LMFDB - Embedded newform 1148.2.ba.a.113.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			113.6
Character	$\chi$	$=$	1148.113
Dual form			1148.2.ba.a.701.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.80180i q^{3} +(-0.0346732 - 0.106713i) q^{5} +(-0.587785 - 0.809017i) q^{7} -0.246466 q^{9} +O(q^{10})$	\(q-1.80180i q^{3} +(-0.0346732 - 0.106713i) q^{5} +(-0.587785 - 0.809017i) q^{7} -0.246466 q^{9} +(-1.80145 - 0.585326i) q^{11} +(1.57378 - 2.16612i) q^{13} +(-0.192275 + 0.0624741i) q^{15} +(-6.98358 - 2.26910i) q^{17} +(2.32100 + 3.19459i) q^{19} +(-1.45768 + 1.05907i) q^{21} +(-5.14309 - 3.73667i) q^{23} +(4.03490 - 2.93153i) q^{25} -4.96130i q^{27} +(-1.26529 + 0.411117i) q^{29} +(-0.816782 + 2.51380i) q^{31} +(-1.05464 + 3.24584i) q^{33} +(-0.0659524 + 0.0907757i) q^{35} +(0.133382 + 0.410509i) q^{37} +(-3.90291 - 2.83563i) q^{39} +(1.09345 + 6.30907i) q^{41} +(-7.59057 - 5.51487i) q^{43} +(0.00854578 + 0.0263012i) q^{45} +(4.38148 - 6.03059i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-4.08846 + 12.5830i) q^{51} +(-7.51371 + 2.44135i) q^{53} +0.212534i q^{55} +(5.75599 - 4.18197i) q^{57} +(-10.7411 - 7.80386i) q^{59} +(4.91011 - 3.56741i) q^{61} +(0.144869 + 0.199395i) q^{63} +(-0.285722 - 0.0928368i) q^{65} +(-10.3008 + 3.34693i) q^{67} +(-6.73272 + 9.26680i) q^{69} +(-1.62924 - 0.529371i) q^{71} +14.0323 q^{73} +(-5.28201 - 7.27006i) q^{75} +(0.585326 + 1.80145i) q^{77} +4.58413i q^{79} -9.67865 q^{81} +7.57146 q^{83} +0.823918i q^{85} +(0.740749 + 2.27979i) q^{87} +(6.75087 + 9.29178i) q^{89} -2.67748 q^{91} +(4.52935 + 1.47167i) q^{93} +(0.260428 - 0.358449i) q^{95} +(-10.6517 + 3.46094i) q^{97} +(0.443996 + 0.144263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	1.80180i		−	1.04027i	−0.854085	−	0.520133i	$-0.825882\pi$
$3$		−	1.80180i		−	1.04027i	0.854085	−	0.520133i	$-0.174118\pi$
$4$		0			0
$5$	−0.0346732	−	0.106713i	−0.0155063	−	0.0477236i	0.943004	−	0.332782i	$-0.107987\pi$
$5$	−0.0346732	−	0.106713i	−0.0155063	−	0.0477236i	−0.958510	+	0.285058i	$0.907987\pi$
$6$		0			0
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$8$		0			0
$9$	−0.246466			−0.0821554
$10$		0			0
$11$	−1.80145	−	0.585326i	−0.543157	−	0.176483i	0.0245716	−	0.999698i	$-0.492178\pi$
$11$	−1.80145	−	0.585326i	−0.543157	−	0.176483i	−0.567729	+	0.823216i	$0.692178\pi$
$12$		0			0
$13$	1.57378	−	2.16612i	0.436488	−	0.600775i	−0.532939	−	0.846154i	$-0.678912\pi$
$13$	1.57378	−	2.16612i	0.436488	−	0.600775i	0.969427	+	0.245379i	$0.0789124\pi$
$14$		0			0
$15$	−0.192275	+	0.0624741i	−0.0496453	+	0.0161307i
$16$		0			0
$17$	−6.98358	−	2.26910i	−1.69377	−	0.550339i	−0.706266	−	0.707946i	$-0.749622\pi$
$17$	−6.98358	−	2.26910i	−1.69377	−	0.550339i	−0.987502	+	0.157608i	$0.949622\pi$
$18$		0			0
$19$	2.32100	+	3.19459i	0.532475	+	0.732889i	0.987505	−	0.157587i	$-0.0503716\pi$
$19$	2.32100	+	3.19459i	0.532475	+	0.732889i	−0.455030	+	0.890476i	$0.650372\pi$
$20$		0			0
$21$	−1.45768	+	1.05907i	−0.318093	+	0.231108i
$22$		0			0
$23$	−5.14309	−	3.73667i	−1.07241	−	0.779150i	−0.0960648	−	0.995375i	$-0.530626\pi$
$23$	−5.14309	−	3.73667i	−1.07241	−	0.779150i	−0.976344	+	0.216225i	$0.930626\pi$
$24$		0			0
$25$	4.03490	−	2.93153i	0.806980	−	0.586305i
$26$		0			0
$27$		−	4.96130i		−	0.954803i
$28$		0			0
$29$	−1.26529	+	0.411117i	−0.234958	+	0.0763426i	−0.424130	−	0.905602i	$-0.639420\pi$
$29$	−1.26529	+	0.411117i	−0.234958	+	0.0763426i	0.189171	+	0.981944i	$0.439420\pi$
$30$		0			0
$31$	−0.816782	+	2.51380i	−0.146698	+	0.451491i	−0.997225	−	0.0744399i	$-0.976283\pi$
$31$	−0.816782	+	2.51380i	−0.146698	+	0.451491i	0.850527	+	0.525931i	$0.176283\pi$
$32$		0			0
$33$	−1.05464	+	3.24584i	−0.183589	+	0.565029i
$34$		0			0
$35$	−0.0659524	+	0.0907757i	−0.0111480	+	0.0153439i
$36$		0			0
$37$	0.133382	+	0.410509i	0.0219279	+	0.0674872i	0.961422	−	0.275079i	$-0.0887040\pi$
$37$	0.133382	+	0.410509i	0.0219279	+	0.0674872i	−0.939494	+	0.342566i	$0.888704\pi$
$38$		0			0
$39$	−3.90291	−	2.83563i	−0.624966	−	0.454065i
$40$		0			0
$41$	1.09345	+	6.30907i	0.170769	+	0.985311i
$41$	1.09345	+	6.30907i	0.170769	+	0.985311i
$42$		0			0
$43$	−7.59057	−	5.51487i	−1.15755	−	0.841010i	−0.168084	−	0.985773i	$-0.553758\pi$
$43$	−7.59057	−	5.51487i	−1.15755	−	0.841010i	−0.989466	+	0.144763i	$0.953758\pi$
$44$		0			0
$45$	0.00854578	+	0.0263012i	0.00127393	+	0.00392075i
$46$		0			0
$47$	4.38148	−	6.03059i	0.639105	−	0.879652i	−0.359463	−	0.933159i	$-0.617040\pi$
$47$	4.38148	−	6.03059i	0.639105	−	0.879652i	0.998567	+	0.0535071i	$0.0170400\pi$
$48$		0			0
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$		0			0
$51$	−4.08846	+	12.5830i	−0.572499	+	1.76197i
$52$		0			0
$53$	−7.51371	+	2.44135i	−1.03209	+	0.335346i	−0.775615	−	0.631206i	$-0.782560\pi$
$53$	−7.51371	+	2.44135i	−1.03209	+	0.335346i	−0.256473	+	0.966551i	$0.582560\pi$
$54$		0			0
$55$			0.212534i			0.0286580i
$56$		0			0
$57$	5.75599	−	4.18197i	0.762400	−	0.553916i
$58$		0			0
$59$	−10.7411	−	7.80386i	−1.39837	−	1.01598i	−0.994888	−	0.100989i	$-0.967799\pi$
$59$	−10.7411	−	7.80386i	−1.39837	−	1.01598i	−0.403483	−	0.914987i	$-0.632201\pi$
$60$		0			0
$61$	4.91011	−	3.56741i	0.628676	−	0.456760i	−0.227266	−	0.973833i	$-0.572979\pi$
$61$	4.91011	−	3.56741i	0.628676	−	0.456760i	0.855941	+	0.517073i	$0.172979\pi$
$62$		0			0
$63$	0.144869	+	0.199395i	0.0182518	+	0.0251214i
$64$		0			0
$65$	−0.285722	−	0.0928368i	−0.0354395	−	0.0115150i
$66$		0			0
$67$	−10.3008	+	3.34693i	−1.25844	+	0.408893i	−0.860939	−	0.508708i	$-0.830123\pi$
$67$	−10.3008	+	3.34693i	−1.25844	+	0.408893i	−0.397503	+	0.917601i	$0.630123\pi$
$68$		0			0
$69$	−6.73272	+	9.26680i	−0.810524	+	1.11559i
$70$		0			0
$71$	−1.62924	−	0.529371i	−0.193355	−	0.0628248i	0.210739	−	0.977542i	$-0.432413\pi$
$71$	−1.62924	−	0.529371i	−0.193355	−	0.0628248i	−0.404094	+	0.914718i	$0.632413\pi$
$72$		0			0
$73$	14.0323			1.64236			0.821181	−	0.570668i	$-0.193316\pi$
$73$	14.0323			1.64236			0.821181	+	0.570668i	$0.193316\pi$
$74$		0			0
$75$	−5.28201	−	7.27006i	−0.609914	−	0.839475i
$76$		0			0
$77$	0.585326	+	1.80145i	0.0667041	+	0.205294i
$78$		0			0
$79$			4.58413i			0.515755i	0.966178	+	0.257877i	$0.0830231\pi$
$79$			4.58413i			0.515755i	−0.966178	+	0.257877i	$0.916977\pi$
$80$		0			0
$81$	−9.67865			−1.07541
$82$		0			0
$83$	7.57146			0.831075			0.415538	−	0.909576i	$-0.363593\pi$
$83$	7.57146			0.831075			0.415538	+	0.909576i	$0.363593\pi$
$84$		0			0
$85$			0.823918i			0.0893665i
$86$		0			0
