LMFDB - Embedded newform 880.2.bo.f.401.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(81,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 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("880.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$8$
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:	no (minimal twist has level 220)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			401.2
Root			$1.33631 + 0.462894i$ of defining polynomial
Character	$\chi$	$=$	880.401
Dual form			880.2.bo.f.801.2

$q$-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 $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.18949	+	1.59076i	1.26410	+	0.918426i	0.998952	−	0.0457808i	$-0.0145776\pi$
$3$	2.18949	+	1.59076i	1.26410	+	0.918426i	0.265153	+	0.964206i	$0.414578\pi$
$4$		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	$-0.448354\pi$
$7$	3.04267	−	2.21063i	1.15002	−	0.835540i	0.988484	+	0.151326i	$0.0483543\pi$
$8$		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	0.987785	+	0.155825i	$0.0498036\pi$
$13$	1.01043	+	3.10977i	0.280242	+	0.862495i	−0.707543	+	0.706670i	$0.750196\pi$
$14$		0			0
$15$	−2.18949	+	1.59076i	−0.565325	+	0.410732i
$16$		0			0
$17$	−1.20785	+	3.71739i	−0.292947	+	0.901599i	0.690956	+	0.722897i	$0.257190\pi$
$17$	−1.20785	+	3.71739i	−0.292947	+	0.901599i	−0.983903	+	0.178702i	$0.942810\pi$
$18$		0			0
$19$	3.49851	+	2.54182i	0.802613	+	0.583133i	0.911680	−	0.410902i	$-0.134786\pi$
$19$	3.49851	+	2.54182i	0.802613	+	0.583133i	−0.109066	+	0.994034i	$0.534786\pi$
$20$		0			0
$21$	10.1785			2.22113
$22$		0			0
$23$	6.41755			1.33815			0.669075	−	0.743194i	$-0.266690\pi$
$23$	6.41755			1.33815			0.669075	+	0.743194i	$0.266690\pi$
$24$		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	−0.956959	−	0.290223i	$-0.906271\pi$
$29$	−5.25946	+	3.82122i	−0.976658	+	0.709583i	−0.0196984	+	0.999806i	$0.506271\pi$
$30$		0			0
$31$	−1.69594	−	5.21956i	−0.304599	−	0.937460i	−0.979826	−	0.199850i	$-0.935954\pi$
$31$	−1.69594	−	5.21956i	−0.304599	−	0.937460i	0.675227	−	0.737610i	$-0.264046\pi$
$32$		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	0.332705	−	0.943031i	$-0.392039\pi$
$37$	8.10463	−	5.88836i	1.33239	−	0.968040i	0.999687	−	0.0250091i	$-0.00796149\pi$
$38$		0			0
$39$	−2.73458	+	8.41617i	−0.437883	+	1.34767i
$40$		0			0
$41$	−6.48659	−	4.71279i	−1.01304	−	0.736014i	−0.0481922	−	0.998838i	$-0.515346\pi$
$41$	−6.48659	−	4.71279i	−1.01304	−	0.736014i	−0.964844	+	0.262824i	$0.915346\pi$
$42$		0			0
$43$	−0.906850			−0.138293			−0.0691467	−	0.997607i	$-0.522028\pi$
$43$	−0.906850			−0.138293			−0.0691467	+	0.997607i	$0.522028\pi$
$44$		0			0
$45$	−4.32440			−0.644643
$46$		0			0
$47$	4.47122	+	3.24853i	0.652194	+	0.473846i	0.864018	−	0.503461i	$-0.167940\pi$
$47$	4.47122	+	3.24853i	0.652194	+	0.473846i	−0.211824	+	0.977308i	$0.567940\pi$
$48$		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	0.971543	−	0.236865i	$-0.0761198\pi$
$53$	0.337233	+	1.03790i	0.0463225	+	0.142566i	−0.925220	+	0.379431i	$0.876120\pi$
$54$		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	$-0.842136\pi$
$59$	−5.36707	+	3.89940i	−0.698733	+	0.507659i	0.180786	+	0.983522i	$0.442136\pi$
$60$		0			0
$61$	−2.78882	+	8.58309i	−0.357071	+	1.09895i	0.597727	+	0.801699i	$0.296071\pi$
$61$	−2.78882	+	8.58309i	−0.357071	+	1.09895i	−0.954799	+	0.297253i	$0.903929\pi$
$62$		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	$-0.825374\pi$
$67$	−13.9684			−1.70651			−0.853254	+	0.521496i	$0.825374\pi$
$68$		0			0
$69$	14.0512	+	10.2088i	1.69156	+	1.22899i
$70$		0			0
$71$	3.20544	−	9.86533i	0.380416	−	1.17080i	−0.559336	−	0.828941i	$-0.688944\pi$
