LMFDB - Embedded newform 880.2.bo.b.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(81,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [4,0,-4,0,1,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	880.81
Dual form			880.2.bo.b.641.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.118034 - 0.363271i) q^{3} +(0.809017 - 0.587785i) q^{5} +(2.30902 + 1.67760i) q^{9} +(3.30902 - 0.224514i) q^{11} +(-5.23607 - 3.80423i) q^{13} +(-0.118034 - 0.363271i) q^{15} +(4.11803 - 2.99193i) q^{17} +(-1.19098 + 3.66547i) q^{19} +6.00000 q^{23} +(0.309017 - 0.951057i) q^{25} +(1.80902 - 1.31433i) q^{27} +(1.47214 + 4.53077i) q^{29} +(-3.00000 - 2.17963i) q^{31} +(0.309017 - 1.22857i) q^{33} +(-0.618034 - 1.90211i) q^{37} +(-2.00000 + 1.45309i) q^{39} +(-1.50000 + 4.61653i) q^{41} +2.85410 q^{43} +2.85410 q^{45} +(3.47214 - 10.6861i) q^{47} +(5.66312 - 4.11450i) q^{49} +(-0.600813 - 1.84911i) q^{51} +(2.85410 + 2.07363i) q^{53} +(2.54508 - 2.12663i) q^{55} +(1.19098 + 0.865300i) q^{57} +(-3.57295 - 10.9964i) q^{59} +(6.23607 - 4.53077i) q^{61} -6.47214 q^{65} +0.618034 q^{67} +(0.708204 - 2.17963i) q^{69} +(-3.85410 + 2.80017i) q^{71} +(0.354102 + 1.08981i) q^{73} +(-0.309017 - 0.224514i) q^{75} +(5.85410 + 4.25325i) q^{79} +(2.38197 + 7.33094i) q^{81} +(-10.0172 + 7.27794i) q^{83} +(1.57295 - 4.84104i) q^{85} +1.81966 q^{87} -4.09017 q^{89} +(-1.14590 + 0.832544i) q^{93} +(1.19098 + 3.66547i) q^{95} +(6.16312 + 4.47777i) q^{97} +(8.01722 + 5.03280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + q^{5} + 7 q^{9} + 11 q^{11} - 12 q^{13} + 4 q^{15} + 12 q^{17} - 7 q^{19} + 24 q^{23} - q^{25} + 5 q^{27} - 12 q^{29} - 12 q^{31} - q^{33} + 2 q^{37} - 8 q^{39} - 6 q^{41} - 2 q^{43}+ \cdots + 3 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + q^5 + 7 * q^9 + 11 * q^11 - 12 * q^13 + 4 * q^15 + 12 * q^17 - 7 * q^19 + 24 * q^23 - q^25 + 5 * q^27 - 12 * q^29 - 12 * q^31 - q^33 + 2 * q^37 - 8 * q^39 - 6 * q^41 - 2 * q^43 - 2 * q^45 - 4 * q^47 + 7 * q^49 - 27 * q^51 - 2 * q^53 - q^55 + 7 * q^57 - 21 * q^59 + 16 * q^61 - 8 * q^65 - 2 * q^67 - 24 * q^69 - 2 * q^71 - 12 * q^73 + q^75 + 10 * q^79 + 14 * q^81 - 11 * q^83 + 13 * q^85 + 52 * q^87 + 6 * q^89 - 18 * q^93 + 7 * q^95 + 9 * q^97 + 3 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.118034	−	0.363271i	0.0681470	−	0.209735i	−0.911184	−	0.412000i	$-0.864830\pi$
$3$	0.118034	−	0.363271i	0.0681470	−	0.209735i	0.979331	+	0.202265i	$0.0648303\pi$
$4$		0			0
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$		0			0
$7$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$7$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$8$		0			0
$9$	2.30902	+	1.67760i	0.769672	+	0.559200i
$10$		0			0
$11$	3.30902	−	0.224514i	0.997706	−	0.0676935i
$11$	3.30902	−	0.224514i	0.997706	−	0.0676935i
$12$		0			0
$13$	−5.23607	−	3.80423i	−1.45222	−	1.05510i	−0.985305	−	0.170802i	$-0.945364\pi$
$13$	−5.23607	−	3.80423i	−1.45222	−	1.05510i	−0.466919	−	0.884300i	$-0.654636\pi$
$14$		0			0
$15$	−0.118034	−	0.363271i	−0.0304762	−	0.0937962i
$16$		0			0
$17$	4.11803	−	2.99193i	0.998770	−	0.725649i	0.0369459	−	0.999317i	$-0.488237\pi$
$17$	4.11803	−	2.99193i	0.998770	−	0.725649i	0.961824	+	0.273668i	$0.0882371\pi$
$18$		0			0
$19$	−1.19098	+	3.66547i	−0.273230	+	0.840916i	0.716452	+	0.697636i	$0.245765\pi$
$19$	−1.19098	+	3.66547i	−0.273230	+	0.840916i	−0.989682	+	0.143280i	$0.954235\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$		0			0
$27$	1.80902	−	1.31433i	0.348145	−	0.252942i
$28$		0			0
$29$	1.47214	+	4.53077i	0.273369	+	0.841343i	0.989646	+	0.143527i	$0.0458444\pi$
$29$	1.47214	+	4.53077i	0.273369	+	0.841343i	−0.716278	+	0.697815i	$0.754156\pi$
$30$		0			0
$31$	−3.00000	−	2.17963i	−0.538816	−	0.391473i	0.284829	−	0.958578i	$-0.408063\pi$
$31$	−3.00000	−	2.17963i	−0.538816	−	0.391473i	−0.823645	+	0.567106i	$0.808063\pi$
$32$		0			0
$33$	0.309017	−	1.22857i	0.0537930	−	0.213867i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.618034	−	1.90211i	−0.101604	−	0.312705i	0.887314	−	0.461165i	$-0.152568\pi$
$37$	−0.618034	−	1.90211i	−0.101604	−	0.312705i	−0.988918	+	0.148460i	$0.952568\pi$
$38$		0			0
$39$	−2.00000	+	1.45309i	−0.320256	+	0.232680i
$40$		0			0
$41$	−1.50000	+	4.61653i	−0.234261	+	0.720980i	0.762958	+	0.646448i	$0.223746\pi$
$41$	−1.50000	+	4.61653i	−0.234261	+	0.720980i	−0.997219	+	0.0745320i	$0.976254\pi$
$42$		0			0
$43$	2.85410			0.435246			0.217623	−	0.976033i	$-0.430170\pi$
$43$	2.85410			0.435246			0.217623	+	0.976033i	$0.430170\pi$
$44$		0			0
$45$	2.85410			0.425464
$46$		0			0
$47$	3.47214	−	10.6861i	0.506463	−	1.55873i	−0.291834	−	0.956469i	$-0.594265\pi$
$47$	3.47214	−	10.6861i	0.506463	−	1.55873i	0.798297	−	0.602264i	$-0.205735\pi$
$48$		0			0
$49$	5.66312	−	4.11450i	0.809017	−	0.587785i
$50$		0			0
$51$	−0.600813	−	1.84911i	−0.0841307	−	0.258928i
$52$		0			0
$53$	2.85410	+	2.07363i	0.392041	+	0.284834i	0.766291	−	0.642493i	$-0.222100\pi$
$53$	2.85410	+	2.07363i	0.392041	+	0.284834i	−0.374250	+	0.927328i	$0.622100\pi$
$54$		0			0
$55$	2.54508	−	2.12663i	0.343179	−	0.286754i
$56$		0			0
$57$	1.19098	+	0.865300i	0.157750	+	0.114612i
$58$		0			0
$59$	−3.57295	−	10.9964i	−0.465158	−	1.43161i	−0.858783	−	0.512339i	$-0.828779\pi$
$59$	−3.57295	−	10.9964i	−0.465158	−	1.43161i	0.393625	−	0.919271i	$-0.371221\pi$
$60$		0			0
$61$	6.23607	−	4.53077i	0.798447	−	0.580105i	−0.112011	−	0.993707i	$-0.535729\pi$
$61$	6.23607	−	4.53077i	0.798447	−	0.580105i	0.910458	+	0.413601i	$0.135729\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.47214			−0.802770
$66$		0			0
$67$	0.618034			0.0755049			0.0377524	−	0.999287i	$-0.487980\pi$
$67$	0.618034			0.0755049			0.0377524	+	0.999287i	$0.487980\pi$
$68$		0			0
$69$	0.708204	−	2.17963i	0.0852577	−	0.262396i
$70$		0			0
$71$	−3.85410	+	2.80017i	−0.457398	+	0.332319i	−0.792510	−	0.609859i	$-0.791226\pi$
$71$	−3.85410	+	2.80017i	−0.457398	+	0.332319i	0.335112	+	0.942178i	$0.391226\pi$
$72$		0			0
$73$	0.354102	+	1.08981i	0.0414445	+	0.127553i	0.969638	−	0.244545i	$-0.0786386\pi$
$73$	0.354102	+	1.08981i	0.0414445	+	0.127553i	−0.928193	+	0.372098i	$0.878639\pi$
$74$		0			0
$75$	−0.309017	−	0.224514i	−0.0356822	−	0.0259246i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	5.85410	+	4.25325i	0.658638	+	0.478528i	0.866203	−	0.499693i	$-0.166554\pi$
$79$	5.85410	+	4.25325i	0.658638	+	0.478528i	−0.207565	+	0.978221i	$0.566554\pi$
$80$		0			0
$81$	2.38197	+	7.33094i	0.264663	+	0.814549i