$87$	0.740749	+	2.27979i	0.0794167	+	0.244419i
$88$		0			0
$89$	6.75087	+	9.29178i	0.715591	+	0.984927i	0.999659	+	0.0261223i	$0.00831593\pi$
$89$	6.75087	+	9.29178i	0.715591	+	0.984927i	−0.284068	+	0.958804i	$0.591684\pi$
$90$		0			0
$91$	−2.67748			−0.280676
$92$		0			0
$93$	4.52935	+	1.47167i	0.469672	+	0.152606i
$94$		0			0
$95$	0.260428	−	0.358449i	0.0267194	−	0.0367760i
$96$		0			0
$97$	−10.6517	+	3.46094i	−1.08151	+	0.351405i	−0.794961	−	0.606660i	$-0.792509\pi$
$97$	−10.6517	+	3.46094i	−1.08151	+	0.351405i	−0.286551	+	0.958065i	$0.592509\pi$
$98$		0			0
$99$	0.443996	+	0.144263i	0.0446233	+	0.0144990i
$100$		0			0
$101$	0.591389	+	0.813978i	0.0588454	+	0.0809938i	0.837426	−	0.546551i	$-0.184060\pi$
$101$	0.591389	+	0.813978i	0.0588454	+	0.0809938i	−0.778580	+	0.627545i	$0.784060\pi$
$102$		0			0
$103$	−4.08508	+	2.96798i	−0.402515	+	0.292444i	−0.770564	−	0.637362i	$-0.780026\pi$
$103$	−4.08508	+	2.96798i	−0.402515	+	0.292444i	0.368050	+	0.929806i	$0.380026\pi$
$104$		0			0
$105$	0.163559	+	0.118833i	0.0159617	+	0.0115969i
$106$		0			0
$107$	−4.15426	+	3.01825i	−0.401608	+	0.291785i	−0.770196	−	0.637808i	$-0.779841\pi$
$107$	−4.15426	+	3.01825i	−0.401608	+	0.291785i	0.368588	+	0.929593i	$0.379841\pi$
$108$		0			0
$109$			10.8078i			1.03520i	0.855622	+	0.517601i	$0.173175\pi$
$109$			10.8078i			1.03520i	−0.855622	+	0.517601i	$0.826825\pi$
$110$		0			0
$111$	0.739653	−	0.240328i	0.0702047	−	0.0228109i
$112$		0			0
$113$	4.55865	−	14.0301i	0.428842	−	1.31984i	−0.470425	−	0.882440i	$-0.655899\pi$
$113$	4.55865	−	14.0301i	0.428842	−	1.31984i	0.899267	−	0.437400i	$-0.144101\pi$
$114$		0			0
$115$	−0.220425	+	0.678398i	−0.0205547	+	0.0632610i
$116$		0			0
$117$	−0.387884	+	0.533876i	−0.0358599	+	0.0493569i
$118$		0			0
$119$	2.26910	+	6.98358i	0.208008	+	0.640184i
$120$		0			0
$121$	−5.99657	−	4.35677i	−0.545143	−	0.396070i
$122$		0			0
$123$	11.3677	−	1.97018i	1.02499	−	0.177645i
$124$		0			0
$125$	−0.906614	−	0.658694i	−0.0810901	−	0.0589154i
$126$		0			0
$127$	−3.72182	−	11.4546i	−0.330258	−	1.01643i	−0.969011	−	0.247018i	$-0.920549\pi$
$127$	−3.72182	−	11.4546i	−0.330258	−	1.01643i	0.638753	−	0.769412i	$-0.279451\pi$
$128$		0			0
$129$	−9.93667	+	13.6767i	−0.874875	+	1.20416i
$130$		0			0
$131$	5.40587	−	16.6376i	0.472313	−	1.45363i	−0.377234	−	0.926118i	$-0.623125\pi$
$131$	5.40587	−	16.6376i	0.472313	−	1.45363i	0.849547	−	0.527513i	$-0.176875\pi$
$132$		0			0
$133$	1.22022	−	3.75546i	0.105807	−	0.325640i
$134$		0			0
$135$	−0.529437	+	0.172024i	−0.0455667	+	0.0148055i
$136$		0			0
$137$		−	6.05678i		−	0.517466i	−0.965949	−	0.258733i	$-0.916695\pi$
$137$		−	6.05678i		−	0.517466i	0.965949	−	0.258733i	$-0.0833050\pi$
$138$		0			0
$139$	11.8192	−	8.58716i	1.00249	−	0.728354i	0.0398717	−	0.999205i	$-0.487305\pi$
$139$	11.8192	−	8.58716i	1.00249	−	0.728354i	0.962621	+	0.270851i	$0.0873051\pi$
$140$		0			0
$141$	−10.8659	−	7.89453i	−0.915073	−	0.664840i
$142$		0			0
$143$	−4.10298	+	2.98099i	−0.343108	+	0.249283i
$144$		0			0
$145$	0.0877434	+	0.120768i	0.00728669	+	0.0100293i
$146$		0			0
$147$	1.71361	+	0.556785i	0.141336	+	0.0459229i
$148$		0			0
$149$	18.2099	−	5.91675i	1.49181	−	0.484719i	0.554195	−	0.832387i	$-0.313026\pi$
$149$	18.2099	−	5.91675i	1.49181	−	0.484719i	0.937618	+	0.347668i	$0.113026\pi$
$150$		0			0
$151$	−2.43892	+	3.35688i	−0.198476	+	0.273179i	−0.896641	−	0.442758i	$-0.854000\pi$
$151$	−2.43892	+	3.35688i	−0.198476	+	0.273179i	0.698165	+	0.715937i	$0.254000\pi$
$152$		0			0
$153$	1.72122	+	0.559257i	0.139152	+	0.0452133i
$154$		0			0
$155$	0.296576			0.0238216
$156$		0			0
$157$	−4.40420	−	6.06187i	−0.351494	−	0.483790i	0.596260	−	0.802791i	$-0.296653\pi$
$157$	−4.40420	−	6.06187i	−0.351494	−	0.483790i	−0.947754	+	0.319001i	$0.896653\pi$
$158$		0			0
$159$	4.39882	+	13.5382i	0.348849	+	1.07365i
$160$		0			0
$161$			6.35721i			0.501018i
$162$		0			0
$163$	−0.0928394			−0.00727174			−0.00363587	−	0.999993i	$-0.501157\pi$
$163$	−0.0928394			−0.00727174			−0.00363587	+	0.999993i	$0.501157\pi$
$164$		0			0
$165$	0.382942			0.0298120
$166$		0			0
$167$			11.6428i			0.900945i	0.892790	+	0.450472i	$0.148744\pi$
$167$			11.6428i			0.900945i	−0.892790	+	0.450472i	$0.851256\pi$
$168$		0			0
$169$	1.80191	+	5.54572i	0.138609	+	0.426594i
$170$		0			0
$171$	−0.572049	−	0.787358i	−0.0437457	−	0.0602107i
$172$		0			0
$173$	21.2662			1.61684			0.808420	−	0.588607i	$-0.200323\pi$
$173$	21.2662			1.61684			0.808420	+	0.588607i	$0.200323\pi$
$174$		0			0
$175$	−4.74331	−	1.54119i	−0.358560	−	0.116503i
$176$		0			0
$177$	−14.0610	+	19.3532i	−1.05689	+	1.45468i
$178$		0			0
$179$	6.05628	−	1.96780i	0.452667	−	0.147081i	−0.0738051	−	0.997273i	$-0.523514\pi$
$179$	6.05628	−	1.96780i	0.452667	−	0.147081i	0.526473	+	0.850192i	$0.323514\pi$
$180$		0			0
$181$	6.50244	+	2.11277i	0.483322	+	0.157041i	0.540536	−	0.841321i	$-0.318222\pi$
$181$	6.50244	+	2.11277i	0.483322	+	0.157041i	−0.0572135	+	0.998362i	$0.518222\pi$
$182$		0			0
$183$	−6.42774	−	8.84702i	−0.475152	−	0.653990i
$184$		0			0
$185$	0.0391819	−	0.0284673i	0.00288071	−	0.00209296i
$186$		0			0
$187$	11.2524	+	8.17535i	0.822857	+	0.597841i
$188$		0			0
$189$	−4.01378	+	2.91618i	−0.291959	+	0.212121i
$190$		0			0
$191$		−	14.8683i		−	1.07583i	−0.842998	−	0.537916i	$-0.819212\pi$
$191$		−	14.8683i		−	1.07583i	0.842998	−	0.537916i	$-0.180788\pi$
$192$		0			0
$193$	14.1221	−	4.58853i	1.01653	−	0.330290i	0.247077	−	0.968996i	$-0.420530\pi$
$193$	14.1221	−	4.58853i	1.01653	−	0.330290i	0.769451	+	0.638706i	$0.220530\pi$
$194$		0			0
$195$	−0.167273	+	0.514813i	−0.0119787	+	0.0368665i
$196$		0			0
$197$	4.82211	−	14.8409i	0.343561	−	1.05737i	−0.618788	−	0.785558i	$-0.712376\pi$
$197$	4.82211	−	14.8409i	0.343561	−	1.05737i	0.962349	−	0.271815i	$-0.0876240\pi$
$198$		0			0
$199$	13.9894	−	19.2548i	0.991684	−	1.36494i	0.0613926	−	0.998114i	$-0.480446\pi$
$199$	13.9894	−	19.2548i	0.991684	−	1.36494i	0.930291	−	0.366822i	$-0.119554\pi$
$200$		0			0
$201$	6.03048	+	18.5599i	0.425358	+	1.30912i
$202$		0			0
$203$	1.07632	+	0.781992i	0.0755428	+	0.0548851i
$204$		0			0
$205$	0.635348	−	0.335442i	0.0443746	−	0.0234283i
$206$		0			0
$207$	1.26760	+	0.920964i	0.0881041	+	0.0640114i
$208$		0			0
$209$	−2.31129	−	7.11343i	−0.159876	−	0.492046i
$210$		0			0
$211$	14.0888	−	19.3916i	0.969913	−	1.33497i	0.0278225	−	0.999613i	$-0.491143\pi$
$211$	14.0888	−	19.3916i	0.969913	−	1.33497i	0.942091	−	0.335358i	$-0.108857\pi$
$212$		0			0
