LMFDB - Embedded newform 756.2.ba.a.575.15

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			575.15
Character	$\chi$	$=$	756.575
Dual form			756.2.ba.a.71.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.412980 - 1.35257i) q^{2} +(-1.65890 + 1.11717i) q^{4} +(-2.51813 + 1.45385i) q^{5} +(0.866025 + 0.500000i) q^{7} +(2.19614 + 1.78241i) q^{8} +O(q^{10})$	\(q+(-0.412980 - 1.35257i) q^{2} +(-1.65890 + 1.11717i) q^{4} +(-2.51813 + 1.45385i) q^{5} +(0.866025 + 0.500000i) q^{7} +(2.19614 + 1.78241i) q^{8} +(3.00637 + 2.80555i) q^{10} +(-1.18430 + 2.05127i) q^{11} +(-0.125913 - 0.218087i) q^{13} +(0.318634 - 1.37785i) q^{14} +(1.50387 - 3.70653i) q^{16} -7.60859i q^{17} -2.60920i q^{19} +(2.55313 - 5.22496i) q^{20} +(3.26359 + 0.754720i) q^{22} +(-4.51674 - 7.82323i) q^{23} +(1.72733 - 2.99183i) q^{25} +(-0.242979 + 0.260371i) q^{26} +(-1.99523 + 0.138049i) q^{28} +(5.53448 + 3.19533i) q^{29} +(-0.0905658 + 0.0522882i) q^{31} +(-5.63441 - 0.503365i) q^{32} +(-10.2912 + 3.14219i) q^{34} -2.90769 q^{35} -3.15261 q^{37} +(-3.52912 + 1.07755i) q^{38} +(-8.12152 - 1.29549i) q^{40} +(7.24183 - 4.18107i) q^{41} +(-7.18102 - 4.14596i) q^{43} +(-0.326984 - 4.72592i) q^{44} +(-8.71615 + 9.34005i) q^{46} +(-0.248282 + 0.430036i) q^{47} +(0.500000 + 0.866025i) q^{49} +(-4.76001 - 1.10078i) q^{50} +(0.452516 + 0.221118i) q^{52} +2.38678i q^{53} -6.88718i q^{55} +(1.01071 + 2.64168i) q^{56} +(2.03629 - 8.80538i) q^{58} +(-3.99487 - 6.91932i) q^{59} +(3.69592 - 6.40151i) q^{61} +(0.108125 + 0.100903i) q^{62} +(1.64606 + 7.82882i) q^{64} +(0.634129 + 0.366115i) q^{65} +(0.444103 - 0.256403i) q^{67} +(8.50008 + 12.6219i) q^{68} +(1.20082 + 3.93286i) q^{70} -1.45233 q^{71} +4.06828 q^{73} +(1.30196 + 4.26412i) q^{74} +(2.91491 + 4.32839i) q^{76} +(-2.05127 + 1.18430i) q^{77} +(-10.0369 - 5.79482i) q^{79} +(1.60178 + 11.5199i) q^{80} +(-8.64592 - 8.06839i) q^{82} +(0.439593 - 0.761398i) q^{83} +(11.0617 + 19.1594i) q^{85} +(-2.64209 + 11.4250i) q^{86} +(-6.25710 + 2.39398i) q^{88} -14.6787i q^{89} -0.251825i q^{91} +(16.2327 + 7.93195i) q^{92} +(0.684190 + 0.158222i) q^{94} +(3.79337 + 6.57031i) q^{95} +(2.88066 - 4.98945i) q^{97} +(0.964871 - 1.03394i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.412980	−	1.35257i	−0.292021	−	0.956412i
$2$	−0.412980	−	1.35257i	−0.292021	−	0.956412i
$3$		0			0
$3$		0			0
$4$	−1.65890	+	1.11717i	−0.829448	+	0.558584i
$5$	−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	−0.987472	−	0.157795i	$-0.949561\pi$
$11$	−1.18430	+	2.05127i	−0.357081	+	0.618483i	0.630391	+	0.776278i	$0.282895\pi$
$12$		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	$0.844452\pi$
$14$	0.318634	−	1.37785i	0.0851586	−	0.368246i
$15$		0			0
$16$	1.50387	−	3.70653i	0.375967	−	0.926633i
$17$		−	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	$-0.903248\pi$
$19$		−	2.60920i		−	0.598591i	0.954160	−	0.299295i	$-0.0967516\pi$
$20$	2.55313	−	5.22496i	0.570897	−	1.16834i
$21$		0			0
$22$	3.26359	+	0.754720i	0.695799	+	0.160907i
$23$	−4.51674	−	7.82323i	−0.941806	−	1.63126i	−0.762024	−	0.647549i	$-0.775794\pi$
$23$	−4.51674	−	7.82323i	−0.941806	−	1.63126i	−0.179782	−	0.983706i	$-0.557539\pi$
$24$		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	−0.508111	−	0.861292i	$-0.669656\pi$
$31$	−0.0905658	+	0.0522882i	−0.0162661	+	0.00939124i	0.491845	+	0.870683i	$0.336323\pi$
$32$	−5.63441	−	0.503365i	−0.996033	−	0.0889831i
$33$		0			0
$34$	−10.2912	+	3.14219i	−1.76492	+	0.538882i
$35$	−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	$0.583440\pi$
$38$	−3.52912	+	1.07755i	−0.572499	+	0.174801i
$39$		0			0
$40$	−8.12152	−	1.29549i	−1.28412	−	0.204835i
$41$	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	−0.160167	−	0.987090i	$-0.551203\pi$
$43$	−7.18102	−	4.14596i	−1.09510	−	0.632254i	−0.934928	+	0.354836i	$0.884537\pi$
$44$	−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	−0.883565	−	0.468308i	$-0.844864\pi$
$47$	−0.248282	+	0.430036i	−0.0362156	+	0.0627273i	0.847349	+	0.531036i	$0.178197\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−4.76001	−	1.10078i	−0.673167	−	0.155673i
$51$		0			0
$52$	0.452516	+	0.221118i	0.0627526	+	0.0306635i
$53$			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
$56$	1.01071	+	2.64168i	0.135062	+	0.353009i
$57$		0			0
$58$	2.03629	−	8.80538i	0.267377	−	1.15620i
$59$	−3.99487	−	6.91932i	−0.520088	−	0.900818i	−0.999727	−	0.0233526i	$-0.992566\pi$
$59$	−3.99487	−	6.91932i	−0.520088	−	0.900818i	0.479640	−	0.877466i	$-0.340767\pi$
$60$		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	−0.472627	−	0.881263i	$-0.656694\pi$
