LMFDB - Embedded newform 880.2.cd.d.609.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(49,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 5, 4]))

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

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

chi := DirichletCharacter("880.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.cd (of order $10$, degree $4$, 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:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 220)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			609.3
Character	$\chi$	$=$	880.609
Dual form			880.2.cd.d.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.989226 - 0.321419i) q^{3} +(1.37039 + 1.76693i) q^{5} +(-2.15207 + 0.699249i) q^{7} +(-1.55179 - 1.12744i) q^{9} +(2.50847 - 2.16969i) q^{11} +(0.157672 - 0.217017i) q^{13} +(-0.787698 - 2.18836i) q^{15} +(3.48212 + 4.79272i) q^{17} +(-1.77525 + 5.46367i) q^{19} +2.35363 q^{21} +2.92836i q^{23} +(-1.24408 + 4.84275i) q^{25} +(3.00682 + 4.13853i) q^{27} +(-2.00268 - 6.16362i) q^{29} +(0.202293 + 0.146974i) q^{31} +(-3.17883 + 1.34004i) q^{33} +(-4.18469 - 2.84431i) q^{35} +(-9.79964 + 3.18410i) q^{37} +(-0.225727 + 0.164000i) q^{39} +(-0.730277 + 2.24756i) q^{41} +7.56763i q^{43} +(-0.134444 - 4.28694i) q^{45} +(-1.07714 - 0.349982i) q^{47} +(-1.52068 + 1.10484i) q^{49} +(-1.90413 - 5.86031i) q^{51} +(-5.99609 + 8.25291i) q^{53} +(7.27127 + 1.45898i) q^{55} +(3.51226 - 4.83421i) q^{57} +(3.52502 + 10.8489i) q^{59} +(3.73924 - 2.71672i) q^{61} +(4.12792 + 1.34124i) q^{63} +(0.599526 - 0.0188020i) q^{65} +6.11229i q^{67} +(0.941231 - 2.89681i) q^{69} +(4.11807 - 2.99195i) q^{71} +(7.75747 - 2.52055i) q^{73} +(2.78723 - 4.39071i) q^{75} +(-3.88125 + 6.42337i) q^{77} +(6.71777 + 4.88074i) q^{79} +(0.133975 + 0.412332i) q^{81} +(-9.65532 - 13.2894i) q^{83} +(-3.69655 + 12.7205i) q^{85} +6.74092i q^{87} +5.73205 q^{89} +(-0.187572 + 0.577288i) q^{91} +(-0.152873 - 0.210411i) q^{93} +(-12.0867 + 4.35060i) q^{95} +(2.65265 - 3.65106i) q^{97} +(-6.33883 + 0.538749i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{5} + 14 q^{9} + 2 q^{11} + q^{15} - 8 q^{19} - 28 q^{21} + 27 q^{25} - 16 q^{29} + 26 q^{31} - 17 q^{35} - 12 q^{39} + 10 q^{41} - 40 q^{45} - 46 q^{49} + 12 q^{51} + 33 q^{55} + 48 q^{59} - 10 q^{61}+ \cdots - 156 q^{99}+O(q^{100}) $ 24 * q + q^5 + 14 * q^9 + 2 * q^11 + q^15 - 8 * q^19 - 28 * q^21 + 27 * q^25 - 16 * q^29 + 26 * q^31 - 17 * q^35 - 12 * q^39 + 10 * q^41 - 40 * q^45 - 46 * q^49 + 12 * q^51 + 33 * q^55 + 48 * q^59 - 10 * q^61 - 22 * q^65 - 58 * q^69 - 42 * q^71 + 17 * q^75 + 64 * q^79 + 36 * q^81 - 17 * q^85 + 72 * q^89 - 10 * q^91 - 67 * q^95 - 156 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.989226	−	0.321419i	−0.571130	−	0.185571i	0.00919303	−	0.999958i	$-0.497074\pi$
$3$	−0.989226	−	0.321419i	−0.571130	−	0.185571i	−0.580323	+	0.814386i	$0.697074\pi$
$4$		0			0
$5$	1.37039	+	1.76693i	0.612856	+	0.790195i
$5$	1.37039	+	1.76693i	0.612856	+	0.790195i
$6$		0			0
$7$	−2.15207	+	0.699249i	−0.813405	+	0.264291i	−0.686039	−	0.727565i	$-0.740652\pi$
$7$	−2.15207	+	0.699249i	−0.813405	+	0.264291i	−0.127365	+	0.991856i	$0.540652\pi$
$8$		0			0
$9$	−1.55179	−	1.12744i	−0.517264	−	0.375814i
$10$		0			0
$11$	2.50847	−	2.16969i	0.756333	−	0.654187i
$11$	2.50847	−	2.16969i	0.756333	−	0.654187i
$12$		0			0
$13$	0.157672	−	0.217017i	0.0437304	−	0.0601897i	−0.786592	−	0.617473i	$-0.788156\pi$
$13$	0.157672	−	0.217017i	0.0437304	−	0.0601897i	0.830322	+	0.557284i	$0.188156\pi$
$14$		0			0
$15$	−0.787698	−	2.18836i	−0.203383	−	0.565033i
$16$		0			0
$17$	3.48212	+	4.79272i	0.844537	+	1.16241i	0.985040	+	0.172326i	$0.0551281\pi$
$17$	3.48212	+	4.79272i	0.844537	+	1.16241i	−0.140503	+	0.990080i	$0.544872\pi$
$18$		0			0
$19$	−1.77525	+	5.46367i	−0.407271	+	1.25345i	0.511712	+	0.859157i	$0.329011\pi$
$19$	−1.77525	+	5.46367i	−0.407271	+	1.25345i	−0.918984	+	0.394296i	$0.870989\pi$
$20$		0			0
$21$	2.35363			0.513605
$22$		0			0
$23$			2.92836i			0.610605i	0.952255	+	0.305303i	$0.0987576\pi$
$23$			2.92836i			0.610605i	−0.952255	+	0.305303i	$0.901242\pi$
$24$		0			0
$25$	−1.24408	+	4.84275i	−0.248815	+	0.968551i
$26$		0			0
$27$	3.00682	+	4.13853i	0.578663	+	0.796461i
$28$		0			0
$29$	−2.00268	−	6.16362i	−0.371889	−	1.14456i	−0.945554	−	0.325466i	$-0.894479\pi$
$29$	−2.00268	−	6.16362i	−0.371889	−	1.14456i	0.573665	−	0.819090i	$-0.305521\pi$
$30$		0			0
$31$	0.202293	+	0.146974i	0.0363328	+	0.0263973i	0.605803	−	0.795614i	$-0.292852\pi$
$31$	0.202293	+	0.146974i	0.0363328	+	0.0263973i	−0.569471	+	0.822012i	$0.692852\pi$
$32$		0			0
$33$	−3.17883	+	1.34004i	−0.553363	+	0.233272i
$34$		0			0
$35$	−4.18469	−	2.84431i	−0.707341	−	0.480776i
$36$		0			0
$37$	−9.79964	+	3.18410i	−1.61105	+	0.523462i	−0.969807	−	0.243874i	$-0.921582\pi$
$37$	−9.79964	+	3.18410i	−1.61105	+	0.523462i	−0.641244	+	0.767337i	$0.721582\pi$
$38$		0			0
$39$	−0.225727	+	0.164000i	−0.0361452	+	0.0262611i
$40$		0			0
$41$	−0.730277	+	2.24756i	−0.114050	+	0.351010i	−0.991748	−	0.128205i	$-0.959079\pi$
$41$	−0.730277	+	2.24756i	−0.114050	+	0.351010i	0.877698	+	0.479215i	$0.159079\pi$
$42$		0			0
$43$			7.56763i			1.15405i	0.816725	+	0.577027i	$0.195787\pi$
$43$			7.56763i			1.15405i	−0.816725	+	0.577027i	$0.804213\pi$
$44$		0			0
$45$	−0.134444	−	4.28694i	−0.0200418	−	0.639059i
$46$		0			0
$47$	−1.07714	−	0.349982i	−0.157116	−	0.0510502i	0.229403	−	0.973332i	$-0.426323\pi$
$47$	−1.07714	−	0.349982i	−0.157116	−	0.0510502i	−0.386519	+	0.922281i	$0.626323\pi$
$48$		0			0
$49$	−1.52068	+	1.10484i	−0.217240	+	0.157834i
$50$		0			0
$51$	−1.90413	−	5.86031i	−0.266631	−	0.820607i
$52$		0			0
$53$	−5.99609	+	8.25291i	−0.823627	+	1.13362i	0.165449	+	0.986218i	$0.447093\pi$
$53$	−5.99609	+	8.25291i	−0.823627	+	1.13362i	−0.989076	+	0.147406i	$0.952907\pi$
$54$		0			0
$55$	7.27127	+	1.45898i	0.980458	+	0.196728i
$56$		0			0
$57$	3.51226	−	4.83421i	0.465210	−	0.640306i
$58$		0			0
$59$	3.52502	+	10.8489i	0.458919	+	1.41241i	0.866473	+	0.499225i	$0.166382\pi$
$59$	3.52502	+	10.8489i	0.458919	+	1.41241i	−0.407554	+	0.913181i	$0.633618\pi$
$60$		0			0
$61$	3.73924	−	2.71672i	0.478761	−	0.347840i	−0.322085	−	0.946711i	$-0.604384\pi$
$61$	3.73924	−	2.71672i	0.478761	−	0.347840i	0.800846	+	0.598871i	$0.204384\pi$
$62$		0			0
$63$	4.12792	+	1.34124i	0.520069	+	0.168981i
$64$		0			0
$65$	0.599526	−	0.0188020i	0.0743621	−	0.00233210i
$66$		0			0
$67$			6.11229i			0.746735i	0.927683	+	0.373368i	$0.121797\pi$
$67$			6.11229i			0.746735i	−0.927683	+	0.373368i	$0.878203\pi$
$68$		0			0
$69$	0.941231	−	2.89681i	0.113311	−	0.348735i
$70$		0			0
$71$	4.11807	−	2.99195i	0.488725	−	0.355079i	−0.315969	−	0.948770i	$-0.602330\pi$
$71$	4.11807	−	2.99195i	0.488725	−	0.355079i	0.804694	+	0.593690i	$0.202330\pi$
$72$		0			0
