LMFDB - Embedded newform 432.2.u.a.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	432.97
Dual form			432.2.u.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70574 + 0.300767i) q^{3} +(-1.26604 - 0.460802i) q^{5} +(0.0209445 - 0.118782i) q^{7} +(2.81908 - 1.02606i) q^{9} +O(q^{10})$	\(q+(-1.70574 + 0.300767i) q^{3} +(-1.26604 - 0.460802i) q^{5} +(0.0209445 - 0.118782i) q^{7} +(2.81908 - 1.02606i) q^{9} +(3.49273 - 1.27125i) q^{11} +(-4.64543 + 3.89798i) q^{13} +(2.29813 + 0.405223i) q^{15} +(2.58512 + 4.47756i) q^{17} +(-2.96064 + 5.12797i) q^{19} +0.208911i q^{21} +(0.826352 + 4.68647i) q^{23} +(-2.43969 - 2.04715i) q^{25} +(-4.50000 + 2.59808i) q^{27} +(4.55303 + 3.82045i) q^{29} +(0.875515 + 4.96529i) q^{31} +(-5.57532 + 3.21891i) q^{33} +(-0.0812519 + 0.140732i) q^{35} +(-0.145430 - 0.251892i) q^{37} +(6.75150 - 8.04612i) q^{39} +(4.44356 - 3.72859i) q^{41} +(0.426022 - 0.155059i) q^{43} -4.04189 q^{45} +(0.134285 - 0.761570i) q^{47} +(6.56418 + 2.38917i) q^{49} +(-5.75624 - 6.86002i) q^{51} -7.29086 q^{53} -5.00774 q^{55} +(3.50774 - 9.63744i) q^{57} +(-1.40033 - 0.509678i) q^{59} +(-0.656574 + 3.72362i) q^{61} +(-0.0628336 - 0.356347i) q^{63} +(7.67752 - 2.79439i) q^{65} +(5.08512 - 4.26692i) q^{67} +(-2.81908 - 7.74535i) q^{69} +(2.87211 + 4.97464i) q^{71} +(-5.20961 + 9.02330i) q^{73} +(4.77719 + 2.75811i) q^{75} +(-0.0778483 - 0.441500i) q^{77} +(-10.7194 - 8.99465i) q^{79} +(6.89440 - 5.78509i) q^{81} +(1.81521 + 1.52314i) q^{83} +(-1.20961 - 6.86002i) q^{85} +(-8.91534 - 5.14728i) q^{87} +(1.08512 - 1.87949i) q^{89} +(0.365715 + 0.633436i) q^{91} +(-2.98680 - 8.20616i) q^{93} +(6.11128 - 5.12797i) q^{95} +(3.21941 - 1.17177i) q^{97} +(8.54189 - 7.16750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 3 q^{7}+O(q^{10}) $ 6 * q - 3 * q^5 - 3 * q^7	$ 6 q - 3 q^{5} - 3 q^{7} + 3 q^{11} - 12 q^{13} - 6 q^{17} - 9 q^{19} + 6 q^{23} - 9 q^{25} - 27 q^{27} + 15 q^{29} + 18 q^{31} - 9 q^{33} - 3 q^{35} + 15 q^{37} - 3 q^{41} + 18 q^{43} - 18 q^{45} - 9 q^{47} + 21 q^{49} - 27 q^{51} - 12 q^{53} + 18 q^{55} - 27 q^{57} + 6 q^{59} + 18 q^{61} + 9 q^{63} + 21 q^{65} + 9 q^{67} - 12 q^{71} + 3 q^{73} + 18 q^{75} + 39 q^{77} - 33 q^{79} + 18 q^{83} + 27 q^{85} - 9 q^{87} - 15 q^{89} + 12 q^{91} + 27 q^{93} - 21 q^{95} - 12 q^{97} + 45 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 - 3 * q^7 + 3 * q^11 - 12 * q^13 - 6 * q^17 - 9 * q^19 + 6 * q^23 - 9 * q^25 - 27 * q^27 + 15 * q^29 + 18 * q^31 - 9 * q^33 - 3 * q^35 + 15 * q^37 - 3 * q^41 + 18 * q^43 - 18 * q^45 - 9 * q^47 + 21 * q^49 - 27 * q^51 - 12 * q^53 + 18 * q^55 - 27 * q^57 + 6 * q^59 + 18 * q^61 + 9 * q^63 + 21 * q^65 + 9 * q^67 - 12 * q^71 + 3 * q^73 + 18 * q^75 + 39 * q^77 - 33 * q^79 + 18 * q^83 + 27 * q^85 - 9 * q^87 - 15 * q^89 + 12 * q^91 + 27 * q^93 - 21 * q^95 - 12 * q^97 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{9}\right)$

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
$3$	−1.70574	+	0.300767i	−0.984808	+	0.173648i
$3$	−1.70574	+	0.300767i	−0.984808	+	0.173648i
$4$		0			0
$5$	−1.26604	−	0.460802i	−0.566192	−	0.206077i	0.0430339	−	0.999074i	$-0.486298\pi$
$5$	−1.26604	−	0.460802i	−0.566192	−	0.206077i	−0.609226	+	0.792996i	$0.708520\pi$
$6$		0			0
$7$	0.0209445	−	0.118782i	0.00791629	−	0.0448955i	−0.980594	−	0.196051i	$-0.937188\pi$
$7$	0.0209445	−	0.118782i	0.00791629	−	0.0448955i	0.988510	+	0.151155i	$0.0482994\pi$
$8$		0			0
$9$	2.81908	−	1.02606i	0.939693	−	0.342020i
$10$		0			0
$11$	3.49273	−	1.27125i	1.05310	−	0.383296i	0.243266	−	0.969960i	$-0.421781\pi$
$11$	3.49273	−	1.27125i	1.05310	−	0.383296i	0.809831	+	0.586664i	$0.199559\pi$
$12$		0			0
$13$	−4.64543	+	3.89798i	−1.28841	+	1.08110i	−0.296385	+	0.955069i	$0.595781\pi$
$13$	−4.64543	+	3.89798i	−1.28841	+	1.08110i	−0.992026	+	0.126036i	$0.959775\pi$
$14$		0			0
$15$	2.29813	+	0.405223i	0.593375	+	0.104628i
$16$		0			0
$17$	2.58512	+	4.47756i	0.626984	+	1.08597i	0.988154	+	0.153468i	$0.0490443\pi$
$17$	2.58512	+	4.47756i	0.626984	+	1.08597i	−0.361169	+	0.932500i	$0.617622\pi$
$18$		0			0
$19$	−2.96064	+	5.12797i	−0.679217	+	1.17644i	0.296000	+	0.955188i	$0.404347\pi$
$19$	−2.96064	+	5.12797i	−0.679217	+	1.17644i	−0.975217	+	0.221250i	$0.928986\pi$
$20$		0			0
$21$			0.208911i			0.0455881i
$22$		0			0
$23$	0.826352	+	4.68647i	0.172306	+	0.977197i	0.941207	+	0.337830i	$0.109693\pi$
$23$	0.826352	+	4.68647i	0.172306	+	0.977197i	−0.768901	+	0.639368i	$0.779196\pi$
$24$		0			0
$25$	−2.43969	−	2.04715i	−0.487939	−	0.409429i
$26$		0			0
$27$	−4.50000	+	2.59808i	−0.866025	+	0.500000i
$28$		0			0
$29$	4.55303	+	3.82045i	0.845477	+	0.709440i	0.958789	−	0.284120i	$-0.0917014\pi$
$29$	4.55303	+	3.82045i	0.845477	+	0.709440i	−0.113312	+	0.993559i	$0.536146\pi$
$30$		0			0
$31$	0.875515	+	4.96529i	0.157247	+	0.891793i	0.956703	+	0.291067i	$0.0940104\pi$
$31$	0.875515	+	4.96529i	0.157247	+	0.891793i	−0.799455	+	0.600725i	$0.794879\pi$
$32$		0			0
$33$	−5.57532	+	3.21891i	−0.970539	+	0.560341i
$34$		0			0
$35$	−0.0812519	+	0.140732i	−0.0137341	+	0.0237881i
$36$		0			0
$37$	−0.145430	−	0.251892i	−0.0239085	−	0.0414107i	0.853824	−	0.520562i	$-0.174278\pi$
$37$	−0.145430	−	0.251892i	−0.0239085	−	0.0414107i	−0.877732	+	0.479152i	$0.840944\pi$
$38$		0			0
$39$	6.75150	−	8.04612i	1.08110	−	1.28841i
$40$		0			0
$41$	4.44356	−	3.72859i	0.693968	−	0.582308i	−0.226082	−	0.974108i	$-0.572592\pi$
$41$	4.44356	−	3.72859i	0.693968	−	0.582308i	0.920050	+	0.391800i	$0.128147\pi$
$42$		0			0
$43$	0.426022	−	0.155059i	0.0649678	−	0.0236463i	−0.309332	−	0.950954i	$-0.600105\pi$
$43$	0.426022	−	0.155059i	0.0649678	−	0.0236463i	0.374300	+	0.927308i	$0.377883\pi$
$44$		0			0
$45$	−4.04189			−0.602529
$46$		0			0
$47$	0.134285	−	0.761570i	0.0195875	−	0.111086i	−0.973446	−	0.228915i	$-0.926482\pi$
$47$	0.134285	−	0.761570i	0.0195875	−	0.111086i	0.993034	+	0.117829i	$0.0375933\pi$
$48$		0			0
$49$	6.56418	+	2.38917i	0.937740	+	0.341309i
$50$		0			0
$51$	−5.75624	−	6.86002i	−0.806035	−	0.960596i
$52$		0			0
$53$	−7.29086			−1.00148			−0.500738	−	0.865599i	$-0.666938\pi$
$53$	−7.29086			−1.00148			−0.500738	+	0.865599i	$0.666938\pi$
$54$		0			0
$55$	−5.00774			−0.675244
$56$		0			0
$57$	3.50774	−	9.63744i	0.464612	−	1.27651i
$58$		0			0
$59$	−1.40033	−	0.509678i	−0.182307	−	0.0663545i	0.249253	−	0.968438i	$-0.419815\pi$
$59$	−1.40033	−	0.509678i	−0.182307	−	0.0663545i	−0.431561	+	0.902084i	$0.642037\pi$
$60$		0			0
$61$	−0.656574	+	3.72362i	−0.0840657	+	0.476760i	0.913489	+	0.406864i	$0.133378\pi$
$61$	−0.656574	+	3.72362i	−0.0840657	+	0.476760i	−0.997554	+	0.0698959i	$0.977733\pi$
$62$		0			0
$63$	−0.0628336	−	0.356347i	−0.00791629	−	0.0448955i
$64$		0			0
$65$	7.67752	−	2.79439i	0.952279	−	0.346601i
$66$		0			0
$67$	5.08512	−	4.26692i	0.621247	−	0.521288i	−0.276949	−	0.960885i	$-0.589323\pi$
$67$	5.08512	−	4.26692i	0.621247	−	0.521288i	0.898195	+	0.439597i	$0.144879\pi$
$68$		0			0
$69$	−2.81908	−	7.74535i	−0.339377	−	0.932431i
$70$		0			0
$71$	2.87211	+	4.97464i	0.340857	+	0.590381i	0.984592	−	0.174867i	$-0.0559495\pi$
