LMFDB - Embedded newform 756.2.ba.a.575.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(71,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("756.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ba (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			575.3
Character	$\chi$	$=$	756.575
Dual form			756.2.ba.a.71.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37785 + 0.318634i) q^{2} +(1.79694 - 0.878061i) q^{4} +(-2.51813 + 1.45385i) q^{5} +(-0.866025 - 0.500000i) q^{7} +(-2.19614 + 1.78241i) q^{8} +O(q^{10})$	\(q+(-1.37785 + 0.318634i) q^{2} +(1.79694 - 0.878061i) q^{4} +(-2.51813 + 1.45385i) q^{5} +(-0.866025 - 0.500000i) q^{7} +(-2.19614 + 1.78241i) q^{8} +(3.00637 - 2.80555i) q^{10} +(1.18430 - 2.05127i) q^{11} +(-0.125913 - 0.218087i) q^{13} +(1.35257 + 0.412980i) q^{14} +(2.45802 - 3.15565i) q^{16} -7.60859i q^{17} +2.60920i q^{19} +(-3.24838 + 4.82355i) q^{20} +(-0.978187 + 3.20371i) q^{22} +(4.51674 + 7.82323i) q^{23} +(1.72733 - 2.99183i) q^{25} +(0.242979 + 0.260371i) q^{26} +(-1.99523 - 0.138049i) q^{28} +(5.53448 + 3.19533i) q^{29} +(0.0905658 - 0.0522882i) q^{31} +(-2.38128 + 5.13123i) q^{32} +(2.42436 + 10.4835i) q^{34} +2.90769 q^{35} -3.15261 q^{37} +(-0.831380 - 3.59508i) q^{38} +(2.93883 - 7.68118i) q^{40} +(7.24183 - 4.18107i) q^{41} +(7.18102 + 4.14596i) q^{43} +(0.326984 - 4.72592i) q^{44} +(-8.71615 - 9.34005i) q^{46} +(0.248282 - 0.430036i) q^{47} +(0.500000 + 0.866025i) q^{49} +(-1.42671 + 4.67268i) q^{50} +(-0.417752 - 0.281331i) q^{52} +2.38678i q^{53} +6.88718i q^{55} +(2.79312 - 0.445538i) q^{56} +(-8.64383 - 2.63922i) q^{58} +(3.99487 + 6.91932i) q^{59} +(3.69592 - 6.40151i) q^{61} +(-0.108125 + 0.100903i) q^{62} +(1.64606 - 7.82882i) q^{64} +(0.634129 + 0.366115i) q^{65} +(-0.444103 + 0.256403i) q^{67} +(-6.68081 - 13.6722i) q^{68} +(-4.00636 + 0.926490i) q^{70} +1.45233 q^{71} +4.06828 q^{73} +(4.34382 - 1.00453i) q^{74} +(2.29103 + 4.68858i) q^{76} +(-2.05127 + 1.18430i) q^{77} +(10.0369 + 5.79482i) q^{79} +(-1.60178 + 11.5199i) q^{80} +(-8.64592 + 8.06839i) q^{82} +(-0.439593 + 0.761398i) q^{83} +(11.0617 + 19.1594i) q^{85} +(-11.2154 - 3.42440i) q^{86} +(1.05531 + 6.61580i) q^{88} -14.6787i q^{89} +0.251825i q^{91} +(14.9856 + 10.0919i) q^{92} +(-0.205071 + 0.671637i) q^{94} +(-3.79337 - 6.57031i) q^{95} +(2.88066 - 4.98945i) q^{97} +(-0.964871 - 1.03394i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) $ 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.37785	+	0.318634i	−0.974287	+	0.225309i
$2$	−1.37785	+	0.318634i	−0.974287	+	0.225309i
$3$		0			0
$3$		0			0
$4$	1.79694	−	0.878061i	0.898472	−	0.439031i
$5$	−2.51813	+	1.45385i	−1.12614	+	0.650179i	−0.942962	−	0.332900i	$-0.891973\pi$
$5$	−2.51813	+	1.45385i	−1.12614	+	0.650179i	−0.183182	+	0.983079i	$0.558640\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$	−2.19614	+	1.78241i	−0.776453	+	0.630175i
$9$		0			0
$10$	3.00637	−	2.80555i	0.950697	−	0.887191i
$11$	1.18430	−	2.05127i	0.357081	−	0.618483i	−0.630391	−	0.776278i	$-0.717105\pi$
$11$	1.18430	−	2.05127i	0.357081	−	0.618483i	0.987472	+	0.157795i	$0.0504387\pi$
$12$		0			0
$13$	−0.125913	−	0.218087i	−0.0349219	−	0.0604864i	0.848036	−	0.529938i	$-0.177785\pi$
$13$	−0.125913	−	0.218087i	−0.0349219	−	0.0604864i	−0.882958	+	0.469452i	$0.844452\pi$
$14$	1.35257	+	0.412980i	0.361490	+	0.110373i
$15$		0			0
$16$	2.45802	−	3.15565i	0.614504	−	0.788913i
$17$		−	7.60859i		−	1.84535i	−0.385574	−	0.922677i	$-0.625997\pi$
$17$		−	7.60859i		−	1.84535i	0.385574	−	0.922677i	$-0.374003\pi$
$18$		0			0
$19$			2.60920i			0.598591i	0.954160	+	0.299295i	$0.0967516\pi$
$19$			2.60920i			0.598591i	−0.954160	+	0.299295i	$0.903248\pi$
$20$	−3.24838	+	4.82355i	−0.726360	+	1.07858i
$21$		0			0
$22$	−0.978187	+	3.20371i	−0.208550	+	0.683033i
$23$	4.51674	+	7.82323i	0.941806	+	1.63126i	0.762024	+	0.647549i	$0.224206\pi$
$23$	4.51674	+	7.82323i	0.941806	+	1.63126i	0.179782	+	0.983706i	$0.442461\pi$
$24$		0			0
$25$	1.72733	−	2.99183i	0.345467	−	0.598366i
$26$	0.242979	+	0.260371i	0.0476520	+	0.0510630i
$27$		0			0
$28$	−1.99523	−	0.138049i	−0.377063	−	0.0260888i
$29$	5.53448	+	3.19533i	1.02773	+	0.593358i	0.916333	−	0.400418i	$-0.131135\pi$
$29$	5.53448	+	3.19533i	1.02773	+	0.593358i	0.111394	+	0.993776i	$0.464468\pi$
$30$		0			0
$31$	0.0905658	−	0.0522882i	0.0162661	−	0.00939124i	−0.491845	−	0.870683i	$-0.663677\pi$
$31$	0.0905658	−	0.0522882i	0.0162661	−	0.00939124i	0.508111	+	0.861292i	$0.330344\pi$
$32$	−2.38128	+	5.13123i	−0.420955	+	0.907082i
$33$		0			0
$34$	2.42436	+	10.4835i	0.415774	+	1.79790i
$35$	2.90769			0.491489
$36$		0			0
$37$	−3.15261			−0.518285			−0.259143	−	0.965839i	$-0.583440\pi$
$37$	−3.15261			−0.518285			−0.259143	+	0.965839i	$0.583440\pi$
$38$	−0.831380	−	3.59508i	−0.134868	−	0.583200i
$39$		0			0
$40$	2.93883	−	7.68118i	0.464670	−	1.21450i
$41$	7.24183	−	4.18107i	1.13098	−	0.652974i	0.186801	−	0.982398i	$-0.440188\pi$
$41$	7.24183	−	4.18107i	1.13098	−	0.652974i	0.944182	+	0.329424i	$0.106855\pi$
$42$		0			0
$43$	7.18102	+	4.14596i	1.09510	+	0.632254i	0.934928	−	0.354836i	$-0.115463\pi$
$43$	7.18102	+	4.14596i	1.09510	+	0.632254i	0.160167	+	0.987090i	$0.448797\pi$
$44$	0.326984	−	4.72592i	0.0492946	−	0.712459i
$45$		0			0
$46$	−8.71615	−	9.34005i	−1.28513	−	1.37712i
$47$	0.248282	−	0.430036i	0.0362156	−	0.0627273i	−0.847349	−	0.531036i	$-0.821803\pi$
$47$	0.248282	−	0.430036i	0.0362156	−	0.0627273i	0.883565	+	0.468308i	$0.155136\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−1.42671	+	4.67268i	−0.201767	+	0.660817i
$51$		0			0
$52$	−0.417752	−	0.281331i	−0.0579317	−	0.0390136i
$53$			2.38678i			0.327849i	0.986473	+	0.163925i	$0.0524154\pi$
$53$			2.38678i			0.327849i	−0.986473	+	0.163925i	$0.947585\pi$
$54$		0			0
$55$			6.88718i			0.928667i
$56$	2.79312	−	0.445538i	0.373246	−	0.0595375i
$57$		0			0
$58$	−8.64383	−	2.63922i	−1.13499	−	0.346546i
$59$	3.99487	+	6.91932i	0.520088	+	0.900818i	0.999727	+	0.0233526i	$0.00743403\pi$
$59$	3.99487	+	6.91932i	0.520088	+	0.900818i	−0.479640	+	0.877466i	$0.659233\pi$
$60$		0			0
$61$	3.69592	−	6.40151i	0.473214	−	0.819630i	−0.526316	−	0.850289i	$-0.676427\pi$
$61$	3.69592	−	6.40151i	0.473214	−	0.819630i	0.999530	+	0.0306589i	$0.00976058\pi$
$62$	−0.108125	+	0.100903i	−0.0137319	+	0.0128147i
$63$		0			0
$64$	1.64606	−	7.82882i	0.205758	−	0.978603i
$65$	0.634129	+	0.366115i	0.0786541	+	0.0454109i
$66$		0			0
$67$	−0.444103	+	0.256403i	−0.0542559	+	0.0313246i	−0.526883	−	0.849938i	$-0.676639\pi$
$67$	−0.444103	+	0.256403i	−0.0542559	+	0.0313246i	0.472627	+	0.881263i	$0.343306\pi$
$68$	−6.68081	−	13.6722i	−0.810167	−	1.65800i
$69$		0			0
$70$	−4.00636	+	0.926490i	−0.478852	+	0.110737i
$71$	1.45233			0.172360			0.0861800	−	0.996280i	$-0.472534\pi$
$71$	1.45233			0.172360			0.0861800	+	0.996280i	$0.472534\pi$
$72$		0			0
$73$	4.06828			0.476157			0.238078	−	0.971246i	$-0.423483\pi$
$73$	4.06828			0.476157			0.238078	+	0.971246i	$0.423483\pi$
$74$	4.34382	−	1.00453i	0.504959	−	0.116774i
$75$		0			0
$76$	2.29103	+	4.68858i	0.262800	+	0.537817i
$77$	−2.05127	+	1.18430i	−0.233764	+	0.134964i
$78$		0			0
$79$	10.0369	+	5.79482i	1.12924	+	0.651968i	0.943744	−	0.330677i	$-0.107277\pi$
$79$	10.0369	+	5.79482i	1.12924	+	0.651968i	0.185498	+	0.982645i	$0.440610\pi$