$71$	3.20544	−	9.86533i	0.380416	−	1.17080i	0.939751	−	0.341858i	$-0.111056\pi$
$72$		0			0
$73$	2.97923	−	2.16454i	0.348692	−	0.253340i	−0.399628	−	0.916677i	$-0.630861\pi$
$73$	2.97923	−	2.16454i	0.348692	−	0.253340i	0.748320	+	0.663338i	$0.230861\pi$
$74$		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	−0.994233	−	0.107244i	$-0.965797\pi$
$79$	−2.24798	−	6.91858i	−0.252918	−	0.778401i	0.741315	−	0.671157i	$-0.234203\pi$
$80$		0			0
$81$	2.64774	−	1.92370i	0.294193	−	0.213744i
$82$		0			0
$83$	1.88933	−	5.81476i	0.207381	−	0.638253i	−0.792226	−	0.610227i	$-0.791078\pi$
$83$	1.88933	−	5.81476i	0.207381	−	0.638253i	0.999607	−	0.0280255i	$-0.00892195\pi$
$84$		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	−0.934904	−	0.354901i	$-0.884514\pi$
$97$	−3.81305	−	11.7354i	−0.387157	−	1.19155i	0.547747	−	0.836644i	$-0.315486\pi$
$98$		0			0
$99$	1.92613	−	14.2125i	0.193583	−	1.42841i
$100$		0			0
$101$	0.0257235	+	0.0791689i	0.00255959	+	0.00787760i	0.952328	−	0.305076i	$-0.0986817\pi$
$101$	0.0257235	+	0.0791689i	0.00255959	+	0.00787760i	−0.949769	+	0.312953i	$0.898682\pi$
$102$		0			0
$103$	8.98269	−	6.52631i	0.885091	−	0.643056i	−0.0495024	−	0.998774i	$-0.515764\pi$
$103$	8.98269	−	6.52631i	0.885091	−	0.643056i	0.934593	+	0.355718i	$0.115764\pi$
$104$		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	$-0.513698\pi$
$107$	−10.4112	−	7.56420i	−1.00649	−	0.731259i	−0.963470	+	0.267815i	$0.913698\pi$
$108$		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	0.569861	−	0.821741i	$-0.306997\pi$
$113$	−0.378065	−	0.274680i	−0.0355654	−	0.0258398i	−0.605426	+	0.795902i	$0.706997\pi$
$114$		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	0.321982	+	0.946746i	$0.395651\pi$
$127$	−5.57825	+	17.1681i	−0.494990	+	1.52342i	−0.816972	+	0.576677i	$0.804349\pi$
$128$		0			0
$129$	−1.98554	−	1.44258i	−0.174817	−	0.127012i
$130$		0			0
$131$	−6.48010			−0.566169			−0.283085	−	0.959095i	$-0.591358\pi$
$131$	−6.48010			−0.566169			−0.283085	+	0.959095i	$0.591358\pi$
$132$		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	−0.922216	−	0.386676i	$-0.873623\pi$
$137$	0.598754	−	1.84278i	0.0511550	−	0.157439i	0.973371	+	0.229237i	$0.0736231\pi$
$138$		0			0
$139$	11.1449	−	8.09724i	0.945297	−	0.686799i	−0.00439260	−	0.999990i	$-0.501398\pi$
$139$	11.1449	−	8.09724i	0.945297	−	0.686799i	0.949690	+	0.313192i	$0.101398\pi$
$140$		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	−0.750317	−	0.661079i	$-0.770099\pi$
$149$	2.99396	−	9.21446i	0.245275	−	0.754878i	0.995591	−	0.0937990i	$-0.0299011\pi$
$150$		0			0
$151$	−13.4658	−	9.78349i	−1.09583	−	0.796169i	−0.115458	−	0.993312i	$-0.536834\pi$
$151$	−13.4658	−	9.78349i	−1.09583	−	0.796169i	−0.980375	+	0.197143i	$0.936834\pi$
$152$		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	0.556422	−	0.830900i	$-0.312174\pi$
$157$	−0.775197	−	0.563214i	−0.0618675	−	0.0449494i	−0.618289	+	0.785951i	$0.712174\pi$
$158$		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	$-0.0443009\pi$
$163$	1.37368	+	4.22775i	0.107595	+	0.331143i	−0.882736	+	0.469870i	$0.844301\pi$
$164$		0			0
$165$	8.83184	−	1.60216i	0.687558	−	0.124728i
$166$		0			0
$167$	−4.31059	−	13.2666i	−0.333563	−	1.02660i	−0.967425	−	0.253156i	$-0.918531\pi$
$167$	−4.31059	−	13.2666i	−0.333563	−	1.02660i	0.633862	−	0.773446i	$-0.281469\pi$
$168$		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	0.960842	−	0.277097i	$-0.0893722\pi$
$173$	13.0770	+	9.50098i	0.994224	+	0.722346i	0.0333821	+	0.999443i	$0.489372\pi$
$174$		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	$-0.0589579\pi$