$82$		0			0
$83$	−10.0172	+	7.27794i	−1.09953	+	0.798857i	−0.980984	−	0.194091i	$-0.937824\pi$
$83$	−10.0172	+	7.27794i	−1.09953	+	0.798857i	−0.118549	+	0.992948i	$0.537824\pi$
$84$		0			0
$85$	1.57295	−	4.84104i	0.170610	−	0.525084i
$86$		0			0
$87$	1.81966			0.195088
$88$		0			0
$89$	−4.09017			−0.433557			−0.216779	−	0.976221i	$-0.569555\pi$
$89$	−4.09017			−0.433557			−0.216779	+	0.976221i	$0.569555\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.14590	+	0.832544i	−0.118824	+	0.0863308i
$94$		0			0
$95$	1.19098	+	3.66547i	0.122192	+	0.376069i
$96$		0			0
$97$	6.16312	+	4.47777i	0.625770	+	0.454648i	0.854932	−	0.518740i	$-0.173599\pi$
$97$	6.16312	+	4.47777i	0.625770	+	0.454648i	−0.229162	+	0.973388i	$0.573599\pi$
$98$		0			0
$99$	8.01722	+	5.03280i	0.805761	+	0.505815i
$100$		0			0
$101$	−8.23607	−	5.98385i	−0.819519	−	0.595416i	0.0970554	−	0.995279i	$-0.469058\pi$
$101$	−8.23607	−	5.98385i	−0.819519	−	0.595416i	−0.916575	+	0.399863i	$0.869058\pi$
$102$		0			0
$103$	4.85410	+	14.9394i	0.478289	+	1.47202i	0.841470	+	0.540303i	$0.181691\pi$
$103$	4.85410	+	14.9394i	0.478289	+	1.47202i	−0.363181	+	0.931718i	$0.618309\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.590170	−	1.81636i	0.0570539	−	0.175594i	−0.918468	−	0.395494i	$-0.870573\pi$
$107$	0.590170	−	1.81636i	0.0570539	−	0.175594i	0.975522	+	0.219901i	$0.0705733\pi$
$108$		0			0
$109$	−17.7082			−1.69614			−0.848069	−	0.529886i	$-0.822235\pi$
$109$	−17.7082			−1.69614			−0.848069	+	0.529886i	$0.822235\pi$
$110$		0			0
$111$	−0.763932			−0.0725092
$112$		0			0
$113$	−2.89919	+	8.92278i	−0.272733	+	0.839385i	0.717078	+	0.696993i	$0.245479\pi$
$113$	−2.89919	+	8.92278i	−0.272733	+	0.839385i	−0.989810	+	0.142391i	$0.954521\pi$
$114$		0			0
$115$	4.85410	−	3.52671i	0.452647	−	0.328868i
$116$		0			0
$117$	−5.70820	−	17.5680i	−0.527724	−	1.62417i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	10.8992	−	1.48584i	0.990835	−	0.135076i
$122$		0			0
$123$	1.50000	+	1.08981i	0.135250	+	0.0982652i
$124$		0			0
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$		0			0
$127$	−6.23607	+	4.53077i	−0.553362	+	0.402041i	−0.829023	−	0.559214i	$-0.811103\pi$
$127$	−6.23607	+	4.53077i	−0.553362	+	0.402041i	0.275662	+	0.961255i	$0.411103\pi$
$128$		0			0
$129$	0.336881	−	1.03681i	0.0296607	−	0.0912863i
$130$		0			0
$131$	0.437694			0.0382415			0.0191208	−	0.999817i	$-0.493913\pi$
$131$	0.437694			0.0382415			0.0191208	+	0.999817i	$0.493913\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.690983	−	2.12663i	0.0594703	−	0.183031i
$136$		0			0
$137$	4.92705	−	3.57971i	0.420946	−	0.305835i	−0.357072	−	0.934077i	$-0.616225\pi$
$137$	4.92705	−	3.57971i	0.420946	−	0.305835i	0.778018	+	0.628241i	$0.216225\pi$
$138$		0			0
$139$	4.00000	+	12.3107i	0.339276	+	1.04418i	0.964577	+	0.263800i	$0.0849759\pi$
$139$	4.00000	+	12.3107i	0.339276	+	1.04418i	−0.625302	+	0.780383i	$0.715024\pi$
$140$		0			0
$141$	−3.47214	−	2.52265i	−0.292407	−	0.212446i
$142$		0			0
$143$	−18.1803	−	11.4127i	−1.52032	−	0.954376i
$144$		0			0
$145$	3.85410	+	2.80017i	0.320066	+	0.232541i
$146$		0			0
$147$	−0.826238	−	2.54290i	−0.0681470	−	0.209735i
$148$		0			0
$149$	−16.7082	+	12.1392i	−1.36879	+	0.994484i	−0.370959	+	0.928649i	$0.620971\pi$
$149$	−16.7082	+	12.1392i	−1.36879	+	0.994484i	−0.997831	+	0.0658344i	$0.979029\pi$
$150$		0			0
$151$	3.85410	−	11.8617i	0.313642	−	0.965292i	−0.662667	−	0.748914i	$-0.730576\pi$
$151$	3.85410	−	11.8617i	0.313642	−	0.965292i	0.976310	−	0.216378i	$-0.0694244\pi$
$152$		0			0
$153$	14.5279			1.17451
$154$		0			0
$155$	−3.70820			−0.297850
$156$		0			0
$157$	2.47214	−	7.60845i	0.197298	−	0.607221i	−0.802644	−	0.596458i	$-0.796574\pi$
$157$	2.47214	−	7.60845i	0.197298	−	0.607221i	0.999942	−	0.0107624i	$-0.00342585\pi$
$158$		0			0
$159$	1.09017	−	0.792055i	0.0864561	−	0.0628140i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−9.20820	−	6.69015i	−0.721242	−	0.524013i	0.165539	−	0.986203i	$-0.447064\pi$
$163$	−9.20820	−	6.69015i	−0.721242	−	0.524013i	−0.886781	+	0.462190i	$0.847064\pi$
$164$		0			0
$165$	−0.472136	−	1.17557i	−0.0367557	−	0.0915180i
$166$		0			0
$167$	−16.3262	−	11.8617i	−1.26336	−	0.917886i	−0.264445	−	0.964401i	$-0.585189\pi$
$167$	−16.3262	−	11.8617i	−1.26336	−	0.917886i	−0.998918	+	0.0465145i	$0.985189\pi$
$168$		0			0
$169$	8.92705	+	27.4746i	0.686696	+	2.11343i
$170$		0			0
$171$	−8.89919	+	6.46564i	−0.680538	+	0.494440i
$172$		0			0
$173$	−1.14590	+	3.52671i	−0.0871210	+	0.268131i	−0.985120	−	0.171866i	$-0.945020\pi$
$173$	−1.14590	+	3.52671i	−0.0871210	+	0.268131i	0.897999	+	0.439997i	$0.145020\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.41641			−0.331958
$178$		0			0
$179$	−7.57295	+	23.3071i	−0.566029	+	1.74206i	0.0988461	+	0.995103i	$0.468485\pi$
$179$	−7.57295	+	23.3071i	−0.566029	+	1.74206i	−0.664875	+	0.746955i	$0.731515\pi$
$180$		0			0
$181$	−7.85410	+	5.70634i	−0.583791	+	0.424149i	−0.840089	−	0.542449i	$-0.817497\pi$
$181$	−7.85410	+	5.70634i	−0.583791	+	0.424149i	0.256298	+	0.966598i	$0.417497\pi$
$182$		0			0
$183$	−0.909830	−	2.80017i	−0.0672566	−	0.206994i
$184$		0			0
$185$	−1.61803	−	1.17557i	−0.118960	−	0.0864297i
$186$		0			0
$187$	12.9549	−	10.8249i	0.947357	−	0.791595i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.00000	+	21.5438i	0.506502	+	1.55885i	0.798230	+	0.602352i	$0.205770\pi$
$191$	7.00000	+	21.5438i	0.506502	+	1.55885i	−0.291728	+	0.956501i	$0.594230\pi$
$192$		0			0
$193$	−14.5623	+	10.5801i	−1.04822	+	0.761575i	−0.971873	−	0.235507i	$-0.924325\pi$
$193$	−14.5623	+	10.5801i	−1.04822	+	0.761575i	−0.0763450	+	0.997081i	$0.524325\pi$
$194$		0			0
$195$	−0.763932	+	2.35114i	−0.0547063	+	0.168369i
$196$		0			0
$197$	1.05573			0.0752175			0.0376088	−	0.999293i	$-0.488026\pi$
$197$	1.05573			0.0752175			0.0376088	+	0.999293i	$0.488026\pi$
$198$		0			0
$199$	−22.1803			−1.57232			−0.786161	−	0.618021i	$-0.787935\pi$
$199$	−22.1803			−1.57232			−0.786161	+	0.618021i	$0.787935\pi$
$200$		0			0
$201$	0.0729490	−	0.224514i	0.00514543	−	0.0158360i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.50000	+	4.61653i	0.104765	+	0.322432i
$206$		0			0
$207$	13.8541	+	10.0656i	0.962927	+	0.699607i
$208$		0			0
$209$	−3.11803	+	12.3965i	−0.215679	+	0.857483i
$210$		0			0
$211$	−15.4894	−	11.2537i	−1.06633	−	0.774735i	−0.0910821	−	0.995843i	$-0.529033\pi$
$211$	−15.4894	−	11.2537i	−1.06633	−	0.774735i	−0.975249	+	0.221108i	$0.929033\pi$