$71$	2.87211	+	4.97464i	0.340857	+	0.590381i	−0.643735	+	0.765248i	$0.722616\pi$
$72$		0			0
$73$	−5.20961	+	9.02330i	−0.609738	+	1.05610i	0.381545	+	0.924350i	$0.375392\pi$
$73$	−5.20961	+	9.02330i	−0.609738	+	1.05610i	−0.991283	+	0.131748i	$0.957941\pi$
$74$		0			0
$75$	4.77719	+	2.75811i	0.551622	+	0.318479i
$76$		0			0
$77$	−0.0778483	−	0.441500i	−0.00887164	−	0.0503136i
$78$		0			0
$79$	−10.7194	−	8.99465i	−1.20603	−	1.01198i	−0.999437	−	0.0335498i	$-0.989319\pi$
$79$	−10.7194	−	8.99465i	−1.20603	−	1.01198i	−0.206591	−	0.978427i	$-0.566237\pi$
$80$		0			0
$81$	6.89440	−	5.78509i	0.766044	−	0.642788i
$82$		0			0
$83$	1.81521	+	1.52314i	0.199245	+	0.167186i	0.736951	−	0.675946i	$-0.236265\pi$
$83$	1.81521	+	1.52314i	0.199245	+	0.167186i	−0.537706	+	0.843132i	$0.680709\pi$
$84$		0			0
$85$	−1.20961	−	6.86002i	−0.131200	−	0.744074i
$86$		0			0
$87$	−8.91534	−	5.14728i	−0.955825	−	0.551846i
$88$		0			0
$89$	1.08512	−	1.87949i	0.115023	−	0.199225i	−0.802766	−	0.596294i	$-0.796639\pi$
$89$	1.08512	−	1.87949i	0.115023	−	0.199225i	0.917789	+	0.397069i	$0.129973\pi$
$90$		0			0
$91$	0.365715	+	0.633436i	0.0383373	+	0.0664022i
$92$		0			0
$93$	−2.98680	−	8.20616i	−0.309716	−	0.850939i
$94$		0			0
$95$	6.11128	−	5.12797i	0.627004	−	0.526119i
$96$		0			0
$97$	3.21941	−	1.17177i	0.326881	−	0.118975i	−0.173366	−	0.984857i	$-0.555464\pi$
$97$	3.21941	−	1.17177i	0.326881	−	0.118975i	0.500248	+	0.865882i	$0.333242\pi$
$98$		0			0
$99$	8.54189	−	7.16750i	0.858492	−	0.720360i
$100$		0			0
$101$	1.49660	−	8.48762i	0.148917	−	0.844550i	−0.815221	−	0.579149i	$-0.803385\pi$
$101$	1.49660	−	8.48762i	0.148917	−	0.844550i	0.964138	−	0.265400i	$-0.0855041\pi$
$102$		0			0
$103$	−2.05303	−	0.747243i	−0.202291	−	0.0736280i	0.238887	−	0.971047i	$-0.423217\pi$
$103$	−2.05303	−	0.747243i	−0.202291	−	0.0736280i	−0.441179	+	0.897419i	$0.645440\pi$
$104$		0			0
$105$	0.0962667	−	0.264490i	0.00939466	−	0.0258116i
$106$		0			0
$107$	10.2909			0.994855			0.497427	−	0.867506i	$-0.334278\pi$
$107$	10.2909			0.994855			0.497427	+	0.867506i	$0.334278\pi$
$108$		0			0
$109$	−11.0915			−1.06237			−0.531187	−	0.847254i	$-0.678254\pi$
$109$	−11.0915			−1.06237			−0.531187	+	0.847254i	$0.678254\pi$
$110$		0			0
$111$	0.323826	+	0.385920i	0.0307362	+	0.0366299i
$112$		0			0
$113$	−5.56670	−	2.02611i	−0.523671	−	0.190601i	0.0666389	−	0.997777i	$-0.478772\pi$
$113$	−5.56670	−	2.02611i	−0.523671	−	0.190601i	−0.590310	+	0.807176i	$0.700995\pi$
$114$		0			0
$115$	1.11334	−	6.31407i	0.103820	−	0.588790i
$116$		0			0
$117$	−9.09627	+	15.7552i	−0.840950	+	1.45657i
$118$		0			0
$119$	0.586000	−	0.213286i	0.0537185	−	0.0195519i
$120$		0			0
$121$	2.15657	−	1.80958i	0.196052	−	0.164507i
$122$		0			0
$123$	−6.45811	+	7.69648i	−0.582308	+	0.693968i
$124$		0			0
$125$	5.51367	+	9.54996i	0.493158	+	0.854174i
$126$		0			0
$127$	−2.86959	+	4.97027i	−0.254634	+	0.441040i	−0.964796	−	0.262999i	$-0.915288\pi$
$127$	−2.86959	+	4.97027i	−0.254634	+	0.441040i	0.710162	+	0.704039i	$0.248622\pi$
$128$		0			0
$129$	−0.680045	+	0.392624i	−0.0598746	+	0.0345686i
$130$		0			0
$131$	−2.99020	−	16.9583i	−0.261255	−	1.48165i	−0.779491	−	0.626413i	$-0.784522\pi$
$131$	−2.99020	−	16.9583i	−0.261255	−	1.48165i	0.518236	−	0.855237i	$-0.326589\pi$
$132$		0			0
$133$	0.547104	+	0.459074i	0.0474399	+	0.0398068i
$134$		0			0
$135$	6.89440	−	1.21567i	0.593375	−	0.104628i
$136$		0			0
$137$	0.0662372	+	0.0555796i	0.00565902	+	0.00474848i	0.645613	−	0.763665i	$-0.276602\pi$
$137$	0.0662372	+	0.0555796i	0.00565902	+	0.00474848i	−0.639954	+	0.768413i	$0.721046\pi$
$138$		0			0
$139$	3.18866	+	18.0838i	0.270459	+	1.53385i	0.753027	+	0.657990i	$0.228593\pi$
$139$	3.18866	+	18.0838i	0.270459	+	1.53385i	−0.482568	+	0.875859i	$0.660296\pi$
$140$		0			0
$141$			1.33943i			0.112800i
$142$		0			0
$143$	−11.2699	+	19.5201i	−0.942438	+	1.63235i
$144$		0			0
$145$	−4.00387	−	6.93491i	−0.332503	−	0.575913i
$146$		0			0
$147$	−11.9153	−	2.10100i	−0.982761	−	0.173287i
$148$		0			0
$149$	−3.75490	+	3.15074i	−0.307613	+	0.258118i	−0.783505	−	0.621386i	$-0.786570\pi$
$149$	−3.75490	+	3.15074i	−0.307613	+	0.258118i	0.475891	+	0.879504i	$0.342126\pi$
$150$		0			0
$151$	1.62701	−	0.592184i	0.132404	−	0.0481912i	−0.274968	−	0.961453i	$-0.588667\pi$
$151$	1.62701	−	0.592184i	0.132404	−	0.0481912i	0.407372	+	0.913262i	$0.366445\pi$
$152$		0			0
$153$	11.8819	+	9.97011i	0.960596	+	0.806035i
$154$		0			0
$155$	1.17958	−	6.68972i	0.0947460	−	0.537331i
$156$		0			0
$157$	5.46451	+	1.98892i	0.436115	+	0.158733i	0.550742	−	0.834676i	$-0.314345\pi$
$157$	5.46451	+	1.98892i	0.436115	+	0.158733i	−0.114627	+	0.993409i	$0.536567\pi$
$158$		0			0
$159$	12.4363	−	2.19285i	0.986262	−	0.173905i
$160$		0			0
$161$	0.573978			0.0452358
$162$		0			0
$163$	2.70914			0.212196			0.106098	−	0.994356i	$-0.466164\pi$
$163$	2.70914			0.212196			0.106098	+	0.994356i	$0.466164\pi$
$164$		0			0
$165$	8.54189	−	1.50617i	0.664985	−	0.117255i
$166$		0			0
$167$	−23.1202	−	8.41507i	−1.78910	−	0.651177i	−0.999284	−	0.0378268i	$-0.987956\pi$
$167$	−23.1202	−	8.41507i	−1.78910	−	0.651177i	−0.789811	−	0.613351i	$-0.789821\pi$
$168$		0			0
$169$	4.12836	−	23.4131i	0.317566	−	1.80101i
$170$		0			0
$171$	−3.08466	+	17.4940i	−0.235890	+	1.33780i
$172$		0			0
$173$	10.0753	−	3.66712i	0.766013	−	0.278806i	0.0706849	−	0.997499i	$-0.477482\pi$
$173$	10.0753	−	3.66712i	0.766013	−	0.278806i	0.695328	+	0.718693i	$0.255259\pi$
$174$		0			0
$175$	−0.294263	+	0.246916i	−0.0222442	+	0.0186651i
$176$		0			0
$177$	2.54189	+	0.448204i	0.191060	+	0.0336890i
$178$		0			0
$179$	−6.92262	−	11.9903i	−0.517421	−	0.896199i	−0.999795	−	0.0202340i	$-0.993559\pi$
$179$	−6.92262	−	11.9903i	−0.517421	−	0.896199i	0.482374	−	0.875965i	$-0.339774\pi$
$180$		0			0
$181$	−1.75490	+	3.03958i	−0.130441	+	0.225930i	−0.923847	−	0.382763i	$-0.874973\pi$
$181$	−1.75490	+	3.03958i	−0.130441	+	0.225930i	0.793406	+	0.608693i	$0.208306\pi$
$182$		0			0
$183$		−	6.54899i		−	0.484115i
$184$		0			0
$185$	0.0680482	+	0.385920i	0.00500300	+	0.0283734i
$186$		0			0
$187$	14.7212	+	12.3526i	1.07652	+	0.903309i
$188$		0			0
$189$	0.214355	+	0.588936i	0.0155920	+	0.0428388i
$190$		0			0
$191$	16.7704	+	14.0720i	1.21346	+	1.01822i	0.999140	+	0.0414526i	$0.0131986\pi$
$191$	16.7704	+	14.0720i	1.21346	+	1.01822i	0.214322	+	0.976763i	$0.431246\pi$
$192$		0			0
$193$	4.44743	+	25.2226i	0.320133	+	1.81557i	0.541873	+	0.840460i	$0.317715\pi$
$193$	4.44743	+	25.2226i	0.320133	+	1.81557i	−0.221740	+	0.975106i	$0.571174\pi$
$194$		0			0
$195$	−12.2554	+	7.07564i	−0.877625	+	0.506697i
$196$		0			0
$197$	−6.84255	+	11.8516i	−0.487511	+	0.844395i	−0.999897	−	0.0143611i	$-0.995429\pi$
$197$	−6.84255	+	11.8516i	−0.487511	+	0.844395i	0.512385	+	0.858756i	$0.328762\pi$
$198$		0			0
$199$	−6.19981	−	10.7384i	−0.439493	−	0.761224i	0.558158	−	0.829735i	$-0.311508\pi$
$199$	−6.19981	−	10.7384i	−0.439493	−	0.761224i	−0.997650	+	0.0685113i	$0.978175\pi$
$200$		0			0
$201$	−7.39053	+	8.80769i	−0.521288	+	0.621247i
$202$		0			0