$179$	14.8705	+	10.8041i	1.11148	+	0.807534i	0.128580	+	0.991699i	$0.458958\pi$
$180$		0			0
$181$	3.42315	−	10.5354i	0.254441	−	0.783088i	−0.739499	−	0.673158i	$-0.764937\pi$
$181$	3.42315	−	10.5354i	0.254441	−	0.783088i	0.993939	−	0.109930i	$-0.0350627\pi$
$182$		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	$-0.586863\pi$
$191$	7.78172	−	5.65375i	0.563066	−	0.409091i	0.832580	+	0.553905i	$0.186863\pi$
$192$		0			0
$193$	−6.07395	+	18.6937i	−0.437213	+	1.34560i	0.453590	+	0.891211i	$0.350143\pi$
$193$	−6.07395	+	18.6937i	−0.437213	+	1.34560i	−0.890802	+	0.454391i	$0.849857\pi$
$194$		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	$-0.596722\pi$
$199$	−8.44164			−0.598412			−0.299206	+	0.954189i	$0.596722\pi$
$200$		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	0.859112	+	0.511788i	$0.171016\pi$
$211$	6.75302	+	20.7837i	0.464897	+	1.43081i	−0.394215	+	0.919018i	$0.628984\pi$
$212$		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	−0.989722	−	0.143002i	$-0.954324\pi$
$223$	−21.3778	−	15.5319i	−1.43157	−	1.04009i	−0.441844	−	0.897092i	$-0.645676\pi$
$224$		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	$-0.593233\pi$
$227$	8.02445	−	5.83010i	0.532601	−	0.386957i	0.821330	+	0.570454i	$0.193233\pi$
$228$		0			0
$229$	−4.01140	−	12.3458i	−0.265081	−	0.815834i	−0.991675	−	0.128767i	$-0.958898\pi$
$229$	−4.01140	−	12.3458i	−0.265081	−	0.815834i	0.726594	−	0.687067i	$-0.241102\pi$
$230$		0			0
$231$	−30.4142	−	14.6491i	−2.00111	−	0.963839i
$232$		0			0
$233$	−2.05800	−	6.33388i	−0.134824	−	0.414946i	0.860738	−	0.509048i	$-0.170002\pi$
$233$	−2.05800	−	6.33388i	−0.134824	−	0.414946i	−0.995563	+	0.0941012i	$0.970002\pi$
$234$		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	$-0.550416\pi$
$239$	−17.7108	−	12.8677i	−1.14562	−	0.832340i	−0.987892	+	0.155143i	$0.950416\pi$
$240$		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	0.996806	+	0.0798576i	$0.0254466\pi$
$251$	3.75973	+	11.5713i	0.237312	+	0.730372i	−0.759494	+	0.650514i	$0.774553\pi$
$252$		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	−0.731271	−	0.682087i	$-0.761073\pi$
$257$	−4.94633	+	3.59372i	−0.308544	+	0.224170i	0.422728	+	0.906257i	$0.361073\pi$
$258$		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	$-0.504382\pi$
$263$	−0.446463			−0.0275301			−0.0137650	+	0.999905i	$0.504382\pi$
$264$		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	−0.950981	−	0.309248i	$-0.899923\pi$
$269$	0.00246118	−	0.00757473i	0.000150061	−	0.000461840i	0.951132	+	0.308786i	$0.0999227\pi$
$270$		0			0
$271$	15.0380	−	10.9257i	0.913493	−	0.663691i	−0.0284029	−	0.999597i	$-0.509042\pi$
$271$	15.0380	−	10.9257i	0.913493	−	0.663691i	0.941896	+	0.335905i	$0.109042\pi$
$272$		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	0.994646	−	0.103339i	$-0.0329528\pi$
$277$	2.15063	+	6.61897i	0.129219	+	0.397695i	−0.865427	+	0.501035i	$0.832953\pi$
$278$		0			0
$279$	19.2004	−	13.9499i	1.14950	−	0.835159i
$280$		0			0
$281$	−6.91031	+	21.2678i	−0.412235	+	1.26873i	0.502466	+	0.864597i	$0.332426\pi$
$281$	−6.91031	+	21.2678i	−0.412235	+	1.26873i	−0.914701	+	0.404131i	$0.867574\pi$
$282$		0			0
$283$	−18.8891	−	13.7237i	−1.12284	−	0.815792i	−0.138204	−	0.990404i	$-0.544133\pi$
$283$	−18.8891	−	13.7237i	−1.12284	−	0.815792i	−0.984637	+	0.174612i	$0.944133\pi$
$284$		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	−0.667443	−	0.744661i	$-0.732611\pi$
$293$	−2.83254	+	2.05796i	−0.165479	+	0.120227i	0.501964	+	0.864889i	$0.332611\pi$
$294$		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	$-0.424224\pi$
$307$	8.26358			0.471628			0.235814	+	0.971798i	$0.424224\pi$