$73$	7.75747	−	2.52055i	0.907943	−	0.295009i	0.182432	−	0.983219i	$-0.441603\pi$
$73$	7.75747	−	2.52055i	0.907943	−	0.295009i	0.725512	+	0.688210i	$0.241603\pi$
$74$		0			0
$75$	2.78723	−	4.39071i	0.321841	−	0.506996i
$76$		0			0
$77$	−3.88125	+	6.42337i	−0.442309	+	0.732011i
$78$		0			0
$79$	6.71777	+	4.88074i	0.755808	+	0.549127i	0.897622	−	0.440767i	$-0.145293\pi$
$79$	6.71777	+	4.88074i	0.755808	+	0.549127i	−0.141814	+	0.989893i	$0.545293\pi$
$80$		0			0
$81$	0.133975	+	0.412332i	0.0148861	+	0.0458147i
$82$		0			0
$83$	−9.65532	−	13.2894i	−1.05981	−	1.45870i	−0.879984	−	0.475003i	$-0.842447\pi$
$83$	−9.65532	−	13.2894i	−1.05981	−	1.45870i	−0.179824	−	0.983699i	$-0.557553\pi$
$84$		0			0
$85$	−3.69655	+	12.7205i	−0.400947	+	1.37974i
$86$		0			0
$87$			6.74092i			0.722702i
$88$		0			0
$89$	5.73205			0.607596			0.303798	−	0.952736i	$-0.401745\pi$
$89$	5.73205			0.607596			0.303798	+	0.952736i	$0.401745\pi$
$90$		0			0
$91$	−0.187572	+	0.577288i	−0.0196629	+	0.0605162i
$92$		0			0
$93$	−0.152873	−	0.210411i	−0.0158522	−	0.0218186i
$94$		0			0
$95$	−12.0867	+	4.35060i	−1.24007	+	0.446362i
$96$		0			0
$97$	2.65265	−	3.65106i	0.269336	−	0.370709i	−0.652830	−	0.757505i	$-0.726418\pi$
$97$	2.65265	−	3.65106i	0.269336	−	0.370709i	0.922165	+	0.386796i	$0.126418\pi$
$98$		0			0
$99$	−6.33883	+	0.538749i	−0.637077	+	0.0541464i
$100$		0			0
$101$	7.58271	+	5.50916i	0.754508	+	0.548182i	0.897221	−	0.441582i	$-0.145583\pi$
$101$	7.58271	+	5.50916i	0.754508	+	0.548182i	−0.142713	+	0.989764i	$0.545583\pi$
$102$		0			0
$103$	6.25332	−	2.03183i	0.616158	−	0.200202i	0.0157244	−	0.999876i	$-0.494995\pi$
$103$	6.25332	−	2.03183i	0.616158	−	0.200202i	0.600434	+	0.799674i	$0.294995\pi$
$104$		0			0
$105$	3.22539	+	4.15870i	0.314766	+	0.405848i
$106$		0			0
$107$	−6.60021	−	2.14454i	−0.638066	−	0.207320i	−0.0279214	−	0.999610i	$-0.508889\pi$
$107$	−6.60021	−	2.14454i	−0.638066	−	0.207320i	−0.610145	+	0.792290i	$0.708889\pi$
$108$		0			0
$109$	−10.0676			−0.964299			−0.482150	−	0.876089i	$-0.660144\pi$
$109$	−10.0676			−0.964299			−0.482150	+	0.876089i	$0.660144\pi$
$110$		0			0
$111$	10.7175			1.01726
$112$		0			0
$113$	17.8596	+	5.80293i	1.68009	+	0.545894i	0.984928	−	0.172962i	$-0.0553339\pi$
$113$	17.8596	+	5.80293i	1.68009	+	0.545894i	0.695159	+	0.718856i	$0.255334\pi$
$114$		0			0
$115$	−5.17421	+	4.01299i	−0.482497	+	0.374213i
$116$		0			0
$117$	−0.489349	+	0.158999i	−0.0452403	+	0.0146995i
$118$		0			0
$119$	−10.8450	−	7.87939i	−0.994164	−	0.722302i
$120$		0			0
$121$	1.58488	−	10.8852i	0.144080	−	0.989566i
$122$		0			0
$123$	1.44482	−	1.98862i	0.130275	−	0.179308i
$124$		0			0
$125$	−10.2617	+	4.43825i	−0.917832	+	0.396969i
$126$		0			0
$127$	−11.2210	−	15.4444i	−0.995707	−	1.37047i	−0.927922	−	0.372773i	$-0.878407\pi$
$127$	−11.2210	−	15.4444i	−0.995707	−	1.37047i	−0.0677847	−	0.997700i	$-0.521593\pi$
$128$		0			0
$129$	2.43238	−	7.48610i	0.214159	−	0.659115i
$130$		0			0
$131$	1.78426			0.155891			0.0779457	−	0.996958i	$-0.475164\pi$
$131$	1.78426			0.155891			0.0779457	+	0.996958i	$0.475164\pi$
$132$		0			0
$133$		−	12.9995i		−	1.12720i
$134$		0			0
$135$	−3.19198	+	10.9842i	−0.274722	+	0.945372i
$136$		0			0
$137$	4.45074	+	6.12592i	0.380252	+	0.523372i	0.955651	−	0.294500i	$-0.0951532\pi$
$137$	4.45074	+	6.12592i	0.380252	+	0.523372i	−0.575399	+	0.817873i	$0.695153\pi$
$138$		0			0
$139$	−3.41970	−	10.5248i	−0.290055	−	0.892698i	−0.984838	−	0.173478i	$-0.944499\pi$
$139$	−3.41970	−	10.5248i	−0.290055	−	0.892698i	0.694783	−	0.719220i	$-0.255501\pi$
$140$		0			0
$141$	0.953039	+	0.692424i	0.0802604	+	0.0583126i
$142$		0			0
$143$	−0.0753438	−	0.886482i	−0.00630056	−	0.0741313i
$144$		0			0
$145$	8.14624	−	11.9852i	0.676508	−	0.995313i
$146$		0			0
$147$	1.85941	−	0.604159i	0.153362	−	0.0498302i
$148$		0			0
$149$	−9.43314	+	6.85358i	−0.772793	+	0.561467i	−0.902807	−	0.430045i	$-0.858498\pi$
$149$	−9.43314	+	6.85358i	−0.772793	+	0.561467i	0.130015	+	0.991512i	$0.458498\pi$
$150$		0			0
$151$	0.0749733	−	0.230744i	0.00610124	−	0.0187777i	−0.947960	−	0.318391i	$-0.896858\pi$
$151$	0.0749733	−	0.230744i	0.00610124	−	0.0187777i	0.954061	+	0.299613i	$0.0968576\pi$
$152$		0			0
$153$		−	11.3632i		−	0.918660i
$154$		0			0
$155$	0.0175262	+	0.558848i	0.00140774	+	0.0448878i
$156$		0			0
$157$	−2.80741	−	0.912183i	−0.224056	−	0.0728001i	0.194838	−	0.980835i	$-0.437582\pi$
$157$	−2.80741	−	0.912183i	−0.224056	−	0.0728001i	−0.418894	+	0.908035i	$0.637582\pi$
$158$		0			0
$159$	8.58414	−	6.23674i	0.680766	−	0.494606i
$160$		0			0
$161$	−2.04765	−	6.30203i	−0.161378	−	0.496669i
$162$		0			0
$163$	6.10996	−	8.40964i	0.478569	−	0.658694i	−0.499660	−	0.866222i	$-0.666542\pi$
$163$	6.10996	−	8.40964i	0.478569	−	0.658694i	0.978229	+	0.207528i	$0.0665417\pi$
$164$		0			0
$165$	−6.72399	−	3.78038i	−0.523462	−	0.294303i
$166$		0			0
$167$	5.81185	−	7.99932i	0.449734	−	0.619006i	−0.522606	−	0.852574i	$-0.675040\pi$
$167$	5.81185	−	7.99932i	0.449734	−	0.619006i	0.972340	+	0.233568i	$0.0750402\pi$
$168$		0			0
$169$	3.99498	+	12.2953i	0.307307	+	0.945792i
$170$		0			0
$171$	8.91481	−	6.47699i	0.681732	−	0.495308i
$172$		0			0
$173$	−15.0185	−	4.87981i	−1.14184	−	0.371005i	−0.323774	−	0.946134i	$-0.604952\pi$
$173$	−15.0185	−	4.87981i	−1.14184	−	0.371005i	−0.818063	+	0.575129i	$0.804952\pi$
$174$		0			0
$175$	−0.708953	−	11.2918i	−0.0535918	−	0.853583i
$176$		0			0
$177$		−	11.8650i		−	0.891830i
$178$		0			0
$179$	1.81268	−	5.57884i	0.135486	−	0.416982i	−0.860180	−	0.509991i	$-0.829649\pi$
$179$	1.81268	−	5.57884i	0.135486	−	0.416982i	0.995665	+	0.0930092i	$0.0296486\pi$
$180$		0			0
$181$	18.2792	−	13.2806i	1.35868	−	0.987138i	0.360151	−	0.932894i	$-0.382725\pi$
$181$	18.2792	−	13.2806i	1.35868	−	0.987138i	0.998528	−	0.0542444i	$-0.0172750\pi$
$182$		0			0
$183$	−4.57216	+	1.48559i	−0.337984	+	0.109818i
$184$		0			0
$185$	−19.0554	−	12.9518i	−1.40098	−	0.952237i
$186$		0			0
$187$	19.1335	+	4.46730i	1.39918	+	0.326681i
$188$		0			0
$189$	−9.36473	−	6.80388i	−0.681184	−	0.494909i
$190$		0			0
$191$	−3.42585	−	10.5437i	−0.247886	−	0.762914i	−0.995148	−	0.0983854i	$-0.968632\pi$
$191$	−3.42585	−	10.5437i	−0.247886	−	0.762914i	0.747262	−	0.664529i	$-0.231368\pi$
$192$		0			0
$193$	−3.76732	−	5.18527i	−0.271178	−	0.373244i	0.651609	−	0.758555i	$-0.274094\pi$
$193$	−3.76732	−	5.18527i	−0.271178	−	0.373244i	−0.922787	+	0.385311i	$0.874094\pi$
$194$		0			0
$195$	−0.599110	−	0.174100i	−0.0429032	−	0.0124675i
$196$		0			0
$197$		−	9.15141i		−	0.652011i	−0.945368	−	0.326005i	$-0.894297\pi$
$197$		−	9.15141i		−	0.652011i	0.945368	−	0.326005i	$-0.105703\pi$
$198$		0			0
$199$	−14.6653			−1.03960			−0.519798	−	0.854289i	$-0.673993\pi$
$199$	−14.6653			−1.03960			−0.519798	+	0.854289i	$0.673993\pi$
$200$		0			0
$201$	1.96461	−	6.04644i	0.138573	−	0.426483i
$202$		0			0
$203$	8.61981	+	11.8642i	0.604992	+	0.832700i
