LMFDB - Embedded newform 220.2.m.a.141.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(81,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("220.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.m (of order $5$, degree $4$, 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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.26265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 $ x^8 - 3x^7 + 2x^6 + x^4 + 8x^2 - 24x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.1
Root			$1.33631 - 0.462894i$ of defining polynomial
Character	$\chi$	$=$	220.141
Dual form			220.2.m.a.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.18949 + 1.59076i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(-3.04267 - 2.21063i) q^{7} +(1.33631 - 4.11275i) q^{9} +(2.98808 - 1.43922i) q^{11} +(1.01043 - 3.10977i) q^{13} +(2.18949 + 1.59076i) q^{15} +(-1.20785 - 3.71739i) q^{17} +(-3.49851 + 2.54182i) q^{19} +10.1785 q^{21} -6.41755 q^{23} +(-0.809017 + 0.587785i) q^{25} +(1.10761 + 3.40887i) q^{27} +(-5.25946 - 3.82122i) q^{29} +(1.69594 - 5.21956i) q^{31} +(-4.25294 + 7.90449i) q^{33} +(-1.16220 + 3.57688i) q^{35} +(8.10463 + 5.88836i) q^{37} +(2.73458 + 8.41617i) q^{39} +(-6.48659 + 4.71279i) q^{41} +0.906850 q^{43} -4.32440 q^{45} +(-4.47122 + 3.24853i) q^{47} +(2.20785 + 6.79507i) q^{49} +(8.55805 + 6.21779i) q^{51} +(0.337233 - 1.03790i) q^{53} +(-2.29215 - 2.39709i) q^{55} +(3.61654 - 11.1306i) q^{57} +(5.36707 + 3.89940i) q^{59} +(-2.78882 - 8.58309i) q^{61} +(-13.1577 + 9.55965i) q^{63} -3.26981 q^{65} +13.9684 q^{67} +(14.0512 - 10.2088i) q^{69} +(-3.20544 - 9.86533i) q^{71} +(2.97923 + 2.16454i) q^{73} +(0.836312 - 2.57390i) q^{75} +(-12.2734 - 2.22648i) q^{77} +(2.24798 - 6.91858i) q^{79} +(2.64774 + 1.92370i) q^{81} +(-1.88933 - 5.81476i) q^{83} +(-3.16220 + 2.29747i) q^{85} +17.5942 q^{87} -12.1209 q^{89} +(-9.94895 + 7.22834i) q^{91} +(4.58982 + 14.1260i) q^{93} +(3.49851 + 2.54182i) q^{95} +(-3.81305 + 11.7354i) q^{97} +(-1.92613 - 14.2125i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{3} + 2 q^{5} + q^{7} + 3 q^{9} + 5 q^{11} + 6 q^{13} + q^{15} - 13 q^{17} - 7 q^{19} + 28 q^{21} - 22 q^{23} - 2 q^{25} + 2 q^{27} + 3 q^{29} - 2 q^{31} - 15 q^{33} + 4 q^{35} + 16 q^{37} - 17 q^{39}+ \cdots - 20 q^{99}+O(q^{100}) $ 8 * q - q^3 + 2 * q^5 + q^7 + 3 * q^9 + 5 * q^11 + 6 * q^13 + q^15 - 13 * q^17 - 7 * q^19 + 28 * q^21 - 22 * q^23 - 2 * q^25 + 2 * q^27 + 3 * q^29 - 2 * q^31 - 15 * q^33 + 4 * q^35 + 16 * q^37 - 17 * q^39 - 12 * q^41 + 10 * q^43 - 8 * q^45 - 18 * q^47 + 21 * q^49 + 21 * q^51 - 23 * q^53 - 15 * q^55 - q^57 - 9 * q^59 - 34 * q^61 - 29 * q^63 - 6 * q^65 + 26 * q^67 - q^69 - 26 * q^71 + q^73 - q^75 - 10 * q^77 + 19 * q^79 + 12 * q^81 - 7 * q^83 - 12 * q^85 + 94 * q^87 - 8 * q^89 - 18 * q^91 + 49 * q^93 + 7 * q^95 - 24 * q^97 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.18949	+	1.59076i	−1.26410	+	0.918426i	−0.998952	−	0.0457808i	$-0.985422\pi$
$3$	−2.18949	+	1.59076i	−1.26410	+	0.918426i	−0.265153	+	0.964206i	$0.585422\pi$
$4$		0			0
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$		0			0
$7$	−3.04267	−	2.21063i	−1.15002	−	0.835540i	−0.161539	−	0.986866i	$-0.551646\pi$
$7$	−3.04267	−	2.21063i	−1.15002	−	0.835540i	−0.988484	+	0.151326i	$0.951646\pi$
$8$		0			0
$9$	1.33631	−	4.11275i	0.445437	−	1.37092i
$10$		0			0
$11$	2.98808	−	1.43922i	0.900941	−	0.433941i
$11$	2.98808	−	1.43922i	0.900941	−	0.433941i
$12$		0			0
$13$	1.01043	−	3.10977i	0.280242	−	0.862495i	−0.707543	−	0.706670i	$-0.750196\pi$
$13$	1.01043	−	3.10977i	0.280242	−	0.862495i	0.987785	−	0.155825i	$-0.0498036\pi$
$14$		0			0
$15$	2.18949	+	1.59076i	0.565325	+	0.410732i
$16$		0			0
$17$	−1.20785	−	3.71739i	−0.292947	−	0.901599i	−0.983903	−	0.178702i	$-0.942810\pi$
$17$	−1.20785	−	3.71739i	−0.292947	−	0.901599i	0.690956	−	0.722897i	$-0.257190\pi$
$18$		0			0
$19$	−3.49851	+	2.54182i	−0.802613	+	0.583133i	−0.911680	−	0.410902i	$-0.865214\pi$
$19$	−3.49851	+	2.54182i	−0.802613	+	0.583133i	0.109066	+	0.994034i	$0.465214\pi$
$20$		0			0
$21$	10.1785			2.22113
$22$		0			0
$23$	−6.41755			−1.33815			−0.669075	−	0.743194i	$-0.733310\pi$
$23$	−6.41755			−1.33815			−0.669075	+	0.743194i	$0.733310\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$		0			0
$27$	1.10761	+	3.40887i	0.213159	+	0.656037i
$28$		0			0
$29$	−5.25946	−	3.82122i	−0.976658	−	0.709583i	−0.0196984	−	0.999806i	$-0.506271\pi$
$29$	−5.25946	−	3.82122i	−0.976658	−	0.709583i	−0.956959	+	0.290223i	$0.906271\pi$
$30$		0			0
$31$	1.69594	−	5.21956i	0.304599	−	0.937460i	−0.675227	−	0.737610i	$-0.735954\pi$
$31$	1.69594	−	5.21956i	0.304599	−	0.937460i	0.979826	−	0.199850i	$-0.0640455\pi$
$32$		0			0
$33$	−4.25294	+	7.90449i	−0.740341	+	1.37599i
$34$		0			0
$35$	−1.16220	+	3.57688i	−0.196447	+	0.604603i
$36$		0			0
$37$	8.10463	+	5.88836i	1.33239	+	0.968040i	0.999687	+	0.0250091i	$0.00796149\pi$
$37$	8.10463	+	5.88836i	1.33239	+	0.968040i	0.332705	+	0.943031i	$0.392039\pi$
$38$		0			0
$39$	2.73458	+	8.41617i	0.437883	+	1.34767i
$40$		0			0
$41$	−6.48659	+	4.71279i	−1.01304	+	0.736014i	−0.964844	−	0.262824i	$-0.915346\pi$
$41$	−6.48659	+	4.71279i	−1.01304	+	0.736014i	−0.0481922	+	0.998838i	$0.515346\pi$
$42$		0			0
$43$	0.906850			0.138293			0.0691467	−	0.997607i	$-0.477972\pi$
$43$	0.906850			0.138293			0.0691467	+	0.997607i	$0.477972\pi$
$44$		0			0
$45$	−4.32440			−0.644643
$46$		0			0
$47$	−4.47122	+	3.24853i	−0.652194	+	0.473846i	−0.864018	−	0.503461i	$-0.832060\pi$
$47$	−4.47122	+	3.24853i	−0.652194	+	0.473846i	0.211824	+	0.977308i	$0.432060\pi$
$48$		0			0
$49$	2.20785	+	6.79507i	0.315407	+	0.970724i
$50$		0			0
$51$	8.55805	+	6.21779i	1.19837	+	0.870665i
$52$		0			0
$53$	0.337233	−	1.03790i	0.0463225	−	0.142566i	−0.925220	−	0.379431i	$-0.876120\pi$
$53$	0.337233	−	1.03790i	0.0463225	−	0.142566i	0.971543	+	0.236865i	$0.0761198\pi$
$54$		0			0
$55$	−2.29215	−	2.39709i	−0.309073	−	0.323224i
$56$		0			0
$57$	3.61654	−	11.1306i	0.479023	−	1.47428i
$58$		0			0
$59$	5.36707	+	3.89940i	0.698733	+	0.507659i	0.879519	−	0.475863i	$-0.157864\pi$
$59$	5.36707	+	3.89940i	0.698733	+	0.507659i	−0.180786	+	0.983522i	$0.557864\pi$
$60$		0			0
$61$	−2.78882	−	8.58309i	−0.357071	−	1.09895i	−0.954799	−	0.297253i	$-0.903929\pi$
$61$	−2.78882	−	8.58309i	−0.357071	−	1.09895i	0.597727	−	0.801699i	$-0.296071\pi$
$62$		0			0
$63$	−13.1577	+	9.55965i	−1.65772	+	1.20440i
$64$		0			0
$65$	−3.26981			−0.405570
$66$		0			0
$67$	13.9684			1.70651			0.853254	−	0.521496i	$-0.174626\pi$
$67$	13.9684			1.70651			0.853254	+	0.521496i	$0.174626\pi$
$68$		0			0
$69$	14.0512	−	10.2088i	1.69156	−	1.22899i
$70$		0			0
$71$	−3.20544	−	9.86533i	−0.380416	−	1.17080i	−0.939751	−	0.341858i	$-0.888944\pi$