$80$	−1.60178	+	11.5199i	−0.179085	+	1.28797i
$81$		0			0
$82$	−8.64592	+	8.06839i	−0.954782	+	0.891004i
$83$	−0.439593	+	0.761398i	−0.0482516	+	0.0835743i	−0.889142	−	0.457630i	$-0.848698\pi$
$83$	−0.439593	+	0.761398i	−0.0482516	+	0.0835743i	0.840891	+	0.541205i	$0.182032\pi$
$84$		0			0
$85$	11.0617	+	19.1594i	1.19981	+	2.07813i
$86$	−11.2154	−	3.42440i	−1.20939	−	0.369262i
$87$		0			0
$88$	1.05531	+	6.61580i	0.112496	+	0.705246i
$89$		−	14.6787i		−	1.55594i	−0.628304	−	0.777968i	$-0.716251\pi$
$89$		−	14.6787i		−	1.55594i	0.628304	−	0.777968i	$-0.283749\pi$
$90$		0			0
$91$			0.251825i			0.0263984i
$92$	14.9856	+	10.0919i	1.56236	+	1.05216i
$93$		0			0
$94$	−0.205071	+	0.671637i	−0.0211514	+	0.0692741i
$95$	−3.79337	−	6.57031i	−0.389191	−	0.674099i
$96$		0			0
$97$	2.88066	−	4.98945i	0.292487	−	0.506602i	−0.681910	−	0.731436i	$-0.738851\pi$
$97$	2.88066	−	4.98945i	0.292487	−	0.506602i	0.974397	+	0.224834i	$0.0721839\pi$
$98$	−0.964871	−	1.03394i	−0.0974667	−	0.104443i
$99$		0			0
$100$	0.476913	−	6.89285i	0.0476913	−	0.689285i
$101$	12.4968	+	7.21504i	1.24348	+	0.717923i	0.969801	−	0.243898i	$-0.0784263\pi$
$101$	12.4968	+	7.21504i	1.24348	+	0.717923i	0.273678	+	0.961821i	$0.411760\pi$
$102$		0			0
$103$	10.3804	−	5.99314i	1.02281	−	0.590521i	0.107896	−	0.994162i	$-0.465589\pi$
$103$	10.3804	−	5.99314i	1.02281	−	0.590521i	0.914918	+	0.403641i	$0.132255\pi$
$104$	0.665241	+	0.254522i	0.0652322	+	0.0249580i
$105$		0			0
$106$	−0.760510	−	3.28862i	−0.0738672	−	0.319419i
$107$	6.10346			0.590043			0.295022	−	0.955491i	$-0.404673\pi$
$107$	6.10346			0.590043			0.295022	+	0.955491i	$0.404673\pi$
$108$		0			0
$109$	6.25509			0.599129			0.299564	−	0.954076i	$-0.403159\pi$
$109$	6.25509			0.599129			0.299564	+	0.954076i	$0.403159\pi$
$110$	−2.19449	−	9.48950i	−0.209237	−	0.904789i
$111$		0			0
$112$	−3.70653	+	1.50387i	−0.350234	+	0.142102i
$113$	−15.8902	+	9.17418i	−1.49482	+	0.863035i	−0.999982	−	0.00595082i	$-0.998106\pi$
$113$	−15.8902	+	9.17418i	−1.49482	+	0.863035i	−0.494838	+	0.868985i	$0.664772\pi$
$114$		0			0
$115$	−22.7475	−	13.1333i	−2.12122	−	1.22469i
$116$	12.7508	+	0.882224i	1.18389	+	0.0819125i
$117$		0			0
$118$	−7.70906	−	8.26088i	−0.709677	−	0.760476i
$119$	−3.80429	+	6.58923i	−0.348739	+	0.604034i
$120$		0			0
$121$	2.69485	+	4.66762i	0.244986	+	0.424329i
$122$	−3.05268	+	9.99798i	−0.276376	+	0.905174i
$123$		0			0
$124$	0.116829	−	0.173481i	0.0104916	−	0.0155791i
$125$		−	4.49335i		−	0.401898i
$126$		0			0
$127$			13.5835i			1.20534i	0.797989	+	0.602672i	$0.205897\pi$
$127$			13.5835i			1.20534i	−0.797989	+	0.602672i	$0.794103\pi$
$128$	0.226504	+	11.3114i	0.0200203	+	0.999800i
$129$		0			0
$130$	−0.990392	−	0.302396i	−0.0868632	−	0.0265219i
$131$	0.740508	+	1.28260i	0.0646985	+	0.112061i	0.896560	−	0.442922i	$-0.146058\pi$
$131$	0.740508	+	1.28260i	0.0646985	+	0.112061i	−0.831862	+	0.554983i	$0.812725\pi$
$132$		0			0
$133$	1.30460	−	2.25963i	0.113123	−	0.195935i
$134$	0.530209	−	0.494792i	0.0458031	−	0.0427435i
$135$		0			0
$136$	13.5616	+	16.7095i	1.16290	+	1.43283i
$137$	−15.5721	−	8.99055i	−1.33041	−	0.768115i	−0.345051	−	0.938584i	$-0.612138\pi$
$137$	−15.5721	−	8.99055i	−1.33041	−	0.768115i	−0.985363	+	0.170469i	$0.945472\pi$
$138$		0			0
$139$	−7.21297	+	4.16441i	−0.611796	+	0.353221i	−0.773668	−	0.633591i	$-0.781580\pi$
$139$	−7.21297	+	4.16441i	−0.611796	+	0.353221i	0.161872	+	0.986812i	$0.448247\pi$
$140$	5.22496	−	2.55313i	0.441590	−	0.215779i
$141$		0			0
$142$	−2.00110	+	0.462763i	−0.167928	+	0.0388342i
$143$	−0.596475			−0.0498797
$144$		0			0
$145$	−18.5821			−1.54316
$146$	−5.60549	+	1.29629i	−0.463913	+	0.107282i
$147$		0			0
$148$	−5.66506	+	2.76818i	−0.465665	+	0.227543i
$149$	2.86752	−	1.65557i	0.234917	−	0.135629i	−0.377921	−	0.925838i	$-0.623361\pi$
$149$	2.86752	−	1.65557i	0.234917	−	0.135629i	0.612838	+	0.790208i	$0.290028\pi$
$150$		0			0
$151$	−5.39261	−	3.11343i	−0.438845	−	0.253367i	0.264263	−	0.964451i	$-0.414871\pi$
$151$	−5.39261	−	3.11343i	−0.438845	−	0.253367i	−0.703107	+	0.711084i	$0.748205\pi$
$152$	−4.65065	−	5.73016i	−0.377217	−	0.464778i
$153$		0			0
$154$	2.44899	−	2.28540i	0.197345	−	0.184163i
$155$	−0.152038	+	0.263337i	−0.0122120	+	0.0211518i
$156$		0			0
$157$	1.48912	+	2.57922i	0.118844	+	0.205844i	0.919310	−	0.393534i	$-0.128748\pi$
$157$	1.48912	+	2.57922i	0.118844	+	0.205844i	−0.800466	+	0.599379i	$0.795414\pi$
$158$	−15.6758	−	4.78629i	−1.24710	−	0.380776i
$159$		0			0
$160$	−1.46363	−	16.3831i	−0.115710	−	1.29520i
$161$		−	9.03348i		−	0.711938i
$162$		0			0
$163$		−	8.29335i		−	0.649585i	−0.945785	−	0.324793i	$-0.894706\pi$
$163$		−	8.29335i		−	0.649585i	0.945785	−	0.324793i	$-0.105294\pi$
$164$	9.34192	−	13.8719i	0.729482	−	1.08321i
$165$		0			0
$166$	0.363086	−	1.18916i	0.0281810	−	0.0922969i
$167$	−9.34971	−	16.1942i	−0.723503	−	1.25314i	−0.959587	−	0.281411i	$-0.909198\pi$
$167$	−9.34971	−	16.1942i	−0.723503	−	1.25314i	0.236085	−	0.971732i	$-0.424136\pi$
$168$		0			0
$169$	6.46829	−	11.2034i	0.497561	−	0.861801i
$170$	−21.3462	−	22.8742i	−1.63718	−	1.75437i
$171$		0			0
$172$	16.5443	+	1.14469i	1.26149	+	0.0872819i
$173$	−7.58848	−	4.38121i	−0.576942	−	0.333097i	0.182975	−	0.983118i	$-0.441427\pi$
$173$	−7.58848	−	4.38121i	−0.576942	−	0.333097i	−0.759917	+	0.650020i	$0.774760\pi$
$174$		0			0
$175$	−2.99183	+	1.72733i	−0.226161	+	0.130574i
$176$	−3.56207	−	8.77932i	−0.268501	−	0.661766i
$177$		0			0
$178$	4.67713	+	20.2250i	0.350566	+	1.51593i
$179$	−2.87709			−0.215044			−0.107522	−	0.994203i	$-0.534292\pi$
$179$	−2.87709			−0.215044			−0.107522	+	0.994203i	$0.534292\pi$
$180$		0			0
$181$	−4.82998			−0.359010			−0.179505	−	0.983757i	$-0.557450\pi$
$181$	−4.82998			−0.359010			−0.179505	+	0.983757i	$0.557450\pi$
$182$	−0.0802401	−	0.346977i	−0.00594780	−	0.0257197i
$183$		0			0
$184$	−23.8636	−	9.13024i	−1.75925	−	0.673090i
$185$	7.93868	−	4.58340i	0.583664	−	0.336978i
$186$		0			0
$187$	−15.6073	−	9.01088i	−1.14132	−	0.658941i
$188$	0.0685500	−	0.990758i	0.00499952	−	0.0722584i
$189$		0			0
$190$	7.32022	+	7.84421i	0.531065	+	0.569078i
$191$	10.2584	−	17.7680i	0.742270	−	1.28565i	−0.209189	−	0.977875i	$-0.567082\pi$
$191$	10.2584	−	17.7680i	0.742270	−	1.28565i	0.951459	−	0.307775i	$-0.0995843\pi$
$192$		0			0
$193$	−9.29894	−	16.1062i	−0.669352	−	1.15935i	−0.978085	−	0.208204i	$-0.933238\pi$
$193$	−9.29894	−	16.1062i	−0.669352	−	1.15935i	0.308733	−	0.951149i	$-0.400095\pi$
$194$	−2.37931	+	7.79260i	−0.170824	+	0.559476i
$195$		0			0
$196$	1.65890	+	1.11717i	0.118493	+	0.0797978i
$197$			17.2523i			1.22917i	0.788850	+	0.614586i	$0.210677\pi$
$197$			17.2523i			1.22917i	−0.788850	+	0.614586i	$0.789323\pi$
$198$		0			0
$199$		−	1.17220i		−	0.0830948i	−0.999137	−	0.0415474i	$-0.986771\pi$
$199$		−	1.17220i		−	0.0830948i	0.999137	−	0.0415474i	$-0.0132288\pi$
$200$	1.53919	+	9.64928i	0.108837	+	0.682307i
$201$		0			0
$202$	−19.5177	−	5.95933i	−1.37326	−	0.419297i
$203$	−3.19533	−	5.53448i	−0.224268	−	0.388444i
$204$		0			0
$205$	−12.1573	+	21.0570i	−0.849100	+	1.47068i
$206$	−12.3930	+	11.5652i	−0.863464	+	0.805786i
$207$		0			0
$208$	−0.997702	−	0.138725i	−0.0691782	−	0.00961885i
$209$	5.35218	+	3.09008i	0.370218	+	0.213745i
$210$		0			0
$211$	8.81152	−	5.08733i	0.606610	−	0.350226i	−0.165028	−	0.986289i	$-0.552771\pi$