$67$	0.444103	−	0.256403i	0.0542559	−	0.0313246i	0.526883	+	0.849938i	$0.323361\pi$
$68$	8.50008	+	12.6219i	1.03079	+	1.53062i
$69$		0			0
$70$	1.20082	+	3.93286i	0.143525	+	0.470066i
$71$	−1.45233			−0.172360			−0.0861800	−	0.996280i	$-0.527466\pi$
$71$	−1.45233			−0.172360			−0.0861800	+	0.996280i	$0.527466\pi$
$72$		0			0
$73$	4.06828			0.476157			0.238078	−	0.971246i	$-0.423483\pi$
$73$	4.06828			0.476157			0.238078	+	0.971246i	$0.423483\pi$
$74$	1.30196	+	4.26412i	0.151350	+	0.495694i
$75$		0			0
$76$	2.91491	+	4.32839i	0.334364	+	0.496500i
$77$	−2.05127	+	1.18430i	−0.233764	+	0.134964i
$78$		0			0
$79$	−10.0369	−	5.79482i	−1.12924	−	0.651968i	−0.185498	−	0.982645i	$-0.559390\pi$
$79$	−10.0369	−	5.79482i	−1.12924	−	0.651968i	−0.943744	+	0.330677i	$0.892723\pi$
$80$	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	−0.840891	−	0.541205i	$-0.817968\pi$
$83$	0.439593	−	0.761398i	0.0482516	−	0.0835743i	0.889142	+	0.457630i	$0.151302\pi$
$84$		0			0
$85$	11.0617	+	19.1594i	1.19981	+	2.07813i
$86$	−2.64209	+	11.4250i	−0.284904	+	1.23199i
$87$		0			0
$88$	−6.25710	+	2.39398i	−0.667009	+	0.255199i
$89$		−	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
$92$	16.2327	+	7.93195i	1.69237	+	0.826963i
$93$		0			0
$94$	0.684190	+	0.158222i	0.0705688	+	0.0163194i
$95$	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	−0.914918	−	0.403641i	$-0.867745\pi$
$103$	−10.3804	+	5.99314i	−1.02281	+	0.590521i	−0.107896	+	0.994162i	$0.534411\pi$
$104$	0.112198	−	0.703377i	0.0110019	−	0.0689718i
$105$		0			0
$106$	3.22829	−	0.985691i	0.313559	−	0.0957388i
$107$	−6.10346			−0.590043			−0.295022	−	0.955491i	$-0.595327\pi$
$107$	−6.10346			−0.590043			−0.295022	+	0.955491i	$0.595327\pi$
$108$		0			0
$109$	6.25509			0.599129			0.299564	−	0.954076i	$-0.403159\pi$
$109$	6.25509			0.599129			0.299564	+	0.954076i	$0.403159\pi$
$110$	−9.31540	+	2.84427i	−0.888188	+	0.271190i
$111$		0			0
$112$	3.15565	−	2.45802i	0.298181	−	0.232261i
$113$	−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
$122$	−10.1848	−	2.35529i	−0.922092	−	0.213238i
$123$		0			0
$124$	0.0918245	−	0.187918i	0.00824608	−	0.0168755i
$125$		−	4.49335i		−	0.401898i
$126$		0			0
$127$		−	13.5835i		−	1.20534i	−0.797989	−	0.602672i	$-0.794103\pi$
$127$		−	13.5835i		−	1.20534i	0.797989	−	0.602672i	$-0.205897\pi$
$128$	9.90925	−	5.45956i	0.875862	−	0.482562i
$129$		0			0
$130$	0.233314	−	1.00890i	0.0204629	−	0.0884866i
$131$	−0.740508	−	1.28260i	−0.0646985	−	0.112061i	0.831862	−	0.554983i	$-0.187275\pi$
$131$	−0.740508	−	1.28260i	−0.0646985	−	0.112061i	−0.896560	+	0.442922i	$0.853942\pi$
$132$		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	−0.161872	−	0.986812i	$-0.551753\pi$
$139$	7.21297	−	4.16441i	0.611796	−	0.353221i	0.773668	+	0.633591i	$0.218420\pi$
$140$	4.82355	−	3.24838i	0.407665	−	0.274538i
$141$		0			0
$142$	0.599783	+	1.96438i	0.0503327	+	0.164847i
$143$	0.596475			0.0498797
$144$		0			0
$145$	−18.5821			−1.54316
$146$	−1.68012	−	5.50264i	−0.139048	−	0.455402i
$147$		0			0
$148$	5.22984	−	3.52199i	0.429890	−	0.289506i
$149$	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	0.703107	−	0.711084i	$-0.251795\pi$
$151$	5.39261	+	3.11343i	0.438845	+	0.253367i	−0.264263	+	0.964451i	$0.585129\pi$
$152$	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	$0.795414\pi$
$158$	−3.69286	+	15.9688i	−0.293788	+	1.27041i
$159$		0			0
$160$	14.9200	−	6.92403i	1.17953	−	0.547392i
$161$		−	9.03348i		−	0.711938i
$162$		0			0
$163$			8.29335i			0.649585i	0.945785	+	0.324793i	$0.105294\pi$
$163$			8.29335i			0.649585i	−0.945785	+	0.324793i	$0.894706\pi$
$164$	−7.34247	+	15.0263i	−0.573351	+	1.17336i
$165$		0			0
$166$	−1.21139	−	0.280139i	−0.0940219	−	0.0217430i
$167$	9.34971	+	16.1942i	0.723503	+	1.25314i	0.959587	+	0.281411i	$0.0908023\pi$
$167$	9.34971	+	16.1942i	0.723503	+	1.25314i	−0.236085	+	0.971732i	$0.575864\pi$
$168$		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
$176$	5.82208	+	7.47451i	0.438856	+	0.563412i
$177$		0			0
$178$	−19.8539	+	6.06199i	−1.48812	+	0.454365i
$179$	2.87709			0.215044			0.107522	−	0.994203i	$-0.465708\pi$
$179$	2.87709			0.215044			0.107522	+	0.994203i	$0.465708\pi$
$180$		0			0
$181$	−4.82998			−0.359010			−0.179505	−	0.983757i	$-0.557450\pi$
$181$	−4.82998			−0.359010			−0.179505	+	0.983757i	$0.557450\pi$
$182$	−0.340611	+	0.103999i	−0.0252478	+	0.00770890i
$183$		0			0
$184$	4.02476	−	25.2316i	0.296709	−	1.86010i
$185$	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	$0.432918\pi$
$191$	−10.2584	+	17.7680i	−0.742270	+	1.28565i	−0.951459	+	0.307775i	$0.900416\pi$