$212$		0			0
$213$	0.562306	+	1.73060i	0.0385286	+	0.118579i
$214$		0			0
$215$	2.30902	−	1.67760i	0.157474	−	0.114411i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	0.437694			0.0295766
$220$		0			0
$221$	−32.9443			−2.21607
$222$		0			0
$223$	−1.23607	+	3.80423i	−0.0827732	+	0.254750i	−0.983875	−	0.178858i	$-0.942760\pi$
$223$	−1.23607	+	3.80423i	−0.0827732	+	0.254750i	0.901102	+	0.433608i	$0.142760\pi$
$224$		0			0
$225$	2.30902	−	1.67760i	0.153934	−	0.111840i
$226$		0			0
$227$	−1.04508	−	3.21644i	−0.0693647	−	0.213483i	0.910365	−	0.413806i	$-0.135801\pi$
$227$	−1.04508	−	3.21644i	−0.0693647	−	0.213483i	−0.979730	+	0.200323i	$0.935801\pi$
$228$		0			0
$229$	−7.70820	−	5.60034i	−0.509372	−	0.370081i	0.303213	−	0.952923i	$-0.401941\pi$
$229$	−7.70820	−	5.60034i	−0.509372	−	0.370081i	−0.812585	+	0.582842i	$0.801941\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−15.3992	−	11.1882i	−1.00883	−	0.732961i	−0.0448700	−	0.998993i	$-0.514287\pi$
$233$	−15.3992	−	11.1882i	−1.00883	−	0.732961i	−0.963964	+	0.266032i	$0.914287\pi$
$234$		0			0
$235$	−3.47214	−	10.6861i	−0.226497	−	0.697087i
$236$		0			0
$237$	2.23607	−	1.62460i	0.145248	−	0.105529i
$238$		0			0
$239$	−4.61803	+	14.2128i	−0.298716	+	0.919353i	0.683232	+	0.730201i	$0.260574\pi$
$239$	−4.61803	+	14.2128i	−0.298716	+	0.919353i	−0.981948	+	0.189151i	$0.939426\pi$
$240$		0			0
$241$	13.8541			0.892421			0.446211	−	0.894928i	$-0.352773\pi$
$241$	13.8541			0.892421			0.446211	+	0.894928i	$0.352773\pi$
$242$		0			0
$243$	9.65248			0.619207
$244$		0			0
$245$	2.16312	−	6.65740i	0.138197	−	0.425325i
$246$		0			0
$247$	20.1803	−	14.6619i	1.28404	−	0.932913i
$248$		0			0
$249$	1.46149	+	4.49801i	0.0926183	+	0.285050i
$250$		0			0
$251$	14.4721	+	10.5146i	0.913473	+	0.663677i	0.941891	−	0.335919i	$-0.109047\pi$
$251$	14.4721	+	10.5146i	0.913473	+	0.663677i	−0.0284177	+	0.999596i	$0.509047\pi$
$252$		0			0
$253$	19.8541	−	1.34708i	1.24822	−	0.0846904i
$254$		0			0
$255$	−1.57295	−	1.14281i	−0.0985019	−	0.0715658i
$256$		0			0
$257$	−2.88197	−	8.86978i	−0.179772	−	0.553282i	0.820047	−	0.572296i	$-0.193947\pi$
$257$	−2.88197	−	8.86978i	−0.179772	−	0.553282i	−0.999819	+	0.0190144i	$0.993947\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−4.20163	+	12.9313i	−0.260074	+	0.800426i
$262$		0			0
$263$	0.180340			0.0111202			0.00556012	−	0.999985i	$-0.498230\pi$
$263$	0.180340			0.0111202			0.00556012	+	0.999985i	$0.498230\pi$
$264$		0			0
$265$	3.52786			0.216715
$266$		0			0
$267$	−0.482779	+	1.48584i	−0.0295456	+	0.0909320i
$268$		0			0
$269$	19.7082	−	14.3188i	1.20163	−	0.873036i	0.207186	−	0.978302i	$-0.433569\pi$
$269$	19.7082	−	14.3188i	1.20163	−	0.873036i	0.994444	+	0.105266i	$0.0335694\pi$
$270$		0			0
$271$	6.18034	+	19.0211i	0.375429	+	1.15545i	0.943189	+	0.332257i	$0.107810\pi$
$271$	6.18034	+	19.0211i	0.375429	+	1.15545i	−0.567760	+	0.823194i	$0.692190\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.809017	−	3.21644i	0.0487856	−	0.193959i
$276$		0			0
$277$	−7.61803	−	5.53483i	−0.457723	−	0.332555i	0.334914	−	0.942249i	$-0.391293\pi$
$277$	−7.61803	−	5.53483i	−0.457723	−	0.332555i	−0.792638	+	0.609693i	$0.791293\pi$
$278$		0			0
$279$	−3.27051	−	10.0656i	−0.195800	−	0.602611i
$280$		0			0
$281$	3.78115	−	2.74717i	0.225565	−	0.163882i	−0.469263	−	0.883058i	$-0.655480\pi$
$281$	3.78115	−	2.74717i	0.225565	−	0.163882i	0.694828	+	0.719176i	$0.255480\pi$
$282$		0			0
$283$	0.763932	−	2.35114i	0.0454110	−	0.139761i	−0.925780	−	0.378062i	$-0.876591\pi$
$283$	0.763932	−	2.35114i	0.0454110	−	0.139761i	0.971191	+	0.238301i	$0.0765906\pi$
$284$		0			0
$285$	1.47214			0.0872018
$286$		0			0
$287$		0			0
$288$		0			0
$289$	2.75329	−	8.47375i	0.161958	−	0.498456i
$290$		0			0
$291$	2.35410	−	1.71036i	0.138000	−	0.100263i
$292$		0			0
$293$	3.47214	+	10.6861i	0.202844	+	0.624291i	0.999795	+	0.0202463i	$0.00644505\pi$
$293$	3.47214	+	10.6861i	0.202844	+	0.624291i	−0.796951	+	0.604044i	$0.793555\pi$
$294$		0			0
$295$	−9.35410	−	6.79615i	−0.544617	−	0.395687i
$296$		0			0
$297$	5.69098	−	4.75528i	0.330224	−	0.275929i
$298$		0			0
$299$	−31.4164	−	22.8254i	−1.81686	−	1.32002i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−3.14590	+	2.28563i	−0.180727	+	0.131306i
$304$		0			0
$305$	2.38197	−	7.33094i	0.136391	−	0.419768i
$306$		0			0
$307$	−12.5623			−0.716969			−0.358484	−	0.933536i	$-0.616706\pi$
$307$	−12.5623			−0.716969			−0.358484	+	0.933536i	$0.616706\pi$
$308$		0			0
$309$	6.00000			0.341328
$310$		0			0
$311$	0.854102	−	2.62866i	0.0484317	−	0.149057i	−0.923916	−	0.382595i	$-0.875030\pi$
$311$	0.854102	−	2.62866i	0.0484317	−	0.149057i	0.972348	+	0.233538i	$0.0750303\pi$
$312$		0			0
$313$	−26.0623	+	18.9354i	−1.47313	+	1.07029i	−0.493437	+	0.869782i	$0.664260\pi$
$313$	−26.0623	+	18.9354i	−1.47313	+	1.07029i	−0.979692	+	0.200509i	$0.935740\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.09017	−	6.60440i	−0.510555	−	0.370940i	0.302479	−	0.953156i	$-0.402186\pi$
$317$	−9.09017	−	6.60440i	−0.510555	−	0.370940i	−0.813034	+	0.582216i	$0.802186\pi$
$318$		0			0
$319$	5.88854	+	14.6619i	0.329695	+	0.820907i
$320$		0			0
$321$	−0.590170	−	0.428784i	−0.0329401	−	0.0239324i
$322$		0			0
$323$	6.06231	+	18.6579i	0.337316	+	1.03815i
$324$		0			0
$325$	−5.23607	+	3.80423i	−0.290445	+	0.211020i
$326$		0			0
$327$	−2.09017	+	6.43288i	−0.115587	+	0.355739i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	14.5623			0.800417			0.400208	−	0.916424i	$-0.368938\pi$
$331$	14.5623			0.800417			0.400208	+	0.916424i	$0.368938\pi$
$332$		0			0
$333$	1.76393	−	5.42882i	0.0966629	−	0.297498i
$334$		0			0
$335$	0.500000	−	0.363271i	0.0273179	−	0.0198476i
$336$		0			0
$337$	8.51722	+	26.2133i	0.463963	+	1.42793i	0.860283	+	0.509818i	$0.170287\pi$
$337$	8.51722	+	26.2133i	0.463963	+	1.42793i	−0.396320	+	0.918112i	$0.629713\pi$
$338$		0			0
$339$	2.89919	+	2.10638i	0.157462	+	0.114403i
$340$		0			0
$341$	−10.4164	−	6.53888i	−0.564080	−	0.354100i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−0.708204	−	2.17963i	−0.0381284	−	0.117347i
$346$		0			0
$347$	7.50000	−	5.44907i	0.402621	−	0.292521i	−0.367987	−	0.929831i	$-0.619953\pi$
$347$	7.50000	−	5.44907i	0.402621	−	0.292521i	0.770608	+	0.637310i	$0.219953\pi$
$348$		0			0
$349$	4.47214	−	13.7638i	0.239388	−	0.736760i	−0.757121	−	0.653275i	$-0.773395\pi$
$349$	4.47214	−	13.7638i	0.239388	−	0.736760i	0.996509	−	0.0834857i	$-0.0266053\pi$
$350$		0			0