$211$	8.81152	−	5.08733i	0.606610	−	0.350226i	0.771637	+	0.636063i	$0.219438\pi$
$212$	2.09574	+	4.28891i	0.143936	+	0.294563i
$213$		0			0
$214$	−8.40965	+	1.94477i	−0.574872	+	0.132942i
$215$	−24.1104			−1.64431
$216$		0			0
$217$	−0.104576			−0.00709911
$218$	−8.61858	+	1.99309i	−0.583724	+	0.134989i
$219$		0			0
$220$	6.04736	+	12.3759i	0.407713	+	0.834381i
$221$	−1.65933	+	0.958017i	−0.111619	+	0.0644432i
$222$		0			0
$223$	−5.28069	−	3.04881i	−0.353621	−	0.204163i	0.312658	−	0.949866i	$-0.398781\pi$
$223$	−5.28069	−	3.04881i	−0.353621	−	0.204163i	−0.666279	+	0.745703i	$0.732114\pi$
$224$	4.62786	−	3.25313i	0.309212	−	0.217359i
$225$		0			0
$226$	18.9710	−	17.7038i	1.26194	−	1.17764i
$227$	−11.1581	+	19.3264i	−0.740589	+	1.28274i	0.211639	+	0.977348i	$0.432120\pi$
$227$	−11.1581	+	19.3264i	−0.740589	+	1.28274i	−0.952228	+	0.305390i	$0.901213\pi$
$228$		0			0
$229$	−2.70895	−	4.69204i	−0.179013	−	0.310059i	0.762530	−	0.646953i	$-0.223957\pi$
$229$	−2.70895	−	4.69204i	−0.179013	−	0.310059i	−0.941543	+	0.336894i	$0.890624\pi$
$230$	35.5274	+	10.8476i	2.34261	+	0.715267i
$231$		0			0
$232$	−17.8499	+	2.84729i	−1.17190	+	0.186933i
$233$			6.08190i			0.398439i	0.979955	+	0.199219i	$0.0638406\pi$
$233$			6.08190i			0.398439i	−0.979955	+	0.199219i	$0.936159\pi$
$234$		0			0
$235$			1.44385i			0.0941865i
$236$	13.2541	+	8.92588i	0.862771	+	0.581026i
$237$		0			0
$238$	3.14219	−	10.2912i	0.203678	−	0.667076i
$239$	−4.58910	−	7.94855i	−0.296844	−	0.514149i	0.678568	−	0.734538i	$-0.262601\pi$
$239$	−4.58910	−	7.94855i	−0.296844	−	0.514149i	−0.975412	+	0.220388i	$0.929268\pi$
$240$		0			0
$241$	−4.60034	+	7.96801i	−0.296334	+	0.513265i	−0.975294	−	0.220910i	$-0.929097\pi$
$241$	−4.60034	+	7.96801i	−0.296334	+	0.513265i	0.678961	+	0.734175i	$0.262431\pi$
$242$	−5.20036	−	5.57260i	−0.334292	−	0.358221i
$243$		0			0
$244$	1.02043	−	14.7484i	0.0653266	−	0.944170i
$245$	−2.51813	−	1.45385i	−0.160878	−	0.0928828i
$246$		0			0
$247$	0.569032	−	0.328531i	0.0362066	−	0.0209039i
$248$	−0.105696	+	0.276257i	−0.00671173	+	0.0175424i
$249$		0			0
$250$	1.43174	+	6.19117i	0.0905510	+	0.391564i
$251$	17.5771			1.10946			0.554729	−	0.832031i	$-0.312822\pi$
$251$	17.5771			1.10946			0.554729	+	0.832031i	$0.312822\pi$
$252$		0			0
$253$	21.3968			1.34520
$254$	−4.32818	−	18.7161i	−0.271574	−	1.17435i
$255$		0			0
$256$	−3.91630	−	15.5133i	−0.244769	−	0.969581i
$257$	9.36418	−	5.40641i	0.584122	−	0.337243i	−0.178648	−	0.983913i	$-0.557172\pi$
$257$	9.36418	−	5.40641i	0.584122	−	0.337243i	0.762770	+	0.646670i	$0.223839\pi$
$258$		0			0
$259$	2.73024	+	1.57630i	0.169649	+	0.0979467i
$260$	1.46097	+	0.101083i	0.0906053	+	0.00626893i
$261$		0			0
$262$	−1.42899	−	1.53128i	−0.0882833	−	0.0946026i
$263$	1.23346	−	2.13642i	0.0760585	−	0.131737i	−0.825488	−	0.564420i	$-0.809100\pi$
$263$	1.23346	−	2.13642i	0.0760585	−	0.131737i	0.901546	+	0.432683i	$0.142433\pi$
$264$		0			0
$265$	−3.47001	−	6.01023i	−0.213161	−	0.369205i
$266$	−1.07755	+	3.52912i	−0.0660686	+	0.216384i
$267$		0			0
$268$	−0.572891	+	0.850692i	−0.0349949	+	0.0519643i
$269$			18.6417i			1.13661i	0.822820	+	0.568303i	$0.192400\pi$
$269$			18.6417i			1.13661i	−0.822820	+	0.568303i	$0.807600\pi$
$270$		0			0
$271$			11.9123i			0.723621i	0.932252	+	0.361811i	$0.117841\pi$
$271$			11.9123i			0.723621i	−0.932252	+	0.361811i	$0.882159\pi$
$272$	−24.0101	−	18.7020i	−1.45582	−	1.13398i
$273$		0			0
$274$	24.3207	+	7.42583i	1.46927	+	0.448611i
$275$	−4.09137	−	7.08647i	−0.246719	−	0.427330i
$276$		0			0
$277$	8.83024	−	15.2944i	0.530558	−	0.918953i	−0.468807	−	0.883301i	$-0.655316\pi$
$277$	8.83024	−	15.2944i	0.530558	−	0.918953i	0.999364	−	0.0356520i	$-0.0113508\pi$
$278$	8.61147	−	8.03624i	0.516482	−	0.481981i
$279$		0			0
$280$	−6.38570	+	5.18268i	−0.381618	+	0.309725i
$281$	16.5651	+	9.56389i	0.988193	+	0.570534i	0.904734	−	0.425977i	$-0.140070\pi$
$281$	16.5651	+	9.56389i	0.988193	+	0.570534i	0.0834596	+	0.996511i	$0.473403\pi$
$282$		0			0
$283$	2.81044	−	1.62261i	0.167063	−	0.0964541i	−0.414137	−	0.910215i	$-0.635917\pi$
$283$	2.81044	−	1.62261i	0.167063	−	0.0964541i	0.581200	+	0.813760i	$0.302583\pi$
$284$	2.60976	−	1.27524i	0.154861	−	0.0756713i
$285$		0			0
$286$	0.821853	−	0.190057i	0.0485972	−	0.0112383i
$287$	−8.36214			−0.493602
$288$		0			0
$289$	−40.8906			−2.40533
$290$	25.6033	−	5.92089i	1.50348	−	0.347687i
$291$		0			0
$292$	7.31048	−	3.57220i	0.427813	−	0.209047i
$293$	−11.1294	+	6.42555i	−0.650185	+	0.375385i	−0.788527	−	0.615000i	$-0.789156\pi$
$293$	−11.1294	+	6.42555i	−0.650185	+	0.375385i	0.138342	+	0.990385i	$0.455823\pi$
$294$		0			0
$295$	−20.1192	−	11.6158i	−1.17139	−	0.676300i
$296$	6.92356	−	5.61922i	0.402424	−	0.326611i
$297$		0			0
$298$	−3.42350	+	3.19481i	−0.198318	+	0.185071i
$299$	1.13743	−	1.97009i	0.0657792	−	0.113933i
$300$		0			0
$301$	−4.14596	−	7.18102i	−0.238969	−	0.413907i
$302$	8.42226	+	2.57156i	0.484647	+	0.147977i
$303$		0			0
$304$	8.23372	+	6.41345i	0.472236	+	0.367837i
$305$			21.4932i			1.23069i
$306$		0			0
$307$			17.7017i			1.01029i	0.863035	+	0.505144i	$0.168561\pi$
$307$			17.7017i			1.01029i	−0.863035	+	0.505144i	$0.831439\pi$
$308$	−2.64613	+	3.92927i	−0.150778	+	0.223891i
$309$		0			0
$310$	0.125577	−	0.411284i	0.00713230	−	0.0233594i
$311$	3.30345	+	5.72174i	0.187321	+	0.324450i	0.944356	−	0.328924i	$-0.106686\pi$
$311$	3.30345	+	5.72174i	0.187321	+	0.324450i	−0.757035	+	0.653374i	$0.773353\pi$
$312$		0			0
$313$	5.34114	−	9.25113i	0.301899	−	0.522905i	−0.674667	−	0.738122i	$-0.735713\pi$
$313$	5.34114	−	9.25113i	0.301899	−	0.522905i	0.976566	+	0.215217i	$0.0690460\pi$
$314$	−2.87361	−	3.07930i	−0.162167	−	0.173775i
$315$		0			0
$316$	23.1240	+	1.59994i	1.30083	+	0.0900034i
$317$	22.1073	+	12.7636i	1.24167	+	0.716878i	0.969434	−	0.245353i	$-0.0789040\pi$
$317$	22.1073	+	12.7636i	1.24167	+	0.716878i	0.272235	+	0.962231i	$0.412237\pi$
$318$		0			0
$319$	13.1090	−	7.56849i	0.733964	−	0.423754i
$320$	7.23689	+	22.1071i	0.404555	+	1.23583i
$321$		0			0
$322$	2.87838	+	12.4468i	0.160406	+	0.693633i
$323$	19.8523			1.10461
$324$		0			0
$325$	−0.869972			−0.0482573
$326$	2.64255	+	11.4270i	0.146357	+	0.632883i
$327$		0			0
$328$	−8.45171	+	22.0901i	−0.466667	+	1.21972i
$329$	−0.430036	+	0.248282i	−0.0237087	+	0.0136882i
$330$		0			0
$331$	23.0921	+	13.3322i	1.26925	+	0.732804i	0.974847	−	0.222876i	$-0.0715445\pi$
$331$	23.0921	+	13.3322i	1.26925	+	0.732804i	0.294407	+	0.955680i	$0.404878\pi$
$332$	−0.121371	+	1.75418i	−0.00666108	+	0.0962731i
$333$		0			0
$334$	18.0425	+	19.3340i	0.987243	+	1.05791i
$335$	0.745541	−	1.29132i	0.0407333	−	0.0705521i
$336$		0			0
$337$	3.17158	+	5.49333i	0.172767	+	0.299241i	0.939386	−	0.342861i	$-0.111396\pi$
$337$	3.17158	+	5.49333i	0.172767	+	0.299241i	−0.766619	+	0.642102i	$0.778063\pi$
$338$	−5.34255	+	17.4976i	−0.290596	+	0.951746i
$339$		0			0
$340$	36.7004	+	24.7156i	1.99036	+	1.34039i
$341$		−	0.247700i		−	0.0134137i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−23.1603	+	3.69437i	−1.24872	+	0.199187i
$345$		0			0
$346$	11.8518	+	3.61871i	0.637157	+	0.194543i
$347$	2.10127	+	3.63950i	0.112802	+	0.195379i	0.916899	−	0.399119i	$-0.130684\pi$
$347$	2.10127	+	3.63950i	0.112802	+	0.195379i	−0.804097	+	0.594498i	$0.797351\pi$
$348$		0			0
$349$	−17.6897	+	30.6395i	−0.946908	+	1.64009i	−0.195023	+	0.980799i	$0.562478\pi$