$192$		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	$-0.400095\pi$
$194$	−7.93824	−	1.83576i	−0.569932	−	0.131800i
$195$		0			0
$196$	−1.79694	−	0.878061i	−0.128353	−	0.0627187i
$197$			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	$0.0132288\pi$
$199$			1.17220i			0.0830948i	−0.999137	+	0.0415474i	$0.986771\pi$
$200$	9.12612	−	3.49167i	0.645314	−	0.246898i
$201$		0			0
$202$	4.59792	−	19.8825i	0.323508	−	1.39893i
$203$	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	−0.771637	−	0.636063i	$-0.780562\pi$
$211$	−8.81152	+	5.08733i	−0.606610	+	0.350226i	0.165028	+	0.986289i	$0.447229\pi$
$212$	−2.66643	−	3.95942i	−0.183131	−	0.271934i
$213$		0			0
$214$	2.52060	+	8.25536i	0.172305	+	0.564325i
$215$	24.1104			1.64431
$216$		0			0
$217$	−0.104576			−0.00709911
$218$	−2.58322	−	8.46045i	−0.174958	−	0.573014i
$219$		0			0
$220$	7.69414	+	11.4251i	0.518739	+	0.770281i
$221$	−1.65933	+	0.958017i	−0.111619	+	0.0644432i
$222$		0			0
$223$	5.28069	+	3.04881i	0.353621	+	0.204163i	0.666279	−	0.745703i	$-0.267886\pi$
$223$	5.28069	+	3.04881i	0.353621	+	0.204163i	−0.312658	+	0.949866i	$0.601219\pi$
$224$	−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	$-0.567880\pi$
$227$	11.1581	−	19.3264i	0.740589	−	1.28274i	0.952228	−	0.305390i	$-0.0987867\pi$
$228$		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	$0.890624\pi$
$230$	8.36944	−	36.1914i	0.551864	−	2.38639i
$231$		0			0
$232$	6.45911	+	16.8821i	0.424062	+	1.10836i
$233$			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
$236$	14.3571	+	7.01548i	0.934568	+	0.456669i
$237$		0			0
$238$	−10.4835	−	2.42436i	−0.679544	−	0.157148i
$239$	4.58910	+	7.94855i	0.296844	+	0.514149i	0.975412	−	0.220388i	$-0.0707325\pi$
$239$	4.58910	+	7.94855i	0.296844	+	0.514149i	−0.678568	+	0.734538i	$0.737399\pi$
$240$		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
$248$	−0.292094	−	0.0465928i	−0.0185480	−	0.00295864i
$249$		0			0
$250$	−6.07758	+	1.85566i	−0.384380	+	0.117363i
$251$	−17.5771			−1.10946			−0.554729	−	0.832031i	$-0.687178\pi$
$251$	−17.5771			−1.10946			−0.554729	+	0.832031i	$0.687178\pi$
$252$		0			0
$253$	21.3968			1.34520
$254$	−18.3727	+	5.60972i	−1.15280	+	0.351985i
$255$		0			0
$256$	−11.4768	−	11.1483i	−0.717298	−	0.696767i
$257$	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	−0.901546	−	0.432683i	$-0.857567\pi$
$263$	−1.23346	+	2.13642i	−0.0760585	+	0.131737i	0.825488	+	0.564420i	$0.190900\pi$
$264$		0			0
$265$	−3.47001	−	6.01023i	−0.213161	−	0.369205i
$266$	−3.59508	−	0.831380i	−0.220429	−	0.0509752i
$267$		0			0
$268$	−0.450275	+	0.921484i	−0.0275049	+	0.0562886i
$269$			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	$-0.882159\pi$
$271$		−	11.9123i		−	0.723621i	0.932252	−	0.361811i	$-0.117841\pi$
$272$	−28.2015	−	11.4423i	−1.70997	−	0.693792i
$273$		0			0
$274$	−5.72940	+	24.7753i	−0.346126	+	1.49673i
$275$	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	−0.581200	−	0.813760i	$-0.697417\pi$
$283$	−2.81044	+	1.62261i	−0.167063	+	0.0964541i	0.414137	+	0.910215i	$0.364083\pi$
$284$	2.40927	−	1.62250i	0.142964	−	0.0962776i
$285$		0			0
$286$	−0.246332	−	0.806775i	−0.0145659	−	0.0477056i
$287$	8.36214			0.493602
$288$		0			0
$289$	−40.8906			−2.40533
$290$	7.67402	+	25.1336i	0.450634	+	1.47589i
$291$		0			0
$292$	−6.74886	+	4.54496i	−0.394947	+	0.265974i
$293$	−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
$302$	1.98409	−	8.57967i	0.114172	−	0.493705i
$303$		0			0
$304$	−9.67107	−	3.92389i	−0.554674	−	0.225050i
$305$			21.4932i			1.23069i
$306$		0			0
$307$		−	17.7017i		−	1.01029i	−0.863035	−	0.505144i	$-0.831439\pi$
$307$		−	17.7017i		−	1.01029i	0.863035	−	0.505144i	$-0.168561\pi$
$308$	2.07978	−	4.25626i	0.118507	−	0.242523i
$309$		0			0
$310$	−0.418971	−	0.0968890i	−0.0237960	−	0.00550293i
$311$	−3.30345	−	5.72174i	−0.187321	−	0.324450i	0.757035	−	0.653374i	$-0.226647\pi$
$311$	−3.30345	−	5.72174i	−0.187321	−	0.324450i	−0.944356	+	0.328924i	$0.893314\pi$
$312$		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
$320$	−15.5269	−	17.3209i	−0.867980	−	0.968268i
$321$		0			0
$322$	−12.2184	+	3.73065i	−0.680906	+	0.207901i
$323$	−19.8523			−1.10461
$324$		0			0
$325$	−0.869972			−0.0482573
$326$	11.2173	−	3.42498i	0.621271	−	0.189692i
$327$		0			0
$328$	23.3564	+	3.72565i	1.28964	+	0.205715i
$329$	−0.430036	+	0.248282i	−0.0237087	+	0.0136882i
$330$		0			0
$331$	−23.0921	−	13.3322i	−1.26925	−	0.732804i	−0.294407	−	0.955680i	$-0.595122\pi$
$331$	−23.0921	−	13.3322i	−1.26925	−	0.732804i	−0.974847	+	0.222876i	$0.928456\pi$
$332$	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	$0.778063\pi$
