LMFDB - Embedded newform 1323.2.h.g.226.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(226,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.6
Root			$-0.474636 - 0.274031i$ of defining polynomial
Character	$\chi$	$=$	1323.226
Dual form			1323.2.h.g.802.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.69963 q^{2} +0.888736 q^{4} +(0.474636 + 0.822093i) q^{5} -1.88874 q^{8} +O(q^{10})$	\(q+1.69963 q^{2} +0.888736 q^{4} +(0.474636 + 0.822093i) q^{5} -1.88874 q^{8} +(0.806704 + 1.39725i) q^{10} +(-0.294182 + 0.509538i) q^{11} +(-2.50987 + 4.34722i) q^{13} -4.98762 q^{16} +(3.79121 + 6.56657i) q^{17} +(-2.23061 + 3.86353i) q^{19} +(0.421826 + 0.730623i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(1.23855 + 2.14523i) q^{23} +(2.04944 - 3.54974i) q^{25} +(-4.26584 + 7.38866i) q^{26} +(2.73855 + 4.74331i) q^{29} +6.07463 q^{31} -4.69963 q^{32} +(6.44364 + 11.1607i) q^{34} +(3.49381 - 6.05146i) q^{37} +(-3.79121 + 6.56657i) q^{38} +(-0.896461 - 1.55272i) q^{40} +(0.527445 - 0.913562i) q^{41} +(-3.49381 - 6.05146i) q^{43} +(-0.261450 + 0.452845i) q^{44} +(2.10507 + 3.64610i) q^{46} -7.47680 q^{47} +(3.48329 - 6.03323i) q^{50} +(-2.23061 + 3.86353i) q^{52} +(3.46108 + 5.99476i) q^{53} -0.558517 q^{55} +(4.65452 + 8.06186i) q^{58} +10.4302 q^{59} -11.6529 q^{61} +10.3246 q^{62} +1.98762 q^{64} -4.76509 q^{65} -11.8640 q^{67} +(3.36938 + 5.83594i) q^{68} -4.30037 q^{71} +(2.23061 + 3.86353i) q^{73} +(5.93818 - 10.2852i) q^{74} +(-1.98242 + 3.43366i) q^{76} -1.33379 q^{79} +(-2.36730 - 4.10029i) q^{80} +(0.896461 - 1.55272i) q^{82} +(2.84194 + 4.92238i) q^{83} +(-3.59888 + 6.23345i) q^{85} +(-5.93818 - 10.2852i) q^{86} +(0.555632 - 0.962383i) q^{88} +(-0.421826 + 0.730623i) q^{89} +(1.10074 + 1.90654i) q^{92} -12.7078 q^{94} -4.23491 q^{95} +(-1.70317 - 2.94997i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 12 q^{4} - 24 q^{8}+O(q^{10}) $ 12 * q - 4 * q^2 + 12 * q^4 - 24 * q^8	$ 12 q - 4 q^{2} + 12 q^{4} - 24 q^{8} + 8 q^{11} + 12 q^{16} - 6 q^{22} + 4 q^{23} - 12 q^{25} + 22 q^{29} - 32 q^{32} + 6 q^{37} - 6 q^{43} - 14 q^{44} - 12 q^{46} + 56 q^{50} + 28 q^{53} - 18 q^{58} - 48 q^{64} + 12 q^{65} - 76 q^{71} + 36 q^{74} - 12 q^{79} + 30 q^{85} - 36 q^{86} + 6 q^{88} + 62 q^{92} - 120 q^{95}+O(q^{100}) $ 12 * q - 4 * q^2 + 12 * q^4 - 24 * q^8 + 8 * q^11 + 12 * q^16 - 6 * q^22 + 4 * q^23 - 12 * q^25 + 22 * q^29 - 32 * q^32 + 6 * q^37 - 6 * q^43 - 14 * q^44 - 12 * q^46 + 56 * q^50 + 28 * q^53 - 18 * q^58 - 48 * q^64 + 12 * q^65 - 76 * q^71 + 36 * q^74 - 12 * q^79 + 30 * q^85 - 36 * q^86 + 6 * q^88 + 62 * q^92 - 120 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.69963			1.20182			0.600909	−	0.799317i	$-0.294805\pi$
$2$	1.69963			1.20182			0.600909	+	0.799317i	$0.294805\pi$
$3$		0			0
$3$		0			0
$4$	0.888736			0.444368
$5$	0.474636	+	0.822093i	0.212263	+	0.367651i	0.952423	−	0.304781i	$-0.0985832\pi$
$5$	0.474636	+	0.822093i	0.212263	+	0.367651i	−0.740159	+	0.672432i	$0.765250\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.88874			−0.667769
$9$		0			0
$10$	0.806704	+	1.39725i	0.255102	+	0.441850i
$11$	−0.294182	+	0.509538i	−0.0886992	+	0.153632i	−0.906962	−	0.421213i	$-0.861604\pi$
$11$	−0.294182	+	0.509538i	−0.0886992	+	0.153632i	0.818262	+	0.574845i	$0.194938\pi$
$12$		0			0
$13$	−2.50987	+	4.34722i	−0.696112	+	1.20570i	0.273692	+	0.961817i	$0.411755\pi$
$13$	−2.50987	+	4.34722i	−0.696112	+	1.20570i	−0.969804	+	0.243885i	$0.921578\pi$
$14$		0			0
$15$		0			0
$16$	−4.98762			−1.24691
$17$	3.79121	+	6.56657i	0.919503	+	1.59263i	0.800171	+	0.599772i	$0.204742\pi$
$17$	3.79121	+	6.56657i	0.919503	+	1.59263i	0.119332	+	0.992854i	$0.461925\pi$
$18$		0			0
$19$	−2.23061	+	3.86353i	−0.511737	+	0.886355i	0.488170	+	0.872748i	$0.337664\pi$
$19$	−2.23061	+	3.86353i	−0.511737	+	0.886355i	−0.999907	+	0.0136063i	$0.995669\pi$
$20$	0.421826	+	0.730623i	0.0943231	+	0.163372i
$21$		0			0
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	1.23855	+	2.14523i	0.258256	+	0.447312i	0.965775	−	0.259382i	$-0.0835190\pi$
$23$	1.23855	+	2.14523i	0.258256	+	0.447312i	−0.707519	+	0.706694i	$0.750186\pi$
$24$		0			0
$25$	2.04944	−	3.54974i	0.409888	−	0.709948i
$26$	−4.26584	+	7.38866i	−0.836601	+	1.44904i
$27$		0			0
$28$		0			0
$29$	2.73855	+	4.74331i	0.508536	+	0.880810i	0.999951	+	0.00988468i	$0.00314644\pi$
$29$	2.73855	+	4.74331i	0.508536	+	0.880810i	−0.491415	+	0.870925i	$0.663520\pi$
$30$		0			0
$31$	6.07463			1.09104			0.545518	−	0.838099i	$-0.316333\pi$
$31$	6.07463			1.09104			0.545518	+	0.838099i	$0.316333\pi$
$32$	−4.69963			−0.830785
$33$		0			0
$34$	6.44364	+	11.1607i	1.10508	+	1.91405i
$35$		0			0
$36$		0			0
$37$	3.49381	−	6.05146i	0.574379	−	0.994853i	−0.421730	−	0.906721i	$-0.638577\pi$
$37$	3.49381	−	6.05146i	0.574379	−	0.994853i	0.996109	−	0.0881319i	$-0.0280897\pi$
$38$	−3.79121	+	6.56657i	−0.615015	+	1.06524i
$39$		0			0
$40$	−0.896461	−	1.55272i	−0.141743	−	0.245506i
$41$	0.527445	−	0.913562i	0.0823731	−	0.142674i	−0.821896	−	0.569638i	$-0.807083\pi$
$41$	0.527445	−	0.913562i	0.0823731	−	0.142674i	0.904269	+	0.426964i	$0.140417\pi$
$42$		0			0
$43$	−3.49381	−	6.05146i	−0.532801	−	0.922838i	−0.999266	−	0.0382990i	$-0.987806\pi$
$43$	−3.49381	−	6.05146i	−0.532801	−	0.922838i	0.466465	−	0.884540i	$-0.345527\pi$
$44$	−0.261450	+	0.452845i	−0.0394151	+	0.0682689i
$45$		0			0
$46$	2.10507	+	3.64610i	0.310376	+	0.537587i
$47$	−7.47680			−1.09060			−0.545301	−	0.838240i	$-0.683585\pi$
$47$	−7.47680			−1.09060			−0.545301	+	0.838240i	$0.683585\pi$
$48$		0			0
$49$		0			0
$50$	3.48329	−	6.03323i	0.492612	−	0.853228i
$51$		0			0
$52$	−2.23061	+	3.86353i	−0.309330	+	0.535775i
$53$	3.46108	+	5.99476i	0.475416	+	0.823444i	0.999603	−	0.0281586i	$-0.00896435\pi$
$53$	3.46108	+	5.99476i	0.475416	+	0.823444i	−0.524188	+	0.851603i	$0.675631\pi$
$54$		0			0
$55$	−0.558517			−0.0753104
$56$		0			0
$57$		0			0
$58$	4.65452	+	8.06186i	0.611168	+	1.05857i
$59$	10.4302			1.35790			0.678950	−	0.734184i	$-0.262435\pi$
$59$	10.4302			1.35790			0.678950	+	0.734184i	$0.262435\pi$
$60$		0			0
$61$	−11.6529			−1.49200			−0.745999	−	0.665947i	$-0.768028\pi$
$61$	−11.6529			−1.49200			−0.745999	+	0.665947i	$0.768028\pi$
$62$	10.3246			1.31123
$63$		0			0
$64$	1.98762			0.248453
$65$	−4.76509			−0.591037
$66$		0			0
$67$	−11.8640			−1.44942			−0.724708	−	0.689056i	$-0.758025\pi$
$67$	−11.8640			−1.44942			−0.724708	+	0.689056i	$0.758025\pi$
$68$	3.36938	+	5.83594i	0.408598	+	0.707712i
$69$		0			0
$70$		0			0
$71$	−4.30037			−0.510360			−0.255180	−	0.966894i	$-0.582135\pi$
$71$	−4.30037			−0.510360			−0.255180	+	0.966894i	$0.582135\pi$
$72$		0			0
$73$	2.23061	+	3.86353i	0.261073	+	0.452192i	0.966527	−	0.256563i	$-0.0825903\pi$
$73$	2.23061	+	3.86353i	0.261073	+	0.452192i	−0.705454	+	0.708756i	$0.749257\pi$
$74$	5.93818	−	10.2852i	0.690299	−	1.19563i
$75$		0			0