$308$		0			0
$309$	30.0493			1.70945
$310$		0			0
$311$	9.35397	+	6.79606i	0.530415	+	0.385369i	0.820513	−	0.571628i	$-0.193688\pi$
$311$	9.35397	+	6.79606i	0.530415	+	0.385369i	−0.290098	+	0.956997i	$0.593688\pi$
$312$		0			0
$313$	−5.96859	+	18.3694i	−0.337364	+	1.03830i	0.628181	+	0.778067i	$0.283800\pi$
$313$	−5.96859	+	18.3694i	−0.337364	+	1.03830i	−0.965546	+	0.260234i	$0.916200\pi$
$314$		0			0
$315$	−13.1577	+	9.55965i	−0.741354	+	0.538625i
$316$		0			0
$317$	6.91381	+	21.2785i	0.388318	+	1.19512i	0.934044	+	0.357157i	$0.116254\pi$
$317$	6.91381	+	21.2785i	0.388318	+	1.19512i	−0.545726	+	0.837964i	$0.683746\pi$
$318$		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	$-0.454542\pi$
$331$	5.17876			0.284650			0.142325	+	0.989820i	$0.454542\pi$
$332$		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	−0.702866	−	0.711322i	$-0.748097\pi$
$337$	−4.47108	+	3.24843i	−0.243555	+	0.176953i	0.459310	+	0.888276i	$0.348097\pi$
$338$		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	$-0.974041\pi$
$347$	−2.65383	+	8.16765i	−0.142465	+	0.438463i	0.854211	+	0.519926i	$0.174041\pi$
$348$		0			0
$349$	−11.8706	−	8.62451i	−0.635419	−	0.461659i	0.222854	−	0.974852i	$-0.428463\pi$
$349$	−11.8706	−	8.62451i	−0.635419	−	0.461659i	−0.858273	+	0.513193i	$0.828463\pi$
$350$		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	$-0.796939\pi$
$359$	−9.19282	+	6.67898i	−0.485179	+	0.352503i	0.318148	+	0.948041i	$0.396939\pi$
$360$		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	$-0.738178\pi$
$367$	−3.70890	+	2.69468i	−0.193603	+	0.140661i	0.486761	+	0.873535i	$0.338178\pi$
$368$		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	−0.633006	−	0.774147i	$-0.718179\pi$
$379$	6.50498	−	20.0203i	0.334139	−	1.02837i	0.967145	−	0.254226i	$-0.0818208\pi$
$380$		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	$-0.0978864\pi$
$383$	0.0803134	+	0.247179i	0.00410382	+	0.0126303i	−0.948984	+	0.315325i	$0.897886\pi$
$384$		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	−0.215561	−	0.976490i	$-0.569158\pi$
$389$	12.7514	−	9.26447i	0.646524	−	0.469727i	0.862085	+	0.506763i	$0.169158\pi$
$390$		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	0.393372	+	0.919379i	$0.371309\pi$
$401$	−9.31703	+	28.6749i	−0.465270	+	1.43195i	−0.858642	+	0.512575i	$0.828691\pi$
$402$		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	0.844688	+	0.535259i	$0.179786\pi$
$409$	9.62526	+	29.6235i	0.475939	+	1.46479i	−0.368749	+	0.929529i	$0.620214\pi$
$410$		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	$-0.605925\pi$
$419$	−13.3733			−0.653328			−0.326664	+	0.945141i	$0.605925\pi$
$420$		0			0
$421$	8.87736	+	6.44978i	0.432656	+	0.314343i	0.782710	−	0.622386i	$-0.213837\pi$
$421$	8.87736	+	6.44978i	0.432656	+	0.314343i	−0.350054	+	0.936730i	$0.613837\pi$
$422$		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	0.996212	+	0.0869561i	$0.0277140\pi$
$431$	5.01099	+	15.4223i	0.241371	+	0.742864i	−0.754841	+	0.655908i	$0.772286\pi$
$432$		0			0
$433$	17.3649	−	12.6163i	0.834503	−	0.606302i	−0.0863271	−	0.996267i	$-0.527513\pi$
$433$	17.3649	−	12.6163i	0.834503	−	0.606302i	0.920830	+	0.389965i	$0.127513\pi$
$434$		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	$-0.545330\pi$
$439$	−5.94741			−0.283855			−0.141927	+	0.989877i	$0.545330\pi$
$440$		0			0
$441$	30.8968			1.47127
$442$		0			0
$443$	−19.2068	−	13.9546i	−0.912545	−	0.663003i	0.0291124	−	0.999576i	$-0.490732\pi$
$443$	−19.2068	−	13.9546i	−0.912545	−	0.663003i	−0.941657	+	0.336574i	$0.890732\pi$
$444$		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	0.805892	+	0.592063i	$0.201686\pi$