$338$	−17.8247	−	4.12204i	−0.969535	−	0.224209i
$339$		0			0
$340$	−39.7546	−	19.4257i	−2.15599	−	1.05351i
$341$		−	0.247700i		−	0.0134137i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−8.38074	−	21.9046i	−0.451859	−	1.18102i
$345$		0			0
$346$	−2.79201	+	12.0733i	−0.150099	+	0.649065i
$347$	−2.10127	−	3.63950i	−0.112802	−	0.195379i	0.804097	−	0.594498i	$-0.202649\pi$
$347$	−2.10127	−	3.63950i	−0.112802	−	0.195379i	−0.916899	+	0.399119i	$0.869316\pi$
$348$		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
$356$	16.3985	+	24.3504i	0.869121	+	1.29057i
$357$		0			0
$358$	−1.18818	−	3.89147i	−0.0627973	−	0.205670i
$359$	−5.48093			−0.289272			−0.144636	−	0.989485i	$-0.546201\pi$
$359$	−5.48093			−0.289272			−0.144636	+	0.989485i	$0.546201\pi$
$360$		0			0
$361$	12.1921			0.641689
$362$	1.99468	+	6.53289i	0.104838	+	0.343361i
$363$		0			0
$364$	0.281331	+	0.417752i	0.0147458	+	0.0218961i
$365$	−10.2445	+	5.91465i	−0.536221	+	0.309587i
$366$		0			0
$367$	−14.7364	−	8.50804i	−0.769232	−	0.444116i	0.0633686	−	0.997990i	$-0.479816\pi$
$367$	−14.7364	−	8.50804i	−0.769232	−	0.444116i	−0.832601	+	0.553874i	$0.813149\pi$
$368$	−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	$0.842734\pi$
$374$	5.74235	−	24.8313i	0.296930	−	1.28400i
$375$		0			0
$376$	−1.31176	+	0.501882i	−0.0676489	+	0.0258826i
$377$		−	1.60933i		−	0.0828847i
$378$		0			0
$379$			26.5456i			1.36356i	0.731559	+	0.681778i	$0.238793\pi$
$379$			26.5456i			1.36356i	−0.731559	+	0.681778i	$0.761207\pi$
$380$	−13.6329	−	6.66162i	−0.699355	−	0.341734i
$381$		0			0
$382$	28.2690	+	6.53735i	1.44637	+	0.334480i
$383$	−17.3272	−	30.0116i	−0.885380	−	1.53352i	−0.845277	−	0.534328i	$-0.820565\pi$
$383$	−17.3272	−	30.0116i	−0.885380	−	1.53352i	−0.0401027	−	0.999196i	$-0.512769\pi$
$384$		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
$392$	−0.445538	+	2.79312i	−0.0225031	+	0.141074i
$393$		0			0
$394$	23.3349	−	7.12483i	1.17559	−	0.358944i
$395$	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	$0.610502\pi$
$398$	1.58548	−	0.484094i	0.0794729	−	0.0242654i
$399$		0			0
$400$	−8.49163	−	10.9017i	−0.424581	−	0.545086i
$401$	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	$0.839776\pi$
$410$	33.5018	+	7.74744i	1.65453	+	0.382619i
$411$		0			0
$412$	10.5247	−	21.5387i	0.518514	−	1.06113i
$413$		−	7.98974i		−	0.393149i
$414$		0			0
$415$			2.55640i			0.125489i
$416$	0.599666	+	1.29217i	0.0294011	+	0.0633540i
$417$		0			0
$418$	1.96921	−	8.51534i	0.0963174	−	0.416499i
$419$	−7.99122	−	13.8412i	−0.390397	−	0.676187i	0.602105	−	0.798417i	$-0.294329\pi$
$419$	−7.99122	−	13.8412i	−0.390397	−	0.676187i	−0.992502	+	0.122230i	$0.960995\pi$
$420$		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
$428$	10.1250	−	6.81859i	0.489410	−	0.329589i
$429$		0			0
$430$	−9.95709	−	32.6110i	−0.480174	−	1.57264i
$431$	32.4604			1.56356			0.781780	−	0.623554i	$-0.214312\pi$
$431$	32.4604			1.56356			0.781780	+	0.623554i	$0.214312\pi$
$432$		0			0
$433$	−18.4266			−0.885525			−0.442762	−	0.896639i	$-0.646001\pi$
$433$	−18.4266			−0.885525			−0.442762	+	0.896639i	$0.646001\pi$
$434$	0.0431879	+	0.141447i	0.00207309	+	0.00678967i
$435$		0			0
$436$	−10.3765	+	6.98799i	−0.496946	+	0.334664i
$437$	−20.4123	+	11.7851i	−0.976455	+	0.563756i
$438$		0			0
$439$	31.5605	+	18.2214i	1.50630	+	0.869662i	0.999973	+	0.00731896i	$0.00232972\pi$
$439$	31.5605	+	18.2214i	1.50630	+	0.869662i	0.506325	+	0.862343i	$0.331004\pi$
$440$	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	$0.348158\pi$
$443$	−11.3610	+	19.6778i	−0.539776	+	0.934919i	−0.998916	+	0.0465549i	$0.985176\pi$
$444$		0			0
$445$	21.3405	+	36.9628i	1.01164	+	1.75221i
$446$	1.94291	−	8.40160i	0.0919994	−	0.397827i
$447$		0			0
$448$	−2.48888	+	7.60299i	−0.117589	+	0.359208i
$449$			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
$452$	16.1110	−	32.9710i	0.757797	−	1.55083i
$453$		0			0
$454$	−30.7484	−	7.11071i	−1.44309	−	0.333722i
$455$	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	−0.248663	−	0.968590i	$-0.579991\pi$
$463$	10.0234	−	5.78704i	0.465829	−	0.268947i	0.714492	+	0.699643i	$0.246658\pi$
$464$	20.1667	−	15.7084i	0.936217	−	0.729243i
$465$		0			0
$466$	8.22620	−	2.51170i	0.381071	−	0.116352i
$467$	−0.571766			−0.0264582			−0.0132291	−	0.999912i	$-0.504211\pi$
$467$	−0.571766			−0.0264582			−0.0132291	+	0.999912i	$0.504211\pi$
$468$		0			0
$469$	0.512806			0.0236792
$470$	−1.95291	+	0.596282i	−0.0900811	+	0.0275044i
$471$		0			0
$472$	3.55973	−	22.3163i	0.163850	−	1.02719i
$473$	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	$0.385779\pi$