$351$	−14.4721			−0.772465
$352$		0			0
$353$	−3.27051			−0.174072			−0.0870358	−	0.996205i	$-0.527739\pi$
$353$	−3.27051			−0.174072			−0.0870358	+	0.996205i	$0.527739\pi$
$354$		0			0
$355$	−1.47214	+	4.53077i	−0.0781329	+	0.240468i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.61803	−	4.97980i	−0.0853966	−	0.262824i	0.899236	−	0.437465i	$-0.144123\pi$
$359$	−1.61803	−	4.97980i	−0.0853966	−	0.262824i	−0.984632	+	0.174641i	$0.944123\pi$
$360$		0			0
$361$	3.35410	+	2.43690i	0.176532	+	0.128258i
$362$		0			0
$363$	0.746711	−	4.13474i	0.0391922	−	0.217018i
$364$		0			0
$365$	0.927051	+	0.673542i	0.0485241	+	0.0352548i
$366$		0			0
$367$	0.708204	+	2.17963i	0.0369679	+	0.113776i	0.967838	−	0.251576i	$-0.0809488\pi$
$367$	0.708204	+	2.17963i	0.0369679	+	0.113776i	−0.930870	+	0.365352i	$0.880949\pi$
$368$		0			0
$369$	−11.2082	+	8.14324i	−0.583476	+	0.423920i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	27.1246			1.40446			0.702230	−	0.711951i	$-0.252188\pi$
$373$	27.1246			1.40446			0.702230	+	0.711951i	$0.252188\pi$
$374$		0			0
$375$	−0.381966			−0.0197246
$376$		0			0
$377$	9.52786	−	29.3238i	0.490710	−	1.51025i
$378$		0			0
$379$	9.16312	−	6.65740i	0.470678	−	0.341967i	−0.327028	−	0.945015i	$-0.606047\pi$
$379$	9.16312	−	6.65740i	0.470678	−	0.341967i	0.797705	+	0.603047i	$0.206047\pi$
$380$		0			0
$381$	0.909830	+	2.80017i	0.0466120	+	0.143457i
$382$		0			0
$383$	−2.85410	−	2.07363i	−0.145838	−	0.105957i	0.512474	−	0.858703i	$-0.328729\pi$
$383$	−2.85410	−	2.07363i	−0.145838	−	0.105957i	−0.658312	+	0.752745i	$0.728729\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.59017	+	4.78804i	0.334997	+	0.243390i
$388$		0			0
$389$	5.43769	+	16.7355i	0.275702	+	0.848524i	0.989033	+	0.147696i	$0.0471857\pi$
$389$	5.43769	+	16.7355i	0.275702	+	0.848524i	−0.713331	+	0.700828i	$0.752814\pi$
$390$		0			0
$391$	24.7082	−	17.9516i	1.24955	−	0.907849i
$392$		0			0
$393$	0.0516628	−	0.159002i	0.00260604	−	0.00802057i
$394$		0			0
$395$	7.23607			0.364086
$396$		0			0
$397$	3.12461			0.156820			0.0784099	−	0.996921i	$-0.475016\pi$
$397$	3.12461			0.156820			0.0784099	+	0.996921i	$0.475016\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	29.3435	−	21.3193i	1.46534	−	1.06463i	0.483412	−	0.875393i	$-0.339397\pi$
$401$	29.3435	−	21.3193i	1.46534	−	1.06463i	0.981931	−	0.189240i	$-0.0606025\pi$
$402$		0			0
$403$	7.41641	+	22.8254i	0.369438	+	1.13701i
$404$		0			0
$405$	6.23607	+	4.53077i	0.309873	+	0.225136i
$406$		0			0
$407$	−2.47214	−	6.15537i	−0.122539	−	0.305110i
$408$		0			0
$409$	−9.32624	−	6.77591i	−0.461153	−	0.335047i	0.332831	−	0.942987i	$-0.391996\pi$
$409$	−9.32624	−	6.77591i	−0.461153	−	0.335047i	−0.793983	+	0.607940i	$0.791996\pi$
$410$		0			0
$411$	−0.718847	−	2.21238i	−0.0354581	−	0.109129i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−3.82624	+	11.7759i	−0.187823	+	0.578059i
$416$		0			0
$417$	4.94427			0.242122
$418$		0			0
$419$	−1.03444			−0.0505358			−0.0252679	−	0.999681i	$-0.508044\pi$
$419$	−1.03444			−0.0505358			−0.0252679	+	0.999681i	$0.508044\pi$
$420$		0			0
$421$	4.90983	−	15.1109i	0.239290	−	0.736460i	−0.757233	−	0.653145i	$-0.773449\pi$
$421$	4.90983	−	15.1109i	0.239290	−	0.736460i	0.996523	−	0.0833152i	$-0.0265508\pi$
$422$		0			0
$423$	25.9443	−	18.8496i	1.26145	−	0.916500i
$424$		0			0
$425$	−1.57295	−	4.84104i	−0.0762992	−	0.234825i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−6.29180	+	5.25731i	−0.303771	+	0.253825i
$430$		0			0
$431$	−8.23607	−	5.98385i	−0.396717	−	0.288232i	0.371485	−	0.928439i	$-0.378849\pi$
$431$	−8.23607	−	5.98385i	−0.396717	−	0.288232i	−0.768203	+	0.640207i	$0.778849\pi$
$432$		0			0
$433$	−9.28115	−	28.5645i	−0.446024	−	1.37272i	−0.881357	−	0.472451i	$-0.843369\pi$
$433$	−9.28115	−	28.5645i	−0.446024	−	1.37272i	0.435333	−	0.900269i	$-0.356631\pi$
$434$		0			0
$435$	1.47214	−	1.06957i	0.0705835	−	0.0512819i
$436$		0			0
$437$	−7.14590	+	21.9928i	−0.341835	+	1.05206i
$438$		0			0
$439$	38.3607			1.83086			0.915428	−	0.402483i	$-0.131853\pi$
$439$	38.3607			1.83086			0.915428	+	0.402483i	$0.131853\pi$
$440$		0			0
$441$	19.9787			0.951367
$442$		0			0
$443$	12.4098	−	38.1935i	0.589609	−	1.81463i	0.00969290	−	0.999953i	$-0.496915\pi$
$443$	12.4098	−	38.1935i	0.589609	−	1.81463i	0.579916	−	0.814676i	$-0.303085\pi$
$444$		0			0
$445$	−3.30902	+	2.40414i	−0.156862	+	0.113967i
$446$		0			0
$447$	2.43769	+	7.50245i	0.115299	+	0.354854i
$448$		0			0
$449$	−14.7361	−	10.7064i	−0.695438	−	0.505265i	0.183005	−	0.983112i	$-0.441417\pi$
$449$	−14.7361	−	10.7064i	−0.695438	−	0.505265i	−0.878443	+	0.477847i	$0.841417\pi$
$450$		0			0
$451$	−3.92705	+	15.6129i	−0.184918	+	0.735184i
$452$		0			0
$453$	−3.85410	−	2.80017i	−0.181082	−	0.131563i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.92705	−	3.57971i	0.230478	−	0.167452i	−0.466553	−	0.884493i	$-0.654504\pi$
$457$	4.92705	−	3.57971i	0.230478	−	0.167452i	0.697030	+	0.717042i	$0.254504\pi$
$458$		0			0
$459$	3.51722	−	10.8249i	0.164170	−	0.505263i
$460$		0			0
$461$	−8.18034			−0.380996			−0.190498	−	0.981688i	$-0.561010\pi$
$461$	−8.18034			−0.380996			−0.190498	+	0.981688i	$0.561010\pi$
$462$		0			0
$463$	−23.1246			−1.07469			−0.537346	−	0.843362i	$-0.680573\pi$
$463$	−23.1246			−1.07469			−0.537346	+	0.843362i	$0.680573\pi$
$464$		0			0
$465$	−0.437694	+	1.34708i	−0.0202976	+	0.0624695i
$466$		0			0
$467$	−32.1803	+	23.3804i	−1.48913	+	1.08192i	−0.514659	+	0.857395i	$0.672082\pi$
$467$	−32.1803	+	23.3804i	−1.48913	+	1.08192i	−0.974469	+	0.224520i	$0.927918\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−2.47214	−	1.79611i	−0.113910	−	0.0827605i
$472$		0			0
$473$	9.44427	−	0.640786i	0.434248	−	0.0294634i
$474$		0			0
$475$	3.11803	+	2.26538i	0.143065	+	0.103943i
$476$		0			0
$477$	3.11146	+	9.57608i	0.142464	+	0.438458i
$478$		0			0
$479$	4.09017	−	2.97168i	0.186885	−	0.135780i	−0.490409	−	0.871492i	$-0.663153\pi$
$479$	4.09017	−	2.97168i	0.186885	−	0.135780i	0.677294	+	0.735713i	$0.263153\pi$
$480$		0			0
$481$	−4.00000	+	12.3107i	−0.182384	+	0.561321i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.61803			0.345917
$486$		0			0
$487$	12.5279	−	38.5568i	0.567692	−	1.74718i	−0.0921236	−	0.995748i	$-0.529365\pi$
$487$	12.5279	−	38.5568i	0.567692	−	1.74718i	0.659815	−	0.751428i	$-0.270635\pi$
$488$		0			0
$489$	−3.51722	+	2.55541i	−0.159054	+	0.115560i
$490$		0			0
$491$	−11.6803	−	35.9484i	−0.527126	−	1.62233i	−0.760072	−	0.649838i	$-0.774837\pi$