$213$	−0.953819	+	2.93555i	−0.0653546	+	0.201141i
$214$		0			0
$215$	−0.325320	+	1.00123i	−0.0221867	+	0.0682835i
$216$		0			0
$217$	2.51380	−	0.816782i	0.170648	−	0.0554468i
$218$		0			0
$219$		−	25.2834i		−	1.70849i
$220$		0			0
$221$	−15.9058	+	11.5562i	−1.06994	+	0.777357i
$222$		0			0
$223$	21.6525	+	15.7314i	1.44996	+	1.05346i	0.985841	+	0.167680i	$0.0536276\pi$
$223$	21.6525	+	15.7314i	1.44996	+	1.05346i	0.464115	+	0.885775i	$0.346372\pi$
$224$		0			0
$225$	−0.994466	+	0.722522i	−0.0662977	+	0.0481681i
$226$		0			0
$227$	−14.6011	−	20.0967i	−0.969110	−	1.33387i	−0.942495	−	0.334220i	$-0.891527\pi$
$227$	−14.6011	−	20.0967i	−0.969110	−	1.33387i	−0.0266150	−	0.999646i	$-0.508473\pi$
$228$		0			0
$229$	28.0376	+	9.10996i	1.85277	+	0.602003i	0.996313	+	0.0857923i	$0.0273422\pi$
$229$	28.0376	+	9.10996i	1.85277	+	0.602003i	0.856462	+	0.516211i	$0.172658\pi$
$230$		0			0
$231$	3.24584	−	1.05464i	0.213561	−	0.0693901i
$232$		0			0
$233$	−16.8196	+	23.1502i	−1.10189	+	1.51662i	−0.269033	+	0.963131i	$0.586704\pi$
$233$	−16.8196	+	23.1502i	−1.10189	+	1.51662i	−0.832856	+	0.553489i	$0.813296\pi$
$234$		0			0
$235$	−0.795464	−	0.258462i	−0.0518904	−	0.0168602i
$236$		0			0
$237$	8.25966			0.536523
$238$		0			0
$239$	2.08036	+	2.86337i	0.134567	+	0.185216i	0.870983	−	0.491314i	$-0.163483\pi$
$239$	2.08036	+	2.86337i	0.134567	+	0.185216i	−0.736415	+	0.676530i	$0.763483\pi$
$240$		0			0
$241$	−4.68866	−	14.4302i	−0.302023	−	0.929532i	−0.980771	−	0.195161i	$-0.937477\pi$
$241$	−4.68866	−	14.4302i	−0.302023	−	0.929532i	0.678748	−	0.734371i	$-0.262523\pi$
$242$		0			0
$243$			2.55504i			0.163906i
$244$		0			0
$245$	0.112205			0.00716851
$246$		0			0
$247$	10.5726			0.672720
$248$		0			0
$249$		−	13.6422i		−	0.864540i
$250$		0			0
$251$	1.25912	+	3.87517i	0.0794750	+	0.244599i	0.982898	−	0.184152i	$-0.0589539\pi$
$251$	1.25912	+	3.87517i	0.0794750	+	0.244599i	−0.903423	+	0.428751i	$0.858954\pi$
$252$		0			0
$253$	7.07784	+	9.74181i	0.444980	+	0.612463i
$254$		0			0
$255$	1.48453			0.0929650
$256$		0			0
$257$	−0.778836	−	0.253059i	−0.0485824	−	0.0157854i	0.284625	−	0.958639i	$-0.408131\pi$
$257$	−0.778836	−	0.253059i	−0.0485824	−	0.0157854i	−0.333207	+	0.942854i	$0.608131\pi$
$258$		0			0
$259$	0.253708	−	0.349200i	0.0157647	−	0.0216982i
$260$		0			0
$261$	0.311851	−	0.101327i	0.0193031	−	0.00627195i
$262$		0			0
$263$	−21.1218	−	6.86289i	−1.30243	−	0.423184i	−0.426001	−	0.904723i	$-0.640078\pi$
$263$	−21.1218	−	6.86289i	−1.30243	−	0.423184i	−0.876425	+	0.481539i	$0.840078\pi$
$264$		0			0
$265$	0.521050	+	0.717163i	0.0320078	+	0.0440550i
$266$		0			0
$267$	16.7419	−	12.1637i	1.02459	−	0.744406i
$268$		0			0
$269$	0.115013	+	0.0835620i	0.00701248	+	0.00509487i	0.591286	−	0.806462i	$-0.298620\pi$
$269$	0.115013	+	0.0835620i	0.00701248	+	0.00509487i	−0.584273	+	0.811557i	$0.698620\pi$
$270$		0			0
$271$	1.24281	−	0.902953i	0.0754952	−	0.0548505i	−0.549397	−	0.835561i	$-0.685143\pi$
$271$	1.24281	−	0.902953i	0.0754952	−	0.0548505i	0.624893	+	0.780711i	$0.285143\pi$
$272$		0			0
$273$			4.82427i			0.291978i
$274$		0			0
$275$	−8.98457	+	2.91926i	−0.541790	+	0.176038i
$276$		0			0
$277$	9.06136	−	27.8880i	0.544444	−	1.67563i	−0.177864	−	0.984055i	$-0.556919\pi$
$277$	9.06136	−	27.8880i	0.544444	−	1.67563i	0.722308	−	0.691572i	$-0.243081\pi$
$278$		0			0
$279$	0.201309	−	0.619566i	0.0120521	−	0.0370924i
$280$		0			0
$281$	−13.2555	+	18.2447i	−0.790759	+	1.08839i	0.203255	+	0.979126i	$0.434848\pi$
$281$	−13.2555	+	18.2447i	−0.790759	+	1.08839i	−0.994013	+	0.109260i	$0.965152\pi$
$282$		0			0
$283$	1.39713	+	4.29993i	0.0830509	+	0.255604i	0.983956	−	0.178412i	$-0.0570960\pi$
$283$	1.39713	+	4.29993i	0.0830509	+	0.255604i	−0.900905	+	0.434016i	$0.857096\pi$
$284$		0			0
$285$	−0.645851	−	0.469238i	−0.0382569	−	0.0277953i
$286$		0			0
$287$	4.46143	−	4.59300i	0.263350	−	0.271116i
$288$		0			0
$289$	29.8683	+	21.7006i	1.75696	+	1.27651i
$290$		0			0
$291$	6.23590	+	19.1921i	0.365555	+	1.12506i
$292$		0			0
$293$	−7.85594	+	10.8128i	−0.458949	+	0.631689i	−0.974290	−	0.225296i	$-0.927665\pi$
$293$	−7.85594	+	10.8128i	−0.458949	+	0.631689i	0.515341	+	0.856985i	$0.327665\pi$
$294$		0			0
$295$	−0.460347	+	1.41680i	−0.0268024	+	0.0824894i
$296$		0			0
$297$	−2.90398	+	8.93754i	−0.168506	+	0.518609i
$298$		0			0
$299$	−16.1882	+	5.25986i	−0.936188	+	0.304186i
$300$		0			0
$301$			9.38246i			0.540796i
$302$		0			0
$303$	1.46662	−	1.06556i	0.0842552	−	0.0612150i
$304$		0			0
$305$	−0.550939	−	0.400281i	−0.0315467	−	0.0229200i
$306$		0			0
$307$	−0.431601	+	0.313576i	−0.0246328	+	0.0178968i	−0.600034	−	0.799975i	$-0.704846\pi$
$307$	−0.431601	+	0.313576i	−0.0246328	+	0.0178968i	0.575401	+	0.817872i	$0.304846\pi$
$308$		0			0
$309$	5.34770	+	7.36047i	0.304220	+	0.418723i
$310$		0			0
$311$	31.2633	+	10.1581i	1.77278	+	0.576011i	0.998391	−	0.0566994i	$-0.0180577\pi$
$311$	31.2633	+	10.1581i	1.77278	+	0.576011i	0.774388	+	0.632710i	$0.218058\pi$
$312$		0			0
$313$	−21.9912	+	7.14538i	−1.24302	+	0.403880i	−0.855413	−	0.517946i	$-0.826697\pi$
$313$	−21.9912	+	7.14538i	−1.24302	+	0.403880i	−0.387603	+	0.921826i	$0.626697\pi$
$314$		0			0
$315$	0.0162550	−	0.0223731i	0.000915868	−	0.00126058i
$316$		0			0
$317$	19.0339	+	6.18448i	1.06905	+	0.347355i	0.790117	−	0.612956i	$-0.210020\pi$
$317$	19.0339	+	6.18448i	1.06905	+	0.347355i	0.278931	+	0.960311i	$0.410020\pi$
$318$		0			0
$319$	2.51999			0.141092
$320$		0			0
$321$	5.43827	+	7.48513i	0.303534	+	0.417779i
$322$		0			0
$323$	−8.96007	−	27.5763i	−0.498552	−	1.53438i
$324$		0			0
$325$		−	13.3537i		−	0.740729i
$326$		0			0
$327$	19.4735			1.07689
$328$		0			0
$329$	−7.45422			−0.410965
$330$		0			0
$331$			6.20469i			0.341041i	0.985354	+	0.170520i	$0.0545448\pi$
$331$			6.20469i			0.341041i	−0.985354	+	0.170520i	$0.945455\pi$
$332$		0			0
$333$	−0.0328742	−	0.101177i	−0.00180150	−	0.00554444i
$334$		0			0
$335$	0.714324	+	0.983182i	0.0390277	+	0.0537170i
$336$		0			0
$337$	−0.239221			−0.0130312			−0.00651560	−	0.999979i	$-0.502074\pi$
$337$	−0.239221			−0.0130312			−0.00651560	+	0.999979i	$0.502074\pi$
$338$		0			0
$339$	−25.2794	−	8.21376i	−1.37299	−	0.446110i
$340$		0			0
$341$	2.94278	−	4.05039i	0.159361	−	0.219341i
$342$		0			0
$343$	0.951057	−	0.309017i	0.0513522	−	0.0166853i
$344$		0			0
$345$	1.22234	+	0.397161i	0.0658083	+	0.0213824i
$346$		0			0
$347$	−4.09662	−	5.63851i	−0.219918	−	0.302691i	0.684776	−	0.728754i	$-0.259900\pi$