$479$	−13.9036	+	24.0818i	−0.635273	+	1.10033i	−0.986457	+	0.164019i	$0.947554\pi$
$480$		0			0
$481$	0.396953	+	0.687542i	0.0180995	+	0.0313492i
$482$	12.6771	+	2.93165i	0.577428	+	0.133533i
$483$		0			0
$484$	−9.68499	−	4.73248i	−0.440227	−	0.215113i
$485$			16.7521i			0.760676i
$486$		0			0
$487$		−	10.3286i		−	0.468031i	−0.972233	−	0.234016i	$-0.924813\pi$
$487$		−	10.3286i		−	0.468031i	0.972233	−	0.234016i	$-0.0751867\pi$
$488$	19.5268	−	7.47100i	0.883939	−	0.338196i
$489$		0			0
$490$	−0.926490	+	4.00636i	−0.0418546	+	0.180989i
$491$	16.9157	+	29.2988i	0.763394	+	1.32224i	0.941091	+	0.338153i	$0.109802\pi$
$491$	16.9157	+	29.2988i	0.763394	+	1.32224i	−0.177697	+	0.984085i	$0.556865\pi$
$492$		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	−0.613391	−	0.789779i	$-0.710195\pi$
$499$	−5.27446	+	3.04521i	−0.236117	+	0.136322i	0.377274	+	0.926102i	$0.376862\pi$
$500$	5.01984	+	7.45400i	0.224494	+	0.333353i
$501$		0			0
$502$	7.25900	+	23.7743i	0.323985	+	1.06110i
$503$	−21.4710			−0.957345			−0.478673	−	0.877993i	$-0.658882\pi$
$503$	−21.4710			−0.957345			−0.478673	+	0.877993i	$0.658882\pi$
$504$		0			0
$505$	−41.9582			−1.86712
$506$	−8.83644	−	28.9407i	−0.392828	−	1.28657i
$507$		0			0
$508$	15.1751	+	22.5337i	0.673286	+	0.999769i
$509$	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
$518$	−1.00453	+	4.34382i	−0.0441365	+	0.190856i
$519$		0			0
$520$	0.740072	+	1.93431i	0.0324543	+	0.0848253i
$521$		−	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	$0.213681\pi$
$523$			28.4494i			1.24401i	−0.783014	+	0.622004i	$0.786319\pi$
$524$	2.66130	+	1.30042i	0.116260	+	0.0568092i
$525$		0			0
$526$	3.39905	+	0.786046i	0.148206	+	0.0342733i
$527$	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
$536$	1.43233	+	0.228475i	0.0618671	+	0.00986861i
$537$		0			0
$538$	25.2142	−	7.69865i	1.08706	−	0.331912i
$539$	−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	$0.285970\pi$
$542$	−16.1122	+	4.91954i	−0.692080	+	0.211312i
$543$		0			0
$544$	−3.82989	+	42.8699i	−0.164205	+	1.83803i
$545$	−15.7512	+	9.09393i	−0.674705	+	0.389541i
$546$		0			0
$547$	−32.0274	−	18.4910i	−1.36939	−	0.790619i	−0.378541	−	0.925584i	$-0.623574\pi$
$547$	−32.0274	−	18.4910i	−1.36939	−	0.790619i	−0.990850	+	0.134966i	$0.956908\pi$
$548$	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
$554$	−24.3335	−	5.62724i	−1.03383	−	0.239078i
$555$		0			0
$556$	−7.31321	+	14.9664i	−0.310149	+	0.634718i
$557$		−	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
$560$	−4.37278	+	10.7774i	−0.184784	+	0.455430i
$561$		0			0
$562$	6.09477	−	26.3552i	0.257092	−	1.11173i
$563$	−2.78657	−	4.82649i	−0.117440	−	0.203412i	0.801312	−	0.598246i	$-0.204135\pi$
$563$	−2.78657	−	4.82649i	−0.117440	−	0.203412i	−0.918753	+	0.394834i	$0.870802\pi$
$564$		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	0.242353	−	0.970188i	$-0.422081\pi$
$571$	28.7640	−	16.6069i	1.20374	−	0.694978i	0.961384	+	0.275211i	$0.0887476\pi$
$572$	−0.989489	+	0.666363i	−0.0413726	+	0.0278620i
$573$		0			0
$574$	−3.45340	−	11.3104i	−0.144142	−	0.472087i
$575$	−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	$0.304771\pi$
$578$	16.8870	+	55.3074i	0.702406	+	2.30049i
$579$		0			0
$580$	30.8257	−	20.7593i	1.27997	−	0.861984i
$581$	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	−0.503717	−	0.863869i	$-0.668035\pi$
$587$	12.0238	−	20.8258i	0.496274	−	0.859571i	0.999991	+	0.00429733i	$0.00136789\pi$
$588$		0			0
$589$	0.136430	+	0.236304i	0.00562151	+	0.00973674i
$590$	7.40241	−	32.0098i	0.304753	−	1.31782i
$591$		0			0
$592$	−4.74110	+	11.6852i	−0.194858	+	0.480260i
$593$		−	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
$596$	−2.90738	+	5.94992i	−0.119091	+	0.243718i
$597$		0			0
$598$	3.13441	+	0.724848i	0.128176	+	0.0296412i
$599$	−14.7689	−	25.5804i	−0.603439	−	1.04519i	−0.992296	−	0.123889i	$-0.960463\pi$
$599$	−14.7689	−	25.5804i	−0.603439	−	1.04519i	0.388857	−	0.921298i	$-0.372870\pi$
$600$		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	0.302748	−	0.953071i	$-0.402096\pi$
$607$	31.5236	−	18.2002i	1.27950	−	0.738722i	0.976757	+	0.214348i	$0.0687628\pi$
$608$	−1.31338	+	14.7013i	−0.0532645	+	0.596216i
$609$		0			0
$610$	29.0710	−	8.87624i	1.17705	−	0.359388i
$611$	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	$0.416394\pi$
$614$	−23.9428	+	7.31043i	−0.966251	+	0.295025i
$615$		0			0
$616$	−6.61580	−	1.05531i	−0.266558	−	0.0425195i
$617$	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	0.481934	−	0.876207i	$-0.339934\pi$
$619$	−0.893596	−	0.515918i	−0.0359167	−	0.0207365i	−0.517851	+	0.855471i	$0.673268\pi$