$203$	0.549163	−	0.460802i	0.0385437	−	0.0323420i
$204$		0			0
$205$	−7.34389	+	2.67296i	−0.512920	+	0.186688i
$206$		0			0
$207$	7.13816	+	12.3636i	0.496136	+	0.859333i
$208$		0			0
$209$	−3.82177	+	21.6743i	−0.264357	+	1.49924i
$210$		0			0
$211$	13.9474	+	5.07645i	0.960181	+	0.349477i	0.774104	−	0.633058i	$-0.218201\pi$
$211$	13.9474	+	5.07645i	0.960181	+	0.349477i	0.186077	+	0.982535i	$0.440423\pi$
$212$		0			0
$213$	−6.39528	−	7.62159i	−0.438197	−	0.522223i
$214$		0			0
$215$	−0.610815			−0.0416572
$216$		0			0
$217$	0.608126			0.0412823
$218$		0			0
$219$	6.17230	−	16.9583i	0.417086	−	1.14593i
$220$		0			0
$221$	−29.4624	−	10.7235i	−1.98186	−	0.721338i
$222$		0			0
$223$	1.16890	−	6.62916i	0.0782754	−	0.443922i	−0.920331	−	0.391141i	$-0.872080\pi$
$223$	1.16890	−	6.62916i	0.0782754	−	0.443922i	0.998606	−	0.0527806i	$-0.0168084\pi$
$224$		0			0
$225$	−8.97818	−	3.26779i	−0.598545	−	0.217853i
$226$		0			0
$227$	13.6211	−	4.95767i	0.904063	−	0.329052i	0.152183	−	0.988352i	$-0.451370\pi$
$227$	13.6211	−	4.95767i	0.904063	−	0.329052i	0.751880	+	0.659300i	$0.229147\pi$
$228$		0			0
$229$	19.7540	−	16.5756i	1.30538	−	1.09535i	0.316194	−	0.948694i	$-0.397595\pi$
$229$	19.7540	−	16.5756i	1.30538	−	1.09535i	0.989188	−	0.146652i	$-0.0468496\pi$
$230$		0			0
$231$	0.265578	+	0.729669i	0.0174737	+	0.0480087i
$232$		0			0
$233$	−5.19846	−	9.00400i	−0.340563	−	0.589872i	0.643975	−	0.765047i	$-0.277284\pi$
$233$	−5.19846	−	9.00400i	−0.340563	−	0.589872i	−0.984537	+	0.175175i	$0.943951\pi$
$234$		0			0
$235$	−0.520945	+	0.902302i	−0.0339827	+	0.0588597i
$236$		0			0
$237$	20.9898	+	12.1185i	1.36343	+	0.787179i
$238$		0			0
$239$	3.97906	+	22.5663i	0.257384	+	1.45970i	0.789879	+	0.613263i	$0.210143\pi$
$239$	3.97906	+	22.5663i	0.257384	+	1.45970i	−0.532495	+	0.846433i	$0.678746\pi$
$240$		0			0
$241$	−9.25150	−	7.76293i	−0.595941	−	0.500054i	0.294197	−	0.955745i	$-0.404948\pi$
$241$	−9.25150	−	7.76293i	−0.595941	−	0.500054i	−0.890138	+	0.455691i	$0.849392\pi$
$242$		0			0
$243$	−10.0201	+	11.9415i	−0.642788	+	0.766044i
$244$		0			0
$245$	−7.20961	−	6.04958i	−0.460605	−	0.386493i
$246$		0			0
$247$	−6.23530	−	35.3621i	−0.396743	−	2.25004i
$248$		0			0
$249$	−3.55438	−	2.05212i	−0.225250	−	0.130048i
$250$		0			0
$251$	−7.02347	+	12.1650i	−0.443318	+	0.767849i	−0.997933	−	0.0642581i	$-0.979532\pi$
$251$	−7.02347	+	12.1650i	−0.443318	+	0.767849i	0.554616	+	0.832107i	$0.312865\pi$
$252$		0			0
$253$	8.84389	+	15.3181i	0.556011	+	0.963039i
$254$		0			0
$255$	4.12654	+	11.3376i	0.258414	+	0.709987i
$256$		0			0
$257$	13.8983	−	11.6620i	0.866950	−	0.727458i	−0.0965034	−	0.995333i	$-0.530766\pi$
$257$	13.8983	−	11.6620i	0.866950	−	0.727458i	0.963454	+	0.267875i	$0.0863214\pi$
$258$		0			0
$259$	−0.0329662	+	0.0119987i	−0.00204842	+	0.000745565i
$260$		0			0
$261$	16.7554	+	6.09845i	1.03713	+	0.377485i
$262$		0			0
$263$	−0.742107	+	4.20870i	−0.0457603	+	0.259519i	−0.999102	−	0.0423745i	$-0.986508\pi$
$263$	−0.742107	+	4.20870i	−0.0457603	+	0.259519i	0.953342	+	0.301894i	$0.0976188\pi$
$264$		0			0
$265$	9.23055	+	3.35965i	0.567028	+	0.206381i
$266$		0			0
$267$	−1.28564	+	3.53228i	−0.0786802	+	0.216172i
$268$		0			0
$269$	13.0615			0.796373			0.398187	−	0.917304i	$-0.369640\pi$
$269$	13.0615			0.796373			0.398187	+	0.917304i	$0.369640\pi$
$270$		0			0
$271$	−8.48751			−0.515580			−0.257790	−	0.966201i	$-0.582994\pi$
$271$	−8.48751			−0.515580			−0.257790	+	0.966201i	$0.582994\pi$
$272$		0			0
$273$	−0.814330	−	0.970481i	−0.0492855	−	0.0587362i
$274$		0			0
$275$	−11.1236	−	4.04866i	−0.670779	−	0.244144i
$276$		0			0
$277$	1.14842	−	6.51303i	0.0690020	−	0.391330i	−0.930673	−	0.365851i	$-0.880778\pi$
$277$	1.14842	−	6.51303i	0.0690020	−	0.391330i	0.999675	−	0.0254787i	$-0.00811100\pi$
$278$		0			0
$279$	7.56283	+	13.0992i	0.452775	+	0.784229i
$280$		0			0
$281$	−27.9320	+	10.1664i	−1.66628	+	0.606478i	−0.991332	−	0.131384i	$-0.958058\pi$
$281$	−27.9320	+	10.1664i	−1.66628	+	0.606478i	−0.674952	+	0.737861i	$0.735836\pi$
$282$		0			0
$283$	2.15657	−	1.80958i	0.128195	−	0.107568i	−0.576436	−	0.817142i	$-0.695557\pi$
$283$	2.15657	−	1.80958i	0.128195	−	0.107568i	0.704631	+	0.709574i	$0.251113\pi$
$284$		0			0
$285$	−8.88191	+	10.5850i	−0.526119	+	0.627004i
$286$		0			0
$287$	−0.349823	−	0.605910i	−0.0206494	−	0.0357658i
$288$		0			0
$289$	−4.86571	+	8.42767i	−0.286219	+	0.495745i
$290$		0			0
$291$	−5.13903	+	2.96702i	−0.301255	+	0.173930i
$292$		0			0
$293$	1.70796	+	9.68631i	0.0997800	+	0.565881i	0.993177	+	0.116613i	$0.0372038\pi$
$293$	1.70796	+	9.68631i	0.0997800	+	0.565881i	−0.893397	+	0.449267i	$0.851685\pi$
$294$		0			0
$295$	1.53802	+	1.29055i	0.0895469	+	0.0751388i
$296$		0			0
$297$	−12.4145	+	14.7950i	−0.720360	+	0.858492i
$298$		0			0
$299$	−22.1065	−	18.5496i	−1.27845	−	1.07275i
$300$		0			0
$301$	−0.00949548	−	0.0538515i	−0.000547310	−	0.00310395i
$302$		0			0
$303$			14.9278i			0.857578i
$304$		0			0
$305$	2.54710	−	4.41171i	0.145847	−	0.252614i
$306$		0			0
$307$	6.78106	+	11.7451i	0.387015	+	0.670330i	0.992047	−	0.125871i	$-0.0401727\pi$
$307$	6.78106	+	11.7451i	0.387015	+	0.670330i	−0.605031	+	0.796202i	$0.706839\pi$
$308$		0			0
$309$	3.72668	+	0.657115i	0.212004	+	0.0373819i
$310$		0			0
$311$	8.10220	−	6.79855i	0.459433	−	0.385510i	−0.383489	−	0.923545i	$-0.625278\pi$
$311$	8.10220	−	6.79855i	0.459433	−	0.385510i	0.842922	+	0.538035i	$0.180833\pi$
$312$		0			0
$313$	10.0544	−	3.65949i	0.568307	−	0.206847i	−0.0418547	−	0.999124i	$-0.513327\pi$
$313$	10.0544	−	3.65949i	0.568307	−	0.206847i	0.610162	+	0.792277i	$0.291104\pi$
$314$		0			0
$315$	−0.0846555	+	0.480105i	−0.00476980	+	0.0270509i
$316$		0			0
$317$	5.06717	−	28.7374i	0.284601	−	1.61405i	−0.422108	−	0.906546i	$-0.638710\pi$
$317$	5.06717	−	28.7374i	0.284601	−	1.61405i	0.706708	−	0.707505i	$-0.250179\pi$
$318$		0			0
$319$	20.7592	+	7.55574i	1.16229	+	0.423040i
$320$		0			0
$321$	−17.5535	+	3.09516i	−0.979741	+	0.172755i
$322$		0			0
$323$	−30.6144			−1.70343
$324$		0			0
$325$	19.3131			1.07130
$326$		0			0
$327$	18.9192	−	3.33597i	1.04623	−	0.184479i
$328$		0			0
$329$	−0.0876485	−	0.0319015i	−0.00483222	−	0.00175878i
$330$		0			0
$331$	1.26739	−	7.18772i	0.0696620	−	0.395073i	−0.929962	−	0.367655i	$-0.880161\pi$
$331$	1.26739	−	7.18772i	0.0696620	−	0.395073i	0.999624	−	0.0274173i	$-0.00872829\pi$
$332$		0			0
$333$	−0.668434	−	0.560882i	−0.0366299	−	0.0307362i
$334$		0			0
$335$	−8.40420	+	3.05888i	−0.459171	+	0.167124i
$336$		0			0
$337$	−1.24376	+	1.04363i	−0.0677517	+	0.0568504i	−0.676035	−	0.736870i	$-0.736303\pi$
$337$	−1.24376	+	1.04363i	−0.0677517	+	0.0568504i	0.608283	+	0.793720i	$0.291859\pi$
$338$		0			0
$339$	10.1047	+	1.78174i	0.548813	+	0.0967706i
$340$		0			0
$341$	9.37005	+	16.2294i	0.507417	+	0.878872i
$342$		0			0
$343$	0.843426	−	1.46086i	0.0455407	−	0.0788788i
$344$		0			0
$345$			11.1050i			0.597873i
$346$		0			0
$347$	0.949655	+	5.38576i	0.0509801	+	0.289123i	0.999630	−	0.0272057i	$-0.00866092\pi$
$347$	0.949655	+	5.38576i	0.0509801	+	0.289123i	−0.948650	+	0.316329i	$0.897550\pi$