$71$	−3.20544	−	9.86533i	−0.380416	−	1.17080i	0.559336	−	0.828941i	$-0.311056\pi$
$72$		0			0
$73$	2.97923	+	2.16454i	0.348692	+	0.253340i	0.748320	−	0.663338i	$-0.230861\pi$
$73$	2.97923	+	2.16454i	0.348692	+	0.253340i	−0.399628	+	0.916677i	$0.630861\pi$
$74$		0			0
$75$	0.836312	−	2.57390i	0.0965690	−	0.297209i
$76$		0			0
$77$	−12.2734	−	2.22648i	−1.39868	−	0.253731i
$78$		0			0
$79$	2.24798	−	6.91858i	0.252918	−	0.778401i	−0.741315	−	0.671157i	$-0.765797\pi$
$79$	2.24798	−	6.91858i	0.252918	−	0.778401i	0.994233	−	0.107244i	$-0.0342026\pi$
$80$		0			0
$81$	2.64774	+	1.92370i	0.294193	+	0.213744i
$82$		0			0
$83$	−1.88933	−	5.81476i	−0.207381	−	0.638253i	−0.999607	−	0.0280255i	$-0.991078\pi$
$83$	−1.88933	−	5.81476i	−0.207381	−	0.638253i	0.792226	−	0.610227i	$-0.208922\pi$
$84$		0			0
$85$	−3.16220	+	2.29747i	−0.342989	+	0.249196i
$86$		0			0
$87$	17.5942			1.88630
$88$		0			0
$89$	−12.1209			−1.28482			−0.642408	−	0.766363i	$-0.722064\pi$
$89$	−12.1209			−1.28482			−0.642408	+	0.766363i	$0.722064\pi$
$90$		0			0
$91$	−9.94895	+	7.22834i	−1.04293	+	0.757736i
$92$		0			0
$93$	4.58982	+	14.1260i	0.475942	+	1.46480i
$94$		0			0
$95$	3.49851	+	2.54182i	0.358940	+	0.260785i
$96$		0			0
$97$	−3.81305	+	11.7354i	−0.387157	+	1.19155i	0.547747	+	0.836644i	$0.315486\pi$
$97$	−3.81305	+	11.7354i	−0.387157	+	1.19155i	−0.934904	+	0.354901i	$0.884514\pi$
$98$		0			0
$99$	−1.92613	−	14.2125i	−0.193583	−	1.42841i
$100$		0			0
$101$	0.0257235	−	0.0791689i	0.00255959	−	0.00787760i	−0.949769	−	0.312953i	$-0.898682\pi$
$101$	0.0257235	−	0.0791689i	0.00255959	−	0.00787760i	0.952328	+	0.305076i	$0.0986817\pi$
$102$		0			0
$103$	−8.98269	−	6.52631i	−0.885091	−	0.643056i	0.0495024	−	0.998774i	$-0.484236\pi$
$103$	−8.98269	−	6.52631i	−0.885091	−	0.643056i	−0.934593	+	0.355718i	$0.884236\pi$
$104$		0			0
$105$	−3.14533	−	9.68033i	−0.306953	−	0.944703i
$106$		0			0
$107$	10.4112	−	7.56420i	1.00649	−	0.731259i	0.0430216	−	0.999074i	$-0.486302\pi$
$107$	10.4112	−	7.56420i	1.00649	−	0.731259i	0.963470	+	0.267815i	$0.0863016\pi$
$108$		0			0
$109$	7.51183			0.719503			0.359752	−	0.933048i	$-0.382861\pi$
$109$	7.51183			0.719503			0.359752	+	0.933048i	$0.382861\pi$
$110$		0			0
$111$	−27.1120			−2.57336
$112$		0			0
$113$	−0.378065	+	0.274680i	−0.0355654	+	0.0258398i	−0.605426	−	0.795902i	$-0.706997\pi$
$113$	−0.378065	+	0.274680i	−0.0355654	+	0.0258398i	0.569861	+	0.821741i	$0.306997\pi$
$114$		0			0
$115$	1.98313	+	6.10345i	0.184928	+	0.569150i
$116$		0			0
$117$	−11.4395	−	8.31125i	−1.05758	−	0.768375i
$118$		0			0
$119$	−4.54267	+	13.9809i	−0.416426	+	1.28163i
$120$		0			0
$121$	6.85729	−	8.60102i	0.623390	−	0.781911i
$122$		0			0
$123$	6.70544	−	20.6372i	0.604609	−	1.86080i
$124$		0			0
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$		0			0
$127$	5.57825	+	17.1681i	0.494990	+	1.52342i	0.816972	+	0.576677i	$0.195651\pi$
$127$	5.57825	+	17.1681i	0.494990	+	1.52342i	−0.321982	+	0.946746i	$0.604349\pi$
$128$		0			0
$129$	−1.98554	+	1.44258i	−0.174817	+	0.127012i
$130$		0			0
$131$	6.48010			0.566169			0.283085	−	0.959095i	$-0.408642\pi$
$131$	6.48010			0.566169			0.283085	+	0.959095i	$0.408642\pi$
$132$		0			0
$133$	16.2638			1.41025
$134$		0			0
$135$	2.89976	−	2.10680i	0.249571	−	0.181324i
$136$		0			0
$137$	0.598754	+	1.84278i	0.0511550	+	0.157439i	0.973371	−	0.229237i	$-0.0736231\pi$
$137$	0.598754	+	1.84278i	0.0511550	+	0.157439i	−0.922216	+	0.386676i	$0.873623\pi$
$138$		0			0
$139$	−11.1449	−	8.09724i	−0.945297	−	0.686799i	0.00439260	−	0.999990i	$-0.498602\pi$
$139$	−11.1449	−	8.09724i	−0.945297	−	0.686799i	−0.949690	+	0.313192i	$0.898602\pi$
$140$		0			0
$141$	4.62207	−	14.2253i	0.389248	−	1.19798i
$142$		0			0
$143$	−1.45641	−	10.7465i	−0.121791	−	0.898666i
$144$		0			0
$145$	−2.00894	+	6.18287i	−0.166833	+	0.513459i
$146$		0			0
$147$	−15.6434	−	11.3656i	−1.29025	−	0.937419i
$148$		0			0
$149$	2.99396	+	9.21446i	0.245275	+	0.754878i	0.995591	+	0.0937990i	$0.0299011\pi$
$149$	2.99396	+	9.21446i	0.245275	+	0.754878i	−0.750317	+	0.661079i	$0.770099\pi$
$150$		0			0
$151$	13.4658	−	9.78349i	1.09583	−	0.796169i	0.115458	−	0.993312i	$-0.463166\pi$
$151$	13.4658	−	9.78349i	1.09583	−	0.796169i	0.980375	+	0.197143i	$0.0631663\pi$
$152$		0			0
$153$	−16.9027			−1.36650
$154$		0			0
$155$	−5.48817			−0.440820
$156$		0			0
$157$	−0.775197	+	0.563214i	−0.0618675	+	0.0449494i	−0.618289	−	0.785951i	$-0.712174\pi$
$157$	−0.775197	+	0.563214i	−0.0618675	+	0.0449494i	0.556422	+	0.830900i	$0.312174\pi$
$158$		0			0
$159$	0.912674	+	2.80892i	0.0723798	+	0.222762i
$160$		0			0
$161$	19.5265	+	14.1868i	1.53890	+	1.11808i
$162$		0			0
$163$	−1.37368	+	4.22775i	−0.107595	+	0.331143i	−0.990331	−	0.138726i	$-0.955699\pi$
$163$	−1.37368	+	4.22775i	−0.107595	+	0.331143i	0.882736	+	0.469870i	$0.155699\pi$
$164$		0			0
$165$	8.83184	+	1.60216i	0.687558	+	0.124728i
$166$		0			0
$167$	4.31059	−	13.2666i	0.333563	−	1.02660i	−0.633862	−	0.773446i	$-0.718531\pi$
$167$	4.31059	−	13.2666i	0.333563	−	1.02660i	0.967425	−	0.253156i	$-0.0814687\pi$
$168$		0			0
$169$	1.86751	+	1.35682i	0.143654	+	0.104371i
$170$		0			0
$171$	5.77874	+	17.7851i	0.441911	+	1.36006i
$172$		0			0
$173$	13.0770	−	9.50098i	0.994224	−	0.722346i	0.0333821	−	0.999443i	$-0.489372\pi$
$173$	13.0770	−	9.50098i	0.994224	−	0.722346i	0.960842	+	0.277097i	$0.0893722\pi$
$174$		0			0
$175$	3.76095			0.284301
$176$		0			0
$177$	−17.9542			−1.34952
$178$		0			0
$179$	−14.8705	+	10.8041i	−1.11148	+	0.807534i	−0.982895	−	0.184165i	$-0.941042\pi$
$179$	−14.8705	+	10.8041i	−1.11148	+	0.807534i	−0.128580	+	0.991699i	$0.541042\pi$
$180$		0			0
$181$	3.42315	+	10.5354i	0.254441	+	0.783088i	0.993939	+	0.109930i	$0.0350627\pi$
$181$	3.42315	+	10.5354i	0.254441	+	0.783088i	−0.739499	+	0.673158i	$0.764937\pi$
$182$		0			0
$183$	19.7597	+	14.3563i	1.46068	+	1.06125i
$184$		0			0
$185$	3.09569	−	9.52756i	0.227600	−	0.700480i
$186$		0			0
$187$	−8.95930	−	9.36950i	−0.655169	−	0.685166i
$188$		0			0
$189$	4.16566	−	12.8206i	0.303007	−	0.932561i
$190$		0			0
$191$	−7.78172	−	5.65375i	−0.563066	−	0.409091i	0.269514	−	0.962996i	$-0.413137\pi$
$191$	−7.78172	−	5.65375i	−0.563066	−	0.409091i	−0.832580	+	0.553905i	$0.813137\pi$
$192$		0			0
$193$	−6.07395	−	18.6937i	−0.437213	−	1.34560i	−0.890802	−	0.454391i	$-0.849857\pi$
$193$	−6.07395	−	18.6937i	−0.437213	−	1.34560i	0.453590	−	0.891211i	$-0.350143\pi$
$194$		0			0
$195$	7.15922	−	5.20148i	0.512682	−	0.372485i
$196$		0			0
$197$	−12.1768			−0.867562			−0.433781	−	0.901018i	$-0.642821\pi$
$197$	−12.1768			−0.867562			−0.433781	+	0.901018i	$0.642821\pi$
$198$		0			0
$199$	8.44164			0.598412			0.299206	−	0.954189i	$-0.403278\pi$
$199$	8.44164			0.598412			0.299206	+	0.954189i	$0.403278\pi$
$200$		0			0