$620$	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
$626$	−14.7186	−	3.40374i	−0.588274	−	0.136041i
$627$		0			0
$628$	−5.35172	−	2.61507i	−0.213557	−	0.104353i
$629$			23.9869i			0.956420i
$630$		0			0
$631$		−	25.4447i		−	1.01294i	−0.862258	−	0.506469i	$-0.830951\pi$
$631$		−	25.4447i		−	1.01294i	0.862258	−	0.506469i	$-0.169049\pi$
$632$	−11.7138	−	30.6161i	−0.465949	−	1.21784i
$633$		0			0
$634$	8.13387	−	35.1728i	0.323037	−	1.39689i
$635$	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	−0.264757	−	0.964315i	$-0.585292\pi$
$643$	11.1062	−	6.41216i	0.437985	−	0.252871i	0.702743	+	0.711444i	$0.251959\pi$
$644$	10.0919	+	14.9856i	0.397678	+	0.590516i
$645$		0			0
$646$	8.19860	+	26.8516i	0.322570	+	1.05646i
$647$	39.1711			1.53998			0.769988	−	0.638058i	$-0.220262\pi$
$647$	39.1711			1.53998			0.769988	+	0.638058i	$0.220262\pi$
$648$		0			0
$649$	18.9246			0.742854
$650$	0.359281	+	1.17670i	0.0140921	+	0.0461539i
$651$		0			0
$652$	−9.26507	−	13.7578i	−0.362848	−	0.538797i
$653$	−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	$-0.664694\pi$
$659$	12.9730	−	22.4699i	0.505357	−	0.875304i	0.999981	−	0.00619658i	$-0.00197245\pi$
$660$		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	$-0.447259\pi$
$662$	−8.49620	+	36.7396i	−0.330214	+	1.42792i
$663$		0			0
$664$	2.32253	−	0.888603i	0.0901316	−	0.0344845i
$665$			7.58674i			0.294201i
$666$		0			0
$667$		−	57.7300i		−	2.23531i
$668$	−33.6018	−	16.4192i	−1.30009	−	0.635279i
$669$		0			0
$670$	2.05449	+	0.475110i	0.0793718	+	0.0183551i
$671$	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
$680$	−9.85683	+	61.7933i	−0.377992	+	2.36966i
$681$		0			0
$682$	−0.335032	+	0.102295i	−0.0128291	+	0.00391709i
$683$	−39.2840			−1.50316			−0.751581	−	0.659641i	$-0.770708\pi$
$683$	−39.2840			−1.50316			−0.751581	+	0.659641i	$0.770708\pi$
$684$		0			0
$685$	52.2835			1.99765
$686$	1.35257	−	0.412980i	0.0516414	−	0.0157676i
$687$		0			0
$688$	−26.1665	+	20.3817i	−0.997587	+	0.777045i
$689$	0.520525	−	0.300525i	0.0198304	−	0.0114491i
$690$		0			0
$691$	−15.8640	−	9.15909i	−0.603495	−	0.348428i	0.166920	−	0.985970i	$-0.446618\pi$
$691$	−15.8640	−	9.15909i	−0.603495	−	0.348428i	−0.770415	+	0.637542i	$0.779951\pi$
$692$	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
$698$	48.7475	+	11.2731i	1.84512	+	0.426693i
$699$		0			0
$700$	−3.03341	+	6.20784i	−0.114652	+	0.234634i
$701$		−	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
$704$	−18.0085	−	5.89518i	−0.678721	−	0.222183i
$705$		0			0
$706$	−9.54362	+	41.2689i	−0.359179	+	1.55317i
$707$	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
$716$	−4.77279	+	3.21419i	−0.178368	+	0.120120i
$717$		0			0
$718$	2.26351	+	7.41334i	0.0844736	+	0.276664i
$719$	7.89549			0.294452			0.147226	−	0.989103i	$-0.452966\pi$
$719$	7.89549			0.294452			0.147226	+	0.989103i	$0.452966\pi$
$720$		0			0
$721$	−11.9863			−0.446392
$722$	−5.03509	−	16.4907i	−0.187387	−	0.613719i
$723$		0			0
$724$	8.01243	−	5.39590i	0.297780	−	0.200537i
$725$	19.1198	−	11.0388i	0.710091	−	0.409971i
$726$		0			0
$727$	9.22490	+	5.32600i	0.342133	+	0.197530i	0.661215	−	0.750197i	$-0.270041\pi$
$727$	9.22490	+	5.32600i	0.342133	+	0.197530i	−0.319082	+	0.947727i	$0.603375\pi$
$728$	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	$0.419141\pi$
$734$	−5.42191	+	23.4456i	−0.200126	+	0.865394i
$735$		0			0
$736$	21.5113	+	46.3529i	0.792916	+	1.70859i
$737$			1.21464i			0.0447417i
$738$		0			0
$739$			34.1328i			1.25560i	0.778376	+	0.627798i	$0.216044\pi$
$739$			34.1328i			1.25560i	−0.778376	+	0.627798i	$0.783956\pi$
$740$	−8.04901	+	16.4722i	−0.295888	+	0.605531i
$741$		0			0
$742$	3.28862	+	0.760510i	0.120729	+	0.0279192i
$743$	−7.11347	−	12.3209i	−0.260968	−	0.452009i	0.705532	−	0.708678i	$-0.250708\pi$
$743$	−7.11347	−	12.3209i	−0.260968	−	0.452009i	−0.966499	+	0.256669i	$0.917375\pi$
$744$		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	0.103844	−	0.994594i	$-0.466886\pi$
$751$	27.8733	−	16.0926i	1.01711	−	0.587228i	0.913265	+	0.407365i	$0.133552\pi$
$752$	1.22056	+	1.56698i	0.0445093	+	0.0571419i
$753$		0			0
$754$	−2.17673	+	0.664621i	−0.0792719	+	0.0242041i
$755$	−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	$0.710555\pi$
$758$	35.9048	−	10.9628i	1.30412	−	0.398187i
$759$		0			0
$760$	−3.38018	+	21.1906i	−0.122612	+	0.768665i
$761$	−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	$0.989865\pi$
$770$	−9.48950	−	2.19449i	−0.341978	−	0.0790840i
$771$		0			0
$772$	33.4194	+	16.3301i	1.20279	+	0.587732i
$773$		−	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
$776$	15.2196	−	5.82303i	0.546350	−	0.209035i