$76$	−1.98242	+	3.43366i	−0.227400	+	0.393868i
$77$		0			0
$78$		0			0
$79$	−1.33379			−0.150063			−0.0750317	−	0.997181i	$-0.523906\pi$
$79$	−1.33379			−0.150063			−0.0750317	+	0.997181i	$0.523906\pi$
$80$	−2.36730	−	4.10029i	−0.264672	−	0.458426i
$81$		0			0
$82$	0.896461	−	1.55272i	0.0989976	−	0.171469i
$83$	2.84194	+	4.92238i	0.311943	+	0.540301i	0.978783	−	0.204900i	$-0.0656868\pi$
$83$	2.84194	+	4.92238i	0.311943	+	0.540301i	−0.666840	+	0.745201i	$0.732353\pi$
$84$		0			0
$85$	−3.59888	+	6.23345i	−0.390354	+	0.676113i
$86$	−5.93818	−	10.2852i	−0.640330	−	1.10908i
$87$		0			0
$88$	0.555632	−	0.962383i	0.0592306	−	0.102590i
$89$	−0.421826	+	0.730623i	−0.0447134	+	0.0774459i	−0.887516	−	0.460777i	$-0.847571\pi$
$89$	−0.421826	+	0.730623i	−0.0447134	+	0.0774459i	0.842803	+	0.538223i	$0.180904\pi$
$90$		0			0
$91$		0			0
$92$	1.10074	+	1.90654i	0.114760	+	0.198771i
$93$		0			0
$94$	−12.7078			−1.31071
$95$	−4.23491			−0.434492
$96$		0			0
$97$	−1.70317	−	2.94997i	−0.172930	−	0.299524i	0.766513	−	0.642229i	$-0.221990\pi$
$97$	−1.70317	−	2.94997i	−0.172930	−	0.299524i	−0.939443	+	0.342705i	$0.888657\pi$
$98$		0			0
$99$		0			0
$100$	1.82141	−	3.15478i	0.182141	−	0.315478i
$101$	4.79329	−	8.30222i	0.476950	−	0.826102i	−0.522701	−	0.852516i	$-0.675076\pi$
$101$	4.79329	−	8.30222i	0.476950	−	0.826102i	0.999651	+	0.0264143i	$0.00840890\pi$
$102$		0			0
$103$	−5.82644	−	10.0917i	−0.574096	−	0.994364i	−0.996139	−	0.0877882i	$-0.972020\pi$
$103$	−5.82644	−	10.0917i	−0.574096	−	0.994364i	0.422043	−	0.906576i	$-0.361313\pi$
$104$	4.74048	−	8.21075i	0.464842	−	0.805130i
$105$		0			0
$106$	5.88255	+	10.1889i	0.571363	+	0.989630i
$107$	−1.89926	+	3.28961i	−0.183608	+	0.318018i	−0.943107	−	0.332491i	$-0.892111\pi$
$107$	−1.89926	+	3.28961i	−0.183608	+	0.318018i	0.759499	+	0.650509i	$0.225444\pi$
$108$		0			0
$109$	6.43199	+	11.1405i	0.616073	+	1.06707i	0.990195	+	0.139690i	$0.0446106\pi$
$109$	6.43199	+	11.1405i	0.616073	+	1.06707i	−0.374123	+	0.927379i	$0.622056\pi$
$110$	−0.949271			−0.0905094
$111$		0			0
$112$		0			0
$113$	4.51052	−	7.81245i	0.424314	−	0.734934i	−0.572042	−	0.820224i	$-0.693849\pi$
$113$	4.51052	−	7.81245i	0.424314	−	0.734934i	0.996356	+	0.0852908i	$0.0271819\pi$
$114$		0			0
$115$	−1.17572	+	2.03641i	−0.109636	+	0.189896i
$116$	2.43385	+	4.21555i	0.225977	+	0.391404i
$117$		0			0
$118$	17.7275			1.63195
$119$		0			0
$120$		0			0
$121$	5.32691	+	9.22649i	0.484265	+	0.838771i
$122$	−19.8056			−1.79311
$123$		0			0
$124$	5.39874			0.484821
$125$	8.63731			0.772544
$126$		0			0
$127$	6.43268			0.570808			0.285404	−	0.958407i	$-0.407872\pi$
$127$	6.43268			0.570808			0.285404	+	0.958407i	$0.407872\pi$
$128$	12.7775			1.12938
$129$		0			0
$130$	−8.09888			−0.710319
$131$	−3.31657	−	5.74447i	−0.289770	−	0.501897i	0.683984	−	0.729497i	$-0.260246\pi$
$131$	−3.31657	−	5.74447i	−0.289770	−	0.501897i	−0.973755	+	0.227600i	$0.926912\pi$
$132$		0			0
$133$		0			0
$134$	−20.1643			−1.74193
$135$		0			0
$136$	−7.16059	−	12.4025i	−0.614016	−	1.06351i
$137$	7.01671	−	12.1533i	0.599478	−	1.03833i	−0.393420	−	0.919359i	$-0.628708\pi$
$137$	7.01671	−	12.1533i	0.599478	−	1.03833i	0.992898	−	0.118968i	$-0.0379585\pi$
$138$		0			0
$139$	4.40254	−	7.62541i	0.373418	−	0.646779i	−0.616671	−	0.787221i	$-0.711519\pi$
$139$	4.40254	−	7.62541i	0.373418	−	0.646779i	0.990089	+	0.140442i	$0.0448523\pi$
$140$		0			0
$141$		0			0
$142$	−7.30903			−0.613360
$143$	−1.47672	−	2.55775i	−0.123489	−	0.213890i
$144$		0			0
$145$	−2.59963	+	4.50268i	−0.215887	+	0.373928i
$146$	3.79121	+	6.56657i	0.313763	+	0.543453i
$147$		0			0
$148$	3.10507	−	5.37815i	0.255236	−	0.442081i
$149$	−2.18292	−	3.78092i	−0.178832	−	0.309745i	0.762649	−	0.646813i	$-0.223898\pi$
$149$	−2.18292	−	3.78092i	−0.178832	−	0.309745i	−0.941481	+	0.337067i	$0.890565\pi$
$150$		0			0
$151$	6.32691	−	10.9585i	0.514877	−	0.891793i	−0.484974	−	0.874529i	$-0.661171\pi$
$151$	6.32691	−	10.9585i	0.514877	−	0.891793i	0.999851	−	0.0172645i	$-0.00549573\pi$
$152$	4.21303	−	7.29719i	0.341722	−	0.591880i
$153$		0			0
$154$		0			0
$155$	2.88323	+	4.99391i	0.231587	+	0.401120i
$156$		0			0
$157$	−11.2739			−0.899754			−0.449877	−	0.893091i	$-0.648532\pi$
$157$	−11.2739			−0.899754			−0.449877	+	0.893091i	$0.648532\pi$
$158$	−2.26695			−0.180349
$159$		0			0
$160$	−2.23061	−	3.86353i	−0.176345	−	0.305439i
$161$		0			0
$162$		0			0
$163$	0.833104	−	1.44298i	0.0652537	−	0.113023i	−0.831553	−	0.555446i	$-0.812548\pi$
$163$	0.833104	−	1.44298i	0.0652537	−	0.113023i	0.896807	+	0.442423i	$0.145881\pi$
$164$	0.468760	−	0.811916i	0.0366040	−	0.0634000i
$165$		0			0
$166$	4.83024	+	8.36622i	0.374899	+	0.649344i
$167$	−1.95135	+	3.37984i	−0.151000	+	0.261540i	−0.931595	−	0.363497i	$-0.881583\pi$
$167$	−1.95135	+	3.37984i	−0.151000	+	0.261540i	0.780595	+	0.625037i	$0.214916\pi$
$168$		0			0
$169$	−6.09888	−	10.5636i	−0.469145	−	0.812583i
$170$	−6.11677	+	10.5945i	−0.469134	+	0.812565i
$171$		0			0
$172$	−3.10507	−	5.37815i	−0.236760	−	0.410080i
$173$	16.1141			1.22513			0.612566	−	0.790419i	$-0.290137\pi$
$173$	16.1141			1.22513			0.612566	+	0.790419i	$0.290137\pi$
$174$		0			0
$175$		0			0
$176$	1.46727	−	2.54138i	0.110599	−	0.191564i
$177$		0			0
$178$	−0.716947	+	1.24179i	−0.0537374	+	0.0930760i
$179$	7.14400	+	12.3738i	0.533967	+	0.924859i	0.999213	+	0.0396767i	$0.0126328\pi$
$179$	7.14400	+	12.3738i	0.533967	+	0.924859i	−0.465245	+	0.885182i	$0.654034\pi$
$180$		0			0
$181$	−12.8873			−0.957905			−0.478952	−	0.877841i	$-0.658983\pi$
$181$	−12.8873			−0.957905			−0.478952	+	0.877841i	$0.658983\pi$
$182$		0			0
$183$		0			0
$184$	−2.33929	−	4.05178i	−0.172455	−	0.298701i
$185$	6.63315			0.487679
$186$		0			0
$187$	−4.46122			−0.326237
$188$	−6.64490			−0.484629
$189$		0			0
$190$	−7.19777			−0.522181
$191$	2.16435			0.156607			0.0783034	−	0.996930i	$-0.475050\pi$
$191$	2.16435			0.156607			0.0783034	+	0.996930i	$0.475050\pi$
$192$		0			0
$193$	10.4313			0.750861			0.375431	−	0.926850i	$-0.377495\pi$
$193$	10.4313			0.750861			0.375431	+	0.926850i	$0.377495\pi$
$194$	−2.89475	−	5.01385i	−0.207831	−	0.359973i
$195$		0			0
$196$		0			0
$197$	18.7848			1.33836			0.669179	−	0.743101i	$-0.266646\pi$
$197$	18.7848			1.33836			0.669179	+	0.743101i	$0.266646\pi$
$198$		0			0
$199$	4.21303	+	7.29719i	0.298654	+	0.517284i	0.975828	−	0.218539i	$-0.0701290\pi$
$199$	4.21303	+	7.29719i	0.298654	+	0.517284i	−0.677174	+	0.735823i	$0.736796\pi$
$200$	−3.87085	+	6.70452i	−0.273711	+	0.474081i
$201$		0			0
$202$	8.14681	−	14.1107i	0.573208	−	0.992825i
$203$		0			0
$204$		0			0
$205$	1.00138			0.0699392
$206$	−9.90278	−	17.1521i	−0.689960	−	1.19505i
$207$		0			0
$208$	12.5183	−	21.6823i	0.867986	−	1.50340i
$209$	−1.31241	−	2.27316i	−0.0907814	−	0.157238i
$210$		0			0
$211$	−5.61126	+	9.71899i	−0.386295	+	0.669083i	−0.991948	−	0.126646i	$-0.959579\pi$