$347$	−4.09662	−	5.63851i	−0.219918	−	0.302691i	−0.904694	+	0.426063i	$0.859900\pi$
$348$		0			0
$349$	0.117288	−	0.0852148i	0.00627829	−	0.00456144i	−0.584642	−	0.811292i	$-0.698765\pi$
$349$	0.117288	−	0.0852148i	0.00627829	−	0.00456144i	0.590920	+	0.806730i	$0.298765\pi$
$350$		0			0
$351$	−10.7468	−	7.80801i	−0.573622	−	0.416761i
$352$		0			0
$353$	6.51049	−	4.73015i	0.346518	−	0.251760i	−0.400889	−	0.916127i	$-0.631299\pi$
$353$	6.51049	−	4.73015i	0.346518	−	0.251760i	0.747407	+	0.664366i	$0.231299\pi$
$354$		0			0
$355$			0.192216i			0.0102018i
$356$		0			0
$357$	12.5830	−	4.08846i	0.665962	−	0.216384i
$358$		0			0
$359$	−1.66872	+	5.13578i	−0.0880715	+	0.271056i	−0.985386	−	0.170335i	$-0.945515\pi$
$359$	−1.66872	+	5.13578i	−0.0880715	+	0.271056i	0.897315	+	0.441391i	$0.145515\pi$
$360$		0			0
$361$	1.05299	−	3.24078i	0.0554206	−	0.170567i
$362$		0			0
$363$	−7.85000	+	10.8046i	−0.412018	+	0.567094i
$364$		0			0
$365$	−0.486547	−	1.49744i	−0.0254670	−	0.0783795i
$366$		0			0
$367$	24.7454	+	17.9786i	1.29170	+	0.938476i	0.999838	−	0.0179839i	$-0.00572478\pi$
$367$	24.7454	+	17.9786i	1.29170	+	0.938476i	0.291863	+	0.956460i	$0.405725\pi$
$368$		0			0
$369$	−0.269499	−	1.55497i	−0.0140296	−	0.0809486i
$370$		0			0
$371$	6.39155	+	4.64373i	0.331833	+	0.241090i
$372$		0			0
$373$	9.98945	+	30.7444i	0.517234	+	1.59188i	0.779180	+	0.626800i	$0.215636\pi$
$373$	9.98945	+	30.7444i	0.517234	+	1.59188i	−0.261946	+	0.965083i	$0.584364\pi$
$374$		0			0
$375$	−1.18683	+	1.63353i	−0.0612877	+	0.0843553i
$376$		0			0
$377$	−1.10076	+	3.38778i	−0.0566919	+	0.174480i
$378$		0			0
$379$	1.36775	−	4.20951i	0.0702568	−	0.216228i	−0.909763	−	0.415128i	$-0.863737\pi$
$379$	1.36775	−	4.20951i	0.0702568	−	0.216228i	0.980020	+	0.198900i	$0.0637368\pi$
$380$		0			0
$381$	−20.6388	+	6.70596i	−1.05736	+	0.343557i
$382$		0			0
$383$			30.8518i			1.57645i	0.615386	+	0.788226i	$0.289000\pi$
$383$			30.8518i			1.57645i	−0.615386	+	0.788226i	$0.711000\pi$
$384$		0			0
$385$	0.171943	−	0.124924i	0.00876304	−	0.00636672i
$386$		0			0
$387$	1.87082	+	1.35923i	0.0950990	+	0.0690935i
$388$		0			0
$389$	20.6252	−	14.9851i	1.04574	−	0.759776i	0.0743433	−	0.997233i	$-0.476314\pi$
$389$	20.6252	−	14.9851i	1.04574	−	0.759776i	0.971398	+	0.237457i	$0.0763140\pi$
$390$		0			0
$391$	27.4383	+	37.7656i	1.38761	+	1.90989i
$392$		0			0
$393$	−29.9775	−	9.74027i	−1.51216	−	0.491332i
$394$		0			0
$395$	0.489187	−	0.158947i	0.0246137	−	0.00799747i
$396$		0			0
$397$	2.71913	−	3.74256i	0.136469	−	0.187834i	−0.735313	−	0.677728i	$-0.762965\pi$
$397$	2.71913	−	3.74256i	0.136469	−	0.187834i	0.871782	+	0.489894i	$0.162965\pi$
$398$		0			0
$399$	−6.76657	−	2.19859i	−0.338752	−	0.110067i
$400$		0			0
$401$	−27.3210			−1.36435			−0.682173	−	0.731190i	$-0.738965\pi$
$401$	−27.3210			−1.36435			−0.682173	+	0.731190i	$0.738965\pi$
$402$		0			0
$403$	4.15976	+	5.72542i	0.207212	+	0.285203i
$404$		0			0
$405$	0.335590	+	1.03284i	0.0166756	+	0.0513223i
$406$		0			0
$407$		−	0.817583i		−	0.0405261i
$408$		0			0
$409$	−10.7717			−0.532628			−0.266314	−	0.963886i	$-0.585806\pi$
$409$	−10.7717			−0.532628			−0.266314	+	0.963886i	$0.585806\pi$
$410$		0			0
$411$	−10.9131			−0.538303
$412$		0			0
$413$			13.2767i			0.653304i
$414$		0			0
$415$	−0.262527	−	0.807975i	−0.0128869	−	0.0396619i
$416$		0			0
$417$	−15.4723	−	21.2958i	−0.757682	−	1.04286i
$418$		0			0
$419$	22.4032			1.09447			0.547233	−	0.836980i	$-0.315681\pi$
$419$	22.4032			1.09447			0.547233	+	0.836980i	$0.315681\pi$
$420$		0			0
$421$	−32.9383	−	10.7023i	−1.60531	−	0.521598i	−0.636899	−	0.770947i	$-0.719783\pi$
$421$	−32.9383	−	10.7023i	−1.60531	−	0.521598i	−0.968414	+	0.249349i	$0.919783\pi$
$422$		0			0
$423$	−1.07989	+	1.48634i	−0.0525059	+	0.0722682i
$424$		0			0
$425$	−34.8300	+	11.3170i	−1.68950	+	0.548953i
$426$		0			0
$427$	−5.77218	−	1.87550i	−0.279336	−	0.0907616i
$428$		0			0
$429$	5.37113	+	7.39272i	0.259321	+	0.356924i
$430$		0			0
$431$	6.58772	−	4.78626i	0.317319	−	0.230546i	−0.417712	−	0.908580i	$-0.637168\pi$
$431$	6.58772	−	4.78626i	0.317319	−	0.230546i	0.735031	+	0.678034i	$0.237168\pi$
$432$		0			0
$433$	−20.7560	−	15.0801i	−0.997472	−	0.724706i	−0.0359272	−	0.999354i	$-0.511438\pi$
$433$	−20.7560	−	15.0801i	−0.997472	−	0.724706i	−0.961545	+	0.274649i	$0.911438\pi$
$434$		0			0
$435$	0.217600	−	0.158096i	0.0104331	−	0.00758010i
$436$		0			0
$437$		−	25.1029i		−	1.20083i
$438$		0			0
$439$	−18.8988	+	6.14058i	−0.901989	+	0.293074i	−0.723058	−	0.690788i	$-0.757264\pi$
$439$	−18.8988	+	6.14058i	−0.901989	+	0.293074i	−0.178931	+	0.983862i	$0.557264\pi$
$440$		0			0
$441$	0.0761622	−	0.234403i	0.00362677	−	0.0111621i
$442$		0			0
$443$	5.83350	−	17.9537i	0.277158	−	0.853004i	−0.711482	−	0.702704i	$-0.751976\pi$
$443$	5.83350	−	17.9537i	0.277158	−	0.853004i	0.988640	−	0.150300i	$-0.0480241\pi$
$444$		0			0
$445$	0.757481	−	1.04258i	0.0359081	−	0.0494232i
$446$		0			0
$447$	−10.6608	−	32.8105i	−0.504237	−	1.55188i
$448$		0			0
$449$	−16.0443	−	11.6569i	−0.757177	−	0.550121i	0.140866	−	0.990029i	$-0.455011\pi$
$449$	−16.0443	−	11.6569i	−0.757177	−	0.550121i	−0.898043	+	0.439908i	$0.855011\pi$
$450$		0			0
$451$	1.72307	−	12.0055i	0.0811360	−	0.565317i
$452$		0			0
$453$	6.04842	+	4.39443i	0.284179	+	0.206468i
$454$		0			0
$455$	0.0928368	+	0.285722i	0.00435226	+	0.0133949i
$456$		0			0
$457$	15.5693	−	21.4293i	0.728302	−	1.00242i	−0.270905	−	0.962606i	$-0.587323\pi$
$457$	15.5693	−	21.4293i	0.728302	−	1.00242i	0.999207	−	0.0398152i	$-0.0126769\pi$
$458$		0			0
$459$	−11.2577	+	34.6477i	−0.525465	+	1.61722i
$460$		0			0
$461$	2.36995	−	7.29396i	0.110380	−	0.339714i	−0.880576	−	0.473906i	$-0.842844\pi$
$461$	2.36995	−	7.29396i	0.110380	−	0.339714i	0.990955	+	0.134192i	$0.0428438\pi$
$462$		0			0
$463$	6.76522	−	2.19815i	0.314406	−	0.102157i	−0.147563	−	0.989053i	$-0.547143\pi$
$463$	6.76522	−	2.19815i	0.314406	−	0.102157i	0.461969	+	0.886896i	$0.347143\pi$
$464$		0			0
$465$		−	0.534369i		−	0.0247808i
$466$		0			0
$467$	−18.9820	+	13.7912i	−0.878382	+	0.638182i	−0.932823	−	0.360335i	$-0.882662\pi$
$467$	−18.9820	+	13.7912i	−0.878382	+	0.638182i	0.0544407	+	0.998517i	$0.482662\pi$
$468$		0			0
$469$	8.76238	+	6.36624i	0.404609	+	0.293966i
$470$		0			0
$471$	−10.9222	+	7.93548i	−0.503270	+	0.365647i
$472$		0			0
$473$	10.4460	+	14.3777i	0.480309	+	0.661088i
$474$		0			0
$475$	18.7300	+	6.08576i	0.859393	+	0.279234i
$476$		0			0
$477$	1.85188	−	0.601711i	0.0847916	−	0.0275505i
$478$		0			0