$449$	10.6354	+	32.7325i	0.501917	+	1.54474i	−0.303975	+	0.952680i	$0.598314\pi$
$450$		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	−0.784825	−	0.619717i	$-0.787247\pi$
$457$	4.58276	−	14.1043i	0.214372	−	0.659770i	0.999198	−	0.0400529i	$-0.0127526\pi$
$458$		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	$-0.448942\pi$
$463$	6.87337			0.319433			0.159716	+	0.987163i	$0.448942\pi$
$464$		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	$-0.889619\pi$
$467$	0.435503	−	1.34034i	0.0201527	−	0.0620236i	0.960627	+	0.277841i	$0.0896188\pi$
$468$		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	−0.641271	−	0.767315i	$-0.721592\pi$
$479$	7.19055	−	22.1302i	0.328544	−	1.01116i	0.969815	−	0.243841i	$-0.0784075\pi$
$480$		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	$-0.161099\pi$
$487$	15.0917	+	10.9647i	0.683868	+	0.496859i	−0.190770	+	0.981635i	$0.561099\pi$
$488$		0			0
$489$	−3.71768	+	11.4418i	−0.168119	+	0.517418i
$490$		0			0
$491$	−33.9898	+	24.6951i	−1.53394	+	1.11447i	−0.579943	+	0.814657i	$0.696925\pi$
$491$	−33.9898	+	24.6951i	−1.53394	+	1.11447i	−0.953997	+	0.299815i	$0.903075\pi$
$492$		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	$-0.737293\pi$
$499$	−4.22493	+	3.06959i	−0.189134	+	0.137414i	0.489189	+	0.872178i	$0.337293\pi$
$500$		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	$-0.0777443\pi$
$503$	23.3289	+	16.9494i	1.04018	+	0.755737i	0.0698614	+	0.997557i	$0.477744\pi$
$504$		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	0.484304	−	0.874900i	$-0.339073\pi$
$509$	−4.46973	−	3.24745i	−0.198117	−	0.143940i	−0.682421	+	0.730959i	$0.739073\pi$
$510$		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	0.0729362	−	0.997337i	$-0.476763\pi$
$521$	23.8297	−	17.3133i	1.04400	−	0.758509i	0.971062	+	0.238828i	$0.0767631\pi$
$522$		0			0
$523$	0.684593	−	2.10696i	0.0299351	−	0.0921309i	−0.934973	−	0.354720i	$-0.884576\pi$
$523$	0.684593	−	2.10696i	0.0299351	−	0.0921309i	0.964908	+	0.262589i	$0.0845763\pi$
$524$		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	0.879292	+	0.476282i	$0.158016\pi$
$541$	10.4175	+	32.0616i	0.447882	+	1.37844i	−0.431411	+	0.902156i	$0.641984\pi$
$542$		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	$-0.504871\pi$
$547$	−22.7092	−	16.4992i	−0.970976	−	0.705455i	−0.955674	+	0.294428i	$0.904871\pi$
$548$		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	−0.821098	−	0.570787i	$-0.806638\pi$
$557$	−12.5552	+	9.12189i	−0.531981	+	0.386507i	0.289117	+	0.957294i	$0.406638\pi$
$558$		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	0.992293	+	0.123915i	$0.0395450\pi$
$563$	6.22486	+	19.1581i	0.262346	+	0.807419i	−0.729946	+	0.683504i	$0.760455\pi$
$564$		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	−0.0919848	−	0.995760i	$-0.529321\pi$
$569$	−25.4623	−	18.4994i	−1.06743	−	0.775536i	−0.975449	+	0.220224i	$0.929321\pi$
$570$		0			0
$571$	14.3295			0.599673			0.299836	−	0.953991i	$-0.403068\pi$
$571$	14.3295			0.599673			0.299836	+	0.953991i	$0.403068\pi$
$572$		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	−0.997317	−	0.0731994i	$-0.976679\pi$
$577$	−3.54175	+	10.9004i	−0.147445	+	0.453789i	0.849872	+	0.526989i	$0.176679\pi$
$578$		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	$-0.637711\pi$
$587$	7.62242	−	5.53801i	0.314611	−	0.228578i	0.733872	+	0.679287i	$0.237711\pi$
$588$		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	$-0.926257\pi$
$599$	−1.24633	+	3.83580i	−0.0509235	+	0.156726i	0.922361	+	0.386329i	$0.126257\pi$
$600$		0			0
$601$	−30.0829	+	21.8565i	−1.22711	+	0.891544i	−0.996670	−	0.0815436i	$-0.974015\pi$