$211$	−5.61126	+	9.71899i	−0.386295	+	0.669083i	0.605653	+	0.795729i	$0.292912\pi$
$212$	3.07598	+	5.32776i	0.211259	+	0.365912i
$213$		0			0
$214$	−3.22803	+	5.59111i	−0.220664	+	0.382200i
$215$	3.31657	−	5.74447i	0.226188	−	0.391770i
$216$		0			0
$217$		0			0
$218$	10.9320	+	18.9348i	0.740408	+	1.28242i
$219$		0			0
$220$	−0.496374			−0.0334655
$221$	−38.0617			−2.56031
$222$		0			0
$223$	−10.3774	−	17.9742i	−0.694923	−	1.20364i	−0.970206	−	0.242279i	$-0.922105\pi$
$223$	−10.3774	−	17.9742i	−0.694923	−	1.20364i	0.275283	−	0.961363i	$-0.411228\pi$
$224$		0			0
$225$		0			0
$226$	7.66621	−	13.2783i	0.509949	−	0.883257i
$227$	5.21512	−	9.03284i	0.346139	−	0.599531i	−0.639421	−	0.768857i	$-0.720826\pi$
$227$	5.21512	−	9.03284i	0.346139	−	0.599531i	0.985560	+	0.169326i	$0.0541591\pi$
$228$		0			0
$229$	7.52961	+	13.0417i	0.497570	+	0.861817i	0.999996	−	0.00280316i	$-0.000892274\pi$
$229$	7.52961	+	13.0417i	0.497570	+	0.861817i	−0.502426	+	0.864620i	$0.667559\pi$
$230$	−1.99829	+	3.46113i	−0.131763	+	0.228220i
$231$		0			0
$232$	−5.17240	−	8.95886i	−0.339585	−	0.588178i
$233$	2.19344	−	3.79915i	0.143697	−	0.248890i	−0.785189	−	0.619256i	$-0.787434\pi$
$233$	2.19344	−	3.79915i	0.143697	−	0.248890i	0.928886	+	0.370366i	$0.120768\pi$
$234$		0			0
$235$	−3.54875	−	6.14662i	−0.231495	−	0.400961i
$236$	9.26972			0.603407
$237$		0			0
$238$		0			0
$239$	−4.77561	+	8.27160i	−0.308909	+	0.535046i	−0.978124	−	0.208023i	$-0.933297\pi$
$239$	−4.77561	+	8.27160i	−0.308909	+	0.535046i	0.669215	+	0.743069i	$0.266630\pi$
$240$		0			0
$241$	5.26792	−	9.12431i	0.339337	−	0.587749i	−0.644971	−	0.764207i	$-0.723131\pi$
$241$	5.26792	−	9.12431i	0.339337	−	0.587749i	0.984308	+	0.176458i	$0.0564640\pi$
$242$	9.05377	+	15.6816i	0.581999	+	1.00805i
$243$		0			0
$244$	−10.3563			−0.662996
$245$		0			0
$246$		0			0
$247$	−11.1971	−	19.3939i	−0.712453	−	1.23401i
$248$	−11.4734			−0.728560
$249$		0			0
$250$	14.6802			0.928458
$251$	−24.4346			−1.54230			−0.771148	−	0.636656i	$-0.780317\pi$
$251$	−24.4346			−1.54230			−0.771148	+	0.636656i	$0.780317\pi$
$252$		0			0
$253$	−1.45744			−0.0916282
$254$	10.9332			0.686007
$255$		0			0
$256$	17.7417			1.10886
$257$	−2.00416	−	3.47131i	−0.125016	−	0.216534i	0.796723	−	0.604345i	$-0.206565\pi$
$257$	−2.00416	−	3.47131i	−0.125016	−	0.216534i	−0.921739	+	0.387810i	$0.873232\pi$
$258$		0			0
$259$		0			0
$260$	−4.23491			−0.262638
$261$		0			0
$262$	−5.63694	−	9.76347i	−0.348251	−	0.603189i
$263$	8.84362	−	15.3176i	0.545321	−	0.944524i	−0.453265	−	0.891376i	$-0.649741\pi$
$263$	8.84362	−	15.3176i	0.545321	−	0.944524i	0.998587	−	0.0531485i	$-0.0169257\pi$
$264$		0			0
$265$	−3.28550	+	5.69066i	−0.201827	+	0.349574i
$266$		0			0
$267$		0			0
$268$	−10.5439			−0.644074
$269$	7.11366	+	12.3212i	0.433727	+	0.751238i	0.997191	−	0.0749032i	$-0.0238648\pi$
$269$	7.11366	+	12.3212i	0.433727	+	0.751238i	−0.563463	+	0.826141i	$0.690531\pi$
$270$		0			0
$271$	−2.69937	+	4.67545i	−0.163975	+	0.284013i	−0.936291	−	0.351226i	$-0.885765\pi$
$271$	−2.69937	+	4.67545i	−0.163975	+	0.284013i	0.772316	+	0.635239i	$0.219098\pi$
$272$	−18.9091	−	32.7515i	−1.14653	−	1.98585i
$273$		0			0
$274$	11.9258	−	20.6561i	0.720464	−	1.24788i
$275$	1.20582	+	2.08854i	0.0727136	+	0.125944i
$276$		0			0
$277$	−3.83310	+	6.63913i	−0.230309	+	0.398907i	−0.957899	−	0.287105i	$-0.907307\pi$
$277$	−3.83310	+	6.63913i	−0.230309	+	0.398907i	0.727590	+	0.686012i	$0.240640\pi$
$278$	7.48267	−	12.9604i	0.448781	−	0.777311i
$279$		0			0
$280$		0			0
$281$	−11.3312	−	19.6263i	−0.675965	−	1.17081i	−0.976186	−	0.216936i	$-0.930394\pi$
$281$	−11.3312	−	19.6263i	−0.675965	−	1.17081i	0.300220	−	0.953870i	$-0.402940\pi$
$282$		0			0
$283$	31.8492			1.89324			0.946619	−	0.322353i	$-0.104474\pi$
$283$	31.8492			1.89324			0.946619	+	0.322353i	$0.104474\pi$
$284$	−3.82189			−0.226788
$285$		0			0
$286$	−2.50987	−	4.34722i	−0.148412	−	0.257057i
$287$		0			0
$288$		0			0
$289$	−20.2465	+	35.0680i	−1.19097	+	2.06282i
$290$	−4.41840	+	7.65289i	−0.259457	+	0.449393i
$291$		0			0
$292$	1.98242	+	3.43366i	0.116013	+	0.200940i
$293$	−13.7468	+	23.8102i	−0.803097	+	1.39100i	0.114472	+	0.993427i	$0.463483\pi$
$293$	−13.7468	+	23.8102i	−0.803097	+	1.39100i	−0.917568	+	0.397578i	$0.869851\pi$
$294$		0			0
$295$	4.95056	+	8.57462i	0.288233	+	0.499234i
$296$	−6.59888	+	11.4296i	−0.383552	+	0.664332i
$297$		0			0
$298$	−3.71015	−	6.42617i	−0.214923	−	0.372258i
$299$	−12.4344			−0.719099
$300$		0			0
$301$		0			0
$302$	10.7534	−	18.6254i	0.618789	−	1.07177i
$303$		0			0
$304$	11.1254	−	19.2698i	0.638088	−	1.10520i
$305$	−5.53087	−	9.57975i	−0.316697	−	0.548535i
$306$		0			0
$307$	−14.8176			−0.845683			−0.422841	−	0.906204i	$-0.638967\pi$
$307$	−14.8176			−0.845683			−0.422841	+	0.906204i	$0.638967\pi$
$308$		0			0
$309$		0			0
$310$	4.90043	+	8.48779i	0.278326	+	0.482074i
$311$	29.0635			1.64804			0.824021	−	0.566559i	$-0.191726\pi$
$311$	29.0635			1.64804			0.824021	+	0.566559i	$0.191726\pi$
$312$		0			0
$313$	24.4780			1.38358			0.691790	−	0.722099i	$-0.256822\pi$
$313$	24.4780			1.38358			0.691790	+	0.722099i	$0.256822\pi$
$314$	−19.1614			−1.08134
$315$		0			0
$316$	−1.18539			−0.0666834
$317$	7.38688			0.414888			0.207444	−	0.978247i	$-0.433485\pi$
$317$	7.38688			0.414888			0.207444	+	0.978247i	$0.433485\pi$
$318$		0			0
$319$	−3.22253			−0.180427
$320$	0.943395	+	1.63401i	0.0527374	+	0.0913438i
$321$		0			0
$322$		0			0
$323$	−33.8268			−1.88218
$324$		0			0
$325$	10.2877	+	17.8188i	0.570657	+	0.988407i
$326$	1.41597	−	2.45253i	0.0784231	−	0.135833i
$327$		0			0
$328$	−0.996205	+	1.72548i	−0.0550062	+	0.0952736i
$329$		0			0
$330$		0			0
$331$	20.0617			1.10269			0.551347	−	0.834276i	$-0.314114\pi$
$331$	20.0617			1.10269			0.551347	+	0.834276i	$0.314114\pi$
$332$	2.52573	+	4.37470i	0.138618	+	0.240093i
$333$		0			0
$334$	−3.31657	+	5.74447i	−0.181475	+	0.314324i
$335$	−5.63106	−	9.75329i	−0.307658	−	0.532879i
$336$		0			0
$337$	−3.20327	+	5.54823i	−0.174493	+	0.302231i	−0.939986	−	0.341214i	$-0.889162\pi$
$337$	−3.20327	+	5.54823i	−0.174493	+	0.302231i	0.765493	+	0.643445i	$0.222495\pi$
$338$	−10.3658	−	17.9542i	−0.563827	−	0.976577i
$339$		0			0
$340$	−3.19846	+	5.53989i	−0.173461	+	0.300443i
$341$	−1.78705	+	3.09526i	−0.0967740	+	0.167617i
$342$		0			0
$343$		0			0
$344$	6.59888	+	11.4296i	0.355788	+	0.616243i
$345$		0			0
$346$	27.3880			1.47239
$347$	29.1927			1.56714			0.783572	−	0.621300i	$-0.213395\pi$
$347$	29.1927			1.56714			0.783572	+	0.621300i	$0.213395\pi$
$348$		0			0
$349$	−2.17192	−	3.76188i	−0.116260	−	0.201369i	0.802022	−	0.597294i	$-0.203757\pi$
$349$	−2.17192	−	3.76188i	−0.116260	−	0.201369i	−0.918283	+	0.395925i	$0.870424\pi$
$350$		0			0
$351$		0			0
$352$	1.38255	−	2.39464i	0.0736899	−	0.127635i
$353$	−12.8503	+	22.2574i	−0.683955	+	1.18464i	0.289809	+	0.957084i	$0.406408\pi$