$201$	−30.5836	+	22.2203i	−2.15720	+	1.56730i
$202$		0			0
$203$	7.55551	+	23.2535i	0.530293	+	1.63207i
$204$		0			0
$205$	6.48659	+	4.71279i	0.453043	+	0.329155i
$206$		0			0
$207$	−8.57584	+	26.3937i	−0.596062	+	1.83449i
$208$		0			0
$209$	−6.79561	+	12.6303i	−0.470062	+	0.873655i
$210$		0			0
$211$	−6.75302	+	20.7837i	−0.464897	+	1.43081i	0.394215	+	0.919018i	$0.371016\pi$
$211$	−6.75302	+	20.7837i	−0.464897	+	1.43081i	−0.859112	+	0.511788i	$0.828984\pi$
$212$		0			0
$213$	22.7117	+	16.5010i	1.55618	+	1.13063i
$214$		0			0
$215$	−0.280232	−	0.862466i	−0.0191117	−	0.0588197i
$216$		0			0
$217$	−16.6987	+	12.1323i	−1.13358	+	0.823595i
$218$		0			0
$219$	−9.96626			−0.673458
$220$		0			0
$221$	−12.7807			−0.859721
$222$		0			0
$223$	21.3778	−	15.5319i	1.43157	−	1.04009i	0.441844	−	0.897092i	$-0.354324\pi$
$223$	21.3778	−	15.5319i	1.43157	−	1.04009i	0.989722	−	0.143002i	$-0.0456756\pi$
$224$		0			0
$225$	1.33631	+	4.11275i	0.0890875	+	0.274183i
$226$		0			0
$227$	−8.02445	−	5.83010i	−0.532601	−	0.386957i	0.288729	−	0.957411i	$-0.406767\pi$
$227$	−8.02445	−	5.83010i	−0.532601	−	0.386957i	−0.821330	+	0.570454i	$0.806767\pi$
$228$		0			0
$229$	−4.01140	+	12.3458i	−0.265081	+	0.815834i	0.726594	+	0.687067i	$0.241102\pi$
$229$	−4.01140	+	12.3458i	−0.265081	+	0.815834i	−0.991675	+	0.128767i	$0.958898\pi$
$230$		0			0
$231$	30.4142	−	14.6491i	2.00111	−	0.963839i
$232$		0			0
$233$	−2.05800	+	6.33388i	−0.134824	+	0.414946i	−0.995563	−	0.0941012i	$-0.970002\pi$
$233$	−2.05800	+	6.33388i	−0.134824	+	0.414946i	0.860738	+	0.509048i	$0.170002\pi$
$234$		0			0
$235$	4.47122	+	3.24853i	0.291670	+	0.211911i
$236$		0			0
$237$	6.08386	+	18.7242i	0.395189	+	1.21627i
$238$		0			0
$239$	17.7108	−	12.8677i	1.14562	−	0.832340i	0.157726	−	0.987483i	$-0.449584\pi$
$239$	17.7108	−	12.8677i	1.14562	−	0.832340i	0.987892	+	0.155143i	$0.0495837\pi$
$240$		0			0
$241$	10.6517			0.686134			0.343067	−	0.939311i	$-0.388534\pi$
$241$	10.6517			0.686134			0.343067	+	0.939311i	$0.388534\pi$
$242$		0			0
$243$	−19.6102			−1.25800
$244$		0			0
$245$	5.78023	−	4.19958i	0.369285	−	0.268302i
$246$		0			0
$247$	4.36948	+	13.4479i	0.278023	+	0.855668i
$248$		0			0
$249$	13.3866	+	9.72591i	0.848339	+	0.616354i
$250$		0			0
$251$	−3.75973	+	11.5713i	−0.237312	+	0.730372i	0.759494	+	0.650514i	$0.225447\pi$
$251$	−3.75973	+	11.5713i	−0.237312	+	0.730372i	−0.996806	+	0.0798576i	$0.974553\pi$
$252$		0			0
$253$	−19.1762	+	9.23626i	−1.20560	+	0.580679i
$254$		0			0
$255$	3.26889	−	10.0606i	0.204706	−	0.630019i
$256$		0			0
$257$	−4.94633	−	3.59372i	−0.308544	−	0.224170i	0.422728	−	0.906257i	$-0.361073\pi$
$257$	−4.94633	−	3.59372i	−0.308544	−	0.224170i	−0.731271	+	0.682087i	$0.761073\pi$
$258$		0			0
$259$	−11.6428	−	35.8327i	−0.723445	−	2.22654i
$260$		0			0
$261$	−22.7440	+	16.5245i	−1.40782	+	1.02284i
$262$		0			0
$263$	0.446463			0.0275301			0.0137650	−	0.999905i	$-0.495618\pi$
$263$	0.446463			0.0275301			0.0137650	+	0.999905i	$0.495618\pi$
$264$		0			0
$265$	−1.09131			−0.0670385
$266$		0			0
$267$	26.5387	−	19.2815i	1.62414	−	1.18001i
$268$		0			0
$269$	0.00246118	+	0.00757473i	0.000150061	+	0.000461840i	0.951132	−	0.308786i	$-0.0999227\pi$
$269$	0.00246118	+	0.00757473i	0.000150061	+	0.000461840i	−0.950981	+	0.309248i	$0.899923\pi$
$270$		0			0
$271$	−15.0380	−	10.9257i	−0.913493	−	0.663691i	0.0284029	−	0.999597i	$-0.490958\pi$
$271$	−15.0380	−	10.9257i	−0.913493	−	0.663691i	−0.941896	+	0.335905i	$0.890958\pi$
$272$		0			0
$273$	10.2846	−	31.6528i	0.622453	−	1.91571i
$274$		0			0
$275$	−1.57146	+	2.92070i	−0.0947625	+	0.176125i
$276$		0			0
$277$	2.15063	−	6.61897i	0.129219	−	0.397695i	−0.865427	−	0.501035i	$-0.832953\pi$
$277$	2.15063	−	6.61897i	0.129219	−	0.397695i	0.994646	+	0.103339i	$0.0329528\pi$
$278$		0			0
$279$	−19.2004	−	13.9499i	−1.14950	−	0.835159i
$280$		0			0
$281$	−6.91031	−	21.2678i	−0.412235	−	1.26873i	−0.914701	−	0.404131i	$-0.867574\pi$
$281$	−6.91031	−	21.2678i	−0.412235	−	1.26873i	0.502466	−	0.864597i	$-0.332426\pi$
$282$		0			0
$283$	18.8891	−	13.7237i	1.12284	−	0.815792i	0.138204	−	0.990404i	$-0.455867\pi$
$283$	18.8891	−	13.7237i	1.12284	−	0.815792i	0.984637	+	0.174612i	$0.0558671\pi$
$284$		0			0
$285$	−11.7034			−0.693249
$286$		0			0
$287$	30.1548			1.77998
$288$		0			0
$289$	1.39323	−	1.01224i	0.0819548	−	0.0595436i
$290$		0			0
$291$	−10.3195	−	31.7601i	−0.604939	−	1.86181i
$292$		0			0
$293$	−2.83254	−	2.05796i	−0.165479	−	0.120227i	0.501964	−	0.864889i	$-0.332611\pi$
$293$	−2.83254	−	2.05796i	−0.165479	−	0.120227i	−0.667443	+	0.744661i	$0.732611\pi$
$294$		0			0
$295$	2.05004	−	6.30937i	0.119358	−	0.367346i
$296$		0			0
$297$	8.21574	+	8.59189i	0.476725	+	0.498552i
$298$		0			0
$299$	−6.48445	+	19.9571i	−0.375006	+	1.15415i
$300$		0			0
$301$	−2.75925	−	2.00471i	−0.159040	−	0.115550i
$302$		0			0
$303$	0.0696172	+	0.214260i	0.00399940	+	0.0123089i
$304$		0			0
$305$	−7.30122	+	5.30464i	−0.418066	+	0.303743i
$306$		0			0
$307$	−8.26358			−0.471628			−0.235814	−	0.971798i	$-0.575776\pi$
$307$	−8.26358			−0.471628			−0.235814	+	0.971798i	$0.575776\pi$
$308$		0			0
$309$	30.0493			1.70945
$310$		0			0
$311$	−9.35397	+	6.79606i	−0.530415	+	0.385369i	−0.820513	−	0.571628i	$-0.806312\pi$
$311$	−9.35397	+	6.79606i	−0.530415	+	0.385369i	0.290098	+	0.956997i	$0.406312\pi$
$312$		0			0
$313$	−5.96859	−	18.3694i	−0.337364	−	1.03830i	−0.965546	−	0.260234i	$-0.916200\pi$
$313$	−5.96859	−	18.3694i	−0.337364	−	1.03830i	0.628181	−	0.778067i	$-0.283800\pi$
$314$		0			0
$315$	13.1577	+	9.55965i	0.741354	+	0.538625i
$316$		0			0
$317$	6.91381	−	21.2785i	0.388318	−	1.19512i	−0.545726	−	0.837964i	$-0.683746\pi$
$317$	6.91381	−	21.2785i	0.388318	−	1.19512i	0.934044	−	0.357157i	$-0.116254\pi$
$318$		0			0
$319$	−21.2153	−	3.84862i	−1.18783	−	0.215481i
$320$		0			0
$321$	−10.7625	+	33.1235i	−0.600704	+	1.84878i
$322$		0			0
$323$	13.6746	+	9.93518i	0.760875	+	0.552808i
$324$		0			0
$325$	1.01043	+	3.10977i	0.0560483	+	0.172499i
$326$		0			0
$327$	−16.4471	+	11.9495i	−0.909527	+	0.660810i
$328$		0			0
$329$	20.7858			1.14596
$330$		0			0
$331$	−5.17876			−0.284650			−0.142325	−	0.989820i	$-0.545458\pi$
$331$	−5.17876			−0.284650			−0.142325	+	0.989820i	$0.545458\pi$
$332$		0			0
$333$	35.0476	−	25.4636i	1.92060	−	1.39540i
$334$		0			0
$335$	−4.31646	−	13.2847i	−0.235834	−	0.725821i
$336$		0			0
$337$	−4.47108	−	3.24843i	−0.243555	−	0.176953i	0.459310	−	0.888276i	$-0.348097\pi$
$337$	−4.47108	−	3.24843i	−0.243555	−	0.176953i	−0.702866	+	0.711322i	$0.748097\pi$
$338$		0			0
$339$	0.390820	−	1.20282i	0.0212264	−	0.0653283i
$340$		0			0
$341$	−2.44448	−	18.0373i	−0.132376	−	0.976774i
$342$		0			0
$343$	0.168240	−	0.517788i	0.00908408	−	0.0279579i
$344$		0			0
$345$	−14.0512	−	10.2088i	−0.756490	−	0.549622i