$204$		0			0
$205$	−4.97205	+	1.78968i	−0.347263	+	0.124997i
$206$		0			0
$207$	3.30156	−	4.54421i	0.229474	−	0.315844i
$208$		0			0
$209$	7.40130	+	17.5572i	0.511959	+	1.21446i
$210$		0			0
$211$	10.0758	+	7.32046i	0.693644	+	0.503962i	0.877856	−	0.478925i	$-0.158973\pi$
$211$	10.0758	+	7.32046i	0.693644	+	0.503962i	−0.184212	+	0.982886i	$0.558973\pi$
$212$		0			0
$213$	−5.03537	+	1.63609i	−0.345018	+	0.112103i
$214$		0			0
$215$	−13.3715	+	10.3706i	−0.911927	+	0.707268i
$216$		0			0
$217$	−0.538118	−	0.174845i	−0.0365299	−	0.0118693i
$218$		0			0
$219$	−8.48405			−0.573299
$220$		0			0
$221$	1.58914			0.106897
$222$		0			0
$223$	11.5954	+	3.76756i	0.776483	+	0.252295i	0.670338	−	0.742056i	$-0.266149\pi$
$223$	11.5954	+	3.76756i	0.776483	+	0.252295i	0.106145	+	0.994351i	$0.466149\pi$
$224$		0			0
$225$	7.39048	−	6.11232i	0.492699	−	0.407488i
$226$		0			0
$227$	−7.32825	+	2.38109i	−0.486393	+	0.158039i	−0.541940	−	0.840417i	$-0.682310\pi$
$227$	−7.32825	+	2.38109i	−0.486393	+	0.158039i	0.0555464	+	0.998456i	$0.482310\pi$
$228$		0			0
$229$	14.7494	+	10.7160i	0.974666	+	0.708136i	0.956510	−	0.291699i	$-0.0942205\pi$
$229$	14.7494	+	10.7160i	0.974666	+	0.708136i	0.0181560	+	0.999835i	$0.494220\pi$
$230$		0			0
$231$	5.90402	−	5.10666i	0.388456	−	0.335993i
$232$		0			0
$233$	2.90808	−	4.00263i	0.190515	−	0.262221i	−0.703065	−	0.711126i	$-0.748186\pi$
$233$	2.90808	−	4.00263i	0.190515	−	0.262221i	0.893580	+	0.448905i	$0.148186\pi$
$234$		0			0
$235$	−0.857698	−	2.38283i	−0.0559501	−	0.155439i
$236$		0			0
$237$	−5.07663	−	6.98738i	−0.329762	−	0.453879i
$238$		0			0
$239$	−5.24855	+	16.1534i	−0.339501	+	1.04488i	0.624962	+	0.780655i	$0.285115\pi$
$239$	−5.24855	+	16.1534i	−0.339501	+	1.04488i	−0.964462	+	0.264220i	$0.914885\pi$
$240$		0			0
$241$	6.72951			0.433486			0.216743	−	0.976229i	$-0.430457\pi$
$241$	6.72951			0.433486			0.216743	+	0.976229i	$0.430457\pi$
$242$		0			0
$243$		−	15.7975i		−	1.01341i
$244$		0			0
$245$	−4.03609	−	1.17288i	−0.257856	−	0.0749323i
$246$		0			0
$247$	0.905803	+	1.24673i	0.0576348	+	0.0793275i
$248$		0			0
$249$	5.27982	+	16.2496i	0.334595	+	1.02978i
$250$		0			0
$251$	15.9920	+	11.6188i	1.00940	+	0.733374i	0.964084	−	0.265598i	$-0.0855695\pi$
$251$	15.9920	+	11.6188i	1.00940	+	0.733374i	0.0453193	+	0.998973i	$0.485569\pi$
$252$		0			0
$253$	6.35364	+	7.34571i	0.399450	+	0.461821i
$254$		0			0
$255$	7.74535	−	11.3953i	0.485033	−	0.713604i
$256$		0			0
$257$	−6.08199	+	1.97616i	−0.379384	+	0.123269i	−0.492500	−	0.870312i	$-0.663917\pi$
$257$	−6.08199	+	1.97616i	−0.379384	+	0.123269i	0.113116	+	0.993582i	$0.463917\pi$
$258$		0			0
$259$	18.8630	−	13.7048i	1.17209	−	0.851573i
$260$		0			0
$261$	−3.84139	+	11.8226i	−0.237776	+	0.731799i
$262$		0			0
$263$			14.6417i			0.902843i	0.892311	+	0.451422i	$0.149083\pi$
$263$			14.6417i			0.902843i	−0.892311	+	0.451422i	$0.850917\pi$
$264$		0			0
$265$	−22.7993	+	0.715017i	−1.40055	+	0.0439231i
$266$		0			0
$267$	−5.67029	−	1.84239i	−0.347016	−	0.112752i
$268$		0			0
$269$	−16.0781	+	11.6814i	−0.980299	+	0.712229i	−0.957775	−	0.287517i	$-0.907170\pi$
$269$	−16.0781	+	11.6814i	−0.980299	+	0.712229i	−0.0225237	+	0.999746i	$0.507170\pi$
$270$		0			0
$271$	5.93702	+	18.2723i	0.360648	+	1.10996i	0.952662	+	0.304033i	$0.0983332\pi$
$271$	5.93702	+	18.2723i	0.360648	+	1.10996i	−0.592014	+	0.805928i	$0.701667\pi$
$272$		0			0
$273$	0.371102	−	0.510779i	0.0224601	−	0.0309137i
$274$		0			0
$275$	7.38655	+	14.8472i	0.445426	+	0.895319i
$276$		0			0
$277$	14.0095	−	19.2825i	0.841751	−	1.15857i	−0.143870	−	0.989597i	$-0.545955\pi$
$277$	14.0095	−	19.2825i	0.841751	−	1.15857i	0.985621	−	0.168974i	$-0.0540453\pi$
$278$		0			0
$279$	−0.148211	−	0.456147i	−0.00887316	−	0.0273088i
$280$		0			0
$281$	14.5045	−	10.5382i	0.865267	−	0.628654i	−0.0640454	−	0.997947i	$-0.520400\pi$
$281$	14.5045	−	10.5382i	0.865267	−	0.628654i	0.929313	+	0.369293i	$0.120400\pi$
$282$		0			0
$283$	−19.9975	−	6.49760i	−1.18873	−	0.386242i	−0.353127	−	0.935575i	$-0.614882\pi$
$283$	−19.9975	−	6.49760i	−1.18873	−	0.386242i	−0.835603	+	0.549333i	$0.814882\pi$
$284$		0			0
$285$	13.3549	−	0.418827i	0.791073	−	0.0248092i
$286$		0			0
$287$		−	5.34755i		−	0.315656i
$288$		0			0
$289$	−5.59176	+	17.2097i	−0.328927	+	1.01233i
$290$		0			0
$291$	−3.79759	+	2.75911i	−0.222619	+	0.161742i
$292$		0			0
$293$	−20.2271	+	6.57220i	−1.18168	+	0.383952i	−0.832991	−	0.553286i	$-0.813374\pi$
$293$	−20.2271	+	6.57220i	−1.18168	+	0.383952i	−0.348691	+	0.937238i	$0.613374\pi$
$294$		0			0
$295$	−14.3386	+	21.0956i	−0.834825	+	1.22824i
$296$		0			0
$297$	16.5219	+	3.85753i	0.958696	+	0.223836i
$298$		0			0
$299$	0.635505	+	0.461721i	0.0367522	+	0.0267020i
$300$		0			0
$301$	−5.29166	−	16.2861i	−0.305006	−	0.938712i
$302$		0			0
$303$	−5.73027	−	7.88704i	−0.329195	−	0.453098i
$304$		0			0
$305$	9.92446	+	2.88402i	0.568273	+	0.165138i
$306$		0			0
$307$		−	32.6823i		−	1.86528i	−0.360812	−	0.932639i	$-0.617500\pi$
$307$		−	32.6823i		−	1.86528i	0.360812	−	0.932639i	$-0.382500\pi$
$308$		0			0
$309$	−6.83902			−0.389058
$310$		0			0
$311$	5.84842	−	17.9996i	0.331634	−	1.02066i	−0.636723	−	0.771093i	$-0.719711\pi$
$311$	5.84842	−	17.9996i	0.331634	−	1.02066i	0.968357	−	0.249571i	$-0.0802895\pi$
$312$		0			0
$313$	7.07138	+	9.73292i	0.399698	+	0.550137i	0.960668	−	0.277699i	$-0.0895717\pi$
$313$	7.07138	+	9.73292i	0.399698	+	0.550137i	−0.560970	+	0.827836i	$0.689572\pi$
$314$		0			0
$315$	3.28697	+	9.13177i	0.185200	+	0.514517i
$316$		0			0
$317$	−5.99585	+	8.25258i	−0.336761	+	0.463511i	−0.943492	−	0.331396i	$-0.892480\pi$
$317$	−5.99585	+	8.25258i	−0.336761	+	0.463511i	0.606731	+	0.794907i	$0.292480\pi$
$318$		0			0
$319$	−18.3968	−	11.1161i	−1.03003	−	0.622381i
$320$		0			0
$321$	5.83981	+	4.24287i	0.325946	+	0.236814i
$322$		0			0
$323$	−32.3675	+	10.5168i	−1.80098	+	0.585173i
$324$		0			0
$325$	0.854805	+	1.03355i	0.0474160	+	0.0573313i
$326$		0			0
$327$	9.95911	+	3.23591i	0.550740	+	0.178946i
$328$		0			0
$329$	2.56279			0.141291
$330$		0			0
$331$	−11.8942			−0.653763			−0.326882	−	0.945065i	$-0.605998\pi$
$331$	−11.8942			−0.653763			−0.326882	+	0.945065i	$0.605998\pi$
$332$		0			0
$333$	18.7969	+	6.10748i	1.03006	+	0.334688i
$334$		0			0
$335$	−10.8000	+	8.37621i	−0.590066	+	0.457641i
$336$		0			0
$337$	9.55843	−	3.10572i	0.520681	−	0.169179i	−0.0368735	−	0.999320i	$-0.511740\pi$
$337$	9.55843	−	3.10572i	0.520681	−	0.169179i	0.557554	+	0.830141i	$0.311740\pi$
$338$		0			0
$339$	−15.8020	−	11.4808i	−0.858246	−	0.623552i
$340$		0			0
$341$	0.826334	−	0.0702317i	0.0447485	−	0.00380326i
$342$		0			0
$343$	11.8104	−	16.2556i	0.637701	−	0.877721i
$344$		0			0
$345$	6.40831	−	2.30666i	0.345012	−	0.124187i
$346$		0			0
$347$	13.6361	+	18.7685i	0.732025	+	1.00755i	0.999038	+	0.0438535i	$0.0139635\pi$