$353$	−12.8503	+	22.2574i	−0.683955	+	1.18464i	−0.973764	+	0.227560i	$0.926925\pi$
$354$		0			0
$355$	−2.04111	−	3.53530i	−0.108331	−	0.187635i
$356$	−0.374892	+	0.649331i	−0.0198692	+	0.0344145i
$357$		0			0
$358$	12.1421	+	21.0308i	0.641732	+	1.11151i
$359$	10.3436	−	17.9157i	0.545916	−	0.945554i	−0.452633	−	0.891697i	$-0.649515\pi$
$359$	10.3436	−	17.9157i	0.545916	−	0.945554i	0.998549	−	0.0538567i	$-0.0171514\pi$
$360$		0			0
$361$	−0.451246	−	0.781582i	−0.0237498	−	0.0411359i
$362$	−21.9036			−1.15123
$363$		0			0
$364$		0			0
$365$	−2.11745	+	3.66754i	−0.110833	+	0.191968i
$366$		0			0
$367$	−1.42391	+	2.46628i	−0.0743273	+	0.128739i	−0.900794	−	0.434248i	$-0.857014\pi$
$367$	−1.42391	+	2.46628i	−0.0743273	+	0.128739i	0.826466	+	0.562986i	$0.190348\pi$
$368$	−6.17742	−	10.6996i	−0.322020	−	0.557755i
$369$		0			0
$370$	11.2739			0.586101
$371$		0			0
$372$		0			0
$373$	−10.7163	−	18.5612i	−0.554871	−	0.961065i	−0.997914	−	0.0645641i	$-0.979434\pi$
$373$	−10.7163	−	18.5612i	−0.554871	−	0.961065i	0.443043	−	0.896501i	$-0.353899\pi$
$374$	−7.58242			−0.392077
$375$		0			0
$376$	14.1217			0.728271
$377$	−27.4936			−1.41599
$378$		0			0
$379$	27.0494			1.38943			0.694716	−	0.719284i	$-0.255530\pi$
$379$	27.0494			1.38943			0.694716	+	0.719284i	$0.255530\pi$
$380$	−3.76371			−0.193074
$381$		0			0
$382$	3.67859			0.188213
$383$	7.21340	+	12.4940i	0.368588	+	0.638412i	0.989345	−	0.145590i	$-0.0465081\pi$
$383$	7.21340	+	12.4940i	0.368588	+	0.638412i	−0.620757	+	0.784003i	$0.713175\pi$
$384$		0			0
$385$		0			0
$386$	17.7293			0.902399
$387$		0			0
$388$	−1.51366	−	2.62174i	−0.0768446	−	0.133099i
$389$	−3.05377	+	5.28929i	−0.154832	+	0.268178i	−0.932998	−	0.359882i	$-0.882817\pi$
$389$	−3.05377	+	5.28929i	−0.154832	+	0.268178i	0.778166	+	0.628059i	$0.216150\pi$
$390$		0			0
$391$	−9.39120	+	16.2660i	−0.474933	+	0.822609i
$392$		0			0
$393$		0			0
$394$	31.9271			1.60846
$395$	−0.633065	−	1.09650i	−0.0318530	−	0.0551710i
$396$		0			0
$397$	−6.44364	+	11.1607i	−0.323397	+	0.560140i	−0.981187	−	0.193061i	$-0.938158\pi$
$397$	−6.44364	+	11.1607i	−0.323397	+	0.560140i	0.657789	+	0.753202i	$0.271492\pi$
$398$	7.16059	+	12.4025i	0.358928	+	0.621682i
$399$		0			0
$400$	−10.2218	+	17.7047i	−0.511092	+	0.885237i
$401$	4.19530	+	7.26647i	0.209503	+	0.362870i	0.951558	−	0.307469i	$-0.0994820\pi$
$401$	4.19530	+	7.26647i	0.209503	+	0.362870i	−0.742055	+	0.670339i	$0.766149\pi$
$402$		0			0
$403$	−15.2465	+	26.4078i	−0.759483	+	1.31546i
$404$	4.25997	−	7.37848i	0.211941	−	0.367093i
$405$		0			0
$406$		0			0
$407$	2.05563	+	3.56046i	0.101894	+	0.176485i
$408$		0			0
$409$	−6.81266			−0.336864			−0.168432	−	0.985713i	$-0.553870\pi$
$409$	−6.81266			−0.336864			−0.168432	+	0.985713i	$0.553870\pi$
$410$	1.70197			0.0840543
$411$		0			0
$412$	−5.17817	−	8.96885i	−0.255110	−	0.441864i
$413$		0			0
$414$		0			0
$415$	−2.69777	+	4.67267i	−0.132428	+	0.229372i
$416$	11.7955	−	20.4303i	0.578320	−	1.00168i
$417$		0			0
$418$	−2.23061	−	3.86353i	−0.109103	−	0.188971i
$419$	5.16231	−	8.94137i	0.252195	−	0.436815i	−0.711935	−	0.702246i	$-0.752181\pi$
$419$	5.16231	−	8.94137i	0.252195	−	0.436815i	0.964130	+	0.265431i	$0.0855142\pi$
$420$		0			0
$421$	−1.56801	−	2.71588i	−0.0764202	−	0.132364i	0.825283	−	0.564720i	$-0.191016\pi$
$421$	−1.56801	−	2.71588i	−0.0764202	−	0.132364i	−0.901703	+	0.432356i	$0.857682\pi$
$422$	−9.53706	+	16.5187i	−0.464257	+	0.804117i
$423$		0			0
$424$	−6.53706	−	11.3225i	−0.317468	−	0.549870i
$425$	31.0795			1.50757
$426$		0			0
$427$		0			0
$428$	−1.68794	+	2.92359i	−0.0815895	+	0.141317i
$429$		0			0
$430$	5.63694	−	9.76347i	0.271837	−	0.470836i
$431$	15.9363	+	27.6025i	0.767625	+	1.32957i	0.938847	+	0.344334i	$0.111895\pi$
$431$	15.9363	+	27.6025i	0.767625	+	1.32957i	−0.171222	+	0.985233i	$0.554771\pi$
$432$		0			0
$433$	−7.48855			−0.359877			−0.179938	−	0.983678i	$-0.557590\pi$
$433$	−7.48855			−0.359877			−0.179938	+	0.983678i	$0.557590\pi$
$434$		0			0
$435$		0			0
$436$	5.71634	+	9.90099i	0.273763	+	0.474171i
$437$	−11.0509			−0.528636
$438$		0			0
$439$	−2.28930			−0.109262			−0.0546311	−	0.998507i	$-0.517398\pi$
$439$	−2.28930			−0.109262			−0.0546311	+	0.998507i	$0.517398\pi$
$440$	1.05489			0.0502900
$441$		0			0
$442$	−64.6908			−3.07703
$443$	−37.3497			−1.77454			−0.887270	−	0.461251i	$-0.847401\pi$
$443$	−37.3497			−1.77454			−0.887270	+	0.461251i	$0.847401\pi$
$444$		0			0
$445$	−0.800854			−0.0379641
$446$	−17.6378	−	30.5495i	−0.835172	−	1.44656i
$447$		0			0
$448$		0			0
$449$	6.20286			0.292731			0.146366	−	0.989231i	$-0.453242\pi$
$449$	6.20286			0.292731			0.146366	+	0.989231i	$0.453242\pi$
$450$		0			0
$451$	0.310330	+	0.537507i	0.0146129	+	0.0253102i
$452$	4.00866	−	6.94320i	0.188552	−	0.326581i
$453$		0			0
$454$	8.86376	−	15.3525i	0.415997	−	0.720527i
$455$		0			0
$456$		0			0
$457$	20.1716			0.943589			0.471795	−	0.881709i	$-0.343606\pi$
$457$	20.1716			0.943589			0.471795	+	0.881709i	$0.343606\pi$
$458$	12.7975	+	22.1660i	0.597989	+	1.03575i
$459$		0			0
$460$	−1.04490	+	1.80983i	−0.0487189	+	0.0843836i
$461$	11.2680	+	19.5168i	0.524803	+	0.908986i	0.999583	+	0.0288813i	$0.00919447\pi$
$461$	11.2680	+	19.5168i	0.524803	+	0.908986i	−0.474780	+	0.880105i	$0.657472\pi$
$462$		0			0
$463$	13.8145	−	23.9275i	0.642016	−	1.11200i	−0.342966	−	0.939348i	$-0.611432\pi$
$463$	13.8145	−	23.9275i	0.642016	−	1.11200i	0.984982	−	0.172656i	$-0.0552350\pi$
$464$	−13.6588	−	23.6578i	−0.634096	−	1.09829i
$465$		0			0
$466$	3.72803	−	6.45714i	0.172698	−	0.299121i
$467$	−10.0612	+	17.4265i	−0.465577	+	0.806404i	−0.999227	−	0.0393016i	$-0.987487\pi$
$467$	−10.0612	+	17.4265i	−0.465577	+	0.806404i	0.533650	+	0.845705i	$0.320820\pi$
$468$		0			0
$469$		0			0
$470$	−6.03156	−	10.4470i	−0.278215	−	0.481883i
$471$		0			0
$472$	−19.6999			−0.906764
$473$	4.11126			0.189036
$474$		0			0
$475$	9.14301	+	15.8362i	0.419510	+	0.726613i
$476$		0			0
$477$		0			0
$478$	−8.11677	+	14.0586i	−0.371252	+	0.643028i
$479$	4.79329	−	8.30222i	0.219011	−	0.379338i	−0.735495	−	0.677530i	$-0.763050\pi$
$479$	4.79329	−	8.30222i	0.219011	−	0.379338i	0.954506	+	0.298192i	$0.0963836\pi$
$480$		0			0
$481$	17.5380	+	30.3767i	0.799664	+	1.38506i
$482$	8.95351	−	15.5079i	0.407821	−	0.706367i
$483$		0			0
$484$	4.73422	+	8.19991i	0.215192	+	0.372723i
$485$	1.61677	−	2.80032i	0.0734135	−	0.127156i
$486$		0			0
$487$	−6.53706	−	11.3225i	−0.296223	−	0.513073i	0.679046	−	0.734096i	$-0.262394\pi$
$487$	−6.53706	−	11.3225i	−0.296223	−	0.513073i	−0.975269	+	0.221023i	$0.929060\pi$
$488$	22.0092			0.996311
$489$		0			0
$490$		0			0
$491$	7.67054	−	13.2858i	0.346167	−	0.599578i	−0.639398	−	0.768876i	$-0.720817\pi$
$491$	7.67054	−	13.2858i	0.346167	−	0.599578i	0.985565	+	0.169298i	$0.0541499\pi$
$492$		0			0
$493$	−20.7648	+	35.9657i	−0.935201	+	1.61982i
$494$	−19.0309	−	32.9624i	−0.856239	−	1.48305i