$346$		0			0
$347$	2.65383	+	8.16765i	0.142465	+	0.438463i	0.996676	−	0.0814636i	$-0.0259594\pi$
$347$	2.65383	+	8.16765i	0.142465	+	0.438463i	−0.854211	+	0.519926i	$0.825959\pi$
$348$		0			0
$349$	−11.8706	+	8.62451i	−0.635419	+	0.461659i	−0.858273	−	0.513193i	$-0.828463\pi$
$349$	−11.8706	+	8.62451i	−0.635419	+	0.461659i	0.222854	+	0.974852i	$0.428463\pi$
$350$		0			0
$351$	11.7200			0.625565
$352$		0			0
$353$	5.79041			0.308192			0.154096	−	0.988056i	$-0.450753\pi$
$353$	5.79041			0.308192			0.154096	+	0.988056i	$0.450753\pi$
$354$		0			0
$355$	−8.39195	+	6.09711i	−0.445399	+	0.323601i
$356$		0			0
$357$	−12.2941	−	37.8374i	−0.650674	−	2.00257i
$358$		0			0
$359$	9.19282	+	6.67898i	0.485179	+	0.352503i	0.803327	−	0.595538i	$-0.203061\pi$
$359$	9.19282	+	6.67898i	0.485179	+	0.352503i	−0.318148	+	0.948041i	$0.603061\pi$
$360$		0			0
$361$	−0.0925809	+	0.284935i	−0.00487268	+	0.0149966i
$362$		0			0
$363$	−1.33185	+	29.7402i	−0.0699038	+	1.56095i
$364$		0			0
$365$	1.13796	−	3.50229i	0.0595638	−	0.183318i
$366$		0			0
$367$	3.70890	+	2.69468i	0.193603	+	0.140661i	0.680364	−	0.732874i	$-0.261822\pi$
$367$	3.70890	+	2.69468i	0.193603	+	0.140661i	−0.486761	+	0.873535i	$0.661822\pi$
$368$		0			0
$369$	10.7144	+	32.9755i	0.557768	+	1.71663i
$370$		0			0
$371$	−3.32050	+	2.41248i	−0.172392	+	0.125250i
$372$		0			0
$373$	−22.8487			−1.18306			−0.591530	−	0.806283i	$-0.701476\pi$
$373$	−22.8487			−1.18306			−0.591530	+	0.806283i	$0.701476\pi$
$374$		0			0
$375$	−2.70636			−0.139756
$376$		0			0
$377$	−17.1974	+	12.4947i	−0.885712	+	0.643508i
$378$		0			0
$379$	−6.50498	−	20.0203i	−0.334139	−	1.02837i	−0.967145	−	0.254226i	$-0.918179\pi$
$379$	−6.50498	−	20.0203i	−0.334139	−	1.02837i	0.633006	−	0.774147i	$-0.281821\pi$
$380$		0			0
$381$	−39.5239	−	28.7158i	−2.02487	−	1.47115i
$382$		0			0
$383$	−0.0803134	+	0.247179i	−0.00410382	+	0.0126303i	−0.953087	−	0.302695i	$-0.902114\pi$
$383$	−0.0803134	+	0.247179i	−0.00410382	+	0.0126303i	0.948984	+	0.315325i	$0.102114\pi$
$384$		0			0
$385$	1.67517	+	12.3607i	0.0853744	+	0.629958i
$386$		0			0
$387$	1.21183	−	3.72964i	0.0616010	−	0.189588i
$388$		0			0
$389$	12.7514	+	9.26447i	0.646524	+	0.469727i	0.862085	−	0.506763i	$-0.169158\pi$
$389$	12.7514	+	9.26447i	0.646524	+	0.469727i	−0.215561	+	0.976490i	$0.569158\pi$
$390$		0			0
$391$	7.75145	+	23.8565i	0.392008	+	1.20648i
$392$		0			0
$393$	−14.1881	+	10.3083i	−0.715697	+	0.519984i
$394$		0			0
$395$	−7.27463			−0.366026
$396$		0			0
$397$	7.62978			0.382928			0.191464	−	0.981500i	$-0.438677\pi$
$397$	7.62978			0.382928			0.191464	+	0.981500i	$0.438677\pi$
$398$		0			0
$399$	−35.6096	+	25.8719i	−1.78271	+	1.29521i
$400$		0			0
$401$	−9.31703	−	28.6749i	−0.465270	−	1.43195i	−0.858642	−	0.512575i	$-0.828691\pi$
$401$	−9.31703	−	28.6749i	−0.465270	−	1.43195i	0.393372	−	0.919379i	$-0.371309\pi$
$402$		0			0
$403$	−14.5180	−	10.5479i	−0.723193	−	0.525431i
$404$		0			0
$405$	1.01135	−	3.11260i	0.0502542	−	0.154667i
$406$		0			0
$407$	32.6919	+	5.93057i	1.62048	+	0.293967i
$408$		0			0
$409$	9.62526	−	29.6235i	0.475939	−	1.46479i	−0.368749	−	0.929529i	$-0.620214\pi$
$409$	9.62526	−	29.6235i	0.475939	−	1.46479i	0.844688	−	0.535259i	$-0.179786\pi$
$410$		0			0
$411$	−4.24238	−	3.08227i	−0.209261	−	0.152037i
$412$		0			0
$413$	−7.71010	−	23.7292i	−0.379389	−	1.16764i
$414$		0			0
$415$	−4.94633	+	3.59372i	−0.242806	+	0.176409i
$416$		0			0
$417$	37.2824			1.82573
$418$		0			0
$419$	13.3733			0.653328			0.326664	−	0.945141i	$-0.394075\pi$
$419$	13.3733			0.653328			0.326664	+	0.945141i	$0.394075\pi$
$420$		0			0
$421$	8.87736	−	6.44978i	0.432656	−	0.314343i	−0.350054	−	0.936730i	$-0.613837\pi$
$421$	8.87736	−	6.44978i	0.432656	−	0.314343i	0.782710	+	0.622386i	$0.213837\pi$
$422$		0			0
$423$	7.38543	+	22.7300i	0.359092	+	1.10517i
$424$		0			0
$425$	3.16220	+	2.29747i	0.153389	+	0.111444i
$426$		0			0
$427$	−10.4886	+	32.2806i	−0.507579	+	1.56217i
$428$		0			0
$429$	20.2839	+	21.2126i	0.979314	+	1.02415i
$430$		0			0
$431$	−5.01099	+	15.4223i	−0.241371	+	0.742864i	0.754841	+	0.655908i	$0.227714\pi$
$431$	−5.01099	+	15.4223i	−0.241371	+	0.742864i	−0.996212	+	0.0869561i	$0.972286\pi$
$432$		0			0
$433$	17.3649	+	12.6163i	0.834503	+	0.606302i	0.920830	−	0.389965i	$-0.127513\pi$
$433$	17.3649	+	12.6163i	0.834503	+	0.606302i	−0.0863271	+	0.996267i	$0.527513\pi$
$434$		0			0
$435$	−5.43691	−	16.7331i	−0.260680	−	0.802290i
$436$		0			0
$437$	22.4518	−	16.3122i	1.07402	−	0.780319i
$438$		0			0
$439$	5.94741			0.283855			0.141927	−	0.989877i	$-0.454670\pi$
$439$	5.94741			0.283855			0.141927	+	0.989877i	$0.454670\pi$
$440$		0			0
$441$	30.8968			1.47127
$442$		0			0
$443$	19.2068	−	13.9546i	0.912545	−	0.663003i	−0.0291124	−	0.999576i	$-0.509268\pi$
$443$	19.2068	−	13.9546i	0.912545	−	0.663003i	0.941657	+	0.336574i	$0.109268\pi$
$444$		0			0
$445$	3.74557	+	11.5277i	0.177557	+	0.546465i
$446$		0			0
$447$	−21.2132	−	15.4123i	−1.00335	−	0.728978i
$448$		0			0
$449$	10.6354	−	32.7325i	0.501917	−	1.54474i	−0.303975	−	0.952680i	$-0.598314\pi$
$449$	10.6354	−	32.7325i	0.501917	−	1.54474i	0.805892	−	0.592063i	$-0.201686\pi$
$450$		0			0
$451$	−12.5998	+	23.4178i	−0.593299	+	1.10270i
$452$		0			0
$453$	−13.9201	+	42.8418i	−0.654025	+	2.01288i
$454$		0			0
$455$	9.94895	+	7.22834i	0.466414	+	0.338870i
$456$		0			0
$457$	4.58276	+	14.1043i	0.214372	+	0.659770i	0.999198	+	0.0400529i	$0.0127526\pi$
$457$	4.58276	+	14.1043i	0.214372	+	0.659770i	−0.784825	+	0.619717i	$0.787247\pi$
$458$		0			0
$459$	11.3343	−	8.23482i	0.529038	−	0.384368i
$460$		0			0
$461$	29.8441			1.38998			0.694990	−	0.719020i	$-0.255409\pi$
$461$	29.8441			1.38998			0.694990	+	0.719020i	$0.255409\pi$
$462$		0			0
$463$	−6.87337			−0.319433			−0.159716	−	0.987163i	$-0.551058\pi$
$463$	−6.87337			−0.319433			−0.159716	+	0.987163i	$0.551058\pi$
$464$		0			0
$465$	12.0163	−	8.73035i	0.557243	−	0.404860i
$466$		0			0
$467$	−0.435503	−	1.34034i	−0.0201527	−	0.0620236i	0.940474	−	0.339864i	$-0.110381\pi$
$467$	−0.435503	−	1.34034i	−0.0201527	−	0.0620236i	−0.960627	+	0.277841i	$0.910381\pi$
$468$		0			0
$469$	−42.5012	−	30.8789i	−1.96252	−	1.42586i
$470$		0			0
$471$	0.801351	−	2.46631i	0.0369243	−	0.113641i
$472$		0			0
$473$	2.70974	−	1.30516i	0.124594	−	0.0600111i
$474$		0			0
$475$	1.33631	−	4.11275i	0.0613142	−	0.188706i
$476$		0			0
$477$	−3.81795	−	2.77391i	−0.174812	−	0.127008i
$478$		0			0
$479$	−7.19055	−	22.1302i	−0.328544	−	1.01116i	−0.969815	−	0.243841i	$-0.921592\pi$
$479$	−7.19055	−	22.1302i	−0.328544	−	1.01116i	0.641271	−	0.767315i	$-0.278408\pi$
$480$		0			0
$481$	26.5006	−	19.2538i	1.20832	−	0.877897i
$482$		0			0
$483$	−65.3210			−2.97221
$484$		0			0
$485$	12.3393			0.560298
$486$		0			0