$601$	−30.0829	+	21.8565i	−1.22711	+	0.891544i	−0.230435	+	0.973088i	$0.574015\pi$
$602$		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	0.998039	+	0.0625883i	$0.0199355\pi$
$607$	5.60247	+	17.2426i	0.227397	+	0.699856i	−0.770642	+	0.637268i	$0.780064\pi$
$608$		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	0.718434	−	0.695595i	$-0.244859\pi$
$613$	6.90505	+	5.01682i	0.278893	+	0.202627i	−0.439542	+	0.898222i	$0.644859\pi$
$614$		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	$-0.579332\pi$
$619$	−30.9640	−	22.4967i	−1.24455	−	0.904218i	−0.997893	+	0.0648846i	$0.979332\pi$
$620$		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	$-0.564872\pi$
$631$	16.7407	−	12.1628i	0.666435	−	0.484194i	0.868830	+	0.495110i	$0.164872\pi$
$632$		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	0.713223	−	0.700937i	$-0.247234\pi$
$641$	6.75967	+	4.91119i	0.266991	+	0.193980i	−0.446232	+	0.894917i	$0.647234\pi$
$642$		0			0
$643$	−9.08552	+	27.9623i	−0.358298	+	1.10273i	0.595775	+	0.803152i	$0.296845\pi$
$643$	−9.08552	+	27.9623i	−0.358298	+	1.10273i	−0.954073	+	0.299576i	$0.903155\pi$
$644$		0			0
$645$	1.98554	−	1.44258i	0.0781806	−	0.0568016i
$646$		0			0
$647$	−7.26160	−	22.3489i	−0.285483	−	0.878626i	−0.986253	−	0.165240i	$-0.947160\pi$
$647$	−7.26160	−	22.3489i	−0.285483	−	0.878626i	0.700770	−	0.713387i	$-0.252840\pi$
$648$		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	−0.804460	−	0.594006i	$-0.797545\pi$
$653$	−12.4733	+	9.06240i	−0.488119	+	0.354639i	0.316342	+	0.948645i	$0.397545\pi$
$654$		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	$-0.576869\pi$
$659$	−12.2785			−0.478301			−0.239151	+	0.970982i	$0.576869\pi$
$660$		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	0.936377	+	0.350997i	$0.114157\pi$
$673$	9.99147	+	30.7506i	0.385143	+	1.18535i	−0.551234	+	0.834351i	$0.685843\pi$
$674$		0			0
$675$	2.89976	−	2.10680i	0.111612	−	0.0810906i
$676$		0			0
$677$	−9.73155	+	29.9506i	−0.374014	+	1.15110i	0.570128	+	0.821556i	$0.306894\pi$
$677$	−9.73155	+	29.9506i	−0.374014	+	1.15110i	−0.944142	+	0.329540i	$0.893106\pi$
$678$		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	$-0.417626\pi$
$683$	13.3758			0.511812			0.255906	+	0.966702i	$0.417626\pi$
$684$		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	0.972471	+	0.233024i	$0.0748622\pi$
$691$	8.48261	+	26.1068i	0.322694	+	0.993149i	−0.649777	+	0.760125i	$0.725138\pi$
$692$		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	0.591087	−	0.806608i	$-0.298699\pi$
$701$	0.175085	+	0.127207i	0.00661287	+	0.00480453i	−0.584474	+	0.811413i	$0.698699\pi$
$702$		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	−0.00882347	+	0.999961i	$0.502809\pi$
$709$	−15.6953	+	48.3050i	−0.589448	+	1.81413i	−0.580624	+	0.814172i	$0.697191\pi$
$710$		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	$-0.918901\pi$
$719$	−27.5398	+	20.0089i	−1.02706	+	0.746204i	−0.0593435	+	0.998238i	$0.518901\pi$
$720$		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	$-0.597348\pi$
$727$	−16.2361			−0.602162			−0.301081	+	0.953599i	$0.597348\pi$
$728$		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	−0.0455508	−	0.998962i	$-0.514504\pi$
$733$	24.1078	−	17.5154i	0.890443	−	0.646944i	0.935993	+	0.352018i	$0.114504\pi$
$734$		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	0.838760	+	0.544501i	$0.183281\pi$
$739$	13.0551	+	40.1794i	0.480239	+	1.47802i	−0.358522	+	0.933521i	$0.616719\pi$
$740$		0			0
$741$	−30.9593	+	22.4932i	−1.13732	+	0.826310i
$742$		0			0
$743$	−6.46233	+	19.8890i	−0.237080	+	0.729657i	0.759759	+	0.650205i	$0.225317\pi$