$349$	−17.6897	+	30.6395i	−0.946908	+	1.64009i	−0.751885	+	0.659294i	$0.770855\pi$
$350$	3.57190	−	3.33331i	0.190926	−	0.178173i
$351$		0			0
$352$	7.70540	+	10.9616i	0.410699	+	0.584255i
$353$	−25.9389	−	14.9758i	−1.38059	−	0.797082i	−0.388358	−	0.921509i	$-0.626958\pi$
$353$	−25.9389	−	14.9758i	−1.38059	−	0.797082i	−0.992229	+	0.124426i	$0.960291\pi$
$354$		0			0
$355$	−3.65716	+	2.11146i	−0.194102	+	0.112065i
$356$	−12.8888	−	26.3767i	−0.683103	−	1.39796i
$357$		0			0
$358$	3.96420	−	0.916740i	0.209514	−	0.0484512i
$359$	5.48093			0.289272			0.144636	−	0.989485i	$-0.453799\pi$
$359$	5.48093			0.289272			0.144636	+	0.989485i	$0.453799\pi$
$360$		0			0
$361$	12.1921			0.641689
$362$	6.65499	−	1.53900i	0.349779	−	0.0808880i
$363$		0			0
$364$	0.221118	+	0.452516i	0.0115897	+	0.0237183i
$365$	−10.2445	+	5.91465i	−0.536221	+	0.309587i
$366$		0			0
$367$	14.7364	+	8.50804i	0.769232	+	0.444116i	0.832601	−	0.553874i	$-0.186851\pi$
$367$	14.7364	+	8.50804i	0.769232	+	0.444116i	−0.0633686	+	0.997990i	$0.520184\pi$
$368$	35.7896	+	4.97635i	1.86566	+	0.259410i
$369$		0			0
$370$	−9.47789	+	8.84478i	−0.492732	+	0.459818i
$371$	1.19339	−	2.06701i	0.0619577	−	0.107314i
$372$		0			0
$373$	−0.570268	−	0.987733i	−0.0295274	−	0.0511429i	0.850884	−	0.525353i	$-0.176067\pi$
$373$	−0.570268	−	0.987733i	−0.0295274	−	0.0511429i	−0.880411	+	0.474211i	$0.842734\pi$
$374$	24.3757	+	7.44262i	1.26044	+	0.384849i
$375$		0			0
$376$	0.221238	+	1.38696i	0.0114095	+	0.0715269i
$377$		−	1.60933i		−	0.0828847i
$378$		0			0
$379$		−	26.5456i		−	1.36356i	−0.731559	−	0.681778i	$-0.761207\pi$
$379$		−	26.5456i		−	1.36356i	0.731559	−	0.681778i	$-0.238793\pi$
$380$	−12.5856	−	8.47567i	−0.645628	−	0.434793i
$381$		0			0
$382$	−8.47301	+	27.7504i	−0.433517	+	1.41983i
$383$	17.3272	+	30.0116i	0.885380	+	1.53352i	0.845277	+	0.534328i	$0.179435\pi$
$383$	17.3272	+	30.0116i	0.885380	+	1.53352i	0.0401027	+	0.999196i	$0.487231\pi$
$384$		0			0
$385$	3.44359	−	5.96447i	0.175502	−	0.303978i
$386$	17.9446	+	19.2290i	0.913354	+	0.978732i
$387$		0			0
$388$	0.795344	−	11.4952i	0.0403775	−	0.583578i
$389$	−10.2165	−	5.89849i	−0.517996	−	0.299065i	0.218118	−	0.975922i	$-0.430008\pi$
$389$	−10.2165	−	5.89849i	−0.517996	−	0.299065i	−0.736114	+	0.676857i	$0.763341\pi$
$390$		0			0
$391$	59.5237	−	34.3660i	3.01024	−	1.73796i
$392$	−2.64168	−	1.01071i	−0.133425	−	0.0510486i
$393$		0			0
$394$	−5.49716	−	23.7710i	−0.276943	−	1.19757i
$395$	−33.6991			−1.69558
$396$		0			0
$397$	−13.5577			−0.680441			−0.340221	−	0.940346i	$-0.610502\pi$
$397$	−13.5577			−0.680441			−0.340221	+	0.940346i	$0.610502\pi$
$398$	0.373502	+	1.61511i	0.0187220	+	0.0809583i
$399$		0			0
$400$	−5.19536	−	12.8048i	−0.259768	−	0.640241i
$401$	5.39384	−	3.11414i	0.269356	−	0.155513i	−0.359239	−	0.933246i	$-0.616964\pi$
$401$	5.39384	−	3.11414i	0.269356	−	0.155513i	0.628595	+	0.777733i	$0.283630\pi$
$402$		0			0
$403$	−0.0228067	−	0.0131675i	−0.00113609	−	0.000655919i
$404$	28.7913	+	1.99206i	1.43242	+	0.0991085i
$405$		0			0
$406$	6.16617	+	6.60754i	0.306022	+	0.327927i
$407$	−3.73364	+	6.46686i	−0.185070	+	0.320550i
$408$		0			0
$409$	−0.409311	−	0.708947i	−0.0202391	−	0.0350552i	0.855728	−	0.517425i	$-0.173109\pi$
$409$	−0.409311	−	0.708947i	−0.0202391	−	0.0350552i	−0.875968	+	0.482370i	$0.839776\pi$
$410$	10.0414	−	32.8871i	0.495910	−	1.62418i
$411$		0			0
$412$	13.3907	−	19.8840i	0.659712	−	0.979613i
$413$		−	7.98974i		−	0.393149i
$414$		0			0
$415$		−	2.55640i		−	0.125489i
$416$	1.41889	−	0.126760i	0.0695667	−	0.00621491i
$417$		0			0
$418$	−8.35911	−	2.55228i	−0.408857	−	0.124836i
$419$	7.99122	+	13.8412i	0.390397	+	0.676187i	0.992502	−	0.122230i	$-0.0390045\pi$
$419$	7.99122	+	13.8412i	0.390397	+	0.676187i	−0.602105	+	0.798417i	$0.705671\pi$
$420$		0			0
$421$	−4.02490	+	6.97133i	−0.196161	+	0.339762i	−0.947281	−	0.320405i	$-0.896181\pi$
$421$	−4.02490	+	6.97133i	−0.196161	+	0.339762i	0.751119	+	0.660167i	$0.229514\pi$
$422$	−10.5200	+	9.81723i	−0.512103	+	0.477896i
$423$		0			0
$424$	−4.25421	−	5.24170i	−0.206603	−	0.254559i
$425$	−22.7636	−	13.1426i	−1.10420	−	0.637508i
$426$		0			0
$427$	−6.40151	+	3.69592i	−0.309791	+	0.178858i
$428$	10.9676	−	5.35921i	0.530138	−	0.259047i
$429$		0			0
$430$	33.2205	−	7.68239i	1.60203	−	0.370478i
$431$	−32.4604			−1.56356			−0.781780	−	0.623554i	$-0.785688\pi$
$431$	−32.4604			−1.56356			−0.781780	+	0.623554i	$0.785688\pi$
$432$		0			0
$433$	−18.4266			−0.885525			−0.442762	−	0.896639i	$-0.646001\pi$
$433$	−18.4266			−0.885525			−0.442762	+	0.896639i	$0.646001\pi$
$434$	0.144091	−	0.0333216i	0.00691657	−	0.00159949i
$435$		0			0
$436$	11.2400	−	5.49235i	0.538301	−	0.263036i
$437$	−20.4123	+	11.7851i	−0.976455	+	0.563756i
$438$		0			0
$439$	−31.5605	−	18.2214i	−1.50630	−	0.869662i	−0.999973	−	0.00731896i	$-0.997670\pi$
$439$	−31.5605	−	18.2214i	−1.50630	−	0.869662i	−0.506325	−	0.862343i	$-0.668996\pi$
$440$	−12.2757	−	15.1252i	−0.585223	−	0.721066i
$441$		0			0
$442$	1.98106	−	1.84872i	0.0942293	−	0.0879349i
$443$	11.3610	−	19.6778i	0.539776	−	0.934919i	−0.459140	−	0.888364i	$-0.651842\pi$
$443$	11.3610	−	19.6778i	0.539776	−	0.934919i	0.998916	−	0.0465549i	$-0.0148243\pi$
$444$		0			0
$445$	21.3405	+	36.9628i	1.01164	+	1.75221i
$446$	8.24745	+	2.51819i	0.390528	+	0.119240i
$447$		0			0
$448$	−5.33994	+	5.95693i	−0.252289	+	0.281438i
$449$			9.26171i			0.437087i	0.975827	+	0.218544i	$0.0701306\pi$
$449$			9.26171i			0.437087i	−0.975827	+	0.218544i	$0.929869\pi$
$450$		0			0
$451$		−	19.8066i		−	0.932658i
$452$	−20.4982	+	30.4380i	−0.964155	+	1.43168i
$453$		0			0
$454$	9.21614	−	30.1842i	0.432535	−	1.41662i
$455$	−0.366115	−	0.634129i	−0.0171637	−	0.0297284i
$456$		0			0
$457$	5.90082	−	10.2205i	0.276029	−	0.478096i	−0.694365	−	0.719623i	$-0.744315\pi$
$457$	5.90082	−	10.2205i	0.276029	−	0.478096i	0.970394	+	0.241527i	$0.0776482\pi$
$458$	5.22758	+	5.60177i	0.244269	+	0.261753i
$459$		0			0
$460$	−52.4079	−	3.62607i	−2.44353	−	0.169066i
$461$	−2.21744	−	1.28024i	−0.103276	−	0.0596266i	0.447472	−	0.894298i	$-0.352324\pi$
$461$	−2.21744	−	1.28024i	−0.103276	−	0.0596266i	−0.550749	+	0.834671i	$0.685658\pi$
$462$		0			0
$463$	−10.0234	+	5.78704i	−0.465829	+	0.268947i	−0.714492	−	0.699643i	$-0.753342\pi$
$463$	−10.0234	+	5.78704i	−0.465829	+	0.268947i	0.248663	+	0.968590i	$0.420009\pi$
$464$	23.6872	−	9.61072i	1.09965	−	0.446166i
$465$		0			0
$466$	−1.93790	−	8.37995i	−0.0897716	−	0.388194i
$467$	0.571766			0.0264582			0.0132291	−	0.999912i	$-0.495789\pi$
$467$	0.571766			0.0264582			0.0132291	+	0.999912i	$0.495789\pi$
$468$		0			0
$469$	0.512806			0.0236792
$470$	−0.460061	−	1.98941i	−0.0212210	−	0.0917648i
$471$		0			0
$472$	−21.1063	−	8.07531i	−0.971497	−	0.371696i
$473$	17.0090	−	9.82016i	0.782076	−	0.451532i
$474$		0			0
$475$	7.80627	+	4.50695i	0.358176	+	0.206793i
$476$	−1.05036	+	15.1809i	−0.0481430	+	0.695815i
$477$		0			0
$478$	8.85578	+	9.48967i	0.405054	+	0.434048i
$479$	13.9036	−	24.0818i	0.635273	−	1.10033i	−0.351184	−	0.936306i	$-0.614221\pi$
$479$	13.9036	−	24.0818i	0.635273	−	1.10033i	0.986457	−	0.164019i	$-0.0524457\pi$
$480$		0			0
$481$	0.396953	+	0.687542i	0.0180995	+	0.0313492i
$482$	3.79969	−	12.4446i	0.173071	−	0.566834i
$483$		0			0
$484$	8.94094	+	6.02120i	0.406407	+	0.273691i