$348$		0			0
$349$	2.37346	+	1.99157i	0.127048	+	0.106606i	0.704098	−	0.710103i	$-0.251352\pi$
$349$	2.37346	+	1.99157i	0.127048	+	0.106606i	−0.577050	+	0.816709i	$0.695796\pi$
$350$		0			0
$351$	10.7772	−	29.6101i	0.575244	−	1.58047i
$352$		0			0
$353$	0.233956	+	0.196312i	0.0124522	+	0.0104486i	0.648992	−	0.760795i	$-0.275191\pi$
$353$	0.233956	+	0.196312i	0.0124522	+	0.0104486i	−0.636540	+	0.771243i	$0.719635\pi$
$354$		0			0
$355$	−1.34389	−	7.62159i	−0.0713264	−	0.404512i
$356$		0			0
$357$	−0.935412	+	0.540060i	−0.0495072	+	0.0285830i
$358$		0			0
$359$	5.28493	−	9.15377i	0.278928	−	0.483117i	−0.692191	−	0.721715i	$-0.743354\pi$
$359$	5.28493	−	9.15377i	0.278928	−	0.483117i	0.971119	+	0.238597i	$0.0766876\pi$
$360$		0			0
$361$	−8.03074	−	13.9097i	−0.422671	−	0.732087i
$362$		0			0
$363$	−3.13429	+	3.73530i	−0.164507	+	0.196052i
$364$		0			0
$365$	10.7536	−	9.02330i	0.562867	−	0.472301i
$366$		0			0
$367$	2.51842	−	0.916629i	0.131460	−	0.0478477i	−0.275452	−	0.961315i	$-0.588828\pi$
$367$	2.51842	−	0.916629i	0.131460	−	0.0478477i	0.406913	+	0.913467i	$0.366605\pi$
$368$		0			0
$369$	8.70099	−	15.0706i	0.452955	−	0.784542i
$370$		0			0
$371$	−0.152704	+	0.866025i	−0.00792798	+	0.0449618i
$372$		0			0
$373$	−22.9008	−	8.33521i	−1.18576	−	0.431581i	−0.327526	−	0.944842i	$-0.606215\pi$
$373$	−22.9008	−	8.33521i	−1.18576	−	0.431581i	−0.858232	+	0.513261i	$0.828437\pi$
$374$		0			0
$375$	−12.2772	−	14.6314i	−0.633991	−	0.755561i
$376$		0			0
$377$	−36.0428			−1.85630
$378$		0			0
$379$	4.08647			0.209908			0.104954	−	0.994477i	$-0.466531\pi$
$379$	4.08647			0.209908			0.104954	+	0.994477i	$0.466531\pi$
$380$		0			0
$381$	3.39986	−	9.34105i	0.174180	−	0.478556i
$382$		0			0
$383$	−15.4017	−	5.60575i	−0.786989	−	0.286440i	−0.0829050	−	0.996557i	$-0.526420\pi$
$383$	−15.4017	−	5.60575i	−0.786989	−	0.286440i	−0.704084	+	0.710117i	$0.748642\pi$
$384$		0			0
$385$	−0.104885	+	0.594831i	−0.00534542	+	0.0303154i
$386$		0			0
$387$	1.04189	−	0.874249i	0.0529622	−	0.0444406i
$388$		0			0
$389$	26.2263	−	9.54558i	1.32972	−	0.483980i	0.423163	−	0.906054i	$-0.360920\pi$
$389$	26.2263	−	9.54558i	1.32972	−	0.483980i	0.906562	+	0.422073i	$0.138698\pi$
$390$		0			0
$391$	−18.8478	+	15.8152i	−0.953172	+	0.799807i
$392$		0			0
$393$	10.2010	+	28.0270i	0.514572	+	1.41377i
$394$		0			0
$395$	9.42649	+	16.3272i	0.474298	+	0.821508i
$396$		0			0
$397$	16.2469	−	28.1405i	0.815409	−	1.41233i	−0.0936247	−	0.995608i	$-0.529845\pi$
$397$	16.2469	−	28.1405i	0.815409	−	1.41233i	0.909034	−	0.416722i	$-0.136821\pi$
$398$		0			0
$399$	−1.07129	−	0.618509i	−0.0536316	−	0.0309642i
$400$		0			0
$401$	2.67096	+	15.1478i	0.133381	+	0.756443i	0.975973	+	0.217891i	$0.0699176\pi$
$401$	2.67096	+	15.1478i	0.133381	+	0.756443i	−0.842592	+	0.538553i	$0.818971\pi$
$402$		0			0
$403$	−23.4217	−	19.6532i	−1.16672	−	0.978994i
$404$		0			0
$405$	−11.3944	+	4.14722i	−0.566192	+	0.206077i
$406$		0			0
$407$	−0.828163	−	0.694911i	−0.0410505	−	0.0344455i
$408$		0			0
$409$	−1.65822	−	9.40425i	−0.0819938	−	0.465010i	−0.997965	−	0.0637658i	$-0.979689\pi$
$409$	−1.65822	−	9.40425i	−0.0819938	−	0.465010i	0.915971	−	0.401244i	$-0.131422\pi$
$410$		0			0
$411$	−0.129700	−	0.0748822i	−0.00639762	−	0.00369366i
$412$		0			0
$413$	−0.0898700	+	0.155659i	−0.00442222	+	0.00765950i
$414$		0			0
$415$	−1.59627	−	2.76481i	−0.0783576	−	0.135719i
$416$		0			0
$417$	−10.8780	−	29.8872i	−0.532700	−	1.46358i
$418$		0			0
$419$	26.0239	−	21.8367i	1.27135	−	1.06679i	0.276977	−	0.960876i	$-0.410667\pi$
$419$	26.0239	−	21.8367i	1.27135	−	1.06679i	0.994375	−	0.105915i	$-0.0337771\pi$
$420$		0			0
$421$	11.8229	−	4.30320i	0.576215	−	0.209725i	−0.0374406	−	0.999299i	$-0.511920\pi$
$421$	11.8229	−	4.30320i	0.576215	−	0.209725i	0.613656	+	0.789574i	$0.289698\pi$
$422$		0			0
$423$	−0.402856	−	2.28471i	−0.0195875	−	0.111086i
$424$		0			0
$425$	2.85932	−	16.2160i	0.138697	−	0.786591i
$426$		0			0
$427$	0.428548	+	0.155979i	0.0207389	+	0.00754834i
$428$		0			0
$429$	13.3525	−	36.6857i	0.644665	−	1.77120i
$430$		0			0
$431$	7.77601			0.374557			0.187279	−	0.982307i	$-0.440033\pi$
$431$	7.77601			0.374557			0.187279	+	0.982307i	$0.440033\pi$
$432$		0			0
$433$	−40.6536			−1.95369			−0.976845	−	0.213950i	$-0.931367\pi$
$433$	−40.6536			−1.95369			−0.976845	+	0.213950i	$0.931367\pi$
$434$		0			0
$435$	8.91534	+	10.6249i	0.427458	+	0.509425i
$436$		0			0
$437$	−26.4786	−	9.63744i	−1.26665	−	0.461021i
$438$		0			0
$439$	3.07280	−	17.4267i	0.146657	−	0.831731i	−0.819366	−	0.573271i	$-0.805674\pi$
$439$	3.07280	−	17.4267i	0.146657	−	0.831731i	0.966022	−	0.258459i	$-0.0832148\pi$
$440$		0			0
$441$	20.9564			0.997922
$442$		0			0
$443$	13.5086	−	4.91673i	0.641814	−	0.233601i	−0.000551343	−	1.00000i	$-0.500175\pi$
$443$	13.5086	−	4.91673i	0.641814	−	0.233601i	0.642365	+	0.766399i	$0.277953\pi$
$444$		0			0
$445$	−2.23989	+	1.87949i	−0.106181	+	0.0890962i
$446$		0			0
$447$	5.45723	−	6.50368i	0.258118	−	0.307613i
$448$		0			0
$449$	−13.9859	−	24.2243i	−0.660036	−	1.14322i	−0.980606	−	0.195991i	$-0.937208\pi$
$449$	−13.9859	−	24.2243i	−0.660036	−	1.14322i	0.320569	−	0.947225i	$-0.396126\pi$
$450$		0			0
$451$	10.7802	−	18.6718i	0.507619	−	0.879222i
$452$		0			0
$453$	−2.59714	+	1.49946i	−0.122024	+	0.0704509i
$454$		0			0
$455$	−0.171122	−	0.970481i	−0.00802232	−	0.0454968i
$456$		0			0
$457$	6.53280	+	5.48167i	0.305592	+	0.256422i	0.782667	−	0.622440i	$-0.213859\pi$
$457$	6.53280	+	5.48167i	0.305592	+	0.256422i	−0.477075	+	0.878862i	$0.658303\pi$
$458$		0			0
$459$	−23.2661	−	13.4327i	−1.08597	−	0.626984i
$460$		0			0
$461$	16.6361	+	13.9593i	0.774820	+	0.650151i	0.941938	−	0.335785i	$-0.109002\pi$
$461$	16.6361	+	13.9593i	0.774820	+	0.650151i	−0.167118	+	0.985937i	$0.553446\pi$
$462$		0			0
$463$	3.43882	+	19.5025i	0.159815	+	0.906358i	0.954250	+	0.299009i	$0.0966559\pi$
$463$	3.43882	+	19.5025i	0.159815	+	0.906358i	−0.794435	+	0.607349i	$0.792233\pi$
$464$		0			0
$465$			11.7657i			0.545620i
$466$		0			0
$467$	18.4927	−	32.0303i	0.855741	−	1.48219i	−0.0202143	−	0.999796i	$-0.506435\pi$
$467$	18.4927	−	32.0303i	0.855741	−	1.48219i	0.875956	−	0.482392i	$-0.160232\pi$
$468$		0			0
$469$	−0.400330	−	0.693392i	−0.0184855	−	0.0320178i
$470$		0			0
$471$	−9.91921	−	1.74903i	−0.457053	−	0.0805908i
$472$		0			0
$473$	1.29086	−	1.08316i	0.0593538	−	0.0498037i
$474$		0			0
$475$	17.7208	−	6.44983i	0.813084	−	0.295938i
$476$		0			0
$477$	−20.5535	+	7.48086i	−0.941080	+	0.342525i
$478$		0			0
$479$	1.97131	−	11.1799i	0.0900717	−	0.510822i	−0.906075	−	0.423117i	$-0.860936\pi$
$479$	1.97131	−	11.1799i	0.0900717	−	0.510822i	0.996147	−	0.0877044i	$-0.0279531\pi$
$480$		0			0
$481$	1.65745	+	0.603263i	0.0755733	+	0.0275064i
$482$		0			0
$483$	−0.979055	+	0.172634i	−0.0445486	+	0.00785511i
$484$		0			0
$485$	−4.61587			−0.209596
$486$		0			0
$487$	−1.13785			−0.0515610			−0.0257805	−	0.999668i	$-0.508207\pi$
$487$	−1.13785			−0.0515610			−0.0257805	+	0.999668i	$0.508207\pi$
$488$		0			0
$489$	−4.62108	+	0.814821i	−0.208973	+	0.0368475i