$777$		0			0
$778$	−3.75892	+	16.2545i	−0.134764	+	0.582751i
$779$	−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	−0.382722	−	0.923863i	$-0.625013\pi$
$787$	6.34026	−	3.66055i	0.226006	−	0.130485i	0.608728	+	0.793379i	$0.291680\pi$
$788$	−19.2737	−	28.6197i	−0.686596	−	1.01953i
$789$		0			0
$790$	−13.9170	−	45.5804i	−0.495146	−	1.62168i
$791$	−18.3484			−0.652393
$792$		0			0
$793$	−1.86145			−0.0661020
$794$	5.59905	+	18.3377i	0.198703	+	0.650782i
$795$		0			0
$796$	−1.30954	−	1.94455i	−0.0464155	−	0.0689228i
$797$	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
$806$	0.00839123	−	0.0362856i	0.000295568	−	0.00127811i
$807$		0			0
$808$	14.5846	+	38.1196i	0.513085	+	1.34104i
$809$		−	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	$-0.633492\pi$
$811$		−	52.0205i		−	1.82669i	0.407192	−	0.913343i	$-0.366508\pi$
$812$	−11.4837	−	5.61140i	−0.402998	−	0.196921i
$813$		0			0
$814$	−10.2888	−	2.37933i	−0.360622	−	0.0833956i
$815$	−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	−0.192361	−	0.981324i	$-0.561614\pi$
$823$	16.1029	−	9.29699i	0.561311	−	0.324073i	0.753671	+	0.657251i	$0.228281\pi$
$824$	−33.4791	−	5.34034i	−1.16630	−	0.186040i
$825$		0			0
$826$	−10.8067	+	3.29960i	−0.376013	+	0.114808i
$827$	22.2626			0.774145			0.387072	−	0.922049i	$-0.373486\pi$
$827$	22.2626			0.774145			0.387072	+	0.922049i	$0.373486\pi$
$828$		0			0
$829$	17.1771			0.596586			0.298293	−	0.954474i	$-0.403583\pi$
$829$	17.1771			0.596586			0.298293	+	0.954474i	$0.403583\pi$
$830$	3.45772	−	1.05574i	0.120019	−	0.0366454i
$831$		0			0
$832$	1.50010	−	1.34473i	0.0520068	−	0.0466202i
$833$	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	$0.435652\pi$
$839$	−21.6662	+	37.5270i	−0.748000	+	1.29557i	−0.948780	+	0.315938i	$0.897681\pi$
$840$		0			0
$841$	5.92031	+	10.2543i	0.204149	+	0.353596i
$842$	11.0914	+	2.56494i	0.382235	+	0.0883937i
$843$		0			0
$844$	8.93398	−	18.2833i	0.307520	−	0.629337i
$845$			37.6156i			1.29402i
$846$		0			0
$847$			5.38970i			0.185192i
$848$	8.84667	+	3.58940i	0.303796	+	0.123260i
$849$		0			0
$850$	−8.37535	+	36.2170i	−0.287272	+	1.24223i
$851$	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	−0.219547	−	0.975602i	$-0.570458\pi$
$859$	15.1108	−	8.72425i	0.515575	−	0.297668i	0.735122	+	0.677934i	$0.237125\pi$
$860$	−39.9966	+	26.9353i	−1.36387	+	0.918488i
$861$		0			0
$862$	−13.4055	−	43.9049i	−0.456592	−	1.49541i
$863$	4.26940			0.145332			0.0726660	−	0.997356i	$-0.476849\pi$
$863$	4.26940			0.145332			0.0726660	+	0.997356i	$0.476849\pi$
$864$		0			0
$865$	25.4784			0.866293
$866$	7.60980	+	24.9232i	0.258592	+	0.846926i
$867$		0			0
$868$	0.173481	−	0.116829i	0.00588834	−	0.00396545i
$869$	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	$0.775888\pi$
$878$	11.6120	−	50.2128i	0.391884	−	1.69460i
$879$		0			0
$880$	−25.5276	−	10.3574i	−0.860534	−	0.349148i
$881$		−	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	$0.0758393\pi$
$883$			14.0261i			0.472017i	−0.971751	+	0.236009i	$0.924161\pi$
$884$	1.68239	−	3.44301i	0.0565851	−	0.115801i
$885$		0			0
$886$	31.3074	+	7.23999i	1.05179	+	0.243232i
$887$	0.0103232	+	0.0178804i	0.000346621	+	0.000600365i	0.866199	−	0.499700i	$-0.166556\pi$
$887$	0.0103232	+	0.0178804i	0.000346621	+	0.000600365i	−0.865852	+	0.500300i	$0.833223\pi$
$888$		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
$896$	11.3114	+	0.226504i	0.377889	+	0.00756696i
$897$		0			0
$898$	12.5271	−	3.82490i	0.418035	−	0.127639i
$899$	−0.668313			−0.0222895
$900$		0			0
$901$	18.1600			0.604998
$902$	26.7899	−	8.17974i	0.892005	−	0.272356i
$903$		0			0
$904$	−51.2491	−	8.17490i	−1.70452	−	0.271893i
$905$	12.1625	−	7.02205i	0.404297	−	0.233421i
$906$		0			0
$907$	40.9665	+	23.6520i	1.36027	+	0.785353i	0.989660	−	0.143436i	$-0.0458150\pi$
$907$	40.9665	+	23.6520i	1.36027	+	0.785353i	0.370611	+	0.928788i	$0.379148\pi$
$908$	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	−0.999553	−	0.0298838i	$-0.990486\pi$
$911$	−14.3035	+	24.7744i	−0.473897	+	0.820813i	0.525657	+	0.850697i	$0.323820\pi$
$912$		0			0
$913$	1.04122	+	1.80345i	0.0344595	+	0.0596856i
$914$	−16.2609	−	3.76041i	−0.537863	−	0.124383i
$915$		0			0
$916$	9.73567	+	4.75725i	0.321676	+	0.157184i
$917$		−	1.48102i		−	0.0489075i
$918$		0			0
$919$			42.1651i			1.39090i	0.718575	+	0.695449i	$0.244795\pi$
$919$			42.1651i			1.39090i	−0.718575	+	0.695449i	$0.755205\pi$
$920$	26.5479	+	69.3879i	0.875259	+	2.28765i
$921$		0			0
$922$	−0.815855	+	3.52795i	−0.0268688	+	0.116187i
$923$	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
$932$	−6.79451	−	10.0892i	−0.222562	−	0.330484i