$485$			16.7521i			0.760676i
$486$		0			0
$487$			10.3286i			0.468031i	0.972233	+	0.234016i	$0.0751867\pi$
$487$			10.3286i			0.468031i	−0.972233	+	0.234016i	$0.924813\pi$
$488$	3.29334	+	20.6462i	0.149083	+	0.934611i
$489$		0			0
$490$	3.93286	+	1.20082i	0.177668	+	0.0542474i
$491$	−16.9157	−	29.2988i	−0.763394	−	1.32224i	−0.941091	−	0.338153i	$-0.890198\pi$
$491$	−16.9157	−	29.2988i	−0.763394	−	1.32224i	0.177697	−	0.984085i	$-0.443135\pi$
$492$		0			0
$493$	24.3120	−	42.1096i	1.09496	−	1.89652i
$494$	−0.679360	+	0.633979i	−0.0305658	+	0.0285241i
$495$		0			0
$496$	0.0576089	−	0.414320i	0.00258672	−	0.0186035i
$497$	−1.25776	−	0.726166i	−0.0564181	−	0.0325730i
$498$		0			0
$499$	5.27446	−	3.04521i	0.236117	−	0.136322i	−0.377274	−	0.926102i	$-0.623138\pi$
$499$	5.27446	−	3.04521i	0.236117	−	0.136322i	0.613391	+	0.789779i	$0.289805\pi$
$500$	−3.94544	−	8.07431i	−0.176445	−	0.361094i
$501$		0			0
$502$	−24.2187	+	5.60068i	−1.08093	+	0.249971i
$503$	21.4710			0.957345			0.478673	−	0.877993i	$-0.341118\pi$
$503$	21.4710			0.957345			0.478673	+	0.877993i	$0.341118\pi$
$504$		0			0
$505$	−41.9582			−1.86712
$506$	−29.4816	+	6.81775i	−1.31062	+	0.303086i
$507$		0			0
$508$	11.9272	+	24.4088i	0.529183	+	1.08297i
$509$	18.4897	−	10.6750i	0.819540	−	0.473161i	−0.0307180	−	0.999528i	$-0.509779\pi$
$509$	18.4897	−	10.6750i	0.819540	−	0.473161i	0.850258	+	0.526367i	$0.176446\pi$
$510$		0			0
$511$	−3.52324	−	2.03414i	−0.155859	−	0.0899851i
$512$	10.3392	+	20.1271i	0.456930	+	0.889503i
$513$		0			0
$514$	−11.1798	+	10.4330i	−0.493119	+	0.460179i
$515$	−17.4262	+	30.1830i	−0.767890	+	1.33002i
$516$		0			0
$517$	−0.588082	−	1.01859i	−0.0258638	−	0.0447974i
$518$	−4.26412	−	1.30196i	−0.187355	−	0.0572050i
$519$		0			0
$520$	−2.04520	+	0.326236i	−0.0896880	+	0.0143064i
$521$		−	30.4799i		−	1.33535i	−0.744453	−	0.667675i	$-0.767290\pi$
$521$		−	30.4799i		−	1.33535i	0.744453	−	0.667675i	$-0.232710\pi$
$522$		0			0
$523$		−	28.4494i		−	1.24401i	−0.783014	−	0.622004i	$-0.786319\pi$
$523$		−	28.4494i		−	1.24401i	0.783014	−	0.622004i	$-0.213681\pi$
$524$	2.45685	+	1.65455i	0.107328	+	0.0722791i
$525$		0			0
$526$	−1.01879	+	3.33669i	−0.0444213	+	0.145486i
$527$	−0.397839	−	0.689078i	−0.0173302	−	0.0300167i
$528$		0			0
$529$	−29.3019	+	50.7524i	−1.27400	+	2.20663i
$530$	6.69622	+	7.17553i	0.290865	+	0.311685i
$531$		0			0
$532$	0.360197	−	5.20595i	0.0156165	−	0.225706i
$533$	−1.82367	−	1.05290i	−0.0789921	−	0.0456061i
$534$		0			0
$535$	−15.3693	+	8.87348i	−0.664474	+	0.383634i
$536$	0.518299	−	1.35467i	0.0223871	−	0.0585128i
$537$		0			0
$538$	−5.93989	−	25.6855i	−0.256087	−	1.10738i
$539$	2.36861			0.102023
$540$		0			0
$541$	28.9747			1.24572			0.622861	−	0.782333i	$-0.285970\pi$
$541$	28.9747			1.24572			0.622861	+	0.782333i	$0.285970\pi$
$542$	−3.79567	−	16.4134i	−0.163038	−	0.705015i
$543$		0			0
$544$	39.0414	+	18.1182i	1.67389	+	0.776811i
$545$	−15.7512	+	9.09393i	−0.674705	+	0.389541i
$546$		0			0
$547$	32.0274	+	18.4910i	1.36939	+	0.790619i	0.990850	−	0.134966i	$-0.0430924\pi$
$547$	32.0274	+	18.4910i	1.36939	+	0.790619i	0.378541	+	0.925584i	$0.376426\pi$
$548$	−35.8764	−	2.48227i	−1.53257	−	0.106037i
$549$		0			0
$550$	7.89529	+	8.46044i	0.336656	+	0.360754i
$551$	−8.33725	+	14.4405i	−0.355179	+	0.615188i
$552$		0			0
$553$	−5.79482	−	10.0369i	−0.246421	−	0.426813i
$554$	−7.29342	+	23.8870i	−0.309868	+	1.01486i
$555$		0			0
$556$	−9.30470	+	13.8166i	−0.394607	+	0.585956i
$557$		−	4.29428i		−	0.181955i	−0.995853	−	0.0909773i	$-0.971001\pi$
$557$		−	4.29428i		−	0.181955i	0.995853	−	0.0909773i	$-0.0289991\pi$
$558$		0			0
$559$		−	2.08812i		−	0.0883179i
$560$	7.14715	−	9.17567i	0.302022	−	0.387743i
$561$		0			0
$562$	−25.8717	−	7.89938i	−1.09133	−	0.333215i
$563$	2.78657	+	4.82649i	0.117440	+	0.203412i	0.918753	−	0.394834i	$-0.129198\pi$
$563$	2.78657	+	4.82649i	0.117440	+	0.203412i	−0.801312	+	0.598246i	$0.795865\pi$
$564$		0			0
$565$	26.6757	−	46.2037i	1.12225	−	1.94380i
$566$	−3.35535	+	3.13122i	−0.141036	+	0.131615i
$567$		0			0
$568$	−3.18952	+	2.58864i	−0.133829	+	0.108617i
$569$	5.72734	+	3.30668i	0.240103	+	0.138623i	0.615224	−	0.788352i	$-0.289066\pi$
$569$	5.72734	+	3.30668i	0.240103	+	0.138623i	−0.375121	+	0.926976i	$0.622399\pi$
$570$		0			0
$571$	−28.7640	+	16.6069i	−1.20374	+	0.694978i	−0.961384	−	0.275211i	$-0.911252\pi$
$571$	−28.7640	+	16.6069i	−1.20374	+	0.694978i	−0.242353	+	0.970188i	$0.577919\pi$
$572$	−1.07183	+	0.523741i	−0.0448156	+	0.0218987i
$573$		0			0
$574$	11.5218	−	2.66447i	0.480910	−	0.111213i
$575$	31.2077			1.30145
$576$		0			0
$577$	27.6524			1.15119			0.575593	−	0.817736i	$-0.304771\pi$
$577$	27.6524			1.15119			0.575593	+	0.817736i	$0.304771\pi$
$578$	56.3411	−	13.0292i	2.34348	−	0.541941i
$579$		0			0
$580$	−33.3910	+	16.3162i	−1.38648	+	0.677494i
$581$	0.761398	−	0.439593i	0.0315881	−	0.0182374i
$582$		0			0
$583$	4.89594	+	2.82667i	0.202769	+	0.117069i
$584$	−8.93452	+	7.25133i	−0.369713	+	0.300062i
$585$		0			0
$586$	13.2872	−	12.3996i	0.548890	−	0.512225i
$587$	−12.0238	+	20.8258i	−0.496274	+	0.859571i	−0.999991	−	0.00429733i	$-0.998632\pi$
$587$	−12.0238	+	20.8258i	−0.496274	+	0.859571i	0.503717	+	0.863869i	$0.331965\pi$
$588$		0			0
$589$	0.136430	+	0.236304i	0.00562151	+	0.00973674i
$590$	31.4225	+	9.59422i	1.29364	+	0.394988i
$591$		0			0
$592$	−7.74916	+	9.94853i	−0.318489	+	0.408882i
$593$		−	7.02971i		−	0.288675i	−0.989528	−	0.144338i	$-0.953895\pi$
$593$		−	7.02971i		−	0.288675i	0.989528	−	0.144338i	$-0.0461052\pi$
$594$		0			0
$595$		−	22.1234i		−	0.906972i
$596$	3.69909	−	5.49282i	0.151521	−	0.224995i
$597$		0			0
$598$	−0.939471	+	3.07691i	−0.0384178	+	0.125824i
$599$	14.7689	+	25.5804i	0.603439	+	1.04519i	0.992296	+	0.123889i	$0.0395366\pi$
$599$	14.7689	+	25.5804i	0.603439	+	1.04519i	−0.388857	+	0.921298i	$0.627130\pi$
$600$		0			0
$601$	−11.2326	+	19.4555i	−0.458188	+	0.793605i	−0.998865	−	0.0476250i	$-0.984835\pi$
$601$	−11.2326	+	19.4555i	−0.458188	+	0.793605i	0.540677	+	0.841230i	$0.318168\pi$
$602$	8.00064	+	8.57333i	0.326082	+	0.349423i
$603$		0			0
$604$	−12.4240	−	0.859610i	−0.505526	−	0.0349770i
$605$	−13.5720	−	7.83579i	−0.551780	−	0.318570i
$606$		0			0
$607$	−31.5236	+	18.2002i	−1.27950	+	0.738722i	−0.976757	−	0.214348i	$-0.931237\pi$
$607$	−31.5236	+	18.2002i	−1.27950	+	0.738722i	−0.302748	+	0.953071i	$0.597904\pi$
$608$	−13.3884	−	6.21323i	−0.542971	−	0.251980i
$609$		0			0
$610$	−6.84846	−	29.6144i	−0.277286	−	1.19905i
$611$	−0.125047			−0.00505886
$612$		0			0
$613$	12.8571			0.519293			0.259646	−	0.965704i	$-0.416394\pi$
$613$	12.8571			0.519293			0.259646	+	0.965704i	$0.416394\pi$
$614$	−5.64036	−	24.3903i	−0.227626	−	0.984310i
$615$		0			0
$616$	2.39398	−	6.25710i	0.0964561	−	0.252106i
$617$	37.5894	−	21.7022i	1.51329	−	0.873699i	0.513412	−	0.858142i	$-0.328381\pi$
$617$	37.5894	−	21.7022i	1.51329	−	0.873699i	0.999879	−	0.0155564i	$-0.00495195\pi$
$618$		0			0
$619$	0.893596	+	0.515918i	0.0359167	+	0.0207365i	0.517851	−	0.855471i	$-0.326732\pi$
$619$	0.893596	+	0.515918i	0.0359167	+	0.0207365i	−0.481934	+	0.876207i	$0.660066\pi$
$620$	−0.0419773	+	0.606701i	−0.00168585	+	0.0243657i
$621$		0			0
$622$	−6.37480	−	6.83111i	−0.255606	−	0.273903i
$623$	−7.33933	+	12.7121i	−0.294044	+	0.509299i
$624$		0			0