$479$	16.0295	−	22.0627i	0.732406	−	1.00807i	−0.266613	−	0.963804i	$-0.585905\pi$
$479$	16.0295	−	22.0627i	0.732406	−	1.00807i	0.999020	−	0.0442673i	$-0.0140953\pi$
$480$		0			0
$481$	1.09913	+	0.357128i	0.0501159	+	0.0162836i
$482$		0			0
$483$	11.4544			0.521193
$484$		0			0
$485$	0.738655	+	1.01667i	0.0335406	+	0.0461647i
$486$		0			0
$487$	−1.00109	−	3.08103i	−0.0453636	−	0.139615i	0.925809	−	0.377991i	$-0.123385\pi$
$487$	−1.00109	−	3.08103i	−0.0453636	−	0.139615i	−0.971173	+	0.238376i	$0.923385\pi$
$488$		0			0
$489$			0.167278i			0.00756456i
$490$		0			0
$491$	−34.6834			−1.56524			−0.782620	−	0.622500i	$-0.786117\pi$
$491$	−34.6834			−1.56524			−0.782620	+	0.622500i	$0.786117\pi$
$492$		0			0
$493$	9.76912			0.439979
$494$		0			0
$495$		−	0.0523824i		−	0.00235441i
$496$		0			0
$497$	0.529371	+	1.62924i	0.0237456	+	0.0730813i
$498$		0			0
$499$	18.8491	+	25.9436i	0.843802	+	1.16139i	0.985195	+	0.171440i	$0.0548421\pi$
$499$	18.8491	+	25.9436i	0.843802	+	1.16139i	−0.141392	+	0.989954i	$0.545158\pi$
$500$		0			0
$501$	20.9779			0.937223
$502$		0			0
$503$	−33.5728	−	10.9085i	−1.49694	−	0.486385i	−0.557815	−	0.829965i	$-0.688360\pi$
$503$	−33.5728	−	10.9085i	−1.49694	−	0.486385i	−0.939123	+	0.343581i	$0.888360\pi$
$504$		0			0
$505$	0.0663568	−	0.0913323i	0.00295284	−	0.00406424i
$506$		0			0
$507$	9.99226	−	3.24668i	0.443772	−	0.144190i
$508$		0			0
$509$	−8.50159	−	2.76233i	−0.376826	−	0.122438i	0.114479	−	0.993426i	$-0.463480\pi$
$509$	−8.50159	−	2.76233i	−0.376826	−	0.122438i	−0.491305	+	0.870987i	$0.663480\pi$
$510$		0			0
$511$	−8.24801	−	11.3524i	−0.364870	−	0.502201i
$512$		0			0
$513$	15.8493	−	11.5152i	0.699765	−	0.508409i
$514$		0			0
$515$	0.458366	+	0.333022i	0.0201980	+	0.0146747i
$516$		0			0
$517$	−11.4229	+	8.29921i	−0.502378	+	0.364999i
$518$		0			0
$519$		−	38.3173i		−	1.68194i
$520$		0			0
$521$	−7.04866	+	2.29025i	−0.308807	+	0.100338i	−0.459321	−	0.888270i	$-0.651907\pi$
$521$	−7.04866	+	2.29025i	−0.308807	+	0.100338i	0.150514	+	0.988608i	$0.451907\pi$
$522$		0			0
$523$	5.16994	−	15.9114i	0.226066	−	0.695759i	−0.772116	−	0.635482i	$-0.780802\pi$
$523$	5.16994	−	15.9114i	0.226066	−	0.695759i	0.998182	−	0.0602773i	$-0.0191985\pi$
$524$		0			0
$525$	−2.77692	+	8.54647i	−0.121195	+	0.372999i
$526$		0			0
$527$	11.4081	−	15.7020i	0.496946	−	0.683988i
$528$		0			0
$529$	5.38125	+	16.5618i	0.233968	+	0.720078i
$530$		0			0
$531$	2.64731	+	1.92339i	0.114884	+	0.0834679i
$532$		0			0
$533$	15.3871	+	7.56054i	0.666489	+	0.327483i
$534$		0			0
$535$	0.466129	+	0.338662i	0.0201525	+	0.0146417i
$536$		0			0
$537$	−3.54558	−	10.9122i	−0.153003	−	0.470895i
$538$		0			0
$539$	1.11336	−	1.53240i	0.0479557	−	0.0660053i
$540$		0			0
$541$	−1.38701	+	4.26877i	−0.0596321	+	0.183529i	−0.976435	−	0.215811i	$-0.930761\pi$
$541$	−1.38701	+	4.26877i	−0.0596321	+	0.183529i	0.916803	+	0.399340i	$0.130761\pi$
$542$		0			0
$543$	3.80678	−	11.7161i	0.163364	−	0.502784i
$544$		0			0
$545$	1.15334	−	0.374742i	0.0494036	−	0.0160522i
$546$		0			0
$547$		−	20.8598i		−	0.891903i	−0.895057	−	0.445951i	$-0.852865\pi$
$547$		−	20.8598i		−	0.891903i	0.895057	−	0.445951i	$-0.147135\pi$
$548$		0			0
$549$	−1.21018	+	0.879245i	−0.0516491	+	0.0375253i
$550$		0			0
$551$	−4.25009	−	3.08787i	−0.181060	−	0.131548i
$552$		0			0
$553$	3.70864	−	2.69448i	0.157707	−	0.114581i
$554$		0			0
$555$	−0.0512923	−	0.0705978i	−0.00217724	−	0.00299671i
$556$		0			0
$557$	16.6524	+	5.41070i	0.705585	+	0.229259i	0.639762	−	0.768573i	$-0.279033\pi$
$557$	16.6524	+	5.41070i	0.705585	+	0.229259i	0.0658230	+	0.997831i	$0.479033\pi$
$558$		0			0
$559$	−23.8918	+	7.76291i	−1.01052	+	0.328336i
$560$		0			0
$561$	14.7303	−	20.2745i	0.621914	−	0.855991i
$562$		0			0
$563$	−5.12592	−	1.66551i	−0.216032	−	0.0701929i	0.199002	−	0.979999i	$-0.436230\pi$
$563$	−5.12592	−	1.66551i	−0.216032	−	0.0701929i	−0.415033	+	0.909806i	$0.636230\pi$
$564$		0			0
$565$	−1.65526			−0.0696373
$566$		0			0
$567$	5.68897	+	7.83019i	0.238914	+	0.328837i
$568$		0			0
$569$	1.14983	+	3.53882i	0.0482035	+	0.148355i	0.972261	−	0.233898i	$-0.0751482\pi$
$569$	1.14983	+	3.53882i	0.0482035	+	0.148355i	−0.924058	+	0.382253i	$0.875148\pi$
$570$		0			0
$571$		−	28.4150i		−	1.18913i	−0.804048	−	0.594565i	$-0.797324\pi$
$571$		−	28.4150i		−	1.18913i	0.804048	−	0.594565i	$-0.202676\pi$
$572$		0			0
$573$	−26.7896			−1.11915
$574$		0			0
$575$	−31.7060			−1.32223
$576$		0			0
$577$			36.1589i			1.50531i	0.658413	+	0.752657i	$0.271228\pi$
$577$			36.1589i			1.50531i	−0.658413	+	0.752657i	$0.728772\pi$
$578$		0			0
$579$	−8.26760	−	25.4450i	−0.343590	−	1.05746i
$580$		0			0
$581$	−4.45039	−	6.12544i	−0.184633	−	0.254126i
$582$		0			0
$583$	14.9646			0.619769
$584$		0			0
$585$	0.0704209	+	0.0228811i	0.00291154	+	0.000946018i
$586$		0			0
$587$	−12.5568	+	17.2829i	−0.518274	+	0.713343i	−0.985287	−	0.170907i	$-0.945330\pi$
$587$	−12.5568	+	17.2829i	−0.518274	+	0.713343i	0.467013	+	0.884250i	$0.345330\pi$
$588$		0			0
$589$	−9.92630	+	3.22525i	−0.409006	+	0.132894i
$590$		0			0
$591$	−26.7403	−	8.68846i	−1.09995	−	0.357396i
$592$		0			0
$593$	−3.34572	−	4.60499i	−0.137392	−	0.189104i	0.734776	−	0.678309i	$-0.237287\pi$
$593$	−3.34572	−	4.60499i	−0.137392	−	0.189104i	−0.872169	+	0.489205i	$0.837287\pi$
$594$		0			0
$595$	0.666564	−	0.484287i	0.0273265	−	0.0198538i
$596$		0			0
$597$	−34.6932	−	25.2061i	−1.41990	−	1.03162i
$598$		0			0
$599$	−13.4135	+	9.74550i	−0.548062	+	0.398190i	−0.827070	−	0.562098i	$-0.809994\pi$
$599$	−13.4135	+	9.74550i	−0.548062	+	0.398190i	0.279008	+	0.960289i	$0.409994\pi$
$600$		0			0
$601$			14.6959i			0.599459i	0.954024	+	0.299729i	$0.0968964\pi$
$601$			14.6959i			0.599459i	−0.954024	+	0.299729i	$0.903104\pi$
$602$		0			0
$603$	2.53880	−	0.824905i	0.103388	−	0.0335927i
$604$		0			0
$605$	−0.257004	+	0.790977i	−0.0104487	+	0.0321578i
$606$		0			0
$607$	−4.60137	+	14.1616i	−0.186764	+	0.574801i	−0.999974	−	0.00716942i	$-0.997718\pi$
$607$	−4.60137	+	14.1616i	−0.186764	+	0.574801i	0.813210	+	0.581970i	$0.197718\pi$
$608$		0			0
$609$	1.40899	−	1.93931i	0.0570951	−	0.0785847i
$610$		0			0
$611$	−6.16752	−	18.9817i	−0.249511	−	0.767916i
$612$		0			0
$613$	−12.9339	−	9.39704i	−0.522396	−	0.379543i	0.295110	−	0.955463i	$-0.404644\pi$
$613$	−12.9339	−	9.39704i	−0.522396	−	0.379543i	−0.817506	+	0.575920i	$0.804644\pi$
$614$		0			0
$615$	−0.604397	−	1.14477i	−0.0243717	−	0.0461615i
$616$		0			0
$617$	17.8526	+	12.9707i	0.718718	+	0.522179i	0.885974	−	0.463734i	$-0.153491\pi$