$491$	−11.6803	−	35.9484i	−0.527126	−	1.62233i	0.232946	−	0.972490i	$-0.425163\pi$
$492$		0			0
$493$	19.6180	+	14.2533i	0.883552	+	0.641938i
$494$		0			0
$495$	9.44427	−	0.640786i	0.424488	−	0.0288012i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	12.4443	+	38.2995i	0.557082	+	1.71452i	0.690380	+	0.723447i	$0.257443\pi$
$499$	12.4443	+	38.2995i	0.557082	+	1.71452i	−0.133298	+	0.991076i	$0.542557\pi$
$500$		0			0
$501$	−6.23607	+	4.53077i	−0.278607	+	0.202420i
$502$		0			0
$503$	−7.43769	+	22.8909i	−0.331630	+	1.02065i	0.636728	+	0.771089i	$0.280288\pi$
$503$	−7.43769	+	22.8909i	−0.331630	+	1.02065i	−0.968358	+	0.249565i	$0.919712\pi$
$504$		0			0
$505$	−10.1803			−0.453019
$506$		0			0
$507$	11.0344			0.490057
$508$		0			0
$509$	−6.14590	+	18.9151i	−0.272412	+	0.838398i	0.717480	+	0.696579i	$0.245295\pi$
$509$	−6.14590	+	18.9151i	−0.272412	+	0.838398i	−0.989893	+	0.141820i	$0.954705\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	2.66312	+	8.19624i	0.117580	+	0.361873i
$514$		0			0
$515$	12.7082	+	9.23305i	0.559990	+	0.406857i
$516$		0			0
$517$	9.09017	−	36.1401i	0.399785	−	1.58944i
$518$		0			0
$519$	1.14590	+	0.832544i	0.0502993	+	0.0365446i
$520$		0			0
$521$	3.80902	+	11.7229i	0.166876	+	0.513592i	0.999170	−	0.0407434i	$-0.0129726\pi$
$521$	3.80902	+	11.7229i	0.166876	+	0.513592i	−0.832294	+	0.554335i	$0.812973\pi$
$522$		0			0
$523$	−8.20820	+	5.96361i	−0.358920	+	0.260770i	−0.752601	−	0.658476i	$-0.771201\pi$
$523$	−8.20820	+	5.96361i	−0.358920	+	0.260770i	0.393682	+	0.919247i	$0.371201\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−18.8754			−0.822225
$528$		0			0
$529$	13.0000			0.565217
$530$		0			0
$531$	10.1976	−	31.3849i	0.442536	−	1.36199i
$532$		0			0
$533$	25.4164	−	18.4661i	1.10091	−	0.799856i
$534$		0			0
$535$	−0.590170	−	1.81636i	−0.0255153	−	0.0785279i
$536$		0			0
$537$	7.57295	+	5.50207i	0.326797	+	0.237432i
$538$		0			0
$539$	17.8156	−	14.8864i	0.767372	−	0.641202i
$540$		0			0
$541$	11.3262	+	8.22899i	0.486953	+	0.353792i	0.804011	−	0.594614i	$-0.202695\pi$
$541$	11.3262	+	8.22899i	0.486953	+	0.353792i	−0.317058	+	0.948406i	$0.602695\pi$
$542$		0			0
$543$	1.14590	+	3.52671i	0.0491752	+	0.151346i
$544$		0			0
$545$	−14.3262	+	10.4086i	−0.613669	+	0.445856i
$546$		0			0
$547$	11.6976	−	36.0014i	0.500152	−	1.53931i	−0.308620	−	0.951185i	$-0.599867\pi$
$547$	11.6976	−	36.0014i	0.500152	−	1.53931i	0.808772	−	0.588123i	$-0.200133\pi$
$548$		0			0
$549$	22.0000			0.938937
$550$		0			0
$551$	−18.3607			−0.782191
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.618034	+	0.449028i	−0.0262341	+	0.0190602i
$556$		0			0
$557$	8.14590	+	25.0705i	0.345153	+	1.06227i	0.961502	+	0.274798i	$0.0886110\pi$
$557$	8.14590	+	25.0705i	0.345153	+	1.06227i	−0.616349	+	0.787473i	$0.711389\pi$
$558$		0			0
$559$	−14.9443	−	10.8576i	−0.632075	−	0.459230i
$560$		0			0
$561$	−2.40325	−	5.98385i	−0.101465	−	0.252638i
$562$		0			0
$563$	1.69098	+	1.22857i	0.0712664	+	0.0517781i	0.622848	−	0.782343i	$-0.285975\pi$
$563$	1.69098	+	1.22857i	0.0712664	+	0.0517781i	−0.551582	+	0.834121i	$0.685975\pi$
$564$		0			0
$565$	2.89919	+	8.92278i	0.121970	+	0.375384i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.39261	−	7.36369i	0.100303	−	0.308702i	−0.888296	−	0.459271i	$-0.848111\pi$
$569$	2.39261	−	7.36369i	0.100303	−	0.308702i	0.988599	+	0.150569i	$0.0481106\pi$
$570$		0			0
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$	8.65248			0.361462
$574$		0			0
$575$	1.85410	−	5.70634i	0.0773214	−	0.237971i
$576$		0			0
$577$	22.5344	−	16.3722i	0.938121	−	0.681585i	−0.00984657	−	0.999952i	$-0.503134\pi$
$577$	22.5344	−	16.3722i	0.938121	−	0.681585i	0.947968	+	0.318367i	$0.103134\pi$
$578$		0			0
$579$	2.12461	+	6.53888i	0.0882959	+	0.271747i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	9.90983	+	6.22088i	0.410423	+	0.257642i
$584$		0			0
$585$	−14.9443	−	10.8576i	−0.617870	−	0.448909i
$586$		0			0
$587$	4.01064	+	12.3435i	0.165537	+	0.509470i	0.999075	−	0.0429910i	$-0.0136887\pi$
$587$	4.01064	+	12.3435i	0.165537	+	0.509470i	−0.833539	+	0.552461i	$0.813689\pi$
$588$		0			0
$589$	11.5623	−	8.40051i	0.476417	−	0.346137i
$590$		0			0
$591$	0.124612	−	0.383516i	0.00512584	−	0.0157757i
$592$		0			0
$593$	−31.8541			−1.30809			−0.654046	−	0.756455i	$-0.726930\pi$
$593$	−31.8541			−1.30809			−0.654046	+	0.756455i	$0.726930\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.61803	+	8.05748i	−0.107149	+	0.329771i
$598$		0			0
$599$	2.38197	−	1.73060i	0.0973245	−	0.0707104i	−0.538059	−	0.842907i	$-0.680842\pi$
$599$	2.38197	−	1.73060i	0.0973245	−	0.0707104i	0.635383	+	0.772197i	$0.280842\pi$
$600$		0			0
$601$	−0.0278640	−	0.0857567i	−0.00113660	−	0.00349809i	0.950487	−	0.310766i	$-0.100585\pi$
$601$	−0.0278640	−	0.0857567i	−0.00113660	−	0.00349809i	−0.951623	+	0.307267i	$0.900585\pi$
$602$		0			0
$603$	1.42705	+	1.03681i	0.0581140	+	0.0422223i
$604$		0			0
$605$	7.94427	−	7.60845i	0.322981	−	0.309328i
$606$		0			0
$607$	10.7082	+	7.77997i	0.434633	+	0.315779i	0.783499	−	0.621394i	$-0.213433\pi$
$607$	10.7082	+	7.77997i	0.434633	+	0.315779i	−0.348866	+	0.937173i	$0.613433\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−58.8328	+	42.7445i	−2.38012	+	1.72926i
$612$		0			0
$613$	4.23607	−	13.0373i	0.171093	−	0.526571i	−0.828340	−	0.560225i	$-0.810715\pi$
$613$	4.23607	−	13.0373i	0.171093	−	0.526571i	0.999434	+	0.0336545i	$0.0107146\pi$
$614$		0			0
$615$	1.85410			0.0747646
$616$		0			0
$617$	−14.9098			−0.600247			−0.300124	−	0.953900i	$-0.597028\pi$
$617$	−14.9098			−0.600247			−0.300124	+	0.953900i	$0.597028\pi$
$618$		0			0
$619$	3.39261	−	10.4414i	0.136360	−	0.419674i	−0.859439	−	0.511239i	$-0.829187\pi$
$619$	3.39261	−	10.4414i	0.136360	−	0.419674i	0.995799	+	0.0915645i	$0.0291868\pi$
$620$		0			0
$621$	10.8541	−	7.88597i	0.435560	−	0.316453i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	4.13525	+	2.59590i	0.165146	+	0.103670i
$628$		0			0
$629$	−8.23607	−	5.98385i	−0.328394	−	0.238592i
$630$		0			0
$631$	−0.527864	−	1.62460i	−0.0210139	−	0.0646742i	0.940000	−	0.341175i	$-0.110825\pi$
$631$	−0.527864	−	1.62460i	−0.0210139	−	0.0646742i	−0.961014	+	0.276501i	$0.910825\pi$
$632$		0			0
$633$	−5.91641	+	4.29852i	−0.235156	+	0.170851i
$634$		0			0
$635$	−2.38197	+	7.33094i	−0.0945254	+	0.290919i
$636$		0			0
$637$	−45.3050			−1.79505
$638$		0			0
$639$	−13.5967			−0.537879
$640$		0			0
