) q^{2} +(1.70128 - 1.05150i) q^{4} +(1.03097 - 1.98421i) q^{5} +3.91927 q^{7} +(-1.90801 + 2.08794i) q^{8} +O(q^{10})\)	\(q+(-1.36038 + 0.386472i) q^{2} +(1.70128 - 1.05150i) q^{4} +(1.03097 - 1.98421i) q^{5} +3.91927 q^{7} +(-1.90801 + 2.08794i) q^{8} +(-0.635669 + 3.09773i) q^{10} +(2.93423 - 2.93423i) q^{11} +(0.732828 - 0.732828i) q^{13} +(-5.33170 + 1.51469i) q^{14} +(1.78869 - 3.57779i) q^{16} +2.89302i q^{17} +(1.67534 + 1.67534i) q^{19} +(-0.332434 - 4.45976i) q^{20} +(-2.85767 + 5.12567i) q^{22} -1.73133 q^{23} +(-2.87420 - 4.09133i) q^{25} +(-0.713708 + 1.28014i) q^{26} +(6.66776 - 4.12111i) q^{28} +(4.99003 + 4.99003i) q^{29} -10.8149 q^{31} +(-1.05059 + 5.55844i) q^{32} +(-1.11807 - 3.93561i) q^{34} +(4.04065 - 7.77666i) q^{35} +(-6.41524 - 6.41524i) q^{37} +(-2.92658 - 1.63163i) q^{38} +(2.17581 + 5.93850i) q^{40} -0.00577512i q^{41} +(2.23930 + 2.23930i) q^{43} +(1.90660 - 8.07728i) q^{44} +(2.35527 - 0.669110i) q^{46} -11.6451i q^{47} +8.36066 q^{49} +(5.49120 + 4.45497i) q^{50} +(0.476175 - 2.01731i) q^{52} +(5.55765 + 5.55765i) q^{53} +(-2.79703 - 8.84724i) q^{55} +(-7.47801 + 8.18319i) q^{56} +(-8.71685 - 4.85983i) q^{58} +(-3.83290 + 3.83290i) q^{59} +(9.30595 + 9.30595i) q^{61} +(14.7123 - 4.17964i) q^{62} +(-0.718981 - 7.96763i) q^{64} +(-0.698563 - 2.20961i) q^{65} +(3.85243 - 3.85243i) q^{67} +(3.04201 + 4.92182i) q^{68} +(-2.49136 + 12.1408i) q^{70} -1.15355i q^{71} +7.98713 q^{73} +(11.2065 + 6.24786i) q^{74} +(4.61185 + 1.08860i) q^{76} +(11.5000 - 11.5000i) q^{77} +0.843960 q^{79} +(-5.25501 - 7.23774i) q^{80} +(0.00223193 + 0.00785637i) q^{82} +(-5.20069 + 5.20069i) q^{83} +(5.74036 + 2.98261i) q^{85} +(-3.91173 - 2.18088i) q^{86} +(0.527948 + 11.7250i) q^{88} +5.40896i q^{89} +(2.87215 - 2.87215i) q^{91} +(-2.94547 + 1.82049i) q^{92} +(4.50051 + 15.8418i) q^{94} +(5.05147 - 1.59701i) q^{95} +2.24154i q^{97} +(-11.3737 + 3.23117i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 48 q^{31} - 28 q^{34} - 24 q^{35} - 16 q^{40} + 40 q^{44} - 4 q^{46} + 48 q^{49} + 32 q^{50} - 48 q^{56} + 32 q^{59} + 16 q^{61} + 48 q^{64} - 16 q^{65} - 40 q^{74} + 60 q^{76} - 96 q^{79} - 72 q^{80} - 16 q^{86} - 32 q^{91} + 44 q^{94} + 48 q^{95}+O(q^{100}) \) 48 * q + 12 * q^10 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 40 * q^26 - 48 * q^31 - 28 * q^34 - 24 * q^35 - 16 * q^40 + 40 * q^44 - 4 * q^46 + 48 * q^49 + 32 * q^50 - 48 * q^56 + 32 * q^59 + 16 * q^61 + 48 * q^64 - 16 * q^65 - 40 * q^74 + 60 * q^76 - 96 * q^79 - 72 * q^80 - 16 * q^86 - 32 * q^91 + 44 * q^94 + 48 * q^95

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