$625$	15.1693	+	26.2740i	0.606772	+	1.05096i
$626$	−4.41157	+	14.4486i	−0.176322	+	0.577480i
$627$		0			0
$628$	4.94057	+	3.32719i	0.197150	+	0.132769i
$629$			23.9869i			0.956420i
$630$		0			0
$631$			25.4447i			1.01294i	0.862258	+	0.506469i	$0.169049\pi$
$631$			25.4447i			1.01294i	−0.862258	+	0.506469i	$0.830951\pi$
$632$	−32.3712	+	5.16363i	−1.28766	+	0.205398i
$633$		0			0
$634$	−34.5275	−	10.5423i	−1.37126	−	0.418686i
$635$	−19.7483	−	34.2051i	−0.783689	−	1.35739i
$636$		0			0
$637$	0.125913	−	0.218087i	0.00498884	−	0.00864092i
$638$	−15.6507	+	14.6052i	−0.619616	+	0.578227i
$639$		0			0
$640$	−17.0155	−	28.1544i	−0.672595	−	1.11290i
$641$	24.3065	+	14.0334i	0.960049	+	0.554284i	0.896188	−	0.443674i	$-0.146325\pi$
$641$	24.3065	+	14.0334i	0.960049	+	0.554284i	0.0638607	+	0.997959i	$0.479659\pi$
$642$		0			0
$643$	−11.1062	+	6.41216i	−0.437985	+	0.252871i	−0.702743	−	0.711444i	$-0.748041\pi$
$643$	−11.1062	+	6.41216i	−0.437985	+	0.252871i	0.264757	+	0.964315i	$0.414708\pi$
$644$	−7.93195	−	16.2327i	−0.312563	−	0.639657i
$645$		0			0
$646$	−27.3535	+	6.32563i	−1.07621	+	0.248878i
$647$	−39.1711			−1.53998			−0.769988	−	0.638058i	$-0.779738\pi$
$647$	−39.1711			−1.53998			−0.769988	+	0.638058i	$0.779738\pi$
$648$		0			0
$649$	18.9246			0.742854
$650$	1.19869	−	0.277203i	0.0470165	−	0.0108728i
$651$		0			0
$652$	−7.28207	−	14.9027i	−0.285188	−	0.583634i
$653$	−5.09574	+	2.94203i	−0.199412	+	0.115130i	−0.596381	−	0.802701i	$-0.703395\pi$
$653$	−5.09574	+	2.94203i	−0.199412	+	0.115130i	0.396969	+	0.917832i	$0.370062\pi$
$654$		0			0
$655$	−3.72940	−	2.15317i	−0.145720	−	0.0841313i
$656$	4.60652	−	33.1298i	0.179855	−	1.29350i
$657$		0			0
$658$	0.513415	−	0.479119i	0.0200150	−	0.0186780i
$659$	−12.9730	+	22.4699i	−0.505357	+	0.875304i	0.494624	+	0.869107i	$0.335306\pi$
$659$	−12.9730	+	22.4699i	−0.505357	+	0.875304i	−0.999981	+	0.00619658i	$0.998028\pi$
$660$		0			0
$661$	−19.8403	−	34.3644i	−0.771699	−	1.33662i	−0.936631	−	0.350316i	$-0.886074\pi$
$661$	−19.8403	−	34.3644i	−0.771699	−	1.33662i	0.164933	−	0.986305i	$-0.447259\pi$
$662$	−36.0655	−	11.0119i	−1.40173	−	0.427988i
$663$		0			0
$664$	−0.391711	−	2.45567i	−0.0152013	−	0.0952985i
$665$			7.58674i			0.294201i
$666$		0			0
$667$			57.7300i			2.23531i
$668$	−31.0204	−	20.8904i	−1.20021	−	0.808274i
$669$		0			0
$670$	−0.615787	+	2.01679i	−0.0237899	+	0.0779156i
$671$	−8.75417	−	15.1627i	−0.337951	−	0.585349i
$672$		0			0
$673$	5.16943	−	8.95371i	0.199267	−	0.345140i	−0.749024	−	0.662543i	$-0.769477\pi$
$673$	5.16943	−	8.95371i	0.199267	−	0.345140i	0.948291	+	0.317403i	$0.102811\pi$
$674$	−6.12032	−	6.55842i	−0.235746	−	0.252621i
$675$		0			0
$676$	1.78588	−	25.8115i	0.0686877	−	0.992748i
$677$	4.67459	+	2.69887i	0.179659	+	0.103726i	0.587132	−	0.809491i	$-0.300257\pi$
$677$	4.67459	+	2.69887i	0.179659	+	0.103726i	−0.407473	+	0.913217i	$0.633590\pi$
$678$		0			0
$679$	−4.98945	+	2.88066i	−0.191478	+	0.110550i
$680$	−58.4430	−	22.3604i	−2.24119	−	0.857481i
$681$		0			0
$682$	0.0789259	+	0.341294i	0.00302223	+	0.0130688i
$683$	39.2840			1.50316			0.751581	−	0.659641i	$-0.229292\pi$
$683$	39.2840			1.50316			0.751581	+	0.659641i	$0.229292\pi$
$684$		0			0
$685$	52.2835			1.99765
$686$	0.318634	+	1.37785i	0.0121655	+	0.0526066i
$687$		0			0
$688$	30.7343	−	12.4700i	1.17173	−	0.475413i
$689$	0.520525	−	0.300525i	0.0198304	−	0.0114491i
$690$		0			0
$691$	15.8640	+	9.15909i	0.603495	+	0.348428i	0.770415	−	0.637542i	$-0.220049\pi$
$691$	15.8640	+	9.15909i	0.603495	+	0.348428i	−0.166920	+	0.985970i	$0.553382\pi$
$692$	−17.4831	−	1.20964i	−0.664606	−	0.0459837i
$693$		0			0
$694$	−4.05490	−	4.34515i	−0.153922	−	0.164940i
$695$	12.1088	−	20.9731i	0.459314	−	0.795555i
$696$		0			0
$697$	−31.8120	−	55.1001i	−1.20497	−	2.08706i
$698$	14.6110	−	47.8532i	0.553034	−	1.81127i
$699$		0			0
$700$	−3.85944	+	5.73093i	−0.145873	+	0.216609i
$701$		−	14.7290i		−	0.556306i	−0.960537	−	0.278153i	$-0.910278\pi$
$701$		−	14.7290i		−	0.556306i	0.960537	−	0.278153i	$-0.0897222\pi$
$702$		0			0
$703$		−	8.22577i		−	0.310241i
$704$	−14.1096	−	12.6482i	−0.531777	−	0.476698i
$705$		0			0
$706$	40.5117	+	12.3694i	1.52468	+	0.465529i
$707$	−7.21504	−	12.4968i	−0.271349	−	0.469991i
$708$		0			0
$709$	−0.246081	+	0.426224i	−0.00924175	+	0.0160072i	−0.870609	−	0.491975i	$-0.836275\pi$
$709$	−0.246081	+	0.426224i	−0.00924175	+	0.0160072i	0.861368	+	0.507982i	$0.169608\pi$
$710$	4.36624	−	4.07458i	0.163862	−	0.152916i
$711$		0			0
$712$	26.1633	+	32.2364i	0.980512	+	1.20811i
$713$	0.818125	+	0.472345i	0.0306390	+	0.0176894i
$714$		0			0
$715$	1.50200	−	0.867182i	0.0561718	−	0.0324308i
$716$	−5.16997	+	2.52626i	−0.193211	+	0.0944108i
$717$		0			0
$718$	−7.55190	+	1.74641i	−0.281834	+	0.0651755i
$719$	−7.89549			−0.294452			−0.147226	−	0.989103i	$-0.547034\pi$
$719$	−7.89549			−0.294452			−0.147226	+	0.989103i	$0.547034\pi$
$720$		0			0
$721$	−11.9863			−0.446392
$722$	−16.7989	+	3.88482i	−0.625189	+	0.144578i
$723$		0			0
$724$	−8.67921	+	4.24102i	−0.322560	+	0.157616i
$725$	19.1198	−	11.0388i	0.710091	−	0.409971i
$726$		0			0
$727$	−9.22490	−	5.32600i	−0.342133	−	0.197530i	0.319082	−	0.947727i	$-0.396625\pi$
$727$	−9.22490	−	5.32600i	−0.342133	−	0.197530i	−0.661215	+	0.750197i	$0.729959\pi$
$728$	−0.448854	−	0.553043i	−0.0166357	−	0.0204971i
$729$		0			0
$730$	12.2308	−	11.4138i	0.452681	−	0.422442i
$731$	31.5449	−	54.6374i	1.16673	−	2.02084i
$732$		0			0
$733$	26.0962	+	45.1999i	0.963885	+	1.66950i	0.712581	+	0.701590i	$0.247526\pi$
$733$	26.0962	+	45.1999i	0.963885	+	1.66950i	0.251304	+	0.967908i	$0.419141\pi$
$734$	−23.0155	−	7.02730i	−0.849516	−	0.259382i
$735$		0			0
$736$	−50.8984	+	4.54714i	−1.87614	+	0.167610i
$737$			1.21464i			0.0447417i
$738$		0			0
$739$		−	34.1328i		−	1.25560i	−0.778376	−	0.627798i	$-0.783956\pi$
$739$		−	34.1328i		−	1.25560i	0.778376	−	0.627798i	$-0.216044\pi$
$740$	10.2409	−	15.2068i	0.376462	−	0.559012i
$741$		0			0
$742$	−0.985691	+	3.22829i	−0.0361859	+	0.118514i
$743$	7.11347	+	12.3209i	0.260968	+	0.452009i	0.966499	−	0.256669i	$-0.0826250\pi$
$743$	7.11347	+	12.3209i	0.260968	+	0.452009i	−0.705532	+	0.708678i	$0.749292\pi$
$744$		0			0
$745$	−4.81387	+	8.33787i	−0.176367	+	0.305476i
$746$	1.10047	+	1.17924i	0.0402911	+	0.0431751i
$747$		0			0
$748$	−35.9576	−	2.48788i	−1.31474	−	0.0909660i
$749$	−5.28575	−	3.05173i	−0.193137	−	0.111508i
$750$		0			0
$751$	−27.8733	+	16.0926i	−1.01711	+	0.587228i	−0.913265	−	0.407365i	$-0.866448\pi$
$751$	−27.8733	+	16.0926i	−1.01711	+	0.587228i	−0.103844	+	0.994594i	$0.533114\pi$
$752$	−0.746765	−	1.84053i	−0.0272317	−	0.0671171i
$753$		0			0
$754$	0.512788	+	2.21742i	0.0186746	+	0.0807536i
$755$	18.1058			0.658936
$756$		0			0
$757$	−33.8024			−1.22857			−0.614284	−	0.789085i	$-0.710555\pi$
$757$	−33.8024			−1.22857			−0.614284	+	0.789085i	$0.710555\pi$
$758$	8.45835	+	36.5759i	0.307221	+	1.32850i
$759$		0			0
$760$	20.0417	+	7.66800i	0.726990	+	0.278147i
$761$	−7.39633	+	4.27027i	−0.268117	+	0.154797i	−0.628031	−	0.778188i	$-0.716139\pi$
$761$	−7.39633	+	4.27027i	−0.268117	+	0.154797i	0.359915	+	0.932985i	$0.382806\pi$
$762$		0			0
$763$	−5.41707	−	3.12754i	−0.196111	−	0.113225i
$764$	2.83232	−	40.9357i	0.102470	−	1.48100i
$765$		0			0
$766$	−33.4371	−	35.8305i	−1.20813	−	1.29461i
$767$	1.00601	−	1.74246i	0.0363249	−	0.0629165i