$641$	−6.15248	+	18.9354i	−0.243008	+	0.747902i	0.752949	+	0.658078i	$0.228630\pi$
$641$	−6.15248	+	18.9354i	−0.243008	+	0.747902i	−0.995958	+	0.0898240i	$0.971370\pi$
$642$		0			0
$643$	4.30902	−	3.13068i	0.169931	−	0.123462i	−0.499569	−	0.866274i	$-0.666508\pi$
$643$	4.30902	−	3.13068i	0.169931	−	0.123462i	0.669500	+	0.742812i	$0.266508\pi$
$644$		0			0
$645$	−0.336881	−	1.03681i	−0.0132647	−	0.0408245i
$646$		0			0
$647$	8.47214	+	6.15537i	0.333074	+	0.241992i	0.741734	−	0.670694i	$-0.234004\pi$
$647$	8.47214	+	6.15537i	0.333074	+	0.241992i	−0.408660	+	0.912687i	$0.634004\pi$
$648$		0			0
$649$	−14.2918	−	35.5851i	−0.561002	−	1.39684i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.00000	−	15.3884i	−0.195665	−	0.602195i	−0.999968	−	0.00797602i	$-0.997461\pi$
$653$	−5.00000	−	15.3884i	−0.195665	−	0.602195i	0.804303	−	0.594219i	$-0.202539\pi$
$654$		0			0
$655$	0.354102	−	0.257270i	0.0138359	−	0.0100524i
$656$		0			0
$657$	−1.01064	+	3.11044i	−0.0394289	+	0.121350i
$658$		0			0
$659$	9.09017			0.354103			0.177051	−	0.984202i	$-0.443344\pi$
$659$	9.09017			0.354103			0.177051	+	0.984202i	$0.443344\pi$
$660$		0			0
$661$	−1.12461			−0.0437423			−0.0218712	−	0.999761i	$-0.506962\pi$
$661$	−1.12461			−0.0437423			−0.0218712	+	0.999761i	$0.506962\pi$
$662$		0			0
$663$	−3.88854	+	11.9677i	−0.151019	+	0.464787i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	8.83282	+	27.1846i	0.342008	+	1.05259i
$668$		0			0
$669$	1.23607	+	0.898056i	0.0477891	+	0.0347208i
$670$		0			0
$671$	19.6180	−	16.3925i	0.757346	−	0.632824i
$672$		0			0
$673$	−32.2426	−	23.4257i	−1.24286	−	0.902993i	−0.245077	−	0.969504i	$-0.578813\pi$
$673$	−32.2426	−	23.4257i	−1.24286	−	0.902993i	−0.997786	+	0.0665110i	$0.978813\pi$
$674$		0			0
$675$	−0.690983	−	2.12663i	−0.0265959	−	0.0818539i
$676$		0			0
$677$	−24.7082	+	17.9516i	−0.949613	+	0.689935i	−0.950715	−	0.310065i	$-0.899649\pi$
$677$	−24.7082	+	17.9516i	−0.949613	+	0.689935i	0.00110199	+	0.999999i	$0.499649\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.29180			−0.0495017
$682$		0			0
$683$	−33.8885			−1.29671			−0.648355	−	0.761339i	$-0.724543\pi$
$683$	−33.8885			−1.29671			−0.648355	+	0.761339i	$0.724543\pi$
$684$		0			0
$685$	1.88197	−	5.79210i	0.0719062	−	0.221305i
$686$		0			0
$687$	−2.94427	+	2.13914i	−0.112331	+	0.0816132i
$688$		0			0
$689$	−7.05573	−	21.7153i	−0.268802	−	0.827287i
$690$		0			0
$691$	36.2426	+	26.3318i	1.37874	+	1.00171i	0.996997	+	0.0774393i	$0.0246744\pi$
$691$	36.2426	+	26.3318i	1.37874	+	1.00171i	0.381738	+	0.924271i	$0.375326\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	10.4721	+	7.60845i	0.397231	+	0.288605i
$696$		0			0
$697$	7.63525	+	23.4989i	0.289206	+	0.890084i
$698$		0			0
$699$	−5.88197	+	4.27350i	−0.222476	+	0.161639i
$700$		0			0
$701$	0.909830	−	2.80017i	0.0343638	−	0.105761i	−0.932403	−	0.361419i	$-0.882292\pi$
$701$	0.909830	−	2.80017i	0.0343638	−	0.105761i	0.966767	+	0.255658i	$0.0822923\pi$
$702$		0			0
$703$	7.70820			0.290720
$704$		0			0
$705$	−4.29180			−0.161638
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−9.00000	+	6.53888i	−0.338002	+	0.245573i	−0.743818	−	0.668382i	$-0.766987\pi$
$709$	−9.00000	+	6.53888i	−0.338002	+	0.245573i	0.405816	+	0.913955i	$0.366987\pi$
$710$		0			0
$711$	6.38197	+	19.6417i	0.239342	+	0.736620i
$712$		0			0
$713$	−18.0000	−	13.0778i	−0.674105	−	0.489766i
$714$		0			0
$715$	−21.4164	+	1.45309i	−0.800928	+	0.0543423i
$716$		0			0
$717$	4.61803	+	3.35520i	0.172464	+	0.125302i
$718$		0			0
$719$	4.81966	+	14.8334i	0.179743	+	0.553192i	0.999818	−	0.0190636i	$-0.00606850\pi$
$719$	4.81966	+	14.8334i	0.179743	+	0.553192i	−0.820075	+	0.572256i	$0.806069\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	1.63525	−	5.03280i	0.0608158	−	0.187172i
$724$		0			0
$725$	4.76393			0.176928
$726$		0			0
$727$	−37.8885			−1.40521			−0.702604	−	0.711581i	$-0.747980\pi$
$727$	−37.8885			−1.40521			−0.702604	+	0.711581i	$0.747980\pi$
$728$		0			0
$729$	−6.00658	+	18.4863i	−0.222466	+	0.684679i
$730$		0			0
$731$	11.7533	−	8.53926i	0.434711	−	0.315836i
$732$		0			0
$733$	9.29180	+	28.5972i	0.343200	+	1.05626i	0.962540	+	0.271139i	$0.0874003\pi$
$733$	9.29180	+	28.5972i	0.343200	+	1.05626i	−0.619340	+	0.785123i	$0.712600\pi$
$734$		0			0
$735$	−2.16312	−	1.57160i	−0.0797878	−	0.0579693i
$736$		0			0
$737$	2.04508	−	0.138757i	0.0753317	−	0.00511119i
$738$		0			0
$739$	−34.0623	−	24.7477i	−1.25300	−	0.910359i	−0.254610	−	0.967044i	$-0.581947\pi$
$739$	−34.0623	−	24.7477i	−1.25300	−	0.910359i	−0.998392	+	0.0566844i	$0.981947\pi$
$740$		0			0
$741$	−2.94427	−	9.06154i	−0.108161	−	0.332884i
$742$		0			0
$743$	35.0344	−	25.4540i	1.28529	−	0.933817i	0.285590	−	0.958352i	$-0.407810\pi$
$743$	35.0344	−	25.4540i	1.28529	−	0.933817i	0.999699	+	0.0245348i	$0.00781044\pi$
$744$		0			0
$745$	−6.38197	+	19.6417i	−0.233817	+	0.719615i
$746$		0			0
$747$	−35.3394			−1.29300
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−4.27051	+	13.1433i	−0.155833	+	0.479605i	−0.998244	−	0.0592301i	$-0.981135\pi$
$751$	−4.27051	+	13.1433i	−0.155833	+	0.479605i	0.842411	+	0.538835i	$0.181135\pi$
$752$		0			0
$753$	5.52786	−	4.01623i	0.201447	−	0.146359i
$754$		0			0
$755$	−3.85410	−	11.8617i	−0.140265	−	0.431692i
$756$		0			0
$757$	27.7082	+	20.1312i	1.00707	+	0.731680i	0.963593	−	0.267374i	$-0.0861559\pi$
$757$	27.7082	+	20.1312i	1.00707	+	0.731680i	0.0434789	+	0.999054i	$0.486156\pi$
$758$		0			0
$759$	1.85410	−	7.37143i	0.0672996	−	0.267566i
$760$		0			0
$761$	0.791796	+	0.575274i	0.0287026	+	0.0208536i	0.602044	−	0.798463i	$-0.294353\pi$
$761$	0.791796	+	0.575274i	0.0287026	+	0.0208536i	−0.573341	+	0.819317i	$0.694353\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	11.7533	−	8.53926i	0.424941	−	0.308738i
$766$		0			0
$767$	−23.1246	+	71.1702i	−0.834981	+	2.56981i
$768$		0			0
$769$	45.7771			1.65076			0.825382	−	0.564575i	$-0.190960\pi$
$769$	45.7771			1.65076			0.825382	+	0.564575i	$0.190960\pi$
$770$		0			0
$771$	−3.56231			−0.128293
$772$		0			0
$773$	−7.38197	+	22.7194i	−0.265511	+	0.817158i	0.726064	+	0.687627i	$0.241347\pi$
$773$	−7.38197	+	22.7194i	−0.265511	+	0.817158i	−0.991575	+	0.129532i	$0.958653\pi$
$774$		0			0
$775$	−3.00000	+	2.17963i	−0.107763	+	0.0782945i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−15.1353	−	10.9964i	−0.542277	−	0.393987i
$780$		0			0
$781$	−12.1246	+	10.1311i	−0.433853	+	0.362519i
$782$		0			0
$783$	8.61803	+	6.26137i	0.307983	+	0.223763i