$490$		0			0
$491$	−14.3880	−	5.23680i	−0.649322	−	0.236334i	−0.00370223	−	0.999993i	$-0.501178\pi$
$491$	−14.3880	−	5.23680i	−0.649322	−	0.236334i	−0.645619	+	0.763659i	$0.723401\pi$
$492$		0			0
$493$	−5.33615	+	30.2628i	−0.240328	+	1.36297i
$494$		0			0
$495$	−14.1172	+	5.13824i	−0.634521	+	0.230947i
$496$		0			0
$497$	0.651055	−	0.236965i	0.0292038	−	0.0106293i
$498$		0			0
$499$	−1.77584	+	1.49011i	−0.0794977	+	0.0667065i	−0.681671	−	0.731659i	$-0.738746\pi$
$499$	−1.77584	+	1.49011i	−0.0794977	+	0.0667065i	0.602173	+	0.798366i	$0.294302\pi$
$500$		0			0
$501$	41.9680	+	7.40008i	1.87499	+	0.330611i
$502$		0			0
$503$	4.02869	+	6.97789i	0.179630	+	0.311129i	0.941754	−	0.336303i	$-0.109177\pi$
$503$	4.02869	+	6.97789i	0.179630	+	0.311129i	−0.762124	+	0.647431i	$0.775843\pi$
$504$		0			0
$505$	−5.80587	+	10.0561i	−0.258358	+	0.447489i
$506$		0			0
$507$			41.1782i			1.82879i
$508$		0			0
$509$	1.24944	+	7.08591i	0.0553803	+	0.314077i	0.999896	−	0.0143875i	$-0.00457984\pi$
$509$	1.24944	+	7.08591i	0.0553803	+	0.314077i	−0.944516	+	0.328465i	$0.893469\pi$
$510$		0			0
$511$	0.962697	+	0.807798i	0.0425872	+	0.0357349i
$512$		0			0
$513$		−	30.7678i		−	1.35843i
$514$		0			0
$515$	2.25490	+	1.89209i	0.0993628	+	0.0833753i
$516$		0			0
$517$	−0.499123	−	2.83067i	−0.0219514	−	0.124493i
$518$		0			0
$519$	−16.0829	+	9.28547i	−0.705961	+	0.407587i
$520$		0			0
$521$	−4.84343	+	8.38906i	−0.212194	+	0.367531i	−0.952401	−	0.304848i	$-0.901394\pi$
$521$	−4.84343	+	8.38906i	−0.212194	+	0.367531i	0.740207	+	0.672379i	$0.234728\pi$
$522$		0			0
$523$	7.29339	+	12.6325i	0.318917	+	0.552381i	0.980262	−	0.197701i	$-0.0633474\pi$
$523$	7.29339	+	12.6325i	0.318917	+	0.552381i	−0.661345	+	0.750082i	$0.730014\pi$
$524$		0			0
$525$	0.427671	−	0.509678i	0.0186651	−	0.0222442i
$526$		0			0
$527$	−19.9691	+	16.7561i	−0.869867	+	0.729905i
$528$		0			0
$529$	0.332748	−	0.121111i	0.0144673	−	0.00526568i
$530$		0			0
$531$	−4.47060			−0.194007
$532$		0			0
$533$	−6.10829	+	34.6418i	−0.264579	+	1.50050i
$534$		0			0
$535$	−13.0287	−	4.74205i	−0.563279	−	0.205017i
$536$		0			0
$537$	15.4145	+	18.3702i	0.665183	+	0.792735i
$538$		0			0
$539$	25.9641			1.11835
$540$		0			0
$541$	23.9786			1.03092			0.515461	−	0.856913i	$-0.327621\pi$
$541$	23.9786			1.03092			0.515461	+	0.856913i	$0.327621\pi$
$542$		0			0
$543$	2.07919	−	5.71253i	0.0892267	−	0.245148i
$544$		0			0
$545$	14.0424	+	5.11100i	0.601508	+	0.218931i
$546$		0			0
$547$	−6.94269	+	39.3739i	−0.296848	+	1.68351i	0.362748	+	0.931887i	$0.381839\pi$
$547$	−6.94269	+	39.3739i	−0.296848	+	1.68351i	−0.659596	+	0.751620i	$0.729273\pi$
$548$		0			0
$549$	1.96972	+	11.1708i	0.0840657	+	0.476760i
$550$		0			0
$551$	−33.0710	+	12.0369i	−1.40887	+	0.512788i
$552$		0			0
$553$	−1.29292	+	1.08489i	−0.0549805	+	0.0461341i
$554$		0			0
$555$	−0.232145	−	0.637812i	−0.00985399	−	0.0270736i
$556$		0			0
$557$	−1.17958	−	2.04309i	−0.0499803	−	0.0865685i	0.839953	−	0.542659i	$-0.182583\pi$
$557$	−1.17958	−	2.04309i	−0.0499803	−	0.0865685i	−0.889933	+	0.456091i	$0.849249\pi$
$558$		0			0
$559$	−1.37464	+	2.38094i	−0.0581410	+	0.100703i
$560$		0			0
$561$	−28.8258	−	16.6426i	−1.21703	−	0.702650i
$562$		0			0
$563$	7.55825	+	42.8650i	0.318542	+	1.80654i	0.551632	+	0.834087i	$0.314005\pi$
$563$	7.55825	+	42.8650i	0.318542	+	1.80654i	−0.233090	+	0.972455i	$0.574884\pi$
$564$		0			0
$565$	6.11406	+	5.13030i	0.257220	+	0.215833i
$566$		0			0
$567$	−0.542766	−	0.940099i	−0.0227940	−	0.0394804i
$568$		0			0
$569$	11.2187	+	9.41360i	0.470312	+	0.394639i	0.846908	−	0.531739i	$-0.178461\pi$
$569$	11.2187	+	9.41360i	0.470312	+	0.394639i	−0.376596	+	0.926377i	$0.622906\pi$
$570$		0			0
$571$	2.57145	+	14.5834i	0.107612	+	0.610297i	0.990145	+	0.140047i	$0.0447253\pi$
$571$	2.57145	+	14.5834i	0.107612	+	0.610297i	−0.882533	+	0.470251i	$0.844164\pi$
$572$		0			0
$573$	−32.8383	−	18.9592i	−1.37184	−	0.792031i
$574$		0			0
$575$	7.57785	−	13.1252i	0.316018	−	0.547359i
$576$		0			0
$577$	16.0706	+	27.8351i	0.669027	+	1.15879i	0.978177	+	0.207775i	$0.0666222\pi$
$577$	16.0706	+	27.8351i	0.669027	+	1.15879i	−0.309150	+	0.951013i	$0.600044\pi$
$578$		0			0
$579$	−15.1723	−	41.6856i	−0.630539	−	1.73239i
$580$		0			0
$581$	0.218941	−	0.183713i	0.00908320	−	0.00762171i
$582$		0			0
$583$	−25.4650	+	9.26849i	−1.05465	+	0.383862i
$584$		0			0
$585$	18.7763	−	15.7552i	0.776305	−	0.651397i
$586$		0			0
$587$	−4.75918	+	26.9907i	−0.196432	+	1.11402i	0.713932	+	0.700215i	$0.246913\pi$
$587$	−4.75918	+	26.9907i	−0.196432	+	1.11402i	−0.910364	+	0.413808i	$0.864198\pi$
$588$		0			0
$589$	−28.0540	−	10.2108i	−1.15594	−	0.420729i
$590$		0			0
$591$	8.10700	−	22.2738i	0.333477	−	0.916222i
$592$		0			0
$593$	36.2377			1.48810			0.744052	−	0.668121i	$-0.232901\pi$
$593$	36.2377			1.48810			0.744052	+	0.668121i	$0.232901\pi$
$594$		0			0
$595$	−0.840185			−0.0344442
$596$		0			0
$597$	13.8050	+	16.4522i	0.565001	+	0.673342i
$598$		0			0
$599$	43.2438	+	15.7395i	1.76689	+	0.643097i	0.999999	+	0.00132449i	$0.000421598\pi$
$599$	43.2438	+	15.7395i	1.76689	+	0.643097i	0.766895	+	0.641772i	$0.221801\pi$
$600$		0			0
$601$	0.294673	−	1.67118i	0.0120200	−	0.0681687i	−0.978208	−	0.207628i	$-0.933425\pi$
$601$	0.294673	−	1.67118i	0.0120200	−	0.0681687i	0.990228	+	0.139460i	$0.0445366\pi$
$602$		0			0
$603$	9.95723	−	17.2464i	0.405490	−	0.702329i
$604$		0			0
$605$	−3.56418	+	1.29725i	−0.144904	+	0.0527409i
$606$		0			0
$607$	10.7779	−	9.04374i	0.437462	−	0.367074i	−0.397297	−	0.917690i	$-0.630052\pi$
$607$	10.7779	−	9.04374i	0.437462	−	0.367074i	0.834758	+	0.550616i	$0.185607\pi$
$608$		0			0
$609$	−0.798133	+	0.951178i	−0.0323420	+	0.0385437i
$610$		0			0
$611$	2.34477	+	4.06126i	0.0948592	+	0.164301i
$612$		0			0
$613$	12.8314	−	22.2246i	0.518256	−	0.897645i	−0.481520	−	0.876435i	$-0.659915\pi$
$613$	12.8314	−	22.2246i	0.518256	−	0.897645i	0.999775	−	0.0212096i	$-0.00675172\pi$
$614$		0			0
$615$	11.7228	−	6.76817i	0.472709	−	0.272919i
$616$		0			0
$617$	5.46822	+	31.0118i	0.220142	+	1.24849i	0.871757	+	0.489938i	$0.162981\pi$
$617$	5.46822	+	31.0118i	0.220142	+	1.24849i	−0.651615	+	0.758550i	$0.725908\pi$
$618$		0			0
$619$	2.42674	+	2.03627i	0.0975388	+	0.0818448i	0.690253	−	0.723568i	$-0.257499\pi$
$619$	2.42674	+	2.03627i	0.0975388	+	0.0818448i	−0.592714	+	0.805413i	$0.701944\pi$
$620$		0			0
$621$	−15.8944	−	18.9422i	−0.637820	−	0.760125i
$622$		0			0
$623$	−0.200522	−	0.168258i	−0.00803376	−	0.00674113i
$624$		0			0
$625$	0.185259	+	1.05066i	0.00741037	+	0.0420263i
$626$		0			0
$627$		−	38.1201i		−	1.52237i
$628$		0			0
$629$	0.751907	−	1.30234i	0.0299805	−	0.0519277i
$630$		0			0
$631$	11.2961	+	19.5654i	0.449690	+	0.778885i	0.998366	−	0.0571498i	$-0.0182013\pi$
$631$	11.2961	+	19.5654i	0.449690	+	0.778885i	−0.548676	+	0.836035i	$0.684868\pi$
$632$		0			0
$633$	−25.3175	−	4.46416i	−1.00628	−	0.177434i
$634$		0			0
$635$	5.92333	−	4.97027i	0.235060	−	0.197239i
$636$		0			0
$637$	−39.8063	+	14.4883i	−1.57718	+	0.574048i
$638$		0			0