$487$	−15.0917	+	10.9647i	−0.683868	+	0.496859i	−0.874639	−	0.484775i	$-0.838901\pi$
$487$	−15.0917	+	10.9647i	−0.683868	+	0.496859i	0.190770	+	0.981635i	$0.438901\pi$
$488$		0			0
$489$	−3.71768	−	11.4418i	−0.168119	−	0.517418i
$490$		0			0
$491$	33.9898	+	24.6951i	1.53394	+	1.11447i	0.953997	+	0.299815i	$0.0969251\pi$
$491$	33.9898	+	24.6951i	1.53394	+	1.11447i	0.579943	+	0.814657i	$0.303075\pi$
$492$		0			0
$493$	−7.85231	+	24.1669i	−0.353650	+	1.08842i
$494$		0			0
$495$	−12.9217	+	6.22375i	−0.580785	+	0.279737i
$496$		0			0
$497$	−12.0555	+	37.1030i	−0.540764	+	1.66430i
$498$		0			0
$499$	4.22493	+	3.06959i	0.189134	+	0.137414i	0.678323	−	0.734764i	$-0.262707\pi$
$499$	4.22493	+	3.06959i	0.189134	+	0.137414i	−0.489189	+	0.872178i	$0.662707\pi$
$500$		0			0
$501$	11.6660	+	35.9043i	0.521199	+	1.60409i
$502$		0			0
$503$	−23.3289	+	16.9494i	−1.04018	+	0.755737i	−0.970321	−	0.241820i	$-0.922256\pi$
$503$	−23.3289	+	16.9494i	−1.04018	+	0.755737i	−0.0698614	+	0.997557i	$0.522256\pi$
$504$		0			0
$505$	−0.0832431			−0.00370427
$506$		0			0
$507$	−6.24728			−0.277451
$508$		0			0
$509$	−4.46973	+	3.24745i	−0.198117	+	0.143940i	−0.682421	−	0.730959i	$-0.739073\pi$
$509$	−4.46973	+	3.24745i	−0.198117	+	0.143940i	0.484304	+	0.874900i	$0.339073\pi$
$510$		0			0
$511$	−4.27983	−	13.1720i	−0.189329	−	0.582693i
$512$		0			0
$513$	−12.5397	−	9.11062i	−0.553641	−	0.402244i
$514$		0			0
$515$	−3.43108	+	10.5598i	−0.151192	+	0.465320i
$516$		0			0
$517$	−8.68502	+	16.1419i	−0.381967	+	0.709921i
$518$		0			0
$519$	−13.5182	+	41.6047i	−0.593382	+	1.82624i
$520$		0			0
$521$	23.8297	+	17.3133i	1.04400	+	0.758509i	0.971062	−	0.238828i	$-0.0767631\pi$
$521$	23.8297	+	17.3133i	1.04400	+	0.758509i	0.0729362	+	0.997337i	$0.476763\pi$
$522$		0			0
$523$	−0.684593	−	2.10696i	−0.0299351	−	0.0921309i	0.934973	−	0.354720i	$-0.115424\pi$
$523$	−0.684593	−	2.10696i	−0.0299351	−	0.0921309i	−0.964908	+	0.262589i	$0.915424\pi$
$524$		0			0
$525$	−8.23458	+	5.98277i	−0.359386	+	0.261110i
$526$		0			0
$527$	−21.4515			−0.934444
$528$		0			0
$529$	18.1849			0.790648
$530$		0			0
$531$	23.2093	−	16.8626i	1.00720	−	0.731773i
$532$		0			0
$533$	8.10146	+	24.9337i	0.350913	+	1.08000i
$534$		0			0
$535$	−10.4112	−	7.56420i	−0.450117	−	0.327029i
$536$		0			0
$537$	15.3722	−	47.3109i	0.663361	−	2.04162i
$538$		0			0
$539$	16.3768	+	17.1267i	0.705401	+	0.737697i
$540$		0			0
$541$	10.4175	−	32.0616i	0.447882	−	1.37844i	−0.431411	−	0.902156i	$-0.641984\pi$
$541$	10.4175	−	32.0616i	0.447882	−	1.37844i	0.879292	−	0.476282i	$-0.158016\pi$
$542$		0			0
$543$	−24.2542	−	17.6217i	−1.04085	−	0.756220i
$544$		0			0
$545$	−2.32128	−	7.14418i	−0.0994329	−	0.306023i
$546$		0			0
$547$	22.7092	−	16.4992i	0.970976	−	0.705455i	0.0153018	−	0.999883i	$-0.495129\pi$
$547$	22.7092	−	16.4992i	0.970976	−	0.705455i	0.955674	+	0.294428i	$0.0951291\pi$
$548$		0			0
$549$	−39.0268			−1.66562
$550$		0			0
$551$	28.1131			1.19766
$552$		0			0
$553$	−22.1343	+	16.0815i	−0.941247	+	0.683856i
$554$		0			0
$555$	8.37807	+	25.7850i	0.355629	+	1.09451i
$556$		0			0
$557$	−12.5552	−	9.12189i	−0.531981	−	0.386507i	0.289117	−	0.957294i	$-0.406638\pi$
$557$	−12.5552	−	9.12189i	−0.531981	−	0.386507i	−0.821098	+	0.570787i	$0.806638\pi$
$558$		0			0
$559$	0.916305	−	2.82010i	0.0387556	−	0.119277i
$560$		0			0
$561$	34.5209	+	6.26236i	1.45748	+	0.264397i
$562$		0			0
$563$	−6.22486	+	19.1581i	−0.262346	+	0.807419i	0.729946	+	0.683504i	$0.239545\pi$
$563$	−6.22486	+	19.1581i	−0.262346	+	0.807419i	−0.992293	+	0.123915i	$0.960455\pi$
$564$		0			0
$565$	0.378065	+	0.274680i	0.0159053	+	0.0115559i
$566$		0			0
$567$	−3.80363	−	11.7064i	−0.159737	−	0.491621i
$568$		0			0
$569$	−25.4623	+	18.4994i	−1.06743	+	0.775536i	−0.975449	−	0.220224i	$-0.929321\pi$
$569$	−25.4623	+	18.4994i	−1.06743	+	0.775536i	−0.0919848	+	0.995760i	$0.529321\pi$
$570$		0			0
$571$	−14.3295			−0.599673			−0.299836	−	0.953991i	$-0.596932\pi$
$571$	−14.3295			−0.599673			−0.299836	+	0.953991i	$0.596932\pi$
$572$		0			0
$573$	26.0318			1.08749
$574$		0			0
$575$	5.19190	−	3.77214i	0.216517	−	0.157309i
$576$		0			0
$577$	−3.54175	−	10.9004i	−0.147445	−	0.453789i	0.849872	−	0.526989i	$-0.176679\pi$
$577$	−3.54175	−	10.9004i	−0.147445	−	0.453789i	−0.997317	+	0.0731994i	$0.976679\pi$
$578$		0			0
$579$	43.0361	+	31.2675i	1.78852	+	1.29943i
$580$		0			0
$581$	−7.10568	+	21.8690i	−0.294793	+	0.907281i
$582$		0			0
$583$	−0.486080	−	3.58667i	−0.0201314	−	0.148545i
$584$		0			0
$585$	−4.36948	+	13.4479i	−0.180656	+	0.556001i
$586$		0			0
$587$	−7.62242	−	5.53801i	−0.314611	−	0.228578i	0.419262	−	0.907865i	$-0.362289\pi$
$587$	−7.62242	−	5.53801i	−0.314611	−	0.228578i	−0.733872	+	0.679287i	$0.762289\pi$
$588$		0			0
$589$	7.33390	+	22.5714i	0.302188	+	0.930039i
$590$		0			0
$591$	26.6611	−	19.3704i	1.09669	−	0.796792i
$592$		0			0
$593$	−28.2270			−1.15914			−0.579571	−	0.814922i	$-0.696780\pi$
$593$	−28.2270			−1.15914			−0.579571	+	0.814922i	$0.696780\pi$
$594$		0			0
$595$	14.7004			0.602658
$596$		0			0
$597$	−18.4829	+	13.4286i	−0.756455	+	0.549597i
$598$		0			0
$599$	1.24633	+	3.83580i	0.0509235	+	0.156726i	0.973284	−	0.229603i	$-0.0737428\pi$
$599$	1.24633	+	3.83580i	0.0509235	+	0.156726i	−0.922361	+	0.386329i	$0.873743\pi$
$600$		0			0
$601$	−30.0829	−	21.8565i	−1.22711	−	0.891544i	−0.230435	−	0.973088i	$-0.574015\pi$
$601$	−30.0829	−	21.8565i	−1.22711	−	0.891544i	−0.996670	+	0.0815436i	$0.974015\pi$
$602$		0			0
$603$	18.6661	−	57.4483i	0.760142	−	2.33948i
$604$		0			0
$605$	−10.2991	−	3.86381i	−0.418717	−	0.157086i
$606$		0			0
$607$	−5.60247	+	17.2426i	−0.227397	+	0.699856i	0.770642	+	0.637268i	$0.219936\pi$
$607$	−5.60247	+	17.2426i	−0.227397	+	0.699856i	−0.998039	+	0.0625883i	$0.980064\pi$
$608$		0			0
$609$	−53.5334	−	38.8943i	−2.16928	−	1.57608i
$610$		0			0
$611$	5.58435	+	17.1868i	0.225918	+	0.695306i
$612$		0			0
$613$	6.90505	−	5.01682i	0.278893	−	0.202627i	−0.439542	−	0.898222i	$-0.644859\pi$
$613$	6.90505	−	5.01682i	0.278893	−	0.202627i	0.718434	+	0.695595i	$0.244859\pi$
$614$		0			0
$615$	−21.6993			−0.874999
$616$		0			0
$617$	−24.5659			−0.988985			−0.494492	−	0.869182i	$-0.664646\pi$
$617$	−24.5659			−0.988985			−0.494492	+	0.869182i	$0.664646\pi$
$618$		0			0
$619$	30.9640	−	22.4967i	1.24455	−	0.904218i	0.246657	−	0.969103i	$-0.420668\pi$
$619$	30.9640	−	22.4967i	1.24455	−	0.904218i	0.997893	+	0.0648846i	$0.0206679\pi$
$620$		0			0
$621$	−7.10813	−	21.8766i	−0.285239	−	0.877876i
$622$		0			0
$623$	36.8800	+	26.7949i	1.47757	+	1.07352i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$		0			0
$627$	−5.21281	−	38.4641i	−0.208179	−	1.53611i
$628$		0			0
$629$	12.1001	−	37.2403i	0.482463	−	1.48487i
$630$		0			0
$631$	−16.7407	−	12.1628i	−0.666435	−	0.484194i	0.202395	−	0.979304i	$-0.435128\pi$