$617$	17.8526	+	12.9707i	0.718718	+	0.522179i	−0.167257	+	0.985913i	$0.553491\pi$
$618$		0			0
$619$	−4.05308	−	12.4741i	−0.162907	−	0.501376i	0.835969	−	0.548777i	$-0.184906\pi$
$619$	−4.05308	−	12.4741i	−0.162907	−	0.501376i	−0.998876	+	0.0474005i	$0.984906\pi$
$620$		0			0
$621$	−18.5388	+	25.5164i	−0.743935	+	1.02394i
$622$		0			0
$623$	3.54914	−	10.9231i	0.142193	−	0.437626i
$624$		0			0
$625$	7.66712	−	23.5970i	0.306685	−	0.943878i
$626$		0			0
$627$	−12.8169	+	4.16448i	−0.511860	+	0.166313i
$628$		0			0
$629$		−	3.16948i		−	0.126375i
$630$		0			0
$631$	−22.2463	+	16.1629i	−0.885611	+	0.643434i	−0.934730	−	0.355359i	$-0.884359\pi$
$631$	−22.2463	+	16.1629i	−0.885611	+	0.643434i	0.0491187	+	0.998793i	$0.484359\pi$
$632$		0			0
$633$	−34.9396	−	25.3851i	−1.38873	−	1.00897i
$634$		0			0
$635$	−1.09331	+	0.794335i	−0.0433866	+	0.0315222i
$636$		0			0
$637$	1.57378	+	2.16612i	0.0623555	+	0.0858250i
$638$		0			0
$639$	0.401552	+	0.130472i	0.0158852	+	0.00516140i
$640$		0			0
$641$	−17.5566	+	5.70450i	−0.693445	+	0.225314i	−0.634472	−	0.772945i	$-0.718783\pi$
$641$	−17.5566	+	5.70450i	−0.693445	+	0.225314i	−0.0589730	+	0.998260i	$0.518783\pi$
$642$		0			0
$643$	−16.2188	+	22.3233i	−0.639609	+	0.880346i	−0.998595	−	0.0529968i	$-0.983123\pi$
$643$	−16.2188	+	22.3233i	−0.639609	+	0.880346i	0.358986	+	0.933343i	$0.383123\pi$
$644$		0			0
$645$	1.80402	+	0.586160i	0.0710331	+	0.0230800i
$646$		0			0
$647$	−6.82820			−0.268444			−0.134222	−	0.990951i	$-0.542854\pi$
$647$	−6.82820			−0.268444			−0.134222	+	0.990951i	$0.542854\pi$
$648$		0			0
$649$	14.7817	+	20.3453i	0.580233	+	0.798623i
$650$		0			0
$651$	−1.47167	−	4.52935i	−0.0576795	−	0.177519i
$652$		0			0
$653$		−	25.7376i		−	1.00719i	−0.863940	−	0.503594i	$-0.832011\pi$
$653$		−	25.7376i		−	1.00719i	0.863940	−	0.503594i	$-0.167989\pi$
$654$		0			0
$655$	−1.96289			−0.0766964
$656$		0			0
$657$	−3.45850			−0.134929
$658$		0			0
$659$			17.9999i			0.701177i	0.936530	+	0.350588i	$0.114018\pi$
$659$			17.9999i			0.701177i	−0.936530	+	0.350588i	$0.885982\pi$
$660$		0			0
$661$	−13.3355	−	41.0424i	−0.518690	−	1.59636i	−0.776466	−	0.630159i	$-0.782990\pi$
$661$	−13.3355	−	41.0424i	−0.518690	−	1.59636i	0.257777	−	0.966205i	$-0.417010\pi$
$662$		0			0
$663$	20.8220	+	28.6590i	0.808659	+	1.11302i
$664$		0			0
$665$	−0.443067			−0.0171814
$666$		0			0
$667$	8.04371	+	2.61356i	0.311454	+	0.101197i
$668$		0			0
$669$	28.3448	−	39.0133i	1.09587	−	1.50834i
$670$		0			0
$671$	−10.9334	+	3.55248i	−0.422080	+	0.137142i
$672$		0			0
$673$	18.4686	+	6.00083i	0.711914	+	0.231315i	0.642514	−	0.766274i	$-0.277892\pi$
$673$	18.4686	+	6.00083i	0.711914	+	0.231315i	0.0694001	+	0.997589i	$0.477892\pi$
$674$		0			0
$675$	−14.5442	−	20.0184i	−0.559806	−	0.770507i
$676$		0			0
$677$	11.7650	−	8.54776i	0.452165	−	0.328517i	−0.338285	−	0.941044i	$-0.609847\pi$
$677$	11.7650	−	8.54776i	0.452165	−	0.328517i	0.790450	+	0.612526i	$0.209847\pi$
$678$		0			0
$679$	9.06085	+	6.58309i	0.347723	+	0.252636i
$680$		0			0
$681$	−36.2102	+	26.3082i	−1.38758	+	1.00813i
$682$		0			0
$683$		−	14.5045i		−	0.555001i	−0.960725	−	0.277500i	$-0.910494\pi$
$683$		−	14.5045i		−	0.555001i	0.960725	−	0.277500i	$-0.0895060\pi$
$684$		0			0
$685$	−0.646339	+	0.210008i	−0.0246954	+	0.00802401i
$686$		0			0
$687$	16.4143	−	50.5180i	0.626244	−	1.92738i
$688$		0			0
$689$	−6.53667	+	20.1178i	−0.249027	+	0.766427i
$690$		0			0
$691$	−20.6508	+	28.4234i	−0.785593	+	1.08128i	0.209050	+	0.977905i	$0.432963\pi$
$691$	−20.6508	+	28.4234i	−0.785593	+	1.08128i	−0.994643	+	0.103371i	$0.967037\pi$
$692$		0			0
$693$	−0.144263	−	0.443996i	−0.00548010	−	0.0168660i
$694$		0			0
$695$	−1.32617	−	0.963522i	−0.0503047	−	0.0365485i
$696$		0			0
$697$	6.67972	−	46.5411i	0.253012	−	1.76287i
$698$		0			0
$699$	41.7119	+	30.3055i	1.57769	+	1.14626i
$700$		0			0
$701$	−6.53588	−	20.1154i	−0.246857	−	0.759747i	−0.995326	−	0.0965767i	$-0.969211\pi$
$701$	−6.53588	−	20.1154i	−0.246857	−	0.759747i	0.748469	−	0.663170i	$-0.230789\pi$
$702$		0			0
$703$	−1.00183	+	1.37889i	−0.0377845	+	0.0520060i
$704$		0			0
$705$	−0.465696	+	1.43326i	−0.0175391	+	0.0539798i
$706$		0			0
$707$	0.310912	−	0.956888i	0.0116930	−	0.0359875i
$708$		0			0
$709$	12.5968	−	4.09294i	0.473082	−	0.153714i	−0.0627658	−	0.998028i	$-0.519992\pi$
$709$	12.5968	−	4.09294i	0.473082	−	0.153714i	0.535848	+	0.844315i	$0.319992\pi$
$710$		0			0
$711$		−	1.12983i		−	0.0423720i
$712$		0			0
$713$	13.5940	−	9.87664i	0.509100	−	0.369883i
$714$		0			0
$715$	0.460374	+	0.334482i	0.0172170	+	0.0125089i
$716$		0			0
$717$	5.15920	−	3.74838i	0.192674	−	0.139986i
$718$		0			0
$719$	6.65804	+	9.16401i	0.248303	+	0.341760i	0.914916	−	0.403644i	$-0.132257\pi$
$719$	6.65804	+	9.16401i	0.248303	+	0.341760i	−0.666613	+	0.745404i	$0.732257\pi$
$720$		0			0
$721$	4.80230	+	1.56036i	0.178847	+	0.0581109i
$722$		0			0
$723$	−26.0003	+	8.44801i	−0.966962	+	0.314185i
$724$		0			0
$725$	−3.90011	+	5.36805i	−0.144847	+	0.199364i
$726$		0			0
$727$	33.1465	+	10.7700i	1.22934	+	0.399436i	0.850474	−	0.526017i	$-0.176315\pi$
$727$	33.1465	+	10.7700i	1.22934	+	0.399436i	0.378863	+	0.925453i	$0.376315\pi$
$728$		0			0
$729$	−24.4323			−0.904900
$730$		0			0
$731$	40.4956	+	55.7374i	1.49778	+	2.06152i
$732$		0			0
$733$	−2.47776	−	7.62576i	−0.0915181	−	0.281664i	0.894813	−	0.446442i	$-0.147309\pi$
$733$	−2.47776	−	7.62576i	−0.0915181	−	0.281664i	−0.986331	+	0.164778i	$0.947309\pi$
$734$		0			0
$735$		−	0.202170i		−	0.00745717i
$736$		0			0
$737$	20.5154			0.755695
$738$		0			0
$739$	−12.4775			−0.458991			−0.229495	−	0.973310i	$-0.573708\pi$
$739$	−12.4775			−0.458991			−0.229495	+	0.973310i	$0.573708\pi$
$740$		0			0
$741$		−	19.0497i		−	0.699808i
$742$		0			0
$743$	8.05974	+	24.8053i	0.295683	+	0.910019i	0.982991	+	0.183653i	$0.0587923\pi$
$743$	8.05974	+	24.8053i	0.295683	+	0.910019i	−0.687308	+	0.726366i	$0.741208\pi$
$744$		0			0
$745$	−1.26279	−	1.73808i	−0.0462651	−	0.0636785i
$746$		0			0
$747$	−1.86611			−0.0682773
$748$		0			0
$749$	4.88363	+	1.58679i	0.178444	+	0.0579799i
$750$		0			0
$751$	−26.5361	+	36.5238i	−0.968315	+	1.33277i	−0.0254221	+	0.999677i	$0.508093\pi$
$751$	−26.5361	+	36.5238i	−0.968315	+	1.33277i	−0.942893	+	0.333095i	$0.891907\pi$
$752$		0			0
$753$	6.98227	−	2.26868i	0.254448	−	0.0826752i
$754$		0			0
$755$	0.442789	+	0.143871i	0.0161148	+	0.00523600i
$756$		0			0
$757$	17.9133	+	24.6555i	0.651070	+	0.896120i	0.999145	−	0.0413462i	$-0.0131647\pi$