$495$		0			0
$496$	−30.2979			−1.36042
$497$		0			0
$498$		0			0
$499$	−2.43268	−	4.21352i	−0.108902	−	0.188623i	0.806424	−	0.591338i	$-0.201400\pi$
$499$	−2.43268	−	4.21352i	−0.108902	−	0.188623i	−0.915326	+	0.402715i	$0.868067\pi$
$500$	7.67628			0.343294
$501$		0			0
$502$	−41.5297			−1.85356
$503$	16.0085			0.713783			0.356892	−	0.934146i	$-0.383837\pi$
$503$	16.0085			0.713783			0.356892	+	0.934146i	$0.383837\pi$
$504$		0			0
$505$	9.10026			0.404956
$506$	−2.47710			−0.110121
$507$		0			0
$508$	5.71695			0.253649
$509$	15.5925	+	27.0071i	0.691127	+	1.19707i	0.971469	+	0.237167i	$0.0762188\pi$
$509$	15.5925	+	27.0071i	0.691127	+	1.19707i	−0.280342	+	0.959900i	$0.590448\pi$
$510$		0			0
$511$		0			0
$512$	4.59937			0.203265
$513$		0			0
$514$	−3.40633	−	5.89994i	−0.150247	−	0.260235i
$515$	5.53087	−	9.57975i	0.243719	−	0.422134i
$516$		0			0
$517$	2.19954	−	3.80971i	0.0967356	−	0.167551i
$518$		0			0
$519$		0			0
$520$	9.00000			0.394676
$521$	−10.4830	−	18.1572i	−0.459270	−	0.795480i	0.539652	−	0.841888i	$-0.318556\pi$
$521$	−10.4830	−	18.1572i	−0.459270	−	0.795480i	−0.998923	+	0.0464085i	$0.985222\pi$
$522$		0			0
$523$	21.7821	−	37.7277i	0.952465	−	1.64972i	0.212401	−	0.977183i	$-0.431872\pi$
$523$	21.7821	−	37.7277i	0.952465	−	1.64972i	0.740064	−	0.672536i	$-0.234795\pi$
$524$	−2.94756	−	5.10532i	−0.128765	−	0.223027i
$525$		0			0
$526$	15.0309	−	26.0342i	0.655377	−	1.13515i
$527$	23.0302	+	39.8894i	1.00321	+	1.73761i
$528$		0			0
$529$	8.43199	−	14.6046i	0.366608	−	0.634984i
$530$	−5.58413	+	9.67200i	−0.242559	+	0.420125i
$531$		0			0
$532$		0			0
$533$	2.64764	+	4.58584i	0.114682	+	0.198635i
$534$		0			0
$535$	−3.60582			−0.155893
$536$	22.4079			0.967875
$537$		0			0
$538$	12.0906	+	20.9415i	0.521262	+	0.902852i
$539$		0			0
$540$		0			0
$541$	−4.93268	+	8.54365i	−0.212072	+	0.367320i	−0.952363	−	0.304967i	$-0.901355\pi$
$541$	−4.93268	+	8.54365i	−0.212072	+	0.367320i	0.740291	+	0.672287i	$0.234688\pi$
$542$	−4.58793	+	7.94652i	−0.197068	+	0.341332i
$543$		0			0
$544$	−17.8173	−	30.8604i	−0.763909	−	1.32313i
$545$	−6.10570	+	10.5754i	−0.261539	+	0.453000i
$546$		0			0
$547$	−0.284350	−	0.492509i	−0.0121579	−	0.0210582i	0.859882	−	0.510492i	$-0.170537\pi$
$547$	−0.284350	−	0.492509i	−0.0121579	−	0.0210582i	−0.872040	+	0.489434i	$0.837203\pi$
$548$	6.23600	−	10.8011i	0.266389	−	0.461399i
$549$		0			0
$550$	2.04944	+	3.54974i	0.0873885	+	0.151361i
$551$	−24.4346			−1.04095
$552$		0			0
$553$		0			0
$554$	−6.51485	+	11.2841i	−0.276789	+	0.479413i
$555$		0			0
$556$	3.91269	−	6.77698i	0.165935	−	0.287408i
$557$	−1.29349	−	2.24040i	−0.0548071	−	0.0949286i	0.837320	−	0.546713i	$-0.184121\pi$
$557$	−1.29349	−	2.24040i	−0.0548071	−	0.0949286i	−0.892127	+	0.451784i	$0.850788\pi$
$558$		0			0
$559$	35.0760			1.48356
$560$		0			0
$561$		0			0
$562$	−19.2589	−	33.3574i	−0.812388	−	1.40710i
$563$	−33.2831			−1.40272			−0.701358	−	0.712809i	$-0.747422\pi$
$563$	−33.2831			−1.40272			−0.701358	+	0.712809i	$0.747422\pi$
$564$		0			0
$565$	8.56341			0.360265
$566$	54.1318			2.27533
$567$		0			0
$568$	8.12227			0.340803
$569$	5.35346			0.224429			0.112214	−	0.993684i	$-0.464206\pi$
$569$	5.35346			0.224429			0.112214	+	0.993684i	$0.464206\pi$
$570$		0			0
$571$	4.90112			0.205105			0.102553	−	0.994728i	$-0.467299\pi$
$571$	4.90112			0.205105			0.102553	+	0.994728i	$0.467299\pi$
$572$	−1.31241	−	2.27316i	−0.0548747	−	0.0950457i
$573$		0			0
$574$		0			0
$575$	10.1533			0.423424
$576$		0			0
$577$	−18.0378	−	31.2425i	−0.750925	−	1.30064i	−0.947375	−	0.320127i	$-0.896275\pi$
$577$	−18.0378	−	31.2425i	−0.750925	−	1.30064i	0.196450	−	0.980514i	$-0.437059\pi$
$578$	−34.4116	+	59.6026i	−1.43133	+	2.47914i
$579$		0			0
$580$	−2.31038	+	4.00170i	−0.0959333	+	0.166161i
$581$		0			0
$582$		0			0
$583$	−4.07275			−0.168676
$584$	−4.21303	−	7.29719i	−0.174337	−	0.301960i
$585$		0			0
$586$	−23.3645	+	40.4684i	−0.965177	+	1.67174i
$587$	−0.527445	−	0.913562i	−0.0217700	−	0.0377068i	0.854935	−	0.518735i	$-0.173597\pi$
$587$	−0.527445	−	0.913562i	−0.0217700	−	0.0377068i	−0.876705	+	0.481028i	$0.840263\pi$
$588$		0			0
$589$	−13.5501	+	23.4695i	−0.558323	+	0.967045i
$590$	8.41411	+	14.5737i	0.346403	+	0.599988i
$591$		0			0
$592$	−17.4258	+	30.1824i	−0.716196	+	1.24049i
$593$	7.53548	−	13.0518i	0.309445	−	0.535975i	−0.668796	−	0.743446i	$-0.733190\pi$
$593$	7.53548	−	13.0518i	0.309445	−	0.535975i	0.978241	+	0.207471i	$0.0665233\pi$
$594$		0			0
$595$		0			0
$596$	−1.94004	−	3.36024i	−0.0794670	−	0.137641i
$597$		0			0
$598$	−21.1338			−0.864227
$599$	−42.0566			−1.71839			−0.859194	−	0.511650i	$-0.829035\pi$
$599$	−42.0566			−1.71839			−0.859194	+	0.511650i	$0.829035\pi$
$600$		0			0
$601$	9.44989	+	16.3677i	0.385469	+	0.667652i	0.991834	−	0.127534i	$-0.0407064\pi$
$601$	9.44989	+	16.3677i	0.385469	+	0.667652i	−0.606365	+	0.795186i	$0.707373\pi$
$602$		0			0
$603$		0			0
$604$	5.62296	−	9.73924i	0.228795	−	0.396284i
$605$	−5.05669	+	8.75844i	−0.205583	+	0.356081i
$606$		0			0
$607$	−14.7213	−	25.4980i	−0.597518	−	1.03493i	−0.993186	−	0.116538i	$-0.962820\pi$
$607$	−14.7213	−	25.4980i	−0.597518	−	1.03493i	0.395668	−	0.918393i	$-0.370513\pi$
$608$	10.4830	−	18.1572i	0.425143	−	0.736370i
$609$		0			0
$610$	−9.40043	−	16.2820i	−0.380612	−	0.659240i
$611$	18.7658	−	32.5033i	0.759182	−	1.31494i
$612$		0			0
$613$	5.83379	+	10.1044i	0.235625	+	0.408114i	0.959454	−	0.281865i	$-0.0909531\pi$
$613$	5.83379	+	10.1044i	0.235625	+	0.408114i	−0.723829	+	0.689979i	$0.757620\pi$
$614$	−25.1843			−1.01636
$615$		0			0
$616$		0			0
$617$	−16.4054	+	28.4151i	−0.660458	+	1.14395i	0.320037	+	0.947405i	$0.396305\pi$
$617$	−16.4054	+	28.4151i	−0.660458	+	1.14395i	−0.980495	+	0.196542i	$0.937029\pi$
$618$		0			0
$619$	−12.0806	+	20.9242i	−0.485560	+	0.841014i	−0.999862	−	0.0165947i	$-0.994717\pi$
$619$	−12.0806	+	20.9242i	−0.485560	+	0.841014i	0.514303	+	0.857609i	$0.328051\pi$
$620$	2.56243	+	4.43827i	0.102910	+	0.178245i
$621$		0			0
$622$	49.3972			1.98065
$623$		0			0
$624$		0			0
$625$	−6.14764	−	10.6480i	−0.245906	−	0.425921i
$626$	41.6035			1.66281
$627$		0			0
$628$	−10.0195			−0.399822
$629$	52.9830			2.11257
$630$		0			0
$631$	−11.1003			−0.441894			−0.220947	−	0.975286i	$-0.570915\pi$
$631$	−11.1003			−0.441894			−0.220947	+	0.975286i	$0.570915\pi$
$632$	2.51918			0.100208
$633$		0			0
$634$	12.5549			0.498620
$635$	3.05318	+	5.28826i	0.121162	+	0.209858i
$636$		0			0
$637$		0			0
$638$	−5.47710			−0.216840
$639$		0			0
$640$	6.06464	+	10.5043i	0.239726	+	0.415218i
$641$	3.65019	−	6.32231i	0.144174	−	0.249716i	−0.784891	−	0.619634i	$-0.787281\pi$
$641$	3.65019	−	6.32231i	0.144174	−	0.249716i	0.929064	+	0.369918i	$0.120614\pi$
$642$		0			0
$643$	10.6256	−	18.4041i	0.419033	−	0.725787i	−0.576809	−	0.816879i	$-0.695702\pi$
$643$	10.6256	−	18.4041i	0.419033	−	0.725787i	0.995842	+	0.0910922i	$0.0290358\pi$