$933$		0			0
$934$	0.236128	+	0.773353i	0.00772633	+	0.0253049i
$935$	−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	$0.447757\pi$
$938$	−0.211779	−	0.693607i	−0.00691482	−	0.0226471i
$939$		0			0
$940$	1.61303	+	2.39520i	0.0526111	+	0.0781228i
$941$	−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	−0.841340	−	0.540507i	$-0.818233\pi$
$947$	1.45936	−	2.52769i	0.0474228	−	0.0821387i	0.888762	+	0.458368i	$0.151566\pi$
$948$		0			0
$949$	−0.512248	−	0.887239i	−0.0166283	−	0.0288010i
$950$	−2.87214	+	12.4198i	−0.0931845	+	0.402952i
$951$		0			0
$952$	20.0994	−	7.69008i	0.651427	−	0.249237i
$953$		−	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
$956$	−16.4927	−	8.05902i	−0.533412	−	0.260647i
$957$		0			0
$958$	38.3142	+	8.86035i	1.23788	+	0.286265i
$959$	−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	−0.484099	−	0.875013i	$-0.660853\pi$
$967$	0.983735	−	0.567960i	0.0316348	−	0.0182644i	0.515734	+	0.856749i	$0.327519\pi$
$968$	−2.40132	+	15.0540i	−0.0771812	+	0.483855i
$969$		0			0
$970$	22.6585	−	6.91830i	0.727519	−	0.222133i
$971$	−7.03338			−0.225712			−0.112856	−	0.993611i	$-0.536000\pi$
$971$	−7.03338			−0.225712			−0.112856	+	0.993611i	$0.536000\pi$
$972$		0			0
$973$	8.32882			0.267010
$974$	−13.9701	+	4.26548i	−0.447631	+	0.136675i
$975$		0			0
$976$	−18.1692	−	23.3261i	−0.581584	−	0.746649i
$977$	−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	$-0.598700\pi$
$983$	21.0741	−	36.5015i	0.672161	−	1.16422i	0.977290	−	0.211905i	$-0.0679669\pi$
$984$		0			0
$985$	−25.0821	−	43.4435i	−0.799182	−	1.38422i
$986$	−66.9965	−	15.4933i	−2.13360	−	0.493406i
$987$		0			0
$988$	0.576940	−	1.18070i	0.0183549	−	0.0375632i
$989$			74.9050i			2.38184i
$990$		0			0
$991$			9.26522i			0.294320i	0.989113	+	0.147160i	$0.0470131\pi$
$991$			9.26522i			0.294320i	−0.989113	+	0.147160i	$0.952987\pi$
$992$	0.536605	−	0.249026i	0.0170372	−	0.00790658i
$993$		0			0
$994$	−0.462763	+	2.00110i	−0.0146779	+	0.0634709i
$995$	−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.575.15		72
3.2	odd	2		252.2.ba.a.155.22	✓	72
4.3	odd	2	inner	756.2.ba.a.575.3		72
9.4	even	3		252.2.ba.a.239.34	yes	72
9.5	odd	6	inner	756.2.ba.a.71.3		72
12.11	even	2		252.2.ba.a.155.34	yes	72
36.23	even	6	inner	756.2.ba.a.71.15		72
36.31	odd	6		252.2.ba.a.239.22	yes	72

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

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)

\(f(q)\)	\(=\)	\(q+(-0.412980 - 1.35257i) q^{2} +(-1.65890 + 1.11717i) q^{4} +(-2.51813 + 1.45385i) q^{5} +(0.866025 + 0.500000i) q^{7} +(2.19614 + 1.78241i) q^{8} +O(q^{10})\)	\(q+(-0.412980 - 1.35257i) q^{2} +(-1.65890 + 1.11717i) q^{4} +(-2.51813 + 1.45385i) q^{5} +(0.866025 + 0.500000i) q^{7} +(2.19614 + 1.78241i) q^{8} +(3.00637 + 2.80555i) q^{10} +(-1.18430 + 2.05127i) q^{11} +(-0.125913 - 0.218087i) q^{13} +(0.318634 - 1.37785i) q^{14} +(1.50387 - 3.70653i) q^{16} -7.60859i q^{17} -2.60920i q^{19} +(2.55313 - 5.22496i) q^{20} +(3.26359 + 0.754720i) q^{22} +(-4.51674 - 7.82323i) q^{23} +(1.72733 - 2.99183i) q^{25} +(-0.242979 + 0.260371i) q^{26} +(-1.99523 + 0.138049i) q^{28} +(5.53448 + 3.19533i) q^{29} +(-0.0905658 + 0.0522882i) q^{31} +(-5.63441 - 0.503365i) q^{32} +(-10.2912 + 3.14219i) q^{34} -2.90769 q^{35} -3.15261 q^{37} +(-3.52912 + 1.07755i) q^{38} +(-8.12152 - 1.29549i) q^{40} +(7.24183 - 4.18107i) q^{41} +(-7.18102 - 4.14596i) q^{43} +(-0.326984 - 4.72592i) q^{44} +(-8.71615 + 9.34005i) q^{46} +(-0.248282 + 0.430036i) q^{47} +(0.500000 + 0.866025i) q^{49} +(-4.76001 - 1.10078i) q^{50} +(0.452516 + 0.221118i) q^{52} +2.38678i q^{53} -6.88718i q^{55} +(1.01071 + 2.64168i) q^{56} +(2.03629 - 8.80538i) q^{58} +(-3.99487 - 6.91932i) q^{59} +(3.69592 - 6.40151i) q^{61} +(0.108125 + 0.100903i) q^{62} +(1.64606 + 7.82882i) q^{64} +(0.634129 + 0.366115i) q^{65} +(0.444103 - 0.256403i) q^{67} +(8.50008 + 12.6219i) q^{68} +(1.20082 + 3.93286i) q^{70} -1.45233 q^{71} +4.06828 q^{73} +(1.30196 + 4.26412i) q^{74} +(2.91491 + 4.32839i) q^{76} +(-2.05127 + 1.18430i) q^{77} +(-10.0369 - 5.79482i) q^{79} +(1.60178 + 11.5199i) q^{80} +(-8.64592 - 8.06839i) q^{82} +(0.439593 - 0.761398i) q^{83} +(11.0617 + 19.1594i) q^{85} +(-2.64209 + 11.4250i) q^{86} +(-6.25710 + 2.39398i) q^{88} -14.6787i q^{89} -0.251825i q^{91} +(16.2327 + 7.93195i) q^{92} +(0.684190 + 0.158222i) q^{94} +(3.79337 + 6.57031i) q^{95} +(2.88066 - 4.98945i) q^{97} +(0.964871 - 1.03394i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 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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