$757$	17.9133	+	24.6555i	0.651070	+	0.896120i	−0.348075	+	0.937467i	$0.613165\pi$
$758$		0			0
$759$	17.5528	−	12.7528i	0.637125	−	0.462898i
$760$		0			0
$761$	13.3360	+	9.68919i	0.483431	+	0.351233i	0.802652	−	0.596447i	$-0.203421\pi$
$761$	13.3360	+	9.68919i	0.483431	+	0.351233i	−0.319222	+	0.947680i	$0.603421\pi$
$762$		0			0
$763$	8.74371	−	6.35268i	0.316544	−	0.229982i
$764$		0			0
$765$		−	0.203068i		−	0.00734194i
$766$		0			0
$767$	−33.8083	+	10.9850i	−1.22075	+	0.396644i
$768$		0			0
$769$	9.30295	−	28.6316i	0.335473	−	1.03248i	−0.631015	−	0.775770i	$-0.717362\pi$
$769$	9.30295	−	28.6316i	0.335473	−	1.03248i	0.966489	−	0.256710i	$-0.0826385\pi$
$770$		0			0
$771$	−0.455961	+	1.40330i	−0.0164210	+	0.0505387i
$772$		0			0
$773$	4.95050	−	6.81378i	0.178057	−	0.245075i	−0.710655	−	0.703541i	$-0.751601\pi$
$773$	4.95050	−	6.81378i	0.178057	−	0.245075i	0.888712	+	0.458467i	$0.151601\pi$
$774$		0			0
$775$	4.07363	+	12.5373i	0.146329	+	0.450354i
$776$		0			0
$777$	−0.629186	−	0.457131i	−0.0225719	−	0.0163995i
$778$		0			0
$779$	−17.6170	+	18.1365i	−0.631193	+	0.649808i
$780$		0			0
$781$	2.62513	+	1.90727i	0.0939347	+	0.0682475i
$782$		0			0
$783$	2.03968	+	6.27749i	0.0728922	+	0.224339i
$784$		0			0
$785$	−0.494174	+	0.680172i	−0.0176378	+	0.0242764i
$786$		0			0
$787$	7.78032	−	23.9454i	0.277338	−	0.853560i	−0.711253	−	0.702936i	$-0.751872\pi$
$787$	7.78032	−	23.9454i	0.277338	−	0.853560i	0.988591	−	0.150624i	$-0.0481282\pi$
$788$		0			0
$789$	−12.3655	+	38.0572i	−0.440224	+	1.35487i
$790$		0			0
$791$	−14.0301	+	4.55865i	−0.498853	+	0.162087i
$792$		0			0
$793$		−	16.2502i		−	0.577063i
$794$		0			0
$795$	1.29218	−	0.938825i	0.0458290	−	0.0332967i
$796$		0			0
$797$	−33.2386	−	24.1492i	−1.17737	−	0.855410i	−0.185498	−	0.982645i	$-0.559390\pi$
$797$	−33.2386	−	24.1492i	−1.17737	−	0.855410i	−0.991873	+	0.127234i	$0.959390\pi$
$798$		0			0
$799$	−44.2825	+	32.1731i	−1.56660	+	1.13820i
$800$		0			0
$801$	−1.66386	−	2.29011i	−0.0587897	−	0.0809170i
$802$		0			0
$803$	−25.2786	−	8.21350i	−0.892061	−	0.289848i
$804$		0			0
$805$	0.678398	−	0.220425i	0.0239104	−	0.00776896i
$806$		0			0
$807$	0.150562	−	0.207230i	0.00530002	−	0.00729485i
$808$		0			0
$809$	−26.8051	−	8.70951i	−0.942418	−	0.306210i	−0.202787	−	0.979223i	$-0.565000\pi$
$809$	−26.8051	−	8.70951i	−0.942418	−	0.306210i	−0.739631	+	0.673013i	$0.765000\pi$
$810$		0			0
$811$	−10.6880			−0.375305			−0.187653	−	0.982235i	$-0.560088\pi$
$811$	−10.6880			−0.375305			−0.187653	+	0.982235i	$0.560088\pi$
$812$		0			0
$813$	−1.62694	−	2.23929i	−0.0570592	−	0.0785352i
$814$		0			0
$815$	0.00321904	+	0.00990720i	0.000112758	+	0.000347034i
$816$		0			0
$817$		−	37.0488i		−	1.29617i
$818$		0			0
$819$	0.659907			0.0230590
$820$		0			0
$821$	13.2815			0.463528			0.231764	−	0.972772i	$-0.425550\pi$
$821$	13.2815			0.463528			0.231764	+	0.972772i	$0.425550\pi$
$822$		0			0
$823$			54.5651i			1.90202i	0.309159	+	0.951010i	$0.399952\pi$
$823$			54.5651i			1.90202i	−0.309159	+	0.951010i	$0.600048\pi$
$824$		0			0
$825$	5.25991	+	16.1883i	0.183127	+	0.563606i
$826$		0			0
$827$	−10.4123	−	14.3313i	−0.362070	−	0.498347i	0.588654	−	0.808385i	$-0.299658\pi$
$827$	−10.4123	−	14.3313i	−0.362070	−	0.498347i	−0.950724	+	0.310039i	$0.899658\pi$
$828$		0			0
$829$	37.9113			1.31672			0.658358	−	0.752705i	$-0.271252\pi$
$829$	37.9113			1.31672			0.658358	+	0.752705i	$0.271252\pi$
$830$		0			0
$831$	−50.2484	−	16.3267i	−1.74310	−	0.566367i
$832$		0			0
$833$	4.31609	−	5.94059i	0.149544	−	0.205829i
$834$		0			0
$835$	1.24244	−	0.403693i	0.0429963	−	0.0139704i
$836$		0			0
$837$	12.4717	+	4.05231i	0.431085	+	0.140068i
$838$		0			0
$839$	13.1978	+	18.1653i	0.455640	+	0.627134i	0.973597	−	0.228272i	$-0.0733075\pi$
$839$	13.1978	+	18.1653i	0.455640	+	0.627134i	−0.517958	+	0.855406i	$0.673308\pi$
$840$		0			0
$841$	−22.0296	+	16.0054i	−0.759640	+	0.551911i
$842$		0			0
$843$	32.8732	+	23.8838i	1.13221	+	0.822600i
$844$		0			0
$845$	0.529324	−	0.384576i	0.0182093	−	0.0132298i
$846$		0			0
$847$			7.41217i			0.254685i
$848$		0			0
$849$	7.74759	−	2.51735i	0.265897	−	0.0863951i
$850$		0			0
$851$	0.847940	−	2.60969i	0.0290670	−	0.0894590i
$852$		0			0
$853$	−9.65885	+	29.7269i	−0.330713	+	1.01783i	0.638083	+	0.769968i	$0.279728\pi$
$853$	−9.65885	+	29.7269i	−0.330713	+	1.01783i	−0.968796	+	0.247861i	$0.920272\pi$
$854$		0			0
$855$	−0.0641867	+	0.0883454i	−0.00219514	+	0.00302135i
$856$		0			0
$857$	11.7247	+	36.0850i	0.400509	+	1.23264i	0.924587	+	0.380970i	$0.124410\pi$
$857$	11.7247	+	36.0850i	0.400509	+	1.23264i	−0.524078	+	0.851670i	$0.675590\pi$
$858$		0			0
$859$	−7.92892	−	5.76069i	−0.270531	−	0.196552i	0.444246	−	0.895905i	$-0.353472\pi$
$859$	−7.92892	−	5.76069i	−0.270531	−	0.196552i	−0.714777	+	0.699353i	$0.753472\pi$
$860$		0			0
$861$	−8.27565	−	8.03858i	−0.282033	−	0.273954i
$862$		0			0
$863$	10.9256	+	7.93793i	0.371913	+	0.270210i	0.758004	−	0.652250i	$-0.226175\pi$
$863$	10.9256	+	7.93793i	0.371913	+	0.270210i	−0.386091	+	0.922461i	$0.626175\pi$
$864$		0			0
$865$	−0.737368	−	2.26939i	−0.0250713	−	0.0771614i
$866$		0			0
$867$	39.1001	−	53.8166i	1.32791	−	1.82771i
$868$		0			0
$869$	2.68321	−	8.25808i	0.0910217	−	0.280136i
$870$		0			0
$871$	−8.96133	+	27.5801i	−0.303643	+	0.934517i
$872$		0			0
$873$	2.62527	−	0.853003i	0.0888521	−	0.0288698i
$874$		0			0
$875$			1.12064i			0.0378844i
$876$		0			0
$877$	27.7364	−	20.1517i	0.936592	−	0.680474i	−0.0110059	−	0.999939i	$-0.503503\pi$
$877$	27.7364	−	20.1517i	0.936592	−	0.680474i	0.947598	+	0.319466i	$0.103503\pi$
$878$		0			0
$879$	19.4824	+	14.1548i	0.657125	+	0.477429i
$880$		0			0
$881$	−27.4813	+	19.9663i	−0.925868	+	0.672682i	−0.944978	−	0.327135i	$-0.893917\pi$
$881$	−27.4813	+	19.9663i	−0.925868	+	0.672682i	0.0191097	+	0.999817i	$0.493917\pi$
$882$		0			0
$883$	−10.2495	−	14.1072i	−0.344922	−	0.474744i	0.600949	−	0.799287i	$-0.294789\pi$
$883$	−10.2495	−	14.1072i	−0.344922	−	0.474744i	−0.945871	+	0.324543i	$0.894789\pi$
$884$		0			0
$885$	2.55279	+	0.829451i	0.0858110	+	0.0278817i
$886$		0			0
$887$	−2.70523	+	0.878982i	−0.0908327	+	0.0295133i	−0.354081	−	0.935215i	$-0.615206\pi$
$887$	−2.70523	+	0.878982i	−0.0908327	+	0.0295133i	0.263248	+	0.964728i	$0.415206\pi$
$888$		0			0
$889$	−7.07932	+	9.74385i	−0.237433	+	0.326798i
$890$		0			0
$891$	17.4356	+	5.66517i	0.584115	+	0.189790i
$892$		0			0
$893$	29.4347			0.984994
$894$		0			0
$895$	−0.419982	−	0.578055i	−0.0140384	−	0.0193222i