$639$	13.2010	+	11.0769i	0.522223	+	0.438197i
$640$		0			0
$641$	−3.04323	+	17.2590i	−0.120200	+	0.681691i	0.863843	+	0.503761i	$0.168051\pi$
$641$	−3.04323	+	17.2590i	−0.120200	+	0.681691i	−0.984043	+	0.177929i	$0.943060\pi$
$642$		0			0
$643$	−26.4923	−	9.64241i	−1.04475	−	0.380260i	−0.238074	−	0.971247i	$-0.576516\pi$
$643$	−26.4923	−	9.64241i	−1.04475	−	0.380260i	−0.806681	+	0.590987i	$0.798738\pi$
$644$		0			0
$645$	1.04189	−	0.183713i	0.0410243	−	0.00723370i
$646$		0			0
$647$	−32.3492			−1.27178			−0.635888	−	0.771781i	$-0.719366\pi$
$647$	−32.3492			−1.27178			−0.635888	+	0.771781i	$0.719366\pi$
$648$		0			0
$649$	−5.53890			−0.217421
$650$		0			0
$651$	−1.03730	+	0.182905i	−0.0406551	+	0.00716860i
$652$		0			0
$653$	25.9329	+	9.43880i	1.01483	+	0.369369i	0.795287	−	0.606234i	$-0.207320\pi$
$653$	25.9329	+	9.43880i	1.01483	+	0.369369i	0.219546	+	0.975602i	$0.429543\pi$
$654$		0			0
$655$	−4.02869	+	22.8478i	−0.157414	+	0.892738i
$656$		0			0
$657$	−5.42783	+	30.7828i	−0.211760	+	1.20095i
$658$		0			0
$659$	−4.90508	+	1.78530i	−0.191075	+	0.0695455i	−0.435785	−	0.900051i	$-0.643529\pi$
$659$	−4.90508	+	1.78530i	−0.191075	+	0.0695455i	0.244711	+	0.969596i	$0.421307\pi$
$660$		0			0
$661$	−36.7294	+	30.8196i	−1.42861	+	1.19875i	−0.482080	+	0.876127i	$0.660119\pi$
$661$	−36.7294	+	30.8196i	−1.42861	+	1.19875i	−0.946529	+	0.322618i	$0.895437\pi$
$662$		0			0
$663$	53.4805	+	9.43005i	2.07701	+	0.366233i
$664$		0			0
$665$	−0.481115	−	0.833315i	−0.0186568	−	0.0323146i
$666$		0			0
$667$	−14.1420	+	24.4947i	−0.547581	+	0.948439i
$668$		0			0
$669$			11.6592i			0.450770i
$670$		0			0
$671$	2.44041	+	13.8402i	0.0942109	+	0.534297i
$672$		0			0
$673$	−8.51960	−	7.14879i	−0.328406	−	0.275566i	0.463644	−	0.886022i	$-0.346542\pi$
$673$	−8.51960	−	7.14879i	−0.328406	−	0.275566i	−0.792050	+	0.610456i	$0.790986\pi$
$674$		0			0
$675$	16.2973	+	2.87365i	0.627282	+	0.110607i
$676$		0			0
$677$	−36.9550	−	31.0089i	−1.42030	−	1.19177i	−0.951181	−	0.308633i	$-0.900128\pi$
$677$	−36.9550	−	31.0089i	−1.42030	−	1.19177i	−0.469115	−	0.883137i	$-0.655427\pi$
$678$		0			0
$679$	−0.0717564	−	0.406951i	−0.00275376	−	0.0156173i
$680$		0			0
$681$	−21.7429	+	12.5533i	−0.833189	+	0.481042i
$682$		0			0
$683$	6.60401	−	11.4385i	0.252695	−	0.437681i	−0.711572	−	0.702614i	$-0.752016\pi$
$683$	6.60401	−	11.4385i	0.252695	−	0.437681i	0.964267	+	0.264932i	$0.0853496\pi$
$684$		0			0
$685$	−0.0582480	−	0.100888i	−0.00222554	−	0.00385475i
$686$		0			0
$687$	−28.7098	+	34.2150i	−1.09535	+	1.30538i
$688$		0			0
$689$	33.8692	−	28.4196i	1.29031	−	1.08270i
$690$		0			0
$691$	−9.37211	+	3.41117i	−0.356532	+	0.129767i	−0.514075	−	0.857745i	$-0.671865\pi$
$691$	−9.37211	+	3.41117i	−0.356532	+	0.129767i	0.157543	+	0.987512i	$0.449643\pi$
$692$		0			0
$693$	−0.672466	−	1.16475i	−0.0255449	−	0.0442450i
$694$		0			0
$695$	4.29607	−	24.3642i	0.162959	−	0.924189i
$696$		0			0
$697$	28.1822	+	10.2575i	1.06748	+	0.388529i
$698$		0			0
$699$	11.5753	+	13.7949i	0.437819	+	0.521772i
$700$		0			0
$701$	46.7588			1.76605			0.883027	−	0.469322i	$-0.155502\pi$
$701$	46.7588			1.76605			0.883027	+	0.469322i	$0.155502\pi$
$702$		0			0
$703$	1.72226			0.0649562
$704$		0			0
$705$	0.617211	−	1.69577i	0.0232455	−	0.0638665i
$706$		0			0
$707$	−0.976834	−	0.355538i	−0.0367376	−	0.0133714i
$708$		0			0
$709$	−6.56907	+	37.2550i	−0.246707	+	1.39914i	0.569789	+	0.821791i	$0.307025\pi$
$709$	−6.56907	+	37.2550i	−0.246707	+	1.39914i	−0.816496	+	0.577351i	$0.804086\pi$
$710$		0			0
$711$	−39.4479	−	14.3579i	−1.47941	−	0.538462i
$712$		0			0
$713$	−22.5462	+	8.20616i	−0.844363	+	0.307323i
$714$		0			0
$715$	23.2631	−	19.5201i	0.869991	−	0.730009i
$716$		0			0
$717$	−13.5744	−	37.2955i	−0.506947	−	1.39283i
$718$		0			0
$719$	1.65048	+	2.85872i	0.0615526	+	0.106612i	0.895160	−	0.445746i	$-0.147061\pi$
$719$	1.65048	+	2.85872i	0.0615526	+	0.106612i	−0.833607	+	0.552358i	$0.813728\pi$
$720$		0			0
$721$	−0.131759	+	0.228213i	−0.00490697	+	0.00849911i
$722$		0			0
$723$	18.1155	+	10.4590i	0.673721	+	0.388973i
$724$		0			0
$725$	−3.28699	−	18.6414i	−0.122076	−	0.692326i
$726$		0			0
$727$	16.0548	+	13.4716i	0.595441	+	0.499635i	0.889977	−	0.456006i	$-0.150720\pi$
$727$	16.0548	+	13.4716i	0.595441	+	0.499635i	−0.294535	+	0.955641i	$0.595165\pi$
$728$		0			0
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$		0			0
$731$	1.79561	+	1.50669i	0.0664129	+	0.0557271i
$732$		0			0
$733$	−3.11943	−	17.6912i	−0.115219	−	0.653439i	−0.986642	−	0.162906i	$-0.947913\pi$
$733$	−3.11943	−	17.6912i	−0.115219	−	0.653439i	0.871423	−	0.490533i	$-0.163198\pi$
$734$		0			0
$735$	14.1172	+	8.15058i	0.520721	+	0.300639i
$736$		0			0
$737$	12.3366	−	21.3677i	0.454425	−	0.787088i
$738$		0			0
$739$	−19.6630	−	34.0573i	−0.723314	−	1.25282i	−0.959664	−	0.281149i	$-0.909285\pi$
$739$	−19.6630	−	34.0573i	−0.723314	−	1.25282i	0.236350	−	0.971668i	$-0.424049\pi$
$740$		0			0
$741$	21.2716	+	58.4431i	0.781430	+	2.14696i
$742$		0			0
$743$	35.7957	−	30.0361i	1.31322	−	1.10192i	0.325519	−	0.945535i	$-0.394461\pi$
$743$	35.7957	−	30.0361i	1.31322	−	1.10192i	0.987696	−	0.156383i	$-0.0499835\pi$
$744$		0			0
$745$	6.20574	−	2.25870i	0.227361	−	0.0827525i
$746$		0			0
$747$	6.68004	+	2.43134i	0.244410	+	0.0889580i
$748$		0			0
$749$	0.215537	−	1.22237i	0.00787556	−	0.0446645i
$750$		0			0
$751$	−31.3184	−	11.3990i	−1.14282	−	0.415954i	−0.299891	−	0.953973i	$-0.596950\pi$
$751$	−31.3184	−	11.3990i	−1.14282	−	0.415954i	−0.842932	+	0.538020i	$0.819173\pi$
$752$		0			0
$753$	8.32136	−	22.8627i	0.303247	−	0.833164i
$754$		0			0
$755$	−2.33275			−0.0848974
$756$		0			0
$757$	32.3354			1.17525			0.587626	−	0.809133i	$-0.300063\pi$
$757$	32.3354			1.17525			0.587626	+	0.809133i	$0.300063\pi$
$758$		0			0
$759$	−19.6925	−	23.4686i	−0.714794	−	0.851858i
$760$		0			0
$761$	−1.81521	−	0.660681i	−0.0658012	−	0.0239497i	0.308910	−	0.951091i	$-0.400036\pi$
$761$	−1.81521	−	0.660681i	−0.0658012	−	0.0239497i	−0.374711	+	0.927142i	$0.622258\pi$
$762$		0			0
$763$	−0.232307	+	1.31748i	−0.00841007	+	0.0476959i
$764$		0			0
$765$	−10.4488	−	18.0978i	−0.377776	−	0.654328i
$766$		0			0
$767$	8.49185	−	3.09078i	0.306623	−	0.111602i
$768$		0			0
$769$	−3.66179	+	3.07261i	−0.132047	+	0.110801i	−0.706419	−	0.707793i	$-0.749691\pi$
$769$	−3.66179	+	3.07261i	−0.132047	+	0.110801i	0.574372	+	0.818594i	$0.305246\pi$
$770$		0			0
$771$	−20.1992	+	24.0725i	−0.727458	+	0.866950i
$772$		0			0
$773$	2.95336	+	5.11538i	0.106225	+	0.183987i	0.914238	−	0.405177i	$-0.132790\pi$
$773$	2.95336	+	5.11538i	0.106225	+	0.183987i	−0.808013	+	0.589165i	$0.799457\pi$
$774$		0			0
$775$	8.02869	−	13.9061i	0.288399	−	0.499522i
$776$		0			0
$777$	0.0526229	−	0.0303818i	0.00188784	−	0.00108994i
$778$		0			0
$779$	5.96435	+	33.8255i	0.213695	+	1.21192i
$780$		0			0
$781$	16.3555	+	13.7239i	0.585246	+	0.491080i
$782$		0			0
$783$	−30.4145	−	5.36289i	−1.08692	−	0.191654i
$784$		0			0
$785$	−6.00181	−	5.03612i	−0.214214	−	0.179747i
$786$		0			0
$787$	−2.29220	−	12.9997i	−0.0817082	−	0.463390i	−0.998018	−	0.0629213i	$-0.979958\pi$