$347$	13.6361	+	18.7685i	0.732025	+	1.00755i	−0.267013	+	0.963693i	$0.586037\pi$
$348$		0			0
$349$	7.82954	−	24.0968i	0.419106	−	1.28987i	−0.489421	−	0.872048i	$-0.662792\pi$
$349$	7.82954	−	24.0968i	0.419106	−	1.28987i	0.908527	−	0.417827i	$-0.137208\pi$
$350$		0			0
$351$	1.37222			0.0732439
$352$		0			0
$353$		−	1.08185i		−	0.0575813i	−0.999585	−	0.0287907i	$-0.990834\pi$
$353$		−	1.08185i		−	0.0575813i	0.999585	−	0.0287907i	$-0.00916562\pi$
$354$		0			0
$355$	10.9299	+	3.17620i	0.580100	+	0.168575i
$356$		0			0
$357$	8.19562	+	11.2803i	0.433758	+	0.597017i
$358$		0			0
$359$	2.84200	+	8.74677i	0.149995	+	0.461637i	0.997619	−	0.0689595i	$-0.0219679\pi$
$359$	2.84200	+	8.74677i	0.149995	+	0.461637i	−0.847624	+	0.530597i	$0.821968\pi$
$360$		0			0
$361$	−11.3289	−	8.23090i	−0.596256	−	0.433205i
$362$		0			0
$363$	−5.06652	+	10.2585i	−0.265924	+	0.538434i
$364$		0			0
$365$	15.0844	+	10.2528i	0.789553	+	0.536654i
$366$		0			0
$367$	−18.4717	+	6.00182i	−0.964215	+	0.313292i	−0.748478	−	0.663159i	$-0.769215\pi$
$367$	−18.4717	+	6.00182i	−0.964215	+	0.313292i	−0.215737	+	0.976452i	$0.569215\pi$
$368$		0			0
$369$	3.66724	−	2.66440i	0.190909	−	0.138703i
$370$		0			0
$371$	7.13315	−	21.9536i	0.370335	−	1.13977i
$372$		0			0
$373$			25.8608i			1.33902i	0.742803	+	0.669510i	$0.233496\pi$
$373$			25.8608i			1.33902i	−0.742803	+	0.669510i	$0.766504\pi$
$374$		0			0
$375$	11.5777	−	1.09214i	0.597868	−	0.0563978i
$376$		0			0
$377$	−1.65338	−	0.537216i	−0.0851534	−	0.0276680i
$378$		0			0
$379$	23.2283	−	16.8764i	1.19316	−	0.866881i	0.199564	−	0.979885i	$-0.436047\pi$
$379$	23.2283	−	16.8764i	1.19316	−	0.866881i	0.993595	+	0.113004i	$0.0360473\pi$
$380$		0			0
$381$	6.13602	+	18.8847i	0.314358	+	0.967493i
$382$		0			0
$383$	−6.56908	+	9.04156i	−0.335664	+	0.462002i	−0.943169	−	0.332314i	$-0.892171\pi$
$383$	−6.56908	+	9.04156i	−0.335664	+	0.462002i	0.607505	+	0.794316i	$0.292171\pi$
$384$		0			0
$385$	−16.6684	+	1.94461i	−0.849503	+	0.0991066i
$386$		0			0
$387$	8.53208	−	11.7434i	0.433710	−	0.596951i
$388$		0			0
$389$	−9.32498	−	28.6994i	−0.472795	−	1.45511i	−0.848908	−	0.528541i	$-0.822739\pi$
$389$	−9.32498	−	28.6994i	−0.472795	−	1.45511i	0.376112	−	0.926574i	$-0.377261\pi$
$390$		0			0
$391$	−14.0348	+	10.1969i	−0.709771	+	0.515679i
$392$		0			0
$393$	−1.76504	−	0.573495i	−0.0890343	−	0.0289290i
$394$		0			0
$395$	0.582015	+	18.5583i	0.0292843	+	0.933771i
$396$		0			0
$397$			28.3518i			1.42293i	0.702719	+	0.711467i	$0.251969\pi$
$397$			28.3518i			1.42293i	−0.702719	+	0.711467i	$0.748031\pi$
$398$		0			0
$399$	−4.17830	+	12.8595i	−0.209176	+	0.643779i
$400$		0			0
$401$	−11.2850	+	8.19906i	−0.563548	+	0.409442i	−0.832756	−	0.553641i	$-0.813238\pi$
$401$	−11.2850	+	8.19906i	−0.563548	+	0.409442i	0.269208	+	0.963082i	$0.413238\pi$
$402$		0			0
$403$	0.0637918	−	0.0207272i	0.00317770	−	0.00103250i
$404$		0			0
$405$	−0.544964	+	0.801779i	−0.0270795	+	0.0398407i
$406$		0			0
$407$	−17.6736	+	29.2494i	−0.876050	+	1.44984i
$408$		0			0
$409$	−10.4677	−	7.60522i	−0.517594	−	0.376054i	0.298103	−	0.954534i	$-0.403646\pi$
$409$	−10.4677	−	7.60522i	−0.517594	−	0.376054i	−0.815697	+	0.578480i	$0.803646\pi$
$410$		0			0
$411$	−2.43380	−	7.49047i	−0.120051	−	0.369478i
$412$		0			0
$413$	−15.1722	−	20.8827i	−0.746573	−	1.02757i
$414$		0			0
$415$	10.2499	−	35.2719i	0.503148	−	1.73143i
$416$		0			0
$417$			11.5105i			0.563673i
$418$		0			0
$419$	−26.6889			−1.30384			−0.651920	−	0.758288i	$-0.726036\pi$
$419$	−26.6889			−1.30384			−0.651920	+	0.758288i	$0.726036\pi$
$420$		0			0
$421$	8.25641	−	25.4106i	0.402393	−	1.23844i	−0.520660	−	0.853764i	$-0.674314\pi$
$421$	8.25641	−	25.4106i	0.402393	−	1.23844i	0.923053	−	0.384673i	$-0.125686\pi$
$422$		0			0
$423$	1.27690	+	1.75751i	0.0620852	+	0.0854530i
$424$		0			0
$425$	−27.5420	+	10.9005i	−1.33598	+	0.528753i
$426$		0			0
$427$	−6.14743	+	8.46122i	−0.297495	+	0.409467i
$428$		0			0
$429$	−0.210400	+	0.901148i	−0.0101582	+	0.0435078i
$430$		0			0
$431$	−12.0756	−	8.77343i	−0.581661	−	0.422601i	0.257662	−	0.966235i	$-0.417048\pi$
$431$	−12.0756	−	8.77343i	−0.581661	−	0.422601i	−0.839322	+	0.543634i	$0.817048\pi$
$432$		0			0
$433$	−18.8500	+	6.12475i	−0.905875	+	0.294337i	−0.724660	−	0.689107i	$-0.758003\pi$
$433$	−18.8500	+	6.12475i	−0.905875	+	0.294337i	−0.181215	+	0.983443i	$0.558003\pi$
$434$		0			0
$435$	−11.9107	+	9.23767i	−0.571076	+	0.442912i
$436$		0			0
$437$	−15.9996	−	5.19859i	−0.765365	−	0.248682i
$438$		0			0
$439$	34.4507			1.64424			0.822122	−	0.569312i	$-0.192790\pi$
$439$	34.4507			1.64424			0.822122	+	0.569312i	$0.192790\pi$
$440$		0			0
$441$	3.60542			0.171687
$442$		0			0
$443$	25.8242	+	8.39080i	1.22695	+	0.398659i	0.849607	−	0.527416i	$-0.176839\pi$
$443$	25.8242	+	8.39080i	1.22695	+	0.398659i	0.377339	+	0.926075i	$0.376839\pi$
$444$		0			0
$445$	7.85513	+	10.1281i	0.372369	+	0.480119i
$446$		0			0
$447$	11.5344	−	3.74775i	0.545557	−	0.177262i
$448$		0			0
$449$	22.1399	+	16.0856i	1.04485	+	0.759125i	0.971225	−	0.238162i	$-0.0765449\pi$
$449$	22.1399	+	16.0856i	1.04485	+	0.759125i	0.0736198	+	0.997286i	$0.476545\pi$
$450$		0			0
$451$	3.04464	+	7.22243i	0.143366	+	0.340091i
$452$		0			0
$453$	−0.148331	+	0.204160i	−0.00696921	+	0.00959229i
$454$		0			0
$455$	−1.27707	+	0.459681i	−0.0598701	+	0.0215502i
$456$		0			0
$457$	−22.6649	−	31.1955i	−1.06022	−	1.45926i	−0.879601	−	0.475711i	$-0.842191\pi$
$457$	−22.6649	−	31.1955i	−1.06022	−	1.45926i	−0.180617	−	0.983554i	$-0.557809\pi$
$458$		0			0
$459$	−9.36473	+	28.8217i	−0.437108	+	1.34528i
$460$		0			0
$461$	−27.7494			−1.29242			−0.646208	−	0.763161i	$-0.723646\pi$
$461$	−27.7494			−1.29242			−0.646208	+	0.763161i	$0.723646\pi$
$462$		0			0
$463$		−	10.9962i		−	0.511035i	−0.966804	−	0.255518i	$-0.917754\pi$
$463$		−	10.9962i		−	0.511035i	0.966804	−	0.255518i	$-0.0822459\pi$
$464$		0			0
$465$	0.162287	−	0.558460i	0.00752588	−	0.0258980i
$466$		0			0
$467$	18.8334	+	25.9219i	0.871504	+	1.19952i	0.978702	+	0.205285i	$0.0658122\pi$
$467$	18.8334	+	25.9219i	0.871504	+	1.19952i	−0.107198	+	0.994238i	$0.534188\pi$
$468$		0			0
$469$	−4.27401	−	13.1541i	−0.197356	−	0.607398i
$470$		0			0
$471$	2.48397	+	1.80471i	0.114455	+	0.0831567i
$472$		0			0
$473$	16.4194	+	18.9832i	0.754966	+	0.872849i
$474$		0			0
$475$	−24.2507	−	15.3944i	−1.11270	−	0.706341i
$476$		0			0
$477$	18.6094	−	6.04655i	0.852065	−	0.276853i
$478$		0			0
$479$	12.4714	−	9.06097i	0.569831	−	0.414006i	−0.265213	−	0.964190i	$-0.585442\pi$
$479$	12.4714	−	9.06097i	0.569831	−	0.414006i	0.835044	+	0.550184i	$0.185442\pi$
$480$		0			0
$481$	−0.854128	+	2.62873i	−0.0389449	+	0.119860i
$482$		0			0
$483$			6.89228i			0.313610i
$484$		0			0
$485$	10.0863	−	0.316321i	0.457996	−	0.0143634i
$486$		0			0
$487$	24.9033	+	8.09158i	1.12848	+	0.366664i	0.812997	−	0.582268i	$-0.197834\pi$