$631$	−16.7407	−	12.1628i	−0.666435	−	0.484194i	−0.868830	+	0.495110i	$0.835128\pi$
$632$		0			0
$633$	−18.2761	−	56.2481i	−0.726410	−	2.23566i
$634$		0			0
$635$	14.6041	−	10.6105i	0.579544	−	0.421064i
$636$		0			0
$637$	23.3620			0.925635
$638$		0			0
$639$	−44.8571			−1.77452
$640$		0			0
$641$	6.75967	−	4.91119i	0.266991	−	0.193980i	−0.446232	−	0.894917i	$-0.647234\pi$
$641$	6.75967	−	4.91119i	0.266991	−	0.193980i	0.713223	+	0.700937i	$0.247234\pi$
$642$		0			0
$643$	9.08552	+	27.9623i	0.358298	+	1.10273i	0.954073	+	0.299576i	$0.0968451\pi$
$643$	9.08552	+	27.9623i	0.358298	+	1.10273i	−0.595775	+	0.803152i	$0.703155\pi$
$644$		0			0
$645$	1.98554	+	1.44258i	0.0781806	+	0.0568016i
$646$		0			0
$647$	7.26160	−	22.3489i	0.285483	−	0.878626i	−0.700770	−	0.713387i	$-0.747160\pi$
$647$	7.26160	−	22.3489i	0.285483	−	0.878626i	0.986253	−	0.165240i	$-0.0528397\pi$
$648$		0			0
$649$	21.6494	+	3.92736i	0.849812	+	0.154162i
$650$		0			0
$651$	17.2621	−	53.1272i	0.676554	−	2.08222i
$652$		0			0
$653$	−12.4733	−	9.06240i	−0.488119	−	0.354639i	0.316342	−	0.948645i	$-0.397545\pi$
$653$	−12.4733	−	9.06240i	−0.488119	−	0.354639i	−0.804460	+	0.594006i	$0.797545\pi$
$654$		0			0
$655$	−2.00246	−	6.16294i	−0.0782426	−	0.240806i
$656$		0			0
$657$	12.8834	−	9.36032i	0.502628	−	0.365181i
$658$		0			0
$659$	12.2785			0.478301			0.239151	−	0.970982i	$-0.423131\pi$
$659$	12.2785			0.478301			0.239151	+	0.970982i	$0.423131\pi$
$660$		0			0
$661$	25.8163			1.00414			0.502070	−	0.864827i	$-0.332572\pi$
$661$	25.8163			1.00414			0.502070	+	0.864827i	$0.332572\pi$
$662$		0			0
$663$	27.9832	−	20.3310i	1.08678	−	0.789589i
$664$		0			0
$665$	−5.02580	−	15.4678i	−0.194892	−	0.599817i
$666$		0			0
$667$	33.7528	+	24.5229i	1.30692	+	0.949529i
$668$		0			0
$669$	−22.0991	+	68.0140i	−0.854401	+	2.62957i
$670$		0			0
$671$	−20.6862	−	21.6333i	−0.798581	−	0.835144i
$672$		0			0
$673$	9.99147	−	30.7506i	0.385143	−	1.18535i	−0.551234	−	0.834351i	$-0.685843\pi$
$673$	9.99147	−	30.7506i	0.385143	−	1.18535i	0.936377	−	0.350997i	$-0.114157\pi$
$674$		0			0
$675$	−2.89976	−	2.10680i	−0.111612	−	0.0810906i
$676$		0			0
$677$	−9.73155	−	29.9506i	−0.374014	−	1.15110i	−0.944142	−	0.329540i	$-0.893106\pi$
$677$	−9.73155	−	29.9506i	−0.374014	−	1.15110i	0.570128	−	0.821556i	$-0.306894\pi$
$678$		0			0
$679$	37.5444	−	27.2776i	1.44082	−	1.04682i
$680$		0			0
$681$	26.8438			1.02866
$682$		0			0
$683$	−13.3758			−0.511812			−0.255906	−	0.966702i	$-0.582374\pi$
$683$	−13.3758			−0.511812			−0.255906	+	0.966702i	$0.582374\pi$
$684$		0			0
$685$	1.56756	−	1.13890i	0.0598933	−	0.0435150i
$686$		0			0
$687$	−10.8563	−	33.4122i	−0.414193	−	1.27476i
$688$		0			0
$689$	−2.88687	−	2.09743i	−0.109981	−	0.0799058i
$690$		0			0
$691$	−8.48261	+	26.1068i	−0.322694	+	0.993149i	0.649777	+	0.760125i	$0.274862\pi$
$691$	−8.48261	+	26.1068i	−0.322694	+	0.993149i	−0.972471	+	0.233024i	$0.925138\pi$
$692$		0			0
$693$	−25.5580	+	47.5019i	−0.970867	+	1.80445i
$694$		0			0
$695$	−4.25697	+	13.1016i	−0.161476	+	0.496972i
$696$		0			0
$697$	25.3541	+	18.4208i	0.960355	+	0.697739i
$698$		0			0
$699$	−5.56970	−	17.1418i	−0.210665	−	0.648362i
$700$		0			0
$701$	0.175085	−	0.127207i	0.00661287	−	0.00480453i	−0.584474	−	0.811413i	$-0.698699\pi$
$701$	0.175085	−	0.127207i	0.00661287	−	0.00480453i	0.591087	+	0.806608i	$0.298699\pi$
$702$		0			0
$703$	−43.3212			−1.63389
$704$		0			0
$705$	−14.9573			−0.563325
$706$		0			0
$707$	−0.253282	+	0.184020i	−0.00952564	+	0.00692078i
$708$		0			0
$709$	−15.6953	−	48.3050i	−0.589448	−	1.81413i	−0.580624	−	0.814172i	$-0.697191\pi$
$709$	−15.6953	−	48.3050i	−0.589448	−	1.81413i	−0.00882347	−	0.999961i	$-0.502809\pi$
$710$		0			0
$711$	−25.4504	−	18.4908i	−0.954463	−	0.693458i
$712$		0			0
$713$	−10.8838	+	33.4967i	−0.407600	+	1.25446i
$714$		0			0
$715$	−9.77046	+	4.70597i	−0.365394	+	0.175993i
$716$		0			0
$717$	−18.3084	+	56.3473i	−0.683738	+	2.10433i
$718$		0			0
$719$	27.5398	+	20.0089i	1.02706	+	0.746204i	0.967719	−	0.252033i	$-0.0810993\pi$
$719$	27.5398	+	20.0089i	1.02706	+	0.746204i	0.0593435	+	0.998238i	$0.481099\pi$
$720$		0			0
$721$	12.9041	+	39.7149i	0.480575	+	1.47906i
$722$		0			0
$723$	−23.3218	+	16.9443i	−0.867346	+	0.630163i
$724$		0			0
$725$	6.50105			0.241443
$726$		0			0
$727$	16.2361			0.602162			0.301081	−	0.953599i	$-0.402652\pi$
$727$	16.2361			0.602162			0.301081	+	0.953599i	$0.402652\pi$
$728$		0			0
$729$	34.9932	−	25.4241i	1.29605	−	0.941633i
$730$		0			0
$731$	−1.09534	−	3.37111i	−0.0405126	−	0.124685i
$732$		0			0
$733$	24.1078	+	17.5154i	0.890443	+	0.646944i	0.935993	−	0.352018i	$-0.114504\pi$
$733$	24.1078	+	17.5154i	0.890443	+	0.646944i	−0.0455508	+	0.998962i	$0.514504\pi$
$734$		0			0
$735$	−5.97525	+	18.3899i	−0.220400	+	0.678322i
$736$		0			0
$737$	41.7387	−	20.1035i	1.53746	−	0.740524i
$738$		0			0
$739$	−13.0551	+	40.1794i	−0.480239	+	1.47802i	0.358522	+	0.933521i	$0.383281\pi$
$739$	−13.0551	+	40.1794i	−0.480239	+	1.47802i	−0.838760	+	0.544501i	$0.816719\pi$
$740$		0			0
$741$	−30.9593	−	22.4932i	−1.13732	−	0.826310i
$742$		0			0
$743$	6.46233	+	19.8890i	0.237080	+	0.729657i	0.996839	+	0.0794519i	$0.0253170\pi$
$743$	6.46233	+	19.8890i	0.237080	+	0.729657i	−0.759759	+	0.650205i	$0.774683\pi$
$744$		0			0
$745$	7.83829	−	5.69485i	0.287173	−	0.208643i
$746$		0			0
$747$	−26.4394			−0.967366
$748$		0			0
$749$	−48.3997			−1.76849
$750$		0			0
$751$	−23.0107	+	16.7182i	−0.839672	+	0.610058i	−0.922279	−	0.386525i	$-0.873675\pi$
$751$	−23.0107	+	16.7182i	−0.839672	+	0.610058i	0.0826069	+	0.996582i	$0.473675\pi$
$752$		0			0
$753$	−10.1752	−	31.3160i	−0.370805	−	1.14122i
$754$		0			0
$755$	−13.4658	−	9.78349i	−0.490072	−	0.356058i
$756$		0			0
$757$	−12.2589	+	37.7291i	−0.445558	+	1.37129i	0.436312	+	0.899795i	$0.356284\pi$
$757$	−12.2589	+	37.7291i	−0.445558	+	1.37129i	−0.881870	+	0.471492i	$0.843716\pi$
$758$		0			0
$759$	27.2934	−	50.7274i	0.990688	−	1.84129i
$760$		0			0
$761$	−15.0740	+	46.3929i	−0.546430	+	1.68174i	0.171134	+	0.985248i	$0.445257\pi$
$761$	−15.0740	+	46.3929i	−0.546430	+	1.68174i	−0.717565	+	0.696492i	$0.754743\pi$
$762$		0			0
$763$	−22.8561	−	16.6059i	−0.827445	−	0.601174i
$764$		0			0
$765$	5.22323	+	16.0755i	0.188846	+	0.581209i
$766$		0			0
$767$	17.5493	−	12.7503i	0.633668	−	0.460387i
$768$		0			0
$769$	−10.7632			−0.388132			−0.194066	−	0.980988i	$-0.562168\pi$
$769$	−10.7632			−0.388132			−0.194066	+	0.980988i	$0.562168\pi$
$770$		0			0
$771$	16.5467			0.595915
$772$		0			0
$773$	−19.7962	+	14.3828i	−0.712021	+	0.517313i	−0.883825	−	0.467818i	$-0.845040\pi$
$773$	−19.7962	+	14.3828i	−0.712021	+	0.517313i	0.171804	+	0.985131i	$0.445040\pi$
$774$		0			0
$775$	1.69594	+	5.21956i	0.0609198	+	0.187492i