$768$		0			0
$769$	−13.0938	−	22.6792i	−0.472176	−	0.817833i	0.527317	−	0.849669i	$-0.323198\pi$
$769$	−13.0938	−	22.6792i	−0.472176	−	0.817833i	−0.999493	+	0.0318354i	$0.989865\pi$
$770$	−2.84427	+	9.31540i	−0.102500	+	0.335704i
$771$		0			0
$772$	−30.8519	−	20.7770i	−1.11039	−	0.747780i
$773$		−	3.16655i		−	0.113893i	−0.998377	−	0.0569464i	$-0.981864\pi$
$773$		−	3.16655i		−	0.113893i	0.998377	−	0.0569464i	$-0.0181364\pi$
$774$		0			0
$775$		−	0.361277i		−	0.0129774i
$776$	2.56689	+	16.0920i	0.0921459	+	0.577671i
$777$		0			0
$778$	15.9562	+	4.87191i	0.572059	+	0.174667i
$779$	10.9092	+	18.8954i	0.390864	+	0.676996i
$780$		0			0
$781$	1.72000	−	2.97913i	0.0615465	−	0.106602i
$782$	−71.0646	+	66.3176i	−2.54126	+	2.37151i
$783$		0			0
$784$	3.96189	+	0.550878i	0.141496	+	0.0196742i
$785$	−7.49959	−	4.32989i	−0.267672	−	0.154540i
$786$		0			0
$787$	−6.34026	+	3.66055i	−0.226006	+	0.130485i	−0.608728	−	0.793379i	$-0.708320\pi$
$787$	−6.34026	+	3.66055i	−0.226006	+	0.130485i	0.382722	+	0.923863i	$0.374987\pi$
$788$	15.1485	+	31.0013i	0.539644	+	1.10438i
$789$		0			0
$790$	46.4323	−	10.7377i	1.65199	−	0.382030i
$791$	18.3484			0.652393
$792$		0			0
$793$	−1.86145			−0.0661020
$794$	18.6805	−	4.31995i	0.662945	−	0.153309i
$795$		0			0
$796$	−1.02926	−	2.10637i	−0.0364812	−	0.0746584i
$797$	10.8713	−	6.27653i	0.385080	−	0.222326i	−0.294946	−	0.955514i	$-0.595302\pi$
$797$	10.8713	−	6.27653i	0.385080	−	0.222326i	0.680026	+	0.733188i	$0.261968\pi$
$798$		0			0
$799$	−3.27197	−	1.88907i	−0.115754	−	0.0668306i
$800$	11.2385	+	15.9877i	0.397341	+	0.565251i
$801$		0			0
$802$	−6.43964	+	6.00948i	−0.227392	+	0.212202i
$803$	4.81808	−	8.34517i	0.170026	−	0.294494i
$804$		0			0
$805$	13.1333	+	22.7475i	0.462888	+	0.801745i
$806$	0.0356199	+	0.0108758i	0.00125466	+	0.000383084i
$807$		0			0
$808$	−40.3049	+	6.42915i	−1.41792	+	0.226177i
$809$		−	42.4323i		−	1.49184i	−0.666036	−	0.745920i	$-0.732010\pi$
$809$		−	42.4323i		−	1.49184i	0.666036	−	0.745920i	$-0.267990\pi$
$810$		0			0
$811$			52.0205i			1.82669i	0.407192	+	0.913343i	$0.366508\pi$
$811$			52.0205i			1.82669i	−0.407192	+	0.913343i	$0.633492\pi$
$812$	−10.6014	−	7.13945i	−0.372038	−	0.250546i
$813$		0			0
$814$	3.08384	−	10.1000i	0.108088	−	0.354006i
$815$	12.0572	+	20.8838i	0.422347	+	0.731526i
$816$		0			0
$817$	−10.8176	+	18.7367i	−0.378461	+	0.655514i
$818$	0.789864	+	0.846402i	0.0276169	+	0.0295938i
$819$		0			0
$820$	−3.35659	+	48.5131i	−0.117217	+	1.69415i
$821$	−2.93634	−	1.69530i	−0.102479	−	0.0591663i	0.447885	−	0.894091i	$-0.352178\pi$
$821$	−2.93634	−	1.69530i	−0.102479	−	0.0591663i	−0.550364	+	0.834925i	$0.685511\pi$
$822$		0			0
$823$	−16.1029	+	9.29699i	−0.561311	+	0.324073i	−0.753671	−	0.657251i	$-0.771719\pi$
$823$	−16.1029	+	9.29699i	−0.561311	+	0.324073i	0.192361	+	0.981324i	$0.438386\pi$
$824$	−12.1147	+	31.6639i	−0.422034	+	1.10306i
$825$		0			0
$826$	2.54580	+	11.0087i	0.0885799	+	0.383040i
$827$	−22.2626			−0.774145			−0.387072	−	0.922049i	$-0.626514\pi$
$827$	−22.2626			−0.774145			−0.387072	+	0.922049i	$0.626514\pi$
$828$		0			0
$829$	17.1771			0.596586			0.298293	−	0.954474i	$-0.403583\pi$
$829$	17.1771			0.596586			0.298293	+	0.954474i	$0.403583\pi$
$830$	0.814558	+	3.52234i	0.0282737	+	0.122262i
$831$		0			0
$832$	−1.91462	+	0.626762i	−0.0663777	+	0.0217291i
$833$	6.58923	−	3.80429i	0.228303	−	0.131811i
$834$		0			0
$835$	47.0877	+	27.1861i	1.62954	+	0.940813i
$836$	12.3308	+	0.853165i	0.426471	+	0.0295073i
$837$		0			0
$838$	−15.4210	−	16.5248i	−0.532709	−	0.570841i
$839$	21.6662	−	37.5270i	0.748000	−	1.29557i	−0.200780	−	0.979636i	$-0.564348\pi$
$839$	21.6662	−	37.5270i	0.748000	−	1.29557i	0.948780	−	0.315938i	$-0.102319\pi$
$840$		0			0
$841$	5.92031	+	10.2543i	0.204149	+	0.353596i
$842$	3.32440	−	10.8879i	0.114566	−	0.375222i
$843$		0			0
$844$	11.3668	−	16.8787i	0.391262	−	0.580989i
$845$			37.6156i			1.29402i
$846$		0			0
$847$		−	5.38970i		−	0.185192i
$848$	7.53185	+	5.86674i	0.258645	+	0.201465i
$849$		0			0
$850$	35.5525	+	10.8552i	1.21944	+	0.372331i
$851$	−14.2395	−	24.6636i	−0.488124	−	0.845456i
$852$		0			0
$853$	−4.55011	+	7.88103i	−0.155793	+	0.269841i	−0.933347	−	0.358974i	$-0.883127\pi$
$853$	−4.55011	+	7.88103i	−0.155793	+	0.269841i	0.777555	+	0.628816i	$0.216460\pi$
$854$	7.64268	−	7.13216i	0.261527	−	0.244058i
$855$		0			0
$856$	−13.4040	+	10.8788i	−0.458141	+	0.371831i
$857$	−12.1291	−	7.00275i	−0.414323	−	0.239209i	0.278323	−	0.960488i	$-0.410222\pi$
$857$	−12.1291	−	7.00275i	−0.414323	−	0.239209i	−0.692645	+	0.721278i	$0.743555\pi$
$858$		0			0
$859$	−15.1108	+	8.72425i	−0.515575	+	0.297668i	−0.735122	−	0.677934i	$-0.762875\pi$
$859$	−15.1108	+	8.72425i	−0.515575	+	0.297668i	0.219547	+	0.975602i	$0.429542\pi$
$860$	−43.3250	+	21.1704i	−1.47737	+	0.721904i
$861$		0			0
$862$	44.7255	−	10.3430i	1.52336	−	0.352283i
$863$	−4.26940			−0.145332			−0.0726660	−	0.997356i	$-0.523151\pi$
$863$	−4.26940			−0.145332			−0.0726660	+	0.997356i	$0.523151\pi$
$864$		0			0
$865$	25.4784			0.866293
$866$	25.3891	−	5.87134i	0.862756	−	0.199516i
$867$		0			0
$868$	−0.187918	+	0.0918245i	−0.00637835	+	0.00311673i
$869$	23.7735	−	13.7256i	0.806462	−	0.465611i
$870$		0			0
$871$	0.111836	+	0.0645688i	0.00378943	+	0.00218783i
$872$	−13.7370	+	11.1491i	−0.465195	+	0.377556i
$873$		0			0
$874$	24.3700	−	22.7421i	0.824329	−	0.769264i
$875$	−2.24668	+	3.89136i	−0.0759516	+	0.131552i
$876$		0			0
$877$	5.31547	+	9.20667i	0.179491	+	0.310887i	0.941706	−	0.336436i	$-0.109222\pi$
$877$	5.31547	+	9.20667i	0.179491	+	0.310887i	−0.762216	+	0.647323i	$0.775888\pi$
$878$	49.2916	+	15.0502i	1.66351	+	0.507919i
$879$		0			0
$880$	21.7336	+	16.9288i	0.732638	+	0.570670i
$881$		−	5.53762i		−	0.186567i	−0.995640	−	0.0932837i	$-0.970264\pi$
$881$		−	5.53762i		−	0.186567i	0.995640	−	0.0932837i	$-0.0297363\pi$
$882$		0			0
$883$		−	14.0261i		−	0.472017i	−0.971751	−	0.236009i	$-0.924161\pi$
$883$		−	14.0261i		−	0.472017i	0.971751	−	0.236009i	$-0.0758393\pi$
$884$	−2.14053	+	3.17850i	−0.0719939	+	0.106904i
$885$		0			0
$886$	−9.38370	+	30.7330i	−0.315251	+	1.03250i
$887$	−0.0103232	−	0.0178804i	−0.000346621	−	0.000600365i	0.865852	−	0.500300i	$-0.166777\pi$
$887$	−0.0103232	−	0.0178804i	−0.000346621	−	0.000600365i	−0.866199	+	0.499700i	$0.833444\pi$
$888$		0			0
$889$	6.79176	−	11.7637i	0.227788	−	0.394541i
$890$	−41.1817	−	44.1295i	−1.38041	−	1.47922i
$891$		0			0
$892$	−12.1661	−	0.841769i	−0.407353	−	0.0281845i
$893$	1.12205	+	0.647816i	0.0375480	+	0.0216783i
$894$		0			0
$895$	7.24490	−	4.18284i	0.242170	−	0.139817i
$896$	5.45956	−	9.90925i	0.182391	−	0.331045i
$897$		0			0
$898$	−2.95110	−	12.7613i	−0.0984795	−	0.425849i
$899$	0.668313			0.0222895
$900$		0			0
$901$	18.1600			0.604998
$902$	6.31107	+	27.2906i	0.210136	+	0.908677i
$903$		0			0
$904$	18.5449	−	48.4705i	0.616794	−	1.61210i
$905$	12.1625	−	7.02205i	0.404297	−	0.233421i
$906$		0			0
$907$	−40.9665	−	23.6520i	−1.36027	−	0.785353i	−0.370611	−	0.928788i	$-0.620852\pi$
$907$	−40.9665	−	23.6520i	−1.36027	−	0.785353i	−0.989660	+	0.143436i	$0.954185\pi$
$908$	−3.08072	+	44.5259i	−0.102237	+	1.47765i
$909$		0			0
$910$	0.706507	+	0.757079i	0.0234205	+	0.0250969i
$911$	14.3035	−	24.7744i	0.473897	−	0.820813i	−0.525657	−	0.850697i	$-0.676180\pi$