$487$	24.9033	+	8.09158i	1.12848	+	0.366664i	0.315480	+	0.948932i	$0.397834\pi$
$488$		0			0
$489$	−8.74716	+	6.35518i	−0.395560	+	0.287391i
$490$		0			0
$491$	2.00100	+	6.15846i	0.0903040	+	0.277927i	0.986001	−	0.166737i	$-0.0533231\pi$
$491$	2.00100	+	6.15846i	0.0903040	+	0.277927i	−0.895697	+	0.444664i	$0.853323\pi$
$492$		0			0
$493$	22.5670	−	31.0608i	1.01636	−	1.39891i
$494$		0			0
$495$	−9.63859	−	10.4620i	−0.433222	−	0.470231i
$496$		0			0
$497$	−6.77024	+	9.31843i	−0.303687	+	0.417989i
$498$		0			0
$499$	7.11586	+	21.9004i	0.318549	+	0.980395i	0.974269	+	0.225390i	$0.0723655\pi$
$499$	7.11586	+	21.9004i	0.318549	+	0.980395i	−0.655719	+	0.755005i	$0.727634\pi$
$500$		0			0
$501$	−8.32036	+	6.04510i	−0.371726	+	0.270075i
$502$		0			0
$503$	26.2022	+	8.51361i	1.16830	+	0.379603i	0.828007	−	0.560717i	$-0.189475\pi$
$503$	26.2022	+	8.51361i	1.16830	+	0.379603i	0.340291	+	0.940320i	$0.389475\pi$
$504$		0			0
$505$	0.656952	+	20.9478i	0.0292340	+	0.932165i
$506$		0			0
$507$		−	13.4469i		−	0.597198i
$508$		0			0
$509$	3.01438	−	9.27730i	0.133610	−	0.411209i	−0.861761	−	0.507314i	$-0.830638\pi$
$509$	3.01438	−	9.27730i	0.133610	−	0.411209i	0.995371	+	0.0961049i	$0.0306384\pi$
$510$		0			0
$511$	−14.9321	+	10.8488i	−0.660557	+	0.479923i
$512$		0			0
$513$	−27.9494	+	9.08132i	−1.23400	+	0.400950i
$514$		0			0
$515$	12.1596	+	8.26479i	0.535815	+	0.364190i
$516$		0			0
$517$	−3.46132	+	1.45913i	−0.152229	+	0.0641724i
$518$		0			0
$519$	13.2882	+	9.65448i	0.583289	+	0.423784i
$520$		0			0
$521$	6.24278	+	19.2133i	0.273501	+	0.841749i	0.989612	+	0.143763i	$0.0459204\pi$
$521$	6.24278	+	19.2133i	0.273501	+	0.841749i	−0.716111	+	0.697986i	$0.754080\pi$
$522$		0			0
$523$	13.4640	+	18.5316i	0.588739	+	0.810330i	0.994619	−	0.103597i	$-0.0330351\pi$
$523$	13.4640	+	18.5316i	0.588739	+	0.810330i	−0.405881	+	0.913926i	$0.633035\pi$
$524$		0			0
$525$	−2.92810	+	11.3981i	−0.127793	+	0.497452i
$526$		0			0
$527$			1.48131i			0.0645270i
$528$		0			0
$529$	14.4247			0.627161
$530$		0			0
$531$	6.76141	−	20.8095i	0.293420	−	0.903055i
$532$		0			0
$533$	0.372615	+	0.512861i	0.0161398	+	0.0222145i
$534$		0			0
$535$	−5.25560	−	14.6010i	−0.227219	−	0.631254i
$536$		0			0
$537$	−3.58629	+	4.93611i	−0.154760	+	0.213009i
$538$		0			0
$539$	−1.41743	+	6.07086i	−0.0610528	+	0.261490i
$540$		0			0
$541$	29.0419	+	21.1002i	1.24861	+	0.907168i	0.998140	−	0.0609571i	$-0.0194153\pi$
$541$	29.0419	+	21.1002i	1.24861	+	0.907168i	0.250469	+	0.968125i	$0.419415\pi$
$542$		0			0
$543$	−22.3509	+	7.26223i	−0.959167	+	0.311652i
$544$		0			0
$545$	−13.7965	−	17.7887i	−0.590976	−	0.761984i
$546$		0			0
$547$	−36.6231	−	11.8996i	−1.56589	−	0.508789i	−0.607517	−	0.794306i	$-0.707835\pi$
$547$	−36.6231	−	11.8996i	−1.56589	−	0.508789i	−0.958373	+	0.285517i	$0.907835\pi$
$548$		0			0
$549$	−8.86547			−0.378369
$550$		0			0
$551$	37.2313			1.58611
$552$		0			0
$553$	−17.8699	−	5.80629i	−0.759907	−	0.246909i
$554$		0			0
$555$	14.6871	+	18.9371i	0.623433	+	0.803833i
$556$		0			0
$557$	−15.1897	+	4.93543i	−0.643608	+	0.209121i	−0.612594	−	0.790398i	$-0.709874\pi$
$557$	−15.1897	+	4.93543i	−0.643608	+	0.209121i	−0.0310143	+	0.999519i	$0.509874\pi$
$558$		0			0
$559$	1.64231	+	1.19321i	0.0694622	+	0.0504672i
$560$		0			0
$561$	−17.4915	−	10.5690i	−0.738492	−	0.446226i
$562$		0			0
$563$	0.335243	−	0.461423i	0.0141288	−	0.0194467i	−0.801894	−	0.597466i	$-0.796174\pi$
$563$	0.335243	−	0.461423i	0.0141288	−	0.0194467i	0.816023	+	0.578019i	$0.196174\pi$
$564$		0			0
$565$	14.2212	+	39.5089i	0.598289	+	1.66215i
$566$		0			0
$567$	−0.576645	−	0.793684i	−0.0242168	−	0.0333316i
$568$		0			0
$569$	14.5218	−	44.6936i	0.608786	−	1.87365i	0.140485	−	0.990083i	$-0.455134\pi$
$569$	14.5218	−	44.6936i	0.608786	−	1.87365i	0.468301	−	0.883569i	$-0.344866\pi$
$570$		0			0
$571$	−39.8308			−1.66687			−0.833434	−	0.552619i	$-0.813628\pi$
$571$	−39.8308			−1.66687			−0.833434	+	0.552619i	$0.813628\pi$
$572$		0			0
$573$			11.5312i			0.481724i
$574$		0			0
$575$	−14.1813	−	3.64311i	−0.591402	−	0.151928i
$576$		0			0
$577$	20.1960	+	27.7974i	0.840770	+	1.15722i	0.985822	+	0.167797i	$0.0536652\pi$
$577$	20.1960	+	27.7974i	0.840770	+	1.15722i	−0.145052	+	0.989424i	$0.546335\pi$
$578$		0			0
$579$	2.06009	+	6.34029i	0.0856143	+	0.263494i
$580$		0			0
$581$	30.0715	+	21.8482i	1.24758	+	0.906416i
$582$		0			0
$583$	2.86524	+	33.7119i	0.118666	+	1.39620i
$584$		0			0
$585$	−0.951538	−	0.646755i	−0.0393413	−	0.0267400i
$586$		0			0
$587$	−30.8485	+	10.0233i	−1.27325	+	0.413705i	−0.866199	−	0.499699i	$-0.833444\pi$
$587$	−30.8485	+	10.0233i	−1.27325	+	0.413705i	−0.407054	+	0.913404i	$0.633444\pi$
$588$		0			0
$589$	−1.16214	+	0.844343i	−0.0478851	+	0.0347906i
$590$		0			0
$591$	−2.94144	+	9.05281i	−0.120995	+	0.372383i
$592$		0			0
$593$			19.9594i			0.819635i	0.912168	+	0.409817i	$0.134408\pi$
$593$			19.9594i			0.819635i	−0.912168	+	0.409817i	$0.865592\pi$
$594$		0			0
$595$	−0.939595	−	29.9602i	−0.0385196	−	1.22825i
$596$		0			0
$597$	14.5073	+	4.71371i	0.593744	+	0.192919i
$598$		0			0
$599$	−9.52358	+	6.91929i	−0.389123	+	0.282714i	−0.765096	−	0.643916i	$-0.777309\pi$
$599$	−9.52358	+	6.91929i	−0.389123	+	0.282714i	0.375973	+	0.926631i	$0.377309\pi$
$600$		0			0
$601$	−1.71529	−	5.27913i	−0.0699683	−	0.215340i	0.909958	−	0.414700i	$-0.136114\pi$
$601$	−1.71529	−	5.27913i	−0.0699683	−	0.215340i	−0.979926	+	0.199360i	$0.936114\pi$
$602$		0			0
$603$	6.89126	−	9.48501i	0.280634	−	0.386259i
$604$		0			0
$605$	21.4053	−	12.1166i	0.870250	−	0.492610i
$606$		0			0
$607$	8.35410	−	11.4984i	0.339083	−	0.466707i	−0.605091	−	0.796157i	$-0.706863\pi$
$607$	8.35410	−	11.4984i	0.339083	−	0.466707i	0.944173	+	0.329449i	$0.106863\pi$
$608$		0			0
$609$	−4.71358	−	14.5069i	−0.191004	−	0.587849i
$610$		0			0
$611$	−0.245787	+	0.178574i	−0.00994346	+	0.00722435i
$612$		0			0
$613$	41.5872	+	13.5125i	1.67969	+	0.545764i	0.984851	−	0.173401i	$-0.0554757\pi$
$613$	41.5872	+	13.5125i	1.67969	+	0.545764i	0.694839	+	0.719165i	$0.255476\pi$
$614$		0			0
$615$	5.49372	−	0.172291i	0.221528	−	0.00694743i
$616$		0			0
$617$			0.0295713i			0.00119050i	1.00000		0.000595249i	$0.000189474\pi$
$617$			0.0295713i			0.00119050i	−1.00000		0.000595249i	$0.999811\pi$
$618$		0			0
$619$	−2.92169	+	8.99204i	−0.117433	+	0.361421i	−0.992447	−	0.122677i	$-0.960852\pi$
$619$	−2.92169	+	8.99204i	−0.117433	+	0.361421i	0.875014	+	0.484098i	$0.160852\pi$
$620$		0			0
$621$	−12.1191	+	8.80505i	−0.486323	+	0.353334i
$622$		0			0
$623$	−12.3358	+	4.00813i	−0.494221	+	0.160582i
$624$		0			0
$625$	−21.9045	−	12.0495i	−0.876182	−	0.481981i
$626$		0			0
$627$	−1.67833	−	19.7470i	−0.0670262	−	0.788619i
$628$		0			0
$629$	−49.3840	−	35.8796i	−1.96907	−	1.43061i
$630$		0			0
$631$	−0.713746	−	2.19668i	−0.0284138	−	0.0874486i	0.935844	−	0.352415i	$-0.114639\pi$