$743$	−6.46233	+	19.8890i	−0.237080	+	0.729657i	−0.996839	+	0.0794519i	$0.974683\pi$
$744$		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	$-0.126325\pi$
$751$	23.0107	+	16.7182i	0.839672	+	0.610058i	−0.0826069	+	0.996582i	$0.526325\pi$
$752$		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	−0.881870	−	0.471492i	$-0.843716\pi$
$757$	−12.2589	−	37.7291i	−0.445558	−	1.37129i	0.436312	−	0.899795i	$-0.356284\pi$
$758$		0			0
$759$	−27.2934	−	50.7274i	−0.990688	−	1.84129i
$760$		0			0
$761$	−15.0740	−	46.3929i	−0.546430	−	1.68174i	−0.717565	−	0.696492i	$-0.754743\pi$
$761$	−15.0740	−	46.3929i	−0.546430	−	1.68174i	0.171134	−	0.985248i	$-0.445257\pi$
$762$		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	0.171804	−	0.985131i	$-0.445040\pi$
$773$	−19.7962	−	14.3828i	−0.712021	−	0.517313i	−0.883825	+	0.467818i	$0.845040\pi$
$774$		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	$-0.872427\pi$
$787$	1.50000	−	4.61653i	0.0534692	−	0.164561i	0.974225	+	0.225578i	$0.0724269\pi$
$788$		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	−0.973099	−	0.230389i	$-0.926000\pi$
$797$	−1.42359	+	4.38135i	−0.0504261	+	0.155195i	0.922673	+	0.385584i	$0.126000\pi$
$798$		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	−0.617549	−	0.786532i	$-0.711874\pi$
$809$	9.79491	−	30.1456i	0.344371	−	1.05986i	0.961920	−	0.273331i	$-0.0881256\pi$
$810$		0			0
$811$	11.6743	+	8.48190i	0.409941	+	0.297840i	0.773578	−	0.633701i	$-0.218465\pi$
$811$	11.6743	+	8.48190i	0.409941	+	0.297840i	−0.363637	+	0.931541i	$0.618465\pi$
$812$		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	−0.585677	+	0.810545i	$0.699171\pi$
$821$	−44.0551	+	32.0079i	−1.53753	+	1.11708i	−0.951858	+	0.306539i	$0.900829\pi$
$822$		0			0
$823$	−0.0187612	−	0.0577411i	−0.000653975	−	0.00201273i	0.950729	−	0.310023i	$-0.100337\pi$
$823$	−0.0187612	−	0.0577411i	−0.000653975	−	0.00201273i	−0.951383	+	0.308010i	$0.900337\pi$
$824$		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	$-0.0340726\pi$
$827$	3.65486	+	11.2485i	0.127092	+	0.391149i	−0.867184	+	0.497987i	$0.834073\pi$
$828$		0			0
$829$	−13.5508	+	9.84525i	−0.470640	+	0.341940i	−0.797691	−	0.603067i	$-0.793945\pi$
$829$	−13.5508	+	9.84525i	−0.470640	+	0.341940i	0.327051	+	0.945007i	$0.393945\pi$
$830$		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	$-0.304988\pi$
$839$	−0.734439	−	0.533601i	−0.0253557	−	0.0184220i	−0.600391	+	0.799707i	$0.704988\pi$
$840$		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	−0.108103	−	0.994140i	$-0.534478\pi$
$853$	16.4634	−	50.6690i	0.563695	−	1.73487i	0.671798	−	0.740735i	$-0.265522\pi$
$854$		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	$-0.651235\pi$
$859$	−26.8141			−0.914887			−0.457443	+	0.889239i	$0.651235\pi$
$860$		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	$-0.803556\pi$
$863$	5.41724	−	16.6726i	0.184405	−	0.567541i	0.999938	+	0.0111706i	$0.00355580\pi$
$864$		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	0.266657	−	0.963792i	$-0.414081\pi$
$877$	−16.8079	−	12.2116i	−0.567562	−	0.412358i	−0.834219	+	0.551434i	$0.814081\pi$
$878$		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	$-0.514600\pi$
$883$	−30.0147	−	21.8070i	−1.01008	−	0.733863i	−0.964225	+	0.265085i	$0.914600\pi$
$884$		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	$-0.579689\pi$
$887$	17.7834	−	12.9204i	0.597109	−	0.433825i	0.844852	+	0.535001i	$0.179689\pi$
$888$		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	0.787150	+	0.616762i	$0.211556\pi$
$907$	−6.39045	+	19.6678i	−0.212191	+	0.653058i	−0.999341	+	0.0362960i	$0.988444\pi$
$908$		0			0