$784$		0			0
$785$	−2.47214	−	7.60845i	−0.0882343	−	0.271557i
$786$		0			0
$787$	−3.79180	+	2.75490i	−0.135163	+	0.0982016i	−0.653312	−	0.757089i	$-0.726621\pi$
$787$	−3.79180	+	2.75490i	−0.135163	+	0.0982016i	0.518149	+	0.855290i	$0.326621\pi$
$788$		0			0
$789$	0.0212862	−	0.0655123i	0.000757810	−	0.00233230i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−49.8885			−1.77159
$794$		0			0
$795$	0.416408	−	1.28157i	0.0147685	−	0.0454527i
$796$		0			0
$797$	−18.4164	+	13.3803i	−0.652343	+	0.473955i	−0.864068	−	0.503374i	$-0.832092\pi$
$797$	−18.4164	+	13.3803i	−0.652343	+	0.473955i	0.211726	+	0.977329i	$0.432092\pi$
$798$		0			0
$799$	−17.6738	−	54.3942i	−0.625253	−	1.92433i
$800$		0			0
$801$	−9.44427	−	6.86167i	−0.333697	−	0.242445i
$802$		0			0
$803$	1.41641	+	3.52671i	0.0499839	+	0.124455i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.87539	−	8.84953i	−0.101218	−	0.311518i
$808$		0			0
$809$	20.3885	−	14.8131i	0.716823	−	0.520802i	−0.168545	−	0.985694i	$-0.553907\pi$
$809$	20.3885	−	14.8131i	0.716823	−	0.520802i	0.885368	+	0.464892i	$0.153907\pi$
$810$		0			0
$811$	10.5000	−	32.3157i	0.368705	−	1.13476i	−0.578924	−	0.815382i	$-0.696527\pi$
$811$	10.5000	−	32.3157i	0.368705	−	1.13476i	0.947628	−	0.319375i	$-0.103473\pi$
$812$		0			0
$813$	7.63932			0.267923
$814$		0			0
$815$	−11.3820			−0.398693
$816$		0			0
$817$	−3.39919	+	10.4616i	−0.118922	+	0.366006i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.43769	+	22.8909i	0.259577	+	0.798897i	0.992893	+	0.119009i	$0.0379717\pi$
$821$	7.43769	+	22.8909i	0.259577	+	0.798897i	−0.733316	+	0.679888i	$0.762028\pi$
$822$		0			0
$823$	−31.9787	−	23.2339i	−1.11471	−	0.809883i	−0.131309	−	0.991341i	$-0.541918\pi$
$823$	−31.9787	−	23.2339i	−1.11471	−	0.809883i	−0.983399	+	0.181459i	$0.941918\pi$
$824$		0			0
$825$	−1.07295	−	0.673542i	−0.0373553	−	0.0234497i
$826$		0			0
$827$	16.6803	+	12.1190i	0.580032	+	0.421418i	0.838736	−	0.544539i	$-0.183295\pi$
$827$	16.6803	+	12.1190i	0.580032	+	0.421418i	−0.258703	+	0.965957i	$0.583295\pi$
$828$		0			0
$829$	0.965558	+	2.97168i	0.0335352	+	0.103211i	0.966423	−	0.256956i	$-0.0827197\pi$
$829$	0.965558	+	2.97168i	0.0335352	+	0.103211i	−0.932888	+	0.360167i	$0.882720\pi$
$830$		0			0
$831$	−2.90983	+	2.11412i	−0.100941	+	0.0733378i
$832$		0			0
$833$	11.0106	−	33.8873i	0.381496	−	1.17412i
$834$		0			0
$835$	−20.1803			−0.698369
$836$		0			0
$837$	−8.29180			−0.286606
$838$		0			0
$839$	−0.763932	+	2.35114i	−0.0263739	+	0.0811704i	−0.963377	−	0.268150i	$-0.913588\pi$
$839$	−0.763932	+	2.35114i	−0.0263739	+	0.0811704i	0.937003	+	0.349321i	$0.113588\pi$
$840$		0			0
$841$	5.10081	−	3.70596i	0.175890	−	0.127792i
$842$		0			0
$843$	−0.551663	−	1.69784i	−0.0190003	−	0.0584768i
$844$		0			0
$845$	23.3713	+	16.9803i	0.803998	+	0.584139i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.763932	−	0.555029i	−0.0262181	−	0.0190485i
$850$		0			0
$851$	−3.70820	−	11.4127i	−0.127116	−	0.391222i
$852$		0			0
$853$	6.00000	−	4.35926i	0.205436	−	0.149258i	−0.480310	−	0.877099i	$-0.659476\pi$
$853$	6.00000	−	4.35926i	0.205436	−	0.149258i	0.685746	+	0.727841i	$0.259476\pi$
$854$		0			0
$855$	−3.39919	+	10.4616i	−0.116250	+	0.357780i
$856$		0			0
$857$	−26.6738			−0.911158			−0.455579	−	0.890195i	$-0.650568\pi$
$857$	−26.6738			−0.911158			−0.455579	+	0.890195i	$0.650568\pi$
$858$		0			0
$859$	34.6180			1.18115			0.590576	−	0.806982i	$-0.298901\pi$
$859$	34.6180			1.18115			0.590576	+	0.806982i	$0.298901\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	34.4164	−	25.0050i	1.17155	−	0.851180i	0.180355	−	0.983602i	$-0.442275\pi$
$863$	34.4164	−	25.0050i	1.17155	−	0.851180i	0.991193	+	0.132422i	$0.0422754\pi$
$864$		0			0
$865$	1.14590	+	3.52671i	0.0389617	+	0.119912i
$866$		0			0
$867$	−2.75329	−	2.00038i	−0.0935066	−	0.0679365i
$868$		0			0
$869$	20.3262	+	12.7598i	0.689520	+	0.432845i
$870$		0			0
$871$	−3.23607	−	2.35114i	−0.109650	−	0.0796654i
$872$		0			0
$873$	6.71885	+	20.6785i	0.227399	+	0.699861i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−13.0557	+	40.1814i	−0.440861	+	1.35683i	0.446099	+	0.894983i	$0.352813\pi$
$877$	−13.0557	+	40.1814i	−0.440861	+	1.35683i	−0.886960	+	0.461846i	$0.847187\pi$
$878$		0			0
$879$	4.29180			0.144759
$880$		0			0
$881$	−26.9230			−0.907058			−0.453529	−	0.891241i	$-0.649835\pi$
$881$	−26.9230			−0.907058			−0.453529	+	0.891241i	$0.649835\pi$
$882$		0			0
$883$	−7.35410	+	22.6336i	−0.247485	+	0.761681i	0.747733	+	0.664000i	$0.231143\pi$
$883$	−7.35410	+	22.6336i	−0.247485	+	0.761681i	−0.995218	+	0.0976812i	$0.968857\pi$
$884$		0			0
$885$	−3.57295	+	2.59590i	−0.120103	+	0.0872602i
$886$		0			0
$887$	−2.88854	−	8.89002i	−0.0969878	−	0.298498i	0.890779	−	0.454437i	$-0.150160\pi$
$887$	−2.88854	−	8.89002i	−0.0969878	−	0.298498i	−0.987767	+	0.155939i	$0.950160\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	9.52786	+	23.7234i	0.319195	+	0.794764i
$892$		0			0
$893$	35.0344	+	25.4540i	1.17238	+	0.851786i
$894$		0			0
$895$	7.57295	+	23.3071i	0.253136	+	0.779072i
$896$		0			0
$897$	−12.0000	+	8.71851i	−0.400668	+	0.291103i
$898$		0			0
$899$	5.45898	−	16.8010i	0.182067	−	0.560345i
$900$		0			0
$901$	17.9574			0.598249
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3.00000	+	9.23305i	−0.0997234	+	0.306917i
$906$		0			0
$907$	−37.3885	+	27.1644i	−1.24147	+	0.901978i	−0.997695	−	0.0678548i	$-0.978385\pi$
$907$	−37.3885	+	27.1644i	−1.24147	+	0.901978i	−0.243771	+	0.969833i	$0.578385\pi$
$908$		0			0
$909$	−8.97871	−	27.6336i	−0.297805	−	0.916550i
$910$		0			0
$911$	−35.9787	−	26.1401i	−1.19203	−	0.866059i	−0.198551	−	0.980091i	$-0.563623\pi$
$911$	−35.9787	−	26.1401i	−1.19203	−	0.866059i	−0.993477	+	0.114032i	$0.963623\pi$
$912$		0			0
$913$	−31.5132	+	26.3318i	−1.04293	+	0.871456i
$914$		0			0
$915$	−2.38197	−	1.73060i	−0.0787454	−	0.0572119i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−20.7984	+	15.1109i	−0.686075	+	0.498463i	−0.875368	−	0.483458i	$-0.839381\pi$
$919$	−20.7984	+	15.1109i	−0.686075	+	0.498463i	0.189292	+	0.981921i	$0.439381\pi$
$920$		0			0
$921$	−1.48278	+	4.56352i	−0.0488592	+	0.150373i
$922$		0			0
$923$	30.8328			1.01487
$924$		0			0
$925$	−2.00000			−0.0657596
$926$		0			0
$927$	−13.8541	+	42.6385i	−0.455028	+	1.40043i
$928$		0			0
$929$	−3.02786	+	2.19987i	−0.0993410	+	0.0721755i	−0.636347	−	0.771403i	$-0.719555\pi$
$929$	−3.02786	+	2.19987i	−0.0993410	+	0.0721755i	0.537006	+	0.843578i	$0.319555\pi$