$631$	−0.713746	−	2.19668i	−0.0284138	−	0.0874486i	−0.964258	+	0.264966i	$0.914639\pi$
$632$		0			0
$633$	−7.61427	−	10.4801i	−0.302640	−	0.416548i
$634$		0			0
$635$	11.9121	−	40.9917i	0.472716	−	1.62671i
$636$		0			0
$637$			0.504216i			0.0199778i
$638$		0			0
$639$	−9.76364			−0.386244
$640$		0			0
$641$	0.489578	−	1.50677i	0.0193372	−	0.0595137i	−0.940922	−	0.338623i	$-0.890039\pi$
$641$	0.489578	−	1.50677i	0.0193372	−	0.0595137i	0.960259	+	0.279109i	$0.0900390\pi$
$642$		0			0
$643$	−6.60550	−	9.09170i	−0.260496	−	0.358542i	0.658657	−	0.752444i	$-0.271125\pi$
$643$	−6.60550	−	9.09170i	−0.260496	−	0.358542i	−0.919152	+	0.393902i	$0.871125\pi$
$644$		0			0
$645$	16.5607	−	5.96101i	0.652078	−	0.234715i
$646$		0			0
$647$	−6.71578	+	9.24348i	−0.264025	+	0.363399i	−0.920361	−	0.391070i	$-0.872105\pi$
$647$	−6.71578	+	9.24348i	−0.264025	+	0.363399i	0.656336	+	0.754468i	$0.272105\pi$
$648$		0			0
$649$	32.3812	+	19.5660i	1.27107	+	0.768031i
$650$		0			0
$651$	0.476122	+	0.345923i	0.0186607	+	0.0135578i
$652$		0			0
$653$	14.0550	−	4.56675i	0.550015	−	0.178711i	−0.0208086	−	0.999783i	$-0.506624\pi$
$653$	14.0550	−	4.56675i	0.550015	−	0.178711i	0.570823	+	0.821073i	$0.306624\pi$
$654$		0			0
$655$	2.44513	+	3.15266i	0.0955390	+	0.123185i
$656$		0			0
$657$	−14.8798	−	4.83473i	−0.580515	−	0.188621i
$658$		0			0
$659$	14.3223			0.557918			0.278959	−	0.960303i	$-0.410011\pi$
$659$	14.3223			0.557918			0.278959	+	0.960303i	$0.410011\pi$
$660$		0			0
$661$	−17.1886			−0.668561			−0.334280	−	0.942474i	$-0.608493\pi$
$661$	−17.1886			−0.668561			−0.334280	+	0.942474i	$0.608493\pi$
$662$		0			0
$663$	−1.57202	−	0.510779i	−0.0610520	−	0.0198370i
$664$		0			0
$665$	22.9692	−	17.8144i	0.890709	−	0.690812i
$666$		0			0
$667$	18.0493	−	5.86458i	0.698872	−	0.227077i
$668$		0			0
$669$	−10.2595	−	7.45394i	−0.396654	−	0.288186i
$670$		0			0
$671$	3.48535	−	14.9278i	0.134550	−	0.576282i
$672$		0			0
$673$	20.2607	−	27.8865i	0.780994	−	1.07495i	−0.214177	−	0.976795i	$-0.568707\pi$
$673$	20.2607	−	27.8865i	0.780994	−	1.07495i	0.995172	−	0.0981513i	$-0.0312929\pi$
$674$		0			0
$675$	−23.7826	+	9.41263i	−0.915393	+	0.362292i
$676$		0			0
$677$	−1.13867	−	1.56724i	−0.0437625	−	0.0602339i	0.786575	−	0.617495i	$-0.211852\pi$
$677$	−1.13867	−	1.56724i	−0.0437625	−	0.0602339i	−0.830337	+	0.557261i	$0.811852\pi$
$678$		0			0
$679$	−3.15568	+	9.71218i	−0.121104	+	0.372719i
$680$		0			0
$681$	8.01463			0.307121
$682$		0			0
$683$		−	19.1445i		−	0.732543i	−0.930508	−	0.366271i	$-0.880634\pi$
$683$		−	19.1445i		−	0.732543i	0.930508	−	0.366271i	$-0.119366\pi$
$684$		0			0
$685$	−4.72483	+	16.2590i	−0.180526	+	0.621225i
$686$		0			0
$687$	−11.1461	−	15.3413i	−0.425251	−	0.585308i
$688$		0			0
$689$	0.845607	+	2.60251i	0.0322151	+	0.0991477i
$690$		0			0
$691$	17.7129	+	12.8692i	0.673832	+	0.489568i	0.871306	−	0.490740i	$-0.163274\pi$
$691$	17.7129	+	12.8692i	0.673832	+	0.489568i	−0.197473	+	0.980308i	$0.563274\pi$
$692$		0			0
$693$	13.2649	−	5.59185i	0.503891	−	0.212417i
$694$		0			0
$695$	13.9102	−	20.4654i	0.527643	−	0.776295i
$696$		0			0
$697$	−13.3149	+	4.32626i	−0.504336	+	0.163869i
$698$		0			0
$699$	−4.16327	+	3.02480i	−0.157469	+	0.114408i
$700$		0			0
$701$	−8.50288	+	26.1692i	−0.321149	+	0.988396i	0.652000	+	0.758219i	$0.273930\pi$
$701$	−8.50288	+	26.1692i	−0.321149	+	0.988396i	−0.973149	+	0.230176i	$0.926070\pi$
$702$		0			0
$703$		−	59.1946i		−	2.23257i
$704$		0			0
$705$	0.0825696	+	2.63284i	0.00310975	+	0.0991586i
$706$		0			0
$707$	−20.1708	−	6.55388i	−0.758600	−	0.246484i
$708$		0			0
$709$	−22.8733	+	16.6185i	−0.859026	+	0.624119i	−0.927620	−	0.373526i	$-0.878149\pi$
$709$	−22.8733	+	16.6185i	−0.859026	+	0.624119i	0.0685937	+	0.997645i	$0.478149\pi$
$710$		0			0
$711$	−4.92182	−	15.1478i	−0.184583	−	0.568087i
$712$		0			0
$713$	−0.430393	+	0.592385i	−0.0161184	+	0.0221850i
$714$		0			0
$715$	1.46310	−	1.34795i	0.0547169	−	0.0504105i
$716$		0			0
$717$	10.3840	−	14.2924i	0.387798	−	0.533758i
$718$		0			0
$719$	−3.38471	−	10.4171i	−0.126228	−	0.388491i	0.867894	−	0.496749i	$-0.165473\pi$
$719$	−3.38471	−	10.4171i	−0.126228	−	0.388491i	−0.994123	+	0.108258i	$0.965473\pi$
$720$		0			0
$721$	−12.0368	+	8.74526i	−0.448274	+	0.325690i
$722$		0			0
$723$	−6.65701	−	2.16299i	−0.247577	−	0.0804426i
$724$		0			0
$725$	32.3404	−	2.03048i	1.20109	−	0.0754100i
$726$		0			0
$727$			26.1233i			0.968860i	0.874830	+	0.484430i	$0.160973\pi$
$727$			26.1233i			0.968860i	−0.874830	+	0.484430i	$0.839027\pi$
$728$		0			0
$729$	−4.67568	+	14.3903i	−0.173173	+	0.532973i
$730$		0			0
$731$	−36.2696	+	26.3514i	−1.34148	+	0.974641i
$732$		0			0
$733$	2.62418	−	0.852648i	0.0969264	−	0.0314933i	−0.260152	−	0.965568i	$-0.583773\pi$
$733$	2.62418	−	0.852648i	0.0969264	−	0.0314933i	0.357079	+	0.934074i	$0.383773\pi$
$734$		0			0
$735$	3.61562	+	2.45752i	0.133364	+	0.0906468i
$736$		0			0
$737$	13.2618	+	15.3325i	0.488504	+	0.564781i
$738$		0			0
$739$	15.6217	+	11.3498i	0.574654	+	0.417511i	0.836793	−	0.547519i	$-0.184428\pi$
$739$	15.6217	+	11.3498i	0.574654	+	0.417511i	−0.262139	+	0.965030i	$0.584428\pi$
$740$		0			0
$741$	−0.495321	−	1.52444i	−0.0181961	−	0.0560017i
$742$		0			0
$743$	−1.76771	−	2.43304i	−0.0648509	−	0.0892596i	0.775360	−	0.631520i	$-0.217569\pi$
$743$	−1.76771	−	2.43304i	−0.0648509	−	0.0892596i	−0.840211	+	0.542260i	$0.817569\pi$
$744$		0			0
$745$	−25.0368	−	7.27563i	−0.917279	−	0.266559i
$746$		0			0
$747$			31.5082i			1.15283i
$748$		0			0
$749$	15.7037			0.573799
$750$		0			0
$751$	−2.86179	+	8.80767i	−0.104428	+	0.321397i	−0.989596	−	0.143876i	$-0.954044\pi$
$751$	−2.86179	+	8.80767i	−0.104428	+	0.321397i	0.885168	+	0.465272i	$0.154044\pi$
$752$		0			0
$753$	−12.0851	−	16.6338i	−0.440407	−	0.606168i
$754$		0			0
$755$	0.510451	−	0.183736i	0.0185772	−	0.00668685i
$756$		0			0
$757$	24.7403	−	34.0522i	0.899203	−	1.23765i	−0.0715183	−	0.997439i	$-0.522784\pi$
$757$	24.7403	−	34.0522i	0.899203	−	1.23765i	0.970722	−	0.240208i	$-0.0772156\pi$
$758$		0			0
$759$	−3.92413	−	9.30875i	−0.142437	−	0.337886i
$760$		0			0
$761$	−36.5243	−	26.5364i	−1.32400	−	0.961945i	−0.999873	−	0.0159331i	$-0.994928\pi$
$761$	−36.5243	−	26.5364i	−1.32400	−	0.961945i	−0.324131	−	0.946012i	$-0.605072\pi$
$762$		0			0
$763$	21.6661	−	7.03974i	0.784365	−	0.254856i
$764$		0			0
$765$	20.0780	−	15.5720i	0.725920	−	0.563006i
$766$		0			0
$767$	2.91019	+	0.945580i	0.105081	+	0.0341429i
$768$		0			0
$769$	45.9031			1.65531			0.827655	−	0.561237i	$-0.189675\pi$
$769$	45.9031			1.65531			0.827655	+	0.561237i	$0.189675\pi$
$770$		0			0
$771$	6.65164			0.239553
$772$		0			0
$773$	−8.07738	−	2.62450i	−0.290523	−	0.0943967i	0.160130	−	0.987096i	$-0.448809\pi$
$773$	−8.07738	−	2.62450i	−0.290523	−	0.0943967i	−0.450653	+	0.892699i	$0.648809\pi$
$774$		0			0
$775$	−0.963427	+	0.796806i	−0.0346073	+	0.0286221i