$911$	14.3035	−	24.7744i	0.473897	−	0.820813i	0.999553	+	0.0298838i	$0.00951371\pi$
$912$		0			0
$913$	1.04122	+	1.80345i	0.0344595	+	0.0596856i
$914$	−4.87384	+	15.9626i	−0.161212	+	0.527994i
$915$		0			0
$916$	−8.98773	−	6.05271i	−0.296963	−	0.199987i
$917$		−	1.48102i		−	0.0489075i
$918$		0			0
$919$		−	42.1651i		−	1.39090i	−0.718575	−	0.695449i	$-0.755205\pi$
$919$		−	42.1651i		−	1.39090i	0.718575	−	0.695449i	$-0.244795\pi$
$920$	73.3656	−	11.7028i	2.41879	−	0.385829i
$921$		0			0
$922$	3.46322	+	1.05742i	0.114055	+	0.0348244i
$923$	−0.182867	−	0.316734i	−0.00601913	−	0.0104254i
$924$		0			0
$925$	−5.44560	+	9.43206i	−0.179050	+	0.310124i
$926$	11.9669	−	11.1675i	0.393256	−	0.366987i
$927$		0			0
$928$	−29.5751	+	20.7897i	−0.970851	+	0.682455i
$929$	−5.09749	−	2.94304i	−0.167243	−	0.0965579i	0.414042	−	0.910258i	$-0.364117\pi$
$929$	−5.09749	−	2.94304i	−0.167243	−	0.0965579i	−0.581285	+	0.813700i	$0.697450\pi$
$930$		0			0
$931$	−2.25963	+	1.30460i	−0.0740564	+	0.0427565i
$932$	5.34028	+	10.9288i	0.174927	+	0.357986i
$933$		0			0
$934$	−0.787807	+	0.182184i	−0.0257778	+	0.00596125i
$935$	52.4017			1.71372
$936$		0			0
$937$	10.0029			0.326781			0.163391	−	0.986561i	$-0.447757\pi$
$937$	10.0029			0.326781			0.163391	+	0.986561i	$0.447757\pi$
$938$	−0.706570	+	0.163398i	−0.0230703	+	0.00533512i
$939$		0			0
$940$	1.26779	+	2.59452i	0.0413508	+	0.0846240i
$941$	−24.7724	+	14.3023i	−0.807557	+	0.466243i	−0.846107	−	0.533014i	$-0.821059\pi$
$941$	−24.7724	+	14.3023i	−0.807557	+	0.466243i	0.0385499	+	0.999257i	$0.487726\pi$
$942$		0			0
$943$	65.4189	+	37.7696i	2.13033	+	1.22995i
$944$	31.6544	+	4.40137i	1.03026	+	0.143253i
$945$		0			0
$946$	−20.3068	+	18.9504i	−0.660233	+	0.616130i
$947$	−1.45936	+	2.52769i	−0.0474228	+	0.0821387i	−0.888762	−	0.458368i	$-0.848434\pi$
$947$	−1.45936	+	2.52769i	−0.0474228	+	0.0821387i	0.841340	+	0.540507i	$0.181767\pi$
$948$		0			0
$949$	−0.512248	−	0.887239i	−0.0166283	−	0.0288010i
$950$	−12.1919	−	3.72256i	−0.395559	−	0.120776i
$951$		0			0
$952$	−3.38992	−	21.2517i	−0.109868	−	0.688770i
$953$		−	24.4516i		−	0.792065i	−0.918236	−	0.396032i	$-0.870387\pi$
$953$		−	24.4516i		−	0.792065i	0.918236	−	0.396032i	$-0.129613\pi$
$954$		0			0
$955$			59.6564i			1.93044i
$956$	−15.2257	−	10.2536i	−0.492433	−	0.331625i
$957$		0			0
$958$	−11.4838	+	37.6113i	−0.371026	+	1.21517i
$959$	8.99055	+	15.5721i	0.290320	+	0.502849i
$960$		0			0
$961$	−15.4945	+	26.8373i	−0.499824	+	0.865720i
$962$	−0.766016	−	0.820848i	−0.0246973	−	0.0264652i
$963$		0			0
$964$	−1.27014	+	18.3575i	−0.0409085	+	0.591254i
$965$	46.8320	+	27.0384i	1.50757	+	0.870398i
$966$		0			0
$967$	−0.983735	+	0.567960i	−0.0316348	+	0.0182644i	−0.515734	−	0.856749i	$-0.672481\pi$
$967$	−0.983735	+	0.567960i	−0.0316348	+	0.0182644i	0.484099	+	0.875013i	$0.339147\pi$
$968$	−14.2378	−	5.44742i	−0.457622	−	0.175087i
$969$		0			0
$970$	−5.33781	−	23.0819i	−0.171387	−	0.741117i
$971$	7.03338			0.225712			0.112856	−	0.993611i	$-0.464000\pi$
$971$	7.03338			0.225712			0.112856	+	0.993611i	$0.464000\pi$
$972$		0			0
$973$	8.32882			0.267010
$974$	−3.29103	−	14.2312i	−0.105451	−	0.455997i
$975$		0			0
$976$	−11.1163	−	27.3981i	−0.355825	−	0.876991i
$977$	−21.1140	+	12.1901i	−0.675495	+	0.389997i	−0.798156	−	0.602451i	$-0.794191\pi$
$977$	−21.1140	+	12.1901i	−0.675495	+	0.389997i	0.122660	+	0.992449i	$0.460857\pi$
$978$		0			0
$979$	−30.1100	−	17.3840i	−0.962319	−	0.555595i
$980$	−5.80151	−	0.401403i	−0.185322	−	0.0128224i
$981$		0			0
$982$	32.6429	+	34.9795i	1.04168	+	1.11624i
$983$	−21.0741	+	36.5015i	−0.672161	+	1.16422i	0.305130	+	0.952311i	$0.401300\pi$
$983$	−21.0741	+	36.5015i	−0.672161	+	1.16422i	−0.977290	+	0.211905i	$0.932033\pi$
$984$		0			0
$985$	−25.0821	−	43.4435i	−0.799182	−	1.38422i
$986$	−20.0807	+	65.7673i	−0.639500	+	2.09446i
$987$		0			0
$988$	0.734048	−	1.09000i	0.0233532	−	0.0346774i
$989$			74.9050i			2.38184i
$990$		0			0
$991$		−	9.26522i		−	0.294320i	−0.989113	−	0.147160i	$-0.952987\pi$
$991$		−	9.26522i		−	0.294320i	0.989113	−	0.147160i	$-0.0470131\pi$
$992$	0.0526401	+	0.589227i	0.00167132	+	0.0187080i
$993$		0			0
$994$	1.96438	+	0.599783i	0.0623064	+	0.0190240i
$995$	1.70419	+	2.95175i	0.0540266	+	0.0935767i
$996$		0			0
$997$	−15.8531	+	27.4584i	−0.502073	+	0.869615i	0.497924	+	0.867220i	$0.334096\pi$
$997$	−15.8531	+	27.4584i	−0.502073	+	0.869615i	−0.999997	+	0.00239501i	$0.999238\pi$
$998$	−6.29711	+	5.87647i	−0.199332	+	0.186016i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ba.a.575.3		72
3.2	odd	2		252.2.ba.a.155.34	yes	72
4.3	odd	2	inner	756.2.ba.a.575.15		72
9.4	even	3		252.2.ba.a.239.22	yes	72
9.5	odd	6	inner	756.2.ba.a.71.15		72
12.11	even	2		252.2.ba.a.155.22	✓	72
36.23	even	6	inner	756.2.ba.a.71.3		72
36.31	odd	6		252.2.ba.a.239.34	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.22	✓	72	12.11	even	2
252.2.ba.a.155.34	yes	72	3.2	odd	2
252.2.ba.a.239.22	yes	72	9.4	even	3
252.2.ba.a.239.34	yes	72	36.31	odd	6
756.2.ba.a.71.3		72	36.23	even	6	inner
756.2.ba.a.71.15		72	9.5	odd	6	inner
756.2.ba.a.575.3		72	1.1	even	1	trivial
756.2.ba.a.575.15		72	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.37785 + 0.318634i) q^{2} +(1.79694 - 0.878061i) q^{4} +(-2.51813 + 1.45385i) q^{5} +(-0.866025 - 0.500000i) q^{7} +(-2.19614 + 1.78241i) q^{8} +O(q^{10})\)	\(q+(-1.37785 + 0.318634i) q^{2} +(1.79694 - 0.878061i) q^{4} +(-2.51813 + 1.45385i) q^{5} +(-0.866025 - 0.500000i) q^{7} +(-2.19614 + 1.78241i) q^{8} +(3.00637 - 2.80555i) q^{10} +(1.18430 - 2.05127i) q^{11} +(-0.125913 - 0.218087i) q^{13} +(1.35257 + 0.412980i) q^{14} +(2.45802 - 3.15565i) q^{16} -7.60859i q^{17} +2.60920i q^{19} +(-3.24838 + 4.82355i) q^{20} +(-0.978187 + 3.20371i) q^{22} +(4.51674 + 7.82323i) q^{23} +(1.72733 - 2.99183i) q^{25} +(0.242979 + 0.260371i) q^{26} +(-1.99523 - 0.138049i) q^{28} +(5.53448 + 3.19533i) q^{29} +(0.0905658 - 0.0522882i) q^{31} +(-2.38128 + 5.13123i) q^{32} +(2.42436 + 10.4835i) q^{34} +2.90769 q^{35} -3.15261 q^{37} +(-0.831380 - 3.59508i) q^{38} +(2.93883 - 7.68118i) q^{40} +(7.24183 - 4.18107i) q^{41} +(7.18102 + 4.14596i) q^{43} +(0.326984 - 4.72592i) q^{44} +(-8.71615 - 9.34005i) q^{46} +(0.248282 - 0.430036i) q^{47} +(0.500000 + 0.866025i) q^{49} +(-1.42671 + 4.67268i) q^{50} +(-0.417752 - 0.281331i) q^{52} +2.38678i q^{53} +6.88718i q^{55} +(2.79312 - 0.445538i) q^{56} +(-8.64383 - 2.63922i) q^{58} +(3.99487 + 6.91932i) q^{59} +(3.69592 - 6.40151i) q^{61} +(-0.108125 + 0.100903i) q^{62} +(1.64606 - 7.82882i) q^{64} +(0.634129 + 0.366115i) q^{65} +(-0.444103 + 0.256403i) q^{67} +(-6.68081 - 13.6722i) q^{68} +(-4.00636 + 0.926490i) q^{70} +1.45233 q^{71} +4.06828 q^{73} +(4.34382 - 1.00453i) q^{74} +(2.29103 + 4.68858i) q^{76} +(-2.05127 + 1.18430i) q^{77} +(10.0369 + 5.79482i) q^{79} +(-1.60178 + 11.5199i) q^{80} +(-8.64592 + 8.06839i) q^{82} +(-0.439593 + 0.761398i) q^{83} +(11.0617 + 19.1594i) q^{85} +(-11.2154 - 3.42440i) q^{86} +(1.05531 + 6.61580i) q^{88} -14.6787i q^{89} +0.251825i q^{91} +(14.9856 + 10.0919i) q^{92} +(-0.205071 + 0.671637i) q^{94} +(-3.79337 - 6.57031i) q^{95} +(2.88066 - 4.98945i) q^{97} +(-0.964871 - 1.03394i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) \) 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

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