$644$		0			0
$645$		0			0
$646$	−57.4930			−2.26203
$647$	−8.47300	−	14.6757i	−0.333108	−	0.576960i	0.650011	−	0.759924i	$-0.274764\pi$
$647$	−8.47300	−	14.6757i	−0.333108	−	0.576960i	−0.983120	+	0.182964i	$0.941431\pi$
$648$		0			0
$649$	−3.06839	+	5.31460i	−0.120445	+	0.208616i
$650$	17.4852	+	30.2853i	0.685826	+	1.18789i
$651$		0			0
$652$	0.740409	−	1.28243i	0.0289967	−	0.0502237i
$653$	−1.86652	−	3.23292i	−0.0730427	−	0.126514i	0.827191	−	0.561921i	$-0.189938\pi$
$653$	−1.86652	−	3.23292i	−0.0730427	−	0.126514i	−0.900233	+	0.435408i	$0.856604\pi$
$654$		0			0
$655$	3.14833	−	5.45306i	0.123015	−	0.213069i
$656$	−2.63070	+	4.55650i	−0.102711	+	0.177902i
$657$		0			0
$658$		0			0
$659$	−11.7992	−	20.4368i	−0.459632	−	0.796105i	0.539310	−	0.842107i	$-0.318685\pi$
$659$	−11.7992	−	20.4368i	−0.459632	−	0.796105i	−0.998941	+	0.0460022i	$0.985352\pi$
$660$		0			0
$661$	−34.5175			−1.34258			−0.671288	−	0.741197i	$-0.734258\pi$
$661$	−34.5175			−1.34258			−0.671288	+	0.741197i	$0.734258\pi$
$662$	34.0975			1.32524
$663$		0			0
$664$	−5.36767	−	9.29708i	−0.208306	−	0.360796i
$665$		0			0
$666$		0			0
$667$	−6.78366	+	11.7496i	−0.262664	+	0.454948i
$668$	−1.73424	+	3.00379i	−0.0670996	+	0.116220i
$669$		0			0
$670$	−9.57072	−	16.5770i	−0.369749	−	0.640424i
$671$	3.42807	−	5.93759i	0.132339	−	0.229218i
$672$		0			0
$673$	12.2287	+	21.1808i	0.471382	+	0.816458i	0.999464	−	0.0327353i	$-0.0104218\pi$
$673$	12.2287	+	21.1808i	0.471382	+	0.816458i	−0.528082	+	0.849194i	$0.677088\pi$
$674$	−5.44437	+	9.42992i	−0.209709	+	0.363227i
$675$		0			0
$676$	−5.42030	−	9.38823i	−0.208473	−	0.361086i
$677$	−8.32045			−0.319781			−0.159890	−	0.987135i	$-0.551114\pi$
$677$	−8.32045			−0.319781			−0.159890	+	0.987135i	$0.551114\pi$
$678$		0			0
$679$		0			0
$680$	6.79734	−	11.7733i	0.260666	−	0.451487i
$681$		0			0
$682$	−3.03731	+	5.26078i	−0.116305	+	0.201446i
$683$	−21.2312	−	36.7735i	−0.812389	−	1.40710i	−0.911188	−	0.411991i	$-0.864833\pi$
$683$	−21.2312	−	36.7735i	−0.812389	−	1.40710i	0.0987988	−	0.995107i	$-0.468500\pi$
$684$		0			0
$685$	13.3215			0.508989
$686$		0			0
$687$		0			0
$688$	17.4258	+	30.1824i	0.664352	+	1.15069i
$689$	−34.7474			−1.32377
$690$		0			0
$691$	−35.3929			−1.34641			−0.673204	−	0.739456i	$-0.735083\pi$
$691$	−35.3929			−1.34641			−0.673204	+	0.739456i	$0.735083\pi$
$692$	14.3212			0.544410
$693$		0			0
$694$	49.6167			1.88342
$695$	8.35840			0.317052
$696$		0			0
$697$	7.99862			0.302969
$698$	−3.69146	−	6.39380i	−0.139724	−	0.242009i
$699$		0			0
$700$		0			0
$701$	7.00372			0.264527			0.132263	−	0.991215i	$-0.457776\pi$
$701$	7.00372			0.264527			0.132263	+	0.991215i	$0.457776\pi$
$702$		0			0
$703$	15.5867	+	26.9969i	0.587862	+	1.01821i
$704$	−0.584722	+	1.01277i	−0.0220375	+	0.0381701i
$705$		0			0
$706$	−21.8408	+	37.8294i	−0.821989	+	1.42373i
$707$		0			0
$708$		0			0
$709$	−2.22253			−0.0834688			−0.0417344	−	0.999129i	$-0.513288\pi$
$709$	−2.22253			−0.0834688			−0.0417344	+	0.999129i	$0.513288\pi$
$710$	−3.46913	−	6.00870i	−0.130194	−	0.225503i
$711$		0			0
$712$	0.796717	−	1.37995i	0.0298582	−	0.0517160i
$713$	7.52373	+	13.0315i	0.281766	+	0.488033i
$714$		0			0
$715$	1.40180	−	2.42800i	0.0524245	−	0.0908019i
$716$	6.34913	+	10.9970i	0.237278	+	0.410977i
$717$		0			0
$718$	17.5803	−	30.4500i	0.656092	−	1.13638i
$719$	−13.0088	+	22.5319i	−0.485145	+	0.840296i	−0.999854	−	0.0170686i	$-0.994567\pi$
$719$	−13.0088	+	22.5319i	−0.485145	+	0.840296i	0.514709	+	0.857365i	$0.327900\pi$
$720$		0			0
$721$		0			0
$722$	−0.766951	−	1.32840i	−0.0285430	−	0.0494379i
$723$		0			0
$724$	−11.4534			−0.425662
$725$	22.4500			0.833772
$726$		0			0
$727$	−0.685875	−	1.18797i	−0.0254377	−	0.0440594i	0.853026	−	0.521868i	$-0.174765\pi$
$727$	−0.685875	−	1.18797i	−0.0254377	−	0.0440594i	−0.878464	+	0.477809i	$0.841431\pi$
$728$		0			0
$729$		0			0
$730$	−3.59888	+	6.23345i	−0.133201	+	0.230710i
$731$	26.4915	−	45.8847i	0.979824	−	1.69711i
$732$		0			0
$733$	−0.400087	−	0.692971i	−0.0147776	−	0.0255955i	0.858542	−	0.512743i	$-0.171371\pi$
$733$	−0.400087	−	0.692971i	−0.0147776	−	0.0255955i	−0.873320	+	0.487148i	$0.838037\pi$
$734$	−2.42011	+	4.19176i	−0.0893280	+	0.154721i
$735$		0			0
$736$	−5.82072	−	10.0818i	−0.214555	−	0.371620i
$737$	3.49017	−	6.04515i	0.128562	−	0.222676i
$738$		0			0
$739$	−2.68547	−	4.65136i	−0.0987865	−	0.171103i	0.812396	−	0.583106i	$-0.198163\pi$
$739$	−2.68547	−	4.65136i	−0.0987865	−	0.171103i	−0.911183	+	0.412003i	$0.864829\pi$
$740$	5.89511			0.216709
$741$		0			0
$742$		0			0
$743$	−6.63162	+	11.4863i	−0.243290	+	0.421391i	−0.961650	−	0.274281i	$-0.911560\pi$
$743$	−6.63162	+	11.4863i	−0.243290	+	0.421391i	0.718359	+	0.695672i	$0.244893\pi$
$744$		0			0
$745$	2.07218	−	3.58912i	0.0759188	−	0.131495i
$746$	−18.2138	−	31.5472i	−0.666854	−	1.15503i
$747$		0			0
$748$	−3.96485			−0.144969
$749$		0			0
$750$		0			0
$751$	−2.77816	−	4.81191i	−0.101377	−	0.175589i	0.810875	−	0.585219i	$-0.198991\pi$
$751$	−2.77816	−	4.81191i	−0.101377	−	0.175589i	−0.912252	+	0.409629i	$0.865658\pi$
$752$	37.2914			1.35988
$753$		0			0
$754$	−46.7289			−1.70177
$755$	12.0119			0.437158
$756$		0			0
$757$	−13.3942			−0.486819			−0.243410	−	0.969924i	$-0.578266\pi$
$757$	−13.3942			−0.486819			−0.243410	+	0.969924i	$0.578266\pi$
$758$	45.9739			1.66985
$759$		0			0
$760$	7.99862			0.290141
$761$	6.42191	+	11.1231i	0.232794	+	0.403211i	0.958629	−	0.284658i	$-0.0918799\pi$
$761$	6.42191	+	11.1231i	0.232794	+	0.403211i	−0.725835	+	0.687868i	$0.758547\pi$
$762$		0			0
$763$		0			0
$764$	1.92353			0.0695910
$765$		0			0
$766$	12.2601	+	21.2351i	0.442975	+	0.767256i
$767$	−26.1785	+	45.3425i	−0.945251	+	1.63722i
$768$		0			0
$769$	1.48259	−	2.56793i	0.0534636	−	0.0926018i	−0.838055	−	0.545586i	$-0.816307\pi$
$769$	1.48259	−	2.56793i	0.0534636	−	0.0926018i	0.891519	+	0.452984i	$0.149641\pi$
$770$		0			0
$771$		0			0
$772$	9.27067			0.333659
$773$	9.63939	+	16.6959i	0.346705	+	0.600510i	0.985662	−	0.168732i	$-0.0539673\pi$
$773$	9.63939	+	16.6959i	0.346705	+	0.600510i	−0.638957	+	0.769242i	$0.720634\pi$
$774$		0			0
$775$	12.4496	−	21.5633i	0.447203	−	0.774578i
$776$	3.21683	+	5.57171i	0.115477	+	0.200013i
$777$		0			0
$778$	−5.19028	+	8.98983i	−0.186080	+	0.322301i
$779$	2.35305	+	4.07560i	0.0843068	+	0.146024i
$780$		0			0
$781$	1.26509	−	2.19120i	0.0452685	−	0.0784074i
$782$	−15.9616	+	27.6462i	−0.570784	+	0.988627i
$783$		0			0
$784$		0			0
$785$	−5.35098	−	9.26818i	−0.190985	−	0.330795i
$786$		0			0
$787$	−13.6453			−0.486402			−0.243201	−	0.969976i	$-0.578197\pi$
$787$	−13.6453			−0.486402			−0.243201	+	0.969976i	$0.578197\pi$
$788$	16.6947			0.594724
$789$		0			0
$790$	−1.07598	−	1.86364i	−0.0382815	−	0.0663055i
$791$		0			0
$792$		0			0
$793$	29.2472	−	50.6577i	1.03860	−	1.79891i
$794$	−10.9518	+	18.9691i	−0.388665	+	0.673187i
$795$		0			0