$776$		0			0
$777$	−23.0648	+	7.49419i	−0.827443	+	0.268853i
$778$		0			0
$779$	−10.9835	−	7.97999i	−0.393525	−	0.285913i
$780$		0			0
$781$	3.83845	−	16.4402i	0.137351	−	0.588276i
$782$		0			0
$783$	19.4866	−	26.8211i	0.696396	−	0.958507i
$784$		0			0
$785$	−2.23548	−	6.21054i	−0.0797876	−	0.221664i
$786$		0			0
$787$	−9.50620	−	13.0842i	−0.338859	−	0.466400i	0.605248	−	0.796037i	$-0.293074\pi$
$787$	−9.50620	−	13.0842i	−0.338859	−	0.466400i	−0.944108	+	0.329637i	$0.893074\pi$
$788$		0			0
$789$	4.70611	−	14.4839i	0.167542	−	0.515641i
$790$		0			0
$791$	−42.4927			−1.51087
$792$		0			0
$793$		−	1.23983i		−	0.0440277i
$794$		0			0
$795$	22.7835	+	6.62081i	0.808046	+	0.234816i
$796$		0			0
$797$	−3.76565	−	5.18298i	−0.133386	−	0.183591i	0.737099	−	0.675785i	$-0.236195\pi$
$797$	−3.76565	−	5.18298i	−0.133386	−	0.183591i	−0.870486	+	0.492194i	$0.836195\pi$
$798$		0			0
$799$	−2.07334	−	6.38109i	−0.0733495	−	0.225747i
$800$		0			0
$801$	−8.89495	−	6.46256i	−0.314288	−	0.228343i
$802$		0			0
$803$	13.9906	−	23.1541i	0.493717	−	0.817089i
$804$		0			0
$805$	8.32916	−	12.2543i	0.293564	−	0.431906i
$806$		0			0
$807$	19.6595	−	6.38776i	0.692048	−	0.224860i
$808$		0			0
$809$	−38.2518	+	27.7915i	−1.34486	+	0.977098i	−0.345610	+	0.938378i	$0.612328\pi$
$809$	−38.2518	+	27.7915i	−1.34486	+	0.977098i	−0.999250	+	0.0387198i	$0.987672\pi$
$810$		0			0
$811$	−7.00564	+	21.5611i	−0.246001	+	0.757114i	0.749469	+	0.662040i	$0.230309\pi$
$811$	−7.00564	+	21.5611i	−0.246001	+	0.757114i	−0.995470	+	0.0950744i	$0.969691\pi$
$812$		0			0
$813$		−	19.9837i		−	0.700858i
$814$		0			0
$815$	23.2323	−	0.728596i	0.813790	−	0.0255216i
$816$		0			0
$817$	−41.3471	−	13.4345i	−1.44655	−	0.470013i
$818$		0			0
$819$	0.941932	−	0.684354i	0.0329138	−	0.0239132i
$820$		0			0
$821$	6.32207	+	19.4573i	0.220642	+	0.679066i	0.998705	+	0.0508794i	$0.0162024\pi$
$821$	6.32207	+	19.4573i	0.220642	+	0.679066i	−0.778063	+	0.628186i	$0.783798\pi$
$822$		0			0
$823$	−15.8680	+	21.8405i	−0.553125	+	0.761311i	−0.990432	−	0.138001i	$-0.955932\pi$
$823$	−15.8680	+	21.8405i	−0.553125	+	0.761311i	0.437307	+	0.899312i	$0.355932\pi$
$824$		0			0
$825$	−2.53480	−	17.0614i	−0.0882504	−	0.594002i
$826$		0			0
$827$	10.9009	−	15.0038i	0.379060	−	0.521732i	−0.576275	−	0.817256i	$-0.695494\pi$
$827$	10.9009	−	15.0038i	0.379060	−	0.521732i	0.955335	+	0.295524i	$0.0954943\pi$
$828$		0			0
$829$	−2.16168	−	6.65296i	−0.0750781	−	0.231067i	0.906474	−	0.422262i	$-0.138764\pi$
$829$	−2.16168	−	6.65296i	−0.0750781	−	0.231067i	−0.981552	+	0.191195i	$0.938764\pi$
$830$		0			0
$831$	−20.0563	+	14.5718i	−0.695747	+	0.505490i
$832$		0			0
$833$	−10.5904	−	3.44102i	−0.366934	−	0.119224i
$834$		0			0
$835$	22.0987	−	0.693046i	0.764757	−	0.0239838i
$836$		0			0
$837$			1.27912i			0.0442128i
$838$		0			0
$839$	4.22625	−	13.0071i	0.145906	−	0.449053i	−0.851220	−	0.524809i	$-0.824137\pi$
$839$	4.22625	−	13.0071i	0.145906	−	0.449053i	0.997126	+	0.0757554i	$0.0241368\pi$
$840$		0			0
$841$	−10.5180	+	7.64180i	−0.362691	+	0.263510i
$842$		0			0
$843$	−17.7354	+	5.76259i	−0.610840	+	0.198474i
$844$		0			0
$845$	−16.2502	+	23.9082i	−0.559025	+	0.822466i
$846$		0			0
$847$	4.20072	+	24.5340i	0.144338	+	0.842997i
$848$		0			0
$849$	17.6936	+	12.8552i	0.607244	+	0.441189i
$850$		0			0
$851$	−9.32418	−	28.6969i	−0.319629	−	0.983716i
$852$		0			0
$853$	−1.94934	−	2.68304i	−0.0667442	−	0.0918656i	0.774340	−	0.632770i	$-0.218082\pi$
$853$	−1.94934	−	2.68304i	−0.0667442	−	0.0918656i	−0.841084	+	0.540904i	$0.818082\pi$
$854$		0			0
$855$	23.6611	+	6.87585i	0.809193	+	0.235149i
$856$		0			0
$857$		−	29.2111i		−	0.997831i	−0.866651	−	0.498915i	$-0.833732\pi$
$857$		−	29.2111i		−	0.997831i	0.866651	−	0.498915i	$-0.166268\pi$
$858$		0			0
$859$	32.2591			1.10067			0.550334	−	0.834945i	$-0.314501\pi$
$859$	32.2591			1.10067			0.550334	+	0.834945i	$0.314501\pi$
$860$		0			0
$861$	−1.71880	+	5.28994i	−0.0585767	+	0.180281i
$862$		0			0
$863$	−16.2453	−	22.3598i	−0.552998	−	0.761136i	0.437417	−	0.899259i	$-0.355893\pi$
$863$	−16.2453	−	22.3598i	−0.552998	−	0.761136i	−0.990415	+	0.138122i	$0.955893\pi$
$864$		0			0
$865$	−11.9589	−	33.2239i	−0.406615	−	1.12965i
$866$		0			0
$867$	11.0630	−	15.2270i	0.375720	−	0.517135i
$868$		0			0
$869$	27.4411	−	2.33227i	0.930874	−	0.0791167i
$870$		0			0
$871$	1.32647	+	0.963739i	0.0449458	+	0.0326550i
$872$		0			0
$873$	−8.23272	+	2.67497i	−0.278635	+	0.0905341i
$874$		0			0
$875$	18.9804	−	16.7269i	0.641653	−	0.565472i
$876$		0			0
$877$	0.812673	+	0.264053i	0.0274420	+	0.00891645i	0.322706	−	0.946499i	$-0.395408\pi$
$877$	0.812673	+	0.264053i	0.0274420	+	0.00891645i	−0.295264	+	0.955416i	$0.595408\pi$
$878$		0			0
$879$	22.1216			0.746145
$880$		0			0
$881$	−7.22437			−0.243395			−0.121698	−	0.992567i	$-0.538834\pi$
$881$	−7.22437			−0.243395			−0.121698	+	0.992567i	$0.538834\pi$
$882$		0			0
$883$	10.8164	+	3.51446i	0.364000	+	0.118271i	0.485306	−	0.874344i	$-0.338708\pi$
$883$	10.8164	+	3.51446i	0.364000	+	0.118271i	−0.121306	+	0.992615i	$0.538708\pi$
$884$		0			0
$885$	20.9647	−	16.2597i	0.704719	−	0.546563i
$886$		0			0
$887$	7.27958	−	2.36528i	0.244424	−	0.0794183i	−0.184243	−	0.982881i	$-0.558983\pi$
$887$	7.27958	−	2.36528i	0.244424	−	0.0794183i	0.428667	+	0.903462i	$0.358983\pi$
$888$		0			0
$889$	34.9480	+	25.3912i	1.17212	+	0.851593i
$890$		0			0
$891$	1.23071	+	0.743640i	0.0412302	+	0.0249129i
$892$		0			0
$893$	3.82438	−	5.26381i	0.127978	−	0.176147i
$894$		0			0
$895$	12.3415	−	4.44230i	0.412530	−	0.148490i
$896$		0			0
$897$	−0.480252	−	0.661010i	−0.0160351	−	0.0220705i
$898$		0			0
$899$	0.500765	−	1.54120i	0.0167015	−	0.0514018i
$900$		0			0
$901$	−60.4330			−2.01332
$902$		0			0
$903$			17.8114i			0.592727i
$904$		0			0
$905$	48.5154	+	14.0984i	1.61271	+	0.468648i
$906$		0			0
$907$	31.9307	+	43.9489i	1.06024	+	1.45930i	0.879578	+	0.475755i	$0.157825\pi$
$907$	31.9307	+	43.9489i	1.06024	+	1.45930i	0.180665	+	0.983545i	$0.442175\pi$
$908$		0			0
$909$	−5.55553	−	17.0982i	−0.184265	−	0.567110i
$910$		0			0
$911$	24.1715	+	17.5616i	0.800836	+	0.581842i	0.911159	−	0.412054i	$-0.135189\pi$
$911$	24.1715	+	17.5616i	0.800836	+	0.581842i	−0.110323	+	0.993896i	$0.535189\pi$
$912$		0			0
$913$	−53.0540	−	12.3871i	−1.75583	−	0.409952i
$914$		0			0
$915$	−8.89056	−	6.04286i	−0.293913	−	0.199771i
$916$		0			0
$917$	−3.83984	+	1.24764i	−0.126803	+	0.0412007i
$918$		0			0
$919$	14.3024	−	10.3913i	0.471793	−	0.342778i	−0.326347	−	0.945250i	$-0.605818\pi$
$919$	14.3024	−	10.3913i	0.471793	−	0.342778i	0.798140	+	0.602473i	$0.205818\pi$
$920$		0			0
$921$	−10.5047	+	32.3302i	−0.346142	+	1.06532i
$922$		0			0
$923$		−	1.36544i		−	0.0449440i
$924$		0			0
$925$	−3.22829	−	51.4185i	−0.106145	−	1.69063i
$926$		0			0
$927$	−11.9946	−	3.89729i	−0.393955	−	0.128004i
$928$		0			0