$776$		0			0
$777$	82.4929	+	59.9346i	2.95942	+	2.15014i
$778$		0			0
$779$	10.7144	−	32.9755i	0.383882	−	1.18147i
$780$		0			0
$781$	−23.7765	−	24.8651i	−0.850790	−	0.889744i
$782$		0			0
$783$	7.20062	−	22.1612i	0.257329	−	0.791978i
$784$		0			0
$785$	0.775197	+	0.563214i	0.0276680	+	0.0201020i
$786$		0			0
$787$	−1.50000	−	4.61653i	−0.0534692	−	0.164561i	0.920756	−	0.390139i	$-0.127573\pi$
$787$	−1.50000	−	4.61653i	−0.0534692	−	0.164561i	−0.974225	+	0.225578i	$0.927573\pi$
$788$		0			0
$789$	−0.977527	+	0.710215i	−0.0348009	+	0.0252843i
$790$		0			0
$791$	1.75755			0.0624911
$792$		0			0
$793$	−29.5093			−1.04791
$794$		0			0
$795$	2.38941	−	1.73601i	0.0847437	−	0.0615699i
$796$		0			0
$797$	−1.42359	−	4.38135i	−0.0504261	−	0.155195i	0.922673	−	0.385584i	$-0.126000\pi$
$797$	−1.42359	−	4.38135i	−0.0504261	−	0.155195i	−0.973099	+	0.230389i	$0.926000\pi$
$798$		0			0
$799$	17.4766	+	12.6975i	0.618278	+	0.449205i
$800$		0			0
$801$	−16.1973	+	49.8503i	−0.572305	+	1.76137i
$802$		0			0
$803$	12.0174	+	2.18005i	0.424086	+	0.0769324i
$804$		0			0
$805$	7.45846	−	22.9548i	0.262876	−	0.809050i
$806$		0			0
$807$	−0.0174383	−	0.0126697i	−0.000613858	−	0.000445994i
$808$		0			0
$809$	9.79491	+	30.1456i	0.344371	+	1.05986i	0.961920	+	0.273331i	$0.0881256\pi$
$809$	9.79491	+	30.1456i	0.344371	+	1.05986i	−0.617549	+	0.786532i	$0.711874\pi$
$810$		0			0
$811$	−11.6743	+	8.48190i	−0.409941	+	0.297840i	−0.773578	−	0.633701i	$-0.781535\pi$
$811$	−11.6743	+	8.48190i	−0.409941	+	0.297840i	0.363637	+	0.931541i	$0.381535\pi$
$812$		0			0
$813$	50.3058			1.76430
$814$		0			0
$815$	4.44532			0.155713
$816$		0			0
$817$	−3.17262	+	2.30505i	−0.110996	+	0.0806434i
$818$		0			0
$819$	16.4334	+	50.5768i	0.574230	+	1.76730i
$820$		0			0
$821$	−44.0551	−	32.0079i	−1.53753	−	1.11708i	−0.951858	−	0.306539i	$-0.900829\pi$
$821$	−44.0551	−	32.0079i	−1.53753	−	1.11708i	−0.585677	−	0.810545i	$-0.699171\pi$
$822$		0			0
$823$	0.0187612	−	0.0577411i	0.000653975	−	0.00201273i	−0.950729	−	0.310023i	$-0.899663\pi$
$823$	0.0187612	−	0.0577411i	0.000653975	−	0.00201273i	0.951383	+	0.308010i	$0.0996632\pi$
$824$		0			0
$825$	−1.20544	−	8.89468i	−0.0419681	−	0.309673i
$826$		0			0
$827$	−3.65486	+	11.2485i	−0.127092	+	0.391149i	−0.994276	−	0.106838i	$-0.965927\pi$
$827$	−3.65486	+	11.2485i	−0.127092	+	0.391149i	0.867184	+	0.497987i	$0.165927\pi$
$828$		0			0
$829$	−13.5508	−	9.84525i	−0.470640	−	0.341940i	0.327051	−	0.945007i	$-0.393945\pi$
$829$	−13.5508	−	9.84525i	−0.470640	−	0.341940i	−0.797691	+	0.603067i	$0.793945\pi$
$830$		0			0
$831$	5.82039	+	17.9133i	0.201907	+	0.621407i
$832$		0			0
$833$	22.5931	−	16.4149i	0.782806	−	0.568742i
$834$		0			0
$835$	−13.9494			−0.482737
$836$		0			0
$837$	19.6712			0.679936
$838$		0			0
$839$	0.734439	−	0.533601i	0.0253557	−	0.0184220i	−0.575035	−	0.818129i	$-0.695012\pi$
$839$	0.734439	−	0.533601i	0.0253557	−	0.0184220i	0.600391	+	0.799707i	$0.295012\pi$
$840$		0			0
$841$	4.09870	+	12.6145i	0.141335	+	0.434983i
$842$		0			0
$843$	48.9620	+	35.5730i	1.68634	+	1.22520i
$844$		0			0
$845$	0.713324	−	2.19539i	0.0245391	−	0.0755236i
$846$		0			0
$847$	−39.8782	+	11.0111i	−1.37023	+	0.378347i
$848$		0			0
$849$	−19.5264	+	60.0961i	−0.670144	+	2.06249i
$850$		0			0
$851$	−52.0118	−	37.7888i	−1.78294	−	1.29538i
$852$		0			0
$853$	16.4634	+	50.6690i	0.563695	+	1.73487i	0.671798	+	0.740735i	$0.265522\pi$
$853$	16.4634	+	50.6690i	0.563695	+	1.73487i	−0.108103	+	0.994140i	$0.534478\pi$
$854$		0			0
$855$	15.1289	−	10.9918i	0.517399	−	0.375912i
$856$		0			0
$857$	37.1487			1.26898			0.634488	−	0.772933i	$-0.281211\pi$
$857$	37.1487			1.26898			0.634488	+	0.772933i	$0.281211\pi$
$858$		0			0
$859$	26.8141			0.914887			0.457443	−	0.889239i	$-0.348765\pi$
$859$	26.8141			0.914887			0.457443	+	0.889239i	$0.348765\pi$
$860$		0			0
$861$	−66.0238	+	47.9691i	−2.25008	+	1.63478i
$862$		0			0
$863$	−5.41724	−	16.6726i	−0.184405	−	0.567541i	0.815532	−	0.578711i	$-0.196444\pi$
$863$	−5.41724	−	16.6726i	−0.184405	−	0.567541i	−0.999938	+	0.0111706i	$0.996444\pi$
$864$		0			0
$865$	−13.0770	−	9.50098i	−0.444631	−	0.323043i
$866$		0			0
$867$	−1.44024	+	4.43259i	−0.0489130	+	0.150539i
$868$		0			0
$869$	−3.24019	−	23.9086i	−0.109916	−	0.811045i
$870$		0			0
$871$	14.1140	−	43.4384i	0.478235	−	1.47185i
$872$		0			0
$873$	43.1691	+	31.3642i	1.46105	+	1.06152i
$874$		0			0
$875$	−1.16220	−	3.57688i	−0.0392895	−	0.120921i
$876$		0			0
$877$	−16.8079	+	12.2116i	−0.567562	+	0.412358i	−0.834219	−	0.551434i	$-0.814081\pi$
$877$	−16.8079	+	12.2116i	−0.567562	+	0.412358i	0.266657	+	0.963792i	$0.414081\pi$
$878$		0			0
$879$	9.47556			0.319603
$880$		0			0
$881$	36.3078			1.22324			0.611621	−	0.791151i	$-0.290518\pi$
$881$	36.3078			1.22324			0.611621	+	0.791151i	$0.290518\pi$
$882$		0			0
$883$	30.0147	−	21.8070i	1.01008	−	0.733863i	0.0458509	−	0.998948i	$-0.485400\pi$
$883$	30.0147	−	21.8070i	1.01008	−	0.733863i	0.964225	+	0.265085i	$0.0854001\pi$
$884$		0			0
$885$	5.54815	+	17.0754i	0.186499	+	0.573985i
$886$		0			0
$887$	−17.7834	−	12.9204i	−0.597109	−	0.433825i	0.247742	−	0.968826i	$-0.420311\pi$
$887$	−17.7834	−	12.9204i	−0.597109	−	0.433825i	−0.844852	+	0.535001i	$0.820311\pi$
$888$		0			0
$889$	20.9795	−	64.5684i	0.703631	−	2.16555i
$890$		0			0
$891$	10.6803	+	1.93749i	0.357803	+	0.0649082i
$892$		0			0
$893$	7.38543	−	22.7300i	0.247144	−	0.760631i
$894$		0			0
$895$	14.8705	+	10.8041i	0.497067	+	0.361140i
$896$		0			0
$897$	−17.5493	−	54.0111i	−0.585953	−	1.80338i
$898$		0			0
$899$	−28.8648	+	20.9715i	−0.962695	+	0.699439i
$900$		0			0
$901$	−4.26559			−0.142107
$902$		0			0
$903$	9.23037			0.307168
$904$		0			0
$905$	8.96192	−	6.51122i	0.297904	−	0.216440i
$906$		0			0
$907$	6.39045	+	19.6678i	0.212191	+	0.653058i	0.999341	+	0.0362960i	$0.0115559\pi$
$907$	6.39045	+	19.6678i	0.212191	+	0.653058i	−0.787150	+	0.616762i	$0.788444\pi$
$908$		0			0
$909$	−0.291227	−	0.211589i	−0.00965939	−	0.00701796i
$910$		0			0
$911$	−10.5882	+	32.5873i	−0.350804	+	1.07966i	0.607598	+	0.794244i	$0.292133\pi$
$911$	−10.5882	+	32.5873i	−0.350804	+	1.07966i	−0.958403	+	0.285420i	$0.907867\pi$
$912$		0			0
$913$	−14.0142	−	14.6558i	−0.463802	−	0.485037i
$914$		0			0
$915$	7.54755	−	23.2290i	0.249514	−	0.767926i
$916$		0			0
$917$	−19.7168	−	14.3251i	−0.651107	−	0.473057i
$918$		0			0
$919$	5.15152	+	15.8548i	0.169933	+	0.523000i	0.999366	−	0.0356062i	$-0.0113362\pi$
$919$	5.15152	+	15.8548i	0.169933	+	0.523000i	−0.829433	+	0.558607i	$0.811336\pi$
$920$		0			0
$921$	18.0931	−	13.1454i	0.596186	−	0.433155i
$922$		0			0
$923$	−33.9178			−1.11642
$924$		0			0
$925$	−10.0179			−0.329386
$926$		0			0
$927$	−38.8447	+	28.2223i	−1.27583	+	0.926943i
$928$		0			0