$796$	3.74427	+	6.48527i	0.132712	+	0.229864i
$797$	11.4792	−	19.8826i	0.406616	−	0.704279i	−0.587892	−	0.808939i	$-0.700042\pi$
$797$	11.4792	−	19.8826i	0.406616	−	0.704279i	0.994508	+	0.104660i	$0.0333755\pi$
$798$		0			0
$799$	−28.3461	−	49.0969i	−1.00281	−	1.73692i
$800$	−9.63162	+	16.6824i	−0.340529	+	0.589814i
$801$		0			0
$802$	7.13045	+	12.3503i	0.251785	+	0.436104i
$803$	−2.62482			−0.0926279
$804$		0			0
$805$		0			0
$806$	−25.9134	+	44.8834i	−0.912761	+	1.58095i
$807$		0			0
$808$	−9.05326	+	15.6807i	−0.318492	+	0.551645i
$809$	19.7291	+	34.1718i	0.693639	+	1.20142i	0.970637	+	0.240548i	$0.0773270\pi$
$809$	19.7291	+	34.1718i	0.693639	+	1.20142i	−0.276998	+	0.960870i	$0.589340\pi$
$810$		0			0
$811$	0.496374			0.0174300			0.00871502	−	0.999962i	$-0.497226\pi$
$811$	0.496374			0.0174300			0.00871502	+	0.999962i	$0.497226\pi$
$812$		0			0
$813$		0			0
$814$	3.49381	+	6.05146i	0.122458	+	0.212103i
$815$	1.58168			0.0554039
$816$		0			0
$817$	31.1733			1.09062
$818$	−11.5790			−0.404850
$819$		0			0
$820$	0.889960			0.0310788
$821$	−47.1038			−1.64393			−0.821967	−	0.569534i	$-0.807124\pi$
$821$	−47.1038			−1.64393			−0.821967	+	0.569534i	$0.807124\pi$
$822$		0			0
$823$	−2.19777			−0.0766094			−0.0383047	−	0.999266i	$-0.512196\pi$
$823$	−2.19777			−0.0766094			−0.0383047	+	0.999266i	$0.512196\pi$
$824$	11.0046	+	19.0605i	0.383364	+	0.664005i
$825$		0			0
$826$		0			0
$827$	55.3360			1.92422			0.962110	−	0.272661i	$-0.0879036\pi$
$827$	55.3360			1.92422			0.962110	+	0.272661i	$0.0879036\pi$
$828$		0			0
$829$	−10.1603	−	17.5982i	−0.352882	−	0.611209i	0.633871	−	0.773439i	$-0.281465\pi$
$829$	−10.1603	−	17.5982i	−0.352882	−	0.611209i	−0.986753	+	0.162229i	$0.948132\pi$
$830$	−4.58520	+	7.94181i	−0.159155	+	0.275664i
$831$		0			0
$832$	−4.98867	+	8.64062i	−0.172951	+	0.299560i
$833$		0			0
$834$		0			0
$835$	−3.70472			−0.128207
$836$	−1.16639	−	2.02024i	−0.0403403	−	0.0698715i
$837$		0			0
$838$	8.77400	−	15.1970i	0.303093	−	0.524972i
$839$	−12.2760	−	21.2626i	−0.423813	−	0.734066i	0.572496	−	0.819908i	$-0.305975\pi$
$839$	−12.2760	−	21.2626i	−0.423813	−	0.734066i	−0.996309	+	0.0858417i	$0.972642\pi$
$840$		0			0
$841$	−0.499311	+	0.864833i	−0.0172176	+	0.0298218i
$842$	−2.66504	−	4.61598i	−0.0918432	−	0.159077i
$843$		0			0
$844$	−4.98693	+	8.63762i	−0.171657	+	0.297319i
$845$	5.78949	−	10.0277i	0.199165	−	0.344963i
$846$		0			0
$847$		0			0
$848$	−17.2625	−	29.8996i	−0.592798	−	1.02676i
$849$		0			0
$850$	52.8235			1.81183
$851$	17.3090			0.593346
$852$		0			0
$853$	26.7708	+	46.3684i	0.916614	+	1.58762i	0.804521	+	0.593925i	$0.202422\pi$
$853$	26.7708	+	46.3684i	0.916614	+	1.58762i	0.112093	+	0.993698i	$0.464244\pi$
$854$		0			0
$855$		0			0
$856$	3.58719	−	6.21320i	0.122608	−	0.212363i
$857$	−27.0777	+	46.8999i	−0.924955	+	1.60207i	−0.133322	+	0.991073i	$0.542564\pi$
$857$	−27.0777	+	46.8999i	−0.924955	+	1.60207i	−0.791633	+	0.610996i	$0.790769\pi$
$858$		0			0
$859$	−0.896461	−	1.55272i	−0.0305869	−	0.0529780i	0.850327	−	0.526255i	$-0.176404\pi$
$859$	−0.896461	−	1.55272i	−0.0305869	−	0.0529780i	−0.880914	+	0.473277i	$0.843071\pi$
$860$	2.94756	−	5.10532i	0.100511	−	0.174090i
$861$		0			0
$862$	27.0858	+	46.9140i	0.922547	+	1.59790i
$863$	−16.2854	+	28.2072i	−0.554363	+	0.960185i	0.443590	+	0.896230i	$0.353705\pi$
$863$	−16.2854	+	28.2072i	−0.554363	+	0.960185i	−0.997953	+	0.0639549i	$0.979629\pi$
$864$		0			0
$865$	7.64833	+	13.2473i	0.260051	+	0.450421i
$866$	−12.7277			−0.432506
$867$		0			0
$868$		0			0
$869$	0.392378	−	0.679618i	0.0133105	−	0.0230545i
$870$		0			0
$871$	29.7770	−	51.5753i	1.00896	−	1.74756i
$872$	−12.1483	−	21.0415i	−0.411394	−	0.712556i
$873$		0			0
$874$	−18.7824			−0.635324
$875$		0			0
$876$		0			0
$877$	18.3647	+	31.8085i	0.620131	+	1.07410i	0.989461	+	0.144800i	$0.0462538\pi$
$877$	18.3647	+	31.8085i	0.620131	+	1.07410i	−0.369330	+	0.929298i	$0.620413\pi$
$878$	−3.89095			−0.131313
$879$		0			0
$880$	2.78567			0.0939049
$881$	−25.3721			−0.854807			−0.427403	−	0.904061i	$-0.640572\pi$
$881$	−25.3721			−0.854807			−0.427403	+	0.904061i	$0.640572\pi$
$882$		0			0
$883$	−16.9381			−0.570012			−0.285006	−	0.958526i	$-0.591996\pi$
$883$	−16.9381			−0.570012			−0.285006	+	0.958526i	$0.591996\pi$
$884$	−33.8268			−1.13772
$885$		0			0
$886$	−63.4807			−2.13267
$887$	−24.0069	−	41.5811i	−0.806071	−	1.39616i	−0.915566	−	0.402169i	$-0.868256\pi$
$887$	−24.0069	−	41.5811i	−0.806071	−	1.39616i	0.109494	−	0.993987i	$-0.465077\pi$
$888$		0			0
$889$		0			0
$890$	−1.36115			−0.0456260
$891$		0			0
$892$	−9.22279	−	15.9743i	−0.308802	−	0.534860i
$893$	16.6778	−	28.8868i	0.558102	−	0.966661i
$894$		0			0
$895$	−6.78159	+	11.7461i	−0.226684	+	0.392627i
$896$		0			0
$897$		0			0
$898$	10.5426			0.351810
$899$	16.6357	+	28.8138i	0.554831	+	0.960995i
$900$		0			0
$901$	−26.2433	+	45.4548i	−0.874292	+	1.51432i
$902$	0.527445	+	0.913562i	0.0175620	+	0.0304183i
$903$		0			0
$904$	−8.51918	+	14.7557i	−0.283344	+	0.490766i
$905$	−6.11677	−	10.5945i	−0.203328	−	0.352175i
$906$		0			0
$907$	12.3887	−	21.4579i	0.411361	−	0.712499i	−0.583678	−	0.811985i	$-0.698387\pi$
$907$	12.3887	−	21.4579i	0.411361	−	0.712499i	0.995039	+	0.0994869i	$0.0317201\pi$
$908$	4.63486	−	8.02781i	0.153813	−	0.266412i
$909$		0			0
$910$		0			0
$911$	15.7916	+	27.3519i	0.523200	+	0.906209i	0.999635	+	0.0269997i	$0.00859533\pi$
$911$	15.7916	+	27.3519i	0.523200	+	0.906209i	−0.476435	+	0.879210i	$0.658071\pi$
$912$		0			0
$913$	−3.34419			−0.110676
$914$	34.2843			1.13402
$915$		0			0
$916$	6.69183	+	11.5906i	0.221104	+	0.382964i
$917$		0			0
$918$		0			0
$919$	−0.796041	+	1.37878i	−0.0262590	+	0.0454819i	−0.878856	−	0.477087i	$-0.841693\pi$
$919$	−0.796041	+	1.37878i	−0.0262590	+	0.0454819i	0.852597	+	0.522569i	$0.175026\pi$
$920$	2.22062	−	3.84623i	0.0732118	−	0.126807i
$921$		0			0
$922$	19.1514	+	33.1712i	0.630718	+	1.09244i
$923$	10.7934	−	18.6947i	0.355268	−	0.615342i
$924$		0			0
$925$	−14.3207	−	24.8042i	−0.470863	−	0.815558i
$926$	23.4796	−	40.6678i	0.771587	−	1.33643i
$927$		0			0
$928$	−12.8702	−	22.2918i	−0.422484	−	0.731764i
$929$	27.0711			0.888175			0.444087	−	0.895983i	$-0.353528\pi$
$929$	27.0711			0.888175			0.444087	+	0.895983i	$0.353528\pi$
$930$		0			0
$931$		0			0
$932$	1.94939	−	3.37644i	0.0638543	−	0.110599i
$933$		0			0
$934$	−17.1003	+	29.6186i	−0.559540	+	0.969151i
$935$	−2.11745	−	3.66754i	−0.0692482	−	0.119941i
$936$		0			0
$937$	−32.6624			−1.06704			−0.533518	−	0.845789i	$-0.679130\pi$
$937$	−32.6624			−1.06704			−0.533518	+	0.845789i	$0.679130\pi$
$938$		0			0
$939$		0			0
$940$	−3.15390	−	5.46272i	−0.102869	−	0.178174i
$941$	4.72285			0.153961			0.0769803	−	0.997033i	$-0.475472\pi$
$941$	4.72285			0.153961			0.0769803	+	0.997033i	$0.475472\pi$
$942$		0			0
$943$	2.61307			0.0850933
$944$	−52.0220			−1.69317
$945$		0			0