$929$	−0.732789	+	0.532403i	−0.0240420	+	0.0174676i	−0.599741	−	0.800194i	$-0.704730\pi$
$929$	−0.732789	+	0.532403i	−0.0240420	+	0.0174676i	0.575699	+	0.817661i	$0.304730\pi$
$930$		0			0
$931$	−3.33688	−	10.2699i	−0.109362	−	0.336581i
$932$		0			0
$933$	−11.5708	+	15.9259i	−0.378812	+	0.521390i
$934$		0			0
$935$	18.3269	+	39.9295i	0.599355	+	1.30583i
$936$		0			0
$937$	−7.57019	+	10.4195i	−0.247307	+	0.340389i	−0.914566	−	0.404437i	$-0.867468\pi$
$937$	−7.57019	+	10.4195i	−0.247307	+	0.340389i	0.667259	+	0.744826i	$0.267468\pi$
$938$		0			0
$939$	−3.86685	−	11.9009i	−0.126190	−	0.388373i
$940$		0			0
$941$	24.9136	−	18.1008i	0.812161	−	0.590069i	−0.102295	−	0.994754i	$-0.532619\pi$
$941$	24.9136	−	18.1008i	0.812161	−	0.590069i	0.914456	+	0.404685i	$0.132619\pi$
$942$		0			0
$943$	−6.58167	−	2.13852i	−0.214329	−	0.0696396i
$944$		0			0
$945$	−0.811343	−	25.8708i	−0.0263930	−	0.841576i
$946$		0			0
$947$		−	27.4841i		−	0.893112i	−0.894756	−	0.446556i	$-0.852650\pi$
$947$		−	27.4841i		−	0.893112i	0.894756	−	0.446556i	$-0.147350\pi$
$948$		0			0
$949$	0.676134	−	2.08093i	0.0219482	−	0.0675497i
$950$		0			0
$951$	8.58379	−	6.23649i	0.278348	−	0.202232i
$952$		0			0
$953$	13.0975	−	4.25565i	0.424271	−	0.137854i	−0.0890962	−	0.996023i	$-0.528398\pi$
$953$	13.0975	−	4.25565i	0.424271	−	0.137854i	0.513367	+	0.858169i	$0.328398\pi$
$954$		0			0
$955$	13.9352	−	20.5022i	0.450933	−	0.663435i
$956$		0			0
$957$	14.6257	+	16.9094i	0.472782	+	0.546604i
$958$		0			0
$959$	−13.8618	−	10.0712i	−0.447622	−	0.325216i
$960$		0			0
$961$	−9.56021	−	29.4233i	−0.308394	−	0.949138i
$962$		0			0
$963$	7.82431	+	10.7692i	0.252135	+	0.347034i
$964$		0			0
$965$	3.99932	−	13.7624i	0.128743	−	0.443028i
$966$		0			0
$967$		−	45.5732i		−	1.46554i	−0.680478	−	0.732768i	$-0.738228\pi$
$967$		−	45.5732i		−	1.46554i	0.680478	−	0.732768i	$-0.261772\pi$
$968$		0			0
$969$	35.3991			1.13718
$970$		0			0
$971$	−14.0933	+	43.3748i	−0.452276	+	1.39196i	0.422028	+	0.906583i	$0.361318\pi$
$971$	−14.0933	+	43.3748i	−0.452276	+	1.39196i	−0.874304	+	0.485379i	$0.838682\pi$
$972$		0			0
$973$	14.7188	+	20.2587i	0.471864	+	0.649466i
$974$		0			0
$975$	−0.513391	−	1.29717i	−0.0164417	−	0.0415427i
$976$		0			0
$977$	−9.95932	+	13.7078i	−0.318627	+	0.438552i	−0.938047	−	0.346507i	$-0.887368\pi$
$977$	−9.95932	+	13.7078i	−0.318627	+	0.438552i	0.619420	+	0.785059i	$0.287368\pi$
$978$		0			0
$979$	14.3787	−	12.4368i	0.459545	−	0.397481i
$980$		0			0
$981$	15.6228	+	11.3506i	0.498797	+	0.362397i
$982$		0			0
$983$	15.2241	−	4.94660i	0.485572	−	0.157772i	−0.0559924	−	0.998431i	$-0.517832\pi$
$983$	15.2241	−	4.94660i	0.485572	−	0.157772i	0.541564	+	0.840659i	$0.317832\pi$
$984$		0			0
$985$	16.1699	−	12.5410i	0.515216	−	0.399589i
$986$		0			0
$987$	−2.53518	−	0.823730i	−0.0806957	−	0.0262196i
$988$		0			0
$989$	−22.1608			−0.704671
$990$		0			0
$991$	−57.8601			−1.83799			−0.918993	−	0.394274i	$-0.870996\pi$
$991$	−57.8601			−1.83799			−0.918993	+	0.394274i	$0.870996\pi$
$992$		0			0
$993$	11.7660	+	3.82302i	0.373384	+	0.121320i
$994$		0			0
$995$	−20.0971	−	25.9125i	−0.637122	−	0.821483i
$996$		0			0
$997$	44.2832	−	14.3885i	1.40246	−	0.455688i	0.492477	−	0.870325i	$-0.336092\pi$
$997$	44.2832	−	14.3885i	1.40246	−	0.455688i	0.909987	+	0.414637i	$0.136092\pi$
$998$		0			0
$999$	−42.6432	−	30.9821i	−1.34917	−	0.980231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.cd.d.609.3		24
4.3	odd	2		220.2.t.a.169.4	yes	24
5.4	even	2	inner	880.2.cd.d.609.4		24
11.3	even	5	inner	880.2.cd.d.289.4		24
20.3	even	4		1100.2.n.f.301.3		24
20.7	even	4		1100.2.n.f.301.4		24
20.19	odd	2		220.2.t.a.169.3	yes	24
44.3	odd	10		220.2.t.a.69.3	✓	24
44.27	odd	10		2420.2.b.i.969.8		12
44.39	even	10		2420.2.b.h.969.8		12
55.14	even	10	inner	880.2.cd.d.289.3		24
220.3	even	20		1100.2.n.f.201.3		24
220.39	even	10		2420.2.b.h.969.5		12
220.47	even	20		1100.2.n.f.201.4		24
220.159	odd	10		2420.2.b.i.969.5		12
220.179	odd	10		220.2.t.a.69.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.t.a.69.3	✓	24	44.3	odd	10
220.2.t.a.69.4	yes	24	220.179	odd	10
220.2.t.a.169.3	yes	24	20.19	odd	2
220.2.t.a.169.4	yes	24	4.3	odd	2
880.2.cd.d.289.3		24	55.14	even	10	inner
880.2.cd.d.289.4		24	11.3	even	5	inner
880.2.cd.d.609.3		24	1.1	even	1	trivial
880.2.cd.d.609.4		24	5.4	even	2	inner
1100.2.n.f.201.3		24	220.3	even	20
1100.2.n.f.201.4		24	220.47	even	20
1100.2.n.f.301.3		24	20.3	even	4
1100.2.n.f.301.4		24	20.7	even	4
2420.2.b.h.969.5		12	220.39	even	10
2420.2.b.h.969.8		12	44.39	even	10
2420.2.b.i.969.5		12	220.159	odd	10
2420.2.b.i.969.8		12	44.27	odd	10

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cd (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.989226 - 0.321419i) q^{3} +(1.37039 + 1.76693i) q^{5} +(-2.15207 + 0.699249i) q^{7} +(-1.55179 - 1.12744i) q^{9} +(2.50847 - 2.16969i) q^{11} +(0.157672 - 0.217017i) q^{13} +(-0.787698 - 2.18836i) q^{15} +(3.48212 + 4.79272i) q^{17} +(-1.77525 + 5.46367i) q^{19} +2.35363 q^{21} +2.92836i q^{23} +(-1.24408 + 4.84275i) q^{25} +(3.00682 + 4.13853i) q^{27} +(-2.00268 - 6.16362i) q^{29} +(0.202293 + 0.146974i) q^{31} +(-3.17883 + 1.34004i) q^{33} +(-4.18469 - 2.84431i) q^{35} +(-9.79964 + 3.18410i) q^{37} +(-0.225727 + 0.164000i) q^{39} +(-0.730277 + 2.24756i) q^{41} +7.56763i q^{43} +(-0.134444 - 4.28694i) q^{45} +(-1.07714 - 0.349982i) q^{47} +(-1.52068 + 1.10484i) q^{49} +(-1.90413 - 5.86031i) q^{51} +(-5.99609 + 8.25291i) q^{53} +(7.27127 + 1.45898i) q^{55} +(3.51226 - 4.83421i) q^{57} +(3.52502 + 10.8489i) q^{59} +(3.73924 - 2.71672i) q^{61} +(4.12792 + 1.34124i) q^{63} +(0.599526 - 0.0188020i) q^{65} +6.11229i q^{67} +(0.941231 - 2.89681i) q^{69} +(4.11807 - 2.99195i) q^{71} +(7.75747 - 2.52055i) q^{73} +(2.78723 - 4.39071i) q^{75} +(-3.88125 + 6.42337i) q^{77} +(6.71777 + 4.88074i) q^{79} +(0.133975 + 0.412332i) q^{81} +(-9.65532 - 13.2894i) q^{83} +(-3.69655 + 12.7205i) q^{85} +6.74092i q^{87} +5.73205 q^{89} +(-0.187572 + 0.577288i) q^{91} +(-0.152873 - 0.210411i) q^{93} +(-12.0867 + 4.35060i) q^{95} +(2.65265 - 3.65106i) q^{97} +(-6.33883 + 0.538749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{5} + 14 q^{9} + 2 q^{11} + q^{15} - 8 q^{19} - 28 q^{21} + 27 q^{25} - 16 q^{29} + 26 q^{31} - 17 q^{35} - 12 q^{39} + 10 q^{41} - 40 q^{45} - 46 q^{49} + 12 q^{51} + 33 q^{55} + 48 q^{59} - 10 q^{61}+ \cdots - 156 q^{99}+O(q^{100}) \) 24 * q + q^5 + 14 * q^9 + 2 * q^11 + q^15 - 8 * q^19 - 28 * q^21 + 27 * q^25 - 16 * q^29 + 26 * q^31 - 17 * q^35 - 12 * q^39 + 10 * q^41 - 40 * q^45 - 46 * q^49 + 12 * q^51 + 33 * q^55 + 48 * q^59 - 10 * q^61 - 22 * q^65 - 58 * q^69 - 42 * q^71 + 17 * q^75 + 64 * q^79 + 36 * q^81 - 17 * q^85 + 72 * q^89 - 10 * q^91 - 67 * q^95 - 156 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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