$896$		0			0
$897$	9.47720	+	29.1678i	0.316434	+	0.973885i
$898$		0			0
$899$		−	3.51647i		−	0.117281i
$900$		0			0
$901$	58.0123			1.93267
$902$		0			0
$903$	16.9053			0.562572
$904$		0			0
$905$		−	0.767153i		−	0.0255010i
$906$		0			0
$907$	5.87356	+	18.0770i	0.195028	+	0.600236i	0.999976	+	0.00689024i	$0.00219325\pi$
$907$	5.87356	+	18.0770i	0.195028	+	0.600236i	−0.804948	+	0.593346i	$0.797807\pi$
$908$		0			0
$909$	−0.145757	−	0.200618i	−0.00483447	−	0.00665408i
$910$		0			0
$911$	25.3171			0.838793			0.419397	−	0.907803i	$-0.362242\pi$
$911$	25.3171			0.838793			0.419397	+	0.907803i	$0.362242\pi$
$912$		0			0
$913$	−13.6396	−	4.43177i	−0.451405	−	0.146670i
$914$		0			0
$915$	−0.721224	+	0.992679i	−0.0238429	+	0.0328170i
$916$		0			0
$917$	−16.6376	+	5.40587i	−0.549421	+	0.178518i
$918$		0			0
$919$	−56.8736	−	18.4793i	−1.87609	−	0.609577i	−0.988988	−	0.147997i	$-0.952717\pi$
$919$	−56.8736	−	18.4793i	−1.87609	−	0.609577i	−0.887099	−	0.461580i	$-0.847283\pi$
$920$		0			0
$921$	0.565001	+	0.777657i	0.0186174	+	0.0256247i
$922$		0			0
$923$	−3.71075	+	2.69602i	−0.122141	+	0.0887405i
$924$		0			0
$925$	1.74160	+	1.26535i	0.0572635	+	0.0416044i
$926$		0			0
$927$	1.00683	−	0.731507i	0.0330687	−	0.0240258i
$928$		0			0
$929$		−	11.5486i		−	0.378897i	−0.981891	−	0.189449i	$-0.939330\pi$
$929$		−	11.5486i		−	0.378897i	0.981891	−	0.189449i	$-0.0606700\pi$
$930$		0			0
$931$	−3.75546	+	1.22022i	−0.123080	+	0.0399912i
$932$		0			0
$933$	18.3028	−	56.3301i	0.599205	−	1.84416i
$934$		0			0
$935$	0.482261	−	1.48425i	0.0157716	−	0.0485401i
$936$		0			0
$937$	1.30217	−	1.79228i	0.0425400	−	0.0585512i	−0.787217	−	0.616676i	$-0.788479\pi$
$937$	1.30217	−	1.79228i	0.0425400	−	0.0585512i	0.829757	+	0.558125i	$0.188479\pi$
$938$		0			0
$939$	12.8745	+	39.6236i	0.420144	+	1.29307i
$940$		0			0
$941$	0.588542	+	0.427601i	0.0191859	+	0.0139394i	0.597337	−	0.801990i	$-0.296226\pi$
$941$	0.588542	+	0.427601i	0.0191859	+	0.0139394i	−0.578151	+	0.815930i	$0.696226\pi$
$942$		0			0
$943$	17.9512	−	36.5340i	0.584572	−	1.18971i
$944$		0			0
$945$	0.450366	+	0.327210i	0.0146504	+	0.0106441i
$946$		0			0
$947$	−3.99560	−	12.2972i	−0.129840	−	0.399605i	0.864912	−	0.501923i	$-0.167374\pi$
$947$	−3.99560	−	12.2972i	−0.129840	−	0.399605i	−0.994752	+	0.102318i	$0.967374\pi$
$948$		0			0
$949$	22.0838	−	30.3958i	0.716872	−	0.986690i
$950$		0			0
$951$	11.1432	−	34.2951i	0.361342	−	1.11210i
$952$		0			0
$953$	2.67607	−	8.23610i	0.0866864	−	0.266793i	−0.898312	−	0.439359i	$-0.855206\pi$
$953$	2.67607	−	8.23610i	0.0866864	−	0.266793i	0.984998	+	0.172566i	$0.0552057\pi$
$954$		0			0
$955$	−1.58665	+	0.515532i	−0.0513426	+	0.0166822i
$956$		0			0
$957$		−	4.54051i		−	0.146774i
$958$		0			0
$959$	−4.90004	+	3.56009i	−0.158231	+	0.114961i
$960$		0			0
$961$	19.4275	+	14.1149i	0.626693	+	0.455319i
$962$		0			0
$963$	1.02389	−	0.743896i	0.0329942	−	0.0239717i
$964$		0			0
$965$	−0.979315	−	1.34791i	−0.0315253	−	0.0433908i
$966$		0			0
$967$	51.9599	+	16.8828i	1.67092	+	0.542914i	0.983116	−	0.182985i	$-0.0585761\pi$
$967$	51.9599	+	16.8828i	1.67092	+	0.542914i	0.687801	+	0.725899i	$0.258576\pi$
$968$		0			0
$969$	−49.6868	+	16.1442i	−1.59617	+	0.518627i
$970$		0			0
$971$	−25.6051	+	35.2425i	−0.821708	+	1.13098i	0.167702	+	0.985838i	$0.446365\pi$
$971$	−25.6051	+	35.2425i	−0.821708	+	1.13098i	−0.989410	+	0.145146i	$0.953635\pi$
$972$		0			0
$973$	−13.8943	−	4.51454i	−0.445432	−	0.144729i
$974$		0			0
$975$	−24.0606			−0.770556
$976$		0			0
$977$	−4.71781	−	6.49351i	−0.150936	−	0.207746i	0.726853	−	0.686793i	$-0.240982\pi$
$977$	−4.71781	−	6.49351i	−0.150936	−	0.207746i	−0.877789	+	0.479047i	$0.840982\pi$
$978$		0			0
$979$	−6.72263	−	20.6901i	−0.214856	−	0.661259i
$980$		0			0
$981$		−	2.66376i		−	0.0850474i
$982$		0			0
$983$	10.5675			0.337050			0.168525	−	0.985697i	$-0.446100\pi$
$983$	10.5675			0.337050			0.168525	+	0.985697i	$0.446100\pi$
$984$		0			0
$985$	−1.75092			−0.0557891
$986$		0			0
$987$			13.4310i			0.427513i
$988$		0			0
$989$	18.4317	+	56.7270i	0.586094	+	1.80381i
$990$		0			0
$991$	21.3919	+	29.4434i	0.679535	+	0.935300i	0.999928	−	0.0119845i	$-0.00381487\pi$
$991$	21.3919	+	29.4434i	0.679535	+	0.935300i	−0.320393	+	0.947285i	$0.603815\pi$
$992$		0			0
$993$	11.1796			0.354773
$994$		0			0
$995$	−2.53980	−	0.825231i	−0.0805171	−	0.0261616i
$996$		0			0
$997$	24.2161	−	33.3306i	0.766931	−	1.05559i	−0.229675	−	0.973267i	$-0.573766\pi$
$997$	24.2161	−	33.3306i	0.766931	−	1.05559i	0.996606	−	0.0823222i	$-0.0262337\pi$
$998$		0			0
$999$	2.03666	−	0.661751i	0.0644370	−	0.0209369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.113.6	✓	80
41.4	even	10	inner	1148.2.ba.a.701.15	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.6	✓	80	1.1	even	1	trivial
1148.2.ba.a.701.15	yes	80	41.4	even	10	inner

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-1.80180i q^{3} +(-0.0346732 - 0.106713i) q^{5} +(-0.587785 - 0.809017i) q^{7} -0.246466 q^{9} +O(q^{10})\)	\(q-1.80180i q^{3} +(-0.0346732 - 0.106713i) q^{5} +(-0.587785 - 0.809017i) q^{7} -0.246466 q^{9} +(-1.80145 - 0.585326i) q^{11} +(1.57378 - 2.16612i) q^{13} +(-0.192275 + 0.0624741i) q^{15} +(-6.98358 - 2.26910i) q^{17} +(2.32100 + 3.19459i) q^{19} +(-1.45768 + 1.05907i) q^{21} +(-5.14309 - 3.73667i) q^{23} +(4.03490 - 2.93153i) q^{25} -4.96130i q^{27} +(-1.26529 + 0.411117i) q^{29} +(-0.816782 + 2.51380i) q^{31} +(-1.05464 + 3.24584i) q^{33} +(-0.0659524 + 0.0907757i) q^{35} +(0.133382 + 0.410509i) q^{37} +(-3.90291 - 2.83563i) q^{39} +(1.09345 + 6.30907i) q^{41} +(-7.59057 - 5.51487i) q^{43} +(0.00854578 + 0.0263012i) q^{45} +(4.38148 - 6.03059i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-4.08846 + 12.5830i) q^{51} +(-7.51371 + 2.44135i) q^{53} +0.212534i q^{55} +(5.75599 - 4.18197i) q^{57} +(-10.7411 - 7.80386i) q^{59} +(4.91011 - 3.56741i) q^{61} +(0.144869 + 0.199395i) q^{63} +(-0.285722 - 0.0928368i) q^{65} +(-10.3008 + 3.34693i) q^{67} +(-6.73272 + 9.26680i) q^{69} +(-1.62924 - 0.529371i) q^{71} +14.0323 q^{73} +(-5.28201 - 7.27006i) q^{75} +(0.585326 + 1.80145i) q^{77} +4.58413i q^{79} -9.67865 q^{81} +7.57146 q^{83} +0.823918i q^{85} +(0.740749 + 2.27979i) q^{87} +(6.75087 + 9.29178i) q^{89} -2.67748 q^{91} +(4.52935 + 1.47167i) q^{93} +(0.260428 - 0.358449i) q^{95} +(-10.6517 + 3.46094i) q^{97} +(0.443996 + 0.144263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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