$930$		0			0
$931$	8.33688	+	25.6583i	0.273230	+	0.840916i
$932$		0			0
$933$	−0.854102	−	0.620541i	−0.0279620	−	0.0203156i
$934$		0			0
$935$	4.11803	−	16.3722i	0.134674	−	0.535429i
$936$		0			0
$937$	10.5344	+	7.65372i	0.344145	+	0.250036i	0.746409	−	0.665488i	$-0.231776\pi$
$937$	10.5344	+	7.65372i	0.344145	+	0.250036i	−0.402264	+	0.915524i	$0.631776\pi$
$938$		0			0
$939$	3.80244	+	11.7027i	0.124088	+	0.381903i
$940$		0			0
$941$	−27.3607	+	19.8787i	−0.891933	+	0.648027i	−0.936381	−	0.350985i	$-0.885847\pi$
$941$	−27.3607	+	19.8787i	−0.891933	+	0.648027i	0.0444485	+	0.999012i	$0.485847\pi$
$942$		0			0
$943$	−9.00000	+	27.6992i	−0.293080	+	0.902008i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	38.5066			1.25130			0.625648	−	0.780106i	$-0.284835\pi$
$947$	38.5066			1.25130			0.625648	+	0.780106i	$0.284835\pi$
$948$		0			0
$949$	2.29180	−	7.05342i	0.0743948	−	0.228964i
$950$		0			0
$951$	−3.47214	+	2.52265i	−0.112592	+	0.0818027i
$952$		0			0
$953$	−13.1180	−	40.3732i	−0.424935	−	1.30781i	−0.903057	−	0.429521i	$-0.858682\pi$
$953$	−13.1180	−	40.3732i	−0.424935	−	1.30781i	0.478122	−	0.878293i	$-0.341318\pi$
$954$		0			0
$955$	18.3262	+	13.3148i	0.593023	+	0.430857i
$956$		0			0
$957$	6.02129	−	0.408539i	0.194641	−	0.0132062i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−5.33030	−	16.4050i	−0.171945	−	0.529193i
$962$		0			0
$963$	4.40983	−	3.20393i	0.142105	−	0.103245i
$964$		0			0
$965$	−5.56231	+	17.1190i	−0.179057	+	0.551081i
$966$		0			0
$967$	20.3607			0.654755			0.327378	−	0.944894i	$-0.393835\pi$
$967$	20.3607			0.654755			0.327378	+	0.944894i	$0.393835\pi$
$968$		0			0
$969$	7.49342			0.240723
$970$		0			0
$971$	−6.00000	+	18.4661i	−0.192549	+	0.592605i	0.807447	+	0.589940i	$0.200849\pi$
$971$	−6.00000	+	18.4661i	−0.192549	+	0.592605i	−0.999996	+	0.00266566i	$0.999151\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	0.763932	+	2.35114i	0.0244654	+	0.0752968i
$976$		0			0
$977$	−29.5066	−	21.4378i	−0.943999	−	0.685855i	0.00538090	−	0.999986i	$-0.498287\pi$
$977$	−29.5066	−	21.4378i	−0.943999	−	0.685855i	−0.949380	+	0.314130i	$0.898287\pi$
$978$		0			0
$979$	−13.5344	+	0.918300i	−0.432563	+	0.0293490i
$980$		0			0
$981$	−40.8885	−	29.7073i	−1.30547	−	0.948480i
$982$		0			0
$983$	−6.03444	−	18.5721i	−0.192469	−	0.592358i	−0.999997	−	0.00252883i	$-0.999195\pi$
$983$	−6.03444	−	18.5721i	−0.192469	−	0.592358i	0.807528	−	0.589829i	$-0.200805\pi$
$984$		0			0
$985$	0.854102	−	0.620541i	0.0272140	−	0.0197721i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	17.1246			0.544531
$990$		0			0
$991$	6.83282			0.217052			0.108526	−	0.994094i	$-0.465387\pi$
$991$	6.83282			0.217052			0.108526	+	0.994094i	$0.465387\pi$
$992$		0			0
$993$	1.71885	−	5.29007i	0.0545460	−	0.167875i
$994$		0			0
$995$	−17.9443	+	13.0373i	−0.568872	+	0.413309i
$996$		0			0
$997$	3.05573	+	9.40456i	0.0967759	+	0.297846i	0.987712	−	0.156282i	$-0.0499509\pi$
$997$	3.05573	+	9.40456i	0.0967759	+	0.297846i	−0.890937	+	0.454128i	$0.849951\pi$
$998$		0			0
$999$	−3.61803	−	2.62866i	−0.114470	−	0.0831670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.b.81.1		4
4.3	odd	2		110.2.g.b.81.1	✓	4
11.3	even	5	inner	880.2.bo.b.641.1		4
11.5	even	5		9680.2.a.bx.1.1		2
11.6	odd	10		9680.2.a.bw.1.1		2
12.11	even	2		990.2.n.c.631.1		4
20.3	even	4		550.2.ba.b.499.2		8
20.7	even	4		550.2.ba.b.499.1		8
20.19	odd	2		550.2.h.b.301.1		4
44.3	odd	10		110.2.g.b.91.1	yes	4
44.27	odd	10		1210.2.a.n.1.2		2
44.39	even	10		1210.2.a.q.1.2		2
132.47	even	10		990.2.n.c.91.1		4
220.3	even	20		550.2.ba.b.399.1		8
220.39	even	10		6050.2.a.ch.1.1		2
220.47	even	20		550.2.ba.b.399.2		8
220.159	odd	10		6050.2.a.cw.1.1		2
220.179	odd	10		550.2.h.b.201.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.b.81.1	✓	4	4.3	odd	2
110.2.g.b.91.1	yes	4	44.3	odd	10
550.2.h.b.201.1		4	220.179	odd	10
550.2.h.b.301.1		4	20.19	odd	2
550.2.ba.b.399.1		8	220.3	even	20
550.2.ba.b.399.2		8	220.47	even	20
550.2.ba.b.499.1		8	20.7	even	4
550.2.ba.b.499.2		8	20.3	even	4
880.2.bo.b.81.1		4	1.1	even	1	trivial
880.2.bo.b.641.1		4	11.3	even	5	inner
990.2.n.c.91.1		4	132.47	even	10
990.2.n.c.631.1		4	12.11	even	2
1210.2.a.n.1.2		2	44.27	odd	10
1210.2.a.q.1.2		2	44.39	even	10
6050.2.a.ch.1.1		2	220.39	even	10
6050.2.a.cw.1.1		2	220.159	odd	10
9680.2.a.bw.1.1		2	11.6	odd	10
9680.2.a.bx.1.1		2	11.5	even	5

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.118034 - 0.363271i) q^{3} +(0.809017 - 0.587785i) q^{5} +(2.30902 + 1.67760i) q^{9} +(3.30902 - 0.224514i) q^{11} +(-5.23607 - 3.80423i) q^{13} +(-0.118034 - 0.363271i) q^{15} +(4.11803 - 2.99193i) q^{17} +(-1.19098 + 3.66547i) q^{19} +6.00000 q^{23} +(0.309017 - 0.951057i) q^{25} +(1.80902 - 1.31433i) q^{27} +(1.47214 + 4.53077i) q^{29} +(-3.00000 - 2.17963i) q^{31} +(0.309017 - 1.22857i) q^{33} +(-0.618034 - 1.90211i) q^{37} +(-2.00000 + 1.45309i) q^{39} +(-1.50000 + 4.61653i) q^{41} +2.85410 q^{43} +2.85410 q^{45} +(3.47214 - 10.6861i) q^{47} +(5.66312 - 4.11450i) q^{49} +(-0.600813 - 1.84911i) q^{51} +(2.85410 + 2.07363i) q^{53} +(2.54508 - 2.12663i) q^{55} +(1.19098 + 0.865300i) q^{57} +(-3.57295 - 10.9964i) q^{59} +(6.23607 - 4.53077i) q^{61} -6.47214 q^{65} +0.618034 q^{67} +(0.708204 - 2.17963i) q^{69} +(-3.85410 + 2.80017i) q^{71} +(0.354102 + 1.08981i) q^{73} +(-0.309017 - 0.224514i) q^{75} +(5.85410 + 4.25325i) q^{79} +(2.38197 + 7.33094i) q^{81} +(-10.0172 + 7.27794i) q^{83} +(1.57295 - 4.84104i) q^{85} +1.81966 q^{87} -4.09017 q^{89} +(-1.14590 + 0.832544i) q^{93} +(1.19098 + 3.66547i) q^{95} +(6.16312 + 4.47777i) q^{97} +(8.01722 + 5.03280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + q^{5} + 7 q^{9} + 11 q^{11} - 12 q^{13} + 4 q^{15} + 12 q^{17} - 7 q^{19} + 24 q^{23} - q^{25} + 5 q^{27} - 12 q^{29} - 12 q^{31} - q^{33} + 2 q^{37} - 8 q^{39} - 6 q^{41} - 2 q^{43}+ \cdots + 3 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + q^5 + 7 * q^9 + 11 * q^11 - 12 * q^13 + 4 * q^15 + 12 * q^17 - 7 * q^19 + 24 * q^23 - q^25 + 5 * q^27 - 12 * q^29 - 12 * q^31 - q^33 + 2 * q^37 - 8 * q^39 - 6 * q^41 - 2 * q^43 - 2 * q^45 - 4 * q^47 + 7 * q^49 - 27 * q^51 - 2 * q^53 - q^55 + 7 * q^57 - 21 * q^59 + 16 * q^61 - 8 * q^65 - 2 * q^67 - 24 * q^69 - 2 * q^71 - 12 * q^73 + q^75 + 10 * q^79 + 14 * q^81 - 11 * q^83 + 13 * q^85 + 52 * q^87 + 6 * q^89 - 18 * q^93 + 7 * q^95 + 9 * q^97 + 3 * q^99

Introduction

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