$946$	6.98762			0.227187
$947$	−56.7810			−1.84514			−0.922568	−	0.385835i	$-0.873913\pi$
$947$	−56.7810			−1.84514			−0.922568	+	0.385835i	$0.873913\pi$
$948$		0			0
$949$	−22.3942			−0.726945
$950$	15.5397	+	26.9156i	0.504175	+	0.873257i
$951$		0			0
$952$		0			0
$953$	47.1693			1.52796			0.763982	−	0.645238i	$-0.223242\pi$
$953$	47.1693			1.52796			0.763982	+	0.645238i	$0.223242\pi$
$954$		0			0
$955$	1.02728	+	1.77930i	0.0332419	+	0.0575766i
$956$	−4.24426	+	7.35127i	−0.137269	+	0.237757i
$957$		0			0
$958$	8.14681	−	14.1107i	0.263211	−	0.455896i
$959$		0			0
$960$		0			0
$961$	5.90112			0.190359
$962$	29.8081	+	51.6291i	0.961052	+	1.66459i
$963$		0			0
$964$	4.68179	−	8.10910i	0.150790	−	0.261177i
$965$	4.95107	+	8.57550i	0.159380	+	0.276055i
$966$		0			0
$967$	−23.6985	+	41.0469i	−0.762091	+	1.31998i	0.179680	+	0.983725i	$0.442494\pi$
$967$	−23.6985	+	41.0469i	−0.762091	+	1.31998i	−0.941771	+	0.336255i	$0.890840\pi$
$968$	−10.0611	−	17.4264i	−0.323377	−	0.560106i
$969$		0			0
$970$	2.74790	−	4.75950i	0.0882297	−	0.152818i
$971$	−11.3736	+	19.6997i	−0.364997	+	0.632193i	−0.988776	−	0.149408i	$-0.952263\pi$
$971$	−11.3736	+	19.6997i	−0.364997	+	0.632193i	0.623779	+	0.781601i	$0.285597\pi$
$972$		0			0
$973$		0			0
$974$	−11.1106	−	19.2441i	−0.356006	−	0.616620i
$975$		0			0
$976$	58.1202			1.86038
$977$	−35.6849			−1.14166			−0.570831	−	0.821068i	$-0.693379\pi$
$977$	−35.6849			−1.14166			−0.570831	+	0.821068i	$0.693379\pi$
$978$		0			0
$979$	−0.248187	−	0.429872i	−0.00793209	−	0.0137388i
$980$		0			0
$981$		0			0
$982$	13.0371	−	22.5809i	0.416029	−	0.720584i
$983$	−12.0067	+	20.7962i	−0.382954	+	0.663296i	−0.991483	−	0.130236i	$-0.958427\pi$
$983$	−12.0067	+	20.7962i	−0.382954	+	0.663296i	0.608529	+	0.793532i	$0.291760\pi$
$984$		0			0
$985$	8.91591	+	15.4428i	0.284085	+	0.492049i
$986$	−35.2925	+	61.1284i	−1.12394	+	1.94672i
$987$		0			0
$988$	−9.95125	−	17.2361i	−0.316591	−	0.548352i
$989$	8.65452	−	14.9901i	0.275198	−	0.476656i
$990$		0			0
$991$	22.2095	+	38.4679i	0.705507	+	1.22197i	0.966508	+	0.256635i	$0.0826139\pi$
$991$	22.2095	+	38.4679i	0.705507	+	1.22197i	−0.261002	+	0.965338i	$0.584053\pi$
$992$	−28.5485			−0.906416
$993$		0			0
$994$		0			0
$995$	−3.99931	+	6.92701i	−0.126787	+	0.219601i
$996$		0			0
$997$	4.52336	−	7.83470i	0.143256	−	0.248127i	−0.785465	−	0.618906i	$-0.787576\pi$
$997$	4.52336	−	7.83470i	0.143256	−	0.248127i	0.928721	+	0.370779i	$0.120909\pi$
$998$	−4.13465	−	7.16142i	−0.130880	−	0.226691i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.h.g.226.6		12
3.2	odd	2		441.2.h.g.373.1		12
7.2	even	3		1323.2.f.g.442.2		12
7.3	odd	6		1323.2.g.g.361.2		12
7.4	even	3		1323.2.g.g.361.1		12
7.5	odd	6		1323.2.f.g.442.1		12
7.6	odd	2	inner	1323.2.h.g.226.5		12
9.2	odd	6		441.2.g.g.79.6		12
9.7	even	3		1323.2.g.g.667.1		12
21.2	odd	6		441.2.f.g.148.5	✓	12
21.5	even	6		441.2.f.g.148.6	yes	12
21.11	odd	6		441.2.g.g.67.6		12
21.17	even	6		441.2.g.g.67.5		12
21.20	even	2		441.2.h.g.373.2		12
63.2	odd	6		441.2.f.g.295.5	yes	12
63.5	even	6		3969.2.a.be.1.1		6
63.11	odd	6		441.2.h.g.214.1		12
63.16	even	3		1323.2.f.g.883.2		12
63.20	even	6		441.2.g.g.79.5		12
63.23	odd	6		3969.2.a.be.1.2		6
63.25	even	3	inner	1323.2.h.g.802.6		12
63.34	odd	6		1323.2.g.g.667.2		12
63.38	even	6		441.2.h.g.214.2		12
63.40	odd	6		3969.2.a.bd.1.6		6
63.47	even	6		441.2.f.g.295.6	yes	12
63.52	odd	6	inner	1323.2.h.g.802.5		12
63.58	even	3		3969.2.a.bd.1.5		6
63.61	odd	6		1323.2.f.g.883.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.5	✓	12	21.2	odd	6
441.2.f.g.148.6	yes	12	21.5	even	6
441.2.f.g.295.5	yes	12	63.2	odd	6
441.2.f.g.295.6	yes	12	63.47	even	6
441.2.g.g.67.5		12	21.17	even	6
441.2.g.g.67.6		12	21.11	odd	6
441.2.g.g.79.5		12	63.20	even	6
441.2.g.g.79.6		12	9.2	odd	6
441.2.h.g.214.1		12	63.11	odd	6
441.2.h.g.214.2		12	63.38	even	6
441.2.h.g.373.1		12	3.2	odd	2
441.2.h.g.373.2		12	21.20	even	2
1323.2.f.g.442.1		12	7.5	odd	6
1323.2.f.g.442.2		12	7.2	even	3
1323.2.f.g.883.1		12	63.61	odd	6
1323.2.f.g.883.2		12	63.16	even	3
1323.2.g.g.361.1		12	7.4	even	3
1323.2.g.g.361.2		12	7.3	odd	6
1323.2.g.g.667.1		12	9.7	even	3
1323.2.g.g.667.2		12	63.34	odd	6
1323.2.h.g.226.5		12	7.6	odd	2	inner
1323.2.h.g.226.6		12	1.1	even	1	trivial
1323.2.h.g.802.5		12	63.52	odd	6	inner
1323.2.h.g.802.6		12	63.25	even	3	inner
3969.2.a.bd.1.5		6	63.58	even	3
3969.2.a.bd.1.6		6	63.40	odd	6
3969.2.a.be.1.1		6	63.5	even	6
3969.2.a.be.1.2		6	63.23	odd	6

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.69963 q^{2} +0.888736 q^{4} +(0.474636 + 0.822093i) q^{5} -1.88874 q^{8} +O(q^{10})\)	\(q+1.69963 q^{2} +0.888736 q^{4} +(0.474636 + 0.822093i) q^{5} -1.88874 q^{8} +(0.806704 + 1.39725i) q^{10} +(-0.294182 + 0.509538i) q^{11} +(-2.50987 + 4.34722i) q^{13} -4.98762 q^{16} +(3.79121 + 6.56657i) q^{17} +(-2.23061 + 3.86353i) q^{19} +(0.421826 + 0.730623i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(1.23855 + 2.14523i) q^{23} +(2.04944 - 3.54974i) q^{25} +(-4.26584 + 7.38866i) q^{26} +(2.73855 + 4.74331i) q^{29} +6.07463 q^{31} -4.69963 q^{32} +(6.44364 + 11.1607i) q^{34} +(3.49381 - 6.05146i) q^{37} +(-3.79121 + 6.56657i) q^{38} +(-0.896461 - 1.55272i) q^{40} +(0.527445 - 0.913562i) q^{41} +(-3.49381 - 6.05146i) q^{43} +(-0.261450 + 0.452845i) q^{44} +(2.10507 + 3.64610i) q^{46} -7.47680 q^{47} +(3.48329 - 6.03323i) q^{50} +(-2.23061 + 3.86353i) q^{52} +(3.46108 + 5.99476i) q^{53} -0.558517 q^{55} +(4.65452 + 8.06186i) q^{58} +10.4302 q^{59} -11.6529 q^{61} +10.3246 q^{62} +1.98762 q^{64} -4.76509 q^{65} -11.8640 q^{67} +(3.36938 + 5.83594i) q^{68} -4.30037 q^{71} +(2.23061 + 3.86353i) q^{73} +(5.93818 - 10.2852i) q^{74} +(-1.98242 + 3.43366i) q^{76} -1.33379 q^{79} +(-2.36730 - 4.10029i) q^{80} +(0.896461 - 1.55272i) q^{82} +(2.84194 + 4.92238i) q^{83} +(-3.59888 + 6.23345i) q^{85} +(-5.93818 - 10.2852i) q^{86} +(0.555632 - 0.962383i) q^{88} +(-0.421826 + 0.730623i) q^{89} +(1.10074 + 1.90654i) q^{92} -12.7078 q^{94} -4.23491 q^{95} +(-1.70317 - 2.94997i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 12 q^{4} - 24 q^{8}+O(q^{10}) \) 12 * q - 4 * q^2 + 12 * q^4 - 24 * q^8	\( 12 q - 4 q^{2} + 12 q^{4} - 24 q^{8} + 8 q^{11} + 12 q^{16} - 6 q^{22} + 4 q^{23} - 12 q^{25} + 22 q^{29} - 32 q^{32} + 6 q^{37} - 6 q^{43} - 14 q^{44} - 12 q^{46} + 56 q^{50} + 28 q^{53} - 18 q^{58} - 48 q^{64} + 12 q^{65} - 76 q^{71} + 36 q^{74} - 12 q^{79} + 30 q^{85} - 36 q^{86} + 6 q^{88} + 62 q^{92} - 120 q^{95}+O(q^{100}) \) 12 * q - 4 * q^2 + 12 * q^4 - 24 * q^8 + 8 * q^11 + 12 * q^16 - 6 * q^22 + 4 * q^23 - 12 * q^25 + 22 * q^29 - 32 * q^32 + 6 * q^37 - 6 * q^43 - 14 * q^44 - 12 * q^46 + 56 * q^50 + 28 * q^53 - 18 * q^58 - 48 * q^64 + 12 * q^65 - 76 * q^71 + 36 * q^74 - 12 * q^79 + 30 * q^85 - 36 * q^86 + 6 * q^88 + 62 * q^92 - 120 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more