$787$	−2.29220	−	12.9997i	−0.0817082	−	0.463390i	0.916310	−	0.400469i	$-0.131153\pi$
$788$		0			0
$789$		−	7.40213i		−	0.263523i
$790$		0			0
$791$	−0.357259	+	0.618790i	−0.0127027	+	0.0220016i
$792$		0			0
$793$	−11.4645	−	19.8571i	−0.407117	−	0.705147i
$794$		0			0
$795$	−16.7554	−	2.95442i	−0.594252	−	0.104783i
$796$		0			0
$797$	6.86959	−	5.76427i	0.243333	−	0.204181i	−0.512962	−	0.858411i	$-0.671452\pi$
$797$	6.86959	−	5.76427i	0.243333	−	0.204181i	0.756295	+	0.654231i	$0.227007\pi$
$798$		0			0
$799$	3.75712	−	1.36748i	0.132917	−	0.0483780i
$800$		0			0
$801$	1.13058	−	6.41182i	0.0399470	−	0.226551i
$802$		0			0
$803$	−6.72487	+	38.1386i	−0.237316	+	1.34588i
$804$		0			0
$805$	−0.726682	−	0.264490i	−0.0256122	−	0.00932206i
$806$		0			0
$807$	−22.2795	+	3.92847i	−0.784274	+	0.138289i
$808$		0			0
$809$	14.9804			0.526683			0.263341	−	0.964703i	$-0.415175\pi$
$809$	14.9804			0.526683			0.263341	+	0.964703i	$0.415175\pi$
$810$		0			0
$811$	−41.7529			−1.46614			−0.733071	−	0.680152i	$-0.761914\pi$
$811$	−41.7529			−1.46614			−0.733071	+	0.680152i	$0.761914\pi$
$812$		0			0
$813$	14.4775	−	2.55277i	0.507747	−	0.0895295i
$814$		0			0
$815$	−3.42989	−	1.24838i	−0.120144	−	0.0437288i
$816$		0			0
$817$	−0.466156	+	2.64370i	−0.0163087	+	0.0924915i
$818$		0			0
$819$	1.68092	+	1.41046i	0.0587362	+	0.0492855i
$820$		0			0
$821$	−7.34730	+	2.67420i	−0.256422	+	0.0933301i	−0.467033	−	0.884240i	$-0.654677\pi$
$821$	−7.34730	+	2.67420i	−0.256422	+	0.0933301i	0.210611	+	0.977570i	$0.432455\pi$
$822$		0			0
$823$	10.4645	−	8.78076i	0.364770	−	0.306078i	−0.441919	−	0.897055i	$-0.645702\pi$
$823$	10.4645	−	8.78076i	0.364770	−	0.306078i	0.806688	+	0.590977i	$0.201258\pi$
$824$		0			0
$825$	20.1917	+	3.56033i	0.702983	+	0.123955i
$826$		0			0
$827$	−10.0679	−	17.4381i	−0.350095	−	0.606382i	0.636171	−	0.771548i	$-0.280517\pi$
$827$	−10.0679	−	17.4381i	−0.350095	−	0.606382i	−0.986266	+	0.165166i	$0.947184\pi$
$828$		0			0
$829$	−20.9491	+	36.2849i	−0.727592	+	1.26023i	0.230307	+	0.973118i	$0.426027\pi$
$829$	−20.9491	+	36.2849i	−0.727592	+	1.26023i	−0.957898	+	0.287108i	$0.907306\pi$
$830$		0			0
$831$			11.4549i			0.397367i
$832$		0			0
$833$	6.27156	+	35.5678i	0.217297	+	1.23235i
$834$		0			0
$835$	25.3935	+	21.3077i	0.878779	+	0.737383i
$836$		0			0
$837$	−16.8400	−	20.0692i	−0.582076	−	0.693692i
$838$		0			0
$839$	30.0480	+	25.2133i	1.03737	+	0.870460i	0.991710	−	0.128497i	$-0.0410153\pi$
$839$	30.0480	+	25.2133i	1.03737	+	0.870460i	0.0456636	+	0.998957i	$0.485460\pi$
$840$		0			0
$841$	1.09849	+	6.22984i	0.0378789	+	0.214822i
$842$		0			0
$843$	44.5869	−	25.7423i	1.53566	−	0.886611i
$844$		0			0
$845$	−16.0155	+	27.7396i	−0.550949	+	0.954272i
$846$		0			0
$847$	−0.169778	−	0.294064i	−0.00583363	−	0.0101041i
$848$		0			0
$849$	−3.13429	+	3.73530i	−0.107568	+	0.128195i
$850$		0			0
$851$	1.06031	−	0.889704i	0.0363469	−	0.0304986i
$852$		0			0
$853$	6.12536	−	2.22945i	0.209728	−	0.0763349i	−0.235020	−	0.971991i	$-0.575515\pi$
$853$	6.12536	−	2.22945i	0.209728	−	0.0763349i	0.444748	+	0.895656i	$0.353293\pi$
$854$		0			0
$855$	11.9666	−	20.7267i	0.409248	−	0.708838i
$856$		0			0
$857$	−3.23514	+	18.3474i	−0.110510	+	0.626734i	0.878365	+	0.477990i	$0.158634\pi$
$857$	−3.23514	+	18.3474i	−0.110510	+	0.626734i	−0.988876	+	0.148745i	$0.952477\pi$
$858$		0			0
$859$	−52.2033	−	19.0004i	−1.78115	−	0.648286i	−0.999704	−	0.0243163i	$-0.992259\pi$
$859$	−52.2033	−	19.0004i	−1.78115	−	0.648286i	−0.781448	−	0.623970i	$-0.785519\pi$
$860$		0			0
$861$	0.778943	+	0.928309i	0.0265463	+	0.0316367i
$862$		0			0
$863$	36.1625			1.23099			0.615493	−	0.788142i	$-0.288957\pi$
$863$	36.1625			1.23099			0.615493	+	0.788142i	$0.288957\pi$
$864$		0			0
$865$	−14.4456			−0.491166
$866$		0			0
$867$	5.76486	−	15.8388i	0.195785	−	0.537915i
$868$		0			0
$869$	−48.8744	−	17.7888i	−1.65795	−	0.603444i
$870$		0			0
$871$	−6.99020	+	39.6434i	−0.236854	+	1.34327i
$872$		0			0
$873$	7.87346	−	6.60661i	0.266476	−	0.223600i
$874$		0			0
$875$	1.24985	−	0.454907i	0.0422526	−	0.0153787i
$876$		0			0
$877$	−14.8719	+	12.4790i	−0.502187	+	0.421385i	−0.858370	−	0.513031i	$-0.828522\pi$
$877$	−14.8719	+	12.4790i	−0.502187	+	0.421385i	0.356183	+	0.934416i	$0.384078\pi$
$878$		0			0
$879$	−5.82666	−	16.0086i	−0.196528	−	0.539957i
$880$		0			0
$881$	−22.9957	−	39.8298i	−0.774745	−	1.34190i	−0.934937	−	0.354813i	$-0.884545\pi$
$881$	−22.9957	−	39.8298i	−0.774745	−	1.34190i	0.160192	−	0.987086i	$-0.448789\pi$
$882$		0			0
$883$	11.9081	−	20.6254i	0.400738	−	0.694099i	−0.593077	−	0.805146i	$-0.702087\pi$
$883$	11.9081	−	20.6254i	0.400738	−	0.694099i	0.993815	+	0.111047i	$0.0354203\pi$
$884$		0			0
$885$	−3.01161	−	1.73875i	−0.101234	−	0.0584476i
$886$		0			0
$887$	−4.57785	−	25.9623i	−0.153709	−	0.871728i	−0.959956	−	0.280149i	$-0.909616\pi$
$887$	−4.57785	−	25.9623i	−0.153709	−	0.871728i	0.806247	−	0.591579i	$-0.201495\pi$
$888$		0			0
$889$	0.530278	+	0.444956i	0.0177849	+	0.0149233i
$890$		0			0
$891$	16.7260	−	28.9702i	0.560341	−	0.970539i
$892$		0			0
$893$	3.50774	+	2.94334i	0.117382	+	0.0984953i
$894$		0			0
$895$	3.23917	+	18.3702i	0.108274	+	0.614050i
$896$		0			0
$897$	43.2870	+	24.9918i	1.44531	+	0.834451i
$898$		0			0
$899$	−14.9834	+	25.9520i	−0.499724	+	0.865548i
$900$		0			0
$901$	−18.8478	−	32.6453i	−0.627910	−	1.08757i
$902$		0			0
$903$	0.0323936	+	0.0890006i	0.00107799	+	0.00296176i
$904$		0			0
$905$	3.62243	−	3.03958i	0.120414	−	0.101039i
$906$		0			0
$907$	−1.99660	+	0.726702i	−0.0662959	+	0.0241297i	−0.374955	−	0.927043i	$-0.622342\pi$
$907$	−1.99660	+	0.726702i	−0.0662959	+	0.0241297i	0.308659	+	0.951173i	$0.400120\pi$
$908$		0			0
$909$	−4.48979	−	25.4629i	−0.148917	−	0.844550i
$910$		0			0
$911$	8.70661	−	49.3777i	0.288463	−	1.63595i	−0.404184	−	0.914678i	$-0.632444\pi$
$911$	8.70661	−	49.3777i	0.288463	−	1.63595i	0.692647	−	0.721277i	$-0.256445\pi$
$912$		0			0
$913$	8.27631	+	3.01233i	0.273906	+	0.0996936i
$914$		0			0
$915$	−3.01779	+	8.29131i	−0.0997650	+	0.274102i
$916$		0			0
$917$	−2.07697			−0.0685876
$918$		0			0
$919$	56.9469			1.87850			0.939252	−	0.343229i	$-0.111521\pi$
$919$	56.9469			1.87850			0.939252	+	0.343229i	$0.111521\pi$
$920$		0			0
$921$	−15.0993	−	17.9946i	−0.497538	−	0.592942i
$922$		0			0
$923$	−32.7332	−	11.9139i	−1.07743	−	0.392152i
$924$		0			0
$925$	−0.160855	+	0.912254i	−0.00528888	+	0.0299947i
$926$		0			0
$927$	−6.55438			−0.215274
$928$		0			0
$929$	−0.236177	+	0.0859614i	−0.00774872	+	0.00282030i	−0.345892	−	0.938274i	$-0.612424\pi$
$929$	−0.236177	+	0.0859614i	−0.00774872	+	0.00282030i	0.338143	+	0.941095i	$0.390201\pi$
$930$		0			0
$931$	−31.6857	+	26.5875i	−1.03846	+	0.871370i
$932$		0			0
$933$	−11.7754	+	14.0334i	−0.385510	+	0.459433i
$934$		0			0
$935$	−12.9456	−	22.4225i	−0.423367	−	0.733293i
$936$		0			0
$937$	18.4662	−	31.9843i	0.603263	−	1.04488i	−0.389060	−	0.921212i	$-0.627200\pi$
$937$	18.4662	−	31.9843i	0.603263	−	1.04488i	0.992323	−	0.123670i	$-0.0394664\pi$
$938$		0			0