$929$	11.4967	+	35.3832i	0.377194	+	1.16089i	0.941986	+	0.335652i	$0.108957\pi$
$929$	11.4967	+	35.3832i	0.377194	+	1.16089i	−0.564792	+	0.825234i	$0.691043\pi$
$930$		0			0
$931$	−24.9960	−	18.1607i	−0.819211	−	0.595192i
$932$		0			0
$933$	9.66956	−	29.7598i	0.316567	−	0.974293i
$934$		0			0
$935$	−6.14235	+	11.4161i	−0.200876	+	0.373348i
$936$		0			0
$937$	4.83539	−	14.8818i	0.157965	−	0.486167i	−0.840484	−	0.541836i	$-0.817729\pi$
$937$	4.83539	−	14.8818i	0.157965	−	0.486167i	0.998449	+	0.0556691i	$0.0177292\pi$
$938$		0			0
$939$	42.2895	+	30.7251i	1.38007	+	1.00268i
$940$		0			0
$941$	−4.47359	−	13.7683i	−0.145835	−	0.448834i	0.851282	−	0.524708i	$-0.175825\pi$
$941$	−4.47359	−	13.7683i	−0.145835	−	0.448834i	−0.997117	+	0.0758737i	$0.975825\pi$
$942$		0			0
$943$	41.6280	−	30.2445i	1.35559	−	0.984897i
$944$		0			0
$945$	−13.4804			−0.438516
$946$		0			0
$947$	−56.2394			−1.82754			−0.913768	−	0.406238i	$-0.866841\pi$
$947$	−56.2394			−1.82754			−0.913768	+	0.406238i	$0.866841\pi$
$948$		0			0
$949$	9.74150	−	7.07762i	0.316223	−	0.229749i
$950$		0			0
$951$	18.7113	+	57.5874i	0.606755	+	1.86740i
$952$		0			0
$953$	17.9028	+	13.0071i	0.579928	+	0.421342i	0.838698	−	0.544597i	$-0.183317\pi$
$953$	17.9028	+	13.0071i	0.579928	+	0.421342i	−0.258770	+	0.965939i	$0.583317\pi$
$954$		0			0
$955$	−2.97235	+	9.14796i	−0.0961831	+	0.296021i
$956$		0			0
$957$	52.5730	−	25.3219i	1.69944	−	0.818541i
$958$		0			0
$959$	2.25188	−	6.93059i	0.0727171	−	0.223800i
$960$		0			0
$961$	0.711966	+	0.517274i	0.0229666	+	0.0166862i
$962$		0			0
$963$	−17.1970	−	52.9269i	−0.554165	−	1.70555i
$964$		0			0
$965$	−15.9018	+	11.5533i	−0.511897	+	0.371915i
$966$		0			0
$967$	32.2808			1.03808			0.519039	−	0.854750i	$-0.326290\pi$
$967$	32.2808			1.03808			0.519039	+	0.854750i	$0.326290\pi$
$968$		0			0
$969$	−45.7449			−1.46954
$970$		0			0
$971$	22.5473	−	16.3816i	0.723576	−	0.525709i	−0.163948	−	0.986469i	$-0.552423\pi$
$971$	22.5473	−	16.3816i	0.723576	−	0.525709i	0.887525	+	0.460760i	$0.152423\pi$
$972$		0			0
$973$	16.0103	+	49.2745i	0.513265	+	1.57967i
$974$		0			0
$975$	−7.15922	−	5.20148i	−0.229278	−	0.166581i
$976$		0			0
$977$	3.29499	−	10.1409i	0.105416	−	0.324437i	−0.884412	−	0.466707i	$-0.845440\pi$
$977$	3.29499	−	10.1409i	0.105416	−	0.324437i	0.989828	+	0.142270i	$0.0454402\pi$
$978$		0			0
$979$	−36.2184	+	17.4447i	−1.15754	+	0.557534i
$980$		0			0
$981$	10.0382	−	30.8943i	0.320494	−	0.986378i
$982$		0			0
$983$	−24.7691	−	17.9958i	−0.790011	−	0.573977i	0.117955	−	0.993019i	$-0.462366\pi$
$983$	−24.7691	−	17.9958i	−0.790011	−	0.573977i	−0.907967	+	0.419042i	$0.862366\pi$
$984$		0			0
$985$	3.76284	+	11.5808i	0.119894	+	0.368996i
$986$		0			0
$987$	−45.5103	+	33.0651i	−1.44861	+	1.05247i
$988$		0			0
$989$	−5.81975			−0.185057
$990$		0			0
$991$	12.2099			0.387859			0.193929	−	0.981015i	$-0.437877\pi$
$991$	12.2099			0.387859			0.193929	+	0.981015i	$0.437877\pi$
$992$		0			0
$993$	11.3389	−	8.23817i	0.359828	−	0.261430i
$994$		0			0
$995$	−2.60861	−	8.02848i	−0.0826985	−	0.254520i
$996$		0			0
$997$	10.9465	+	7.95313i	0.346681	+	0.251878i	0.747475	−	0.664290i	$-0.231266\pi$
$997$	10.9465	+	7.95313i	0.346681	+	0.251878i	−0.400795	+	0.916168i	$0.631266\pi$
$998$		0			0
$999$	−11.0959	+	34.1496i	−0.351058	+	1.08045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.m.a.141.1	✓	8
3.2	odd	2		1980.2.z.c.361.1		8
4.3	odd	2		880.2.bo.f.801.2		8
5.2	odd	4		1100.2.cb.c.449.4		16
5.3	odd	4		1100.2.cb.c.449.1		16
5.4	even	2		1100.2.n.c.801.2		8
11.4	even	5		2420.2.a.n.1.4		4
11.5	even	5	inner	220.2.m.a.181.1	yes	8
11.7	odd	10		2420.2.a.m.1.4		4
33.5	odd	10		1980.2.z.c.181.1		8
44.7	even	10		9680.2.a.cl.1.1		4
44.15	odd	10		9680.2.a.ck.1.1		4
44.27	odd	10		880.2.bo.f.401.2		8
55.27	odd	20		1100.2.cb.c.49.1		16
55.38	odd	20		1100.2.cb.c.49.4		16
55.49	even	10		1100.2.n.c.401.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.m.a.141.1	✓	8	1.1	even	1	trivial
220.2.m.a.181.1	yes	8	11.5	even	5	inner
880.2.bo.f.401.2		8	44.27	odd	10
880.2.bo.f.801.2		8	4.3	odd	2
1100.2.n.c.401.2		8	55.49	even	10
1100.2.n.c.801.2		8	5.4	even	2
1100.2.cb.c.49.1		16	55.27	odd	20
1100.2.cb.c.49.4		16	55.38	odd	20
1100.2.cb.c.449.1		16	5.3	odd	4
1100.2.cb.c.449.4		16	5.2	odd	4
1980.2.z.c.181.1		8	33.5	odd	10
1980.2.z.c.361.1		8	3.2	odd	2
2420.2.a.m.1.4		4	11.7	odd	10
2420.2.a.n.1.4		4	11.4	even	5
9680.2.a.ck.1.1		4	44.15	odd	10
9680.2.a.cl.1.1		4	44.7	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.18949 + 1.59076i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(-3.04267 - 2.21063i) q^{7} +(1.33631 - 4.11275i) q^{9} +(2.98808 - 1.43922i) q^{11} +(1.01043 - 3.10977i) q^{13} +(2.18949 + 1.59076i) q^{15} +(-1.20785 - 3.71739i) q^{17} +(-3.49851 + 2.54182i) q^{19} +10.1785 q^{21} -6.41755 q^{23} +(-0.809017 + 0.587785i) q^{25} +(1.10761 + 3.40887i) q^{27} +(-5.25946 - 3.82122i) q^{29} +(1.69594 - 5.21956i) q^{31} +(-4.25294 + 7.90449i) q^{33} +(-1.16220 + 3.57688i) q^{35} +(8.10463 + 5.88836i) q^{37} +(2.73458 + 8.41617i) q^{39} +(-6.48659 + 4.71279i) q^{41} +0.906850 q^{43} -4.32440 q^{45} +(-4.47122 + 3.24853i) q^{47} +(2.20785 + 6.79507i) q^{49} +(8.55805 + 6.21779i) q^{51} +(0.337233 - 1.03790i) q^{53} +(-2.29215 - 2.39709i) q^{55} +(3.61654 - 11.1306i) q^{57} +(5.36707 + 3.89940i) q^{59} +(-2.78882 - 8.58309i) q^{61} +(-13.1577 + 9.55965i) q^{63} -3.26981 q^{65} +13.9684 q^{67} +(14.0512 - 10.2088i) q^{69} +(-3.20544 - 9.86533i) q^{71} +(2.97923 + 2.16454i) q^{73} +(0.836312 - 2.57390i) q^{75} +(-12.2734 - 2.22648i) q^{77} +(2.24798 - 6.91858i) q^{79} +(2.64774 + 1.92370i) q^{81} +(-1.88933 - 5.81476i) q^{83} +(-3.16220 + 2.29747i) q^{85} +17.5942 q^{87} -12.1209 q^{89} +(-9.94895 + 7.22834i) q^{91} +(4.58982 + 14.1260i) q^{93} +(3.49851 + 2.54182i) q^{95} +(-3.81305 + 11.7354i) q^{97} +(-1.92613 - 14.2125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} + 2 q^{5} + q^{7} + 3 q^{9} + 5 q^{11} + 6 q^{13} + q^{15} - 13 q^{17} - 7 q^{19} + 28 q^{21} - 22 q^{23} - 2 q^{25} + 2 q^{27} + 3 q^{29} - 2 q^{31} - 15 q^{33} + 4 q^{35} + 16 q^{37} - 17 q^{39}+ \cdots - 20 q^{99}+O(q^{100}) \) 8 * q - q^3 + 2 * q^5 + q^7 + 3 * q^9 + 5 * q^11 + 6 * q^13 + q^15 - 13 * q^17 - 7 * q^19 + 28 * q^21 - 22 * q^23 - 2 * q^25 + 2 * q^27 + 3 * q^29 - 2 * q^31 - 15 * q^33 + 4 * q^35 + 16 * q^37 - 17 * q^39 - 12 * q^41 + 10 * q^43 - 8 * q^45 - 18 * q^47 + 21 * q^49 + 21 * q^51 - 23 * q^53 - 15 * q^55 - q^57 - 9 * q^59 - 34 * q^61 - 29 * q^63 - 6 * q^65 + 26 * q^67 - q^69 - 26 * q^71 + q^73 - q^75 - 10 * q^77 + 19 * q^79 + 12 * q^81 - 7 * q^83 - 12 * q^85 + 94 * q^87 - 8 * q^89 - 18 * q^91 + 49 * q^93 + 7 * q^95 - 24 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

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