$909$	−0.291227	+	0.211589i	−0.00965939	+	0.00701796i
$910$		0			0
$911$	10.5882	+	32.5873i	0.350804	+	1.07966i	0.958403	+	0.285420i	$0.0921330\pi$
$911$	10.5882	+	32.5873i	0.350804	+	1.07966i	−0.607598	+	0.794244i	$0.707867\pi$
$912$		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	$-0.988664\pi$
$919$	−5.15152	+	15.8548i	−0.169933	+	0.523000i	0.829433	+	0.558607i	$0.188664\pi$
$920$		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	−0.564792	−	0.825234i	$-0.691043\pi$
$929$	11.4967	−	35.3832i	0.377194	−	1.16089i	0.941986	−	0.335652i	$-0.108957\pi$
$930$		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	0.998449	−	0.0556691i	$-0.0177292\pi$
$937$	4.83539	+	14.8818i	0.157965	+	0.486167i	−0.840484	+	0.541836i	$0.817729\pi$
$938$		0			0
$939$	−42.2895	+	30.7251i	−1.38007	+	1.00268i
$940$		0			0
$941$	−4.47359	+	13.7683i	−0.145835	+	0.448834i	−0.997117	−	0.0758737i	$-0.975825\pi$
$941$	−4.47359	+	13.7683i	−0.145835	+	0.448834i	0.851282	+	0.524708i	$0.175825\pi$
$942$		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	$-0.133159\pi$
$947$	56.2394			1.82754			0.913768	+	0.406238i	$0.133159\pi$
$948$		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	−0.258770	−	0.965939i	$-0.583317\pi$
$953$	17.9028	−	13.0071i	0.579928	−	0.421342i	0.838698	+	0.544597i	$0.183317\pi$
$954$		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	$-0.673710\pi$
$967$	−32.2808			−1.03808			−0.519039	+	0.854750i	$0.673710\pi$
$968$		0			0
$969$	−45.7449			−1.46954
$970$		0			0
$971$	−22.5473	−	16.3816i	−0.723576	−	0.525709i	0.163948	−	0.986469i	$-0.447577\pi$
$971$	−22.5473	−	16.3816i	−0.723576	−	0.525709i	−0.887525	+	0.460760i	$0.847577\pi$
$972$		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	0.989828	−	0.142270i	$-0.0454402\pi$
$977$	3.29499	+	10.1409i	0.105416	+	0.324437i	−0.884412	+	0.466707i	$0.845440\pi$
$978$		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	$-0.537634\pi$
$983$	24.7691	−	17.9958i	0.790011	−	0.573977i	0.907967	+	0.419042i	$0.137634\pi$
$984$		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	$-0.562123\pi$
$991$	−12.2099			−0.387859			−0.193929	+	0.981015i	$0.562123\pi$
$992$		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	−0.400795	−	0.916168i	$-0.631266\pi$
$997$	10.9465	−	7.95313i	0.346681	−	0.251878i	0.747475	+	0.664290i	$0.231266\pi$
$998$		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	880.2.bo.f.401.2		8
4.3	odd	2		220.2.m.a.181.1	yes	8
11.3	even	5		9680.2.a.ck.1.1		4
11.8	odd	10		9680.2.a.cl.1.1		4
11.9	even	5	inner	880.2.bo.f.801.2		8
12.11	even	2		1980.2.z.c.181.1		8
20.3	even	4		1100.2.cb.c.49.4		16
20.7	even	4		1100.2.cb.c.49.1		16
20.19	odd	2		1100.2.n.c.401.2		8
44.3	odd	10		2420.2.a.n.1.4		4
44.19	even	10		2420.2.a.m.1.4		4
44.31	odd	10		220.2.m.a.141.1	✓	8
132.119	even	10		1980.2.z.c.361.1		8
220.119	odd	10		1100.2.n.c.801.2		8
220.163	even	20		1100.2.cb.c.449.1		16
220.207	even	20		1100.2.cb.c.449.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.m.a.141.1	✓	8	44.31	odd	10
220.2.m.a.181.1	yes	8	4.3	odd	2
880.2.bo.f.401.2		8	1.1	even	1	trivial
880.2.bo.f.801.2		8	11.9	even	5	inner
1100.2.n.c.401.2		8	20.19	odd	2
1100.2.n.c.801.2		8	220.119	odd	10
1100.2.cb.c.49.1		16	20.7	even	4
1100.2.cb.c.49.4		16	20.3	even	4
1100.2.cb.c.449.1		16	220.163	even	20
1100.2.cb.c.449.4		16	220.207	even	20
1980.2.z.c.181.1		8	12.11	even	2
1980.2.z.c.361.1		8	132.119	even	10
2420.2.a.m.1.4		4	44.19	even	10
2420.2.a.n.1.4		4	44.3	odd	10
9680.2.a.ck.1.1		4	11.3	even	5
9680.2.a.cl.1.1		4	11.8	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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