$939$	−16.0495	+	9.26616i	−0.523755	+	0.302390i
$940$		0			0
$941$	7.50118	+	42.5413i	0.244532	+	1.38681i	0.821578	+	0.570096i	$0.193094\pi$
$941$	7.50118	+	42.5413i	0.244532	+	1.38681i	−0.577047	+	0.816711i	$0.695795\pi$
$942$		0			0
$943$	21.1459	+	17.7435i	0.688605	+	0.577808i
$944$		0			0
$945$		−	0.844395i		−	0.0274682i
$946$		0			0
$947$	−36.3562	−	30.5065i	−1.18142	−	0.991328i	−0.999969	−	0.00792752i	$-0.997477\pi$
$947$	−36.3562	−	30.5065i	−1.18142	−	0.991328i	−0.181450	−	0.983400i	$-0.558079\pi$
$948$		0			0
$949$	−10.9718	−	62.2241i	−0.356159	−	2.01988i
$950$		0			0
$951$			50.5424i			1.63895i
$952$		0			0
$953$	22.6575	−	39.2440i	0.733949	−	1.27124i	−0.221234	−	0.975221i	$-0.571009\pi$
$953$	22.6575	−	39.2440i	0.733949	−	1.27124i	0.955183	−	0.296016i	$-0.0956581\pi$
$954$		0			0
$955$	−14.7476	−	25.5436i	−0.477222	−	0.826573i
$956$		0			0
$957$	−37.6823	−	6.64441i	−1.21810	−	0.214783i
$958$		0			0
$959$	0.00798918	−	0.00670372i	0.000257984	−	0.000216474i
$960$		0			0
$961$	5.24288	−	1.90825i	0.169125	−	0.0615565i
$962$		0			0
$963$	29.0107	−	10.5590i	0.934858	−	0.340260i
$964$		0			0
$965$	5.99201	−	33.9824i	0.192890	−	1.09393i
$966$		0			0
$967$	42.1559	+	15.3435i	1.35564	+	0.493413i	0.914704	−	0.404125i	$-0.132424\pi$
$967$	42.1559	+	15.3435i	1.35564	+	0.493413i	0.440937	+	0.897538i	$0.354646\pi$
$968$		0			0
$969$	52.2202	−	9.20783i	1.67755	−	0.295798i
$970$		0			0
$971$	6.55438			0.210340			0.105170	−	0.994454i	$-0.466461\pi$
$971$	6.55438			0.210340			0.105170	+	0.994454i	$0.466461\pi$
$972$		0			0
$973$	2.21482			0.0710039
$974$		0			0
$975$	−32.9432	+	5.80877i	−1.05503	+	0.186029i
$976$		0			0
$977$	44.3940	+	16.1581i	1.42029	+	0.516943i	0.934132	−	0.356928i	$-0.116176\pi$
$977$	44.3940	+	16.1581i	1.42029	+	0.516943i	0.486158	+	0.873871i	$0.338398\pi$
$978$		0			0
$979$	1.40074	−	7.94399i	0.0447679	−	0.253891i
$980$		0			0
$981$	−31.2679	+	11.3806i	−0.998306	+	0.363354i
$982$		0			0
$983$	−29.5197	+	10.7443i	−0.941531	+	0.342689i	−0.766770	−	0.641922i	$-0.778137\pi$
$983$	−29.5197	+	10.7443i	−0.941531	+	0.342689i	−0.174761	+	0.984611i	$0.555915\pi$
$984$		0			0
$985$	14.1242	−	11.8516i	0.450036	−	0.377625i
$986$		0			0
$987$	0.159100	+	0.0280537i	0.00506422	+	0.000892958i
$988$		0			0
$989$	1.07873	+	1.86841i	0.0343015	+	0.0594119i
$990$		0			0
$991$	23.2126	−	40.2054i	0.737373	−	1.27717i	−0.216302	−	0.976327i	$-0.569400\pi$
$991$	23.2126	−	40.2054i	0.737373	−	1.27717i	0.953675	−	0.300840i	$-0.0972671\pi$
$992$		0			0
$993$			12.6415i			0.401167i
$994$		0			0
$995$	2.90096	+	16.4522i	0.0919666	+	0.521568i
$996$		0			0
$997$	−20.5797	−	17.2684i	−0.651764	−	0.546895i	0.255841	−	0.966719i	$-0.417648\pi$
$997$	−20.5797	−	17.2684i	−0.651764	−	0.546895i	−0.907606	+	0.419824i	$0.862092\pi$
$998$		0			0
$999$	1.30887	+	0.755675i	0.0414107	+	0.0239085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.a.97.1		6
4.3	odd	2		54.2.e.a.43.1	✓	6
12.11	even	2		162.2.e.a.127.1		6
27.22	even	9	inner	432.2.u.a.49.1		6
36.7	odd	6		486.2.e.b.217.1		6
36.11	even	6		486.2.e.c.217.1		6
36.23	even	6		486.2.e.a.55.1		6
36.31	odd	6		486.2.e.d.55.1		6
108.7	odd	18		1458.2.a.a.1.2		3
108.11	even	18		1458.2.c.a.487.2		6
108.23	even	18		486.2.e.c.271.1		6
108.31	odd	18		486.2.e.b.271.1		6
108.43	odd	18		1458.2.c.d.487.2		6
108.47	even	18		1458.2.a.d.1.2		3
108.59	even	18		162.2.e.a.37.1		6
108.67	odd	18		486.2.e.d.433.1		6
108.79	odd	18		1458.2.c.d.973.2		6
108.83	even	18		1458.2.c.a.973.2		6
108.95	even	18		486.2.e.a.433.1		6
108.103	odd	18		54.2.e.a.49.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.a.43.1	✓	6	4.3	odd	2
54.2.e.a.49.1	yes	6	108.103	odd	18
162.2.e.a.37.1		6	108.59	even	18
162.2.e.a.127.1		6	12.11	even	2
432.2.u.a.49.1		6	27.22	even	9	inner
432.2.u.a.97.1		6	1.1	even	1	trivial
486.2.e.a.55.1		6	36.23	even	6
486.2.e.a.433.1		6	108.95	even	18
486.2.e.b.217.1		6	36.7	odd	6
486.2.e.b.271.1		6	108.31	odd	18
486.2.e.c.217.1		6	36.11	even	6
486.2.e.c.271.1		6	108.23	even	18
486.2.e.d.55.1		6	36.31	odd	6
486.2.e.d.433.1		6	108.67	odd	18
1458.2.a.a.1.2		3	108.7	odd	18
1458.2.a.d.1.2		3	108.47	even	18
1458.2.c.a.487.2		6	108.11	even	18
1458.2.c.a.973.2		6	108.83	even	18
1458.2.c.d.487.2		6	108.43	odd	18
1458.2.c.d.973.2		6	108.79	odd	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.70574 + 0.300767i) q^{3} +(-1.26604 - 0.460802i) q^{5} +(0.0209445 - 0.118782i) q^{7} +(2.81908 - 1.02606i) q^{9} +O(q^{10})\)	\(q+(-1.70574 + 0.300767i) q^{3} +(-1.26604 - 0.460802i) q^{5} +(0.0209445 - 0.118782i) q^{7} +(2.81908 - 1.02606i) q^{9} +(3.49273 - 1.27125i) q^{11} +(-4.64543 + 3.89798i) q^{13} +(2.29813 + 0.405223i) q^{15} +(2.58512 + 4.47756i) q^{17} +(-2.96064 + 5.12797i) q^{19} +0.208911i q^{21} +(0.826352 + 4.68647i) q^{23} +(-2.43969 - 2.04715i) q^{25} +(-4.50000 + 2.59808i) q^{27} +(4.55303 + 3.82045i) q^{29} +(0.875515 + 4.96529i) q^{31} +(-5.57532 + 3.21891i) q^{33} +(-0.0812519 + 0.140732i) q^{35} +(-0.145430 - 0.251892i) q^{37} +(6.75150 - 8.04612i) q^{39} +(4.44356 - 3.72859i) q^{41} +(0.426022 - 0.155059i) q^{43} -4.04189 q^{45} +(0.134285 - 0.761570i) q^{47} +(6.56418 + 2.38917i) q^{49} +(-5.75624 - 6.86002i) q^{51} -7.29086 q^{53} -5.00774 q^{55} +(3.50774 - 9.63744i) q^{57} +(-1.40033 - 0.509678i) q^{59} +(-0.656574 + 3.72362i) q^{61} +(-0.0628336 - 0.356347i) q^{63} +(7.67752 - 2.79439i) q^{65} +(5.08512 - 4.26692i) q^{67} +(-2.81908 - 7.74535i) q^{69} +(2.87211 + 4.97464i) q^{71} +(-5.20961 + 9.02330i) q^{73} +(4.77719 + 2.75811i) q^{75} +(-0.0778483 - 0.441500i) q^{77} +(-10.7194 - 8.99465i) q^{79} +(6.89440 - 5.78509i) q^{81} +(1.81521 + 1.52314i) q^{83} +(-1.20961 - 6.86002i) q^{85} +(-8.91534 - 5.14728i) q^{87} +(1.08512 - 1.87949i) q^{89} +(0.365715 + 0.633436i) q^{91} +(-2.98680 - 8.20616i) q^{93} +(6.11128 - 5.12797i) q^{95} +(3.21941 - 1.17177i) q^{97} +(8.54189 - 7.16750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 3 q^{7}+O(q^{10}) \) 6 * q - 3 * q^5 - 3 * q^7	\( 6 q - 3 q^{5} - 3 q^{7} + 3 q^{11} - 12 q^{13} - 6 q^{17} - 9 q^{19} + 6 q^{23} - 9 q^{25} - 27 q^{27} + 15 q^{29} + 18 q^{31} - 9 q^{33} - 3 q^{35} + 15 q^{37} - 3 q^{41} + 18 q^{43} - 18 q^{45} - 9 q^{47} + 21 q^{49} - 27 q^{51} - 12 q^{53} + 18 q^{55} - 27 q^{57} + 6 q^{59} + 18 q^{61} + 9 q^{63} + 21 q^{65} + 9 q^{67} - 12 q^{71} + 3 q^{73} + 18 q^{75} + 39 q^{77} - 33 q^{79} + 18 q^{83} + 27 q^{85} - 9 q^{87} - 15 q^{89} + 12 q^{91} + 27 q^{93} - 21 q^{95} - 12 q^{97} + 45 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 - 3 * q^7 + 3 * q^11 - 12 * q^13 - 6 * q^17 - 9 * q^19 + 6 * q^23 - 9 * q^25 - 27 * q^27 + 15 * q^29 + 18 * q^31 - 9 * q^33 - 3 * q^35 + 15 * q^37 - 3 * q^41 + 18 * q^43 - 18 * q^45 - 9 * q^47 + 21 * q^49 - 27 * q^51 - 12 * q^53 + 18 * q^55 - 27 * q^57 + 6 * q^59 + 18 * q^61 + 9 * q^63 + 21 * q^65 + 9 * q^67 - 12 * q^71 + 3 * q^73 + 18 * q^75 + 39 * q^77 - 33 * q^79 + 18 * q^83 + 27 * q^85 - 9 * q^87 - 15 * q^89 + 12 * q^91 + 27 * q^93 - 21 * q^95 - 12 * q^97 + 45 * q^99

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